Current Status of Second Generation Intact Stability Criteria Development and Some Recent Efforts

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1 1 Current Status of Second Generaton Intact Stablty Crtera Development and Some Recent Efforts Naoya UMEDA Osaka Unversty ABSTRACT The paper summarses the current status of the second generaton ntact stablty crtera development for all fve falure modes n the correspondence group establshed at SLF 55. Some ponts to be dscussed n publc are remarked and some recent works for them by the author are also presented. The dscusson ponts ncludes that desgn measures for avodng parametrc roll of contanershps and car carrers, safety levels of three layers and the methodology for excessve acceleraton ssues. KEYWORDS Parametrc rollng, pure loss of stablty, broachng, dead shp, excessve acceleraton INTRODUCTION At the Internatonal Martme Organzaton (IMO), the second generaton ntact stablty crtera are now under development. These crtera are based on physcs so that they are expected to be applcable to any shps n prncple. Thus the use of new crtera could allow us to desgn completely new shps sutable for new era wthout emprcal restrctons. The new crtera wll be mandatory n the long run by beng referred n the SOLAS and LL conventons for passenger and cargo shps of 24 meters or longer. (Francescutto and Umeda, 2010) The second generaton crtera deal wth fve falure modes: pure loss of stablty n astern waves, parametrc rollng, broachng, harmonc resonance under dead shp condton and excessve acceleraton. For each falure mode, the frst and second level vulnerablty crtera and the drect stablty assessment procedure as the thrd level wll be developed. A shp s requred to comply wth one of the three crtera for each falure mode. Here the lower level crtera requre smaller effort for the desgner but wth larger safety margn. In case the shp fals to comply wth the second or thrd level crtera, operatonal lmtaton or gudance shall be developed based on the outcomes of the appled crtera For pure loss of stablty n astern waves, parametrc rollng and broachng, the drafts of the frst and second level crtera are agreed except for some remaned tems. For dead shp stablty, consoldated proposal wll be avalable for fnalsng the second level crtera. For excessve acceleraton, t was confrmed that exstng proposals cannot be used as they are now. Ths paper summarses the current status of the second generaton ntact stablty crtera development and presents some ponts to be dscussed n publc and recent works by the author for resolvng the problems for realsng the new crtera.

2 2 PURE LOSS OF STABILITY IN ASTERN WAVES Roll restorng moment of a shp n longtudnal waves could be reduced when a wave crest s stuated n the shp centre and the wave length s comparable to the shp length. In case of astern waves, the shp could start to roll as a result of the restorng reducton wth low wave encounter and natural roll frequences and then the roll nduces addtonal hydrodynamc roll moment due to the unsymmetrcal underwater hull shape. Based on the above mechansm of pure loss of stablty, the IMO agreed the frst and second level crtera n prncple. The current draft s set out as the Annex 2 (SLF 55/WP.3) wth the square brackets whch ndcate undecded tems. balance n snkage and trm s used. Here three stablty ndces n one wave cycle shall be examned: the mnmum GM, the largest loll and the smallest value of maxmum GZ. However, t was agreed to exclude the GM because t s equvalent to non-exstence of loll. As ts alternatve, one delegaton proposed to use the angle of vanshng stablty. The requred value for the maxmum GZ dependng on the Froude number represents addtonal hydrodynamc roll moment due to the unsymmetrcal underwater hull shape. n calm water wth lowest draught n calm water n waves (wave crest at mdshp) Frst and second level crteron In the frst level crteron, the metacentrc heght, GM, n longtudnal waves s requred to be postve n prncple. If GM n longtudnal waves s suffcently postve, most lkely GZ n waves s suffcently large. If GM n waves s negatve wth larger freeboard, GZ could be suffcent. Thus the requrement of GM could be more conservatve. The GM n longtudnal waves can be calculated by a smplfed method except for tumblehome topsde vessels. Here the moment of nerta of waterplane n waves can be approxmated wth that n calm water but wth lowest draught. Ths s because the restorng reducton n longtudnal waves depends on manly bow and stern parts, as shown n Fg. 1, so that we can gnore the effect of mdshp part for ths purpose. As a result, the conventonal hydrostatc curves are suffcent for the applcaton of the frst level crteron. Ths could avod unnecessary ncrease of shp desgners loads because most of ol tankers and bulk carrers are not relevant to ths falure mode at all. In the second level, drect calculaton of GZ n longtudnal waves s requred for a shp but the Froude-Krylov approxmaton wth statc Fg. 1 Smplfed estmaton of restorng reducton on a wave crest. For the reference wave heghts and reference wave lengths, two canddates are avalable for fnal decson at the IMO. One s the 16 representatve wave cases. The other s Grm s effectve wave heght (Grm, 1961) calculated for all possble sgnfcant wave heghts and zero-crossng wave perod appeared n the wave scatterng dagram of the North Atlantc wth the wave length equal to the shp length. Snce the latter s more strngent than the former, the requred probablty (standard) of dangerous sea states should depend on the selecton of reference waves as follows: R [0.06 n the former] [or 0.15n the latter]. PL0

