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32 GUN FRIGATE
HMS SOUTHAMPTON
STABILITY ANALYSIS
R. Braithwaite
Issue 01
Oct 2009
HMS Southampton Stability Analysis
R.Braithwaite Page 2 Issue 01
Contents 1 Introduction ........................................................................................................ 3
2 Stability Model ................................................................................................... 4 3 Downflooding Points .......................................................................................... 7
4 Hydrostatic Tables ............................................................................................. 8 5 KN Tables ........................................................................................................ 10
6 Load Conditions ............................................................................................... 12 7 Weight Estimate ............................................................................................... 13
7.1 Hull ........................................................................................................... 14 7.2 Armament ................................................................................................. 15
7.3 Top Hamper .............................................................................................. 16 7.4 Ground Tackle .......................................................................................... 17
7.5 Boats ......................................................................................................... 17 7.6 Stowage .................................................................................................... 17
7.7 Men and Effects ........................................................................................ 18 7.8 Ballast ....................................................................................................... 18
8 Stability Criteria ............................................................................................... 19 9 Results ............................................................................................................. 22
9.1 Departure Condition (Foreign Service 6 months) ....................................... 23 9.2 Arrival Condition ...................................................................................... 24
9.3 Design Condition ...................................................................................... 26 10 Discussion .................................................................................................... 28
References ............................................................................................................... 30 Appendix 1 Hydrostatic Tables................................................................................ 31
Appendix 2 – KN Tables ......................................................................................... 38 Appendix 3 Weight Estimate ................................................................................... 42
HMS Southampton Stability Analysis
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1 Introduction
This report relates to a reconstruction of the 32 gun frigate HMS Southampton (built
in 1757) described in Ref.9.
Data used for this reconstruction and the reconstructed drawings were used to analyse
the vessels stability.
A critical part of the study involved reconstructing a weight estimate for the vessel.
Whilst contemporary data (together with hydrostatics from the stability model)
enables a good estimate to be made of total displacement and longitudinal center of
gravity (LCG), the vertical center of gravity (VCG) had to be derived by detailed
calculation which included a number of assumptions (discussed in the report). The
VCG is critical in determining the stability of any floating vessel, so the reliability of
this stability analysis is highly dependent on the validity of these assumptions.
The results of the analysis are compared with current UK stability criteria for sail
training vessels and some of the implications on the operation of the vessel are
discussed.
Data generated from this analysis has been used in a velocity prediction study (Ref.
10).
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2 Stability Model
A 3D surface model was created using Maxsurf Software. This was created by fitting
a hull surface to imported images of the hull moulded sections, waterlines and
buttock lines.
Figure 1 and Figure 2 show views of the Maxsurf model surfaces with sections,
waterlines and buttocks positioned as shown in the design draught reconstruction
(Ref. 9).
Stability Analysis was conducted in Hydromax software. Figure 3 shows the sections
interpolated by this software from the Maxsurf Surface model (with the 3“ skin
thickness added).
A free flood area was added to represent the space between the upper deck and the
quaterdeck/forecastle (shaded area in Figure 4). This was assigned a permeability of
95% (in line with MCA/MoD recommendation for permeability of accommodation
spaces Ref. 3).
The origin is taken at the underside of keel at the aft perpendicular. The x axis is
taken as positive forwards. The y axis positive to port and the z axis positive upwards.
All units are metric unless otherwise stated.
The Aft draught marks are at the aft perpendicular and the forward draught marks are
at the forward perpendicular (x= 37.897 m)
Density of water taken at 1.0252 tonnes/m3
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Figure 1 HMS Southampton Maxsurf Model Stern
Figure 2 HMS Southampton Maxsurf Model Bow
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Figure 3 Hydromax Sections
Figure 4 Midship Section Showing Extent of Freeflood Space
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3 Downflooding Points
Down flooding points were positioned at the corners of the centerline hatch at
midships. A downflood point is defined as an opening which, when immersed will
cause progressive flooding of the vessel.
A warning point was also set at the lower corner of the midships gun port. It is
obviously desirable not to immerse the gunports (particularly when these are open).
However, these openings will not cause downflooding if immersed and any water
taken on board should make its way back overboard through the upper deck scuppers.
X (m) Y (m) Z (m)
Centerline Hatch 20.700 0.760 6.600
Aft Hatch Corner 7.363 0.760 7.045
Forward Hatch Corner 26.959 0.760 6.979
Midship Gunport sill 20.990 4.496 7.032
Table 1 Downflood/Warning points
Figure 5 Key Points
Midship
Gunport
Downflood points
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4 Hydrostatic Tables
Hydrostatic tables derived from the Maxsurf model are presented in Appendix 1.
These are tabulated for a mean draughts ranging from 4 to 5 meters and trim of 0m to
0.5m by the stern.
The displacement (and any other hydrostatic property) can be calculated for from any
set of draught mark readings as follows:
1. Calculate the draught at amidships as being the mean of the draught at the AP
and that at the FP.
2. Calculate the trim as the difference between the draught at the AP and that at
the FP
3. Interpolate for the calculated mean draught from the hydrostatic tables with a
trim both greater and lower than the calculated trim interpolated for the
calculated midship draught.
4. Interpolate between these values for the calculated trim to find the
displacement at the required mean draught and trim.
If the vertical center of gravity (KG) is known the initial stability of the vessel can be
calculated.
Initial stability is measured by a quantity known as the metacentic height (GMT).
This can be calculated from the value KMT interpolated from the hydrostatic tables
(as above) and the vertical center of gravity as follows:
GMT= KMT-KG
If GMT is greater than zero the vessel is stable, if it is less than zero the vessel is
unstable.
Other hydrostatic parameters presented in the results section area as follows:
CB: Block Coefficient: An indication of the fullness of the hull and equal to
the Displacement Volume divided by Waterline length x beam x
draught.
CP: Prismatic Coefficient: an indication of the distribution of the volume of
the underwater hull . A low Cp indicates a full midship section with
fine ends. It is evaluated by dividing the displacement volume by
Waterline length x midship section area.
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LCB: Longitudinal Center of Buoyancy, corresponding to the longitudinal
center of the immersed volume of the hull
LCF: Longitudinal Center of Flotation: weights added or removed at this
point will cause the vessel to rise or sink in the water without changing
trim.
TPC: Tonnes Per Centimetre immersion. The number of tonnes, added at the
LCF which will cause the vessel to sink by 1 centimeter.
MCT: Moment to Change Trim: The moment of weights added about the
LCF which will cause the trim to change by 1 cm.
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5 KN Tables
These tables can be used to calculate the large angle stability of the vessel.
The stability of a vessel is determined by the tendency for the center of buoyancy (CB
in Figure 6) to move as the vessel heels. If this movement is such that the line of
action of the buoyancy force and the line of action of the weight of the vessel (acting
through the center of gravity (CG) form a couple that opposes the heel angle then the
vessel is said to be stable. The distance apart of the line of action of these two forces
is termed the righting lever or GZ. A graph of the righting lever (GZ) against heel
angle is called a GZ curve.
The distance KN can be calculated directly from the Maxsurf model (without
knowledge of the vertical center of gravity KG). The distance KN is the righting lever
assuming a KG of zero (i.e. CG on the keel)
Once the vertical center of gravity is known the GZ value can be calculated from the
KN value as follows:
GZ=KN-KGsinθ
Figure 6 Righting Lever GZ
As with initial stability, the key to determining the stability of the vessel is its vertical
center of gravity.
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Once this is known and having found the displacement from the hydrostatic tables the
GZ curve can be derived from these tables (for displacements ranging from 706 to
1037 tonnes) as follows:
For each heel angle:
1. Interpolate KN for displacement from the two tables with trim below and
above the calculated trim.
2. Interpolate for the calculated trim to find the KN, at that heel angle for the
required displacement and trim.
3. Calculate the GZ value from the KG using the above formula.
Plot the calculated GZ values against heel angle to generate the GZ curve for that
loading condition.
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6 Load Conditions
The load conditions considered are shown in Table 2.
The draughts for the first two load conditions are given on contemporary sailing trial
reports (Ref.1). These draughts were used to derive corresponding displacements and
longitudinal centers of gravity using the Maxsurf model.
The draughts for the design condition were scaled from the design draught and these
were used to derive the design displacement and LCG as above.
The vertical centers of gravity were calculated from the weight estimate as described
below.
The arrival condition displacement and vertical center of gravity were calculated from
the weight estimate assuming:
The quantities of stowage items given in Table 8.
Fully depleted shot and powder (as this gives a worst case for stability)
The same trim as the design condition (i.e. parallel rise)
Load Condition Draught
(AP)
Draught
(FP)
Displacement
(tonnes)
LCG VCG
Stored for 4 months
(Channel Service)
4.953 4.648 968 19.727 4.567
Stored for 6 months
(Foreign Service)
5.131 4.826 1029 19.694
4.411
Design Condition 4.851 4.496 925 19.708 4.681
Arrival Condition 4.504 4.148 809 19.777 5.085 Table 2 Load Conditions
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7 Weight Estimate
As described above the displacement and LCG for a given set of draughts can be
derived from the geometry of the Maxsurf surface model. The purpose of creating a
weight breakdown is to estimate the vertical center of gravity and derive alternative
loading conditions.
