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8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 167
Damage Stability
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 267
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8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 367
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8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 467
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8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 567
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8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 667
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8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 767
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8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 867
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8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 967
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8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 1067
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8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 1167
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8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 1267
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8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 1367
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8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 1467
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8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 1567
Permability is the ratio of amount of water that can a enter or a
compartment or tank to the total volume of compartment or tank
VOLUME TOTAL
VOLUME AVAILABLE TY PERMEABILI =
983120983141983154983149983141983137983138983145983148983145983156983161 μ
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 1667
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Surface permability is the percentage of a waterplane that can be
occupied by water
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 1767
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 1867
A cargo hold with dimensions of l = 1524m w = 914 m
h=61 m is completely flooded Determine the volume of the
space and the corrected flooded volume
Volume = 1524 m x 914 m x 61 m = 8497 m3
Flooded volume = Volume x permeability
Flooded volume = 8497 m3 x 60
Flooded volume = 5098 m3
Example 1
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 1967
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8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 2067
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8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 2167
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8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 2267
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8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 2367
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8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 2467
D983141983156983141983154983149983145983150983137983156983145983151983150 983151983142 983156983144983141 983148983151983139983137983156983145983151983150 983151983142 983156983144983141 983158983151983148983157983149983141 983139983141983150983156983154983141 983151983142
983140983137983149983137983143983141983140 983139983151983149983152983137983154983156983149983141983150983156
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 2567
D983141983156983141983154983149983145983150983137983156983145983151983150 983151983142 983156983144983141 983158983151983148983157983149983141 983151983142 983159983137983156983141983154 983141983150983156983141983154983145983150983143 983156983144983141 983158983141983155983155983141983148
Initial displacement and longitudinal centre of buoyancy (LCB) can be read from hydrostatcic curves
However displacement and LCB are unknown after damaged
Therefore if trim forward and aft draught are known trimmed waterline can be drawn over Bonjean
area curves
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 2667
983108983141983156983141983154983149983145983150983137983156983145983151983150 983151983142 983140983137983149983137983143983141983140 983148983141983150983143983156983144 983137983150983140 983148983151983139983137983156983145983151983150 983151983142 983149983145983140
983151983142 983139983151983149983152983137983154983156983149983141983150983156
vw The volume of water entering the vessel
xw Distance of volume centre of damaged compartment from maestory
micro Permability of the compartment
v0 Volume of the compartment
xm Distance of the volume centre of the compartment to the mid of damaged length
xl Distance of the mid of damaged length of compartment to maestory
xc Distance of the computed volume centre of compartment to maestory (xc=xl-xm)
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 2767
983108983141983156983141983154983149983145983150983137983156983145983151983150 983151983142 983140983137983149983137983143983141983140 983148983141983150983143983156983144 983137983150983140 983148983151983139983137983156983145983151983150 983151983142 983149983145983140
983151983142 983139983151983149983152983137983154983156983149983141983150983156
Damaged length and location of compartment can be determined by iterative
procedure
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 2867
bull The volume of water entering the vessel (vw)
bull Distance of volume centre of damaged compartment from amidships Θ ( xw)
bull Volume of the compartment (v0
= vw
μ)
First trial
1) Assume xm=0 (xl=xw)
2) Damaged Length l1 = (Volume of the compartment v0) (mean sec Area Amean)
where Amean is determined from trimmed sectional area curve
983108983141983156983141983154983149983145983150983137983156983145983151983150 983151983142 983140983137983149983137983143983141983140 983148983141983150983143983156983144 983137983150983140 983148983151983139983137983156983145983151983150 983151983142 983149983145983140
983151983142 983139983151983149983152983137983154983156983149983141983150983156
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 2967
3) In order to determine vm and xm
s = l1 4
vm = (s 3) sum3
xm = s sum4 sum3
xc = xl ndash xm
|vm-v0| le Tolarence for volume
|xc-xw| le Tolarence for location of volume centre
l=l1 xl=xw
983108983141983156983141983154983149983145983150983137983156983145983151983150 983151983142 983140983137983149983137983143983141983140 983148983141983150983143983156983144 983137983150983140 983148983151983139983137983156983145983151983150 983151983142 983149983145983140
983151983142 983139983151983149983152983137983154983156983149983141983150983156
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 3067
983108983141983156983141983154983149983145983150983137983156983145983151983150 983151983142 983140983137983149983137983143983141983140 983148983141983150983143983156983144 983137983150983140 983148983151983139983137983156983145983151983150 983151983142 983149983145983140
983151983142 983139983151983149983152983137983154983156983149983141983150983156Second Trial
Damaged length is changed proportionally by the volume
l2 = l1 times (v0v
m)
vm Computed volume at first trial
If the value of xm computed at first trial is negative then the mid of the
compartment slides to the bow
xl = xw+xm
where xm is the distance of the volume centre of compartment to amidship
computed at first trial
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 3167
In order to determine vm and xm
983108983141983156983141983154983149983145983150983137983156983145983151983150 983151983142 983140983137983149983137983143983141983140 983148983141983150983143983156983144 983137983150983140 983148983151983139983137983156983145983151983150 983151983142 983149983145983140
983151983142 983139983151983149983152983137983154983156983149983141983150983156
s = l2 4
vm = (s 3) sum3
xm = s sum4 sum3
xc = xl ndash xm
|vm-v0| le Tolarence for volume
|xc-xw| le Tolarence for location of volume centre
l=l2
If tolarances for both volume and location are not satisfied third fourthtrials are made similar to
second trial
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 3267
If either tolarence for volume or tolarance for location are satisfied at a trial
satisfied one is fixed trials are continued to make for the other one
983108983141983156983141983154983149983145983150983137983156983145983151983150 983151983142 983140983137983149983137983143983141983140 983148983141983150983143983156983144 983137983150983140 983148983151983139983137983156983145983151983150 983151983142 983149983145983140
983151983142 983139983151983149983152983137983154983156983149983141983150983156
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 3367
A ship is 116 meter long and displaces 7842 ton in salt water (ρ1=1025 tm3)
when her mean draught is 64m Longitudinal Centre of Buoyancy (LCB) is
0615 m aft from amidships After one of her stern compartment is damaged
she floats trimmed to the aft Her sectional areas after damaged are given in the
following table
a) Determine the volume of water entering the vessel (vw) and the location of
volume centre of damaged compartment (xw)
b) Assume permability of compartment micro is 1 Determine damaged length
and Distance of the mid of damaged length of compartment to amidship
983109983160983137983149983152983148983141 2
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 3467
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 3567
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 3667
Predicted xw
is between section 2 and section 3
983123983141983139 N983151 983123983141983139 A983154983141983137 D983145983155983156 A9831499831459831559831449831459831522 10135 983085348
3 1208 983085232
983123983141983139 A983154983141983137 983137983156 98308524983149 983142983154983151983149 983137983149983145983140983155983144983145983152 = 11959831492
l1=v0Amean=204081195=17078 m
s=l14=427 m
983109983160983137983149983152983148983141 2983085983123983119983116983125983124983113983119983118
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 3767
983161983145 L983151983139 A983149983141983137983150 983123M M A983154983149
9831311983133 9831312983133 98313119831339832559831312983133 9831313983133 983131198313398325598313129831339832559831313983133
0 9830853254 1051 1 1051 2 21021 9830852827 1123 4 4492 1 4492
2 98308524 1195 2 239 0 0
3 9830851973 1219 4 4876 9830851 9830854876
4 9830851546 1233 1 1233 9830852 9830852466
sum983091983101 14042 sum983092983101 983085748
vm
= (s3) sum3= 199864479831493
xm
=s sum4sum3= 9830850227983149
v0-vm=20408-19986=422 m3
Error=422times10020408=207
983109983160983137983149983152983148983141 2983085983123983119983116983125983124983113983119983118
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 3867
Methods of Calculation
There two available method calculating the
final stage of the damaged vessel
bull Lost Buoyancy Method
bull Added Weight Method
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 3967
Comparision of Lost Buoyancy and Added
Weight Methods
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 4067
Consider a vessel that has been damaged such
that a portion of the bottom is now open to the
sea
The vesselrsquos draft will increase because an amount
of the buoyancy was lost
Added Weight Method
Added Weight Method
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 4167
Added Weight Method
In this method flood water is treated as a fixed weight (for example the
weight of water of volume ABEF) This added weight is balanced by the
additional buoyant force of the layer WL1WL
The added weight can be determined by either the volume ABEF or
waterline WL1 Therefore WL1 waterline is not known can be just guessed
For the predicted waterline added weight and additional buoyant force
caculation are done iteratively until both of them are equal This method is
known as Added weight method
Determination of Added Weight
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 4267
Determination of Added Weight
vc Volume of damaged compartment (DCEF)
ac The surface area (AB) of damaged compartment on the waterline
micro The volume permability of damaged compartment
microa The area permability of the surface of damaged compartment
∆ The initial displacement
∆1 The displacement at final stage
vw The volume of water entering the vessel (ABEH)
w The weight of water entering the vessel
p The value of parallel sinkage
If th t th l l i k i h f t l f
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 4367
If we assume that the paralel sinkage cause a minor change of water plane area of a
ship (Awp
asymp Awp1
) we can determine the paralel sinkage by equating the volume of
the layer WL1WL to the volume of ABEF
If the damaged compartment is bounded on top
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 4467
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 4567
Longitudinal Metacentre Radius at final stage
Free Surface Effect
Damaged compartment can be considered as a half filled tank
Free Contact Effect
Damaged compartment can be considered as a half filled tank
T M H i h
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 4667
Transverse Metacentre Height
The angle of heel
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 4767
L it di l M t t H i ht
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 4867
Longitudinal Metacentre Height
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 4967
E983160983137983149983152983148983141 A 983138983137983154983143983141
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 5067
E983160983137983149983152983148983141 A 983138983137983154983143983141
991266 L = 20 983149991266 B = 5 983149
991266 983124 = 15 983149
991266 KG = 15 983149
I983150983156983137983139983156 C983151983150983140983145983156983145983151983150
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 5167
I983150983156983137983139983156 C983151983150983140983145983156983145983151983150
991266 983124983144983141 983140983145983155983152983148983137983139983141983149983141983150983156 983158983151983148983157983149983141
991266 983124983144983141 983149983137983155983155 983140983145983155983152983148983137983139983141983149983141983150983156
991266 983124983144983141 983149983151983149983141983150983156 983151983142 983145983150983141983154983156983145983137 983151983142 983156983144983141 983159983137983156983141983154983152983148983137983150983141 983137983154983141983137983137983138983151983157983156 CL
3
15051520 m x xT B L
I I
==sdotsdot=nabla
tons x I
751531500251 ==nablasdot=∆ ρ
433
33208
12
205
12
m x L B
I I
===
I983150983156983137983139983156 C983151983150983140983145983156983145983151983150
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 5267
I983150983156983137983139983156 C983151983150983140983145983156983145983151983150
991266 M983141983156983137983139983141983150983156983154983145983139 983154983137983140983145983157983155
991266 O983154 983145983156 983139983151983157983148983140 983138983141 983139983137983148983139983157983148983137983156983141983140 983140983145983154983141983139983156983148983161 983137983155
991266 H983141983145983143983144983156 983151983142 983156983144983141 983139983141983150983156983141983154 983151983142 983138983157983151983161983137983150983139983161
m I
BM
I
I 3891
150
33208==
nabla
=
m xT
B
LBT
L B BM
I I
I 3891
5112
5
12
12 223
====
mT
KB I
I 750
2
==
I983150983156983137983139983156 C983151983150983140983145983156983145983151983150
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 5367
991266 983124983144983141 983149983141983156983137983139983141983150983156983154983145983139 983144983141983145983143983144983156
991266 F983151983154 983155983149983137983148983148 983137983150983143983148983141983155 983151983142 983144983141983141983148 983156983144983141 983154983145983143983144983156983145983150983143 983149983151983149983141983150983156
m KG BM KBGM I I 63905013891750 =minus+=minus+=
sin22998sin693075153sin mt x xGM M I I
φ φ φ ==∆=
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 5467
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 5567
983116983119983123983124 983106983125983119983129983105983118983107983129 983117983109983124983112983119983108
Paralel Sinkage
Volume (DCEF)=Volume (W1ADW+BL1LC)
Damaged compartment is bounded on top
983116983119983123983124 983106983125983119983129983105983118983107983129 983117983109983124983112983119983108
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 5667
983116983119983123983124 983106983125983119983129983105983118983107983129 983117983109983124983112983119983108
bull It is assumed that displacement and location of vertical centre
of gravity does not change after damaged
983116983119983123983124 983106983125983119983129983105983118983107983129 983117983109983124983112983119983108
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 5767
983116983119983123983124 983106983125983119983129983105983118983107983129 983117983109983124983112983119983108
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 5867
The heel angle of damaged ship is determined by
where
d is the distance between the volume centre of damaged compartment
and the new longitudinal centre of floatation
wc=vc μ ρ
983116983119983123983124 983106983125983119983129983105983118983107983129 983117983109983124983112983119983108
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 5967
983116983119983123983124 983106983125983119983129983105983118983107983129 983117983109983124983112983119983108
983116983119983123983124 983106983125983119983129983105983118983107983129 983117983109983124983112983119983108
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 6067
Longitudinal Metacentre Height of a Damaged Ship
983116983119983123983124 983106983125983119983129983105983118983107983129 983117983109983124983112983119983108
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 6167
983110983151983154983159983137983154983140 983137983150983140 983137983142983156 983140983154983137983157983143983144983156983155 983137983142983156983141983154 983140983137983149983137983143983141983140
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 6267
983120983151983154983156 983105983142983156 983120983151983154983156 983110983151983154983141 983123983156983137983154983138983151983137983154983140 983105983142983156 983123983156983137983154983138983151983137983154983140 983110983151983154983159983137983154983140
I983150983145983156983145983137983148 D983154983137983157983143983144983156 983124 983124 983124 983124
983120983137983154983137983148983141983148 983123983145983150983147983137983143983141 +983152 +983152 +983152 +983120
H983141983141983148 983085983149983145 983085983149983145 +983149983155 +983149983155
983124983154983145983149 983085983156983147 +983156983138 983085983156983147 +983156983138
F983145983150983137983148 D983154983137983157983143983144983156 983124+983152983085983149983145983085983156983147 983124+983152983085983149983145+983156983138 983124+983152+983149983155983085983156983147 983124+983152+983149983155+983156983138
Table 1 Final Draughts for a starboard side damaged ship
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 6367
L983151983155983156 B983157983151983161983137983150983139983161 M983141983156983144983151983140
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 6467
L983151983155983156 B983157983151983161983137983150983139983161 M983141983156983144983151983140
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 6567
991266 A983142983156983141983154 983148983151983151983155983145983150983143 983156983144983141 983139983141983150983156983154983137983148 983139983151983149983152983137983154983156983149983141983150983156 983156983144983141
983159983137983156983141983154983152983148983137983150983141 983137983154983141983137 983145983155
991266 983124983151 983139983151983149983152983141983150983155983137983156983141 983142983151983154 983156983144983141 983148983151983155983155 983151983142 983138983157983151983161983137983150983139983161 983151983142 983156983144983141
983139983141983150983156983154983137983148 983139983151983149983152983137983154983156983149983141983150983156 983156983144983141 983140983154983137983142983156 983145983150983139983154983141983137983155983141983155 983156983151
2805)420()( m x Bl L A L
=minus=minus=
m A
T
L
I
L 875180
150==
nabla=
L983151983155983156 B983157983151983161983137983150983139983161 M983141983156983144983151983140
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 6667
991266 983124983144983141 983144983141983145983143983144983156 983151983142 983156983144983141 983139983141983150983156983141983154 983151983142 983138983157983151983161983137983150983139983161 983145983150983139983154983141983137983155983141983155 983156983151
991266 983124983144983141 983149983151983149983141983150983156 983151983142 983145983150983141983154983156983145983137 983151983142 983156983144983141 983159983137983156983141983154983152983148983137983150983141 983137983154983141983137
991266 983124983144983141 983149983141983156983137983139983141983150983156983154983145983139 983154983137983140983145983157983155
m
T
KB L
L 93802
8751
2 ===
433
6716612
)420(5
12
)(m
l L B I L
=minus
=minus
=
m I
BM
I
L
L 1111150
67166==
nabla
=
L983151983155983156 B983157983151983161983137983150983139983161 M983141983156983144983151983140
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 6767
991266 983124983144983141 983149983141983156983137983139983141983150983156983154983145983139 983144983141983145983143983144983156
991266 983122983145983143983144983156983145983150983143 983149983151983149983141983150983156 983142983151983154 983155983149983137983148983148 983144983141983141983148 983137983150983143983148983141983155
m KG BM KBGM L L L 54905111119380 =minus+=minus+=
mt xGM M L
sin34984sin549075153sin φ φ φ ==∆=
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 267
983127A983124E983122983124IGH983124 IN983124EG983122I983124983129
bull 983123983144983145983152 983145983155 983140983145983158983145983140983141983140 983145983150983156983151 983159983137983156983141983154983156983145983143983144983156 983139983151983149983152983137983154983156983149983141983150983156983155 983138983161 983149983141983137983150983155 983151983142
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bull 983127983144983141983150 983137 983159983137983156983141983154983156983145983143983144983156 983139983151983149983152983137983154983156983149983141983150983156 (983151983154 983137 983143983154983151983157983152 983151983142
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8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 367
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8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 467
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A983150983161 983151983152983141983150983145983150983143 983145983150 983156983144983141 983159983137983156983141983154983156983145983143983144983156 983138983157983148983147983144983141983137983140983155 983149983157983155983156 983138983141 983141983153983157983145983152983152983141983140 983159983145983156983144
983159983137983156983141983154983156983145983143983144983156 983141983153983157983145983152983149983141983150983156983155 (983140983151983151983154983155 983159983145983150983140983151983159983155 983158983137983148983158983141983155 983141983156983139)
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 567
983127A983124E983122983124IGH983124 DOO983122983123
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 667
983127A983124E983122983124IGH983124 DOO983122983123
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 767
983127A983124E983122983124IGH983124 DOO983122983123
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 867
D983137983149983137983143983141
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8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 967
D983137983149983137983143983141
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 1067
983127983137983156983141983154983156983145983143983144983156 983138983157983148983147983144983141983137983140983155 983098 983156983144983141 983144983157983148983148 983145983155 983155983157983138983140983145983158983145983140983141983140 983145983150983156983151 983159983137983156983141983154983156983145983143983144983156
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8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 1167
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8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 1267
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A983142983156983141983154 983142983148983151983151983140983145983150983143 983151983142 983137 983152983154983141983155983139983154983145983138983141983140 983150983157983149983138983141983154 983151983142 983139983151983149983152983137983154983156983149983141983150983156983155 983156983144983141 983155983144983145983152 983155983144983137983148983148 983150983151983156
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8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 1367
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8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 1467
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8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 1567
Permability is the ratio of amount of water that can a enter or a
compartment or tank to the total volume of compartment or tank
VOLUME TOTAL
VOLUME AVAILABLE TY PERMEABILI =
983120983141983154983149983141983137983138983145983148983145983156983161 μ
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 1667
983123983157983154983142983137983139983141 983120983141983154983149983141983137983138983145983148983145983156983161 μ983137
Surface permability is the percentage of a waterplane that can be
occupied by water
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 1767
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 1867
A cargo hold with dimensions of l = 1524m w = 914 m
h=61 m is completely flooded Determine the volume of the
space and the corrected flooded volume
Volume = 1524 m x 914 m x 61 m = 8497 m3
Flooded volume = Volume x permeability
Flooded volume = 8497 m3 x 60
Flooded volume = 5098 m3
Example 1
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 1967
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8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 2067
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8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 2167
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8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 2267
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8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 2367
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Δ I983150983145983156983145983137983148 983140983145983155983152983148983137983139983141983149983141983150983156 Δ1 D983145983155983152983148983137983139983141983149983141983150983156 983137983142983156983141983154 983140983137983149983137983143983141983140
B I983150983145983156983145983137983148 983139983141983150983156983154983141 983151983142 983138983157983151983161983137983150983139983161
G I983150983145983156983145983137983148 983139983141983150983156983154983141 983151983142 9831439831549831379831589831459831569831619831600 I983150983145983156983145983137983148 983139983141983150983156983154983141 983151983142 983148983151983150983143983145983156983157983140983145983150983137983148 983138983157983151983161983137983150983139983161 LCB
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8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 2467
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8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 2567
D983141983156983141983154983149983145983150983137983156983145983151983150 983151983142 983156983144983141 983158983151983148983157983149983141 983151983142 983159983137983156983141983154 983141983150983156983141983154983145983150983143 983156983144983141 983158983141983155983155983141983148
Initial displacement and longitudinal centre of buoyancy (LCB) can be read from hydrostatcic curves
However displacement and LCB are unknown after damaged
Therefore if trim forward and aft draught are known trimmed waterline can be drawn over Bonjean
area curves
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 2667
983108983141983156983141983154983149983145983150983137983156983145983151983150 983151983142 983140983137983149983137983143983141983140 983148983141983150983143983156983144 983137983150983140 983148983151983139983137983156983145983151983150 983151983142 983149983145983140
983151983142 983139983151983149983152983137983154983156983149983141983150983156
vw The volume of water entering the vessel
xw Distance of volume centre of damaged compartment from maestory
micro Permability of the compartment
v0 Volume of the compartment
xm Distance of the volume centre of the compartment to the mid of damaged length
xl Distance of the mid of damaged length of compartment to maestory
xc Distance of the computed volume centre of compartment to maestory (xc=xl-xm)
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 2767
983108983141983156983141983154983149983145983150983137983156983145983151983150 983151983142 983140983137983149983137983143983141983140 983148983141983150983143983156983144 983137983150983140 983148983151983139983137983156983145983151983150 983151983142 983149983145983140
983151983142 983139983151983149983152983137983154983156983149983141983150983156
Damaged length and location of compartment can be determined by iterative
procedure
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 2867
bull The volume of water entering the vessel (vw)
bull Distance of volume centre of damaged compartment from amidships Θ ( xw)
bull Volume of the compartment (v0
= vw
μ)
First trial
1) Assume xm=0 (xl=xw)
2) Damaged Length l1 = (Volume of the compartment v0) (mean sec Area Amean)
where Amean is determined from trimmed sectional area curve
983108983141983156983141983154983149983145983150983137983156983145983151983150 983151983142 983140983137983149983137983143983141983140 983148983141983150983143983156983144 983137983150983140 983148983151983139983137983156983145983151983150 983151983142 983149983145983140
983151983142 983139983151983149983152983137983154983156983149983141983150983156
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 2967
3) In order to determine vm and xm
s = l1 4
vm = (s 3) sum3
xm = s sum4 sum3
xc = xl ndash xm
|vm-v0| le Tolarence for volume
|xc-xw| le Tolarence for location of volume centre
l=l1 xl=xw
983108983141983156983141983154983149983145983150983137983156983145983151983150 983151983142 983140983137983149983137983143983141983140 983148983141983150983143983156983144 983137983150983140 983148983151983139983137983156983145983151983150 983151983142 983149983145983140
983151983142 983139983151983149983152983137983154983156983149983141983150983156
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 3067
983108983141983156983141983154983149983145983150983137983156983145983151983150 983151983142 983140983137983149983137983143983141983140 983148983141983150983143983156983144 983137983150983140 983148983151983139983137983156983145983151983150 983151983142 983149983145983140
983151983142 983139983151983149983152983137983154983156983149983141983150983156Second Trial
Damaged length is changed proportionally by the volume
l2 = l1 times (v0v
m)
vm Computed volume at first trial
If the value of xm computed at first trial is negative then the mid of the
compartment slides to the bow
xl = xw+xm
where xm is the distance of the volume centre of compartment to amidship
computed at first trial
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 3167
In order to determine vm and xm
983108983141983156983141983154983149983145983150983137983156983145983151983150 983151983142 983140983137983149983137983143983141983140 983148983141983150983143983156983144 983137983150983140 983148983151983139983137983156983145983151983150 983151983142 983149983145983140
983151983142 983139983151983149983152983137983154983156983149983141983150983156
s = l2 4
vm = (s 3) sum3
xm = s sum4 sum3
xc = xl ndash xm
|vm-v0| le Tolarence for volume
|xc-xw| le Tolarence for location of volume centre
l=l2
If tolarances for both volume and location are not satisfied third fourthtrials are made similar to
second trial
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 3267
If either tolarence for volume or tolarance for location are satisfied at a trial
satisfied one is fixed trials are continued to make for the other one
983108983141983156983141983154983149983145983150983137983156983145983151983150 983151983142 983140983137983149983137983143983141983140 983148983141983150983143983156983144 983137983150983140 983148983151983139983137983156983145983151983150 983151983142 983149983145983140
983151983142 983139983151983149983152983137983154983156983149983141983150983156
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 3367
A ship is 116 meter long and displaces 7842 ton in salt water (ρ1=1025 tm3)
when her mean draught is 64m Longitudinal Centre of Buoyancy (LCB) is
0615 m aft from amidships After one of her stern compartment is damaged
she floats trimmed to the aft Her sectional areas after damaged are given in the
following table
a) Determine the volume of water entering the vessel (vw) and the location of
volume centre of damaged compartment (xw)
b) Assume permability of compartment micro is 1 Determine damaged length
and Distance of the mid of damaged length of compartment to amidship
983109983160983137983149983152983148983141 2
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 3467
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 3567
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 3667
Predicted xw
is between section 2 and section 3
983123983141983139 N983151 983123983141983139 A983154983141983137 D983145983155983156 A9831499831459831559831449831459831522 10135 983085348
3 1208 983085232
983123983141983139 A983154983141983137 983137983156 98308524983149 983142983154983151983149 983137983149983145983140983155983144983145983152 = 11959831492
l1=v0Amean=204081195=17078 m
s=l14=427 m
983109983160983137983149983152983148983141 2983085983123983119983116983125983124983113983119983118
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 3767
983161983145 L983151983139 A983149983141983137983150 983123M M A983154983149
9831311983133 9831312983133 98313119831339832559831312983133 9831313983133 983131198313398325598313129831339832559831313983133
0 9830853254 1051 1 1051 2 21021 9830852827 1123 4 4492 1 4492
2 98308524 1195 2 239 0 0
3 9830851973 1219 4 4876 9830851 9830854876
4 9830851546 1233 1 1233 9830852 9830852466
sum983091983101 14042 sum983092983101 983085748
vm
= (s3) sum3= 199864479831493
xm
=s sum4sum3= 9830850227983149
v0-vm=20408-19986=422 m3
Error=422times10020408=207
983109983160983137983149983152983148983141 2983085983123983119983116983125983124983113983119983118
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 3867
Methods of Calculation
There two available method calculating the
final stage of the damaged vessel
bull Lost Buoyancy Method
bull Added Weight Method
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 3967
Comparision of Lost Buoyancy and Added
Weight Methods
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 4067
Consider a vessel that has been damaged such
that a portion of the bottom is now open to the
sea
The vesselrsquos draft will increase because an amount
of the buoyancy was lost
Added Weight Method
Added Weight Method
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 4167
Added Weight Method
In this method flood water is treated as a fixed weight (for example the
weight of water of volume ABEF) This added weight is balanced by the
additional buoyant force of the layer WL1WL
The added weight can be determined by either the volume ABEF or
waterline WL1 Therefore WL1 waterline is not known can be just guessed
For the predicted waterline added weight and additional buoyant force
caculation are done iteratively until both of them are equal This method is
known as Added weight method
Determination of Added Weight
8162019 Damaged Stability
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Determination of Added Weight
vc Volume of damaged compartment (DCEF)
ac The surface area (AB) of damaged compartment on the waterline
micro The volume permability of damaged compartment
microa The area permability of the surface of damaged compartment
∆ The initial displacement
∆1 The displacement at final stage
vw The volume of water entering the vessel (ABEH)
w The weight of water entering the vessel
p The value of parallel sinkage
If th t th l l i k i h f t l f
8162019 Damaged Stability
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If we assume that the paralel sinkage cause a minor change of water plane area of a
ship (Awp
asymp Awp1
) we can determine the paralel sinkage by equating the volume of
the layer WL1WL to the volume of ABEF
If the damaged compartment is bounded on top
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 4467
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 4567
Longitudinal Metacentre Radius at final stage
Free Surface Effect
Damaged compartment can be considered as a half filled tank
Free Contact Effect
Damaged compartment can be considered as a half filled tank
T M H i h
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 4667
Transverse Metacentre Height
The angle of heel
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 4767
L it di l M t t H i ht
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 4867
Longitudinal Metacentre Height
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 4967
E983160983137983149983152983148983141 A 983138983137983154983143983141
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 5067
E983160983137983149983152983148983141 A 983138983137983154983143983141
991266 L = 20 983149991266 B = 5 983149
991266 983124 = 15 983149
991266 KG = 15 983149
I983150983156983137983139983156 C983151983150983140983145983156983145983151983150
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 5167
I983150983156983137983139983156 C983151983150983140983145983156983145983151983150
991266 983124983144983141 983140983145983155983152983148983137983139983141983149983141983150983156 983158983151983148983157983149983141
991266 983124983144983141 983149983137983155983155 983140983145983155983152983148983137983139983141983149983141983150983156
991266 983124983144983141 983149983151983149983141983150983156 983151983142 983145983150983141983154983156983145983137 983151983142 983156983144983141 983159983137983156983141983154983152983148983137983150983141 983137983154983141983137983137983138983151983157983156 CL
3
15051520 m x xT B L
I I
==sdotsdot=nabla
tons x I
751531500251 ==nablasdot=∆ ρ
433
33208
12
205
12
m x L B
I I
===
I983150983156983137983139983156 C983151983150983140983145983156983145983151983150
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 5267
I983150983156983137983139983156 C983151983150983140983145983156983145983151983150
991266 M983141983156983137983139983141983150983156983154983145983139 983154983137983140983145983157983155
991266 O983154 983145983156 983139983151983157983148983140 983138983141 983139983137983148983139983157983148983137983156983141983140 983140983145983154983141983139983156983148983161 983137983155
991266 H983141983145983143983144983156 983151983142 983156983144983141 983139983141983150983156983141983154 983151983142 983138983157983151983161983137983150983139983161
m I
BM
I
I 3891
150
33208==
nabla
=
m xT
B
LBT
L B BM
I I
I 3891
5112
5
12
12 223
====
mT
KB I
I 750
2
==
I983150983156983137983139983156 C983151983150983140983145983156983145983151983150
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 5367
991266 983124983144983141 983149983141983156983137983139983141983150983156983154983145983139 983144983141983145983143983144983156
991266 F983151983154 983155983149983137983148983148 983137983150983143983148983141983155 983151983142 983144983141983141983148 983156983144983141 983154983145983143983144983156983145983150983143 983149983151983149983141983150983156
m KG BM KBGM I I 63905013891750 =minus+=minus+=
sin22998sin693075153sin mt x xGM M I I
φ φ φ ==∆=
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 5467
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 5567
983116983119983123983124 983106983125983119983129983105983118983107983129 983117983109983124983112983119983108
Paralel Sinkage
Volume (DCEF)=Volume (W1ADW+BL1LC)
Damaged compartment is bounded on top
983116983119983123983124 983106983125983119983129983105983118983107983129 983117983109983124983112983119983108
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 5667
983116983119983123983124 983106983125983119983129983105983118983107983129 983117983109983124983112983119983108
bull It is assumed that displacement and location of vertical centre
of gravity does not change after damaged
983116983119983123983124 983106983125983119983129983105983118983107983129 983117983109983124983112983119983108
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 5767
983116983119983123983124 983106983125983119983129983105983118983107983129 983117983109983124983112983119983108
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 5867
The heel angle of damaged ship is determined by
where
d is the distance between the volume centre of damaged compartment
and the new longitudinal centre of floatation
wc=vc μ ρ
983116983119983123983124 983106983125983119983129983105983118983107983129 983117983109983124983112983119983108
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 5967
983116983119983123983124 983106983125983119983129983105983118983107983129 983117983109983124983112983119983108
983116983119983123983124 983106983125983119983129983105983118983107983129 983117983109983124983112983119983108
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 6067
Longitudinal Metacentre Height of a Damaged Ship
983116983119983123983124 983106983125983119983129983105983118983107983129 983117983109983124983112983119983108
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 6167
983110983151983154983159983137983154983140 983137983150983140 983137983142983156 983140983154983137983157983143983144983156983155 983137983142983156983141983154 983140983137983149983137983143983141983140
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 6267
983120983151983154983156 983105983142983156 983120983151983154983156 983110983151983154983141 983123983156983137983154983138983151983137983154983140 983105983142983156 983123983156983137983154983138983151983137983154983140 983110983151983154983159983137983154983140
I983150983145983156983145983137983148 D983154983137983157983143983144983156 983124 983124 983124 983124
983120983137983154983137983148983141983148 983123983145983150983147983137983143983141 +983152 +983152 +983152 +983120
H983141983141983148 983085983149983145 983085983149983145 +983149983155 +983149983155
983124983154983145983149 983085983156983147 +983156983138 983085983156983147 +983156983138
F983145983150983137983148 D983154983137983157983143983144983156 983124+983152983085983149983145983085983156983147 983124+983152983085983149983145+983156983138 983124+983152+983149983155983085983156983147 983124+983152+983149983155+983156983138
Table 1 Final Draughts for a starboard side damaged ship
8162019 Damaged Stability
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L983151983155983156 B983157983151983161983137983150983139983161 M983141983156983144983151983140
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 6467
L983151983155983156 B983157983151983161983137983150983139983161 M983141983156983144983151983140
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 6567
991266 A983142983156983141983154 983148983151983151983155983145983150983143 983156983144983141 983139983141983150983156983154983137983148 983139983151983149983152983137983154983156983149983141983150983156 983156983144983141
983159983137983156983141983154983152983148983137983150983141 983137983154983141983137 983145983155
991266 983124983151 983139983151983149983152983141983150983155983137983156983141 983142983151983154 983156983144983141 983148983151983155983155 983151983142 983138983157983151983161983137983150983139983161 983151983142 983156983144983141
983139983141983150983156983154983137983148 983139983151983149983152983137983154983156983149983141983150983156 983156983144983141 983140983154983137983142983156 983145983150983139983154983141983137983155983141983155 983156983151
2805)420()( m x Bl L A L
=minus=minus=
m A
T
L
I
L 875180
150==
nabla=
L983151983155983156 B983157983151983161983137983150983139983161 M983141983156983144983151983140
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 6667
991266 983124983144983141 983144983141983145983143983144983156 983151983142 983156983144983141 983139983141983150983156983141983154 983151983142 983138983157983151983161983137983150983139983161 983145983150983139983154983141983137983155983141983155 983156983151
991266 983124983144983141 983149983151983149983141983150983156 983151983142 983145983150983141983154983156983145983137 983151983142 983156983144983141 983159983137983156983141983154983152983148983137983150983141 983137983154983141983137
991266 983124983144983141 983149983141983156983137983139983141983150983156983154983145983139 983154983137983140983145983157983155
m
T
KB L
L 93802
8751
2 ===
433
6716612
)420(5
12
)(m
l L B I L
=minus
=minus
=
m I
BM
I
L
L 1111150
67166==
nabla
=
L983151983155983156 B983157983151983161983137983150983139983161 M983141983156983144983151983140
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 6767
991266 983124983144983141 983149983141983156983137983139983141983150983156983154983145983139 983144983141983145983143983144983156
991266 983122983145983143983144983156983145983150983143 983149983151983149983141983150983156 983142983151983154 983155983149983137983148983148 983144983141983141983148 983137983150983143983148983141983155
m KG BM KBGM L L L 54905111119380 =minus+=minus+=
mt xGM M L
sin34984sin549075153sin φ φ φ ==∆=
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 367
983127A983124E983122983124IGH983124 IN983124EG983122I983124983129
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 467
983127A983124E983122983124IGH983124NE983123983123983127983137983156983141983154983156983145983143983144983156 983149983141983137983150983155 983154983141983155983145983155983156983137983150983139983141 983151983142 983156983144983141 983155983156983154983157983139983156983157983154983141 983137983143983137983145983150983155983156 983155983156983137983156983145983139 983159983137983156983141983154
983152983154983141983155983155983157983154983141 983159983145983156983144983151983157983156 983137983150983161 983148983141983137983147983137983143983141
I983156 983152983154983141983158983141983150983156983155 983159983137983156983141983154 983151983154 983137983150983161 983151983156983144983141983154 983148983145983153983157983145983140 983156983151 983142983148983151983159 983151983156983144983141983154 983139983151983149983152983137983154983156983149983141983150983156983155
(983151983154 983145983150 983156983144983141 983151983152983152983151983155983145983156983141 983140983145983154983141983139983156983145983151983150)
983124983144983141 983149983137983145983150 983140983141983139983147 983137983150983140 983149983137983145983150 983138983157983148983147983144983141983137983140983155 983151983142 983137 983155983144983145983152 983149983157983155983156 983138983141 983159983137983156983141983154983156983145983143983144983156
983127983137983156983141983154983156983145983143983144983156 983138983157983148983147983144983141983137983140983155 983149983157983155983156 983141983160983156983141983150983140 983156983151 983156983144983141 983149983137983145983150 983140983141983139983147
A983150983161 983151983152983141983150983145983150983143 983145983150 983156983144983141 983159983137983156983141983154983156983145983143983144983156 983138983157983148983147983144983141983137983140983155 983149983157983155983156 983138983141 983141983153983157983145983152983152983141983140 983159983145983156983144
983159983137983156983141983154983156983145983143983144983156 983141983153983157983145983152983149983141983150983156983155 (983140983151983151983154983155 983159983145983150983140983151983159983155 983158983137983148983158983141983155 983141983156983139)
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 567
983127A983124E983122983124IGH983124 DOO983122983123
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 667
983127A983124E983122983124IGH983124 DOO983122983123
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 767
983127A983124E983122983124IGH983124 DOO983122983123
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 867
D983137983149983137983143983141
991266 I983142 983156983144983141 983155983144983141983148983148 983151983142 983137 983155983144983145983152 983145983155 983140983137983149983137983143983141983140 983148983141983137983147983137983143983141 983159983145983148983148 983156983137983147983141 983152983148983137983139983141
983138983141983156983159983141983141983150 983156983144983141 983155983141983137 983137983150983140 983156983144983141 983140983137983149983137983143983141983140 983155983152983137983139983141983155 983157983150983156983145983148 983155983156983137983138983148983141
983141983153983157983145983148983145983138983154983145983157983149 983145983155 983141983155983156983137983138983148983145983155983144983141983140 983151983154 983157983150983156983145983148 983156983144983141 983155983144983145983152 983139983137983152983155983145983162983141983155 983151983154 983155983145983150983147983155
991266 I983156 983145983155 983145983149983152983154983137983139983156983145983139983137983148 983156983151 983140983141983155983145983143983150 983137 983155983144983145983152 983156983151 983159983145983156983144983155983156983137983150983140 983137983150983161 983152983151983155983155983145983138983148983141
983140983137983149983137983143983141 983140983157983141 983156983151 983139983151983148983148983145983155983145983151983150 983143983154983151983157983150983140983145983150983143 983151983154 983149983145983148983145983156983137983154983161 983137983139983156983145983151983150
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 967
D983137983149983137983143983141
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 1067
983127983137983156983141983154983156983145983143983144983156 983138983157983148983147983144983141983137983140983155 983098 983156983144983141 983144983157983148983148 983145983155 983155983157983138983140983145983158983145983140983141983140 983145983150983156983151 983159983137983156983141983154983156983145983143983144983156
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983127983137983156983141983154983156983145983143983144983156 983106983157983148983147983144983141983137983140983155
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 1167
983106983157983148983147983144983141983137983140 983108983141983139983147983155
983106983157983148983147983144983141983137983140 983140983141983139983147983155 983098 983156983144983141 983140983141983139983147 983157983152 983156983151 983159983144983145983139983144 983156983144983141983155983141 983138983157983148983147983144983141983137983140983155 983141983160983156983141983150983140983155
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 1267
983117983137983154983143983145983150 983116983145983150983141
983117983137983154983143983145983150 983148983145983150983141 983145983155 983137 983148983145983150983141 983140983141983142983145983150983145983150983143 983156983144983141 983144983145983143983144983141983155983156 983152983141983154983149983141983155983155983145983138983148983141 983148983151983139983137983156983145983151983150 983151983150 983156983144983141 983155983145983140983141 983151983142 983156983144983141
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A983142983156983141983154 983142983148983151983151983140983145983150983143 983151983142 983137 983152983154983141983155983139983154983145983138983141983140 983150983157983149983138983141983154 983151983142 983139983151983149983152983137983154983156983149983141983150983156983155 983156983144983141 983155983144983145983152 983155983144983137983148983148 983150983151983156
983155983157983138983149983141983154983143983141 983138983141983161983151983150983140 983137 983148983145983150983141 983155983145983156983157983137983156983141983140 983137983156 983148983141983137983155983156 76 983149983149 B983141983148983151983159 983156983144983141 983140983141983139983147 983137983156 983155983145983140983141
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 1367
983117983137983154983143983145983150 983116983145983150983141
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 1467
983117983137983154983143983145983150 983116983145983150983141
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 1567
Permability is the ratio of amount of water that can a enter or a
compartment or tank to the total volume of compartment or tank
VOLUME TOTAL
VOLUME AVAILABLE TY PERMEABILI =
983120983141983154983149983141983137983138983145983148983145983156983161 μ
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 1667
983123983157983154983142983137983139983141 983120983141983154983149983141983137983138983145983148983145983156983161 μ983137
Surface permability is the percentage of a waterplane that can be
occupied by water
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 1767
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 1867
A cargo hold with dimensions of l = 1524m w = 914 m
h=61 m is completely flooded Determine the volume of the
space and the corrected flooded volume
Volume = 1524 m x 914 m x 61 m = 8497 m3
Flooded volume = Volume x permeability
Flooded volume = 8497 m3 x 60
Flooded volume = 5098 m3
Example 1
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 1967
983110983148983151983151983140983137983138983148983141 983116983141983150983143983156983144
983110983148983151983151983140983137983138983148983141 983148983141983150983143983156983144983098 983137983156 983137 983143983145983158983141983150 983152983151983145983150983156 983151983142 983156983144983141 983155983144983145983152 983148983141983150983143983156983144 983145983155 983156983144983141 983149983137983160983145983149983157983149 983148983141983150983143983156983144
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983155983144983145983152 983138983141983161983151983150983140 983149983137983154983143983145983150 983148983145983150983141
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8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 2067
983110983148983151983151983140983137983138983148983141 983116983141983150983143983156983144 983107983157983154983158983141
983110983148983151983151983140983137983138983148983141 983116983141983150983143983156983144 983107983157983154983158983141983098 I983156 983145983155 983151983138983156983137983145983150983141983140 983138983161 983156983144983141 983139983151983150983150983141983139983156983145983151983150 983151983142 983142983148983151983151983140983137983138983148983141 983148983141983150983143983156983144983155 983137983156
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8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 2167
983110983137983139983156983151983154 983151983142 983123983157983138983140983145983158983145983155983145983151983150
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8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 2267
983120983141983154983149983145983155983155983145983138983148983141 983116983141983150983143983156983144
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8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 2367
D983141983156983141983154983149983145983150983137983156983145983151983150 983151983142 983156983144983141 983148983151983139983137983156983145983151983150 983151983142 983156983144983141 983158983151983148983157983149983141 983139983141983150983156983154983141 983151983142
983140983137983149983137983143983141983140 983139983151983149983152983137983154983156983149983141983150983156
Δ I983150983145983156983145983137983148 983140983145983155983152983148983137983139983141983149983141983150983156 Δ1 D983145983155983152983148983137983139983141983149983141983150983156 983137983142983156983141983154 983140983137983149983137983143983141983140
B I983150983145983156983145983137983148 983139983141983150983156983154983141 983151983142 983138983157983151983161983137983150983139983161
G I983150983145983156983145983137983148 983139983141983150983156983154983141 983151983142 9831439831549831379831589831459831569831619831600 I983150983145983156983145983137983148 983139983141983150983156983154983141 983151983142 983148983151983150983143983145983156983157983140983145983150983137983148 983138983157983151983161983137983150983139983161 LCB
983158983159 983124983144983141 983158983151983148983157983149983141 983151983142 983159983137983156983141983154 983141983150983156983141983154983145983150983143 983156983144983141 983158983141983155983155983141983148
983160983159 D983145983155983156983137983150983139983141 983151983142 983158983151983148983157983149983141 983139983141983150983156983154983141 983151983142 983140983137983149983137983143983141983140 983139983151983149983152983137983154983156983149983141983150983156 983142983154983151983149 983149983137983141983155983156983151983154983161
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 2467
D983141983156983141983154983149983145983150983137983156983145983151983150 983151983142 983156983144983141 983148983151983139983137983156983145983151983150 983151983142 983156983144983141 983158983151983148983157983149983141 983139983141983150983156983154983141 983151983142
983140983137983149983137983143983141983140 983139983151983149983152983137983154983156983149983141983150983156
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 2567
D983141983156983141983154983149983145983150983137983156983145983151983150 983151983142 983156983144983141 983158983151983148983157983149983141 983151983142 983159983137983156983141983154 983141983150983156983141983154983145983150983143 983156983144983141 983158983141983155983155983141983148
Initial displacement and longitudinal centre of buoyancy (LCB) can be read from hydrostatcic curves
However displacement and LCB are unknown after damaged
Therefore if trim forward and aft draught are known trimmed waterline can be drawn over Bonjean
area curves
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 2667
983108983141983156983141983154983149983145983150983137983156983145983151983150 983151983142 983140983137983149983137983143983141983140 983148983141983150983143983156983144 983137983150983140 983148983151983139983137983156983145983151983150 983151983142 983149983145983140
983151983142 983139983151983149983152983137983154983156983149983141983150983156
vw The volume of water entering the vessel
xw Distance of volume centre of damaged compartment from maestory
micro Permability of the compartment
v0 Volume of the compartment
xm Distance of the volume centre of the compartment to the mid of damaged length
xl Distance of the mid of damaged length of compartment to maestory
xc Distance of the computed volume centre of compartment to maestory (xc=xl-xm)
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 2767
983108983141983156983141983154983149983145983150983137983156983145983151983150 983151983142 983140983137983149983137983143983141983140 983148983141983150983143983156983144 983137983150983140 983148983151983139983137983156983145983151983150 983151983142 983149983145983140
983151983142 983139983151983149983152983137983154983156983149983141983150983156
Damaged length and location of compartment can be determined by iterative
procedure
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 2867
bull The volume of water entering the vessel (vw)
bull Distance of volume centre of damaged compartment from amidships Θ ( xw)
bull Volume of the compartment (v0
= vw
μ)
First trial
1) Assume xm=0 (xl=xw)
2) Damaged Length l1 = (Volume of the compartment v0) (mean sec Area Amean)
where Amean is determined from trimmed sectional area curve
983108983141983156983141983154983149983145983150983137983156983145983151983150 983151983142 983140983137983149983137983143983141983140 983148983141983150983143983156983144 983137983150983140 983148983151983139983137983156983145983151983150 983151983142 983149983145983140
983151983142 983139983151983149983152983137983154983156983149983141983150983156
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 2967
3) In order to determine vm and xm
s = l1 4
vm = (s 3) sum3
xm = s sum4 sum3
xc = xl ndash xm
|vm-v0| le Tolarence for volume
|xc-xw| le Tolarence for location of volume centre
l=l1 xl=xw
983108983141983156983141983154983149983145983150983137983156983145983151983150 983151983142 983140983137983149983137983143983141983140 983148983141983150983143983156983144 983137983150983140 983148983151983139983137983156983145983151983150 983151983142 983149983145983140
983151983142 983139983151983149983152983137983154983156983149983141983150983156
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 3067
983108983141983156983141983154983149983145983150983137983156983145983151983150 983151983142 983140983137983149983137983143983141983140 983148983141983150983143983156983144 983137983150983140 983148983151983139983137983156983145983151983150 983151983142 983149983145983140
983151983142 983139983151983149983152983137983154983156983149983141983150983156Second Trial
Damaged length is changed proportionally by the volume
l2 = l1 times (v0v
m)
vm Computed volume at first trial
If the value of xm computed at first trial is negative then the mid of the
compartment slides to the bow
xl = xw+xm
where xm is the distance of the volume centre of compartment to amidship
computed at first trial
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 3167
In order to determine vm and xm
983108983141983156983141983154983149983145983150983137983156983145983151983150 983151983142 983140983137983149983137983143983141983140 983148983141983150983143983156983144 983137983150983140 983148983151983139983137983156983145983151983150 983151983142 983149983145983140
983151983142 983139983151983149983152983137983154983156983149983141983150983156
s = l2 4
vm = (s 3) sum3
xm = s sum4 sum3
xc = xl ndash xm
|vm-v0| le Tolarence for volume
|xc-xw| le Tolarence for location of volume centre
l=l2
If tolarances for both volume and location are not satisfied third fourthtrials are made similar to
second trial
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 3267
If either tolarence for volume or tolarance for location are satisfied at a trial
satisfied one is fixed trials are continued to make for the other one
983108983141983156983141983154983149983145983150983137983156983145983151983150 983151983142 983140983137983149983137983143983141983140 983148983141983150983143983156983144 983137983150983140 983148983151983139983137983156983145983151983150 983151983142 983149983145983140
983151983142 983139983151983149983152983137983154983156983149983141983150983156
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 3367
A ship is 116 meter long and displaces 7842 ton in salt water (ρ1=1025 tm3)
when her mean draught is 64m Longitudinal Centre of Buoyancy (LCB) is
0615 m aft from amidships After one of her stern compartment is damaged
she floats trimmed to the aft Her sectional areas after damaged are given in the
following table
a) Determine the volume of water entering the vessel (vw) and the location of
volume centre of damaged compartment (xw)
b) Assume permability of compartment micro is 1 Determine damaged length
and Distance of the mid of damaged length of compartment to amidship
983109983160983137983149983152983148983141 2
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 3467
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 3567
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 3667
Predicted xw
is between section 2 and section 3
983123983141983139 N983151 983123983141983139 A983154983141983137 D983145983155983156 A9831499831459831559831449831459831522 10135 983085348
3 1208 983085232
983123983141983139 A983154983141983137 983137983156 98308524983149 983142983154983151983149 983137983149983145983140983155983144983145983152 = 11959831492
l1=v0Amean=204081195=17078 m
s=l14=427 m
983109983160983137983149983152983148983141 2983085983123983119983116983125983124983113983119983118
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 3767
983161983145 L983151983139 A983149983141983137983150 983123M M A983154983149
9831311983133 9831312983133 98313119831339832559831312983133 9831313983133 983131198313398325598313129831339832559831313983133
0 9830853254 1051 1 1051 2 21021 9830852827 1123 4 4492 1 4492
2 98308524 1195 2 239 0 0
3 9830851973 1219 4 4876 9830851 9830854876
4 9830851546 1233 1 1233 9830852 9830852466
sum983091983101 14042 sum983092983101 983085748
vm
= (s3) sum3= 199864479831493
xm
=s sum4sum3= 9830850227983149
v0-vm=20408-19986=422 m3
Error=422times10020408=207
983109983160983137983149983152983148983141 2983085983123983119983116983125983124983113983119983118
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 3867
Methods of Calculation
There two available method calculating the
final stage of the damaged vessel
bull Lost Buoyancy Method
bull Added Weight Method
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 3967
Comparision of Lost Buoyancy and Added
Weight Methods
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 4067
Consider a vessel that has been damaged such
that a portion of the bottom is now open to the
sea
The vesselrsquos draft will increase because an amount
of the buoyancy was lost
Added Weight Method
Added Weight Method
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 4167
Added Weight Method
In this method flood water is treated as a fixed weight (for example the
weight of water of volume ABEF) This added weight is balanced by the
additional buoyant force of the layer WL1WL
The added weight can be determined by either the volume ABEF or
waterline WL1 Therefore WL1 waterline is not known can be just guessed
For the predicted waterline added weight and additional buoyant force
caculation are done iteratively until both of them are equal This method is
known as Added weight method
Determination of Added Weight
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 4267
Determination of Added Weight
vc Volume of damaged compartment (DCEF)
ac The surface area (AB) of damaged compartment on the waterline
micro The volume permability of damaged compartment
microa The area permability of the surface of damaged compartment
∆ The initial displacement
∆1 The displacement at final stage
vw The volume of water entering the vessel (ABEH)
w The weight of water entering the vessel
p The value of parallel sinkage
If th t th l l i k i h f t l f
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 4367
If we assume that the paralel sinkage cause a minor change of water plane area of a
ship (Awp
asymp Awp1
) we can determine the paralel sinkage by equating the volume of
the layer WL1WL to the volume of ABEF
If the damaged compartment is bounded on top
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 4467
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 4567
Longitudinal Metacentre Radius at final stage
Free Surface Effect
Damaged compartment can be considered as a half filled tank
Free Contact Effect
Damaged compartment can be considered as a half filled tank
T M H i h
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 4667
Transverse Metacentre Height
The angle of heel
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 4767
L it di l M t t H i ht
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 4867
Longitudinal Metacentre Height
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 4967
E983160983137983149983152983148983141 A 983138983137983154983143983141
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 5067
E983160983137983149983152983148983141 A 983138983137983154983143983141
991266 L = 20 983149991266 B = 5 983149
991266 983124 = 15 983149
991266 KG = 15 983149
I983150983156983137983139983156 C983151983150983140983145983156983145983151983150
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 5167
I983150983156983137983139983156 C983151983150983140983145983156983145983151983150
991266 983124983144983141 983140983145983155983152983148983137983139983141983149983141983150983156 983158983151983148983157983149983141
991266 983124983144983141 983149983137983155983155 983140983145983155983152983148983137983139983141983149983141983150983156
991266 983124983144983141 983149983151983149983141983150983156 983151983142 983145983150983141983154983156983145983137 983151983142 983156983144983141 983159983137983156983141983154983152983148983137983150983141 983137983154983141983137983137983138983151983157983156 CL
3
15051520 m x xT B L
I I
==sdotsdot=nabla
tons x I
751531500251 ==nablasdot=∆ ρ
433
33208
12
205
12
m x L B
I I
===
I983150983156983137983139983156 C983151983150983140983145983156983145983151983150
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 5267
I983150983156983137983139983156 C983151983150983140983145983156983145983151983150
991266 M983141983156983137983139983141983150983156983154983145983139 983154983137983140983145983157983155
991266 O983154 983145983156 983139983151983157983148983140 983138983141 983139983137983148983139983157983148983137983156983141983140 983140983145983154983141983139983156983148983161 983137983155
991266 H983141983145983143983144983156 983151983142 983156983144983141 983139983141983150983156983141983154 983151983142 983138983157983151983161983137983150983139983161
m I
BM
I
I 3891
150
33208==
nabla
=
m xT
B
LBT
L B BM
I I
I 3891
5112
5
12
12 223
====
mT
KB I
I 750
2
==
I983150983156983137983139983156 C983151983150983140983145983156983145983151983150
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 5367
991266 983124983144983141 983149983141983156983137983139983141983150983156983154983145983139 983144983141983145983143983144983156
991266 F983151983154 983155983149983137983148983148 983137983150983143983148983141983155 983151983142 983144983141983141983148 983156983144983141 983154983145983143983144983156983145983150983143 983149983151983149983141983150983156
m KG BM KBGM I I 63905013891750 =minus+=minus+=
sin22998sin693075153sin mt x xGM M I I
φ φ φ ==∆=
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 5467
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 5567
983116983119983123983124 983106983125983119983129983105983118983107983129 983117983109983124983112983119983108
Paralel Sinkage
Volume (DCEF)=Volume (W1ADW+BL1LC)
Damaged compartment is bounded on top
983116983119983123983124 983106983125983119983129983105983118983107983129 983117983109983124983112983119983108
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 5667
983116983119983123983124 983106983125983119983129983105983118983107983129 983117983109983124983112983119983108
bull It is assumed that displacement and location of vertical centre
of gravity does not change after damaged
983116983119983123983124 983106983125983119983129983105983118983107983129 983117983109983124983112983119983108
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 5767
983116983119983123983124 983106983125983119983129983105983118983107983129 983117983109983124983112983119983108
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 5867
The heel angle of damaged ship is determined by
where
d is the distance between the volume centre of damaged compartment
and the new longitudinal centre of floatation
wc=vc μ ρ
983116983119983123983124 983106983125983119983129983105983118983107983129 983117983109983124983112983119983108
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 5967
983116983119983123983124 983106983125983119983129983105983118983107983129 983117983109983124983112983119983108
983116983119983123983124 983106983125983119983129983105983118983107983129 983117983109983124983112983119983108
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 6067
Longitudinal Metacentre Height of a Damaged Ship
983116983119983123983124 983106983125983119983129983105983118983107983129 983117983109983124983112983119983108
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 6167
983110983151983154983159983137983154983140 983137983150983140 983137983142983156 983140983154983137983157983143983144983156983155 983137983142983156983141983154 983140983137983149983137983143983141983140
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 6267
983120983151983154983156 983105983142983156 983120983151983154983156 983110983151983154983141 983123983156983137983154983138983151983137983154983140 983105983142983156 983123983156983137983154983138983151983137983154983140 983110983151983154983159983137983154983140
I983150983145983156983145983137983148 D983154983137983157983143983144983156 983124 983124 983124 983124
983120983137983154983137983148983141983148 983123983145983150983147983137983143983141 +983152 +983152 +983152 +983120
H983141983141983148 983085983149983145 983085983149983145 +983149983155 +983149983155
983124983154983145983149 983085983156983147 +983156983138 983085983156983147 +983156983138
F983145983150983137983148 D983154983137983157983143983144983156 983124+983152983085983149983145983085983156983147 983124+983152983085983149983145+983156983138 983124+983152+983149983155983085983156983147 983124+983152+983149983155+983156983138
Table 1 Final Draughts for a starboard side damaged ship
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 6367
L983151983155983156 B983157983151983161983137983150983139983161 M983141983156983144983151983140
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 6467
L983151983155983156 B983157983151983161983137983150983139983161 M983141983156983144983151983140
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 6567
991266 A983142983156983141983154 983148983151983151983155983145983150983143 983156983144983141 983139983141983150983156983154983137983148 983139983151983149983152983137983154983156983149983141983150983156 983156983144983141
983159983137983156983141983154983152983148983137983150983141 983137983154983141983137 983145983155
991266 983124983151 983139983151983149983152983141983150983155983137983156983141 983142983151983154 983156983144983141 983148983151983155983155 983151983142 983138983157983151983161983137983150983139983161 983151983142 983156983144983141
983139983141983150983156983154983137983148 983139983151983149983152983137983154983156983149983141983150983156 983156983144983141 983140983154983137983142983156 983145983150983139983154983141983137983155983141983155 983156983151
2805)420()( m x Bl L A L
=minus=minus=
m A
T
L
I
L 875180
150==
nabla=
L983151983155983156 B983157983151983161983137983150983139983161 M983141983156983144983151983140
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 6667
991266 983124983144983141 983144983141983145983143983144983156 983151983142 983156983144983141 983139983141983150983156983141983154 983151983142 983138983157983151983161983137983150983139983161 983145983150983139983154983141983137983155983141983155 983156983151
991266 983124983144983141 983149983151983149983141983150983156 983151983142 983145983150983141983154983156983145983137 983151983142 983156983144983141 983159983137983156983141983154983152983148983137983150983141 983137983154983141983137
991266 983124983144983141 983149983141983156983137983139983141983150983156983154983145983139 983154983137983140983145983157983155
m
T
KB L
L 93802
8751
2 ===
433
6716612
)420(5
12
)(m
l L B I L
=minus
=minus
=
m I
BM
I
L
L 1111150
67166==
nabla
=
L983151983155983156 B983157983151983161983137983150983139983161 M983141983156983144983151983140
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 6767
991266 983124983144983141 983149983141983156983137983139983141983150983156983154983145983139 983144983141983145983143983144983156
991266 983122983145983143983144983156983145983150983143 983149983151983149983141983150983156 983142983151983154 983155983149983137983148983148 983144983141983141983148 983137983150983143983148983141983155
m KG BM KBGM L L L 54905111119380 =minus+=minus+=
mt xGM M L
sin34984sin549075153sin φ φ φ ==∆=
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 467
983127A983124E983122983124IGH983124NE983123983123983127983137983156983141983154983156983145983143983144983156 983149983141983137983150983155 983154983141983155983145983155983156983137983150983139983141 983151983142 983156983144983141 983155983156983154983157983139983156983157983154983141 983137983143983137983145983150983155983156 983155983156983137983156983145983139 983159983137983156983141983154
983152983154983141983155983155983157983154983141 983159983145983156983144983151983157983156 983137983150983161 983148983141983137983147983137983143983141
I983156 983152983154983141983158983141983150983156983155 983159983137983156983141983154 983151983154 983137983150983161 983151983156983144983141983154 983148983145983153983157983145983140 983156983151 983142983148983151983159 983151983156983144983141983154 983139983151983149983152983137983154983156983149983141983150983156983155
(983151983154 983145983150 983156983144983141 983151983152983152983151983155983145983156983141 983140983145983154983141983139983156983145983151983150)
983124983144983141 983149983137983145983150 983140983141983139983147 983137983150983140 983149983137983145983150 983138983157983148983147983144983141983137983140983155 983151983142 983137 983155983144983145983152 983149983157983155983156 983138983141 983159983137983156983141983154983156983145983143983144983156
983127983137983156983141983154983156983145983143983144983156 983138983157983148983147983144983141983137983140983155 983149983157983155983156 983141983160983156983141983150983140 983156983151 983156983144983141 983149983137983145983150 983140983141983139983147
A983150983161 983151983152983141983150983145983150983143 983145983150 983156983144983141 983159983137983156983141983154983156983145983143983144983156 983138983157983148983147983144983141983137983140983155 983149983157983155983156 983138983141 983141983153983157983145983152983152983141983140 983159983145983156983144
983159983137983156983141983154983156983145983143983144983156 983141983153983157983145983152983149983141983150983156983155 (983140983151983151983154983155 983159983145983150983140983151983159983155 983158983137983148983158983141983155 983141983156983139)
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 567
983127A983124E983122983124IGH983124 DOO983122983123
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 667
983127A983124E983122983124IGH983124 DOO983122983123
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 767
983127A983124E983122983124IGH983124 DOO983122983123
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 867
D983137983149983137983143983141
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8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 967
D983137983149983137983143983141
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 1067
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8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 1167
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8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 1267
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8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 1367
983117983137983154983143983145983150 983116983145983150983141
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 1467
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8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 1567
Permability is the ratio of amount of water that can a enter or a
compartment or tank to the total volume of compartment or tank
VOLUME TOTAL
VOLUME AVAILABLE TY PERMEABILI =
983120983141983154983149983141983137983138983145983148983145983156983161 μ
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 1667
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Surface permability is the percentage of a waterplane that can be
occupied by water
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 1767
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 1867
A cargo hold with dimensions of l = 1524m w = 914 m
h=61 m is completely flooded Determine the volume of the
space and the corrected flooded volume
Volume = 1524 m x 914 m x 61 m = 8497 m3
Flooded volume = Volume x permeability
Flooded volume = 8497 m3 x 60
Flooded volume = 5098 m3
Example 1
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 1967
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8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 2067
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8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 2167
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8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 2267
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8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 2367
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Δ I983150983145983156983145983137983148 983140983145983155983152983148983137983139983141983149983141983150983156 Δ1 D983145983155983152983148983137983139983141983149983141983150983156 983137983142983156983141983154 983140983137983149983137983143983141983140
B I983150983145983156983145983137983148 983139983141983150983156983154983141 983151983142 983138983157983151983161983137983150983139983161
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8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 2467
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8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 2567
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Initial displacement and longitudinal centre of buoyancy (LCB) can be read from hydrostatcic curves
However displacement and LCB are unknown after damaged
Therefore if trim forward and aft draught are known trimmed waterline can be drawn over Bonjean
area curves
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 2667
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vw The volume of water entering the vessel
xw Distance of volume centre of damaged compartment from maestory
micro Permability of the compartment
v0 Volume of the compartment
xm Distance of the volume centre of the compartment to the mid of damaged length
xl Distance of the mid of damaged length of compartment to maestory
xc Distance of the computed volume centre of compartment to maestory (xc=xl-xm)
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 2767
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Damaged length and location of compartment can be determined by iterative
procedure
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 2867
bull The volume of water entering the vessel (vw)
bull Distance of volume centre of damaged compartment from amidships Θ ( xw)
bull Volume of the compartment (v0
= vw
μ)
First trial
1) Assume xm=0 (xl=xw)
2) Damaged Length l1 = (Volume of the compartment v0) (mean sec Area Amean)
where Amean is determined from trimmed sectional area curve
983108983141983156983141983154983149983145983150983137983156983145983151983150 983151983142 983140983137983149983137983143983141983140 983148983141983150983143983156983144 983137983150983140 983148983151983139983137983156983145983151983150 983151983142 983149983145983140
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8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 2967
3) In order to determine vm and xm
s = l1 4
vm = (s 3) sum3
xm = s sum4 sum3
xc = xl ndash xm
|vm-v0| le Tolarence for volume
|xc-xw| le Tolarence for location of volume centre
l=l1 xl=xw
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8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 3067
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983151983142 983139983151983149983152983137983154983156983149983141983150983156Second Trial
Damaged length is changed proportionally by the volume
l2 = l1 times (v0v
m)
vm Computed volume at first trial
If the value of xm computed at first trial is negative then the mid of the
compartment slides to the bow
xl = xw+xm
where xm is the distance of the volume centre of compartment to amidship
computed at first trial
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 3167
In order to determine vm and xm
983108983141983156983141983154983149983145983150983137983156983145983151983150 983151983142 983140983137983149983137983143983141983140 983148983141983150983143983156983144 983137983150983140 983148983151983139983137983156983145983151983150 983151983142 983149983145983140
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s = l2 4
vm = (s 3) sum3
xm = s sum4 sum3
xc = xl ndash xm
|vm-v0| le Tolarence for volume
|xc-xw| le Tolarence for location of volume centre
l=l2
If tolarances for both volume and location are not satisfied third fourthtrials are made similar to
second trial
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 3267
If either tolarence for volume or tolarance for location are satisfied at a trial
satisfied one is fixed trials are continued to make for the other one
983108983141983156983141983154983149983145983150983137983156983145983151983150 983151983142 983140983137983149983137983143983141983140 983148983141983150983143983156983144 983137983150983140 983148983151983139983137983156983145983151983150 983151983142 983149983145983140
983151983142 983139983151983149983152983137983154983156983149983141983150983156
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 3367
A ship is 116 meter long and displaces 7842 ton in salt water (ρ1=1025 tm3)
when her mean draught is 64m Longitudinal Centre of Buoyancy (LCB) is
0615 m aft from amidships After one of her stern compartment is damaged
she floats trimmed to the aft Her sectional areas after damaged are given in the
following table
a) Determine the volume of water entering the vessel (vw) and the location of
volume centre of damaged compartment (xw)
b) Assume permability of compartment micro is 1 Determine damaged length
and Distance of the mid of damaged length of compartment to amidship
983109983160983137983149983152983148983141 2
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 3467
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 3567
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 3667
Predicted xw
is between section 2 and section 3
983123983141983139 N983151 983123983141983139 A983154983141983137 D983145983155983156 A9831499831459831559831449831459831522 10135 983085348
3 1208 983085232
983123983141983139 A983154983141983137 983137983156 98308524983149 983142983154983151983149 983137983149983145983140983155983144983145983152 = 11959831492
l1=v0Amean=204081195=17078 m
s=l14=427 m
983109983160983137983149983152983148983141 2983085983123983119983116983125983124983113983119983118
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 3767
983161983145 L983151983139 A983149983141983137983150 983123M M A983154983149
9831311983133 9831312983133 98313119831339832559831312983133 9831313983133 983131198313398325598313129831339832559831313983133
0 9830853254 1051 1 1051 2 21021 9830852827 1123 4 4492 1 4492
2 98308524 1195 2 239 0 0
3 9830851973 1219 4 4876 9830851 9830854876
4 9830851546 1233 1 1233 9830852 9830852466
sum983091983101 14042 sum983092983101 983085748
vm
= (s3) sum3= 199864479831493
xm
=s sum4sum3= 9830850227983149
v0-vm=20408-19986=422 m3
Error=422times10020408=207
983109983160983137983149983152983148983141 2983085983123983119983116983125983124983113983119983118
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 3867
Methods of Calculation
There two available method calculating the
final stage of the damaged vessel
bull Lost Buoyancy Method
bull Added Weight Method
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 3967
Comparision of Lost Buoyancy and Added
Weight Methods
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 4067
Consider a vessel that has been damaged such
that a portion of the bottom is now open to the
sea
The vesselrsquos draft will increase because an amount
of the buoyancy was lost
Added Weight Method
Added Weight Method
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 4167
Added Weight Method
In this method flood water is treated as a fixed weight (for example the
weight of water of volume ABEF) This added weight is balanced by the
additional buoyant force of the layer WL1WL
The added weight can be determined by either the volume ABEF or
waterline WL1 Therefore WL1 waterline is not known can be just guessed
For the predicted waterline added weight and additional buoyant force
caculation are done iteratively until both of them are equal This method is
known as Added weight method
Determination of Added Weight
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 4267
Determination of Added Weight
vc Volume of damaged compartment (DCEF)
ac The surface area (AB) of damaged compartment on the waterline
micro The volume permability of damaged compartment
microa The area permability of the surface of damaged compartment
∆ The initial displacement
∆1 The displacement at final stage
vw The volume of water entering the vessel (ABEH)
w The weight of water entering the vessel
p The value of parallel sinkage
If th t th l l i k i h f t l f
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 4367
If we assume that the paralel sinkage cause a minor change of water plane area of a
ship (Awp
asymp Awp1
) we can determine the paralel sinkage by equating the volume of
the layer WL1WL to the volume of ABEF
If the damaged compartment is bounded on top
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 4467
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 4567
Longitudinal Metacentre Radius at final stage
Free Surface Effect
Damaged compartment can be considered as a half filled tank
Free Contact Effect
Damaged compartment can be considered as a half filled tank
T M H i h
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 4667
Transverse Metacentre Height
The angle of heel
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 4767
L it di l M t t H i ht
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 4867
Longitudinal Metacentre Height
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 4967
E983160983137983149983152983148983141 A 983138983137983154983143983141
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 5067
E983160983137983149983152983148983141 A 983138983137983154983143983141
991266 L = 20 983149991266 B = 5 983149
991266 983124 = 15 983149
991266 KG = 15 983149
I983150983156983137983139983156 C983151983150983140983145983156983145983151983150
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 5167
I983150983156983137983139983156 C983151983150983140983145983156983145983151983150
991266 983124983144983141 983140983145983155983152983148983137983139983141983149983141983150983156 983158983151983148983157983149983141
991266 983124983144983141 983149983137983155983155 983140983145983155983152983148983137983139983141983149983141983150983156
991266 983124983144983141 983149983151983149983141983150983156 983151983142 983145983150983141983154983156983145983137 983151983142 983156983144983141 983159983137983156983141983154983152983148983137983150983141 983137983154983141983137983137983138983151983157983156 CL
3
15051520 m x xT B L
I I
==sdotsdot=nabla
tons x I
751531500251 ==nablasdot=∆ ρ
433
33208
12
205
12
m x L B
I I
===
I983150983156983137983139983156 C983151983150983140983145983156983145983151983150
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 5267
I983150983156983137983139983156 C983151983150983140983145983156983145983151983150
991266 M983141983156983137983139983141983150983156983154983145983139 983154983137983140983145983157983155
991266 O983154 983145983156 983139983151983157983148983140 983138983141 983139983137983148983139983157983148983137983156983141983140 983140983145983154983141983139983156983148983161 983137983155
991266 H983141983145983143983144983156 983151983142 983156983144983141 983139983141983150983156983141983154 983151983142 983138983157983151983161983137983150983139983161
m I
BM
I
I 3891
150
33208==
nabla
=
m xT
B
LBT
L B BM
I I
I 3891
5112
5
12
12 223
====
mT
KB I
I 750
2
==
I983150983156983137983139983156 C983151983150983140983145983156983145983151983150
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 5367
991266 983124983144983141 983149983141983156983137983139983141983150983156983154983145983139 983144983141983145983143983144983156
991266 F983151983154 983155983149983137983148983148 983137983150983143983148983141983155 983151983142 983144983141983141983148 983156983144983141 983154983145983143983144983156983145983150983143 983149983151983149983141983150983156
m KG BM KBGM I I 63905013891750 =minus+=minus+=
sin22998sin693075153sin mt x xGM M I I
φ φ φ ==∆=
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 5467
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 5567
983116983119983123983124 983106983125983119983129983105983118983107983129 983117983109983124983112983119983108
Paralel Sinkage
Volume (DCEF)=Volume (W1ADW+BL1LC)
Damaged compartment is bounded on top
983116983119983123983124 983106983125983119983129983105983118983107983129 983117983109983124983112983119983108
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 5667
983116983119983123983124 983106983125983119983129983105983118983107983129 983117983109983124983112983119983108
bull It is assumed that displacement and location of vertical centre
of gravity does not change after damaged
983116983119983123983124 983106983125983119983129983105983118983107983129 983117983109983124983112983119983108
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 5767
983116983119983123983124 983106983125983119983129983105983118983107983129 983117983109983124983112983119983108
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 5867
The heel angle of damaged ship is determined by
where
d is the distance between the volume centre of damaged compartment
and the new longitudinal centre of floatation
wc=vc μ ρ
983116983119983123983124 983106983125983119983129983105983118983107983129 983117983109983124983112983119983108
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 5967
983116983119983123983124 983106983125983119983129983105983118983107983129 983117983109983124983112983119983108
983116983119983123983124 983106983125983119983129983105983118983107983129 983117983109983124983112983119983108
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 6067
Longitudinal Metacentre Height of a Damaged Ship
983116983119983123983124 983106983125983119983129983105983118983107983129 983117983109983124983112983119983108
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 6167
983110983151983154983159983137983154983140 983137983150983140 983137983142983156 983140983154983137983157983143983144983156983155 983137983142983156983141983154 983140983137983149983137983143983141983140
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 6267
983120983151983154983156 983105983142983156 983120983151983154983156 983110983151983154983141 983123983156983137983154983138983151983137983154983140 983105983142983156 983123983156983137983154983138983151983137983154983140 983110983151983154983159983137983154983140
I983150983145983156983145983137983148 D983154983137983157983143983144983156 983124 983124 983124 983124
983120983137983154983137983148983141983148 983123983145983150983147983137983143983141 +983152 +983152 +983152 +983120
H983141983141983148 983085983149983145 983085983149983145 +983149983155 +983149983155
983124983154983145983149 983085983156983147 +983156983138 983085983156983147 +983156983138
F983145983150983137983148 D983154983137983157983143983144983156 983124+983152983085983149983145983085983156983147 983124+983152983085983149983145+983156983138 983124+983152+983149983155983085983156983147 983124+983152+983149983155+983156983138
Table 1 Final Draughts for a starboard side damaged ship
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 6367
L983151983155983156 B983157983151983161983137983150983139983161 M983141983156983144983151983140
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 6467
L983151983155983156 B983157983151983161983137983150983139983161 M983141983156983144983151983140
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 6567
991266 A983142983156983141983154 983148983151983151983155983145983150983143 983156983144983141 983139983141983150983156983154983137983148 983139983151983149983152983137983154983156983149983141983150983156 983156983144983141
983159983137983156983141983154983152983148983137983150983141 983137983154983141983137 983145983155
991266 983124983151 983139983151983149983152983141983150983155983137983156983141 983142983151983154 983156983144983141 983148983151983155983155 983151983142 983138983157983151983161983137983150983139983161 983151983142 983156983144983141
983139983141983150983156983154983137983148 983139983151983149983152983137983154983156983149983141983150983156 983156983144983141 983140983154983137983142983156 983145983150983139983154983141983137983155983141983155 983156983151
2805)420()( m x Bl L A L
=minus=minus=
m A
T
L
I
L 875180
150==
nabla=
L983151983155983156 B983157983151983161983137983150983139983161 M983141983156983144983151983140
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 6667
991266 983124983144983141 983144983141983145983143983144983156 983151983142 983156983144983141 983139983141983150983156983141983154 983151983142 983138983157983151983161983137983150983139983161 983145983150983139983154983141983137983155983141983155 983156983151
991266 983124983144983141 983149983151983149983141983150983156 983151983142 983145983150983141983154983156983145983137 983151983142 983156983144983141 983159983137983156983141983154983152983148983137983150983141 983137983154983141983137
991266 983124983144983141 983149983141983156983137983139983141983150983156983154983145983139 983154983137983140983145983157983155
m
T
KB L
L 93802
8751
2 ===
433
6716612
)420(5
12
)(m
l L B I L
=minus
=minus
=
m I
BM
I
L
L 1111150
67166==
nabla
=
L983151983155983156 B983157983151983161983137983150983139983161 M983141983156983144983151983140
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 6767
991266 983124983144983141 983149983141983156983137983139983141983150983156983154983145983139 983144983141983145983143983144983156
991266 983122983145983143983144983156983145983150983143 983149983151983149983141983150983156 983142983151983154 983155983149983137983148983148 983144983141983141983148 983137983150983143983148983141983155
m KG BM KBGM L L L 54905111119380 =minus+=minus+=
mt xGM M L
sin34984sin549075153sin φ φ φ ==∆=
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 567
983127A983124E983122983124IGH983124 DOO983122983123
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 667
983127A983124E983122983124IGH983124 DOO983122983123
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 767
983127A983124E983122983124IGH983124 DOO983122983123
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 867
D983137983149983137983143983141
991266 I983142 983156983144983141 983155983144983141983148983148 983151983142 983137 983155983144983145983152 983145983155 983140983137983149983137983143983141983140 983148983141983137983147983137983143983141 983159983145983148983148 983156983137983147983141 983152983148983137983139983141
983138983141983156983159983141983141983150 983156983144983141 983155983141983137 983137983150983140 983156983144983141 983140983137983149983137983143983141983140 983155983152983137983139983141983155 983157983150983156983145983148 983155983156983137983138983148983141
983141983153983157983145983148983145983138983154983145983157983149 983145983155 983141983155983156983137983138983148983145983155983144983141983140 983151983154 983157983150983156983145983148 983156983144983141 983155983144983145983152 983139983137983152983155983145983162983141983155 983151983154 983155983145983150983147983155
991266 I983156 983145983155 983145983149983152983154983137983139983156983145983139983137983148 983156983151 983140983141983155983145983143983150 983137 983155983144983145983152 983156983151 983159983145983156983144983155983156983137983150983140 983137983150983161 983152983151983155983155983145983138983148983141
983140983137983149983137983143983141 983140983157983141 983156983151 983139983151983148983148983145983155983145983151983150 983143983154983151983157983150983140983145983150983143 983151983154 983149983145983148983145983156983137983154983161 983137983139983156983145983151983150
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 967
D983137983149983137983143983141
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 1067
983127983137983156983141983154983156983145983143983144983156 983138983157983148983147983144983141983137983140983155 983098 983156983144983141 983144983157983148983148 983145983155 983155983157983138983140983145983158983145983140983141983140 983145983150983156983151 983159983137983156983141983154983156983145983143983144983156
983139983151983149983152983137983154983156983149983141983150983156983155 983138983161 983149983141983137983150983155 983151983142 983159983137983156983141983154983156983145983143983144983156 983138983157983148983147983144983141983137983140983155 983137983150983140 983140983141983139983147983155
983127983137983156983141983154983156983145983143983144983156 983106983157983148983147983144983141983137983140983155
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 1167
983106983157983148983147983144983141983137983140 983108983141983139983147983155
983106983157983148983147983144983141983137983140 983140983141983139983147983155 983098 983156983144983141 983140983141983139983147 983157983152 983156983151 983159983144983145983139983144 983156983144983141983155983141 983138983157983148983147983144983141983137983140983155 983141983160983156983141983150983140983155
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 1267
983117983137983154983143983145983150 983116983145983150983141
983117983137983154983143983145983150 983148983145983150983141 983145983155 983137 983148983145983150983141 983140983141983142983145983150983145983150983143 983156983144983141 983144983145983143983144983141983155983156 983152983141983154983149983141983155983155983145983138983148983141 983148983151983139983137983156983145983151983150 983151983150 983156983144983141 983155983145983140983141 983151983142 983156983144983141
983158983141983155983155983141983148 983151983142 983137983150983161 983140983137983149983137983143983141983140 983159983137983156983141983154983152983148983137983150983141 983145983150 983156983144983141 983142983145983150983137983148 983139983151983150983140983145983156983145983151983150 983151983142 983155983145983150983147983137983143983141983156983154983145983149 983137983150983140 983144983141983141983148
A983142983156983141983154 983142983148983151983151983140983145983150983143 983151983142 983137 983152983154983141983155983139983154983145983138983141983140 983150983157983149983138983141983154 983151983142 983139983151983149983152983137983154983156983149983141983150983156983155 983156983144983141 983155983144983145983152 983155983144983137983148983148 983150983151983156
983155983157983138983149983141983154983143983141 983138983141983161983151983150983140 983137 983148983145983150983141 983155983145983156983157983137983156983141983140 983137983156 983148983141983137983155983156 76 983149983149 B983141983148983151983159 983156983144983141 983140983141983139983147 983137983156 983155983145983140983141
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 1367
983117983137983154983143983145983150 983116983145983150983141
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 1467
983117983137983154983143983145983150 983116983145983150983141
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 1567
Permability is the ratio of amount of water that can a enter or a
compartment or tank to the total volume of compartment or tank
VOLUME TOTAL
VOLUME AVAILABLE TY PERMEABILI =
983120983141983154983149983141983137983138983145983148983145983156983161 μ
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 1667
983123983157983154983142983137983139983141 983120983141983154983149983141983137983138983145983148983145983156983161 μ983137
Surface permability is the percentage of a waterplane that can be
occupied by water
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 1767
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 1867
A cargo hold with dimensions of l = 1524m w = 914 m
h=61 m is completely flooded Determine the volume of the
space and the corrected flooded volume
Volume = 1524 m x 914 m x 61 m = 8497 m3
Flooded volume = Volume x permeability
Flooded volume = 8497 m3 x 60
Flooded volume = 5098 m3
Example 1
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 1967
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8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 2067
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8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 2167
983110983137983139983156983151983154 983151983142 983123983157983138983140983145983158983145983155983145983151983150
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983138983161 983156983144983141 983137983152983152983148983145983139983137983138983148983141 983154983141983143983157983148983137983156983145983151983150983155 983137983150983140 983138983161 983145983150983156983141983154983150983137983156983145983151983150983137983148 983139983151983150983158983141983150983156983145983151983150 983156983144983137983156
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8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 2267
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983120983141983154983149983145983155983155983145983138983148983141 L983141983150983143983156983144 983145983155 983151983138983156983137983145983150983141983140 983138983161 983149983157983148983156983145983152983148983161983145983150983143 983156983144983141 983142983148983151983151983140983137983138983148983141 983148983141983150983143983156983144 983137983156
983156983144983137983156 983152983151983145983150983156 983138983161 983156983144983141 983142983137983139983156983151983154 983151983142 983155983157983138983140983145983158983145983155983145983151983150
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 2367
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983140983137983149983137983143983141983140 983139983151983149983152983137983154983156983149983141983150983156
Δ I983150983145983156983145983137983148 983140983145983155983152983148983137983139983141983149983141983150983156 Δ1 D983145983155983152983148983137983139983141983149983141983150983156 983137983142983156983141983154 983140983137983149983137983143983141983140
B I983150983145983156983145983137983148 983139983141983150983156983154983141 983151983142 983138983157983151983161983137983150983139983161
G I983150983145983156983145983137983148 983139983141983150983156983154983141 983151983142 9831439831549831379831589831459831569831619831600 I983150983145983156983145983137983148 983139983141983150983156983154983141 983151983142 983148983151983150983143983145983156983157983140983145983150983137983148 983138983157983151983161983137983150983139983161 LCB
983158983159 983124983144983141 983158983151983148983157983149983141 983151983142 983159983137983156983141983154 983141983150983156983141983154983145983150983143 983156983144983141 983158983141983155983155983141983148
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8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 2467
D983141983156983141983154983149983145983150983137983156983145983151983150 983151983142 983156983144983141 983148983151983139983137983156983145983151983150 983151983142 983156983144983141 983158983151983148983157983149983141 983139983141983150983156983154983141 983151983142
983140983137983149983137983143983141983140 983139983151983149983152983137983154983156983149983141983150983156
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 2567
D983141983156983141983154983149983145983150983137983156983145983151983150 983151983142 983156983144983141 983158983151983148983157983149983141 983151983142 983159983137983156983141983154 983141983150983156983141983154983145983150983143 983156983144983141 983158983141983155983155983141983148
Initial displacement and longitudinal centre of buoyancy (LCB) can be read from hydrostatcic curves
However displacement and LCB are unknown after damaged
Therefore if trim forward and aft draught are known trimmed waterline can be drawn over Bonjean
area curves
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 2667
983108983141983156983141983154983149983145983150983137983156983145983151983150 983151983142 983140983137983149983137983143983141983140 983148983141983150983143983156983144 983137983150983140 983148983151983139983137983156983145983151983150 983151983142 983149983145983140
983151983142 983139983151983149983152983137983154983156983149983141983150983156
vw The volume of water entering the vessel
xw Distance of volume centre of damaged compartment from maestory
micro Permability of the compartment
v0 Volume of the compartment
xm Distance of the volume centre of the compartment to the mid of damaged length
xl Distance of the mid of damaged length of compartment to maestory
xc Distance of the computed volume centre of compartment to maestory (xc=xl-xm)
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 2767
983108983141983156983141983154983149983145983150983137983156983145983151983150 983151983142 983140983137983149983137983143983141983140 983148983141983150983143983156983144 983137983150983140 983148983151983139983137983156983145983151983150 983151983142 983149983145983140
983151983142 983139983151983149983152983137983154983156983149983141983150983156
Damaged length and location of compartment can be determined by iterative
procedure
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 2867
bull The volume of water entering the vessel (vw)
bull Distance of volume centre of damaged compartment from amidships Θ ( xw)
bull Volume of the compartment (v0
= vw
μ)
First trial
1) Assume xm=0 (xl=xw)
2) Damaged Length l1 = (Volume of the compartment v0) (mean sec Area Amean)
where Amean is determined from trimmed sectional area curve
983108983141983156983141983154983149983145983150983137983156983145983151983150 983151983142 983140983137983149983137983143983141983140 983148983141983150983143983156983144 983137983150983140 983148983151983139983137983156983145983151983150 983151983142 983149983145983140
983151983142 983139983151983149983152983137983154983156983149983141983150983156
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 2967
3) In order to determine vm and xm
s = l1 4
vm = (s 3) sum3
xm = s sum4 sum3
xc = xl ndash xm
|vm-v0| le Tolarence for volume
|xc-xw| le Tolarence for location of volume centre
l=l1 xl=xw
983108983141983156983141983154983149983145983150983137983156983145983151983150 983151983142 983140983137983149983137983143983141983140 983148983141983150983143983156983144 983137983150983140 983148983151983139983137983156983145983151983150 983151983142 983149983145983140
983151983142 983139983151983149983152983137983154983156983149983141983150983156
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 3067
983108983141983156983141983154983149983145983150983137983156983145983151983150 983151983142 983140983137983149983137983143983141983140 983148983141983150983143983156983144 983137983150983140 983148983151983139983137983156983145983151983150 983151983142 983149983145983140
983151983142 983139983151983149983152983137983154983156983149983141983150983156Second Trial
Damaged length is changed proportionally by the volume
l2 = l1 times (v0v
m)
vm Computed volume at first trial
If the value of xm computed at first trial is negative then the mid of the
compartment slides to the bow
xl = xw+xm
where xm is the distance of the volume centre of compartment to amidship
computed at first trial
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 3167
In order to determine vm and xm
983108983141983156983141983154983149983145983150983137983156983145983151983150 983151983142 983140983137983149983137983143983141983140 983148983141983150983143983156983144 983137983150983140 983148983151983139983137983156983145983151983150 983151983142 983149983145983140
983151983142 983139983151983149983152983137983154983156983149983141983150983156
s = l2 4
vm = (s 3) sum3
xm = s sum4 sum3
xc = xl ndash xm
|vm-v0| le Tolarence for volume
|xc-xw| le Tolarence for location of volume centre
l=l2
If tolarances for both volume and location are not satisfied third fourthtrials are made similar to
second trial
8162019 Damaged Stability
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If either tolarence for volume or tolarance for location are satisfied at a trial
satisfied one is fixed trials are continued to make for the other one
983108983141983156983141983154983149983145983150983137983156983145983151983150 983151983142 983140983137983149983137983143983141983140 983148983141983150983143983156983144 983137983150983140 983148983151983139983137983156983145983151983150 983151983142 983149983145983140
983151983142 983139983151983149983152983137983154983156983149983141983150983156
8162019 Damaged Stability
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A ship is 116 meter long and displaces 7842 ton in salt water (ρ1=1025 tm3)
when her mean draught is 64m Longitudinal Centre of Buoyancy (LCB) is
0615 m aft from amidships After one of her stern compartment is damaged
she floats trimmed to the aft Her sectional areas after damaged are given in the
following table
a) Determine the volume of water entering the vessel (vw) and the location of
volume centre of damaged compartment (xw)
b) Assume permability of compartment micro is 1 Determine damaged length
and Distance of the mid of damaged length of compartment to amidship
983109983160983137983149983152983148983141 2
8162019 Damaged Stability
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8162019 Damaged Stability
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8162019 Damaged Stability
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Predicted xw
is between section 2 and section 3
983123983141983139 N983151 983123983141983139 A983154983141983137 D983145983155983156 A9831499831459831559831449831459831522 10135 983085348
3 1208 983085232
983123983141983139 A983154983141983137 983137983156 98308524983149 983142983154983151983149 983137983149983145983140983155983144983145983152 = 11959831492
l1=v0Amean=204081195=17078 m
s=l14=427 m
983109983160983137983149983152983148983141 2983085983123983119983116983125983124983113983119983118
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 3767
983161983145 L983151983139 A983149983141983137983150 983123M M A983154983149
9831311983133 9831312983133 98313119831339832559831312983133 9831313983133 983131198313398325598313129831339832559831313983133
0 9830853254 1051 1 1051 2 21021 9830852827 1123 4 4492 1 4492
2 98308524 1195 2 239 0 0
3 9830851973 1219 4 4876 9830851 9830854876
4 9830851546 1233 1 1233 9830852 9830852466
sum983091983101 14042 sum983092983101 983085748
vm
= (s3) sum3= 199864479831493
xm
=s sum4sum3= 9830850227983149
v0-vm=20408-19986=422 m3
Error=422times10020408=207
983109983160983137983149983152983148983141 2983085983123983119983116983125983124983113983119983118
8162019 Damaged Stability
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Methods of Calculation
There two available method calculating the
final stage of the damaged vessel
bull Lost Buoyancy Method
bull Added Weight Method
8162019 Damaged Stability
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Comparision of Lost Buoyancy and Added
Weight Methods
8162019 Damaged Stability
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Consider a vessel that has been damaged such
that a portion of the bottom is now open to the
sea
The vesselrsquos draft will increase because an amount
of the buoyancy was lost
Added Weight Method
Added Weight Method
8162019 Damaged Stability
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Added Weight Method
In this method flood water is treated as a fixed weight (for example the
weight of water of volume ABEF) This added weight is balanced by the
additional buoyant force of the layer WL1WL
The added weight can be determined by either the volume ABEF or
waterline WL1 Therefore WL1 waterline is not known can be just guessed
For the predicted waterline added weight and additional buoyant force
caculation are done iteratively until both of them are equal This method is
known as Added weight method
Determination of Added Weight
8162019 Damaged Stability
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Determination of Added Weight
vc Volume of damaged compartment (DCEF)
ac The surface area (AB) of damaged compartment on the waterline
micro The volume permability of damaged compartment
microa The area permability of the surface of damaged compartment
∆ The initial displacement
∆1 The displacement at final stage
vw The volume of water entering the vessel (ABEH)
w The weight of water entering the vessel
p The value of parallel sinkage
If th t th l l i k i h f t l f
8162019 Damaged Stability
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If we assume that the paralel sinkage cause a minor change of water plane area of a
ship (Awp
asymp Awp1
) we can determine the paralel sinkage by equating the volume of
the layer WL1WL to the volume of ABEF
If the damaged compartment is bounded on top
8162019 Damaged Stability
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8162019 Damaged Stability
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Longitudinal Metacentre Radius at final stage
Free Surface Effect
Damaged compartment can be considered as a half filled tank
Free Contact Effect
Damaged compartment can be considered as a half filled tank
T M H i h
8162019 Damaged Stability
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Transverse Metacentre Height
The angle of heel
8162019 Damaged Stability
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L it di l M t t H i ht
8162019 Damaged Stability
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Longitudinal Metacentre Height
8162019 Damaged Stability
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E983160983137983149983152983148983141 A 983138983137983154983143983141
8162019 Damaged Stability
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E983160983137983149983152983148983141 A 983138983137983154983143983141
991266 L = 20 983149991266 B = 5 983149
991266 983124 = 15 983149
991266 KG = 15 983149
I983150983156983137983139983156 C983151983150983140983145983156983145983151983150
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 5167
I983150983156983137983139983156 C983151983150983140983145983156983145983151983150
991266 983124983144983141 983140983145983155983152983148983137983139983141983149983141983150983156 983158983151983148983157983149983141
991266 983124983144983141 983149983137983155983155 983140983145983155983152983148983137983139983141983149983141983150983156
991266 983124983144983141 983149983151983149983141983150983156 983151983142 983145983150983141983154983156983145983137 983151983142 983156983144983141 983159983137983156983141983154983152983148983137983150983141 983137983154983141983137983137983138983151983157983156 CL
3
15051520 m x xT B L
I I
==sdotsdot=nabla
tons x I
751531500251 ==nablasdot=∆ ρ
433
33208
12
205
12
m x L B
I I
===
I983150983156983137983139983156 C983151983150983140983145983156983145983151983150
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 5267
I983150983156983137983139983156 C983151983150983140983145983156983145983151983150
991266 M983141983156983137983139983141983150983156983154983145983139 983154983137983140983145983157983155
991266 O983154 983145983156 983139983151983157983148983140 983138983141 983139983137983148983139983157983148983137983156983141983140 983140983145983154983141983139983156983148983161 983137983155
991266 H983141983145983143983144983156 983151983142 983156983144983141 983139983141983150983156983141983154 983151983142 983138983157983151983161983137983150983139983161
m I
BM
I
I 3891
150
33208==
nabla
=
m xT
B
LBT
L B BM
I I
I 3891
5112
5
12
12 223
====
mT
KB I
I 750
2
==
I983150983156983137983139983156 C983151983150983140983145983156983145983151983150
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 5367
991266 983124983144983141 983149983141983156983137983139983141983150983156983154983145983139 983144983141983145983143983144983156
991266 F983151983154 983155983149983137983148983148 983137983150983143983148983141983155 983151983142 983144983141983141983148 983156983144983141 983154983145983143983144983156983145983150983143 983149983151983149983141983150983156
m KG BM KBGM I I 63905013891750 =minus+=minus+=
sin22998sin693075153sin mt x xGM M I I
φ φ φ ==∆=
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 5467
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 5567
983116983119983123983124 983106983125983119983129983105983118983107983129 983117983109983124983112983119983108
Paralel Sinkage
Volume (DCEF)=Volume (W1ADW+BL1LC)
Damaged compartment is bounded on top
983116983119983123983124 983106983125983119983129983105983118983107983129 983117983109983124983112983119983108
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 5667
983116983119983123983124 983106983125983119983129983105983118983107983129 983117983109983124983112983119983108
bull It is assumed that displacement and location of vertical centre
of gravity does not change after damaged
983116983119983123983124 983106983125983119983129983105983118983107983129 983117983109983124983112983119983108
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 5767
983116983119983123983124 983106983125983119983129983105983118983107983129 983117983109983124983112983119983108
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 5867
The heel angle of damaged ship is determined by
where
d is the distance between the volume centre of damaged compartment
and the new longitudinal centre of floatation
wc=vc μ ρ
983116983119983123983124 983106983125983119983129983105983118983107983129 983117983109983124983112983119983108
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 5967
983116983119983123983124 983106983125983119983129983105983118983107983129 983117983109983124983112983119983108
983116983119983123983124 983106983125983119983129983105983118983107983129 983117983109983124983112983119983108
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 6067
Longitudinal Metacentre Height of a Damaged Ship
983116983119983123983124 983106983125983119983129983105983118983107983129 983117983109983124983112983119983108
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 6167
983110983151983154983159983137983154983140 983137983150983140 983137983142983156 983140983154983137983157983143983144983156983155 983137983142983156983141983154 983140983137983149983137983143983141983140
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 6267
983120983151983154983156 983105983142983156 983120983151983154983156 983110983151983154983141 983123983156983137983154983138983151983137983154983140 983105983142983156 983123983156983137983154983138983151983137983154983140 983110983151983154983159983137983154983140
I983150983145983156983145983137983148 D983154983137983157983143983144983156 983124 983124 983124 983124
983120983137983154983137983148983141983148 983123983145983150983147983137983143983141 +983152 +983152 +983152 +983120
H983141983141983148 983085983149983145 983085983149983145 +983149983155 +983149983155
983124983154983145983149 983085983156983147 +983156983138 983085983156983147 +983156983138
F983145983150983137983148 D983154983137983157983143983144983156 983124+983152983085983149983145983085983156983147 983124+983152983085983149983145+983156983138 983124+983152+983149983155983085983156983147 983124+983152+983149983155+983156983138
Table 1 Final Draughts for a starboard side damaged ship
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 6367
L983151983155983156 B983157983151983161983137983150983139983161 M983141983156983144983151983140
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 6467