3 3 Drect stablty assessment For the drect stablty assessment, we can use numercal smulaton of nonlnear roll moton coupled wth manoeuvrng motons (SLF 55/INF.15). Thus t s possble to dentfy the case that a shp havng smaller maxmum GZ could survve n realstc ocean waves wth hydrodynamc effect other than the hydrostatc restorng moment. PARAMETRIC ROLLING The roll restorng varaton n longtudnal waves could nduce sgnfcant roll moton as a parametrc roll resonance. The current draft s set out as the Annex 1 (SLF 55/WP.3) wth the square brackets whch ndcate undecded tems. Frst level crteron If we apply an averagng method or equvalent to the uncoupled roll model wth snusodal GM varaton and nonlnear roll restorng and dampng moment, the ampltude of the parametrc roll can be analytcally determned (e.g. Sato, 1970). If the nonlneartes of roll restorng and dampng are excluded, the occurrence condton of parametrc roll can be obtaned as GM GM R PR. (1) Here R PR represents the lnear roll dampng for a steady state or the combnaton of the lnear roll dampng and wave group effect for a transent state. In the frst level crteron, the GM can be calculated by a smplfed method except for tumblehome topsde vessels. Here the moment of nerta of waterplane n waves can be approxmated wth that n calm water but wth lowest or hghest draught. Ths s because the restorng varaton n longtudnal waves depends on bow and stern parts, as shown n Fg. 1, so that we can gnore the effect of mdshp part for ths purpose. As a result, the conventonal hydrostatc curves are suffcent for the applcaton of the frst level crteron. Here the roll dampng s assumed to be always a constant regardless actual hull forms or to be a smple emprcal estmate but dependng on the area of blge keel and blge crcle effect. And the wave steepness s assumed to be Second level crteron The second level crteron conssts of two checks. A shp s requested to comply wth one of them. Its frst check s based on the same methodology used n the frst level crteron but drect calculaton of GM n longtudnal waves and the examnaton wth 16 wave cases are requred. In addton, the effect of forward speed wth related to wave and roll frequences s ncluded. In ts second check, the judgement s gven wth the calculaton of ampltude of parametrc roll n snusodal waves. Here drect calculaton of GM n longtudnal waves and that of roll dampng moment usng the smplfed verson of Ikeda s sem-emprcal method (Kawahara et al., 2009) or the equvalent are used. The GZ curve n calm water s ftted wth a quntc formula and the dampng s ftted wth a cubc formula. In prncple, the ampltude of parametrc roll s calculated by usng an averagng method. Alternatvely, tme doman numercal smulaton could be used f the GZ curve s too complcated. The use of tme doman numercal smulaton for transent effect s also under dscusson. In ths case, the used wave heghts are Grm s effectve wave heght calculated for all possble sgnfcant wave heghts and zero-crossng wave perod appeared n the wave scatterng dagram of the North Atlantc and the wave length s equal to the shp length. Thus, we can obtan the roll ampltude for all possble shortterm sea states n the North Atlantc. Then the probablty to meet dangerous sea states where

4 4 the roll ampltude s greater than the crtcal angle can be calculated and s compared wth the requred value. If the shp fals to comply wth ths check, these data could be used for the operatonal lmtaton. Drect stablty assessment For the drect stablty assessment, we can use numercal smulaton of nonlnear roll moton coupled wth vertcal motons. Ths approach allows us to take account of the effect of vertcal motons on roll restorng varaton. Ths effect could reduce the possblty of parametrc roll. Thus the drect stablty assessment s less conservatve than the second level crtera. BROACHING Broachng s a phenomenon that a shp cannot keep a constant course even wth the maxmum steerng effort. It often occurs when a shp s surf-rdded n followng waves and the centrfugal force due to accelerated shp forward velocty and large yaw angular velocty could result n capszng. Thus the frst and the second crtera were agreed to use crtera for preventng surf-rdng as shown n SLF 54/WP.3. Broachng tself could happen wthout surf-rdng but the forward velocty s generally low so that danger for capszng s not so hgh. Frst level crteron The frst level crteron for broachng s already agreed at the IMO as follows. If the operatonal Froude number s larger than 0.3 and the shp length s smaller than 200 metres, the shp s judged as vulnerable to broachng. The former requrement s exactly the same as that n MSC/Crc. 707 developed n 1995, whch was superseded as MSC.1/Crc It s based on the smallest value of surf-rdng threshold calculated by global bfurcaton analyses of several shps wth the wave steepness of 0.1 and the wave length to shp length rato of 1 or over. The latter shows smaller possblty of occurrence of wave length of 200 metres or over. Second level crteron In the second level, drect estmatons of surfrdng threshold for a gven shp n snusodal waves are requred. Here the Melnkov method (Kan, 1990; Spyrou, 2006) or equvalent as a global bfurcaton analyss can be used. The wave condtons shall cover varous wave heghts and lengths. Then the short-term probablty of surf-rdng can be calculated wth Longuet-Hggns (1983) s theoretcal formula of the jont probablty densty of local wave heght and length. The long-term probablty of surf-rdng s requred to be calculated wth the wave scatterng dagram n the North Atlantc and to be compared wth acceptable value. At the IMO, the undecded tems are only two: one s the value of acceptable probablty and the other s a way for fttng calm-water resstance test data. Drect stablty assessment For the drect stablty assessment, we can use numercal smulaton of nonlnear roll moton coupled wth manoeuvrng motons. Here we can dscuss the danger of broachng drectly. If the probablty of stablty falure due to broachng wth assocated wth surf-rdng s smaller than that of surf-rdng, the drect stablty assessment s less conservatve than the second level crtera. DEAD SHIP STABILITY If a shp loses her propulsve power, the shp could suffer beam wnd and waves as the worst case for harmonc resonance for longer duraton. Or the shp master would select ths stuaton for avodng pure loss of stablty, parametrc rollng or broachng wth possble operatonal gudance. Thus the shp desgner shall guarantee the stablty safety of shps under dead shp condton at least. Its frst level crteron was already agreed at the IMO as the current weather crteron but wth

