ABSTRACT Ortogonal Tipping in Conventional Offsore Stability Evaluations J. Andrew Breuer* Cief Engineer, Offsore Engineering Department, ABS Amerias Karl-Gustav Sjölund Consultant Researer, Seasafe AB, Sweden Originally presented at te STAB 2006 onferene eld in Rio de Janeiro, Brazil September 22-29, 2006 and reprinted wit te kind permission of te International Conferene on Stability of Sips and Oean Veiles Ortogonal tipping is a penomenon tat frequently auses problems in te appliation of onventional stability evaluation metods wen applied in all diretions as is done for offsore strutures. Experiene sows tat often it is diffiult to find an interpretation of te stability rules tat allows te alulation of a relevant free trim rigting lever urve overing a suffiient range of eel. In te ligt of reent additions to te damage stability riteria for jak-ups introdued by ABS, te paper presents te nature of ortogonal tipping, te limitations of onventional stability analysis proedures, and an alternative metod to evaluate te Range of Stability witout expliit use of a rigting lever urve. Altoug equivalent to te onventional metods based on te rigting lever urve, tis metod avoids te ortogonal tipping problem, and tus onsistently produes relevant results. Te paper also investigates te possibilities to generalize te metod to over oter types of stability riteria. Keywords: offsore, stability, mobile offsore unit, damage, range of stability. INTRODUCTION Beause most offsore units and floating installations ave omparable lengt and breadt, transverse stability is not suffiient to establis te safety of te floating vessel. Tis as been resolved by following onventional transverse stability metodology to any orientations. Te metodology inludes te development of rigting arm urves wit te ull rotating about an axis tat is sequentially sifted at regular angular intervals for all 360 degrees. Te omplexity brougt in by inorporating a tird dimension to te metod an only be resolved wit omputers. Tis approa applies to all offsore vessels, drilling units and offsore prodution installations. Tis inludes jak-up and semisubmersible drilling units, drill sips, spar and semisubmersible prodution installations, and almost any vessel dediated to te offsore oil industry. Figure Semi-submersible Drilling Rig Ortogonal Tipping in Conventional Offsore Stability Evaluations 327
2. HISTORY Wile te offsore oil ativities an be traed bak to te early 900 s, drilling from a floating vessel was first aieved in 947. Early mobile offsore drilling units (MODU) onsisted of a dek barge wit te industrial equipment set on dek. Te first jak-up rig was ommissioned 954 and te first purpose built semi-submersible was built in 964. A group formed by regulators, naval aritets, and rig designers took on te task of developing te first rules for MODU; te rules were first publised in 968 []. allowable eigt of te enter of Gravity (AVCG) as a funtion of draft. Te usual proedure is to alulate te AVCG based on te intat stability riteria and separately te AVCG based on damage stability riteria. Te AVCG is presented to te onboard operating personnel eiter as a table or as grap. MODU are usually designed to operate in two different modes; normal operations and storm survival. Wile te intat stability riteria are te same, te former is based on a 36 m / s wind and te latter on a 5 m / s wind veloity. Calulations are performed for a sequene of wind diretions defined by te azimut angle to establis te Rule requirement to ave suffiient stability (rigting stability) to witstand te overturning moment equivalent to te one produed by a wind from any orizontal diretion[]. Figure 2 A four leg Jak-up drilling unit in operation Te Rules inluded many innovations; most notably te introdutions of stability requirements; intat and damage. Te main reason for tese innovations was te lak of statutory standards to resolve te unique proportions and subdivision of MODU. Wile it is lear tat onventional stability standards ave little appliation to MODU, te metodology and approa to sip stability ontinues to influene te subjet in te offsore industry. 3. METHODOLOGY Stability analysis for offsore units is usually direted to te determination of te maximum Figure 3 Axis system for stability evaluation of a MODU For ea azimut angle Ψ, te rigting arm (GZ) is alulated for a sequene of angles of inlination about te axis ξ. Te axis oinides wit eeling moment vetor imparted by te wind. As te ull eels around te axis, te enter of buoyany (CB) sifts in te diretion of wind and in te diretion perpendiular to te wind diretion. Following te free trim standard, te perpendiular to te wind sift of te CB is neutralized by trimming te azimut axis su 328 Ortogonal Tipping in Conventional Offsore Stability Evaluations