The approach that was adopted for HMS Southampton was as follows:
A high level weight estimate for HMS Pearl (Ref. 1) provided a weight breakdown
for a similar sized frigate built soon after HMS Southampton. A comparison of the
principal particulars of the two vessels is given below:
HMS Pearl HMS Southampton
Gundeck Length (feet) 125.00 124.33
Length on keel (feet) 103.33 102.29
Breadth (feet) 35.17 34.67
Depth in hold (feet) 12.00 12.00
Tonnage 679 652
Table 3 Principal Particulars
It should be noted that the tonnage quoted in Table 3 is not the displacement of the
vessel but is a quantity calculated from the principal particulars and is related to the
total enclosed volume of the vessel.
The first level weight groups derived for HMS Southampton (as stored for 4 months
channel service) is shown in Table 4.
A detailed weight estimate is presented in Appendix 3.
Weight Group HMS Pearl
(tons)
HMS Pearl
(tonnes)
HMS Southampton
(tonnes)
HULL 516.400 524.662 479.229
ARMAMENT 73.450 74.625 74.625
TOP HAMPER 58.550 59.457 53.480
GROUND TACKLE 32.250 32.766 32.766
BOATS 2.290 2.997 2.997
STOWAGE 132.100 152.705 180.842
MEN AND EFFECTS 23.050 23.419 23.419
BALLAST 130.000 132.080 120.642
TOTAL 968.750 1002.741 968.000
Table 4 Weight Breakdown
For HMS Southampton a weight and center of gravity was calculated for each weight
group as follows:
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7.1 Hull
Figure 7 CAD Surface Model used to estimate hull areas and vcg’s
The total weight of this group (together with the Top Hamper and ballast groups) was
determined by scaling the HMS Pearl weights with a common factor determined by
making the total displacement equal the 4 month stowed condition in Table 2, with
the stowage weights set to their 4 month values (See Section 7.6). This factor worked
out at approximately 0.91 (compared to the ratio of design displacements of 0.92).
The drawings were used to calculate the weights and center of gravity of the hull and
deck structure together with some of the fittings. A 3D CAD surface model was
created to help estimate the vertical centers and areas of the major planked areas
(outer and inner planking, decks and bulkheads see Figure 7). Other weights were
estimated by taking measurements from the drawings (e.g. calculating areas and
centroids using regions (AutoCad) and applying a thickness).
Appendix 3 contains comments on the method used to estimate the various
components in this group.
The balance between the calculated total and the scaled weight for the whole group
was added at a vertical center of gravity equal to the VCG of the combined total of the
calculated components. It should be noted that a number of approximations were
made in this weight estimate (e.g. inner planking thickness taken as 3” inside rather
than taking account of the varying thicknesses of the individual strakes). This could
be improved upon by building a mode detailed CAD model, or a detailed scale model
in wood.
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7.2 Armament
The maximum amount of shot carried for channel and foreign service are given in
Ref. 1 as follows:
Ammunition Channel Service Foreign Service
Number Weight Number Weight
12 pounder round 1820 9.828 2600 14040
12 pounder grape 260 2.691 260 2.691
12 pounder dismantling 78 0.842 78 0.842
6 pounder round 420 1.134 600 1620
½ pounder round 600 0.135 720 162
TOTAL 14.630 TOTAL 19.355
Table 5 Ammunition - Shot
This shot was all located at the center of the shot locker in the weight estimate.
The HMS Pearl estimate divides this group into the groups shown in Table 6. As both
vessels are 32gun 12 pounder frigates the same weights were assumed for both
vessels.
Special 12 pounder guns were fitted to the 12 pounder 32 gun frigates weighing 28.5
cwt (1448 kg). These were shorter than the standard gun to allow room for the guns to
be worked on the relatively narrow upper decks of these ships. These were
individually positioned at VCG’s derived from the drawings. The six 6 pounder long
guns (16.5 cwt, 838kg) were centered 20” above the upper deck. The weight of the
swivel guns was scaled from a model of a swivel gun built for a model of the
schooner HMS Halifax (80 kg), and the VCG taken from the drawings. This only left
5kg to be added to align with the HMS Pearl data.
Powder and Gunners Stores assumed to be equal to the Pearl breakdown (and
constant for channel/foreign service) and were located in the magazine.
For the arrival condition it was assumed that all shot and powder had been consumed
(conservative).
The total weights of Armament for channel and foreign service departure load
conditions and the arrival conditions were, therefore, as set out in Table 6
HMS Pearl
(Tonnes)
HMS Southampton
Channel
Departure
Foreign
Departure
Arrival
Guns 43.637 43.637 43.637 43.637
Shot 14.630 14.630 19.355 0
Powder 6.909 6.909 6.909 0
Gunners
Stores
9.449 9.449 9.449 9.449
Table 6 Armament
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7.3 Top Hamper
The data for HMS Pearl and as scaled for HMS Southampton is shown in Table 7.
A 3D model of the spars (excluding studding sail booms) was produced from the sail
plan, which was used to determine the vcg and weight (together with an assumed
density). Other weights (e.g. cross trees and caps) were calculated from the spar plan
(Ref.9). All yards were hoisted to the hounds. An additional 5.24 tonnes was added at
the same vcg to make up the required total.
Figure 8 3D Solid model used to calculate volume and vcg of Spars
Rigging was all assigned the same vcg.
The sail weight was divided between a vcg for the sail plan and the center of the sail
room. The weight of each sail was calculated from the sail area as measured from the
sail plan and the weight of cloth used (taken from Ref.2) with an additional 60%
HMS Southampton Stability Analysis
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(guess) to account for overlaps, bolt ropes, reef points etc. The vcg of each sail was
measured from the sail plan. This assumed all plain sails hoisted (Fore and Aft and
square but excluding studding sails) at a weight of 2.100 tonnes, with 3.679 tonnes in
the sail room (to reflect studding sails, spare sails, tarpaulins, spare cloth etc.)
HMS Pearl (tonnes) HMS Southampton
(tonnes)
Spars 30.074 26.939
Rigging 22.962 20.568
Sails 6.452 5.779 Table 7 Top Hamper
7.4 Ground Tackle
Ground Tackle was assumed as HMS Pearl:
Cables 25.298 tonnes vcg on cable tier (mid orlop platform).
Anchors 7.468 tonnes vcg from drawings
7.5 Boats
Weight assumed as HMS Pearl
7.6 Stowage
The HMS Pearl data breaks Stowage down into the 4 groups shown in Table 8. The
usage/month was calculated by assuming that Sea Stores are not consumed with time
and that the other groups are consumed at the same proportional rate. The difference
between the 6 month and 4 month stored conditions (Table 2) was used to define this
rate after correcting for the different ammunition carried for foreign and channel
service (hence ignoring any difference in stowage for channel and foreign service).
The arrival condition was calculated as 10% of the quantity calculated for foreign
service (stored for 6 months) departure.
HMS Pearl (3
months stores)
(tonnes)
1 months
usage
(tonnes)
HMS Southampton
6 months 4 months Arrival
Sea Stores 21.844 0.000 21.844 21.844 21.844
Water 43.434 9.339 71.451 52.773 7.145
Provisions 68.936 14.822 113.403 83.758 11.340
Fuel 18.491 3.976 30.419 22.467 3.042
Table 8 Stowage
All Stores were assumed to be located underneath the orlop deck.
HMS Southampton Stability Analysis
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These assumptions on stores were used to calculate the displacement and vertical
center of gravity at any stored condition.
7.7 Men and Effects
Men and effects were assumed the same weight as HMS Pearl shared equally between
the upper and lower decks.
7.8 Ballast
Ballast was scaled by the scaling factor. Iron Ballast was located in the hold (two pigs
deep) with shingle ballast at half depth of the hold.
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8 Stability Criteria
Following a number of losses of sail training vessels due to capsize, work was carried
out by the Wolfson Unit at Southampton University to develop new stability criteria
for these vessels (Ref. 4). These were made part of the UK standards for Sailing
Vessels including a code of Large Yachts and Sail Training Vessels (Ref. 5)
The study found that:
Vessels with a range of stability of less than 90° degrees are vulnerable to
wind induced capsize, with the capsize arrested by the rig art 90° . They will
then remain at his angle until they sink through downflooding. This was the
means by which a number of sail training vessels have been lost (Ref. 6,7,8)
Wind tunnel tests on models found that wind heeling moments vary from a
maximum at 0° to approx zero at 90° with a good fit to a cos1.3
θ curve.