5 5 the modfed wave steepness table n MSC.1/Crc For the second level crteron, two proposals by two delegatons were submtted: one s Method A and the other s Method B. Method A uses the lnearsaton of the GZ curve n the vcnty of the equlbrum heel angle under the acton of mean wnd. In order to estmate the falure probablty, Method A utlses the concept of equvalent area. Gven the actual crtcal heel angle (n general, f relevant, the mnmum between the angle of progressve floodng, the angle of vanshng stablty under the acton of mean wnd and a reference absolute crtcal angle, e.g. 50deg), Method A defnes an equvalent crtcal heel angle n such a way that the area under the resdual lnearsed GZ curve from the equlbrum heel angle up to the equvalent crtcal heel angle s the same as the area under the actual resdual GZ curve from the equlbrum heel angle up to the actual crtcal heel angle. Method B approxmates the orgnal GZ curve wth pece-wse lnear curves. Here the maxmum rghtng arm, the averaged slope of GZ curve up to the maxmum rghtng arm and the angle of vanshng stablty are kept n the approxmaton so that the area of approxmated GZ curve up to the angle of vanshng stablty s slghtly smaller than that of the orgnal GZ curve. At the SLF 55 n 2013, however, these two delegatons (SLF 55/3/11), as a result of ther comparson study on two methods, submtted a consoldated proposal as follows: - The level 2 vulnerablty crteron should be based on the calculaton of the weghted average total stablty falure probablty, consderng a reference exposure tme of one hour, takng nto account all possble statonary sea states appearng n the reference wave scatter dagram wth ther respectve probabltes of occurrence. Each statonary sea state s represented by the mean wnd velocty, the sgnfcant wave heght, the mean wave perod, and the approprate wnd velocty spectrum and wave spectrum; - Method A should be used because Method A provdes outcomes smlar to the smplfed verson of Method B and the use of Method A s smpler. For some statonary sea states havng large total stablty falure probablty among them, the non-smplfed verson of Method B can be used as an alternatve; - The roll dampng coeffcent s to be calculated, as a bass, usng the Ikeda's smplfed method (Kawahara et al. 2009). However, methods whch are deemed to be at least equvalently relable can be used as well; - The effectve wave slope coeffcent s to be calculated, as a bass, usng an analytcal approxmate conservatve formulaton. However, methods whch are deemed to be at least equvalently relable can be used as well; - The wnd heelng moment ncludng hydrodynamc reacton force s to be calculated, as a bass, smlarly to the current weather crteron. However, methods whch are deemed to be at least equvalently relable can be used as well; - For the determnaton of the parameters mentoned above, use can be made of model experments or calculaton methods whch are deemed to provde a suffcent level of accuracy. When consderng model experments, the gudelnes reported n MSC.1/Crc.1200 can be used as a bass. EXCESSIVE ACCELERATION If a shp has excessve GM, the natural roll perod becomes very small so that excessve acceleraton occurs at the wheel house and the cargo space. Ths excessve acceleraton results n death or serous njury of crew and the cargo damage. For the frst and second level crtera, two proposals were submtted to the correspondence group but the sample calculatons usng actual shps submtted to the correspondence group (SLF 55/3/1) reported that the maxmum GM specfed by these draft crtera can be smaller than the mnmum GM specfed by damage stablty requrement.