tat te enter of gravity (CG) and CB remain on te same vertial Plane. For te purpose of tis paper, and following te ommon pratie in industry, te following notation is used: Generalized Heel (G-eel) is te angle of rotation of te ull about te Azimut axis ξ. If te azimut angle is nil, eel follows te definition used in sipbuilding. Generalized Trim (G-trim) is te angle of te azimut axis wit respet to te orizontal. If te azimut angle is nil, trim follows te definition used in sipbuilding. Inlination is te angle between te ull base plane and te orizontal. 4. RECENT DEVELOPMENTS In 956 QATAR I beame te first jak-up lost wile in transit. Following tat loss, not less tan twenty-four oter jak-ups were lost in transit; last one in 998.[2] Te investigation of tese inidents resulted in many anges in te way tese rigs are transported and operated. From a regulatory point of view, it was determined tat most jakup are well subdivided despite te lak of adequate subdivision standards. Te main weakness of most standards is te assumption tat jak-up rigs are mainly exposed to damage by way of ollision or from leakage troug te bottom sell. Tis approa, tat strongly emulates te earlier standards for onventional vessels, does not reflet te flooding troug te dek tat was determined to be te most frequent ause of loss of jak-up in transit. Industry, gatered in various working groups, ontinued te resear of te auses of tese inidents. Based on te findings, new proedures for towing jak-up publised in te early 990 s greatly redued te frequeny of tese inidents. Anoter onlusion from tis investigation establised te need to develop adequate standards of internal subdivision of Jak-up. An ad-o ommittee formed by representatives of Industry was reported in two papers presented at te International Conferene in te jak-up platform [2], [3]. Te main ange brougt in troug te findings of te Ad-o ommittee is a new subdivision standard wit te following notable aspets:. In addition to te ompartments exposed to ollision, all oter ompartments are subjet to a single ompartment flooding standard. 2. Te pre-existing standard of positive stability and no down flooding under a 50-knot wind applies to all ompartments regardless of loation. 3. Te unit after damage must ave a residual stability wit a minimum range of stability (RoS) of: RoS o. 5 7 ϕ or S o RoS 0 Wiever is greater. Were φ S is te stati angle of eel after damage Figure 4 Residual stability standard for Jak-up Te new standard, publised in 2005 4, applies to onstrution ontrats signed after January, 2005. Te new standard produed unexpeted results wen applied to on ertain damaged onditions and diretion of stability as a peuliar alulation penomenon ourred. Even wen te unexpeted event was reported in 986 by Van Santen [5], te problem aused mu onern. 5. ORTHOGONAL TIPPING Te first indiation of tis alulation problem manifested wen te GZ alulations failed to Ortogonal Tipping in Conventional Offsore Stability Evaluations 329
yield results for te full range of angles of inlination speified for te alulation run. Wen plotted, a typial GZ urve would look as in Figure 6. Beause offsore strutures are irregular in sape, waterline properties used to balane te ull by way of multiple approximations do not onform to a ontinuous funtion. Tis lak of ontinuity is often te reason for failure to onverge to a solution. Depending on te software, failure to onverge sometimes results in an inomplete GZ urve su as tose experiened wen alulating stability urves to determine te RoS of damaged jak-up. Figure 5 illustrates an inomplete urve. Te termination of te urve will be referred as te fading stability point and te angle as FA intat ull forms, were not adequate under te new riteria. Questioning te adequay of te onventional metods te investigation led to a return to first priniples of engineering. Tis also involved te development of new omputational tools for existing offsore stability software 6. ISO-ENERGY CONTOURS 6. Energy to eel and trim Te onventional approa to alulating te energy to eel te vessel onsists in te integration of te rigting arm moment frequently referred to as te Area under te rigting arm urve E θ P Θ EP = GZ dϕ () 0 0 Tis metod is so generalized tat most intat stability, and sometime damage stability, standards will express requirements of eeling energy in terms of Radian-meters or Footdegrees as opposed orret ones in Lengtfore