L983151983155983156 B983157983151983161983137983150983139983161 M983141983156983144983151983140
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 6567
991266 A983142983156983141983154 983148983151983151983155983145983150983143 983156983144983141 983139983141983150983156983154983137983148 983139983151983149983152983137983154983156983149983141983150983156 983156983144983141
983159983137983156983141983154983152983148983137983150983141 983137983154983141983137 983145983155
991266 983124983151 983139983151983149983152983141983150983155983137983156983141 983142983151983154 983156983144983141 983148983151983155983155 983151983142 983138983157983151983161983137983150983139983161 983151983142 983156983144983141
983139983141983150983156983154983137983148 983139983151983149983152983137983154983156983149983141983150983156 983156983144983141 983140983154983137983142983156 983145983150983139983154983141983137983155983141983155 983156983151
2805)420()( m x Bl L A L
=minus=minus=
m A
T
L
I
L 875180
150==
nabla=
L983151983155983156 B983157983151983161983137983150983139983161 M983141983156983144983151983140
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 6667
991266 983124983144983141 983144983141983145983143983144983156 983151983142 983156983144983141 983139983141983150983156983141983154 983151983142 983138983157983151983161983137983150983139983161 983145983150983139983154983141983137983155983141983155 983156983151
991266 983124983144983141 983149983151983149983141983150983156 983151983142 983145983150983141983154983156983145983137 983151983142 983156983144983141 983159983137983156983141983154983152983148983137983150983141 983137983154983141983137
991266 983124983144983141 983149983141983156983137983139983141983150983156983154983145983139 983154983137983140983145983157983155
m
T
KB L
L 93802
8751
2 ===
433
6716612
)420(5
12
)(m
l L B I L
=minus
=minus
=
m I
BM
I
L
L 1111150
67166==
nabla
=
L983151983155983156 B983157983151983161983137983150983139983161 M983141983156983144983151983140
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 6767
991266 983124983144983141 983149983141983156983137983139983141983150983156983154983145983139 983144983141983145983143983144983156
991266 983122983145983143983144983156983145983150983143 983149983151983149983141983150983156 983142983151983154 983155983149983137983148983148 983144983141983141983148 983137983150983143983148983141983155
m KG BM KBGM L L L 54905111119380 =minus+=minus+=
mt xGM M L
sin34984sin549075153sin φ φ φ ==∆=
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 667
983127A983124E983122983124IGH983124 DOO983122983123
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 767
983127A983124E983122983124IGH983124 DOO983122983123
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 867
D983137983149983137983143983141
991266 I983142 983156983144983141 983155983144983141983148983148 983151983142 983137 983155983144983145983152 983145983155 983140983137983149983137983143983141983140 983148983141983137983147983137983143983141 983159983145983148983148 983156983137983147983141 983152983148983137983139983141
983138983141983156983159983141983141983150 983156983144983141 983155983141983137 983137983150983140 983156983144983141 983140983137983149983137983143983141983140 983155983152983137983139983141983155 983157983150983156983145983148 983155983156983137983138983148983141
983141983153983157983145983148983145983138983154983145983157983149 983145983155 983141983155983156983137983138983148983145983155983144983141983140 983151983154 983157983150983156983145983148 983156983144983141 983155983144983145983152 983139983137983152983155983145983162983141983155 983151983154 983155983145983150983147983155
991266 I983156 983145983155 983145983149983152983154983137983139983156983145983139983137983148 983156983151 983140983141983155983145983143983150 983137 983155983144983145983152 983156983151 983159983145983156983144983155983156983137983150983140 983137983150983161 983152983151983155983155983145983138983148983141
983140983137983149983137983143983141 983140983157983141 983156983151 983139983151983148983148983145983155983145983151983150 983143983154983151983157983150983140983145983150983143 983151983154 983149983145983148983145983156983137983154983161 983137983139983156983145983151983150
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 967
D983137983149983137983143983141
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 1067
983127983137983156983141983154983156983145983143983144983156 983138983157983148983147983144983141983137983140983155 983098 983156983144983141 983144983157983148983148 983145983155 983155983157983138983140983145983158983145983140983141983140 983145983150983156983151 983159983137983156983141983154983156983145983143983144983156
983139983151983149983152983137983154983156983149983141983150983156983155 983138983161 983149983141983137983150983155 983151983142 983159983137983156983141983154983156983145983143983144983156 983138983157983148983147983144983141983137983140983155 983137983150983140 983140983141983139983147983155
983127983137983156983141983154983156983145983143983144983156 983106983157983148983147983144983141983137983140983155
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 1167
983106983157983148983147983144983141983137983140 983108983141983139983147983155
983106983157983148983147983144983141983137983140 983140983141983139983147983155 983098 983156983144983141 983140983141983139983147 983157983152 983156983151 983159983144983145983139983144 983156983144983141983155983141 983138983157983148983147983144983141983137983140983155 983141983160983156983141983150983140983155
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 1267
983117983137983154983143983145983150 983116983145983150983141
983117983137983154983143983145983150 983148983145983150983141 983145983155 983137 983148983145983150983141 983140983141983142983145983150983145983150983143 983156983144983141 983144983145983143983144983141983155983156 983152983141983154983149983141983155983155983145983138983148983141 983148983151983139983137983156983145983151983150 983151983150 983156983144983141 983155983145983140983141 983151983142 983156983144983141
983158983141983155983155983141983148 983151983142 983137983150983161 983140983137983149983137983143983141983140 983159983137983156983141983154983152983148983137983150983141 983145983150 983156983144983141 983142983145983150983137983148 983139983151983150983140983145983156983145983151983150 983151983142 983155983145983150983147983137983143983141983156983154983145983149 983137983150983140 983144983141983141983148
A983142983156983141983154 983142983148983151983151983140983145983150983143 983151983142 983137 983152983154983141983155983139983154983145983138983141983140 983150983157983149983138983141983154 983151983142 983139983151983149983152983137983154983156983149983141983150983156983155 983156983144983141 983155983144983145983152 983155983144983137983148983148 983150983151983156
983155983157983138983149983141983154983143983141 983138983141983161983151983150983140 983137 983148983145983150983141 983155983145983156983157983137983156983141983140 983137983156 983148983141983137983155983156 76 983149983149 B983141983148983151983159 983156983144983141 983140983141983139983147 983137983156 983155983145983140983141
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 1367
983117983137983154983143983145983150 983116983145983150983141
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 1467
983117983137983154983143983145983150 983116983145983150983141
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 1567
Permability is the ratio of amount of water that can a enter or a
compartment or tank to the total volume of compartment or tank
VOLUME TOTAL
VOLUME AVAILABLE TY PERMEABILI =
983120983141983154983149983141983137983138983145983148983145983156983161 μ
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 1667
983123983157983154983142983137983139983141 983120983141983154983149983141983137983138983145983148983145983156983161 μ983137
Surface permability is the percentage of a waterplane that can be
occupied by water
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 1767
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 1867
A cargo hold with dimensions of l = 1524m w = 914 m
h=61 m is completely flooded Determine the volume of the
space and the corrected flooded volume
Volume = 1524 m x 914 m x 61 m = 8497 m3
Flooded volume = Volume x permeability
Flooded volume = 8497 m3 x 60
Flooded volume = 5098 m3
Example 1
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 1967
983110983148983151983151983140983137983138983148983141 983116983141983150983143983156983144
983110983148983151983151983140983137983138983148983141 983148983141983150983143983156983144983098 983137983156 983137 983143983145983158983141983150 983152983151983145983150983156 983151983142 983156983144983141 983155983144983145983152 983148983141983150983143983156983144 983145983155 983156983144983141 983149983137983160983145983149983157983149 983148983141983150983143983156983144
983159983145983156983144 983156983144983141 983139983141983150983156983141983154 983137983156 983156983144983137983156 983152983151983145983150983156 983156983144983137983156 983139983137983150 983138983141 983142983148983151983151983140983141983140 983159983145983156983144983151983157983156 983155983157983138983149983141983154983143983145983150983143 983156983144983141
983155983144983145983152 983138983141983161983151983150983140 983149983137983154983143983145983150 983148983145983150983141
983129983137983154983137983148ı 983106983286983148983149983141 983106983151983161983157983098 G983141983149983145 983138983151983161983157983150983139983137 983144983141983154983144983137983150983143983145 983138983145983154 983150983151983147983156983137983140983137 983138983157 983150983151983147983156983137 983149983141983154983147983141983162
983151983148983149983137983147 983292983162983141983154983141 983143983141983149983145983161983145 983155ı983150ı983154 983144983137983156983156ı983150983137 983156983141ğ983141983156 983144983137983148983141 983143983141983156983145983154983141983139983141983147 983141983150 983138983292983161983292983147 983138983286983148983149983141 983138983151983161983157983150983137
983151 983150983151983147983156983137983140983137983147983145 983161983137983154983137983148ı 983138983286983148983149983141 983138983151983161983157 983140983141983150983145983154
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 2067
983110983148983151983151983140983137983138983148983141 983116983141983150983143983156983144 983107983157983154983158983141
983110983148983151983151983140983137983138983148983141 983116983141983150983143983156983144 983107983157983154983158983141983098 I983156 983145983155 983151983138983156983137983145983150983141983140 983138983161 983156983144983141 983139983151983150983150983141983139983156983145983151983150 983151983142 983142983148983151983151983140983137983138983148983141 983148983141983150983143983156983144983155 983137983156
983140983145983142983142983141983154983141983150983156 983152983151983145983150983156983155 983137983148983151983150983143 983156983144983141 983155983144983145983152 983148983141983150983143983156983144
983129983137983154983137983148ı 983106983286983148983149983141 983106983151983161983157 983109ğ983154983145983155983145983098 G983141983149983145 983138983151983161983157983150983139983137 983140983141ğ983145ş983145983147 983150983151983147983156983137983148983137983154983140983137 983144983141983155983137983152983148983137983150983137983150 983161983137983154983137983148ı
983138983286983148983149983141 983138983151983161983157 983140983141ğ983141983154983148983141983154983145983150983145983150 983138983145983154983148983141ş983156983145983154983145983148983149983141983155983145 983145983148983141 983141983148983140983141 983141983140983145983148983145983154
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 2167
983110983137983139983156983151983154 983151983142 983123983157983138983140983145983158983145983155983145983151983150
F983137983139983156983151983154 983151983142 983123983157983138983140983145983158983145983155983145983151983150 983124983144983141 983142983137983139983156983151983154 983151983142 983155983157983138983140983145983158983145983155983145983151983150 983145983155 983137 983142983137983139983156983151983154 983152983154983141983155983139983154983145983138983141983140
983138983161 983156983144983141 983137983152983152983148983145983139983137983138983148983141 983154983141983143983157983148983137983156983145983151983150983155 983137983150983140 983138983161 983145983150983156983141983154983150983137983156983145983151983150983137983148 983139983151983150983158983141983150983156983145983151983150 983156983144983137983156
983140983141983152983141983150983140983155 983151983150 983155983144983145983152 983148983141983150983143983156983144 983137983150983140 983139983154983145983156983141983154983145983151983150 983151983142 983155983141983154983158983145983139983141
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 2267
983120983141983154983149983145983155983155983145983138983148983141 983116983141983150983143983156983144
983120983141983154983149983145983155983155983145983138983148983141 L983141983150983143983156983144 983145983155 983151983138983156983137983145983150983141983140 983138983161 983149983157983148983156983145983152983148983161983145983150983143 983156983144983141 983142983148983151983151983140983137983138983148983141 983148983141983150983143983156983144 983137983156
983156983144983137983156 983152983151983145983150983156 983138983161 983156983144983141 983142983137983139983156983151983154 983151983142 983155983157983138983140983145983158983145983155983145983151983150
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 2367
D983141983156983141983154983149983145983150983137983156983145983151983150 983151983142 983156983144983141 983148983151983139983137983156983145983151983150 983151983142 983156983144983141 983158983151983148983157983149983141 983139983141983150983156983154983141 983151983142
983140983137983149983137983143983141983140 983139983151983149983152983137983154983156983149983141983150983156
Δ I983150983145983156983145983137983148 983140983145983155983152983148983137983139983141983149983141983150983156 Δ1 D983145983155983152983148983137983139983141983149983141983150983156 983137983142983156983141983154 983140983137983149983137983143983141983140
B I983150983145983156983145983137983148 983139983141983150983156983154983141 983151983142 983138983157983151983161983137983150983139983161
G I983150983145983156983145983137983148 983139983141983150983156983154983141 983151983142 9831439831549831379831589831459831569831619831600 I983150983145983156983145983137983148 983139983141983150983156983154983141 983151983142 983148983151983150983143983145983156983157983140983145983150983137983148 983138983157983151983161983137983150983139983161 LCB
983158983159 983124983144983141 983158983151983148983157983149983141 983151983142 983159983137983156983141983154 983141983150983156983141983154983145983150983143 983156983144983141 983158983141983155983155983141983148
983160983159 D983145983155983156983137983150983139983141 983151983142 983158983151983148983157983149983141 983139983141983150983156983154983141 983151983142 983140983137983149983137983143983141983140 983139983151983149983152983137983154983156983149983141983150983156 983142983154983151983149 983149983137983141983155983156983151983154983161
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 2467
D983141983156983141983154983149983145983150983137983156983145983151983150 983151983142 983156983144983141 983148983151983139983137983156983145983151983150 983151983142 983156983144983141 983158983151983148983157983149983141 983139983141983150983156983154983141 983151983142
983140983137983149983137983143983141983140 983139983151983149983152983137983154983156983149983141983150983156
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 2567
D983141983156983141983154983149983145983150983137983156983145983151983150 983151983142 983156983144983141 983158983151983148983157983149983141 983151983142 983159983137983156983141983154 983141983150983156983141983154983145983150983143 983156983144983141 983158983141983155983155983141983148
Initial displacement and longitudinal centre of buoyancy (LCB) can be read from hydrostatcic curves
However displacement and LCB are unknown after damaged
Therefore if trim forward and aft draught are known trimmed waterline can be drawn over Bonjean
area curves
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 2667
983108983141983156983141983154983149983145983150983137983156983145983151983150 983151983142 983140983137983149983137983143983141983140 983148983141983150983143983156983144 983137983150983140 983148983151983139983137983156983145983151983150 983151983142 983149983145983140
983151983142 983139983151983149983152983137983154983156983149983141983150983156
vw The volume of water entering the vessel
xw Distance of volume centre of damaged compartment from maestory
micro Permability of the compartment
v0 Volume of the compartment
xm Distance of the volume centre of the compartment to the mid of damaged length
xl Distance of the mid of damaged length of compartment to maestory
xc Distance of the computed volume centre of compartment to maestory (xc=xl-xm)
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 2767
983108983141983156983141983154983149983145983150983137983156983145983151983150 983151983142 983140983137983149983137983143983141983140 983148983141983150983143983156983144 983137983150983140 983148983151983139983137983156983145983151983150 983151983142 983149983145983140
983151983142 983139983151983149983152983137983154983156983149983141983150983156
Damaged length and location of compartment can be determined by iterative
procedure
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 2867
bull The volume of water entering the vessel (vw)
bull Distance of volume centre of damaged compartment from amidships Θ ( xw)
bull Volume of the compartment (v0
= vw
μ)
First trial
1) Assume xm=0 (xl=xw)
2) Damaged Length l1 = (Volume of the compartment v0) (mean sec Area Amean)
where Amean is determined from trimmed sectional area curve
983108983141983156983141983154983149983145983150983137983156983145983151983150 983151983142 983140983137983149983137983143983141983140 983148983141983150983143983156983144 983137983150983140 983148983151983139983137983156983145983151983150 983151983142 983149983145983140
983151983142 983139983151983149983152983137983154983156983149983141983150983156
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 2967
3) In order to determine vm and xm
s = l1 4
vm = (s 3) sum3
xm = s sum4 sum3
xc = xl ndash xm
|vm-v0| le Tolarence for volume
|xc-xw| le Tolarence for location of volume centre
l=l1 xl=xw
983108983141983156983141983154983149983145983150983137983156983145983151983150 983151983142 983140983137983149983137983143983141983140 983148983141983150983143983156983144 983137983150983140 983148983151983139983137983156983145983151983150 983151983142 983149983145983140
983151983142 983139983151983149983152983137983154983156983149983141983150983156
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 3067
983108983141983156983141983154983149983145983150983137983156983145983151983150 983151983142 983140983137983149983137983143983141983140 983148983141983150983143983156983144 983137983150983140 983148983151983139983137983156983145983151983150 983151983142 983149983145983140
983151983142 983139983151983149983152983137983154983156983149983141983150983156Second Trial
Damaged length is changed proportionally by the volume
l2 = l1 times (v0v
m)
vm Computed volume at first trial
If the value of xm computed at first trial is negative then the mid of the
compartment slides to the bow
xl = xw+xm
where xm is the distance of the volume centre of compartment to amidship
computed at first trial
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 3167
In order to determine vm and xm
983108983141983156983141983154983149983145983150983137983156983145983151983150 983151983142 983140983137983149983137983143983141983140 983148983141983150983143983156983144 983137983150983140 983148983151983139983137983156983145983151983150 983151983142 983149983145983140
983151983142 983139983151983149983152983137983154983156983149983141983150983156
s = l2 4
vm = (s 3) sum3
xm = s sum4 sum3
xc = xl ndash xm
|vm-v0| le Tolarence for volume
|xc-xw| le Tolarence for location of volume centre
l=l2
If tolarances for both volume and location are not satisfied third fourthtrials are made similar to
second trial
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 3267
If either tolarence for volume or tolarance for location are satisfied at a trial
satisfied one is fixed trials are continued to make for the other one
983108983141983156983141983154983149983145983150983137983156983145983151983150 983151983142 983140983137983149983137983143983141983140 983148983141983150983143983156983144 983137983150983140 983148983151983139983137983156983145983151983150 983151983142 983149983145983140
983151983142 983139983151983149983152983137983154983156983149983141983150983156
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 3367
A ship is 116 meter long and displaces 7842 ton in salt water (ρ1=1025 tm3)
when her mean draught is 64m Longitudinal Centre of Buoyancy (LCB) is
0615 m aft from amidships After one of her stern compartment is damaged
she floats trimmed to the aft Her sectional areas after damaged are given in the
following table
a) Determine the volume of water entering the vessel (vw) and the location of
volume centre of damaged compartment (xw)
b) Assume permability of compartment micro is 1 Determine damaged length
and Distance of the mid of damaged length of compartment to amidship
983109983160983137983149983152983148983141 2
8162019 Damaged Stability
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8162019 Damaged Stability
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8162019 Damaged Stability
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Predicted xw
is between section 2 and section 3
983123983141983139 N983151 983123983141983139 A983154983141983137 D983145983155983156 A9831499831459831559831449831459831522 10135 983085348
3 1208 983085232
983123983141983139 A983154983141983137 983137983156 98308524983149 983142983154983151983149 983137983149983145983140983155983144983145983152 = 11959831492
l1=v0Amean=204081195=17078 m
s=l14=427 m
983109983160983137983149983152983148983141 2983085983123983119983116983125983124983113983119983118
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 3767
983161983145 L983151983139 A983149983141983137983150 983123M M A983154983149
9831311983133 9831312983133 98313119831339832559831312983133 9831313983133 983131198313398325598313129831339832559831313983133
0 9830853254 1051 1 1051 2 21021 9830852827 1123 4 4492 1 4492
2 98308524 1195 2 239 0 0
3 9830851973 1219 4 4876 9830851 9830854876
4 9830851546 1233 1 1233 9830852 9830852466
sum983091983101 14042 sum983092983101 983085748
vm
= (s3) sum3= 199864479831493
xm
=s sum4sum3= 9830850227983149
v0-vm=20408-19986=422 m3
Error=422times10020408=207
983109983160983137983149983152983148983141 2983085983123983119983116983125983124983113983119983118
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 3867
Methods of Calculation
There two available method calculating the
final stage of the damaged vessel
bull Lost Buoyancy Method
bull Added Weight Method
8162019 Damaged Stability
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Comparision of Lost Buoyancy and Added
Weight Methods
8162019 Damaged Stability
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Consider a vessel that has been damaged such
that a portion of the bottom is now open to the
sea
The vesselrsquos draft will increase because an amount
of the buoyancy was lost
Added Weight Method
Added Weight Method
8162019 Damaged Stability
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Added Weight Method
In this method flood water is treated as a fixed weight (for example the
weight of water of volume ABEF) This added weight is balanced by the
additional buoyant force of the layer WL1WL
The added weight can be determined by either the volume ABEF or
waterline WL1 Therefore WL1 waterline is not known can be just guessed
For the predicted waterline added weight and additional buoyant force
caculation are done iteratively until both of them are equal This method is
known as Added weight method
Determination of Added Weight
8162019 Damaged Stability
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Determination of Added Weight
vc Volume of damaged compartment (DCEF)
ac The surface area (AB) of damaged compartment on the waterline
micro The volume permability of damaged compartment
microa The area permability of the surface of damaged compartment
∆ The initial displacement
∆1 The displacement at final stage
vw The volume of water entering the vessel (ABEH)
w The weight of water entering the vessel
p The value of parallel sinkage
If th t th l l i k i h f t l f
8162019 Damaged Stability
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If we assume that the paralel sinkage cause a minor change of water plane area of a
ship (Awp
asymp Awp1
) we can determine the paralel sinkage by equating the volume of
the layer WL1WL to the volume of ABEF
If the damaged compartment is bounded on top
8162019 Damaged Stability
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8162019 Damaged Stability
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Longitudinal Metacentre Radius at final stage
Free Surface Effect
Damaged compartment can be considered as a half filled tank
Free Contact Effect
Damaged compartment can be considered as a half filled tank
T M H i h
8162019 Damaged Stability
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Transverse Metacentre Height
The angle of heel
8162019 Damaged Stability
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L it di l M t t H i ht
8162019 Damaged Stability
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Longitudinal Metacentre Height
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 4967
E983160983137983149983152983148983141 A 983138983137983154983143983141
8162019 Damaged Stability
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E983160983137983149983152983148983141 A 983138983137983154983143983141
991266 L = 20 983149991266 B = 5 983149
991266 983124 = 15 983149
991266 KG = 15 983149
I983150983156983137983139983156 C983151983150983140983145983156983145983151983150
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 5167
I983150983156983137983139983156 C983151983150983140983145983156983145983151983150
991266 983124983144983141 983140983145983155983152983148983137983139983141983149983141983150983156 983158983151983148983157983149983141
991266 983124983144983141 983149983137983155983155 983140983145983155983152983148983137983139983141983149983141983150983156
991266 983124983144983141 983149983151983149983141983150983156 983151983142 983145983150983141983154983156983145983137 983151983142 983156983144983141 983159983137983156983141983154983152983148983137983150983141 983137983154983141983137983137983138983151983157983156 CL
3
15051520 m x xT B L
I I
==sdotsdot=nabla
tons x I
751531500251 ==nablasdot=∆ ρ
433
33208
12
205
12
m x L B
I I
===
I983150983156983137983139983156 C983151983150983140983145983156983145983151983150
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 5267
I983150983156983137983139983156 C983151983150983140983145983156983145983151983150
991266 M983141983156983137983139983141983150983156983154983145983139 983154983137983140983145983157983155
991266 O983154 983145983156 983139983151983157983148983140 983138983141 983139983137983148983139983157983148983137983156983141983140 983140983145983154983141983139983156983148983161 983137983155
991266 H983141983145983143983144983156 983151983142 983156983144983141 983139983141983150983156983141983154 983151983142 983138983157983151983161983137983150983139983161
m I
BM
I
I 3891
150
33208==
nabla
=
m xT
B
LBT
L B BM
I I
I 3891
5112
5
12
12 223
====
mT
KB I
I 750
2
==
I983150983156983137983139983156 C983151983150983140983145983156983145983151983150
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 5367
991266 983124983144983141 983149983141983156983137983139983141983150983156983154983145983139 983144983141983145983143983144983156
991266 F983151983154 983155983149983137983148983148 983137983150983143983148983141983155 983151983142 983144983141983141983148 983156983144983141 983154983145983143983144983156983145983150983143 983149983151983149983141983150983156
m KG BM KBGM I I 63905013891750 =minus+=minus+=
sin22998sin693075153sin mt x xGM M I I
φ φ φ ==∆=
8162019 Damaged Stability
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8162019 Damaged Stability
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983116983119983123983124 983106983125983119983129983105983118983107983129 983117983109983124983112983119983108
Paralel Sinkage
Volume (DCEF)=Volume (W1ADW+BL1LC)
Damaged compartment is bounded on top
983116983119983123983124 983106983125983119983129983105983118983107983129 983117983109983124983112983119983108
8162019 Damaged Stability
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983116983119983123983124 983106983125983119983129983105983118983107983129 983117983109983124983112983119983108
bull It is assumed that displacement and location of vertical centre
of gravity does not change after damaged
983116983119983123983124 983106983125983119983129983105983118983107983129 983117983109983124983112983119983108
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 5767
983116983119983123983124 983106983125983119983129983105983118983107983129 983117983109983124983112983119983108
8162019 Damaged Stability
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The heel angle of damaged ship is determined by
where
d is the distance between the volume centre of damaged compartment
and the new longitudinal centre of floatation
wc=vc μ ρ
983116983119983123983124 983106983125983119983129983105983118983107983129 983117983109983124983112983119983108
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 5967
983116983119983123983124 983106983125983119983129983105983118983107983129 983117983109983124983112983119983108
983116983119983123983124 983106983125983119983129983105983118983107983129 983117983109983124983112983119983108
8162019 Damaged Stability
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Longitudinal Metacentre Height of a Damaged Ship
983116983119983123983124 983106983125983119983129983105983118983107983129 983117983109983124983112983119983108
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 6167
983110983151983154983159983137983154983140 983137983150983140 983137983142983156 983140983154983137983157983143983144983156983155 983137983142983156983141983154 983140983137983149983137983143983141983140
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 6267
983120983151983154983156 983105983142983156 983120983151983154983156 983110983151983154983141 983123983156983137983154983138983151983137983154983140 983105983142983156 983123983156983137983154983138983151983137983154983140 983110983151983154983159983137983154983140
I983150983145983156983145983137983148 D983154983137983157983143983144983156 983124 983124 983124 983124
983120983137983154983137983148983141983148 983123983145983150983147983137983143983141 +983152 +983152 +983152 +983120
H983141983141983148 983085983149983145 983085983149983145 +983149983155 +983149983155
983124983154983145983149 983085983156983147 +983156983138 983085983156983147 +983156983138
F983145983150983137983148 D983154983137983157983143983144983156 983124+983152983085983149983145983085983156983147 983124+983152983085983149983145+983156983138 983124+983152+983149983155983085983156983147 983124+983152+983149983155+983156983138
Table 1 Final Draughts for a starboard side damaged ship
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 6367
L983151983155983156 B983157983151983161983137983150983139983161 M983141983156983144983151983140
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 6467
L983151983155983156 B983157983151983161983137983150983139983161 M983141983156983144983151983140
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 6567
991266 A983142983156983141983154 983148983151983151983155983145983150983143 983156983144983141 983139983141983150983156983154983137983148 983139983151983149983152983137983154983156983149983141983150983156 983156983144983141
983159983137983156983141983154983152983148983137983150983141 983137983154983141983137 983145983155
991266 983124983151 983139983151983149983152983141983150983155983137983156983141 983142983151983154 983156983144983141 983148983151983155983155 983151983142 983138983157983151983161983137983150983139983161 983151983142 983156983144983141
983139983141983150983156983154983137983148 983139983151983149983152983137983154983156983149983141983150983156 983156983144983141 983140983154983137983142983156 983145983150983139983154983141983137983155983141983155 983156983151
2805)420()( m x Bl L A L
=minus=minus=
m A
T
L
I
L 875180
150==
nabla=
L983151983155983156 B983157983151983161983137983150983139983161 M983141983156983144983151983140
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 6667
991266 983124983144983141 983144983141983145983143983144983156 983151983142 983156983144983141 983139983141983150983156983141983154 983151983142 983138983157983151983161983137983150983139983161 983145983150983139983154983141983137983155983141983155 983156983151
991266 983124983144983141 983149983151983149983141983150983156 983151983142 983145983150983141983154983156983145983137 983151983142 983156983144983141 983159983137983156983141983154983152983148983137983150983141 983137983154983141983137
991266 983124983144983141 983149983141983156983137983139983141983150983156983154983145983139 983154983137983140983145983157983155
m
T
KB L
L 93802
8751
2 ===
433
6716612
)420(5
12
)(m
l L B I L
=minus
=minus
=
m I
BM
I
L
L 1111150
67166==
nabla
=
L983151983155983156 B983157983151983161983137983150983139983161 M983141983156983144983151983140
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 6767
991266 983124983144983141 983149983141983156983137983139983141983150983156983154983145983139 983144983141983145983143983144983156
991266 983122983145983143983144983156983145983150983143 983149983151983149983141983150983156 983142983151983154 983155983149983137983148983148 983144983141983141983148 983137983150983143983148983141983155
m KG BM KBGM L L L 54905111119380 =minus+=minus+=
mt xGM M L
sin34984sin549075153sin φ φ φ ==∆=
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 767
983127A983124E983122983124IGH983124 DOO983122983123
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 867
D983137983149983137983143983141
991266 I983142 983156983144983141 983155983144983141983148983148 983151983142 983137 983155983144983145983152 983145983155 983140983137983149983137983143983141983140 983148983141983137983147983137983143983141 983159983145983148983148 983156983137983147983141 983152983148983137983139983141
983138983141983156983159983141983141983150 983156983144983141 983155983141983137 983137983150983140 983156983144983141 983140983137983149983137983143983141983140 983155983152983137983139983141983155 983157983150983156983145983148 983155983156983137983138983148983141
983141983153983157983145983148983145983138983154983145983157983149 983145983155 983141983155983156983137983138983148983145983155983144983141983140 983151983154 983157983150983156983145983148 983156983144983141 983155983144983145983152 983139983137983152983155983145983162983141983155 983151983154 983155983145983150983147983155
991266 I983156 983145983155 983145983149983152983154983137983139983156983145983139983137983148 983156983151 983140983141983155983145983143983150 983137 983155983144983145983152 983156983151 983159983145983156983144983155983156983137983150983140 983137983150983161 983152983151983155983155983145983138983148983141
983140983137983149983137983143983141 983140983157983141 983156983151 983139983151983148983148983145983155983145983151983150 983143983154983151983157983150983140983145983150983143 983151983154 983149983145983148983145983156983137983154983161 983137983139983156983145983151983150
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 967
D983137983149983137983143983141
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 1067
983127983137983156983141983154983156983145983143983144983156 983138983157983148983147983144983141983137983140983155 983098 983156983144983141 983144983157983148983148 983145983155 983155983157983138983140983145983158983145983140983141983140 983145983150983156983151 983159983137983156983141983154983156983145983143983144983156
983139983151983149983152983137983154983156983149983141983150983156983155 983138983161 983149983141983137983150983155 983151983142 983159983137983156983141983154983156983145983143983144983156 983138983157983148983147983144983141983137983140983155 983137983150983140 983140983141983139983147983155
983127983137983156983141983154983156983145983143983144983156 983106983157983148983147983144983141983137983140983155
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 1167
983106983157983148983147983144983141983137983140 983108983141983139983147983155
983106983157983148983147983144983141983137983140 983140983141983139983147983155 983098 983156983144983141 983140983141983139983147 983157983152 983156983151 983159983144983145983139983144 983156983144983141983155983141 983138983157983148983147983144983141983137983140983155 983141983160983156983141983150983140983155
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 1267
983117983137983154983143983145983150 983116983145983150983141
983117983137983154983143983145983150 983148983145983150983141 983145983155 983137 983148983145983150983141 983140983141983142983145983150983145983150983143 983156983144983141 983144983145983143983144983141983155983156 983152983141983154983149983141983155983155983145983138983148983141 983148983151983139983137983156983145983151983150 983151983150 983156983144983141 983155983145983140983141 983151983142 983156983144983141
983158983141983155983155983141983148 983151983142 983137983150983161 983140983137983149983137983143983141983140 983159983137983156983141983154983152983148983137983150983141 983145983150 983156983144983141 983142983145983150983137983148 983139983151983150983140983145983156983145983151983150 983151983142 983155983145983150983147983137983143983141983156983154983145983149 983137983150983140 983144983141983141983148
A983142983156983141983154 983142983148983151983151983140983145983150983143 983151983142 983137 983152983154983141983155983139983154983145983138983141983140 983150983157983149983138983141983154 983151983142 983139983151983149983152983137983154983156983149983141983150983156983155 983156983144983141 983155983144983145983152 983155983144983137983148983148 983150983151983156
983155983157983138983149983141983154983143983141 983138983141983161983151983150983140 983137 983148983145983150983141 983155983145983156983157983137983156983141983140 983137983156 983148983141983137983155983156 76 983149983149 B983141983148983151983159 983156983144983141 983140983141983139983147 983137983156 983155983145983140983141
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 1367
983117983137983154983143983145983150 983116983145983150983141
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 1467
983117983137983154983143983145983150 983116983145983150983141
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 1567
Permability is the ratio of amount of water that can a enter or a
compartment or tank to the total volume of compartment or tank
VOLUME TOTAL
VOLUME AVAILABLE TY PERMEABILI =
983120983141983154983149983141983137983138983145983148983145983156983161 μ
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 1667
983123983157983154983142983137983139983141 983120983141983154983149983141983137983138983145983148983145983156983161 μ983137
Surface permability is the percentage of a waterplane that can be
occupied by water
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 1767
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 1867
A cargo hold with dimensions of l = 1524m w = 914 m
h=61 m is completely flooded Determine the volume of the
space and the corrected flooded volume
Volume = 1524 m x 914 m x 61 m = 8497 m3
Flooded volume = Volume x permeability
Flooded volume = 8497 m3 x 60
Flooded volume = 5098 m3
Example 1
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 1967
983110983148983151983151983140983137983138983148983141 983116983141983150983143983156983144
983110983148983151983151983140983137983138983148983141 983148983141983150983143983156983144983098 983137983156 983137 983143983145983158983141983150 983152983151983145983150983156 983151983142 983156983144983141 983155983144983145983152 983148983141983150983143983156983144 983145983155 983156983144983141 983149983137983160983145983149983157983149 983148983141983150983143983156983144
983159983145983156983144 983156983144983141 983139983141983150983156983141983154 983137983156 983156983144983137983156 983152983151983145983150983156 983156983144983137983156 983139983137983150 983138983141 983142983148983151983151983140983141983140 983159983145983156983144983151983157983156 983155983157983138983149983141983154983143983145983150983143 983156983144983141
983155983144983145983152 983138983141983161983151983150983140 983149983137983154983143983145983150 983148983145983150983141
983129983137983154983137983148ı 983106983286983148983149983141 983106983151983161983157983098 G983141983149983145 983138983151983161983157983150983139983137 983144983141983154983144983137983150983143983145 983138983145983154 983150983151983147983156983137983140983137 983138983157 983150983151983147983156983137 983149983141983154983147983141983162
983151983148983149983137983147 983292983162983141983154983141 983143983141983149983145983161983145 983155ı983150ı983154 983144983137983156983156ı983150983137 983156983141ğ983141983156 983144983137983148983141 983143983141983156983145983154983141983139983141983147 983141983150 983138983292983161983292983147 983138983286983148983149983141 983138983151983161983157983150983137
983151 983150983151983147983156983137983140983137983147983145 983161983137983154983137983148ı 983138983286983148983149983141 983138983151983161983157 983140983141983150983145983154
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 2067
983110983148983151983151983140983137983138983148983141 983116983141983150983143983156983144 983107983157983154983158983141
983110983148983151983151983140983137983138983148983141 983116983141983150983143983156983144 983107983157983154983158983141983098 I983156 983145983155 983151983138983156983137983145983150983141983140 983138983161 983156983144983141 983139983151983150983150983141983139983156983145983151983150 983151983142 983142983148983151983151983140983137983138983148983141 983148983141983150983143983156983144983155 983137983156
983140983145983142983142983141983154983141983150983156 983152983151983145983150983156983155 983137983148983151983150983143 983156983144983141 983155983144983145983152 983148983141983150983143983156983144
983129983137983154983137983148ı 983106983286983148983149983141 983106983151983161983157 983109ğ983154983145983155983145983098 G983141983149983145 983138983151983161983157983150983139983137 983140983141ğ983145ş983145983147 983150983151983147983156983137983148983137983154983140983137 983144983141983155983137983152983148983137983150983137983150 983161983137983154983137983148ı
983138983286983148983149983141 983138983151983161983157 983140983141ğ983141983154983148983141983154983145983150983145983150 983138983145983154983148983141ş983156983145983154983145983148983149983141983155983145 983145983148983141 983141983148983140983141 983141983140983145983148983145983154
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 2167
983110983137983139983156983151983154 983151983142 983123983157983138983140983145983158983145983155983145983151983150
F983137983139983156983151983154 983151983142 983123983157983138983140983145983158983145983155983145983151983150 983124983144983141 983142983137983139983156983151983154 983151983142 983155983157983138983140983145983158983145983155983145983151983150 983145983155 983137 983142983137983139983156983151983154 983152983154983141983155983139983154983145983138983141983140
983138983161 983156983144983141 983137983152983152983148983145983139983137983138983148983141 983154983141983143983157983148983137983156983145983151983150983155 983137983150983140 983138983161 983145983150983156983141983154983150983137983156983145983151983150983137983148 983139983151983150983158983141983150983156983145983151983150 983156983144983137983156
983140983141983152983141983150983140983155 983151983150 983155983144983145983152 983148983141983150983143983156983144 983137983150983140 983139983154983145983156983141983154983145983151983150 983151983142 983155983141983154983158983145983139983141
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 2267
983120983141983154983149983145983155983155983145983138983148983141 983116983141983150983143983156983144
983120983141983154983149983145983155983155983145983138983148983141 L983141983150983143983156983144 983145983155 983151983138983156983137983145983150983141983140 983138983161 983149983157983148983156983145983152983148983161983145983150983143 983156983144983141 983142983148983151983151983140983137983138983148983141 983148983141983150983143983156983144 983137983156
983156983144983137983156 983152983151983145983150983156 983138983161 983156983144983141 983142983137983139983156983151983154 983151983142 983155983157983138983140983145983158983145983155983145983151983150
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 2367
D983141983156983141983154983149983145983150983137983156983145983151983150 983151983142 983156983144983141 983148983151983139983137983156983145983151983150 983151983142 983156983144983141 983158983151983148983157983149983141 983139983141983150983156983154983141 983151983142
983140983137983149983137983143983141983140 983139983151983149983152983137983154983156983149983141983150983156
Δ I983150983145983156983145983137983148 983140983145983155983152983148983137983139983141983149983141983150983156 Δ1 D983145983155983152983148983137983139983141983149983141983150983156 983137983142983156983141983154 983140983137983149983137983143983141983140
B I983150983145983156983145983137983148 983139983141983150983156983154983141 983151983142 983138983157983151983161983137983150983139983161
G I983150983145983156983145983137983148 983139983141983150983156983154983141 983151983142 9831439831549831379831589831459831569831619831600 I983150983145983156983145983137983148 983139983141983150983156983154983141 983151983142 983148983151983150983143983145983156983157983140983145983150983137983148 983138983157983151983161983137983150983139983161 LCB
983158983159 983124983144983141 983158983151983148983157983149983141 983151983142 983159983137983156983141983154 983141983150983156983141983154983145983150983143 983156983144983141 983158983141983155983155983141983148
983160983159 D983145983155983156983137983150983139983141 983151983142 983158983151983148983157983149983141 983139983141983150983156983154983141 983151983142 983140983137983149983137983143983141983140 983139983151983149983152983137983154983156983149983141983150983156 983142983154983151983149 983149983137983141983155983156983151983154983161
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 2467
D983141983156983141983154983149983145983150983137983156983145983151983150 983151983142 983156983144983141 983148983151983139983137983156983145983151983150 983151983142 983156983144983141 983158983151983148983157983149983141 983139983141983150983156983154983141 983151983142
983140983137983149983137983143983141983140 983139983151983149983152983137983154983156983149983141983150983156
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 2567
D983141983156983141983154983149983145983150983137983156983145983151983150 983151983142 983156983144983141 983158983151983148983157983149983141 983151983142 983159983137983156983141983154 983141983150983156983141983154983145983150983143 983156983144983141 983158983141983155983155983141983148
Initial displacement and longitudinal centre of buoyancy (LCB) can be read from hydrostatcic curves
However displacement and LCB are unknown after damaged
Therefore if trim forward and aft draught are known trimmed waterline can be drawn over Bonjean
area curves
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 2667
983108983141983156983141983154983149983145983150983137983156983145983151983150 983151983142 983140983137983149983137983143983141983140 983148983141983150983143983156983144 983137983150983140 983148983151983139983137983156983145983151983150 983151983142 983149983145983140
983151983142 983139983151983149983152983137983154983156983149983141983150983156
vw The volume of water entering the vessel
xw Distance of volume centre of damaged compartment from maestory
micro Permability of the compartment
v0 Volume of the compartment
xm Distance of the volume centre of the compartment to the mid of damaged length
xl Distance of the mid of damaged length of compartment to maestory
xc Distance of the computed volume centre of compartment to maestory (xc=xl-xm)
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 2767
983108983141983156983141983154983149983145983150983137983156983145983151983150 983151983142 983140983137983149983137983143983141983140 983148983141983150983143983156983144 983137983150983140 983148983151983139983137983156983145983151983150 983151983142 983149983145983140
983151983142 983139983151983149983152983137983154983156983149983141983150983156
Damaged length and location of compartment can be determined by iterative
procedure
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 2867
bull The volume of water entering the vessel (vw)
bull Distance of volume centre of damaged compartment from amidships Θ ( xw)
bull Volume of the compartment (v0
= vw
μ)
First trial
1) Assume xm=0 (xl=xw)
2) Damaged Length l1 = (Volume of the compartment v0) (mean sec Area Amean)
where Amean is determined from trimmed sectional area curve
983108983141983156983141983154983149983145983150983137983156983145983151983150 983151983142 983140983137983149983137983143983141983140 983148983141983150983143983156983144 983137983150983140 983148983151983139983137983156983145983151983150 983151983142 983149983145983140
983151983142 983139983151983149983152983137983154983156983149983141983150983156
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 2967
3) In order to determine vm and xm
s = l1 4
vm = (s 3) sum3
xm = s sum4 sum3
xc = xl ndash xm
|vm-v0| le Tolarence for volume
|xc-xw| le Tolarence for location of volume centre
l=l1 xl=xw
983108983141983156983141983154983149983145983150983137983156983145983151983150 983151983142 983140983137983149983137983143983141983140 983148983141983150983143983156983144 983137983150983140 983148983151983139983137983156983145983151983150 983151983142 983149983145983140
983151983142 983139983151983149983152983137983154983156983149983141983150983156
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 3067
983108983141983156983141983154983149983145983150983137983156983145983151983150 983151983142 983140983137983149983137983143983141983140 983148983141983150983143983156983144 983137983150983140 983148983151983139983137983156983145983151983150 983151983142 983149983145983140
983151983142 983139983151983149983152983137983154983156983149983141983150983156Second Trial
Damaged length is changed proportionally by the volume
l2 = l1 times (v0v
m)
vm Computed volume at first trial
If the value of xm computed at first trial is negative then the mid of the
compartment slides to the bow
xl = xw+xm
where xm is the distance of the volume centre of compartment to amidship
computed at first trial
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 3167
In order to determine vm and xm
983108983141983156983141983154983149983145983150983137983156983145983151983150 983151983142 983140983137983149983137983143983141983140 983148983141983150983143983156983144 983137983150983140 983148983151983139983137983156983145983151983150 983151983142 983149983145983140
983151983142 983139983151983149983152983137983154983156983149983141983150983156
s = l2 4
vm = (s 3) sum3
xm = s sum4 sum3
xc = xl ndash xm
|vm-v0| le Tolarence for volume
|xc-xw| le Tolarence for location of volume centre
l=l2
If tolarances for both volume and location are not satisfied third fourthtrials are made similar to
second trial
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 3267
If either tolarence for volume or tolarance for location are satisfied at a trial
satisfied one is fixed trials are continued to make for the other one
983108983141983156983141983154983149983145983150983137983156983145983151983150 983151983142 983140983137983149983137983143983141983140 983148983141983150983143983156983144 983137983150983140 983148983151983139983137983156983145983151983150 983151983142 983149983145983140
983151983142 983139983151983149983152983137983154983156983149983141983150983156
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 3367
A ship is 116 meter long and displaces 7842 ton in salt water (ρ1=1025 tm3)
when her mean draught is 64m Longitudinal Centre of Buoyancy (LCB) is
0615 m aft from amidships After one of her stern compartment is damaged
she floats trimmed to the aft Her sectional areas after damaged are given in the
following table
a) Determine the volume of water entering the vessel (vw) and the location of
volume centre of damaged compartment (xw)
b) Assume permability of compartment micro is 1 Determine damaged length
and Distance of the mid of damaged length of compartment to amidship
983109983160983137983149983152983148983141 2
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 3467
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 3567
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 3667
Predicted xw
is between section 2 and section 3
983123983141983139 N983151 983123983141983139 A983154983141983137 D983145983155983156 A9831499831459831559831449831459831522 10135 983085348
3 1208 983085232
983123983141983139 A983154983141983137 983137983156 98308524983149 983142983154983151983149 983137983149983145983140983155983144983145983152 = 11959831492
l1=v0Amean=204081195=17078 m
s=l14=427 m
983109983160983137983149983152983148983141 2983085983123983119983116983125983124983113983119983118
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 3767
983161983145 L983151983139 A983149983141983137983150 983123M M A983154983149
9831311983133 9831312983133 98313119831339832559831312983133 9831313983133 983131198313398325598313129831339832559831313983133
0 9830853254 1051 1 1051 2 21021 9830852827 1123 4 4492 1 4492
2 98308524 1195 2 239 0 0
3 9830851973 1219 4 4876 9830851 9830854876
4 9830851546 1233 1 1233 9830852 9830852466
sum983091983101 14042 sum983092983101 983085748
vm
= (s3) sum3= 199864479831493
xm
=s sum4sum3= 9830850227983149
v0-vm=20408-19986=422 m3
Error=422times10020408=207
983109983160983137983149983152983148983141 2983085983123983119983116983125983124983113983119983118
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 3867
Methods of Calculation
There two available method calculating the
final stage of the damaged vessel
bull Lost Buoyancy Method
bull Added Weight Method
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 3967
Comparision of Lost Buoyancy and Added
Weight Methods
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 4067
Consider a vessel that has been damaged such
that a portion of the bottom is now open to the
sea
The vesselrsquos draft will increase because an amount
of the buoyancy was lost
Added Weight Method
Added Weight Method
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 4167
Added Weight Method
In this method flood water is treated as a fixed weight (for example the
weight of water of volume ABEF) This added weight is balanced by the
additional buoyant force of the layer WL1WL
The added weight can be determined by either the volume ABEF or
waterline WL1 Therefore WL1 waterline is not known can be just guessed
For the predicted waterline added weight and additional buoyant force
caculation are done iteratively until both of them are equal This method is
known as Added weight method
Determination of Added Weight
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 4267
Determination of Added Weight
vc Volume of damaged compartment (DCEF)
ac The surface area (AB) of damaged compartment on the waterline
micro The volume permability of damaged compartment
microa The area permability of the surface of damaged compartment
∆ The initial displacement
∆1 The displacement at final stage
vw The volume of water entering the vessel (ABEH)
w The weight of water entering the vessel
p The value of parallel sinkage
If th t th l l i k i h f t l f
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 4367
If we assume that the paralel sinkage cause a minor change of water plane area of a
ship (Awp
asymp Awp1
) we can determine the paralel sinkage by equating the volume of
the layer WL1WL to the volume of ABEF
If the damaged compartment is bounded on top
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 4467
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 4567
Longitudinal Metacentre Radius at final stage
Free Surface Effect
Damaged compartment can be considered as a half filled tank
Free Contact Effect
Damaged compartment can be considered as a half filled tank
T M H i h
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 4667
Transverse Metacentre Height
The angle of heel
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 4767
L it di l M t t H i ht
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 4867
Longitudinal Metacentre Height
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 4967
E983160983137983149983152983148983141 A 983138983137983154983143983141
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 5067
E983160983137983149983152983148983141 A 983138983137983154983143983141
991266 L = 20 983149991266 B = 5 983149
991266 983124 = 15 983149
991266 KG = 15 983149
I983150983156983137983139983156 C983151983150983140983145983156983145983151983150
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 5167
I983150983156983137983139983156 C983151983150983140983145983156983145983151983150
991266 983124983144983141 983140983145983155983152983148983137983139983141983149983141983150983156 983158983151983148983157983149983141
991266 983124983144983141 983149983137983155983155 983140983145983155983152983148983137983139983141983149983141983150983156
991266 983124983144983141 983149983151983149983141983150983156 983151983142 983145983150983141983154983156983145983137 983151983142 983156983144983141 983159983137983156983141983154983152983148983137983150983141 983137983154983141983137983137983138983151983157983156 CL
3
15051520 m x xT B L
I I
==sdotsdot=nabla
tons x I
751531500251 ==nablasdot=∆ ρ
433
33208
12
205
12
m x L B
I I
===
I983150983156983137983139983156 C983151983150983140983145983156983145983151983150
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 5267
I983150983156983137983139983156 C983151983150983140983145983156983145983151983150
991266 M983141983156983137983139983141983150983156983154983145983139 983154983137983140983145983157983155
991266 O983154 983145983156 983139983151983157983148983140 983138983141 983139983137983148983139983157983148983137983156983141983140 983140983145983154983141983139983156983148983161 983137983155
991266 H983141983145983143983144983156 983151983142 983156983144983141 983139983141983150983156983141983154 983151983142 983138983157983151983161983137983150983139983161
m I
BM
I
I 3891
150
33208==
nabla
=
m xT
B
LBT
L B BM
I I
I 3891
5112
5
12
12 223
====
mT
KB I
I 750
2
==
I983150983156983137983139983156 C983151983150983140983145983156983145983151983150
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 5367
991266 983124983144983141 983149983141983156983137983139983141983150983156983154983145983139 983144983141983145983143983144983156
991266 F983151983154 983155983149983137983148983148 983137983150983143983148983141983155 983151983142 983144983141983141983148 983156983144983141 983154983145983143983144983156983145983150983143 983149983151983149983141983150983156
m KG BM KBGM I I 63905013891750 =minus+=minus+=
sin22998sin693075153sin mt x xGM M I I
φ φ φ ==∆=
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 5467
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 5567
983116983119983123983124 983106983125983119983129983105983118983107983129 983117983109983124983112983119983108
Paralel Sinkage
Volume (DCEF)=Volume (W1ADW+BL1LC)
Damaged compartment is bounded on top
983116983119983123983124 983106983125983119983129983105983118983107983129 983117983109983124983112983119983108
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 5667
983116983119983123983124 983106983125983119983129983105983118983107983129 983117983109983124983112983119983108
bull It is assumed that displacement and location of vertical centre
of gravity does not change after damaged
983116983119983123983124 983106983125983119983129983105983118983107983129 983117983109983124983112983119983108
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 5767
983116983119983123983124 983106983125983119983129983105983118983107983129 983117983109983124983112983119983108
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 5867
The heel angle of damaged ship is determined by
where
d is the distance between the volume centre of damaged compartment
and the new longitudinal centre of floatation
wc=vc μ ρ
983116983119983123983124 983106983125983119983129983105983118983107983129 983117983109983124983112983119983108
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 5967
983116983119983123983124 983106983125983119983129983105983118983107983129 983117983109983124983112983119983108
983116983119983123983124 983106983125983119983129983105983118983107983129 983117983109983124983112983119983108
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 6067
Longitudinal Metacentre Height of a Damaged Ship
983116983119983123983124 983106983125983119983129983105983118983107983129 983117983109983124983112983119983108
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 6167
983110983151983154983159983137983154983140 983137983150983140 983137983142983156 983140983154983137983157983143983144983156983155 983137983142983156983141983154 983140983137983149983137983143983141983140
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 6267
983120983151983154983156 983105983142983156 983120983151983154983156 983110983151983154983141 983123983156983137983154983138983151983137983154983140 983105983142983156 983123983156983137983154983138983151983137983154983140 983110983151983154983159983137983154983140
I983150983145983156983145983137983148 D983154983137983157983143983144983156 983124 983124 983124 983124
983120983137983154983137983148983141983148 983123983145983150983147983137983143983141 +983152 +983152 +983152 +983120
H983141983141983148 983085983149983145 983085983149983145 +983149983155 +983149983155
983124983154983145983149 983085983156983147 +983156983138 983085983156983147 +983156983138
F983145983150983137983148 D983154983137983157983143983144983156 983124+983152983085983149983145983085983156983147 983124+983152983085983149983145+983156983138 983124+983152+983149983155983085983156983147 983124+983152+983149983155+983156983138
Table 1 Final Draughts for a starboard side damaged ship
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 6367
L983151983155983156 B983157983151983161983137983150983139983161 M983141983156983144983151983140
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 6467
L983151983155983156 B983157983151983161983137983150983139983161 M983141983156983144983151983140
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 6567
991266 A983142983156983141983154 983148983151983151983155983145983150983143 983156983144983141 983139983141983150983156983154983137983148 983139983151983149983152983137983154983156983149983141983150983156 983156983144983141
983159983137983156983141983154983152983148983137983150983141 983137983154983141983137 983145983155
991266 983124983151 983139983151983149983152983141983150983155983137983156983141 983142983151983154 983156983144983141 983148983151983155983155 983151983142 983138983157983151983161983137983150983139983161 983151983142 983156983144983141
983139983141983150983156983154983137983148 983139983151983149983152983137983154983156983149983141983150983156 983156983144983141 983140983154983137983142983156 983145983150983139983154983141983137983155983141983155 983156983151
2805)420()( m x Bl L A L
=minus=minus=
m A
T
L
I
L 875180
150==
nabla=
L983151983155983156 B983157983151983161983137983150983139983161 M983141983156983144983151983140
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 6667
991266 983124983144983141 983144983141983145983143983144983156 983151983142 983156983144983141 983139983141983150983156983141983154 983151983142 983138983157983151983161983137983150983139983161 983145983150983139983154983141983137983155983141983155 983156983151
991266 983124983144983141 983149983151983149983141983150983156 983151983142 983145983150983141983154983156983145983137 983151983142 983156983144983141 983159983137983156983141983154983152983148983137983150983141 983137983154983141983137
991266 983124983144983141 983149983141983156983137983139983141983150983156983154983145983139 983154983137983140983145983157983155
m
T
KB L
L 93802
8751
2 ===
433
6716612
)420(5
12
)(m
l L B I L
=minus
=minus
=
m I
BM
I
L
L 1111150
67166==
nabla
=
L983151983155983156 B983157983151983161983137983150983139983161 M983141983156983144983151983140
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 6767
991266 983124983144983141 983149983141983156983137983139983141983150983156983154983145983139 983144983141983145983143983144983156
991266 983122983145983143983144983156983145983150983143 983149983151983149983141983150983156 983142983151983154 983155983149983137983148983148 983144983141983141983148 983137983150983143983148983141983155
m KG BM KBGM L L L 54905111119380 =minus+=minus+=
mt xGM M L
sin34984sin549075153sin φ φ φ ==∆=
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 867
D983137983149983137983143983141
991266 I983142 983156983144983141 983155983144983141983148983148 983151983142 983137 983155983144983145983152 983145983155 983140983137983149983137983143983141983140 983148983141983137983147983137983143983141 983159983145983148983148 983156983137983147983141 983152983148983137983139983141
983138983141983156983159983141983141983150 983156983144983141 983155983141983137 983137983150983140 983156983144983141 983140983137983149983137983143983141983140 983155983152983137983139983141983155 983157983150983156983145983148 983155983156983137983138983148983141
983141983153983157983145983148983145983138983154983145983157983149 983145983155 983141983155983156983137983138983148983145983155983144983141983140 983151983154 983157983150983156983145983148 983156983144983141 983155983144983145983152 983139983137983152983155983145983162983141983155 983151983154 983155983145983150983147983155
991266 I983156 983145983155 983145983149983152983154983137983139983156983145983139983137983148 983156983151 983140983141983155983145983143983150 983137 983155983144983145983152 983156983151 983159983145983156983144983155983156983137983150983140 983137983150983161 983152983151983155983155983145983138983148983141
983140983137983149983137983143983141 983140983157983141 983156983151 983139983151983148983148983145983155983145983151983150 983143983154983151983157983150983140983145983150983143 983151983154 983149983145983148983145983156983137983154983161 983137983139983156983145983151983150
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 967
D983137983149983137983143983141
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 1067
983127983137983156983141983154983156983145983143983144983156 983138983157983148983147983144983141983137983140983155 983098 983156983144983141 983144983157983148983148 983145983155 983155983157983138983140983145983158983145983140983141983140 983145983150983156983151 983159983137983156983141983154983156983145983143983144983156
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983127983137983156983141983154983156983145983143983144983156 983106983157983148983147983144983141983137983140983155
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 1167
983106983157983148983147983144983141983137983140 983108983141983139983147983155
983106983157983148983147983144983141983137983140 983140983141983139983147983155 983098 983156983144983141 983140983141983139983147 983157983152 983156983151 983159983144983145983139983144 983156983144983141983155983141 983138983157983148983147983144983141983137983140983155 983141983160983156983141983150983140983155
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 1267
983117983137983154983143983145983150 983116983145983150983141
983117983137983154983143983145983150 983148983145983150983141 983145983155 983137 983148983145983150983141 983140983141983142983145983150983145983150983143 983156983144983141 983144983145983143983144983141983155983156 983152983141983154983149983141983155983155983145983138983148983141 983148983151983139983137983156983145983151983150 983151983150 983156983144983141 983155983145983140983141 983151983142 983156983144983141
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A983142983156983141983154 983142983148983151983151983140983145983150983143 983151983142 983137 983152983154983141983155983139983154983145983138983141983140 983150983157983149983138983141983154 983151983142 983139983151983149983152983137983154983156983149983141983150983156983155 983156983144983141 983155983144983145983152 983155983144983137983148983148 983150983151983156
983155983157983138983149983141983154983143983141 983138983141983161983151983150983140 983137 983148983145983150983141 983155983145983156983157983137983156983141983140 983137983156 983148983141983137983155983156 76 983149983149 B983141983148983151983159 983156983144983141 983140983141983139983147 983137983156 983155983145983140983141
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 1367
983117983137983154983143983145983150 983116983145983150983141
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 1467
983117983137983154983143983145983150 983116983145983150983141
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 1567
Permability is the ratio of amount of water that can a enter or a
compartment or tank to the total volume of compartment or tank
VOLUME TOTAL
VOLUME AVAILABLE TY PERMEABILI =
983120983141983154983149983141983137983138983145983148983145983156983161 μ
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 1667
983123983157983154983142983137983139983141 983120983141983154983149983141983137983138983145983148983145983156983161 μ983137
Surface permability is the percentage of a waterplane that can be
occupied by water
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 1767
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 1867
A cargo hold with dimensions of l = 1524m w = 914 m
h=61 m is completely flooded Determine the volume of the
space and the corrected flooded volume
Volume = 1524 m x 914 m x 61 m = 8497 m3
Flooded volume = Volume x permeability
Flooded volume = 8497 m3 x 60
Flooded volume = 5098 m3
Example 1
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 1967
983110983148983151983151983140983137983138983148983141 983116983141983150983143983156983144
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983155983144983145983152 983138983141983161983151983150983140 983149983137983154983143983145983150 983148983145983150983141
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8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 2067
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983140983145983142983142983141983154983141983150983156 983152983151983145983150983156983155 983137983148983151983150983143 983156983144983141 983155983144983145983152 983148983141983150983143983156983144
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8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 2167
983110983137983139983156983151983154 983151983142 983123983157983138983140983145983158983145983155983145983151983150
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983138983161 983156983144983141 983137983152983152983148983145983139983137983138983148983141 983154983141983143983157983148983137983156983145983151983150983155 983137983150983140 983138983161 983145983150983156983141983154983150983137983156983145983151983150983137983148 983139983151983150983158983141983150983156983145983151983150 983156983144983137983156
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8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 2267
983120983141983154983149983145983155983155983145983138983148983141 983116983141983150983143983156983144
983120983141983154983149983145983155983155983145983138983148983141 L983141983150983143983156983144 983145983155 983151983138983156983137983145983150983141983140 983138983161 983149983157983148983156983145983152983148983161983145983150983143 983156983144983141 983142983148983151983151983140983137983138983148983141 983148983141983150983143983156983144 983137983156
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8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 2367
D983141983156983141983154983149983145983150983137983156983145983151983150 983151983142 983156983144983141 983148983151983139983137983156983145983151983150 983151983142 983156983144983141 983158983151983148983157983149983141 983139983141983150983156983154983141 983151983142
983140983137983149983137983143983141983140 983139983151983149983152983137983154983156983149983141983150983156
Δ I983150983145983156983145983137983148 983140983145983155983152983148983137983139983141983149983141983150983156 Δ1 D983145983155983152983148983137983139983141983149983141983150983156 983137983142983156983141983154 983140983137983149983137983143983141983140
B I983150983145983156983145983137983148 983139983141983150983156983154983141 983151983142 983138983157983151983161983137983150983139983161
G I983150983145983156983145983137983148 983139983141983150983156983154983141 983151983142 9831439831549831379831589831459831569831619831600 I983150983145983156983145983137983148 983139983141983150983156983154983141 983151983142 983148983151983150983143983145983156983157983140983145983150983137983148 983138983157983151983161983137983150983139983161 LCB
983158983159 983124983144983141 983158983151983148983157983149983141 983151983142 983159983137983156983141983154 983141983150983156983141983154983145983150983143 983156983144983141 983158983141983155983155983141983148
983160983159 D983145983155983156983137983150983139983141 983151983142 983158983151983148983157983149983141 983139983141983150983156983154983141 983151983142 983140983137983149983137983143983141983140 983139983151983149983152983137983154983156983149983141983150983156 983142983154983151983149 983149983137983141983155983156983151983154983161
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 2467
D983141983156983141983154983149983145983150983137983156983145983151983150 983151983142 983156983144983141 983148983151983139983137983156983145983151983150 983151983142 983156983144983141 983158983151983148983157983149983141 983139983141983150983156983154983141 983151983142
983140983137983149983137983143983141983140 983139983151983149983152983137983154983156983149983141983150983156
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 2567
D983141983156983141983154983149983145983150983137983156983145983151983150 983151983142 983156983144983141 983158983151983148983157983149983141 983151983142 983159983137983156983141983154 983141983150983156983141983154983145983150983143 983156983144983141 983158983141983155983155983141983148
Initial displacement and longitudinal centre of buoyancy (LCB) can be read from hydrostatcic curves
However displacement and LCB are unknown after damaged
Therefore if trim forward and aft draught are known trimmed waterline can be drawn over Bonjean
area curves
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 2667
983108983141983156983141983154983149983145983150983137983156983145983151983150 983151983142 983140983137983149983137983143983141983140 983148983141983150983143983156983144 983137983150983140 983148983151983139983137983156983145983151983150 983151983142 983149983145983140
983151983142 983139983151983149983152983137983154983156983149983141983150983156
vw The volume of water entering the vessel
xw Distance of volume centre of damaged compartment from maestory
micro Permability of the compartment
v0 Volume of the compartment
xm Distance of the volume centre of the compartment to the mid of damaged length
xl Distance of the mid of damaged length of compartment to maestory
xc Distance of the computed volume centre of compartment to maestory (xc=xl-xm)
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 2767
983108983141983156983141983154983149983145983150983137983156983145983151983150 983151983142 983140983137983149983137983143983141983140 983148983141983150983143983156983144 983137983150983140 983148983151983139983137983156983145983151983150 983151983142 983149983145983140
983151983142 983139983151983149983152983137983154983156983149983141983150983156
Damaged length and location of compartment can be determined by iterative
procedure
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 2867
bull The volume of water entering the vessel (vw)
bull Distance of volume centre of damaged compartment from amidships Θ ( xw)
bull Volume of the compartment (v0
= vw
μ)
First trial
1) Assume xm=0 (xl=xw)
2) Damaged Length l1 = (Volume of the compartment v0) (mean sec Area Amean)
where Amean is determined from trimmed sectional area curve
983108983141983156983141983154983149983145983150983137983156983145983151983150 983151983142 983140983137983149983137983143983141983140 983148983141983150983143983156983144 983137983150983140 983148983151983139983137983156983145983151983150 983151983142 983149983145983140
983151983142 983139983151983149983152983137983154983156983149983141983150983156
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 2967
3) In order to determine vm and xm
s = l1 4
vm = (s 3) sum3
xm = s sum4 sum3
xc = xl ndash xm
|vm-v0| le Tolarence for volume
|xc-xw| le Tolarence for location of volume centre
l=l1 xl=xw
983108983141983156983141983154983149983145983150983137983156983145983151983150 983151983142 983140983137983149983137983143983141983140 983148983141983150983143983156983144 983137983150983140 983148983151983139983137983156983145983151983150 983151983142 983149983145983140
983151983142 983139983151983149983152983137983154983156983149983141983150983156
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 3067
983108983141983156983141983154983149983145983150983137983156983145983151983150 983151983142 983140983137983149983137983143983141983140 983148983141983150983143983156983144 983137983150983140 983148983151983139983137983156983145983151983150 983151983142 983149983145983140
983151983142 983139983151983149983152983137983154983156983149983141983150983156Second Trial
Damaged length is changed proportionally by the volume
l2 = l1 times (v0v
m)
vm Computed volume at first trial
If the value of xm computed at first trial is negative then the mid of the
compartment slides to the bow
xl = xw+xm
where xm is the distance of the volume centre of compartment to amidship
computed at first trial
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 3167
In order to determine vm and xm
983108983141983156983141983154983149983145983150983137983156983145983151983150 983151983142 983140983137983149983137983143983141983140 983148983141983150983143983156983144 983137983150983140 983148983151983139983137983156983145983151983150 983151983142 983149983145983140
983151983142 983139983151983149983152983137983154983156983149983141983150983156
s = l2 4
vm = (s 3) sum3
xm = s sum4 sum3
xc = xl ndash xm
|vm-v0| le Tolarence for volume
|xc-xw| le Tolarence for location of volume centre
l=l2
If tolarances for both volume and location are not satisfied third fourthtrials are made similar to
second trial
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 3267
If either tolarence for volume or tolarance for location are satisfied at a trial
satisfied one is fixed trials are continued to make for the other one
983108983141983156983141983154983149983145983150983137983156983145983151983150 983151983142 983140983137983149983137983143983141983140 983148983141983150983143983156983144 983137983150983140 983148983151983139983137983156983145983151983150 983151983142 983149983145983140
983151983142 983139983151983149983152983137983154983156983149983141983150983156
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 3367
A ship is 116 meter long and displaces 7842 ton in salt water (ρ1=1025 tm3)
when her mean draught is 64m Longitudinal Centre of Buoyancy (LCB) is
0615 m aft from amidships After one of her stern compartment is damaged
she floats trimmed to the aft Her sectional areas after damaged are given in the
following table
a) Determine the volume of water entering the vessel (vw) and the location of
volume centre of damaged compartment (xw)
b) Assume permability of compartment micro is 1 Determine damaged length
and Distance of the mid of damaged length of compartment to amidship
983109983160983137983149983152983148983141 2
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 3467
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 3567
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 3667
Predicted xw
is between section 2 and section 3
983123983141983139 N983151 983123983141983139 A983154983141983137 D983145983155983156 A9831499831459831559831449831459831522 10135 983085348
3 1208 983085232
983123983141983139 A983154983141983137 983137983156 98308524983149 983142983154983151983149 983137983149983145983140983155983144983145983152 = 11959831492
l1=v0Amean=204081195=17078 m
s=l14=427 m
983109983160983137983149983152983148983141 2983085983123983119983116983125983124983113983119983118
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 3767
983161983145 L983151983139 A983149983141983137983150 983123M M A983154983149
9831311983133 9831312983133 98313119831339832559831312983133 9831313983133 983131198313398325598313129831339832559831313983133
0 9830853254 1051 1 1051 2 21021 9830852827 1123 4 4492 1 4492
2 98308524 1195 2 239 0 0
3 9830851973 1219 4 4876 9830851 9830854876
4 9830851546 1233 1 1233 9830852 9830852466
sum983091983101 14042 sum983092983101 983085748
vm
= (s3) sum3= 199864479831493
xm
=s sum4sum3= 9830850227983149
v0-vm=20408-19986=422 m3
Error=422times10020408=207
983109983160983137983149983152983148983141 2983085983123983119983116983125983124983113983119983118
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 3867
Methods of Calculation
There two available method calculating the
final stage of the damaged vessel
bull Lost Buoyancy Method
bull Added Weight Method
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 3967
Comparision of Lost Buoyancy and Added
Weight Methods
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 4067
Consider a vessel that has been damaged such
that a portion of the bottom is now open to the
sea
The vesselrsquos draft will increase because an amount
of the buoyancy was lost
Added Weight Method
Added Weight Method
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 4167
Added Weight Method
In this method flood water is treated as a fixed weight (for example the
weight of water of volume ABEF) This added weight is balanced by the
additional buoyant force of the layer WL1WL
The added weight can be determined by either the volume ABEF or
waterline WL1 Therefore WL1 waterline is not known can be just guessed
For the predicted waterline added weight and additional buoyant force
caculation are done iteratively until both of them are equal This method is
known as Added weight method
Determination of Added Weight
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 4267
Determination of Added Weight
vc Volume of damaged compartment (DCEF)
ac The surface area (AB) of damaged compartment on the waterline
micro The volume permability of damaged compartment
microa The area permability of the surface of damaged compartment
∆ The initial displacement
∆1 The displacement at final stage
vw The volume of water entering the vessel (ABEH)
w The weight of water entering the vessel
p The value of parallel sinkage
If th t th l l i k i h f t l f
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 4367
If we assume that the paralel sinkage cause a minor change of water plane area of a
ship (Awp
asymp Awp1
) we can determine the paralel sinkage by equating the volume of
the layer WL1WL to the volume of ABEF
If the damaged compartment is bounded on top
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 4467
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 4567
Longitudinal Metacentre Radius at final stage
Free Surface Effect
Damaged compartment can be considered as a half filled tank
Free Contact Effect
Damaged compartment can be considered as a half filled tank
T M H i h
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 4667
Transverse Metacentre Height
The angle of heel
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 4767
L it di l M t t H i ht
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 4867
Longitudinal Metacentre Height
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 4967
E983160983137983149983152983148983141 A 983138983137983154983143983141
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 5067
E983160983137983149983152983148983141 A 983138983137983154983143983141
991266 L = 20 983149991266 B = 5 983149
991266 983124 = 15 983149
991266 KG = 15 983149
I983150983156983137983139983156 C983151983150983140983145983156983145983151983150
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 5167
I983150983156983137983139983156 C983151983150983140983145983156983145983151983150
991266 983124983144983141 983140983145983155983152983148983137983139983141983149983141983150983156 983158983151983148983157983149983141
991266 983124983144983141 983149983137983155983155 983140983145983155983152983148983137983139983141983149983141983150983156
991266 983124983144983141 983149983151983149983141983150983156 983151983142 983145983150983141983154983156983145983137 983151983142 983156983144983141 983159983137983156983141983154983152983148983137983150983141 983137983154983141983137983137983138983151983157983156 CL
3
15051520 m x xT B L
I I
==sdotsdot=nabla
tons x I
751531500251 ==nablasdot=∆ ρ
433
33208
12
205
12
m x L B
I I
===
I983150983156983137983139983156 C983151983150983140983145983156983145983151983150
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 5267
I983150983156983137983139983156 C983151983150983140983145983156983145983151983150
991266 M983141983156983137983139983141983150983156983154983145983139 983154983137983140983145983157983155
991266 O983154 983145983156 983139983151983157983148983140 983138983141 983139983137983148983139983157983148983137983156983141983140 983140983145983154983141983139983156983148983161 983137983155
991266 H983141983145983143983144983156 983151983142 983156983144983141 983139983141983150983156983141983154 983151983142 983138983157983151983161983137983150983139983161
m I
BM
I
I 3891
150
33208==
nabla
=
m xT
B
LBT
L B BM
I I
I 3891
5112
5
12
12 223
====
mT
KB I
I 750
2
==
I983150983156983137983139983156 C983151983150983140983145983156983145983151983150
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 5367
991266 983124983144983141 983149983141983156983137983139983141983150983156983154983145983139 983144983141983145983143983144983156
991266 F983151983154 983155983149983137983148983148 983137983150983143983148983141983155 983151983142 983144983141983141983148 983156983144983141 983154983145983143983144983156983145983150983143 983149983151983149983141983150983156
m KG BM KBGM I I 63905013891750 =minus+=minus+=
sin22998sin693075153sin mt x xGM M I I
φ φ φ ==∆=
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 5467
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 5567
983116983119983123983124 983106983125983119983129983105983118983107983129 983117983109983124983112983119983108
Paralel Sinkage
Volume (DCEF)=Volume (W1ADW+BL1LC)
Damaged compartment is bounded on top
983116983119983123983124 983106983125983119983129983105983118983107983129 983117983109983124983112983119983108
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 5667
983116983119983123983124 983106983125983119983129983105983118983107983129 983117983109983124983112983119983108
bull It is assumed that displacement and location of vertical centre
of gravity does not change after damaged
983116983119983123983124 983106983125983119983129983105983118983107983129 983117983109983124983112983119983108
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 5767
983116983119983123983124 983106983125983119983129983105983118983107983129 983117983109983124983112983119983108
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 5867
The heel angle of damaged ship is determined by
where
d is the distance between the volume centre of damaged compartment
and the new longitudinal centre of floatation
wc=vc μ ρ
983116983119983123983124 983106983125983119983129983105983118983107983129 983117983109983124983112983119983108
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 5967
983116983119983123983124 983106983125983119983129983105983118983107983129 983117983109983124983112983119983108
983116983119983123983124 983106983125983119983129983105983118983107983129 983117983109983124983112983119983108
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 6067
Longitudinal Metacentre Height of a Damaged Ship
983116983119983123983124 983106983125983119983129983105983118983107983129 983117983109983124983112983119983108
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 6167
983110983151983154983159983137983154983140 983137983150983140 983137983142983156 983140983154983137983157983143983144983156983155 983137983142983156983141983154 983140983137983149983137983143983141983140
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 6267
983120983151983154983156 983105983142983156 983120983151983154983156 983110983151983154983141 983123983156983137983154983138983151983137983154983140 983105983142983156 983123983156983137983154983138983151983137983154983140 983110983151983154983159983137983154983140
I983150983145983156983145983137983148 D983154983137983157983143983144983156 983124 983124 983124 983124
983120983137983154983137983148983141983148 983123983145983150983147983137983143983141 +983152 +983152 +983152 +983120
H983141983141983148 983085983149983145 983085983149983145 +983149983155 +983149983155
983124983154983145983149 983085983156983147 +983156983138 983085983156983147 +983156983138
F983145983150983137983148 D983154983137983157983143983144983156 983124+983152983085983149983145983085983156983147 983124+983152983085983149983145+983156983138 983124+983152+983149983155983085983156983147 983124+983152+983149983155+983156983138
Table 1 Final Draughts for a starboard side damaged ship
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 6367
L983151983155983156 B983157983151983161983137983150983139983161 M983141983156983144983151983140
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 6467
L983151983155983156 B983157983151983161983137983150983139983161 M983141983156983144983151983140
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 6567
991266 A983142983156983141983154 983148983151983151983155983145983150983143 983156983144983141 983139983141983150983156983154983137983148 983139983151983149983152983137983154983156983149983141983150983156 983156983144983141
983159983137983156983141983154983152983148983137983150983141 983137983154983141983137 983145983155
991266 983124983151 983139983151983149983152983141983150983155983137983156983141 983142983151983154 983156983144983141 983148983151983155983155 983151983142 983138983157983151983161983137983150983139983161 983151983142 983156983144983141
983139983141983150983156983154983137983148 983139983151983149983152983137983154983156983149983141983150983156 983156983144983141 983140983154983137983142983156 983145983150983139983154983141983137983155983141983155 983156983151
2805)420()( m x Bl L A L
=minus=minus=
m A
T
L
I
L 875180
150==
nabla=
L983151983155983156 B983157983151983161983137983150983139983161 M983141983156983144983151983140
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 6667
991266 983124983144983141 983144983141983145983143983144983156 983151983142 983156983144983141 983139983141983150983156983141983154 983151983142 983138983157983151983161983137983150983139983161 983145983150983139983154983141983137983155983141983155 983156983151
991266 983124983144983141 983149983151983149983141983150983156 983151983142 983145983150983141983154983156983145983137 983151983142 983156983144983141 983159983137983156983141983154983152983148983137983150983141 983137983154983141983137
991266 983124983144983141 983149983141983156983137983139983141983150983156983154983145983139 983154983137983140983145983157983155
m
T
KB L
L 93802
8751
2 ===
433
6716612
)420(5
12
)(m
l L B I L
=minus
=minus
=
m I
BM
I
L
L 1111150
67166==
nabla
=
L983151983155983156 B983157983151983161983137983150983139983161 M983141983156983144983151983140
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 6767
991266 983124983144983141 983149983141983156983137983139983141983150983156983154983145983139 983144983141983145983143983144983156
991266 983122983145983143983144983156983145983150983143 983149983151983149983141983150983156 983142983151983154 983155983149983137983148983148 983144983141983141983148 983137983150983143983148983141983155
m KG BM KBGM L L L 54905111119380 =minus+=minus+=
mt xGM M L
sin34984sin549075153sin φ φ φ ==∆=
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 967
D983137983149983137983143983141
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 1067
983127983137983156983141983154983156983145983143983144983156 983138983157983148983147983144983141983137983140983155 983098 983156983144983141 983144983157983148983148 983145983155 983155983157983138983140983145983158983145983140983141983140 983145983150983156983151 983159983137983156983141983154983156983145983143983144983156
983139983151983149983152983137983154983156983149983141983150983156983155 983138983161 983149983141983137983150983155 983151983142 983159983137983156983141983154983156983145983143983144983156 983138983157983148983147983144983141983137983140983155 983137983150983140 983140983141983139983147983155
983127983137983156983141983154983156983145983143983144983156 983106983157983148983147983144983141983137983140983155
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 1167
983106983157983148983147983144983141983137983140 983108983141983139983147983155
983106983157983148983147983144983141983137983140 983140983141983139983147983155 983098 983156983144983141 983140983141983139983147 983157983152 983156983151 983159983144983145983139983144 983156983144983141983155983141 983138983157983148983147983144983141983137983140983155 983141983160983156983141983150983140983155
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 1267
983117983137983154983143983145983150 983116983145983150983141
983117983137983154983143983145983150 983148983145983150983141 983145983155 983137 983148983145983150983141 983140983141983142983145983150983145983150983143 983156983144983141 983144983145983143983144983141983155983156 983152983141983154983149983141983155983155983145983138983148983141 983148983151983139983137983156983145983151983150 983151983150 983156983144983141 983155983145983140983141 983151983142 983156983144983141
983158983141983155983155983141983148 983151983142 983137983150983161 983140983137983149983137983143983141983140 983159983137983156983141983154983152983148983137983150983141 983145983150 983156983144983141 983142983145983150983137983148 983139983151983150983140983145983156983145983151983150 983151983142 983155983145983150983147983137983143983141983156983154983145983149 983137983150983140 983144983141983141983148
A983142983156983141983154 983142983148983151983151983140983145983150983143 983151983142 983137 983152983154983141983155983139983154983145983138983141983140 983150983157983149983138983141983154 983151983142 983139983151983149983152983137983154983156983149983141983150983156983155 983156983144983141 983155983144983145983152 983155983144983137983148983148 983150983151983156
983155983157983138983149983141983154983143983141 983138983141983161983151983150983140 983137 983148983145983150983141 983155983145983156983157983137983156983141983140 983137983156 983148983141983137983155983156 76 983149983149 B983141983148983151983159 983156983144983141 983140983141983139983147 983137983156 983155983145983140983141
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 1367
983117983137983154983143983145983150 983116983145983150983141
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 1467
983117983137983154983143983145983150 983116983145983150983141
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 1567
Permability is the ratio of amount of water that can a enter or a
compartment or tank to the total volume of compartment or tank
VOLUME TOTAL
VOLUME AVAILABLE TY PERMEABILI =
983120983141983154983149983141983137983138983145983148983145983156983161 μ
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 1667
983123983157983154983142983137983139983141 983120983141983154983149983141983137983138983145983148983145983156983161 μ983137
Surface permability is the percentage of a waterplane that can be
occupied by water
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 1767
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 1867
A cargo hold with dimensions of l = 1524m w = 914 m
h=61 m is completely flooded Determine the volume of the
space and the corrected flooded volume
Volume = 1524 m x 914 m x 61 m = 8497 m3
Flooded volume = Volume x permeability
Flooded volume = 8497 m3 x 60
Flooded volume = 5098 m3
Example 1
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 1967
983110983148983151983151983140983137983138983148983141 983116983141983150983143983156983144
983110983148983151983151983140983137983138983148983141 983148983141983150983143983156983144983098 983137983156 983137 983143983145983158983141983150 983152983151983145983150983156 983151983142 983156983144983141 983155983144983145983152 983148983141983150983143983156983144 983145983155 983156983144983141 983149983137983160983145983149983157983149 983148983141983150983143983156983144
983159983145983156983144 983156983144983141 983139983141983150983156983141983154 983137983156 983156983144983137983156 983152983151983145983150983156 983156983144983137983156 983139983137983150 983138983141 983142983148983151983151983140983141983140 983159983145983156983144983151983157983156 983155983157983138983149983141983154983143983145983150983143 983156983144983141
983155983144983145983152 983138983141983161983151983150983140 983149983137983154983143983145983150 983148983145983150983141
983129983137983154983137983148ı 983106983286983148983149983141 983106983151983161983157983098 G983141983149983145 983138983151983161983157983150983139983137 983144983141983154983144983137983150983143983145 983138983145983154 983150983151983147983156983137983140983137 983138983157 983150983151983147983156983137 983149983141983154983147983141983162
983151983148983149983137983147 983292983162983141983154983141 983143983141983149983145983161983145 983155ı983150ı983154 983144983137983156983156ı983150983137 983156983141ğ983141983156 983144983137983148983141 983143983141983156983145983154983141983139983141983147 983141983150 983138983292983161983292983147 983138983286983148983149983141 983138983151983161983157983150983137
983151 983150983151983147983156983137983140983137983147983145 983161983137983154983137983148ı 983138983286983148983149983141 983138983151983161983157 983140983141983150983145983154
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 2067
983110983148983151983151983140983137983138983148983141 983116983141983150983143983156983144 983107983157983154983158983141
983110983148983151983151983140983137983138983148983141 983116983141983150983143983156983144 983107983157983154983158983141983098 I983156 983145983155 983151983138983156983137983145983150983141983140 983138983161 983156983144983141 983139983151983150983150983141983139983156983145983151983150 983151983142 983142983148983151983151983140983137983138983148983141 983148983141983150983143983156983144983155 983137983156
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8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 2167
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F983137983139983156983151983154 983151983142 983123983157983138983140983145983158983145983155983145983151983150 983124983144983141 983142983137983139983156983151983154 983151983142 983155983157983138983140983145983158983145983155983145983151983150 983145983155 983137 983142983137983139983156983151983154 983152983154983141983155983139983154983145983138983141983140
983138983161 983156983144983141 983137983152983152983148983145983139983137983138983148983141 983154983141983143983157983148983137983156983145983151983150983155 983137983150983140 983138983161 983145983150983156983141983154983150983137983156983145983151983150983137983148 983139983151983150983158983141983150983156983145983151983150 983156983144983137983156
983140983141983152983141983150983140983155 983151983150 983155983144983145983152 983148983141983150983143983156983144 983137983150983140 983139983154983145983156983141983154983145983151983150 983151983142 983155983141983154983158983145983139983141
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 2267
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983120983141983154983149983145983155983155983145983138983148983141 L983141983150983143983156983144 983145983155 983151983138983156983137983145983150983141983140 983138983161 983149983157983148983156983145983152983148983161983145983150983143 983156983144983141 983142983148983151983151983140983137983138983148983141 983148983141983150983143983156983144 983137983156
983156983144983137983156 983152983151983145983150983156 983138983161 983156983144983141 983142983137983139983156983151983154 983151983142 983155983157983138983140983145983158983145983155983145983151983150
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 2367
D983141983156983141983154983149983145983150983137983156983145983151983150 983151983142 983156983144983141 983148983151983139983137983156983145983151983150 983151983142 983156983144983141 983158983151983148983157983149983141 983139983141983150983156983154983141 983151983142
983140983137983149983137983143983141983140 983139983151983149983152983137983154983156983149983141983150983156
Δ I983150983145983156983145983137983148 983140983145983155983152983148983137983139983141983149983141983150983156 Δ1 D983145983155983152983148983137983139983141983149983141983150983156 983137983142983156983141983154 983140983137983149983137983143983141983140
B I983150983145983156983145983137983148 983139983141983150983156983154983141 983151983142 983138983157983151983161983137983150983139983161
G I983150983145983156983145983137983148 983139983141983150983156983154983141 983151983142 9831439831549831379831589831459831569831619831600 I983150983145983156983145983137983148 983139983141983150983156983154983141 983151983142 983148983151983150983143983145983156983157983140983145983150983137983148 983138983157983151983161983137983150983139983161 LCB
983158983159 983124983144983141 983158983151983148983157983149983141 983151983142 983159983137983156983141983154 983141983150983156983141983154983145983150983143 983156983144983141 983158983141983155983155983141983148
983160983159 D983145983155983156983137983150983139983141 983151983142 983158983151983148983157983149983141 983139983141983150983156983154983141 983151983142 983140983137983149983137983143983141983140 983139983151983149983152983137983154983156983149983141983150983156 983142983154983151983149 983149983137983141983155983156983151983154983161
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 2467
D983141983156983141983154983149983145983150983137983156983145983151983150 983151983142 983156983144983141 983148983151983139983137983156983145983151983150 983151983142 983156983144983141 983158983151983148983157983149983141 983139983141983150983156983154983141 983151983142
983140983137983149983137983143983141983140 983139983151983149983152983137983154983156983149983141983150983156
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 2567
D983141983156983141983154983149983145983150983137983156983145983151983150 983151983142 983156983144983141 983158983151983148983157983149983141 983151983142 983159983137983156983141983154 983141983150983156983141983154983145983150983143 983156983144983141 983158983141983155983155983141983148
Initial displacement and longitudinal centre of buoyancy (LCB) can be read from hydrostatcic curves
However displacement and LCB are unknown after damaged
Therefore if trim forward and aft draught are known trimmed waterline can be drawn over Bonjean
area curves
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 2667
983108983141983156983141983154983149983145983150983137983156983145983151983150 983151983142 983140983137983149983137983143983141983140 983148983141983150983143983156983144 983137983150983140 983148983151983139983137983156983145983151983150 983151983142 983149983145983140
983151983142 983139983151983149983152983137983154983156983149983141983150983156
vw The volume of water entering the vessel
xw Distance of volume centre of damaged compartment from maestory
micro Permability of the compartment
v0 Volume of the compartment
xm Distance of the volume centre of the compartment to the mid of damaged length
xl Distance of the mid of damaged length of compartment to maestory
xc Distance of the computed volume centre of compartment to maestory (xc=xl-xm)
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 2767
983108983141983156983141983154983149983145983150983137983156983145983151983150 983151983142 983140983137983149983137983143983141983140 983148983141983150983143983156983144 983137983150983140 983148983151983139983137983156983145983151983150 983151983142 983149983145983140
983151983142 983139983151983149983152983137983154983156983149983141983150983156
Damaged length and location of compartment can be determined by iterative
procedure
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 2867
bull The volume of water entering the vessel (vw)
bull Distance of volume centre of damaged compartment from amidships Θ ( xw)
bull Volume of the compartment (v0
= vw
μ)
First trial
1) Assume xm=0 (xl=xw)
2) Damaged Length l1 = (Volume of the compartment v0) (mean sec Area Amean)
where Amean is determined from trimmed sectional area curve
983108983141983156983141983154983149983145983150983137983156983145983151983150 983151983142 983140983137983149983137983143983141983140 983148983141983150983143983156983144 983137983150983140 983148983151983139983137983156983145983151983150 983151983142 983149983145983140
983151983142 983139983151983149983152983137983154983156983149983141983150983156
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 2967
3) In order to determine vm and xm
s = l1 4
vm = (s 3) sum3
xm = s sum4 sum3
xc = xl ndash xm
|vm-v0| le Tolarence for volume
|xc-xw| le Tolarence for location of volume centre
l=l1 xl=xw
983108983141983156983141983154983149983145983150983137983156983145983151983150 983151983142 983140983137983149983137983143983141983140 983148983141983150983143983156983144 983137983150983140 983148983151983139983137983156983145983151983150 983151983142 983149983145983140
983151983142 983139983151983149983152983137983154983156983149983141983150983156
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 3067
983108983141983156983141983154983149983145983150983137983156983145983151983150 983151983142 983140983137983149983137983143983141983140 983148983141983150983143983156983144 983137983150983140 983148983151983139983137983156983145983151983150 983151983142 983149983145983140
983151983142 983139983151983149983152983137983154983156983149983141983150983156Second Trial
Damaged length is changed proportionally by the volume
l2 = l1 times (v0v
m)
vm Computed volume at first trial
If the value of xm computed at first trial is negative then the mid of the
compartment slides to the bow
xl = xw+xm
where xm is the distance of the volume centre of compartment to amidship
computed at first trial
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 3167
In order to determine vm and xm
983108983141983156983141983154983149983145983150983137983156983145983151983150 983151983142 983140983137983149983137983143983141983140 983148983141983150983143983156983144 983137983150983140 983148983151983139983137983156983145983151983150 983151983142 983149983145983140
983151983142 983139983151983149983152983137983154983156983149983141983150983156
s = l2 4
vm = (s 3) sum3
xm = s sum4 sum3
xc = xl ndash xm
|vm-v0| le Tolarence for volume
|xc-xw| le Tolarence for location of volume centre
l=l2
If tolarances for both volume and location are not satisfied third fourthtrials are made similar to
second trial
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 3267
If either tolarence for volume or tolarance for location are satisfied at a trial
satisfied one is fixed trials are continued to make for the other one
983108983141983156983141983154983149983145983150983137983156983145983151983150 983151983142 983140983137983149983137983143983141983140 983148983141983150983143983156983144 983137983150983140 983148983151983139983137983156983145983151983150 983151983142 983149983145983140
983151983142 983139983151983149983152983137983154983156983149983141983150983156
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 3367
A ship is 116 meter long and displaces 7842 ton in salt water (ρ1=1025 tm3)
when her mean draught is 64m Longitudinal Centre of Buoyancy (LCB) is
0615 m aft from amidships After one of her stern compartment is damaged
she floats trimmed to the aft Her sectional areas after damaged are given in the
following table
a) Determine the volume of water entering the vessel (vw) and the location of
volume centre of damaged compartment (xw)
b) Assume permability of compartment micro is 1 Determine damaged length
and Distance of the mid of damaged length of compartment to amidship
983109983160983137983149983152983148983141 2
8162019 Damaged Stability
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8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 3567
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 3667
Predicted xw
is between section 2 and section 3
983123983141983139 N983151 983123983141983139 A983154983141983137 D983145983155983156 A9831499831459831559831449831459831522 10135 983085348
3 1208 983085232
983123983141983139 A983154983141983137 983137983156 98308524983149 983142983154983151983149 983137983149983145983140983155983144983145983152 = 11959831492
l1=v0Amean=204081195=17078 m
s=l14=427 m
983109983160983137983149983152983148983141 2983085983123983119983116983125983124983113983119983118
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 3767
983161983145 L983151983139 A983149983141983137983150 983123M M A983154983149
9831311983133 9831312983133 98313119831339832559831312983133 9831313983133 983131198313398325598313129831339832559831313983133
0 9830853254 1051 1 1051 2 21021 9830852827 1123 4 4492 1 4492
2 98308524 1195 2 239 0 0
3 9830851973 1219 4 4876 9830851 9830854876
4 9830851546 1233 1 1233 9830852 9830852466
sum983091983101 14042 sum983092983101 983085748
vm
= (s3) sum3= 199864479831493
xm
=s sum4sum3= 9830850227983149
v0-vm=20408-19986=422 m3
Error=422times10020408=207
983109983160983137983149983152983148983141 2983085983123983119983116983125983124983113983119983118
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 3867
Methods of Calculation
There two available method calculating the
final stage of the damaged vessel
bull Lost Buoyancy Method
bull Added Weight Method
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 3967
Comparision of Lost Buoyancy and Added
Weight Methods
8162019 Damaged Stability
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Consider a vessel that has been damaged such
that a portion of the bottom is now open to the
sea
The vesselrsquos draft will increase because an amount
of the buoyancy was lost
Added Weight Method
Added Weight Method
8162019 Damaged Stability
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Added Weight Method
In this method flood water is treated as a fixed weight (for example the
weight of water of volume ABEF) This added weight is balanced by the
additional buoyant force of the layer WL1WL
The added weight can be determined by either the volume ABEF or
waterline WL1 Therefore WL1 waterline is not known can be just guessed
For the predicted waterline added weight and additional buoyant force
caculation are done iteratively until both of them are equal This method is
known as Added weight method
Determination of Added Weight
8162019 Damaged Stability
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Determination of Added Weight
vc Volume of damaged compartment (DCEF)
ac The surface area (AB) of damaged compartment on the waterline
micro The volume permability of damaged compartment
microa The area permability of the surface of damaged compartment
∆ The initial displacement
∆1 The displacement at final stage
vw The volume of water entering the vessel (ABEH)
w The weight of water entering the vessel
p The value of parallel sinkage
If th t th l l i k i h f t l f
8162019 Damaged Stability
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If we assume that the paralel sinkage cause a minor change of water plane area of a
ship (Awp
asymp Awp1
) we can determine the paralel sinkage by equating the volume of
the layer WL1WL to the volume of ABEF
If the damaged compartment is bounded on top
8162019 Damaged Stability
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8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 4567
Longitudinal Metacentre Radius at final stage
Free Surface Effect
Damaged compartment can be considered as a half filled tank
Free Contact Effect
Damaged compartment can be considered as a half filled tank
T M H i h
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 4667
Transverse Metacentre Height
The angle of heel
8162019 Damaged Stability
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L it di l M t t H i ht
8162019 Damaged Stability
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Longitudinal Metacentre Height
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 4967
E983160983137983149983152983148983141 A 983138983137983154983143983141
8162019 Damaged Stability
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E983160983137983149983152983148983141 A 983138983137983154983143983141
991266 L = 20 983149991266 B = 5 983149
991266 983124 = 15 983149
991266 KG = 15 983149
I983150983156983137983139983156 C983151983150983140983145983156983145983151983150
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 5167
I983150983156983137983139983156 C983151983150983140983145983156983145983151983150
991266 983124983144983141 983140983145983155983152983148983137983139983141983149983141983150983156 983158983151983148983157983149983141
991266 983124983144983141 983149983137983155983155 983140983145983155983152983148983137983139983141983149983141983150983156
991266 983124983144983141 983149983151983149983141983150983156 983151983142 983145983150983141983154983156983145983137 983151983142 983156983144983141 983159983137983156983141983154983152983148983137983150983141 983137983154983141983137983137983138983151983157983156 CL
3
15051520 m x xT B L
I I
==sdotsdot=nabla
tons x I
751531500251 ==nablasdot=∆ ρ
433
33208
12
205
12
m x L B
I I
===
I983150983156983137983139983156 C983151983150983140983145983156983145983151983150
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 5267
I983150983156983137983139983156 C983151983150983140983145983156983145983151983150
991266 M983141983156983137983139983141983150983156983154983145983139 983154983137983140983145983157983155
991266 O983154 983145983156 983139983151983157983148983140 983138983141 983139983137983148983139983157983148983137983156983141983140 983140983145983154983141983139983156983148983161 983137983155
991266 H983141983145983143983144983156 983151983142 983156983144983141 983139983141983150983156983141983154 983151983142 983138983157983151983161983137983150983139983161
m I
BM
I
I 3891
150
33208==
nabla
=
m xT
B
LBT
L B BM
I I
I 3891
5112
5
12
12 223
====
mT
KB I
I 750
2
==
I983150983156983137983139983156 C983151983150983140983145983156983145983151983150
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 5367
991266 983124983144983141 983149983141983156983137983139983141983150983156983154983145983139 983144983141983145983143983144983156
991266 F983151983154 983155983149983137983148983148 983137983150983143983148983141983155 983151983142 983144983141983141983148 983156983144983141 983154983145983143983144983156983145983150983143 983149983151983149983141983150983156
m KG BM KBGM I I 63905013891750 =minus+=minus+=
sin22998sin693075153sin mt x xGM M I I
φ φ φ ==∆=
8162019 Damaged Stability
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8162019 Damaged Stability
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983116983119983123983124 983106983125983119983129983105983118983107983129 983117983109983124983112983119983108
Paralel Sinkage
Volume (DCEF)=Volume (W1ADW+BL1LC)
Damaged compartment is bounded on top
983116983119983123983124 983106983125983119983129983105983118983107983129 983117983109983124983112983119983108
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 5667
983116983119983123983124 983106983125983119983129983105983118983107983129 983117983109983124983112983119983108
bull It is assumed that displacement and location of vertical centre
of gravity does not change after damaged
983116983119983123983124 983106983125983119983129983105983118983107983129 983117983109983124983112983119983108
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 5767
983116983119983123983124 983106983125983119983129983105983118983107983129 983117983109983124983112983119983108
8162019 Damaged Stability
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The heel angle of damaged ship is determined by
where
d is the distance between the volume centre of damaged compartment
and the new longitudinal centre of floatation
wc=vc μ ρ
983116983119983123983124 983106983125983119983129983105983118983107983129 983117983109983124983112983119983108
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 5967
983116983119983123983124 983106983125983119983129983105983118983107983129 983117983109983124983112983119983108
983116983119983123983124 983106983125983119983129983105983118983107983129 983117983109983124983112983119983108
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 6067
Longitudinal Metacentre Height of a Damaged Ship
983116983119983123983124 983106983125983119983129983105983118983107983129 983117983109983124983112983119983108
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 6167
983110983151983154983159983137983154983140 983137983150983140 983137983142983156 983140983154983137983157983143983144983156983155 983137983142983156983141983154 983140983137983149983137983143983141983140
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 6267
983120983151983154983156 983105983142983156 983120983151983154983156 983110983151983154983141 983123983156983137983154983138983151983137983154983140 983105983142983156 983123983156983137983154983138983151983137983154983140 983110983151983154983159983137983154983140
I983150983145983156983145983137983148 D983154983137983157983143983144983156 983124 983124 983124 983124
983120983137983154983137983148983141983148 983123983145983150983147983137983143983141 +983152 +983152 +983152 +983120
H983141983141983148 983085983149983145 983085983149983145 +983149983155 +983149983155
983124983154983145983149 983085983156983147 +983156983138 983085983156983147 +983156983138
F983145983150983137983148 D983154983137983157983143983144983156 983124+983152983085983149983145983085983156983147 983124+983152983085983149983145+983156983138 983124+983152+983149983155983085983156983147 983124+983152+983149983155+983156983138
Table 1 Final Draughts for a starboard side damaged ship
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 6367
L983151983155983156 B983157983151983161983137983150983139983161 M983141983156983144983151983140
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 6467
L983151983155983156 B983157983151983161983137983150983139983161 M983141983156983144983151983140
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 6567
991266 A983142983156983141983154 983148983151983151983155983145983150983143 983156983144983141 983139983141983150983156983154983137983148 983139983151983149983152983137983154983156983149983141983150983156 983156983144983141
983159983137983156983141983154983152983148983137983150983141 983137983154983141983137 983145983155
991266 983124983151 983139983151983149983152983141983150983155983137983156983141 983142983151983154 983156983144983141 983148983151983155983155 983151983142 983138983157983151983161983137983150983139983161 983151983142 983156983144983141
983139983141983150983156983154983137983148 983139983151983149983152983137983154983156983149983141983150983156 983156983144983141 983140983154983137983142983156 983145983150983139983154983141983137983155983141983155 983156983151
2805)420()( m x Bl L A L
=minus=minus=
m A
T
L
I
L 875180
150==
nabla=
L983151983155983156 B983157983151983161983137983150983139983161 M983141983156983144983151983140
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 6667
991266 983124983144983141 983144983141983145983143983144983156 983151983142 983156983144983141 983139983141983150983156983141983154 983151983142 983138983157983151983161983137983150983139983161 983145983150983139983154983141983137983155983141983155 983156983151
991266 983124983144983141 983149983151983149983141983150983156 983151983142 983145983150983141983154983156983145983137 983151983142 983156983144983141 983159983137983156983141983154983152983148983137983150983141 983137983154983141983137
991266 983124983144983141 983149983141983156983137983139983141983150983156983154983145983139 983154983137983140983145983157983155
m
T
KB L
L 93802
8751
2 ===
433
6716612
)420(5
12
)(m
l L B I L
=minus
=minus
=
m I
BM
I
L
L 1111150
67166==
nabla
=
L983151983155983156 B983157983151983161983137983150983139983161 M983141983156983144983151983140
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 6767
991266 983124983144983141 983149983141983156983137983139983141983150983156983154983145983139 983144983141983145983143983144983156
991266 983122983145983143983144983156983145983150983143 983149983151983149983141983150983156 983142983151983154 983155983149983137983148983148 983144983141983141983148 983137983150983143983148983141983155
m KG BM KBGM L L L 54905111119380 =minus+=minus+=
mt xGM M L
sin34984sin549075153sin φ φ φ ==∆=
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 1067
983127983137983156983141983154983156983145983143983144983156 983138983157983148983147983144983141983137983140983155 983098 983156983144983141 983144983157983148983148 983145983155 983155983157983138983140983145983158983145983140983141983140 983145983150983156983151 983159983137983156983141983154983156983145983143983144983156
983139983151983149983152983137983154983156983149983141983150983156983155 983138983161 983149983141983137983150983155 983151983142 983159983137983156983141983154983156983145983143983144983156 983138983157983148983147983144983141983137983140983155 983137983150983140 983140983141983139983147983155
983127983137983156983141983154983156983145983143983144983156 983106983157983148983147983144983141983137983140983155
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 1167
983106983157983148983147983144983141983137983140 983108983141983139983147983155