6 6 Thus the correspondence group concluded that smple applcaton of the exstng draft crtera seems to be not feasble and SLF 55 agreed wth ths concluson. Thus t s urgent to develop a new proposal on ths falure mode. DESIGN MEASURE FOR PARAMETRIC ROLLING As an actvty of the ntersessonal correspondence group on ths ssue, several delegatons executed sample calculatons of the level 1 and 2 crtera for parametrc rollng and pure loss of stablty usng more than 150 sample shps n total (SLF 55/3/1). Ths number s comparable to those used for the current crtera of the 2008 IS Code Part A,.e. the crtera regardng rghtng lever curve propertes and the weather crteron. The sample shps used here ncludes ol tankers, chemcal tankers, bulk carrers, LNG carrers, contanershps, RoPax shps, car carrers, passenger shps, general cargo shps, reefers, offshore supply vessels, super yachts, fshng vessels and naval shps. The results ndcate that most of ol tankers and bulk carrers comply wth the level 1 crtera so that no problem exsts for desgnng these shp-types. On the other hand, most of contanershps and car carrers used n the submtted sample calculatons fal to pass the level 2 parametrc roll crteron. Snce the applcaton of the drect stablty assessment s not so easy, t s desrable for desgners to resolve the falure problem for contanershp and car carrers wthn the stage of level 2. Therefore we have to explore ways to resolve t by desgn measures usng the C11 class contanershp and a car carrer as examples. These sample shps do not comply wth the level 2 crteron for parametrc rollng. Although several ways for reducng the danger of parametrc rollng are avalable, effects of blge keel area and allowable roll angle are presented n Fgs Here the smallest values of the blge keel area rato among the symbols ndcate the actual desgn. When the blge keel area sze ncreases or the allowable roll angle ncreases, the C2 value of the level 2 crteron for parametrc rollng decreases. If we keep 25 degrees as the allowable roll angle, very small ncrease of blge keel sze s suffcent to realse the complance of the car carrer. Ths would result n only 0.4 per cent of propulsve power ncrease so that t could be a margnally acceptable soluton. For the C11 class contanershp, however, ths soluton could result n 1.6 per cent of propulsve power ncrease so that t mght not be feasble. If we adopt 30 degrees as the allowable roll angle by nstallng two-tered lashng brdges, the power ncrease due to the blge keel sze ncrease could be 0.5 per cent so that t could not be mpractcable. Fg.2 Effect of blge keel area on C2 value for the C11 class contanershp wth dfferent allowable roll angles. (Umeda et al., 2013) Fg.3 Effect of blge keel area on C2 value for the car carrer wth dfferent allowable roll angles. (Umeda et al., 2013)

7 Capszng probablty Surf-rdng prob. Internatonal Shp Stablty Workshop VERIFICATION OF SAFETY LEVELS Snce the second generaton ntact stablty crtera have three-layered structures, t s mportant to keep consstency of judgements among them. For the level 1 and 2 crtera for parametrc rollng and pure loss of stablty, sample calculaton results usng actual 35 shps coverng both full and ballast condtons by a certan delegaton (SLF 55/INF.15) reported that no false negatve case s found f the requrement of GM mn for CR1 of pure loss of stablty s excluded and the effect of blge keel s properly evaluated n the parametrc roll level 1 crteron. For broachng, ts sample calculaton results usng seven shps (SLF 55/3/12) also shows no false negatve case f the requred value s adequately selected. These consstences are guaranteed wth the systematc structure of the crtera and the adequate selecton of requred values. Here the sample calculatons and the feedback from them are ndspensable. 1.E E E-02 1.E-03 1.E-04 1.E-05 1.E-06 Beaufort No. Fn=0.31 Fn=0.32 Fn=0.33 Fg. 4 Probabllty of surf-rdng when the ITTC Shp A-2 meets a encounter wave cycle n pure followng waves. (Umeda et al., 2008) E+00 1.E-01 1.E-02 1.E-03 1.E-04 1.E-05 1.E-06 Beaufort No. Fn=0.30 Fn=0.35 Fn=0.40 Fg. 5 Probabllty of stablty falure due to broachng assocated wth surf-rdng for the ITTC Shp A-2 n stern quarterng waves wth the desred course of 5 degrees from the wave drecton. (Umeda et al., 2008) Consstency between the level 2 crtera and drect stablty assessment depends on the physcs to be realsed n dfferent levels. For example, the broachng level 2 crteron requres the calculaton of surf-rdng probablty and the drect stablty assessment of broachng does that of probablty of stablty falure due to broachng assocated wth surf-rdng. Fgs. 4 and 5 demonstrate that the surf-rdng probablty s much larger than the probablty of stablty falure due to broachng assocated wth surf-rdng (Umeda et al., 2008). Therefore, we can conclude that the broachng level 2 crteron s more conservatve than the drect stablty assessment for broachng. METHODOLOGY FOR EXCESSIVE ACCELERATION There are two dfferent proposals for excessve acceleraton but these specfy wave condtons as wave steepness tables,.e. the table n the current weather crteron or upper boundary of the wave scatterng dagram. Consderng the current stuaton n whch the maxmum allowable GMs by the current proposals could be occasonally smaller than the mnmum allowable GM by the exstng crtera, safety margn of the current proposals for excessve acceleraton seems to be too large. Thus the use of operatonal lmtaton from the level 2 crteron could be a feasble approach. If so, t s worth whle nvestgatng the evaluaton of acceleraton at the wheel house for all possble sgnfcant wave heght and zero-crossng perod n the level 2 crteron for ths mode. CONCLUDING REMARKS The man remarks from ths work are summarzed as follows: (1) The level 1 and 2 crtera for pure loss of stablty, parametrc rollng and broachng are almost agreed at the IMO