units. Figure 5 Inomplete GZ Curve Furter analysis of oter results of te alulation, sowed tat te trim onsistently grew to very large values as te ull was inlined towards FA. A first evaluation of tis penomenon interpreted as equivalent to a apsizing not in te diretion to wi te unit was inlined but in te ortogonal diretion. Te onventional RoS is establised as a differene between te zero-rossing angles of te GZ urve as sown in Figure 2. However, a apsizing, regardless of diretion, is equivalent to a zero-rossing and effetively te upper end of te RoS. Tis onlusion, wile plausible, lead to te unexpeted and wrong onlusion tat subdivision arrangements, and even well tested Figure 6 Conventional alulation of energy to eel Te work needed to inline (furter referened as energy to inline) orresponds to te inrease in potential energy (E P ) and an be determined by rigorous metod. Tis proedure requires an aurate determination of te position of CB. Manual alulations seldom meet tis standard and te need for omputers may explain wy tis metodology is rarely found in traditional text. 330 Ortogonal Tipping in Conventional Offsore Stability Evaluations
Figure 7 Rigorous determination of te energy to eel For a onstant displaement, te energy to inline is determined by te ange in potential energy from te equilibrium position to te inlined position. Te inrease is proportional to te ange in vertial distane between te enter of gravity and te enter of buoyany. Figure 7 illustrates te metodology and te E P equation is: ( BZ BG ) ( B Z BG) δ EP = (2) EP ~ (3) Were is te displaement Te rigorous metod to alulate te energy to inline ompares te inlined-ondition wit te ondition-of-equilibrium. Terefore, te alulation is independent of te pat of integration and is not affeted by te diretions of stability, initial onditions, or te effetiveness of te iterative proess to aieve balane. 6.2 Representing of te Energy to Inline To visualize te energy we developed a model of a fititious jak-up. A typial void ompartment adjaent to te aft end of te ull is also flooded wit diret ommuniation wit te sea. Figure 8 Model used for alulations and illustration For te seleted damage ondition, wit a onstant position of te enter of gravity and onstant displaement, an azimut of 270 o, te energy to inline was alulated for a matrix of G-eel-G-trim ombinations. Te alulated energy to inline, represented in an Ortogonal system of G-Heel (X axis), G- Trim (Y axis), and E P (Z axis). Te energy at te position of stati equilibrium after damage (PSE) is used as te energy baseline. Figure 9 Energy to eel surfae In an ortogonal 3-axis system, te matrix of results of G-eel, G-trim, and Energy, represent a surfae. Te same surfae an also be represented as a topograpi art by presenting E P in terms of iso-energy ontours. Having establised te inrease in vertial distane between te enters of Buoyany and Gravity (BG), te analogy between te energy surfae and te motions of a partile on a Ortogonal Tipping in Conventional Offsore Stability Evaluations 33
pysial surfae is evident and is used to understand statis of stability afloat. Figure 0 Iso-Energy ontours 6.3 Nature of Ortogonal Tipping To understand te subjet event, te sequene of G-eel and G-trim alulated in te development of te GZ urve illustrated in Figure 5 is plotted in Figure. It an be seen tat as te ull is G-eeled, te initial G-trim (2 o approximately) remains relatively onstant but after 3 degrees of G-eel beyond te position of stati equilibrium, G-trim inreases to a point were te rotation is only in te Gtrim diretion wit no inrease of G-eel. 6.4 Observations on te Energy Surfae Te general sape of te energy surfae will ange dramatially for ea of te intat or damage ases and te parameters of te alulation. However, a number of notable points and lines is found on all surfaes. Beause te undisturbed ull will balane at te lowest point of energy aievable, te low point in a depression will always be te representation of a stati position of equilibrium. If a surfae is developed for a full range of G-eel and G-trim, more tan one position of equilibrium will likely be found; usually orresponding to te uprigt and apsized onditions. Hulls wit a CG below te CB, su as spars, submarines, drydok gates, will result in a single depression, On onventional offsore ulls te general sape will ave te depression wit several peaks around tem and te peaks will be onneted by ridge lines. Te ridge lines are notable in tat are te slope divide and terefore onstitute a watersed. Tis means tat a partile will roll down one side of te ill or te oter, depending on wi side of te watersed line it starts its motion. Figure G-Heel - G-Trim pat for GZ alulation Beause motions of te ull will not be toward an inreased G-eel, te point of fading stability an also desribed as a point of refusal. Figure 2 Notable points of te energy surfae Following te analogy of floating stability and partile motions on a surfae, te watersed line is te limit of positive stability. A ull inlined beyond a ombination of G-eel and G-trim will not return to te position of stati equilibrium. Terefore, te watersed line 332 Ortogonal Tipping in Conventional Offsore Stability Evaluations