983106983157983148983147983144983141983137983140 983140983141983139983147983155 983098 983156983144983141 983140983141983139983147 983157983152 983156983151 983159983144983145983139983144 983156983144983141983155983141 983138983157983148983147983144983141983137983140983155 983141983160983156983141983150983140983155
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 1267
983117983137983154983143983145983150 983116983145983150983141
983117983137983154983143983145983150 983148983145983150983141 983145983155 983137 983148983145983150983141 983140983141983142983145983150983145983150983143 983156983144983141 983144983145983143983144983141983155983156 983152983141983154983149983141983155983155983145983138983148983141 983148983151983139983137983156983145983151983150 983151983150 983156983144983141 983155983145983140983141 983151983142 983156983144983141
983158983141983155983155983141983148 983151983142 983137983150983161 983140983137983149983137983143983141983140 983159983137983156983141983154983152983148983137983150983141 983145983150 983156983144983141 983142983145983150983137983148 983139983151983150983140983145983156983145983151983150 983151983142 983155983145983150983147983137983143983141983156983154983145983149 983137983150983140 983144983141983141983148
A983142983156983141983154 983142983148983151983151983140983145983150983143 983151983142 983137 983152983154983141983155983139983154983145983138983141983140 983150983157983149983138983141983154 983151983142 983139983151983149983152983137983154983156983149983141983150983156983155 983156983144983141 983155983144983145983152 983155983144983137983148983148 983150983151983156
983155983157983138983149983141983154983143983141 983138983141983161983151983150983140 983137 983148983145983150983141 983155983145983156983157983137983156983141983140 983137983156 983148983141983137983155983156 76 983149983149 B983141983148983151983159 983156983144983141 983140983141983139983147 983137983156 983155983145983140983141
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 1367
983117983137983154983143983145983150 983116983145983150983141
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 1467
983117983137983154983143983145983150 983116983145983150983141
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 1567
Permability is the ratio of amount of water that can a enter or a
compartment or tank to the total volume of compartment or tank
VOLUME TOTAL
VOLUME AVAILABLE TY PERMEABILI =
983120983141983154983149983141983137983138983145983148983145983156983161 μ
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 1667
983123983157983154983142983137983139983141 983120983141983154983149983141983137983138983145983148983145983156983161 μ983137
Surface permability is the percentage of a waterplane that can be
occupied by water
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 1767
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 1867
A cargo hold with dimensions of l = 1524m w = 914 m
h=61 m is completely flooded Determine the volume of the
space and the corrected flooded volume
Volume = 1524 m x 914 m x 61 m = 8497 m3
Flooded volume = Volume x permeability
Flooded volume = 8497 m3 x 60
Flooded volume = 5098 m3
Example 1
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 1967
983110983148983151983151983140983137983138983148983141 983116983141983150983143983156983144
983110983148983151983151983140983137983138983148983141 983148983141983150983143983156983144983098 983137983156 983137 983143983145983158983141983150 983152983151983145983150983156 983151983142 983156983144983141 983155983144983145983152 983148983141983150983143983156983144 983145983155 983156983144983141 983149983137983160983145983149983157983149 983148983141983150983143983156983144
983159983145983156983144 983156983144983141 983139983141983150983156983141983154 983137983156 983156983144983137983156 983152983151983145983150983156 983156983144983137983156 983139983137983150 983138983141 983142983148983151983151983140983141983140 983159983145983156983144983151983157983156 983155983157983138983149983141983154983143983145983150983143 983156983144983141
983155983144983145983152 983138983141983161983151983150983140 983149983137983154983143983145983150 983148983145983150983141
983129983137983154983137983148ı 983106983286983148983149983141 983106983151983161983157983098 G983141983149983145 983138983151983161983157983150983139983137 983144983141983154983144983137983150983143983145 983138983145983154 983150983151983147983156983137983140983137 983138983157 983150983151983147983156983137 983149983141983154983147983141983162
983151983148983149983137983147 983292983162983141983154983141 983143983141983149983145983161983145 983155ı983150ı983154 983144983137983156983156ı983150983137 983156983141ğ983141983156 983144983137983148983141 983143983141983156983145983154983141983139983141983147 983141983150 983138983292983161983292983147 983138983286983148983149983141 983138983151983161983157983150983137
983151 983150983151983147983156983137983140983137983147983145 983161983137983154983137983148ı 983138983286983148983149983141 983138983151983161983157 983140983141983150983145983154
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 2067
983110983148983151983151983140983137983138983148983141 983116983141983150983143983156983144 983107983157983154983158983141
983110983148983151983151983140983137983138983148983141 983116983141983150983143983156983144 983107983157983154983158983141983098 I983156 983145983155 983151983138983156983137983145983150983141983140 983138983161 983156983144983141 983139983151983150983150983141983139983156983145983151983150 983151983142 983142983148983151983151983140983137983138983148983141 983148983141983150983143983156983144983155 983137983156
983140983145983142983142983141983154983141983150983156 983152983151983145983150983156983155 983137983148983151983150983143 983156983144983141 983155983144983145983152 983148983141983150983143983156983144
983129983137983154983137983148ı 983106983286983148983149983141 983106983151983161983157 983109ğ983154983145983155983145983098 G983141983149983145 983138983151983161983157983150983139983137 983140983141ğ983145ş983145983147 983150983151983147983156983137983148983137983154983140983137 983144983141983155983137983152983148983137983150983137983150 983161983137983154983137983148ı
983138983286983148983149983141 983138983151983161983157 983140983141ğ983141983154983148983141983154983145983150983145983150 983138983145983154983148983141ş983156983145983154983145983148983149983141983155983145 983145983148983141 983141983148983140983141 983141983140983145983148983145983154
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 2167
983110983137983139983156983151983154 983151983142 983123983157983138983140983145983158983145983155983145983151983150
F983137983139983156983151983154 983151983142 983123983157983138983140983145983158983145983155983145983151983150 983124983144983141 983142983137983139983156983151983154 983151983142 983155983157983138983140983145983158983145983155983145983151983150 983145983155 983137 983142983137983139983156983151983154 983152983154983141983155983139983154983145983138983141983140
983138983161 983156983144983141 983137983152983152983148983145983139983137983138983148983141 983154983141983143983157983148983137983156983145983151983150983155 983137983150983140 983138983161 983145983150983156983141983154983150983137983156983145983151983150983137983148 983139983151983150983158983141983150983156983145983151983150 983156983144983137983156
983140983141983152983141983150983140983155 983151983150 983155983144983145983152 983148983141983150983143983156983144 983137983150983140 983139983154983145983156983141983154983145983151983150 983151983142 983155983141983154983158983145983139983141
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 2267
983120983141983154983149983145983155983155983145983138983148983141 983116983141983150983143983156983144
983120983141983154983149983145983155983155983145983138983148983141 L983141983150983143983156983144 983145983155 983151983138983156983137983145983150983141983140 983138983161 983149983157983148983156983145983152983148983161983145983150983143 983156983144983141 983142983148983151983151983140983137983138983148983141 983148983141983150983143983156983144 983137983156
983156983144983137983156 983152983151983145983150983156 983138983161 983156983144983141 983142983137983139983156983151983154 983151983142 983155983157983138983140983145983158983145983155983145983151983150
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 2367
D983141983156983141983154983149983145983150983137983156983145983151983150 983151983142 983156983144983141 983148983151983139983137983156983145983151983150 983151983142 983156983144983141 983158983151983148983157983149983141 983139983141983150983156983154983141 983151983142
983140983137983149983137983143983141983140 983139983151983149983152983137983154983156983149983141983150983156
Δ I983150983145983156983145983137983148 983140983145983155983152983148983137983139983141983149983141983150983156 Δ1 D983145983155983152983148983137983139983141983149983141983150983156 983137983142983156983141983154 983140983137983149983137983143983141983140
B I983150983145983156983145983137983148 983139983141983150983156983154983141 983151983142 983138983157983151983161983137983150983139983161
G I983150983145983156983145983137983148 983139983141983150983156983154983141 983151983142 9831439831549831379831589831459831569831619831600 I983150983145983156983145983137983148 983139983141983150983156983154983141 983151983142 983148983151983150983143983145983156983157983140983145983150983137983148 983138983157983151983161983137983150983139983161 LCB
983158983159 983124983144983141 983158983151983148983157983149983141 983151983142 983159983137983156983141983154 983141983150983156983141983154983145983150983143 983156983144983141 983158983141983155983155983141983148
983160983159 D983145983155983156983137983150983139983141 983151983142 983158983151983148983157983149983141 983139983141983150983156983154983141 983151983142 983140983137983149983137983143983141983140 983139983151983149983152983137983154983156983149983141983150983156 983142983154983151983149 983149983137983141983155983156983151983154983161
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 2467
D983141983156983141983154983149983145983150983137983156983145983151983150 983151983142 983156983144983141 983148983151983139983137983156983145983151983150 983151983142 983156983144983141 983158983151983148983157983149983141 983139983141983150983156983154983141 983151983142
983140983137983149983137983143983141983140 983139983151983149983152983137983154983156983149983141983150983156
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 2567
D983141983156983141983154983149983145983150983137983156983145983151983150 983151983142 983156983144983141 983158983151983148983157983149983141 983151983142 983159983137983156983141983154 983141983150983156983141983154983145983150983143 983156983144983141 983158983141983155983155983141983148
Initial displacement and longitudinal centre of buoyancy (LCB) can be read from hydrostatcic curves
However displacement and LCB are unknown after damaged
Therefore if trim forward and aft draught are known trimmed waterline can be drawn over Bonjean
area curves
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 2667
983108983141983156983141983154983149983145983150983137983156983145983151983150 983151983142 983140983137983149983137983143983141983140 983148983141983150983143983156983144 983137983150983140 983148983151983139983137983156983145983151983150 983151983142 983149983145983140
983151983142 983139983151983149983152983137983154983156983149983141983150983156
vw The volume of water entering the vessel
xw Distance of volume centre of damaged compartment from maestory
micro Permability of the compartment
v0 Volume of the compartment
xm Distance of the volume centre of the compartment to the mid of damaged length
xl Distance of the mid of damaged length of compartment to maestory
xc Distance of the computed volume centre of compartment to maestory (xc=xl-xm)
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 2767
983108983141983156983141983154983149983145983150983137983156983145983151983150 983151983142 983140983137983149983137983143983141983140 983148983141983150983143983156983144 983137983150983140 983148983151983139983137983156983145983151983150 983151983142 983149983145983140
983151983142 983139983151983149983152983137983154983156983149983141983150983156
Damaged length and location of compartment can be determined by iterative
procedure
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 2867
bull The volume of water entering the vessel (vw)
bull Distance of volume centre of damaged compartment from amidships Θ ( xw)
bull Volume of the compartment (v0
= vw
μ)
First trial
1) Assume xm=0 (xl=xw)
2) Damaged Length l1 = (Volume of the compartment v0) (mean sec Area Amean)
where Amean is determined from trimmed sectional area curve
983108983141983156983141983154983149983145983150983137983156983145983151983150 983151983142 983140983137983149983137983143983141983140 983148983141983150983143983156983144 983137983150983140 983148983151983139983137983156983145983151983150 983151983142 983149983145983140
983151983142 983139983151983149983152983137983154983156983149983141983150983156
8162019 Damaged Stability
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3) In order to determine vm and xm
s = l1 4
vm = (s 3) sum3
xm = s sum4 sum3
xc = xl ndash xm
|vm-v0| le Tolarence for volume
|xc-xw| le Tolarence for location of volume centre
l=l1 xl=xw
983108983141983156983141983154983149983145983150983137983156983145983151983150 983151983142 983140983137983149983137983143983141983140 983148983141983150983143983156983144 983137983150983140 983148983151983139983137983156983145983151983150 983151983142 983149983145983140
983151983142 983139983151983149983152983137983154983156983149983141983150983156
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 3067
983108983141983156983141983154983149983145983150983137983156983145983151983150 983151983142 983140983137983149983137983143983141983140 983148983141983150983143983156983144 983137983150983140 983148983151983139983137983156983145983151983150 983151983142 983149983145983140
983151983142 983139983151983149983152983137983154983156983149983141983150983156Second Trial
Damaged length is changed proportionally by the volume
l2 = l1 times (v0v
m)
vm Computed volume at first trial
If the value of xm computed at first trial is negative then the mid of the
compartment slides to the bow
xl = xw+xm
where xm is the distance of the volume centre of compartment to amidship
computed at first trial
8162019 Damaged Stability
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In order to determine vm and xm
983108983141983156983141983154983149983145983150983137983156983145983151983150 983151983142 983140983137983149983137983143983141983140 983148983141983150983143983156983144 983137983150983140 983148983151983139983137983156983145983151983150 983151983142 983149983145983140
983151983142 983139983151983149983152983137983154983156983149983141983150983156
s = l2 4
vm = (s 3) sum3
xm = s sum4 sum3
xc = xl ndash xm
|vm-v0| le Tolarence for volume
|xc-xw| le Tolarence for location of volume centre
l=l2
If tolarances for both volume and location are not satisfied third fourthtrials are made similar to
second trial
8162019 Damaged Stability
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If either tolarence for volume or tolarance for location are satisfied at a trial
satisfied one is fixed trials are continued to make for the other one
983108983141983156983141983154983149983145983150983137983156983145983151983150 983151983142 983140983137983149983137983143983141983140 983148983141983150983143983156983144 983137983150983140 983148983151983139983137983156983145983151983150 983151983142 983149983145983140
983151983142 983139983151983149983152983137983154983156983149983141983150983156
8162019 Damaged Stability
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A ship is 116 meter long and displaces 7842 ton in salt water (ρ1=1025 tm3)
when her mean draught is 64m Longitudinal Centre of Buoyancy (LCB) is
0615 m aft from amidships After one of her stern compartment is damaged
she floats trimmed to the aft Her sectional areas after damaged are given in the
following table
a) Determine the volume of water entering the vessel (vw) and the location of
volume centre of damaged compartment (xw)
b) Assume permability of compartment micro is 1 Determine damaged length
and Distance of the mid of damaged length of compartment to amidship
983109983160983137983149983152983148983141 2
8162019 Damaged Stability
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8162019 Damaged Stability
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8162019 Damaged Stability
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Predicted xw
is between section 2 and section 3
983123983141983139 N983151 983123983141983139 A983154983141983137 D983145983155983156 A9831499831459831559831449831459831522 10135 983085348
3 1208 983085232
983123983141983139 A983154983141983137 983137983156 98308524983149 983142983154983151983149 983137983149983145983140983155983144983145983152 = 11959831492
l1=v0Amean=204081195=17078 m
s=l14=427 m
983109983160983137983149983152983148983141 2983085983123983119983116983125983124983113983119983118
8162019 Damaged Stability
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983161983145 L983151983139 A983149983141983137983150 983123M M A983154983149
9831311983133 9831312983133 98313119831339832559831312983133 9831313983133 983131198313398325598313129831339832559831313983133
0 9830853254 1051 1 1051 2 21021 9830852827 1123 4 4492 1 4492
2 98308524 1195 2 239 0 0
3 9830851973 1219 4 4876 9830851 9830854876
4 9830851546 1233 1 1233 9830852 9830852466
sum983091983101 14042 sum983092983101 983085748
vm
= (s3) sum3= 199864479831493
xm
=s sum4sum3= 9830850227983149
v0-vm=20408-19986=422 m3
Error=422times10020408=207
983109983160983137983149983152983148983141 2983085983123983119983116983125983124983113983119983118
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 3867
Methods of Calculation
There two available method calculating the
final stage of the damaged vessel
bull Lost Buoyancy Method
bull Added Weight Method
8162019 Damaged Stability
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Comparision of Lost Buoyancy and Added
Weight Methods
8162019 Damaged Stability
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Consider a vessel that has been damaged such
that a portion of the bottom is now open to the
sea
The vesselrsquos draft will increase because an amount
of the buoyancy was lost
Added Weight Method
Added Weight Method
8162019 Damaged Stability
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Added Weight Method
In this method flood water is treated as a fixed weight (for example the
weight of water of volume ABEF) This added weight is balanced by the
additional buoyant force of the layer WL1WL
The added weight can be determined by either the volume ABEF or
waterline WL1 Therefore WL1 waterline is not known can be just guessed
For the predicted waterline added weight and additional buoyant force
caculation are done iteratively until both of them are equal This method is
known as Added weight method
Determination of Added Weight
8162019 Damaged Stability
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Determination of Added Weight
vc Volume of damaged compartment (DCEF)
ac The surface area (AB) of damaged compartment on the waterline
micro The volume permability of damaged compartment
microa The area permability of the surface of damaged compartment
∆ The initial displacement
∆1 The displacement at final stage
vw The volume of water entering the vessel (ABEH)
w The weight of water entering the vessel
p The value of parallel sinkage
If th t th l l i k i h f t l f
8162019 Damaged Stability
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If we assume that the paralel sinkage cause a minor change of water plane area of a
ship (Awp
asymp Awp1
) we can determine the paralel sinkage by equating the volume of
the layer WL1WL to the volume of ABEF
If the damaged compartment is bounded on top
8162019 Damaged Stability
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8162019 Damaged Stability
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Longitudinal Metacentre Radius at final stage
Free Surface Effect
Damaged compartment can be considered as a half filled tank
Free Contact Effect
Damaged compartment can be considered as a half filled tank
T M H i h
8162019 Damaged Stability
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Transverse Metacentre Height
The angle of heel
8162019 Damaged Stability
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L it di l M t t H i ht
8162019 Damaged Stability
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Longitudinal Metacentre Height
8162019 Damaged Stability
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E983160983137983149983152983148983141 A 983138983137983154983143983141
8162019 Damaged Stability
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E983160983137983149983152983148983141 A 983138983137983154983143983141
991266 L = 20 983149991266 B = 5 983149
991266 983124 = 15 983149
991266 KG = 15 983149
I983150983156983137983139983156 C983151983150983140983145983156983145983151983150
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 5167
I983150983156983137983139983156 C983151983150983140983145983156983145983151983150
991266 983124983144983141 983140983145983155983152983148983137983139983141983149983141983150983156 983158983151983148983157983149983141
991266 983124983144983141 983149983137983155983155 983140983145983155983152983148983137983139983141983149983141983150983156
991266 983124983144983141 983149983151983149983141983150983156 983151983142 983145983150983141983154983156983145983137 983151983142 983156983144983141 983159983137983156983141983154983152983148983137983150983141 983137983154983141983137983137983138983151983157983156 CL
3
15051520 m x xT B L
I I
==sdotsdot=nabla
tons x I
751531500251 ==nablasdot=∆ ρ
433
33208
12
205
12
m x L B
I I
===
I983150983156983137983139983156 C983151983150983140983145983156983145983151983150
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 5267
I983150983156983137983139983156 C983151983150983140983145983156983145983151983150
991266 M983141983156983137983139983141983150983156983154983145983139 983154983137983140983145983157983155
991266 O983154 983145983156 983139983151983157983148983140 983138983141 983139983137983148983139983157983148983137983156983141983140 983140983145983154983141983139983156983148983161 983137983155
991266 H983141983145983143983144983156 983151983142 983156983144983141 983139983141983150983156983141983154 983151983142 983138983157983151983161983137983150983139983161
m I
BM
I
I 3891
150
33208==
nabla
=
m xT
B
LBT
L B BM
I I
I 3891
5112
5
12
12 223
====
mT
KB I
I 750
2
==
I983150983156983137983139983156 C983151983150983140983145983156983145983151983150
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 5367
991266 983124983144983141 983149983141983156983137983139983141983150983156983154983145983139 983144983141983145983143983144983156
991266 F983151983154 983155983149983137983148983148 983137983150983143983148983141983155 983151983142 983144983141983141983148 983156983144983141 983154983145983143983144983156983145983150983143 983149983151983149983141983150983156
m KG BM KBGM I I 63905013891750 =minus+=minus+=
sin22998sin693075153sin mt x xGM M I I
φ φ φ ==∆=
8162019 Damaged Stability
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8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 5567
983116983119983123983124 983106983125983119983129983105983118983107983129 983117983109983124983112983119983108
Paralel Sinkage
Volume (DCEF)=Volume (W1ADW+BL1LC)
Damaged compartment is bounded on top
983116983119983123983124 983106983125983119983129983105983118983107983129 983117983109983124983112983119983108
8162019 Damaged Stability
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983116983119983123983124 983106983125983119983129983105983118983107983129 983117983109983124983112983119983108
bull It is assumed that displacement and location of vertical centre
of gravity does not change after damaged
983116983119983123983124 983106983125983119983129983105983118983107983129 983117983109983124983112983119983108
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 5767
983116983119983123983124 983106983125983119983129983105983118983107983129 983117983109983124983112983119983108
8162019 Damaged Stability
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The heel angle of damaged ship is determined by
where
d is the distance between the volume centre of damaged compartment
and the new longitudinal centre of floatation
wc=vc μ ρ
983116983119983123983124 983106983125983119983129983105983118983107983129 983117983109983124983112983119983108
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 5967
983116983119983123983124 983106983125983119983129983105983118983107983129 983117983109983124983112983119983108
983116983119983123983124 983106983125983119983129983105983118983107983129 983117983109983124983112983119983108
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 6067
Longitudinal Metacentre Height of a Damaged Ship
983116983119983123983124 983106983125983119983129983105983118983107983129 983117983109983124983112983119983108
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 6167
983110983151983154983159983137983154983140 983137983150983140 983137983142983156 983140983154983137983157983143983144983156983155 983137983142983156983141983154 983140983137983149983137983143983141983140
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 6267
983120983151983154983156 983105983142983156 983120983151983154983156 983110983151983154983141 983123983156983137983154983138983151983137983154983140 983105983142983156 983123983156983137983154983138983151983137983154983140 983110983151983154983159983137983154983140
I983150983145983156983145983137983148 D983154983137983157983143983144983156 983124 983124 983124 983124
983120983137983154983137983148983141983148 983123983145983150983147983137983143983141 +983152 +983152 +983152 +983120
H983141983141983148 983085983149983145 983085983149983145 +983149983155 +983149983155
983124983154983145983149 983085983156983147 +983156983138 983085983156983147 +983156983138
F983145983150983137983148 D983154983137983157983143983144983156 983124+983152983085983149983145983085983156983147 983124+983152983085983149983145+983156983138 983124+983152+983149983155983085983156983147 983124+983152+983149983155+983156983138
Table 1 Final Draughts for a starboard side damaged ship
8162019 Damaged Stability
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L983151983155983156 B983157983151983161983137983150983139983161 M983141983156983144983151983140
8162019 Damaged Stability
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L983151983155983156 B983157983151983161983137983150983139983161 M983141983156983144983151983140
8162019 Damaged Stability
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991266 A983142983156983141983154 983148983151983151983155983145983150983143 983156983144983141 983139983141983150983156983154983137983148 983139983151983149983152983137983154983156983149983141983150983156 983156983144983141
983159983137983156983141983154983152983148983137983150983141 983137983154983141983137 983145983155
991266 983124983151 983139983151983149983152983141983150983155983137983156983141 983142983151983154 983156983144983141 983148983151983155983155 983151983142 983138983157983151983161983137983150983139983161 983151983142 983156983144983141
983139983141983150983156983154983137983148 983139983151983149983152983137983154983156983149983141983150983156 983156983144983141 983140983154983137983142983156 983145983150983139983154983141983137983155983141983155 983156983151
2805)420()( m x Bl L A L
=minus=minus=
m A
T
L
I
L 875180
150==
nabla=
L983151983155983156 B983157983151983161983137983150983139983161 M983141983156983144983151983140
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 6667
991266 983124983144983141 983144983141983145983143983144983156 983151983142 983156983144983141 983139983141983150983156983141983154 983151983142 983138983157983151983161983137983150983139983161 983145983150983139983154983141983137983155983141983155 983156983151
991266 983124983144983141 983149983151983149983141983150983156 983151983142 983145983150983141983154983156983145983137 983151983142 983156983144983141 983159983137983156983141983154983152983148983137983150983141 983137983154983141983137
991266 983124983144983141 983149983141983156983137983139983141983150983156983154983145983139 983154983137983140983145983157983155
m
T
KB L
L 93802
8751
2 ===
433
6716612
)420(5
12
)(m
l L B I L
=minus
=minus
=
m I
BM
I
L
L 1111150
67166==
nabla
=
L983151983155983156 B983157983151983161983137983150983139983161 M983141983156983144983151983140
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 6767
991266 983124983144983141 983149983141983156983137983139983141983150983156983154983145983139 983144983141983145983143983144983156
991266 983122983145983143983144983156983145983150983143 983149983151983149983141983150983156 983142983151983154 983155983149983137983148983148 983144983141983141983148 983137983150983143983148983141983155
m KG BM KBGM L L L 54905111119380 =minus+=minus+=
mt xGM M L
sin34984sin549075153sin φ φ φ ==∆=
8162019 Damaged Stability
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983106983157983148983147983144983141983137983140 983108983141983139983147983155
983106983157983148983147983144983141983137983140 983140983141983139983147983155 983098 983156983144983141 983140983141983139983147 983157983152 983156983151 983159983144983145983139983144 983156983144983141983155983141 983138983157983148983147983144983141983137983140983155 983141983160983156983141983150983140983155
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 1267
983117983137983154983143983145983150 983116983145983150983141
983117983137983154983143983145983150 983148983145983150983141 983145983155 983137 983148983145983150983141 983140983141983142983145983150983145983150983143 983156983144983141 983144983145983143983144983141983155983156 983152983141983154983149983141983155983155983145983138983148983141 983148983151983139983137983156983145983151983150 983151983150 983156983144983141 983155983145983140983141 983151983142 983156983144983141
983158983141983155983155983141983148 983151983142 983137983150983161 983140983137983149983137983143983141983140 983159983137983156983141983154983152983148983137983150983141 983145983150 983156983144983141 983142983145983150983137983148 983139983151983150983140983145983156983145983151983150 983151983142 983155983145983150983147983137983143983141983156983154983145983149 983137983150983140 983144983141983141983148
A983142983156983141983154 983142983148983151983151983140983145983150983143 983151983142 983137 983152983154983141983155983139983154983145983138983141983140 983150983157983149983138983141983154 983151983142 983139983151983149983152983137983154983156983149983141983150983156983155 983156983144983141 983155983144983145983152 983155983144983137983148983148 983150983151983156
983155983157983138983149983141983154983143983141 983138983141983161983151983150983140 983137 983148983145983150983141 983155983145983156983157983137983156983141983140 983137983156 983148983141983137983155983156 76 983149983149 B983141983148983151983159 983156983144983141 983140983141983139983147 983137983156 983155983145983140983141
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 1367
983117983137983154983143983145983150 983116983145983150983141
8162019 Damaged Stability
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983117983137983154983143983145983150 983116983145983150983141
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 1567
Permability is the ratio of amount of water that can a enter or a
compartment or tank to the total volume of compartment or tank
VOLUME TOTAL
VOLUME AVAILABLE TY PERMEABILI =
983120983141983154983149983141983137983138983145983148983145983156983161 μ
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 1667
983123983157983154983142983137983139983141 983120983141983154983149983141983137983138983145983148983145983156983161 μ983137
Surface permability is the percentage of a waterplane that can be
occupied by water
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 1767
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 1867
A cargo hold with dimensions of l = 1524m w = 914 m
h=61 m is completely flooded Determine the volume of the
space and the corrected flooded volume
Volume = 1524 m x 914 m x 61 m = 8497 m3
Flooded volume = Volume x permeability
Flooded volume = 8497 m3 x 60
Flooded volume = 5098 m3
Example 1
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 1967
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983155983144983145983152 983138983141983161983151983150983140 983149983137983154983143983145983150 983148983145983150983141
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8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 2067
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8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 2167
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983138983161 983156983144983141 983137983152983152983148983145983139983137983138983148983141 983154983141983143983157983148983137983156983145983151983150983155 983137983150983140 983138983161 983145983150983156983141983154983150983137983156983145983151983150983137983148 983139983151983150983158983141983150983156983145983151983150 983156983144983137983156
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8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 2267
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983120983141983154983149983145983155983155983145983138983148983141 L983141983150983143983156983144 983145983155 983151983138983156983137983145983150983141983140 983138983161 983149983157983148983156983145983152983148983161983145983150983143 983156983144983141 983142983148983151983151983140983137983138983148983141 983148983141983150983143983156983144 983137983156
983156983144983137983156 983152983151983145983150983156 983138983161 983156983144983141 983142983137983139983156983151983154 983151983142 983155983157983138983140983145983158983145983155983145983151983150
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 2367
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983140983137983149983137983143983141983140 983139983151983149983152983137983154983156983149983141983150983156
Δ I983150983145983156983145983137983148 983140983145983155983152983148983137983139983141983149983141983150983156 Δ1 D983145983155983152983148983137983139983141983149983141983150983156 983137983142983156983141983154 983140983137983149983137983143983141983140
B I983150983145983156983145983137983148 983139983141983150983156983154983141 983151983142 983138983157983151983161983137983150983139983161
G I983150983145983156983145983137983148 983139983141983150983156983154983141 983151983142 9831439831549831379831589831459831569831619831600 I983150983145983156983145983137983148 983139983141983150983156983154983141 983151983142 983148983151983150983143983145983156983157983140983145983150983137983148 983138983157983151983161983137983150983139983161 LCB
983158983159 983124983144983141 983158983151983148983157983149983141 983151983142 983159983137983156983141983154 983141983150983156983141983154983145983150983143 983156983144983141 983158983141983155983155983141983148
983160983159 D983145983155983156983137983150983139983141 983151983142 983158983151983148983157983149983141 983139983141983150983156983154983141 983151983142 983140983137983149983137983143983141983140 983139983151983149983152983137983154983156983149983141983150983156 983142983154983151983149 983149983137983141983155983156983151983154983161
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 2467
D983141983156983141983154983149983145983150983137983156983145983151983150 983151983142 983156983144983141 983148983151983139983137983156983145983151983150 983151983142 983156983144983141 983158983151983148983157983149983141 983139983141983150983156983154983141 983151983142
983140983137983149983137983143983141983140 983139983151983149983152983137983154983156983149983141983150983156
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 2567
D983141983156983141983154983149983145983150983137983156983145983151983150 983151983142 983156983144983141 983158983151983148983157983149983141 983151983142 983159983137983156983141983154 983141983150983156983141983154983145983150983143 983156983144983141 983158983141983155983155983141983148
Initial displacement and longitudinal centre of buoyancy (LCB) can be read from hydrostatcic curves
However displacement and LCB are unknown after damaged
Therefore if trim forward and aft draught are known trimmed waterline can be drawn over Bonjean
area curves
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 2667
983108983141983156983141983154983149983145983150983137983156983145983151983150 983151983142 983140983137983149983137983143983141983140 983148983141983150983143983156983144 983137983150983140 983148983151983139983137983156983145983151983150 983151983142 983149983145983140
983151983142 983139983151983149983152983137983154983156983149983141983150983156
vw The volume of water entering the vessel
xw Distance of volume centre of damaged compartment from maestory
micro Permability of the compartment
v0 Volume of the compartment
xm Distance of the volume centre of the compartment to the mid of damaged length
xl Distance of the mid of damaged length of compartment to maestory
xc Distance of the computed volume centre of compartment to maestory (xc=xl-xm)
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 2767
983108983141983156983141983154983149983145983150983137983156983145983151983150 983151983142 983140983137983149983137983143983141983140 983148983141983150983143983156983144 983137983150983140 983148983151983139983137983156983145983151983150 983151983142 983149983145983140
983151983142 983139983151983149983152983137983154983156983149983141983150983156
Damaged length and location of compartment can be determined by iterative
procedure
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 2867
bull The volume of water entering the vessel (vw)
bull Distance of volume centre of damaged compartment from amidships Θ ( xw)
bull Volume of the compartment (v0
= vw
μ)
First trial
1) Assume xm=0 (xl=xw)
2) Damaged Length l1 = (Volume of the compartment v0) (mean sec Area Amean)
where Amean is determined from trimmed sectional area curve
983108983141983156983141983154983149983145983150983137983156983145983151983150 983151983142 983140983137983149983137983143983141983140 983148983141983150983143983156983144 983137983150983140 983148983151983139983137983156983145983151983150 983151983142 983149983145983140
983151983142 983139983151983149983152983137983154983156983149983141983150983156
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 2967
3) In order to determine vm and xm
s = l1 4
vm = (s 3) sum3
xm = s sum4 sum3
xc = xl ndash xm
|vm-v0| le Tolarence for volume
|xc-xw| le Tolarence for location of volume centre
l=l1 xl=xw
983108983141983156983141983154983149983145983150983137983156983145983151983150 983151983142 983140983137983149983137983143983141983140 983148983141983150983143983156983144 983137983150983140 983148983151983139983137983156983145983151983150 983151983142 983149983145983140
983151983142 983139983151983149983152983137983154983156983149983141983150983156
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 3067
983108983141983156983141983154983149983145983150983137983156983145983151983150 983151983142 983140983137983149983137983143983141983140 983148983141983150983143983156983144 983137983150983140 983148983151983139983137983156983145983151983150 983151983142 983149983145983140
983151983142 983139983151983149983152983137983154983156983149983141983150983156Second Trial
Damaged length is changed proportionally by the volume
l2 = l1 times (v0v
m)
vm Computed volume at first trial
If the value of xm computed at first trial is negative then the mid of the
compartment slides to the bow
xl = xw+xm
where xm is the distance of the volume centre of compartment to amidship
computed at first trial
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 3167
In order to determine vm and xm
983108983141983156983141983154983149983145983150983137983156983145983151983150 983151983142 983140983137983149983137983143983141983140 983148983141983150983143983156983144 983137983150983140 983148983151983139983137983156983145983151983150 983151983142 983149983145983140
983151983142 983139983151983149983152983137983154983156983149983141983150983156
s = l2 4
vm = (s 3) sum3
xm = s sum4 sum3
xc = xl ndash xm
|vm-v0| le Tolarence for volume
|xc-xw| le Tolarence for location of volume centre
l=l2
If tolarances for both volume and location are not satisfied third fourthtrials are made similar to
second trial
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 3267
If either tolarence for volume or tolarance for location are satisfied at a trial
satisfied one is fixed trials are continued to make for the other one
983108983141983156983141983154983149983145983150983137983156983145983151983150 983151983142 983140983137983149983137983143983141983140 983148983141983150983143983156983144 983137983150983140 983148983151983139983137983156983145983151983150 983151983142 983149983145983140
983151983142 983139983151983149983152983137983154983156983149983141983150983156
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 3367
A ship is 116 meter long and displaces 7842 ton in salt water (ρ1=1025 tm3)
when her mean draught is 64m Longitudinal Centre of Buoyancy (LCB) is
0615 m aft from amidships After one of her stern compartment is damaged
she floats trimmed to the aft Her sectional areas after damaged are given in the
following table
a) Determine the volume of water entering the vessel (vw) and the location of
volume centre of damaged compartment (xw)
b) Assume permability of compartment micro is 1 Determine damaged length
and Distance of the mid of damaged length of compartment to amidship
983109983160983137983149983152983148983141 2
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 3467
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 3567
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 3667
Predicted xw
is between section 2 and section 3
983123983141983139 N983151 983123983141983139 A983154983141983137 D983145983155983156 A9831499831459831559831449831459831522 10135 983085348
3 1208 983085232
983123983141983139 A983154983141983137 983137983156 98308524983149 983142983154983151983149 983137983149983145983140983155983144983145983152 = 11959831492
l1=v0Amean=204081195=17078 m
s=l14=427 m
983109983160983137983149983152983148983141 2983085983123983119983116983125983124983113983119983118
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 3767
983161983145 L983151983139 A983149983141983137983150 983123M M A983154983149
9831311983133 9831312983133 98313119831339832559831312983133 9831313983133 983131198313398325598313129831339832559831313983133
0 9830853254 1051 1 1051 2 21021 9830852827 1123 4 4492 1 4492
2 98308524 1195 2 239 0 0
3 9830851973 1219 4 4876 9830851 9830854876
4 9830851546 1233 1 1233 9830852 9830852466
sum983091983101 14042 sum983092983101 983085748
vm
= (s3) sum3= 199864479831493
xm
=s sum4sum3= 9830850227983149
v0-vm=20408-19986=422 m3
Error=422times10020408=207
983109983160983137983149983152983148983141 2983085983123983119983116983125983124983113983119983118
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 3867
Methods of Calculation
There two available method calculating the
final stage of the damaged vessel
bull Lost Buoyancy Method
bull Added Weight Method
8162019 Damaged Stability
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Comparision of Lost Buoyancy and Added
Weight Methods
8162019 Damaged Stability
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Consider a vessel that has been damaged such
that a portion of the bottom is now open to the
sea
The vesselrsquos draft will increase because an amount
of the buoyancy was lost
Added Weight Method
Added Weight Method
8162019 Damaged Stability
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Added Weight Method
In this method flood water is treated as a fixed weight (for example the
weight of water of volume ABEF) This added weight is balanced by the
additional buoyant force of the layer WL1WL
The added weight can be determined by either the volume ABEF or
waterline WL1 Therefore WL1 waterline is not known can be just guessed
For the predicted waterline added weight and additional buoyant force
caculation are done iteratively until both of them are equal This method is
known as Added weight method
Determination of Added Weight
8162019 Damaged Stability
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Determination of Added Weight
vc Volume of damaged compartment (DCEF)
ac The surface area (AB) of damaged compartment on the waterline
micro The volume permability of damaged compartment
microa The area permability of the surface of damaged compartment
∆ The initial displacement
∆1 The displacement at final stage
vw The volume of water entering the vessel (ABEH)
w The weight of water entering the vessel
p The value of parallel sinkage
If th t th l l i k i h f t l f
8162019 Damaged Stability
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If we assume that the paralel sinkage cause a minor change of water plane area of a
ship (Awp
asymp Awp1
) we can determine the paralel sinkage by equating the volume of
the layer WL1WL to the volume of ABEF
If the damaged compartment is bounded on top
8162019 Damaged Stability
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8162019 Damaged Stability
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Longitudinal Metacentre Radius at final stage
Free Surface Effect
Damaged compartment can be considered as a half filled tank
Free Contact Effect
Damaged compartment can be considered as a half filled tank
T M H i h
8162019 Damaged Stability
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Transverse Metacentre Height
The angle of heel
8162019 Damaged Stability
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L it di l M t t H i ht
8162019 Damaged Stability
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Longitudinal Metacentre Height
8162019 Damaged Stability
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E983160983137983149983152983148983141 A 983138983137983154983143983141
8162019 Damaged Stability
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E983160983137983149983152983148983141 A 983138983137983154983143983141
991266 L = 20 983149991266 B = 5 983149
991266 983124 = 15 983149
991266 KG = 15 983149
I983150983156983137983139983156 C983151983150983140983145983156983145983151983150
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 5167
I983150983156983137983139983156 C983151983150983140983145983156983145983151983150
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991266 983124983144983141 983149983137983155983155 983140983145983155983152983148983137983139983141983149983141983150983156
991266 983124983144983141 983149983151983149983141983150983156 983151983142 983145983150983141983154983156983145983137 983151983142 983156983144983141 983159983137983156983141983154983152983148983137983150983141 983137983154983141983137983137983138983151983157983156 CL
3
15051520 m x xT B L
I I
==sdotsdot=nabla
tons x I
751531500251 ==nablasdot=∆ ρ
433
33208
12
205
12
m x L B
I I
===
I983150983156983137983139983156 C983151983150983140983145983156983145983151983150
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 5267
I983150983156983137983139983156 C983151983150983140983145983156983145983151983150
991266 M983141983156983137983139983141983150983156983154983145983139 983154983137983140983145983157983155
991266 O983154 983145983156 983139983151983157983148983140 983138983141 983139983137983148983139983157983148983137983156983141983140 983140983145983154983141983139983156983148983161 983137983155
991266 H983141983145983143983144983156 983151983142 983156983144983141 983139983141983150983156983141983154 983151983142 983138983157983151983161983137983150983139983161
m I
BM
I
I 3891
150
33208==
nabla
=
m xT
B
LBT
L B BM
I I
I 3891
5112
5
12
12 223
====
mT
KB I
I 750
2
==
I983150983156983137983139983156 C983151983150983140983145983156983145983151983150
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 5367
991266 983124983144983141 983149983141983156983137983139983141983150983156983154983145983139 983144983141983145983143983144983156
991266 F983151983154 983155983149983137983148983148 983137983150983143983148983141983155 983151983142 983144983141983141983148 983156983144983141 983154983145983143983144983156983145983150983143 983149983151983149983141983150983156
m KG BM KBGM I I 63905013891750 =minus+=minus+=
sin22998sin693075153sin mt x xGM M I I
φ φ φ ==∆=
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 5467
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 5567
983116983119983123983124 983106983125983119983129983105983118983107983129 983117983109983124983112983119983108
Paralel Sinkage
Volume (DCEF)=Volume (W1ADW+BL1LC)
Damaged compartment is bounded on top
983116983119983123983124 983106983125983119983129983105983118983107983129 983117983109983124983112983119983108
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 5667
983116983119983123983124 983106983125983119983129983105983118983107983129 983117983109983124983112983119983108
bull It is assumed that displacement and location of vertical centre
of gravity does not change after damaged
983116983119983123983124 983106983125983119983129983105983118983107983129 983117983109983124983112983119983108
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 5767
983116983119983123983124 983106983125983119983129983105983118983107983129 983117983109983124983112983119983108
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 5867
The heel angle of damaged ship is determined by
where
d is the distance between the volume centre of damaged compartment
and the new longitudinal centre of floatation
wc=vc μ ρ
983116983119983123983124 983106983125983119983129983105983118983107983129 983117983109983124983112983119983108
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 5967
983116983119983123983124 983106983125983119983129983105983118983107983129 983117983109983124983112983119983108
983116983119983123983124 983106983125983119983129983105983118983107983129 983117983109983124983112983119983108
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 6067
Longitudinal Metacentre Height of a Damaged Ship
983116983119983123983124 983106983125983119983129983105983118983107983129 983117983109983124983112983119983108
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 6167
983110983151983154983159983137983154983140 983137983150983140 983137983142983156 983140983154983137983157983143983144983156983155 983137983142983156983141983154 983140983137983149983137983143983141983140
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 6267
983120983151983154983156 983105983142983156 983120983151983154983156 983110983151983154983141 983123983156983137983154983138983151983137983154983140 983105983142983156 983123983156983137983154983138983151983137983154983140 983110983151983154983159983137983154983140
I983150983145983156983145983137983148 D983154983137983157983143983144983156 983124 983124 983124 983124
983120983137983154983137983148983141983148 983123983145983150983147983137983143983141 +983152 +983152 +983152 +983120
H983141983141983148 983085983149983145 983085983149983145 +983149983155 +983149983155
983124983154983145983149 983085983156983147 +983156983138 983085983156983147 +983156983138
F983145983150983137983148 D983154983137983157983143983144983156 983124+983152983085983149983145983085983156983147 983124+983152983085983149983145+983156983138 983124+983152+983149983155983085983156983147 983124+983152+983149983155+983156983138
Table 1 Final Draughts for a starboard side damaged ship
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 6367
L983151983155983156 B983157983151983161983137983150983139983161 M983141983156983144983151983140
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 6467
L983151983155983156 B983157983151983161983137983150983139983161 M983141983156983144983151983140
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 6567
991266 A983142983156983141983154 983148983151983151983155983145983150983143 983156983144983141 983139983141983150983156983154983137983148 983139983151983149983152983137983154983156983149983141983150983156 983156983144983141
983159983137983156983141983154983152983148983137983150983141 983137983154983141983137 983145983155
991266 983124983151 983139983151983149983152983141983150983155983137983156983141 983142983151983154 983156983144983141 983148983151983155983155 983151983142 983138983157983151983161983137983150983139983161 983151983142 983156983144983141
983139983141983150983156983154983137983148 983139983151983149983152983137983154983156983149983141983150983156 983156983144983141 983140983154983137983142983156 983145983150983139983154983141983137983155983141983155 983156983151
2805)420()( m x Bl L A L
=minus=minus=
m A
T
L
I
L 875180
150==
nabla=
L983151983155983156 B983157983151983161983137983150983139983161 M983141983156983144983151983140
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 6667
991266 983124983144983141 983144983141983145983143983144983156 983151983142 983156983144983141 983139983141983150983156983141983154 983151983142 983138983157983151983161983137983150983139983161 983145983150983139983154983141983137983155983141983155 983156983151
991266 983124983144983141 983149983151983149983141983150983156 983151983142 983145983150983141983154983156983145983137 983151983142 983156983144983141 983159983137983156983141983154983152983148983137983150983141 983137983154983141983137
991266 983124983144983141 983149983141983156983137983139983141983150983156983154983145983139 983154983137983140983145983157983155
m
T
KB L
L 93802
8751
2 ===
433
6716612
)420(5
12
)(m
l L B I L
=minus
=minus
=
m I
BM
I
L
L 1111150
67166==
nabla
=
L983151983155983156 B983157983151983161983137983150983139983161 M983141983156983144983151983140
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 6767
991266 983124983144983141 983149983141983156983137983139983141983150983156983154983145983139 983144983141983145983143983144983156
991266 983122983145983143983144983156983145983150983143 983149983151983149983141983150983156 983142983151983154 983155983149983137983148983148 983144983141983141983148 983137983150983143983148983141983155
m KG BM KBGM L L L 54905111119380 =minus+=minus+=
mt xGM M L
sin34984sin549075153sin φ φ φ ==∆=
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 1267
983117983137983154983143983145983150 983116983145983150983141
983117983137983154983143983145983150 983148983145983150983141 983145983155 983137 983148983145983150983141 983140983141983142983145983150983145983150983143 983156983144983141 983144983145983143983144983141983155983156 983152983141983154983149983141983155983155983145983138983148983141 983148983151983139983137983156983145983151983150 983151983150 983156983144983141 983155983145983140983141 983151983142 983156983144983141
983158983141983155983155983141983148 983151983142 983137983150983161 983140983137983149983137983143983141983140 983159983137983156983141983154983152983148983137983150983141 983145983150 983156983144983141 983142983145983150983137983148 983139983151983150983140983145983156983145983151983150 983151983142 983155983145983150983147983137983143983141983156983154983145983149 983137983150983140 983144983141983141983148
A983142983156983141983154 983142983148983151983151983140983145983150983143 983151983142 983137 983152983154983141983155983139983154983145983138983141983140 983150983157983149983138983141983154 983151983142 983139983151983149983152983137983154983156983149983141983150983156983155 983156983144983141 983155983144983145983152 983155983144983137983148983148 983150983151983156
983155983157983138983149983141983154983143983141 983138983141983161983151983150983140 983137 983148983145983150983141 983155983145983156983157983137983156983141983140 983137983156 983148983141983137983155983156 76 983149983149 B983141983148983151983159 983156983144983141 983140983141983139983147 983137983156 983155983145983140983141
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 1367
983117983137983154983143983145983150 983116983145983150983141
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 1467
983117983137983154983143983145983150 983116983145983150983141
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 1567
Permability is the ratio of amount of water that can a enter or a
compartment or tank to the total volume of compartment or tank
VOLUME TOTAL
VOLUME AVAILABLE TY PERMEABILI =
983120983141983154983149983141983137983138983145983148983145983156983161 μ
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 1667
983123983157983154983142983137983139983141 983120983141983154983149983141983137983138983145983148983145983156983161 μ983137
Surface permability is the percentage of a waterplane that can be
occupied by water
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 1767
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 1867
A cargo hold with dimensions of l = 1524m w = 914 m
h=61 m is completely flooded Determine the volume of the
space and the corrected flooded volume
Volume = 1524 m x 914 m x 61 m = 8497 m3
Flooded volume = Volume x permeability
Flooded volume = 8497 m3 x 60
Flooded volume = 5098 m3
Example 1
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 1967
983110983148983151983151983140983137983138983148983141 983116983141983150983143983156983144
983110983148983151983151983140983137983138983148983141 983148983141983150983143983156983144983098 983137983156 983137 983143983145983158983141983150 983152983151983145983150983156 983151983142 983156983144983141 983155983144983145983152 983148983141983150983143983156983144 983145983155 983156983144983141 983149983137983160983145983149983157983149 983148983141983150983143983156983144
983159983145983156983144 983156983144983141 983139983141983150983156983141983154 983137983156 983156983144983137983156 983152983151983145983150983156 983156983144983137983156 983139983137983150 983138983141 983142983148983151983151983140983141983140 983159983145983156983144983151983157983156 983155983157983138983149983141983154983143983145983150983143 983156983144983141
983155983144983145983152 983138983141983161983151983150983140 983149983137983154983143983145983150 983148983145983150983141
983129983137983154983137983148ı 983106983286983148983149983141 983106983151983161983157983098 G983141983149983145 983138983151983161983157983150983139983137 983144983141983154983144983137983150983143983145 983138983145983154 983150983151983147983156983137983140983137 983138983157 983150983151983147983156983137 983149983141983154983147983141983162
983151983148983149983137983147 983292983162983141983154983141 983143983141983149983145983161983145 983155ı983150ı983154 983144983137983156983156ı983150983137 983156983141ğ983141983156 983144983137983148983141 983143983141983156983145983154983141983139983141983147 983141983150 983138983292983161983292983147 983138983286983148983149983141 983138983151983161983157983150983137
983151 983150983151983147983156983137983140983137983147983145 983161983137983154983137983148ı 983138983286983148983149983141 983138983151983161983157 983140983141983150983145983154
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 2067
983110983148983151983151983140983137983138983148983141 983116983141983150983143983156983144 983107983157983154983158983141
983110983148983151983151983140983137983138983148983141 983116983141983150983143983156983144 983107983157983154983158983141983098 I983156 983145983155 983151983138983156983137983145983150983141983140 983138983161 983156983144983141 983139983151983150983150983141983139983156983145983151983150 983151983142 983142983148983151983151983140983137983138983148983141 983148983141983150983143983156983144983155 983137983156
983140983145983142983142983141983154983141983150983156 983152983151983145983150983156983155 983137983148983151983150983143 983156983144983141 983155983144983145983152 983148983141983150983143983156983144
983129983137983154983137983148ı 983106983286983148983149983141 983106983151983161983157 983109ğ983154983145983155983145983098 G983141983149983145 983138983151983161983157983150983139983137 983140983141ğ983145ş983145983147 983150983151983147983156983137983148983137983154983140983137 983144983141983155983137983152983148983137983150983137983150 983161983137983154983137983148ı
983138983286983148983149983141 983138983151983161983157 983140983141ğ983141983154983148983141983154983145983150983145983150 983138983145983154983148983141ş983156983145983154983145983148983149983141983155983145 983145983148983141 983141983148983140983141 983141983140983145983148983145983154
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 2167
983110983137983139983156983151983154 983151983142 983123983157983138983140983145983158983145983155983145983151983150
F983137983139983156983151983154 983151983142 983123983157983138983140983145983158983145983155983145983151983150 983124983144983141 983142983137983139983156983151983154 983151983142 983155983157983138983140983145983158983145983155983145983151983150 983145983155 983137 983142983137983139983156983151983154 983152983154983141983155983139983154983145983138983141983140
983138983161 983156983144983141 983137983152983152983148983145983139983137983138983148983141 983154983141983143983157983148983137983156983145983151983150983155 983137983150983140 983138983161 983145983150983156983141983154983150983137983156983145983151983150983137983148 983139983151983150983158983141983150983156983145983151983150 983156983144983137983156
983140983141983152983141983150983140983155 983151983150 983155983144983145983152 983148983141983150983143983156983144 983137983150983140 983139983154983145983156983141983154983145983151983150 983151983142 983155983141983154983158983145983139983141
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 2267
983120983141983154983149983145983155983155983145983138983148983141 983116983141983150983143983156983144
983120983141983154983149983145983155983155983145983138983148983141 L983141983150983143983156983144 983145983155 983151983138983156983137983145983150983141983140 983138983161 983149983157983148983156983145983152983148983161983145983150983143 983156983144983141 983142983148983151983151983140983137983138983148983141 983148983141983150983143983156983144 983137983156
983156983144983137983156 983152983151983145983150983156 983138983161 983156983144983141 983142983137983139983156983151983154 983151983142 983155983157983138983140983145983158983145983155983145983151983150
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 2367
D983141983156983141983154983149983145983150983137983156983145983151983150 983151983142 983156983144983141 983148983151983139983137983156983145983151983150 983151983142 983156983144983141 983158983151983148983157983149983141 983139983141983150983156983154983141 983151983142
983140983137983149983137983143983141983140 983139983151983149983152983137983154983156983149983141983150983156
Δ I983150983145983156983145983137983148 983140983145983155983152983148983137983139983141983149983141983150983156 Δ1 D983145983155983152983148983137983139983141983149983141983150983156 983137983142983156983141983154 983140983137983149983137983143983141983140
B I983150983145983156983145983137983148 983139983141983150983156983154983141 983151983142 983138983157983151983161983137983150983139983161
G I983150983145983156983145983137983148 983139983141983150983156983154983141 983151983142 9831439831549831379831589831459831569831619831600 I983150983145983156983145983137983148 983139983141983150983156983154983141 983151983142 983148983151983150983143983145983156983157983140983145983150983137983148 983138983157983151983161983137983150983139983161 LCB
983158983159 983124983144983141 983158983151983148983157983149983141 983151983142 983159983137983156983141983154 983141983150983156983141983154983145983150983143 983156983144983141 983158983141983155983155983141983148
983160983159 D983145983155983156983137983150983139983141 983151983142 983158983151983148983157983149983141 983139983141983150983156983154983141 983151983142 983140983137983149983137983143983141983140 983139983151983149983152983137983154983156983149983141983150983156 983142983154983151983149 983149983137983141983155983156983151983154983161
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 2467
D983141983156983141983154983149983145983150983137983156983145983151983150 983151983142 983156983144983141 983148983151983139983137983156983145983151983150 983151983142 983156983144983141 983158983151983148983157983149983141 983139983141983150983156983154983141 983151983142
983140983137983149983137983143983141983140 983139983151983149983152983137983154983156983149983141983150983156
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 2567
D983141983156983141983154983149983145983150983137983156983145983151983150 983151983142 983156983144983141 983158983151983148983157983149983141 983151983142 983159983137983156983141983154 983141983150983156983141983154983145983150983143 983156983144983141 983158983141983155983155983141983148
Initial displacement and longitudinal centre of buoyancy (LCB) can be read from hydrostatcic curves
However displacement and LCB are unknown after damaged
Therefore if trim forward and aft draught are known trimmed waterline can be drawn over Bonjean
area curves
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 2667
983108983141983156983141983154983149983145983150983137983156983145983151983150 983151983142 983140983137983149983137983143983141983140 983148983141983150983143983156983144 983137983150983140 983148983151983139983137983156983145983151983150 983151983142 983149983145983140
983151983142 983139983151983149983152983137983154983156983149983141983150983156
vw The volume of water entering the vessel
xw Distance of volume centre of damaged compartment from maestory
micro Permability of the compartment
v0 Volume of the compartment
xm Distance of the volume centre of the compartment to the mid of damaged length
xl Distance of the mid of damaged length of compartment to maestory
xc Distance of the computed volume centre of compartment to maestory (xc=xl-xm)
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 2767
983108983141983156983141983154983149983145983150983137983156983145983151983150 983151983142 983140983137983149983137983143983141983140 983148983141983150983143983156983144 983137983150983140 983148983151983139983137983156983145983151983150 983151983142 983149983145983140
983151983142 983139983151983149983152983137983154983156983149983141983150983156
Damaged length and location of compartment can be determined by iterative
procedure
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 2867
bull The volume of water entering the vessel (vw)
bull Distance of volume centre of damaged compartment from amidships Θ ( xw)
bull Volume of the compartment (v0
= vw
μ)
First trial
1) Assume xm=0 (xl=xw)
2) Damaged Length l1 = (Volume of the compartment v0) (mean sec Area Amean)
where Amean is determined from trimmed sectional area curve
983108983141983156983141983154983149983145983150983137983156983145983151983150 983151983142 983140983137983149983137983143983141983140 983148983141983150983143983156983144 983137983150983140 983148983151983139983137983156983145983151983150 983151983142 983149983145983140
983151983142 983139983151983149983152983137983154983156983149983141983150983156
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 2967
3) In order to determine vm and xm
s = l1 4
vm = (s 3) sum3
xm = s sum4 sum3
xc = xl ndash xm
|vm-v0| le Tolarence for volume
|xc-xw| le Tolarence for location of volume centre
l=l1 xl=xw
983108983141983156983141983154983149983145983150983137983156983145983151983150 983151983142 983140983137983149983137983143983141983140 983148983141983150983143983156983144 983137983150983140 983148983151983139983137983156983145983151983150 983151983142 983149983145983140
983151983142 983139983151983149983152983137983154983156983149983141983150983156
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 3067
983108983141983156983141983154983149983145983150983137983156983145983151983150 983151983142 983140983137983149983137983143983141983140 983148983141983150983143983156983144 983137983150983140 983148983151983139983137983156983145983151983150 983151983142 983149983145983140
983151983142 983139983151983149983152983137983154983156983149983141983150983156Second Trial
Damaged length is changed proportionally by the volume
l2 = l1 times (v0v
m)
vm Computed volume at first trial
If the value of xm computed at first trial is negative then the mid of the
compartment slides to the bow
xl = xw+xm
where xm is the distance of the volume centre of compartment to amidship
computed at first trial
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 3167
In order to determine vm and xm
983108983141983156983141983154983149983145983150983137983156983145983151983150 983151983142 983140983137983149983137983143983141983140 983148983141983150983143983156983144 983137983150983140 983148983151983139983137983156983145983151983150 983151983142 983149983145983140
983151983142 983139983151983149983152983137983154983156983149983141983150983156
s = l2 4
vm = (s 3) sum3
xm = s sum4 sum3
xc = xl ndash xm
|vm-v0| le Tolarence for volume
|xc-xw| le Tolarence for location of volume centre
l=l2
If tolarances for both volume and location are not satisfied third fourthtrials are made similar to
second trial
8162019 Damaged Stability
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If either tolarence for volume or tolarance for location are satisfied at a trial
satisfied one is fixed trials are continued to make for the other one
983108983141983156983141983154983149983145983150983137983156983145983151983150 983151983142 983140983137983149983137983143983141983140 983148983141983150983143983156983144 983137983150983140 983148983151983139983137983156983145983151983150 983151983142 983149983145983140
983151983142 983139983151983149983152983137983154983156983149983141983150983156
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 3367
A ship is 116 meter long and displaces 7842 ton in salt water (ρ1=1025 tm3)
when her mean draught is 64m Longitudinal Centre of Buoyancy (LCB) is
0615 m aft from amidships After one of her stern compartment is damaged
she floats trimmed to the aft Her sectional areas after damaged are given in the
following table
a) Determine the volume of water entering the vessel (vw) and the location of
volume centre of damaged compartment (xw)
b) Assume permability of compartment micro is 1 Determine damaged length
and Distance of the mid of damaged length of compartment to amidship
983109983160983137983149983152983148983141 2
8162019 Damaged Stability
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8162019 Damaged Stability
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8162019 Damaged Stability
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Predicted xw
is between section 2 and section 3
983123983141983139 N983151 983123983141983139 A983154983141983137 D983145983155983156 A9831499831459831559831449831459831522 10135 983085348
3 1208 983085232
983123983141983139 A983154983141983137 983137983156 98308524983149 983142983154983151983149 983137983149983145983140983155983144983145983152 = 11959831492
l1=v0Amean=204081195=17078 m
s=l14=427 m
983109983160983137983149983152983148983141 2983085983123983119983116983125983124983113983119983118
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 3767
983161983145 L983151983139 A983149983141983137983150 983123M M A983154983149
9831311983133 9831312983133 98313119831339832559831312983133 9831313983133 983131198313398325598313129831339832559831313983133
0 9830853254 1051 1 1051 2 21021 9830852827 1123 4 4492 1 4492
2 98308524 1195 2 239 0 0
3 9830851973 1219 4 4876 9830851 9830854876
4 9830851546 1233 1 1233 9830852 9830852466
sum983091983101 14042 sum983092983101 983085748
vm
= (s3) sum3= 199864479831493
xm
=s sum4sum3= 9830850227983149
v0-vm=20408-19986=422 m3
Error=422times10020408=207
983109983160983137983149983152983148983141 2983085983123983119983116983125983124983113983119983118
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 3867
Methods of Calculation
There two available method calculating the
final stage of the damaged vessel
bull Lost Buoyancy Method
bull Added Weight Method
8162019 Damaged Stability
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Comparision of Lost Buoyancy and Added
Weight Methods
8162019 Damaged Stability
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Consider a vessel that has been damaged such
that a portion of the bottom is now open to the
sea
The vesselrsquos draft will increase because an amount
of the buoyancy was lost
Added Weight Method
Added Weight Method
8162019 Damaged Stability
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Added Weight Method
In this method flood water is treated as a fixed weight (for example the
weight of water of volume ABEF) This added weight is balanced by the
additional buoyant force of the layer WL1WL
The added weight can be determined by either the volume ABEF or
waterline WL1 Therefore WL1 waterline is not known can be just guessed
For the predicted waterline added weight and additional buoyant force
caculation are done iteratively until both of them are equal This method is
known as Added weight method
Determination of Added Weight
8162019 Damaged Stability
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Determination of Added Weight
vc Volume of damaged compartment (DCEF)
ac The surface area (AB) of damaged compartment on the waterline
micro The volume permability of damaged compartment
microa The area permability of the surface of damaged compartment
∆ The initial displacement
∆1 The displacement at final stage
vw The volume of water entering the vessel (ABEH)
w The weight of water entering the vessel
p The value of parallel sinkage
If th t th l l i k i h f t l f
8162019 Damaged Stability
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If we assume that the paralel sinkage cause a minor change of water plane area of a
ship (Awp
asymp Awp1
) we can determine the paralel sinkage by equating the volume of
the layer WL1WL to the volume of ABEF
If the damaged compartment is bounded on top
8162019 Damaged Stability
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8162019 Damaged Stability
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Longitudinal Metacentre Radius at final stage
Free Surface Effect
Damaged compartment can be considered as a half filled tank
Free Contact Effect
Damaged compartment can be considered as a half filled tank
T M H i h
8162019 Damaged Stability
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Transverse Metacentre Height
The angle of heel
8162019 Damaged Stability
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L it di l M t t H i ht
8162019 Damaged Stability
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Longitudinal Metacentre Height
8162019 Damaged Stability
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E983160983137983149983152983148983141 A 983138983137983154983143983141
8162019 Damaged Stability
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E983160983137983149983152983148983141 A 983138983137983154983143983141
991266 L = 20 983149991266 B = 5 983149
991266 983124 = 15 983149
991266 KG = 15 983149
I983150983156983137983139983156 C983151983150983140983145983156983145983151983150
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 5167
I983150983156983137983139983156 C983151983150983140983145983156983145983151983150
991266 983124983144983141 983140983145983155983152983148983137983139983141983149983141983150983156 983158983151983148983157983149983141
991266 983124983144983141 983149983137983155983155 983140983145983155983152983148983137983139983141983149983141983150983156
991266 983124983144983141 983149983151983149983141983150983156 983151983142 983145983150983141983154983156983145983137 983151983142 983156983144983141 983159983137983156983141983154983152983148983137983150983141 983137983154983141983137983137983138983151983157983156 CL
3
15051520 m x xT B L
I I
==sdotsdot=nabla
tons x I
751531500251 ==nablasdot=∆ ρ
433
33208
12
205
12
m x L B
I I
===
I983150983156983137983139983156 C983151983150983140983145983156983145983151983150
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 5267
I983150983156983137983139983156 C983151983150983140983145983156983145983151983150
991266 M983141983156983137983139983141983150983156983154983145983139 983154983137983140983145983157983155
991266 O983154 983145983156 983139983151983157983148983140 983138983141 983139983137983148983139983157983148983137983156983141983140 983140983145983154983141983139983156983148983161 983137983155
991266 H983141983145983143983144983156 983151983142 983156983144983141 983139983141983150983156983141983154 983151983142 983138983157983151983161983137983150983139983161
m I
BM
I
I 3891
150
33208==
nabla
=
m xT
B
LBT
L B BM
I I
I 3891
5112
5
12
12 223
====
mT
KB I
I 750
2
==
I983150983156983137983139983156 C983151983150983140983145983156983145983151983150
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 5367
991266 983124983144983141 983149983141983156983137983139983141983150983156983154983145983139 983144983141983145983143983144983156
991266 F983151983154 983155983149983137983148983148 983137983150983143983148983141983155 983151983142 983144983141983141983148 983156983144983141 983154983145983143983144983156983145983150983143 983149983151983149983141983150983156
m KG BM KBGM I I 63905013891750 =minus+=minus+=
sin22998sin693075153sin mt x xGM M I I
φ φ φ ==∆=
8162019 Damaged Stability
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8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 5567
983116983119983123983124 983106983125983119983129983105983118983107983129 983117983109983124983112983119983108
Paralel Sinkage
Volume (DCEF)=Volume (W1ADW+BL1LC)
Damaged compartment is bounded on top
983116983119983123983124 983106983125983119983129983105983118983107983129 983117983109983124983112983119983108
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 5667
983116983119983123983124 983106983125983119983129983105983118983107983129 983117983109983124983112983119983108
bull It is assumed that displacement and location of vertical centre
of gravity does not change after damaged
983116983119983123983124 983106983125983119983129983105983118983107983129 983117983109983124983112983119983108
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 5767
983116983119983123983124 983106983125983119983129983105983118983107983129 983117983109983124983112983119983108
8162019 Damaged Stability
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The heel angle of damaged ship is determined by
where
d is the distance between the volume centre of damaged compartment
and the new longitudinal centre of floatation
wc=vc μ ρ
983116983119983123983124 983106983125983119983129983105983118983107983129 983117983109983124983112983119983108
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 5967
983116983119983123983124 983106983125983119983129983105983118983107983129 983117983109983124983112983119983108
983116983119983123983124 983106983125983119983129983105983118983107983129 983117983109983124983112983119983108
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 6067
Longitudinal Metacentre Height of a Damaged Ship
983116983119983123983124 983106983125983119983129983105983118983107983129 983117983109983124983112983119983108
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 6167
983110983151983154983159983137983154983140 983137983150983140 983137983142983156 983140983154983137983157983143983144983156983155 983137983142983156983141983154 983140983137983149983137983143983141983140
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 6267
983120983151983154983156 983105983142983156 983120983151983154983156 983110983151983154983141 983123983156983137983154983138983151983137983154983140 983105983142983156 983123983156983137983154983138983151983137983154983140 983110983151983154983159983137983154983140
I983150983145983156983145983137983148 D983154983137983157983143983144983156 983124 983124 983124 983124
983120983137983154983137983148983141983148 983123983145983150983147983137983143983141 +983152 +983152 +983152 +983120
H983141983141983148 983085983149983145 983085983149983145 +983149983155 +983149983155
983124983154983145983149 983085983156983147 +983156983138 983085983156983147 +983156983138
F983145983150983137983148 D983154983137983157983143983144983156 983124+983152983085983149983145983085983156983147 983124+983152983085983149983145+983156983138 983124+983152+983149983155983085983156983147 983124+983152+983149983155+983156983138
Table 1 Final Draughts for a starboard side damaged ship
8162019 Damaged Stability
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L983151983155983156 B983157983151983161983137983150983139983161 M983141983156983144983151983140
8162019 Damaged Stability
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L983151983155983156 B983157983151983161983137983150983139983161 M983141983156983144983151983140
8162019 Damaged Stability
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991266 A983142983156983141983154 983148983151983151983155983145983150983143 983156983144983141 983139983141983150983156983154983137983148 983139983151983149983152983137983154983156983149983141983150983156 983156983144983141
983159983137983156983141983154983152983148983137983150983141 983137983154983141983137 983145983155
991266 983124983151 983139983151983149983152983141983150983155983137983156983141 983142983151983154 983156983144983141 983148983151983155983155 983151983142 983138983157983151983161983137983150983139983161 983151983142 983156983144983141
983139983141983150983156983154983137983148 983139983151983149983152983137983154983156983149983141983150983156 983156983144983141 983140983154983137983142983156 983145983150983139983154983141983137983155983141983155 983156983151
2805)420()( m x Bl L A L
=minus=minus=
m A
T
L
I
L 875180
150==
nabla=
L983151983155983156 B983157983151983161983137983150983139983161 M983141983156983144983151983140
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 6667
991266 983124983144983141 983144983141983145983143983144983156 983151983142 983156983144983141 983139983141983150983156983141983154 983151983142 983138983157983151983161983137983150983139983161 983145983150983139983154983141983137983155983141983155 983156983151
991266 983124983144983141 983149983151983149983141983150983156 983151983142 983145983150983141983154983156983145983137 983151983142 983156983144983141 983159983137983156983141983154983152983148983137983150983141 983137983154983141983137
991266 983124983144983141 983149983141983156983137983139983141983150983156983154983145983139 983154983137983140983145983157983155
m
T
KB L
L 93802
8751
2 ===
433
6716612
)420(5
12
)(m
l L B I L
=minus
=minus
=
m I
BM
I
L
L 1111150
67166==
nabla
=
L983151983155983156 B983157983151983161983137983150983139983161 M983141983156983144983151983140
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 6767
991266 983124983144983141 983149983141983156983137983139983141983150983156983154983145983139 983144983141983145983143983144983156
991266 983122983145983143983144983156983145983150983143 983149983151983149983141983150983156 983142983151983154 983155983149983137983148983148 983144983141983141983148 983137983150983143983148983141983155
m KG BM KBGM L L L 54905111119380 =minus+=minus+=
mt xGM M L
sin34984sin549075153sin φ φ φ ==∆=
8162019 Damaged Stability
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983117983137983154983143983145983150 983116983145983150983141
8162019 Damaged Stability
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983117983137983154983143983145983150 983116983145983150983141
8162019 Damaged Stability
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Permability is the ratio of amount of water that can a enter or a
compartment or tank to the total volume of compartment or tank
VOLUME TOTAL
VOLUME AVAILABLE TY PERMEABILI =
983120983141983154983149983141983137983138983145983148983145983156983161 μ
8162019 Damaged Stability
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983123983157983154983142983137983139983141 983120983141983154983149983141983137983138983145983148983145983156983161 μ983137
Surface permability is the percentage of a waterplane that can be
occupied by water
8162019 Damaged Stability
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8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 1867
A cargo hold with dimensions of l = 1524m w = 914 m
h=61 m is completely flooded Determine the volume of the
space and the corrected flooded volume
Volume = 1524 m x 914 m x 61 m = 8497 m3
Flooded volume = Volume x permeability
Flooded volume = 8497 m3 x 60
Flooded volume = 5098 m3
Example 1
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 1967
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8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 2067
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8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 2167
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8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 2267
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8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 2367
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Δ I983150983145983156983145983137983148 983140983145983155983152983148983137983139983141983149983141983150983156 Δ1 D983145983155983152983148983137983139983141983149983141983150983156 983137983142983156983141983154 983140983137983149983137983143983141983140
B I983150983145983156983145983137983148 983139983141983150983156983154983141 983151983142 983138983157983151983161983137983150983139983161
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8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 2467
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983140983137983149983137983143983141983140 983139983151983149983152983137983154983156983149983141983150983156
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 2567
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Initial displacement and longitudinal centre of buoyancy (LCB) can be read from hydrostatcic curves
However displacement and LCB are unknown after damaged
Therefore if trim forward and aft draught are known trimmed waterline can be drawn over Bonjean
area curves
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 2667
983108983141983156983141983154983149983145983150983137983156983145983151983150 983151983142 983140983137983149983137983143983141983140 983148983141983150983143983156983144 983137983150983140 983148983151983139983137983156983145983151983150 983151983142 983149983145983140
983151983142 983139983151983149983152983137983154983156983149983141983150983156
vw The volume of water entering the vessel
xw Distance of volume centre of damaged compartment from maestory
micro Permability of the compartment
v0 Volume of the compartment
xm Distance of the volume centre of the compartment to the mid of damaged length
xl Distance of the mid of damaged length of compartment to maestory
xc Distance of the computed volume centre of compartment to maestory (xc=xl-xm)
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 2767
983108983141983156983141983154983149983145983150983137983156983145983151983150 983151983142 983140983137983149983137983143983141983140 983148983141983150983143983156983144 983137983150983140 983148983151983139983137983156983145983151983150 983151983142 983149983145983140
983151983142 983139983151983149983152983137983154983156983149983141983150983156
Damaged length and location of compartment can be determined by iterative
procedure
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 2867
bull The volume of water entering the vessel (vw)
bull Distance of volume centre of damaged compartment from amidships Θ ( xw)
bull Volume of the compartment (v0
= vw
μ)
First trial
1) Assume xm=0 (xl=xw)
2) Damaged Length l1 = (Volume of the compartment v0) (mean sec Area Amean)
where Amean is determined from trimmed sectional area curve
983108983141983156983141983154983149983145983150983137983156983145983151983150 983151983142 983140983137983149983137983143983141983140 983148983141983150983143983156983144 983137983150983140 983148983151983139983137983156983145983151983150 983151983142 983149983145983140
983151983142 983139983151983149983152983137983154983156983149983141983150983156
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 2967
3) In order to determine vm and xm
s = l1 4
vm = (s 3) sum3
xm = s sum4 sum3
xc = xl ndash xm
|vm-v0| le Tolarence for volume
|xc-xw| le Tolarence for location of volume centre
l=l1 xl=xw
983108983141983156983141983154983149983145983150983137983156983145983151983150 983151983142 983140983137983149983137983143983141983140 983148983141983150983143983156983144 983137983150983140 983148983151983139983137983156983145983151983150 983151983142 983149983145983140
983151983142 983139983151983149983152983137983154983156983149983141983150983156
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 3067
983108983141983156983141983154983149983145983150983137983156983145983151983150 983151983142 983140983137983149983137983143983141983140 983148983141983150983143983156983144 983137983150983140 983148983151983139983137983156983145983151983150 983151983142 983149983145983140
983151983142 983139983151983149983152983137983154983156983149983141983150983156Second Trial
Damaged length is changed proportionally by the volume
l2 = l1 times (v0v
m)
vm Computed volume at first trial
If the value of xm computed at first trial is negative then the mid of the
compartment slides to the bow
xl = xw+xm
where xm is the distance of the volume centre of compartment to amidship
computed at first trial
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 3167
In order to determine vm and xm
983108983141983156983141983154983149983145983150983137983156983145983151983150 983151983142 983140983137983149983137983143983141983140 983148983141983150983143983156983144 983137983150983140 983148983151983139983137983156983145983151983150 983151983142 983149983145983140
983151983142 983139983151983149983152983137983154983156983149983141983150983156
s = l2 4
vm = (s 3) sum3
xm = s sum4 sum3
xc = xl ndash xm
|vm-v0| le Tolarence for volume
|xc-xw| le Tolarence for location of volume centre
l=l2
If tolarances for both volume and location are not satisfied third fourthtrials are made similar to
second trial
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 3267
If either tolarence for volume or tolarance for location are satisfied at a trial
satisfied one is fixed trials are continued to make for the other one
983108983141983156983141983154983149983145983150983137983156983145983151983150 983151983142 983140983137983149983137983143983141983140 983148983141983150983143983156983144 983137983150983140 983148983151983139983137983156983145983151983150 983151983142 983149983145983140
983151983142 983139983151983149983152983137983154983156983149983141983150983156
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 3367
A ship is 116 meter long and displaces 7842 ton in salt water (ρ1=1025 tm3)
when her mean draught is 64m Longitudinal Centre of Buoyancy (LCB) is
0615 m aft from amidships After one of her stern compartment is damaged
she floats trimmed to the aft Her sectional areas after damaged are given in the
following table
a) Determine the volume of water entering the vessel (vw) and the location of
volume centre of damaged compartment (xw)
b) Assume permability of compartment micro is 1 Determine damaged length
and Distance of the mid of damaged length of compartment to amidship
983109983160983137983149983152983148983141 2
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 3467
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 3567
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 3667
Predicted xw
is between section 2 and section 3
983123983141983139 N983151 983123983141983139 A983154983141983137 D983145983155983156 A9831499831459831559831449831459831522 10135 983085348
3 1208 983085232
983123983141983139 A983154983141983137 983137983156 98308524983149 983142983154983151983149 983137983149983145983140983155983144983145983152 = 11959831492
l1=v0Amean=204081195=17078 m
s=l14=427 m
983109983160983137983149983152983148983141 2983085983123983119983116983125983124983113983119983118
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 3767
983161983145 L983151983139 A983149983141983137983150 983123M M A983154983149
9831311983133 9831312983133 98313119831339832559831312983133 9831313983133 983131198313398325598313129831339832559831313983133
0 9830853254 1051 1 1051 2 21021 9830852827 1123 4 4492 1 4492
2 98308524 1195 2 239 0 0
3 9830851973 1219 4 4876 9830851 9830854876
4 9830851546 1233 1 1233 9830852 9830852466
sum983091983101 14042 sum983092983101 983085748
vm
= (s3) sum3= 199864479831493
xm
=s sum4sum3= 9830850227983149
v0-vm=20408-19986=422 m3
Error=422times10020408=207
983109983160983137983149983152983148983141 2983085983123983119983116983125983124983113983119983118
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 3867
Methods of Calculation
There two available method calculating the
final stage of the damaged vessel
bull Lost Buoyancy Method
bull Added Weight Method
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 3967
Comparision of Lost Buoyancy and Added
Weight Methods
8162019 Damaged Stability
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Consider a vessel that has been damaged such
that a portion of the bottom is now open to the
sea
The vesselrsquos draft will increase because an amount
of the buoyancy was lost
Added Weight Method
Added Weight Method
8162019 Damaged Stability
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Added Weight Method
In this method flood water is treated as a fixed weight (for example the
weight of water of volume ABEF) This added weight is balanced by the
additional buoyant force of the layer WL1WL
The added weight can be determined by either the volume ABEF or
waterline WL1 Therefore WL1 waterline is not known can be just guessed
For the predicted waterline added weight and additional buoyant force
caculation are done iteratively until both of them are equal This method is
known as Added weight method
Determination of Added Weight
8162019 Damaged Stability
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Determination of Added Weight
vc Volume of damaged compartment (DCEF)
ac The surface area (AB) of damaged compartment on the waterline
micro The volume permability of damaged compartment
microa The area permability of the surface of damaged compartment
∆ The initial displacement
∆1 The displacement at final stage
vw The volume of water entering the vessel (ABEH)
w The weight of water entering the vessel
p The value of parallel sinkage
If th t th l l i k i h f t l f
8162019 Damaged Stability
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If we assume that the paralel sinkage cause a minor change of water plane area of a
ship (Awp
asymp Awp1
) we can determine the paralel sinkage by equating the volume of
the layer WL1WL to the volume of ABEF
If the damaged compartment is bounded on top
8162019 Damaged Stability
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8162019 Damaged Stability
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Longitudinal Metacentre Radius at final stage
Free Surface Effect
Damaged compartment can be considered as a half filled tank
Free Contact Effect
Damaged compartment can be considered as a half filled tank
T M H i h
8162019 Damaged Stability
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Transverse Metacentre Height
The angle of heel
8162019 Damaged Stability
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L it di l M t t H i ht
8162019 Damaged Stability
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Longitudinal Metacentre Height
8162019 Damaged Stability
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E983160983137983149983152983148983141 A 983138983137983154983143983141
8162019 Damaged Stability
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E983160983137983149983152983148983141 A 983138983137983154983143983141
991266 L = 20 983149991266 B = 5 983149
991266 983124 = 15 983149
991266 KG = 15 983149
I983150983156983137983139983156 C983151983150983140983145983156983145983151983150
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 5167
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3
15051520 m x xT B L
I I
==sdotsdot=nabla
tons x I
751531500251 ==nablasdot=∆ ρ
433
33208
12
205
12
m x L B
I I
===
I983150983156983137983139983156 C983151983150983140983145983156983145983151983150
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 5267
I983150983156983137983139983156 C983151983150983140983145983156983145983151983150
991266 M983141983156983137983139983141983150983156983154983145983139 983154983137983140983145983157983155
991266 O983154 983145983156 983139983151983157983148983140 983138983141 983139983137983148983139983157983148983137983156983141983140 983140983145983154983141983139983156983148983161 983137983155
991266 H983141983145983143983144983156 983151983142 983156983144983141 983139983141983150983156983141983154 983151983142 983138983157983151983161983137983150983139983161
m I
BM
I
I 3891
150
33208==
nabla
=
m xT
B
LBT
L B BM
I I
I 3891
5112
5
12
12 223
====
mT
KB I
I 750
2
==
I983150983156983137983139983156 C983151983150983140983145983156983145983151983150
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 5367
991266 983124983144983141 983149983141983156983137983139983141983150983156983154983145983139 983144983141983145983143983144983156
991266 F983151983154 983155983149983137983148983148 983137983150983143983148983141983155 983151983142 983144983141983141983148 983156983144983141 983154983145983143983144983156983145983150983143 983149983151983149983141983150983156
m KG BM KBGM I I 63905013891750 =minus+=minus+=
sin22998sin693075153sin mt x xGM M I I
φ φ φ ==∆=
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 5467
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 5567
983116983119983123983124 983106983125983119983129983105983118983107983129 983117983109983124983112983119983108
Paralel Sinkage
Volume (DCEF)=Volume (W1ADW+BL1LC)
Damaged compartment is bounded on top
983116983119983123983124 983106983125983119983129983105983118983107983129 983117983109983124983112983119983108
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 5667
983116983119983123983124 983106983125983119983129983105983118983107983129 983117983109983124983112983119983108
bull It is assumed that displacement and location of vertical centre
of gravity does not change after damaged
983116983119983123983124 983106983125983119983129983105983118983107983129 983117983109983124983112983119983108
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 5767
983116983119983123983124 983106983125983119983129983105983118983107983129 983117983109983124983112983119983108
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 5867
The heel angle of damaged ship is determined by
where
d is the distance between the volume centre of damaged compartment
and the new longitudinal centre of floatation
wc=vc μ ρ
983116983119983123983124 983106983125983119983129983105983118983107983129 983117983109983124983112983119983108
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 5967
983116983119983123983124 983106983125983119983129983105983118983107983129 983117983109983124983112983119983108
983116983119983123983124 983106983125983119983129983105983118983107983129 983117983109983124983112983119983108
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 6067
Longitudinal Metacentre Height of a Damaged Ship
983116983119983123983124 983106983125983119983129983105983118983107983129 983117983109983124983112983119983108
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 6167
983110983151983154983159983137983154983140 983137983150983140 983137983142983156 983140983154983137983157983143983144983156983155 983137983142983156983141983154 983140983137983149983137983143983141983140
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 6267
983120983151983154983156 983105983142983156 983120983151983154983156 983110983151983154983141 983123983156983137983154983138983151983137983154983140 983105983142983156 983123983156983137983154983138983151983137983154983140 983110983151983154983159983137983154983140
I983150983145983156983145983137983148 D983154983137983157983143983144983156 983124 983124 983124 983124
983120983137983154983137983148983141983148 983123983145983150983147983137983143983141 +983152 +983152 +983152 +983120
H983141983141983148 983085983149983145 983085983149983145 +983149983155 +983149983155
983124983154983145983149 983085983156983147 +983156983138 983085983156983147 +983156983138
F983145983150983137983148 D983154983137983157983143983144983156 983124+983152983085983149983145983085983156983147 983124+983152983085983149983145+983156983138 983124+983152+983149983155983085983156983147 983124+983152+983149983155+983156983138
Table 1 Final Draughts for a starboard side damaged ship
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 6367
L983151983155983156 B983157983151983161983137983150983139983161 M983141983156983144983151983140
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 6467
L983151983155983156 B983157983151983161983137983150983139983161 M983141983156983144983151983140
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 6567
991266 A983142983156983141983154 983148983151983151983155983145983150983143 983156983144983141 983139983141983150983156983154983137983148 983139983151983149983152983137983154983156983149983141983150983156 983156983144983141
983159983137983156983141983154983152983148983137983150983141 983137983154983141983137 983145983155
991266 983124983151 983139983151983149983152983141983150983155983137983156983141 983142983151983154 983156983144983141 983148983151983155983155 983151983142 983138983157983151983161983137983150983139983161 983151983142 983156983144983141
983139983141983150983156983154983137983148 983139983151983149983152983137983154983156983149983141983150983156 983156983144983141 983140983154983137983142983156 983145983150983139983154983141983137983155983141983155 983156983151
2805)420()( m x Bl L A L
=minus=minus=
m A
T
L
I
L 875180
150==
nabla=
L983151983155983156 B983157983151983161983137983150983139983161 M983141983156983144983151983140
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 6667
991266 983124983144983141 983144983141983145983143983144983156 983151983142 983156983144983141 983139983141983150983156983141983154 983151983142 983138983157983151983161983137983150983139983161 983145983150983139983154983141983137983155983141983155 983156983151
991266 983124983144983141 983149983151983149983141983150983156 983151983142 983145983150983141983154983156983145983137 983151983142 983156983144983141 983159983137983156983141983154983152983148983137983150983141 983137983154983141983137
991266 983124983144983141 983149983141983156983137983139983141983150983156983154983145983139 983154983137983140983145983157983155
m
T
KB L
L 93802
8751
2 ===
433
6716612
)420(5
12
)(m
l L B I L
=minus
=minus
=
m I
BM
I
L
L 1111150
67166==
nabla
=
L983151983155983156 B983157983151983161983137983150983139983161 M983141983156983144983151983140
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 6767
991266 983124983144983141 983149983141983156983137983139983141983150983156983154983145983139 983144983141983145983143983144983156
991266 983122983145983143983144983156983145983150983143 983149983151983149983141983150983156 983142983151983154 983155983149983137983148983148 983144983141983141983148 983137983150983143983148983141983155
m KG BM KBGM L L L 54905111119380 =minus+=minus+=
mt xGM M L
sin34984sin549075153sin φ φ φ ==∆=
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 1467
983117983137983154983143983145983150 983116983145983150983141
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 1567
Permability is the ratio of amount of water that can a enter or a
compartment or tank to the total volume of compartment or tank
VOLUME TOTAL
VOLUME AVAILABLE TY PERMEABILI =
983120983141983154983149983141983137983138983145983148983145983156983161 μ
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 1667
983123983157983154983142983137983139983141 983120983141983154983149983141983137983138983145983148983145983156983161 μ983137
Surface permability is the percentage of a waterplane that can be
occupied by water
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 1767
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 1867
A cargo hold with dimensions of l = 1524m w = 914 m
h=61 m is completely flooded Determine the volume of the
space and the corrected flooded volume
Volume = 1524 m x 914 m x 61 m = 8497 m3
Flooded volume = Volume x permeability
Flooded volume = 8497 m3 x 60
Flooded volume = 5098 m3
Example 1
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 1967
983110983148983151983151983140983137983138983148983141 983116983141983150983143983156983144
983110983148983151983151983140983137983138983148983141 983148983141983150983143983156983144983098 983137983156 983137 983143983145983158983141983150 983152983151983145983150983156 983151983142 983156983144983141 983155983144983145983152 983148983141983150983143983156983144 983145983155 983156983144983141 983149983137983160983145983149983157983149 983148983141983150983143983156983144
983159983145983156983144 983156983144983141 983139983141983150983156983141983154 983137983156 983156983144983137983156 983152983151983145983150983156 983156983144983137983156 983139983137983150 983138983141 983142983148983151983151983140983141983140 983159983145983156983144983151983157983156 983155983157983138983149983141983154983143983145983150983143 983156983144983141
983155983144983145983152 983138983141983161983151983150983140 983149983137983154983143983145983150 983148983145983150983141
983129983137983154983137983148ı 983106983286983148983149983141 983106983151983161983157983098 G983141983149983145 983138983151983161983157983150983139983137 983144983141983154983144983137983150983143983145 983138983145983154 983150983151983147983156983137983140983137 983138983157 983150983151983147983156983137 983149983141983154983147983141983162
983151983148983149983137983147 983292983162983141983154983141 983143983141983149983145983161983145 983155ı983150ı983154 983144983137983156983156ı983150983137 983156983141ğ983141983156 983144983137983148983141 983143983141983156983145983154983141983139983141983147 983141983150 983138983292983161983292983147 983138983286983148983149983141 983138983151983161983157983150983137
983151 983150983151983147983156983137983140983137983147983145 983161983137983154983137983148ı 983138983286983148983149983141 983138983151983161983157 983140983141983150983145983154
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 2067
983110983148983151983151983140983137983138983148983141 983116983141983150983143983156983144 983107983157983154983158983141
983110983148983151983151983140983137983138983148983141 983116983141983150983143983156983144 983107983157983154983158983141983098 I983156 983145983155 983151983138983156983137983145983150983141983140 983138983161 983156983144983141 983139983151983150983150983141983139983156983145983151983150 983151983142 983142983148983151983151983140983137983138983148983141 983148983141983150983143983156983144983155 983137983156
983140983145983142983142983141983154983141983150983156 983152983151983145983150983156983155 983137983148983151983150983143 983156983144983141 983155983144983145983152 983148983141983150983143983156983144
983129983137983154983137983148ı 983106983286983148983149983141 983106983151983161983157 983109ğ983154983145983155983145983098 G983141983149983145 983138983151983161983157983150983139983137 983140983141ğ983145ş983145983147 983150983151983147983156983137983148983137983154983140983137 983144983141983155983137983152983148983137983150983137983150 983161983137983154983137983148ı
983138983286983148983149983141 983138983151983161983157 983140983141ğ983141983154983148983141983154983145983150983145983150 983138983145983154983148983141ş983156983145983154983145983148983149983141983155983145 983145983148983141 983141983148983140983141 983141983140983145983148983145983154
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 2167
983110983137983139983156983151983154 983151983142 983123983157983138983140983145983158983145983155983145983151983150
F983137983139983156983151983154 983151983142 983123983157983138983140983145983158983145983155983145983151983150 983124983144983141 983142983137983139983156983151983154 983151983142 983155983157983138983140983145983158983145983155983145983151983150 983145983155 983137 983142983137983139983156983151983154 983152983154983141983155983139983154983145983138983141983140
983138983161 983156983144983141 983137983152983152983148983145983139983137983138983148983141 983154983141983143983157983148983137983156983145983151983150983155 983137983150983140 983138983161 983145983150983156983141983154983150983137983156983145983151983150983137983148 983139983151983150983158983141983150983156983145983151983150 983156983144983137983156
983140983141983152983141983150983140983155 983151983150 983155983144983145983152 983148983141983150983143983156983144 983137983150983140 983139983154983145983156983141983154983145983151983150 983151983142 983155983141983154983158983145983139983141
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 2267
983120983141983154983149983145983155983155983145983138983148983141 983116983141983150983143983156983144
983120983141983154983149983145983155983155983145983138983148983141 L983141983150983143983156983144 983145983155 983151983138983156983137983145983150983141983140 983138983161 983149983157983148983156983145983152983148983161983145983150983143 983156983144983141 983142983148983151983151983140983137983138983148983141 983148983141983150983143983156983144 983137983156
983156983144983137983156 983152983151983145983150983156 983138983161 983156983144983141 983142983137983139983156983151983154 983151983142 983155983157983138983140983145983158983145983155983145983151983150
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 2367
D983141983156983141983154983149983145983150983137983156983145983151983150 983151983142 983156983144983141 983148983151983139983137983156983145983151983150 983151983142 983156983144983141 983158983151983148983157983149983141 983139983141983150983156983154983141 983151983142
983140983137983149983137983143983141983140 983139983151983149983152983137983154983156983149983141983150983156
Δ I983150983145983156983145983137983148 983140983145983155983152983148983137983139983141983149983141983150983156 Δ1 D983145983155983152983148983137983139983141983149983141983150983156 983137983142983156983141983154 983140983137983149983137983143983141983140
B I983150983145983156983145983137983148 983139983141983150983156983154983141 983151983142 983138983157983151983161983137983150983139983161
G I983150983145983156983145983137983148 983139983141983150983156983154983141 983151983142 9831439831549831379831589831459831569831619831600 I983150983145983156983145983137983148 983139983141983150983156983154983141 983151983142 983148983151983150983143983145983156983157983140983145983150983137983148 983138983157983151983161983137983150983139983161 LCB
983158983159 983124983144983141 983158983151983148983157983149983141 983151983142 983159983137983156983141983154 983141983150983156983141983154983145983150983143 983156983144983141 983158983141983155983155983141983148
983160983159 D983145983155983156983137983150983139983141 983151983142 983158983151983148983157983149983141 983139983141983150983156983154983141 983151983142 983140983137983149983137983143983141983140 983139983151983149983152983137983154983156983149983141983150983156 983142983154983151983149 983149983137983141983155983156983151983154983161
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 2467
D983141983156983141983154983149983145983150983137983156983145983151983150 983151983142 983156983144983141 983148983151983139983137983156983145983151983150 983151983142 983156983144983141 983158983151983148983157983149983141 983139983141983150983156983154983141 983151983142
983140983137983149983137983143983141983140 983139983151983149983152983137983154983156983149983141983150983156
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 2567
D983141983156983141983154983149983145983150983137983156983145983151983150 983151983142 983156983144983141 983158983151983148983157983149983141 983151983142 983159983137983156983141983154 983141983150983156983141983154983145983150983143 983156983144983141 983158983141983155983155983141983148
Initial displacement and longitudinal centre of buoyancy (LCB) can be read from hydrostatcic curves
However displacement and LCB are unknown after damaged
Therefore if trim forward and aft draught are known trimmed waterline can be drawn over Bonjean
area curves
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 2667
983108983141983156983141983154983149983145983150983137983156983145983151983150 983151983142 983140983137983149983137983143983141983140 983148983141983150983143983156983144 983137983150983140 983148983151983139983137983156983145983151983150 983151983142 983149983145983140
983151983142 983139983151983149983152983137983154983156983149983141983150983156
vw The volume of water entering the vessel
xw Distance of volume centre of damaged compartment from maestory
micro Permability of the compartment
v0 Volume of the compartment
xm Distance of the volume centre of the compartment to the mid of damaged length
xl Distance of the mid of damaged length of compartment to maestory
xc Distance of the computed volume centre of compartment to maestory (xc=xl-xm)
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 2767
983108983141983156983141983154983149983145983150983137983156983145983151983150 983151983142 983140983137983149983137983143983141983140 983148983141983150983143983156983144 983137983150983140 983148983151983139983137983156983145983151983150 983151983142 983149983145983140
983151983142 983139983151983149983152983137983154983156983149983141983150983156
Damaged length and location of compartment can be determined by iterative
procedure
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 2867
bull The volume of water entering the vessel (vw)
bull Distance of volume centre of damaged compartment from amidships Θ ( xw)
bull Volume of the compartment (v0
= vw
μ)
First trial
1) Assume xm=0 (xl=xw)
2) Damaged Length l1 = (Volume of the compartment v0) (mean sec Area Amean)
where Amean is determined from trimmed sectional area curve
983108983141983156983141983154983149983145983150983137983156983145983151983150 983151983142 983140983137983149983137983143983141983140 983148983141983150983143983156983144 983137983150983140 983148983151983139983137983156983145983151983150 983151983142 983149983145983140
983151983142 983139983151983149983152983137983154983156983149983141983150983156
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 2967
3) In order to determine vm and xm
s = l1 4
vm = (s 3) sum3
xm = s sum4 sum3
xc = xl ndash xm
|vm-v0| le Tolarence for volume
|xc-xw| le Tolarence for location of volume centre
l=l1 xl=xw
983108983141983156983141983154983149983145983150983137983156983145983151983150 983151983142 983140983137983149983137983143983141983140 983148983141983150983143983156983144 983137983150983140 983148983151983139983137983156983145983151983150 983151983142 983149983145983140
983151983142 983139983151983149983152983137983154983156983149983141983150983156
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 3067
983108983141983156983141983154983149983145983150983137983156983145983151983150 983151983142 983140983137983149983137983143983141983140 983148983141983150983143983156983144 983137983150983140 983148983151983139983137983156983145983151983150 983151983142 983149983145983140
983151983142 983139983151983149983152983137983154983156983149983141983150983156Second Trial
Damaged length is changed proportionally by the volume
l2 = l1 times (v0v
m)
vm Computed volume at first trial
If the value of xm computed at first trial is negative then the mid of the
compartment slides to the bow
xl = xw+xm
where xm is the distance of the volume centre of compartment to amidship
computed at first trial
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 3167
In order to determine vm and xm
983108983141983156983141983154983149983145983150983137983156983145983151983150 983151983142 983140983137983149983137983143983141983140 983148983141983150983143983156983144 983137983150983140 983148983151983139983137983156983145983151983150 983151983142 983149983145983140
983151983142 983139983151983149983152983137983154983156983149983141983150983156
s = l2 4
vm = (s 3) sum3
xm = s sum4 sum3
xc = xl ndash xm
|vm-v0| le Tolarence for volume
|xc-xw| le Tolarence for location of volume centre
l=l2
If tolarances for both volume and location are not satisfied third fourthtrials are made similar to
second trial
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 3267
If either tolarence for volume or tolarance for location are satisfied at a trial
satisfied one is fixed trials are continued to make for the other one
983108983141983156983141983154983149983145983150983137983156983145983151983150 983151983142 983140983137983149983137983143983141983140 983148983141983150983143983156983144 983137983150983140 983148983151983139983137983156983145983151983150 983151983142 983149983145983140
983151983142 983139983151983149983152983137983154983156983149983141983150983156
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 3367
A ship is 116 meter long and displaces 7842 ton in salt water (ρ1=1025 tm3)
when her mean draught is 64m Longitudinal Centre of Buoyancy (LCB) is
0615 m aft from amidships After one of her stern compartment is damaged
she floats trimmed to the aft Her sectional areas after damaged are given in the
following table
a) Determine the volume of water entering the vessel (vw) and the location of
volume centre of damaged compartment (xw)
b) Assume permability of compartment micro is 1 Determine damaged length
and Distance of the mid of damaged length of compartment to amidship
983109983160983137983149983152983148983141 2
8162019 Damaged Stability
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8162019 Damaged Stability
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8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 3667
Predicted xw
is between section 2 and section 3
983123983141983139 N983151 983123983141983139 A983154983141983137 D983145983155983156 A9831499831459831559831449831459831522 10135 983085348
3 1208 983085232
983123983141983139 A983154983141983137 983137983156 98308524983149 983142983154983151983149 983137983149983145983140983155983144983145983152 = 11959831492
l1=v0Amean=204081195=17078 m
s=l14=427 m
983109983160983137983149983152983148983141 2983085983123983119983116983125983124983113983119983118
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 3767
983161983145 L983151983139 A983149983141983137983150 983123M M A983154983149
9831311983133 9831312983133 98313119831339832559831312983133 9831313983133 983131198313398325598313129831339832559831313983133
0 9830853254 1051 1 1051 2 21021 9830852827 1123 4 4492 1 4492
2 98308524 1195 2 239 0 0
3 9830851973 1219 4 4876 9830851 9830854876
4 9830851546 1233 1 1233 9830852 9830852466
sum983091983101 14042 sum983092983101 983085748
vm
= (s3) sum3= 199864479831493
xm
=s sum4sum3= 9830850227983149
v0-vm=20408-19986=422 m3
Error=422times10020408=207
983109983160983137983149983152983148983141 2983085983123983119983116983125983124983113983119983118
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 3867
Methods of Calculation
There two available method calculating the
final stage of the damaged vessel
bull Lost Buoyancy Method
bull Added Weight Method
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 3967
Comparision of Lost Buoyancy and Added
Weight Methods
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 4067
Consider a vessel that has been damaged such
that a portion of the bottom is now open to the
sea
The vesselrsquos draft will increase because an amount
of the buoyancy was lost
Added Weight Method
Added Weight Method
8162019 Damaged Stability
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Added Weight Method
In this method flood water is treated as a fixed weight (for example the
weight of water of volume ABEF) This added weight is balanced by the
additional buoyant force of the layer WL1WL
The added weight can be determined by either the volume ABEF or
waterline WL1 Therefore WL1 waterline is not known can be just guessed
For the predicted waterline added weight and additional buoyant force
caculation are done iteratively until both of them are equal This method is
known as Added weight method
Determination of Added Weight
8162019 Damaged Stability
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Determination of Added Weight
vc Volume of damaged compartment (DCEF)
ac The surface area (AB) of damaged compartment on the waterline
micro The volume permability of damaged compartment
microa The area permability of the surface of damaged compartment
∆ The initial displacement
∆1 The displacement at final stage
vw The volume of water entering the vessel (ABEH)
w The weight of water entering the vessel
p The value of parallel sinkage
If th t th l l i k i h f t l f
8162019 Damaged Stability
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If we assume that the paralel sinkage cause a minor change of water plane area of a
ship (Awp
asymp Awp1
) we can determine the paralel sinkage by equating the volume of
the layer WL1WL to the volume of ABEF
If the damaged compartment is bounded on top
8162019 Damaged Stability
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8162019 Damaged Stability
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Longitudinal Metacentre Radius at final stage
Free Surface Effect
Damaged compartment can be considered as a half filled tank
Free Contact Effect
Damaged compartment can be considered as a half filled tank
T M H i h
8162019 Damaged Stability
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Transverse Metacentre Height
The angle of heel
8162019 Damaged Stability
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L it di l M t t H i ht
8162019 Damaged Stability
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Longitudinal Metacentre Height
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 4967
E983160983137983149983152983148983141 A 983138983137983154983143983141
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 5067
E983160983137983149983152983148983141 A 983138983137983154983143983141
991266 L = 20 983149991266 B = 5 983149
991266 983124 = 15 983149
991266 KG = 15 983149
I983150983156983137983139983156 C983151983150983140983145983156983145983151983150
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 5167
I983150983156983137983139983156 C983151983150983140983145983156983145983151983150
991266 983124983144983141 983140983145983155983152983148983137983139983141983149983141983150983156 983158983151983148983157983149983141
991266 983124983144983141 983149983137983155983155 983140983145983155983152983148983137983139983141983149983141983150983156
991266 983124983144983141 983149983151983149983141983150983156 983151983142 983145983150983141983154983156983145983137 983151983142 983156983144983141 983159983137983156983141983154983152983148983137983150983141 983137983154983141983137983137983138983151983157983156 CL
3
15051520 m x xT B L
I I
==sdotsdot=nabla
tons x I
751531500251 ==nablasdot=∆ ρ
433
33208
12
205
12
m x L B
I I
===
