Int. Journal of Applie Sciences an Engineering Research, Vol. 3, Issue 6, 04 www.ijaser.com 04 by the authors Licensee IJASER- Uner Creative Commons License 3.0 eitorial@ijaser.com Research article ISSN 77 944 Numerical an experimental analysis for the stability of a 500 tonnes offshore work boat Department of Marine Engineering, Rivers State University of Science an Technology Port Harcourt, Rivers State, Nigeria DOI: 0.6088/ijaser.030600004 Abstract: The esign of work Boat have become very important in the worl especially in the Niger Delta region of Nigeria, now that oil exploration is moving graually from the onshore to the offshore. Hence the stability of the vessel at sea becomes critical for the safety of life an properties onboar the work boat. The esign of a 500 Tonnes offshore work boat, etermination of optimal scantling for goo stability characteristics, estimation of principal imension an the analysis of the stability of the work boat in an offshore working conition was carrie out. The stability characteristics of a rectangular work boat of imension 4m x 7.5m x 5m were etermine an analyze using International coes an stanars. The hyrostatic curves for the boat were plotte an use to etermine the optimal values for safe operation of the work Boat. Furthermore the analysis of the stability of the entire work boat was one to ascertain the maximum loa the vessel coul carry not to excee a safe value this shows the esign is worth will. This was also verifie using an inclining experiment moel. Key wors: Stability Analysis, Stability characteristics, Offshore Work Boat, Volume Displacement, Metacentric height, Centre of Buoyancy, Static Forces an Dynamic Forces.. Introuction The esign an realization of Sea going vessels like the 500 tonnes offshore work boat coul not be achieve all alone without the consieration of the concept of stability as the vessel woul efinitely be affecte by the isturbances create by water boies usually terme waves when it is floating. Therefore, at this point, the concept of stability has become important both in the esign an construction of vessels an also in the operational moes. On a broa note, ship stability is an area of naval architecture an ship esign that eals with how a ship behaves at sea; both in still water an in waves generate when the boies of waters are isturbe. The instability of a boat is initiate when a ship is subjecte to a number of forces causing the structure to istort. These forces are basically ivie into categories with respect to the conitions of the water, whether it is in still water an isturbing waves which are static forces an ynamic 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 an the buoyant force. The later, the ynamic forces are set of forces acting on the ship when it s in motion. This latter category of forces, the ynamic forces coul be subivie into six (6) egree of freeom with three linear an three rotational forces. Pawlowski et al (009) consiere all the three linear forces uner ynamic forces as (swaging, heaving, an surging) an the rotational forces as pitching, yawing an rolling). There forces are largely ue to isturbing waves an coul come from any irection. These former an later set of forces coul be illustrate briefly with the sketches below. *Corresponing author (e-mail: nitonyes@yahoo.com) 04 Receive on August, 04; Publishe on November, 04