orresponds to te seond zero-rossing on te rigting arm urve. Matematially, if Θ ~ GZ dϕ EP (4) Ten 0 EP GZ ~ (5) ϕ Tus E P will ave a maximum value wen GZ = 0. Te watersed line segment between peaks will ave a low point or minimum. Tese saddle points are speial points of apsizing as tey are at relative low levels of energy. In te partiular ase sown in Figure 2, tree saddle points are identified. Te distane between te position of stati equilibrium and ea of te saddle points onstitute a range of stability. Furter, it is easy to establis tat su distane is te minimum range for te family of rigting arm urves alulated for tat general diretion. 6.5 Waterplane parameters in te Isoenergy ontours Assuming te ull fixed to te oordinate system, te waterplane may be desribed by te vetor normal to te plane: N r d = 0 N = Sin θ iˆ ( Cos θ Sin ϕ ) ˆj ( Cos θ Cos ϕ )kˆ (6) (7) Were: N : is te Plane s normal r : is a vetor from te origin to any point in te plane d: is te distane of te origin to te plane θ: is te angle of G-Trim φ is te angle of G-Heel Te angle Ψ from te axis of azimut to te axis of inlination an be alulated as: π ArTan ( N / N 2 ) if N 2 < 0 ψ = sign ( N ) π / 2 if N 2 = 0 (8) ArTan ( N / N 2 ) if N 2 > 0 or, for inlinations less tan π/2 radians, π ArTan ( Tanθ / Sinϕ) ψ = sign( θ ) π / 2 ArTan ( Tanθ / Sinϕ) if ϕ < 0 if ϕ = 0 if ϕ > 0 (9) Figure 3 RoS on iso-energy ontours Going bak to Figure 0 te GZ alulation sowing te sequene of G-eel - G-trim ombinations, it an be seen tat te point of fading stability is reaed before te point of apsizing. Beause te latter point will not be reaed by inlining te ull around te establised axis, te onept of range of stability annot be applied to te ase. Te most important onlusion from tis is tat GZ urves tat fade annot be used to establis RoS. Te angle ψ between te vessel s longitudinal axis and te axis of inlination is: ψ = ψ ξ (0) 6.6 Range of Stability - Redefined It is lear tat determining RoS by developing a onventional rigting arm urve is not adequate. Furtermore, te approa to evaluating stability by rotating te ull about a fixed axis is questioned. If floating stability is defined as te ability of te ull to return to te position of equilibrium after it as been disturbed, we an define Range Ortogonal Tipping in Conventional Offsore Stability Evaluations 333
of Stability to be te angle to wi te ull an be inlined and return to te position of equilibrium. In aepting tis premise, te pat troug wi te ull returns, is not signifiant as long as it does not go beyond te boundaries of stable positions. A furter onlusion tat drawn from tis premise is tat beause te onept of rotation about a fixed axis is moot, we must aept tat te range of stability is te differene between te inlination of te waterplane between te position of stati equilibrium and te angle of apsizing. To illustrate tis point, Figure 3 sows te watersed lines and a line representing an inlination of 0 o beyond te angle of stati equilibrium. RoS in te Iso-energy ontours orresponds to te inlination of te ull at te position of stati equilibrium and te losest point on te watersed line most likely at te nearest saddle point In Matematial terms, RoS an be alulated as follows: N N RoS = Sin iˆ 7. ALTERNATIVE INCLINING PATH 7. Dynami desent θ () ( Cos θ Sin ϕ ˆ ) j ( Cos θ Cos ϕ ) kˆ = Sin iˆ ( Cos θ Sinϕ ) ˆj Having establised tat te onventional approa to stability follows an unlikely θ (2) ( Cos θ Cos ϕ ) kˆ = ArCos ( N N ) RoS = ArCos ( Sinθ Sinθ Cosθ Cosθ Cos ( ϕ ϕ )) (3) (4) sequene of eel-trim ombinations, te question to resolve is wi sequene is te teoretially orret pat and wat assumptions we must make to rea tat answer. Following te analogy of te partile moving on a surfae, we ould assume tat a spere in te position of stati equilibrium, reeives an impulse to roll upill. Dismissing te effet of frition, we an expet te spere to rea a ertain elevation and ten endlessly roll down and up te ill. Wit su motion, te sum of potential and