Ocean Engng, Vol. 12, No.1, pp.45-97,1985.0029-8018/85 $3.00 +,00 Printed in Great Britain.1985 Pergamon Press Ltd. ACOMP ARI S ONOFME T HODS FORCAL CUL AT I NGTHE MOTI ONOFAS EMI - S UBMERS I BLE MATAO TAKAGI andSHIN-ICHI ARAI Hitachi Zosen Corporation, Technical Research Institute, 1-3-22 Sakurajima, Konohana-ku, Osaka, Japan SEIJI TAKEZAWA YokohamaNationalUniversity,Faculty ofEngineering,Department ofNaval Architecture&Ocean Engineering, 156 Tokiwadai, Hodogaya-ku, Yokohama, Japan KUNIO TANAKA Ishikawajima-HarimaHeavyIndustriesCo.,Ltd,ResearchInstitute(Yokohama),1Shin-nakaharacho, Isogo-ku, Yokohama, Japan and NAONOSUKE TAKARADA Sumitomo Heavy Industries, Ltd, Hiratsuka Research Laboratory, 63-30 Yuhigaoka, Hiratsuka, Japan Al~traet--The17th I'I~C Ocean Engineering Committee undertook the comparison of methods for calculating semi-submersible wave motion, and 34 programs from 28 different organizations participated in the project. The summary of the results are reported in the Technical Reportof the17th ITTC (ITTC,1984). In this paper, the details of the project are described. Namely, almost all the calculation results of the 34 programs are shown and examined from the viewpoints of the validity of the program itself and of the correlation between the differences in the various calculation methods and the differencesinthecalculationresults.Thecalculation resultsarealso compared with the experiments, the details of which arealso illustrated. 1.I NTRODUCTI ON ASEMI-submersibleisutilizedinvariouskindsof oceanstructuresbecauseitsmot i onin wavesissmallcomparedwithasurfaceship.Henceitisveryi mport ant toestablisha met hodforcalculatingthemot i onsofasemi-submersiblefromthevi ewpoi nt ofthe designofthistypeofoceanstructure. Ther earemanymet hodsforcalculatingthewaveforces actinguponoceanstructures and, t herefore, themot i onof semi-submersiblesarealsoestimatedbyvariousmet hods.The17thI TTCOceanEngi neeri ngCommi t t eeconduct edacompari sonofsemi- submersiblewavemot i oncalculationmet hodsinordertoexaminenotonlytheoverall validityofthevariouscalculationprogramsbutalsoacorrel at i onbet weenthe differencesinthevariouscalculationmet hodsandthedifferencesinthecalculation results. Thesemi-submersibleusedasthecalculationmodel wasthesameasthatusedina seriesofexperi ment sperformedbyProjectNo. 192oftheShipbuildingResearch Associ at i onofJapan(abbrevi at edSR192hereafter). Thecommi t t eeofSR192kindly provi dedtheOceanEngi neeri ngCommi t t eewiththeresultsofthoseexperiments.Asummaryof theresultsexami nedabovewasreport edbythe17thI' VFC.However ,inordertomaketheresultsmorefruitful,thedetailsarepublishedherewiththe 45 46M. TAKAGI e t a l .permi ssi onof t heOceanEngi neer i ngCommi t t eeandtheedi t orofOcean Engineering. 2.DATAFORCALCULATI ON Theshapeandprincipaldi mensi onsoftheSR192model usedinthecal cul at i onsare showninFig.1andTabl e1.Thecal cul at i oncondi t i onsarealsoshowninTabl e1.The model waschosenfort hei nvest i gat i onofstabilityinasemi -submersi bl edrillingrigin SR192.Thescaleof themodel wasassumedtobe1/64andt hedraft wast hat fora survivalcondi t i on. Theexper i ment sinwaveswereper f or medint hreeseakeepi ngt anks wi t h awat erdept hofabout t hr eemet ers. Thedetails oftheexper i ment sarei l l ust rat edin Appendi xA.Thei t emsr equest edforthecompar i