Numerical and experimental analysis for the stability of a 2500

Int. Journal of Applied Sciences and Engineering Research, Vol. 3, Issue 6, 2014 www.ijaser.com

© 2014 by the authors – Licensee IJASER- Under Creative Commons License 3.0 [email protected]

Research article ISSN 2277 – 9442

—————————————

*Corresponding author (e-mail: [email protected]) 1041

Received on August, 2014; Published on November, 2014

Numerical and experimental analysis for the stability of a 2500

tonnes offshore work boat

Nitonye Samson and Adumene Sidum

Department of Marine Engineering, Rivers State University of Science and Technology Port Harcourt,

Rivers State, Nigeria

DOI: 10.6088/ijaser.030600004

Abstract: The design of work Boat have become very important in the world especially in the Niger Delta

region of Nigeria, now that oil exploration is moving gradually from the onshore to the offshore. Hence the

stability of the vessel at sea becomes critical for the safety of life and properties onboard the work boat. The

design of a 2500 Tonnes offshore work boat, determination of optimal scantling for good stability

characteristics, estimation of principal dimension and the analysis of the stability of the work boat in an

offshore working condition was carried out. The stability characteristics of a rectangular work boat of

dimension 42m x 7.5m x 5m were determined and analyzed using International codes and standards. The

hydrostatic curves for the boat were plotted and used to determine the optimal values for safe operation of the

work Boat. Furthermore the analysis of the stability of the entire work boat was done to ascertain the

maximum load the vessel could carry not to exceed a safe value this shows the design is worth will. This was

also verified using an inclining experiment model.

Key words: Stability Analysis, Stability characteristics, Offshore Work Boat, Volume Displacement,

Metacentric height, Centre of Buoyancy, Static Forces and Dynamic Forces.

1. Introduction

The design and realization of Sea going vessels like the 2500 tonnes offshore work boat could not be

achieved all alone without the consideration of the concept of stability as the vessel would definitely be

affected by the disturbances created by water bodies usually termed ‘waves’ when it is floating. Therefore, at

this point, the concept of stability has become important both in the design and construction of vessels and

also in the operational modes. On a broad note, ship stability is an area of naval architecture and ship design

that deals with how a ship behaves at sea; both in still water and in waves generated when the bodies of

waters are disturbed. The instability of a boat is initiated when a ship is subjected to a number of forces

causing the structure to distort. These forces are basically divided into categories with respect to the

conditions of the water, whether it is in still water and disturbing waves which are static forces and dynamic

forces respectively. The former categories of forces, the static forces are forcing acting on the ship when it is

floating at rest in still water. These static forces comprises of the weight and the buoyant force. The later, the

dynamic forces are set of forces acting on the ship when it’s in motion. This latter category of forces, the

dynamic forces could be subdivided into six (6) degree of freedom with three linear and three rotational

forces. Pawlowski et al (2009) considered all the three linear forces under dynamic forces as (swaging,

heaving, and surging) and the rotational forces as pitching, yawing and rolling). There forces are largely due

to disturbing waves and could come from any direction. These former and later set of forces could be

illustrated briefly with the sketches below.

Numerical and experimental analysis for the stability of a 2500 tonnes offshore work boat


Int. Journal of Applied Sciences and Engineering Research, Vol. 3, No. 6, 2014

1042

Figure 1: Dynamic forces in a 3-dimensional plane Figure 2: Static Forces.

However, the concept of equilibrium cannot be ruled out when the stability of a floating vessel is mentioned

or considered. The three types of equilibrium conditions usually considered are the stable, neutral and

unstable equilibrium with respect to a few number of hydrostatic parameters such as the center of gravity

(GG), the metacentric height (GM), metacentre (M) and the centre of buoyancy (CG) easily determined. Not

forgetting the Righting lever (+GZ) and the overturning lever (-GZ) as monitored by Edward (1988) which

was looked at by Norrbin (1950) many years ago and agree with the Lloyd’s (1997) on ship classification..

The stability of vessel could also be considered through the concept of the angle of lift, across two planes and

two degrees of freedom. The longitudinal section usually referred to as rolling and the transverse section

which is called pitching. So to consider the basic concept of the analysis of stability of a rectangular work

Boat, we must look at it when it is floating.