kineti energy remains onstant. Wile speial ases ould result on an endless repeat of te same pat, most likely, te spere will roll following an apparently random pat. 7.2 Steepest desent metod. Te alternative to a dynami approa is a quasi-stati pat. Tis means tat as te partile returns to te position of equilibrium, te loss of potential energy does not onvert to kineti energy. Under su a premise, te partile would follow te steepest desent pat (SDP) su tat te potential energy will deplete troug te most effiient pat. Te pat is a funtion of te starting point and te initial diretion imparted to te partile. If te floating stability evaluation ase is assumed a stati event, te SDP is a realisti solution; inluding te evaluation of RoS. Were dynamis are part of te event, te SDP departs from teory but follows first priniples better tan te onventional stability analysis. Te SDP as te simpliity needed to resolve stability expediently and it follows aeptable priniples of pysis. A dynami approa, wile possible, is extremely omplex and still separated from reality due to te random nature of te environmental fores and exitations. Wit te SDP approa, te starting point and te initial diretion of motion determine te pat. Te pat is perfetly reversible; meaning tat te pat does not depend on te diretion of te motion, and tat te pat of energy buildup will be idential to te pat of energy depletion. 334 Ortogonal Tipping in Conventional Offsore Stability Evaluations
If te vessel is displaed from its equilibrium to an arbitrary point somewere witin te watersed desribed, te moment resulting from te gravitational fores will always tend to rotate te vessel along a SDP. Tis is beause te moment vetor is always parallel to te SDP. Wen te steepest desent metod is used, we intrinsially allow te ull freedom to rotate relative te diretion of te eeling and rigting moments. Tis is te fundamental differene between te SDP metod and te onventional free trim rotation tat fixes te moment diretion relative te sip geometry. Te freedom to rotate prevents te ourrene of fading stability in SDP and te lak of it is te ause in te onventional approa Figure 4 sows te families of pats tat follow te SDP priniple. We an note te following properties of te SDP: Figure 4 Steepest Desent Pats. All pats pass troug te extreme points of te E P surfae - peaks and position of stati equilibrium. 2. Te pat are perpendiular to te ontour lines at te point of intersetion. 3. Boundary lines between families of lines, a dividing line onneting te point of stati equilibrium wit te saddles, define te diretion of minimum range of stability. 4. Te boundary lines are a singular ase of a SDP but beause te line reaes te saddle, te ull apsizes witout progressing on te watersed line. 5. Tere is no fixed relation between te moment diretion and te inlination axis. 6. Tere is no fixed relation between te moment diretion and a body-fixed axis. 7.3 Analysis of stability along a SDP A Stability urve an be developed in assoiation wit any SDP under ertain assumptions. Te GZ-urve is a funtion of one parameter ξ. For te steepest desent rotation pat, te natural oie of ξ is te rotation along te SDP, i.e. a rotation tat is parallel to te moment vetor at all times. Te value of ξ in a given point tus equals te lengt of te pat measured from te point ξ = 0. Tis oie as te following two important advantages:. Only troug tis oie will te area below te GZ-urve be proportional to te buildup in energy. Tis is beause te rotation is always parallel to te moment vetor along te SDP. 2. It is always possible to present GZ as a funtion of ξ irrespetive of ow te pat twists and turns, sine te value of ξ always inreases along te rotation pat. Terefore, te GZ urve never fades, and ortogonal tipping does not our. Te urve allows evaluation of range of stability and oter stability parameters. A typial SDP Rigting arm urve GZ = f(ξ) is illustrated in Figure 5. As indiated before, te boundary line between families of SDP is a singular pat tat must be paid speial attention. Beause tey terminate at te saddle point, a relative minimum E P, tis pat is likely to be a ritial one. Ortogonal Tipping in Conventional Offsore Stability Evaluations 335