sonofcal cul at i onsweretheampl i t udesand phasesoft he6modesof mot i onatthecent erofgravi t yof themodel freel yfl oat i ngin regul arwaves. Inor der t obeablet ocompar edi rect l yt hecal cul at i onresultswitht hose of t hemodel exper i ment , thepart i ci pant swerer equest edtomaket hei rmot i on predi ct i onsfort hemodel scale, andnot fortheassumedpr ot ot ype.Thei nput dat aof t hei nci dent wavesareWavesI-IIIshowninTabl e1.Fort he wave- i nducedmot i ons, t heresponsefunct i ons wi t hperi odsoflesst han3.5sec(28secin t hepr ot ot ype) areenough; however somewi t hperi odsof upt o10secarer equest edfor vari ousreferences. Inor der toi nvest i gat e t heeffectof wavehei ght , WaveIandWaveII arespecified.Thechoiceoft hecal cul at i onpoi nt sint ermsofperi odsislefttothe part i ci pant ssot hat t heycanobt ai nsmoot hcurves.WaveIIIisamargi nal l yhighwave fort hewavemaker sint heseakeepi ngt anks. Thecoor di nat esyst em for t hecal cul at i ons isshowninFig.1. Z L0.~36L0.575_I_0.575 _~0.575_l~0.5,'361 W~J- _035fii_0.575_ _0.575_ _0.375__03~6,II~ WOVe Elevotion~= ~acos (t.dt -kX~) Motion ofRigX: XAcos(t.0t-Ex) FIG.1.Se mi - s ubme r s i bl e a ndc oor di na t e s ys t e mus e dincal cul at i on.Methods forcalculating semi-submersible wavemotion TABLE1.DATA FOR CALCULATION 47 L e n g t hD r a f tC e n t e rM e t a c e n t r i c h e i g h t ,R a d i u s ofg y r a t i o n ,D i s p l a c e m e n t in W a t e r d e p t hW a v e d i r e c t i o nW a v eofl o w e r h u l l , L:1 . 7 9 7 m:0 . 3 1 3 mofg r a v i t y , x G:att h eY G :att h ez G:0 . 2 7 3 m( a b o v eL o n g i . (LGM):0 . 0 3 7 mT r a n s . (TGM):0 . 0 4 5 mR o l l :0 . 5 3 6 mP i t c h :0 . 5 5 6 mY a w :0 . 6 3 4 mf r e s h w a t e r :1 3 0 . 3 k g fh:3 . 0 mX:045 h e i g h t (2~ A)a n d w a v e p e r i o d (T): W a v e s I-2~ A=0 . 0 4 6 m , 0 . 5 ~T~i 0 . 0S W a v e s ~-2 ~ A =0 . 1 6 0 m , 1 . 0 !T (conltl. ) Progr Ul, V W X ..__ ___I-._ -. ._ - --.- Reference __- - Hooft (1971). Hooft (1971). Seakeeping Quality of Semi-Submersible Drilling Rig BINGO 4000M, Nippon Kokan Tech. Rep. Overseas, Nc>38. 1983. __-___ _____- KATAYAMA, M. et al. 1978. On Structural Response Analysis of Semi-Submersible Offshore Structures in Waves, MHI Technical Review, Vol. 125, No. 2. WAHAB, R. 1974. Wave Induced Motions and Drift Forces on a Floating Structure. Netherlands Ship Research Centre TNO, Report No. 186s. Hooft (19711, Hooft (1972). NOJIRI, N. and INOUE, Y. 1981. Dynamic Behavior of Semi-submersible Platforms in Waves IHI Engineering Review Vol. No. 2. SUN, F. 1980. Analysis of Motions of Semi-submersible in Sea Waves, Offshore Technology Conference, Vol. 4. BORISOV, R.V. and MOLODOZHNIKOV, A.B. 1980. Calculation of Motions of Moored Floating Drilling Units in Regular and Irregular tiaves, Trudy LSL. KOKKINOWRACHOS, K. 1978. Hydrodynamic Analysis of Large Offshore Structures, 5. Intern. Ocean Development Conf. Tokyo. KOKKINOWRACHOS, K., ASORAKOS, S. and MAVRAKOS, S. 1980, Belastungen und Bewegungen gro8volumiger Seebauwerke durch Weilen, Research Report of the State of North-Rhine-Westfalia, No.2905, Opladen. KOKKINOWRACHOS, K. and HOEFELD, J. 1980. Theoretische und experimentelle Untersuchungen des Bewegungsver- haltens van Halbtauchern, Research Report of the State of North-Rhine-Westfalia, No. 