8 8 except for some undecded tems. (2) For contanershps and car carrers whch fal to comply wth the level 2 parametrc rollng crteron, a feasble desgn measures could be provded. (3) The level 1 crteron for dead shp stablty was agreed at the IMO and the consoldated proposal for the level 2 dead shp stablty crteron would be presented. (4) For the level 2 crteron for excessve acceleraton, a new proposal based on the wave scatterng dagram s requred for facltatng the use of operatonal lmtaton. (5) The consstency among the dfferent level requrements could be realsed f we use systematc crteron structure n physcs and adopt adequate requred probablty levels. ACKNOWLEDGEMENTS Ths work was supported by a Grant-n Ad for Scentfc Research of the Japan Socety for Promoton of Scence (No ). It was partly carred out as a research actvty of Goal- Based Stablty Crteron Project of Japan Shp Technology Research Assocaton n the fscal year of 2012, funded by the Nppon Foundaton. REFERENCES Francescutto, A. and N. Umeda: Current Status of New Generaton Intact Stablty Crtera Development, Proceedngs of the 11th Internatonal Shp stablty Workshop, Wagenngen, Jun. 2010, pp.1-5. Grm, O. : Betrag zu dem Problem der Scherhet des Schffes n Seegang, Schff und Hafen, Heft 6, 1961 S Kan, M.: Surgng of Large Ampltude and Surf-rdng of Shps n Followng Seas, Naval Archtecture and Ocean Engneerng, Vol. 28, 1990, pp Kawahara, Y., K. Maekawa and Y. Ikeda: Smple Predcton Formula of Roll Dampng of Conventonal Cargo Shps on the Bass of Ikeda s Method and Its Lmtaton, Proceedngs of the 10th Internatonal Conference on Stablty of Shps and Ocean Vehcles Sat. Petersburg, 2009, pp Longuet-Hggns, M.S.: On the Jont Dstrbuton of Wave Perods and Ampltudes n a Random Wave Feld, Proceedngs of the Royal Socety of London, Seres A, Vol. 389, 1983, pp Sato, C.: Nonlnear Vbraton, Asakura Shoten (Tokyo), 1970, (n Japanese). SLF 54/WP.3, Report of the Workng Group (Part 1), IMO (London), SLF 55/3/1, Report of the Correspondence Group on Intact Stablty (Part I: Second Generaton Intact Stablty Crtera), submtted by Japan, IMO (London), SLF 55/3/11, Comparson Study of Draft Level 2 Vulnerablty Crtera for Stablty Under Dead Shp Condton, submtted by Italy and Japan, IMO (London), SLF 55/3/12, Comments on Draft Level 2 Vulnerablty Crtera for Broachng, submtted by Japan, IMO (London), SLF 55/INF.15, Informaton Collected by the Correspondence Group on Intact Stablty, submtted by Japan, IMO (London), SLF 55/WP.3, Report of the Workng Group (Part 1), IMO (London), Spyrou, K.J., Asymmetrc Surgng of Shps n Followng Seas and ts Repercusson for Safety, Nonlnear Dynamcs, Vol.43, 2006, pp Umeda, N., S. Ikejma, M. Arak and Y. Ikeda: Desgn Measures for Avodng Parametrc Rollng n Longtudnal Waves, Proceedngs of 5th Internatonal Martme Conference on Desgn for Safety, Shangha, Nov. 2013, (to be appeared). Umeda, N., A. Mak and M. Arak: Some Issues on Broachng Phenomenon n Followng and Quarterng Seas, Proceedngs of the 10th Internatonal Shp Stablty Workshop, Daejeon, Mar. 2008, p

9 9 ANNEX 1 PROPOSED AMENDMENTS TO PART B OF THE 2008 IS CODE TO ASSESS THE VULNERABILITY OF SHIPS TO THE PARAMETRIC ROLLING STABILITY FAILURE MODE 2.11 Shp assessment of vulnerablty to the parametrc rollng stablty falure mode Applcaton The provsons gven hereunder apply to all shps of 24 meters and greater n length For all condtons of loadng, a shp that:.1 meets the standard contaned n the crtera contaned n s consdered not to be vulnerable to the parametrc rollng stablty falure mode;.2 does not meet the standard contaned n the crtera contaned n should be subject to more detaled assessment of vulnerablty to the parametrc rollng stablty falure mode by applyng the crtera contaned n For each condton of loadng, a shp that nether meets the crtera contaned n nor meets the crtera contaned n should be subject to ether a drect stablty assessment for the parametrc rollng stablty falure mode that s performed accordng to the specfcatons provded n Chapter [X] [or should follow the gudance to the master to avod dangerous envronmental condtons [provded n operatonal lmtaton document] [developed from the outcomes of the applcaton of the crtera contaned n ]].[If crtera are not satsfed, the consdered loadng condton s subject to operatonal lmtatons, or drect stablty assessment/operatonal gudance procedures, to the satsfacton of the Admnstraton. (Refer to the gudelne to be developed.)] Level 1 Vulnerablty Crtera for Parametrc Rollng A shp s consdered not to be vulnerable to the parametrc rollng stablty falure mode f GM GM R PR Where, R PR = [0.5] 100ABk 0 m LB [or C 1.7 ; the value of 100A Bk should not exceed 4 and the value of LB blge.] RPR but s 1.87 for a shp havng sharp GM = ampltude of the varaton of the metacentrc heght as a longtudnal wave passes the shp calculated as provded n