I983150983156983137983139983156 C983151983150983140983145983156983145983151983150
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 5267
I983150983156983137983139983156 C983151983150983140983145983156983145983151983150
991266 M983141983156983137983139983141983150983156983154983145983139 983154983137983140983145983157983155
991266 O983154 983145983156 983139983151983157983148983140 983138983141 983139983137983148983139983157983148983137983156983141983140 983140983145983154983141983139983156983148983161 983137983155
991266 H983141983145983143983144983156 983151983142 983156983144983141 983139983141983150983156983141983154 983151983142 983138983157983151983161983137983150983139983161
m I
BM
I
I 3891
150
33208==
nabla
=
m xT
B
LBT
L B BM
I I
I 3891
5112
5
12
12 223
====
mT
KB I
I 750
2
==
I983150983156983137983139983156 C983151983150983140983145983156983145983151983150
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 5367
991266 983124983144983141 983149983141983156983137983139983141983150983156983154983145983139 983144983141983145983143983144983156
991266 F983151983154 983155983149983137983148983148 983137983150983143983148983141983155 983151983142 983144983141983141983148 983156983144983141 983154983145983143983144983156983145983150983143 983149983151983149983141983150983156
m KG BM KBGM I I 63905013891750 =minus+=minus+=
sin22998sin693075153sin mt x xGM M I I
φ φ φ ==∆=
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 5467
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 5567
983116983119983123983124 983106983125983119983129983105983118983107983129 983117983109983124983112983119983108
Paralel Sinkage
Volume (DCEF)=Volume (W1ADW+BL1LC)
Damaged compartment is bounded on top
983116983119983123983124 983106983125983119983129983105983118983107983129 983117983109983124983112983119983108
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 5667
983116983119983123983124 983106983125983119983129983105983118983107983129 983117983109983124983112983119983108
bull It is assumed that displacement and location of vertical centre
of gravity does not change after damaged
983116983119983123983124 983106983125983119983129983105983118983107983129 983117983109983124983112983119983108
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 5767
983116983119983123983124 983106983125983119983129983105983118983107983129 983117983109983124983112983119983108
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 5867
The heel angle of damaged ship is determined by
where
d is the distance between the volume centre of damaged compartment
and the new longitudinal centre of floatation
wc=vc μ ρ
983116983119983123983124 983106983125983119983129983105983118983107983129 983117983109983124983112983119983108
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 5967
983116983119983123983124 983106983125983119983129983105983118983107983129 983117983109983124983112983119983108
983116983119983123983124 983106983125983119983129983105983118983107983129 983117983109983124983112983119983108
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 6067
Longitudinal Metacentre Height of a Damaged Ship
983116983119983123983124 983106983125983119983129983105983118983107983129 983117983109983124983112983119983108
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 6167
983110983151983154983159983137983154983140 983137983150983140 983137983142983156 983140983154983137983157983143983144983156983155 983137983142983156983141983154 983140983137983149983137983143983141983140
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 6267
983120983151983154983156 983105983142983156 983120983151983154983156 983110983151983154983141 983123983156983137983154983138983151983137983154983140 983105983142983156 983123983156983137983154983138983151983137983154983140 983110983151983154983159983137983154983140
I983150983145983156983145983137983148 D983154983137983157983143983144983156 983124 983124 983124 983124
983120983137983154983137983148983141983148 983123983145983150983147983137983143983141 +983152 +983152 +983152 +983120
H983141983141983148 983085983149983145 983085983149983145 +983149983155 +983149983155
983124983154983145983149 983085983156983147 +983156983138 983085983156983147 +983156983138
F983145983150983137983148 D983154983137983157983143983144983156 983124+983152983085983149983145983085983156983147 983124+983152983085983149983145+983156983138 983124+983152+983149983155983085983156983147 983124+983152+983149983155+983156983138
Table 1 Final Draughts for a starboard side damaged ship
8162019 Damaged Stability
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L983151983155983156 B983157983151983161983137983150983139983161 M983141983156983144983151983140
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 6467
L983151983155983156 B983157983151983161983137983150983139983161 M983141983156983144983151983140
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 6567
991266 A983142983156983141983154 983148983151983151983155983145983150983143 983156983144983141 983139983141983150983156983154983137983148 983139983151983149983152983137983154983156983149983141983150983156 983156983144983141
983159983137983156983141983154983152983148983137983150983141 983137983154983141983137 983145983155
991266 983124983151 983139983151983149983152983141983150983155983137983156983141 983142983151983154 983156983144983141 983148983151983155983155 983151983142 983138983157983151983161983137983150983139983161 983151983142 983156983144983141
983139983141983150983156983154983137983148 983139983151983149983152983137983154983156983149983141983150983156 983156983144983141 983140983154983137983142983156 983145983150983139983154983141983137983155983141983155 983156983151
2805)420()( m x Bl L A L
=minus=minus=
m A
T
L
I
L 875180
150==
nabla=
L983151983155983156 B983157983151983161983137983150983139983161 M983141983156983144983151983140
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 6667
991266 983124983144983141 983144983141983145983143983144983156 983151983142 983156983144983141 983139983141983150983156983141983154 983151983142 983138983157983151983161983137983150983139983161 983145983150983139983154983141983137983155983141983155 983156983151
991266 983124983144983141 983149983151983149983141983150983156 983151983142 983145983150983141983154983156983145983137 983151983142 983156983144983141 983159983137983156983141983154983152983148983137983150983141 983137983154983141983137
991266 983124983144983141 983149983141983156983137983139983141983150983156983154983145983139 983154983137983140983145983157983155
m
T
KB L
L 93802
8751
2 ===
433
6716612
)420(5
12
)(m
l L B I L
=minus
=minus
=
m I
BM
I
L
L 1111150
67166==
nabla
=
L983151983155983156 B983157983151983161983137983150983139983161 M983141983156983144983151983140
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 6767
991266 983124983144983141 983149983141983156983137983139983141983150983156983154983145983139 983144983141983145983143983144983156
991266 983122983145983143983144983156983145983150983143 983149983151983149983141983150983156 983142983151983154 983155983149983137983148983148 983144983141983141983148 983137983150983143983148983141983155
m KG BM KBGM L L L 54905111119380 =minus+=minus+=
mt xGM M L
sin34984sin549075153sin φ φ φ ==∆=
8162019 Damaged Stability
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Permability is the ratio of amount of water that can a enter or a
compartment or tank to the total volume of compartment or tank
VOLUME TOTAL
VOLUME AVAILABLE TY PERMEABILI =
983120983141983154983149983141983137983138983145983148983145983156983161 μ
8162019 Damaged Stability
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983123983157983154983142983137983139983141 983120983141983154983149983141983137983138983145983148983145983156983161 μ983137
Surface permability is the percentage of a waterplane that can be
occupied by water
8162019 Damaged Stability
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8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 1867
A cargo hold with dimensions of l = 1524m w = 914 m
h=61 m is completely flooded Determine the volume of the
space and the corrected flooded volume
Volume = 1524 m x 914 m x 61 m = 8497 m3
Flooded volume = Volume x permeability
Flooded volume = 8497 m3 x 60
Flooded volume = 5098 m3
Example 1
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 1967
983110983148983151983151983140983137983138983148983141 983116983141983150983143983156983144
983110983148983151983151983140983137983138983148983141 983148983141983150983143983156983144983098 983137983156 983137 983143983145983158983141983150 983152983151983145983150983156 983151983142 983156983144983141 983155983144983145983152 983148983141983150983143983156983144 983145983155 983156983144983141 983149983137983160983145983149983157983149 983148983141983150983143983156983144
983159983145983156983144 983156983144983141 983139983141983150983156983141983154 983137983156 983156983144983137983156 983152983151983145983150983156 983156983144983137983156 983139983137983150 983138983141 983142983148983151983151983140983141983140 983159983145983156983144983151983157983156 983155983157983138983149983141983154983143983145983150983143 983156983144983141
983155983144983145983152 983138983141983161983151983150983140 983149983137983154983143983145983150 983148983145983150983141
983129983137983154983137983148ı 983106983286983148983149983141 983106983151983161983157983098 G983141983149983145 983138983151983161983157983150983139983137 983144983141983154983144983137983150983143983145 983138983145983154 983150983151983147983156983137983140983137 983138983157 983150983151983147983156983137 983149983141983154983147983141983162
983151983148983149983137983147 983292983162983141983154983141 983143983141983149983145983161983145 983155ı983150ı983154 983144983137983156983156ı983150983137 983156983141ğ983141983156 983144983137983148983141 983143983141983156983145983154983141983139983141983147 983141983150 983138983292983161983292983147 983138983286983148983149983141 983138983151983161983157983150983137
983151 983150983151983147983156983137983140983137983147983145 983161983137983154983137983148ı 983138983286983148983149983141 983138983151983161983157 983140983141983150983145983154
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 2067
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8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 2167
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8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 2267
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8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 2367
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983140983137983149983137983143983141983140 983139983151983149983152983137983154983156983149983141983150983156
Δ I983150983145983156983145983137983148 983140983145983155983152983148983137983139983141983149983141983150983156 Δ1 D983145983155983152983148983137983139983141983149983141983150983156 983137983142983156983141983154 983140983137983149983137983143983141983140
B I983150983145983156983145983137983148 983139983141983150983156983154983141 983151983142 983138983157983151983161983137983150983139983161
G I983150983145983156983145983137983148 983139983141983150983156983154983141 983151983142 9831439831549831379831589831459831569831619831600 I983150983145983156983145983137983148 983139983141983150983156983154983141 983151983142 983148983151983150983143983145983156983157983140983145983150983137983148 983138983157983151983161983137983150983139983161 LCB
983158983159 983124983144983141 983158983151983148983157983149983141 983151983142 983159983137983156983141983154 983141983150983156983141983154983145983150983143 983156983144983141 983158983141983155983155983141983148
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8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 2467
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983140983137983149983137983143983141983140 983139983151983149983152983137983154983156983149983141983150983156
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 2567
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Initial displacement and longitudinal centre of buoyancy (LCB) can be read from hydrostatcic curves
However displacement and LCB are unknown after damaged
Therefore if trim forward and aft draught are known trimmed waterline can be drawn over Bonjean
area curves
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 2667
983108983141983156983141983154983149983145983150983137983156983145983151983150 983151983142 983140983137983149983137983143983141983140 983148983141983150983143983156983144 983137983150983140 983148983151983139983137983156983145983151983150 983151983142 983149983145983140
983151983142 983139983151983149983152983137983154983156983149983141983150983156
vw The volume of water entering the vessel
xw Distance of volume centre of damaged compartment from maestory
micro Permability of the compartment
v0 Volume of the compartment
xm Distance of the volume centre of the compartment to the mid of damaged length
xl Distance of the mid of damaged length of compartment to maestory
xc Distance of the computed volume centre of compartment to maestory (xc=xl-xm)
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 2767
983108983141983156983141983154983149983145983150983137983156983145983151983150 983151983142 983140983137983149983137983143983141983140 983148983141983150983143983156983144 983137983150983140 983148983151983139983137983156983145983151983150 983151983142 983149983145983140
983151983142 983139983151983149983152983137983154983156983149983141983150983156
Damaged length and location of compartment can be determined by iterative
procedure
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 2867
bull The volume of water entering the vessel (vw)
bull Distance of volume centre of damaged compartment from amidships Θ ( xw)
bull Volume of the compartment (v0
= vw
μ)
First trial
1) Assume xm=0 (xl=xw)
2) Damaged Length l1 = (Volume of the compartment v0) (mean sec Area Amean)
where Amean is determined from trimmed sectional area curve
983108983141983156983141983154983149983145983150983137983156983145983151983150 983151983142 983140983137983149983137983143983141983140 983148983141983150983143983156983144 983137983150983140 983148983151983139983137983156983145983151983150 983151983142 983149983145983140
983151983142 983139983151983149983152983137983154983156983149983141983150983156
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 2967
3) In order to determine vm and xm
s = l1 4
vm = (s 3) sum3
xm = s sum4 sum3
xc = xl ndash xm
|vm-v0| le Tolarence for volume
|xc-xw| le Tolarence for location of volume centre
l=l1 xl=xw
983108983141983156983141983154983149983145983150983137983156983145983151983150 983151983142 983140983137983149983137983143983141983140 983148983141983150983143983156983144 983137983150983140 983148983151983139983137983156983145983151983150 983151983142 983149983145983140
983151983142 983139983151983149983152983137983154983156983149983141983150983156
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 3067
983108983141983156983141983154983149983145983150983137983156983145983151983150 983151983142 983140983137983149983137983143983141983140 983148983141983150983143983156983144 983137983150983140 983148983151983139983137983156983145983151983150 983151983142 983149983145983140
983151983142 983139983151983149983152983137983154983156983149983141983150983156Second Trial
Damaged length is changed proportionally by the volume
l2 = l1 times (v0v
m)
vm Computed volume at first trial
If the value of xm computed at first trial is negative then the mid of the
compartment slides to the bow
xl = xw+xm
where xm is the distance of the volume centre of compartment to amidship
computed at first trial
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 3167
In order to determine vm and xm
983108983141983156983141983154983149983145983150983137983156983145983151983150 983151983142 983140983137983149983137983143983141983140 983148983141983150983143983156983144 983137983150983140 983148983151983139983137983156983145983151983150 983151983142 983149983145983140
983151983142 983139983151983149983152983137983154983156983149983141983150983156
s = l2 4
vm = (s 3) sum3
xm = s sum4 sum3
xc = xl ndash xm
|vm-v0| le Tolarence for volume
|xc-xw| le Tolarence for location of volume centre
l=l2
If tolarances for both volume and location are not satisfied third fourthtrials are made similar to
second trial
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 3267
If either tolarence for volume or tolarance for location are satisfied at a trial
satisfied one is fixed trials are continued to make for the other one
983108983141983156983141983154983149983145983150983137983156983145983151983150 983151983142 983140983137983149983137983143983141983140 983148983141983150983143983156983144 983137983150983140 983148983151983139983137983156983145983151983150 983151983142 983149983145983140
983151983142 983139983151983149983152983137983154983156983149983141983150983156
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 3367
A ship is 116 meter long and displaces 7842 ton in salt water (ρ1=1025 tm3)
when her mean draught is 64m Longitudinal Centre of Buoyancy (LCB) is
0615 m aft from amidships After one of her stern compartment is damaged
she floats trimmed to the aft Her sectional areas after damaged are given in the
following table
a) Determine the volume of water entering the vessel (vw) and the location of
volume centre of damaged compartment (xw)
b) Assume permability of compartment micro is 1 Determine damaged length
and Distance of the mid of damaged length of compartment to amidship
983109983160983137983149983152983148983141 2
8162019 Damaged Stability
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8162019 Damaged Stability
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8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 3667
Predicted xw
is between section 2 and section 3
983123983141983139 N983151 983123983141983139 A983154983141983137 D983145983155983156 A9831499831459831559831449831459831522 10135 983085348
3 1208 983085232
983123983141983139 A983154983141983137 983137983156 98308524983149 983142983154983151983149 983137983149983145983140983155983144983145983152 = 11959831492
l1=v0Amean=204081195=17078 m
s=l14=427 m
983109983160983137983149983152983148983141 2983085983123983119983116983125983124983113983119983118
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 3767
983161983145 L983151983139 A983149983141983137983150 983123M M A983154983149
9831311983133 9831312983133 98313119831339832559831312983133 9831313983133 983131198313398325598313129831339832559831313983133
0 9830853254 1051 1 1051 2 21021 9830852827 1123 4 4492 1 4492
2 98308524 1195 2 239 0 0
3 9830851973 1219 4 4876 9830851 9830854876
4 9830851546 1233 1 1233 9830852 9830852466
sum983091983101 14042 sum983092983101 983085748
vm
= (s3) sum3= 199864479831493
xm
=s sum4sum3= 9830850227983149
v0-vm=20408-19986=422 m3
Error=422times10020408=207
983109983160983137983149983152983148983141 2983085983123983119983116983125983124983113983119983118
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 3867
Methods of Calculation
There two available method calculating the
final stage of the damaged vessel
bull Lost Buoyancy Method
bull Added Weight Method
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 3967
Comparision of Lost Buoyancy and Added
Weight Methods
8162019 Damaged Stability
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Consider a vessel that has been damaged such
that a portion of the bottom is now open to the
sea
The vesselrsquos draft will increase because an amount
of the buoyancy was lost
Added Weight Method
Added Weight Method
8162019 Damaged Stability
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Added Weight Method
In this method flood water is treated as a fixed weight (for example the
weight of water of volume ABEF) This added weight is balanced by the
additional buoyant force of the layer WL1WL
The added weight can be determined by either the volume ABEF or
waterline WL1 Therefore WL1 waterline is not known can be just guessed
For the predicted waterline added weight and additional buoyant force
caculation are done iteratively until both of them are equal This method is
known as Added weight method
Determination of Added Weight
8162019 Damaged Stability
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Determination of Added Weight
vc Volume of damaged compartment (DCEF)
ac The surface area (AB) of damaged compartment on the waterline
micro The volume permability of damaged compartment
microa The area permability of the surface of damaged compartment
∆ The initial displacement
∆1 The displacement at final stage
vw The volume of water entering the vessel (ABEH)
w The weight of water entering the vessel
p The value of parallel sinkage
If th t th l l i k i h f t l f
8162019 Damaged Stability
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If we assume that the paralel sinkage cause a minor change of water plane area of a
ship (Awp
asymp Awp1
) we can determine the paralel sinkage by equating the volume of
the layer WL1WL to the volume of ABEF
If the damaged compartment is bounded on top
8162019 Damaged Stability
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8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 4567
Longitudinal Metacentre Radius at final stage
Free Surface Effect
Damaged compartment can be considered as a half filled tank
Free Contact Effect
Damaged compartment can be considered as a half filled tank
T M H i h
8162019 Damaged Stability
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Transverse Metacentre Height
The angle of heel
8162019 Damaged Stability
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L it di l M t t H i ht
8162019 Damaged Stability
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Longitudinal Metacentre Height
8162019 Damaged Stability
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E983160983137983149983152983148983141 A 983138983137983154983143983141
8162019 Damaged Stability
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E983160983137983149983152983148983141 A 983138983137983154983143983141
991266 L = 20 983149991266 B = 5 983149
991266 983124 = 15 983149
991266 KG = 15 983149
I983150983156983137983139983156 C983151983150983140983145983156983145983151983150
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 5167
I983150983156983137983139983156 C983151983150983140983145983156983145983151983150
991266 983124983144983141 983140983145983155983152983148983137983139983141983149983141983150983156 983158983151983148983157983149983141
991266 983124983144983141 983149983137983155983155 983140983145983155983152983148983137983139983141983149983141983150983156
991266 983124983144983141 983149983151983149983141983150983156 983151983142 983145983150983141983154983156983145983137 983151983142 983156983144983141 983159983137983156983141983154983152983148983137983150983141 983137983154983141983137983137983138983151983157983156 CL
3
15051520 m x xT B L
I I
==sdotsdot=nabla
tons x I
751531500251 ==nablasdot=∆ ρ
433
33208
12
205
12
m x L B
I I
===
I983150983156983137983139983156 C983151983150983140983145983156983145983151983150
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 5267
I983150983156983137983139983156 C983151983150983140983145983156983145983151983150
991266 M983141983156983137983139983141983150983156983154983145983139 983154983137983140983145983157983155
991266 O983154 983145983156 983139983151983157983148983140 983138983141 983139983137983148983139983157983148983137983156983141983140 983140983145983154983141983139983156983148983161 983137983155
991266 H983141983145983143983144983156 983151983142 983156983144983141 983139983141983150983156983141983154 983151983142 983138983157983151983161983137983150983139983161
m I
BM
I
I 3891
150
33208==
nabla
=
m xT
B
LBT
L B BM
I I
I 3891
5112
5
12
12 223
====
mT
KB I
I 750
2
==
I983150983156983137983139983156 C983151983150983140983145983156983145983151983150
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 5367
991266 983124983144983141 983149983141983156983137983139983141983150983156983154983145983139 983144983141983145983143983144983156
991266 F983151983154 983155983149983137983148983148 983137983150983143983148983141983155 983151983142 983144983141983141983148 983156983144983141 983154983145983143983144983156983145983150983143 983149983151983149983141983150983156
m KG BM KBGM I I 63905013891750 =minus+=minus+=
sin22998sin693075153sin mt x xGM M I I
φ φ φ ==∆=
8162019 Damaged Stability
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8162019 Damaged Stability
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983116983119983123983124 983106983125983119983129983105983118983107983129 983117983109983124983112983119983108
Paralel Sinkage
Volume (DCEF)=Volume (W1ADW+BL1LC)
Damaged compartment is bounded on top
983116983119983123983124 983106983125983119983129983105983118983107983129 983117983109983124983112983119983108
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 5667
983116983119983123983124 983106983125983119983129983105983118983107983129 983117983109983124983112983119983108
bull It is assumed that displacement and location of vertical centre
of gravity does not change after damaged
983116983119983123983124 983106983125983119983129983105983118983107983129 983117983109983124983112983119983108
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 5767
983116983119983123983124 983106983125983119983129983105983118983107983129 983117983109983124983112983119983108
8162019 Damaged Stability
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The heel angle of damaged ship is determined by
where
d is the distance between the volume centre of damaged compartment
and the new longitudinal centre of floatation
wc=vc μ ρ
983116983119983123983124 983106983125983119983129983105983118983107983129 983117983109983124983112983119983108
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 5967
983116983119983123983124 983106983125983119983129983105983118983107983129 983117983109983124983112983119983108
983116983119983123983124 983106983125983119983129983105983118983107983129 983117983109983124983112983119983108
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 6067
Longitudinal Metacentre Height of a Damaged Ship
983116983119983123983124 983106983125983119983129983105983118983107983129 983117983109983124983112983119983108
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 6167
983110983151983154983159983137983154983140 983137983150983140 983137983142983156 983140983154983137983157983143983144983156983155 983137983142983156983141983154 983140983137983149983137983143983141983140
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 6267
983120983151983154983156 983105983142983156 983120983151983154983156 983110983151983154983141 983123983156983137983154983138983151983137983154983140 983105983142983156 983123983156983137983154983138983151983137983154983140 983110983151983154983159983137983154983140
I983150983145983156983145983137983148 D983154983137983157983143983144983156 983124 983124 983124 983124
983120983137983154983137983148983141983148 983123983145983150983147983137983143983141 +983152 +983152 +983152 +983120
H983141983141983148 983085983149983145 983085983149983145 +983149983155 +983149983155
983124983154983145983149 983085983156983147 +983156983138 983085983156983147 +983156983138
F983145983150983137983148 D983154983137983157983143983144983156 983124+983152983085983149983145983085983156983147 983124+983152983085983149983145+983156983138 983124+983152+983149983155983085983156983147 983124+983152+983149983155+983156983138
Table 1 Final Draughts for a starboard side damaged ship
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 6367
L983151983155983156 B983157983151983161983137983150983139983161 M983141983156983144983151983140
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 6467
L983151983155983156 B983157983151983161983137983150983139983161 M983141983156983144983151983140
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 6567
991266 A983142983156983141983154 983148983151983151983155983145983150983143 983156983144983141 983139983141983150983156983154983137983148 983139983151983149983152983137983154983156983149983141983150983156 983156983144983141
983159983137983156983141983154983152983148983137983150983141 983137983154983141983137 983145983155
991266 983124983151 983139983151983149983152983141983150983155983137983156983141 983142983151983154 983156983144983141 983148983151983155983155 983151983142 983138983157983151983161983137983150983139983161 983151983142 983156983144983141
983139983141983150983156983154983137983148 983139983151983149983152983137983154983156983149983141983150983156 983156983144983141 983140983154983137983142983156 983145983150983139983154983141983137983155983141983155 983156983151
2805)420()( m x Bl L A L
=minus=minus=
m A
T
L
I
L 875180
150==
nabla=
L983151983155983156 B983157983151983161983137983150983139983161 M983141983156983144983151983140
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 6667
991266 983124983144983141 983144983141983145983143983144983156 983151983142 983156983144983141 983139983141983150983156983141983154 983151983142 983138983157983151983161983137983150983139983161 983145983150983139983154983141983137983155983141983155 983156983151
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991266 983124983144983141 983149983141983156983137983139983141983150983156983154983145983139 983154983137983140983145983157983155
m
T
KB L
L 93802
8751
2 ===
433
6716612
)420(5
12
)(m
l L B I L
=minus
=minus
=
m I
BM
I
L
L 1111150
67166==
nabla
=
L983151983155983156 B983157983151983161983137983150983139983161 M983141983156983144983151983140
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 6767
991266 983124983144983141 983149983141983156983137983139983141983150983156983154983145983139 983144983141983145983143983144983156
991266 983122983145983143983144983156983145983150983143 983149983151983149983141983150983156 983142983151983154 983155983149983137983148983148 983144983141983141983148 983137983150983143983148983141983155
m KG BM KBGM L L L 54905111119380 =minus+=minus+=
mt xGM M L
sin34984sin549075153sin φ φ φ ==∆=
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 1667
983123983157983154983142983137983139983141 983120983141983154983149983141983137983138983145983148983145983156983161 μ983137
Surface permability is the percentage of a waterplane that can be
occupied by water
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 1767
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 1867
A cargo hold with dimensions of l = 1524m w = 914 m
h=61 m is completely flooded Determine the volume of the
space and the corrected flooded volume
Volume = 1524 m x 914 m x 61 m = 8497 m3
Flooded volume = Volume x permeability
Flooded volume = 8497 m3 x 60
Flooded volume = 5098 m3
Example 1
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 1967
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983155983144983145983152 983138983141983161983151983150983140 983149983137983154983143983145983150 983148983145983150983141
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8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 2067
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983140983145983142983142983141983154983141983150983156 983152983151983145983150983156983155 983137983148983151983150983143 983156983144983141 983155983144983145983152 983148983141983150983143983156983144
983129983137983154983137983148ı 983106983286983148983149983141 983106983151983161983157 983109ğ983154983145983155983145983098 G983141983149983145 983138983151983161983157983150983139983137 983140983141ğ983145ş983145983147 983150983151983147983156983137983148983137983154983140983137 983144983141983155983137983152983148983137983150983137983150 983161983137983154983137983148ı
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8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 2167
983110983137983139983156983151983154 983151983142 983123983157983138983140983145983158983145983155983145983151983150
F983137983139983156983151983154 983151983142 983123983157983138983140983145983158983145983155983145983151983150 983124983144983141 983142983137983139983156983151983154 983151983142 983155983157983138983140983145983158983145983155983145983151983150 983145983155 983137 983142983137983139983156983151983154 983152983154983141983155983139983154983145983138983141983140
983138983161 983156983144983141 983137983152983152983148983145983139983137983138983148983141 983154983141983143983157983148983137983156983145983151983150983155 983137983150983140 983138983161 983145983150983156983141983154983150983137983156983145983151983150983137983148 983139983151983150983158983141983150983156983145983151983150 983156983144983137983156
983140983141983152983141983150983140983155 983151983150 983155983144983145983152 983148983141983150983143983156983144 983137983150983140 983139983154983145983156983141983154983145983151983150 983151983142 983155983141983154983158983145983139983141
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 2267
983120983141983154983149983145983155983155983145983138983148983141 983116983141983150983143983156983144
983120983141983154983149983145983155983155983145983138983148983141 L983141983150983143983156983144 983145983155 983151983138983156983137983145983150983141983140 983138983161 983149983157983148983156983145983152983148983161983145983150983143 983156983144983141 983142983148983151983151983140983137983138983148983141 983148983141983150983143983156983144 983137983156
983156983144983137983156 983152983151983145983150983156 983138983161 983156983144983141 983142983137983139983156983151983154 983151983142 983155983157983138983140983145983158983145983155983145983151983150
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 2367
D983141983156983141983154983149983145983150983137983156983145983151983150 983151983142 983156983144983141 983148983151983139983137983156983145983151983150 983151983142 983156983144983141 983158983151983148983157983149983141 983139983141983150983156983154983141 983151983142
983140983137983149983137983143983141983140 983139983151983149983152983137983154983156983149983141983150983156
Δ I983150983145983156983145983137983148 983140983145983155983152983148983137983139983141983149983141983150983156 Δ1 D983145983155983152983148983137983139983141983149983141983150983156 983137983142983156983141983154 983140983137983149983137983143983141983140
B I983150983145983156983145983137983148 983139983141983150983156983154983141 983151983142 983138983157983151983161983137983150983139983161
G I983150983145983156983145983137983148 983139983141983150983156983154983141 983151983142 9831439831549831379831589831459831569831619831600 I983150983145983156983145983137983148 983139983141983150983156983154983141 983151983142 983148983151983150983143983145983156983157983140983145983150983137983148 983138983157983151983161983137983150983139983161 LCB
983158983159 983124983144983141 983158983151983148983157983149983141 983151983142 983159983137983156983141983154 983141983150983156983141983154983145983150983143 983156983144983141 983158983141983155983155983141983148
983160983159 D983145983155983156983137983150983139983141 983151983142 983158983151983148983157983149983141 983139983141983150983156983154983141 983151983142 983140983137983149983137983143983141983140 983139983151983149983152983137983154983156983149983141983150983156 983142983154983151983149 983149983137983141983155983156983151983154983161
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 2467
D983141983156983141983154983149983145983150983137983156983145983151983150 983151983142 983156983144983141 983148983151983139983137983156983145983151983150 983151983142 983156983144983141 983158983151983148983157983149983141 983139983141983150983156983154983141 983151983142
983140983137983149983137983143983141983140 983139983151983149983152983137983154983156983149983141983150983156
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 2567
D983141983156983141983154983149983145983150983137983156983145983151983150 983151983142 983156983144983141 983158983151983148983157983149983141 983151983142 983159983137983156983141983154 983141983150983156983141983154983145983150983143 983156983144983141 983158983141983155983155983141983148
Initial displacement and longitudinal centre of buoyancy (LCB) can be read from hydrostatcic curves
However displacement and LCB are unknown after damaged
Therefore if trim forward and aft draught are known trimmed waterline can be drawn over Bonjean
area curves
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 2667
983108983141983156983141983154983149983145983150983137983156983145983151983150 983151983142 983140983137983149983137983143983141983140 983148983141983150983143983156983144 983137983150983140 983148983151983139983137983156983145983151983150 983151983142 983149983145983140
983151983142 983139983151983149983152983137983154983156983149983141983150983156
vw The volume of water entering the vessel
xw Distance of volume centre of damaged compartment from maestory
micro Permability of the compartment
v0 Volume of the compartment
xm Distance of the volume centre of the compartment to the mid of damaged length
xl Distance of the mid of damaged length of compartment to maestory
xc Distance of the computed volume centre of compartment to maestory (xc=xl-xm)
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 2767
983108983141983156983141983154983149983145983150983137983156983145983151983150 983151983142 983140983137983149983137983143983141983140 983148983141983150983143983156983144 983137983150983140 983148983151983139983137983156983145983151983150 983151983142 983149983145983140
983151983142 983139983151983149983152983137983154983156983149983141983150983156
Damaged length and location of compartment can be determined by iterative
procedure
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 2867
bull The volume of water entering the vessel (vw)
bull Distance of volume centre of damaged compartment from amidships Θ ( xw)
bull Volume of the compartment (v0
= vw
μ)
First trial
1) Assume xm=0 (xl=xw)
2) Damaged Length l1 = (Volume of the compartment v0) (mean sec Area Amean)
where Amean is determined from trimmed sectional area curve
983108983141983156983141983154983149983145983150983137983156983145983151983150 983151983142 983140983137983149983137983143983141983140 983148983141983150983143983156983144 983137983150983140 983148983151983139983137983156983145983151983150 983151983142 983149983145983140
983151983142 983139983151983149983152983137983154983156983149983141983150983156
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 2967
3) In order to determine vm and xm
s = l1 4
vm = (s 3) sum3
xm = s sum4 sum3
xc = xl ndash xm
|vm-v0| le Tolarence for volume
|xc-xw| le Tolarence for location of volume centre
l=l1 xl=xw
983108983141983156983141983154983149983145983150983137983156983145983151983150 983151983142 983140983137983149983137983143983141983140 983148983141983150983143983156983144 983137983150983140 983148983151983139983137983156983145983151983150 983151983142 983149983145983140
983151983142 983139983151983149983152983137983154983156983149983141983150983156
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 3067
983108983141983156983141983154983149983145983150983137983156983145983151983150 983151983142 983140983137983149983137983143983141983140 983148983141983150983143983156983144 983137983150983140 983148983151983139983137983156983145983151983150 983151983142 983149983145983140
983151983142 983139983151983149983152983137983154983156983149983141983150983156Second Trial
Damaged length is changed proportionally by the volume
l2 = l1 times (v0v
m)
vm Computed volume at first trial
If the value of xm computed at first trial is negative then the mid of the
compartment slides to the bow
xl = xw+xm
where xm is the distance of the volume centre of compartment to amidship
computed at first trial
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 3167
In order to determine vm and xm
983108983141983156983141983154983149983145983150983137983156983145983151983150 983151983142 983140983137983149983137983143983141983140 983148983141983150983143983156983144 983137983150983140 983148983151983139983137983156983145983151983150 983151983142 983149983145983140
983151983142 983139983151983149983152983137983154983156983149983141983150983156
s = l2 4
vm = (s 3) sum3
xm = s sum4 sum3
xc = xl ndash xm
|vm-v0| le Tolarence for volume
|xc-xw| le Tolarence for location of volume centre
l=l2
If tolarances for both volume and location are not satisfied third fourthtrials are made similar to
second trial
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 3267
If either tolarence for volume or tolarance for location are satisfied at a trial
satisfied one is fixed trials are continued to make for the other one
983108983141983156983141983154983149983145983150983137983156983145983151983150 983151983142 983140983137983149983137983143983141983140 983148983141983150983143983156983144 983137983150983140 983148983151983139983137983156983145983151983150 983151983142 983149983145983140
983151983142 983139983151983149983152983137983154983156983149983141983150983156
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 3367
A ship is 116 meter long and displaces 7842 ton in salt water (ρ1=1025 tm3)
when her mean draught is 64m Longitudinal Centre of Buoyancy (LCB) is
0615 m aft from amidships After one of her stern compartment is damaged
she floats trimmed to the aft Her sectional areas after damaged are given in the
following table
a) Determine the volume of water entering the vessel (vw) and the location of
volume centre of damaged compartment (xw)
b) Assume permability of compartment micro is 1 Determine damaged length
and Distance of the mid of damaged length of compartment to amidship
983109983160983137983149983152983148983141 2
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 3467
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 3567
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 3667
Predicted xw
is between section 2 and section 3
983123983141983139 N983151 983123983141983139 A983154983141983137 D983145983155983156 A9831499831459831559831449831459831522 10135 983085348
3 1208 983085232
983123983141983139 A983154983141983137 983137983156 98308524983149 983142983154983151983149 983137983149983145983140983155983144983145983152 = 11959831492
l1=v0Amean=204081195=17078 m
s=l14=427 m
983109983160983137983149983152983148983141 2983085983123983119983116983125983124983113983119983118
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 3767
983161983145 L983151983139 A983149983141983137983150 983123M M A983154983149
9831311983133 9831312983133 98313119831339832559831312983133 9831313983133 983131198313398325598313129831339832559831313983133
0 9830853254 1051 1 1051 2 21021 9830852827 1123 4 4492 1 4492
2 98308524 1195 2 239 0 0
3 9830851973 1219 4 4876 9830851 9830854876
4 9830851546 1233 1 1233 9830852 9830852466
sum983091983101 14042 sum983092983101 983085748
vm
= (s3) sum3= 199864479831493
xm
=s sum4sum3= 9830850227983149
v0-vm=20408-19986=422 m3
Error=422times10020408=207
983109983160983137983149983152983148983141 2983085983123983119983116983125983124983113983119983118
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 3867
Methods of Calculation
There two available method calculating the
final stage of the damaged vessel
bull Lost Buoyancy Method
bull Added Weight Method
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 3967
Comparision of Lost Buoyancy and Added
Weight Methods
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 4067
Consider a vessel that has been damaged such
that a portion of the bottom is now open to the
sea
The vesselrsquos draft will increase because an amount
of the buoyancy was lost
Added Weight Method
Added Weight Method
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 4167
Added Weight Method
In this method flood water is treated as a fixed weight (for example the
weight of water of volume ABEF) This added weight is balanced by the
additional buoyant force of the layer WL1WL
The added weight can be determined by either the volume ABEF or
waterline WL1 Therefore WL1 waterline is not known can be just guessed
For the predicted waterline added weight and additional buoyant force
caculation are done iteratively until both of them are equal This method is
known as Added weight method
Determination of Added Weight
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 4267
Determination of Added Weight
vc Volume of damaged compartment (DCEF)
ac The surface area (AB) of damaged compartment on the waterline
micro The volume permability of damaged compartment
microa The area permability of the surface of damaged compartment
∆ The initial displacement
∆1 The displacement at final stage
vw The volume of water entering the vessel (ABEH)
w The weight of water entering the vessel
p The value of parallel sinkage
If th t th l l i k i h f t l f
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 4367
If we assume that the paralel sinkage cause a minor change of water plane area of a
ship (Awp
asymp Awp1
) we can determine the paralel sinkage by equating the volume of
the layer WL1WL to the volume of ABEF
If the damaged compartment is bounded on top
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 4467
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 4567
Longitudinal Metacentre Radius at final stage
Free Surface Effect
Damaged compartment can be considered as a half filled tank
Free Contact Effect
Damaged compartment can be considered as a half filled tank
T M H i h
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 4667
Transverse Metacentre Height
The angle of heel
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 4767
L it di l M t t H i ht
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 4867
Longitudinal Metacentre Height
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 4967
E983160983137983149983152983148983141 A 983138983137983154983143983141
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 5067
E983160983137983149983152983148983141 A 983138983137983154983143983141
991266 L = 20 983149991266 B = 5 983149
991266 983124 = 15 983149
991266 KG = 15 983149
I983150983156983137983139983156 C983151983150983140983145983156983145983151983150
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 5167
I983150983156983137983139983156 C983151983150983140983145983156983145983151983150
991266 983124983144983141 983140983145983155983152983148983137983139983141983149983141983150983156 983158983151983148983157983149983141
991266 983124983144983141 983149983137983155983155 983140983145983155983152983148983137983139983141983149983141983150983156
991266 983124983144983141 983149983151983149983141983150983156 983151983142 983145983150983141983154983156983145983137 983151983142 983156983144983141 983159983137983156983141983154983152983148983137983150983141 983137983154983141983137983137983138983151983157983156 CL
3
15051520 m x xT B L
I I
==sdotsdot=nabla
tons x I
751531500251 ==nablasdot=∆ ρ
433
33208
12
205
12
m x L B
I I
===
I983150983156983137983139983156 C983151983150983140983145983156983145983151983150
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 5267
I983150983156983137983139983156 C983151983150983140983145983156983145983151983150
991266 M983141983156983137983139983141983150983156983154983145983139 983154983137983140983145983157983155
991266 O983154 983145983156 983139983151983157983148983140 983138983141 983139983137983148983139983157983148983137983156983141983140 983140983145983154983141983139983156983148983161 983137983155
991266 H983141983145983143983144983156 983151983142 983156983144983141 983139983141983150983156983141983154 983151983142 983138983157983151983161983137983150983139983161
m I
BM
I
I 3891
150
33208==
nabla
=
m xT
B
LBT
L B BM
I I
I 3891
5112
5
12
12 223
====
mT
KB I
I 750
2
==
I983150983156983137983139983156 C983151983150983140983145983156983145983151983150
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 5367
991266 983124983144983141 983149983141983156983137983139983141983150983156983154983145983139 983144983141983145983143983144983156
991266 F983151983154 983155983149983137983148983148 983137983150983143983148983141983155 983151983142 983144983141983141983148 983156983144983141 983154983145983143983144983156983145983150983143 983149983151983149983141983150983156
m KG BM KBGM I I 63905013891750 =minus+=minus+=
sin22998sin693075153sin mt x xGM M I I
φ φ φ ==∆=
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 5467
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 5567
983116983119983123983124 983106983125983119983129983105983118983107983129 983117983109983124983112983119983108
Paralel Sinkage
Volume (DCEF)=Volume (W1ADW+BL1LC)
Damaged compartment is bounded on top
983116983119983123983124 983106983125983119983129983105983118983107983129 983117983109983124983112983119983108
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 5667
983116983119983123983124 983106983125983119983129983105983118983107983129 983117983109983124983112983119983108
bull It is assumed that displacement and location of vertical centre
of gravity does not change after damaged
983116983119983123983124 983106983125983119983129983105983118983107983129 983117983109983124983112983119983108
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 5767
983116983119983123983124 983106983125983119983129983105983118983107983129 983117983109983124983112983119983108
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 5867
The heel angle of damaged ship is determined by
where
d is the distance between the volume centre of damaged compartment
and the new longitudinal centre of floatation
wc=vc μ ρ
983116983119983123983124 983106983125983119983129983105983118983107983129 983117983109983124983112983119983108
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 5967
983116983119983123983124 983106983125983119983129983105983118983107983129 983117983109983124983112983119983108
983116983119983123983124 983106983125983119983129983105983118983107983129 983117983109983124983112983119983108
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 6067
Longitudinal Metacentre Height of a Damaged Ship
983116983119983123983124 983106983125983119983129983105983118983107983129 983117983109983124983112983119983108
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 6167
983110983151983154983159983137983154983140 983137983150983140 983137983142983156 983140983154983137983157983143983144983156983155 983137983142983156983141983154 983140983137983149983137983143983141983140
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 6267
983120983151983154983156 983105983142983156 983120983151983154983156 983110983151983154983141 983123983156983137983154983138983151983137983154983140 983105983142983156 983123983156983137983154983138983151983137983154983140 983110983151983154983159983137983154983140
I983150983145983156983145983137983148 D983154983137983157983143983144983156 983124 983124 983124 983124
983120983137983154983137983148983141983148 983123983145983150983147983137983143983141 +983152 +983152 +983152 +983120
H983141983141983148 983085983149983145 983085983149983145 +983149983155 +983149983155
983124983154983145983149 983085983156983147 +983156983138 983085983156983147 +983156983138
F983145983150983137983148 D983154983137983157983143983144983156 983124+983152983085983149983145983085983156983147 983124+983152983085983149983145+983156983138 983124+983152+983149983155983085983156983147 983124+983152+983149983155+983156983138
Table 1 Final Draughts for a starboard side damaged ship
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 6367
L983151983155983156 B983157983151983161983137983150983139983161 M983141983156983144983151983140
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 6467
L983151983155983156 B983157983151983161983137983150983139983161 M983141983156983144983151983140
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 6567
991266 A983142983156983141983154 983148983151983151983155983145983150983143 983156983144983141 983139983141983150983156983154983137983148 983139983151983149983152983137983154983156983149983141983150983156 983156983144983141
983159983137983156983141983154983152983148983137983150983141 983137983154983141983137 983145983155
991266 983124983151 983139983151983149983152983141983150983155983137983156983141 983142983151983154 983156983144983141 983148983151983155983155 983151983142 983138983157983151983161983137983150983139983161 983151983142 983156983144983141
983139983141983150983156983154983137983148 983139983151983149983152983137983154983156983149983141983150983156 983156983144983141 983140983154983137983142983156 983145983150983139983154983141983137983155983141983155 983156983151
2805)420()( m x Bl L A L
=minus=minus=
m A
T
L
I
L 875180
150==
nabla=
L983151983155983156 B983157983151983161983137983150983139983161 M983141983156983144983151983140
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 6667
991266 983124983144983141 983144983141983145983143983144983156 983151983142 983156983144983141 983139983141983150983156983141983154 983151983142 983138983157983151983161983137983150983139983161 983145983150983139983154983141983137983155983141983155 983156983151
991266 983124983144983141 983149983151983149983141983150983156 983151983142 983145983150983141983154983156983145983137 983151983142 983156983144983141 983159983137983156983141983154983152983148983137983150983141 983137983154983141983137
991266 983124983144983141 983149983141983156983137983139983141983150983156983154983145983139 983154983137983140983145983157983155
m
T
KB L
L 93802
8751
2 ===
433
6716612
)420(5
12
)(m
l L B I L
=minus
=minus
=
m I
BM
I
L
L 1111150
67166==
nabla
=
L983151983155983156 B983157983151983161983137983150983139983161 M983141983156983144983151983140
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 6767
991266 983124983144983141 983149983141983156983137983139983141983150983156983154983145983139 983144983141983145983143983144983156
991266 983122983145983143983144983156983145983150983143 983149983151983149983141983150983156 983142983151983154 983155983149983137983148983148 983144983141983141983148 983137983150983143983148983141983155
m KG BM KBGM L L L 54905111119380 =minus+=minus+=
mt xGM M L
sin34984sin549075153sin φ φ φ ==∆=
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 1767
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 1867
A cargo hold with dimensions of l = 1524m w = 914 m
h=61 m is completely flooded Determine the volume of the
space and the corrected flooded volume
Volume = 1524 m x 914 m x 61 m = 8497 m3
Flooded volume = Volume x permeability
Flooded volume = 8497 m3 x 60
Flooded volume = 5098 m3
Example 1
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 1967
983110983148983151983151983140983137983138983148983141 983116983141983150983143983156983144
983110983148983151983151983140983137983138983148983141 983148983141983150983143983156983144983098 983137983156 983137 983143983145983158983141983150 983152983151983145983150983156 983151983142 983156983144983141 983155983144983145983152 983148983141983150983143983156983144 983145983155 983156983144983141 983149983137983160983145983149983157983149 983148983141983150983143983156983144
983159983145983156983144 983156983144983141 983139983141983150983156983141983154 983137983156 983156983144983137983156 983152983151983145983150983156 983156983144983137983156 983139983137983150 983138983141 983142983148983151983151983140983141983140 983159983145983156983144983151983157983156 983155983157983138983149983141983154983143983145983150983143 983156983144983141
983155983144983145983152 983138983141983161983151983150983140 983149983137983154983143983145983150 983148983145983150983141
983129983137983154983137983148ı 983106983286983148983149983141 983106983151983161983157983098 G983141983149983145 983138983151983161983157983150983139983137 983144983141983154983144983137983150983143983145 983138983145983154 983150983151983147983156983137983140983137 983138983157 983150983151983147983156983137 983149983141983154983147983141983162
983151983148983149983137983147 983292983162983141983154983141 983143983141983149983145983161983145 983155ı983150ı983154 983144983137983156983156ı983150983137 983156983141ğ983141983156 983144983137983148983141 983143983141983156983145983154983141983139983141983147 983141983150 983138983292983161983292983147 983138983286983148983149983141 983138983151983161983157983150983137
983151 983150983151983147983156983137983140983137983147983145 983161983137983154983137983148ı 983138983286983148983149983141 983138983151983161983157 983140983141983150983145983154
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 2067
983110983148983151983151983140983137983138983148983141 983116983141983150983143983156983144 983107983157983154983158983141
983110983148983151983151983140983137983138983148983141 983116983141983150983143983156983144 983107983157983154983158983141983098 I983156 983145983155 983151983138983156983137983145983150983141983140 983138983161 983156983144983141 983139983151983150983150983141983139983156983145983151983150 983151983142 983142983148983151983151983140983137983138983148983141 983148983141983150983143983156983144983155 983137983156
983140983145983142983142983141983154983141983150983156 983152983151983145983150983156983155 983137983148983151983150983143 983156983144983141 983155983144983145983152 983148983141983150983143983156983144
983129983137983154983137983148ı 983106983286983148983149983141 983106983151983161983157 983109ğ983154983145983155983145983098 G983141983149983145 983138983151983161983157983150983139983137 983140983141ğ983145ş983145983147 983150983151983147983156983137983148983137983154983140983137 983144983141983155983137983152983148983137983150983137983150 983161983137983154983137983148ı
983138983286983148983149983141 983138983151983161983157 983140983141ğ983141983154983148983141983154983145983150983145983150 983138983145983154983148983141ş983156983145983154983145983148983149983141983155983145 983145983148983141 983141983148983140983141 983141983140983145983148983145983154
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 2167
983110983137983139983156983151983154 983151983142 983123983157983138983140983145983158983145983155983145983151983150
F983137983139983156983151983154 983151983142 983123983157983138983140983145983158983145983155983145983151983150 983124983144983141 983142983137983139983156983151983154 983151983142 983155983157983138983140983145983158983145983155983145983151983150 983145983155 983137 983142983137983139983156983151983154 983152983154983141983155983139983154983145983138983141983140
983138983161 983156983144983141 983137983152983152983148983145983139983137983138983148983141 983154983141983143983157983148983137983156983145983151983150983155 983137983150983140 983138983161 983145983150983156983141983154983150983137983156983145983151983150983137983148 983139983151983150983158983141983150983156983145983151983150 983156983144983137983156
983140983141983152983141983150983140983155 983151983150 983155983144983145983152 983148983141983150983143983156983144 983137983150983140 983139983154983145983156983141983154983145983151983150 983151983142 983155983141983154983158983145983139983141
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 2267
983120983141983154983149983145983155983155983145983138983148983141 983116983141983150983143983156983144
983120983141983154983149983145983155983155983145983138983148983141 L983141983150983143983156983144 983145983155 983151983138983156983137983145983150983141983140 983138983161 983149983157983148983156983145983152983148983161983145983150983143 983156983144983141 983142983148983151983151983140983137983138983148983141 983148983141983150983143983156983144 983137983156
983156983144983137983156 983152983151983145983150983156 983138983161 983156983144983141 983142983137983139983156983151983154 983151983142 983155983157983138983140983145983158983145983155983145983151983150
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 2367
D983141983156983141983154983149983145983150983137983156983145983151983150 983151983142 983156983144983141 983148983151983139983137983156983145983151983150 983151983142 983156983144983141 983158983151983148983157983149983141 983139983141983150983156983154983141 983151983142
983140983137983149983137983143983141983140 983139983151983149983152983137983154983156983149983141983150983156
Δ I983150983145983156983145983137983148 983140983145983155983152983148983137983139983141983149983141983150983156 Δ1 D983145983155983152983148983137983139983141983149983141983150983156 983137983142983156983141983154 983140983137983149983137983143983141983140
B I983150983145983156983145983137983148 983139983141983150983156983154983141 983151983142 983138983157983151983161983137983150983139983161
G I983150983145983156983145983137983148 983139983141983150983156983154983141 983151983142 9831439831549831379831589831459831569831619831600 I983150983145983156983145983137983148 983139983141983150983156983154983141 983151983142 983148983151983150983143983145983156983157983140983145983150983137983148 983138983157983151983161983137983150983139983161 LCB
983158983159 983124983144983141 983158983151983148983157983149983141 983151983142 983159983137983156983141983154 983141983150983156983141983154983145983150983143 983156983144983141 983158983141983155983155983141983148
983160983159 D983145983155983156983137983150983139983141 983151983142 983158983151983148983157983149983141 983139983141983150983156983154983141 983151983142 983140983137983149983137983143983141983140 983139983151983149983152983137983154983156983149983141983150983156 983142983154983151983149 983149983137983141983155983156983151983154983161
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 2467
D983141983156983141983154983149983145983150983137983156983145983151983150 983151983142 983156983144983141 983148983151983139983137983156983145983151983150 983151983142 983156983144983141 983158983151983148983157983149983141 983139983141983150983156983154983141 983151983142
983140983137983149983137983143983141983140 983139983151983149983152983137983154983156983149983141983150983156
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 2567
D983141983156983141983154983149983145983150983137983156983145983151983150 983151983142 983156983144983141 983158983151983148983157983149983141 983151983142 983159983137983156983141983154 983141983150983156983141983154983145983150983143 983156983144983141 983158983141983155983155983141983148
Initial displacement and longitudinal centre of buoyancy (LCB) can be read from hydrostatcic curves
However displacement and LCB are unknown after damaged
Therefore if trim forward and aft draught are known trimmed waterline can be drawn over Bonjean
area curves
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 2667
983108983141983156983141983154983149983145983150983137983156983145983151983150 983151983142 983140983137983149983137983143983141983140 983148983141983150983143983156983144 983137983150983140 983148983151983139983137983156983145983151983150 983151983142 983149983145983140
983151983142 983139983151983149983152983137983154983156983149983141983150983156
vw The volume of water entering the vessel
xw Distance of volume centre of damaged compartment from maestory
micro Permability of the compartment
v0 Volume of the compartment
xm Distance of the volume centre of the compartment to the mid of damaged length
xl Distance of the mid of damaged length of compartment to maestory
xc Distance of the computed volume centre of compartment to maestory (xc=xl-xm)
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 2767
983108983141983156983141983154983149983145983150983137983156983145983151983150 983151983142 983140983137983149983137983143983141983140 983148983141983150983143983156983144 983137983150983140 983148983151983139983137983156983145983151983150 983151983142 983149983145983140
983151983142 983139983151983149983152983137983154983156983149983141983150983156
Damaged length and location of compartment can be determined by iterative
procedure
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 2867
bull The volume of water entering the vessel (vw)
bull Distance of volume centre of damaged compartment from amidships Θ ( xw)
bull Volume of the compartment (v0
= vw
μ)
First trial
1) Assume xm=0 (xl=xw)
2) Damaged Length l1 = (Volume of the compartment v0) (mean sec Area Amean)
where Amean is determined from trimmed sectional area curve
983108983141983156983141983154983149983145983150983137983156983145983151983150 983151983142 983140983137983149983137983143983141983140 983148983141983150983143983156983144 983137983150983140 983148983151983139983137983156983145983151983150 983151983142 983149983145983140
983151983142 983139983151983149983152983137983154983156983149983141983150983156
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 2967
3) In order to determine vm and xm
s = l1 4
vm = (s 3) sum3
xm = s sum4 sum3
xc = xl ndash xm
|vm-v0| le Tolarence for volume
|xc-xw| le Tolarence for location of volume centre
l=l1 xl=xw
983108983141983156983141983154983149983145983150983137983156983145983151983150 983151983142 983140983137983149983137983143983141983140 983148983141983150983143983156983144 983137983150983140 983148983151983139983137983156983145983151983150 983151983142 983149983145983140
983151983142 983139983151983149983152983137983154983156983149983141983150983156
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 3067
983108983141983156983141983154983149983145983150983137983156983145983151983150 983151983142 983140983137983149983137983143983141983140 983148983141983150983143983156983144 983137983150983140 983148983151983139983137983156983145983151983150 983151983142 983149983145983140
983151983142 983139983151983149983152983137983154983156983149983141983150983156Second Trial
Damaged length is changed proportionally by the volume
l2 = l1 times (v0v
m)
vm Computed volume at first trial
If the value of xm computed at first trial is negative then the mid of the
compartment slides to the bow
xl = xw+xm
where xm is the distance of the volume centre of compartment to amidship
computed at first trial
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 3167
In order to determine vm and xm
983108983141983156983141983154983149983145983150983137983156983145983151983150 983151983142 983140983137983149983137983143983141983140 983148983141983150983143983156983144 983137983150983140 983148983151983139983137983156983145983151983150 983151983142 983149983145983140
983151983142 983139983151983149983152983137983154983156983149983141983150983156
s = l2 4
vm = (s 3) sum3
xm = s sum4 sum3
xc = xl ndash xm
|vm-v0| le Tolarence for volume
|xc-xw| le Tolarence for location of volume centre
l=l2
If tolarances for both volume and location are not satisfied third fourthtrials are made similar to
second trial
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 3267
If either tolarence for volume or tolarance for location are satisfied at a trial
satisfied one is fixed trials are continued to make for the other one
983108983141983156983141983154983149983145983150983137983156983145983151983150 983151983142 983140983137983149983137983143983141983140 983148983141983150983143983156983144 983137983150983140 983148983151983139983137983156983145983151983150 983151983142 983149983145983140
983151983142 983139983151983149983152983137983154983156983149983141983150983156
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 3367
A ship is 116 meter long and displaces 7842 ton in salt water (ρ1=1025 tm3)
when her mean draught is 64m Longitudinal Centre of Buoyancy (LCB) is
0615 m aft from amidships After one of her stern compartment is damaged
she floats trimmed to the aft Her sectional areas after damaged are given in the
following table
a) Determine the volume of water entering the vessel (vw) and the location of
volume centre of damaged compartment (xw)
b) Assume permability of compartment micro is 1 Determine damaged length
and Distance of the mid of damaged length of compartment to amidship
983109983160983137983149983152983148983141 2
8162019 Damaged Stability
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8162019 Damaged Stability
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8162019 Damaged Stability
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Predicted xw
is between section 2 and section 3
983123983141983139 N983151 983123983141983139 A983154983141983137 D983145983155983156 A9831499831459831559831449831459831522 10135 983085348
3 1208 983085232
983123983141983139 A983154983141983137 983137983156 98308524983149 983142983154983151983149 983137983149983145983140983155983144983145983152 = 11959831492
l1=v0Amean=204081195=17078 m
s=l14=427 m
983109983160983137983149983152983148983141 2983085983123983119983116983125983124983113983119983118
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 3767
983161983145 L983151983139 A983149983141983137983150 983123M M A983154983149
9831311983133 9831312983133 98313119831339832559831312983133 9831313983133 983131198313398325598313129831339832559831313983133
0 9830853254 1051 1 1051 2 21021 9830852827 1123 4 4492 1 4492
2 98308524 1195 2 239 0 0
3 9830851973 1219 4 4876 9830851 9830854876
4 9830851546 1233 1 1233 9830852 9830852466
sum983091983101 14042 sum983092983101 983085748
vm
= (s3) sum3= 199864479831493
xm
=s sum4sum3= 9830850227983149
v0-vm=20408-19986=422 m3
Error=422times10020408=207
983109983160983137983149983152983148983141 2983085983123983119983116983125983124983113983119983118
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 3867
Methods of Calculation
There two available method calculating the
final stage of the damaged vessel
bull Lost Buoyancy Method
bull Added Weight Method
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 3967
Comparision of Lost Buoyancy and Added
Weight Methods
8162019 Damaged Stability
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Consider a vessel that has been damaged such
that a portion of the bottom is now open to the
sea
The vesselrsquos draft will increase because an amount
of the buoyancy was lost
Added Weight Method
Added Weight Method
8162019 Damaged Stability
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Added Weight Method
In this method flood water is treated as a fixed weight (for example the
weight of water of volume ABEF) This added weight is balanced by the
additional buoyant force of the layer WL1WL
The added weight can be determined by either the volume ABEF or
waterline WL1 Therefore WL1 waterline is not known can be just guessed
For the predicted waterline added weight and additional buoyant force
caculation are done iteratively until both of them are equal This method is
known as Added weight method
Determination of Added Weight
8162019 Damaged Stability
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Determination of Added Weight
vc Volume of damaged compartment (DCEF)
ac The surface area (AB) of damaged compartment on the waterline
micro The volume permability of damaged compartment
microa The area permability of the surface of damaged compartment
∆ The initial displacement
∆1 The displacement at final stage
vw The volume of water entering the vessel (ABEH)
w The weight of water entering the vessel
p The value of parallel sinkage
If th t th l l i k i h f t l f
8162019 Damaged Stability
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If we assume that the paralel sinkage cause a minor change of water plane area of a
ship (Awp
asymp Awp1
) we can determine the paralel sinkage by equating the volume of
the layer WL1WL to the volume of ABEF
If the damaged compartment is bounded on top
8162019 Damaged Stability
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8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 4567
Longitudinal Metacentre Radius at final stage
Free Surface Effect
Damaged compartment can be considered as a half filled tank
Free Contact Effect
Damaged compartment can be considered as a half filled tank
T M H i h
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 4667
Transverse Metacentre Height
The angle of heel
8162019 Damaged Stability
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L it di l M t t H i ht
8162019 Damaged Stability
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Longitudinal Metacentre Height
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 4967
E983160983137983149983152983148983141 A 983138983137983154983143983141
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 5067
E983160983137983149983152983148983141 A 983138983137983154983143983141
991266 L = 20 983149991266 B = 5 983149
991266 983124 = 15 983149
991266 KG = 15 983149
I983150983156983137983139983156 C983151983150983140983145983156983145983151983150
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 5167
I983150983156983137983139983156 C983151983150983140983145983156983145983151983150
991266 983124983144983141 983140983145983155983152983148983137983139983141983149983141983150983156 983158983151983148983157983149983141
991266 983124983144983141 983149983137983155983155 983140983145983155983152983148983137983139983141983149983141983150983156
991266 983124983144983141 983149983151983149983141983150983156 983151983142 983145983150983141983154983156983145983137 983151983142 983156983144983141 983159983137983156983141983154983152983148983137983150983141 983137983154983141983137983137983138983151983157983156 CL
3
15051520 m x xT B L
I I
==sdotsdot=nabla
tons x I
751531500251 ==nablasdot=∆ ρ
433
33208
12
205
12
m x L B
I I
===
I983150983156983137983139983156 C983151983150983140983145983156983145983151983150
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 5267
I983150983156983137983139983156 C983151983150983140983145983156983145983151983150
991266 M983141983156983137983139983141983150983156983154983145983139 983154983137983140983145983157983155
991266 O983154 983145983156 983139983151983157983148983140 983138983141 983139983137983148983139983157983148983137983156983141983140 983140983145983154983141983139983156983148983161 983137983155
991266 H983141983145983143983144983156 983151983142 983156983144983141 983139983141983150983156983141983154 983151983142 983138983157983151983161983137983150983139983161
m I
BM
I
I 3891
150
33208==
nabla
=
m xT
B
LBT
L B BM
I I
I 3891
5112
5
12
12 223
====
mT
KB I
I 750
2
==
I983150983156983137983139983156 C983151983150983140983145983156983145983151983150
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 5367
991266 983124983144983141 983149983141983156983137983139983141983150983156983154983145983139 983144983141983145983143983144983156
991266 F983151983154 983155983149983137983148983148 983137983150983143983148983141983155 983151983142 983144983141983141983148 983156983144983141 983154983145983143983144983156983145983150983143 983149983151983149983141983150983156
m KG BM KBGM I I 63905013891750 =minus+=minus+=
sin22998sin693075153sin mt x xGM M I I
φ φ φ ==∆=
8162019 Damaged Stability
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8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 5567
983116983119983123983124 983106983125983119983129983105983118983107983129 983117983109983124983112983119983108
Paralel Sinkage
Volume (DCEF)=Volume (W1ADW+BL1LC)
Damaged compartment is bounded on top
983116983119983123983124 983106983125983119983129983105983118983107983129 983117983109983124983112983119983108
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 5667
983116983119983123983124 983106983125983119983129983105983118983107983129 983117983109983124983112983119983108
bull It is assumed that displacement and location of vertical centre
of gravity does not change after damaged
983116983119983123983124 983106983125983119983129983105983118983107983129 983117983109983124983112983119983108
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 5767
983116983119983123983124 983106983125983119983129983105983118983107983129 983117983109983124983112983119983108
8162019 Damaged Stability
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The heel angle of damaged ship is determined by
where
d is the distance between the volume centre of damaged compartment
and the new longitudinal centre of floatation
wc=vc μ ρ
983116983119983123983124 983106983125983119983129983105983118983107983129 983117983109983124983112983119983108
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 5967
983116983119983123983124 983106983125983119983129983105983118983107983129 983117983109983124983112983119983108
983116983119983123983124 983106983125983119983129983105983118983107983129 983117983109983124983112983119983108
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 6067
Longitudinal Metacentre Height of a Damaged Ship
983116983119983123983124 983106983125983119983129983105983118983107983129 983117983109983124983112983119983108
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 6167
983110983151983154983159983137983154983140 983137983150983140 983137983142983156 983140983154983137983157983143983144983156983155 983137983142983156983141983154 983140983137983149983137983143983141983140
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 6267
983120983151983154983156 983105983142983156 983120983151983154983156 983110983151983154983141 983123983156983137983154983138983151983137983154983140 983105983142983156 983123983156983137983154983138983151983137983154983140 983110983151983154983159983137983154983140
I983150983145983156983145983137983148 D983154983137983157983143983144983156 983124 983124 983124 983124
983120983137983154983137983148983141983148 983123983145983150983147983137983143983141 +983152 +983152 +983152 +983120
H983141983141983148 983085983149983145 983085983149983145 +983149983155 +983149983155
983124983154983145983149 983085983156983147 +983156983138 983085983156983147 +983156983138
F983145983150983137983148 D983154983137983157983143983144983156 983124+983152983085983149983145983085983156983147 983124+983152983085983149983145+983156983138 983124+983152+983149983155983085983156983147 983124+983152+983149983155+983156983138
Table 1 Final Draughts for a starboard side damaged ship
8162019 Damaged Stability
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L983151983155983156 B983157983151983161983137983150983139983161 M983141983156983144983151983140
8162019 Damaged Stability
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L983151983155983156 B983157983151983161983137983150983139983161 M983141983156983144983151983140
8162019 Damaged Stability
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991266 A983142983156983141983154 983148983151983151983155983145983150983143 983156983144983141 983139983141983150983156983154983137983148 983139983151983149983152983137983154983156983149983141983150983156 983156983144983141
983159983137983156983141983154983152983148983137983150983141 983137983154983141983137 983145983155
991266 983124983151 983139983151983149983152983141983150983155983137983156983141 983142983151983154 983156983144983141 983148983151983155983155 983151983142 983138983157983151983161983137983150983139983161 983151983142 983156983144983141
983139983141983150983156983154983137983148 983139983151983149983152983137983154983156983149983141983150983156 983156983144983141 983140983154983137983142983156 983145983150983139983154983141983137983155983141983155 983156983151
2805)420()( m x Bl L A L
=minus=minus=
m A
T
L
I
L 875180
150==
nabla=
L983151983155983156 B983157983151983161983137983150983139983161 M983141983156983144983151983140
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 6667
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m
T
KB L
L 93802
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2 ===
433
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12
)(m
l L B I L
=minus
=minus
=
m I
BM
I
L
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nabla
=
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8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 6767
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m KG BM KBGM L L L 54905111119380 =minus+=minus+=
mt xGM M L
sin34984sin549075153sin φ φ φ ==∆=
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 1867
A cargo hold with dimensions of l = 1524m w = 914 m
h=61 m is completely flooded Determine the volume of the
space and the corrected flooded volume
Volume = 1524 m x 914 m x 61 m = 8497 m3
Flooded volume = Volume x permeability
Flooded volume = 8497 m3 x 60
Flooded volume = 5098 m3
Example 1
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 1967
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8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 2067
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8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 2167
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8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 2267
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8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 2367
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8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 2467
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983140983137983149983137983143983141983140 983139983151983149983152983137983154983156983149983141983150983156
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 2567
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Initial displacement and longitudinal centre of buoyancy (LCB) can be read from hydrostatcic curves
However displacement and LCB are unknown after damaged
Therefore if trim forward and aft draught are known trimmed waterline can be drawn over Bonjean
area curves
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 2667
983108983141983156983141983154983149983145983150983137983156983145983151983150 983151983142 983140983137983149983137983143983141983140 983148983141983150983143983156983144 983137983150983140 983148983151983139983137983156983145983151983150 983151983142 983149983145983140
983151983142 983139983151983149983152983137983154983156983149983141983150983156
vw The volume of water entering the vessel
xw Distance of volume centre of damaged compartment from maestory
micro Permability of the compartment
v0 Volume of the compartment
xm Distance of the volume centre of the compartment to the mid of damaged length
xl Distance of the mid of damaged length of compartment to maestory
xc Distance of the computed volume centre of compartment to maestory (xc=xl-xm)
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 2767
983108983141983156983141983154983149983145983150983137983156983145983151983150 983151983142 983140983137983149983137983143983141983140 983148983141983150983143983156983144 983137983150983140 983148983151983139983137983156983145983151983150 983151983142 983149983145983140
983151983142 983139983151983149983152983137983154983156983149983141983150983156
Damaged length and location of compartment can be determined by iterative
procedure
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 2867
bull The volume of water entering the vessel (vw)
bull Distance of volume centre of damaged compartment from amidships Θ ( xw)
bull Volume of the compartment (v0
= vw
μ)
First trial
1) Assume xm=0 (xl=xw)
2) Damaged Length l1 = (Volume of the compartment v0) (mean sec Area Amean)
where Amean is determined from trimmed sectional area curve
983108983141983156983141983154983149983145983150983137983156983145983151983150 983151983142 983140983137983149983137983143983141983140 983148983141983150983143983156983144 983137983150983140 983148983151983139983137983156983145983151983150 983151983142 983149983145983140
983151983142 983139983151983149983152983137983154983156983149983141983150983156
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 2967
3) In order to determine vm and xm
s = l1 4
vm = (s 3) sum3
xm = s sum4 sum3
xc = xl ndash xm
|vm-v0| le Tolarence for volume
|xc-xw| le Tolarence for location of volume centre
l=l1 xl=xw
983108983141983156983141983154983149983145983150983137983156983145983151983150 983151983142 983140983137983149983137983143983141983140 983148983141983150983143983156983144 983137983150983140 983148983151983139983137983156983145983151983150 983151983142 983149983145983140
983151983142 983139983151983149983152983137983154983156983149983141983150983156
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 3067
983108983141983156983141983154983149983145983150983137983156983145983151983150 983151983142 983140983137983149983137983143983141983140 983148983141983150983143983156983144 983137983150983140 983148983151983139983137983156983145983151983150 983151983142 983149983145983140
983151983142 983139983151983149983152983137983154983156983149983141983150983156Second Trial
Damaged length is changed proportionally by the volume
l2 = l1 times (v0v
m)
vm Computed volume at first trial
If the value of xm computed at first trial is negative then the mid of the
compartment slides to the bow
xl = xw+xm
where xm is the distance of the volume centre of compartment to amidship
computed at first trial
8162019 Damaged Stability
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In order to determine vm and xm
983108983141983156983141983154983149983145983150983137983156983145983151983150 983151983142 983140983137983149983137983143983141983140 983148983141983150983143983156983144 983137983150983140 983148983151983139983137983156983145983151983150 983151983142 983149983145983140
983151983142 983139983151983149983152983137983154983156983149983141983150983156
s = l2 4
vm = (s 3) sum3
xm = s sum4 sum3
xc = xl ndash xm
|vm-v0| le Tolarence for volume
|xc-xw| le Tolarence for location of volume centre
l=l2
If tolarances for both volume and location are not satisfied third fourthtrials are made similar to
second trial
8162019 Damaged Stability
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If either tolarence for volume or tolarance for location are satisfied at a trial
satisfied one is fixed trials are continued to make for the other one
983108983141983156983141983154983149983145983150983137983156983145983151983150 983151983142 983140983137983149983137983143983141983140 983148983141983150983143983156983144 983137983150983140 983148983151983139983137983156983145983151983150 983151983142 983149983145983140
983151983142 983139983151983149983152983137983154983156983149983141983150983156
8162019 Damaged Stability
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A ship is 116 meter long and displaces 7842 ton in salt water (ρ1=1025 tm3)
when her mean draught is 64m Longitudinal Centre of Buoyancy (LCB) is
0615 m aft from amidships After one of her stern compartment is damaged
she floats trimmed to the aft Her sectional areas after damaged are given in the
following table
a) Determine the volume of water entering the vessel (vw) and the location of
volume centre of damaged compartment (xw)
b) Assume permability of compartment micro is 1 Determine damaged length
and Distance of the mid of damaged length of compartment to amidship
983109983160983137983149983152983148983141 2
8162019 Damaged Stability
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8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 3567
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 3667
Predicted xw
is between section 2 and section 3
983123983141983139 N983151 983123983141983139 A983154983141983137 D983145983155983156 A9831499831459831559831449831459831522 10135 983085348
3 1208 983085232
983123983141983139 A983154983141983137 983137983156 98308524983149 983142983154983151983149 983137983149983145983140983155983144983145983152 = 11959831492
l1=v0Amean=204081195=17078 m
s=l14=427 m
983109983160983137983149983152983148983141 2983085983123983119983116983125983124983113983119983118
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 3767
983161983145 L983151983139 A983149983141983137983150 983123M M A983154983149
9831311983133 9831312983133 98313119831339832559831312983133 9831313983133 983131198313398325598313129831339832559831313983133
0 9830853254 1051 1 1051 2 21021 9830852827 1123 4 4492 1 4492
2 98308524 1195 2 239 0 0
3 9830851973 1219 4 4876 9830851 9830854876
4 9830851546 1233 1 1233 9830852 9830852466
sum983091983101 14042 sum983092983101 983085748
vm
= (s3) sum3= 199864479831493
xm
=s sum4sum3= 9830850227983149
v0-vm=20408-19986=422 m3
Error=422times10020408=207
983109983160983137983149983152983148983141 2983085983123983119983116983125983124983113983119983118
8162019 Damaged Stability
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Methods of Calculation
There two available method calculating the
final stage of the damaged vessel
bull Lost Buoyancy Method
bull Added Weight Method
8162019 Damaged Stability
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Comparision of Lost Buoyancy and Added
Weight Methods
8162019 Damaged Stability
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Consider a vessel that has been damaged such
that a portion of the bottom is now open to the
sea
The vesselrsquos draft will increase because an amount
of the buoyancy was lost
Added Weight Method
Added Weight Method
8162019 Damaged Stability
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Added Weight Method
In this method flood water is treated as a fixed weight (for example the
weight of water of volume ABEF) This added weight is balanced by the
additional buoyant force of the layer WL1WL
The added weight can be determined by either the volume ABEF or
waterline WL1 Therefore WL1 waterline is not known can be just guessed
For the predicted waterline added weight and additional buoyant force
caculation are done iteratively until both of them are equal This method is
known as Added weight method
Determination of Added Weight
8162019 Damaged Stability
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Determination of Added Weight
vc Volume of damaged compartment (DCEF)
ac The surface area (AB) of damaged compartment on the waterline
micro The volume permability of damaged compartment
microa The area permability of the surface of damaged compartment
∆ The initial displacement
∆1 The displacement at final stage
vw The volume of water entering the vessel (ABEH)
w The weight of water entering the vessel
p The value of parallel sinkage
If th t th l l i k i h f t l f
8162019 Damaged Stability
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If we assume that the paralel sinkage cause a minor change of water plane area of a
ship (Awp
asymp Awp1
) we can determine the paralel sinkage by equating the volume of
the layer WL1WL to the volume of ABEF
If the damaged compartment is bounded on top
8162019 Damaged Stability
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8162019 Damaged Stability
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Longitudinal Metacentre Radius at final stage
Free Surface Effect
Damaged compartment can be considered as a half filled tank
Free Contact Effect
Damaged compartment can be considered as a half filled tank
T M H i h
8162019 Damaged Stability
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Transverse Metacentre Height
The angle of heel
8162019 Damaged Stability
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L it di l M t t H i ht
8162019 Damaged Stability
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Longitudinal Metacentre Height
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E983160983137983149983152983148983141 A 983138983137983154983143983141
8162019 Damaged Stability
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E983160983137983149983152983148983141 A 983138983137983154983143983141
991266 L = 20 983149991266 B = 5 983149
991266 983124 = 15 983149
991266 KG = 15 983149
I983150983156983137983139983156 C983151983150983140983145983156983145983151983150
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 5167
I983150983156983137983139983156 C983151983150983140983145983156983145983151983150
991266 983124983144983141 983140983145983155983152983148983137983139983141983149983141983150983156 983158983151983148983157983149983141
991266 983124983144983141 983149983137983155983155 983140983145983155983152983148983137983139983141983149983141983150983156
991266 983124983144983141 983149983151983149983141983150983156 983151983142 983145983150983141983154983156983145983137 983151983142 983156983144983141 983159983137983156983141983154983152983148983137983150983141 983137983154983141983137983137983138983151983157983156 CL
3
15051520 m x xT B L
I I
==sdotsdot=nabla
tons x I
751531500251 ==nablasdot=∆ ρ
433
33208
12
205
12
m x L B
I I
===
I983150983156983137983139983156 C983151983150983140983145983156983145983151983150
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 5267
I983150983156983137983139983156 C983151983150983140983145983156983145983151983150
991266 M983141983156983137983139983141983150983156983154983145983139 983154983137983140983145983157983155
991266 O983154 983145983156 983139983151983157983148983140 983138983141 983139983137983148983139983157983148983137983156983141983140 983140983145983154983141983139983156983148983161 983137983155
991266 H983141983145983143983144983156 983151983142 983156983144983141 983139983141983150983156983141983154 983151983142 983138983157983151983161983137983150983139983161
m I
BM
I
I 3891
150
33208==
nabla
=
m xT
B
LBT
L B BM
I I
I 3891
5112
5
12
12 223
====
mT
KB I
I 750
2
==
I983150983156983137983139983156 C983151983150983140983145983156983145983151983150
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 5367
991266 983124983144983141 983149983141983156983137983139983141983150983156983154983145983139 983144983141983145983143983144983156
991266 F983151983154 983155983149983137983148983148 983137983150983143983148983141983155 983151983142 983144983141983141983148 983156983144983141 983154983145983143983144983156983145983150983143 983149983151983149983141983150983156
m KG BM KBGM I I 63905013891750 =minus+=minus+=
sin22998sin693075153sin mt x xGM M I I
φ φ φ ==∆=
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 5467
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 5567
983116983119983123983124 983106983125983119983129983105983118983107983129 983117983109983124983112983119983108
Paralel Sinkage
Volume (DCEF)=Volume (W1ADW+BL1LC)
Damaged compartment is bounded on top
983116983119983123983124 983106983125983119983129983105983118983107983129 983117983109983124983112983119983108
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 5667
983116983119983123983124 983106983125983119983129983105983118983107983129 983117983109983124983112983119983108
bull It is assumed that displacement and location of vertical centre
of gravity does not change after damaged
983116983119983123983124 983106983125983119983129983105983118983107983129 983117983109983124983112983119983108
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 5767
983116983119983123983124 983106983125983119983129983105983118983107983129 983117983109983124983112983119983108
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 5867
The heel angle of damaged ship is determined by
where
d is the distance between the volume centre of damaged compartment
and the new longitudinal centre of floatation
wc=vc μ ρ
983116983119983123983124 983106983125983119983129983105983118983107983129 983117983109983124983112983119983108
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 5967
983116983119983123983124 983106983125983119983129983105983118983107983129 983117983109983124983112983119983108
983116983119983123983124 983106983125983119983129983105983118983107983129 983117983109983124983112983119983108
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 6067
Longitudinal Metacentre Height of a Damaged Ship
983116983119983123983124 983106983125983119983129983105983118983107983129 983117983109983124983112983119983108
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 6167
983110983151983154983159983137983154983140 983137983150983140 983137983142983156 983140983154983137983157983143983144983156983155 983137983142983156983141983154 983140983137983149983137983143983141983140
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 6267
983120983151983154983156 983105983142983156 983120983151983154983156 983110983151983154983141 983123983156983137983154983138983151983137983154983140 983105983142983156 983123983156983137983154983138983151983137983154983140 983110983151983154983159983137983154983140
I983150983145983156983145983137983148 D983154983137983157983143983144983156 983124 983124 983124 983124
983120983137983154983137983148983141983148 983123983145983150983147983137983143983141 +983152 +983152 +983152 +983120
H983141983141983148 983085983149983145 983085983149983145 +983149983155 +983149983155
983124983154983145983149 983085983156983147 +983156983138 983085983156983147 +983156983138
F983145983150983137983148 D983154983137983157983143983144983156 983124+983152983085983149983145983085983156983147 983124+983152983085983149983145+983156983138 983124+983152+983149983155983085983156983147 983124+983152+983149983155+983156983138
Table 1 Final Draughts for a starboard side damaged ship
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 6367
L983151983155983156 B983157983151983161983137983150983139983161 M983141983156983144983151983140
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 6467
L983151983155983156 B983157983151983161983137983150983139983161 M983141983156983144983151983140
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 6567
991266 A983142983156983141983154 983148983151983151983155983145983150983143 983156983144983141 983139983141983150983156983154983137983148 983139983151983149983152983137983154983156983149983141983150983156 983156983144983141
983159983137983156983141983154983152983148983137983150983141 983137983154983141983137 983145983155
991266 983124983151 983139983151983149983152983141983150983155983137983156983141 983142983151983154 983156983144983141 983148983151983155983155 983151983142 983138983157983151983161983137983150983139983161 983151983142 983156983144983141
983139983141983150983156983154983137983148 983139983151983149983152983137983154983156983149983141983150983156 983156983144983141 983140983154983137983142983156 983145983150983139983154983141983137983155983141983155 983156983151
2805)420()( m x Bl L A L
=minus=minus=
m A
T
L
I
L 875180
150==
nabla=
L983151983155983156 B983157983151983161983137983150983139983161 M983141983156983144983151983140
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 6667
991266 983124983144983141 983144983141983145983143983144983156 983151983142 983156983144983141 983139983141983150983156983141983154 983151983142 983138983157983151983161983137983150983139983161 983145983150983139983154983141983137983155983141983155 983156983151
991266 983124983144983141 983149983151983149983141983150983156 983151983142 983145983150983141983154983156983145983137 983151983142 983156983144983141 983159983137983156983141983154983152983148983137983150983141 983137983154983141983137
991266 983124983144983141 983149983141983156983137983139983141983150983156983154983145983139 983154983137983140983145983157983155
m
T
KB L
L 93802
8751
2 ===
433
6716612
)420(5
12
)(m
l L B I L
=minus
=minus
=
m I
BM
I
L
L 1111150
67166==
nabla
=
L983151983155983156 B983157983151983161983137983150983139983161 M983141983156983144983151983140
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 6767
991266 983124983144983141 983149983141983156983137983139983141983150983156983154983145983139 983144983141983145983143983144983156
991266 983122983145983143983144983156983145983150983143 983149983151983149983141983150983156 983142983151983154 983155983149983137983148983148 983144983141983141983148 983137983150983143983148983141983155
m KG BM KBGM L L L 54905111119380 =minus+=minus+=
mt xGM M L
sin34984sin549075153sin φ φ φ ==∆=
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 1967
983110983148983151983151983140983137983138983148983141 983116983141983150983143983156983144
983110983148983151983151983140983137983138983148983141 983148983141983150983143983156983144983098 983137983156 983137 983143983145983158983141983150 983152983151983145983150983156 983151983142 983156983144983141 983155983144983145983152 983148983141983150983143983156983144 983145983155 983156983144983141 983149983137983160983145983149983157983149 983148983141983150983143983156983144
983159983145983156983144 983156983144983141 983139983141983150983156983141983154 983137983156 983156983144983137983156 983152983151983145983150983156 983156983144983137983156 983139983137983150 983138983141 983142983148983151983151983140983141983140 983159983145983156983144983151983157983156 983155983157983138983149983141983154983143983145983150983143 983156983144983141
983155983144983145983152 983138983141983161983151983150983140 983149983137983154983143983145983150 983148983145983150983141
983129983137983154983137983148ı 983106983286983148983149983141 983106983151983161983157983098 G983141983149983145 983138983151983161983157983150983139983137 983144983141983154983144983137983150983143983145 983138983145983154 983150983151983147983156983137983140983137 983138983157 983150983151983147983156983137 983149983141983154983147983141983162
983151983148983149983137983147 983292983162983141983154983141 983143983141983149983145983161983145 983155ı983150ı983154 983144983137983156983156ı983150983137 983156983141ğ983141983156 983144983137983148983141 983143983141983156983145983154983141983139983141983147 983141983150 983138983292983161983292983147 983138983286983148983149983141 983138983151983161983157983150983137
983151 983150983151983147983156983137983140983137983147983145 983161983137983154983137983148ı 983138983286983148983149983141 983138983151983161983157 983140983141983150983145983154
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 2067
983110983148983151983151983140983137983138983148983141 983116983141983150983143983156983144 983107983157983154983158983141
983110983148983151983151983140983137983138983148983141 983116983141983150983143983156983144 983107983157983154983158983141983098 I983156 983145983155 983151983138983156983137983145983150983141983140 983138983161 983156983144983141 983139983151983150983150983141983139983156983145983151983150 983151983142 983142983148983151983151983140983137983138983148983141 983148983141983150983143983156983144983155 983137983156
983140983145983142983142983141983154983141983150983156 983152983151983145983150983156983155 983137983148983151983150983143 983156983144983141 983155983144983145983152 983148983141983150983143983156983144
983129983137983154983137983148ı 983106983286983148983149983141 983106983151983161983157 983109ğ983154983145983155983145983098 G983141983149983145 983138983151983161983157983150983139983137 983140983141ğ983145ş983145983147 983150983151983147983156983137983148983137983154983140983137 983144983141983155983137983152983148983137983150983137983150 983161983137983154983137983148ı
983138983286983148983149983141 983138983151983161983157 983140983141ğ983141983154983148983141983154983145983150983145983150 983138983145983154983148983141ş983156983145983154983145983148983149983141983155983145 983145983148983141 983141983148983140983141 983141983140983145983148983145983154
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 2167
983110983137983139983156983151983154 983151983142 983123983157983138983140983145983158983145983155983145983151983150
F983137983139983156983151983154 983151983142 983123983157983138983140983145983158983145983155983145983151983150 983124983144983141 983142983137983139983156983151983154 983151983142 983155983157983138983140983145983158983145983155983145983151983150 983145983155 983137 983142983137983139983156983151983154 983152983154983141983155983139983154983145983138983141983140
983138983161 983156983144983141 983137983152983152983148983145983139983137983138983148983141 983154983141983143983157983148983137983156983145983151983150983155 983137983150983140 983138983161 983145983150983156983141983154983150983137983156983145983151983150983137983148 983139983151983150983158983141983150983156983145983151983150 983156983144983137983156
983140983141983152983141983150983140983155 983151983150 983155983144983145983152 983148983141983150983143983156983144 983137983150983140 983139983154983145983156983141983154983145983151983150 983151983142 983155983141983154983158983145983139983141
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 2267
983120983141983154983149983145983155983155983145983138983148983141 983116983141983150983143983156983144
983120983141983154983149983145983155983155983145983138983148983141 L983141983150983143983156983144 983145983155 983151983138983156983137983145983150983141983140 983138983161 983149983157983148983156983145983152983148983161983145983150983143 983156983144983141 983142983148983151983151983140983137983138983148983141 983148983141983150983143983156983144 983137983156
983156983144983137983156 983152983151983145983150983156 983138983161 983156983144983141 983142983137983139983156983151983154 983151983142 983155983157983138983140983145983158983145983155983145983151983150
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 2367
D983141983156983141983154983149983145983150983137983156983145983151983150 983151983142 983156983144983141 983148983151983139983137983156983145983151983150 983151983142 983156983144983141 983158983151983148983157983149983141 983139983141983150983156983154983141 983151983142
983140983137983149983137983143983141983140 983139983151983149983152983137983154983156983149983141983150983156
Δ I983150983145983156983145983137983148 983140983145983155983152983148983137983139983141983149983141983150983156 Δ1 D983145983155983152983148983137983139983141983149983141983150983156 983137983142983156983141983154 983140983137983149983137983143983141983140
B I983150983145983156983145983137983148 983139983141983150983156983154983141 983151983142 983138983157983151983161983137983150983139983161
G I983150983145983156983145983137983148 983139983141983150983156983154983141 983151983142 9831439831549831379831589831459831569831619831600 I983150983145983156983145983137983148 983139983141983150983156983154983141 983151983142 983148983151983150983143983145983156983157983140983145983150983137983148 983138983157983151983161983137983150983139983161 LCB
983158983159 983124983144983141 983158983151983148983157983149983141 983151983142 983159983137983156983141983154 983141983150983156983141983154983145983150983143 983156983144983141 983158983141983155983155983141983148
983160983159 D983145983155983156983137983150983139983141 983151983142 983158983151983148983157983149983141 983139983141983150983156983154983141 983151983142 983140983137983149983137983143983141983140 983139983151983149983152983137983154983156983149983141983150983156 983142983154983151983149 983149983137983141983155983156983151983154983161
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 2467
D983141983156983141983154983149983145983150983137983156983145983151983150 983151983142 983156983144983141 983148983151983139983137983156983145983151983150 983151983142 983156983144983141 983158983151983148983157983149983141 983139983141983150983156983154983141 983151983142
983140983137983149983137983143983141983140 983139983151983149983152983137983154983156983149983141983150983156
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 2567
D983141983156983141983154983149983145983150983137983156983145983151983150 983151983142 983156983144983141 983158983151983148983157983149983141 983151983142 983159983137983156983141983154 983141983150983156983141983154983145983150983143 983156983144983141 983158983141983155983155983141983148
Initial displacement and longitudinal centre of buoyancy (LCB) can be read from hydrostatcic curves
However displacement and LCB are unknown after damaged
Therefore if trim forward and aft draught are known trimmed waterline can be drawn over Bonjean
area curves
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 2667
983108983141983156983141983154983149983145983150983137983156983145983151983150 983151983142 983140983137983149983137983143983141983140 983148983141983150983143983156983144 983137983150983140 983148983151983139983137983156983145983151983150 983151983142 983149983145983140
983151983142 983139983151983149983152983137983154983156983149983141983150983156
vw The volume of water entering the vessel
xw Distance of volume centre of damaged compartment from maestory
micro Permability of the compartment
v0 Volume of the compartment
xm Distance of the volume centre of the compartment to the mid of damaged length
xl Distance of the mid of damaged length of compartment to maestory
xc Distance of the computed volume centre of compartment to maestory (xc=xl-xm)
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 2767
983108983141983156983141983154983149983145983150983137983156983145983151983150 983151983142 983140983137983149983137983143983141983140 983148983141983150983143983156983144 983137983150983140 983148983151983139983137983156983145983151983150 983151983142 983149983145983140
983151983142 983139983151983149983152983137983154983156983149983141983150983156
Damaged length and location of compartment can be determined by iterative
procedure
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 2867
bull The volume of water entering the vessel (vw)
bull Distance of volume centre of damaged compartment from amidships Θ ( xw)
bull Volume of the compartment (v0
= vw
μ)
First trial
1) Assume xm=0 (xl=xw)
2) Damaged Length l1 = (Volume of the compartment v0) (mean sec Area Amean)
where Amean is determined from trimmed sectional area curve
983108983141983156983141983154983149983145983150983137983156983145983151983150 983151983142 983140983137983149983137983143983141983140 983148983141983150983143983156983144 983137983150983140 983148983151983139983137983156983145983151983150 983151983142 983149983145983140
983151983142 983139983151983149983152983137983154983156983149983141983150983156
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 2967
3) In order to determine vm and xm
s = l1 4
vm = (s 3) sum3
xm = s sum4 sum3
xc = xl ndash xm
|vm-v0| le Tolarence for volume
|xc-xw| le Tolarence for location of volume centre
l=l1 xl=xw
983108983141983156983141983154983149983145983150983137983156983145983151983150 983151983142 983140983137983149983137983143983141983140 983148983141983150983143983156983144 983137983150983140 983148983151983139983137983156983145983151983150 983151983142 983149983145983140
983151983142 983139983151983149983152983137983154983156983149983141983150983156
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 3067
983108983141983156983141983154983149983145983150983137983156983145983151983150 983151983142 983140983137983149983137983143983141983140 983148983141983150983143983156983144 983137983150983140 983148983151983139983137983156983145983151983150 983151983142 983149983145983140
983151983142 983139983151983149983152983137983154983156983149983141983150983156Second Trial
Damaged length is changed proportionally by the volume
l2 = l1 times (v0v
m)
vm Computed volume at first trial
If the value of xm computed at first trial is negative then the mid of the
compartment slides to the bow
xl = xw+xm
where xm is the distance of the volume centre of compartment to amidship
computed at first trial
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 3167
In order to determine vm and xm
983108983141983156983141983154983149983145983150983137983156983145983151983150 983151983142 983140983137983149983137983143983141983140 983148983141983150983143983156983144 983137983150983140 983148983151983139983137983156983145983151983150 983151983142 983149983145983140
983151983142 983139983151983149983152983137983154983156983149983141983150983156
s = l2 4
vm = (s 3) sum3
xm = s sum4 sum3
xc = xl ndash xm
|vm-v0| le Tolarence for volume
|xc-xw| le Tolarence for location of volume centre
l=l2
If tolarances for both volume and location are not satisfied third fourthtrials are made similar to
second trial
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 3267
If either tolarence for volume or tolarance for location are satisfied at a trial
satisfied one is fixed trials are continued to make for the other one
983108983141983156983141983154983149983145983150983137983156983145983151983150 983151983142 983140983137983149983137983143983141983140 983148983141983150983143983156983144 983137983150983140 983148983151983139983137983156983145983151983150 983151983142 983149983145983140
983151983142 983139983151983149983152983137983154983156983149983141983150983156
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 3367
A ship is 116 meter long and displaces 7842 ton in salt water (ρ1=1025 tm3)
when her mean draught is 64m Longitudinal Centre of Buoyancy (LCB) is
0615 m aft from amidships After one of her stern compartment is damaged
she floats trimmed to the aft Her sectional areas after damaged are given in the
following table
a) Determine the volume of water entering the vessel (vw) and the location of
volume centre of damaged compartment (xw)
b) Assume permability of compartment micro is 1 Determine damaged length
and Distance of the mid of damaged length of compartment to amidship
983109983160983137983149983152983148983141 2
8162019 Damaged Stability
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8162019 Damaged Stability
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8162019 Damaged Stability
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Predicted xw
is between section 2 and section 3
983123983141983139 N983151 983123983141983139 A983154983141983137 D983145983155983156 A9831499831459831559831449831459831522 10135 983085348
3 1208 983085232
983123983141983139 A983154983141983137 983137983156 98308524983149 983142983154983151983149 983137983149983145983140983155983144983145983152 = 11959831492
l1=v0Amean=204081195=17078 m
s=l14=427 m
983109983160983137983149983152983148983141 2983085983123983119983116983125983124983113983119983118
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 3767
983161983145 L983151983139 A983149983141983137983150 983123M M A983154983149
9831311983133 9831312983133 98313119831339832559831312983133 9831313983133 983131198313398325598313129831339832559831313983133
0 9830853254 1051 1 1051 2 21021 9830852827 1123 4 4492 1 4492
2 98308524 1195 2 239 0 0
3 9830851973 1219 4 4876 9830851 9830854876
4 9830851546 1233 1 1233 9830852 9830852466
sum983091983101 14042 sum983092983101 983085748
vm
= (s3) sum3= 199864479831493
xm
=s sum4sum3= 9830850227983149
v0-vm=20408-19986=422 m3
Error=422times10020408=207
983109983160983137983149983152983148983141 2983085983123983119983116983125983124983113983119983118
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 3867
Methods of Calculation
There two available method calculating the
final stage of the damaged vessel
bull Lost Buoyancy Method
bull Added Weight Method
8162019 Damaged Stability
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Comparision of Lost Buoyancy and Added
Weight Methods
8162019 Damaged Stability
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Consider a vessel that has been damaged such
that a portion of the bottom is now open to the
sea
The vesselrsquos draft will increase because an amount
of the buoyancy was lost
Added Weight Method
Added Weight Method
8162019 Damaged Stability
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Added Weight Method
In this method flood water is treated as a fixed weight (for example the
weight of water of volume ABEF) This added weight is balanced by the
additional buoyant force of the layer WL1WL
The added weight can be determined by either the volume ABEF or
waterline WL1 Therefore WL1 waterline is not known can be just guessed
For the predicted waterline added weight and additional buoyant force
caculation are done iteratively until both of them are equal This method is
known as Added weight method
Determination of Added Weight
8162019 Damaged Stability
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Determination of Added Weight
vc Volume of damaged compartment (DCEF)
ac The surface area (AB) of damaged compartment on the waterline
micro The volume permability of damaged compartment
microa The area permability of the surface of damaged compartment
∆ The initial displacement
∆1 The displacement at final stage
vw The volume of water entering the vessel (ABEH)
w The weight of water entering the vessel
p The value of parallel sinkage
If th t th l l i k i h f t l f
8162019 Damaged Stability
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If we assume that the paralel sinkage cause a minor change of water plane area of a
ship (Awp
asymp Awp1
) we can determine the paralel sinkage by equating the volume of
the layer WL1WL to the volume of ABEF
If the damaged compartment is bounded on top
8162019 Damaged Stability
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8162019 Damaged Stability
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Longitudinal Metacentre Radius at final stage
Free Surface Effect
Damaged compartment can be considered as a half filled tank
Free Contact Effect
Damaged compartment can be considered as a half filled tank
T M H i h
8162019 Damaged Stability
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Transverse Metacentre Height
The angle of heel
8162019 Damaged Stability
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L it di l M t t H i ht
8162019 Damaged Stability
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Longitudinal Metacentre Height
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 4967
E983160983137983149983152983148983141 A 983138983137983154983143983141
8162019 Damaged Stability
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E983160983137983149983152983148983141 A 983138983137983154983143983141
991266 L = 20 983149991266 B = 5 983149
991266 983124 = 15 983149
991266 KG = 15 983149
I983150983156983137983139983156 C983151983150983140983145983156983145983151983150
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 5167
I983150983156983137983139983156 C983151983150983140983145983156983145983151983150
991266 983124983144983141 983140983145983155983152983148983137983139983141983149983141983150983156 983158983151983148983157983149983141
991266 983124983144983141 983149983137983155983155 983140983145983155983152983148983137983139983141983149983141983150983156
991266 983124983144983141 983149983151983149983141983150983156 983151983142 983145983150983141983154983156983145983137 983151983142 983156983144983141 983159983137983156983141983154983152983148983137983150983141 983137983154983141983137983137983138983151983157983156 CL
3
15051520 m x xT B L
I I
==sdotsdot=nabla
tons x I
751531500251 ==nablasdot=∆ ρ
433
33208
12
205
12
m x L B
I I
===
I983150983156983137983139983156 C983151983150983140983145983156983145983151983150
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 5267
I983150983156983137983139983156 C983151983150983140983145983156983145983151983150
991266 M983141983156983137983139983141983150983156983154983145983139 983154983137983140983145983157983155
991266 O983154 983145983156 983139983151983157983148983140 983138983141 983139983137983148983139983157983148983137983156983141983140 983140983145983154983141983139983156983148983161 983137983155
991266 H983141983145983143983144983156 983151983142 983156983144983141 983139983141983150983156983141983154 983151983142 983138983157983151983161983137983150983139983161
m I
BM
I
I 3891
150
33208==
nabla
=
m xT
B
LBT
L B BM
I I
I 3891
5112
5
12
12 223
====
mT
KB I
I 750
2
==
I983150983156983137983139983156 C983151983150983140983145983156983145983151983150
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 5367
991266 983124983144983141 983149983141983156983137983139983141983150983156983154983145983139 983144983141983145983143983144983156
991266 F983151983154 983155983149983137983148983148 983137983150983143983148983141983155 983151983142 983144983141983141983148 983156983144983141 983154983145983143983144983156983145983150983143 983149983151983149983141983150983156
m KG BM KBGM I I 63905013891750 =minus+=minus+=
sin22998sin693075153sin mt x xGM M I I
φ φ φ ==∆=
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 5467
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 5567
983116983119983123983124 983106983125983119983129983105983118983107983129 983117983109983124983112983119983108
Paralel Sinkage
Volume (DCEF)=Volume (W1ADW+BL1LC)
Damaged compartment is bounded on top
983116983119983123983124 983106983125983119983129983105983118983107983129 983117983109983124983112983119983108
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 5667
983116983119983123983124 983106983125983119983129983105983118983107983129 983117983109983124983112983119983108
bull It is assumed that displacement and location of vertical centre
of gravity does not change after damaged
983116983119983123983124 983106983125983119983129983105983118983107983129 983117983109983124983112983119983108
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 5767
983116983119983123983124 983106983125983119983129983105983118983107983129 983117983109983124983112983119983108
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 5867
The heel angle of damaged ship is determined by
where
d is the distance between the volume centre of damaged compartment
and the new longitudinal centre of floatation
wc=vc μ ρ
983116983119983123983124 983106983125983119983129983105983118983107983129 983117983109983124983112983119983108
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 5967
983116983119983123983124 983106983125983119983129983105983118983107983129 983117983109983124983112983119983108
983116983119983123983124 983106983125983119983129983105983118983107983129 983117983109983124983112983119983108
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 6067
Longitudinal Metacentre Height of a Damaged Ship
983116983119983123983124 983106983125983119983129983105983118983107983129 983117983109983124983112983119983108
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 6167
983110983151983154983159983137983154983140 983137983150983140 983137983142983156 983140983154983137983157983143983144983156983155 983137983142983156983141983154 983140983137983149983137983143983141983140
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 6267
983120983151983154983156 983105983142983156 983120983151983154983156 983110983151983154983141 983123983156983137983154983138983151983137983154983140 983105983142983156 983123983156983137983154983138983151983137983154983140 983110983151983154983159983137983154983140
I983150983145983156983145983137983148 D983154983137983157983143983144983156 983124 983124 983124 983124
983120983137983154983137983148983141983148 983123983145983150983147983137983143983141 +983152 +983152 +983152 +983120
H983141983141983148 983085983149983145 983085983149983145 +983149983155 +983149983155
983124983154983145983149 983085983156983147 +983156983138 983085983156983147 +983156983138
F983145983150983137983148 D983154983137983157983143983144983156 983124+983152983085983149983145983085983156983147 983124+983152983085983149983145+983156983138 983124+983152+983149983155983085983156983147 983124+983152+983149983155+983156983138
Table 1 Final Draughts for a starboard side damaged ship
8162019 Damaged Stability
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L983151983155983156 B983157983151983161983137983150983139983161 M983141983156983144983151983140
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 6467
L983151983155983156 B983157983151983161983137983150983139983161 M983141983156983144983151983140
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 6567
991266 A983142983156983141983154 983148983151983151983155983145983150983143 983156983144983141 983139983141983150983156983154983137983148 983139983151983149983152983137983154983156983149983141983150983156 983156983144983141
983159983137983156983141983154983152983148983137983150983141 983137983154983141983137 983145983155
991266 983124983151 983139983151983149983152983141983150983155983137983156983141 983142983151983154 983156983144983141 983148983151983155983155 983151983142 983138983157983151983161983137983150983139983161 983151983142 983156983144983141
983139983141983150983156983154983137983148 983139983151983149983152983137983154983156983149983141983150983156 983156983144983141 983140983154983137983142983156 983145983150983139983154983141983137983155983141983155 983156983151
2805)420()( m x Bl L A L
=minus=minus=
m A
T
L
I
L 875180
150==
nabla=
L983151983155983156 B983157983151983161983137983150983139983161 M983141983156983144983151983140