Gusts caused by turbulence in the atmospheric boundary layer commonly give
rise to short duration gusts which rarely exceed a velocity of 1.4 times the
hourly mean.
Squalls, caused by small scale weather systems can last for longer periods and
can give rise to wind speeds up to 10 times the mean for the previous hour.
The findings of the study were used to develop some very simple criteria. Firstly a
range of stability of 90° is required to reduce the risk of wind induced capsize.
Secondly, a maximum safe steady heel angle is calculated and recorded in the vessels
stability book. If the master of the vessel sets sail to ensure that the steady heel angle
does not exceed this value he can be confident that likelihood of encountering a gust
that will cause serious downflooding is very small. A further requirement of the
stability book is a graphical presentation of the maximum heel angle at which the
vessel may be sailed in a given wind speed in order to withstand a squall of a certain
strength. The intention being to provide the master with a tool to judge a safe heel
angle if conditions suggest that squalls are an imminent threat.
These criteria are defined in (Ref. 5) as follows:
1. GZ curves should be produced for Loaded Departure (100% consumables)
and Loaded Arrival (10% consumables) conditions. In the case of Military
Vessels the UK Navy’s approach is to consider the worst case distribution of
ammunition in the arrival condition
2. GZ curve should have a range of not less than 90°. A range of less than 90°
may be considered for vessels over 45m subject to agreed operational criteria.
HMS Southampton Stability Analysis
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3. The angle of steady heel should be greater than 15°. The angle of steady heel
is obtained from the intersection of a “derived heeling lever” curve with the
GZ curve
dwhl = derived wind heeling lever = 0.5 x WLO x cos1.3
θ
Where WLO = f
f
Cos
GZ3/1
Noting that
WLO Is the magnitude of the actual wind heeling lever at 0° which
would cause the vessel to heel to the down flooding angle θf or
60° whichever is least
GZf Is the lever of the vessel’s GZ at the down flooding angle θf or 60°
whichever is least
θd Is the angle at which the “derived wind heeling” curve intersects
the GZ curve (if θd is less than 15° the vessel is considered to have
insufficient stability).
θf The “down flooding angle is the angle of heel causing immersion
of the lower edge of openings having and aggregate area, in
square meters, greater than:
It might be noted that that if the vessel is sailed at an angle of heel no greater than
the “derived angle of heel”, it should be capable of withstanding a wind gust equal
to 1.4 times the steady wind speed (i.e. twice the steady wind pressure) without
immersing any downflooding openings or heeling beyond 60°.
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Ref.5 also requires that sail training vessels should be subdivided into watertight
compartments such that they can survive flooding of any one compartment. HMS
Southampton was not fitted with any watertight bulkheads so would not be able to
comply. Survival following damage below the waterline would be down to the
rate at which the bilge pump could remove water and the speed at which holes
could be plugged.
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9 Results
Results are presented for three of the loading conditions:
Loaded Departure (6 months foreign service)
Arrival Condition
Design Condition
It should be noted that none of these conditions have a range of stability of greater
than 90 degrees. This has the effect, in the latter two conditions, that it is not possible
to calcualate a WLO that would cause the vessel to heel to the downflood angle (or 60
degrees) . In these cases the WLO has been calculated as the minimum that would
cause the vessel to capsize (and the “effective downflood angle” becomes the angle at
which the gust heeling lever curve is tangential to the GZ curve).
Curves of maximum heel angle to prevent downflooding in gusts and squalls are
presented for the latter two conditions.
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9.1 Departure Condition (Foreign Service 6 months)
Hydrostatics
Displacement Draft at FP
Draft at AP CP CB LCB LCF GMT TPC MCT
(tonnes) m m m m m tonne/cm tonne.m/cm
1029.44 4.826 5.131 0.640 0.460 0.746 0.174 1.430 3.475 8.303
GZ Curve
Heel angle 0 10 20 30 40 50 60 70 80 90 100
GZ m 0.000 0.247 0.471 0.599 0.628 0.580 0.469 0.315 0.137 -
0.048 -0.195
GZ Range 86.65 degrees
Gunport Imersion 26.03 degrees
Hatch Immersion 60.53 degrees
Max Steady Heel Angle 22.81 degrees
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9.2 Arrival Condition
Hydrostatics
Displacement Draft at FP
Draft at AP CP CB LCB LCF GMT TPC MCT
(tonnes) m m m m m tonne/cm tonne.m/cm
809.00 4.148 4.504 0.618 0.418 0.829 0.422 0.732 3.261 6.942
GZ Curve
Heel angle 0 10 20 30 40 50 60 70 80 90 100
GZ m 0.000 0.124 0.229 0.305 0.296 0.209 0.046 -0.168 -0.392 -0.582 -0.800
GZ Range 62.38 degrees
Gunport Imersion 34.08 degrees
Hatch Immersion 80.24 degrees
Effective Downflood angle 42.00 degrees
Max Steady Heel Angle 16.94 degrees
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0
5
10
15
20
25
30
0 10 20 30 40 50 60
Ste
ad
y o
r M
ean
H
eel
An
gle
Mean Apparent Wind Speed
Curves of Maximum Steady Heel Angle to Prevent Downflooding in SquallsArrival Condition
30 knot squall
45 knot squall
60 knot squall
MSHA
Region B - Vulnerable to Gusts in this region
Region A – Vulnerable to Gusts
and Squalls in this region
Region C – Vulnerable
to Squalls in this region
Region D – Not Vulnerable to
Downflooding in this region
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9.3 Design Condition
Hydrostatics
Displacement Draft at FP
Draft at AP CP CB LCB LCF GMT TPC MCT
(tonnes) m m m m m tonne/cm tonne.m/cm
924.67 4.496 4.851 0.631 0.440 0.760 0.270 1.153 3.388 7.703
GZ Curve
Heel angle 0 10 20 30 40 50 60 70 80 90 100
GZ m 0.000 0.198 0.376 0.495 0.507 0.446 0.310 0.125 -0.080 -0.264 -0.428
GZ Range 75.81 degrees
Gunport Imersion 29.53 degrees
Hatch Immersion 69.78 degrees
Effective Downflood Angle 53.00 degrees
Max Steady Heel Angle 19.60 degrees
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0
5
10
15
20
25
30
0 10 20 30 40 50 60
Ste
ad
y o
r M
ean
H
eel
An
gle
Mean Apparent Wind Speed
Curves of Maximum Steady Heel Angle to Prevent Downflooding in SquallsDesign Condition
30 knot squall
45 knot squall
60 knot squall
MSHA
Region B - Vulnerable to Gusts in this region
Region A – Vulnerable to Gusts
and Squalls in this region
Region C – Vulnerable
to Squalls in this region
Region D – Not Vulnerable to
Downflooding in this region
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10 Discussion
Curves of stability were not calculated for ships in the 18th century. The importance of
large angle stability only becoming seriously recognised after the capsize of HMS
Captain in 1870. Figure 9 presents GZ curves for HMS Captain and HMS Monarch
(which was considered to have adequate stability)Ref.11. Whilst these ships were
substantially different from HMS Southampton, they were both military sailing ships
(albeit with steam auxiliary power) and so form some basis for comparison.
As can be seen from Figure 9 HMS Captain had a range of stability of 54.5 degrees.
However the GZ curve peaks at only 21 degrees meaning that if heeled beyond this
point the vessel would continue to heel over until its progress was stopped by the
rigging (at 90 degrees) at which point it would remain at 90 degrees until sinking by
downflooding. This was, in fact, what happened to HMS Captain.
Figure 9 GZ Curve for HMS Captain and HMS Monarch
This can be understood by looking at the GZ curve for HMS Southampton in the
arrival condition. It can be seen that a wind strength that can heel the vessel to more
than 40 degrees will continue to capsize the vessel, since at heel angles greater than
40 the wind heeling moment will be greater than the righting moment.
HMS Southampton, in the design condition, has a GZ curve similar to than of HMS
Monmouth (a similar angle of maximum GZ and a slightly greater range of stability).
A range of stability of 90 degrees is still not achieved, but the stability of the vessel
would have been considered adequate at the time (as it was with HMS Monarch). In
fact HMS Southampton was considered a stiff and seaworthy vessel in comparison
with similar vessels (Ref.1).
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It is likely that the stability presented for the arrival condition would not have been
considered adequate in that the ability of the vessel to carry sail at moderate heel
angles would have been poor. It was common practice to fill empty casks with
seawater to maintain trim and stiffness as fresh water was consumed (Ref. 12). If this
was done such that the design draught and trim were maintained then the GZ curve
presented for the design condition would be the worst case in practice.
This gives a maximum steady heel angle to prevent capsize or downflooding in gusts
of 19.6 degrees. However gunport immersion occurs at around 30 degrees and so a
practical maximum heel angle of 15 degrees would have been sensible to minimise
risk of their immersion. Further work on a velocity prediction spreadsheet for HMS
Southampton (Ref. 13) suggests that this heel angle gives reasonable wind strengths
for reducing sail.