10 10 Or I H I L VD V GM only f 1. 0 ; 2V AW ( D d), GM = metacentrc heght of the loadng condton n calm water ; A BK = total overall area of the blge keels (no other appendages), m 2 ; L = Length between perpendculars, m B = moulded breadth of the shp, m; D = moulded depth at sde to the weather deck; V D = volume of dsplacement at waterlne equal to D A W = waterplane area at the draft equal to d. d H L SW Mn( D d, ) 2 C m = mdshp secton coeffcent; d = draft correspondng to the loadng condton under consderaton; d d d ; H d H d L d L ; I H = moment of nerta of the waterplane at the draft d H ; I L = moment of nerta of the waterplane at the draft d L ; V = volume of dsplacement correspondng to the loadng condton under consderaton; d L L SW Mn( d 0.25d full, ) 2 [ d full = draft correspondng to the full load condton] S W [Whether Intal trm and free surface effect are taken nto account or not should be specfed.] As provded by , GM may be determned as half the dfference between the maxmum and mnmum values of the metacentrc heght calculated for the shp, correspondng to the loadng condton under consderaton, consderng the shp to be balanced n snkage and trm on a seres of waves wth the followng characterstcs:

11 11 wavelength wave heght L ; h L S W ; and the wave crest centered at the longtudnal center of gravty and at each 0.1L forward and aft thereof Level 2 Vulnerablty Crtera for Parametrc Roll A shp s consdered not to be vulnerable to the parametrc rollng stablty falure mode f the value of C1 calculated accordng to paragraph s less than R PR 0. If the value of C1 s larger than R PR 0 but the value of C2 calculated accordng to paragraph s less than R PR1, the shp s judged as non-vulnerable. RPR 0 and PR1 or 0.1] R s the standard that s the boundary between acceptable and unacceptable. [ R 0. PR0 06 [ R PR or 0.25] The value for C1 s calculated as a weghted average from a set of waves specfed n N C 1 1 W C Where, W = the weghtng factor for the respectve wave specfed n ; C = 0, f the requrements of any of and are satsfed, and = 1, f not The requrement for the varaton of GM n waves s satsfed f, for each wave specfed n : Where, GM( H GM( H, ), ) 0 and RPR, GM( H, ) R PR = as defned n ; GM(H, λ ) GM(H, λ ) = half the dfference between the maxmum and mnmum values of the metacentrc heght calculated for the shp, correspondng to the loadng condton under consderaton, consderng the shp to be balanced n snkage and trm on a seres of waves charactersed by a H, and a λ ; = the average value of the metacentrc heght calculated for the shp, correspondng to the loadng condton under consderaton, consderng the shp to be balanced n snkage and trm on a seres of waves characterzed by a H, and a λ ;

12 12 H = a wave heght specfed n ; and λ = a wave length specfed n The requrement for the shp speed n a wave s satsfed f, for a wave specfed n : V V PR D Where, VD = the [servce /desgn] speed; and VPR = the reference shp speed (m/s) correspondng to parametrc resonance condtons, when GM(H, )>0: V PR 2 GM( H, ) g T GM 2 Where, T = the roll natural perod n calm water (s); GM = the metacentrc heght n calm water (m); GM(H, λ ) = as defned n ; λ = a wave length specfed n ; and = the absolute value operaton/operand Specfed wave cases for evaluaton of the requrements contaned n and are presented n Table 3-A-1. For use n , N s to taken as 16. In ths table, W, H, are as defned n and

13 13 Table 3-A-1 Wave cases for parametrc rollng evaluaton Case number Weght W Wave length [m] Wave heght H [m] E E E E E E E E E E E E E E E E The value for C2 s calculated as a weghted average from a set of waves specfed n , for dfferent Froude numbers and for both head and followng waves. N C 2 1W C Where, W = the weghtng factor for the respectve wave specfed n ; C = 1, f the roll angle specfed n exceedng [25] degrees, and = 0, f not. Then average of the above C2 values for dfferent speeds and drectons are used for judgement n Roll response, assessed as the maxmum roll ampltude n head and followng seas, s evaluated for a range of speeds n whch the calculaton of stablty n waves s expected to account for nfluence of ptch and heave quas-statcally and the wave heght, H, and the wave length, I, are taken as specfed n In the absence of roll decay test data, roll dampng may be modelled, usng ether smplfed Ikeda's method or type-specfc emprcal data (wth blge keels geometry effect ncluded), f approprate. [The roll response s determned usng the roll moton equaton accordng to one of three soluton methods:.1 a numercal transent soluton that provdes evaluaton of between four and eght waves n a wave group;