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 6667
991266 983124983144983141 983144983141983145983143983144983156 983151983142 983156983144983141 983139983141983150983156983141983154 983151983142 983138983157983151983161983137983150983139983161 983145983150983139983154983141983137983155983141983155 983156983151
991266 983124983144983141 983149983151983149983141983150983156 983151983142 983145983150983141983154983156983145983137 983151983142 983156983144983141 983159983137983156983141983154983152983148983137983150983141 983137983154983141983137
991266 983124983144983141 983149983141983156983137983139983141983150983156983154983145983139 983154983137983140983145983157983155
m
T
KB L
L 93802
8751
2 ===
433
6716612
)420(5
12
)(m
l L B I L
=minus
=minus
=
m I
BM
I
L
L 1111150
67166==
nabla
=
L983151983155983156 B983157983151983161983137983150983139983161 M983141983156983144983151983140
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 6767
991266 983124983144983141 983149983141983156983137983139983141983150983156983154983145983139 983144983141983145983143983144983156
991266 983122983145983143983144983156983145983150983143 983149983151983149983141983150983156 983142983151983154 983155983149983137983148983148 983144983141983141983148 983137983150983143983148983141983155
m KG BM KBGM L L L 54905111119380 =minus+=minus+=
mt xGM M L
sin34984sin549075153sin φ φ φ ==∆=
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 2067
983110983148983151983151983140983137983138983148983141 983116983141983150983143983156983144 983107983157983154983158983141
983110983148983151983151983140983137983138983148983141 983116983141983150983143983156983144 983107983157983154983158983141983098 I983156 983145983155 983151983138983156983137983145983150983141983140 983138983161 983156983144983141 983139983151983150983150983141983139983156983145983151983150 983151983142 983142983148983151983151983140983137983138983148983141 983148983141983150983143983156983144983155 983137983156
983140983145983142983142983141983154983141983150983156 983152983151983145983150983156983155 983137983148983151983150983143 983156983144983141 983155983144983145983152 983148983141983150983143983156983144
983129983137983154983137983148ı 983106983286983148983149983141 983106983151983161983157 983109ğ983154983145983155983145983098 G983141983149983145 983138983151983161983157983150983139983137 983140983141ğ983145ş983145983147 983150983151983147983156983137983148983137983154983140983137 983144983141983155983137983152983148983137983150983137983150 983161983137983154983137983148ı
983138983286983148983149983141 983138983151983161983157 983140983141ğ983141983154983148983141983154983145983150983145983150 983138983145983154983148983141ş983156983145983154983145983148983149983141983155983145 983145983148983141 983141983148983140983141 983141983140983145983148983145983154
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 2167
983110983137983139983156983151983154 983151983142 983123983157983138983140983145983158983145983155983145983151983150
F983137983139983156983151983154 983151983142 983123983157983138983140983145983158983145983155983145983151983150 983124983144983141 983142983137983139983156983151983154 983151983142 983155983157983138983140983145983158983145983155983145983151983150 983145983155 983137 983142983137983139983156983151983154 983152983154983141983155983139983154983145983138983141983140
983138983161 983156983144983141 983137983152983152983148983145983139983137983138983148983141 983154983141983143983157983148983137983156983145983151983150983155 983137983150983140 983138983161 983145983150983156983141983154983150983137983156983145983151983150983137983148 983139983151983150983158983141983150983156983145983151983150 983156983144983137983156
983140983141983152983141983150983140983155 983151983150 983155983144983145983152 983148983141983150983143983156983144 983137983150983140 983139983154983145983156983141983154983145983151983150 983151983142 983155983141983154983158983145983139983141
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 2267
983120983141983154983149983145983155983155983145983138983148983141 983116983141983150983143983156983144
983120983141983154983149983145983155983155983145983138983148983141 L983141983150983143983156983144 983145983155 983151983138983156983137983145983150983141983140 983138983161 983149983157983148983156983145983152983148983161983145983150983143 983156983144983141 983142983148983151983151983140983137983138983148983141 983148983141983150983143983156983144 983137983156
983156983144983137983156 983152983151983145983150983156 983138983161 983156983144983141 983142983137983139983156983151983154 983151983142 983155983157983138983140983145983158983145983155983145983151983150
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 2367
D983141983156983141983154983149983145983150983137983156983145983151983150 983151983142 983156983144983141 983148983151983139983137983156983145983151983150 983151983142 983156983144983141 983158983151983148983157983149983141 983139983141983150983156983154983141 983151983142
983140983137983149983137983143983141983140 983139983151983149983152983137983154983156983149983141983150983156
Δ I983150983145983156983145983137983148 983140983145983155983152983148983137983139983141983149983141983150983156 Δ1 D983145983155983152983148983137983139983141983149983141983150983156 983137983142983156983141983154 983140983137983149983137983143983141983140
B I983150983145983156983145983137983148 983139983141983150983156983154983141 983151983142 983138983157983151983161983137983150983139983161
G I983150983145983156983145983137983148 983139983141983150983156983154983141 983151983142 9831439831549831379831589831459831569831619831600 I983150983145983156983145983137983148 983139983141983150983156983154983141 983151983142 983148983151983150983143983145983156983157983140983145983150983137983148 983138983157983151983161983137983150983139983161 LCB
983158983159 983124983144983141 983158983151983148983157983149983141 983151983142 983159983137983156983141983154 983141983150983156983141983154983145983150983143 983156983144983141 983158983141983155983155983141983148
983160983159 D983145983155983156983137983150983139983141 983151983142 983158983151983148983157983149983141 983139983141983150983156983154983141 983151983142 983140983137983149983137983143983141983140 983139983151983149983152983137983154983156983149983141983150983156 983142983154983151983149 983149983137983141983155983156983151983154983161
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 2467
D983141983156983141983154983149983145983150983137983156983145983151983150 983151983142 983156983144983141 983148983151983139983137983156983145983151983150 983151983142 983156983144983141 983158983151983148983157983149983141 983139983141983150983156983154983141 983151983142
983140983137983149983137983143983141983140 983139983151983149983152983137983154983156983149983141983150983156
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 2567
D983141983156983141983154983149983145983150983137983156983145983151983150 983151983142 983156983144983141 983158983151983148983157983149983141 983151983142 983159983137983156983141983154 983141983150983156983141983154983145983150983143 983156983144983141 983158983141983155983155983141983148
Initial displacement and longitudinal centre of buoyancy (LCB) can be read from hydrostatcic curves
However displacement and LCB are unknown after damaged
Therefore if trim forward and aft draught are known trimmed waterline can be drawn over Bonjean
area curves
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 2667
983108983141983156983141983154983149983145983150983137983156983145983151983150 983151983142 983140983137983149983137983143983141983140 983148983141983150983143983156983144 983137983150983140 983148983151983139983137983156983145983151983150 983151983142 983149983145983140
983151983142 983139983151983149983152983137983154983156983149983141983150983156
vw The volume of water entering the vessel
xw Distance of volume centre of damaged compartment from maestory
micro Permability of the compartment
v0 Volume of the compartment
xm Distance of the volume centre of the compartment to the mid of damaged length
xl Distance of the mid of damaged length of compartment to maestory
xc Distance of the computed volume centre of compartment to maestory (xc=xl-xm)
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 2767
983108983141983156983141983154983149983145983150983137983156983145983151983150 983151983142 983140983137983149983137983143983141983140 983148983141983150983143983156983144 983137983150983140 983148983151983139983137983156983145983151983150 983151983142 983149983145983140
983151983142 983139983151983149983152983137983154983156983149983141983150983156
Damaged length and location of compartment can be determined by iterative
procedure
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 2867
bull The volume of water entering the vessel (vw)
bull Distance of volume centre of damaged compartment from amidships Θ ( xw)
bull Volume of the compartment (v0
= vw
μ)
First trial
1) Assume xm=0 (xl=xw)
2) Damaged Length l1 = (Volume of the compartment v0) (mean sec Area Amean)
where Amean is determined from trimmed sectional area curve
983108983141983156983141983154983149983145983150983137983156983145983151983150 983151983142 983140983137983149983137983143983141983140 983148983141983150983143983156983144 983137983150983140 983148983151983139983137983156983145983151983150 983151983142 983149983145983140
983151983142 983139983151983149983152983137983154983156983149983141983150983156
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 2967
3) In order to determine vm and xm
s = l1 4
vm = (s 3) sum3
xm = s sum4 sum3
xc = xl ndash xm
|vm-v0| le Tolarence for volume
|xc-xw| le Tolarence for location of volume centre
l=l1 xl=xw
983108983141983156983141983154983149983145983150983137983156983145983151983150 983151983142 983140983137983149983137983143983141983140 983148983141983150983143983156983144 983137983150983140 983148983151983139983137983156983145983151983150 983151983142 983149983145983140
983151983142 983139983151983149983152983137983154983156983149983141983150983156
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 3067
983108983141983156983141983154983149983145983150983137983156983145983151983150 983151983142 983140983137983149983137983143983141983140 983148983141983150983143983156983144 983137983150983140 983148983151983139983137983156983145983151983150 983151983142 983149983145983140
983151983142 983139983151983149983152983137983154983156983149983141983150983156Second Trial
Damaged length is changed proportionally by the volume
l2 = l1 times (v0v
m)
vm Computed volume at first trial
If the value of xm computed at first trial is negative then the mid of the
compartment slides to the bow
xl = xw+xm
where xm is the distance of the volume centre of compartment to amidship
computed at first trial
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 3167
In order to determine vm and xm
983108983141983156983141983154983149983145983150983137983156983145983151983150 983151983142 983140983137983149983137983143983141983140 983148983141983150983143983156983144 983137983150983140 983148983151983139983137983156983145983151983150 983151983142 983149983145983140
983151983142 983139983151983149983152983137983154983156983149983141983150983156
s = l2 4
vm = (s 3) sum3
xm = s sum4 sum3
xc = xl ndash xm
|vm-v0| le Tolarence for volume
|xc-xw| le Tolarence for location of volume centre
l=l2
If tolarances for both volume and location are not satisfied third fourthtrials are made similar to
second trial
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 3267
If either tolarence for volume or tolarance for location are satisfied at a trial
satisfied one is fixed trials are continued to make for the other one
983108983141983156983141983154983149983145983150983137983156983145983151983150 983151983142 983140983137983149983137983143983141983140 983148983141983150983143983156983144 983137983150983140 983148983151983139983137983156983145983151983150 983151983142 983149983145983140
983151983142 983139983151983149983152983137983154983156983149983141983150983156
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 3367
A ship is 116 meter long and displaces 7842 ton in salt water (ρ1=1025 tm3)
when her mean draught is 64m Longitudinal Centre of Buoyancy (LCB) is
0615 m aft from amidships After one of her stern compartment is damaged
she floats trimmed to the aft Her sectional areas after damaged are given in the
following table
a) Determine the volume of water entering the vessel (vw) and the location of
volume centre of damaged compartment (xw)
b) Assume permability of compartment micro is 1 Determine damaged length
and Distance of the mid of damaged length of compartment to amidship
983109983160983137983149983152983148983141 2
8162019 Damaged Stability
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8162019 Damaged Stability
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8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 3667
Predicted xw
is between section 2 and section 3
983123983141983139 N983151 983123983141983139 A983154983141983137 D983145983155983156 A9831499831459831559831449831459831522 10135 983085348
3 1208 983085232
983123983141983139 A983154983141983137 983137983156 98308524983149 983142983154983151983149 983137983149983145983140983155983144983145983152 = 11959831492
l1=v0Amean=204081195=17078 m
s=l14=427 m
983109983160983137983149983152983148983141 2983085983123983119983116983125983124983113983119983118
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 3767
983161983145 L983151983139 A983149983141983137983150 983123M M A983154983149
9831311983133 9831312983133 98313119831339832559831312983133 9831313983133 983131198313398325598313129831339832559831313983133
0 9830853254 1051 1 1051 2 21021 9830852827 1123 4 4492 1 4492
2 98308524 1195 2 239 0 0
3 9830851973 1219 4 4876 9830851 9830854876
4 9830851546 1233 1 1233 9830852 9830852466
sum983091983101 14042 sum983092983101 983085748
vm
= (s3) sum3= 199864479831493
xm
=s sum4sum3= 9830850227983149
v0-vm=20408-19986=422 m3
Error=422times10020408=207
983109983160983137983149983152983148983141 2983085983123983119983116983125983124983113983119983118
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 3867
Methods of Calculation
There two available method calculating the
final stage of the damaged vessel
bull Lost Buoyancy Method
bull Added Weight Method
8162019 Damaged Stability
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Comparision of Lost Buoyancy and Added
Weight Methods
8162019 Damaged Stability
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Consider a vessel that has been damaged such
that a portion of the bottom is now open to the
sea
The vesselrsquos draft will increase because an amount
of the buoyancy was lost
Added Weight Method
Added Weight Method
8162019 Damaged Stability
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Added Weight Method
In this method flood water is treated as a fixed weight (for example the
weight of water of volume ABEF) This added weight is balanced by the
additional buoyant force of the layer WL1WL
The added weight can be determined by either the volume ABEF or
waterline WL1 Therefore WL1 waterline is not known can be just guessed
For the predicted waterline added weight and additional buoyant force
caculation are done iteratively until both of them are equal This method is
known as Added weight method
Determination of Added Weight
8162019 Damaged Stability
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Determination of Added Weight
vc Volume of damaged compartment (DCEF)
ac The surface area (AB) of damaged compartment on the waterline
micro The volume permability of damaged compartment
microa The area permability of the surface of damaged compartment
∆ The initial displacement
∆1 The displacement at final stage
vw The volume of water entering the vessel (ABEH)
w The weight of water entering the vessel
p The value of parallel sinkage
If th t th l l i k i h f t l f
8162019 Damaged Stability
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If we assume that the paralel sinkage cause a minor change of water plane area of a
ship (Awp
asymp Awp1
) we can determine the paralel sinkage by equating the volume of
the layer WL1WL to the volume of ABEF
If the damaged compartment is bounded on top
8162019 Damaged Stability
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8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 4567
Longitudinal Metacentre Radius at final stage
Free Surface Effect
Damaged compartment can be considered as a half filled tank
Free Contact Effect
Damaged compartment can be considered as a half filled tank
T M H i h
8162019 Damaged Stability
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Transverse Metacentre Height
The angle of heel
8162019 Damaged Stability
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L it di l M t t H i ht
8162019 Damaged Stability
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Longitudinal Metacentre Height
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 4967
E983160983137983149983152983148983141 A 983138983137983154983143983141
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 5067
E983160983137983149983152983148983141 A 983138983137983154983143983141
991266 L = 20 983149991266 B = 5 983149
991266 983124 = 15 983149
991266 KG = 15 983149
I983150983156983137983139983156 C983151983150983140983145983156983145983151983150
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 5167
I983150983156983137983139983156 C983151983150983140983145983156983145983151983150
991266 983124983144983141 983140983145983155983152983148983137983139983141983149983141983150983156 983158983151983148983157983149983141
991266 983124983144983141 983149983137983155983155 983140983145983155983152983148983137983139983141983149983141983150983156
991266 983124983144983141 983149983151983149983141983150983156 983151983142 983145983150983141983154983156983145983137 983151983142 983156983144983141 983159983137983156983141983154983152983148983137983150983141 983137983154983141983137983137983138983151983157983156 CL
3
15051520 m x xT B L
I I
==sdotsdot=nabla
tons x I
751531500251 ==nablasdot=∆ ρ
433
33208
12
205
12
m x L B
I I
===
I983150983156983137983139983156 C983151983150983140983145983156983145983151983150
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 5267
I983150983156983137983139983156 C983151983150983140983145983156983145983151983150
991266 M983141983156983137983139983141983150983156983154983145983139 983154983137983140983145983157983155
991266 O983154 983145983156 983139983151983157983148983140 983138983141 983139983137983148983139983157983148983137983156983141983140 983140983145983154983141983139983156983148983161 983137983155
991266 H983141983145983143983144983156 983151983142 983156983144983141 983139983141983150983156983141983154 983151983142 983138983157983151983161983137983150983139983161
m I
BM
I
I 3891
150
33208==
nabla
=
m xT
B
LBT
L B BM
I I
I 3891
5112
5
12
12 223
====
mT
KB I
I 750
2
==
I983150983156983137983139983156 C983151983150983140983145983156983145983151983150
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 5367
991266 983124983144983141 983149983141983156983137983139983141983150983156983154983145983139 983144983141983145983143983144983156
991266 F983151983154 983155983149983137983148983148 983137983150983143983148983141983155 983151983142 983144983141983141983148 983156983144983141 983154983145983143983144983156983145983150983143 983149983151983149983141983150983156
m KG BM KBGM I I 63905013891750 =minus+=minus+=
sin22998sin693075153sin mt x xGM M I I
φ φ φ ==∆=
8162019 Damaged Stability
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8162019 Damaged Stability
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983116983119983123983124 983106983125983119983129983105983118983107983129 983117983109983124983112983119983108
Paralel Sinkage
Volume (DCEF)=Volume (W1ADW+BL1LC)
Damaged compartment is bounded on top
983116983119983123983124 983106983125983119983129983105983118983107983129 983117983109983124983112983119983108
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 5667
983116983119983123983124 983106983125983119983129983105983118983107983129 983117983109983124983112983119983108
bull It is assumed that displacement and location of vertical centre
of gravity does not change after damaged
983116983119983123983124 983106983125983119983129983105983118983107983129 983117983109983124983112983119983108
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 5767
983116983119983123983124 983106983125983119983129983105983118983107983129 983117983109983124983112983119983108
8162019 Damaged Stability
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The heel angle of damaged ship is determined by
where
d is the distance between the volume centre of damaged compartment
and the new longitudinal centre of floatation
wc=vc μ ρ
983116983119983123983124 983106983125983119983129983105983118983107983129 983117983109983124983112983119983108
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 5967
983116983119983123983124 983106983125983119983129983105983118983107983129 983117983109983124983112983119983108
983116983119983123983124 983106983125983119983129983105983118983107983129 983117983109983124983112983119983108
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 6067
Longitudinal Metacentre Height of a Damaged Ship
983116983119983123983124 983106983125983119983129983105983118983107983129 983117983109983124983112983119983108
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 6167
983110983151983154983159983137983154983140 983137983150983140 983137983142983156 983140983154983137983157983143983144983156983155 983137983142983156983141983154 983140983137983149983137983143983141983140
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 6267
983120983151983154983156 983105983142983156 983120983151983154983156 983110983151983154983141 983123983156983137983154983138983151983137983154983140 983105983142983156 983123983156983137983154983138983151983137983154983140 983110983151983154983159983137983154983140
I983150983145983156983145983137983148 D983154983137983157983143983144983156 983124 983124 983124 983124
983120983137983154983137983148983141983148 983123983145983150983147983137983143983141 +983152 +983152 +983152 +983120
H983141983141983148 983085983149983145 983085983149983145 +983149983155 +983149983155
983124983154983145983149 983085983156983147 +983156983138 983085983156983147 +983156983138
F983145983150983137983148 D983154983137983157983143983144983156 983124+983152983085983149983145983085983156983147 983124+983152983085983149983145+983156983138 983124+983152+983149983155983085983156983147 983124+983152+983149983155+983156983138
Table 1 Final Draughts for a starboard side damaged ship
8162019 Damaged Stability
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L983151983155983156 B983157983151983161983137983150983139983161 M983141983156983144983151983140
8162019 Damaged Stability
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L983151983155983156 B983157983151983161983137983150983139983161 M983141983156983144983151983140
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 6567
991266 A983142983156983141983154 983148983151983151983155983145983150983143 983156983144983141 983139983141983150983156983154983137983148 983139983151983149983152983137983154983156983149983141983150983156 983156983144983141
983159983137983156983141983154983152983148983137983150983141 983137983154983141983137 983145983155
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2805)420()( m x Bl L A L
=minus=minus=
m A
T
L
I
L 875180
150==
nabla=
L983151983155983156 B983157983151983161983137983150983139983161 M983141983156983144983151983140
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 6667
991266 983124983144983141 983144983141983145983143983144983156 983151983142 983156983144983141 983139983141983150983156983141983154 983151983142 983138983157983151983161983137983150983139983161 983145983150983139983154983141983137983155983141983155 983156983151
991266 983124983144983141 983149983151983149983141983150983156 983151983142 983145983150983141983154983156983145983137 983151983142 983156983144983141 983159983137983156983141983154983152983148983137983150983141 983137983154983141983137
991266 983124983144983141 983149983141983156983137983139983141983150983156983154983145983139 983154983137983140983145983157983155
m
T
KB L
L 93802
8751
2 ===
433
6716612
)420(5
12
)(m
l L B I L
=minus
=minus
=
m I
BM
I
L
L 1111150
67166==
nabla
=
L983151983155983156 B983157983151983161983137983150983139983161 M983141983156983144983151983140
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 6767
991266 983124983144983141 983149983141983156983137983139983141983150983156983154983145983139 983144983141983145983143983144983156
991266 983122983145983143983144983156983145983150983143 983149983151983149983141983150983156 983142983151983154 983155983149983137983148983148 983144983141983141983148 983137983150983143983148983141983155
m KG BM KBGM L L L 54905111119380 =minus+=minus+=
mt xGM M L
sin34984sin549075153sin φ φ φ ==∆=
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 2167
983110983137983139983156983151983154 983151983142 983123983157983138983140983145983158983145983155983145983151983150
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983138983161 983156983144983141 983137983152983152983148983145983139983137983138983148983141 983154983141983143983157983148983137983156983145983151983150983155 983137983150983140 983138983161 983145983150983156983141983154983150983137983156983145983151983150983137983148 983139983151983150983158983141983150983156983145983151983150 983156983144983137983156
983140983141983152983141983150983140983155 983151983150 983155983144983145983152 983148983141983150983143983156983144 983137983150983140 983139983154983145983156983141983154983145983151983150 983151983142 983155983141983154983158983145983139983141
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 2267
983120983141983154983149983145983155983155983145983138983148983141 983116983141983150983143983156983144
983120983141983154983149983145983155983155983145983138983148983141 L983141983150983143983156983144 983145983155 983151983138983156983137983145983150983141983140 983138983161 983149983157983148983156983145983152983148983161983145983150983143 983156983144983141 983142983148983151983151983140983137983138983148983141 983148983141983150983143983156983144 983137983156
983156983144983137983156 983152983151983145983150983156 983138983161 983156983144983141 983142983137983139983156983151983154 983151983142 983155983157983138983140983145983158983145983155983145983151983150
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 2367
D983141983156983141983154983149983145983150983137983156983145983151983150 983151983142 983156983144983141 983148983151983139983137983156983145983151983150 983151983142 983156983144983141 983158983151983148983157983149983141 983139983141983150983156983154983141 983151983142
983140983137983149983137983143983141983140 983139983151983149983152983137983154983156983149983141983150983156
Δ I983150983145983156983145983137983148 983140983145983155983152983148983137983139983141983149983141983150983156 Δ1 D983145983155983152983148983137983139983141983149983141983150983156 983137983142983156983141983154 983140983137983149983137983143983141983140
B I983150983145983156983145983137983148 983139983141983150983156983154983141 983151983142 983138983157983151983161983137983150983139983161
G I983150983145983156983145983137983148 983139983141983150983156983154983141 983151983142 9831439831549831379831589831459831569831619831600 I983150983145983156983145983137983148 983139983141983150983156983154983141 983151983142 983148983151983150983143983145983156983157983140983145983150983137983148 983138983157983151983161983137983150983139983161 LCB
983158983159 983124983144983141 983158983151983148983157983149983141 983151983142 983159983137983156983141983154 983141983150983156983141983154983145983150983143 983156983144983141 983158983141983155983155983141983148
983160983159 D983145983155983156983137983150983139983141 983151983142 983158983151983148983157983149983141 983139983141983150983156983154983141 983151983142 983140983137983149983137983143983141983140 983139983151983149983152983137983154983156983149983141983150983156 983142983154983151983149 983149983137983141983155983156983151983154983161
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 2467
D983141983156983141983154983149983145983150983137983156983145983151983150 983151983142 983156983144983141 983148983151983139983137983156983145983151983150 983151983142 983156983144983141 983158983151983148983157983149983141 983139983141983150983156983154983141 983151983142
983140983137983149983137983143983141983140 983139983151983149983152983137983154983156983149983141983150983156
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 2567
D983141983156983141983154983149983145983150983137983156983145983151983150 983151983142 983156983144983141 983158983151983148983157983149983141 983151983142 983159983137983156983141983154 983141983150983156983141983154983145983150983143 983156983144983141 983158983141983155983155983141983148
Initial displacement and longitudinal centre of buoyancy (LCB) can be read from hydrostatcic curves
However displacement and LCB are unknown after damaged
Therefore if trim forward and aft draught are known trimmed waterline can be drawn over Bonjean
area curves
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 2667
983108983141983156983141983154983149983145983150983137983156983145983151983150 983151983142 983140983137983149983137983143983141983140 983148983141983150983143983156983144 983137983150983140 983148983151983139983137983156983145983151983150 983151983142 983149983145983140
983151983142 983139983151983149983152983137983154983156983149983141983150983156
vw The volume of water entering the vessel
xw Distance of volume centre of damaged compartment from maestory
micro Permability of the compartment
v0 Volume of the compartment
xm Distance of the volume centre of the compartment to the mid of damaged length
xl Distance of the mid of damaged length of compartment to maestory
xc Distance of the computed volume centre of compartment to maestory (xc=xl-xm)
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 2767
983108983141983156983141983154983149983145983150983137983156983145983151983150 983151983142 983140983137983149983137983143983141983140 983148983141983150983143983156983144 983137983150983140 983148983151983139983137983156983145983151983150 983151983142 983149983145983140
983151983142 983139983151983149983152983137983154983156983149983141983150983156
Damaged length and location of compartment can be determined by iterative
procedure
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 2867
bull The volume of water entering the vessel (vw)
bull Distance of volume centre of damaged compartment from amidships Θ ( xw)
bull Volume of the compartment (v0
= vw
μ)
First trial
1) Assume xm=0 (xl=xw)
2) Damaged Length l1 = (Volume of the compartment v0) (mean sec Area Amean)
where Amean is determined from trimmed sectional area curve
983108983141983156983141983154983149983145983150983137983156983145983151983150 983151983142 983140983137983149983137983143983141983140 983148983141983150983143983156983144 983137983150983140 983148983151983139983137983156983145983151983150 983151983142 983149983145983140
983151983142 983139983151983149983152983137983154983156983149983141983150983156
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 2967
3) In order to determine vm and xm
s = l1 4
vm = (s 3) sum3
xm = s sum4 sum3
xc = xl ndash xm
|vm-v0| le Tolarence for volume
|xc-xw| le Tolarence for location of volume centre
l=l1 xl=xw
983108983141983156983141983154983149983145983150983137983156983145983151983150 983151983142 983140983137983149983137983143983141983140 983148983141983150983143983156983144 983137983150983140 983148983151983139983137983156983145983151983150 983151983142 983149983145983140
983151983142 983139983151983149983152983137983154983156983149983141983150983156
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 3067
983108983141983156983141983154983149983145983150983137983156983145983151983150 983151983142 983140983137983149983137983143983141983140 983148983141983150983143983156983144 983137983150983140 983148983151983139983137983156983145983151983150 983151983142 983149983145983140
983151983142 983139983151983149983152983137983154983156983149983141983150983156Second Trial
Damaged length is changed proportionally by the volume
l2 = l1 times (v0v
m)
vm Computed volume at first trial
If the value of xm computed at first trial is negative then the mid of the
compartment slides to the bow
xl = xw+xm
where xm is the distance of the volume centre of compartment to amidship
computed at first trial
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 3167
In order to determine vm and xm
983108983141983156983141983154983149983145983150983137983156983145983151983150 983151983142 983140983137983149983137983143983141983140 983148983141983150983143983156983144 983137983150983140 983148983151983139983137983156983145983151983150 983151983142 983149983145983140
983151983142 983139983151983149983152983137983154983156983149983141983150983156
s = l2 4
vm = (s 3) sum3
xm = s sum4 sum3
xc = xl ndash xm
|vm-v0| le Tolarence for volume
|xc-xw| le Tolarence for location of volume centre
l=l2
If tolarances for both volume and location are not satisfied third fourthtrials are made similar to
second trial
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 3267
If either tolarence for volume or tolarance for location are satisfied at a trial
satisfied one is fixed trials are continued to make for the other one
983108983141983156983141983154983149983145983150983137983156983145983151983150 983151983142 983140983137983149983137983143983141983140 983148983141983150983143983156983144 983137983150983140 983148983151983139983137983156983145983151983150 983151983142 983149983145983140
983151983142 983139983151983149983152983137983154983156983149983141983150983156
8162019 Damaged Stability
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A ship is 116 meter long and displaces 7842 ton in salt water (ρ1=1025 tm3)
when her mean draught is 64m Longitudinal Centre of Buoyancy (LCB) is
0615 m aft from amidships After one of her stern compartment is damaged
she floats trimmed to the aft Her sectional areas after damaged are given in the
following table
a) Determine the volume of water entering the vessel (vw) and the location of
volume centre of damaged compartment (xw)
b) Assume permability of compartment micro is 1 Determine damaged length
and Distance of the mid of damaged length of compartment to amidship
983109983160983137983149983152983148983141 2
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 3467
8162019 Damaged Stability
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8162019 Damaged Stability
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Predicted xw
is between section 2 and section 3
983123983141983139 N983151 983123983141983139 A983154983141983137 D983145983155983156 A9831499831459831559831449831459831522 10135 983085348
3 1208 983085232
983123983141983139 A983154983141983137 983137983156 98308524983149 983142983154983151983149 983137983149983145983140983155983144983145983152 = 11959831492
l1=v0Amean=204081195=17078 m
s=l14=427 m
983109983160983137983149983152983148983141 2983085983123983119983116983125983124983113983119983118
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 3767
983161983145 L983151983139 A983149983141983137983150 983123M M A983154983149
9831311983133 9831312983133 98313119831339832559831312983133 9831313983133 983131198313398325598313129831339832559831313983133
0 9830853254 1051 1 1051 2 21021 9830852827 1123 4 4492 1 4492
2 98308524 1195 2 239 0 0
3 9830851973 1219 4 4876 9830851 9830854876
4 9830851546 1233 1 1233 9830852 9830852466
sum983091983101 14042 sum983092983101 983085748
vm
= (s3) sum3= 199864479831493
xm
=s sum4sum3= 9830850227983149
v0-vm=20408-19986=422 m3
Error=422times10020408=207
983109983160983137983149983152983148983141 2983085983123983119983116983125983124983113983119983118
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 3867
Methods of Calculation
There two available method calculating the
final stage of the damaged vessel
bull Lost Buoyancy Method
bull Added Weight Method
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 3967
Comparision of Lost Buoyancy and Added
Weight Methods
8162019 Damaged Stability
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Consider a vessel that has been damaged such
that a portion of the bottom is now open to the
sea
The vesselrsquos draft will increase because an amount
of the buoyancy was lost
Added Weight Method
Added Weight Method
8162019 Damaged Stability
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Added Weight Method
In this method flood water is treated as a fixed weight (for example the
weight of water of volume ABEF) This added weight is balanced by the
additional buoyant force of the layer WL1WL
The added weight can be determined by either the volume ABEF or
waterline WL1 Therefore WL1 waterline is not known can be just guessed
For the predicted waterline added weight and additional buoyant force
caculation are done iteratively until both of them are equal This method is
known as Added weight method
Determination of Added Weight
8162019 Damaged Stability
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Determination of Added Weight
vc Volume of damaged compartment (DCEF)
ac The surface area (AB) of damaged compartment on the waterline
micro The volume permability of damaged compartment
microa The area permability of the surface of damaged compartment
∆ The initial displacement
∆1 The displacement at final stage
vw The volume of water entering the vessel (ABEH)
w The weight of water entering the vessel
p The value of parallel sinkage
If th t th l l i k i h f t l f
8162019 Damaged Stability
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If we assume that the paralel sinkage cause a minor change of water plane area of a
ship (Awp
asymp Awp1
) we can determine the paralel sinkage by equating the volume of
the layer WL1WL to the volume of ABEF
If the damaged compartment is bounded on top
8162019 Damaged Stability
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8162019 Damaged Stability
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Longitudinal Metacentre Radius at final stage
Free Surface Effect
Damaged compartment can be considered as a half filled tank
Free Contact Effect
Damaged compartment can be considered as a half filled tank
T M H i h
8162019 Damaged Stability
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Transverse Metacentre Height
The angle of heel
8162019 Damaged Stability
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L it di l M t t H i ht
8162019 Damaged Stability
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Longitudinal Metacentre Height
8162019 Damaged Stability
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E983160983137983149983152983148983141 A 983138983137983154983143983141
8162019 Damaged Stability
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E983160983137983149983152983148983141 A 983138983137983154983143983141
991266 L = 20 983149991266 B = 5 983149
991266 983124 = 15 983149
991266 KG = 15 983149
I983150983156983137983139983156 C983151983150983140983145983156983145983151983150
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 5167
I983150983156983137983139983156 C983151983150983140983145983156983145983151983150
991266 983124983144983141 983140983145983155983152983148983137983139983141983149983141983150983156 983158983151983148983157983149983141
991266 983124983144983141 983149983137983155983155 983140983145983155983152983148983137983139983141983149983141983150983156
991266 983124983144983141 983149983151983149983141983150983156 983151983142 983145983150983141983154983156983145983137 983151983142 983156983144983141 983159983137983156983141983154983152983148983137983150983141 983137983154983141983137983137983138983151983157983156 CL
3
15051520 m x xT B L
I I
==sdotsdot=nabla
tons x I
751531500251 ==nablasdot=∆ ρ
433
33208
12
205
12
m x L B
I I
===
I983150983156983137983139983156 C983151983150983140983145983156983145983151983150
8162019 Damaged Stability
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I983150983156983137983139983156 C983151983150983140983145983156983145983151983150
991266 M983141983156983137983139983141983150983156983154983145983139 983154983137983140983145983157983155
991266 O983154 983145983156 983139983151983157983148983140 983138983141 983139983137983148983139983157983148983137983156983141983140 983140983145983154983141983139983156983148983161 983137983155
991266 H983141983145983143983144983156 983151983142 983156983144983141 983139983141983150983156983141983154 983151983142 983138983157983151983161983137983150983139983161
m I
BM
I
I 3891
150
33208==
nabla
=
m xT
B
LBT
L B BM
I I
I 3891
5112
5
12
12 223
====
mT
KB I
I 750
2
==
I983150983156983137983139983156 C983151983150983140983145983156983145983151983150
8162019 Damaged Stability
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991266 983124983144983141 983149983141983156983137983139983141983150983156983154983145983139 983144983141983145983143983144983156
991266 F983151983154 983155983149983137983148983148 983137983150983143983148983141983155 983151983142 983144983141983141983148 983156983144983141 983154983145983143983144983156983145983150983143 983149983151983149983141983150983156
m KG BM KBGM I I 63905013891750 =minus+=minus+=
sin22998sin693075153sin mt x xGM M I I
φ φ φ ==∆=
8162019 Damaged Stability
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8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 5567
983116983119983123983124 983106983125983119983129983105983118983107983129 983117983109983124983112983119983108
Paralel Sinkage
Volume (DCEF)=Volume (W1ADW+BL1LC)
Damaged compartment is bounded on top
983116983119983123983124 983106983125983119983129983105983118983107983129 983117983109983124983112983119983108
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 5667
983116983119983123983124 983106983125983119983129983105983118983107983129 983117983109983124983112983119983108
bull It is assumed that displacement and location of vertical centre
of gravity does not change after damaged
983116983119983123983124 983106983125983119983129983105983118983107983129 983117983109983124983112983119983108
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 5767
983116983119983123983124 983106983125983119983129983105983118983107983129 983117983109983124983112983119983108
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 5867
The heel angle of damaged ship is determined by
where
d is the distance between the volume centre of damaged compartment
and the new longitudinal centre of floatation
wc=vc μ ρ
983116983119983123983124 983106983125983119983129983105983118983107983129 983117983109983124983112983119983108
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 5967
983116983119983123983124 983106983125983119983129983105983118983107983129 983117983109983124983112983119983108
983116983119983123983124 983106983125983119983129983105983118983107983129 983117983109983124983112983119983108
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 6067
Longitudinal Metacentre Height of a Damaged Ship
983116983119983123983124 983106983125983119983129983105983118983107983129 983117983109983124983112983119983108
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 6167
983110983151983154983159983137983154983140 983137983150983140 983137983142983156 983140983154983137983157983143983144983156983155 983137983142983156983141983154 983140983137983149983137983143983141983140
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 6267
983120983151983154983156 983105983142983156 983120983151983154983156 983110983151983154983141 983123983156983137983154983138983151983137983154983140 983105983142983156 983123983156983137983154983138983151983137983154983140 983110983151983154983159983137983154983140
I983150983145983156983145983137983148 D983154983137983157983143983144983156 983124 983124 983124 983124
983120983137983154983137983148983141983148 983123983145983150983147983137983143983141 +983152 +983152 +983152 +983120
H983141983141983148 983085983149983145 983085983149983145 +983149983155 +983149983155
983124983154983145983149 983085983156983147 +983156983138 983085983156983147 +983156983138
F983145983150983137983148 D983154983137983157983143983144983156 983124+983152983085983149983145983085983156983147 983124+983152983085983149983145+983156983138 983124+983152+983149983155983085983156983147 983124+983152+983149983155+983156983138
Table 1 Final Draughts for a starboard side damaged ship
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 6367
L983151983155983156 B983157983151983161983137983150983139983161 M983141983156983144983151983140
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 6467
L983151983155983156 B983157983151983161983137983150983139983161 M983141983156983144983151983140
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 6567
991266 A983142983156983141983154 983148983151983151983155983145983150983143 983156983144983141 983139983141983150983156983154983137983148 983139983151983149983152983137983154983156983149983141983150983156 983156983144983141
983159983137983156983141983154983152983148983137983150983141 983137983154983141983137 983145983155
991266 983124983151 983139983151983149983152983141983150983155983137983156983141 983142983151983154 983156983144983141 983148983151983155983155 983151983142 983138983157983151983161983137983150983139983161 983151983142 983156983144983141
983139983141983150983156983154983137983148 983139983151983149983152983137983154983156983149983141983150983156 983156983144983141 983140983154983137983142983156 983145983150983139983154983141983137983155983141983155 983156983151
2805)420()( m x Bl L A L
=minus=minus=
m A
T
L
I
L 875180
150==
nabla=
L983151983155983156 B983157983151983161983137983150983139983161 M983141983156983144983151983140
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 6667
991266 983124983144983141 983144983141983145983143983144983156 983151983142 983156983144983141 983139983141983150983156983141983154 983151983142 983138983157983151983161983137983150983139983161 983145983150983139983154983141983137983155983141983155 983156983151
991266 983124983144983141 983149983151983149983141983150983156 983151983142 983145983150983141983154983156983145983137 983151983142 983156983144983141 983159983137983156983141983154983152983148983137983150983141 983137983154983141983137
991266 983124983144983141 983149983141983156983137983139983141983150983156983154983145983139 983154983137983140983145983157983155
m
T
KB L
L 93802
8751
2 ===
433
6716612
)420(5
12
)(m
l L B I L
=minus
=minus
=
m I
BM
I
L
L 1111150
67166==
nabla
=
L983151983155983156 B983157983151983161983137983150983139983161 M983141983156983144983151983140
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 6767
991266 983124983144983141 983149983141983156983137983139983141983150983156983154983145983139 983144983141983145983143983144983156
991266 983122983145983143983144983156983145983150983143 983149983151983149983141983150983156 983142983151983154 983155983149983137983148983148 983144983141983141983148 983137983150983143983148983141983155
m KG BM KBGM L L L 54905111119380 =minus+=minus+=
mt xGM M L
sin34984sin549075153sin φ φ φ ==∆=
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 2267
983120983141983154983149983145983155983155983145983138983148983141 983116983141983150983143983156983144
983120983141983154983149983145983155983155983145983138983148983141 L983141983150983143983156983144 983145983155 983151983138983156983137983145983150983141983140 983138983161 983149983157983148983156983145983152983148983161983145983150983143 983156983144983141 983142983148983151983151983140983137983138983148983141 983148983141983150983143983156983144 983137983156
983156983144983137983156 983152983151983145983150983156 983138983161 983156983144983141 983142983137983139983156983151983154 983151983142 983155983157983138983140983145983158983145983155983145983151983150
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 2367
D983141983156983141983154983149983145983150983137983156983145983151983150 983151983142 983156983144983141 983148983151983139983137983156983145983151983150 983151983142 983156983144983141 983158983151983148983157983149983141 983139983141983150983156983154983141 983151983142
983140983137983149983137983143983141983140 983139983151983149983152983137983154983156983149983141983150983156
Δ I983150983145983156983145983137983148 983140983145983155983152983148983137983139983141983149983141983150983156 Δ1 D983145983155983152983148983137983139983141983149983141983150983156 983137983142983156983141983154 983140983137983149983137983143983141983140
B I983150983145983156983145983137983148 983139983141983150983156983154983141 983151983142 983138983157983151983161983137983150983139983161
G I983150983145983156983145983137983148 983139983141983150983156983154983141 983151983142 9831439831549831379831589831459831569831619831600 I983150983145983156983145983137983148 983139983141983150983156983154983141 983151983142 983148983151983150983143983145983156983157983140983145983150983137983148 983138983157983151983161983137983150983139983161 LCB
983158983159 983124983144983141 983158983151983148983157983149983141 983151983142 983159983137983156983141983154 983141983150983156983141983154983145983150983143 983156983144983141 983158983141983155983155983141983148
983160983159 D983145983155983156983137983150983139983141 983151983142 983158983151983148983157983149983141 983139983141983150983156983154983141 983151983142 983140983137983149983137983143983141983140 983139983151983149983152983137983154983156983149983141983150983156 983142983154983151983149 983149983137983141983155983156983151983154983161
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 2467
D983141983156983141983154983149983145983150983137983156983145983151983150 983151983142 983156983144983141 983148983151983139983137983156983145983151983150 983151983142 983156983144983141 983158983151983148983157983149983141 983139983141983150983156983154983141 983151983142
983140983137983149983137983143983141983140 983139983151983149983152983137983154983156983149983141983150983156
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 2567
D983141983156983141983154983149983145983150983137983156983145983151983150 983151983142 983156983144983141 983158983151983148983157983149983141 983151983142 983159983137983156983141983154 983141983150983156983141983154983145983150983143 983156983144983141 983158983141983155983155983141983148
Initial displacement and longitudinal centre of buoyancy (LCB) can be read from hydrostatcic curves
However displacement and LCB are unknown after damaged
Therefore if trim forward and aft draught are known trimmed waterline can be drawn over Bonjean
area curves
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 2667
983108983141983156983141983154983149983145983150983137983156983145983151983150 983151983142 983140983137983149983137983143983141983140 983148983141983150983143983156983144 983137983150983140 983148983151983139983137983156983145983151983150 983151983142 983149983145983140
983151983142 983139983151983149983152983137983154983156983149983141983150983156
vw The volume of water entering the vessel
xw Distance of volume centre of damaged compartment from maestory
micro Permability of the compartment
v0 Volume of the compartment
xm Distance of the volume centre of the compartment to the mid of damaged length
xl Distance of the mid of damaged length of compartment to maestory
xc Distance of the computed volume centre of compartment to maestory (xc=xl-xm)
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 2767
983108983141983156983141983154983149983145983150983137983156983145983151983150 983151983142 983140983137983149983137983143983141983140 983148983141983150983143983156983144 983137983150983140 983148983151983139983137983156983145983151983150 983151983142 983149983145983140
983151983142 983139983151983149983152983137983154983156983149983141983150983156
Damaged length and location of compartment can be determined by iterative
procedure
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 2867
bull The volume of water entering the vessel (vw)
bull Distance of volume centre of damaged compartment from amidships Θ ( xw)
bull Volume of the compartment (v0
= vw
μ)
First trial
1) Assume xm=0 (xl=xw)
2) Damaged Length l1 = (Volume of the compartment v0) (mean sec Area Amean)
where Amean is determined from trimmed sectional area curve
983108983141983156983141983154983149983145983150983137983156983145983151983150 983151983142 983140983137983149983137983143983141983140 983148983141983150983143983156983144 983137983150983140 983148983151983139983137983156983145983151983150 983151983142 983149983145983140
983151983142 983139983151983149983152983137983154983156983149983141983150983156
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 2967
3) In order to determine vm and xm
s = l1 4
vm = (s 3) sum3
xm = s sum4 sum3
xc = xl ndash xm
|vm-v0| le Tolarence for volume
|xc-xw| le Tolarence for location of volume centre
l=l1 xl=xw
983108983141983156983141983154983149983145983150983137983156983145983151983150 983151983142 983140983137983149983137983143983141983140 983148983141983150983143983156983144 983137983150983140 983148983151983139983137983156983145983151983150 983151983142 983149983145983140
983151983142 983139983151983149983152983137983154983156983149983141983150983156
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 3067
983108983141983156983141983154983149983145983150983137983156983145983151983150 983151983142 983140983137983149983137983143983141983140 983148983141983150983143983156983144 983137983150983140 983148983151983139983137983156983145983151983150 983151983142 983149983145983140
983151983142 983139983151983149983152983137983154983156983149983141983150983156Second Trial
Damaged length is changed proportionally by the volume
l2 = l1 times (v0v
m)
vm Computed volume at first trial
If the value of xm computed at first trial is negative then the mid of the
compartment slides to the bow
xl = xw+xm
where xm is the distance of the volume centre of compartment to amidship
computed at first trial
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 3167
In order to determine vm and xm
983108983141983156983141983154983149983145983150983137983156983145983151983150 983151983142 983140983137983149983137983143983141983140 983148983141983150983143983156983144 983137983150983140 983148983151983139983137983156983145983151983150 983151983142 983149983145983140
983151983142 983139983151983149983152983137983154983156983149983141983150983156
s = l2 4
vm = (s 3) sum3
xm = s sum4 sum3
xc = xl ndash xm
|vm-v0| le Tolarence for volume
|xc-xw| le Tolarence for location of volume centre
l=l2
If tolarances for both volume and location are not satisfied third fourthtrials are made similar to
second trial
8162019 Damaged Stability
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If either tolarence for volume or tolarance for location are satisfied at a trial
satisfied one is fixed trials are continued to make for the other one
983108983141983156983141983154983149983145983150983137983156983145983151983150 983151983142 983140983137983149983137983143983141983140 983148983141983150983143983156983144 983137983150983140 983148983151983139983137983156983145983151983150 983151983142 983149983145983140
983151983142 983139983151983149983152983137983154983156983149983141983150983156
8162019 Damaged Stability
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A ship is 116 meter long and displaces 7842 ton in salt water (ρ1=1025 tm3)
when her mean draught is 64m Longitudinal Centre of Buoyancy (LCB) is
0615 m aft from amidships After one of her stern compartment is damaged
she floats trimmed to the aft Her sectional areas after damaged are given in the
following table
a) Determine the volume of water entering the vessel (vw) and the location of
volume centre of damaged compartment (xw)
b) Assume permability of compartment micro is 1 Determine damaged length
and Distance of the mid of damaged length of compartment to amidship
983109983160983137983149983152983148983141 2
8162019 Damaged Stability
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8162019 Damaged Stability
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8162019 Damaged Stability
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Predicted xw
is between section 2 and section 3
983123983141983139 N983151 983123983141983139 A983154983141983137 D983145983155983156 A9831499831459831559831449831459831522 10135 983085348
3 1208 983085232
983123983141983139 A983154983141983137 983137983156 98308524983149 983142983154983151983149 983137983149983145983140983155983144983145983152 = 11959831492
l1=v0Amean=204081195=17078 m
s=l14=427 m
983109983160983137983149983152983148983141 2983085983123983119983116983125983124983113983119983118
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 3767
983161983145 L983151983139 A983149983141983137983150 983123M M A983154983149
9831311983133 9831312983133 98313119831339832559831312983133 9831313983133 983131198313398325598313129831339832559831313983133
0 9830853254 1051 1 1051 2 21021 9830852827 1123 4 4492 1 4492
2 98308524 1195 2 239 0 0
3 9830851973 1219 4 4876 9830851 9830854876
4 9830851546 1233 1 1233 9830852 9830852466
sum983091983101 14042 sum983092983101 983085748
vm
= (s3) sum3= 199864479831493
xm
=s sum4sum3= 9830850227983149
v0-vm=20408-19986=422 m3
Error=422times10020408=207
983109983160983137983149983152983148983141 2983085983123983119983116983125983124983113983119983118
8162019 Damaged Stability
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Methods of Calculation
There two available method calculating the
final stage of the damaged vessel
bull Lost Buoyancy Method
bull Added Weight Method
8162019 Damaged Stability
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Comparision of Lost Buoyancy and Added
Weight Methods
8162019 Damaged Stability
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Consider a vessel that has been damaged such
that a portion of the bottom is now open to the
sea
The vesselrsquos draft will increase because an amount
of the buoyancy was lost
Added Weight Method
Added Weight Method
8162019 Damaged Stability
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Added Weight Method
In this method flood water is treated as a fixed weight (for example the
weight of water of volume ABEF) This added weight is balanced by the
additional buoyant force of the layer WL1WL
The added weight can be determined by either the volume ABEF or
waterline WL1 Therefore WL1 waterline is not known can be just guessed
For the predicted waterline added weight and additional buoyant force
caculation are done iteratively until both of them are equal This method is
known as Added weight method
Determination of Added Weight
8162019 Damaged Stability
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Determination of Added Weight
vc Volume of damaged compartment (DCEF)
ac The surface area (AB) of damaged compartment on the waterline
micro The volume permability of damaged compartment
microa The area permability of the surface of damaged compartment
∆ The initial displacement
∆1 The displacement at final stage
vw The volume of water entering the vessel (ABEH)
w The weight of water entering the vessel
p The value of parallel sinkage
If th t th l l i k i h f t l f
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If we assume that the paralel sinkage cause a minor change of water plane area of a
ship (Awp
asymp Awp1
) we can determine the paralel sinkage by equating the volume of
the layer WL1WL to the volume of ABEF
If the damaged compartment is bounded on top
8162019 Damaged Stability
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8162019 Damaged Stability
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Longitudinal Metacentre Radius at final stage
Free Surface Effect
Damaged compartment can be considered as a half filled tank
Free Contact Effect
Damaged compartment can be considered as a half filled tank
T M H i h
8162019 Damaged Stability
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Transverse Metacentre Height
The angle of heel
8162019 Damaged Stability
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L it di l M t t H i ht
8162019 Damaged Stability
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Longitudinal Metacentre Height
8162019 Damaged Stability
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E983160983137983149983152983148983141 A 983138983137983154983143983141
8162019 Damaged Stability
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E983160983137983149983152983148983141 A 983138983137983154983143983141
991266 L = 20 983149991266 B = 5 983149
991266 983124 = 15 983149
991266 KG = 15 983149
I983150983156983137983139983156 C983151983150983140983145983156983145983151983150
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 5167
I983150983156983137983139983156 C983151983150983140983145983156983145983151983150
991266 983124983144983141 983140983145983155983152983148983137983139983141983149983141983150983156 983158983151983148983157983149983141
991266 983124983144983141 983149983137983155983155 983140983145983155983152983148983137983139983141983149983141983150983156
991266 983124983144983141 983149983151983149983141983150983156 983151983142 983145983150983141983154983156983145983137 983151983142 983156983144983141 983159983137983156983141983154983152983148983137983150983141 983137983154983141983137983137983138983151983157983156 CL
3
15051520 m x xT B L
I I
==sdotsdot=nabla
tons x I
751531500251 ==nablasdot=∆ ρ
433
33208
12
205
12
m x L B
I I
===
I983150983156983137983139983156 C983151983150983140983145983156983145983151983150
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 5267
I983150983156983137983139983156 C983151983150983140983145983156983145983151983150
991266 M983141983156983137983139983141983150983156983154983145983139 983154983137983140983145983157983155
991266 O983154 983145983156 983139983151983157983148983140 983138983141 983139983137983148983139983157983148983137983156983141983140 983140983145983154983141983139983156983148983161 983137983155
991266 H983141983145983143983144983156 983151983142 983156983144983141 983139983141983150983156983141983154 983151983142 983138983157983151983161983137983150983139983161
m I
BM
I
I 3891
150
33208==
nabla
=
m xT
B
LBT
L B BM
I I
I 3891
5112
5
12
12 223
====
mT
KB I
I 750
2
==
I983150983156983137983139983156 C983151983150983140983145983156983145983151983150
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 5367
991266 983124983144983141 983149983141983156983137983139983141983150983156983154983145983139 983144983141983145983143983144983156
991266 F983151983154 983155983149983137983148983148 983137983150983143983148983141983155 983151983142 983144983141983141983148 983156983144983141 983154983145983143983144983156983145983150983143 983149983151983149983141983150983156
m KG BM KBGM I I 63905013891750 =minus+=minus+=
sin22998sin693075153sin mt x xGM M I I
φ φ φ ==∆=
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 5467
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 5567
983116983119983123983124 983106983125983119983129983105983118983107983129 983117983109983124983112983119983108
Paralel Sinkage
Volume (DCEF)=Volume (W1ADW+BL1LC)
Damaged compartment is bounded on top
983116983119983123983124 983106983125983119983129983105983118983107983129 983117983109983124983112983119983108
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 5667
983116983119983123983124 983106983125983119983129983105983118983107983129 983117983109983124983112983119983108
bull It is assumed that displacement and location of vertical centre
of gravity does not change after damaged
983116983119983123983124 983106983125983119983129983105983118983107983129 983117983109983124983112983119983108
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 5767
983116983119983123983124 983106983125983119983129983105983118983107983129 983117983109983124983112983119983108
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 5867
The heel angle of damaged ship is determined by
where
d is the distance between the volume centre of damaged compartment
and the new longitudinal centre of floatation
wc=vc μ ρ
983116983119983123983124 983106983125983119983129983105983118983107983129 983117983109983124983112983119983108
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 5967
983116983119983123983124 983106983125983119983129983105983118983107983129 983117983109983124983112983119983108
983116983119983123983124 983106983125983119983129983105983118983107983129 983117983109983124983112983119983108
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 6067
Longitudinal Metacentre Height of a Damaged Ship
983116983119983123983124 983106983125983119983129983105983118983107983129 983117983109983124983112983119983108
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 6167
983110983151983154983159983137983154983140 983137983150983140 983137983142983156 983140983154983137983157983143983144983156983155 983137983142983156983141983154 983140983137983149983137983143983141983140
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 6267
983120983151983154983156 983105983142983156 983120983151983154983156 983110983151983154983141 983123983156983137983154983138983151983137983154983140 983105983142983156 983123983156983137983154983138983151983137983154983140 983110983151983154983159983137983154983140
I983150983145983156983145983137983148 D983154983137983157983143983144983156 983124 983124 983124 983124
983120983137983154983137983148983141983148 983123983145983150983147983137983143983141 +983152 +983152 +983152 +983120
H983141983141983148 983085983149983145 983085983149983145 +983149983155 +983149983155
983124983154983145983149 983085983156983147 +983156983138 983085983156983147 +983156983138
F983145983150983137983148 D983154983137983157983143983144983156 983124+983152983085983149983145983085983156983147 983124+983152983085983149983145+983156983138 983124+983152+983149983155983085983156983147 983124+983152+983149983155+983156983138
Table 1 Final Draughts for a starboard side damaged ship
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 6367
L983151983155983156 B983157983151983161983137983150983139983161 M983141983156983144983151983140
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 6467
L983151983155983156 B983157983151983161983137983150983139983161 M983141983156983144983151983140
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 6567
991266 A983142983156983141983154 983148983151983151983155983145983150983143 983156983144983141 983139983141983150983156983154983137983148 983139983151983149983152983137983154983156983149983141983150983156 983156983144983141
983159983137983156983141983154983152983148983137983150983141 983137983154983141983137 983145983155
991266 983124983151 983139983151983149983152983141983150983155983137983156983141 983142983151983154 983156983144983141 983148983151983155983155 983151983142 983138983157983151983161983137983150983139983161 983151983142 983156983144983141
983139983141983150983156983154983137983148 983139983151983149983152983137983154983156983149983141983150983156 983156983144983141 983140983154983137983142983156 983145983150983139983154983141983137983155983141983155 983156983151
2805)420()( m x Bl L A L
=minus=minus=
m A
T
L
I
L 875180
150==
nabla=
L983151983155983156 B983157983151983161983137983150983139983161 M983141983156983144983151983140
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 6667
991266 983124983144983141 983144983141983145983143983144983156 983151983142 983156983144983141 983139983141983150983156983141983154 983151983142 983138983157983151983161983137983150983139983161 983145983150983139983154983141983137983155983141983155 983156983151
991266 983124983144983141 983149983151983149983141983150983156 983151983142 983145983150983141983154983156983145983137 983151983142 983156983144983141 983159983137983156983141983154983152983148983137983150983141 983137983154983141983137
991266 983124983144983141 983149983141983156983137983139983141983150983156983154983145983139 983154983137983140983145983157983155
m
T
KB L
L 93802
8751
2 ===
433
6716612
)420(5
12
)(m
l L B I L
=minus
=minus
=
m I
BM
I
L
L 1111150
67166==
nabla
=
L983151983155983156 B983157983151983161983137983150983139983161 M983141983156983144983151983140
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 6767
991266 983124983144983141 983149983141983156983137983139983141983150983156983154983145983139 983144983141983145983143983144983156
991266 983122983145983143983144983156983145983150983143 983149983151983149983141983150983156 983142983151983154 983155983149983137983148983148 983144983141983141983148 983137983150983143983148983141983155
m KG BM KBGM L L L 54905111119380 =minus+=minus+=
mt xGM M L
sin34984sin549075153sin φ φ φ ==∆=
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 2367
D983141983156983141983154983149983145983150983137983156983145983151983150 983151983142 983156983144983141 983148983151983139983137983156983145983151983150 983151983142 983156983144983141 983158983151983148983157983149983141 983139983141983150983156983154983141 983151983142
983140983137983149983137983143983141983140 983139983151983149983152983137983154983156983149983141983150983156
Δ I983150983145983156983145983137983148 983140983145983155983152983148983137983139983141983149983141983150983156 Δ1 D983145983155983152983148983137983139983141983149983141983150983156 983137983142983156983141983154 983140983137983149983137983143983141983140
B I983150983145983156983145983137983148 983139983141983150983156983154983141 983151983142 983138983157983151983161983137983150983139983161
G I983150983145983156983145983137983148 983139983141983150983156983154983141 983151983142 9831439831549831379831589831459831569831619831600 I983150983145983156983145983137983148 983139983141983150983156983154983141 983151983142 983148983151983150983143983145983156983157983140983145983150983137983148 983138983157983151983161983137983150983139983161 LCB
983158983159 983124983144983141 983158983151983148983157983149983141 983151983142 983159983137983156983141983154 983141983150983156983141983154983145983150983143 983156983144983141 983158983141983155983155983141983148
983160983159 D983145983155983156983137983150983139983141 983151983142 983158983151983148983157983149983141 983139983141983150983156983154983141 983151983142 983140983137983149983137983143983141983140 983139983151983149983152983137983154983156983149983141983150983156 983142983154983151983149 983149983137983141983155983156983151983154983161
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 2467
D983141983156983141983154983149983145983150983137983156983145983151983150 983151983142 983156983144983141 983148983151983139983137983156983145983151983150 983151983142 983156983144983141 983158983151983148983157983149983141 983139983141983150983156983154983141 983151983142
983140983137983149983137983143983141983140 983139983151983149983152983137983154983156983149983141983150983156
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 2567
D983141983156983141983154983149983145983150983137983156983145983151983150 983151983142 983156983144983141 983158983151983148983157983149983141 983151983142 983159983137983156983141983154 983141983150983156983141983154983145983150983143 983156983144983141 983158983141983155983155983141983148
Initial displacement and longitudinal centre of buoyancy (LCB) can be read from hydrostatcic curves
However displacement and LCB are unknown after damaged
Therefore if trim forward and aft draught are known trimmed waterline can be drawn over Bonjean
area curves
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 2667
983108983141983156983141983154983149983145983150983137983156983145983151983150 983151983142 983140983137983149983137983143983141983140 983148983141983150983143983156983144 983137983150983140 983148983151983139983137983156983145983151983150 983151983142 983149983145983140
983151983142 983139983151983149983152983137983154983156983149983141983150983156
vw The volume of water entering the vessel
xw Distance of volume centre of damaged compartment from maestory
micro Permability of the compartment
v0 Volume of the compartment
xm Distance of the volume centre of the compartment to the mid of damaged length
xl Distance of the mid of damaged length of compartment to maestory
xc Distance of the computed volume centre of compartment to maestory (xc=xl-xm)
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 2767
983108983141983156983141983154983149983145983150983137983156983145983151983150 983151983142 983140983137983149983137983143983141983140 983148983141983150983143983156983144 983137983150983140 983148983151983139983137983156983145983151983150 983151983142 983149983145983140
983151983142 983139983151983149983152983137983154983156983149983141983150983156
Damaged length and location of compartment can be determined by iterative
procedure
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 2867
bull The volume of water entering the vessel (vw)
bull Distance of volume centre of damaged compartment from amidships Θ ( xw)
bull Volume of the compartment (v0
= vw
μ)
First trial
1) Assume xm=0 (xl=xw)
2) Damaged Length l1 = (Volume of the compartment v0) (mean sec Area Amean)
where Amean is determined from trimmed sectional area curve
983108983141983156983141983154983149983145983150983137983156983145983151983150 983151983142 983140983137983149983137983143983141983140 983148983141983150983143983156983144 983137983150983140 983148983151983139983137983156983145983151983150 983151983142 983149983145983140
983151983142 983139983151983149983152983137983154983156983149983141983150983156
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 2967
3) In order to determine vm and xm
s = l1 4
vm = (s 3) sum3
xm = s sum4 sum3
xc = xl ndash xm
|vm-v0| le Tolarence for volume
|xc-xw| le Tolarence for location of volume centre
l=l1 xl=xw
983108983141983156983141983154983149983145983150983137983156983145983151983150 983151983142 983140983137983149983137983143983141983140 983148983141983150983143983156983144 983137983150983140 983148983151983139983137983156983145983151983150 983151983142 983149983145983140
983151983142 983139983151983149983152983137983154983156983149983141983150983156
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 3067
983108983141983156983141983154983149983145983150983137983156983145983151983150 983151983142 983140983137983149983137983143983141983140 983148983141983150983143983156983144 983137983150983140 983148983151983139983137983156983145983151983150 983151983142 983149983145983140
983151983142 983139983151983149983152983137983154983156983149983141983150983156Second Trial
Damaged length is changed proportionally by the volume
l2 = l1 times (v0v
m)
vm Computed volume at first trial
If the value of xm computed at first trial is negative then the mid of the
compartment slides to the bow
xl = xw+xm
where xm is the distance of the volume centre of compartment to amidship
computed at first trial
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 3167
In order to determine vm and xm
983108983141983156983141983154983149983145983150983137983156983145983151983150 983151983142 983140983137983149983137983143983141983140 983148983141983150983143983156983144 983137983150983140 983148983151983139983137983156983145983151983150 983151983142 983149983145983140
983151983142 983139983151983149983152983137983154983156983149983141983150983156
s = l2 4
vm = (s 3) sum3
xm = s sum4 sum3
xc = xl ndash xm
|vm-v0| le Tolarence for volume
|xc-xw| le Tolarence for location of volume centre
l=l2
If tolarances for both volume and location are not satisfied third fourthtrials are made similar to
second trial
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 3267
If either tolarence for volume or tolarance for location are satisfied at a trial
satisfied one is fixed trials are continued to make for the other one
983108983141983156983141983154983149983145983150983137983156983145983151983150 983151983142 983140983137983149983137983143983141983140 983148983141983150983143983156983144 983137983150983140 983148983151983139983137983156983145983151983150 983151983142 983149983145983140
983151983142 983139983151983149983152983137983154983156983149983141983150983156
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 3367
A ship is 116 meter long and displaces 7842 ton in salt water (ρ1=1025 tm3)
when her mean draught is 64m Longitudinal Centre of Buoyancy (LCB) is
0615 m aft from amidships After one of her stern compartment is damaged
she floats trimmed to the aft Her sectional areas after damaged are given in the
following table
a) Determine the volume of water entering the vessel (vw) and the location of
volume centre of damaged compartment (xw)
b) Assume permability of compartment micro is 1 Determine damaged length
and Distance of the mid of damaged length of compartment to amidship
983109983160983137983149983152983148983141 2
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 3467
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 3567
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 3667
Predicted xw
is between section 2 and section 3
983123983141983139 N983151 983123983141983139 A983154983141983137 D983145983155983156 A9831499831459831559831449831459831522 10135 983085348
3 1208 983085232
983123983141983139 A983154983141983137 983137983156 98308524983149 983142983154983151983149 983137983149983145983140983155983144983145983152 = 11959831492
l1=v0Amean=204081195=17078 m
s=l14=427 m
983109983160983137983149983152983148983141 2983085983123983119983116983125983124983113983119983118
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 3767
983161983145 L983151983139 A983149983141983137983150 983123M M A983154983149
9831311983133 9831312983133 98313119831339832559831312983133 9831313983133 983131198313398325598313129831339832559831313983133
0 9830853254 1051 1 1051 2 21021 9830852827 1123 4 4492 1 4492
2 98308524 1195 2 239 0 0
3 9830851973 1219 4 4876 9830851 9830854876
4 9830851546 1233 1 1233 9830852 9830852466
sum983091983101 14042 sum983092983101 983085748
vm
= (s3) sum3= 199864479831493
xm
=s sum4sum3= 9830850227983149
v0-vm=20408-19986=422 m3
Error=422times10020408=207
983109983160983137983149983152983148983141 2983085983123983119983116983125983124983113983119983118
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 3867
Methods of Calculation
There two available method calculating the
final stage of the damaged vessel
bull Lost Buoyancy Method
bull Added Weight Method
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 3967
Comparision of Lost Buoyancy and Added
Weight Methods
8162019 Damaged Stability
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Consider a vessel that has been damaged such
that a portion of the bottom is now open to the
sea
The vesselrsquos draft will increase because an amount
of the buoyancy was lost
Added Weight Method
Added Weight Method
8162019 Damaged Stability
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Added Weight Method
In this method flood water is treated as a fixed weight (for example the
weight of water of volume ABEF) This added weight is balanced by the
additional buoyant force of the layer WL1WL
The added weight can be determined by either the volume ABEF or
waterline WL1 Therefore WL1 waterline is not known can be just guessed
For the predicted waterline added weight and additional buoyant force
caculation are done iteratively until both of them are equal This method is
known as Added weight method
Determination of Added Weight
8162019 Damaged Stability
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Determination of Added Weight
vc Volume of damaged compartment (DCEF)
ac The surface area (AB) of damaged compartment on the waterline
micro The volume permability of damaged compartment
microa The area permability of the surface of damaged compartment
∆ The initial displacement
∆1 The displacement at final stage
vw The volume of water entering the vessel (ABEH)
w The weight of water entering the vessel
p The value of parallel sinkage
If th t th l l i k i h f t l f
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 4367
If we assume that the paralel sinkage cause a minor change of water plane area of a
ship (Awp
asymp Awp1
) we can determine the paralel sinkage by equating the volume of
the layer WL1WL to the volume of ABEF
If the damaged compartment is bounded on top
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 4467
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 4567
Longitudinal Metacentre Radius at final stage
Free Surface Effect
Damaged compartment can be considered as a half filled tank
Free Contact Effect
Damaged compartment can be considered as a half filled tank
T M H i h
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 4667
Transverse Metacentre Height
The angle of heel
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 4767
L it di l M t t H i ht
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 4867
Longitudinal Metacentre Height
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 4967
E983160983137983149983152983148983141 A 983138983137983154983143983141
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 5067
E983160983137983149983152983148983141 A 983138983137983154983143983141
991266 L = 20 983149991266 B = 5 983149
991266 983124 = 15 983149
991266 KG = 15 983149
I983150983156983137983139983156 C983151983150983140983145983156983145983151983150
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 5167
I983150983156983137983139983156 C983151983150983140983145983156983145983151983150
991266 983124983144983141 983140983145983155983152983148983137983139983141983149983141983150983156 983158983151983148983157983149983141
991266 983124983144983141 983149983137983155983155 983140983145983155983152983148983137983139983141983149983141983150983156
991266 983124983144983141 983149983151983149983141983150983156 983151983142 983145983150983141983154983156983145983137 983151983142 983156983144983141 983159983137983156983141983154983152983148983137983150983141 983137983154983141983137983137983138983151983157983156 CL
3
15051520 m x xT B L
I I
==sdotsdot=nabla
tons x I
751531500251 ==nablasdot=∆ ρ
433
33208
12
205
12
m x L B
I I
===
I983150983156983137983139983156 C983151983150983140983145983156983145983151983150
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 5267
I983150983156983137983139983156 C983151983150983140983145983156983145983151983150
991266 M983141983156983137983139983141983150983156983154983145983139 983154983137983140983145983157983155
991266 O983154 983145983156 983139983151983157983148983140 983138983141 983139983137983148983139983157983148983137983156983141983140 983140983145983154983141983139983156983148983161 983137983155
991266 H983141983145983143983144983156 983151983142 983156983144983141 983139983141983150983156983141983154 983151983142 983138983157983151983161983137983150983139983161
m I
BM
I
I 3891
150
33208==
nabla
=
m xT
B
LBT
L B BM
I I
I 3891
5112
5
12
12 223
====
mT
KB I
I 750
2
==
I983150983156983137983139983156 C983151983150983140983145983156983145983151983150
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 5367
991266 983124983144983141 983149983141983156983137983139983141983150983156983154983145983139 983144983141983145983143983144983156
991266 F983151983154 983155983149983137983148983148 983137983150983143983148983141983155 983151983142 983144983141983141983148 983156983144983141 983154983145983143983144983156983145983150983143 983149983151983149983141983150983156
m KG BM KBGM I I 63905013891750 =minus+=minus+=
sin22998sin693075153sin mt x xGM M I I
φ φ φ ==∆=
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 5467
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 5567
983116983119983123983124 983106983125983119983129983105983118983107983129 983117983109983124983112983119983108
Paralel Sinkage
Volume (DCEF)=Volume (W1ADW+BL1LC)
Damaged compartment is bounded on top
983116983119983123983124 983106983125983119983129983105983118983107983129 983117983109983124983112983119983108
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 5667
983116983119983123983124 983106983125983119983129983105983118983107983129 983117983109983124983112983119983108
bull It is assumed that displacement and location of vertical centre
of gravity does not change after damaged
983116983119983123983124 983106983125983119983129983105983118983107983129 983117983109983124983112983119983108
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 5767
983116983119983123983124 983106983125983119983129983105983118983107983129 983117983109983124983112983119983108
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 5867
The heel angle of damaged ship is determined by
where
d is the distance between the volume centre of damaged compartment
and the new longitudinal centre of floatation
wc=vc μ ρ
983116983119983123983124 983106983125983119983129983105983118983107983129 983117983109983124983112983119983108
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 5967
983116983119983123983124 983106983125983119983129983105983118983107983129 983117983109983124983112983119983108
983116983119983123983124 983106983125983119983129983105983118983107983129 983117983109983124983112983119983108
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 6067
Longitudinal Metacentre Height of a Damaged Ship
983116983119983123983124 983106983125983119983129983105983118983107983129 983117983109983124983112983119983108
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 6167
983110983151983154983159983137983154983140 983137983150983140 983137983142983156 983140983154983137983157983143983144983156983155 983137983142983156983141983154 983140983137983149983137983143983141983140
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 6267
983120983151983154983156 983105983142983156 983120983151983154983156 983110983151983154983141 983123983156983137983154983138983151983137983154983140 983105983142983156 983123983156983137983154983138983151983137983154983140 983110983151983154983159983137983154983140
I983150983145983156983145983137983148 D983154983137983157983143983144983156 983124 983124 983124 983124
983120983137983154983137983148983141983148 983123983145983150983147983137983143983141 +983152 +983152 +983152 +983120
H983141983141983148 983085983149983145 983085983149983145 +983149983155 +983149983155
983124983154983145983149 983085983156983147 +983156983138 983085983156983147 +983156983138
F983145983150983137983148 D983154983137983157983143983144983156 983124+983152983085983149983145983085983156983147 983124+983152983085983149983145+983156983138 983124+983152+983149983155983085983156983147 983124+983152+983149983155+983156983138
Table 1 Final Draughts for a starboard side damaged ship
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 6367
L983151983155983156 B983157983151983161983137983150983139983161 M983141983156983144983151983140
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 6467
L983151983155983156 B983157983151983161983137983150983139983161 M983141983156983144983151983140
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 6567
991266 A983142983156983141983154 983148983151983151983155983145983150983143 983156983144983141 983139983141983150983156983154983137983148 983139983151983149983152983137983154983156983149983141983150983156 983156983144983141
983159983137983156983141983154983152983148983137983150983141 983137983154983141983137 983145983155
991266 983124983151 983139983151983149983152983141983150983155983137983156983141 983142983151983154 983156983144983141 983148983151983155983155 983151983142 983138983157983151983161983137983150983139983161 983151983142 983156983144983141
983139983141983150983156983154983137983148 983139983151983149983152983137983154983156983149983141983150983156 983156983144983141 983140983154983137983142983156 983145983150983139983154983141983137983155983141983155 983156983151
2805)420()( m x Bl L A L
=minus=minus=
m A
T
L
I
L 875180
150==
nabla=
L983151983155983156 B983157983151983161983137983150983139983161 M983141983156983144983151983140
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 6667
991266 983124983144983141 983144983141983145983143983144983156 983151983142 983156983144983141 983139983141983150983156983141983154 983151983142 983138983157983151983161983137983150983139983161 983145983150983139983154983141983137983155983141983155 983156983151
991266 983124983144983141 983149983151983149983141983150983156 983151983142 983145983150983141983154983156983145983137 983151983142 983156983144983141 983159983137983156983141983154983152983148983137983150983141 983137983154983141983137
991266 983124983144983141 983149983141983156983137983139983141983150983156983154983145983139 983154983137983140983145983157983155
m
T
KB L
L 93802
8751
2 ===
433
6716612
)420(5
12
)(m
l L B I L
=minus
=minus
=
m I
BM
I
L
L 1111150
67166==
nabla
=
L983151983155983156 B983157983151983161983137983150983139983161 M983141983156983144983151983140
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 6767
991266 983124983144983141 983149983141983156983137983139983141983150983156983154983145983139 983144983141983145983143983144983156
991266 983122983145983143983144983156983145983150983143 983149983151983149983141983150983156 983142983151983154 983155983149983137983148983148 983144983141983141983148 983137983150983143983148983141983155
m KG BM KBGM L L L 54905111119380 =minus+=minus+=
mt xGM M L
sin34984sin549075153sin φ φ φ ==∆=
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 2467
D983141983156983141983154983149983145983150983137983156983145983151983150 983151983142 983156983144983141 983148983151983139983137983156983145983151983150 983151983142 983156983144983141 983158983151983148983157983149983141 983139983141983150983156983154983141 983151983142
983140983137983149983137983143983141983140 983139983151983149983152983137983154983156983149983141983150983156
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 2567
D983141983156983141983154983149983145983150983137983156983145983151983150 983151983142 983156983144983141 983158983151983148983157983149983141 983151983142 983159983137983156983141983154 983141983150983156983141983154983145983150983143 983156983144983141 983158983141983155983155983141983148
Initial displacement and longitudinal centre of buoyancy (LCB) can be read from hydrostatcic curves
However displacement and LCB are unknown after damaged
Therefore if trim forward and aft draught are known trimmed waterline can be drawn over Bonjean
area curves
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 2667
983108983141983156983141983154983149983145983150983137983156983145983151983150 983151983142 983140983137983149983137983143983141983140 983148983141983150983143983156983144 983137983150983140 983148983151983139983137983156983145983151983150 983151983142 983149983145983140
983151983142 983139983151983149983152983137983154983156983149983141983150983156
vw The volume of water entering the vessel
xw Distance of volume centre of damaged compartment from maestory
micro Permability of the compartment
v0 Volume of the compartment
xm Distance of the volume centre of the compartment to the mid of damaged length
xl Distance of the mid of damaged length of compartment to maestory
xc Distance of the computed volume centre of compartment to maestory (xc=xl-xm)
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 2767
983108983141983156983141983154983149983145983150983137983156983145983151983150 983151983142 983140983137983149983137983143983141983140 983148983141983150983143983156983144 983137983150983140 983148983151983139983137983156983145983151983150 983151983142 983149983145983140
983151983142 983139983151983149983152983137983154983156983149983141983150983156
Damaged length and location of compartment can be determined by iterative
procedure
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 2867
bull The volume of water entering the vessel (vw)
bull Distance of volume centre of damaged compartment from amidships Θ ( xw)
bull Volume of the compartment (v0
= vw
μ)
First trial
1) Assume xm=0 (xl=xw)
2) Damaged Length l1 = (Volume of the compartment v0) (mean sec Area Amean)
where Amean is determined from trimmed sectional area curve
983108983141983156983141983154983149983145983150983137983156983145983151983150 983151983142 983140983137983149983137983143983141983140 983148983141983150983143983156983144 983137983150983140 983148983151983139983137983156983145983151983150 983151983142 983149983145983140
983151983142 983139983151983149983152983137983154983156983149983141983150983156
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 2967
3) In order to determine vm and xm
s = l1 4
vm = (s 3) sum3
xm = s sum4 sum3
xc = xl ndash xm
|vm-v0| le Tolarence for volume
|xc-xw| le Tolarence for location of volume centre
l=l1 xl=xw
983108983141983156983141983154983149983145983150983137983156983145983151983150 983151983142 983140983137983149983137983143983141983140 983148983141983150983143983156983144 983137983150983140 983148983151983139983137983156983145983151983150 983151983142 983149983145983140
983151983142 983139983151983149983152983137983154983156983149983141983150983156
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 3067
983108983141983156983141983154983149983145983150983137983156983145983151983150 983151983142 983140983137983149983137983143983141983140 983148983141983150983143983156983144 983137983150983140 983148983151983139983137983156983145983151983150 983151983142 983149983145983140
983151983142 983139983151983149983152983137983154983156983149983141983150983156Second Trial
Damaged length is changed proportionally by the volume
l2 = l1 times (v0v
m)
vm Computed volume at first trial
If the value of xm computed at first trial is negative then the mid of the
compartment slides to the bow
xl = xw+xm
where xm is the distance of the volume centre of compartment to amidship
computed at first trial
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 3167
In order to determine vm and xm
983108983141983156983141983154983149983145983150983137983156983145983151983150 983151983142 983140983137983149983137983143983141983140 983148983141983150983143983156983144 983137983150983140 983148983151983139983137983156983145983151983150 983151983142 983149983145983140
983151983142 983139983151983149983152983137983154983156983149983141983150983156
s = l2 4
vm = (s 3) sum3
xm = s sum4 sum3
xc = xl ndash xm
|vm-v0| le Tolarence for volume
|xc-xw| le Tolarence for location of volume centre
l=l2
If tolarances for both volume and location are not satisfied third fourthtrials are made similar to
second trial
8162019 Damaged Stability
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If either tolarence for volume or tolarance for location are satisfied at a trial
satisfied one is fixed trials are continued to make for the other one
983108983141983156983141983154983149983145983150983137983156983145983151983150 983151983142 983140983137983149983137983143983141983140 983148983141983150983143983156983144 983137983150983140 983148983151983139983137983156983145983151983150 983151983142 983149983145983140
983151983142 983139983151983149983152983137983154983156983149983141983150983156
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 3367
A ship is 116 meter long and displaces 7842 ton in salt water (ρ1=1025 tm3)
when her mean draught is 64m Longitudinal Centre of Buoyancy (LCB) is
0615 m aft from amidships After one of her stern compartment is damaged
she floats trimmed to the aft Her sectional areas after damaged are given in the
following table
a) Determine the volume of water entering the vessel (vw) and the location of
volume centre of damaged compartment (xw)
b) Assume permability of compartment micro is 1 Determine damaged length
and Distance of the mid of damaged length of compartment to amidship
983109983160983137983149983152983148983141 2
8162019 Damaged Stability
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8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 3567
8162019 Damaged Stability
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Predicted xw
is between section 2 and section 3
983123983141983139 N983151 983123983141983139 A983154983141983137 D983145983155983156 A9831499831459831559831449831459831522 10135 983085348
3 1208 983085232
983123983141983139 A983154983141983137 983137983156 98308524983149 983142983154983151983149 983137983149983145983140983155983144983145983152 = 11959831492
l1=v0Amean=204081195=17078 m
s=l14=427 m
983109983160983137983149983152983148983141 2983085983123983119983116983125983124983113983119983118
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 3767
983161983145 L983151983139 A983149983141983137983150 983123M M A983154983149
9831311983133 9831312983133 98313119831339832559831312983133 9831313983133 983131198313398325598313129831339832559831313983133
0 9830853254 1051 1 1051 2 21021 9830852827 1123 4 4492 1 4492
2 98308524 1195 2 239 0 0
3 9830851973 1219 4 4876 9830851 9830854876
4 9830851546 1233 1 1233 9830852 9830852466
sum983091983101 14042 sum983092983101 983085748
vm
= (s3) sum3= 199864479831493
xm
=s sum4sum3= 9830850227983149
v0-vm=20408-19986=422 m3
Error=422times10020408=207
983109983160983137983149983152983148983141 2983085983123983119983116983125983124983113983119983118
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 3867
Methods of Calculation
There two available method calculating the
final stage of the damaged vessel
bull Lost Buoyancy Method
bull Added Weight Method
8162019 Damaged Stability
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Comparision of Lost Buoyancy and Added
Weight Methods
8162019 Damaged Stability
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Consider a vessel that has been damaged such
that a portion of the bottom is now open to the
sea
The vesselrsquos draft will increase because an amount
of the buoyancy was lost
Added Weight Method
Added Weight Method
8162019 Damaged Stability
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Added Weight Method
In this method flood water is treated as a fixed weight (for example the
weight of water of volume ABEF) This added weight is balanced by the
additional buoyant force of the layer WL1WL
The added weight can be determined by either the volume ABEF or
waterline WL1 Therefore WL1 waterline is not known can be just guessed
For the predicted waterline added weight and additional buoyant force
caculation are done iteratively until both of them are equal This method is
known as Added weight method
Determination of Added Weight
8162019 Damaged Stability
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Determination of Added Weight
vc Volume of damaged compartment (DCEF)
ac The surface area (AB) of damaged compartment on the waterline
micro The volume permability of damaged compartment
microa The area permability of the surface of damaged compartment
∆ The initial displacement
∆1 The displacement at final stage
vw The volume of water entering the vessel (ABEH)
w The weight of water entering the vessel
p The value of parallel sinkage
If th t th l l i k i h f t l f
8162019 Damaged Stability
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If we assume that the paralel sinkage cause a minor change of water plane area of a
ship (Awp
asymp Awp1
) we can determine the paralel sinkage by equating the volume of
the layer WL1WL to the volume of ABEF
If the damaged compartment is bounded on top
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 4467
8162019 Damaged Stability
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Longitudinal Metacentre Radius at final stage
Free Surface Effect
Damaged compartment can be considered as a half filled tank
Free Contact Effect
Damaged compartment can be considered as a half filled tank
T M H i h
8162019 Damaged Stability
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Transverse Metacentre Height
The angle of heel
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 4767
L it di l M t t H i ht
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 4867
Longitudinal Metacentre Height
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 4967
E983160983137983149983152983148983141 A 983138983137983154983143983141
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 5067
E983160983137983149983152983148983141 A 983138983137983154983143983141
991266 L = 20 983149991266 B = 5 983149
991266 983124 = 15 983149
991266 KG = 15 983149
I983150983156983137983139983156 C983151983150983140983145983156983145983151983150
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 5167
I983150983156983137983139983156 C983151983150983140983145983156983145983151983150
991266 983124983144983141 983140983145983155983152983148983137983139983141983149983141983150983156 983158983151983148983157983149983141
991266 983124983144983141 983149983137983155983155 983140983145983155983152983148983137983139983141983149983141983150983156
991266 983124983144983141 983149983151983149983141983150983156 983151983142 983145983150983141983154983156983145983137 983151983142 983156983144983141 983159983137983156983141983154983152983148983137983150983141 983137983154983141983137983137983138983151983157983156 CL
3
15051520 m x xT B L
I I
==sdotsdot=nabla
tons x I
751531500251 ==nablasdot=∆ ρ
433
33208
12
205
12
m x L B
I I
===
I983150983156983137983139983156 C983151983150983140983145983156983145983151983150
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 5267
I983150983156983137983139983156 C983151983150983140983145983156983145983151983150
991266 M983141983156983137983139983141983150983156983154983145983139 983154983137983140983145983157983155
991266 O983154 983145983156 983139983151983157983148983140 983138983141 983139983137983148983139983157983148983137983156983141983140 983140983145983154983141983139983156983148983161 983137983155
991266 H983141983145983143983144983156 983151983142 983156983144983141 983139983141983150983156983141983154 983151983142 983138983157983151983161983137983150983139983161
m I
BM
I
I 3891
150
33208==
nabla
=
m xT
B
LBT
L B BM
I I
I 3891
5112
5
12
12 223
====
mT
KB I
I 750
2
==
I983150983156983137983139983156 C983151983150983140983145983156983145983151983150
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 5367
991266 983124983144983141 983149983141983156983137983139983141983150983156983154983145983139 983144983141983145983143983144983156
991266 F983151983154 983155983149983137983148983148 983137983150983143983148983141983155 983151983142 983144983141983141983148 983156983144983141 983154983145983143983144983156983145983150983143 983149983151983149983141983150983156
m KG BM KBGM I I 63905013891750 =minus+=minus+=
sin22998sin693075153sin mt x xGM M I I
φ φ φ ==∆=
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 5467
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 5567
983116983119983123983124 983106983125983119983129983105983118983107983129 983117983109983124983112983119983108
Paralel Sinkage
Volume (DCEF)=Volume (W1ADW+BL1LC)
Damaged compartment is bounded on top
983116983119983123983124 983106983125983119983129983105983118983107983129 983117983109983124983112983119983108
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 5667
983116983119983123983124 983106983125983119983129983105983118983107983129 983117983109983124983112983119983108
bull It is assumed that displacement and location of vertical centre
of gravity does not change after damaged
983116983119983123983124 983106983125983119983129983105983118983107983129 983117983109983124983112983119983108
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 5767
983116983119983123983124 983106983125983119983129983105983118983107983129 983117983109983124983112983119983108
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 5867
The heel angle of damaged ship is determined by
where
d is the distance between the volume centre of damaged compartment
and the new longitudinal centre of floatation
wc=vc μ ρ
983116983119983123983124 983106983125983119983129983105983118983107983129 983117983109983124983112983119983108
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 5967
983116983119983123983124 983106983125983119983129983105983118983107983129 983117983109983124983112983119983108
983116983119983123983124 983106983125983119983129983105983118983107983129 983117983109983124983112983119983108
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 6067
Longitudinal Metacentre Height of a Damaged Ship
983116983119983123983124 983106983125983119983129983105983118983107983129 983117983109983124983112983119983108
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 6167
983110983151983154983159983137983154983140 983137983150983140 983137983142983156 983140983154983137983157983143983144983156983155 983137983142983156983141983154 983140983137983149983137983143983141983140
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 6267
983120983151983154983156 983105983142983156 983120983151983154983156 983110983151983154983141 983123983156983137983154983138983151983137983154983140 983105983142983156 983123983156983137983154983138983151983137983154983140 983110983151983154983159983137983154983140
I983150983145983156983145983137983148 D983154983137983157983143983144983156 983124 983124 983124 983124
983120983137983154983137983148983141983148 983123983145983150983147983137983143983141 +983152 +983152 +983152 +983120
H983141983141983148 983085983149983145 983085983149983145 +983149983155 +983149983155
983124983154983145983149 983085983156983147 +983156983138 983085983156983147 +983156983138
F983145983150983137983148 D983154983137983157983143983144983156 983124+983152983085983149983145983085983156983147 983124+983152983085983149983145+983156983138 983124+983152+983149983155983085983156983147 983124+983152+983149983155+983156983138
Table 1 Final Draughts for a starboard side damaged ship
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 6367
L983151983155983156 B983157983151983161983137983150983139983161 M983141983156983144983151983140
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 6467
L983151983155983156 B983157983151983161983137983150983139983161 M983141983156983144983151983140
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 6567
991266 A983142983156983141983154 983148983151983151983155983145983150983143 983156983144983141 983139983141983150983156983154983137983148 983139983151983149983152983137983154983156983149983141983150983156 983156983144983141
983159983137983156983141983154983152983148983137983150983141 983137983154983141983137 983145983155
991266 983124983151 983139983151983149983152983141983150983155983137983156983141 983142983151983154 983156983144983141 983148983151983155983155 983151983142 983138983157983151983161983137983150983139983161 983151983142 983156983144983141
983139983141983150983156983154983137983148 983139983151983149983152983137983154983156983149983141983150983156 983156983144983141 983140983154983137983142983156 983145983150983139983154983141983137983155983141983155 983156983151
2805)420()( m x Bl L A L
=minus=minus=
m A
T
L
I
L 875180
150==
nabla=
L983151983155983156 B983157983151983161983137983150983139983161 M983141983156983144983151983140
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 6667
991266 983124983144983141 983144983141983145983143983144983156 983151983142 983156983144983141 983139983141983150983156983141983154 983151983142 983138983157983151983161983137983150983139983161 983145983150983139983154983141983137983155983141983155 983156983151
991266 983124983144983141 983149983151983149983141983150983156 983151983142 983145983150983141983154983156983145983137 983151983142 983156983144983141 983159983137983156983141983154983152983148983137983150983141 983137983154983141983137
991266 983124983144983141 983149983141983156983137983139983141983150983156983154983145983139 983154983137983140983145983157983155
m
T
KB L
L 93802
8751
2 ===
433
6716612
)420(5
12
)(m
l L B I L
=minus
=minus
=
m I
BM
I
L
L 1111150
67166==
nabla
=
L983151983155983156 B983157983151983161983137983150983139983161 M983141983156983144983151983140
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 6767
991266 983124983144983141 983149983141983156983137983139983141983150983156983154983145983139 983144983141983145983143983144983156
991266 983122983145983143983144983156983145983150983143 983149983151983149983141983150983156 983142983151983154 983155983149983137983148983148 983144983141983141983148 983137983150983143983148983141983155
m KG BM KBGM L L L 54905111119380 =minus+=minus+=
mt xGM M L
sin34984sin549075153sin φ φ φ ==∆=
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 2567
D983141983156983141983154983149983145983150983137983156983145983151983150 983151983142 983156983144983141 983158983151983148983157983149983141 983151983142 983159983137983156983141983154 983141983150983156983141983154983145983150983143 983156983144983141 983158983141983155983155983141983148
Initial displacement and longitudinal centre of buoyancy (LCB) can be read from hydrostatcic curves
However displacement and LCB are unknown after damaged
Therefore if trim forward and aft draught are known trimmed waterline can be drawn over Bonjean
area curves
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 2667
983108983141983156983141983154983149983145983150983137983156983145983151983150 983151983142 983140983137983149983137983143983141983140 983148983141983150983143983156983144 983137983150983140 983148983151983139983137983156983145983151983150 983151983142 983149983145983140
983151983142 983139983151983149983152983137983154983156983149983141983150983156
vw The volume of water entering the vessel
xw Distance of volume centre of damaged compartment from maestory
micro Permability of the compartment
v0 Volume of the compartment
xm Distance of the volume centre of the compartment to the mid of damaged length
xl Distance of the mid of damaged length of compartment to maestory
xc Distance of the computed volume centre of compartment to maestory (xc=xl-xm)
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 2767
983108983141983156983141983154983149983145983150983137983156983145983151983150 983151983142 983140983137983149983137983143983141983140 983148983141983150983143983156983144 983137983150983140 983148983151983139983137983156983145983151983150 983151983142 983149983145983140
983151983142 983139983151983149983152983137983154983156983149983141983150983156
Damaged length and location of compartment can be determined by iterative
procedure
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 2867
bull The volume of water entering the vessel (vw)
bull Distance of volume centre of damaged compartment from amidships Θ ( xw)
bull Volume of the compartment (v0
= vw
μ)
First trial
1) Assume xm=0 (xl=xw)
2) Damaged Length l1 = (Volume of the compartment v0) (mean sec Area Amean)
where Amean is determined from trimmed sectional area curve
983108983141983156983141983154983149983145983150983137983156983145983151983150 983151983142 983140983137983149983137983143983141983140 983148983141983150983143983156983144 983137983150983140 983148983151983139983137983156983145983151983150 983151983142 983149983145983140
983151983142 983139983151983149983152983137983154983156983149983141983150983156
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 2967
3) In order to determine vm and xm
s = l1 4
vm = (s 3) sum3
xm = s sum4 sum3
xc = xl ndash xm
|vm-v0| le Tolarence for volume
|xc-xw| le Tolarence for location of volume centre
l=l1 xl=xw
983108983141983156983141983154983149983145983150983137983156983145983151983150 983151983142 983140983137983149983137983143983141983140 983148983141983150983143983156983144 983137983150983140 983148983151983139983137983156983145983151983150 983151983142 983149983145983140
983151983142 983139983151983149983152983137983154983156983149983141983150983156
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 3067
983108983141983156983141983154983149983145983150983137983156983145983151983150 983151983142 983140983137983149983137983143983141983140 983148983141983150983143983156983144 983137983150983140 983148983151983139983137983156983145983151983150 983151983142 983149983145983140
983151983142 983139983151983149983152983137983154983156983149983141983150983156Second Trial
Damaged length is changed proportionally by the volume
l2 = l1 times (v0v
m)
vm Computed volume at first trial
If the value of xm computed at first trial is negative then the mid of the
compartment slides to the bow
xl = xw+xm
where xm is the distance of the volume centre of compartment to amidship
computed at first trial
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 3167
In order to determine vm and xm
983108983141983156983141983154983149983145983150983137983156983145983151983150 983151983142 983140983137983149983137983143983141983140 983148983141983150983143983156983144 983137983150983140 983148983151983139983137983156983145983151983150 983151983142 983149983145983140
983151983142 983139983151983149983152983137983154983156983149983141983150983156
s = l2 4
vm = (s 3) sum3
xm = s sum4 sum3
xc = xl ndash xm
|vm-v0| le Tolarence for volume
|xc-xw| le Tolarence for location of volume centre
l=l2
If tolarances for both volume and location are not satisfied third fourthtrials are made similar to
second trial
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 3267
If either tolarence for volume or tolarance for location are satisfied at a trial
satisfied one is fixed trials are continued to make for the other one
983108983141983156983141983154983149983145983150983137983156983145983151983150 983151983142 983140983137983149983137983143983141983140 983148983141983150983143983156983144 983137983150983140 983148983151983139983137983156983145983151983150 983151983142 983149983145983140
983151983142 983139983151983149983152983137983154983156983149983141983150983156
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 3367
A ship is 116 meter long and displaces 7842 ton in salt water (ρ1=1025 tm3)
when her mean draught is 64m Longitudinal Centre of Buoyancy (LCB) is
0615 m aft from amidships After one of her stern compartment is damaged
she floats trimmed to the aft Her sectional areas after damaged are given in the
following table
a) Determine the volume of water entering the vessel (vw) and the location of
volume centre of damaged compartment (xw)
b) Assume permability of compartment micro is 1 Determine damaged length
and Distance of the mid of damaged length of compartment to amidship
983109983160983137983149983152983148983141 2
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 3467
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 3567
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 3667
Predicted xw
is between section 2 and section 3
983123983141983139 N983151 983123983141983139 A983154983141983137 D983145983155983156 A9831499831459831559831449831459831522 10135 983085348
3 1208 983085232
983123983141983139 A983154983141983137 983137983156 98308524983149 983142983154983151983149 983137983149983145983140983155983144983145983152 = 11959831492
l1=v0Amean=204081195=17078 m
s=l14=427 m
983109983160983137983149983152983148983141 2983085983123983119983116983125983124983113983119983118
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 3767
983161983145 L983151983139 A983149983141983137983150 983123M M A983154983149
9831311983133 9831312983133 98313119831339832559831312983133 9831313983133 983131198313398325598313129831339832559831313983133
0 9830853254 1051 1 1051 2 21021 9830852827 1123 4 4492 1 4492
2 98308524 1195 2 239 0 0
3 9830851973 1219 4 4876 9830851 9830854876
4 9830851546 1233 1 1233 9830852 9830852466
sum983091983101 14042 sum983092983101 983085748
vm
= (s3) sum3= 199864479831493
xm
=s sum4sum3= 9830850227983149
v0-vm=20408-19986=422 m3
Error=422times10020408=207
983109983160983137983149983152983148983141 2983085983123983119983116983125983124983113983119983118
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 3867
Methods of Calculation
There two available method calculating the
final stage of the damaged vessel
bull Lost Buoyancy Method
bull Added Weight Method
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 3967
Comparision of Lost Buoyancy and Added
Weight Methods
8162019 Damaged Stability
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Consider a vessel that has been damaged such
that a portion of the bottom is now open to the
sea
The vesselrsquos draft will increase because an amount
of the buoyancy was lost
Added Weight Method
Added Weight Method
8162019 Damaged Stability
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Added Weight Method
In this method flood water is treated as a fixed weight (for example the
weight of water of volume ABEF) This added weight is balanced by the
additional buoyant force of the layer WL1WL
The added weight can be determined by either the volume ABEF or
waterline WL1 Therefore WL1 waterline is not known can be just guessed
For the predicted waterline added weight and additional buoyant force
caculation are done iteratively until both of them are equal This method is
known as Added weight method
Determination of Added Weight
8162019 Damaged Stability
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Determination of Added Weight
vc Volume of damaged compartment (DCEF)
ac The surface area (AB) of damaged compartment on the waterline
micro The volume permability of damaged compartment
microa The area permability of the surface of damaged compartment
∆ The initial displacement
∆1 The displacement at final stage
vw The volume of water entering the vessel (ABEH)
w The weight of water entering the vessel
p The value of parallel sinkage
If th t th l l i k i h f t l f
8162019 Damaged Stability
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If we assume that the paralel sinkage cause a minor change of water plane area of a
ship (Awp
asymp Awp1
) we can determine the paralel sinkage by equating the volume of
the layer WL1WL to the volume of ABEF
If the damaged compartment is bounded on top
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 4467
8162019 Damaged Stability
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Longitudinal Metacentre Radius at final stage
Free Surface Effect
Damaged compartment can be considered as a half filled tank
Free Contact Effect
Damaged compartment can be considered as a half filled tank
T M H i h
8162019 Damaged Stability
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Transverse Metacentre Height
The angle of heel
8162019 Damaged Stability
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L it di l M t t H i ht
8162019 Damaged Stability
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Longitudinal Metacentre Height
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 4967
E983160983137983149983152983148983141 A 983138983137983154983143983141
8162019 Damaged Stability
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E983160983137983149983152983148983141 A 983138983137983154983143983141
991266 L = 20 983149991266 B = 5 983149
991266 983124 = 15 983149
991266 KG = 15 983149
I983150983156983137983139983156 C983151983150983140983145983156983145983151983150
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 5167
I983150983156983137983139983156 C983151983150983140983145983156983145983151983150
991266 983124983144983141 983140983145983155983152983148983137983139983141983149983141983150983156 983158983151983148983157983149983141
991266 983124983144983141 983149983137983155983155 983140983145983155983152983148983137983139983141983149983141983150983156
991266 983124983144983141 983149983151983149983141983150983156 983151983142 983145983150983141983154983156983145983137 983151983142 983156983144983141 983159983137983156983141983154983152983148983137983150983141 983137983154983141983137983137983138983151983157983156 CL
3
15051520 m x xT B L
I I
==sdotsdot=nabla
tons x I
751531500251 ==nablasdot=∆ ρ
433
33208
12
205
12
m x L B
I I
===
I983150983156983137983139983156 C983151983150983140983145983156983145983151983150
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 5267
I983150983156983137983139983156 C983151983150983140983145983156983145983151983150
991266 M983141983156983137983139983141983150983156983154983145983139 983154983137983140983145983157983155
991266 O983154 983145983156 983139983151983157983148983140 983138983141 983139983137983148983139983157983148983137983156983141983140 983140983145983154983141983139983156983148983161 983137983155
991266 H983141983145983143983144983156 983151983142 983156983144983141 983139983141983150983156983141983154 983151983142 983138983157983151983161983137983150983139983161
m I
BM
I
I 3891
150
33208==
nabla
=
m xT
B
LBT
L B BM
I I
I 3891
5112
5
12
12 223
====
mT
KB I
I 750
2
==
I983150983156983137983139983156 C983151983150983140983145983156983145983151983150
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 5367
991266 983124983144983141 983149983141983156983137983139983141983150983156983154983145983139 983144983141983145983143983144983156
991266 F983151983154 983155983149983137983148983148 983137983150983143983148983141983155 983151983142 983144983141983141983148 983156983144983141 983154983145983143983144983156983145983150983143 983149983151983149983141983150983156
m KG BM KBGM I I 63905013891750 =minus+=minus+=
sin22998sin693075153sin mt x xGM M I I
φ φ φ ==∆=
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 5467
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 5567
983116983119983123983124 983106983125983119983129983105983118983107983129 983117983109983124983112983119983108
Paralel Sinkage
Volume (DCEF)=Volume (W1ADW+BL1LC)
Damaged compartment is bounded on top
983116983119983123983124 983106983125983119983129983105983118983107983129 983117983109983124983112983119983108
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 5667
983116983119983123983124 983106983125983119983129983105983118983107983129 983117983109983124983112983119983108
bull It is assumed that displacement and location of vertical centre
of gravity does not change after damaged
983116983119983123983124 983106983125983119983129983105983118983107983129 983117983109983124983112983119983108
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 5767
983116983119983123983124 983106983125983119983129983105983118983107983129 983117983109983124983112983119983108
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 5867
The heel angle of damaged ship is determined by
where
d is the distance between the volume centre of damaged compartment
and the new longitudinal centre of floatation
wc=vc μ ρ
983116983119983123983124 983106983125983119983129983105983118983107983129 983117983109983124983112983119983108
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 5967
983116983119983123983124 983106983125983119983129983105983118983107983129 983117983109983124983112983119983108
983116983119983123983124 983106983125983119983129983105983118983107983129 983117983109983124983112983119983108
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 6067
Longitudinal Metacentre Height of a Damaged Ship
983116983119983123983124 983106983125983119983129983105983118983107983129 983117983109983124983112983119983108
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 6167
983110983151983154983159983137983154983140 983137983150983140 983137983142983156 983140983154983137983157983143983144983156983155 983137983142983156983141983154 983140983137983149983137983143983141983140
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 6267
983120983151983154983156 983105983142983156 983120983151983154983156 983110983151983154983141 983123983156983137983154983138983151983137983154983140 983105983142983156 983123983156983137983154983138983151983137983154983140 983110983151983154983159983137983154983140
I983150983145983156983145983137983148 D983154983137983157983143983144983156 983124 983124 983124 983124
983120983137983154983137983148983141983148 983123983145983150983147983137983143983141 +983152 +983152 +983152 +983120
H983141983141983148 983085983149983145 983085983149983145 +983149983155 +983149983155