2915, Opladen. KOKKINOWRACHOS, K. and HOEFELD, J. 1983. Systematic Evaluation of the Seakeeping Characteristics of Semi- Submersibles, PRADS '83, Tokyo, Seoul, Oct. 16-22. KOKKINOWRACHOS, K. and ZIBELL, H.G. 1984. Wave Interaction with Multiple Cross-Sections in Finite Water Depth. To be presented at the 3rd Intern. Symposium on Offshore Mechanics and Arctic Engineering, New Orleans Febr INGLIS, R.B. and PRICE, W.G. 1981. A Three-Dimensional Ship Motion Theory - Comparison tiettween Theoretical Predictions and Experimental Data of the Hydrodynamic Coefficients with Forward Speed. RENA. No reference Semi-Submersible Design: The effect of Differing Geometries on Heaving Response and Stability. RINA Trans. 1976. (contd.) Program Y1 Y2 Z ZA ZB Reference PAULLING, J. R. 1970. Wave Induced Forces and Motions of Tubular Structures, Eighth Symposium, Naval Hydro- dynamics, Rome, Italy, August 24-28. STIANSEN, S.G. and CHEN, H.H. 1981. Computational Methods for Predicting Motions and Dynamic Loads of Tension Leg Platforms, Second International Symposium on Integrity of Offshore Structures, Glasgow, Scotland, 3 July PAULLING, J.R., HONG, Y.S., CHEN, H.H. and STIANSEN, S.G. 1977. Analysis of Semlsubmerslble Catamaran-type Platforms, OTC 2975, Proceedings of Offshore Technology Conference, Houston. PAULING, J.R. 1981. The Sensitivity of Predicted Loads and Responses of Floating Platforms to Computational Methods, Second International Symposium of Integrity of Offshore Structures, Glassgow, Scotland, 3 July. No reference Paulling et al. (1977) No reference > > t~ Methods for calculating semi-submersible wavemotion53 tothecalculation methods of thehydrodynamic forces onthecolumns andlowerhulls: (1)Useofathree-dimensionalpotentialtheorywithorwithoutviscousdamping correction:A,B,C2,D,El , E2,F,G2,I,U2,VandW. (2)UseofHooft' sMethod(Hooft,1971) withtheMorisonFormula:C1,G1,H,J, L1,M,O,P,S,Y1andZB. (3)UseofHooft' sMethodwithatwo-dimensional potentialtheory withorwithout viscousdampingcorrection:K,T,X,ZandZA. (4)Amixtureof(1)and(3):U1andY2. (5)Amixtureof(2)and(3):L2,N,QandR. In the above classifications, the term "Hooft' s Method" is used to mean the conception that thehydrodynamic forces of asemi-submersible arecalculated by dividing the whole structureintosomesimplemembers,e.g.thecolumn,lowerhull,etc.However,some calculation programs consider a partial interaction between the members.In method (2), thehydrodynamicforcesonthemembersareobtainedbytheuseoftheMorison Formula,wheretheaddedmasscoefficientCmanddragcoefficientCoareobtained t heoret i cal l y, experi ment al l y, orasdefinedregulations. Inmet hod(3),the hydrodynamic forcesonthemembersareobtainedbytheuseofatwo-dimensional diffractionandradiationtheory.Inmethods(1)and(3),mostprogramsconsidera viscousdampingcorrection.Inmanyoftheprograms,asshowninTable3,the correctionisdoneinsuchawaythattheviscousforcesarecalculatedbyusingthe relativevelocity betweenthemembersandthewaterparticles,andthenlinearized. Most programsusethe frequency domain analysis method.InC1andF,time domain analysis isusedandthecoefficients of thehydrodynamic forcesareconstants. Since Fpresentedtheresults of high waves only, they arenot shown in the figures but inTable5.Moreover,althoughthecalculationsforthemodelwererequested,H presentedtheresultsfortheassumedprototype. 