Numerical an experimental analysis for the stability of a 500 tonnes offshore work boat Figure : Dynamic forces in a 3-imensional plane Figure : Static Forces. However, the concept of equilibrium cannot be rule out when the stability of a floating vessel is mentione or consiere. The three types of equilibrium conitions usually consiere are the stable, neutral an unstable equilibrium with respect to a few number of hyrostatic parameters such as the center of gravity (GG), the metacentric height (GM), metacentre (M) an the centre of buoyancy (CG) easily etermine. Not forgetting the Righting lever (+GZ) an the overturning lever (-GZ) as monitore by Ewar (988) which was looke at by Norrbin (950) many years ago an agree with the Lloy s (997) on ship classification.. The stability of vessel coul also be consiere through the concept of the angle of lift, across two planes an two egrees of freeom. The longituinal section usually referre to as rolling an the transverse section which is calle pitching. So to consier the basic concept of the analysis of stability of a rectangular work Boat, we must look at it when it is floating.. Materials an methos. Determination of metacentric raius (M) with respect to the raft The transverse section of a rectangular an triangular barge an her water plane shape is heele to a small angle of inclination by an external moment, so that she floats at the waterline W L instea of W L Figure 3: The transverse section of the barge. The istance between the two centers of buoyancy, BB is given by W BB X g g () w Volume isplacement of the wege (3) () Int. Journal of Applie Sciences an Engineering Research, Vol. 3, No. 6, 04 04
Numerical an experimental analysis for the stability of a 500 tonnes offshore work boat Height of wege, L B tan (4) Substituting equation 4 into equation 3, the Volume isplace of the wege will be B L tan B B L tan (5) 8 Substituting equation 5 into equation, Substituting equation 6 into equation, W W BB B λ λ x + tan L (6) 8 B tan L g g λ + an δ L (7) 3 λ Also the istance between the centre of the gravity of the weges Substituting for g g into equation 7, From the iagram, BB BB tan δl 8 λ B x B 3 λ B tan δ L 3 Metacentric raius, BB BM (8) tan α So, (9) Substituting equation 8 into 9 we have, BMx λ B 3 L tan α (0) But Volume isplacement An In case of longituinal stability. Determination of center of buoyancy from keel (KG) B 3 L I Substituting into 0 BM I () I BM L () L By the Geometry of the submerge section: The center of buoyancy is the centroi of the area of the submerge section: for a barge as of raft : the Buoyancy is given by: KB Centroi of the submerge section KB (3).3 Determination of height of metacenter above Keel (KM) Again from the Geometry: Substituting equations 3 for KB an λ B 3 L for BM Int. Journal of Applie Sciences an Engineering Research, Vol. 3, No. 6, 04 043
Numerical an experimental analysis for the stability of a 500 tonnes offshore work boat Alreay formulate expression, we have.4 Determination of metacentric height (GM) KM + λ B 3 L (4) From the Geometry of the barge, through the transverse section of the pontoon: By substituting the expression of KM from equation 4 so GM λ (5) 3 B L KG.5 Metacentric iagram KB an BM epens upon the raft, their values for any ship or barge can be calculate for a number of ifferent raughts an plotte to form the metacentric iagram for the ship, the KM curve is the meta centric iagram..5 Tonne per centimeter immersion Paulling et al (007) in their paper motion an capsizing in Astern Sea looke at the amount of cargoes loae on a vessel that woul to cause a parallel sinkage of one () cm which were supporte by Grochwalski et al (007) an Hanshin (008). Mathematically, it is expresse as tonne per C on immersion Area of water plan ensity TPC Ton 00 cm A w λ ton (6) 00 cm Where A w Area of water plane Density of sea water IF ρ.05 ton cm Substituting into 6 TPC A w.05 00 ton cm A W x0. 05 ton cm (7).6 Preliminary calculations from the hull forms The principal particulars of the barge are given as follows Length overall, LOA 4m Beam moule, B 7.5m Depth moule, D 5m Light barge raft,.6m KG.0m Dea weight 500 tons Int. Journal of Applie Sciences an Engineering Research, Vol. 3, No. 6, 04 044