983124983154983145983149 983085983156983147 +983156983138 983085983156983147 +983156983138
F983145983150983137983148 D983154983137983157983143983144983156 983124+983152983085983149983145983085983156983147 983124+983152983085983149983145+983156983138 983124+983152+983149983155983085983156983147 983124+983152+983149983155+983156983138
Table 1 Final Draughts for a starboard side damaged ship
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 6367
L983151983155983156 B983157983151983161983137983150983139983161 M983141983156983144983151983140
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 6467
L983151983155983156 B983157983151983161983137983150983139983161 M983141983156983144983151983140
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 6567
991266 A983142983156983141983154 983148983151983151983155983145983150983143 983156983144983141 983139983141983150983156983154983137983148 983139983151983149983152983137983154983156983149983141983150983156 983156983144983141
983159983137983156983141983154983152983148983137983150983141 983137983154983141983137 983145983155
991266 983124983151 983139983151983149983152983141983150983155983137983156983141 983142983151983154 983156983144983141 983148983151983155983155 983151983142 983138983157983151983161983137983150983139983161 983151983142 983156983144983141
983139983141983150983156983154983137983148 983139983151983149983152983137983154983156983149983141983150983156 983156983144983141 983140983154983137983142983156 983145983150983139983154983141983137983155983141983155 983156983151
2805)420()( m x Bl L A L
=minus=minus=
m A
T
L
I
L 875180
150==
nabla=
L983151983155983156 B983157983151983161983137983150983139983161 M983141983156983144983151983140
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 6667
991266 983124983144983141 983144983141983145983143983144983156 983151983142 983156983144983141 983139983141983150983156983141983154 983151983142 983138983157983151983161983137983150983139983161 983145983150983139983154983141983137983155983141983155 983156983151
991266 983124983144983141 983149983151983149983141983150983156 983151983142 983145983150983141983154983156983145983137 983151983142 983156983144983141 983159983137983156983141983154983152983148983137983150983141 983137983154983141983137
991266 983124983144983141 983149983141983156983137983139983141983150983156983154983145983139 983154983137983140983145983157983155
m
T
KB L
L 93802
8751
2 ===
433
6716612
)420(5
12
)(m
l L B I L
=minus
=minus
=
m I
BM
I
L
L 1111150
67166==
nabla
=
L983151983155983156 B983157983151983161983137983150983139983161 M983141983156983144983151983140
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 6767
991266 983124983144983141 983149983141983156983137983139983141983150983156983154983145983139 983144983141983145983143983144983156
991266 983122983145983143983144983156983145983150983143 983149983151983149983141983150983156 983142983151983154 983155983149983137983148983148 983144983141983141983148 983137983150983143983148983141983155
m KG BM KBGM L L L 54905111119380 =minus+=minus+=
mt xGM M L
sin34984sin549075153sin φ φ φ ==∆=
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 2667
983108983141983156983141983154983149983145983150983137983156983145983151983150 983151983142 983140983137983149983137983143983141983140 983148983141983150983143983156983144 983137983150983140 983148983151983139983137983156983145983151983150 983151983142 983149983145983140
983151983142 983139983151983149983152983137983154983156983149983141983150983156
vw The volume of water entering the vessel
xw Distance of volume centre of damaged compartment from maestory
micro Permability of the compartment
v0 Volume of the compartment
xm Distance of the volume centre of the compartment to the mid of damaged length
xl Distance of the mid of damaged length of compartment to maestory
xc Distance of the computed volume centre of compartment to maestory (xc=xl-xm)
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 2767
983108983141983156983141983154983149983145983150983137983156983145983151983150 983151983142 983140983137983149983137983143983141983140 983148983141983150983143983156983144 983137983150983140 983148983151983139983137983156983145983151983150 983151983142 983149983145983140
983151983142 983139983151983149983152983137983154983156983149983141983150983156
Damaged length and location of compartment can be determined by iterative
procedure
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 2867
bull The volume of water entering the vessel (vw)
bull Distance of volume centre of damaged compartment from amidships Θ ( xw)
bull Volume of the compartment (v0
= vw
μ)
First trial
1) Assume xm=0 (xl=xw)
2) Damaged Length l1 = (Volume of the compartment v0) (mean sec Area Amean)
where Amean is determined from trimmed sectional area curve
983108983141983156983141983154983149983145983150983137983156983145983151983150 983151983142 983140983137983149983137983143983141983140 983148983141983150983143983156983144 983137983150983140 983148983151983139983137983156983145983151983150 983151983142 983149983145983140
983151983142 983139983151983149983152983137983154983156983149983141983150983156
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 2967
3) In order to determine vm and xm
s = l1 4
vm = (s 3) sum3
xm = s sum4 sum3
xc = xl ndash xm
|vm-v0| le Tolarence for volume
|xc-xw| le Tolarence for location of volume centre
l=l1 xl=xw
983108983141983156983141983154983149983145983150983137983156983145983151983150 983151983142 983140983137983149983137983143983141983140 983148983141983150983143983156983144 983137983150983140 983148983151983139983137983156983145983151983150 983151983142 983149983145983140
983151983142 983139983151983149983152983137983154983156983149983141983150983156
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 3067
983108983141983156983141983154983149983145983150983137983156983145983151983150 983151983142 983140983137983149983137983143983141983140 983148983141983150983143983156983144 983137983150983140 983148983151983139983137983156983145983151983150 983151983142 983149983145983140
983151983142 983139983151983149983152983137983154983156983149983141983150983156Second Trial
Damaged length is changed proportionally by the volume
l2 = l1 times (v0v
m)
vm Computed volume at first trial
If the value of xm computed at first trial is negative then the mid of the
compartment slides to the bow
xl = xw+xm
where xm is the distance of the volume centre of compartment to amidship
computed at first trial
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 3167
In order to determine vm and xm
983108983141983156983141983154983149983145983150983137983156983145983151983150 983151983142 983140983137983149983137983143983141983140 983148983141983150983143983156983144 983137983150983140 983148983151983139983137983156983145983151983150 983151983142 983149983145983140
983151983142 983139983151983149983152983137983154983156983149983141983150983156
s = l2 4
vm = (s 3) sum3
xm = s sum4 sum3
xc = xl ndash xm
|vm-v0| le Tolarence for volume
|xc-xw| le Tolarence for location of volume centre
l=l2
If tolarances for both volume and location are not satisfied third fourthtrials are made similar to
second trial
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 3267
If either tolarence for volume or tolarance for location are satisfied at a trial
satisfied one is fixed trials are continued to make for the other one
983108983141983156983141983154983149983145983150983137983156983145983151983150 983151983142 983140983137983149983137983143983141983140 983148983141983150983143983156983144 983137983150983140 983148983151983139983137983156983145983151983150 983151983142 983149983145983140
983151983142 983139983151983149983152983137983154983156983149983141983150983156
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 3367
A ship is 116 meter long and displaces 7842 ton in salt water (ρ1=1025 tm3)
when her mean draught is 64m Longitudinal Centre of Buoyancy (LCB) is
0615 m aft from amidships After one of her stern compartment is damaged
she floats trimmed to the aft Her sectional areas after damaged are given in the
following table
a) Determine the volume of water entering the vessel (vw) and the location of
volume centre of damaged compartment (xw)
b) Assume permability of compartment micro is 1 Determine damaged length
and Distance of the mid of damaged length of compartment to amidship
983109983160983137983149983152983148983141 2
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 3467
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 3567
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 3667
Predicted xw
is between section 2 and section 3
983123983141983139 N983151 983123983141983139 A983154983141983137 D983145983155983156 A9831499831459831559831449831459831522 10135 983085348
3 1208 983085232
983123983141983139 A983154983141983137 983137983156 98308524983149 983142983154983151983149 983137983149983145983140983155983144983145983152 = 11959831492
l1=v0Amean=204081195=17078 m
s=l14=427 m
983109983160983137983149983152983148983141 2983085983123983119983116983125983124983113983119983118
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 3767
983161983145 L983151983139 A983149983141983137983150 983123M M A983154983149
9831311983133 9831312983133 98313119831339832559831312983133 9831313983133 983131198313398325598313129831339832559831313983133
0 9830853254 1051 1 1051 2 21021 9830852827 1123 4 4492 1 4492
2 98308524 1195 2 239 0 0
3 9830851973 1219 4 4876 9830851 9830854876
4 9830851546 1233 1 1233 9830852 9830852466
sum983091983101 14042 sum983092983101 983085748
vm
= (s3) sum3= 199864479831493
xm
=s sum4sum3= 9830850227983149
v0-vm=20408-19986=422 m3
Error=422times10020408=207
983109983160983137983149983152983148983141 2983085983123983119983116983125983124983113983119983118
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 3867
Methods of Calculation
There two available method calculating the
final stage of the damaged vessel
bull Lost Buoyancy Method
bull Added Weight Method
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 3967
Comparision of Lost Buoyancy and Added
Weight Methods
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 4067
Consider a vessel that has been damaged such
that a portion of the bottom is now open to the
sea
The vesselrsquos draft will increase because an amount
of the buoyancy was lost
Added Weight Method
Added Weight Method
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 4167
Added Weight Method
In this method flood water is treated as a fixed weight (for example the
weight of water of volume ABEF) This added weight is balanced by the
additional buoyant force of the layer WL1WL
The added weight can be determined by either the volume ABEF or
waterline WL1 Therefore WL1 waterline is not known can be just guessed
For the predicted waterline added weight and additional buoyant force
caculation are done iteratively until both of them are equal This method is
known as Added weight method
Determination of Added Weight
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 4267
Determination of Added Weight
vc Volume of damaged compartment (DCEF)
ac The surface area (AB) of damaged compartment on the waterline
micro The volume permability of damaged compartment
microa The area permability of the surface of damaged compartment
∆ The initial displacement
∆1 The displacement at final stage
vw The volume of water entering the vessel (ABEH)
w The weight of water entering the vessel
p The value of parallel sinkage
If th t th l l i k i h f t l f
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 4367
If we assume that the paralel sinkage cause a minor change of water plane area of a
ship (Awp
asymp Awp1
) we can determine the paralel sinkage by equating the volume of
the layer WL1WL to the volume of ABEF
If the damaged compartment is bounded on top
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 4467
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 4567
Longitudinal Metacentre Radius at final stage
Free Surface Effect
Damaged compartment can be considered as a half filled tank
Free Contact Effect
Damaged compartment can be considered as a half filled tank
T M H i h
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 4667
Transverse Metacentre Height
The angle of heel
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 4767
L it di l M t t H i ht
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 4867
Longitudinal Metacentre Height
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 4967
E983160983137983149983152983148983141 A 983138983137983154983143983141
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 5067
E983160983137983149983152983148983141 A 983138983137983154983143983141
991266 L = 20 983149991266 B = 5 983149
991266 983124 = 15 983149
991266 KG = 15 983149
I983150983156983137983139983156 C983151983150983140983145983156983145983151983150
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 5167
I983150983156983137983139983156 C983151983150983140983145983156983145983151983150
991266 983124983144983141 983140983145983155983152983148983137983139983141983149983141983150983156 983158983151983148983157983149983141
991266 983124983144983141 983149983137983155983155 983140983145983155983152983148983137983139983141983149983141983150983156
991266 983124983144983141 983149983151983149983141983150983156 983151983142 983145983150983141983154983156983145983137 983151983142 983156983144983141 983159983137983156983141983154983152983148983137983150983141 983137983154983141983137983137983138983151983157983156 CL
3
15051520 m x xT B L
I I
==sdotsdot=nabla
tons x I
751531500251 ==nablasdot=∆ ρ
433
33208
12
205
12
m x L B
I I
===
I983150983156983137983139983156 C983151983150983140983145983156983145983151983150
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 5267
I983150983156983137983139983156 C983151983150983140983145983156983145983151983150
991266 M983141983156983137983139983141983150983156983154983145983139 983154983137983140983145983157983155
991266 O983154 983145983156 983139983151983157983148983140 983138983141 983139983137983148983139983157983148983137983156983141983140 983140983145983154983141983139983156983148983161 983137983155
991266 H983141983145983143983144983156 983151983142 983156983144983141 983139983141983150983156983141983154 983151983142 983138983157983151983161983137983150983139983161
m I
BM
I
I 3891
150
33208==
nabla
=
m xT
B
LBT
L B BM
I I
I 3891
5112
5
12
12 223
====
mT
KB I
I 750
2
==
I983150983156983137983139983156 C983151983150983140983145983156983145983151983150
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 5367
991266 983124983144983141 983149983141983156983137983139983141983150983156983154983145983139 983144983141983145983143983144983156
991266 F983151983154 983155983149983137983148983148 983137983150983143983148983141983155 983151983142 983144983141983141983148 983156983144983141 983154983145983143983144983156983145983150983143 983149983151983149983141983150983156
m KG BM KBGM I I 63905013891750 =minus+=minus+=
sin22998sin693075153sin mt x xGM M I I
φ φ φ ==∆=
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 5467
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 5567
983116983119983123983124 983106983125983119983129983105983118983107983129 983117983109983124983112983119983108
Paralel Sinkage
Volume (DCEF)=Volume (W1ADW+BL1LC)
Damaged compartment is bounded on top
983116983119983123983124 983106983125983119983129983105983118983107983129 983117983109983124983112983119983108
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 5667
983116983119983123983124 983106983125983119983129983105983118983107983129 983117983109983124983112983119983108
bull It is assumed that displacement and location of vertical centre
of gravity does not change after damaged
983116983119983123983124 983106983125983119983129983105983118983107983129 983117983109983124983112983119983108
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 5767
983116983119983123983124 983106983125983119983129983105983118983107983129 983117983109983124983112983119983108
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 5867
The heel angle of damaged ship is determined by
where
d is the distance between the volume centre of damaged compartment
and the new longitudinal centre of floatation
wc=vc μ ρ
983116983119983123983124 983106983125983119983129983105983118983107983129 983117983109983124983112983119983108
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 5967
983116983119983123983124 983106983125983119983129983105983118983107983129 983117983109983124983112983119983108
983116983119983123983124 983106983125983119983129983105983118983107983129 983117983109983124983112983119983108
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 6067
Longitudinal Metacentre Height of a Damaged Ship
983116983119983123983124 983106983125983119983129983105983118983107983129 983117983109983124983112983119983108
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 6167
983110983151983154983159983137983154983140 983137983150983140 983137983142983156 983140983154983137983157983143983144983156983155 983137983142983156983141983154 983140983137983149983137983143983141983140
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 6267
983120983151983154983156 983105983142983156 983120983151983154983156 983110983151983154983141 983123983156983137983154983138983151983137983154983140 983105983142983156 983123983156983137983154983138983151983137983154983140 983110983151983154983159983137983154983140
I983150983145983156983145983137983148 D983154983137983157983143983144983156 983124 983124 983124 983124
983120983137983154983137983148983141983148 983123983145983150983147983137983143983141 +983152 +983152 +983152 +983120
H983141983141983148 983085983149983145 983085983149983145 +983149983155 +983149983155
983124983154983145983149 983085983156983147 +983156983138 983085983156983147 +983156983138
F983145983150983137983148 D983154983137983157983143983144983156 983124+983152983085983149983145983085983156983147 983124+983152983085983149983145+983156983138 983124+983152+983149983155983085983156983147 983124+983152+983149983155+983156983138
Table 1 Final Draughts for a starboard side damaged ship
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 6367
L983151983155983156 B983157983151983161983137983150983139983161 M983141983156983144983151983140
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 6467
L983151983155983156 B983157983151983161983137983150983139983161 M983141983156983144983151983140
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 6567
991266 A983142983156983141983154 983148983151983151983155983145983150983143 983156983144983141 983139983141983150983156983154983137983148 983139983151983149983152983137983154983156983149983141983150983156 983156983144983141
983159983137983156983141983154983152983148983137983150983141 983137983154983141983137 983145983155
991266 983124983151 983139983151983149983152983141983150983155983137983156983141 983142983151983154 983156983144983141 983148983151983155983155 983151983142 983138983157983151983161983137983150983139983161 983151983142 983156983144983141
983139983141983150983156983154983137983148 983139983151983149983152983137983154983156983149983141983150983156 983156983144983141 983140983154983137983142983156 983145983150983139983154983141983137983155983141983155 983156983151
2805)420()( m x Bl L A L
=minus=minus=
m A
T
L
I
L 875180
150==
nabla=
L983151983155983156 B983157983151983161983137983150983139983161 M983141983156983144983151983140
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 6667
991266 983124983144983141 983144983141983145983143983144983156 983151983142 983156983144983141 983139983141983150983156983141983154 983151983142 983138983157983151983161983137983150983139983161 983145983150983139983154983141983137983155983141983155 983156983151
991266 983124983144983141 983149983151983149983141983150983156 983151983142 983145983150983141983154983156983145983137 983151983142 983156983144983141 983159983137983156983141983154983152983148983137983150983141 983137983154983141983137
991266 983124983144983141 983149983141983156983137983139983141983150983156983154983145983139 983154983137983140983145983157983155
m
T
KB L
L 93802
8751
2 ===
433
6716612
)420(5
12
)(m
l L B I L
=minus
=minus
=
m I
BM
I
L
L 1111150
67166==
nabla
=
L983151983155983156 B983157983151983161983137983150983139983161 M983141983156983144983151983140
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 6767
991266 983124983144983141 983149983141983156983137983139983141983150983156983154983145983139 983144983141983145983143983144983156
991266 983122983145983143983144983156983145983150983143 983149983151983149983141983150983156 983142983151983154 983155983149983137983148983148 983144983141983141983148 983137983150983143983148983141983155
m KG BM KBGM L L L 54905111119380 =minus+=minus+=
mt xGM M L
sin34984sin549075153sin φ φ φ ==∆=
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 2767
983108983141983156983141983154983149983145983150983137983156983145983151983150 983151983142 983140983137983149983137983143983141983140 983148983141983150983143983156983144 983137983150983140 983148983151983139983137983156983145983151983150 983151983142 983149983145983140
983151983142 983139983151983149983152983137983154983156983149983141983150983156
Damaged length and location of compartment can be determined by iterative
procedure
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 2867
bull The volume of water entering the vessel (vw)
bull Distance of volume centre of damaged compartment from amidships Θ ( xw)
bull Volume of the compartment (v0
= vw
μ)
First trial
1) Assume xm=0 (xl=xw)
2) Damaged Length l1 = (Volume of the compartment v0) (mean sec Area Amean)
where Amean is determined from trimmed sectional area curve
983108983141983156983141983154983149983145983150983137983156983145983151983150 983151983142 983140983137983149983137983143983141983140 983148983141983150983143983156983144 983137983150983140 983148983151983139983137983156983145983151983150 983151983142 983149983145983140
983151983142 983139983151983149983152983137983154983156983149983141983150983156
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 2967
3) In order to determine vm and xm
s = l1 4
vm = (s 3) sum3
xm = s sum4 sum3
xc = xl ndash xm
|vm-v0| le Tolarence for volume
|xc-xw| le Tolarence for location of volume centre
l=l1 xl=xw
983108983141983156983141983154983149983145983150983137983156983145983151983150 983151983142 983140983137983149983137983143983141983140 983148983141983150983143983156983144 983137983150983140 983148983151983139983137983156983145983151983150 983151983142 983149983145983140
983151983142 983139983151983149983152983137983154983156983149983141983150983156
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 3067
983108983141983156983141983154983149983145983150983137983156983145983151983150 983151983142 983140983137983149983137983143983141983140 983148983141983150983143983156983144 983137983150983140 983148983151983139983137983156983145983151983150 983151983142 983149983145983140
983151983142 983139983151983149983152983137983154983156983149983141983150983156Second Trial
Damaged length is changed proportionally by the volume
l2 = l1 times (v0v
m)
vm Computed volume at first trial
If the value of xm computed at first trial is negative then the mid of the
compartment slides to the bow
xl = xw+xm
where xm is the distance of the volume centre of compartment to amidship
computed at first trial
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 3167
In order to determine vm and xm
983108983141983156983141983154983149983145983150983137983156983145983151983150 983151983142 983140983137983149983137983143983141983140 983148983141983150983143983156983144 983137983150983140 983148983151983139983137983156983145983151983150 983151983142 983149983145983140
983151983142 983139983151983149983152983137983154983156983149983141983150983156
s = l2 4
vm = (s 3) sum3
xm = s sum4 sum3
xc = xl ndash xm
|vm-v0| le Tolarence for volume
|xc-xw| le Tolarence for location of volume centre
l=l2
If tolarances for both volume and location are not satisfied third fourthtrials are made similar to
second trial
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 3267
If either tolarence for volume or tolarance for location are satisfied at a trial
satisfied one is fixed trials are continued to make for the other one
983108983141983156983141983154983149983145983150983137983156983145983151983150 983151983142 983140983137983149983137983143983141983140 983148983141983150983143983156983144 983137983150983140 983148983151983139983137983156983145983151983150 983151983142 983149983145983140
983151983142 983139983151983149983152983137983154983156983149983141983150983156
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 3367
A ship is 116 meter long and displaces 7842 ton in salt water (ρ1=1025 tm3)
when her mean draught is 64m Longitudinal Centre of Buoyancy (LCB) is
0615 m aft from amidships After one of her stern compartment is damaged
she floats trimmed to the aft Her sectional areas after damaged are given in the
following table
a) Determine the volume of water entering the vessel (vw) and the location of
volume centre of damaged compartment (xw)
b) Assume permability of compartment micro is 1 Determine damaged length
and Distance of the mid of damaged length of compartment to amidship
983109983160983137983149983152983148983141 2
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 3467
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 3567
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 3667
Predicted xw
is between section 2 and section 3
983123983141983139 N983151 983123983141983139 A983154983141983137 D983145983155983156 A9831499831459831559831449831459831522 10135 983085348
3 1208 983085232
983123983141983139 A983154983141983137 983137983156 98308524983149 983142983154983151983149 983137983149983145983140983155983144983145983152 = 11959831492
l1=v0Amean=204081195=17078 m
s=l14=427 m
983109983160983137983149983152983148983141 2983085983123983119983116983125983124983113983119983118
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 3767
983161983145 L983151983139 A983149983141983137983150 983123M M A983154983149
9831311983133 9831312983133 98313119831339832559831312983133 9831313983133 983131198313398325598313129831339832559831313983133
0 9830853254 1051 1 1051 2 21021 9830852827 1123 4 4492 1 4492
2 98308524 1195 2 239 0 0
3 9830851973 1219 4 4876 9830851 9830854876
4 9830851546 1233 1 1233 9830852 9830852466
sum983091983101 14042 sum983092983101 983085748
vm
= (s3) sum3= 199864479831493
xm
=s sum4sum3= 9830850227983149
v0-vm=20408-19986=422 m3
Error=422times10020408=207
983109983160983137983149983152983148983141 2983085983123983119983116983125983124983113983119983118
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 3867
Methods of Calculation
There two available method calculating the
final stage of the damaged vessel
bull Lost Buoyancy Method
bull Added Weight Method
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 3967
Comparision of Lost Buoyancy and Added
Weight Methods
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 4067
Consider a vessel that has been damaged such
that a portion of the bottom is now open to the
sea
The vesselrsquos draft will increase because an amount
of the buoyancy was lost
Added Weight Method
Added Weight Method
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 4167
Added Weight Method
In this method flood water is treated as a fixed weight (for example the
weight of water of volume ABEF) This added weight is balanced by the
additional buoyant force of the layer WL1WL
The added weight can be determined by either the volume ABEF or
waterline WL1 Therefore WL1 waterline is not known can be just guessed
For the predicted waterline added weight and additional buoyant force
caculation are done iteratively until both of them are equal This method is
known as Added weight method
Determination of Added Weight
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 4267
Determination of Added Weight
vc Volume of damaged compartment (DCEF)
ac The surface area (AB) of damaged compartment on the waterline
micro The volume permability of damaged compartment
microa The area permability of the surface of damaged compartment
∆ The initial displacement
∆1 The displacement at final stage
vw The volume of water entering the vessel (ABEH)
w The weight of water entering the vessel
p The value of parallel sinkage
If th t th l l i k i h f t l f
8162019 Damaged Stability
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If we assume that the paralel sinkage cause a minor change of water plane area of a
ship (Awp
asymp Awp1
) we can determine the paralel sinkage by equating the volume of
the layer WL1WL to the volume of ABEF
If the damaged compartment is bounded on top
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 4467
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 4567
Longitudinal Metacentre Radius at final stage
Free Surface Effect
Damaged compartment can be considered as a half filled tank
Free Contact Effect
Damaged compartment can be considered as a half filled tank
T M H i h
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 4667
Transverse Metacentre Height
The angle of heel
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 4767
L it di l M t t H i ht
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 4867
Longitudinal Metacentre Height
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 4967
E983160983137983149983152983148983141 A 983138983137983154983143983141
8162019 Damaged Stability
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E983160983137983149983152983148983141 A 983138983137983154983143983141
991266 L = 20 983149991266 B = 5 983149
991266 983124 = 15 983149
991266 KG = 15 983149
I983150983156983137983139983156 C983151983150983140983145983156983145983151983150
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 5167
I983150983156983137983139983156 C983151983150983140983145983156983145983151983150
991266 983124983144983141 983140983145983155983152983148983137983139983141983149983141983150983156 983158983151983148983157983149983141
991266 983124983144983141 983149983137983155983155 983140983145983155983152983148983137983139983141983149983141983150983156
991266 983124983144983141 983149983151983149983141983150983156 983151983142 983145983150983141983154983156983145983137 983151983142 983156983144983141 983159983137983156983141983154983152983148983137983150983141 983137983154983141983137983137983138983151983157983156 CL
3
15051520 m x xT B L
I I
==sdotsdot=nabla
tons x I
751531500251 ==nablasdot=∆ ρ
433
33208
12
205
12
m x L B
I I
===
I983150983156983137983139983156 C983151983150983140983145983156983145983151983150
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 5267
I983150983156983137983139983156 C983151983150983140983145983156983145983151983150
991266 M983141983156983137983139983141983150983156983154983145983139 983154983137983140983145983157983155
991266 O983154 983145983156 983139983151983157983148983140 983138983141 983139983137983148983139983157983148983137983156983141983140 983140983145983154983141983139983156983148983161 983137983155
991266 H983141983145983143983144983156 983151983142 983156983144983141 983139983141983150983156983141983154 983151983142 983138983157983151983161983137983150983139983161
m I
BM
I
I 3891
150
33208==
nabla
=
m xT
B
LBT
L B BM
I I
I 3891
5112
5
12
12 223
====
mT
KB I
I 750
2
==
I983150983156983137983139983156 C983151983150983140983145983156983145983151983150
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 5367
991266 983124983144983141 983149983141983156983137983139983141983150983156983154983145983139 983144983141983145983143983144983156
991266 F983151983154 983155983149983137983148983148 983137983150983143983148983141983155 983151983142 983144983141983141983148 983156983144983141 983154983145983143983144983156983145983150983143 983149983151983149983141983150983156
m KG BM KBGM I I 63905013891750 =minus+=minus+=
sin22998sin693075153sin mt x xGM M I I
φ φ φ ==∆=
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 5467
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 5567
983116983119983123983124 983106983125983119983129983105983118983107983129 983117983109983124983112983119983108
Paralel Sinkage
Volume (DCEF)=Volume (W1ADW+BL1LC)
Damaged compartment is bounded on top
983116983119983123983124 983106983125983119983129983105983118983107983129 983117983109983124983112983119983108
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 5667
983116983119983123983124 983106983125983119983129983105983118983107983129 983117983109983124983112983119983108
bull It is assumed that displacement and location of vertical centre
of gravity does not change after damaged
983116983119983123983124 983106983125983119983129983105983118983107983129 983117983109983124983112983119983108
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 5767
983116983119983123983124 983106983125983119983129983105983118983107983129 983117983109983124983112983119983108
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 5867
The heel angle of damaged ship is determined by
where
d is the distance between the volume centre of damaged compartment
and the new longitudinal centre of floatation
wc=vc μ ρ
983116983119983123983124 983106983125983119983129983105983118983107983129 983117983109983124983112983119983108
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 5967
983116983119983123983124 983106983125983119983129983105983118983107983129 983117983109983124983112983119983108
983116983119983123983124 983106983125983119983129983105983118983107983129 983117983109983124983112983119983108
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 6067
Longitudinal Metacentre Height of a Damaged Ship
983116983119983123983124 983106983125983119983129983105983118983107983129 983117983109983124983112983119983108
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 6167
983110983151983154983159983137983154983140 983137983150983140 983137983142983156 983140983154983137983157983143983144983156983155 983137983142983156983141983154 983140983137983149983137983143983141983140
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 6267
983120983151983154983156 983105983142983156 983120983151983154983156 983110983151983154983141 983123983156983137983154983138983151983137983154983140 983105983142983156 983123983156983137983154983138983151983137983154983140 983110983151983154983159983137983154983140
I983150983145983156983145983137983148 D983154983137983157983143983144983156 983124 983124 983124 983124
983120983137983154983137983148983141983148 983123983145983150983147983137983143983141 +983152 +983152 +983152 +983120
H983141983141983148 983085983149983145 983085983149983145 +983149983155 +983149983155
983124983154983145983149 983085983156983147 +983156983138 983085983156983147 +983156983138
F983145983150983137983148 D983154983137983157983143983144983156 983124+983152983085983149983145983085983156983147 983124+983152983085983149983145+983156983138 983124+983152+983149983155983085983156983147 983124+983152+983149983155+983156983138
Table 1 Final Draughts for a starboard side damaged ship
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 6367
L983151983155983156 B983157983151983161983137983150983139983161 M983141983156983144983151983140
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 6467
L983151983155983156 B983157983151983161983137983150983139983161 M983141983156983144983151983140
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 6567
991266 A983142983156983141983154 983148983151983151983155983145983150983143 983156983144983141 983139983141983150983156983154983137983148 983139983151983149983152983137983154983156983149983141983150983156 983156983144983141
983159983137983156983141983154983152983148983137983150983141 983137983154983141983137 983145983155
991266 983124983151 983139983151983149983152983141983150983155983137983156983141 983142983151983154 983156983144983141 983148983151983155983155 983151983142 983138983157983151983161983137983150983139983161 983151983142 983156983144983141
983139983141983150983156983154983137983148 983139983151983149983152983137983154983156983149983141983150983156 983156983144983141 983140983154983137983142983156 983145983150983139983154983141983137983155983141983155 983156983151
2805)420()( m x Bl L A L
=minus=minus=
m A
T
L
I
L 875180
150==
nabla=
L983151983155983156 B983157983151983161983137983150983139983161 M983141983156983144983151983140
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 6667
991266 983124983144983141 983144983141983145983143983144983156 983151983142 983156983144983141 983139983141983150983156983141983154 983151983142 983138983157983151983161983137983150983139983161 983145983150983139983154983141983137983155983141983155 983156983151
991266 983124983144983141 983149983151983149983141983150983156 983151983142 983145983150983141983154983156983145983137 983151983142 983156983144983141 983159983137983156983141983154983152983148983137983150983141 983137983154983141983137
991266 983124983144983141 983149983141983156983137983139983141983150983156983154983145983139 983154983137983140983145983157983155
m
T
KB L
L 93802
8751
2 ===
433
6716612
)420(5
12
)(m
l L B I L
=minus
=minus
=
m I
BM
I
L
L 1111150
67166==
nabla
=
L983151983155983156 B983157983151983161983137983150983139983161 M983141983156983144983151983140
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 6767
991266 983124983144983141 983149983141983156983137983139983141983150983156983154983145983139 983144983141983145983143983144983156
991266 983122983145983143983144983156983145983150983143 983149983151983149983141983150983156 983142983151983154 983155983149983137983148983148 983144983141983141983148 983137983150983143983148983141983155
m KG BM KBGM L L L 54905111119380 =minus+=minus+=
mt xGM M L
sin34984sin549075153sin φ φ φ ==∆=
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 2867
bull The volume of water entering the vessel (vw)
bull Distance of volume centre of damaged compartment from amidships Θ ( xw)
bull Volume of the compartment (v0
= vw
μ)
First trial
1) Assume xm=0 (xl=xw)
2) Damaged Length l1 = (Volume of the compartment v0) (mean sec Area Amean)
where Amean is determined from trimmed sectional area curve
983108983141983156983141983154983149983145983150983137983156983145983151983150 983151983142 983140983137983149983137983143983141983140 983148983141983150983143983156983144 983137983150983140 983148983151983139983137983156983145983151983150 983151983142 983149983145983140
983151983142 983139983151983149983152983137983154983156983149983141983150983156
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 2967
3) In order to determine vm and xm
s = l1 4
vm = (s 3) sum3
xm = s sum4 sum3
xc = xl ndash xm
|vm-v0| le Tolarence for volume
|xc-xw| le Tolarence for location of volume centre
l=l1 xl=xw
983108983141983156983141983154983149983145983150983137983156983145983151983150 983151983142 983140983137983149983137983143983141983140 983148983141983150983143983156983144 983137983150983140 983148983151983139983137983156983145983151983150 983151983142 983149983145983140
983151983142 983139983151983149983152983137983154983156983149983141983150983156
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 3067
983108983141983156983141983154983149983145983150983137983156983145983151983150 983151983142 983140983137983149983137983143983141983140 983148983141983150983143983156983144 983137983150983140 983148983151983139983137983156983145983151983150 983151983142 983149983145983140
983151983142 983139983151983149983152983137983154983156983149983141983150983156Second Trial
Damaged length is changed proportionally by the volume
l2 = l1 times (v0v
m)
vm Computed volume at first trial
If the value of xm computed at first trial is negative then the mid of the
compartment slides to the bow
xl = xw+xm
where xm is the distance of the volume centre of compartment to amidship
computed at first trial
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 3167
In order to determine vm and xm
983108983141983156983141983154983149983145983150983137983156983145983151983150 983151983142 983140983137983149983137983143983141983140 983148983141983150983143983156983144 983137983150983140 983148983151983139983137983156983145983151983150 983151983142 983149983145983140
983151983142 983139983151983149983152983137983154983156983149983141983150983156
s = l2 4
vm = (s 3) sum3
xm = s sum4 sum3
xc = xl ndash xm
|vm-v0| le Tolarence for volume
|xc-xw| le Tolarence for location of volume centre
l=l2
If tolarances for both volume and location are not satisfied third fourthtrials are made similar to
second trial
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 3267
If either tolarence for volume or tolarance for location are satisfied at a trial
satisfied one is fixed trials are continued to make for the other one
983108983141983156983141983154983149983145983150983137983156983145983151983150 983151983142 983140983137983149983137983143983141983140 983148983141983150983143983156983144 983137983150983140 983148983151983139983137983156983145983151983150 983151983142 983149983145983140
983151983142 983139983151983149983152983137983154983156983149983141983150983156
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 3367
A ship is 116 meter long and displaces 7842 ton in salt water (ρ1=1025 tm3)
when her mean draught is 64m Longitudinal Centre of Buoyancy (LCB) is
0615 m aft from amidships After one of her stern compartment is damaged
she floats trimmed to the aft Her sectional areas after damaged are given in the
following table
a) Determine the volume of water entering the vessel (vw) and the location of
volume centre of damaged compartment (xw)
b) Assume permability of compartment micro is 1 Determine damaged length
and Distance of the mid of damaged length of compartment to amidship
983109983160983137983149983152983148983141 2
8162019 Damaged Stability
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8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 3567
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 3667
Predicted xw
is between section 2 and section 3
983123983141983139 N983151 983123983141983139 A983154983141983137 D983145983155983156 A9831499831459831559831449831459831522 10135 983085348
3 1208 983085232
983123983141983139 A983154983141983137 983137983156 98308524983149 983142983154983151983149 983137983149983145983140983155983144983145983152 = 11959831492
l1=v0Amean=204081195=17078 m
s=l14=427 m
983109983160983137983149983152983148983141 2983085983123983119983116983125983124983113983119983118
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 3767
983161983145 L983151983139 A983149983141983137983150 983123M M A983154983149
9831311983133 9831312983133 98313119831339832559831312983133 9831313983133 983131198313398325598313129831339832559831313983133
0 9830853254 1051 1 1051 2 21021 9830852827 1123 4 4492 1 4492
2 98308524 1195 2 239 0 0
3 9830851973 1219 4 4876 9830851 9830854876
4 9830851546 1233 1 1233 9830852 9830852466
sum983091983101 14042 sum983092983101 983085748
vm
= (s3) sum3= 199864479831493
xm
=s sum4sum3= 9830850227983149
v0-vm=20408-19986=422 m3
Error=422times10020408=207
983109983160983137983149983152983148983141 2983085983123983119983116983125983124983113983119983118
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 3867
Methods of Calculation
There two available method calculating the
final stage of the damaged vessel
bull Lost Buoyancy Method
bull Added Weight Method
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 3967
Comparision of Lost Buoyancy and Added
Weight Methods
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 4067
Consider a vessel that has been damaged such
that a portion of the bottom is now open to the
sea
The vesselrsquos draft will increase because an amount
of the buoyancy was lost
Added Weight Method
Added Weight Method
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 4167
Added Weight Method
In this method flood water is treated as a fixed weight (for example the
weight of water of volume ABEF) This added weight is balanced by the
additional buoyant force of the layer WL1WL
The added weight can be determined by either the volume ABEF or
waterline WL1 Therefore WL1 waterline is not known can be just guessed
For the predicted waterline added weight and additional buoyant force
caculation are done iteratively until both of them are equal This method is
known as Added weight method
Determination of Added Weight
8162019 Damaged Stability
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Determination of Added Weight
vc Volume of damaged compartment (DCEF)
ac The surface area (AB) of damaged compartment on the waterline
micro The volume permability of damaged compartment
microa The area permability of the surface of damaged compartment
∆ The initial displacement
∆1 The displacement at final stage
vw The volume of water entering the vessel (ABEH)
w The weight of water entering the vessel
p The value of parallel sinkage
If th t th l l i k i h f t l f
8162019 Damaged Stability
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If we assume that the paralel sinkage cause a minor change of water plane area of a
ship (Awp
asymp Awp1
) we can determine the paralel sinkage by equating the volume of
the layer WL1WL to the volume of ABEF
If the damaged compartment is bounded on top
8162019 Damaged Stability
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8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 4567
Longitudinal Metacentre Radius at final stage
Free Surface Effect
Damaged compartment can be considered as a half filled tank
Free Contact Effect
Damaged compartment can be considered as a half filled tank
T M H i h
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 4667
Transverse Metacentre Height
The angle of heel
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 4767
L it di l M t t H i ht
8162019 Damaged Stability
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Longitudinal Metacentre Height
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 4967
E983160983137983149983152983148983141 A 983138983137983154983143983141
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 5067
E983160983137983149983152983148983141 A 983138983137983154983143983141
991266 L = 20 983149991266 B = 5 983149
991266 983124 = 15 983149
991266 KG = 15 983149
I983150983156983137983139983156 C983151983150983140983145983156983145983151983150
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 5167
I983150983156983137983139983156 C983151983150983140983145983156983145983151983150
991266 983124983144983141 983140983145983155983152983148983137983139983141983149983141983150983156 983158983151983148983157983149983141
991266 983124983144983141 983149983137983155983155 983140983145983155983152983148983137983139983141983149983141983150983156
991266 983124983144983141 983149983151983149983141983150983156 983151983142 983145983150983141983154983156983145983137 983151983142 983156983144983141 983159983137983156983141983154983152983148983137983150983141 983137983154983141983137983137983138983151983157983156 CL
3
15051520 m x xT B L
I I
==sdotsdot=nabla
tons x I
751531500251 ==nablasdot=∆ ρ
433
33208
12
205
12
m x L B
I I
===
I983150983156983137983139983156 C983151983150983140983145983156983145983151983150
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 5267
I983150983156983137983139983156 C983151983150983140983145983156983145983151983150
991266 M983141983156983137983139983141983150983156983154983145983139 983154983137983140983145983157983155
991266 O983154 983145983156 983139983151983157983148983140 983138983141 983139983137983148983139983157983148983137983156983141983140 983140983145983154983141983139983156983148983161 983137983155
991266 H983141983145983143983144983156 983151983142 983156983144983141 983139983141983150983156983141983154 983151983142 983138983157983151983161983137983150983139983161
m I
BM
I
I 3891
150
33208==
nabla
=
m xT
B
LBT
L B BM
I I
I 3891
5112
5
12
12 223
====
mT
KB I
I 750
2
==
I983150983156983137983139983156 C983151983150983140983145983156983145983151983150
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 5367
991266 983124983144983141 983149983141983156983137983139983141983150983156983154983145983139 983144983141983145983143983144983156
991266 F983151983154 983155983149983137983148983148 983137983150983143983148983141983155 983151983142 983144983141983141983148 983156983144983141 983154983145983143983144983156983145983150983143 983149983151983149983141983150983156
m KG BM KBGM I I 63905013891750 =minus+=minus+=
sin22998sin693075153sin mt x xGM M I I
φ φ φ ==∆=
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 5467
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 5567
983116983119983123983124 983106983125983119983129983105983118983107983129 983117983109983124983112983119983108
Paralel Sinkage
Volume (DCEF)=Volume (W1ADW+BL1LC)
Damaged compartment is bounded on top
983116983119983123983124 983106983125983119983129983105983118983107983129 983117983109983124983112983119983108
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 5667
983116983119983123983124 983106983125983119983129983105983118983107983129 983117983109983124983112983119983108
bull It is assumed that displacement and location of vertical centre
of gravity does not change after damaged
983116983119983123983124 983106983125983119983129983105983118983107983129 983117983109983124983112983119983108
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 5767
983116983119983123983124 983106983125983119983129983105983118983107983129 983117983109983124983112983119983108
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 5867
The heel angle of damaged ship is determined by
where
d is the distance between the volume centre of damaged compartment
and the new longitudinal centre of floatation
wc=vc μ ρ
983116983119983123983124 983106983125983119983129983105983118983107983129 983117983109983124983112983119983108
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 5967
983116983119983123983124 983106983125983119983129983105983118983107983129 983117983109983124983112983119983108
983116983119983123983124 983106983125983119983129983105983118983107983129 983117983109983124983112983119983108
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 6067
Longitudinal Metacentre Height of a Damaged Ship
983116983119983123983124 983106983125983119983129983105983118983107983129 983117983109983124983112983119983108
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 6167
983110983151983154983159983137983154983140 983137983150983140 983137983142983156 983140983154983137983157983143983144983156983155 983137983142983156983141983154 983140983137983149983137983143983141983140
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 6267
983120983151983154983156 983105983142983156 983120983151983154983156 983110983151983154983141 983123983156983137983154983138983151983137983154983140 983105983142983156 983123983156983137983154983138983151983137983154983140 983110983151983154983159983137983154983140
I983150983145983156983145983137983148 D983154983137983157983143983144983156 983124 983124 983124 983124
983120983137983154983137983148983141983148 983123983145983150983147983137983143983141 +983152 +983152 +983152 +983120
H983141983141983148 983085983149983145 983085983149983145 +983149983155 +983149983155
983124983154983145983149 983085983156983147 +983156983138 983085983156983147 +983156983138
F983145983150983137983148 D983154983137983157983143983144983156 983124+983152983085983149983145983085983156983147 983124+983152983085983149983145+983156983138 983124+983152+983149983155983085983156983147 983124+983152+983149983155+983156983138
Table 1 Final Draughts for a starboard side damaged ship
8162019 Damaged Stability
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L983151983155983156 B983157983151983161983137983150983139983161 M983141983156983144983151983140
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 6467
L983151983155983156 B983157983151983161983137983150983139983161 M983141983156983144983151983140
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 6567
991266 A983142983156983141983154 983148983151983151983155983145983150983143 983156983144983141 983139983141983150983156983154983137983148 983139983151983149983152983137983154983156983149983141983150983156 983156983144983141
983159983137983156983141983154983152983148983137983150983141 983137983154983141983137 983145983155
991266 983124983151 983139983151983149983152983141983150983155983137983156983141 983142983151983154 983156983144983141 983148983151983155983155 983151983142 983138983157983151983161983137983150983139983161 983151983142 983156983144983141
983139983141983150983156983154983137983148 983139983151983149983152983137983154983156983149983141983150983156 983156983144983141 983140983154983137983142983156 983145983150983139983154983141983137983155983141983155 983156983151
2805)420()( m x Bl L A L
=minus=minus=
m A
T
L
I
L 875180
150==
nabla=
L983151983155983156 B983157983151983161983137983150983139983161 M983141983156983144983151983140
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 6667
991266 983124983144983141 983144983141983145983143983144983156 983151983142 983156983144983141 983139983141983150983156983141983154 983151983142 983138983157983151983161983137983150983139983161 983145983150983139983154983141983137983155983141983155 983156983151
991266 983124983144983141 983149983151983149983141983150983156 983151983142 983145983150983141983154983156983145983137 983151983142 983156983144983141 983159983137983156983141983154983152983148983137983150983141 983137983154983141983137
991266 983124983144983141 983149983141983156983137983139983141983150983156983154983145983139 983154983137983140983145983157983155
m
T
KB L
L 93802
8751
2 ===
433
6716612
)420(5
12
)(m
l L B I L
=minus
=minus
=
m I
BM
I
L
L 1111150
67166==
nabla
=
L983151983155983156 B983157983151983161983137983150983139983161 M983141983156983144983151983140
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 6767
991266 983124983144983141 983149983141983156983137983139983141983150983156983154983145983139 983144983141983145983143983144983156
991266 983122983145983143983144983156983145983150983143 983149983151983149983141983150983156 983142983151983154 983155983149983137983148983148 983144983141983141983148 983137983150983143983148983141983155
m KG BM KBGM L L L 54905111119380 =minus+=minus+=
mt xGM M L
sin34984sin549075153sin φ φ φ ==∆=
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 2967
3) In order to determine vm and xm
s = l1 4
vm = (s 3) sum3
xm = s sum4 sum3
xc = xl ndash xm
|vm-v0| le Tolarence for volume
|xc-xw| le Tolarence for location of volume centre
l=l1 xl=xw
983108983141983156983141983154983149983145983150983137983156983145983151983150 983151983142 983140983137983149983137983143983141983140 983148983141983150983143983156983144 983137983150983140 983148983151983139983137983156983145983151983150 983151983142 983149983145983140
983151983142 983139983151983149983152983137983154983156983149983141983150983156
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 3067
983108983141983156983141983154983149983145983150983137983156983145983151983150 983151983142 983140983137983149983137983143983141983140 983148983141983150983143983156983144 983137983150983140 983148983151983139983137983156983145983151983150 983151983142 983149983145983140
983151983142 983139983151983149983152983137983154983156983149983141983150983156Second Trial
Damaged length is changed proportionally by the volume
l2 = l1 times (v0v
m)
vm Computed volume at first trial
If the value of xm computed at first trial is negative then the mid of the
compartment slides to the bow
xl = xw+xm
where xm is the distance of the volume centre of compartment to amidship
computed at first trial
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 3167
In order to determine vm and xm
983108983141983156983141983154983149983145983150983137983156983145983151983150 983151983142 983140983137983149983137983143983141983140 983148983141983150983143983156983144 983137983150983140 983148983151983139983137983156983145983151983150 983151983142 983149983145983140
983151983142 983139983151983149983152983137983154983156983149983141983150983156
s = l2 4
vm = (s 3) sum3
xm = s sum4 sum3
xc = xl ndash xm
|vm-v0| le Tolarence for volume
|xc-xw| le Tolarence for location of volume centre
l=l2
If tolarances for both volume and location are not satisfied third fourthtrials are made similar to
second trial
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 3267
If either tolarence for volume or tolarance for location are satisfied at a trial
satisfied one is fixed trials are continued to make for the other one
983108983141983156983141983154983149983145983150983137983156983145983151983150 983151983142 983140983137983149983137983143983141983140 983148983141983150983143983156983144 983137983150983140 983148983151983139983137983156983145983151983150 983151983142 983149983145983140
983151983142 983139983151983149983152983137983154983156983149983141983150983156
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 3367
A ship is 116 meter long and displaces 7842 ton in salt water (ρ1=1025 tm3)
when her mean draught is 64m Longitudinal Centre of Buoyancy (LCB) is
0615 m aft from amidships After one of her stern compartment is damaged
she floats trimmed to the aft Her sectional areas after damaged are given in the
following table
a) Determine the volume of water entering the vessel (vw) and the location of
volume centre of damaged compartment (xw)
b) Assume permability of compartment micro is 1 Determine damaged length
and Distance of the mid of damaged length of compartment to amidship
983109983160983137983149983152983148983141 2
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 3467
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 3567
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 3667
Predicted xw
is between section 2 and section 3
983123983141983139 N983151 983123983141983139 A983154983141983137 D983145983155983156 A9831499831459831559831449831459831522 10135 983085348
3 1208 983085232
983123983141983139 A983154983141983137 983137983156 98308524983149 983142983154983151983149 983137983149983145983140983155983144983145983152 = 11959831492
l1=v0Amean=204081195=17078 m
s=l14=427 m
983109983160983137983149983152983148983141 2983085983123983119983116983125983124983113983119983118
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 3767
983161983145 L983151983139 A983149983141983137983150 983123M M A983154983149
9831311983133 9831312983133 98313119831339832559831312983133 9831313983133 983131198313398325598313129831339832559831313983133
0 9830853254 1051 1 1051 2 21021 9830852827 1123 4 4492 1 4492
2 98308524 1195 2 239 0 0
3 9830851973 1219 4 4876 9830851 9830854876
4 9830851546 1233 1 1233 9830852 9830852466
sum983091983101 14042 sum983092983101 983085748
vm
= (s3) sum3= 199864479831493
xm
=s sum4sum3= 9830850227983149
v0-vm=20408-19986=422 m3
Error=422times10020408=207
983109983160983137983149983152983148983141 2983085983123983119983116983125983124983113983119983118
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 3867
Methods of Calculation
There two available method calculating the
final stage of the damaged vessel
bull Lost Buoyancy Method
bull Added Weight Method
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 3967
Comparision of Lost Buoyancy and Added
Weight Methods
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 4067
Consider a vessel that has been damaged such
that a portion of the bottom is now open to the
sea
The vesselrsquos draft will increase because an amount
of the buoyancy was lost
Added Weight Method
Added Weight Method
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 4167
Added Weight Method
In this method flood water is treated as a fixed weight (for example the
weight of water of volume ABEF) This added weight is balanced by the
additional buoyant force of the layer WL1WL
The added weight can be determined by either the volume ABEF or
waterline WL1 Therefore WL1 waterline is not known can be just guessed
For the predicted waterline added weight and additional buoyant force
caculation are done iteratively until both of them are equal This method is
known as Added weight method
Determination of Added Weight
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 4267
Determination of Added Weight
vc Volume of damaged compartment (DCEF)
ac The surface area (AB) of damaged compartment on the waterline
micro The volume permability of damaged compartment
microa The area permability of the surface of damaged compartment
∆ The initial displacement
∆1 The displacement at final stage
vw The volume of water entering the vessel (ABEH)
w The weight of water entering the vessel
p The value of parallel sinkage
If th t th l l i k i h f t l f
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 4367
If we assume that the paralel sinkage cause a minor change of water plane area of a
ship (Awp
asymp Awp1
) we can determine the paralel sinkage by equating the volume of
the layer WL1WL to the volume of ABEF
If the damaged compartment is bounded on top
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 4467
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 4567
Longitudinal Metacentre Radius at final stage
Free Surface Effect
Damaged compartment can be considered as a half filled tank
Free Contact Effect
Damaged compartment can be considered as a half filled tank
T M H i h
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 4667
Transverse Metacentre Height
The angle of heel
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 4767
L it di l M t t H i ht
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 4867
Longitudinal Metacentre Height
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 4967
E983160983137983149983152983148983141 A 983138983137983154983143983141
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 5067
E983160983137983149983152983148983141 A 983138983137983154983143983141
991266 L = 20 983149991266 B = 5 983149
991266 983124 = 15 983149
991266 KG = 15 983149
I983150983156983137983139983156 C983151983150983140983145983156983145983151983150
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 5167
I983150983156983137983139983156 C983151983150983140983145983156983145983151983150
991266 983124983144983141 983140983145983155983152983148983137983139983141983149983141983150983156 983158983151983148983157983149983141
991266 983124983144983141 983149983137983155983155 983140983145983155983152983148983137983139983141983149983141983150983156
991266 983124983144983141 983149983151983149983141983150983156 983151983142 983145983150983141983154983156983145983137 983151983142 983156983144983141 983159983137983156983141983154983152983148983137983150983141 983137983154983141983137983137983138983151983157983156 CL
3
15051520 m x xT B L
I I
==sdotsdot=nabla
tons x I
751531500251 ==nablasdot=∆ ρ
433
33208
12
205
12
m x L B
I I
===
I983150983156983137983139983156 C983151983150983140983145983156983145983151983150
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 5267
I983150983156983137983139983156 C983151983150983140983145983156983145983151983150
991266 M983141983156983137983139983141983150983156983154983145983139 983154983137983140983145983157983155
991266 O983154 983145983156 983139983151983157983148983140 983138983141 983139983137983148983139983157983148983137983156983141983140 983140983145983154983141983139983156983148983161 983137983155
991266 H983141983145983143983144983156 983151983142 983156983144983141 983139983141983150983156983141983154 983151983142 983138983157983151983161983137983150983139983161
m I
BM
I
I 3891
150
33208==
nabla
=
m xT
B
LBT
L B BM
I I
I 3891
5112
5
12
12 223
====
mT
KB I
I 750
2
==
I983150983156983137983139983156 C983151983150983140983145983156983145983151983150
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 5367
991266 983124983144983141 983149983141983156983137983139983141983150983156983154983145983139 983144983141983145983143983144983156
991266 F983151983154 983155983149983137983148983148 983137983150983143983148983141983155 983151983142 983144983141983141983148 983156983144983141 983154983145983143983144983156983145983150983143 983149983151983149983141983150983156
m KG BM KBGM I I 63905013891750 =minus+=minus+=
sin22998sin693075153sin mt x xGM M I I
φ φ φ ==∆=
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 5467
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 5567
983116983119983123983124 983106983125983119983129983105983118983107983129 983117983109983124983112983119983108
Paralel Sinkage
Volume (DCEF)=Volume (W1ADW+BL1LC)
Damaged compartment is bounded on top
983116983119983123983124 983106983125983119983129983105983118983107983129 983117983109983124983112983119983108
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 5667
983116983119983123983124 983106983125983119983129983105983118983107983129 983117983109983124983112983119983108
bull It is assumed that displacement and location of vertical centre
of gravity does not change after damaged
983116983119983123983124 983106983125983119983129983105983118983107983129 983117983109983124983112983119983108
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 5767
983116983119983123983124 983106983125983119983129983105983118983107983129 983117983109983124983112983119983108
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 5867
The heel angle of damaged ship is determined by
where
d is the distance between the volume centre of damaged compartment
and the new longitudinal centre of floatation
wc=vc μ ρ
983116983119983123983124 983106983125983119983129983105983118983107983129 983117983109983124983112983119983108
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 5967
983116983119983123983124 983106983125983119983129983105983118983107983129 983117983109983124983112983119983108
983116983119983123983124 983106983125983119983129983105983118983107983129 983117983109983124983112983119983108
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 6067
Longitudinal Metacentre Height of a Damaged Ship
983116983119983123983124 983106983125983119983129983105983118983107983129 983117983109983124983112983119983108
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 6167
983110983151983154983159983137983154983140 983137983150983140 983137983142983156 983140983154983137983157983143983144983156983155 983137983142983156983141983154 983140983137983149983137983143983141983140
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 6267
983120983151983154983156 983105983142983156 983120983151983154983156 983110983151983154983141 983123983156983137983154983138983151983137983154983140 983105983142983156 983123983156983137983154983138983151983137983154983140 983110983151983154983159983137983154983140
I983150983145983156983145983137983148 D983154983137983157983143983144983156 983124 983124 983124 983124
983120983137983154983137983148983141983148 983123983145983150983147983137983143983141 +983152 +983152 +983152 +983120
H983141983141983148 983085983149983145 983085983149983145 +983149983155 +983149983155
983124983154983145983149 983085983156983147 +983156983138 983085983156983147 +983156983138
F983145983150983137983148 D983154983137983157983143983144983156 983124+983152983085983149983145983085983156983147 983124+983152983085983149983145+983156983138 983124+983152+983149983155983085983156983147 983124+983152+983149983155+983156983138
Table 1 Final Draughts for a starboard side damaged ship
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 6367
L983151983155983156 B983157983151983161983137983150983139983161 M983141983156983144983151983140
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 6467
L983151983155983156 B983157983151983161983137983150983139983161 M983141983156983144983151983140
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 6567
991266 A983142983156983141983154 983148983151983151983155983145983150983143 983156983144983141 983139983141983150983156983154983137983148 983139983151983149983152983137983154983156983149983141983150983156 983156983144983141
983159983137983156983141983154983152983148983137983150983141 983137983154983141983137 983145983155
991266 983124983151 983139983151983149983152983141983150983155983137983156983141 983142983151983154 983156983144983141 983148983151983155983155 983151983142 983138983157983151983161983137983150983139983161 983151983142 983156983144983141
983139983141983150983156983154983137983148 983139983151983149983152983137983154983156983149983141983150983156 983156983144983141 983140983154983137983142983156 983145983150983139983154983141983137983155983141983155 983156983151
2805)420()( m x Bl L A L
=minus=minus=
m A
T
L
I
L 875180
150==
nabla=
L983151983155983156 B983157983151983161983137983150983139983161 M983141983156983144983151983140
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 6667
991266 983124983144983141 983144983141983145983143983144983156 983151983142 983156983144983141 983139983141983150983156983141983154 983151983142 983138983157983151983161983137983150983139983161 983145983150983139983154983141983137983155983141983155 983156983151
991266 983124983144983141 983149983151983149983141983150983156 983151983142 983145983150983141983154983156983145983137 983151983142 983156983144983141 983159983137983156983141983154983152983148983137983150983141 983137983154983141983137
991266 983124983144983141 983149983141983156983137983139983141983150983156983154983145983139 983154983137983140983145983157983155
m
T
KB L
L 93802
8751
2 ===
433
6716612
)420(5
12
)(m
l L B I L
=minus
=minus
=
m I
BM
I
L
L 1111150
67166==
nabla
=
L983151983155983156 B983157983151983161983137983150983139983161 M983141983156983144983151983140
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 6767
991266 983124983144983141 983149983141983156983137983139983141983150983156983154983145983139 983144983141983145983143983144983156
991266 983122983145983143983144983156983145983150983143 983149983151983149983141983150983156 983142983151983154 983155983149983137983148983148 983144983141983141983148 983137983150983143983148983141983155
m KG BM KBGM L L L 54905111119380 =minus+=minus+=
mt xGM M L
sin34984sin549075153sin φ φ φ ==∆=
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 3067
983108983141983156983141983154983149983145983150983137983156983145983151983150 983151983142 983140983137983149983137983143983141983140 983148983141983150983143983156983144 983137983150983140 983148983151983139983137983156983145983151983150 983151983142 983149983145983140
983151983142 983139983151983149983152983137983154983156983149983141983150983156Second Trial
Damaged length is changed proportionally by the volume
l2 = l1 times (v0v
m)
vm Computed volume at first trial
If the value of xm computed at first trial is negative then the mid of the
compartment slides to the bow
xl = xw+xm
where xm is the distance of the volume centre of compartment to amidship
computed at first trial
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 3167
In order to determine vm and xm
983108983141983156983141983154983149983145983150983137983156983145983151983150 983151983142 983140983137983149983137983143983141983140 983148983141983150983143983156983144 983137983150983140 983148983151983139983137983156983145983151983150 983151983142 983149983145983140
983151983142 983139983151983149983152983137983154983156983149983141983150983156
s = l2 4
vm = (s 3) sum3
xm = s sum4 sum3
xc = xl ndash xm
|vm-v0| le Tolarence for volume
|xc-xw| le Tolarence for location of volume centre
l=l2
If tolarances for both volume and location are not satisfied third fourthtrials are made similar to
second trial
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 3267
If either tolarence for volume or tolarance for location are satisfied at a trial
satisfied one is fixed trials are continued to make for the other one
983108983141983156983141983154983149983145983150983137983156983145983151983150 983151983142 983140983137983149983137983143983141983140 983148983141983150983143983156983144 983137983150983140 983148983151983139983137983156983145983151983150 983151983142 983149983145983140
983151983142 983139983151983149983152983137983154983156983149983141983150983156
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 3367
A ship is 116 meter long and displaces 7842 ton in salt water (ρ1=1025 tm3)
when her mean draught is 64m Longitudinal Centre of Buoyancy (LCB) is
0615 m aft from amidships After one of her stern compartment is damaged
she floats trimmed to the aft Her sectional areas after damaged are given in the
following table
a) Determine the volume of water entering the vessel (vw) and the location of
volume centre of damaged compartment (xw)
b) Assume permability of compartment micro is 1 Determine damaged length
and Distance of the mid of damaged length of compartment to amidship
983109983160983137983149983152983148983141 2
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 3467
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 3567
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 3667
Predicted xw
is between section 2 and section 3
983123983141983139 N983151 983123983141983139 A983154983141983137 D983145983155983156 A9831499831459831559831449831459831522 10135 983085348
3 1208 983085232
983123983141983139 A983154983141983137 983137983156 98308524983149 983142983154983151983149 983137983149983145983140983155983144983145983152 = 11959831492
l1=v0Amean=204081195=17078 m
s=l14=427 m
983109983160983137983149983152983148983141 2983085983123983119983116983125983124983113983119983118
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 3767
983161983145 L983151983139 A983149983141983137983150 983123M M A983154983149
9831311983133 9831312983133 98313119831339832559831312983133 9831313983133 983131198313398325598313129831339832559831313983133
0 9830853254 1051 1 1051 2 21021 9830852827 1123 4 4492 1 4492
2 98308524 1195 2 239 0 0
3 9830851973 1219 4 4876 9830851 9830854876
4 9830851546 1233 1 1233 9830852 9830852466
sum983091983101 14042 sum983092983101 983085748
vm
= (s3) sum3= 199864479831493
xm
=s sum4sum3= 9830850227983149
v0-vm=20408-19986=422 m3
Error=422times10020408=207
983109983160983137983149983152983148983141 2983085983123983119983116983125983124983113983119983118
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 3867
Methods of Calculation
There two available method calculating the
final stage of the damaged vessel
bull Lost Buoyancy Method
bull Added Weight Method
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 3967
Comparision of Lost Buoyancy and Added
Weight Methods
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 4067
Consider a vessel that has been damaged such
that a portion of the bottom is now open to the
sea
The vesselrsquos draft will increase because an amount
of the buoyancy was lost
Added Weight Method
Added Weight Method
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 4167
Added Weight Method
In this method flood water is treated as a fixed weight (for example the
weight of water of volume ABEF) This added weight is balanced by the
additional buoyant force of the layer WL1WL
The added weight can be determined by either the volume ABEF or
waterline WL1 Therefore WL1 waterline is not known can be just guessed
For the predicted waterline added weight and additional buoyant force
caculation are done iteratively until both of them are equal This method is
known as Added weight method
Determination of Added Weight
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 4267
Determination of Added Weight
vc Volume of damaged compartment (DCEF)
ac The surface area (AB) of damaged compartment on the waterline
micro The volume permability of damaged compartment
microa The area permability of the surface of damaged compartment
∆ The initial displacement
∆1 The displacement at final stage
vw The volume of water entering the vessel (ABEH)
w The weight of water entering the vessel
p The value of parallel sinkage
If th t th l l i k i h f t l f
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 4367
If we assume that the paralel sinkage cause a minor change of water plane area of a
ship (Awp
asymp Awp1
) we can determine the paralel sinkage by equating the volume of
the layer WL1WL to the volume of ABEF
If the damaged compartment is bounded on top
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 4467
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 4567
Longitudinal Metacentre Radius at final stage
Free Surface Effect
Damaged compartment can be considered as a half filled tank
Free Contact Effect
Damaged compartment can be considered as a half filled tank
T M H i h
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 4667
Transverse Metacentre Height
The angle of heel
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 4767
L it di l M t t H i ht
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 4867
Longitudinal Metacentre Height
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 4967
E983160983137983149983152983148983141 A 983138983137983154983143983141
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 5067
E983160983137983149983152983148983141 A 983138983137983154983143983141
991266 L = 20 983149991266 B = 5 983149
991266 983124 = 15 983149
991266 KG = 15 983149
I983150983156983137983139983156 C983151983150983140983145983156983145983151983150
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 5167
I983150983156983137983139983156 C983151983150983140983145983156983145983151983150
991266 983124983144983141 983140983145983155983152983148983137983139983141983149983141983150983156 983158983151983148983157983149983141
991266 983124983144983141 983149983137983155983155 983140983145983155983152983148983137983139983141983149983141983150983156
991266 983124983144983141 983149983151983149983141983150983156 983151983142 983145983150983141983154983156983145983137 983151983142 983156983144983141 983159983137983156983141983154983152983148983137983150983141 983137983154983141983137983137983138983151983157983156 CL
3
15051520 m x xT B L
I I
==sdotsdot=nabla
tons x I
751531500251 ==nablasdot=∆ ρ
433
33208
12
205
12
m x L B
I I
===
I983150983156983137983139983156 C983151983150983140983145983156983145983151983150
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 5267
I983150983156983137983139983156 C983151983150983140983145983156983145983151983150
991266 M983141983156983137983139983141983150983156983154983145983139 983154983137983140983145983157983155
991266 O983154 983145983156 983139983151983157983148983140 983138983141 983139983137983148983139983157983148983137983156983141983140 983140983145983154983141983139983156983148983161 983137983155
991266 H983141983145983143983144983156 983151983142 983156983144983141 983139983141983150983156983141983154 983151983142 983138983157983151983161983137983150983139983161
m I
BM
I
I 3891
150
33208==
nabla
=
m xT
B
LBT
L B BM
I I
I 3891
5112
5
12
12 223
====
mT
KB I
I 750
2
==
I983150983156983137983139983156 C983151983150983140983145983156983145983151983150
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 5367
991266 983124983144983141 983149983141983156983137983139983141983150983156983154983145983139 983144983141983145983143983144983156
991266 F983151983154 983155983149983137983148983148 983137983150983143983148983141983155 983151983142 983144983141983141983148 983156983144983141 983154983145983143983144983156983145983150983143 983149983151983149983141983150983156
m KG BM KBGM I I 63905013891750 =minus+=minus+=
sin22998sin693075153sin mt x xGM M I I
φ φ φ ==∆=
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 5467
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 5567
983116983119983123983124 983106983125983119983129983105983118983107983129 983117983109983124983112983119983108
Paralel Sinkage
Volume (DCEF)=Volume (W1ADW+BL1LC)
Damaged compartment is bounded on top
983116983119983123983124 983106983125983119983129983105983118983107983129 983117983109983124983112983119983108
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 5667
983116983119983123983124 983106983125983119983129983105983118983107983129 983117983109983124983112983119983108
bull It is assumed that displacement and location of vertical centre
of gravity does not change after damaged
983116983119983123983124 983106983125983119983129983105983118983107983129 983117983109983124983112983119983108
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 5767
983116983119983123983124 983106983125983119983129983105983118983107983129 983117983109983124983112983119983108
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 5867
The heel angle of damaged ship is determined by
where
d is the distance between the volume centre of damaged compartment
and the new longitudinal centre of floatation
wc=vc μ ρ
983116983119983123983124 983106983125983119983129983105983118983107983129 983117983109983124983112983119983108
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 5967
983116983119983123983124 983106983125983119983129983105983118983107983129 983117983109983124983112983119983108
983116983119983123983124 983106983125983119983129983105983118983107983129 983117983109983124983112983119983108
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 6067
Longitudinal Metacentre Height of a Damaged Ship
983116983119983123983124 983106983125983119983129983105983118983107983129 983117983109983124983112983119983108
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 6167
983110983151983154983159983137983154983140 983137983150983140 983137983142983156 983140983154983137983157983143983144983156983155 983137983142983156983141983154 983140983137983149983137983143983141983140
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 6267
983120983151983154983156 983105983142983156 983120983151983154983156 983110983151983154983141 983123983156983137983154983138983151983137983154983140 983105983142983156 983123983156983137983154983138983151983137983154983140 983110983151983154983159983137983154983140
I983150983145983156983145983137983148 D983154983137983157983143983144983156 983124 983124 983124 983124
983120983137983154983137983148983141983148 983123983145983150983147983137983143983141 +983152 +983152 +983152 +983120
H983141983141983148 983085983149983145 983085983149983145 +983149983155 +983149983155
983124983154983145983149 983085983156983147 +983156983138 983085983156983147 +983156983138
F983145983150983137983148 D983154983137983157983143983144983156 983124+983152983085983149983145983085983156983147 983124+983152983085983149983145+983156983138 983124+983152+983149983155983085983156983147 983124+983152+983149983155+983156983138
Table 1 Final Draughts for a starboard side damaged ship
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 6367
L983151983155983156 B983157983151983161983137983150983139983161 M983141983156983144983151983140
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 6467
L983151983155983156 B983157983151983161983137983150983139983161 M983141983156983144983151983140
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 6567
991266 A983142983156983141983154 983148983151983151983155983145983150983143 983156983144983141 983139983141983150983156983154983137983148 983139983151983149983152983137983154983156983149983141983150983156 983156983144983141
983159983137983156983141983154983152983148983137983150983141 983137983154983141983137 983145983155
991266 983124983151 983139983151983149983152983141983150983155983137983156983141 983142983151983154 983156983144983141 983148983151983155983155 983151983142 983138983157983151983161983137983150983139983161 983151983142 983156983144983141
983139983141983150983156983154983137983148 983139983151983149983152983137983154983156983149983141983150983156 983156983144983141 983140983154983137983142983156 983145983150983139983154983141983137983155983141983155 983156983151
2805)420()( m x Bl L A L
=minus=minus=
m A
T
L
I
L 875180
150==
nabla=
L983151983155983156 B983157983151983161983137983150983139983161 M983141983156983144983151983140
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 6667
991266 983124983144983141 983144983141983145983143983144983156 983151983142 983156983144983141 983139983141983150983156983141983154 983151983142 983138983157983151983161983137983150983139983161 983145983150983139983154983141983137983155983141983155 983156983151
991266 983124983144983141 983149983151983149983141983150983156 983151983142 983145983150983141983154983156983145983137 983151983142 983156983144983141 983159983137983156983141983154983152983148983137983150983141 983137983154983141983137
991266 983124983144983141 983149983141983156983137983139983141983150983156983154983145983139 983154983137983140983145983157983155
m
T
KB L
L 93802
8751
2 ===
433
6716612
)420(5
12
)(m
l L B I L
=minus
=minus
=
m I
BM
I
L
L 1111150
67166==
nabla
=
L983151983155983156 B983157983151983161983137983150983139983161 M983141983156983144983151983140
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 6767
991266 983124983144983141 983149983141983156983137983139983141983150983156983154983145983139 983144983141983145983143983144983156
991266 983122983145983143983144983156983145983150983143 983149983151983149983141983150983156 983142983151983154 983155983149983137983148983148 983144983141983141983148 983137983150983143983148983141983155
m KG BM KBGM L L L 54905111119380 =minus+=minus+=
mt xGM M L
sin34984sin549075153sin φ φ φ ==∆=
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 3167
In order to determine vm and xm
983108983141983156983141983154983149983145983150983137983156983145983151983150 983151983142 983140983137983149983137983143983141983140 983148983141983150983143983156983144 983137983150983140 983148983151983139983137983156983145983151983150 983151983142 983149983145983140
983151983142 983139983151983149983152983137983154983156983149983141983150983156
s = l2 4
vm = (s 3) sum3
xm = s sum4 sum3
xc = xl ndash xm
|vm-v0| le Tolarence for volume
|xc-xw| le Tolarence for location of volume centre
l=l2
If tolarances for both volume and location are not satisfied third fourthtrials are made similar to
second trial
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 3267
If either tolarence for volume or tolarance for location are satisfied at a trial
satisfied one is fixed trials are continued to make for the other one
983108983141983156983141983154983149983145983150983137983156983145983151983150 983151983142 983140983137983149983137983143983141983140 983148983141983150983143983156983144 983137983150983140 983148983151983139983137983156983145983151983150 983151983142 983149983145983140
983151983142 983139983151983149983152983137983154983156983149983141983150983156
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 3367
A ship is 116 meter long and displaces 7842 ton in salt water (ρ1=1025 tm3)
when her mean draught is 64m Longitudinal Centre of Buoyancy (LCB) is
0615 m aft from amidships After one of her stern compartment is damaged
she floats trimmed to the aft Her sectional areas after damaged are given in the
following table
a) Determine the volume of water entering the vessel (vw) and the location of
volume centre of damaged compartment (xw)
b) Assume permability of compartment micro is 1 Determine damaged length
and Distance of the mid of damaged length of compartment to amidship
983109983160983137983149983152983148983141 2
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 3467
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 3567
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 3667
Predicted xw
is between section 2 and section 3
983123983141983139 N983151 983123983141983139 A983154983141983137 D983145983155983156 A9831499831459831559831449831459831522 10135 983085348
3 1208 983085232
983123983141983139 A983154983141983137 983137983156 98308524983149 983142983154983151983149 983137983149983145983140983155983144983145983152 = 11959831492
l1=v0Amean=204081195=17078 m
s=l14=427 m
983109983160983137983149983152983148983141 2983085983123983119983116983125983124983113983119983118
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 3767
983161983145 L983151983139 A983149983141983137983150 983123M M A983154983149
9831311983133 9831312983133 98313119831339832559831312983133 9831313983133 983131198313398325598313129831339832559831313983133
0 9830853254 1051 1 1051 2 21021 9830852827 1123 4 4492 1 4492
2 98308524 1195 2 239 0 0
3 9830851973 1219 4 4876 9830851 9830854876
4 9830851546 1233 1 1233 9830852 9830852466
sum983091983101 14042 sum983092983101 983085748
vm
= (s3) sum3= 199864479831493
xm
=s sum4sum3= 9830850227983149
v0-vm=20408-19986=422 m3
Error=422times10020408=207
983109983160983137983149983152983148983141 2983085983123983119983116983125983124983113983119983118
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 3867
Methods of Calculation
There two available method calculating the
final stage of the damaged vessel
bull Lost Buoyancy Method
bull Added Weight Method
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 3967
Comparision of Lost Buoyancy and Added
Weight Methods
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 4067
Consider a vessel that has been damaged such
that a portion of the bottom is now open to the
sea
The vesselrsquos draft will increase because an amount
of the buoyancy was lost
Added Weight Method
Added Weight Method
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 4167
Added Weight Method
In this method flood water is treated as a fixed weight (for example the
weight of water of volume ABEF) This added weight is balanced by the
additional buoyant force of the layer WL1WL
The added weight can be determined by either the volume ABEF or
waterline WL1 Therefore WL1 waterline is not known can be just guessed
For the predicted waterline added weight and additional buoyant force
caculation are done iteratively until both of them are equal This method is
known as Added weight method
Determination of Added Weight
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 4267
Determination of Added Weight
vc Volume of damaged compartment (DCEF)
ac The surface area (AB) of damaged compartment on the waterline
micro The volume permability of damaged compartment
microa The area permability of the surface of damaged compartment
∆ The initial displacement
∆1 The displacement at final stage
vw The volume of water entering the vessel (ABEH)
w The weight of water entering the vessel
p The value of parallel sinkage
If th t th l l i k i h f t l f
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 4367
If we assume that the paralel sinkage cause a minor change of water plane area of a
ship (Awp
asymp Awp1
) we can determine the paralel sinkage by equating the volume of
the layer WL1WL to the volume of ABEF
If the damaged compartment is bounded on top
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 4467
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 4567
Longitudinal Metacentre Radius at final stage
Free Surface Effect
Damaged compartment can be considered as a half filled tank
Free Contact Effect
Damaged compartment can be considered as a half filled tank
T M H i h
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 4667
Transverse Metacentre Height
The angle of heel
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 4767
L it di l M t t H i ht
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 4867
Longitudinal Metacentre Height
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 4967
E983160983137983149983152983148983141 A 983138983137983154983143983141
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 5067
E983160983137983149983152983148983141 A 983138983137983154983143983141
991266 L = 20 983149991266 B = 5 983149
991266 983124 = 15 983149
991266 KG = 15 983149
I983150983156983137983139983156 C983151983150983140983145983156983145983151983150
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 5167
I983150983156983137983139983156 C983151983150983140983145983156983145983151983150
991266 983124983144983141 983140983145983155983152983148983137983139983141983149983141983150983156 983158983151983148983157983149983141
991266 983124983144983141 983149983137983155983155 983140983145983155983152983148983137983139983141983149983141983150983156
991266 983124983144983141 983149983151983149983141983150983156 983151983142 983145983150983141983154983156983145983137 983151983142 983156983144983141 983159983137983156983141983154983152983148983137983150983141 983137983154983141983137983137983138983151983157983156 CL
3
15051520 m x xT B L
I I
==sdotsdot=nabla
tons x I
751531500251 ==nablasdot=∆ ρ
433
33208
12
205
12
m x L B
I I
===
I983150983156983137983139983156 C983151983150983140983145983156983145983151983150
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 5267
I983150983156983137983139983156 C983151983150983140983145983156983145983151983150
991266 M983141983156983137983139983141983150983156983154983145983139 983154983137983140983145983157983155
991266 O983154 983145983156 983139983151983157983148983140 983138983141 983139983137983148983139983157983148983137983156983141983140 983140983145983154983141983139983156983148983161 983137983155
991266 H983141983145983143983144983156 983151983142 983156983144983141 983139983141983150983156983141983154 983151983142 983138983157983151983161983137983150983139983161
m I
BM
I
I 3891
150
33208==
nabla
=
m xT
B
LBT
L B BM
I I
I 3891
5112
5
12
12 223
====
mT
KB I
I 750
2
==
I983150983156983137983139983156 C983151983150983140983145983156983145983151983150
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 5367
991266 983124983144983141 983149983141983156983137983139983141983150983156983154983145983139 983144983141983145983143983144983156
991266 F983151983154 983155983149983137983148983148 983137983150983143983148983141983155 983151983142 983144983141983141983148 983156983144983141 983154983145983143983144983156983145983150983143 983149983151983149983141983150983156
m KG BM KBGM I I 63905013891750 =minus+=minus+=
sin22998sin693075153sin mt x xGM M I I
φ φ φ ==∆=
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 5467
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 5567
983116983119983123983124 983106983125983119983129983105983118983107983129 983117983109983124983112983119983108
Paralel Sinkage
Volume (DCEF)=Volume (W1ADW+BL1LC)
Damaged compartment is bounded on top
983116983119983123983124 983106983125983119983129983105983118983107983129 983117983109983124983112983119983108
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 5667
983116983119983123983124 983106983125983119983129983105983118983107983129 983117983109983124983112983119983108
bull It is assumed that displacement and location of vertical centre
of gravity does not change after damaged
983116983119983123983124 983106983125983119983129983105983118983107983129 983117983109983124983112983119983108
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 5767
983116983119983123983124 983106983125983119983129983105983118983107983129 983117983109983124983112983119983108
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 5867
The heel angle of damaged ship is determined by
where
d is the distance between the volume centre of damaged compartment
and the new longitudinal centre of floatation
wc=vc μ ρ
983116983119983123983124 983106983125983119983129983105983118983107983129 983117983109983124983112983119983108
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 5967
983116983119983123983124 983106983125983119983129983105983118983107983129 983117983109983124983112983119983108
983116983119983123983124 983106983125983119983129983105983118983107983129 983117983109983124983112983119983108
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 6067
Longitudinal Metacentre Height of a Damaged Ship
983116983119983123983124 983106983125983119983129983105983118983107983129 983117983109983124983112983119983108
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 6167
983110983151983154983159983137983154983140 983137983150983140 983137983142983156 983140983154983137983157983143983144983156983155 983137983142983156983141983154 983140983137983149983137983143983141983140
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 6267
983120983151983154983156 983105983142983156 983120983151983154983156 983110983151983154983141 983123983156983137983154983138983151983137983154983140 983105983142983156 983123983156983137983154983138983151983137983154983140 983110983151983154983159983137983154983140
I983150983145983156983145983137983148 D983154983137983157983143983144983156 983124 983124 983124 983124
983120983137983154983137983148983141983148 983123983145983150983147983137983143983141 +983152 +983152 +983152 +983120
H983141983141983148 983085983149983145 983085983149983145 +983149983155 +983149983155
983124983154983145983149 983085983156983147 +983156983138 983085983156983147 +983156983138
F983145983150983137983148 D983154983137983157983143983144983156 983124+983152983085983149983145983085983156983147 983124+983152983085983149983145+983156983138 983124+983152+983149983155983085983156983147 983124+983152+983149983155+983156983138
Table 1 Final Draughts for a starboard side damaged ship
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 6367
L983151983155983156 B983157983151983161983137983150983139983161 M983141983156983144983151983140
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 6467
L983151983155983156 B983157983151983161983137983150983139983161 M983141983156983144983151983140
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 6567
991266 A983142983156983141983154 983148983151983151983155983145983150983143 983156983144983141 983139983141983150983156983154983137983148 983139983151983149983152983137983154983156983149983141983150983156 983156983144983141
983159983137983156983141983154983152983148983137983150983141 983137983154983141983137 983145983155
991266 983124983151 983139983151983149983152983141983150983155983137983156983141 983142983151983154 983156983144983141 983148983151983155983155 983151983142 983138983157983151983161983137983150983139983161 983151983142 983156983144983141
983139983141983150983156983154983137983148 983139983151983149983152983137983154983156983149983141983150983156 983156983144983141 983140983154983137983142983156 983145983150983139983154983141983137983155983141983155 983156983151
2805)420()( m x Bl L A L
=minus=minus=
m A
T
L
I
L 875180
150==
nabla=
L983151983155983156 B983157983151983161983137983150983139983161 M983141983156983144983151983140
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 6667
991266 983124983144983141 983144983141983145983143983144983156 983151983142 983156983144983141 983139983141983150983156983141983154 983151983142 983138983157983151983161983137983150983139983161 983145983150983139983154983141983137983155983141983155 983156983151
991266 983124983144983141 983149983151983149983141983150983156 983151983142 983145983150983141983154983156983145983137 983151983142 983156983144983141 983159983137983156983141983154983152983148983137983150983141 983137983154983141983137
991266 983124983144983141 983149983141983156983137983139983141983150983156983154983145983139 983154983137983140983145983157983155
m
T
KB L
L 93802
8751
2 ===
433
6716612
)420(5
12
)(m
l L B I L
=minus
=minus
=
m I
BM
I
L
L 1111150
67166==
nabla
=
L983151983155983156 B983157983151983161983137983150983139983161 M983141983156983144983151983140
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 6767
991266 983124983144983141 983149983141983156983137983139983141983150983156983154983145983139 983144983141983145983143983144983156
991266 983122983145983143983144983156983145983150983143 983149983151983149983141983150983156 983142983151983154 983155983149983137983148983148 983144983141983141983148 983137983150983143983148983141983155
m KG BM KBGM L L L 54905111119380 =minus+=minus+=
mt xGM M L
sin34984sin549075153sin φ φ φ ==∆=
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 3267
If either tolarence for volume or tolarance for location are satisfied at a trial
satisfied one is fixed trials are continued to make for the other one
983108983141983156983141983154983149983145983150983137983156983145983151983150 983151983142 983140983137983149983137983143983141983140 983148983141983150983143983156983144 983137983150983140 983148983151983139983137983156983145983151983150 983151983142 983149983145983140
983151983142 983139983151983149983152983137983154983156983149983141983150983156
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 3367
A ship is 116 meter long and displaces 7842 ton in salt water (ρ1=1025 tm3)
when her mean draught is 64m Longitudinal Centre of Buoyancy (LCB) is
0615 m aft from amidships After one of her stern compartment is damaged
she floats trimmed to the aft Her sectional areas after damaged are given in the
following table
a) Determine the volume of water entering the vessel (vw) and the location of
volume centre of damaged compartment (xw)
b) Assume permability of compartment micro is 1 Determine damaged length
and Distance of the mid of damaged length of compartment to amidship
983109983160983137983149983152983148983141 2
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 3467
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 3567
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 3667
Predicted xw
is between section 2 and section 3
983123983141983139 N983151 983123983141983139 A983154983141983137 D983145983155983156 A9831499831459831559831449831459831522 10135 983085348
3 1208 983085232
983123983141983139 A983154983141983137 983137983156 98308524983149 983142983154983151983149 983137983149983145983140983155983144983145983152 = 11959831492
l1=v0Amean=204081195=17078 m
s=l14=427 m
983109983160983137983149983152983148983141 2983085983123983119983116983125983124983113983119983118
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 3767
983161983145 L983151983139 A983149983141983137983150 983123M M A983154983149
9831311983133 9831312983133 98313119831339832559831312983133 9831313983133 983131198313398325598313129831339832559831313983133
0 9830853254 1051 1 1051 2 21021 9830852827 1123 4 4492 1 4492
2 98308524 1195 2 239 0 0
3 9830851973 1219 4 4876 9830851 9830854876
4 9830851546 1233 1 1233 9830852 9830852466
sum983091983101 14042 sum983092983101 983085748
vm
= (s3) sum3= 199864479831493
xm
=s sum4sum3= 9830850227983149
v0-vm=20408-19986=422 m3
Error=422times10020408=207
983109983160983137983149983152983148983141 2983085983123983119983116983125983124983113983119983118
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 3867
Methods of Calculation
There two available method calculating the
final stage of the damaged vessel
bull Lost Buoyancy Method
bull Added Weight Method
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 3967
Comparision of Lost Buoyancy and Added
Weight Methods
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 4067
Consider a vessel that has been damaged such
that a portion of the bottom is now open to the
sea
The vesselrsquos draft will increase because an amount
of the buoyancy was lost
Added Weight Method
Added Weight Method
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 4167
Added Weight Method
In this method flood water is treated as a fixed weight (for example the
weight of water of volume ABEF) This added weight is balanced by the
additional buoyant force of the layer WL1WL
The added weight can be determined by either the volume ABEF or
waterline WL1 Therefore WL1 waterline is not known can be just guessed
For the predicted waterline added weight and additional buoyant force
caculation are done iteratively until both of them are equal This method is
known as Added weight method
Determination of Added Weight
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 4267
Determination of Added Weight
vc Volume of damaged compartment (DCEF)
ac The surface area (AB) of damaged compartment on the waterline
micro The volume permability of damaged compartment
microa The area permability of the surface of damaged compartment
∆ The initial displacement
∆1 The displacement at final stage
vw The volume of water entering the vessel (ABEH)
w The weight of water entering the vessel
p The value of parallel sinkage
If th t th l l i k i h f t l f
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 4367
If we assume that the paralel sinkage cause a minor change of water plane area of a
ship (Awp
asymp Awp1
) we can determine the paralel sinkage by equating the volume of
the layer WL1WL to the volume of ABEF
If the damaged compartment is bounded on top
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 4467
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 4567
Longitudinal Metacentre Radius at final stage
Free Surface Effect
Damaged compartment can be considered as a half filled tank
Free Contact Effect
Damaged compartment can be considered as a half filled tank
T M H i h
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 4667
Transverse Metacentre Height
The angle of heel
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 4767
L it di l M t t H i ht
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 4867
Longitudinal Metacentre Height
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 4967
E983160983137983149983152983148983141 A 983138983137983154983143983141
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 5067
E983160983137983149983152983148983141 A 983138983137983154983143983141
991266 L = 20 983149991266 B = 5 983149
991266 983124 = 15 983149
991266 KG = 15 983149
I983150983156983137983139983156 C983151983150983140983145983156983145983151983150
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 5167
I983150983156983137983139983156 C983151983150983140983145983156983145983151983150
991266 983124983144983141 983140983145983155983152983148983137983139983141983149983141983150983156 983158983151983148983157983149983141
991266 983124983144983141 983149983137983155983155 983140983145983155983152983148983137983139983141983149983141983150983156
991266 983124983144983141 983149983151983149983141983150983156 983151983142 983145983150983141983154983156983145983137 983151983142 983156983144983141 983159983137983156983141983154983152983148983137983150983141 983137983154983141983137983137983138983151983157983156 CL
3
15051520 m x xT B L
I I
==sdotsdot=nabla
tons x I
751531500251 ==nablasdot=∆ ρ
433
33208
12
205
12
m x L B
I I
===
I983150983156983137983139983156 C983151983150983140983145983156983145983151983150
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 5267
I983150983156983137983139983156 C983151983150983140983145983156983145983151983150
991266 M983141983156983137983139983141983150983156983154983145983139 983154983137983140983145983157983155
991266 O983154 983145983156 983139983151983157983148983140 983138983141 983139983137983148983139983157983148983137983156983141983140 983140983145983154983141983139983156983148983161 983137983155
991266 H983141983145983143983144983156 983151983142 983156983144983141 983139983141983150983156983141983154 983151983142 983138983157983151983161983137983150983139983161
m I
BM
I
I 3891
150
33208==
nabla
=
m xT
B
LBT
L B BM
I I
I 3891
5112
5
12
12 223
====
mT
KB I
I 750
2
==
I983150983156983137983139983156 C983151983150983140983145983156983145983151983150
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 5367
991266 983124983144983141 983149983141983156983137983139983141983150983156983154983145983139 983144983141983145983143983144983156
991266 F983151983154 983155983149983137983148983148 983137983150983143983148983141983155 983151983142 983144983141983141983148 983156983144983141 983154983145983143983144983156983145983150983143 983149983151983149983141983150983156
m KG BM KBGM I I 63905013891750 =minus+=minus+=
sin22998sin693075153sin mt x xGM M I I
φ φ φ ==∆=
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 5467
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 5567
983116983119983123983124 983106983125983119983129983105983118983107983129 983117983109983124983112983119983108
Paralel Sinkage
Volume (DCEF)=Volume (W1ADW+BL1LC)
Damaged compartment is bounded on top
983116983119983123983124 983106983125983119983129983105983118983107983129 983117983109983124983112983119983108
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 5667
983116983119983123983124 983106983125983119983129983105983118983107983129 983117983109983124983112983119983108
bull It is assumed that displacement and location of vertical centre
of gravity does not change after damaged
983116983119983123983124 983106983125983119983129983105983118983107983129 983117983109983124983112983119983108
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 5767
983116983119983123983124 983106983125983119983129983105983118983107983129 983117983109983124983112983119983108
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 5867
The heel angle of damaged ship is determined by
where
d is the distance between the volume centre of damaged compartment
and the new longitudinal centre of floatation
wc=vc μ ρ
983116983119983123983124 983106983125983119983129983105983118983107983129 983117983109983124983112983119983108
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 5967
983116983119983123983124 983106983125983119983129983105983118983107983129 983117983109983124983112983119983108
983116983119983123983124 983106983125983119983129983105983118983107983129 983117983109983124983112983119983108
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 6067
Longitudinal Metacentre Height of a Damaged Ship
983116983119983123983124 983106983125983119983129983105983118983107983129 983117983109983124983112983119983108
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 6167
983110983151983154983159983137983154983140 983137983150983140 983137983142983156 983140983154983137983157983143983144983156983155 983137983142983156983141983154 983140983137983149983137983143983141983140
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 6267
983120983151983154983156 983105983142983156 983120983151983154983156 983110983151983154983141 983123983156983137983154983138983151983137983154983140 983105983142983156 983123983156983137983154983138983151983137983154983140 983110983151983154983159983137983154983140
I983150983145983156983145983137983148 D983154983137983157983143983144983156 983124 983124 983124 983124
983120983137983154983137983148983141983148 983123983145983150983147983137983143983141 +983152 +983152 +983152 +983120
H983141983141983148 983085983149983145 983085983149983145 +983149983155 +983149983155
983124983154983145983149 983085983156983147 +983156983138 983085983156983147 +983156983138
F983145983150983137983148 D983154983137983157983143983144983156 983124+983152983085983149983145983085983156983147 983124+983152983085983149983145+983156983138 983124+983152+983149983155983085983156983147 983124+983152+983149983155+983156983138
Table 1 Final Draughts for a starboard side damaged ship
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 6367
L983151983155983156 B983157983151983161983137983150983139983161 M983141983156983144983151983140
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 6467
L983151983155983156 B983157983151983161983137983150983139983161 M983141983156983144983151983140
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 6567
991266 A983142983156983141983154 983148983151983151983155983145983150983143 983156983144983141 983139983141983150983156983154983137983148 983139983151983149983152983137983154983156983149983141983150983156 983156983144983141
983159983137983156983141983154983152983148983137983150983141 983137983154983141983137 983145983155
991266 983124983151 983139983151983149983152983141983150983155983137983156983141 983142983151983154 983156983144983141 983148983151983155983155 983151983142 983138983157983151983161983137983150983139983161 983151983142 983156983144983141
983139983141983150983156983154983137983148 983139983151983149983152983137983154983156983149983141983150983156 983156983144983141 983140983154983137983142983156 983145983150983139983154983141983137983155983141983155 983156983151
2805)420()( m x Bl L A L
=minus=minus=
m A
T
L
I
L 875180
150==
nabla=
L983151983155983156 B983157983151983161983137983150983139983161 M983141983156983144983151983140
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 6667
991266 983124983144983141 983144983141983145983143983144983156 983151983142 983156983144983141 983139983141983150983156983141983154 983151983142 983138983157983151983161983137983150983139983161 983145983150983139983154983141983137983155983141983155 983156983151
991266 983124983144983141 983149983151983149983141983150983156 983151983142 983145983150983141983154983156983145983137 983151983142 983156983144983141 983159983137983156983141983154983152983148983137983150983141 983137983154983141983137
991266 983124983144983141 983149983141983156983137983139983141983150983156983154983145983139 983154983137983140983145983157983155
m
T
KB L
L 93802
8751
2 ===
433
6716612
)420(5
12
)(m
l L B I L
=minus
=minus
=
m I
BM
I
L
L 1111150
67166==
nabla
=
L983151983155983156 B983157983151983161983137983150983139983161 M983141983156983144983151983140
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 6767
991266 983124983144983141 983149983141983156983137983139983141983150983156983154983145983139 983144983141983145983143983144983156
991266 983122983145983143983144983156983145983150983143 983149983151983149983141983150983156 983142983151983154 983155983149983137983148983148 983144983141983141983148 983137983150983143983148983141983155
m KG BM KBGM L L L 54905111119380 =minus+=minus+=
mt xGM M L
sin34984sin549075153sin φ φ φ ==∆=
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 3367
A ship is 116 meter long and displaces 7842 ton in salt water (ρ1=1025 tm3)
when her mean draught is 64m Longitudinal Centre of Buoyancy (LCB) is
0615 m aft from amidships After one of her stern compartment is damaged
she floats trimmed to the aft Her sectional areas after damaged are given in the
following table
a) Determine the volume of water entering the vessel (vw) and the location of
volume centre of damaged compartment (xw)
b) Assume permability of compartment micro is 1 Determine damaged length
and Distance of the mid of damaged length of compartment to amidship
983109983160983137983149983152983148983141 2
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 3467
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 3567
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 3667
Predicted xw
is between section 2 and section 3
983123983141983139 N983151 983123983141983139 A983154983141983137 D983145983155983156 A9831499831459831559831449831459831522 10135 983085348
3 1208 983085232
983123983141983139 A983154983141983137 983137983156 98308524983149 983142983154983151983149 983137983149983145983140983155983144983145983152 = 11959831492
l1=v0Amean=204081195=17078 m
s=l14=427 m
983109983160983137983149983152983148983141 2983085983123983119983116983125983124983113983119983118
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 3767
983161983145 L983151983139 A983149983141983137983150 983123M M A983154983149
9831311983133 9831312983133 98313119831339832559831312983133 9831313983133 983131198313398325598313129831339832559831313983133
0 9830853254 1051 1 1051 2 21021 9830852827 1123 4 4492 1 4492
2 98308524 1195 2 239 0 0
3 9830851973 1219 4 4876 9830851 9830854876
4 9830851546 1233 1 1233 9830852 9830852466
sum983091983101 14042 sum983092983101 983085748
vm
= (s3) sum3= 199864479831493
xm
=s sum4sum3= 9830850227983149
v0-vm=20408-19986=422 m3
Error=422times10020408=207
983109983160983137983149983152983148983141 2983085983123983119983116983125983124983113983119983118
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 3867
Methods of Calculation
There two available method calculating the
final stage of the damaged vessel
bull Lost Buoyancy Method
bull Added Weight Method
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 3967
Comparision of Lost Buoyancy and Added
Weight Methods
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 4067
Consider a vessel that has been damaged such
that a portion of the bottom is now open to the
sea
The vesselrsquos draft will increase because an amount
of the buoyancy was lost
Added Weight Method
Added Weight Method
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 4167
Added Weight Method
In this method flood water is treated as a fixed weight (for example the
weight of water of volume ABEF) This added weight is balanced by the
additional buoyant force of the layer WL1WL
The added weight can be determined by either the volume ABEF or
waterline WL1 Therefore WL1 waterline is not known can be just guessed
For the predicted waterline added weight and additional buoyant force
caculation are done iteratively until both of them are equal This method is
known as Added weight method
Determination of Added Weight
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 4267
Determination of Added Weight
vc Volume of damaged compartment (DCEF)
ac The surface area (AB) of damaged compartment on the waterline
micro The volume permability of damaged compartment
microa The area permability of the surface of damaged compartment
∆ The initial displacement
∆1 The displacement at final stage
vw The volume of water entering the vessel (ABEH)
w The weight of water entering the vessel
p The value of parallel sinkage
If th t th l l i k i h f t l f
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 4367
If we assume that the paralel sinkage cause a minor change of water plane area of a
ship (Awp
asymp Awp1
) we can determine the paralel sinkage by equating the volume of
the layer WL1WL to the volume of ABEF
If the damaged compartment is bounded on top
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 4467
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 4567
Longitudinal Metacentre Radius at final stage
Free Surface Effect
Damaged compartment can be considered as a half filled tank
Free Contact Effect
Damaged compartment can be considered as a half filled tank
T M H i h
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 4667
Transverse Metacentre Height
The angle of heel
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 4767
L it di l M t t H i ht
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 4867
Longitudinal Metacentre Height
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 4967
E983160983137983149983152983148983141 A 983138983137983154983143983141
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 5067
E983160983137983149983152983148983141 A 983138983137983154983143983141
991266 L = 20 983149991266 B = 5 983149
991266 983124 = 15 983149
991266 KG = 15 983149
I983150983156983137983139983156 C983151983150983140983145983156983145983151983150
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 5167
I983150983156983137983139983156 C983151983150983140983145983156983145983151983150
991266 983124983144983141 983140983145983155983152983148983137983139983141983149983141983150983156 983158983151983148983157983149983141
991266 983124983144983141 983149983137983155983155 983140983145983155983152983148983137983139983141983149983141983150983156
991266 983124983144983141 983149983151983149983141983150983156 983151983142 983145983150983141983154983156983145983137 983151983142 983156983144983141 983159983137983156983141983154983152983148983137983150983141 983137983154983141983137983137983138983151983157983156 CL
3
15051520 m x xT B L
I I
==sdotsdot=nabla
tons x I
751531500251 ==nablasdot=∆ ρ
433
33208
12
205
12
m x L B
I I
===
I983150983156983137983139983156 C983151983150983140983145983156983145983151983150
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 5267
I983150983156983137983139983156 C983151983150983140983145983156983145983151983150
991266 M983141983156983137983139983141983150983156983154983145983139 983154983137983140983145983157983155
991266 O983154 983145983156 983139983151983157983148983140 983138983141 983139983137983148983139983157983148983137983156983141983140 983140983145983154983141983139983156983148983161 983137983155
991266 H983141983145983143983144983156 983151983142 983156983144983141 983139983141983150983156983141983154 983151983142 983138983157983151983161983137983150983139983161
m I
BM
I
I 3891
150
33208==
nabla
=
m xT
B
LBT
L B BM
I I
I 3891
5112
5
12
12 223
====
mT
KB I
I 750
2
==
I983150983156983137983139983156 C983151983150983140983145983156983145983151983150
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 5367
991266 983124983144983141 983149983141983156983137983139983141983150983156983154983145983139 983144983141983145983143983144983156
991266 F983151983154 983155983149983137983148983148 983137983150983143983148983141983155 983151983142 983144983141983141983148 983156983144983141 983154983145983143983144983156983145983150983143 983149983151983149983141983150983156
m KG BM KBGM I I 63905013891750 =minus+=minus+=
sin22998sin693075153sin mt x xGM M I I
φ φ φ ==∆=
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 5467
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 5567
983116983119983123983124 983106983125983119983129983105983118983107983129 983117983109983124983112983119983108
Paralel Sinkage
Volume (DCEF)=Volume (W1ADW+BL1LC)
Damaged compartment is bounded on top
983116983119983123983124 983106983125983119983129983105983118983107983129 983117983109983124983112983119983108
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 5667
983116983119983123983124 983106983125983119983129983105983118983107983129 983117983109983124983112983119983108
bull It is assumed that displacement and location of vertical centre
of gravity does not change after damaged
983116983119983123983124 983106983125983119983129983105983118983107983129 983117983109983124983112983119983108
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 5767
983116983119983123983124 983106983125983119983129983105983118983107983129 983117983109983124983112983119983108
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 5867
The heel angle of damaged ship is determined by
where
d is the distance between the volume centre of damaged compartment
and the new longitudinal centre of floatation
wc=vc μ ρ
983116983119983123983124 983106983125983119983129983105983118983107983129 983117983109983124983112983119983108
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 5967
983116983119983123983124 983106983125983119983129983105983118983107983129 983117983109983124983112983119983108
983116983119983123983124 983106983125983119983129983105983118983107983129 983117983109983124983112983119983108
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 6067
Longitudinal Metacentre Height of a Damaged Ship
983116983119983123983124 983106983125983119983129983105983118983107983129 983117983109983124983112983119983108
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 6167
983110983151983154983159983137983154983140 983137983150983140 983137983142983156 983140983154983137983157983143983144983156983155 983137983142983156983141983154 983140983137983149983137983143983141983140
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 6267
983120983151983154983156 983105983142983156 983120983151983154983156 983110983151983154983141 983123983156983137983154983138983151983137983154983140 983105983142983156 983123983156983137983154983138983151983137983154983140 983110983151983154983159983137983154983140
I983150983145983156983145983137983148 D983154983137983157983143983144983156 983124 983124 983124 983124
983120983137983154983137983148983141983148 983123983145983150983147983137983143983141 +983152 +983152 +983152 +983120
H983141983141983148 983085983149983145 983085983149983145 +983149983155 +983149983155
983124983154983145983149 983085983156983147 +983156983138 983085983156983147 +983156983138
F983145983150983137983148 D983154983137983157983143983144983156 983124+983152983085983149983145983085983156983147 983124+983152983085983149983145+983156983138 983124+983152+983149983155983085983156983147 983124+983152+983149983155+983156983138
Table 1 Final Draughts for a starboard side damaged ship
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 6367
L983151983155983156 B983157983151983161983137983150983139983161 M983141983156983144983151983140
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 6467
L983151983155983156 B983157983151983161983137983150983139983161 M983141983156983144983151983140
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 6567
991266 A983142983156983141983154 983148983151983151983155983145983150983143 983156983144983141 983139983141983150983156983154983137983148 983139983151983149983152983137983154983156983149983141983150983156 983156983144983141
983159983137983156983141983154983152983148983137983150983141 983137983154983141983137 983145983155