14 14.2 an analytcal steady state soluton that may be appled only f both the angle of the maxmum rghtng lever n calm water exceeds 30º and the devaton between a 5th degree polynomal fttng of the rghtng lever curve n calm water from uprght to a heel angle of 30º and the actual rghtng lever curve does not exceed 5 per cent or 0.005m, whchever s greater, at each nterval of 2º;.3 a numercal steady state soluton that s concluded only when the dfference between successve maxmum roll ampltudes s less than [0.5]º. [The detals of the calculatons methods (ntal condtons, wave tran ampltude) related to the transent and steady numercal approaches are to be developed ntersessonally]; For each numercal soluton, the rghtng lever curve at each poston of the wave as t passes the shp s approxmated by modulaton of the calm water rghtng lever curve by the rato of the nstantaneous metacentrc heght to the calm water metacentrc heght.] Roll response should be calculated wth an equaton of uncoupled roll moton. Here the followng component s should be ncluded: - nerta term ncludng added moment of nerta n roll n calm water; - lnear and nonlnear roll dampng moment n calm water; - lnear and nonlnear roll restorng moment n calm water; - wave effect on roll restorng moment. The evaluaton of roll ampltude should be carred out [ether] by analytcal [or numercal] method wth relable gudance for users] wth the steady state roll ampltude [or the maxmum roll angle wthn [4] roll cycles ntated wth approprate ntal roll angle and roll angular velocty]. For calculatng the roll ampltude [or the maxmum roll angle] usng the above formula, the followng wavelength and wave heght should be used: Length L Heght h 0.01L, 0,1,...,10 The Froude number of shp forward speed shall range from 0 to the servce Froude number wth the ncrement of [0.1]. For roll dampng, the forward speed effect could be taken nto account wth Ikeda's method for lft component or equvalent Specfed wave cases for evaluaton of the requrements contaned n are presented n table 3-B-1. For use n , N s to taken as 306. For each combnaton of H s and T z, W s obtaned as the value n table 3-B-1 dvded by , whch s assocated wth a H calculated as provded n and s taken as equal to L. Then the roll ampltude [or the maxmum roll angle] for each H, should be nterpolated from the relatonshp between h and the roll ampltude obtaned n

15 15 Table 3-B-1 Wave cases for parametrc rollng evaluaton The sgnfcant effectve wave heght, H, for use n evaluaton of the requrements n s calculated by flterng ocean waves wthn shp length. Here approprate wave spectrum shape s assumed. The detals wll be descrbed n the explanatory note to be developed. ***

16 16 ANNEX 2 PROPOSED AMENDMENTS TO PART B OF THE 2008 IS CODE TO ASSESS THE VULNERABILITY OF SHIPS TO THE PURE LOSS OF STABILITY FAILURE MODE 2.10 Assessment of shp vulnerablty to the pure loss of stablty falure mode Applcaton The provsons gven hereunder apply to all shps of 24 meters and greater n length for whch the Froude number, F N, correspondng to the servce speed exceeds [ or 0.26]. For the purpose of ths secton, F N s determned for the followng formula: F N V s gl Where, Vs = Servce speed [at 90%MCR], m/s L = Shp length, m g = acceleraton due to gravty, 9.81 m/s For all condtons of loadng, a shp that:.1 meets the standard contaned n the crtera contaned n s consdered not to be vulnerable to the pure loss of stablty falure mode;.2 does not meet the standard contaned n the crtera contaned n should be subject to more detaled assessment of vulnerablty to the pure loss of stablty falure mode by applyng the crtera contaned n For each condton of loadng, a shp that nether meets the crtera contaned n nor meets the crtera contaned n should be subject to ether a drect stablty assessment for the pure loss of stablty falure mode that s performed accordng to the specfcatons provded n Chapter [X] [or should follow the gudance to the master to avod dangerous envronmental condtons [provded n operatonal lmtaton document] [developed from the outcomes of the applcaton of the crtera contaned n ]].[If crtera are not satsfed, the consdered loadng condton s subject to operatonal lmtatons, or drect stablty assessment/operatonal gudance procedures, to the satsfacton of the Admnstraton (ref: gudelne to be developed for passenger and cargo vessels.)] (In explanatory note, mportance of crtcal loadng condton should be mentoned.) Level 1 Vulnerablty Crtera for Pure Loss of Stablty A shp s consdered not to be vulnerable to the pure loss of stablty falure mode f GMmn R PLA Where, R PLA = [mn(1.83 d (F N ) 2, 0.05)] m; and GM mn = the mnmum value of the metacentrc heght [on level trm and wthout takng consderaton of free surface effects] as a longtudnal wave passes the shp calculated as provded n ,