Numerical an experimental analysis for the stability of a 500 tonnes offshore work boat 3. Calculation of the mass isplacement of the barge 3. Port Sie of the barge an starboar sie Figure 4: The form of the Barge The Area of the part sie A p From the iagram A Also, A 6m (.5 + 5) m. 5m But So But note that Area of part sie of the large is equal to that of the starboar sie. so total Area of part an starboar sie is 3. Top an 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 an Aft sie of the barge Area of the fore sie of the barge A F But Area of the fore sie of the barge A F equal to the Area of the Aft sie of the barge A a 3.4 Area of Comportment sie of the barge If one part of the barge is flooe to prevent the other comportment from flooing, comportment are place at every 5meter along the barge. Area of comportment A cv But we have 7 (seven) comportment Total Volume of the barge Total Area of the barge A T Int. Journal of Applie Sciences an Engineering Research, Vol. 3, No. 6, 04 045
Numerical an experimental analysis for the stability of a 500 tonnes offshore work boat The thickness of the plate use for the barge throughout to be mm Volume of barge (V b ) A T x thickness Total Volume of the Weling plate use for the barge V.F a 6m by 6m plate is to be use an thickness of the place mm. Volume of plate Total Number of Plate use for construction Barge Number of Plate (N P) Number of plate N p 38 for 6m by 6m by mm 3.5 Mathematical relation for isplacement with respect to raft The mass isplacement ( ) is the height of the water isplace by the rectangular barge. It is etermine by isplacement Displacement Light weight, 3.6 Inclining experiment moel This was performe to obtain accurately the vertical height of the center of gravity above the keel (KG & KG ) an verify with the analytical moel. This was carrie out at various loae weight an the barge inclination was also analyse at ifferent angle of heeling. The righting arm (GZ) was then estimate from the point of inclination of the work barge. Derrett (999) gave aequate recommenation on the principles of incline experiment in his material Ship stability for masters an mates Figure 5: Incline Experiment iagram The above figure escribes the position of the work barge at various heeling angles of 0, 5, 30, 45, 60, 75, 85 an the righting moment GZ have corresponing value of 0,.m,.85m,.5m,.5m, 0.45m, 0 respectively. The Analysis is one with ifferent loaing conition of the work barge an is plotte as shown in figure 6. Int. Journal of Applie Sciences an Engineering Research, Vol. 3, No. 6, 04 046
Numerical an experimental analysis for the stability of a 500 tonnes offshore work boat Figure 6: Graph of righting arm versus heeling angles Determining the stability ratio of the work barge from the experiment is one using the (Dave Gerr Estimation). This gives the positive energy area of the curve (PEA) AVS x Max GZ x 0.63 85 x.5 x 0.63 0.4875 egree-metres. While the negative energy area (NEA) of the curve (80-85) x Min. GZ x 0.66 95 x -0.475 x 0.66 9.785 egree-metres. The Stability ratio of the work barge 0.4875/9.785 4.05. As a general rule, Pawlowski et al (009) sai a stability ratio of at least 3 is consiere aequate for coastal work barge. 4. Results an iscussions 4. Analytical Calculation for maximum loaing of weight Cramic (000) in his paper Service Network esign in freight transportation sai at all times, it is of paramount importance for the naval architect to know exactly the maximum loa to be ae to a vessel an the rectangular barge here is not an exception, in orer to avoi capsizes of the barge. The coax of this work is base on etermining the maximum loa that can be ae for parallel sinkage at a height of five meters above the base that will not cause the barge to become unstable. Table : Displacement with Draft Relationship S/NO 3 4 5 6 7 8 Draft T (m 0.5 0.5 0.75.5.5.75 3.875 80.79 6.438 4.56 3.875 403.594 484.33 565.03 645.75 S/NO. 9 0 3 4 5 6 Draft T (m.5.5.75 3 3.5 3.5 3.75 4 3.875 76.469 807.88 887.907 968.65 049.344 30.063 0.78 9.5 S/NO 7 8 9 0 Draft T (m 4.5 4.5 4.75 5 3.875 37.9 45.938 533.656 64.375 Int. Journal of Applie Sciences an Engineering Research, Vol. 3, No. 6, 04 047