HMS Southampton Stability Analysis
R.Braithwaite Page 30 Issue 01
References
1. Gardiner, The first Frigates, Nine Pounder and Twelve Pounder Frigates,
1748-1815, Conway Maritime Press 1992.
2. David Steel, The Elements and Practice of Rigging and Seamanship, 1794
3. Stability of Surface Ships, Part 1 Conventional Ships, MAP 01-024, Sea
Systems Directorate, MoD Abbey Wood
4. B.Deakin, The Development of Stability Standards for UK Sailing Vessels,
Transactions of the Royal Institution of Naval Architects, 1991
5. Maritime and Coastguard Agency, LY2 The Large Commercial Yacht Code
6. Accident Report on the sinking of the Isaac H.Evans, U.S.Coastguard¸Jan
1985
7. Accident Report on the capsizing and sinking of the US Sailing Vessel Pride
of Baltimore, U.S.National Transportation Safety Board, March 1987
8. Grieg. C and Sutton F, The last voyage of the Albatross, Ducell, Sloan and
Pearce
9. R.Braithwaite, Notes to accompany the reconstructed drawings of HMS
Southampton. http://richardsmodelboats.webs.com
10. R.Braithwaite, Velocity Prediction of the 32 Gun Frigate HMS Southampton.
http://richardsmodelboats.webs.com
11. L Attwood, Theoretical Naval Architecture, Edward 1922
12. B Lavery, The Arming and Fitting of English Ships of War 1600-
1815,Conway 1987.
13. R.Braithwaite, HMS Southampton, Velocity Prediction
HMS Southampton Stability Analysis
R.Braithwaite Page 31 Issue 01
Appendix 1 Hydrostatic Tables
HMS Southampton Stability Analysis
R.Braithwaite Page 32 Issue 01
Hydrostatics for Trim =0
Midship Draught 4 4.1 4.2 4.3 4.4 4.5 4.6 4.7 4.8 4.9 5
Displacement tonne 706.8 738.1 769.9 802.1 834.5 867.5 900.9 934.6 968.6 1003 1037
Heel to Starboard degrees 0 0 0 0 0 0 0 0 0 0 0
Draft at FP m 4 4.1 4.2 4.3 4.4 4.5 4.6 4.7 4.8 4.9 5
Draft at AP m 4 4.1 4.2 4.3 4.4 4.5 4.6 4.7 4.8 4.9 5
Draft at LCF m 4 4.1 4.2 4.3 4.4 4.5 4.6 4.7 4.8 4.9 5
Trim (+ve by stern) m 0 0 0 0 0 0 0 0 0 0 0
WL Length m 39.807 39.86 39.91 39.968 39.949 39.901 39.949 40.013 40.088 40.166 40.243
WL Beam m 10.43 10.483 10.513 10.539 10.564 10.576 10.588 10.598 10.601 10.604 10.602
Wetted Area m^2 469.912 479.467 488.993 498.442 507.254 513.552 522.777 531.996 541.168 550.279 559.536
Waterpl. Area m^2 303.005 307.516 311.783 315.828 319.713 323.318 326.75 330.015 333.056 335.872 338.474
Prismatic Coeff. 0.601 0.605 0.608 0.612 0.617 0.622 0.626 0.629 0.633 0.636 0.639
Block Coeff. 0.415 0.42 0.426 0.432 0.438 0.446 0.452 0.457 0.463 0.469 0.474
Midship Area Coeff. 0.692 0.696 0.702 0.707 0.712 0.717 0.723 0.728 0.733 0.738 0.743
Waterpl. Area Coeff. 0.73 0.736 0.743 0.75 0.758 0.766 0.772 0.778 0.784 0.789 0.793
LCB from Amidsh. (+ve fwd) m 1.223 1.202 1.181 1.16 1.134 1.111 1.087 1.063 1.039 1.015 0.991
LCF from Amidsh. (+ve fwd) m 0.768 0.717 0.663 0.609 0.556 0.508 0.459 0.408 0.359 0.313 0.266
KB m 2.602 2.663 2.725 2.786 2.847 2.908 2.968 3.029 3.089 3.15 3.21
BMt m 3.161 3.118 3.068 3.016 2.964 2.909 2.853 2.797 2.739 2.681 2.622
BML m 35.864 35.366 34.899 34.444 34.004 33.537 33.095 32.666 32.237 31.8 31.364
KMt m 5.763 5.781 5.793 5.802 5.811 5.817 5.822 5.826 5.829 5.831 5.832
KML m 38.466 38.029 37.624 37.23 36.851 36.445 36.063 35.695 35.326 34.949 34.573
Immersion (TPc) tonne/cm 3.106 3.153 3.196 3.238 3.278 3.315 3.35 3.383 3.414 3.443 3.47
MTc tonne.m 6.363 6.559 6.76 6.959 7.157 7.347 7.539 7.73 7.917 8.098 8.274
RM at 1deg = GMt.Disp.sin(1) tonne.m 17.434 18.434 19.387 20.322 21.273 22.207 23.139 24.07 24.994 25.917 26.83
Max deck inclination deg 0 0 0 0 0 0 0 0 0 0 0
Trim angle (+ve by stern) deg 0 0 0 0 0 0 0 0 0 0 0
HMS Southampton Stability Analysis
R.Braithwaite Page 33 Issue 01
Hydrostatics for Trim =0.1m
Midship Draught 4 4.1 4.2 4.3 4.4 4.5 4.6 4.7 4.8 4.9 5
Displacement tonne 706.2 737.5 769.3 801.6 834.2 867.1 900.5 934.2 968.3 1003 1037
Heel to Starboard degrees 0 0 0 0 0 0 0 0 0 0 0
Draft at FP m 3.95 4.05 4.15 4.25 4.35 4.45 4.55 4.65 4.75 4.85 4.95
Draft at AP m 4.05 4.15 4.25 4.35 4.45 4.55 4.65 4.75 4.85 4.95 5.05
Draft at LCF m 3.998 4.098 4.198 4.299 4.399 4.499 4.599 4.699 4.799 4.899 4.999
Trim (+ve by stern) m 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1
WL Length m 39.779 39.827 39.876 39.911 39.847 39.85 39.914 39.978 40.046 40.124 40.201
WL Beam m 10.429 10.482 10.513 10.538 10.564 10.576 10.588 10.598 10.601 10.604 10.602
Wetted Area m^2 470.141 479.712 489.228 498.682 508.107 513.814 523.053 532.26 541.419 550.525 559.69
Waterpl. Area m^2 303.326 307.865 312.159 316.202 320.101 323.697 327.151 330.412 333.432 336.246 338.814
Prismatic Coeff. 0.601 0.605 0.609 0.613 0.619 0.623 0.627 0.63 0.633 0.636 0.639
Block Coeff. 0.41 0.415 0.421 0.427 0.434 0.441 0.447 0.453 0.459 0.464 0.47
Midship Area Coeff. 0.691 0.695 0.7 0.705 0.71 0.716 0.721 0.727 0.732 0.737 0.743
Waterpl. Area Coeff. 0.731 0.737 0.745 0.752 0.76 0.768 0.774 0.78 0.785 0.79 0.795
LCB from Amidsh. (+ve fwd) m 1.128 1.109 1.089 1.069 1.047 1.022 1 0.977 0.954 0.931 0.908
LCF from Amidsh. (+ve fwd) m 0.715 0.665 0.611 0.56 0.508 0.462 0.414 0.366 0.319 0.276 0.23
KB m 2.601 2.662 2.724 2.785 2.846 2.907 2.968 3.028 3.089 3.149 3.209
BMt m 3.166 3.123 3.073 3.02 2.967 2.913 2.857 2.8 2.742 2.684 2.625
BML m 36.009 35.514 35.047 34.589 34.144 33.675 33.238 32.802 32.363 31.922 31.467
KMt m 5.767 5.785 5.797 5.805 5.814 5.82 5.825 5.829 5.831 5.833 5.835
KML m 38.61 38.177 37.771 37.374 36.991 36.582 36.206 35.831 35.452 35.071 34.677
Immersion (TPc) tonne/cm 3.11 3.156 3.2 3.242 3.282 3.319 3.354 3.387 3.418 3.447 3.474
MTc tonne.m 6.385 6.584 6.785 6.986 7.186 7.376 7.57 7.761 7.947 8.128 8.301
RM at 1deg = GMt.Disp.sin(1) tonne.m 17.503 18.507 19.468 20.401 21.351 22.285 23.216 24.151 25.072 25.996 26.917
Max deck inclination deg 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2
Trim angle (+ve by stern) deg 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2
HMS Southampton Stability Analysis
R.Braithwaite Page 34 Issue 01
Hydrostatics for Trim =0.2m