2. Materials and methods

2.1 Determination of metacentric radius (M) with respect to the draft

The transverse section of a rectangular and triangular barge and her water plane shape is heeled to a small

angle of inclination by an external moment, so that she floats at the waterline W2 L2 instead of W1L1

Figure 3: The transverse section of the barge.

The distance between the two centers of buoyancy, BB1 is given by

21

1ggX

WBB w

∆= (1)

(2)

Volume displacement of the wedge (3)




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Height of wedge, ∂= tan2

BL (4)

Substituting equation 4 into equation 3, the Volume displace of the wedge will be

∂×××=∆ tan222

1 BLB

∂×××=∆ tan8

1 2 LB (5)

Substituting equation 5 into equation 2, LB

xWW ∂+=∆= tan8

2

λλ (6)

Substituting equation 6 into equation 1, LanggLB

BB δ+∆

=3

2tan 21

21 λ

λ (7)

Also the distance between the centre of the gravity of the wedges

Substituting for g1g2 into equation 7, 3

2

8

tan21 BxLB

BB∆

=δλ

∆=

12

tan31 LB

BBδλ

From the diagram, Metacentric radius, αtan

1BBBM = (8)

So, (9)

Substituting equation 8 into 9 we have, ∆

=12

tan3 LB

BMxλ

α (10)

But Volume displacement

And 12

3 LBI = Substituting into 10

∇=

IBM (11)

In case of longitudinal stability

∇= L

L

IBM (12)

2.2 Determination of center of buoyancy from keel (KG)

By the Geometry of the submerged section: The center of buoyancy is the centroid of the area of the

submerged section: for a barge as of draft d: the Buoyancy is given by:

KB = Centroid of the submerged section 2

dKB = (13)

2.3 Determination of height of metacenter above Keel (KM)

Again from the Geometry:

Substituting equations 13 for KB and ∆12

3 LBλ for BM




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Already formulated expression, we have ∆

+=122

3LBdKM

λ (14)

2.4 Determination of metacentric height (GM)

From the Geometry of the barge, through the transverse section of the pontoon:

By substituting the expression of KM from equation 14 so

KGLBdGM −

∆=

122

3λ (15)

2.5 Metacentric diagram

KB and BM depends upon the draft, their values for any ship or barge can be calculated for a number of

different draughts and plotted to form the metacentric diagram for the ship, the KM curve is the meta centric

diagram.

2.5 Tonne per centimeter immersion

Paulling et al (2007) in their paper motion and capsizing in Astern Sea looked at the amount of cargoes

loaded on a vessel that would to cause a parallel sinkage of one (1) cm which were supported by Grochwalski

et al (2007) and Hanshind (2008).

Mathematically, it is expressed as tonne per C on immersion

cmTondensityplanwaterofArea

TPC100

×=

= cm

tonA w

100

λ× (16)

Where Aw = Area of water – plane

= Density of sea water

IF cm

ton025.1=ρ

Substituting into 16 cm

tonATPC w

100

025.1×=

cm

tonxAW 0125.0= (17)

2.6 Preliminary calculations from the hull forms

The principal particulars of the barge are given as follows

Length overall, LOA = 42m

Beam moulded, B = 7.5m

Depth moulded, D = 5m

Light barge draft, d = 1.62m

KG = 2.02m

Dead weight = 2500 tons




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3. Calculation of the mass displacement of the barge

3.1 Port Side of the barge and starboard side

Figure 4: The form of the Barge

The Area of the part side Ap

From the diagram A1

Also, 2

2 5.22)55.2(62

12 mmmA =+×=

But

So

But note that Area of part side of the large is equal to that of the starboard side.

so total Area of part and starboard side is

3.2 Top and bottom of the barge

Area of the top of the barge

But Area of the top is equal to the Area of the bottom

3.3 Fore and Aft side of the barge

Area of the fore side of the barge AF

But Area of the fore side of the barge AF equal to the Area of the Aft side of the barge Aa

3.4 Area of Comportment side of the barge

If one part of the barge is flooded to prevent the other comportment from flooding, comportment are

placed at every 5meter along the barge.