Numerical an experimental analysis for the stability of a 500 tonnes offshore work boat A graph of Displacement against Draft is shown below 6 5 Displacement (tonnes) 4 3 0 0 00 400 600 800 000 00 400 600 800 Draft Figure 7: Graph of Displacement versus Draft The Analytical proceure are outline below 500 tones at.6m Distance of center of buoyancy from metacenter BM BM B ( 7.5).6 Distance of buoyancy from the keel KB.6 m Distance of meta-center from the keel, Meta-centric height, GM After aing weight W, the new raft, becomes New raft ( + W ) (8) Substituting values for an initial raft into equation substituting values for an initial raft, into equation (8) above.6 ( 53.0575 + W ) 53.0575 847.3535 +.6 W 53.0575 53.0575 + W 3.875 (9) But BM B Int. Journal of Applie Sciences an Engineering Research, Vol. 3, No. 6, 04 048
Numerical an experimental analysis for the stability of a 500 tonnes offshore work boat New But New KB BM BM B 847.3535 +.6 53.0575 53.476563 (0) 53.0575 + W 53.0575 + W 3.875 W New New KM New BM + New KB Aing equation 0 an, we have New KG New KG 53.0575 + W KB () 645.75 KM KG 53.476563 53.0575 + W + () 53.0575 + W 645.75 KG + + WKG W 53.0575.0 + 5 W 53.0575 + W 056.576 + 5 W KG (3) 53.0575 + W But New GM (4) But if the barge will be Neutral stable, GM 0 Therefore the equation became that (5) Substituting equation an 3 into equation 5 53.476563 53.0575 Applying the Almighty formula to the above quaratic equation (6) ( 056.576 + 5W ) 53.0575 + W + + W 645.75 53.0575 + W 0 (6) W b ± b 4 ac a W ( 8.68 ) ± (8.638 ) 4 56863.63 The loa require on boar the barge will be 393.7 tonnes, while 97.5 tonnes will cause the barge to capsize, so the value 97.5 tonnes is neglecte. Hence W max 393.7 tonnes 4. Variation of GM with change in raft Ephraim an Douglas (99) in their technical report on analysis an esign of support system for weather for Golf Master looke at the loaing conition of a crane on a rig an sai whenever a loa, W is place Int. Journal of Applie Sciences an Engineering Research, Vol. 3, No. 6, 04 049
Numerical an experimental analysis for the stability of a 500 tonnes offshore work boat on boar centrally, it causes an aitional isplacement, ( ) which in turn shifts the center of gravity G of the barge to G an affects the metacentric height (GM). The transverse metacentric height falls until a point is reache where GM 0 an 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 avisable to operate the barge. 4.3 Determination of KG Sheng (000) looke at Change in raft as being equal to (.60m) cause by assume aition of weight, W. Volume of aitional weight (.6) x L x B, while the Weight of isplace volume is (7) But Shift in center of gravity ue to aition of weight, W with raft is expresse us GG WTG Substituting equation 8, 7 into 9 an noting that TG (5.0.0). 98m GG GG 3.875 (.6 ) x (5.0 ) 3.875 (.6 ) (.98 ) 4.876 (30) Hence KG KG + GG 4.3. Determination of BM (3) BM (8) (9) 4.876 4.876.6 + 3.6 (3) B Substituting values 4( 7.5) 4.4 Determination of GM GM KB + BM KG GM BM 4.6875 + 4.6875 3.6 4.876 + 9.55 + 3.6 (33) Equation (0), (5), (3), an (3) are use to obtain the table below an figure 7. The relationship between the raft an isplacement is an importance one especially when the subject of stability is mentione. From the isplacement raft graph of figure 7. It is observe that the slop of the graph gives the tonne per cm immersion for parallel sinkage. Slope of the isplacement raft graph of figure.7 isplaceme nt 049.344 4.56 Slope raft 3.5 0.75 Int. Journal of Applie Sciences an Engineering Research, Vol. 3, No. 6, 04 050