Midship Draught 4 4.1 4.2 4.3 4.4 4.5 4.6 4.7 4.8 4.9 5
Displacement tonne 705.6 737 768.9 801.1 833.8 866.8 900.2 933.9 968 1002 1037
Heel to Starboard degrees 0 0 0 0 0 0 0 0 0 0 0
Draft at FP m 3.9 4 4.1 4.2 4.3 4.4 4.5 4.6 4.7 4.8 4.9
Draft at AP m 4.1 4.2 4.3 4.4 4.5 4.6 4.7 4.8 4.9 5 5.1
Draft at LCF m 3.997 4.097 4.197 4.297 4.398 4.498 4.598 4.698 4.799 4.899 4.999
Trim (+ve by stern) m 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2
WL Length m 39.746 39.795 39.844 39.81 39.766 39.816 39.88 39.944 40.008 40.083 40.16
WL Beam m 10.429 10.482 10.513 10.538 10.563 10.576 10.588 10.598 10.601 10.604 10.602
Wetted Area m^2 470.373 479.96 489.471 498.933 505.331 514.06 523.325 532.528 541.663 550.789 559.828
Waterpl. Area m^2 303.642 308.206 312.519 316.58 320.407 324.041 327.526 330.801 333.783 336.621 339.185
Prismatic Coeff. 0.602 0.606 0.609 0.615 0.62 0.624 0.627 0.631 0.634 0.637 0.64
Block Coeff. 0.404 0.41 0.416 0.423 0.43 0.436 0.442 0.448 0.454 0.46 0.466
Midship Area Coeff. 0.691 0.695 0.7 0.705 0.71 0.716 0.721 0.726 0.732 0.737 0.743
Waterpl. Area Coeff. 0.733 0.739 0.746 0.755 0.763 0.77 0.776 0.781 0.787 0.792 0.797
LCB from Amidsh. (+ve fwd) m 1.033 1.015 0.997 0.977 0.957 0.933 0.912 0.89 0.869 0.847 0.824
LCF from Amidsh. (+ve fwd) m 0.662 0.611 0.56 0.509 0.464 0.417 0.369 0.324 0.28 0.238 0.199
KB m 2.6 2.662 2.723 2.785 2.846 2.907 2.968 3.028 3.089 3.149 3.209
BMt m 3.171 3.127 3.078 3.025 2.971 2.916 2.86 2.803 2.745 2.687 2.628
BML m 36.148 35.661 35.191 34.732 34.249 33.801 33.372 32.934 32.482 32.044 31.583
KMt m 5.771 5.789 5.801 5.81 5.817 5.823 5.827 5.832 5.834 5.836 5.837
KML m 38.748 38.323 37.914 37.516 37.094 36.707 36.34 35.963 35.571 35.193 34.792
Immersion (TPc) tonne/cm 3.113 3.16 3.204 3.246 3.285 3.322 3.358 3.391 3.422 3.451 3.477
MTc tonne.m 6.406 6.608 6.811 7.012 7.206 7.402 7.6 7.792 7.976 8.16 8.332
RM at 1deg = GMt.Disp.sin(1) tonne.m 17.571 18.573 19.541 20.479 21.425 22.355 23.287 24.229 25.143 26.072 26.995
Max deck inclination deg 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3
Trim angle (+ve by stern) deg 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3
HMS Southampton Stability Analysis
R.Braithwaite Page 35 Issue 01
Hydrostatics for Trim =0.3m
Midship Draught 4 4.1 4.2 4.3 4.4 4.5 4.6 4.7 4.8 4.9 5
Displacement tonne 705.1 736.5 768.4 800.7 833.5 866.6 899.9 933.7 967.8 1002 1037
Heel to Starboard degrees 0 0 0 0 0 0 0 0 0 0 0
Draft at FP m 3.85 3.95 4.05 4.15 4.25 4.35 4.45 4.55 4.65 4.75 4.85
Draft at AP m 4.15 4.25 4.35 4.45 4.55 4.65 4.75 4.85 4.95 5.05 5.15
Draft at LCF m 3.995 4.096 4.196 4.296 4.397 4.497 4.597 4.698 4.798 4.898 4.999
Trim (+ve by stern) m 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3
WL Length m 39.714 39.763 39.785 39.713 39.719 39.783 39.847 39.911 39.975 40.042 40.119
WL Beam m 10.428 10.481 10.512 10.538 10.563 10.576 10.588 10.598 10.601 10.604 10.602
Wetted Area m^2 470.622 480.195 489.72 499.191 505.574 514.913 523.591 532.793 541.914 551.027 557.643
Waterpl. Area m^2 303.968 308.541 312.872 316.95 320.777 324.42 327.879 331.158 334.137 336.949 339.439
Prismatic Coeff. 0.602 0.606 0.61 0.616 0.621 0.624 0.628 0.631 0.635 0.638 0.641
Block Coeff. 0.399 0.405 0.411 0.419 0.426 0.432 0.438 0.444 0.45 0.456 0.461
Midship Area Coeff. 0.691 0.695 0.7 0.705 0.71 0.716 0.721 0.726 0.732 0.737 0.743
Waterpl. Area Coeff. 0.734 0.74 0.748 0.757 0.765 0.771 0.777 0.783 0.788 0.794 0.798
LCB from Amidsh. (+ve fwd) m 0.937 0.921 0.904 0.885 0.867 0.847 0.824 0.803 0.783 0.762 0.747
LCF from Amidsh. (+ve fwd) m 0.607 0.558 0.508 0.459 0.415 0.37 0.325 0.282 0.241 0.201 0.169
KB m 2.6 2.661 2.723 2.784 2.846 2.907 2.968 3.028 3.089 3.149 3.21
BMt m 3.176 3.131 3.082 3.029 2.975 2.919 2.863 2.806 2.747 2.689 2.631
BML m 36.288 35.801 35.33 34.873 34.384 33.932 33.498 33.057 32.6 32.151 31.67
KMt m 5.776 5.793 5.805 5.813 5.821 5.826 5.83 5.835 5.836 5.838 5.841
KML m 38.888 38.462 38.053 37.658 37.23 36.839 36.466 36.086 35.689 35.301 34.88
Immersion (TPc) tonne/cm 3.116 3.163 3.208 3.249 3.289 3.326 3.361 3.395 3.426 3.454 3.48
MTc tonne.m 6.427 6.631 6.835 7.039 7.233 7.431 7.628 7.821 8.005 8.187 8.353
RM at 1deg = GMt.Disp.sin(1) tonne.m 17.638 18.638 19.611 20.55 21.498 22.426 23.353 24.297 25.213 26.139 27.074
Max deck inclination deg 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5
Trim angle (+ve by stern) deg 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5
HMS Southampton Stability Analysis
R.Braithwaite Page 36 Issue 01
Hydrostatics for Trim =0.4m
Midship Draught 4 4.1 4.2 4.3 4.4 4.5 4.6 4.7 4.8 4.9 5
Displacement tonne 704.7 736.1 768 800.4 833.2 866.3 899.7 933.5 967.7 1002 1037
Heel to Starboard degrees 0 0 0 0 0 0 0 0 0 0 0
Draft at FP m 3.8 3.9 4 4.1 4.2 4.3 4.4 4.5 4.6 4.7 4.8
Draft at AP m 4.2 4.3 4.4 4.5 4.6 4.7 4.8 4.9 5 5.1 5.2
Draft at LCF m 3.994 4.095 4.195 4.296 4.396 4.497 4.597 4.697 4.798 4.898 4.999
Trim (+ve by stern) m 0.4 0.4 0.4 0.4 0.4 0.4 0.4 0.4 0.4 0.4 0.4
WL Length m 39.683 39.731 39.689 39.642 39.686 39.75 39.814 39.877 39.941 40.005 40.078
WL Beam m 10.427 10.48 10.512 10.537 10.563 10.576 10.588 10.598 10.601 10.604 10.602
Wetted Area m^2 470.854 480.428 489.952 496.389 505.774 515.137 523.837 533.022 542.168 551.231 557.845
Waterpl. Area m^2 304.293 308.888 313.225 317.23 321.11 324.786 328.227 331.486 334.502 337.241 339.783
Prismatic Coeff. 0.602 0.606 0.612 0.617 0.621 0.625 0.628 0.632 0.635 0.639 0.642
Block Coeff. 0.394 0.4 0.407 0.415 0.421 0.427 0.433 0.439 0.445 0.451 0.457
Midship Area Coeff. 0.69 0.695 0.7 0.705 0.71 0.716 0.721 0.726 0.732 0.737 0.742
Waterpl. Area Coeff. 0.735 0.742 0.751 0.759 0.766 0.773 0.779 0.784 0.79 0.795 0.8
LCB from Amidsh. (+ve fwd) m 0.842 0.826 0.81 0.793 0.775 0.757 0.735 0.716 0.697 0.677 0.664
LCF from Amidsh. (+ve fwd) m 0.552 0.504 0.456 0.413 0.368 0.322 0.28 0.24 0.2 0.165 0.133
KB m 2.6 2.661 2.723 2.785 2.846 2.907 2.968 3.029 3.09 3.15 3.21
BMt m 3.18 3.136 3.086 3.033 2.979 2.922 2.865 2.808 2.75 2.691 2.633