17 17 I Or GM KB L VD V mn KG only f 1. 0 ;, V AW ( D d) d = draft correspondng to the loadng condton under consderaton; I L = moment of nerta of the waterplane at the draft d L ; d d L d L ; KB = heght of the vertcal centre of buoyancy correspondng to the loadng condton under consderaton; KG = heght of the vertcal centre of gravty correspondng to the loadng condton under consderaton; V = volume of dsplacement correspondng to the loadng condton under consderaton; d L L SW Mn( d 0.25d full, ) 2 S W D = Depth V D = volume of dsplacement at waterlne equal to D A W = waterplane area at the draft equal to d. [If VD V 1.0 AW ( D d), n each case specfed heren, the rghtng lever at a heel angle of 30 degrees must be postve.] As provded by , GM mn may be determned as the mnmum value calculated for the shp, correspondng to the loadng condton under consderaton, consderng the shp to be balanced n snkage and trm on waves wth the followng characterstcs: wavelength wave heght L ; h S W L ; and wave crest centred at the longtudnal centre of gravty and at each 0.1L forward and aft thereof.

18 Level 2 Vulnerablty Crtera for Pure Loss of Stablty A shp s consdered not to be vulnerable to the pure loss of stablty falure mode f the maxmum value of CR 1, CR 2, and CR 3, calculated accordng to paragraphs , , and under the servce speed, respectvely, s less than R PL 0. RPL 0 s the standard that s the boundary between acceptable and unacceptable. R PL0 [0.06 n case Opton 6 - A] (dependng on future decson of the reference waves) [or 0.15n case of Opton 6 - B] Each of the three crtera, CR 1, CR 2, and CR 3, represent a weghted average of certan stablty parameters for a shp consdered to be statcally postoned n waves of defned heght (H ) and length (λ ) obtaned from table Where, [ CR CR CR W C1 1 N W C2 1 N N W C3 1 Weghted crteron 1; ] Weghted crteron 2; Weghted crteron 3; (20) W = a weghtng factor obtaned from Table [6-A-1 or 3-B-1]; N = number of wave cases for whch C1, C2, C3 are evaluated = [16 n case of Opton 6-A, 306 n case of Opton 6-B]; C1 = Crteron 1 evaluated accordng to ; C2 = Crteron 2 evaluated accordng to ; and C3 = Crteron 3 evaluated accordng to (CR 1 should be reformulated.) Opton 6-A

19 19 Table 6-A-1 Wave cases for pure loss of stablty Case Wave length Wave heght number Weght W [m] H [m] E E E E E E E E E E E E E E E E Opton 6-B For calculatng the restorng moment n waves, the followng wavelength and wave heght should be used: Length L Heght h 0.01L, 0,1,...,10 Then the ndexes for the Crterons [1]-3 are calculated wth the above as descrbed n [3]-5. Specfed wave cases for evaluaton of the requrements are presented n Table 3-B-1. For use n [3]-5, N s to taken as 306. For each combnaton of H s and T z, W s obtaned as the value n table 3- B-1 dvded by , whch s assocated wth a H calculated below and s taken as equal to L. Then the ndexes for each H, should be nterpolated from the relatonshp between h and the ndexes obtaned above. The 3 per cent largest effectve wave heght, H, for use n evaluaton of the requrements s calculated by flterng ocean waves wthn shp length. Here approprate wave spectrum shape s assumed. The detals wll be descrbed n the explanatory note to be developed Crteron 1 [Crteron 1 s a crteron as provded n the followng formula:

20 20 C1 1 0 [ [ R V PL1 otherwse ]; The angle of vanshng stablty may be determned as the mnmum value/calculated for the shp, correspondng to the loadng condton under consderaton, consderng the shp to be balanced n snkage and trm on a seres of waves wth the characterstcs dentfed n table and wth the wave crest centred at the longtudnal centre of gravty and at each 0.1forward and aft thereof. R PL1 = [30 degrees]] Crteron 2 Crteron 2 s a based on a calculaton of the shp's angle of loll as provded n the followng formula: C2 1 0 (deg rees) [ R loll otherwse PL 2 ] loll s a maxmum loll angle determned from the rghtng lever curve calculated for the shp, correspondng to the loadng condton under consderaton, consderng the shp to be balanced n snkage and trm on a seres of waves wth the characterstcs dentfed n table and wth the wave crest centered at the longtudnal center of gravty and at each 0.1L forward and aft thereof. R PL 2 = [25 degrees] Crteron 3 Crteron 3 s a based on a calculaton of the maxmum value of the rghtng lever curve as provded n the followng formula: C3 1 0 GZ max ( m) [ R otherwse PL3 ] (24) GZ max s determned as the smallest of maxma of the rghtng lever curves calculated for the shp, correspondng to the loadng condton under consderaton, consderng the shp to be balanced n snkage and trm on a seres of waves wth the characterstcs dentfed n table n and wth the wave crest centered at the longtudnal center of gravty and at each 0.1forward and aft thereof. R PL3 = [8(H/λ)dF 2 N ]. **