4.COMPARISON OF CALCULATION RESULTS Themotion under the wave conditions (X=0,45,90; Waves I,II,III)shown in Table 1 werecalculated by 34 programs.It would take too much space to show all theresults in thisreport,butageneralviewof thecalculation resultsrevealedthat: (a)Withafew exceptions,theeffect of thewaveheight onheavemotion waslarge, butvirtually nonexistent inallothermodesof motion. (b)Changesintheangleofincidenceofthewavescausedverylittlechangeinthe heave. TheabovematterscanbealsoseenintheexperimentalresultsshowninAppendixA. Therefore, only thecalculation results of the wave height 2gA=0.046mareall shown in theappendices.In Appendix B, the results of amplitudes of periodT =0.5 -4 sec are shown.However only the cases of =45 areshown for heavemotion.InAppendix C, the calculation results of phases for periodT =1.0 -10 sec and =45 areshown.Since it isdifficult to show theresults of 34 programs in one figure, they aredivided into three groups and shown in three figures. The axis of the abscissa in the figure is the wave period in model scale, which is one-eighth of that which corresponds to the assumed prototype. Nowwewillanalysethecalculationresults.Figures2-11showthecasesofwave height2~A=0.046m.Theshadedareasinthefiguresindicatetheregionscoveredby many of theprogramresults.Theresultsof waterdepthh=0 whichdonotfall inthe 54M. TAKAGI e t a t .'~Sur geat4 5 . . . . . . . : h=oo 1.0L- - - : Exp. 0.5 0I23T ( s ) 4 X 1.0 0.5 0 1.0 0.5 0 Fl ~. 2.Sur gea mpl i t ude (2~A=0. 046m) .I I ISur geat0 =O 0 .~ t ~ ' ~ . < x ~ , . '~ f. . . .I25T ( s ) 4 F16.3.Sur gea mpl i t ude (2~A=0. 046m) .I I ISwayat4 5 . . . . . . . :h = O O: E x p . . . . - I25T(s)4 F~6.4 . S w a y a m p l i t u d e ( 2 ~ A=0 . 0 4 6 m ) .Methodsforcalculatingsemi-submersiblewavemotion 0I23T( s)4 FIG.5.Swayamplitude(25,,=0.046m). 2. c G l a LC 0 II Heaveat45" 2h=O. O46m________: h =( - J - J- - - - :Exp. I23T( s)3 / / _z FIG.6.Heaveamplitude(2cn=0.046m). aboveregionsareindicatedbythedottedlines.Theexperimentalresultsareindicatedby thebroadbrokenlines.thevaluesofwhicharethemeanvaluesoftheresultsshownin AppendixA. Forsurgeandsway,thereisasatisfactorydegreeofmutualagreementamongthe calculationresults.whichalsoagreewiththeexperimentalresults.Itcanbeseenthatthe effectofthewaterdepthappearsinlongerperiods. Forheave,roll,pitchandyaw,thereisnotagoodmutualagreementamongthe calculationresults.Exceptforheave.however,thecentralvaluesofthecalculation 56M. TAKAGI e t al .1.0 0 50 1.0 Q5 0 1.0 Q5 0 I IR o l l Qt45 . . . . . . . . : h : c o- - - : E x p .I25T( s ) 4 FIG.7.Rol l a mpl i t ude (2~A=0. 046m) .I I IRollat90 . . . . . . . h = o o- - - - " E x p . --1 I25 T ( s 4 FIG.8.Rol l a mpl i t ude (2~a=0. 046m). 1 IPi t chat4 5 . . . . . . . . : h : o o- - - : E x p .FIG.9. I II 2 :5T ( s )Pi t cha mpl i t ude (2~A=0. 046m) .4 Methods forcalculating semi-submersible wavemotion57