BML m 36.428 35.942 35.467 34.969 34.505 34.063 33.62 33.17 32.722 32.247 31.781
KMt m 5.78 5.797 5.81 5.817 5.825 5.83 5.834 5.837 5.839 5.841 5.843
KML m 39.028 38.603 38.19 37.753 37.351 36.97 36.588 36.199 35.811 35.397 34.991
Immersion (TPc) tonne/cm 3.12 3.167 3.211 3.252 3.292 3.33 3.365 3.398 3.429 3.457 3.483
MTc tonne.m 6.45 6.655 6.86 7.057 7.257 7.459 7.655 7.847 8.035 8.212 8.383
RM at 1deg = GMt.Disp.sin(1) tonne.m 17.698 18.704 19.679 20.614 21.564 22.493 23.417 24.358 25.279 26.199 27.139
Max deck inclination deg 0.6 0.6 0.6 0.6 0.6 0.6 0.6 0.6 0.6 0.6 0.6
Trim angle (+ve by stern) deg 0.6 0.6 0.6 0.6 0.6 0.6 0.6 0.6 0.6 0.6 0.6
HMS Southampton Stability Analysis
R.Braithwaite Page 37 Issue 01
Hydrostatics for Trim =0.5m
Midship Draught 4 4.1 4.2 4.3 4.4 4.5 4.6 4.7 4.8 4.9 5
Displacement tonne 704.3 735.8 767.7 800.1 832.9 866.1 899.6 933.4 967.6 1002 1036
Heel to Starboard degrees 0 0 0 0 0 0 0 0 0 0 0
Draft at FP m 3.75 3.85 3.95 4.05 4.15 4.25 4.35 4.45 4.55 4.65 4.75
Draft at AP m 4.25 4.35 4.45 4.55 4.65 4.75 4.85 4.95 5.05 5.15 5.25
Draft at LCF m 3.993 4.094 4.195 4.295 4.396 4.496 4.597 4.697 4.798 4.898 4.999
Trim (+ve by stern) m 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5
WL Length m 39.651 39.666 39.594 39.603 39.658 39.717 39.781 39.845 39.908 39.972 40.038
WL Beam m 10.427 10.48 10.512 10.537 10.562 10.576 10.588 10.598 10.601 10.604 10.602
Wetted Area m^2 471.122 480.714 490.242 496.663 506.054 515.408 524.703 533.293 542.446 549.075 558.02
Waterpl. Area m^2 304.614 309.224 313.579 317.579 321.468 325.133 328.561 331.786 334.808 337.472 340.03
Prismatic Coeff. 0.603 0.607 0.613 0.618 0.622 0.625 0.629 0.633 0.636 0.639 0.642
Block Coeff. 0.39 0.396 0.403 0.41 0.417 0.423 0.429 0.435 0.441 0.447 0.453
Midship Area Coeff. 0.69 0.695 0.7 0.705 0.71 0.716 0.721 0.726 0.732 0.737 0.742
Waterpl. Area Coeff. 0.737 0.744 0.753 0.761 0.767 0.774 0.78 0.786 0.791 0.796 0.801
LCB from Amidsh. (+ve fwd) m 0.745 0.731 0.716 0.701 0.684 0.667 0.649 0.628 0.61 0.598 0.58
LCF from Amidsh. (+ve fwd) m 0.496 0.449 0.403 0.362 0.318 0.275 0.234 0.198 0.162 0.133 0.101
KB m 2.6 2.662 2.724 2.785 2.847 2.908 2.969 3.03 3.09 3.151 3.211
BMt m 3.185 3.14 3.091 3.036 2.982 2.925 2.868 2.81 2.752 2.693 2.634
BML m 36.562 36.076 35.601 35.098 34.636 34.186 33.732 33.274 32.825 32.33 31.859
KMt m 5.785 5.802 5.814 5.822 5.829 5.833 5.837 5.84 5.842 5.844 5.846
KML m 39.162 38.738 38.324 37.883 37.483 37.093 36.701 36.304 35.915 35.481 35.07
Immersion (TPc) tonne/cm 3.123 3.17 3.215 3.256 3.296 3.333 3.368 3.401 3.432 3.46 3.486
MTc tonne.m 6.471 6.678 6.884 7.082 7.284 7.485 7.682 7.872 8.061 8.231 8.404
RM at 1deg = GMt.Disp.sin(1) tonne.m 17.758 18.767 19.745 20.679 21.628 22.556 23.476 24.412 25.334 26.265 27.196
Max deck inclination deg 0.8 0.8 0.8 0.8 0.8 0.8 0.8 0.8 0.8 0.8 0.8
Trim angle (+ve by stern) deg 0.8 0.8 0.8 0.8 0.8 0.8 0.8 0.8 0.8 0.8 0.8
HMS Southampton Stability Analysis
R.Braithwaite Page 38 Issue 01
Appendix 2 – KN Tables
HMS Southampton Stability Analysis
R.Braithwaite Page 39 Issue 01
KN Values
Initial Trim 0.0 m
Displacement 0 10 20 30 40 50 60 70 80 90 100
706.8 0 0.998 1.952 2.836 3.589 4.153 4.524 4.702 4.728 4.555 4.223
739.8 0 1 1.956 2.84 3.58 4.135 4.497 4.668 4.691 4.537 4.215
772.8 0 1.002 1.96 2.842 3.569 4.117 4.47 4.637 4.655 4.52 4.208
805.9 0 1.004 1.963 2.842 3.558 4.099 4.444 4.608 4.621 4.499 4.201
838.9 0 1.006 1.967 2.841 3.546 4.079 4.419 4.581 4.591 4.477 4.194
871.9 0 1.007 1.969 2.838 3.532 4.058 4.394 4.556 4.566 4.455 4.187
904.9 0 1.008 1.972 2.833 3.518 4.036 4.369 4.532 4.543 4.433 4.179
937.9 0 1.009 1.974 2.827 3.502 4.014 4.344 4.51 4.523 4.412 4.171
971 0 1.01 1.976 2.819 3.486 3.992 4.322 4.489 4.504 4.393 4.163
1004 0 1.01 1.977 2.809 3.47 3.968 4.299 4.469 4.488 4.376 4.154
1037 0 1.011 1.976 2.797 3.453 3.945 4.276 4.45 4.472 4.361 4.146
Initial Trim 0.1 m Displacement 0 10 20 30 40 50 60 70 80 90 100
706.2 0 0.998 1.953 2.837 3.591 4.155 4.527 4.703 4.732 4.559 4.224
739.3 0 1.001 1.957 2.841 3.582 4.137 4.499 4.67 4.693 4.539 4.217
772.4 0 1.003 1.961 2.843 3.572 4.12 4.472 4.639 4.656 4.522 4.21
805.4 0 1.005 1.964 2.844 3.561 4.101 4.447 4.61 4.621 4.502 4.203
838.5 0 1.006 1.968 2.843 3.548 4.082 4.421 4.583 4.591 4.48 4.196
871.6 0 1.008 1.971 2.84 3.534 4.061 4.396 4.558 4.565 4.456 4.189
904.7 0 1.009 1.973 2.835 3.52 4.039 4.371 4.534 4.543 4.433 4.182
937.8 0 1.01 1.975 2.829 3.505 4.017 4.348 4.512 4.523 4.411 4.173
970.8 0 1.01 1.977 2.82 3.489 3.995 4.325 4.491 4.505 4.391 4.164
1004 0 1.011 1.978 2.81 3.472 3.971 4.301 4.471 4.489 4.374 4.155
1037 0 1.011 1.977 2.799 3.455 3.948 4.278 4.451 4.474 4.36 4.146
HMS Southampton Stability Analysis
R.Braithwaite Page 40 Issue 01
KN Values
Initial Trim 0.2 m Displacement 0 10 20 30 40 50 60 70 80 90 100
705.6 0 0.999 1.954 2.838 3.593 4.157 4.529 4.706 4.736 4.562 4.226
738.7 0 1.001 1.958 2.842 3.584 4.139 4.502 4.672 4.695 4.542 4.219
771.9 0 1.003 1.962 2.844 3.574 4.122 4.475 4.641 4.656 4.523 4.212
805 0 1.005 1.965 2.845 3.563 4.104 4.449 4.612 4.621 4.504 4.205
838.2 0 1.007 1.969 2.844 3.55 4.084 4.424 4.585 4.59 4.482 4.198
871.3 0 1.008 1.972 2.841 3.536 4.063 4.399 4.559 4.564 4.458 4.191
904.4 0 1.009 1.974 2.837 3.522 4.042 4.374 4.536 4.542 4.433 4.184
937.6 0 1.01 1.977 2.83 3.507 4.02 4.351 4.513 4.523 4.41 4.176
970.7 0 1.011 1.978 2.822 3.491 3.997 4.327 4.492 4.506 4.39 4.166
1004 0 1.012 1.979 2.812 3.474 3.974 4.304 4.472 4.49 4.373 4.156
1037 0 1.012 1.979 2.801 3.457 3.951 4.281 4.453 4.475 4.36 4.146
Initial Trim 0.3 m Displacement 0 10 20 30 40 50 60 70 80 90 100
705.1 0 0.999 1.955 2.84 3.594 4.159 4.532 4.707 4.74 4.564 4.227
738.3 0 1.002 1.959 2.843 3.586 4.141 4.505 4.674 4.697 4.544 4.221
771.5 0 1.004 1.963 2.846 3.576 4.124 4.478 4.642 4.656 4.524 4.214
804.7 0 1.006 1.967 2.847 3.565 4.106 4.452 4.613 4.621 4.506 4.208
837.9 0 1.007 1.97 2.846 3.552 4.087 4.427 4.586 4.59 4.484 4.2