991266 983124983151 983139983151983149983152983141983150983155983137983156983141 983142983151983154 983156983144983141 983148983151983155983155 983151983142 983138983157983151983161983137983150983139983161 983151983142 983156983144983141
983139983141983150983156983154983137983148 983139983151983149983152983137983154983156983149983141983150983156 983156983144983141 983140983154983137983142983156 983145983150983139983154983141983137983155983141983155 983156983151
2805)420()( m x Bl L A L
=minus=minus=
m A
T
L
I
L 875180
150==
nabla=
L983151983155983156 B983157983151983161983137983150983139983161 M983141983156983144983151983140
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 6667
991266 983124983144983141 983144983141983145983143983144983156 983151983142 983156983144983141 983139983141983150983156983141983154 983151983142 983138983157983151983161983137983150983139983161 983145983150983139983154983141983137983155983141983155 983156983151
991266 983124983144983141 983149983151983149983141983150983156 983151983142 983145983150983141983154983156983145983137 983151983142 983156983144983141 983159983137983156983141983154983152983148983137983150983141 983137983154983141983137
991266 983124983144983141 983149983141983156983137983139983141983150983156983154983145983139 983154983137983140983145983157983155
m
T
KB L
L 93802
8751
2 ===
433
6716612
)420(5
12
)(m
l L B I L
=minus
=minus
=
m I
BM
I
L
L 1111150
67166==
nabla
=
L983151983155983156 B983157983151983161983137983150983139983161 M983141983156983144983151983140
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 6767
991266 983124983144983141 983149983141983156983137983139983141983150983156983154983145983139 983144983141983145983143983144983156
991266 983122983145983143983144983156983145983150983143 983149983151983149983141983150983156 983142983151983154 983155983149983137983148983148 983144983141983141983148 983137983150983143983148983141983155
m KG BM KBGM L L L 54905111119380 =minus+=minus+=
mt xGM M L
sin34984sin549075153sin φ φ φ ==∆=
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 3467
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 3567
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 3667
Predicted xw
is between section 2 and section 3
983123983141983139 N983151 983123983141983139 A983154983141983137 D983145983155983156 A9831499831459831559831449831459831522 10135 983085348
3 1208 983085232
983123983141983139 A983154983141983137 983137983156 98308524983149 983142983154983151983149 983137983149983145983140983155983144983145983152 = 11959831492
l1=v0Amean=204081195=17078 m
s=l14=427 m
983109983160983137983149983152983148983141 2983085983123983119983116983125983124983113983119983118
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 3767
983161983145 L983151983139 A983149983141983137983150 983123M M A983154983149
9831311983133 9831312983133 98313119831339832559831312983133 9831313983133 983131198313398325598313129831339832559831313983133
0 9830853254 1051 1 1051 2 21021 9830852827 1123 4 4492 1 4492
2 98308524 1195 2 239 0 0
3 9830851973 1219 4 4876 9830851 9830854876
4 9830851546 1233 1 1233 9830852 9830852466
sum983091983101 14042 sum983092983101 983085748
vm
= (s3) sum3= 199864479831493
xm
=s sum4sum3= 9830850227983149
v0-vm=20408-19986=422 m3
Error=422times10020408=207
983109983160983137983149983152983148983141 2983085983123983119983116983125983124983113983119983118
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 3867
Methods of Calculation
There two available method calculating the
final stage of the damaged vessel
bull Lost Buoyancy Method
bull Added Weight Method
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 3967
Comparision of Lost Buoyancy and Added
Weight Methods
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 4067
Consider a vessel that has been damaged such
that a portion of the bottom is now open to the
sea
The vesselrsquos draft will increase because an amount
of the buoyancy was lost
Added Weight Method
Added Weight Method
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 4167
Added Weight Method
In this method flood water is treated as a fixed weight (for example the
weight of water of volume ABEF) This added weight is balanced by the
additional buoyant force of the layer WL1WL
The added weight can be determined by either the volume ABEF or
waterline WL1 Therefore WL1 waterline is not known can be just guessed
For the predicted waterline added weight and additional buoyant force
caculation are done iteratively until both of them are equal This method is
known as Added weight method
Determination of Added Weight
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 4267
Determination of Added Weight
vc Volume of damaged compartment (DCEF)
ac The surface area (AB) of damaged compartment on the waterline
micro The volume permability of damaged compartment
microa The area permability of the surface of damaged compartment
∆ The initial displacement
∆1 The displacement at final stage
vw The volume of water entering the vessel (ABEH)
w The weight of water entering the vessel
p The value of parallel sinkage
If th t th l l i k i h f t l f
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 4367
If we assume that the paralel sinkage cause a minor change of water plane area of a
ship (Awp
asymp Awp1
) we can determine the paralel sinkage by equating the volume of
the layer WL1WL to the volume of ABEF
If the damaged compartment is bounded on top
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 4467
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 4567
Longitudinal Metacentre Radius at final stage
Free Surface Effect
Damaged compartment can be considered as a half filled tank
Free Contact Effect
Damaged compartment can be considered as a half filled tank
T M H i h
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 4667
Transverse Metacentre Height
The angle of heel
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 4767
L it di l M t t H i ht
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 4867
Longitudinal Metacentre Height
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 4967
E983160983137983149983152983148983141 A 983138983137983154983143983141
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 5067
E983160983137983149983152983148983141 A 983138983137983154983143983141
991266 L = 20 983149991266 B = 5 983149
991266 983124 = 15 983149
991266 KG = 15 983149
I983150983156983137983139983156 C983151983150983140983145983156983145983151983150
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 5167
I983150983156983137983139983156 C983151983150983140983145983156983145983151983150
991266 983124983144983141 983140983145983155983152983148983137983139983141983149983141983150983156 983158983151983148983157983149983141
991266 983124983144983141 983149983137983155983155 983140983145983155983152983148983137983139983141983149983141983150983156
991266 983124983144983141 983149983151983149983141983150983156 983151983142 983145983150983141983154983156983145983137 983151983142 983156983144983141 983159983137983156983141983154983152983148983137983150983141 983137983154983141983137983137983138983151983157983156 CL
3
15051520 m x xT B L
I I
==sdotsdot=nabla
tons x I
751531500251 ==nablasdot=∆ ρ
433
33208
12
205
12
m x L B
I I
===
I983150983156983137983139983156 C983151983150983140983145983156983145983151983150
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 5267
I983150983156983137983139983156 C983151983150983140983145983156983145983151983150
991266 M983141983156983137983139983141983150983156983154983145983139 983154983137983140983145983157983155
991266 O983154 983145983156 983139983151983157983148983140 983138983141 983139983137983148983139983157983148983137983156983141983140 983140983145983154983141983139983156983148983161 983137983155
991266 H983141983145983143983144983156 983151983142 983156983144983141 983139983141983150983156983141983154 983151983142 983138983157983151983161983137983150983139983161
m I
BM
I
I 3891
150
33208==
nabla
=
m xT
B
LBT
L B BM
I I
I 3891
5112
5
12
12 223
====
mT
KB I
I 750
2
==
I983150983156983137983139983156 C983151983150983140983145983156983145983151983150
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 5367
991266 983124983144983141 983149983141983156983137983139983141983150983156983154983145983139 983144983141983145983143983144983156
991266 F983151983154 983155983149983137983148983148 983137983150983143983148983141983155 983151983142 983144983141983141983148 983156983144983141 983154983145983143983144983156983145983150983143 983149983151983149983141983150983156
m KG BM KBGM I I 63905013891750 =minus+=minus+=
sin22998sin693075153sin mt x xGM M I I
φ φ φ ==∆=
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 5467
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 5567
983116983119983123983124 983106983125983119983129983105983118983107983129 983117983109983124983112983119983108
Paralel Sinkage
Volume (DCEF)=Volume (W1ADW+BL1LC)
Damaged compartment is bounded on top
983116983119983123983124 983106983125983119983129983105983118983107983129 983117983109983124983112983119983108
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 5667
983116983119983123983124 983106983125983119983129983105983118983107983129 983117983109983124983112983119983108
bull It is assumed that displacement and location of vertical centre
of gravity does not change after damaged
983116983119983123983124 983106983125983119983129983105983118983107983129 983117983109983124983112983119983108
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 5767
983116983119983123983124 983106983125983119983129983105983118983107983129 983117983109983124983112983119983108
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 5867
The heel angle of damaged ship is determined by
where
d is the distance between the volume centre of damaged compartment
and the new longitudinal centre of floatation
wc=vc μ ρ
983116983119983123983124 983106983125983119983129983105983118983107983129 983117983109983124983112983119983108
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 5967
983116983119983123983124 983106983125983119983129983105983118983107983129 983117983109983124983112983119983108
983116983119983123983124 983106983125983119983129983105983118983107983129 983117983109983124983112983119983108
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 6067
Longitudinal Metacentre Height of a Damaged Ship
983116983119983123983124 983106983125983119983129983105983118983107983129 983117983109983124983112983119983108
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 6167
983110983151983154983159983137983154983140 983137983150983140 983137983142983156 983140983154983137983157983143983144983156983155 983137983142983156983141983154 983140983137983149983137983143983141983140
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 6267
983120983151983154983156 983105983142983156 983120983151983154983156 983110983151983154983141 983123983156983137983154983138983151983137983154983140 983105983142983156 983123983156983137983154983138983151983137983154983140 983110983151983154983159983137983154983140
I983150983145983156983145983137983148 D983154983137983157983143983144983156 983124 983124 983124 983124
983120983137983154983137983148983141983148 983123983145983150983147983137983143983141 +983152 +983152 +983152 +983120
H983141983141983148 983085983149983145 983085983149983145 +983149983155 +983149983155
983124983154983145983149 983085983156983147 +983156983138 983085983156983147 +983156983138
F983145983150983137983148 D983154983137983157983143983144983156 983124+983152983085983149983145983085983156983147 983124+983152983085983149983145+983156983138 983124+983152+983149983155983085983156983147 983124+983152+983149983155+983156983138
Table 1 Final Draughts for a starboard side damaged ship
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 6367
L983151983155983156 B983157983151983161983137983150983139983161 M983141983156983144983151983140
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 6467
L983151983155983156 B983157983151983161983137983150983139983161 M983141983156983144983151983140
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 6567
991266 A983142983156983141983154 983148983151983151983155983145983150983143 983156983144983141 983139983141983150983156983154983137983148 983139983151983149983152983137983154983156983149983141983150983156 983156983144983141
983159983137983156983141983154983152983148983137983150983141 983137983154983141983137 983145983155
991266 983124983151 983139983151983149983152983141983150983155983137983156983141 983142983151983154 983156983144983141 983148983151983155983155 983151983142 983138983157983151983161983137983150983139983161 983151983142 983156983144983141
983139983141983150983156983154983137983148 983139983151983149983152983137983154983156983149983141983150983156 983156983144983141 983140983154983137983142983156 983145983150983139983154983141983137983155983141983155 983156983151
2805)420()( m x Bl L A L
=minus=minus=
m A
T
L
I
L 875180
150==
nabla=
L983151983155983156 B983157983151983161983137983150983139983161 M983141983156983144983151983140
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 6667
991266 983124983144983141 983144983141983145983143983144983156 983151983142 983156983144983141 983139983141983150983156983141983154 983151983142 983138983157983151983161983137983150983139983161 983145983150983139983154983141983137983155983141983155 983156983151
991266 983124983144983141 983149983151983149983141983150983156 983151983142 983145983150983141983154983156983145983137 983151983142 983156983144983141 983159983137983156983141983154983152983148983137983150983141 983137983154983141983137
991266 983124983144983141 983149983141983156983137983139983141983150983156983154983145983139 983154983137983140983145983157983155
m
T
KB L
L 93802
8751
2 ===
433
6716612
)420(5
12
)(m
l L B I L
=minus
=minus
=
m I
BM
I
L
L 1111150
67166==
nabla
=
L983151983155983156 B983157983151983161983137983150983139983161 M983141983156983144983151983140
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 6767
991266 983124983144983141 983149983141983156983137983139983141983150983156983154983145983139 983144983141983145983143983144983156
991266 983122983145983143983144983156983145983150983143 983149983151983149983141983150983156 983142983151983154 983155983149983137983148983148 983144983141983141983148 983137983150983143983148983141983155
m KG BM KBGM L L L 54905111119380 =minus+=minus+=
mt xGM M L
sin34984sin549075153sin φ φ φ ==∆=
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 3567
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 3667
Predicted xw
is between section 2 and section 3
983123983141983139 N983151 983123983141983139 A983154983141983137 D983145983155983156 A9831499831459831559831449831459831522 10135 983085348
3 1208 983085232
983123983141983139 A983154983141983137 983137983156 98308524983149 983142983154983151983149 983137983149983145983140983155983144983145983152 = 11959831492
l1=v0Amean=204081195=17078 m
s=l14=427 m
983109983160983137983149983152983148983141 2983085983123983119983116983125983124983113983119983118
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 3767
983161983145 L983151983139 A983149983141983137983150 983123M M A983154983149
9831311983133 9831312983133 98313119831339832559831312983133 9831313983133 983131198313398325598313129831339832559831313983133
0 9830853254 1051 1 1051 2 21021 9830852827 1123 4 4492 1 4492
2 98308524 1195 2 239 0 0
3 9830851973 1219 4 4876 9830851 9830854876
4 9830851546 1233 1 1233 9830852 9830852466
sum983091983101 14042 sum983092983101 983085748
vm
= (s3) sum3= 199864479831493
xm
=s sum4sum3= 9830850227983149
v0-vm=20408-19986=422 m3
Error=422times10020408=207
983109983160983137983149983152983148983141 2983085983123983119983116983125983124983113983119983118
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 3867
Methods of Calculation
There two available method calculating the
final stage of the damaged vessel
bull Lost Buoyancy Method
bull Added Weight Method
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 3967
Comparision of Lost Buoyancy and Added
Weight Methods
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 4067
Consider a vessel that has been damaged such
that a portion of the bottom is now open to the
sea
The vesselrsquos draft will increase because an amount
of the buoyancy was lost
Added Weight Method
Added Weight Method
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 4167
Added Weight Method
In this method flood water is treated as a fixed weight (for example the
weight of water of volume ABEF) This added weight is balanced by the
additional buoyant force of the layer WL1WL
The added weight can be determined by either the volume ABEF or
waterline WL1 Therefore WL1 waterline is not known can be just guessed
For the predicted waterline added weight and additional buoyant force
caculation are done iteratively until both of them are equal This method is
known as Added weight method
Determination of Added Weight
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 4267
Determination of Added Weight
vc Volume of damaged compartment (DCEF)
ac The surface area (AB) of damaged compartment on the waterline
micro The volume permability of damaged compartment
microa The area permability of the surface of damaged compartment
∆ The initial displacement
∆1 The displacement at final stage
vw The volume of water entering the vessel (ABEH)
w The weight of water entering the vessel
p The value of parallel sinkage
If th t th l l i k i h f t l f
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 4367
If we assume that the paralel sinkage cause a minor change of water plane area of a
ship (Awp
asymp Awp1
) we can determine the paralel sinkage by equating the volume of
the layer WL1WL to the volume of ABEF
If the damaged compartment is bounded on top
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 4467
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 4567
Longitudinal Metacentre Radius at final stage
Free Surface Effect
Damaged compartment can be considered as a half filled tank
Free Contact Effect
Damaged compartment can be considered as a half filled tank
T M H i h
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 4667
Transverse Metacentre Height
The angle of heel
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 4767
L it di l M t t H i ht
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 4867
Longitudinal Metacentre Height
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 4967
E983160983137983149983152983148983141 A 983138983137983154983143983141
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 5067
E983160983137983149983152983148983141 A 983138983137983154983143983141
991266 L = 20 983149991266 B = 5 983149
991266 983124 = 15 983149
991266 KG = 15 983149
I983150983156983137983139983156 C983151983150983140983145983156983145983151983150
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 5167
I983150983156983137983139983156 C983151983150983140983145983156983145983151983150
991266 983124983144983141 983140983145983155983152983148983137983139983141983149983141983150983156 983158983151983148983157983149983141
991266 983124983144983141 983149983137983155983155 983140983145983155983152983148983137983139983141983149983141983150983156
991266 983124983144983141 983149983151983149983141983150983156 983151983142 983145983150983141983154983156983145983137 983151983142 983156983144983141 983159983137983156983141983154983152983148983137983150983141 983137983154983141983137983137983138983151983157983156 CL
3
15051520 m x xT B L
I I
==sdotsdot=nabla
tons x I
751531500251 ==nablasdot=∆ ρ
433
33208
12
205
12
m x L B
I I
===
I983150983156983137983139983156 C983151983150983140983145983156983145983151983150
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 5267
I983150983156983137983139983156 C983151983150983140983145983156983145983151983150
991266 M983141983156983137983139983141983150983156983154983145983139 983154983137983140983145983157983155
991266 O983154 983145983156 983139983151983157983148983140 983138983141 983139983137983148983139983157983148983137983156983141983140 983140983145983154983141983139983156983148983161 983137983155
991266 H983141983145983143983144983156 983151983142 983156983144983141 983139983141983150983156983141983154 983151983142 983138983157983151983161983137983150983139983161
m I
BM
I
I 3891
150
33208==
nabla
=
m xT
B
LBT
L B BM
I I
I 3891
5112
5
12
12 223
====
mT
KB I
I 750
2
==
I983150983156983137983139983156 C983151983150983140983145983156983145983151983150
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 5367
991266 983124983144983141 983149983141983156983137983139983141983150983156983154983145983139 983144983141983145983143983144983156
991266 F983151983154 983155983149983137983148983148 983137983150983143983148983141983155 983151983142 983144983141983141983148 983156983144983141 983154983145983143983144983156983145983150983143 983149983151983149983141983150983156
m KG BM KBGM I I 63905013891750 =minus+=minus+=
sin22998sin693075153sin mt x xGM M I I
φ φ φ ==∆=
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 5467
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 5567
983116983119983123983124 983106983125983119983129983105983118983107983129 983117983109983124983112983119983108
Paralel Sinkage
Volume (DCEF)=Volume (W1ADW+BL1LC)
Damaged compartment is bounded on top
983116983119983123983124 983106983125983119983129983105983118983107983129 983117983109983124983112983119983108
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 5667
983116983119983123983124 983106983125983119983129983105983118983107983129 983117983109983124983112983119983108
bull It is assumed that displacement and location of vertical centre
of gravity does not change after damaged
983116983119983123983124 983106983125983119983129983105983118983107983129 983117983109983124983112983119983108
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 5767
983116983119983123983124 983106983125983119983129983105983118983107983129 983117983109983124983112983119983108
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 5867
The heel angle of damaged ship is determined by
where
d is the distance between the volume centre of damaged compartment
and the new longitudinal centre of floatation
wc=vc μ ρ
983116983119983123983124 983106983125983119983129983105983118983107983129 983117983109983124983112983119983108
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 5967
983116983119983123983124 983106983125983119983129983105983118983107983129 983117983109983124983112983119983108
983116983119983123983124 983106983125983119983129983105983118983107983129 983117983109983124983112983119983108
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 6067
Longitudinal Metacentre Height of a Damaged Ship
983116983119983123983124 983106983125983119983129983105983118983107983129 983117983109983124983112983119983108
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 6167
983110983151983154983159983137983154983140 983137983150983140 983137983142983156 983140983154983137983157983143983144983156983155 983137983142983156983141983154 983140983137983149983137983143983141983140
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 6267
983120983151983154983156 983105983142983156 983120983151983154983156 983110983151983154983141 983123983156983137983154983138983151983137983154983140 983105983142983156 983123983156983137983154983138983151983137983154983140 983110983151983154983159983137983154983140
I983150983145983156983145983137983148 D983154983137983157983143983144983156 983124 983124 983124 983124
983120983137983154983137983148983141983148 983123983145983150983147983137983143983141 +983152 +983152 +983152 +983120
H983141983141983148 983085983149983145 983085983149983145 +983149983155 +983149983155
983124983154983145983149 983085983156983147 +983156983138 983085983156983147 +983156983138
F983145983150983137983148 D983154983137983157983143983144983156 983124+983152983085983149983145983085983156983147 983124+983152983085983149983145+983156983138 983124+983152+983149983155983085983156983147 983124+983152+983149983155+983156983138
Table 1 Final Draughts for a starboard side damaged ship
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 6367
L983151983155983156 B983157983151983161983137983150983139983161 M983141983156983144983151983140
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 6467
L983151983155983156 B983157983151983161983137983150983139983161 M983141983156983144983151983140
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 6567
991266 A983142983156983141983154 983148983151983151983155983145983150983143 983156983144983141 983139983141983150983156983154983137983148 983139983151983149983152983137983154983156983149983141983150983156 983156983144983141
983159983137983156983141983154983152983148983137983150983141 983137983154983141983137 983145983155
991266 983124983151 983139983151983149983152983141983150983155983137983156983141 983142983151983154 983156983144983141 983148983151983155983155 983151983142 983138983157983151983161983137983150983139983161 983151983142 983156983144983141
983139983141983150983156983154983137983148 983139983151983149983152983137983154983156983149983141983150983156 983156983144983141 983140983154983137983142983156 983145983150983139983154983141983137983155983141983155 983156983151
2805)420()( m x Bl L A L
=minus=minus=
m A
T
L
I
L 875180
150==
nabla=
L983151983155983156 B983157983151983161983137983150983139983161 M983141983156983144983151983140
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 6667
991266 983124983144983141 983144983141983145983143983144983156 983151983142 983156983144983141 983139983141983150983156983141983154 983151983142 983138983157983151983161983137983150983139983161 983145983150983139983154983141983137983155983141983155 983156983151
991266 983124983144983141 983149983151983149983141983150983156 983151983142 983145983150983141983154983156983145983137 983151983142 983156983144983141 983159983137983156983141983154983152983148983137983150983141 983137983154983141983137
991266 983124983144983141 983149983141983156983137983139983141983150983156983154983145983139 983154983137983140983145983157983155
m
T
KB L
L 93802
8751
2 ===
433
6716612
)420(5
12
)(m
l L B I L
=minus
=minus
=
m I
BM
I
L
L 1111150
67166==
nabla
=
L983151983155983156 B983157983151983161983137983150983139983161 M983141983156983144983151983140
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 6767
991266 983124983144983141 983149983141983156983137983139983141983150983156983154983145983139 983144983141983145983143983144983156
991266 983122983145983143983144983156983145983150983143 983149983151983149983141983150983156 983142983151983154 983155983149983137983148983148 983144983141983141983148 983137983150983143983148983141983155
m KG BM KBGM L L L 54905111119380 =minus+=minus+=
mt xGM M L
sin34984sin549075153sin φ φ φ ==∆=
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 3667
Predicted xw
is between section 2 and section 3
983123983141983139 N983151 983123983141983139 A983154983141983137 D983145983155983156 A9831499831459831559831449831459831522 10135 983085348
3 1208 983085232
983123983141983139 A983154983141983137 983137983156 98308524983149 983142983154983151983149 983137983149983145983140983155983144983145983152 = 11959831492
l1=v0Amean=204081195=17078 m
s=l14=427 m
983109983160983137983149983152983148983141 2983085983123983119983116983125983124983113983119983118
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 3767
983161983145 L983151983139 A983149983141983137983150 983123M M A983154983149
9831311983133 9831312983133 98313119831339832559831312983133 9831313983133 983131198313398325598313129831339832559831313983133
0 9830853254 1051 1 1051 2 21021 9830852827 1123 4 4492 1 4492
2 98308524 1195 2 239 0 0
3 9830851973 1219 4 4876 9830851 9830854876
4 9830851546 1233 1 1233 9830852 9830852466
sum983091983101 14042 sum983092983101 983085748
vm
= (s3) sum3= 199864479831493
xm
=s sum4sum3= 9830850227983149
v0-vm=20408-19986=422 m3
Error=422times10020408=207
983109983160983137983149983152983148983141 2983085983123983119983116983125983124983113983119983118
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 3867
Methods of Calculation
There two available method calculating the
final stage of the damaged vessel
bull Lost Buoyancy Method
bull Added Weight Method
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 3967
Comparision of Lost Buoyancy and Added
Weight Methods
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 4067
Consider a vessel that has been damaged such
that a portion of the bottom is now open to the
sea
The vesselrsquos draft will increase because an amount
of the buoyancy was lost
Added Weight Method
Added Weight Method
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 4167
Added Weight Method
In this method flood water is treated as a fixed weight (for example the
weight of water of volume ABEF) This added weight is balanced by the
additional buoyant force of the layer WL1WL
The added weight can be determined by either the volume ABEF or
waterline WL1 Therefore WL1 waterline is not known can be just guessed
For the predicted waterline added weight and additional buoyant force
caculation are done iteratively until both of them are equal This method is
known as Added weight method
Determination of Added Weight
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 4267
Determination of Added Weight
vc Volume of damaged compartment (DCEF)
ac The surface area (AB) of damaged compartment on the waterline
micro The volume permability of damaged compartment
microa The area permability of the surface of damaged compartment
∆ The initial displacement
∆1 The displacement at final stage
vw The volume of water entering the vessel (ABEH)
w The weight of water entering the vessel
p The value of parallel sinkage
If th t th l l i k i h f t l f
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 4367
If we assume that the paralel sinkage cause a minor change of water plane area of a
ship (Awp
asymp Awp1
) we can determine the paralel sinkage by equating the volume of
the layer WL1WL to the volume of ABEF
If the damaged compartment is bounded on top
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 4467
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 4567
Longitudinal Metacentre Radius at final stage
Free Surface Effect
Damaged compartment can be considered as a half filled tank
Free Contact Effect
Damaged compartment can be considered as a half filled tank
T M H i h
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 4667
Transverse Metacentre Height
The angle of heel
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 4767
L it di l M t t H i ht
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 4867
Longitudinal Metacentre Height
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 4967
E983160983137983149983152983148983141 A 983138983137983154983143983141
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 5067
E983160983137983149983152983148983141 A 983138983137983154983143983141
991266 L = 20 983149991266 B = 5 983149
991266 983124 = 15 983149
991266 KG = 15 983149
I983150983156983137983139983156 C983151983150983140983145983156983145983151983150
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 5167
I983150983156983137983139983156 C983151983150983140983145983156983145983151983150
991266 983124983144983141 983140983145983155983152983148983137983139983141983149983141983150983156 983158983151983148983157983149983141
991266 983124983144983141 983149983137983155983155 983140983145983155983152983148983137983139983141983149983141983150983156
991266 983124983144983141 983149983151983149983141983150983156 983151983142 983145983150983141983154983156983145983137 983151983142 983156983144983141 983159983137983156983141983154983152983148983137983150983141 983137983154983141983137983137983138983151983157983156 CL
3
15051520 m x xT B L
I I
==sdotsdot=nabla
tons x I
751531500251 ==nablasdot=∆ ρ
433
33208
12
205
12
m x L B
I I
===
I983150983156983137983139983156 C983151983150983140983145983156983145983151983150
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 5267
I983150983156983137983139983156 C983151983150983140983145983156983145983151983150
991266 M983141983156983137983139983141983150983156983154983145983139 983154983137983140983145983157983155
991266 O983154 983145983156 983139983151983157983148983140 983138983141 983139983137983148983139983157983148983137983156983141983140 983140983145983154983141983139983156983148983161 983137983155
991266 H983141983145983143983144983156 983151983142 983156983144983141 983139983141983150983156983141983154 983151983142 983138983157983151983161983137983150983139983161
m I
BM
I
I 3891
150
33208==
nabla
=
m xT
B
LBT
L B BM
I I
I 3891
5112
5
12
12 223
====
mT
KB I
I 750
2
==
I983150983156983137983139983156 C983151983150983140983145983156983145983151983150
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 5367
991266 983124983144983141 983149983141983156983137983139983141983150983156983154983145983139 983144983141983145983143983144983156
991266 F983151983154 983155983149983137983148983148 983137983150983143983148983141983155 983151983142 983144983141983141983148 983156983144983141 983154983145983143983144983156983145983150983143 983149983151983149983141983150983156
m KG BM KBGM I I 63905013891750 =minus+=minus+=
sin22998sin693075153sin mt x xGM M I I
φ φ φ ==∆=
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 5467
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 5567
983116983119983123983124 983106983125983119983129983105983118983107983129 983117983109983124983112983119983108
Paralel Sinkage
Volume (DCEF)=Volume (W1ADW+BL1LC)
Damaged compartment is bounded on top
983116983119983123983124 983106983125983119983129983105983118983107983129 983117983109983124983112983119983108
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 5667
983116983119983123983124 983106983125983119983129983105983118983107983129 983117983109983124983112983119983108
bull It is assumed that displacement and location of vertical centre
of gravity does not change after damaged
983116983119983123983124 983106983125983119983129983105983118983107983129 983117983109983124983112983119983108
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 5767
983116983119983123983124 983106983125983119983129983105983118983107983129 983117983109983124983112983119983108
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 5867
The heel angle of damaged ship is determined by
where
d is the distance between the volume centre of damaged compartment
and the new longitudinal centre of floatation
wc=vc μ ρ
983116983119983123983124 983106983125983119983129983105983118983107983129 983117983109983124983112983119983108
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 5967
983116983119983123983124 983106983125983119983129983105983118983107983129 983117983109983124983112983119983108
983116983119983123983124 983106983125983119983129983105983118983107983129 983117983109983124983112983119983108
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 6067
Longitudinal Metacentre Height of a Damaged Ship
983116983119983123983124 983106983125983119983129983105983118983107983129 983117983109983124983112983119983108
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 6167
983110983151983154983159983137983154983140 983137983150983140 983137983142983156 983140983154983137983157983143983144983156983155 983137983142983156983141983154 983140983137983149983137983143983141983140
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 6267
983120983151983154983156 983105983142983156 983120983151983154983156 983110983151983154983141 983123983156983137983154983138983151983137983154983140 983105983142983156 983123983156983137983154983138983151983137983154983140 983110983151983154983159983137983154983140
I983150983145983156983145983137983148 D983154983137983157983143983144983156 983124 983124 983124 983124
983120983137983154983137983148983141983148 983123983145983150983147983137983143983141 +983152 +983152 +983152 +983120
H983141983141983148 983085983149983145 983085983149983145 +983149983155 +983149983155
983124983154983145983149 983085983156983147 +983156983138 983085983156983147 +983156983138
F983145983150983137983148 D983154983137983157983143983144983156 983124+983152983085983149983145983085983156983147 983124+983152983085983149983145+983156983138 983124+983152+983149983155983085983156983147 983124+983152+983149983155+983156983138
Table 1 Final Draughts for a starboard side damaged ship
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 6367
L983151983155983156 B983157983151983161983137983150983139983161 M983141983156983144983151983140
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 6467
L983151983155983156 B983157983151983161983137983150983139983161 M983141983156983144983151983140
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 6567
991266 A983142983156983141983154 983148983151983151983155983145983150983143 983156983144983141 983139983141983150983156983154983137983148 983139983151983149983152983137983154983156983149983141983150983156 983156983144983141
983159983137983156983141983154983152983148983137983150983141 983137983154983141983137 983145983155
991266 983124983151 983139983151983149983152983141983150983155983137983156983141 983142983151983154 983156983144983141 983148983151983155983155 983151983142 983138983157983151983161983137983150983139983161 983151983142 983156983144983141
983139983141983150983156983154983137983148 983139983151983149983152983137983154983156983149983141983150983156 983156983144983141 983140983154983137983142983156 983145983150983139983154983141983137983155983141983155 983156983151
2805)420()( m x Bl L A L
=minus=minus=
m A
T
L
I
L 875180
150==
nabla=
L983151983155983156 B983157983151983161983137983150983139983161 M983141983156983144983151983140
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 6667
991266 983124983144983141 983144983141983145983143983144983156 983151983142 983156983144983141 983139983141983150983156983141983154 983151983142 983138983157983151983161983137983150983139983161 983145983150983139983154983141983137983155983141983155 983156983151
991266 983124983144983141 983149983151983149983141983150983156 983151983142 983145983150983141983154983156983145983137 983151983142 983156983144983141 983159983137983156983141983154983152983148983137983150983141 983137983154983141983137
991266 983124983144983141 983149983141983156983137983139983141983150983156983154983145983139 983154983137983140983145983157983155
m
T
KB L
L 93802
8751
2 ===
433
6716612
)420(5
12
)(m
l L B I L
=minus
=minus
=
m I
BM
I
L
L 1111150
67166==
nabla
=
L983151983155983156 B983157983151983161983137983150983139983161 M983141983156983144983151983140
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 6767
991266 983124983144983141 983149983141983156983137983139983141983150983156983154983145983139 983144983141983145983143983144983156
991266 983122983145983143983144983156983145983150983143 983149983151983149983141983150983156 983142983151983154 983155983149983137983148983148 983144983141983141983148 983137983150983143983148983141983155
m KG BM KBGM L L L 54905111119380 =minus+=minus+=
mt xGM M L
sin34984sin549075153sin φ φ φ ==∆=
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 3767
983161983145 L983151983139 A983149983141983137983150 983123M M A983154983149
9831311983133 9831312983133 98313119831339832559831312983133 9831313983133 983131198313398325598313129831339832559831313983133
0 9830853254 1051 1 1051 2 21021 9830852827 1123 4 4492 1 4492
2 98308524 1195 2 239 0 0
3 9830851973 1219 4 4876 9830851 9830854876
4 9830851546 1233 1 1233 9830852 9830852466
sum983091983101 14042 sum983092983101 983085748
vm
= (s3) sum3= 199864479831493
xm
=s sum4sum3= 9830850227983149
v0-vm=20408-19986=422 m3
Error=422times10020408=207
983109983160983137983149983152983148983141 2983085983123983119983116983125983124983113983119983118
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 3867
Methods of Calculation
There two available method calculating the
final stage of the damaged vessel
bull Lost Buoyancy Method
bull Added Weight Method
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 3967
Comparision of Lost Buoyancy and Added
Weight Methods
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 4067
Consider a vessel that has been damaged such
that a portion of the bottom is now open to the
sea
The vesselrsquos draft will increase because an amount
of the buoyancy was lost
Added Weight Method
Added Weight Method
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 4167
Added Weight Method
In this method flood water is treated as a fixed weight (for example the
weight of water of volume ABEF) This added weight is balanced by the
additional buoyant force of the layer WL1WL
The added weight can be determined by either the volume ABEF or
waterline WL1 Therefore WL1 waterline is not known can be just guessed
For the predicted waterline added weight and additional buoyant force
caculation are done iteratively until both of them are equal This method is
known as Added weight method
Determination of Added Weight
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 4267
Determination of Added Weight
vc Volume of damaged compartment (DCEF)
ac The surface area (AB) of damaged compartment on the waterline
micro The volume permability of damaged compartment
microa The area permability of the surface of damaged compartment
∆ The initial displacement
∆1 The displacement at final stage
vw The volume of water entering the vessel (ABEH)
w The weight of water entering the vessel
p The value of parallel sinkage
If th t th l l i k i h f t l f
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 4367
If we assume that the paralel sinkage cause a minor change of water plane area of a
ship (Awp
asymp Awp1
) we can determine the paralel sinkage by equating the volume of
the layer WL1WL to the volume of ABEF
If the damaged compartment is bounded on top
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 4467
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 4567
Longitudinal Metacentre Radius at final stage
Free Surface Effect
Damaged compartment can be considered as a half filled tank
Free Contact Effect
Damaged compartment can be considered as a half filled tank
T M H i h
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 4667
Transverse Metacentre Height
The angle of heel
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 4767
L it di l M t t H i ht
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 4867
Longitudinal Metacentre Height
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 4967
E983160983137983149983152983148983141 A 983138983137983154983143983141
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 5067
E983160983137983149983152983148983141 A 983138983137983154983143983141
991266 L = 20 983149991266 B = 5 983149
991266 983124 = 15 983149
991266 KG = 15 983149
I983150983156983137983139983156 C983151983150983140983145983156983145983151983150
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 5167
I983150983156983137983139983156 C983151983150983140983145983156983145983151983150
991266 983124983144983141 983140983145983155983152983148983137983139983141983149983141983150983156 983158983151983148983157983149983141
991266 983124983144983141 983149983137983155983155 983140983145983155983152983148983137983139983141983149983141983150983156
991266 983124983144983141 983149983151983149983141983150983156 983151983142 983145983150983141983154983156983145983137 983151983142 983156983144983141 983159983137983156983141983154983152983148983137983150983141 983137983154983141983137983137983138983151983157983156 CL
3
15051520 m x xT B L
I I
==sdotsdot=nabla
tons x I
751531500251 ==nablasdot=∆ ρ
433
33208
12
205
12
m x L B
I I
===
I983150983156983137983139983156 C983151983150983140983145983156983145983151983150
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 5267
I983150983156983137983139983156 C983151983150983140983145983156983145983151983150
991266 M983141983156983137983139983141983150983156983154983145983139 983154983137983140983145983157983155
991266 O983154 983145983156 983139983151983157983148983140 983138983141 983139983137983148983139983157983148983137983156983141983140 983140983145983154983141983139983156983148983161 983137983155
991266 H983141983145983143983144983156 983151983142 983156983144983141 983139983141983150983156983141983154 983151983142 983138983157983151983161983137983150983139983161
m I
BM
I
I 3891
150
33208==
nabla
=
m xT
B
LBT
L B BM
I I
I 3891
5112
5
12
12 223
====
mT
KB I
I 750
2
==
I983150983156983137983139983156 C983151983150983140983145983156983145983151983150
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 5367
991266 983124983144983141 983149983141983156983137983139983141983150983156983154983145983139 983144983141983145983143983144983156
991266 F983151983154 983155983149983137983148983148 983137983150983143983148983141983155 983151983142 983144983141983141983148 983156983144983141 983154983145983143983144983156983145983150983143 983149983151983149983141983150983156
m KG BM KBGM I I 63905013891750 =minus+=minus+=
sin22998sin693075153sin mt x xGM M I I
φ φ φ ==∆=
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 5467
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 5567
983116983119983123983124 983106983125983119983129983105983118983107983129 983117983109983124983112983119983108
Paralel Sinkage
Volume (DCEF)=Volume (W1ADW+BL1LC)
Damaged compartment is bounded on top
983116983119983123983124 983106983125983119983129983105983118983107983129 983117983109983124983112983119983108
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 5667
983116983119983123983124 983106983125983119983129983105983118983107983129 983117983109983124983112983119983108
bull It is assumed that displacement and location of vertical centre
of gravity does not change after damaged
983116983119983123983124 983106983125983119983129983105983118983107983129 983117983109983124983112983119983108
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 5767
983116983119983123983124 983106983125983119983129983105983118983107983129 983117983109983124983112983119983108
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 5867
The heel angle of damaged ship is determined by
where
d is the distance between the volume centre of damaged compartment
and the new longitudinal centre of floatation
wc=vc μ ρ
983116983119983123983124 983106983125983119983129983105983118983107983129 983117983109983124983112983119983108
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 5967
983116983119983123983124 983106983125983119983129983105983118983107983129 983117983109983124983112983119983108
983116983119983123983124 983106983125983119983129983105983118983107983129 983117983109983124983112983119983108
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 6067
Longitudinal Metacentre Height of a Damaged Ship
983116983119983123983124 983106983125983119983129983105983118983107983129 983117983109983124983112983119983108
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 6167
983110983151983154983159983137983154983140 983137983150983140 983137983142983156 983140983154983137983157983143983144983156983155 983137983142983156983141983154 983140983137983149983137983143983141983140
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 6267
983120983151983154983156 983105983142983156 983120983151983154983156 983110983151983154983141 983123983156983137983154983138983151983137983154983140 983105983142983156 983123983156983137983154983138983151983137983154983140 983110983151983154983159983137983154983140
I983150983145983156983145983137983148 D983154983137983157983143983144983156 983124 983124 983124 983124
983120983137983154983137983148983141983148 983123983145983150983147983137983143983141 +983152 +983152 +983152 +983120
H983141983141983148 983085983149983145 983085983149983145 +983149983155 +983149983155
983124983154983145983149 983085983156983147 +983156983138 983085983156983147 +983156983138
F983145983150983137983148 D983154983137983157983143983144983156 983124+983152983085983149983145983085983156983147 983124+983152983085983149983145+983156983138 983124+983152+983149983155983085983156983147 983124+983152+983149983155+983156983138
Table 1 Final Draughts for a starboard side damaged ship
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 6367
L983151983155983156 B983157983151983161983137983150983139983161 M983141983156983144983151983140
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 6467
L983151983155983156 B983157983151983161983137983150983139983161 M983141983156983144983151983140
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 6567
991266 A983142983156983141983154 983148983151983151983155983145983150983143 983156983144983141 983139983141983150983156983154983137983148 983139983151983149983152983137983154983156983149983141983150983156 983156983144983141
983159983137983156983141983154983152983148983137983150983141 983137983154983141983137 983145983155
991266 983124983151 983139983151983149983152983141983150983155983137983156983141 983142983151983154 983156983144983141 983148983151983155983155 983151983142 983138983157983151983161983137983150983139983161 983151983142 983156983144983141
983139983141983150983156983154983137983148 983139983151983149983152983137983154983156983149983141983150983156 983156983144983141 983140983154983137983142983156 983145983150983139983154983141983137983155983141983155 983156983151
2805)420()( m x Bl L A L
=minus=minus=
m A
T
L
I
L 875180
150==
nabla=
L983151983155983156 B983157983151983161983137983150983139983161 M983141983156983144983151983140
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 6667
991266 983124983144983141 983144983141983145983143983144983156 983151983142 983156983144983141 983139983141983150983156983141983154 983151983142 983138983157983151983161983137983150983139983161 983145983150983139983154983141983137983155983141983155 983156983151
991266 983124983144983141 983149983151983149983141983150983156 983151983142 983145983150983141983154983156983145983137 983151983142 983156983144983141 983159983137983156983141983154983152983148983137983150983141 983137983154983141983137
991266 983124983144983141 983149983141983156983137983139983141983150983156983154983145983139 983154983137983140983145983157983155
m
T
KB L
L 93802
8751
2 ===
433
6716612
)420(5
12
)(m
l L B I L
=minus
=minus
=
m I
BM
I
L
L 1111150
67166==
nabla
=
L983151983155983156 B983157983151983161983137983150983139983161 M983141983156983144983151983140
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 6767
991266 983124983144983141 983149983141983156983137983139983141983150983156983154983145983139 983144983141983145983143983144983156
991266 983122983145983143983144983156983145983150983143 983149983151983149983141983150983156 983142983151983154 983155983149983137983148983148 983144983141983141983148 983137983150983143983148983141983155
m KG BM KBGM L L L 54905111119380 =minus+=minus+=
mt xGM M L
sin34984sin549075153sin φ φ φ ==∆=
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 3867
Methods of Calculation
There two available method calculating the
final stage of the damaged vessel
bull Lost Buoyancy Method
bull Added Weight Method
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 3967
Comparision of Lost Buoyancy and Added
Weight Methods
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 4067
Consider a vessel that has been damaged such
that a portion of the bottom is now open to the
sea
The vesselrsquos draft will increase because an amount
of the buoyancy was lost
Added Weight Method
Added Weight Method
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 4167
Added Weight Method
In this method flood water is treated as a fixed weight (for example the
weight of water of volume ABEF) This added weight is balanced by the
additional buoyant force of the layer WL1WL
The added weight can be determined by either the volume ABEF or
waterline WL1 Therefore WL1 waterline is not known can be just guessed
For the predicted waterline added weight and additional buoyant force
caculation are done iteratively until both of them are equal This method is
known as Added weight method
Determination of Added Weight
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 4267
Determination of Added Weight
vc Volume of damaged compartment (DCEF)
ac The surface area (AB) of damaged compartment on the waterline
micro The volume permability of damaged compartment
microa The area permability of the surface of damaged compartment
∆ The initial displacement
∆1 The displacement at final stage
vw The volume of water entering the vessel (ABEH)
w The weight of water entering the vessel
p The value of parallel sinkage
If th t th l l i k i h f t l f
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 4367
If we assume that the paralel sinkage cause a minor change of water plane area of a
ship (Awp
asymp Awp1
) we can determine the paralel sinkage by equating the volume of
the layer WL1WL to the volume of ABEF
If the damaged compartment is bounded on top
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 4467
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 4567
Longitudinal Metacentre Radius at final stage
Free Surface Effect
Damaged compartment can be considered as a half filled tank
Free Contact Effect
Damaged compartment can be considered as a half filled tank
T M H i h
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 4667
Transverse Metacentre Height
The angle of heel
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 4767
L it di l M t t H i ht
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 4867
Longitudinal Metacentre Height
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 4967
E983160983137983149983152983148983141 A 983138983137983154983143983141
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 5067
E983160983137983149983152983148983141 A 983138983137983154983143983141
991266 L = 20 983149991266 B = 5 983149
991266 983124 = 15 983149
991266 KG = 15 983149
I983150983156983137983139983156 C983151983150983140983145983156983145983151983150
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 5167
I983150983156983137983139983156 C983151983150983140983145983156983145983151983150
991266 983124983144983141 983140983145983155983152983148983137983139983141983149983141983150983156 983158983151983148983157983149983141
991266 983124983144983141 983149983137983155983155 983140983145983155983152983148983137983139983141983149983141983150983156
991266 983124983144983141 983149983151983149983141983150983156 983151983142 983145983150983141983154983156983145983137 983151983142 983156983144983141 983159983137983156983141983154983152983148983137983150983141 983137983154983141983137983137983138983151983157983156 CL
3
15051520 m x xT B L
I I
==sdotsdot=nabla
tons x I
751531500251 ==nablasdot=∆ ρ
433
33208
12
205
12
m x L B
I I
===
I983150983156983137983139983156 C983151983150983140983145983156983145983151983150
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 5267
I983150983156983137983139983156 C983151983150983140983145983156983145983151983150
991266 M983141983156983137983139983141983150983156983154983145983139 983154983137983140983145983157983155
991266 O983154 983145983156 983139983151983157983148983140 983138983141 983139983137983148983139983157983148983137983156983141983140 983140983145983154983141983139983156983148983161 983137983155
991266 H983141983145983143983144983156 983151983142 983156983144983141 983139983141983150983156983141983154 983151983142 983138983157983151983161983137983150983139983161
m I
BM
I
I 3891
150
33208==
nabla
=
m xT
B
LBT
L B BM
I I
I 3891
5112
5
12
12 223
====
mT
KB I
I 750
2
==
I983150983156983137983139983156 C983151983150983140983145983156983145983151983150
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 5367
991266 983124983144983141 983149983141983156983137983139983141983150983156983154983145983139 983144983141983145983143983144983156
991266 F983151983154 983155983149983137983148983148 983137983150983143983148983141983155 983151983142 983144983141983141983148 983156983144983141 983154983145983143983144983156983145983150983143 983149983151983149983141983150983156
m KG BM KBGM I I 63905013891750 =minus+=minus+=
sin22998sin693075153sin mt x xGM M I I
φ φ φ ==∆=
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 5467
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 5567
983116983119983123983124 983106983125983119983129983105983118983107983129 983117983109983124983112983119983108
Paralel Sinkage
Volume (DCEF)=Volume (W1ADW+BL1LC)
Damaged compartment is bounded on top
983116983119983123983124 983106983125983119983129983105983118983107983129 983117983109983124983112983119983108
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 5667
983116983119983123983124 983106983125983119983129983105983118983107983129 983117983109983124983112983119983108
bull It is assumed that displacement and location of vertical centre
of gravity does not change after damaged
983116983119983123983124 983106983125983119983129983105983118983107983129 983117983109983124983112983119983108
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 5767
983116983119983123983124 983106983125983119983129983105983118983107983129 983117983109983124983112983119983108
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 5867
The heel angle of damaged ship is determined by
where
d is the distance between the volume centre of damaged compartment
and the new longitudinal centre of floatation
wc=vc μ ρ
983116983119983123983124 983106983125983119983129983105983118983107983129 983117983109983124983112983119983108
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 5967
983116983119983123983124 983106983125983119983129983105983118983107983129 983117983109983124983112983119983108
983116983119983123983124 983106983125983119983129983105983118983107983129 983117983109983124983112983119983108
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 6067
Longitudinal Metacentre Height of a Damaged Ship
983116983119983123983124 983106983125983119983129983105983118983107983129 983117983109983124983112983119983108
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 6167
983110983151983154983159983137983154983140 983137983150983140 983137983142983156 983140983154983137983157983143983144983156983155 983137983142983156983141983154 983140983137983149983137983143983141983140
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 6267
983120983151983154983156 983105983142983156 983120983151983154983156 983110983151983154983141 983123983156983137983154983138983151983137983154983140 983105983142983156 983123983156983137983154983138983151983137983154983140 983110983151983154983159983137983154983140
I983150983145983156983145983137983148 D983154983137983157983143983144983156 983124 983124 983124 983124
983120983137983154983137983148983141983148 983123983145983150983147983137983143983141 +983152 +983152 +983152 +983120
H983141983141983148 983085983149983145 983085983149983145 +983149983155 +983149983155
983124983154983145983149 983085983156983147 +983156983138 983085983156983147 +983156983138
F983145983150983137983148 D983154983137983157983143983144983156 983124+983152983085983149983145983085983156983147 983124+983152983085983149983145+983156983138 983124+983152+983149983155983085983156983147 983124+983152+983149983155+983156983138
Table 1 Final Draughts for a starboard side damaged ship
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 6367
L983151983155983156 B983157983151983161983137983150983139983161 M983141983156983144983151983140
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 6467
L983151983155983156 B983157983151983161983137983150983139983161 M983141983156983144983151983140
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 6567
991266 A983142983156983141983154 983148983151983151983155983145983150983143 983156983144983141 983139983141983150983156983154983137983148 983139983151983149983152983137983154983156983149983141983150983156 983156983144983141
983159983137983156983141983154983152983148983137983150983141 983137983154983141983137 983145983155
991266 983124983151 983139983151983149983152983141983150983155983137983156983141 983142983151983154 983156983144983141 983148983151983155983155 983151983142 983138983157983151983161983137983150983139983161 983151983142 983156983144983141
983139983141983150983156983154983137983148 983139983151983149983152983137983154983156983149983141983150983156 983156983144983141 983140983154983137983142983156 983145983150983139983154983141983137983155983141983155 983156983151
2805)420()( m x Bl L A L
=minus=minus=
m A
T
L
I
L 875180
150==
nabla=
L983151983155983156 B983157983151983161983137983150983139983161 M983141983156983144983151983140
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 6667
991266 983124983144983141 983144983141983145983143983144983156 983151983142 983156983144983141 983139983141983150983156983141983154 983151983142 983138983157983151983161983137983150983139983161 983145983150983139983154983141983137983155983141983155 983156983151
991266 983124983144983141 983149983151983149983141983150983156 983151983142 983145983150983141983154983156983145983137 983151983142 983156983144983141 983159983137983156983141983154983152983148983137983150983141 983137983154983141983137
991266 983124983144983141 983149983141983156983137983139983141983150983156983154983145983139 983154983137983140983145983157983155
m
T
KB L
L 93802
8751
2 ===
433
6716612
)420(5
12
)(m
l L B I L
=minus
=minus
=
m I
BM
I
L
L 1111150
67166==
nabla
=
L983151983155983156 B983157983151983161983137983150983139983161 M983141983156983144983151983140
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 6767
991266 983124983144983141 983149983141983156983137983139983141983150983156983154983145983139 983144983141983145983143983144983156
991266 983122983145983143983144983156983145983150983143 983149983151983149983141983150983156 983142983151983154 983155983149983137983148983148 983144983141983141983148 983137983150983143983148983141983155
m KG BM KBGM L L L 54905111119380 =minus+=minus+=
mt xGM M L
sin34984sin549075153sin φ φ φ ==∆=
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 3967
Comparision of Lost Buoyancy and Added
Weight Methods
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 4067
Consider a vessel that has been damaged such
that a portion of the bottom is now open to the
sea
The vesselrsquos draft will increase because an amount
of the buoyancy was lost
Added Weight Method
Added Weight Method
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 4167
Added Weight Method
In this method flood water is treated as a fixed weight (for example the
weight of water of volume ABEF) This added weight is balanced by the
additional buoyant force of the layer WL1WL
The added weight can be determined by either the volume ABEF or
waterline WL1 Therefore WL1 waterline is not known can be just guessed
For the predicted waterline added weight and additional buoyant force
caculation are done iteratively until both of them are equal This method is
known as Added weight method
Determination of Added Weight
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 4267
Determination of Added Weight
vc Volume of damaged compartment (DCEF)
ac The surface area (AB) of damaged compartment on the waterline
micro The volume permability of damaged compartment
microa The area permability of the surface of damaged compartment
∆ The initial displacement
∆1 The displacement at final stage
vw The volume of water entering the vessel (ABEH)
w The weight of water entering the vessel
p The value of parallel sinkage
If th t th l l i k i h f t l f
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 4367
If we assume that the paralel sinkage cause a minor change of water plane area of a
ship (Awp
asymp Awp1
) we can determine the paralel sinkage by equating the volume of
the layer WL1WL to the volume of ABEF
If the damaged compartment is bounded on top
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 4467
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 4567
Longitudinal Metacentre Radius at final stage
Free Surface Effect
Damaged compartment can be considered as a half filled tank
Free Contact Effect
Damaged compartment can be considered as a half filled tank
T M H i h
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 4667
Transverse Metacentre Height
The angle of heel
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 4767
L it di l M t t H i ht
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 4867
Longitudinal Metacentre Height
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 4967
E983160983137983149983152983148983141 A 983138983137983154983143983141
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 5067
E983160983137983149983152983148983141 A 983138983137983154983143983141
991266 L = 20 983149991266 B = 5 983149
991266 983124 = 15 983149
991266 KG = 15 983149
I983150983156983137983139983156 C983151983150983140983145983156983145983151983150
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 5167
I983150983156983137983139983156 C983151983150983140983145983156983145983151983150
991266 983124983144983141 983140983145983155983152983148983137983139983141983149983141983150983156 983158983151983148983157983149983141
991266 983124983144983141 983149983137983155983155 983140983145983155983152983148983137983139983141983149983141983150983156
991266 983124983144983141 983149983151983149983141983150983156 983151983142 983145983150983141983154983156983145983137 983151983142 983156983144983141 983159983137983156983141983154983152983148983137983150983141 983137983154983141983137983137983138983151983157983156 CL
3
15051520 m x xT B L
I I
==sdotsdot=nabla
tons x I
751531500251 ==nablasdot=∆ ρ
433
33208
12
205
12
m x L B
I I
===
I983150983156983137983139983156 C983151983150983140983145983156983145983151983150
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 5267
I983150983156983137983139983156 C983151983150983140983145983156983145983151983150
991266 M983141983156983137983139983141983150983156983154983145983139 983154983137983140983145983157983155
991266 O983154 983145983156 983139983151983157983148983140 983138983141 983139983137983148983139983157983148983137983156983141983140 983140983145983154983141983139983156983148983161 983137983155
991266 H983141983145983143983144983156 983151983142 983156983144983141 983139983141983150983156983141983154 983151983142 983138983157983151983161983137983150983139983161
m I
BM
I
I 3891
150
33208==
nabla
=
m xT
B
LBT
L B BM
I I
I 3891
5112
5
12
12 223
====
mT
KB I
I 750
2
==
I983150983156983137983139983156 C983151983150983140983145983156983145983151983150
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 5367
991266 983124983144983141 983149983141983156983137983139983141983150983156983154983145983139 983144983141983145983143983144983156
991266 F983151983154 983155983149983137983148983148 983137983150983143983148983141983155 983151983142 983144983141983141983148 983156983144983141 983154983145983143983144983156983145983150983143 983149983151983149983141983150983156
m KG BM KBGM I I 63905013891750 =minus+=minus+=
sin22998sin693075153sin mt x xGM M I I
φ φ φ ==∆=
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 5467
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 5567
983116983119983123983124 983106983125983119983129983105983118983107983129 983117983109983124983112983119983108
Paralel Sinkage
Volume (DCEF)=Volume (W1ADW+BL1LC)
Damaged compartment is bounded on top
983116983119983123983124 983106983125983119983129983105983118983107983129 983117983109983124983112983119983108
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 5667
983116983119983123983124 983106983125983119983129983105983118983107983129 983117983109983124983112983119983108
bull It is assumed that displacement and location of vertical centre
of gravity does not change after damaged
983116983119983123983124 983106983125983119983129983105983118983107983129 983117983109983124983112983119983108
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 5767
983116983119983123983124 983106983125983119983129983105983118983107983129 983117983109983124983112983119983108
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 5867
The heel angle of damaged ship is determined by
where
d is the distance between the volume centre of damaged compartment
and the new longitudinal centre of floatation
wc=vc μ ρ
983116983119983123983124 983106983125983119983129983105983118983107983129 983117983109983124983112983119983108
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 5967
983116983119983123983124 983106983125983119983129983105983118983107983129 983117983109983124983112983119983108
983116983119983123983124 983106983125983119983129983105983118983107983129 983117983109983124983112983119983108
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 6067
Longitudinal Metacentre Height of a Damaged Ship
983116983119983123983124 983106983125983119983129983105983118983107983129 983117983109983124983112983119983108
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 6167
983110983151983154983159983137983154983140 983137983150983140 983137983142983156 983140983154983137983157983143983144983156983155 983137983142983156983141983154 983140983137983149983137983143983141983140
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 6267
983120983151983154983156 983105983142983156 983120983151983154983156 983110983151983154983141 983123983156983137983154983138983151983137983154983140 983105983142983156 983123983156983137983154983138983151983137983154983140 983110983151983154983159983137983154983140
I983150983145983156983145983137983148 D983154983137983157983143983144983156 983124 983124 983124 983124
983120983137983154983137983148983141983148 983123983145983150983147983137983143983141 +983152 +983152 +983152 +983120
H983141983141983148 983085983149983145 983085983149983145 +983149983155 +983149983155
983124983154983145983149 983085983156983147 +983156983138 983085983156983147 +983156983138
F983145983150983137983148 D983154983137983157983143983144983156 983124+983152983085983149983145983085983156983147 983124+983152983085983149983145+983156983138 983124+983152+983149983155983085983156983147 983124+983152+983149983155+983156983138
Table 1 Final Draughts for a starboard side damaged ship
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 6367
L983151983155983156 B983157983151983161983137983150983139983161 M983141983156983144983151983140
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 6467
L983151983155983156 B983157983151983161983137983150983139983161 M983141983156983144983151983140
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 6567
991266 A983142983156983141983154 983148983151983151983155983145983150983143 983156983144983141 983139983141983150983156983154983137983148 983139983151983149983152983137983154983156983149983141983150983156 983156983144983141
983159983137983156983141983154983152983148983137983150983141 983137983154983141983137 983145983155
991266 983124983151 983139983151983149983152983141983150983155983137983156983141 983142983151983154 983156983144983141 983148983151983155983155 983151983142 983138983157983151983161983137983150983139983161 983151983142 983156983144983141
983139983141983150983156983154983137983148 983139983151983149983152983137983154983156983149983141983150983156 983156983144983141 983140983154983137983142983156 983145983150983139983154983141983137983155983141983155 983156983151
2805)420()( m x Bl L A L
=minus=minus=
m A
T
L
I
L 875180
150==
nabla=
L983151983155983156 B983157983151983161983137983150983139983161 M983141983156983144983151983140
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 6667
991266 983124983144983141 983144983141983145983143983144983156 983151983142 983156983144983141 983139983141983150983156983141983154 983151983142 983138983157983151983161983137983150983139983161 983145983150983139983154983141983137983155983141983155 983156983151
991266 983124983144983141 983149983151983149983141983150983156 983151983142 983145983150983141983154983156983145983137 983151983142 983156983144983141 983159983137983156983141983154983152983148983137983150983141 983137983154983141983137
991266 983124983144983141 983149983141983156983137983139983141983150983156983154983145983139 983154983137983140983145983157983155
m
T
KB L
L 93802
8751
2 ===
433
6716612
)420(5
12
)(m
l L B I L
=minus
=minus
=
m I
BM
I
L
L 1111150
67166==
nabla
=
L983151983155983156 B983157983151983161983137983150983139983161 M983141983156983144983151983140
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 6767
991266 983124983144983141 983149983141983156983137983139983141983150983156983154983145983139 983144983141983145983143983144983156
991266 983122983145983143983144983156983145983150983143 983149983151983149983141983150983156 983142983151983154 983155983149983137983148983148 983144983141983141983148 983137983150983143983148983141983155
m KG BM KBGM L L L 54905111119380 =minus+=minus+=
mt xGM M L
sin34984sin549075153sin φ φ φ ==∆=
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 4067
Consider a vessel that has been damaged such
that a portion of the bottom is now open to the
sea
The vesselrsquos draft will increase because an amount
of the buoyancy was lost
Added Weight Method
Added Weight Method
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 4167
Added Weight Method
In this method flood water is treated as a fixed weight (for example the
weight of water of volume ABEF) This added weight is balanced by the
additional buoyant force of the layer WL1WL
The added weight can be determined by either the volume ABEF or
waterline WL1 Therefore WL1 waterline is not known can be just guessed
For the predicted waterline added weight and additional buoyant force
caculation are done iteratively until both of them are equal This method is
known as Added weight method
Determination of Added Weight
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 4267
Determination of Added Weight
vc Volume of damaged compartment (DCEF)
ac The surface area (AB) of damaged compartment on the waterline
micro The volume permability of damaged compartment
microa The area permability of the surface of damaged compartment
∆ The initial displacement
∆1 The displacement at final stage
vw The volume of water entering the vessel (ABEH)
w The weight of water entering the vessel
p The value of parallel sinkage
If th t th l l i k i h f t l f
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 4367
If we assume that the paralel sinkage cause a minor change of water plane area of a
ship (Awp
asymp Awp1
) we can determine the paralel sinkage by equating the volume of
the layer WL1WL to the volume of ABEF
If the damaged compartment is bounded on top
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 4467
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 4567
Longitudinal Metacentre Radius at final stage
Free Surface Effect
Damaged compartment can be considered as a half filled tank
Free Contact Effect
Damaged compartment can be considered as a half filled tank
T M H i h
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 4667
Transverse Metacentre Height
The angle of heel
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 4767
L it di l M t t H i ht
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 4867
Longitudinal Metacentre Height
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 4967
E983160983137983149983152983148983141 A 983138983137983154983143983141
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 5067
E983160983137983149983152983148983141 A 983138983137983154983143983141
991266 L = 20 983149991266 B = 5 983149
991266 983124 = 15 983149
991266 KG = 15 983149
I983150983156983137983139983156 C983151983150983140983145983156983145983151983150
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 5167
I983150983156983137983139983156 C983151983150983140983145983156983145983151983150
991266 983124983144983141 983140983145983155983152983148983137983139983141983149983141983150983156 983158983151983148983157983149983141
991266 983124983144983141 983149983137983155983155 983140983145983155983152983148983137983139983141983149983141983150983156
991266 983124983144983141 983149983151983149983141983150983156 983151983142 983145983150983141983154983156983145983137 983151983142 983156983144983141 983159983137983156983141983154983152983148983137983150983141 983137983154983141983137983137983138983151983157983156 CL
3
15051520 m x xT B L
I I
==sdotsdot=nabla
tons x I
751531500251 ==nablasdot=∆ ρ
433
33208
12
205
12
m x L B
I I
===
I983150983156983137983139983156 C983151983150983140983145983156983145983151983150
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 5267
I983150983156983137983139983156 C983151983150983140983145983156983145983151983150
991266 M983141983156983137983139983141983150983156983154983145983139 983154983137983140983145983157983155
991266 O983154 983145983156 983139983151983157983148983140 983138983141 983139983137983148983139983157983148983137983156983141983140 983140983145983154983141983139983156983148983161 983137983155
991266 H983141983145983143983144983156 983151983142 983156983144983141 983139983141983150983156983141983154 983151983142 983138983157983151983161983137983150983139983161
m I
BM
I
I 3891
150
33208==
nabla
=
m xT
B
LBT
L B BM
I I
I 3891
5112
5
12
12 223
====
mT
KB I
I 750
2
==
I983150983156983137983139983156 C983151983150983140983145983156983145983151983150
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 5367
991266 983124983144983141 983149983141983156983137983139983141983150983156983154983145983139 983144983141983145983143983144983156
991266 F983151983154 983155983149983137983148983148 983137983150983143983148983141983155 983151983142 983144983141983141983148 983156983144983141 983154983145983143983144983156983145983150983143 983149983151983149983141983150983156
m KG BM KBGM I I 63905013891750 =minus+=minus+=
sin22998sin693075153sin mt x xGM M I I
φ φ φ ==∆=
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 5467
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 5567
983116983119983123983124 983106983125983119983129983105983118983107983129 983117983109983124983112983119983108
Paralel Sinkage
Volume (DCEF)=Volume (W1ADW+BL1LC)
Damaged compartment is bounded on top
983116983119983123983124 983106983125983119983129983105983118983107983129 983117983109983124983112983119983108
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 5667
983116983119983123983124 983106983125983119983129983105983118983107983129 983117983109983124983112983119983108
bull It is assumed that displacement and location of vertical centre
of gravity does not change after damaged
983116983119983123983124 983106983125983119983129983105983118983107983129 983117983109983124983112983119983108
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 5767
983116983119983123983124 983106983125983119983129983105983118983107983129 983117983109983124983112983119983108
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 5867
The heel angle of damaged ship is determined by
where
d is the distance between the volume centre of damaged compartment
and the new longitudinal centre of floatation
wc=vc μ ρ
983116983119983123983124 983106983125983119983129983105983118983107983129 983117983109983124983112983119983108
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 5967
983116983119983123983124 983106983125983119983129983105983118983107983129 983117983109983124983112983119983108
983116983119983123983124 983106983125983119983129983105983118983107983129 983117983109983124983112983119983108
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 6067
Longitudinal Metacentre Height of a Damaged Ship
983116983119983123983124 983106983125983119983129983105983118983107983129 983117983109983124983112983119983108
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 6167
983110983151983154983159983137983154983140 983137983150983140 983137983142983156 983140983154983137983157983143983144983156983155 983137983142983156983141983154 983140983137983149983137983143983141983140
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 6267
983120983151983154983156 983105983142983156 983120983151983154983156 983110983151983154983141 983123983156983137983154983138983151983137983154983140 983105983142983156 983123983156983137983154983138983151983137983154983140 983110983151983154983159983137983154983140
I983150983145983156983145983137983148 D983154983137983157983143983144983156 983124 983124 983124 983124
983120983137983154983137983148983141983148 983123983145983150983147983137983143983141 +983152 +983152 +983152 +983120
H983141983141983148 983085983149983145 983085983149983145 +983149983155 +983149983155
983124983154983145983149 983085983156983147 +983156983138 983085983156983147 +983156983138
F983145983150983137983148 D983154983137983157983143983144983156 983124+983152983085983149983145983085983156983147 983124+983152983085983149983145+983156983138 983124+983152+983149983155983085983156983147 983124+983152+983149983155+983156983138
Table 1 Final Draughts for a starboard side damaged ship
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 6367
L983151983155983156 B983157983151983161983137983150983139983161 M983141983156983144983151983140
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 6467
L983151983155983156 B983157983151983161983137983150983139983161 M983141983156983144983151983140
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 6567
991266 A983142983156983141983154 983148983151983151983155983145983150983143 983156983144983141 983139983141983150983156983154983137983148 983139983151983149983152983137983154983156983149983141983150983156 983156983144983141
983159983137983156983141983154983152983148983137983150983141 983137983154983141983137 983145983155
991266 983124983151 983139983151983149983152983141983150983155983137983156983141 983142983151983154 983156983144983141 983148983151983155983155 983151983142 983138983157983151983161983137983150983139983161 983151983142 983156983144983141
983139983141983150983156983154983137983148 983139983151983149983152983137983154983156983149983141983150983156 983156983144983141 983140983154983137983142983156 983145983150983139983154983141983137983155983141983155 983156983151
2805)420()( m x Bl L A L
=minus=minus=
m A
T
L
I
L 875180
150==
nabla=
L983151983155983156 B983157983151983161983137983150983139983161 M983141983156983144983151983140
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 6667
991266 983124983144983141 983144983141983145983143983144983156 983151983142 983156983144983141 983139983141983150983156983141983154 983151983142 983138983157983151983161983137983150983139983161 983145983150983139983154983141983137983155983141983155 983156983151
991266 983124983144983141 983149983151983149983141983150983156 983151983142 983145983150983141983154983156983145983137 983151983142 983156983144983141 983159983137983156983141983154983152983148983137983150983141 983137983154983141983137
991266 983124983144983141 983149983141983156983137983139983141983150983156983154983145983139 983154983137983140983145983157983155
m
T
KB L
L 93802
8751
2 ===
433
6716612
)420(5
12
)(m
l L B I L
=minus
=minus
=
m I
BM
I
L
L 1111150
67166==
nabla
=
L983151983155983156 B983157983151983161983137983150983139983161 M983141983156983144983151983140
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 6767
991266 983124983144983141 983149983141983156983137983139983141983150983156983154983145983139 983144983141983145983143983144983156
991266 983122983145983143983144983156983145983150983143 983149983151983149983141983150983156 983142983151983154 983155983149983137983148983148 983144983141983141983148 983137983150983143983148983141983155
m KG BM KBGM L L L 54905111119380 =minus+=minus+=
mt xGM M L
sin34984sin549075153sin φ φ φ ==∆=
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 4167
Added Weight Method
In this method flood water is treated as a fixed weight (for example the
weight of water of volume ABEF) This added weight is balanced by the
additional buoyant force of the layer WL1WL
The added weight can be determined by either the volume ABEF or
waterline WL1 Therefore WL1 waterline is not known can be just guessed
For the predicted waterline added weight and additional buoyant force
caculation are done iteratively until both of them are equal This method is
known as Added weight method
Determination of Added Weight
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 4267
Determination of Added Weight
vc Volume of damaged compartment (DCEF)
ac The surface area (AB) of damaged compartment on the waterline
micro The volume permability of damaged compartment
microa The area permability of the surface of damaged compartment
∆ The initial displacement
∆1 The displacement at final stage
vw The volume of water entering the vessel (ABEH)
w The weight of water entering the vessel
p The value of parallel sinkage
If th t th l l i k i h f t l f
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 4367
If we assume that the paralel sinkage cause a minor change of water plane area of a
ship (Awp
asymp Awp1
) we can determine the paralel sinkage by equating the volume of
the layer WL1WL to the volume of ABEF
If the damaged compartment is bounded on top
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 4467
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 4567
Longitudinal Metacentre Radius at final stage
Free Surface Effect
Damaged compartment can be considered as a half filled tank
Free Contact Effect
Damaged compartment can be considered as a half filled tank
T M H i h
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 4667
Transverse Metacentre Height
The angle of heel
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 4767
L it di l M t t H i ht
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 4867
Longitudinal Metacentre Height
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 4967
E983160983137983149983152983148983141 A 983138983137983154983143983141
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 5067
E983160983137983149983152983148983141 A 983138983137983154983143983141
991266 L = 20 983149991266 B = 5 983149
991266 983124 = 15 983149
991266 KG = 15 983149
I983150983156983137983139983156 C983151983150983140983145983156983145983151983150
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 5167
I983150983156983137983139983156 C983151983150983140983145983156983145983151983150
991266 983124983144983141 983140983145983155983152983148983137983139983141983149983141983150983156 983158983151983148983157983149983141
991266 983124983144983141 983149983137983155983155 983140983145983155983152983148983137983139983141983149983141983150983156
991266 983124983144983141 983149983151983149983141983150983156 983151983142 983145983150983141983154983156983145983137 983151983142 983156983144983141 983159983137983156983141983154983152983148983137983150983141 983137983154983141983137983137983138983151983157983156 CL
3
15051520 m x xT B L
I I
==sdotsdot=nabla
tons x I
751531500251 ==nablasdot=∆ ρ
433
33208
12
205
12
m x L B
I I
===
I983150983156983137983139983156 C983151983150983140983145983156983145983151983150
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 5267
I983150983156983137983139983156 C983151983150983140983145983156983145983151983150
991266 M983141983156983137983139983141983150983156983154983145983139 983154983137983140983145983157983155
991266 O983154 983145983156 983139983151983157983148983140 983138983141 983139983137983148983139983157983148983137983156983141983140 983140983145983154983141983139983156983148983161 983137983155
991266 H983141983145983143983144983156 983151983142 983156983144983141 983139983141983150983156983141983154 983151983142 983138983157983151983161983137983150983139983161
m I
BM
I
I 3891
150
33208==
nabla
=
m xT
B
LBT
L B BM
I I
I 3891
5112
5
12
12 223
====
mT
KB I
I 750
2
==
I983150983156983137983139983156 C983151983150983140983145983156983145983151983150
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 5367
991266 983124983144983141 983149983141983156983137983139983141983150983156983154983145983139 983144983141983145983143983144983156
991266 F983151983154 983155983149983137983148983148 983137983150983143983148983141983155 983151983142 983144983141983141983148 983156983144983141 983154983145983143983144983156983145983150983143 983149983151983149983141983150983156
m KG BM KBGM I I 63905013891750 =minus+=minus+=
sin22998sin693075153sin mt x xGM M I I
φ φ φ ==∆=
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 5467
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 5567
983116983119983123983124 983106983125983119983129983105983118983107983129 983117983109983124983112983119983108
Paralel Sinkage
Volume (DCEF)=Volume (W1ADW+BL1LC)
Damaged compartment is bounded on top
983116983119983123983124 983106983125983119983129983105983118983107983129 983117983109983124983112983119983108
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 5667
983116983119983123983124 983106983125983119983129983105983118983107983129 983117983109983124983112983119983108
bull It is assumed that displacement and location of vertical centre
of gravity does not change after damaged
983116983119983123983124 983106983125983119983129983105983118983107983129 983117983109983124983112983119983108
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 5767
983116983119983123983124 983106983125983119983129983105983118983107983129 983117983109983124983112983119983108
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 5867
The heel angle of damaged ship is determined by
where
d is the distance between the volume centre of damaged compartment
and the new longitudinal centre of floatation
wc=vc μ ρ
983116983119983123983124 983106983125983119983129983105983118983107983129 983117983109983124983112983119983108
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 5967
983116983119983123983124 983106983125983119983129983105983118983107983129 983117983109983124983112983119983108
983116983119983123983124 983106983125983119983129983105983118983107983129 983117983109983124983112983119983108
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 6067
Longitudinal Metacentre Height of a Damaged Ship
983116983119983123983124 983106983125983119983129983105983118983107983129 983117983109983124983112983119983108
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 6167
983110983151983154983159983137983154983140 983137983150983140 983137983142983156 983140983154983137983157983143983144983156983155 983137983142983156983141983154 983140983137983149983137983143983141983140
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 6267
983120983151983154983156 983105983142983156 983120983151983154983156 983110983151983154983141 983123983156983137983154983138983151983137983154983140 983105983142983156 983123983156983137983154983138983151983137983154983140 983110983151983154983159983137983154983140
I983150983145983156983145983137983148 D983154983137983157983143983144983156 983124 983124 983124 983124
983120983137983154983137983148983141983148 983123983145983150983147983137983143983141 +983152 +983152 +983152 +983120
H983141983141983148 983085983149983145 983085983149983145 +983149983155 +983149983155
983124983154983145983149 983085983156983147 +983156983138 983085983156983147 +983156983138
F983145983150983137983148 D983154983137983157983143983144983156 983124+983152983085983149983145983085983156983147 983124+983152983085983149983145+983156983138 983124+983152+983149983155983085983156983147 983124+983152+983149983155+983156983138
Table 1 Final Draughts for a starboard side damaged ship
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 6367
L983151983155983156 B983157983151983161983137983150983139983161 M983141983156983144983151983140
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 6467
L983151983155983156 B983157983151983161983137983150983139983161 M983141983156983144983151983140
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 6567
991266 A983142983156983141983154 983148983151983151983155983145983150983143 983156983144983141 983139983141983150983156983154983137983148 983139983151983149983152983137983154983156983149983141983150983156 983156983144983141
983159983137983156983141983154983152983148983137983150983141 983137983154983141983137 983145983155
991266 983124983151 983139983151983149983152983141983150983155983137983156983141 983142983151983154 983156983144983141 983148983151983155983155 983151983142 983138983157983151983161983137983150983139983161 983151983142 983156983144983141
983139983141983150983156983154983137983148 983139983151983149983152983137983154983156983149983141983150983156 983156983144983141 983140983154983137983142983156 983145983150983139983154983141983137983155983141983155 983156983151
2805)420()( m x Bl L A L
=minus=minus=
m A
T
L
I
L 875180
150==
nabla=
L983151983155983156 B983157983151983161983137983150983139983161 M983141983156983144983151983140
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 6667
991266 983124983144983141 983144983141983145983143983144983156 983151983142 983156983144983141 983139983141983150983156983141983154 983151983142 983138983157983151983161983137983150983139983161 983145983150983139983154983141983137983155983141983155 983156983151
991266 983124983144983141 983149983151983149983141983150983156 983151983142 983145983150983141983154983156983145983137 983151983142 983156983144983141 983159983137983156983141983154983152983148983137983150983141 983137983154983141983137
991266 983124983144983141 983149983141983156983137983139983141983150983156983154983145983139 983154983137983140983145983157983155
m
T
KB L
L 93802
8751
2 ===
433
6716612
)420(5
12
)(m
l L B I L
=minus
=minus
=
m I
BM
I
L
L 1111150
67166==
nabla
=
L983151983155983156 B983157983151983161983137983150983139983161 M983141983156983144983151983140
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 6767
991266 983124983144983141 983149983141983156983137983139983141983150983156983154983145983139 983144983141983145983143983144983156
991266 983122983145983143983144983156983145983150983143 983149983151983149983141983150983156 983142983151983154 983155983149983137983148983148 983144983141983141983148 983137983150983143983148983141983155
m KG BM KBGM L L L 54905111119380 =minus+=minus+=
mt xGM M L
sin34984sin549075153sin φ φ φ ==∆=
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 4267
Determination of Added Weight
vc Volume of damaged compartment (DCEF)
ac The surface area (AB) of damaged compartment on the waterline
micro The volume permability of damaged compartment
microa The area permability of the surface of damaged compartment
∆ The initial displacement
∆1 The displacement at final stage
vw The volume of water entering the vessel (ABEH)
w The weight of water entering the vessel
p The value of parallel sinkage
If th t th l l i k i h f t l f
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 4367
If we assume that the paralel sinkage cause a minor change of water plane area of a
ship (Awp
asymp Awp1
) we can determine the paralel sinkage by equating the volume of
the layer WL1WL to the volume of ABEF
If the damaged compartment is bounded on top
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 4467
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 4567
Longitudinal Metacentre Radius at final stage
Free Surface Effect
Damaged compartment can be considered as a half filled tank
Free Contact Effect
Damaged compartment can be considered as a half filled tank
T M H i h
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 4667
Transverse Metacentre Height
The angle of heel
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 4767
L it di l M t t H i ht
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 4867
Longitudinal Metacentre Height
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 4967
E983160983137983149983152983148983141 A 983138983137983154983143983141
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 5067
E983160983137983149983152983148983141 A 983138983137983154983143983141
991266 L = 20 983149991266 B = 5 983149
991266 983124 = 15 983149
991266 KG = 15 983149
I983150983156983137983139983156 C983151983150983140983145983156983145983151983150
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 5167
I983150983156983137983139983156 C983151983150983140983145983156983145983151983150
991266 983124983144983141 983140983145983155983152983148983137983139983141983149983141983150983156 983158983151983148983157983149983141
991266 983124983144983141 983149983137983155983155 983140983145983155983152983148983137983139983141983149983141983150983156
991266 983124983144983141 983149983151983149983141983150983156 983151983142 983145983150983141983154983156983145983137 983151983142 983156983144983141 983159983137983156983141983154983152983148983137983150983141 983137983154983141983137983137983138983151983157983156 CL
3
15051520 m x xT B L
I I
==sdotsdot=nabla
tons x I
751531500251 ==nablasdot=∆ ρ
433
33208
12
205
12
m x L B
I I
===
I983150983156983137983139983156 C983151983150983140983145983156983145983151983150
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 5267
I983150983156983137983139983156 C983151983150983140983145983156983145983151983150
991266 M983141983156983137983139983141983150983156983154983145983139 983154983137983140983145983157983155
991266 O983154 983145983156 983139983151983157983148983140 983138983141 983139983137983148983139983157983148983137983156983141983140 983140983145983154983141983139983156983148983161 983137983155
991266 H983141983145983143983144983156 983151983142 983156983144983141 983139983141983150983156983141983154 983151983142 983138983157983151983161983137983150983139983161
m I
BM
I
I 3891
150
33208==
nabla
=
m xT
B
LBT
L B BM
I I
I 3891
5112
5
12
12 223
====
mT
KB I
I 750
2
==
I983150983156983137983139983156 C983151983150983140983145983156983145983151983150
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 5367
991266 983124983144983141 983149983141983156983137983139983141983150983156983154983145983139 983144983141983145983143983144983156
991266 F983151983154 983155983149983137983148983148 983137983150983143983148983141983155 983151983142 983144983141983141983148 983156983144983141 983154983145983143983144983156983145983150983143 983149983151983149983141983150983156
m KG BM KBGM I I 63905013891750 =minus+=minus+=
sin22998sin693075153sin mt x xGM M I I
φ φ φ ==∆=
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 5467
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 5567
983116983119983123983124 983106983125983119983129983105983118983107983129 983117983109983124983112983119983108
Paralel Sinkage
Volume (DCEF)=Volume (W1ADW+BL1LC)
Damaged compartment is bounded on top
983116983119983123983124 983106983125983119983129983105983118983107983129 983117983109983124983112983119983108
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 5667
983116983119983123983124 983106983125983119983129983105983118983107983129 983117983109983124983112983119983108
bull It is assumed that displacement and location of vertical centre
of gravity does not change after damaged
983116983119983123983124 983106983125983119983129983105983118983107983129 983117983109983124983112983119983108
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 5767
983116983119983123983124 983106983125983119983129983105983118983107983129 983117983109983124983112983119983108
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 5867
The heel angle of damaged ship is determined by
where
d is the distance between the volume centre of damaged compartment
and the new longitudinal centre of floatation
wc=vc μ ρ
983116983119983123983124 983106983125983119983129983105983118983107983129 983117983109983124983112983119983108
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 5967
983116983119983123983124 983106983125983119983129983105983118983107983129 983117983109983124983112983119983108
983116983119983123983124 983106983125983119983129983105983118983107983129 983117983109983124983112983119983108
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 6067
Longitudinal Metacentre Height of a Damaged Ship
983116983119983123983124 983106983125983119983129983105983118983107983129 983117983109983124983112983119983108
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 6167
983110983151983154983159983137983154983140 983137983150983140 983137983142983156 983140983154983137983157983143983144983156983155 983137983142983156983141983154 983140983137983149983137983143983141983140
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 6267
983120983151983154983156 983105983142983156 983120983151983154983156 983110983151983154983141 983123983156983137983154983138983151983137983154983140 983105983142983156 983123983156983137983154983138983151983137983154983140 983110983151983154983159983137983154983140
I983150983145983156983145983137983148 D983154983137983157983143983144983156 983124 983124 983124 983124
983120983137983154983137983148983141983148 983123983145983150983147983137983143983141 +983152 +983152 +983152 +983120
H983141983141983148 983085983149983145 983085983149983145 +983149983155 +983149983155
983124983154983145983149 983085983156983147 +983156983138 983085983156983147 +983156983138
F983145983150983137983148 D983154983137983157983143983144983156 983124+983152983085983149983145983085983156983147 983124+983152983085983149983145+983156983138 983124+983152+983149983155983085983156983147 983124+983152+983149983155+983156983138
Table 1 Final Draughts for a starboard side damaged ship
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 6367
L983151983155983156 B983157983151983161983137983150983139983161 M983141983156983144983151983140
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 6467
L983151983155983156 B983157983151983161983137983150983139983161 M983141983156983144983151983140
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 6567
991266 A983142983156983141983154 983148983151983151983155983145983150983143 983156983144983141 983139983141983150983156983154983137983148 983139983151983149983152983137983154983156983149983141983150983156 983156983144983141
983159983137983156983141983154983152983148983137983150983141 983137983154983141983137 983145983155
991266 983124983151 983139983151983149983152983141983150983155983137983156983141 983142983151983154 983156983144983141 983148983151983155983155 983151983142 983138983157983151983161983137983150983139983161 983151983142 983156983144983141
983139983141983150983156983154983137983148 983139983151983149983152983137983154983156983149983141983150983156 983156983144983141 983140983154983137983142983156 983145983150983139983154983141983137983155983141983155 983156983151
2805)420()( m x Bl L A L
=minus=minus=
m A
T
L
I
L 875180
150==
nabla=
L983151983155983156 B983157983151983161983137983150983139983161 M983141983156983144983151983140
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 6667
991266 983124983144983141 983144983141983145983143983144983156 983151983142 983156983144983141 983139983141983150983156983141983154 983151983142 983138983157983151983161983137983150983139983161 983145983150983139983154983141983137983155983141983155 983156983151
991266 983124983144983141 983149983151983149983141983150983156 983151983142 983145983150983141983154983156983145983137 983151983142 983156983144983141 983159983137983156983141983154983152983148983137983150983141 983137983154983141983137
991266 983124983144983141 983149983141983156983137983139983141983150983156983154983145983139 983154983137983140983145983157983155
m
T
KB L
L 93802
8751
2 ===
433
6716612
)420(5
12
)(m
l L B I L
=minus
=minus
=
m I
BM
I
L
L 1111150
67166==
nabla
=
L983151983155983156 B983157983151983161983137983150983139983161 M983141983156983144983151983140
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 6767
991266 983124983144983141 983149983141983156983137983139983141983150983156983154983145983139 983144983141983145983143983144983156
991266 983122983145983143983144983156983145983150983143 983149983151983149983141983150983156 983142983151983154 983155983149983137983148983148 983144983141983141983148 983137983150983143983148983141983155
m KG BM KBGM L L L 54905111119380 =minus+=minus+=
mt xGM M L
sin34984sin549075153sin φ φ φ ==∆=
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 4367
If we assume that the paralel sinkage cause a minor change of water plane area of a
ship (Awp
asymp Awp1
) we can determine the paralel sinkage by equating the volume of
the layer WL1WL to the volume of ABEF
If the damaged compartment is bounded on top
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 4467
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 4567
Longitudinal Metacentre Radius at final stage
Free Surface Effect
Damaged compartment can be considered as a half filled tank
Free Contact Effect
Damaged compartment can be considered as a half filled tank
T M H i h
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 4667
Transverse Metacentre Height
The angle of heel
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 4767
L it di l M t t H i ht
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 4867
Longitudinal Metacentre Height
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 4967
E983160983137983149983152983148983141 A 983138983137983154983143983141
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 5067
E983160983137983149983152983148983141 A 983138983137983154983143983141
991266 L = 20 983149991266 B = 5 983149
991266 983124 = 15 983149
991266 KG = 15 983149
I983150983156983137983139983156 C983151983150983140983145983156983145983151983150
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 5167
I983150983156983137983139983156 C983151983150983140983145983156983145983151983150
991266 983124983144983141 983140983145983155983152983148983137983139983141983149983141983150983156 983158983151983148983157983149983141
991266 983124983144983141 983149983137983155983155 983140983145983155983152983148983137983139983141983149983141983150983156
991266 983124983144983141 983149983151983149983141983150983156 983151983142 983145983150983141983154983156983145983137 983151983142 983156983144983141 983159983137983156983141983154983152983148983137983150983141 983137983154983141983137983137983138983151983157983156 CL
3
15051520 m x xT B L
I I
==sdotsdot=nabla
tons x I
751531500251 ==nablasdot=∆ ρ
433
33208
12
205
12
m x L B
I I
===
I983150983156983137983139983156 C983151983150983140983145983156983145983151983150
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 5267
I983150983156983137983139983156 C983151983150983140983145983156983145983151983150
991266 M983141983156983137983139983141983150983156983154983145983139 983154983137983140983145983157983155
991266 O983154 983145983156 983139983151983157983148983140 983138983141 983139983137983148983139983157983148983137983156983141983140 983140983145983154983141983139983156983148983161 983137983155
991266 H983141983145983143983144983156 983151983142 983156983144983141 983139983141983150983156983141983154 983151983142 983138983157983151983161983137983150983139983161
m I
BM
I
I 3891
150
33208==
nabla
=
m xT
B
LBT
L B BM
I I
I 3891
5112
5
12
12 223
====
mT
KB I
I 750
2
==
I983150983156983137983139983156 C983151983150983140983145983156983145983151983150
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 5367
991266 983124983144983141 983149983141983156983137983139983141983150983156983154983145983139 983144983141983145983143983144983156
991266 F983151983154 983155983149983137983148983148 983137983150983143983148983141983155 983151983142 983144983141983141983148 983156983144983141 983154983145983143983144983156983145983150983143 983149983151983149983141983150983156
m KG BM KBGM I I 63905013891750 =minus+=minus+=
sin22998sin693075153sin mt x xGM M I I
φ φ φ ==∆=
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 5467
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 5567
983116983119983123983124 983106983125983119983129983105983118983107983129 983117983109983124983112983119983108
Paralel Sinkage
Volume (DCEF)=Volume (W1ADW+BL1LC)
Damaged compartment is bounded on top
983116983119983123983124 983106983125983119983129983105983118983107983129 983117983109983124983112983119983108
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 5667
983116983119983123983124 983106983125983119983129983105983118983107983129 983117983109983124983112983119983108
bull It is assumed that displacement and location of vertical centre
of gravity does not change after damaged
983116983119983123983124 983106983125983119983129983105983118983107983129 983117983109983124983112983119983108
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 5767
983116983119983123983124 983106983125983119983129983105983118983107983129 983117983109983124983112983119983108
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 5867
The heel angle of damaged ship is determined by
where
d is the distance between the volume centre of damaged compartment
and the new longitudinal centre of floatation
wc=vc μ ρ
983116983119983123983124 983106983125983119983129983105983118983107983129 983117983109983124983112983119983108
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 5967
983116983119983123983124 983106983125983119983129983105983118983107983129 983117983109983124983112983119983108
983116983119983123983124 983106983125983119983129983105983118983107983129 983117983109983124983112983119983108
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 6067
Longitudinal Metacentre Height of a Damaged Ship
983116983119983123983124 983106983125983119983129983105983118983107983129 983117983109983124983112983119983108
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 6167
983110983151983154983159983137983154983140 983137983150983140 983137983142983156 983140983154983137983157983143983144983156983155 983137983142983156983141983154 983140983137983149983137983143983141983140
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 6267
983120983151983154983156 983105983142983156 983120983151983154983156 983110983151983154983141 983123983156983137983154983138983151983137983154983140 983105983142983156 983123983156983137983154983138983151983137983154983140 983110983151983154983159983137983154983140
I983150983145983156983145983137983148 D983154983137983157983143983144983156 983124 983124 983124 983124
983120983137983154983137983148983141983148 983123983145983150983147983137983143983141 +983152 +983152 +983152 +983120
H983141983141983148 983085983149983145 983085983149983145 +983149983155 +983149983155
983124983154983145983149 983085983156983147 +983156983138 983085983156983147 +983156983138
F983145983150983137983148 D983154983137983157983143983144983156 983124+983152983085983149983145983085983156983147 983124+983152983085983149983145+983156983138 983124+983152+983149983155983085983156983147 983124+983152+983149983155+983156983138
Table 1 Final Draughts for a starboard side damaged ship
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 6367
L983151983155983156 B983157983151983161983137983150983139983161 M983141983156983144983151983140
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 6467
L983151983155983156 B983157983151983161983137983150983139983161 M983141983156983144983151983140
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 6567
991266 A983142983156983141983154 983148983151983151983155983145983150983143 983156983144983141 983139983141983150983156983154983137983148 983139983151983149983152983137983154983156983149983141983150983156 983156983144983141
983159983137983156983141983154983152983148983137983150983141 983137983154983141983137 983145983155
991266 983124983151 983139983151983149983152983141983150983155983137983156983141 983142983151983154 983156983144983141 983148983151983155983155 983151983142 983138983157983151983161983137983150983139983161 983151983142 983156983144983141
983139983141983150983156983154983137983148 983139983151983149983152983137983154983156983149983141983150983156 983156983144983141 983140983154983137983142983156 983145983150983139983154983141983137983155983141983155 983156983151
2805)420()( m x Bl L A L
=minus=minus=
m A
T
L
I
L 875180
150==
nabla=
L983151983155983156 B983157983151983161983137983150983139983161 M983141983156983144983151983140
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 6667
991266 983124983144983141 983144983141983145983143983144983156 983151983142 983156983144983141 983139983141983150983156983141983154 983151983142 983138983157983151983161983137983150983139983161 983145983150983139983154983141983137983155983141983155 983156983151
991266 983124983144983141 983149983151983149983141983150983156 983151983142 983145983150983141983154983156983145983137 983151983142 983156983144983141 983159983137983156983141983154983152983148983137983150983141 983137983154983141983137
991266 983124983144983141 983149983141983156983137983139983141983150983156983154983145983139 983154983137983140983145983157983155
m
T
KB L
L 93802
8751
2 ===
433
6716612
)420(5
12
)(m
l L B I L
=minus
=minus
=
m I
BM
I
L
L 1111150
67166==
nabla
=
L983151983155983156 B983157983151983161983137983150983139983161 M983141983156983144983151983140
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 6767
991266 983124983144983141 983149983141983156983137983139983141983150983156983154983145983139 983144983141983145983143983144983156
991266 983122983145983143983144983156983145983150983143 983149983151983149983141983150983156 983142983151983154 983155983149983137983148983148 983144983141983141983148 983137983150983143983148983141983155
m KG BM KBGM L L L 54905111119380 =minus+=minus+=
mt xGM M L
sin34984sin549075153sin φ φ φ ==∆=
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 4467
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 4567
Longitudinal Metacentre Radius at final stage
Free Surface Effect
Damaged compartment can be considered as a half filled tank
Free Contact Effect
Damaged compartment can be considered as a half filled tank
T M H i h
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 4667
Transverse Metacentre Height
The angle of heel
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 4767
L it di l M t t H i ht
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 4867
Longitudinal Metacentre Height
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 4967
E983160983137983149983152983148983141 A 983138983137983154983143983141
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 5067
E983160983137983149983152983148983141 A 983138983137983154983143983141
991266 L = 20 983149991266 B = 5 983149
991266 983124 = 15 983149
991266 KG = 15 983149
I983150983156983137983139983156 C983151983150983140983145983156983145983151983150
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 5167
I983150983156983137983139983156 C983151983150983140983145983156983145983151983150
991266 983124983144983141 983140983145983155983152983148983137983139983141983149983141983150983156 983158983151983148983157983149983141
991266 983124983144983141 983149983137983155983155 983140983145983155983152983148983137983139983141983149983141983150983156
991266 983124983144983141 983149983151983149983141983150983156 983151983142 983145983150983141983154983156983145983137 983151983142 983156983144983141 983159983137983156983141983154983152983148983137983150983141 983137983154983141983137983137983138983151983157983156 CL
3
15051520 m x xT B L
I I
==sdotsdot=nabla
tons x I
751531500251 ==nablasdot=∆ ρ
433
33208
12
205
12
m x L B
I I
===
I983150983156983137983139983156 C983151983150983140983145983156983145983151983150
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 5267
I983150983156983137983139983156 C983151983150983140983145983156983145983151983150
991266 M983141983156983137983139983141983150983156983154983145983139 983154983137983140983145983157983155
991266 O983154 983145983156 983139983151983157983148983140 983138983141 983139983137983148983139983157983148983137983156983141983140 983140983145983154983141983139983156983148983161 983137983155
991266 H983141983145983143983144983156 983151983142 983156983144983141 983139983141983150983156983141983154 983151983142 983138983157983151983161983137983150983139983161
m I
BM
I
I 3891
150
33208==
nabla
=
m xT
B
LBT
L B BM
I I
I 3891
5112
5
12
12 223
====
mT
KB I
I 750
2
==
I983150983156983137983139983156 C983151983150983140983145983156983145983151983150
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 5367
991266 983124983144983141 983149983141983156983137983139983141983150983156983154983145983139 983144983141983145983143983144983156
991266 F983151983154 983155983149983137983148983148 983137983150983143983148983141983155 983151983142 983144983141983141983148 983156983144983141 983154983145983143983144983156983145983150983143 983149983151983149983141983150983156
m KG BM KBGM I I 63905013891750 =minus+=minus+=
sin22998sin693075153sin mt x xGM M I I
φ φ φ ==∆=
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 5467
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 5567
983116983119983123983124 983106983125983119983129983105983118983107983129 983117983109983124983112983119983108
Paralel Sinkage
Volume (DCEF)=Volume (W1ADW+BL1LC)
Damaged compartment is bounded on top
983116983119983123983124 983106983125983119983129983105983118983107983129 983117983109983124983112983119983108
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 5667
983116983119983123983124 983106983125983119983129983105983118983107983129 983117983109983124983112983119983108
bull It is assumed that displacement and location of vertical centre
of gravity does not change after damaged
983116983119983123983124 983106983125983119983129983105983118983107983129 983117983109983124983112983119983108
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 5767
983116983119983123983124 983106983125983119983129983105983118983107983129 983117983109983124983112983119983108
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 5867
The heel angle of damaged ship is determined by
where
d is the distance between the volume centre of damaged compartment
and the new longitudinal centre of floatation
wc=vc μ ρ
983116983119983123983124 983106983125983119983129983105983118983107983129 983117983109983124983112983119983108
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 5967
983116983119983123983124 983106983125983119983129983105983118983107983129 983117983109983124983112983119983108
983116983119983123983124 983106983125983119983129983105983118983107983129 983117983109983124983112983119983108
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 6067
Longitudinal Metacentre Height of a Damaged Ship
983116983119983123983124 983106983125983119983129983105983118983107983129 983117983109983124983112983119983108
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 6167
983110983151983154983159983137983154983140 983137983150983140 983137983142983156 983140983154983137983157983143983144983156983155 983137983142983156983141983154 983140983137983149983137983143983141983140
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 6267
983120983151983154983156 983105983142983156 983120983151983154983156 983110983151983154983141 983123983156983137983154983138983151983137983154983140 983105983142983156 983123983156983137983154983138983151983137983154983140 983110983151983154983159983137983154983140
I983150983145983156983145983137983148 D983154983137983157983143983144983156 983124 983124 983124 983124
983120983137983154983137983148983141983148 983123983145983150983147983137983143983141 +983152 +983152 +983152 +983120
H983141983141983148 983085983149983145 983085983149983145 +983149983155 +983149983155
983124983154983145983149 983085983156983147 +983156983138 983085983156983147 +983156983138
F983145983150983137983148 D983154983137983157983143983144983156 983124+983152983085983149983145983085983156983147 983124+983152983085983149983145+983156983138 983124+983152+983149983155983085983156983147 983124+983152+983149983155+983156983138
Table 1 Final Draughts for a starboard side damaged ship
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 6367
L983151983155983156 B983157983151983161983137983150983139983161 M983141983156983144983151983140
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 6467
L983151983155983156 B983157983151983161983137983150983139983161 M983141983156983144983151983140
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 6567
991266 A983142983156983141983154 983148983151983151983155983145983150983143 983156983144983141 983139983141983150983156983154983137983148 983139983151983149983152983137983154983156983149983141983150983156 983156983144983141
983159983137983156983141983154983152983148983137983150983141 983137983154983141983137 983145983155
991266 983124983151 983139983151983149983152983141983150983155983137983156983141 983142983151983154 983156983144983141 983148983151983155983155 983151983142 983138983157983151983161983137983150983139983161 983151983142 983156983144983141
983139983141983150983156983154983137983148 983139983151983149983152983137983154983156983149983141983150983156 983156983144983141 983140983154983137983142983156 983145983150983139983154983141983137983155983141983155 983156983151
2805)420()( m x Bl L A L
=minus=minus=
m A
T
L
I
L 875180
150==
nabla=
L983151983155983156 B983157983151983161983137983150983139983161 M983141983156983144983151983140
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 6667
991266 983124983144983141 983144983141983145983143983144983156 983151983142 983156983144983141 983139983141983150983156983141983154 983151983142 983138983157983151983161983137983150983139983161 983145983150983139983154983141983137983155983141983155 983156983151
991266 983124983144983141 983149983151983149983141983150983156 983151983142 983145983150983141983154983156983145983137 983151983142 983156983144983141 983159983137983156983141983154983152983148983137983150983141 983137983154983141983137
991266 983124983144983141 983149983141983156983137983139983141983150983156983154983145983139 983154983137983140983145983157983155
m
T
KB L
L 93802
8751
2 ===
433
6716612
)420(5
12
)(m
l L B I L
=minus
=minus
=
m I
BM
I
L
L 1111150
67166==
nabla
=
L983151983155983156 B983157983151983161983137983150983139983161 M983141983156983144983151983140
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 6767
991266 983124983144983141 983149983141983156983137983139983141983150983156983154983145983139 983144983141983145983143983144983156
991266 983122983145983143983144983156983145983150983143 983149983151983149983141983150983156 983142983151983154 983155983149983137983148983148 983144983141983141983148 983137983150983143983148983141983155
m KG BM KBGM L L L 54905111119380 =minus+=minus+=
mt xGM M L
sin34984sin549075153sin φ φ φ ==∆=
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 4567
Longitudinal Metacentre Radius at final stage
Free Surface Effect
Damaged compartment can be considered as a half filled tank
Free Contact Effect
Damaged compartment can be considered as a half filled tank
T M H i h
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 4667
Transverse Metacentre Height
The angle of heel
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 4767
L it di l M t t H i ht
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 4867
Longitudinal Metacentre Height
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 4967
E983160983137983149983152983148983141 A 983138983137983154983143983141
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 5067
E983160983137983149983152983148983141 A 983138983137983154983143983141
991266 L = 20 983149991266 B = 5 983149
991266 983124 = 15 983149
991266 KG = 15 983149
I983150983156983137983139983156 C983151983150983140983145983156983145983151983150
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 5167
I983150983156983137983139983156 C983151983150983140983145983156983145983151983150
991266 983124983144983141 983140983145983155983152983148983137983139983141983149983141983150983156 983158983151983148983157983149983141
991266 983124983144983141 983149983137983155983155 983140983145983155983152983148983137983139983141983149983141983150983156
991266 983124983144983141 983149983151983149983141983150983156 983151983142 983145983150983141983154983156983145983137 983151983142 983156983144983141 983159983137983156983141983154983152983148983137983150983141 983137983154983141983137983137983138983151983157983156 CL
3
15051520 m x xT B L
I I
==sdotsdot=nabla
tons x I
751531500251 ==nablasdot=∆ ρ
433
33208
12
205
12
m x L B
I I
===
I983150983156983137983139983156 C983151983150983140983145983156983145983151983150
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 5267
I983150983156983137983139983156 C983151983150983140983145983156983145983151983150
991266 M983141983156983137983139983141983150983156983154983145983139 983154983137983140983145983157983155