Area of comportment Acv

But we have 7 (seven) comportment

Total Volume of the barge

Total Area of the barge AT




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The thickness of the plate use for the barge throughout to be 12mm

Volume of barge (Vb ) = AT x thickness

Total Volume of the Welding plate used for the barge

V.F a 6m by 6m plate is to be used and thickness of the place 12mm.

Volume of plate

Total Number of Plate used for construction

Barge Number of Plate (NP)

Number of plate Np ≈ 38

for 6m by 6m by 12mm

3.5 Mathematical relation for displacement with respect to draft

The mass displacement ( ∆ ) is the height of the water displaced by the rectangular barge. It is determined

by displacement

Displacement ∆

Light weight,

3.6 Inclining experiment model

This was performed to obtain accurately the vertical height of the center of gravity above the keel (KG &

KG1) and verify with the analytical model. This was carried out at various loaded weight and the barge

inclination was also analysed at different angle of heeling. The righting arm (GZ) was then estimated from

the point of inclination of the work barge. Derrett (1999) gave adequate recommendation on the principles

of inclined experiment in his material Ship stability for masters and mates

Figure 5: Inclined Experiment diagram

The above figure describes the position of the work barge at various heeling angles of 0, 15, 30, 45, 60, 75,

85 and the righting moment GZ have corresponding value of 0, 1.22m, 1.85m, 2.25m, 1.25m, 0.45m, 0

respectively. The Analysis is done with different loading condition of the work barge and is plotted as

shown in figure 6.




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Figure 6: Graph of righting arm versus heeling angles

Determining the stability ratio of the work barge from the experiment is done using the (Dave Gerr

Estimation). This gives the positive energy area of the curve (PEA) = AVS x Max GZ x 0.63 = 85 x 2.25 x

0.63 = 120.4875 degree-metres. While the negative energy area (NEA) of the curve = (180-85) x Min. GZ

x 0.66 = 95 x -0.475 x 0.66 = 29.7825 degree-metres.

The Stability ratio of the work barge = 120.4875/29.7825 = 4.05.

As a general rule, Pawlowski et al (2009) said a stability ratio of at least 3 is considered adequate for

coastal work barge.

4. Results and discussions

4.1 Analytical Calculation for maximum loading of weight

Cramic (2000) in his paper Service Network design in freight transportation said at all times, it is of

paramount importance for the naval architect to know exactly the maximum load to be added to a vessel

and the rectangular barge here is not an exception, in order to avoid capsizes of the barge. The coax of this

work is based on determining the maximum load that can be added for parallel sinkage at a height of five

meters above the base that will not cause the barge to become unstable.

Table 1: Displacement with Draft Relationship

S/NO 1 2 3 4 5 6 7 8

Draft T (m 0.25 0.5 0.75 1 1.25 1.5 1.75 2

∆=322.875 80.719 161.438 242.156 322.875 403.594 484.313 565.031 645.75

S/NO. 9 10 11 12 13 14 15 16

Draft T

(m 2.25 2.5 2.75 3 3.25 3.5 3.75 4

∆=322.875 726.469 807.188 887.907 968.625 1049.344 1130.063 1210.781 1291.5

S/NO 17 18 19 20

Draft T

(m 4.25 4.5 4.75 5

∆=322.875 1372.219 1452.938 1533.656 1614.375




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A graph of Displacement against Draft is shown below

0

1

2

3

4

5

6

0 200 400 600 800 1000 1200 1400 1600 1800

tonnes /cm

Draft

Figure 7: Graph of Displacement versus Draft

The Analytical procedure are outlined below

2500 tones at 1.62m

Distance of center of buoyancy from metacenter

( )62.112

5.7

122

2

×=

=

BM

d

BBM

Distance of buoyancy from the keel 2

62.1

2

mdKB ==

Distance of meta-center from the keel,

Meta-centric height, GM

After adding weight W, the new draft, d1 becomes

New draft ( )∆

+∆=

Wdd 1

(18)

Substituting values for ∆ and initial draft d into equation substituting values for ∆ and initial draft, d into

equation (18) above

( )0575.523

0575.52362.11

Wd

+=

875.322

0575.523

0575.523

62.135315.847

W

W

+=

+= (19)