> Remark R z = Z / Z c, Zc = ZA / CA (CA = 0.046m) Methodsfor calculating semi-submersible wavemotion63 ( 5) F o r y a w, t h e Mo r i s o n p r o g r a ms g a v e s ma l l e r a mp l i t u d e s t h a n o t h e r p r o g r a mswh i c h us e at h r e e - d i me n s i o n a l a n d / o r t wo - d i me n s i o n a l p o t e n t i a l t h e o r y .( 6) E x c e p t f or t h e h e a v e mo t i o n a r o u n d t h e p e a k , t h e wa v e h e i g h t h a s v i r t u a l l y n oe f f e c t onmo t i o n , e i t h e r i nt h e c a l c u l a t i o n s o r i nt h e e x p e r i me n t .( 7) F u r t h e r i n v e s t i g a t i o n s i n t o a d d e d ma s s a n d d a mp i n g f o r c e a r e n e e d e d i no r d e r t oe x p l a i n t h e d i f f e r e n c e s a mo n g t h e p r o g r a ms .Acknowledgements--Theauthorswishtoexpresstheirgratitudetotheorganizationsandpersonswho contributed thecomparative calculations, tothe17th ITTCOceanEngineering Committee,andto theSR192 Committee. R E F E R E NC E S17th ITTCReportoftheOceanEngineeringCommittee.1984. HroFT,J.P.1971.Amathematicalmethodofdetermininghydrodynamicallyinducedforcesona semisubmersible.TransactionsofSNAME79,28--70. AP P E NDI XA MODE L EXP ERI MENTS1.I NT R ODUC T I ON Themodel exper i ment s wer epe r f or me dint hef ol l owi ngt hr eet anks:TheTowi ngandSeakeepi ngTank(100( L) x8(B)x3.5( D) m)of Yo k o h a ma Nat i onalUni ver si t y.TheSeakeepi ngandManeuver i ngBasi n(56( L) x30(B)2.5( D) m)of Sumi t omoHe a vy I ndust r i es, Lt d.TheSeakeepi ngandManeuver i ngTank(70( L) 30(B)3( D) m)of I s hi ka wa j i ma - Ha r i maHeavyI ndust r i esCo. , Lt d.Theset hr eeor gani zat i onsar er ef er r edt oher eaf t er asYNU, SHI , andI HI r espect i vel y.Themeas ur edr esul t sobt ai nedint heexper i ment al t ankswer es ummar i zedandc ompa r e d.2.E XP E R I ME NT AL AR R ANGE ME NT2.1.ModelAcommonmodel wasusedbyt het hr eeor gani zat i onsinor de r t oel i mi nat eer r or s causedby usi ngdi f f er ent model s. Themodel isanexact r epr es ent at i onoft het heor et i cal ful l -scal e vessel . I tisc ompos e dof t wol ower hul l sandei ght col umnss uppor t i ngaboxt ypeupper hul l . Themai n di mensi onsar eshowninTabl eA1.Themodel iss t r i ppedof anchor r acksint hes ubmer gedpor t i onandof st r uct ur esont heuppe rdeckexcept forahel i por t . Thel ower hul l sandt hecol umnsar ema de of FRPandt heuppe r hul l ,t hebr aci ngs, andt hehel i por t ont heuppe r deckaremadeof wood.2.2.Experi ment al condi t i ons (1)Draf t conditions. Themodel wasbal l ast edbyeachor gani zat i ont ost i mul at easurvi val dr af tcondi t i on. Thedr af t condi t i onsar eshowninTabl eA1. Thet hr eeor gani zat i ons s ucceededin at t ai ni ngt hedr af t condi t i onswhi chpr ovi det het ar get val uesof t hepar t i cul ar sof t heful l -scal e condi t i onsasshowninTabl eA1.Tabl eA1al soshowst henat ur al per i odsof heave, rol l , pi t ch, andyawobt ai nedf r omf r ee decayi ngosci l l at i ont est sof t hemodel .6 4 M. TAKAGIe t al .TABLEA1 . MAI NDI MENSI ONSANDEXPERIMENTALBALLASTCONDI TI ONSOFTHEMODEL DesignationUnitActual Lengthoverall Breadthmoul ded Upperdeckelevation Lowerhulls (2) Columns (8) Length B e a mHeight Large col umns Diameter SmallColumns Diameter Draft(Survival cond.) D i s p l a c e m e n tCenterof gravity Metacentric height Vert.,VCG above thebase line Longi.,LCG at themidship Trans., TCG at thecenterline Longi.,LGM Trans.,TG M Roll,Kx x Radius of gyrationPitch,KY Y Yaw, KZZ Heave NaturalRoll periodPitch Yaw Waterdepthat thet i meofthe modelexperiments m m m m m m m m m Ton kg m m m m m m m m S S S S m 115 751.172 430.672 1151.797 150.234 9.750.125 100.156 80.125 2O 35,000 Model (Scale ratio1/64) Y N U I SHIIIHI 1.797 0.313 131.8131. 