Numerical an experimental analysis for the stability of a 500 tonnes offshore work boat tonnes 3.875 m 3.9 tonnes cm The slope signifies that a loa of 3.9 tonnes will cause a parallel sinkage of one cm. Also from the stability calculation, it is observe that for a barge of 000 tonnes (ea weight) with length of 4m, beams of 7.5m an epth of 5m, the maximum loa at which the barge becomes unstable is 393.7 tonnes. This can be verify by using the below formula to check. The reason why I i not get 500 tonnes remain the fact that in practical light weight have to o with the weight of the metal plate an weight of weling which is not consiere here. So practically, So, any loa on the barge above 373.7 tonnes will cause the barge to sink or capsize. Table : Some stability parameters S/NO Draft (m) KB(m) BM (m) KM(m) KG (m) GM (m) 0.5 0. 9 9 5.7 3.6 0.5 0.3 9.4 9.6 4.3 4 3 0.75 0.4 6.3 6.6-4.7 7.88 4 0.5 4.7 5. -.4 4.88 5.5 0.6 3.8 4.4 0.7 3.3 6.5 0.8 3. 3.9.4 7.75 0.9.7 3.6.78.3 8.3 3.3.4 0.69 9.5.. 3..59 0.9 0.5.3.9 3..85 0.75.4.7 3. 3.07-0. 3.5.6 3. 3.4-0.4 Int. Journal of Applie Sciences an Engineering Research, Vol. 3, No. 6, 04 05
Numerical an experimental analysis for the stability of a 500 tonnes offshore work boat Figure 8: Draft versus the metacentric raius Figure 9: Graph of KM versus Draft Figure 0: Graph of BM versus Draft Figure : Graph of KB versus Draft 5. Conclusions The stability of the work boat in an offshore working conition was carrie out. The stability haracteristics of a rectangular work boat of imension 4m x 7.5m x 5m were etermine mathematically an analyze using International coes an stanars. The hyrostatic curves for the boat were plotte an use to etermine the optimal values for safe operation of the work Boat at sea operating conitions.. The stability analysis of a rectangular barge of imension 4m x 7.5m x 5m to avoi it from capsize provies results that meet safety requirements uring operations.. It is therefore emphasize from the research that within the loaing range less than 373.7 tonnes, the work barge shows a healthy stability ratio of 4.05. 3. It was further observe that an aition of weight to 373.7 tonnes will cause the work barge to capsize. 4. From the metacentric iagram, it is notice that the barge will become unstable when the rafts starts exceeing.45m as the variation of the isplacement against the raft gives a goo notice that per 3, tonnes of loa on the barge a parallel sinkage of one () cm will occur. 5. This approach presente here can be use to preict the loa range of the barge to a reasonable extent. 6. References Int. Journal of Applie Sciences an Engineering Research, Vol. 3, No. 6, 04 05
Numerical an experimental analysis for the stability of a 500 tonnes offshore work boat. Crainic, T. G, 000. Service network esign in freight transportation. European Journal of operational Research,.. Derrett D. R, 999. Ship Stability for masters an mates, Revise by Dr. C.B Ree Eucational an Professional Publishing Lt Barras, Oxfor Aucklan Boston Johannesburg Melbourne New Delhi, 3. Ewar, V. L, 988. Principle of Naval Architecture Secon Revision: Stability an Strength Volume I. The Society of Naval Architecture an Marine Engineers. New Jersey, 4. Ephraim M. E, an Douglas, I. E, 99. Technical Report on Analysis an Design of support system for weather for Gulf master G 5F Crane on the Anini- Rig, 5. Grochwalski, S, Rask, I, an Soerberg, P, 007. An Experimental Technique for investigation into Physics of ship capsizing in Proceeings. Thir International Conference on stability of ship an Ocean vehicles, STAB 86, Gansk, Polan. 6. Hanshin, M. D. 008. Hyroynamics Theory of ship motions. Publishe by Nauks, Moscow, (in Russian). 7. Lloy s Register, 997. Classification of Ship Rules an Regulations Part 3: Ship Structure Lonon,. 8. Norrbin, N. H., 950. The Design of Sea kinly Ships. North-East Coast Institution of Engineers an Ship-owners, Newcastle upon Tyne, Unite Kingom. 9. Pauling.J. R, Oakley, O. H, an Woo P. D, 007. Motion an Capsizing in Astern Sea in Proceeings. Tenth Symposium on Naval hyroynamics. 0. Pawlowski, J. S, Bass, D. W, an Grochowalski, S. A, 009. Time Domain Simulation of ship motion in Waves in Proceeings. 7 th Symposium on Naval Hyroynamics, The Hague, Netherlans.. SHENG Zhenbang 00. Principle of Ship (M). Shanghai. Shanghai Jiaotong University press,. Int. Journal of Applie Sciences an Engineering Research, Vol. 3, No. 6, 04 053