But

1

2

12 d

BBM =

Dis

pla

cem

ent

(to

nn

es)




1049

New

+=

0575.523

62.135315.847

12 1

2WB

BM

W

BM+

=0575.523

476563.1513 (20)

But New KB

875.322

0575.523

2

1

W

d

+=

=

New 75.645

0575.523 WKB

+= (21)

New KM = New BM + New KB

Adding equation 20 and 21, we have 75.645

0575.523

0575.523

476563.1513 W

WKM

++

+= (22)

New KG W

WKGKGKG

+∆

+∆=

W

W

+

×+×=

0575.523

502.20575.523

New KG W

WKG

+

+=

0575.523

55761.1056 (23)

But New GM (24)

But if the barge will be Neutral stable, GM = 0

Therefore the equation became that (25)

Substituting equation 22 and 23 into equation 25

( )0

0575.523

55761.1056

75.645

0575.523

0575.523

476563.1513=

+

+−

++

+ W

WW

W

(26)

Applying the Almighty formula to the above quadratic equation (26)

a

acbbW

2

42 −±−=

12

6223.56863214)638.2182()628.2182(

2

×

××−−±−=W

The load required on board the barge will be 1393.72 tonnes, while 2971.52 tonnes will cause the barge to

capsize, so the value 2971.52 tonnes is neglected. Hence Wmax = 1393.72 tonnes

4.2 Variation of GM with change in draft

Ephraim and Douglas (1991) in their technical report on analysis and design of support system for weather

for Golf Master looked at the loading condition of a crane on a rig and said whenever a load, W is placed




1050

on board centrally, it causes an additional displacement, ( ∆ ) which in turn shifts the center of gravity G of

the barge to G1 and affects the metacentric height (GM). The transverse metacentric height falls until a

point is reached where GM = 0 and below this point, instability begins to set in. The aim of this project

work is also to establish this point below which it is not advisable to operate the barge.

4.3 Determination of KG1

Sheng (2000) looked at Change in draft as being equal to (d – 1.620m) caused by assumed addition of

weight, W. Volume of additional weight = (d – 1.62) x L x B, while the Weight of displaced volume is

(27)

(28)

But Shift in center of gravity due to addition of weight, W with draft is expressed us

1

1∆

=WTG

GG

(29)

Substituting equation 28, 27 into 29 and noting that TG = (5.0 – 2.02) = 2. 98m

d

xdGG

875.322

)02.25()62.1(875.3221

−−=

d

d )98.2()62.1( −=

dGG

8276.411 −= (30)

Hence KG1 = KG + GG1 dd

8276.462.3

8276.4162.2 −=−+= (31)

4.3.1 Determination of BM d

BBM

12

2

=

(32)

Substituting values ( )

ddBM

6875.4

12

5.742

==

4.4 Determination of GM

GM = KB + BM – KG1 dd

dGM8276.4

62.36875.4

2+−+=

62.3515.9

2−+=

dd (33)

Equation (10), (15), (31), and (32) are used to obtain the table 2 below and figure 7. The relationship

between the draft and displacement is an importance one especially when the subject of stability is

mentioned. From the displacement – draft graph of figure 7. It is observed that the slop of the graph gives

the tonne per cm immersion for parallel sinkage.

Slope of the displacement draft – graph of figure.7

75.025.3

156.242344.1049

1 −

−=

∆=

draftd

ntdisplacemeSlope




1051

cm

tonnes

m

tonnes229.3875.322 ==

The slope signifies that a load of 3.229 tonnes will cause a parallel sinkage of one cm.

Also from the stability calculation, it is observed that for a barge of 2000 tonnes (dead weight) with length

of 42m, beams of 7.5m and depth of 5m, the maximum load at which the barge becomes unstable is

1393.72 tonnes. This can be verify by using the below formula to check.

The reason why I did not get 2500 tonnes remain the fact that in practical light weight have to do with the

weight of the metal plate and weight of welding which is not considered here.

So practically,

So, any load on the barge above 1373.72 tonnes will cause the barge to sink or capsize.