1131.7 17.50.2730.2730.274 0000 0000 2.370.0370.0370.036 2.870.0450.0450.044 -0.5180.5080.504 -0.5560.5530.554 -0.6650.6420.654 -3.02.982.99 6.546.846.18 7.257.807.18 -9.426.61 3.52.53.O Methodsforcalculating semi-submersible wavemotion65 (2)Wave conditions.Themodel exper i ment s wer econduct edint wot ypesof waves: r egul arwat er wavesat SHI andI HI , andt r ansi ent wat er wavesatYNU. Ther egul ar wat er wavescoverwaveper i ods r angi ngf r om0.5t o3.5seci ncl udi ng t henat ur al per i odof heave, wi t hsever al wave hei ght sforsomeof t hewaveper i ods asshowninTabl eA2.TABLE A2.REGULARWAVE CONDITIONS Mode iWaveheght Hw=2~A,m Waveperiod T w, s a0. 0460. 5t o3. 5 b0. 1600. 75t o3. 5 c0. 2801.5 d0. 3102. 0 Modes (a)and(b)ar eforobt ai ni ngf r equencyr esponsechar act er i st i csandforst udyi ngt he i nfl uenceof t hewavehei ght onmot i on. Modes (c)and(d)cor r es pondt ot hemaxi mumwave hei ght sfort hespeci fi edwaveper i ods t hat canbegener at edbyt hewavemaker s. As fort he t r ansi ent wat er waves, t wot ypeswer eused: onewi t haconst ant wavehei ght andonewi t ha const ant wavesl opein~ e Four i e r Spect r um. Thet hr eewavedi r ect i onsspeci fi edfort hemode lexper i ment s ar easfol l ows:He a dwaves: =0deg.Bowquar t er i ngwaves: =45deg.Beamwaves: =90deg.SHI andI HI car r i edout exper i ment s inallt hr eest at es, whi l et heYNUexper i ment s wer efor headandbeamwaves.2.3.Experimental procedure Mot i oninallsix degr ees off r eedomoft hemodel inwaveswasmeas ur edbyusi ngt hef ol l owi ng t womet hods :(1)Mechanical measuring system (at SHI andI HI ) . As i l l ust r at edinFi gsA1. 1andA1. 2, t he model isconnect edwi t hmeas ur i ngequi pment consi st i ngof car r i ages, aver t i cal ( heave) r od, and gi mbal s. St eady f or ces( dr i f t i ng f or ces andmome nt ) ont hemodel ar ebal ancedby acount er wei ghtandsoft spri ngst okeept hemodel posi t i onwi t hi nt hespeci fi c measur i ngr angeoft heequi pment .Thever t i cal r odandot her mechani cal movi ngpar t sar el i ght inwei ght , t he r e byr educi ngt hei ri nfl uenceonmot i on. Thesix component s ofmot i onoft hemodel ar eme a s ur e dmechani cal l y f r om t her el at i vedi s pl acement s bet weent hecar r i agesandt hemodel byusi ngpot ent i omet er s .(2)Opto-electronic measuring system(at YNU) . Wi t ht hi smeas ur i ngsyst em, t hemodel issetcompl et el yf r eeasseeninFi g. A1. 3. Thesyst emconsi st sof l i ght - emi t t i ngdi odes ( LEDs ) anda posi t i onsensor devi ce( PSD) . TheLEDs ar eat t achedt ot hemodel andi l l umi nat econt i nuousl y.ThePSDusest wocamer aheadst oobser vet hemovement of t hel i ght sf r omt heLEDs . Thesix component s of mot i onoft hemodel ar eder i vedf r omt het r ansl at i onal mot i onof t hepoi nt s obs er vedasmovement s of t helightsof t heLEDs .66M.TAKAG!e t al ., ' b ' ~ O 0 0 0 0 0 0 ~~ ' ~ ; p r in g~ '\ P u l l e y~T~ Heaver o dW i r er o p eI IW e i g h t\ = c ~Wave J "J FIG. AI. 1. Schemeof apparatusfor themodel experiment(SHI). H e a v e r o dWire rope~ / Yaw spring for drifting moment \ ~ ~ - - ~ Pulley ~ W e i g h t Gi mt ~ ~ ~ , ~ ' ' ' - - - ~-~fordriftingforce ~~WaveFiG. AI. 2. Schemeof apparatusforthemodelexperiment(IHI). Meas ur ement s oft hemot i onweremadeont h e u p p e r deckas showninFi gs A1. 1-A1. 