871.1 0 1.009 1.973 2.843 3.539 4.066 4.401 4.561 4.564 4.459 4.193
904.2 0 1.01 1.975 2.839 3.524 4.045 4.378 4.537 4.542 4.433 4.186
937.4 0 1.011 1.978 2.832 3.509 4.023 4.354 4.515 4.523 4.409 4.178
970.6 0 1.012 1.98 2.824 3.493 4 4.33 4.494 4.507 4.389 4.168
1004 0 1.012 1.98 2.814 3.476 3.977 4.306 4.474 4.491 4.372 4.157
1037 0 1.013 1.98 2.802 3.459 3.953 4.283 4.455 4.477 4.36 4.146
HMS Southampton Stability Analysis
R.Braithwaite Page 41 Issue 01
KN Values
Initial Trim 0.4 m Displacement 0 10 20 30 40 50 60 70 80 90 100
704.7 0 1 1.956 2.841 3.596 4.161 4.534 4.709 4.743 4.567 4.229
737.9 0 1.002 1.96 2.845 3.588 4.144 4.507 4.675 4.698 4.547 4.223
771.2 0 1.005 1.964 2.847 3.578 4.127 4.481 4.644 4.656 4.527 4.216
804.4 0 1.007 1.968 2.848 3.567 4.109 4.455 4.615 4.62 4.507 4.21
837.6 0 1.008 1.971 2.847 3.554 4.089 4.429 4.588 4.59 4.486 4.203
870.9 0 1.009 1.974 2.845 3.541 4.068 4.404 4.563 4.564 4.461 4.195
904.1 0 1.011 1.977 2.84 3.526 4.047 4.38 4.539 4.542 4.433 4.188
937.3 0 1.012 1.979 2.834 3.511 4.025 4.356 4.516 4.524 4.408 4.18
970.5 0 1.012 1.981 2.825 3.495 4.002 4.333 4.495 4.507 4.388 4.17
1004 0 1.013 1.981 2.815 3.478 3.979 4.309 4.475 4.492 4.372 4.159
1037 0 1.013 1.981 2.804 3.461 3.955 4.285 4.456 4.479 4.361 4.146
Initial Trim 0.5 m Displacement 0 10 20 30 40 50 60 70 80 90 100
704.3 0 1.001 1.957 2.842 3.599 4.163 4.537 4.711 4.746 4.57 4.23
737.5 0 1.003 1.961 2.846 3.59 4.146 4.51 4.677 4.699 4.549 4.224
770.6 0 1.005 1.965 2.849 3.58 4.129 4.484 4.646 4.656 4.529 4.218
803.8 0 1.007 1.969 2.85 3.569 4.111 4.458 4.617 4.621 4.509 4.212
837 0 1.009 1.972 2.849 3.556 4.092 4.432 4.59 4.59 4.487 4.205
870.1 0 1.01 1.975 2.846 3.543 4.071 4.408 4.565 4.565 4.462 4.197
903.3 0 1.011 1.978 2.842 3.528 4.05 4.384 4.541 4.543 4.432 4.19
936.5 0 1.012 1.98 2.835 3.513 4.028 4.36 4.518 4.525 4.407 4.181
969.7 0 1.013 1.982 2.827 3.497 4.005 4.336 4.497 4.509 4.387 4.172
1003 0 1.013 1.983 2.817 3.48 3.982 4.312 4.477 4.494 4.373 4.16
1036 0 1.014 1.982 2.805 3.463 3.958 4.288 4.458 4.48 4.362 4.147
HMS Southampton Stability Analysis
R.Braithwaite Page 42 Issue 01
Appendix 3 Weight Estimate
Load Condition:
Foreign Service
Stored for 6 months
HMS Southampton Stability Analysis
R.Braithwaite Page 43 Issue 01
HULL 479229 4.399 scaled
weight VCG COMMENTS
Item (kg) (m)
Hull
Outer hull planking bottom 33387 2.499
Area and vcg from Surface model trimmed under wale
Outer hull planking wale 7960 5.351 Area and vcg from Surface model trimmed to wale
Outer hull planking topsides 13588 7.243
Area and vcg from Surface model trimmed above wale
Inner Hull Planking 48779 4.449
Area and vcg from Surface model assumed 3" overall
Stern planking (external) 1101 7.637 Area and vcg from Surface model (2")
Stern planking (internal) 1101 7.637 "
Crutch 157 2.896
Hull Frames 121000 3.284 weight & cg calculated from drg
Stern Timbers 911 7.795
area and vcg calculated from drawing (region) thickness from contract
Transoms 1188 5.551 "
Hawse Timbers 4169 5.553 "
Keel 4788 0.227 "
stem 458 3.011 "
knee of stem etc 2029 5.125 "
stemson etc 711 3.995 "
sternpost 1029 3.176 "
deadwood 5848 1.320 "
keelson 3567 1.422 "
breasthooks below lower deck 684 3.861 weight & cg calc form drg/Eolus Contract
Head rails 482 7.290 weight & cg calc form drg
Main Channels 412 8.115 weight & cg calc form drg/Eolus Contract
Fore Channels 328 8.204 "
Mizzen Channels 226 8.585 "
0 0.000
Bulkheads 0 0.000
Beakhead Bulkhead planking 468 8.128 weight & cg calc form drg
Beakhead bulkhead stiffeners 301 8.128 "
Upper deck divisions -panels 956 7.777 Area and vcg from surface model
-stanchions 199 7.777 Assumed 3'spacing
Lower deck divisions -panels 2732 5.703 Area and vcg from surface model
-stanchions 253 5.703 Assumed 3'spacing
below lower deck divisions -panels 3276 3.985
Area and vcg from surface model
-stanchions 181 3.985 Assumed 3'spacing
Wells 1030 1.895 weight & cg calc form drg
Shot Locker 315 1.895 "
Magazine bulkheads 3016 2.828 Area and vcg from surface model
Magazine stiffeners 126 2.828
0 0.000
HMS Southampton Stability Analysis
R.Braithwaite Page 44 Issue 01
weight VCG COMMENTS
Item (kg) (m)
Decks 0 0.000
Quarter Deck 0 0.000
Quarter Deck Planking 5236 8.789 Area and vcg from surface model
quarterdeck lodging knees 534 8.732 weight & cg calc from drg
quarterdeck hanging knees 749 7.950 "
Quarterdeck beams 3365 8.707 "
stern beam? 264 8.697 "
carlings 326 8.707 "
0 0.000
Foredeck 0 0.000
Foredeck planks 2506 8.522 Area and vcg from surface model
foredeck lodging knees 437 8.465 weight & cg calc from drg
foredeck hanging knees 613 8.459 "
Foredeck beams 1529 8.440 "
Forward Beam 463 8.440 "
carlings 55 8.440 "
cathead Beam 657 8.376 "
0 0.000
0 0.000
Upper Deck 0 0.000
Upper Deck Planking 21377 6.669 Area and vcg from Surface model
breasthook 474 6.862 wt from drg cg from surface
transom 626 6.869 "
Curvrd beams 1206 6.555 "
lodging knees 3514 6.580 "
hanging knees 3096 6.580 "
Mast Partners 1369 6.555 "
Upper Deck Beams (main) 11614 6.555 "
Upper Deck Beams (minor aft) 440 6.599 "
carlings (longitudinal) 2218 6.599 "
Ledges 2523 6.628 "
0 0.000
Lower Deck 0 0.000
Lower Deck Planking 16722 4.779 Area and vcg from surface model
breasthook 322 5.004 weight & cg calc from drg
transom 0 0.000 "
Curvrd beams 652 4.677 "
lodging knees 3275 4.690 "
hanging knees 3301 4.690 "
Mast Partners 1100 4.677 "
Lower Deck Beams 8601 4.677 "
carlings (longitudinal) 2755 4.710 "
Ledges 2624 4.738 "
Standards 747 5.328
HMS Southampton Stability Analysis
R.Braithwaite Page 45 Issue 01
weight VCG COMMENTS
Item (kg) (m)
Orlop Platforms 0 0.000
0 0.000
Fwd Platform planks 1905 3.180 Area and vcg from surface model
lodging knees 1176 3.091 area from drawing, vcg 1/2 thickness fro deck
Fwd Platform beams 2555 3.066 total length measured from drawing
0 0.000
Mid Platform planks 2983 3.128 Area and vcg from surface model
lodging knees 588 3.039 area from drawing, vcg 1/2 thickness fro deck