Te SDP stability urve allows evaluation in te same way as a onventionally alulated stability. Tis inludes te typial ritial angles su as, first (ξ ) and seond interepts (ξ 2 ), first (ξ 0 ) and seond zero-rossing (ξ - stati equilibrium and apsizing), and te angle of maximum rigting arm (ξ m ). However, te onept of diretionality, eel and trim is no longer relevant as te angle evaluated is te inlination of te ull and te onepts of eeling about an azimut axis and te trimming of te axis are no longer valid. Figure 5 Steepest Desent Pat Stability Curves If te analysis assumes te superposition of a wind overturning moment, a relative rotation of te ull about a vertial axis must be aepted as te diretionality of wind must be onsistent wit te rotation along te SDP. 7.4 Implementing te SDP onept In priniple, te evaluation of intat or damage stability based on te SDP metod is not vastly different from evaluation based on free trim GZ-urves, but te notable differene in oie of rotation pat(s) as a signifiant effet on te alulation algoritm. Obviously, tere will be various solutions to te problem, and a detailed algoritm is outside te sope of tis paper. However, for a vessel were no assumptions an be made regarding ritial evaluation diretions, te proedure ould involve te following steps:. Analyze te funtion Ep to find any extreme points witin a relevant definition region, e.g. all inlinations < 40 degrees. Sine te omponents of te moment vetor M are te partial derivatives of Ep, te most straigtforward approa is to find all solutions to te equation M = 0 witin te definition range. Te funtions Ep and M an be approximated using a grid of triangular faets. Ea value point in te grid orresponds to a ertain eel and trim and te buoyany and displaement need to be balaned for ea knot in tis grid. 2. Determine te rotation pats. In setors of te definition region were te watersed line ours, ea pat will pass troug eiter a saddle-point or a loal maximum (See figure 4). Te pats must be distributed in su a way tat tey over te entire definition region in order to ensure tat ritial ase will be identified during te riteria evaluation. Care sould be taken to inlude te singular pats tat pass te saddle points. 3. Generate te stability urve orresponding to ea pat. Tese urve plots te magnitude of M (divided by te displaement) as a funtion of ξ, te rotation along te SDP (See setion 7.3). 4. For ea of te stability urves, verify a set of riteria. 5. If te task is to establis a limiting KG, steps -4 need to be repeated to arrive at te limiting value. One possibility is to vary KG using bisetion. Te balaning of buoyany and displaement is performed only one, and need not be repeated in tis iteration. 8. CONCLUSIONS Experiene sows frequent problems to establis Free-Trim GZ-urves for different types of offsore units. Tis makes stability evaluation problemati. Te evaluation of ABS new damage stability standards depending on te Range of Stability (RoS) is signifiantly affeted by tis problem. Conventional free to trim stability proedures are inadequate to establis Range of Stability beause it assumes an unrealisti sequene of eel-trim ombination. Conventionally obtained rigting arm urves in offsore an terminate at unexpeted angles of eel. Te fading of tese urves is not an indiation of apsizing and do not onstitute a seond zero-rossing of te GZ urve. If 336 Ortogonal Tipping in Conventional Offsore Stability Evaluations
onventional metods are applied, fading GZ urves sould be disregarded. Te energy to inline a ull is a funtion of te initial and final position of te ull and not a funtion of te sequene of eel trim ombinations. Range of stability and oter stability properties an be determined by analysis of te energy to inline surfae. Applying te steepest desent pat to te evaluation of intat and damage stability appears to be more rational tat te onventional free to trim. Te steepest Desent Pat allows te rotation of te azimut axis and resolves te problem of ortogonal tipping. 9. ACKNOWLEDMENTS Te autors wis to aknowledge te unrelenting support of te ABS Amerias Offsore Stability Team, inluding, T.S. Bus, R. dos Santos, B. Radanovi, and J.H. Rousseau. 0. REFERENCES [] ABS Rules for Building and Classing Offsore Mobile Drilling Units, 968 (setion 3.3.2, Stability Afloat, [2] Breuer, J.A., Bowie, R., 2003, Te Future of Jak-up Stability Learning from Our Past, Nint International Conferene on te Jak-up Platform, City University, September 2003 [3] Breuer, J.A., Bowie, R., Bowes, J., Internal Subdivision of Jak-upsa new standard to resolve an old onern, Tent International Conferene on te Jakup Platform, City University, September 2005 [4] ABS Rules for Building and Classing Mobile Offsore Drilling Units, 2005 [5] Joost van Santen, Stability alulations for jak-ups and semi-submersibles, Conferene on Computer Aided Design, Manufature and Operation in te Marine and Offsore Industries, September 986 Ortogonal Tipping in Conventional Offsore Stability Evaluations 337