3andt he meas ur edresul t swer et r ansl at edi nt omot i onatt hemodel ' s cent er of gravi t y.Thewaveprofi l eswer emeas ur edatt wopoi nt sint heexper i ment al t anks: onenear t hemodelandt heot her at afixedposi t i onnear t heflapof t hewavemaker .3.C OMP AR I S ONOF ME AS UR E DRE S UL T STheresul t sof t hemeas ur ement s of t het hr eeor gani zat i onsandt hecal cul at i onsof I HI with r espect t ot hef r equencyr esponsechar act er i st i cs( ampl i t udeandphasechar act er i st i cs) of t he mot i onabout t hecent er of gravi t yar egi veninFi gsA3( a) -Al 0 ( b ) ; (a)showst heampl i t ude char act er i st i cs and(b)t hephasecharact eri st i cs. Int hesefigures, t hemeas ur edresul t sobt a i ne dby Methodsforcalculating semi-submersible wavemotion67 R e m o t e M e a s u r e m e n t b y P o s i t i o n S e n s o r D e v i c e (YNU) TIr - S , " - ~ C l~~B"=I' SEI ! L M A I N C A R R I A G E E S U B C A R R I A G E--Rail - - Wave3,500 A , B , B~-C a m e r aC-W a v e P r o b eD-W a v e P r o v eE-L . E . D ( t a r g e t for p o s i t i o n s e n s o r d e v i c e )F- NylonropeforguLde FIG. A1.3.Schemeof apparatusfor themodelexperiment(YNU). t het hr eeor gani zat i ons ar epl ot t edt oget her . Themar ks usedint hesefiguresar ei l l ust r at edinFi g.A2. For t hemeas ur edresul t sf r omYNU, onl yt heampl i t udechar act er i st i csar ei ndi cat edher e.Theampl i t udeandphaseangl eof mot i onar ede t e r mi ne df r omt hemeas ur eddat abymeans of a har moni canal ysi st echni queat SHI andI HI .Ther esul t sar epr es ent edint hef or mof anon- di mens i onalf r equencyr esponseoft heampl i t ude oft hemot i ont oabaseoft hewaveper i ods. Thephaseangl esoft hemot i onar egi venindegr ees ,al sot oabaseof t hewaveper i ods.As fort hecompar i s onof t heresul t sof t het hr eeor gani zat i ons, t henat ur al per i odof heave agr eedver ywel l , wher eas t hoseof pi t chandrol l hadslightdi f f er ences.Meas ur ement s of t henat ur al per i ods wer econduct edat YNUandI HI under acompl et el y f r ee- f l oat i ngcondi t i onandSHI car r i edout t hemeas ur ement s byus i ngt hemode l andt he meas ur i ngequi pment fort hemot i on. Thedi ffi cul t yof pr eci semeas ur ement s duet ot hef r ee decayi ng osci l l at i on ofal ong per i od wi t hfastdecayi ng is cons i der edt obeoneoft hef act or s fort he di f f er encesint henat ur al per i odfort hepi t chandrol l amongt het hr eeor gani zat i ons.Thenat ur al per i odof yawist henat ur al per i odof t hemechani cal meas ur i ngsyst emas me nt i one dabove. Al argedi f f er ence int henat ur al per i od ofyaw bet weent wooft heor gani zat i ons( SHI andI HI ) isduet ot hedi f f er ent st i ffnessof t hesoft spri ngsusedbyeachor gani zat i on.a t t o n0 . 0 4 60 . 1 6 00 . 2 8 00 . 3 1 0SHtIHI Wat erDeDth 2. 5m3. 0m RegularWaterWave EXP. CAL. EXP. CAL.0 ZX+ [ ]0 YNU 3. 5m Transi entWat er Wave EXP. CAL.FIG. A2.Explanation of marksusedinFigs A3 -A10. 68 1 . f i rM.TAKAGI e t al .SURGE X =0deg'0. 5 o 0 F I G . A3(a). o~~~ I,eo8 ~ 7 /i 1. 02. 03. 0 Tw,s Surgemotioninregularheadwaves. SURGE X:0deg" 180r 90 z~ i0e1.0 o,x - 1 8 00 ' ~ i o ' 3 1 oTw,s FIG. A3(b).Surgemotioninregularheadwaves. Methods forcalculating semi-submersible wavemotion SWAY 1.5rX=90 de~ 69 1.0 0.5 0o ~ IIIL 6 1.02.03.0 Tw,$ FiG.A4(a).Swaymotioninregularbeamwaves. "10 180 90 - 9 0- 1 8 0i z~1.0 SWAY X =90 deg O o~A2 ~ ~ t t ~t ~ iiiii 2.03.0 Tw. s FIG. A4(b).Swaymotioninregularbeamwaves. 