Table 2: Some stability parameters

S/NO Draft

d(m) KB(m) BM (m) KM(m) KG1(m) GM (m)

1 0.25 0.1 19 19 15.7 32.6

2 0.5 0.3 9.4 9.6 14.3 14

3 0.75 0.4 6.3 6.6 -4.7 7.88

4 1 0.5 4.7 5.2 -1.4 4.88

5 1.25 0.6 3.8 4.4 0.17 3.13

6 1.5 0.8 3.1 3.9 1.14 2

7 1.75 0.9 2.7 3.6 1.78 1.23

8 2 1 2.3 3.3 2.24 0.69

9 2.25 1.2 2.1 3.2 2.59 0.29

10 2.5 1.3 1.9 3.1 2.85 0

11 2.75 1.4 1.7 3.1 3.07 -0.2

12 3 1.5 1.6 3.1 3.24 -0.4




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Figure 8: Draft versus the metacentric radius Figure 9: Graph of KM versus Draft

Figure 10: Graph of BM versus Draft Figure 11: Graph of KB versus Draft

5. Conclusions The stability of the work boat in an offshore working condition was carried out. The stability haracteristics

of a rectangular work boat of dimension 42m x 7.5m x 5m were determined mathematically and analyzed

using International codes and standards. The hydrostatic curves for the boat were plotted and used to

determine the optimal values for safe operation of the work Boat at sea operating conditions.

1. The stability analysis of a rectangular barge of dimension 42m x 7.5m x 5m to avoid it from

capsize provides results that meet safety requirements during operations.

2. It is therefore emphasized from the research that within the loading range less than 1373.72 tonnes,

the work barge shows a healthy stability ratio of 4.05.

3. It was further observed that an addition of weight to 1373.72 tonnes will cause the work barge to

capsize.

4. From the metacentric diagram, it is noticed that the barge will become unstable when the drafts

starts exceeding 2.45m as the variation of the displacement against the draft gives a good notice

that per 3,22 tonnes of load on the barge a parallel sinkage of one (1) cm will occur.

5. This approach presented here can be used to predict the load range of the barge to a reasonable

extent.

6. References




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1. Crainic, T. G, 2000. Service network design in freight transportation. European Journal of

operational Research, 122.

2. Derrett D. R, 1999. Ship Stability for masters and mates, Revised by Dr. C.B Reed Educational

and Professional Publishing Ltd Barras, Oxford Auckland Boston Johannesburg Melbourne New

Delhi,

3. Edward, V. L, 1988. Principle of Naval Architecture Second Revision: Stability and Strength

Volume I. The Society of Naval Architecture and Marine Engineers. New Jersey,

4. Ephraim M. E, and Douglas, I. E, 1991. Technical Report on Analysis and Design of support

system for weather ford Gulf master G 1 5F Crane on the Anini-1 Rig,

5. Grochwalski, S, Rask, I, and Soderberg, P, 2007. An Experimental Technique for investigation into

Physics of ship capsizing in Proceedings. Third International Conference on stability of ship and

Ocean vehicles, STAB’86, Gdansk, Poland.

6. Hanshind, M. D. 2008. Hydrodynamics Theory of ship motions. Published by Nauks, Moscow, (in

Russian).

7. Lloyd’s Register, 1997. Classification of Ship Rules and Regulations Part 3: Ship Structure

London,.

8. Norrbin, N. H. , 1950. The Design of Sea kindly Ships. North-East Coast Institution of Engineers

and Ship-owners, Newcastle upon Tyne, United Kingdom.

9. Pauling .J. R, Oakley, O. H, and Wood P. D, 2007. Motion and Capsizing in Astern Sea” in

Proceedings. Tenth Symposium on Naval hydrodynamics.

10. Pawlowski, J. S, Bass, D. W, and Grochowalski, S. A, 2009. Time Domain Simulation of ship

motion in Waves” in Proceedings. 17th Symposium on Naval Hydrodynamics, The Hague,

Netherlands.

11. SHENG Zhenbang 2002. Principle of Ship (M). Shanghai. Shanghai Jiaotong University press,.

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Numerical and experimental analysis for the stability of a 2500