991266 O983154 983145983156 983139983151983157983148983140 983138983141 983139983137983148983139983157983148983137983156983141983140 983140983145983154983141983139983156983148983161 983137983155
991266 H983141983145983143983144983156 983151983142 983156983144983141 983139983141983150983156983141983154 983151983142 983138983157983151983161983137983150983139983161
m I
BM
I
I 3891
150
33208==
nabla
=
m xT
B
LBT
L B BM
I I
I 3891
5112
5
12
12 223
====
mT
KB I
I 750
2
==
I983150983156983137983139983156 C983151983150983140983145983156983145983151983150
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 5367
991266 983124983144983141 983149983141983156983137983139983141983150983156983154983145983139 983144983141983145983143983144983156
991266 F983151983154 983155983149983137983148983148 983137983150983143983148983141983155 983151983142 983144983141983141983148 983156983144983141 983154983145983143983144983156983145983150983143 983149983151983149983141983150983156
m KG BM KBGM I I 63905013891750 =minus+=minus+=
sin22998sin693075153sin mt x xGM M I I
φ φ φ ==∆=
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 5467
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 5567
983116983119983123983124 983106983125983119983129983105983118983107983129 983117983109983124983112983119983108
Paralel Sinkage
Volume (DCEF)=Volume (W1ADW+BL1LC)
Damaged compartment is bounded on top
983116983119983123983124 983106983125983119983129983105983118983107983129 983117983109983124983112983119983108
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 5667
983116983119983123983124 983106983125983119983129983105983118983107983129 983117983109983124983112983119983108
bull It is assumed that displacement and location of vertical centre
of gravity does not change after damaged
983116983119983123983124 983106983125983119983129983105983118983107983129 983117983109983124983112983119983108
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 5767
983116983119983123983124 983106983125983119983129983105983118983107983129 983117983109983124983112983119983108
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 5867
The heel angle of damaged ship is determined by
where
d is the distance between the volume centre of damaged compartment
and the new longitudinal centre of floatation
wc=vc μ ρ
983116983119983123983124 983106983125983119983129983105983118983107983129 983117983109983124983112983119983108
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 5967
983116983119983123983124 983106983125983119983129983105983118983107983129 983117983109983124983112983119983108
983116983119983123983124 983106983125983119983129983105983118983107983129 983117983109983124983112983119983108
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 6067
Longitudinal Metacentre Height of a Damaged Ship
983116983119983123983124 983106983125983119983129983105983118983107983129 983117983109983124983112983119983108
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 6167
983110983151983154983159983137983154983140 983137983150983140 983137983142983156 983140983154983137983157983143983144983156983155 983137983142983156983141983154 983140983137983149983137983143983141983140
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 6267
983120983151983154983156 983105983142983156 983120983151983154983156 983110983151983154983141 983123983156983137983154983138983151983137983154983140 983105983142983156 983123983156983137983154983138983151983137983154983140 983110983151983154983159983137983154983140
I983150983145983156983145983137983148 D983154983137983157983143983144983156 983124 983124 983124 983124
983120983137983154983137983148983141983148 983123983145983150983147983137983143983141 +983152 +983152 +983152 +983120
H983141983141983148 983085983149983145 983085983149983145 +983149983155 +983149983155
983124983154983145983149 983085983156983147 +983156983138 983085983156983147 +983156983138
F983145983150983137983148 D983154983137983157983143983144983156 983124+983152983085983149983145983085983156983147 983124+983152983085983149983145+983156983138 983124+983152+983149983155983085983156983147 983124+983152+983149983155+983156983138
Table 1 Final Draughts for a starboard side damaged ship
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 6367
L983151983155983156 B983157983151983161983137983150983139983161 M983141983156983144983151983140
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 6467
L983151983155983156 B983157983151983161983137983150983139983161 M983141983156983144983151983140
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 6567
991266 A983142983156983141983154 983148983151983151983155983145983150983143 983156983144983141 983139983141983150983156983154983137983148 983139983151983149983152983137983154983156983149983141983150983156 983156983144983141
983159983137983156983141983154983152983148983137983150983141 983137983154983141983137 983145983155
991266 983124983151 983139983151983149983152983141983150983155983137983156983141 983142983151983154 983156983144983141 983148983151983155983155 983151983142 983138983157983151983161983137983150983139983161 983151983142 983156983144983141
983139983141983150983156983154983137983148 983139983151983149983152983137983154983156983149983141983150983156 983156983144983141 983140983154983137983142983156 983145983150983139983154983141983137983155983141983155 983156983151
2805)420()( m x Bl L A L
=minus=minus=
m A
T
L
I
L 875180
150==
nabla=
L983151983155983156 B983157983151983161983137983150983139983161 M983141983156983144983151983140
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 6667
991266 983124983144983141 983144983141983145983143983144983156 983151983142 983156983144983141 983139983141983150983156983141983154 983151983142 983138983157983151983161983137983150983139983161 983145983150983139983154983141983137983155983141983155 983156983151
991266 983124983144983141 983149983151983149983141983150983156 983151983142 983145983150983141983154983156983145983137 983151983142 983156983144983141 983159983137983156983141983154983152983148983137983150983141 983137983154983141983137
991266 983124983144983141 983149983141983156983137983139983141983150983156983154983145983139 983154983137983140983145983157983155
m
T
KB L
L 93802
8751
2 ===
433
6716612
)420(5
12
)(m
l L B I L
=minus
=minus
=
m I
BM
I
L
L 1111150
67166==
nabla
=
L983151983155983156 B983157983151983161983137983150983139983161 M983141983156983144983151983140
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 6767
991266 983124983144983141 983149983141983156983137983139983141983150983156983154983145983139 983144983141983145983143983144983156
991266 983122983145983143983144983156983145983150983143 983149983151983149983141983150983156 983142983151983154 983155983149983137983148983148 983144983141983141983148 983137983150983143983148983141983155
m KG BM KBGM L L L 54905111119380 =minus+=minus+=
mt xGM M L
sin34984sin549075153sin φ φ φ ==∆=
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 4667
Transverse Metacentre Height
The angle of heel
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 4767
L it di l M t t H i ht
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 4867
Longitudinal Metacentre Height
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 4967
E983160983137983149983152983148983141 A 983138983137983154983143983141
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 5067
E983160983137983149983152983148983141 A 983138983137983154983143983141
991266 L = 20 983149991266 B = 5 983149
991266 983124 = 15 983149
991266 KG = 15 983149
I983150983156983137983139983156 C983151983150983140983145983156983145983151983150
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 5167
I983150983156983137983139983156 C983151983150983140983145983156983145983151983150
991266 983124983144983141 983140983145983155983152983148983137983139983141983149983141983150983156 983158983151983148983157983149983141
991266 983124983144983141 983149983137983155983155 983140983145983155983152983148983137983139983141983149983141983150983156
991266 983124983144983141 983149983151983149983141983150983156 983151983142 983145983150983141983154983156983145983137 983151983142 983156983144983141 983159983137983156983141983154983152983148983137983150983141 983137983154983141983137983137983138983151983157983156 CL
3
15051520 m x xT B L
I I
==sdotsdot=nabla
tons x I
751531500251 ==nablasdot=∆ ρ
433
33208
12
205
12
m x L B
I I
===
I983150983156983137983139983156 C983151983150983140983145983156983145983151983150
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 5267
I983150983156983137983139983156 C983151983150983140983145983156983145983151983150
991266 M983141983156983137983139983141983150983156983154983145983139 983154983137983140983145983157983155
991266 O983154 983145983156 983139983151983157983148983140 983138983141 983139983137983148983139983157983148983137983156983141983140 983140983145983154983141983139983156983148983161 983137983155
991266 H983141983145983143983144983156 983151983142 983156983144983141 983139983141983150983156983141983154 983151983142 983138983157983151983161983137983150983139983161
m I
BM
I
I 3891
150
33208==
nabla
=
m xT
B
LBT
L B BM
I I
I 3891
5112
5
12
12 223
====
mT
KB I
I 750
2
==
I983150983156983137983139983156 C983151983150983140983145983156983145983151983150
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 5367
991266 983124983144983141 983149983141983156983137983139983141983150983156983154983145983139 983144983141983145983143983144983156
991266 F983151983154 983155983149983137983148983148 983137983150983143983148983141983155 983151983142 983144983141983141983148 983156983144983141 983154983145983143983144983156983145983150983143 983149983151983149983141983150983156
m KG BM KBGM I I 63905013891750 =minus+=minus+=
sin22998sin693075153sin mt x xGM M I I
φ φ φ ==∆=
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 5467
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 5567
983116983119983123983124 983106983125983119983129983105983118983107983129 983117983109983124983112983119983108
Paralel Sinkage
Volume (DCEF)=Volume (W1ADW+BL1LC)
Damaged compartment is bounded on top
983116983119983123983124 983106983125983119983129983105983118983107983129 983117983109983124983112983119983108
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 5667
983116983119983123983124 983106983125983119983129983105983118983107983129 983117983109983124983112983119983108
bull It is assumed that displacement and location of vertical centre
of gravity does not change after damaged
983116983119983123983124 983106983125983119983129983105983118983107983129 983117983109983124983112983119983108
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 5767
983116983119983123983124 983106983125983119983129983105983118983107983129 983117983109983124983112983119983108
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 5867
The heel angle of damaged ship is determined by
where
d is the distance between the volume centre of damaged compartment
and the new longitudinal centre of floatation
wc=vc μ ρ
983116983119983123983124 983106983125983119983129983105983118983107983129 983117983109983124983112983119983108
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 5967
983116983119983123983124 983106983125983119983129983105983118983107983129 983117983109983124983112983119983108
983116983119983123983124 983106983125983119983129983105983118983107983129 983117983109983124983112983119983108
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 6067
Longitudinal Metacentre Height of a Damaged Ship
983116983119983123983124 983106983125983119983129983105983118983107983129 983117983109983124983112983119983108
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 6167
983110983151983154983159983137983154983140 983137983150983140 983137983142983156 983140983154983137983157983143983144983156983155 983137983142983156983141983154 983140983137983149983137983143983141983140
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 6267
983120983151983154983156 983105983142983156 983120983151983154983156 983110983151983154983141 983123983156983137983154983138983151983137983154983140 983105983142983156 983123983156983137983154983138983151983137983154983140 983110983151983154983159983137983154983140
I983150983145983156983145983137983148 D983154983137983157983143983144983156 983124 983124 983124 983124
983120983137983154983137983148983141983148 983123983145983150983147983137983143983141 +983152 +983152 +983152 +983120
H983141983141983148 983085983149983145 983085983149983145 +983149983155 +983149983155
983124983154983145983149 983085983156983147 +983156983138 983085983156983147 +983156983138
F983145983150983137983148 D983154983137983157983143983144983156 983124+983152983085983149983145983085983156983147 983124+983152983085983149983145+983156983138 983124+983152+983149983155983085983156983147 983124+983152+983149983155+983156983138
Table 1 Final Draughts for a starboard side damaged ship
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 6367
L983151983155983156 B983157983151983161983137983150983139983161 M983141983156983144983151983140
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 6467
L983151983155983156 B983157983151983161983137983150983139983161 M983141983156983144983151983140
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 6567
991266 A983142983156983141983154 983148983151983151983155983145983150983143 983156983144983141 983139983141983150983156983154983137983148 983139983151983149983152983137983154983156983149983141983150983156 983156983144983141
983159983137983156983141983154983152983148983137983150983141 983137983154983141983137 983145983155
991266 983124983151 983139983151983149983152983141983150983155983137983156983141 983142983151983154 983156983144983141 983148983151983155983155 983151983142 983138983157983151983161983137983150983139983161 983151983142 983156983144983141
983139983141983150983156983154983137983148 983139983151983149983152983137983154983156983149983141983150983156 983156983144983141 983140983154983137983142983156 983145983150983139983154983141983137983155983141983155 983156983151
2805)420()( m x Bl L A L
=minus=minus=
m A
T
L
I
L 875180
150==
nabla=
L983151983155983156 B983157983151983161983137983150983139983161 M983141983156983144983151983140
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 6667
991266 983124983144983141 983144983141983145983143983144983156 983151983142 983156983144983141 983139983141983150983156983141983154 983151983142 983138983157983151983161983137983150983139983161 983145983150983139983154983141983137983155983141983155 983156983151
991266 983124983144983141 983149983151983149983141983150983156 983151983142 983145983150983141983154983156983145983137 983151983142 983156983144983141 983159983137983156983141983154983152983148983137983150983141 983137983154983141983137
991266 983124983144983141 983149983141983156983137983139983141983150983156983154983145983139 983154983137983140983145983157983155
m
T
KB L
L 93802
8751
2 ===
433
6716612
)420(5
12
)(m
l L B I L
=minus
=minus
=
m I
BM
I
L
L 1111150
67166==
nabla
=
L983151983155983156 B983157983151983161983137983150983139983161 M983141983156983144983151983140
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 6767
991266 983124983144983141 983149983141983156983137983139983141983150983156983154983145983139 983144983141983145983143983144983156
991266 983122983145983143983144983156983145983150983143 983149983151983149983141983150983156 983142983151983154 983155983149983137983148983148 983144983141983141983148 983137983150983143983148983141983155
m KG BM KBGM L L L 54905111119380 =minus+=minus+=
mt xGM M L
sin34984sin549075153sin φ φ φ ==∆=
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 4767
L it di l M t t H i ht
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 4867
Longitudinal Metacentre Height
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 4967
E983160983137983149983152983148983141 A 983138983137983154983143983141
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 5067
E983160983137983149983152983148983141 A 983138983137983154983143983141
991266 L = 20 983149991266 B = 5 983149
991266 983124 = 15 983149
991266 KG = 15 983149
I983150983156983137983139983156 C983151983150983140983145983156983145983151983150
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 5167
I983150983156983137983139983156 C983151983150983140983145983156983145983151983150
991266 983124983144983141 983140983145983155983152983148983137983139983141983149983141983150983156 983158983151983148983157983149983141
991266 983124983144983141 983149983137983155983155 983140983145983155983152983148983137983139983141983149983141983150983156
991266 983124983144983141 983149983151983149983141983150983156 983151983142 983145983150983141983154983156983145983137 983151983142 983156983144983141 983159983137983156983141983154983152983148983137983150983141 983137983154983141983137983137983138983151983157983156 CL
3
15051520 m x xT B L
I I
==sdotsdot=nabla
tons x I
751531500251 ==nablasdot=∆ ρ
433
33208
12
205
12
m x L B
I I
===
I983150983156983137983139983156 C983151983150983140983145983156983145983151983150
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 5267
I983150983156983137983139983156 C983151983150983140983145983156983145983151983150
991266 M983141983156983137983139983141983150983156983154983145983139 983154983137983140983145983157983155
991266 O983154 983145983156 983139983151983157983148983140 983138983141 983139983137983148983139983157983148983137983156983141983140 983140983145983154983141983139983156983148983161 983137983155
991266 H983141983145983143983144983156 983151983142 983156983144983141 983139983141983150983156983141983154 983151983142 983138983157983151983161983137983150983139983161
m I
BM
I
I 3891
150
33208==
nabla
=
m xT
B
LBT
L B BM
I I
I 3891
5112
5
12
12 223
====
mT
KB I
I 750
2
==
I983150983156983137983139983156 C983151983150983140983145983156983145983151983150
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 5367
991266 983124983144983141 983149983141983156983137983139983141983150983156983154983145983139 983144983141983145983143983144983156
991266 F983151983154 983155983149983137983148983148 983137983150983143983148983141983155 983151983142 983144983141983141983148 983156983144983141 983154983145983143983144983156983145983150983143 983149983151983149983141983150983156
m KG BM KBGM I I 63905013891750 =minus+=minus+=
sin22998sin693075153sin mt x xGM M I I
φ φ φ ==∆=
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 5467
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 5567
983116983119983123983124 983106983125983119983129983105983118983107983129 983117983109983124983112983119983108
Paralel Sinkage
Volume (DCEF)=Volume (W1ADW+BL1LC)
Damaged compartment is bounded on top
983116983119983123983124 983106983125983119983129983105983118983107983129 983117983109983124983112983119983108
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 5667
983116983119983123983124 983106983125983119983129983105983118983107983129 983117983109983124983112983119983108
bull It is assumed that displacement and location of vertical centre
of gravity does not change after damaged
983116983119983123983124 983106983125983119983129983105983118983107983129 983117983109983124983112983119983108
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 5767
983116983119983123983124 983106983125983119983129983105983118983107983129 983117983109983124983112983119983108
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 5867
The heel angle of damaged ship is determined by
where
d is the distance between the volume centre of damaged compartment
and the new longitudinal centre of floatation
wc=vc μ ρ
983116983119983123983124 983106983125983119983129983105983118983107983129 983117983109983124983112983119983108
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 5967
983116983119983123983124 983106983125983119983129983105983118983107983129 983117983109983124983112983119983108
983116983119983123983124 983106983125983119983129983105983118983107983129 983117983109983124983112983119983108
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 6067
Longitudinal Metacentre Height of a Damaged Ship
983116983119983123983124 983106983125983119983129983105983118983107983129 983117983109983124983112983119983108
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 6167
983110983151983154983159983137983154983140 983137983150983140 983137983142983156 983140983154983137983157983143983144983156983155 983137983142983156983141983154 983140983137983149983137983143983141983140
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 6267
983120983151983154983156 983105983142983156 983120983151983154983156 983110983151983154983141 983123983156983137983154983138983151983137983154983140 983105983142983156 983123983156983137983154983138983151983137983154983140 983110983151983154983159983137983154983140
I983150983145983156983145983137983148 D983154983137983157983143983144983156 983124 983124 983124 983124
983120983137983154983137983148983141983148 983123983145983150983147983137983143983141 +983152 +983152 +983152 +983120
H983141983141983148 983085983149983145 983085983149983145 +983149983155 +983149983155
983124983154983145983149 983085983156983147 +983156983138 983085983156983147 +983156983138
F983145983150983137983148 D983154983137983157983143983144983156 983124+983152983085983149983145983085983156983147 983124+983152983085983149983145+983156983138 983124+983152+983149983155983085983156983147 983124+983152+983149983155+983156983138
Table 1 Final Draughts for a starboard side damaged ship
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 6367
L983151983155983156 B983157983151983161983137983150983139983161 M983141983156983144983151983140
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 6467
L983151983155983156 B983157983151983161983137983150983139983161 M983141983156983144983151983140
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 6567
991266 A983142983156983141983154 983148983151983151983155983145983150983143 983156983144983141 983139983141983150983156983154983137983148 983139983151983149983152983137983154983156983149983141983150983156 983156983144983141
983159983137983156983141983154983152983148983137983150983141 983137983154983141983137 983145983155
991266 983124983151 983139983151983149983152983141983150983155983137983156983141 983142983151983154 983156983144983141 983148983151983155983155 983151983142 983138983157983151983161983137983150983139983161 983151983142 983156983144983141
983139983141983150983156983154983137983148 983139983151983149983152983137983154983156983149983141983150983156 983156983144983141 983140983154983137983142983156 983145983150983139983154983141983137983155983141983155 983156983151
2805)420()( m x Bl L A L
=minus=minus=
m A
T
L
I
L 875180
150==
nabla=
L983151983155983156 B983157983151983161983137983150983139983161 M983141983156983144983151983140
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 6667
991266 983124983144983141 983144983141983145983143983144983156 983151983142 983156983144983141 983139983141983150983156983141983154 983151983142 983138983157983151983161983137983150983139983161 983145983150983139983154983141983137983155983141983155 983156983151
991266 983124983144983141 983149983151983149983141983150983156 983151983142 983145983150983141983154983156983145983137 983151983142 983156983144983141 983159983137983156983141983154983152983148983137983150983141 983137983154983141983137
991266 983124983144983141 983149983141983156983137983139983141983150983156983154983145983139 983154983137983140983145983157983155
m
T
KB L
L 93802
8751
2 ===
433
6716612
)420(5
12
)(m
l L B I L
=minus
=minus
=
m I
BM
I
L
L 1111150
67166==
nabla
=
L983151983155983156 B983157983151983161983137983150983139983161 M983141983156983144983151983140
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 6767
991266 983124983144983141 983149983141983156983137983139983141983150983156983154983145983139 983144983141983145983143983144983156
991266 983122983145983143983144983156983145983150983143 983149983151983149983141983150983156 983142983151983154 983155983149983137983148983148 983144983141983141983148 983137983150983143983148983141983155
m KG BM KBGM L L L 54905111119380 =minus+=minus+=
mt xGM M L
sin34984sin549075153sin φ φ φ ==∆=
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 4867
Longitudinal Metacentre Height
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 4967
E983160983137983149983152983148983141 A 983138983137983154983143983141
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 5067
E983160983137983149983152983148983141 A 983138983137983154983143983141
991266 L = 20 983149991266 B = 5 983149
991266 983124 = 15 983149
991266 KG = 15 983149
I983150983156983137983139983156 C983151983150983140983145983156983145983151983150
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 5167
I983150983156983137983139983156 C983151983150983140983145983156983145983151983150
991266 983124983144983141 983140983145983155983152983148983137983139983141983149983141983150983156 983158983151983148983157983149983141
991266 983124983144983141 983149983137983155983155 983140983145983155983152983148983137983139983141983149983141983150983156
991266 983124983144983141 983149983151983149983141983150983156 983151983142 983145983150983141983154983156983145983137 983151983142 983156983144983141 983159983137983156983141983154983152983148983137983150983141 983137983154983141983137983137983138983151983157983156 CL
3
15051520 m x xT B L
I I
==sdotsdot=nabla
tons x I
751531500251 ==nablasdot=∆ ρ
433
33208
12
205
12
m x L B
I I
===
I983150983156983137983139983156 C983151983150983140983145983156983145983151983150
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 5267
I983150983156983137983139983156 C983151983150983140983145983156983145983151983150
991266 M983141983156983137983139983141983150983156983154983145983139 983154983137983140983145983157983155
991266 O983154 983145983156 983139983151983157983148983140 983138983141 983139983137983148983139983157983148983137983156983141983140 983140983145983154983141983139983156983148983161 983137983155
991266 H983141983145983143983144983156 983151983142 983156983144983141 983139983141983150983156983141983154 983151983142 983138983157983151983161983137983150983139983161
m I
BM
I
I 3891
150
33208==
nabla
=
m xT
B
LBT
L B BM
I I
I 3891
5112
5
12
12 223
====
mT
KB I
I 750
2
==
I983150983156983137983139983156 C983151983150983140983145983156983145983151983150
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 5367
991266 983124983144983141 983149983141983156983137983139983141983150983156983154983145983139 983144983141983145983143983144983156
991266 F983151983154 983155983149983137983148983148 983137983150983143983148983141983155 983151983142 983144983141983141983148 983156983144983141 983154983145983143983144983156983145983150983143 983149983151983149983141983150983156
m KG BM KBGM I I 63905013891750 =minus+=minus+=
sin22998sin693075153sin mt x xGM M I I
φ φ φ ==∆=
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 5467
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 5567
983116983119983123983124 983106983125983119983129983105983118983107983129 983117983109983124983112983119983108
Paralel Sinkage
Volume (DCEF)=Volume (W1ADW+BL1LC)
Damaged compartment is bounded on top
983116983119983123983124 983106983125983119983129983105983118983107983129 983117983109983124983112983119983108
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 5667
983116983119983123983124 983106983125983119983129983105983118983107983129 983117983109983124983112983119983108
bull It is assumed that displacement and location of vertical centre
of gravity does not change after damaged
983116983119983123983124 983106983125983119983129983105983118983107983129 983117983109983124983112983119983108
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 5767
983116983119983123983124 983106983125983119983129983105983118983107983129 983117983109983124983112983119983108
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 5867
The heel angle of damaged ship is determined by
where
d is the distance between the volume centre of damaged compartment
and the new longitudinal centre of floatation
wc=vc μ ρ
983116983119983123983124 983106983125983119983129983105983118983107983129 983117983109983124983112983119983108
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 5967
983116983119983123983124 983106983125983119983129983105983118983107983129 983117983109983124983112983119983108
983116983119983123983124 983106983125983119983129983105983118983107983129 983117983109983124983112983119983108
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 6067
Longitudinal Metacentre Height of a Damaged Ship
983116983119983123983124 983106983125983119983129983105983118983107983129 983117983109983124983112983119983108
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 6167
983110983151983154983159983137983154983140 983137983150983140 983137983142983156 983140983154983137983157983143983144983156983155 983137983142983156983141983154 983140983137983149983137983143983141983140
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 6267
983120983151983154983156 983105983142983156 983120983151983154983156 983110983151983154983141 983123983156983137983154983138983151983137983154983140 983105983142983156 983123983156983137983154983138983151983137983154983140 983110983151983154983159983137983154983140
I983150983145983156983145983137983148 D983154983137983157983143983144983156 983124 983124 983124 983124
983120983137983154983137983148983141983148 983123983145983150983147983137983143983141 +983152 +983152 +983152 +983120
H983141983141983148 983085983149983145 983085983149983145 +983149983155 +983149983155
983124983154983145983149 983085983156983147 +983156983138 983085983156983147 +983156983138
F983145983150983137983148 D983154983137983157983143983144983156 983124+983152983085983149983145983085983156983147 983124+983152983085983149983145+983156983138 983124+983152+983149983155983085983156983147 983124+983152+983149983155+983156983138
Table 1 Final Draughts for a starboard side damaged ship
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 6367
L983151983155983156 B983157983151983161983137983150983139983161 M983141983156983144983151983140
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 6467
L983151983155983156 B983157983151983161983137983150983139983161 M983141983156983144983151983140
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 6567
991266 A983142983156983141983154 983148983151983151983155983145983150983143 983156983144983141 983139983141983150983156983154983137983148 983139983151983149983152983137983154983156983149983141983150983156 983156983144983141
983159983137983156983141983154983152983148983137983150983141 983137983154983141983137 983145983155
991266 983124983151 983139983151983149983152983141983150983155983137983156983141 983142983151983154 983156983144983141 983148983151983155983155 983151983142 983138983157983151983161983137983150983139983161 983151983142 983156983144983141
983139983141983150983156983154983137983148 983139983151983149983152983137983154983156983149983141983150983156 983156983144983141 983140983154983137983142983156 983145983150983139983154983141983137983155983141983155 983156983151
2805)420()( m x Bl L A L
=minus=minus=
m A
T
L
I
L 875180
150==
nabla=
L983151983155983156 B983157983151983161983137983150983139983161 M983141983156983144983151983140
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 6667
991266 983124983144983141 983144983141983145983143983144983156 983151983142 983156983144983141 983139983141983150983156983141983154 983151983142 983138983157983151983161983137983150983139983161 983145983150983139983154983141983137983155983141983155 983156983151
991266 983124983144983141 983149983151983149983141983150983156 983151983142 983145983150983141983154983156983145983137 983151983142 983156983144983141 983159983137983156983141983154983152983148983137983150983141 983137983154983141983137
991266 983124983144983141 983149983141983156983137983139983141983150983156983154983145983139 983154983137983140983145983157983155
m
T
KB L
L 93802
8751
2 ===
433
6716612
)420(5
12
)(m
l L B I L
=minus
=minus
=
m I
BM
I
L
L 1111150
67166==
nabla
=
L983151983155983156 B983157983151983161983137983150983139983161 M983141983156983144983151983140
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 6767
991266 983124983144983141 983149983141983156983137983139983141983150983156983154983145983139 983144983141983145983143983144983156
991266 983122983145983143983144983156983145983150983143 983149983151983149983141983150983156 983142983151983154 983155983149983137983148983148 983144983141983141983148 983137983150983143983148983141983155
m KG BM KBGM L L L 54905111119380 =minus+=minus+=
mt xGM M L
sin34984sin549075153sin φ φ φ ==∆=
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 4967
E983160983137983149983152983148983141 A 983138983137983154983143983141
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 5067
E983160983137983149983152983148983141 A 983138983137983154983143983141
991266 L = 20 983149991266 B = 5 983149
991266 983124 = 15 983149
991266 KG = 15 983149
I983150983156983137983139983156 C983151983150983140983145983156983145983151983150
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 5167
I983150983156983137983139983156 C983151983150983140983145983156983145983151983150
991266 983124983144983141 983140983145983155983152983148983137983139983141983149983141983150983156 983158983151983148983157983149983141
991266 983124983144983141 983149983137983155983155 983140983145983155983152983148983137983139983141983149983141983150983156
991266 983124983144983141 983149983151983149983141983150983156 983151983142 983145983150983141983154983156983145983137 983151983142 983156983144983141 983159983137983156983141983154983152983148983137983150983141 983137983154983141983137983137983138983151983157983156 CL
3
15051520 m x xT B L
I I
==sdotsdot=nabla
tons x I
751531500251 ==nablasdot=∆ ρ
433
33208
12
205
12
m x L B
I I
===
I983150983156983137983139983156 C983151983150983140983145983156983145983151983150
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 5267
I983150983156983137983139983156 C983151983150983140983145983156983145983151983150
991266 M983141983156983137983139983141983150983156983154983145983139 983154983137983140983145983157983155
991266 O983154 983145983156 983139983151983157983148983140 983138983141 983139983137983148983139983157983148983137983156983141983140 983140983145983154983141983139983156983148983161 983137983155
991266 H983141983145983143983144983156 983151983142 983156983144983141 983139983141983150983156983141983154 983151983142 983138983157983151983161983137983150983139983161
m I
BM
I
I 3891
150
33208==
nabla
=
m xT
B
LBT
L B BM
I I
I 3891
5112
5
12
12 223
====
mT
KB I
I 750
2
==
I983150983156983137983139983156 C983151983150983140983145983156983145983151983150
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 5367
991266 983124983144983141 983149983141983156983137983139983141983150983156983154983145983139 983144983141983145983143983144983156
991266 F983151983154 983155983149983137983148983148 983137983150983143983148983141983155 983151983142 983144983141983141983148 983156983144983141 983154983145983143983144983156983145983150983143 983149983151983149983141983150983156
m KG BM KBGM I I 63905013891750 =minus+=minus+=
sin22998sin693075153sin mt x xGM M I I
φ φ φ ==∆=
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 5467
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 5567
983116983119983123983124 983106983125983119983129983105983118983107983129 983117983109983124983112983119983108
Paralel Sinkage
Volume (DCEF)=Volume (W1ADW+BL1LC)
Damaged compartment is bounded on top
983116983119983123983124 983106983125983119983129983105983118983107983129 983117983109983124983112983119983108
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 5667
983116983119983123983124 983106983125983119983129983105983118983107983129 983117983109983124983112983119983108
bull It is assumed that displacement and location of vertical centre
of gravity does not change after damaged
983116983119983123983124 983106983125983119983129983105983118983107983129 983117983109983124983112983119983108
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 5767
983116983119983123983124 983106983125983119983129983105983118983107983129 983117983109983124983112983119983108
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 5867
The heel angle of damaged ship is determined by
where
d is the distance between the volume centre of damaged compartment
and the new longitudinal centre of floatation
wc=vc μ ρ
983116983119983123983124 983106983125983119983129983105983118983107983129 983117983109983124983112983119983108
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 5967
983116983119983123983124 983106983125983119983129983105983118983107983129 983117983109983124983112983119983108
983116983119983123983124 983106983125983119983129983105983118983107983129 983117983109983124983112983119983108
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 6067
Longitudinal Metacentre Height of a Damaged Ship
983116983119983123983124 983106983125983119983129983105983118983107983129 983117983109983124983112983119983108
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 6167
983110983151983154983159983137983154983140 983137983150983140 983137983142983156 983140983154983137983157983143983144983156983155 983137983142983156983141983154 983140983137983149983137983143983141983140
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 6267
983120983151983154983156 983105983142983156 983120983151983154983156 983110983151983154983141 983123983156983137983154983138983151983137983154983140 983105983142983156 983123983156983137983154983138983151983137983154983140 983110983151983154983159983137983154983140
I983150983145983156983145983137983148 D983154983137983157983143983144983156 983124 983124 983124 983124
983120983137983154983137983148983141983148 983123983145983150983147983137983143983141 +983152 +983152 +983152 +983120
H983141983141983148 983085983149983145 983085983149983145 +983149983155 +983149983155
983124983154983145983149 983085983156983147 +983156983138 983085983156983147 +983156983138
F983145983150983137983148 D983154983137983157983143983144983156 983124+983152983085983149983145983085983156983147 983124+983152983085983149983145+983156983138 983124+983152+983149983155983085983156983147 983124+983152+983149983155+983156983138
Table 1 Final Draughts for a starboard side damaged ship
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 6367
L983151983155983156 B983157983151983161983137983150983139983161 M983141983156983144983151983140
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 6467
L983151983155983156 B983157983151983161983137983150983139983161 M983141983156983144983151983140
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 6567
991266 A983142983156983141983154 983148983151983151983155983145983150983143 983156983144983141 983139983141983150983156983154983137983148 983139983151983149983152983137983154983156983149983141983150983156 983156983144983141
983159983137983156983141983154983152983148983137983150983141 983137983154983141983137 983145983155
991266 983124983151 983139983151983149983152983141983150983155983137983156983141 983142983151983154 983156983144983141 983148983151983155983155 983151983142 983138983157983151983161983137983150983139983161 983151983142 983156983144983141
983139983141983150983156983154983137983148 983139983151983149983152983137983154983156983149983141983150983156 983156983144983141 983140983154983137983142983156 983145983150983139983154983141983137983155983141983155 983156983151
2805)420()( m x Bl L A L
=minus=minus=
m A
T
L
I
L 875180
150==
nabla=
L983151983155983156 B983157983151983161983137983150983139983161 M983141983156983144983151983140
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 6667
991266 983124983144983141 983144983141983145983143983144983156 983151983142 983156983144983141 983139983141983150983156983141983154 983151983142 983138983157983151983161983137983150983139983161 983145983150983139983154983141983137983155983141983155 983156983151
991266 983124983144983141 983149983151983149983141983150983156 983151983142 983145983150983141983154983156983145983137 983151983142 983156983144983141 983159983137983156983141983154983152983148983137983150983141 983137983154983141983137
991266 983124983144983141 983149983141983156983137983139983141983150983156983154983145983139 983154983137983140983145983157983155
m
T
KB L
L 93802
8751
2 ===
433
6716612
)420(5
12
)(m
l L B I L
=minus
=minus
=
m I
BM
I
L
L 1111150
67166==
nabla
=
L983151983155983156 B983157983151983161983137983150983139983161 M983141983156983144983151983140
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 6767
991266 983124983144983141 983149983141983156983137983139983141983150983156983154983145983139 983144983141983145983143983144983156
991266 983122983145983143983144983156983145983150983143 983149983151983149983141983150983156 983142983151983154 983155983149983137983148983148 983144983141983141983148 983137983150983143983148983141983155
m KG BM KBGM L L L 54905111119380 =minus+=minus+=
mt xGM M L
sin34984sin549075153sin φ φ φ ==∆=
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 5067
E983160983137983149983152983148983141 A 983138983137983154983143983141
991266 L = 20 983149991266 B = 5 983149
991266 983124 = 15 983149
991266 KG = 15 983149
I983150983156983137983139983156 C983151983150983140983145983156983145983151983150
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 5167
I983150983156983137983139983156 C983151983150983140983145983156983145983151983150
991266 983124983144983141 983140983145983155983152983148983137983139983141983149983141983150983156 983158983151983148983157983149983141
991266 983124983144983141 983149983137983155983155 983140983145983155983152983148983137983139983141983149983141983150983156
991266 983124983144983141 983149983151983149983141983150983156 983151983142 983145983150983141983154983156983145983137 983151983142 983156983144983141 983159983137983156983141983154983152983148983137983150983141 983137983154983141983137983137983138983151983157983156 CL
3
15051520 m x xT B L
I I
==sdotsdot=nabla
tons x I
751531500251 ==nablasdot=∆ ρ
433
33208
12
205
12
m x L B
I I
===
I983150983156983137983139983156 C983151983150983140983145983156983145983151983150
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 5267
I983150983156983137983139983156 C983151983150983140983145983156983145983151983150
991266 M983141983156983137983139983141983150983156983154983145983139 983154983137983140983145983157983155
991266 O983154 983145983156 983139983151983157983148983140 983138983141 983139983137983148983139983157983148983137983156983141983140 983140983145983154983141983139983156983148983161 983137983155
991266 H983141983145983143983144983156 983151983142 983156983144983141 983139983141983150983156983141983154 983151983142 983138983157983151983161983137983150983139983161
m I
BM
I
I 3891
150
33208==
nabla
=
m xT
B
LBT
L B BM
I I
I 3891
5112
5
12
12 223
====
mT
KB I
I 750
2
==
I983150983156983137983139983156 C983151983150983140983145983156983145983151983150
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 5367
991266 983124983144983141 983149983141983156983137983139983141983150983156983154983145983139 983144983141983145983143983144983156
991266 F983151983154 983155983149983137983148983148 983137983150983143983148983141983155 983151983142 983144983141983141983148 983156983144983141 983154983145983143983144983156983145983150983143 983149983151983149983141983150983156
m KG BM KBGM I I 63905013891750 =minus+=minus+=
sin22998sin693075153sin mt x xGM M I I
φ φ φ ==∆=
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 5467
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 5567
983116983119983123983124 983106983125983119983129983105983118983107983129 983117983109983124983112983119983108
Paralel Sinkage
Volume (DCEF)=Volume (W1ADW+BL1LC)
Damaged compartment is bounded on top
983116983119983123983124 983106983125983119983129983105983118983107983129 983117983109983124983112983119983108
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 5667
983116983119983123983124 983106983125983119983129983105983118983107983129 983117983109983124983112983119983108
bull It is assumed that displacement and location of vertical centre
of gravity does not change after damaged
983116983119983123983124 983106983125983119983129983105983118983107983129 983117983109983124983112983119983108
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 5767
983116983119983123983124 983106983125983119983129983105983118983107983129 983117983109983124983112983119983108
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 5867
The heel angle of damaged ship is determined by
where
d is the distance between the volume centre of damaged compartment
and the new longitudinal centre of floatation
wc=vc μ ρ
983116983119983123983124 983106983125983119983129983105983118983107983129 983117983109983124983112983119983108
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 5967
983116983119983123983124 983106983125983119983129983105983118983107983129 983117983109983124983112983119983108
983116983119983123983124 983106983125983119983129983105983118983107983129 983117983109983124983112983119983108
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 6067
Longitudinal Metacentre Height of a Damaged Ship
983116983119983123983124 983106983125983119983129983105983118983107983129 983117983109983124983112983119983108
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 6167
983110983151983154983159983137983154983140 983137983150983140 983137983142983156 983140983154983137983157983143983144983156983155 983137983142983156983141983154 983140983137983149983137983143983141983140
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 6267
983120983151983154983156 983105983142983156 983120983151983154983156 983110983151983154983141 983123983156983137983154983138983151983137983154983140 983105983142983156 983123983156983137983154983138983151983137983154983140 983110983151983154983159983137983154983140
I983150983145983156983145983137983148 D983154983137983157983143983144983156 983124 983124 983124 983124
983120983137983154983137983148983141983148 983123983145983150983147983137983143983141 +983152 +983152 +983152 +983120
H983141983141983148 983085983149983145 983085983149983145 +983149983155 +983149983155
983124983154983145983149 983085983156983147 +983156983138 983085983156983147 +983156983138
F983145983150983137983148 D983154983137983157983143983144983156 983124+983152983085983149983145983085983156983147 983124+983152983085983149983145+983156983138 983124+983152+983149983155983085983156983147 983124+983152+983149983155+983156983138
Table 1 Final Draughts for a starboard side damaged ship
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 6367
L983151983155983156 B983157983151983161983137983150983139983161 M983141983156983144983151983140
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 6467
L983151983155983156 B983157983151983161983137983150983139983161 M983141983156983144983151983140
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 6567
991266 A983142983156983141983154 983148983151983151983155983145983150983143 983156983144983141 983139983141983150983156983154983137983148 983139983151983149983152983137983154983156983149983141983150983156 983156983144983141
983159983137983156983141983154983152983148983137983150983141 983137983154983141983137 983145983155
991266 983124983151 983139983151983149983152983141983150983155983137983156983141 983142983151983154 983156983144983141 983148983151983155983155 983151983142 983138983157983151983161983137983150983139983161 983151983142 983156983144983141
983139983141983150983156983154983137983148 983139983151983149983152983137983154983156983149983141983150983156 983156983144983141 983140983154983137983142983156 983145983150983139983154983141983137983155983141983155 983156983151
2805)420()( m x Bl L A L
=minus=minus=
m A
T
L
I
L 875180
150==
nabla=
L983151983155983156 B983157983151983161983137983150983139983161 M983141983156983144983151983140
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 6667
991266 983124983144983141 983144983141983145983143983144983156 983151983142 983156983144983141 983139983141983150983156983141983154 983151983142 983138983157983151983161983137983150983139983161 983145983150983139983154983141983137983155983141983155 983156983151
991266 983124983144983141 983149983151983149983141983150983156 983151983142 983145983150983141983154983156983145983137 983151983142 983156983144983141 983159983137983156983141983154983152983148983137983150983141 983137983154983141983137
991266 983124983144983141 983149983141983156983137983139983141983150983156983154983145983139 983154983137983140983145983157983155
m
T
KB L
L 93802
8751
2 ===
433
6716612
)420(5
12
)(m
l L B I L
=minus
=minus
=
m I
BM
I
L
L 1111150
67166==
nabla
=
L983151983155983156 B983157983151983161983137983150983139983161 M983141983156983144983151983140
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 6767
991266 983124983144983141 983149983141983156983137983139983141983150983156983154983145983139 983144983141983145983143983144983156
991266 983122983145983143983144983156983145983150983143 983149983151983149983141983150983156 983142983151983154 983155983149983137983148983148 983144983141983141983148 983137983150983143983148983141983155
m KG BM KBGM L L L 54905111119380 =minus+=minus+=
mt xGM M L
sin34984sin549075153sin φ φ φ ==∆=
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 5167
I983150983156983137983139983156 C983151983150983140983145983156983145983151983150
991266 983124983144983141 983140983145983155983152983148983137983139983141983149983141983150983156 983158983151983148983157983149983141
991266 983124983144983141 983149983137983155983155 983140983145983155983152983148983137983139983141983149983141983150983156
991266 983124983144983141 983149983151983149983141983150983156 983151983142 983145983150983141983154983156983145983137 983151983142 983156983144983141 983159983137983156983141983154983152983148983137983150983141 983137983154983141983137983137983138983151983157983156 CL
3
15051520 m x xT B L
I I
==sdotsdot=nabla
tons x I
751531500251 ==nablasdot=∆ ρ
433
33208
12
205
12
m x L B
I I
===
I983150983156983137983139983156 C983151983150983140983145983156983145983151983150
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 5267
I983150983156983137983139983156 C983151983150983140983145983156983145983151983150
991266 M983141983156983137983139983141983150983156983154983145983139 983154983137983140983145983157983155
991266 O983154 983145983156 983139983151983157983148983140 983138983141 983139983137983148983139983157983148983137983156983141983140 983140983145983154983141983139983156983148983161 983137983155
991266 H983141983145983143983144983156 983151983142 983156983144983141 983139983141983150983156983141983154 983151983142 983138983157983151983161983137983150983139983161
m I
BM
I
I 3891
150
33208==
nabla
=
m xT
B
LBT
L B BM
I I
I 3891
5112
5
12
12 223
====
mT
KB I
I 750
2
==
I983150983156983137983139983156 C983151983150983140983145983156983145983151983150
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 5367
991266 983124983144983141 983149983141983156983137983139983141983150983156983154983145983139 983144983141983145983143983144983156
991266 F983151983154 983155983149983137983148983148 983137983150983143983148983141983155 983151983142 983144983141983141983148 983156983144983141 983154983145983143983144983156983145983150983143 983149983151983149983141983150983156
m KG BM KBGM I I 63905013891750 =minus+=minus+=
sin22998sin693075153sin mt x xGM M I I
φ φ φ ==∆=
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 5467
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 5567
983116983119983123983124 983106983125983119983129983105983118983107983129 983117983109983124983112983119983108
Paralel Sinkage
Volume (DCEF)=Volume (W1ADW+BL1LC)
Damaged compartment is bounded on top
983116983119983123983124 983106983125983119983129983105983118983107983129 983117983109983124983112983119983108
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 5667
983116983119983123983124 983106983125983119983129983105983118983107983129 983117983109983124983112983119983108
bull It is assumed that displacement and location of vertical centre
of gravity does not change after damaged
983116983119983123983124 983106983125983119983129983105983118983107983129 983117983109983124983112983119983108
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 5767
983116983119983123983124 983106983125983119983129983105983118983107983129 983117983109983124983112983119983108
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 5867
The heel angle of damaged ship is determined by
where
d is the distance between the volume centre of damaged compartment
and the new longitudinal centre of floatation
wc=vc μ ρ
983116983119983123983124 983106983125983119983129983105983118983107983129 983117983109983124983112983119983108
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 5967
983116983119983123983124 983106983125983119983129983105983118983107983129 983117983109983124983112983119983108
983116983119983123983124 983106983125983119983129983105983118983107983129 983117983109983124983112983119983108
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 6067
Longitudinal Metacentre Height of a Damaged Ship
983116983119983123983124 983106983125983119983129983105983118983107983129 983117983109983124983112983119983108
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 6167
983110983151983154983159983137983154983140 983137983150983140 983137983142983156 983140983154983137983157983143983144983156983155 983137983142983156983141983154 983140983137983149983137983143983141983140
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 6267
983120983151983154983156 983105983142983156 983120983151983154983156 983110983151983154983141 983123983156983137983154983138983151983137983154983140 983105983142983156 983123983156983137983154983138983151983137983154983140 983110983151983154983159983137983154983140
I983150983145983156983145983137983148 D983154983137983157983143983144983156 983124 983124 983124 983124
983120983137983154983137983148983141983148 983123983145983150983147983137983143983141 +983152 +983152 +983152 +983120
H983141983141983148 983085983149983145 983085983149983145 +983149983155 +983149983155
983124983154983145983149 983085983156983147 +983156983138 983085983156983147 +983156983138
F983145983150983137983148 D983154983137983157983143983144983156 983124+983152983085983149983145983085983156983147 983124+983152983085983149983145+983156983138 983124+983152+983149983155983085983156983147 983124+983152+983149983155+983156983138
Table 1 Final Draughts for a starboard side damaged ship
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 6367
L983151983155983156 B983157983151983161983137983150983139983161 M983141983156983144983151983140
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 6467
L983151983155983156 B983157983151983161983137983150983139983161 M983141983156983144983151983140
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 6567
991266 A983142983156983141983154 983148983151983151983155983145983150983143 983156983144983141 983139983141983150983156983154983137983148 983139983151983149983152983137983154983156983149983141983150983156 983156983144983141
983159983137983156983141983154983152983148983137983150983141 983137983154983141983137 983145983155
991266 983124983151 983139983151983149983152983141983150983155983137983156983141 983142983151983154 983156983144983141 983148983151983155983155 983151983142 983138983157983151983161983137983150983139983161 983151983142 983156983144983141
983139983141983150983156983154983137983148 983139983151983149983152983137983154983156983149983141983150983156 983156983144983141 983140983154983137983142983156 983145983150983139983154983141983137983155983141983155 983156983151
2805)420()( m x Bl L A L
=minus=minus=
m A
T
L
I
L 875180
150==
nabla=
L983151983155983156 B983157983151983161983137983150983139983161 M983141983156983144983151983140
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 6667
991266 983124983144983141 983144983141983145983143983144983156 983151983142 983156983144983141 983139983141983150983156983141983154 983151983142 983138983157983151983161983137983150983139983161 983145983150983139983154983141983137983155983141983155 983156983151
991266 983124983144983141 983149983151983149983141983150983156 983151983142 983145983150983141983154983156983145983137 983151983142 983156983144983141 983159983137983156983141983154983152983148983137983150983141 983137983154983141983137
991266 983124983144983141 983149983141983156983137983139983141983150983156983154983145983139 983154983137983140983145983157983155
m
T
KB L
L 93802
8751
2 ===
433
6716612
)420(5
12
)(m
l L B I L
=minus
=minus
=
m I
BM
I
L
L 1111150
67166==
nabla
=
L983151983155983156 B983157983151983161983137983150983139983161 M983141983156983144983151983140
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 6767
991266 983124983144983141 983149983141983156983137983139983141983150983156983154983145983139 983144983141983145983143983144983156
991266 983122983145983143983144983156983145983150983143 983149983151983149983141983150983156 983142983151983154 983155983149983137983148983148 983144983141983141983148 983137983150983143983148983141983155
m KG BM KBGM L L L 54905111119380 =minus+=minus+=
mt xGM M L
sin34984sin549075153sin φ φ φ ==∆=
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 5267
I983150983156983137983139983156 C983151983150983140983145983156983145983151983150
991266 M983141983156983137983139983141983150983156983154983145983139 983154983137983140983145983157983155
991266 O983154 983145983156 983139983151983157983148983140 983138983141 983139983137983148983139983157983148983137983156983141983140 983140983145983154983141983139983156983148983161 983137983155
991266 H983141983145983143983144983156 983151983142 983156983144983141 983139983141983150983156983141983154 983151983142 983138983157983151983161983137983150983139983161
m I
BM
I
I 3891
150
33208==
nabla
=
m xT
B
LBT
L B BM
I I
I 3891
5112
5
12
12 223
====
mT
KB I
I 750
2
==
I983150983156983137983139983156 C983151983150983140983145983156983145983151983150
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 5367
991266 983124983144983141 983149983141983156983137983139983141983150983156983154983145983139 983144983141983145983143983144983156
991266 F983151983154 983155983149983137983148983148 983137983150983143983148983141983155 983151983142 983144983141983141983148 983156983144983141 983154983145983143983144983156983145983150983143 983149983151983149983141983150983156
m KG BM KBGM I I 63905013891750 =minus+=minus+=
sin22998sin693075153sin mt x xGM M I I
φ φ φ ==∆=
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 5467
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 5567
983116983119983123983124 983106983125983119983129983105983118983107983129 983117983109983124983112983119983108
Paralel Sinkage
Volume (DCEF)=Volume (W1ADW+BL1LC)
Damaged compartment is bounded on top
983116983119983123983124 983106983125983119983129983105983118983107983129 983117983109983124983112983119983108
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 5667
983116983119983123983124 983106983125983119983129983105983118983107983129 983117983109983124983112983119983108
bull It is assumed that displacement and location of vertical centre
of gravity does not change after damaged
983116983119983123983124 983106983125983119983129983105983118983107983129 983117983109983124983112983119983108
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 5767
983116983119983123983124 983106983125983119983129983105983118983107983129 983117983109983124983112983119983108
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 5867
The heel angle of damaged ship is determined by
where
d is the distance between the volume centre of damaged compartment
and the new longitudinal centre of floatation
wc=vc μ ρ
983116983119983123983124 983106983125983119983129983105983118983107983129 983117983109983124983112983119983108
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 5967
983116983119983123983124 983106983125983119983129983105983118983107983129 983117983109983124983112983119983108
983116983119983123983124 983106983125983119983129983105983118983107983129 983117983109983124983112983119983108
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 6067
Longitudinal Metacentre Height of a Damaged Ship
983116983119983123983124 983106983125983119983129983105983118983107983129 983117983109983124983112983119983108
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 6167
983110983151983154983159983137983154983140 983137983150983140 983137983142983156 983140983154983137983157983143983144983156983155 983137983142983156983141983154 983140983137983149983137983143983141983140
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 6267
983120983151983154983156 983105983142983156 983120983151983154983156 983110983151983154983141 983123983156983137983154983138983151983137983154983140 983105983142983156 983123983156983137983154983138983151983137983154983140 983110983151983154983159983137983154983140
I983150983145983156983145983137983148 D983154983137983157983143983144983156 983124 983124 983124 983124
983120983137983154983137983148983141983148 983123983145983150983147983137983143983141 +983152 +983152 +983152 +983120
H983141983141983148 983085983149983145 983085983149983145 +983149983155 +983149983155
983124983154983145983149 983085983156983147 +983156983138 983085983156983147 +983156983138
F983145983150983137983148 D983154983137983157983143983144983156 983124+983152983085983149983145983085983156983147 983124+983152983085983149983145+983156983138 983124+983152+983149983155983085983156983147 983124+983152+983149983155+983156983138
Table 1 Final Draughts for a starboard side damaged ship
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 6367
L983151983155983156 B983157983151983161983137983150983139983161 M983141983156983144983151983140
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 6467
L983151983155983156 B983157983151983161983137983150983139983161 M983141983156983144983151983140
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 6567
991266 A983142983156983141983154 983148983151983151983155983145983150983143 983156983144983141 983139983141983150983156983154983137983148 983139983151983149983152983137983154983156983149983141983150983156 983156983144983141
983159983137983156983141983154983152983148983137983150983141 983137983154983141983137 983145983155
991266 983124983151 983139983151983149983152983141983150983155983137983156983141 983142983151983154 983156983144983141 983148983151983155983155 983151983142 983138983157983151983161983137983150983139983161 983151983142 983156983144983141
983139983141983150983156983154983137983148 983139983151983149983152983137983154983156983149983141983150983156 983156983144983141 983140983154983137983142983156 983145983150983139983154983141983137983155983141983155 983156983151
2805)420()( m x Bl L A L
=minus=minus=
m A
T
L
I
L 875180
150==
nabla=
L983151983155983156 B983157983151983161983137983150983139983161 M983141983156983144983151983140
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 6667
991266 983124983144983141 983144983141983145983143983144983156 983151983142 983156983144983141 983139983141983150983156983141983154 983151983142 983138983157983151983161983137983150983139983161 983145983150983139983154983141983137983155983141983155 983156983151
991266 983124983144983141 983149983151983149983141983150983156 983151983142 983145983150983141983154983156983145983137 983151983142 983156983144983141 983159983137983156983141983154983152983148983137983150983141 983137983154983141983137
991266 983124983144983141 983149983141983156983137983139983141983150983156983154983145983139 983154983137983140983145983157983155
m
T
KB L
L 93802
8751
2 ===
433
6716612
)420(5
12
)(m
l L B I L
=minus
=minus
=
m I
BM
I
L
L 1111150
67166==
nabla
=
L983151983155983156 B983157983151983161983137983150983139983161 M983141983156983144983151983140
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 6767
991266 983124983144983141 983149983141983156983137983139983141983150983156983154983145983139 983144983141983145983143983144983156
991266 983122983145983143983144983156983145983150983143 983149983151983149983141983150983156 983142983151983154 983155983149983137983148983148 983144983141983141983148 983137983150983143983148983141983155
m KG BM KBGM L L L 54905111119380 =minus+=minus+=
mt xGM M L
sin34984sin549075153sin φ φ φ ==∆=
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 5367
991266 983124983144983141 983149983141983156983137983139983141983150983156983154983145983139 983144983141983145983143983144983156
991266 F983151983154 983155983149983137983148983148 983137983150983143983148983141983155 983151983142 983144983141983141983148 983156983144983141 983154983145983143983144983156983145983150983143 983149983151983149983141983150983156
m KG BM KBGM I I 63905013891750 =minus+=minus+=
sin22998sin693075153sin mt x xGM M I I
φ φ φ ==∆=
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 5467
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 5567
983116983119983123983124 983106983125983119983129983105983118983107983129 983117983109983124983112983119983108
Paralel Sinkage
Volume (DCEF)=Volume (W1ADW+BL1LC)
Damaged compartment is bounded on top
983116983119983123983124 983106983125983119983129983105983118983107983129 983117983109983124983112983119983108
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 5667
983116983119983123983124 983106983125983119983129983105983118983107983129 983117983109983124983112983119983108
bull It is assumed that displacement and location of vertical centre
of gravity does not change after damaged
983116983119983123983124 983106983125983119983129983105983118983107983129 983117983109983124983112983119983108
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 5767
983116983119983123983124 983106983125983119983129983105983118983107983129 983117983109983124983112983119983108
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 5867
The heel angle of damaged ship is determined by
where
d is the distance between the volume centre of damaged compartment
and the new longitudinal centre of floatation
wc=vc μ ρ
983116983119983123983124 983106983125983119983129983105983118983107983129 983117983109983124983112983119983108
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 5967
983116983119983123983124 983106983125983119983129983105983118983107983129 983117983109983124983112983119983108
983116983119983123983124 983106983125983119983129983105983118983107983129 983117983109983124983112983119983108
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 6067
Longitudinal Metacentre Height of a Damaged Ship
983116983119983123983124 983106983125983119983129983105983118983107983129 983117983109983124983112983119983108
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 6167
983110983151983154983159983137983154983140 983137983150983140 983137983142983156 983140983154983137983157983143983144983156983155 983137983142983156983141983154 983140983137983149983137983143983141983140
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 6267
983120983151983154983156 983105983142983156 983120983151983154983156 983110983151983154983141 983123983156983137983154983138983151983137983154983140 983105983142983156 983123983156983137983154983138983151983137983154983140 983110983151983154983159983137983154983140
I983150983145983156983145983137983148 D983154983137983157983143983144983156 983124 983124 983124 983124
983120983137983154983137983148983141983148 983123983145983150983147983137983143983141 +983152 +983152 +983152 +983120
H983141983141983148 983085983149983145 983085983149983145 +983149983155 +983149983155
983124983154983145983149 983085983156983147 +983156983138 983085983156983147 +983156983138
F983145983150983137983148 D983154983137983157983143983144983156 983124+983152983085983149983145983085983156983147 983124+983152983085983149983145+983156983138 983124+983152+983149983155983085983156983147 983124+983152+983149983155+983156983138
Table 1 Final Draughts for a starboard side damaged ship
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 6367
L983151983155983156 B983157983151983161983137983150983139983161 M983141983156983144983151983140
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 6467
L983151983155983156 B983157983151983161983137983150983139983161 M983141983156983144983151983140
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 6567
991266 A983142983156983141983154 983148983151983151983155983145983150983143 983156983144983141 983139983141983150983156983154983137983148 983139983151983149983152983137983154983156983149983141983150983156 983156983144983141
983159983137983156983141983154983152983148983137983150983141 983137983154983141983137 983145983155
991266 983124983151 983139983151983149983152983141983150983155983137983156983141 983142983151983154 983156983144983141 983148983151983155983155 983151983142 983138983157983151983161983137983150983139983161 983151983142 983156983144983141
983139983141983150983156983154983137983148 983139983151983149983152983137983154983156983149983141983150983156 983156983144983141 983140983154983137983142983156 983145983150983139983154983141983137983155983141983155 983156983151
2805)420()( m x Bl L A L
=minus=minus=
m A
T
L
I
L 875180
150==
nabla=
L983151983155983156 B983157983151983161983137983150983139983161 M983141983156983144983151983140
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 6667
991266 983124983144983141 983144983141983145983143983144983156 983151983142 983156983144983141 983139983141983150983156983141983154 983151983142 983138983157983151983161983137983150983139983161 983145983150983139983154983141983137983155983141983155 983156983151
991266 983124983144983141 983149983151983149983141983150983156 983151983142 983145983150983141983154983156983145983137 983151983142 983156983144983141 983159983137983156983141983154983152983148983137983150983141 983137983154983141983137
991266 983124983144983141 983149983141983156983137983139983141983150983156983154983145983139 983154983137983140983145983157983155
m
T
KB L
L 93802
8751
2 ===
433
6716612
)420(5
12
)(m
l L B I L
=minus
=minus
=
m I
BM
I
L
L 1111150
67166==
nabla
=
L983151983155983156 B983157983151983161983137983150983139983161 M983141983156983144983151983140
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 6767
991266 983124983144983141 983149983141983156983137983139983141983150983156983154983145983139 983144983141983145983143983144983156
991266 983122983145983143983144983156983145983150983143 983149983151983149983141983150983156 983142983151983154 983155983149983137983148983148 983144983141983141983148 983137983150983143983148983141983155
m KG BM KBGM L L L 54905111119380 =minus+=minus+=
mt xGM M L
sin34984sin549075153sin φ φ φ ==∆=
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 5467
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 5567
983116983119983123983124 983106983125983119983129983105983118983107983129 983117983109983124983112983119983108
Paralel Sinkage
Volume (DCEF)=Volume (W1ADW+BL1LC)
Damaged compartment is bounded on top
983116983119983123983124 983106983125983119983129983105983118983107983129 983117983109983124983112983119983108
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 5667
983116983119983123983124 983106983125983119983129983105983118983107983129 983117983109983124983112983119983108
bull It is assumed that displacement and location of vertical centre
of gravity does not change after damaged
983116983119983123983124 983106983125983119983129983105983118983107983129 983117983109983124983112983119983108
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 5767
983116983119983123983124 983106983125983119983129983105983118983107983129 983117983109983124983112983119983108
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 5867
The heel angle of damaged ship is determined by
where
d is the distance between the volume centre of damaged compartment
and the new longitudinal centre of floatation
wc=vc μ ρ
983116983119983123983124 983106983125983119983129983105983118983107983129 983117983109983124983112983119983108
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 5967
983116983119983123983124 983106983125983119983129983105983118983107983129 983117983109983124983112983119983108
983116983119983123983124 983106983125983119983129983105983118983107983129 983117983109983124983112983119983108
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 6067
Longitudinal Metacentre Height of a Damaged Ship
983116983119983123983124 983106983125983119983129983105983118983107983129 983117983109983124983112983119983108
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 6167
983110983151983154983159983137983154983140 983137983150983140 983137983142983156 983140983154983137983157983143983144983156983155 983137983142983156983141983154 983140983137983149983137983143983141983140
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 6267
983120983151983154983156 983105983142983156 983120983151983154983156 983110983151983154983141 983123983156983137983154983138983151983137983154983140 983105983142983156 983123983156983137983154983138983151983137983154983140 983110983151983154983159983137983154983140
I983150983145983156983145983137983148 D983154983137983157983143983144983156 983124 983124 983124 983124
983120983137983154983137983148983141983148 983123983145983150983147983137983143983141 +983152 +983152 +983152 +983120
H983141983141983148 983085983149983145 983085983149983145 +983149983155 +983149983155
983124983154983145983149 983085983156983147 +983156983138 983085983156983147 +983156983138
F983145983150983137983148 D983154983137983157983143983144983156 983124+983152983085983149983145983085983156983147 983124+983152983085983149983145+983156983138 983124+983152+983149983155983085983156983147 983124+983152+983149983155+983156983138
Table 1 Final Draughts for a starboard side damaged ship
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 6367
L983151983155983156 B983157983151983161983137983150983139983161 M983141983156983144983151983140
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 6467
L983151983155983156 B983157983151983161983137983150983139983161 M983141983156983144983151983140
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 6567
991266 A983142983156983141983154 983148983151983151983155983145983150983143 983156983144983141 983139983141983150983156983154983137983148 983139983151983149983152983137983154983156983149983141983150983156 983156983144983141
983159983137983156983141983154983152983148983137983150983141 983137983154983141983137 983145983155
991266 983124983151 983139983151983149983152983141983150983155983137983156983141 983142983151983154 983156983144983141 983148983151983155983155 983151983142 983138983157983151983161983137983150983139983161 983151983142 983156983144983141
983139983141983150983156983154983137983148 983139983151983149983152983137983154983156983149983141983150983156 983156983144983141 983140983154983137983142983156 983145983150983139983154983141983137983155983141983155 983156983151
2805)420()( m x Bl L A L
=minus=minus=
m A
T
L
I
L 875180
150==
nabla=
L983151983155983156 B983157983151983161983137983150983139983161 M983141983156983144983151983140
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 6667
991266 983124983144983141 983144983141983145983143983144983156 983151983142 983156983144983141 983139983141983150983156983141983154 983151983142 983138983157983151983161983137983150983139983161 983145983150983139983154983141983137983155983141983155 983156983151
991266 983124983144983141 983149983151983149983141983150983156 983151983142 983145983150983141983154983156983145983137 983151983142 983156983144983141 983159983137983156983141983154983152983148983137983150983141 983137983154983141983137
991266 983124983144983141 983149983141983156983137983139983141983150983156983154983145983139 983154983137983140983145983157983155
m
T
KB L
L 93802
8751
2 ===
433
6716612
)420(5
12
)(m
l L B I L
=minus
=minus
=
m I
BM
I
L
L 1111150
67166==
nabla
=
L983151983155983156 B983157983151983161983137983150983139983161 M983141983156983144983151983140
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 6767
991266 983124983144983141 983149983141983156983137983139983141983150983156983154983145983139 983144983141983145983143983144983156
991266 983122983145983143983144983156983145983150983143 983149983151983149983141983150983156 983142983151983154 983155983149983137983148983148 983144983141983141983148 983137983150983143983148983141983155
m KG BM KBGM L L L 54905111119380 =minus+=minus+=
mt xGM M L
sin34984sin549075153sin φ φ φ ==∆=
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 5567
983116983119983123983124 983106983125983119983129983105983118983107983129 983117983109983124983112983119983108
Paralel Sinkage
Volume (DCEF)=Volume (W1ADW+BL1LC)
Damaged compartment is bounded on top
983116983119983123983124 983106983125983119983129983105983118983107983129 983117983109983124983112983119983108
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 5667
983116983119983123983124 983106983125983119983129983105983118983107983129 983117983109983124983112983119983108
bull It is assumed that displacement and location of vertical centre
of gravity does not change after damaged
983116983119983123983124 983106983125983119983129983105983118983107983129 983117983109983124983112983119983108
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 5767
983116983119983123983124 983106983125983119983129983105983118983107983129 983117983109983124983112983119983108
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 5867
The heel angle of damaged ship is determined by
where
d is the distance between the volume centre of damaged compartment
and the new longitudinal centre of floatation
wc=vc μ ρ
983116983119983123983124 983106983125983119983129983105983118983107983129 983117983109983124983112983119983108
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 5967
983116983119983123983124 983106983125983119983129983105983118983107983129 983117983109983124983112983119983108
983116983119983123983124 983106983125983119983129983105983118983107983129 983117983109983124983112983119983108
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 6067
Longitudinal Metacentre Height of a Damaged Ship
983116983119983123983124 983106983125983119983129983105983118983107983129 983117983109983124983112983119983108
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 6167
983110983151983154983159983137983154983140 983137983150983140 983137983142983156 983140983154983137983157983143983144983156983155 983137983142983156983141983154 983140983137983149983137983143983141983140
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 6267
983120983151983154983156 983105983142983156 983120983151983154983156 983110983151983154983141 983123983156983137983154983138983151983137983154983140 983105983142983156 983123983156983137983154983138983151983137983154983140 983110983151983154983159983137983154983140
I983150983145983156983145983137983148 D983154983137983157983143983144983156 983124 983124 983124 983124
983120983137983154983137983148983141983148 983123983145983150983147983137983143983141 +983152 +983152 +983152 +983120
H983141983141983148 983085983149983145 983085983149983145 +983149983155 +983149983155
983124983154983145983149 983085983156983147 +983156983138 983085983156983147 +983156983138
F983145983150983137983148 D983154983137983157983143983144983156 983124+983152983085983149983145983085983156983147 983124+983152983085983149983145+983156983138 983124+983152+983149983155983085983156983147 983124+983152+983149983155+983156983138
Table 1 Final Draughts for a starboard side damaged ship
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 6367
L983151983155983156 B983157983151983161983137983150983139983161 M983141983156983144983151983140
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 6467
L983151983155983156 B983157983151983161983137983150983139983161 M983141983156983144983151983140
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 6567
991266 A983142983156983141983154 983148983151983151983155983145983150983143 983156983144983141 983139983141983150983156983154983137983148 983139983151983149983152983137983154983156983149983141983150983156 983156983144983141
983159983137983156983141983154983152983148983137983150983141 983137983154983141983137 983145983155
991266 983124983151 983139983151983149983152983141983150983155983137983156983141 983142983151983154 983156983144983141 983148983151983155983155 983151983142 983138983157983151983161983137983150983139983161 983151983142 983156983144983141
983139983141983150983156983154983137983148 983139983151983149983152983137983154983156983149983141983150983156 983156983144983141 983140983154983137983142983156 983145983150983139983154983141983137983155983141983155 983156983151
2805)420()( m x Bl L A L
=minus=minus=
m A
T
L
I
L 875180
150==
nabla=
L983151983155983156 B983157983151983161983137983150983139983161 M983141983156983144983151983140
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 6667
991266 983124983144983141 983144983141983145983143983144983156 983151983142 983156983144983141 983139983141983150983156983141983154 983151983142 983138983157983151983161983137983150983139983161 983145983150983139983154983141983137983155983141983155 983156983151
991266 983124983144983141 983149983151983149983141983150983156 983151983142 983145983150983141983154983156983145983137 983151983142 983156983144983141 983159983137983156983141983154983152983148983137983150983141 983137983154983141983137
991266 983124983144983141 983149983141983156983137983139983141983150983156983154983145983139 983154983137983140983145983157983155
m
T
KB L
L 93802
8751
2 ===
433
6716612
)420(5
12
)(m
l L B I L
=minus
=minus
=
m I
BM
I
L
L 1111150
67166==
nabla
=
L983151983155983156 B983157983151983161983137983150983139983161 M983141983156983144983151983140
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 6767
991266 983124983144983141 983149983141983156983137983139983141983150983156983154983145983139 983144983141983145983143983144983156
991266 983122983145983143983144983156983145983150983143 983149983151983149983141983150983156 983142983151983154 983155983149983137983148983148 983144983141983141983148 983137983150983143983148983141983155
m KG BM KBGM L L L 54905111119380 =minus+=minus+=
mt xGM M L
sin34984sin549075153sin φ φ φ ==∆=
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 5667
983116983119983123983124 983106983125983119983129983105983118983107983129 983117983109983124983112983119983108
bull It is assumed that displacement and location of vertical centre
of gravity does not change after damaged
983116983119983123983124 983106983125983119983129983105983118983107983129 983117983109983124983112983119983108
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 5767
983116983119983123983124 983106983125983119983129983105983118983107983129 983117983109983124983112983119983108
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 5867
The heel angle of damaged ship is determined by
where
d is the distance between the volume centre of damaged compartment
and the new longitudinal centre of floatation
wc=vc μ ρ
983116983119983123983124 983106983125983119983129983105983118983107983129 983117983109983124983112983119983108
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 5967
983116983119983123983124 983106983125983119983129983105983118983107983129 983117983109983124983112983119983108
983116983119983123983124 983106983125983119983129983105983118983107983129 983117983109983124983112983119983108
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 6067
Longitudinal Metacentre Height of a Damaged Ship
983116983119983123983124 983106983125983119983129983105983118983107983129 983117983109983124983112983119983108
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 6167
983110983151983154983159983137983154983140 983137983150983140 983137983142983156 983140983154983137983157983143983144983156983155 983137983142983156983141983154 983140983137983149983137983143983141983140
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 6267
983120983151983154983156 983105983142983156 983120983151983154983156 983110983151983154983141 983123983156983137983154983138983151983137983154983140 983105983142983156 983123983156983137983154983138983151983137983154983140 983110983151983154983159983137983154983140
I983150983145983156983145983137983148 D983154983137983157983143983144983156 983124 983124 983124 983124
983120983137983154983137983148983141983148 983123983145983150983147983137983143983141 +983152 +983152 +983152 +983120
H983141983141983148 983085983149983145 983085983149983145 +983149983155 +983149983155
983124983154983145983149 983085983156983147 +983156983138 983085983156983147 +983156983138
F983145983150983137983148 D983154983137983157983143983144983156 983124+983152983085983149983145983085983156983147 983124+983152983085983149983145+983156983138 983124+983152+983149983155983085983156983147 983124+983152+983149983155+983156983138
Table 1 Final Draughts for a starboard side damaged ship
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 6367
L983151983155983156 B983157983151983161983137983150983139983161 M983141983156983144983151983140
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 6467
L983151983155983156 B983157983151983161983137983150983139983161 M983141983156983144983151983140
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 6567
991266 A983142983156983141983154 983148983151983151983155983145983150983143 983156983144983141 983139983141983150983156983154983137983148 983139983151983149983152983137983154983156983149983141983150983156 983156983144983141
983159983137983156983141983154983152983148983137983150983141 983137983154983141983137 983145983155
991266 983124983151 983139983151983149983152983141983150983155983137983156983141 983142983151983154 983156983144983141 983148983151983155983155 983151983142 983138983157983151983161983137983150983139983161 983151983142 983156983144983141
983139983141983150983156983154983137983148 983139983151983149983152983137983154983156983149983141983150983156 983156983144983141 983140983154983137983142983156 983145983150983139983154983141983137983155983141983155 983156983151
2805)420()( m x Bl L A L
=minus=minus=
m A
T
L
I
L 875180
150==
nabla=
L983151983155983156 B983157983151983161983137983150983139983161 M983141983156983144983151983140
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 6667
991266 983124983144983141 983144983141983145983143983144983156 983151983142 983156983144983141 983139983141983150983156983141983154 983151983142 983138983157983151983161983137983150983139983161 983145983150983139983154983141983137983155983141983155 983156983151
991266 983124983144983141 983149983151983149983141983150983156 983151983142 983145983150983141983154983156983145983137 983151983142 983156983144983141 983159983137983156983141983154983152983148983137983150983141 983137983154983141983137
991266 983124983144983141 983149983141983156983137983139983141983150983156983154983145983139 983154983137983140983145983157983155
m
T
KB L
L 93802
8751
2 ===
433
6716612
)420(5
12
)(m
l L B I L
=minus
=minus
=
m I
BM
I
L
L 1111150
67166==
nabla
=
L983151983155983156 B983157983151983161983137983150983139983161 M983141983156983144983151983140
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 6767
991266 983124983144983141 983149983141983156983137983139983141983150983156983154983145983139 983144983141983145983143983144983156
991266 983122983145983143983144983156983145983150983143 983149983151983149983141983150983156 983142983151983154 983155983149983137983148983148 983144983141983141983148 983137983150983143983148983141983155
m KG BM KBGM L L L 54905111119380 =minus+=minus+=
mt xGM M L
sin34984sin549075153sin φ φ φ ==∆=
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 5767
983116983119983123983124 983106983125983119983129983105983118983107983129 983117983109983124983112983119983108
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 5867
The heel angle of damaged ship is determined by
where
d is the distance between the volume centre of damaged compartment
and the new longitudinal centre of floatation
wc=vc μ ρ
983116983119983123983124 983106983125983119983129983105983118983107983129 983117983109983124983112983119983108
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 5967
983116983119983123983124 983106983125983119983129983105983118983107983129 983117983109983124983112983119983108
983116983119983123983124 983106983125983119983129983105983118983107983129 983117983109983124983112983119983108
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 6067
Longitudinal Metacentre Height of a Damaged Ship
983116983119983123983124 983106983125983119983129983105983118983107983129 983117983109983124983112983119983108
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 6167
983110983151983154983159983137983154983140 983137983150983140 983137983142983156 983140983154983137983157983143983144983156983155 983137983142983156983141983154 983140983137983149983137983143983141983140
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 6267
983120983151983154983156 983105983142983156 983120983151983154983156 983110983151983154983141 983123983156983137983154983138983151983137983154983140 983105983142983156 983123983156983137983154983138983151983137983154983140 983110983151983154983159983137983154983140
I983150983145983156983145983137983148 D983154983137983157983143983144983156 983124 983124 983124 983124
983120983137983154983137983148983141983148 983123983145983150983147983137983143983141 +983152 +983152 +983152 +983120
H983141983141983148 983085983149983145 983085983149983145 +983149983155 +983149983155
983124983154983145983149 983085983156983147 +983156983138 983085983156983147 +983156983138
F983145983150983137983148 D983154983137983157983143983144983156 983124+983152983085983149983145983085983156983147 983124+983152983085983149983145+983156983138 983124+983152+983149983155983085983156983147 983124+983152+983149983155+983156983138
Table 1 Final Draughts for a starboard side damaged ship
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 6367
L983151983155983156 B983157983151983161983137983150983139983161 M983141983156983144983151983140
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 6467
L983151983155983156 B983157983151983161983137983150983139983161 M983141983156983144983151983140
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 6567
991266 A983142983156983141983154 983148983151983151983155983145983150983143 983156983144983141 983139983141983150983156983154983137983148 983139983151983149983152983137983154983156983149983141983150983156 983156983144983141
983159983137983156983141983154983152983148983137983150983141 983137983154983141983137 983145983155
991266 983124983151 983139983151983149983152983141983150983155983137983156983141 983142983151983154 983156983144983141 983148983151983155983155 983151983142 983138983157983151983161983137983150983139983161 983151983142 983156983144983141
983139983141983150983156983154983137983148 983139983151983149983152983137983154983156983149983141983150983156 983156983144983141 983140983154983137983142983156 983145983150983139983154983141983137983155983141983155 983156983151
2805)420()( m x Bl L A L
=minus=minus=
m A
T
L
I
L 875180
150==
nabla=
L983151983155983156 B983157983151983161983137983150983139983161 M983141983156983144983151983140
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 6667
991266 983124983144983141 983144983141983145983143983144983156 983151983142 983156983144983141 983139983141983150983156983141983154 983151983142 983138983157983151983161983137983150983139983161 983145983150983139983154983141983137983155983141983155 983156983151
991266 983124983144983141 983149983151983149983141983150983156 983151983142 983145983150983141983154983156983145983137 983151983142 983156983144983141 983159983137983156983141983154983152983148983137983150983141 983137983154983141983137
991266 983124983144983141 983149983141983156983137983139983141983150983156983154983145983139 983154983137983140983145983157983155
m
T
KB L
L 93802
8751
2 ===
433
6716612
)420(5
12
)(m
l L B I L
=minus
=minus
=
m I
BM
I
L
L 1111150
67166==
nabla
=
L983151983155983156 B983157983151983161983137983150983139983161 M983141983156983144983151983140
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 6767
991266 983124983144983141 983149983141983156983137983139983141983150983156983154983145983139 983144983141983145983143983144983156
991266 983122983145983143983144983156983145983150983143 983149983151983149983141983150983156 983142983151983154 983155983149983137983148983148 983144983141983141983148 983137983150983143983148983141983155
m KG BM KBGM L L L 54905111119380 =minus+=minus+=
mt xGM M L
sin34984sin549075153sin φ φ φ ==∆=
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 5867
The heel angle of damaged ship is determined by
where
d is the distance between the volume centre of damaged compartment
and the new longitudinal centre of floatation
wc=vc μ ρ
983116983119983123983124 983106983125983119983129983105983118983107983129 983117983109983124983112983119983108
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 5967
983116983119983123983124 983106983125983119983129983105983118983107983129 983117983109983124983112983119983108
983116983119983123983124 983106983125983119983129983105983118983107983129 983117983109983124983112983119983108
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 6067
Longitudinal Metacentre Height of a Damaged Ship
983116983119983123983124 983106983125983119983129983105983118983107983129 983117983109983124983112983119983108
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 6167
983110983151983154983159983137983154983140 983137983150983140 983137983142983156 983140983154983137983157983143983144983156983155 983137983142983156983141983154 983140983137983149983137983143983141983140
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 6267
983120983151983154983156 983105983142983156 983120983151983154983156 983110983151983154983141 983123983156983137983154983138983151983137983154983140 983105983142983156 983123983156983137983154983138983151983137983154983140 983110983151983154983159983137983154983140
I983150983145983156983145983137983148 D983154983137983157983143983144983156 983124 983124 983124 983124
983120983137983154983137983148983141983148 983123983145983150983147983137983143983141 +983152 +983152 +983152 +983120
H983141983141983148 983085983149983145 983085983149983145 +983149983155 +983149983155
983124983154983145983149 983085983156983147 +983156983138 983085983156983147 +983156983138
F983145983150983137983148 D983154983137983157983143983144983156 983124+983152983085983149983145983085983156983147 983124+983152983085983149983145+983156983138 983124+983152+983149983155983085983156983147 983124+983152+983149983155+983156983138
Table 1 Final Draughts for a starboard side damaged ship
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 6367
L983151983155983156 B983157983151983161983137983150983139983161 M983141983156983144983151983140
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 6467
L983151983155983156 B983157983151983161983137983150983139983161 M983141983156983144983151983140
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 6567
991266 A983142983156983141983154 983148983151983151983155983145983150983143 983156983144983141 983139983141983150983156983154983137983148 983139983151983149983152983137983154983156983149983141983150983156 983156983144983141
983159983137983156983141983154983152983148983137983150983141 983137983154983141983137 983145983155
991266 983124983151 983139983151983149983152983141983150983155983137983156983141 983142983151983154 983156983144983141 983148983151983155983155 983151983142 983138983157983151983161983137983150983139983161 983151983142 983156983144983141
983139983141983150983156983154983137983148 983139983151983149983152983137983154983156983149983141983150983156 983156983144983141 983140983154983137983142983156 983145983150983139983154983141983137983155983141983155 983156983151
2805)420()( m x Bl L A L
=minus=minus=
m A
T
L
I
L 875180
150==
nabla=
L983151983155983156 B983157983151983161983137983150983139983161 M983141983156983144983151983140
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 6667
991266 983124983144983141 983144983141983145983143983144983156 983151983142 983156983144983141 983139983141983150983156983141983154 983151983142 983138983157983151983161983137983150983139983161 983145983150983139983154983141983137983155983141983155 983156983151
991266 983124983144983141 983149983151983149983141983150983156 983151983142 983145983150983141983154983156983145983137 983151983142 983156983144983141 983159983137983156983141983154983152983148983137983150983141 983137983154983141983137
991266 983124983144983141 983149983141983156983137983139983141983150983156983154983145983139 983154983137983140983145983157983155
m
T
KB L
L 93802
8751
2 ===
433
6716612
)420(5
12
)(m
l L B I L
=minus
=minus
=
m I
BM
I
L
L 1111150
67166==
nabla
=
L983151983155983156 B983157983151983161983137983150983139983161 M983141983156983144983151983140
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 6767
991266 983124983144983141 983149983141983156983137983139983141983150983156983154983145983139 983144983141983145983143983144983156
991266 983122983145983143983144983156983145983150983143 983149983151983149983141983150983156 983142983151983154 983155983149983137983148983148 983144983141983141983148 983137983150983143983148983141983155
m KG BM KBGM L L L 54905111119380 =minus+=minus+=
mt xGM M L
sin34984sin549075153sin φ φ φ ==∆=
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 5967
983116983119983123983124 983106983125983119983129983105983118983107983129 983117983109983124983112983119983108
983116983119983123983124 983106983125983119983129983105983118983107983129 983117983109983124983112983119983108
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 6067
Longitudinal Metacentre Height of a Damaged Ship
983116983119983123983124 983106983125983119983129983105983118983107983129 983117983109983124983112983119983108
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 6167
983110983151983154983159983137983154983140 983137983150983140 983137983142983156 983140983154983137983157983143983144983156983155 983137983142983156983141983154 983140983137983149983137983143983141983140
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 6267
983120983151983154983156 983105983142983156 983120983151983154983156 983110983151983154983141 983123983156983137983154983138983151983137983154983140 983105983142983156 983123983156983137983154983138983151983137983154983140 983110983151983154983159983137983154983140
I983150983145983156983145983137983148 D983154983137983157983143983144983156 983124 983124 983124 983124
983120983137983154983137983148983141983148 983123983145983150983147983137983143983141 +983152 +983152 +983152 +983120
H983141983141983148 983085983149983145 983085983149983145 +983149983155 +983149983155
983124983154983145983149 983085983156983147 +983156983138 983085983156983147 +983156983138
F983145983150983137983148 D983154983137983157983143983144983156 983124+983152983085983149983145983085983156983147 983124+983152983085983149983145+983156983138 983124+983152+983149983155983085983156983147 983124+983152+983149983155+983156983138
Table 1 Final Draughts for a starboard side damaged ship
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 6367
L983151983155983156 B983157983151983161983137983150983139983161 M983141983156983144983151983140
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 6467
L983151983155983156 B983157983151983161983137983150983139983161 M983141983156983144983151983140
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 6567
991266 A983142983156983141983154 983148983151983151983155983145983150983143 983156983144983141 983139983141983150983156983154983137983148 983139983151983149983152983137983154983156983149983141983150983156 983156983144983141
983159983137983156983141983154983152983148983137983150983141 983137983154983141983137 983145983155
991266 983124983151 983139983151983149983152983141983150983155983137983156983141 983142983151983154 983156983144983141 983148983151983155983155 983151983142 983138983157983151983161983137983150983139983161 983151983142 983156983144983141
983139983141983150983156983154983137983148 983139983151983149983152983137983154983156983149983141983150983156 983156983144983141 983140983154983137983142983156 983145983150983139983154983141983137983155983141983155 983156983151
2805)420()( m x Bl L A L
=minus=minus=
m A
T
L
I
L 875180
150==
nabla=
L983151983155983156 B983157983151983161983137983150983139983161 M983141983156983144983151983140
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 6667
991266 983124983144983141 983144983141983145983143983144983156 983151983142 983156983144983141 983139983141983150983156983141983154 983151983142 983138983157983151983161983137983150983139983161 983145983150983139983154983141983137983155983141983155 983156983151
991266 983124983144983141 983149983151983149983141983150983156 983151983142 983145983150983141983154983156983145983137 983151983142 983156983144983141 983159983137983156983141983154983152983148983137983150983141 983137983154983141983137
991266 983124983144983141 983149983141983156983137983139983141983150983156983154983145983139 983154983137983140983145983157983155
m
T
KB L
L 93802
8751
2 ===
433
6716612
)420(5
12
)(m
l L B I L
=minus
=minus
=
m I
BM
I
L
L 1111150
67166==
nabla
=
L983151983155983156 B983157983151983161983137983150983139983161 M983141983156983144983151983140
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 6767
991266 983124983144983141 983149983141983156983137983139983141983150983156983154983145983139 983144983141983145983143983144983156
991266 983122983145983143983144983156983145983150983143 983149983151983149983141983150983156 983142983151983154 983155983149983137983148983148 983144983141983141983148 983137983150983143983148983141983155
m KG BM KBGM L L L 54905111119380 =minus+=minus+=
mt xGM M L
sin34984sin549075153sin φ φ φ ==∆=
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 6067
Longitudinal Metacentre Height of a Damaged Ship
983116983119983123983124 983106983125983119983129983105983118983107983129 983117983109983124983112983119983108
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 6167
983110983151983154983159983137983154983140 983137983150983140 983137983142983156 983140983154983137983157983143983144983156983155 983137983142983156983141983154 983140983137983149983137983143983141983140
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 6267
983120983151983154983156 983105983142983156 983120983151983154983156 983110983151983154983141 983123983156983137983154983138983151983137983154983140 983105983142983156 983123983156983137983154983138983151983137983154983140 983110983151983154983159983137983154983140
I983150983145983156983145983137983148 D983154983137983157983143983144983156 983124 983124 983124 983124
983120983137983154983137983148983141983148 983123983145983150983147983137983143983141 +983152 +983152 +983152 +983120
H983141983141983148 983085983149983145 983085983149983145 +983149983155 +983149983155
983124983154983145983149 983085983156983147 +983156983138 983085983156983147 +983156983138
F983145983150983137983148 D983154983137983157983143983144983156 983124+983152983085983149983145983085983156983147 983124+983152983085983149983145+983156983138 983124+983152+983149983155983085983156983147 983124+983152+983149983155+983156983138
Table 1 Final Draughts for a starboard side damaged ship
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 6367
L983151983155983156 B983157983151983161983137983150983139983161 M983141983156983144983151983140
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 6467
L983151983155983156 B983157983151983161983137983150983139983161 M983141983156983144983151983140
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 6567
991266 A983142983156983141983154 983148983151983151983155983145983150983143 983156983144983141 983139983141983150983156983154983137983148 983139983151983149983152983137983154983156983149983141983150983156 983156983144983141
983159983137983156983141983154983152983148983137983150983141 983137983154983141983137 983145983155
991266 983124983151 983139983151983149983152983141983150983155983137983156983141 983142983151983154 983156983144983141 983148983151983155983155 983151983142 983138983157983151983161983137983150983139983161 983151983142 983156983144983141
983139983141983150983156983154983137983148 983139983151983149983152983137983154983156983149983141983150983156 983156983144983141 983140983154983137983142983156 983145983150983139983154983141983137983155983141983155 983156983151
2805)420()( m x Bl L A L
=minus=minus=
m A
T
L
I
L 875180
150==
nabla=
L983151983155983156 B983157983151983161983137983150983139983161 M983141983156983144983151983140
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 6667
991266 983124983144983141 983144983141983145983143983144983156 983151983142 983156983144983141 983139983141983150983156983141983154 983151983142 983138983157983151983161983137983150983139983161 983145983150983139983154983141983137983155983141983155 983156983151
991266 983124983144983141 983149983151983149983141983150983156 983151983142 983145983150983141983154983156983145983137 983151983142 983156983144983141 983159983137983156983141983154983152983148983137983150983141 983137983154983141983137
991266 983124983144983141 983149983141983156983137983139983141983150983156983154983145983139 983154983137983140983145983157983155
m
T
KB L
L 93802
8751
2 ===
433
6716612
)420(5
12
)(m
l L B I L
=minus
=minus
=
m I
BM
I
L
L 1111150
67166==
nabla
=
L983151983155983156 B983157983151983161983137983150983139983161 M983141983156983144983151983140
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 6767
991266 983124983144983141 983149983141983156983137983139983141983150983156983154983145983139 983144983141983145983143983144983156
991266 983122983145983143983144983156983145983150983143 983149983151983149983141983150983156 983142983151983154 983155983149983137983148983148 983144983141983141983148 983137983150983143983148983141983155
m KG BM KBGM L L L 54905111119380 =minus+=minus+=
mt xGM M L
sin34984sin549075153sin φ φ φ ==∆=
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 6167
983110983151983154983159983137983154983140 983137983150983140 983137983142983156 983140983154983137983157983143983144983156983155 983137983142983156983141983154 983140983137983149983137983143983141983140
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 6267
983120983151983154983156 983105983142983156 983120983151983154983156 983110983151983154983141 983123983156983137983154983138983151983137983154983140 983105983142983156 983123983156983137983154983138983151983137983154983140 983110983151983154983159983137983154983140
I983150983145983156983145983137983148 D983154983137983157983143983144983156 983124 983124 983124 983124
983120983137983154983137983148983141983148 983123983145983150983147983137983143983141 +983152 +983152 +983152 +983120
H983141983141983148 983085983149983145 983085983149983145 +983149983155 +983149983155
983124983154983145983149 983085983156983147 +983156983138 983085983156983147 +983156983138
F983145983150983137983148 D983154983137983157983143983144983156 983124+983152983085983149983145983085983156983147 983124+983152983085983149983145+983156983138 983124+983152+983149983155983085983156983147 983124+983152+983149983155+983156983138
Table 1 Final Draughts for a starboard side damaged ship
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 6367
L983151983155983156 B983157983151983161983137983150983139983161 M983141983156983144983151983140
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 6467
L983151983155983156 B983157983151983161983137983150983139983161 M983141983156983144983151983140
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 6567
991266 A983142983156983141983154 983148983151983151983155983145983150983143 983156983144983141 983139983141983150983156983154983137983148 983139983151983149983152983137983154983156983149983141983150983156 983156983144983141
983159983137983156983141983154983152983148983137983150983141 983137983154983141983137 983145983155
991266 983124983151 983139983151983149983152983141983150983155983137983156983141 983142983151983154 983156983144983141 983148983151983155983155 983151983142 983138983157983151983161983137983150983139983161 983151983142 983156983144983141
983139983141983150983156983154983137983148 983139983151983149983152983137983154983156983149983141983150983156 983156983144983141 983140983154983137983142983156 983145983150983139983154983141983137983155983141983155 983156983151
2805)420()( m x Bl L A L
=minus=minus=
m A
T
L
I
L 875180
150==
nabla=
L983151983155983156 B983157983151983161983137983150983139983161 M983141983156983144983151983140
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 6667
991266 983124983144983141 983144983141983145983143983144983156 983151983142 983156983144983141 983139983141983150983156983141983154 983151983142 983138983157983151983161983137983150983139983161 983145983150983139983154983141983137983155983141983155 983156983151
991266 983124983144983141 983149983151983149983141983150983156 983151983142 983145983150983141983154983156983145983137 983151983142 983156983144983141 983159983137983156983141983154983152983148983137983150983141 983137983154983141983137
991266 983124983144983141 983149983141983156983137983139983141983150983156983154983145983139 983154983137983140983145983157983155
m
T
KB L
L 93802
8751
2 ===
433
6716612
)420(5
12
)(m
l L B I L
=minus
=minus
=
m I
BM
I
L
L 1111150
67166==
nabla
=
L983151983155983156 B983157983151983161983137983150983139983161 M983141983156983144983151983140
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 6767
991266 983124983144983141 983149983141983156983137983139983141983150983156983154983145983139 983144983141983145983143983144983156
991266 983122983145983143983144983156983145983150983143 983149983151983149983141983150983156 983142983151983154 983155983149983137983148983148 983144983141983141983148 983137983150983143983148983141983155
m KG BM KBGM L L L 54905111119380 =minus+=minus+=
mt xGM M L
sin34984sin549075153sin φ φ φ ==∆=
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 6267
983120983151983154983156 983105983142983156 983120983151983154983156 983110983151983154983141 983123983156983137983154983138983151983137983154983140 983105983142983156 983123983156983137983154983138983151983137983154983140 983110983151983154983159983137983154983140
I983150983145983156983145983137983148 D983154983137983157983143983144983156 983124 983124 983124 983124
983120983137983154983137983148983141983148 983123983145983150983147983137983143983141 +983152 +983152 +983152 +983120
H983141983141983148 983085983149983145 983085983149983145 +983149983155 +983149983155
983124983154983145983149 983085983156983147 +983156983138 983085983156983147 +983156983138
F983145983150983137983148 D983154983137983157983143983144983156 983124+983152983085983149983145983085983156983147 983124+983152983085983149983145+983156983138 983124+983152+983149983155983085983156983147 983124+983152+983149983155+983156983138
Table 1 Final Draughts for a starboard side damaged ship
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 6367
L983151983155983156 B983157983151983161983137983150983139983161 M983141983156983144983151983140
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 6467
L983151983155983156 B983157983151983161983137983150983139983161 M983141983156983144983151983140
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 6567
991266 A983142983156983141983154 983148983151983151983155983145983150983143 983156983144983141 983139983141983150983156983154983137983148 983139983151983149983152983137983154983156983149983141983150983156 983156983144983141
983159983137983156983141983154983152983148983137983150983141 983137983154983141983137 983145983155
991266 983124983151 983139983151983149983152983141983150983155983137983156983141 983142983151983154 983156983144983141 983148983151983155983155 983151983142 983138983157983151983161983137983150983139983161 983151983142 983156983144983141
983139983141983150983156983154983137983148 983139983151983149983152983137983154983156983149983141983150983156 983156983144983141 983140983154983137983142983156 983145983150983139983154983141983137983155983141983155 983156983151
2805)420()( m x Bl L A L
=minus=minus=
m A
T
L
I
L 875180
150==
nabla=
L983151983155983156 B983157983151983161983137983150983139983161 M983141983156983144983151983140
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 6667
991266 983124983144983141 983144983141983145983143983144983156 983151983142 983156983144983141 983139983141983150983156983141983154 983151983142 983138983157983151983161983137983150983139983161 983145983150983139983154983141983137983155983141983155 983156983151
991266 983124983144983141 983149983151983149983141983150983156 983151983142 983145983150983141983154983156983145983137 983151983142 983156983144983141 983159983137983156983141983154983152983148983137983150983141 983137983154983141983137
991266 983124983144983141 983149983141983156983137983139983141983150983156983154983145983139 983154983137983140983145983157983155
m
T
KB L
L 93802
8751
2 ===
433
6716612
)420(5
12
)(m
l L B I L
=minus
=minus
=
m I
BM
I
L
L 1111150
67166==
nabla
=
L983151983155983156 B983157983151983161983137983150983139983161 M983141983156983144983151983140
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 6767
991266 983124983144983141 983149983141983156983137983139983141983150983156983154983145983139 983144983141983145983143983144983156
991266 983122983145983143983144983156983145983150983143 983149983151983149983141983150983156 983142983151983154 983155983149983137983148983148 983144983141983141983148 983137983150983143983148983141983155
m KG BM KBGM L L L 54905111119380 =minus+=minus+=
mt xGM M L
sin34984sin549075153sin φ φ φ ==∆=
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 6367
L983151983155983156 B983157983151983161983137983150983139983161 M983141983156983144983151983140
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 6467
L983151983155983156 B983157983151983161983137983150983139983161 M983141983156983144983151983140
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 6567
991266 A983142983156983141983154 983148983151983151983155983145983150983143 983156983144983141 983139983141983150983156983154983137983148 983139983151983149983152983137983154983156983149983141983150983156 983156983144983141
983159983137983156983141983154983152983148983137983150983141 983137983154983141983137 983145983155
991266 983124983151 983139983151983149983152983141983150983155983137983156983141 983142983151983154 983156983144983141 983148983151983155983155 983151983142 983138983157983151983161983137983150983139983161 983151983142 983156983144983141
983139983141983150983156983154983137983148 983139983151983149983152983137983154983156983149983141983150983156 983156983144983141 983140983154983137983142983156 983145983150983139983154983141983137983155983141983155 983156983151
2805)420()( m x Bl L A L
=minus=minus=
m A
T
L
I
L 875180
150==
nabla=
L983151983155983156 B983157983151983161983137983150983139983161 M983141983156983144983151983140
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 6667
991266 983124983144983141 983144983141983145983143983144983156 983151983142 983156983144983141 983139983141983150983156983141983154 983151983142 983138983157983151983161983137983150983139983161 983145983150983139983154983141983137983155983141983155 983156983151
991266 983124983144983141 983149983151983149983141983150983156 983151983142 983145983150983141983154983156983145983137 983151983142 983156983144983141 983159983137983156983141983154983152983148983137983150983141 983137983154983141983137
991266 983124983144983141 983149983141983156983137983139983141983150983156983154983145983139 983154983137983140983145983157983155
m
T
KB L
L 93802
8751
2 ===
433
6716612
)420(5
12
)(m
l L B I L
=minus
=minus
=
m I
BM
I
L
L 1111150
67166==
nabla
=
L983151983155983156 B983157983151983161983137983150983139983161 M983141983156983144983151983140
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 6767
991266 983124983144983141 983149983141983156983137983139983141983150983156983154983145983139 983144983141983145983143983144983156
991266 983122983145983143983144983156983145983150983143 983149983151983149983141983150983156 983142983151983154 983155983149983137983148983148 983144983141983141983148 983137983150983143983148983141983155
m KG BM KBGM L L L 54905111119380 =minus+=minus+=
mt xGM M L
sin34984sin549075153sin φ φ φ ==∆=
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 6467
L983151983155983156 B983157983151983161983137983150983139983161 M983141983156983144983151983140
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 6567
991266 A983142983156983141983154 983148983151983151983155983145983150983143 983156983144983141 983139983141983150983156983154983137983148 983139983151983149983152983137983154983156983149983141983150983156 983156983144983141
983159983137983156983141983154983152983148983137983150983141 983137983154983141983137 983145983155
991266 983124983151 983139983151983149983152983141983150983155983137983156983141 983142983151983154 983156983144983141 983148983151983155983155 983151983142 983138983157983151983161983137983150983139983161 983151983142 983156983144983141
983139983141983150983156983154983137983148 983139983151983149983152983137983154983156983149983141983150983156 983156983144983141 983140983154983137983142983156 983145983150983139983154983141983137983155983141983155 983156983151
2805)420()( m x Bl L A L
=minus=minus=
m A
T
L
I
L 875180
150==
nabla=
L983151983155983156 B983157983151983161983137983150983139983161 M983141983156983144983151983140
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 6667
991266 983124983144983141 983144983141983145983143983144983156 983151983142 983156983144983141 983139983141983150983156983141983154 983151983142 983138983157983151983161983137983150983139983161 983145983150983139983154983141983137983155983141983155 983156983151
991266 983124983144983141 983149983151983149983141983150983156 983151983142 983145983150983141983154983156983145983137 983151983142 983156983144983141 983159983137983156983141983154983152983148983137983150983141 983137983154983141983137
991266 983124983144983141 983149983141983156983137983139983141983150983156983154983145983139 983154983137983140983145983157983155
m
T
KB L
L 93802
8751
2 ===
433
6716612
)420(5
12
)(m
l L B I L
=minus
=minus
=
m I
BM
I
L
L 1111150
67166==
nabla
=
L983151983155983156 B983157983151983161983137983150983139983161 M983141983156983144983151983140
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 6767
991266 983124983144983141 983149983141983156983137983139983141983150983156983154983145983139 983144983141983145983143983144983156
991266 983122983145983143983144983156983145983150983143 983149983151983149983141983150983156 983142983151983154 983155983149983137983148983148 983144983141983141983148 983137983150983143983148983141983155
m KG BM KBGM L L L 54905111119380 =minus+=minus+=
mt xGM M L
sin34984sin549075153sin φ φ φ ==∆=
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 6567
991266 A983142983156983141983154 983148983151983151983155983145983150983143 983156983144983141 983139983141983150983156983154983137983148 983139983151983149983152983137983154983156983149983141983150983156 983156983144983141
983159983137983156983141983154983152983148983137983150983141 983137983154983141983137 983145983155
991266 983124983151 983139983151983149983152983141983150983155983137983156983141 983142983151983154 983156983144983141 983148983151983155983155 983151983142 983138983157983151983161983137983150983139983161 983151983142 983156983144983141
983139983141983150983156983154983137983148 983139983151983149983152983137983154983156983149983141983150983156 983156983144983141 983140983154983137983142983156 983145983150983139983154983141983137983155983141983155 983156983151
2805)420()( m x Bl L A L
=minus=minus=
m A
T
L
I
L 875180
150==
nabla=
L983151983155983156 B983157983151983161983137983150983139983161 M983141983156983144983151983140
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 6667
991266 983124983144983141 983144983141983145983143983144983156 983151983142 983156983144983141 983139983141983150983156983141983154 983151983142 983138983157983151983161983137983150983139983161 983145983150983139983154983141983137983155983141983155 983156983151
991266 983124983144983141 983149983151983149983141983150983156 983151983142 983145983150983141983154983156983145983137 983151983142 983156983144983141 983159983137983156983141983154983152983148983137983150983141 983137983154983141983137
991266 983124983144983141 983149983141983156983137983139983141983150983156983154983145983139 983154983137983140983145983157983155
m
T
KB L
L 93802
8751
2 ===
433
6716612
)420(5
12
)(m
l L B I L
=minus
=minus
=
m I
BM
I
L
L 1111150
67166==
nabla
=
L983151983155983156 B983157983151983161983137983150983139983161 M983141983156983144983151983140
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 6767
991266 983124983144983141 983149983141983156983137983139983141983150983156983154983145983139 983144983141983145983143983144983156
991266 983122983145983143983144983156983145983150983143 983149983151983149983141983150983156 983142983151983154 983155983149983137983148983148 983144983141983141983148 983137983150983143983148983141983155
m KG BM KBGM L L L 54905111119380 =minus+=minus+=
mt xGM M L
sin34984sin549075153sin φ φ φ ==∆=
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 6667
991266 983124983144983141 983144983141983145983143983144983156 983151983142 983156983144983141 983139983141983150983156983141983154 983151983142 983138983157983151983161983137983150983139983161 983145983150983139983154983141983137983155983141983155 983156983151
991266 983124983144983141 983149983151983149983141983150983156 983151983142 983145983150983141983154983156983145983137 983151983142 983156983144983141 983159983137983156983141983154983152983148983137983150983141 983137983154983141983137
991266 983124983144983141 983149983141983156983137983139983141983150983156983154983145983139 983154983137983140983145983157983155
m
T
KB L
L 93802
8751
2 ===
433
6716612
)420(5
12
)(m
l L B I L
=minus
=minus
=
m I
BM
I
L
L 1111150
67166==
nabla
=
L983151983155983156 B983157983151983161983137983150983139983161 M983141983156983144983151983140
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 6767
991266 983124983144983141 983149983141983156983137983139983141983150983156983154983145983139 983144983141983145983143983144983156
991266 983122983145983143983144983156983145983150983143 983149983151983149983141983150983156 983142983151983154 983155983149983137983148983148 983144983141983141983148 983137983150983143983148983141983155
m KG BM KBGM L L L 54905111119380 =minus+=minus+=
mt xGM M L
sin34984sin549075153sin φ φ φ ==∆=
8162019 Damaged Stability
httpslidepdfcomreaderfulldamaged-stability 6767
991266 983124983144983141 983149983141983156983137983139983141983150983156983154983145983139 983144983141983145983143983144983156
991266 983122983145983143983144983156983145983150983143 983149983151983149983141983150983156 983142983151983154 983155983149983137983148983148 983144983141983141983148 983137983150983143983148983141983155
m KG BM KBGM L L L 54905111119380 =minus+=minus+=
mt xGM M L
sin34984sin549075153sin φ φ φ ==∆=
![Ch acl yo - PERU - Copernicus EMS · Crisis! Information Transportation! Grading Road, !Destroyed Road,! Highly! Damaged Road,! Moderately Damaged Destroyed [100%] Highly! Damaged](https://img.pdfslide.us/doc/110x75/5e40cd31a78927343e264038/ch-acl-yo-peru-copernicus-ems-crisis-information-transportation-grading-road.jpg)
![Recent Advances in Damage Stability Assessment with ... · E SOLAS damaged stability rules post-2009 Probabilistic ‘Regulation A’ is described in MSN 1698M (MCA, 1998) [9]. A](https://img.pdfslide.us/doc/110x75/5e7160a7113e3a6b9a622b2d/recent-advances-in-damage-stability-assessment-with-e-solas-damaged-stability.jpg)
![Designing for Damage Stability and Survivability ...of damaged Ro-Ro vessel dynamic stability and survivability [2]. The subject of dynamic ship stability in waves with the hull breached](https://img.pdfslide.us/doc/110x75/5e715e0900257f3e3e6c2c7c/designing-for-damage-stability-and-survivability-of-damaged-ro-ro-vessel-dynamic.jpg)