Mid Platform beams 1988 3.014 total length measured from drawing
0 0.000 "
Aft Platform planks 1149 2.946 Area and vcg from surface model
lodging knees 588 2.857 area from drawing, vcg 1/2 thickness fro deck
Aft Platform beams 1103 2.832 total length measured from drawing
0 0.000
Fittings 0 0.000
Foremast step 838 2.087 weight & cg calc from drg/Eolus Contract
Mainmast step 915 1.380 "
Mizzen mast step 214 2.058 "
Bowsprit step 162 5.867 "
0 0.000
0 0.000
Bits 0 0.000
Lower ~Deck aft 0 0.000
Stanchions 670 3.943 weight & cg calc from drg/Eolus Contract
Standard 181 5.146
area and vcg calculated from drawing (region) thickness from contract
Cross piece 28 5.480 weight & cg calc from drg/Eolus Contract
Lower Deck fwd 0 0.000
Standard 306 5.424
area and vcg calculated from drawing (region) thickness from contract
Cross Piece 28 5.555 weight & cg calc from drg/Eolus Contract
Upper Deck aft 0 0.000
0 0.000
0 0.000
Upper Deck Fwd 0 0.000
0 0.000
Stove 1000 7.169 Guess
Chain Pumps 1000 2.946 Guess
Capstans 1725 6.525 weight and cg from 3d model
0 0.000
Pillars 0 0.000
Lower Deck 792 2.921 weight & cg calc from drg/Eolus Contract
Upper Deck 216 5.639 "
HMS Southampton Stability Analysis
R.Braithwaite Page 46 Issue 01
weight VCG COMMENTS
Item (kg) (m)
Ladders 0 0.000
lower-upper- 1 Sides 29 5.592 weight & cg calc from drg
- rungs 35 5.592 weight & cg calc from drg
lower-upper- 2 Sides 29 5.592 weight & cg calc from drg
- rungs 35 5.592 weight & cg calc from drg
orlop-lower- 1 Sides 29 3.763 weight & cg calc from drg
- rungs 35 3.763 weight & cg calc from drg
orlop-lower- 2 Sides 29 3.763 weight & cg calc from drg
- rungs 35 3.763 weight & cg calc from drg
0 0.000
0 0.000
Rails 497 8.433 weight & cg calc from drg
0 0.000
Rudder 1326 3.062
area and vcg calculated from drawing (region) thickness from contract
Tiller 378 6.375 weight and cg from drawing
Wheel 110 9.728 weight and cg from 3d model
0 0.000
0 0.000
0 0.000
Fastenings 20000 4.400 Guess
Misc 62508 4.450
to make total up to scaled value, c.g as calculated items above
HMS Southampton Stability Analysis
R.Braithwaite Page 47 Issue 01
ARMAMENT 79350 6.243
Guns 43637 7.796 as Pearl cg calculatd
weight VCG COMMENTS
Item (kg) (m)
12 pdr bow port 2896 7.821 28.5cwt gun centered in port
12 pdr port 2 2896 7.664 "
12 pdr port 3 2896 7.566 "
12 pdr port 4 2896 7.498 "
12 pdr port 5 2896 7.439 "
12 pdr port 6 2896 7.395 "
12 pdr port 7 2896 7.381 "
12 pdr port 8 2896 7.394 "
12 pdr port 9 2896 7.440 "
12 pdr port 10 2896 7.504 "
12 pdr port 11 2896 7.576 "
12 pdr port 12 2896 7.663 "
12 pdr port 13 2896 7.787 "
6pdr (foredeck) 1676 9.017 16.5cwt gun 20" above deck
6 pdr (quarterdeck) 3353 9.322 "
swivel guns 960 10.033 scaled from a 1/16 model
Misc 5 7.796 to make up total
0 0.000
Shot 19355 5.850 as Pearl
weight VCG COMMENTS
Item (kg) (m)
12 pounder shot 14040 1.895 Calculated positioned in shot locker
12 pounder grape 2691 1.895 "
12 pounder double 842 1.895 "
6 pounder shot 1620 1.895 "
1/2 pounder shot 162 1.895 "
Powder 6909 2.565 as Pearl
Gunners Stores 9449 2.565 as Pearl
HMS Southampton Stability Analysis
R.Braithwaite Page 48 Issue 01
TOP HAMPER 53480 17.149 scaled
Spars 27037 17.977 scaled
weight VCG COMMENTS
Item (kg) (m)
Main mast 4090 12.649 3d solid CAD Model
Main topmast 961 29.362 "
Main topgallant 197 41.072 "
Fore mast 2875 12.243 "
Fore topmast 842 26.949 "
Fore topgallant 135 37.323 "
Mizzen mast 1514 12.044 "
Mizzen topmast 412 27.924 "
Bowsprit 2674 9.578 "
Jibboom 441 14.517 "
Main yard 1577 21.370 "
Main topsail yard 541 35.200 "
Main topgallant yard 109 42.955 "
Fore yard 1093 19.788 "
Fore topsail yard 372 32.171 "
Fore topgallant yard 79 39.141 "
Mizzen Yard 738 19.042 "
Mizzen topsail yard 101 31.007 "
Mizzen crossjack 364 20.161 "
Spritsail yard 369 11.066 "
Sprit topsail yard 0 0.000 "
Fittings 0 0.000
Mainmast Trestle trees 333 23.231 calculated weight and cg from dwg
Mainmast Cross Trees 287 23.231 "
Mainmast cap 314 26.756 "
Maintopmast Trestle trees 26 36.590 "
Maintopmast Cross Trees 56 36.590 "
Maintopmast cap 54 38.080 "
Foremast Trestle trees 235 21.708 "
Foremast Cross Trees 202 21.708 "
Foremast cap 292 24.548 "
Foretopmast Trestle trees 19 33.542 "
Foretopmast Cross Trees 40 33.542 "
Foretopmast cap 37 34.920 "
Mizzenmast Trestle trees 107 21.619 "
Mizzenmast Cross Trees 91 21.619 "
Mizzenmast cap 87 23.860 "
Bowsprit Cap 37 13.989 "
0 0.000
Misc 5338 17.977 to make up total
0 0.000
Rigging 20643 17.977 scaled weight vcg as spars
Sails 5800 10.345 scaled
HMS Southampton Stability Analysis
R.Braithwaite Page 49 Issue 01
weight VCG COMMENTS
Item (kg) (m)
Square
Main Course 317 15.792
Area and vcg from drg. Weight taken as area x cloth weight x 1.6
Main topsail 304 28.053 "
Main Topgallant 74 38.923 "
Fore course 225 15.185 "
Fore topsail 238 25.824 "
Fore topgallant 58 35.536 "
Mizzen Topsail 126 25.708 "
Spritsail 94 8.315 "
Fore and Aft 0 0.000 "
Mizzen Course 105 16.743 "
Main Staysail 91 14.850 "
Main topmast Staysail 127 20.961 "
Main topgallant Staysail 63 32.598 "
Fore Staysail 51 14.945 "
Fore Topmast Staysail 43 17.724 "
Jib 68 21.229 "
Mizzen Staysail 76 14.395 "
Mizzen topmast staysail 42 22.407 "
0 0.000
Sails, tarpaulins etc. in Sail room 3700 4.094
to make up total placed in sail room 36" above orlop
0 0.000
HMS Southampton Stability Analysis
R.Braithwaite Page 50 Issue 01
GROUND TACKLE 32766 4.416 as Pearl
Cables 25298 3.328 as Pearl vcg 200mm above orlop
Anchors 7468 8.103 as Pearl
BOATS 2997 8.128 as Pearl
STOWAGE 237117 2.100
Sea Stores 21844 2.100
Calculated based on stored condition. Located In hold
Water 71451 2.100 "
Provisions 113403 2.100 "
Fuel 30419 2.100 "
0 0.000
0 0.000
0 0.000
0 0.000
MEN AND EFFECTS 23419 6.024 as Pearl vcg 300mm above upper and lower deck
BALLAST 120642 1.740 Scaled
Iron 46401 1.130 Scaled vcg 6" above inner planks at midships
Shingle 74241 2.121
Scaled vcg 1/2 depth from top of iron ballast to underside of orlop beams
TOTAL 1029000 4.411