7 0 M.TAKAGI e t al . 2 . 0 -1.5 < N 1.0 0. 5 H E A V E :~ X=0a e 9 0 & Z, +, ,1.02. 03. 0 Tw,s Fm.A5(a). H e a v e mo t i o n inr e g u l a r h e a d w a v e s .HEAVE X=0d i g .m o V oO Oo 9O o i l ; ~ ~ o o ~ o ,+. "~ 1.o"~" o e3 . 0 - Tw.s - - ' I i- 1 8 0 c FZC;. A 5 ( b ) . He a v e mot i oninr egul ar headwaves. Met hodsforcalculatingsemi -submersi bl ewavemot i on71 HEAVE 2 . 0 X=4 5 deo.e o1.5 1.0 0.5 r ,o9 0 P~ 2 *~ - ~ c / LJ ~ o1. 02 . 0T w , s FIG.A6(a).1 8 0/ x 3 1 0 'Heavemot i oninregul arbowquar t er i ngwaves. HEAVE x=4 5 de~. 9 0" oO 0 ~G - 9 0O O \1.0~"2.0o3.0 O oT w , s . !- 1 8 0FIG.A6( b) . Heavemot i oninregul arbowquar t er i ngwaves. 72M. TAKAG[ et al .2.0 1.5 HEAVE X=90deg . 1.0 0.5~ 0tItt 01.02.03.0 Tw,s He a v e mot i oninr egul ar b e a mwaves .HEAVE X =90 deg' FIG.A7( a ) .& 0 1. 0 - 9 0e @Q~. -+~0@ +\~@. & 6 # J O O 4 lo S ' 2 . 2.03.0 Tw, s Fl~.A7( b) . He a ve mot i oninr egul ar b e a mwaves.Methods for calculating semi-submersible wavemotion73 ROLL 1. 5X=90d' g- 1.0 0 i01.02.03.0 Tw,s FIG.A8(a).Rollmotioninregularbeamwaves. '1o 1 8 00 90 - 9 0-180 R O L LX=9 0 d e oAii 1.0 0 00~ 'I i i i2.03.0 Tw,s FIG. A8(b).Rollmotioninregularbeamwaves. 7 41. 5 M. TAKAGI e t al .PITCH X =0dee. 1.0 0.5 FIG.A9( a ) .O ^ ~0O0 0 J 1 . o 2 ' . o ' a l o 'T w , s Pi t chmo t i o n inr e gul a r h e a d waves .180- eO 9 00 O A - 180 FIG.A9( b) .P I T CH X=0aeu. , . o . 210'310' T w . s Pi t chmo t i o n inr egul ar he a dwaves .Met hodsforcalculatingsemi -submersi bl ewavemot i on75 0. 3 I Q5 0 0 1.0 XO5 0 6i iAMPLITUDES OF SURGE % =45, 2~,A=OO46m A *B 25T(S)4 FIG.B2.1 iAMPLITUDES OF SURGE % =45~, 2~A=QO46m - - ~- K,R --. --LI. . . . L2 2 _ * -I 2 5 T ( S ) 4FiG.B2.2 80M.TAKAGI e t al .1.0 050! I.O ,# Q5 I.O 05 O o ii AMPLITUDESOF SURGE % :45 ~,2~A:OO46m S T Ul . . . . U2 V . . . . . W . . . . . . X YI --+--Y2 Z . . . . . . o. . . . . .F I G . B 2 . 3I 3T(S)4 AMPLITUDES OF S W A YA o8%= 4 5, 2 ~ A = O . O 4 6 mC I GL_ ~ ............I -"G2/ ~ . . . . . . . . . . I : i i : ! /. . . . . ZA I23T ( S ) 4 Fio.B3.1 AMPLI TUDESOFSWAY %:4 5,2~A = OO4 6 m - - M - - L I , L 2 _ , ~ z ~ . . . . . . . - . . . . .. . . .ZB I25T ( S ) 4 FIG.B3.2 Methods for calculating semi-submersible wavemotion81 , f0.5 0 01.0 %Q5 1.0 4 0.5 o 6 i IAMPLITUDES OF SWAY %=4 5, 2BA =0 0 4 6m i x,. ~ o o - - 7 - - ~2, , . ~~ #" i LI 25T(S)4 F i G. B3.3 AMPLITUDESOFSWAY o~9(, =90, 2~A=OO46m/ _ ~ - . . ~ " 'oC I . ~ ' o__._~ 2 ~ L \ . . . . . ._:_~,~ ' ~ -. . . . . . J p , ." .,A !,.25T ( S ) 4 FiG.B4.1 AMPLITUDES OF SWAY % = 9 0 , 2 z ; A = O 0 4 6 m , ~ ' ~ , +K. , , ~ " ~ ' ' b ' ' ' ~ ' ' A~"'1~'= .--..ii~~'/ I 2 . 5 T ( S ) 4F i G. B4.2 82M.TAKAGI et at .1.0 ~ t>.- 05 00 AMPLITUDESOF SWAY i(, =90~2~A =0.046m s - - - T._ ~ - : = - : t : _ z ~UIt ~ = : - - o . . . . U 2oV . . . . . W . . . . . . X/,~'o- ~ Y I " " , ~ i- - : - - ~ 2 /f i i I i s 'I i 5 T ( S ) 4FIG.B4.3 2 I.O 0 AMPLITUDESOF HEAVE! % =45~ 2~A :0.046m"~ i J "+ ~ ~I~,o. F_2.*I!J[ , l , / I rI25T ( S ) 4 FIG.B5.1 Methodsforcalculating semi-submersible wavemotion83 2.0 N I.C 0 ' ' IAMPLITUDES OFHEAVE 3(, = 45? 2~A =QO46m - - , ~ - - K . . . . L L ~_.--= . . . . . . .~ZB , I II25T ( S ) 4 FIG.B5.2 2.0 r . , JI.( 0 AMPLITUDES OFHEAVE % =45, 2~A=O.O46m - - S- - - - - - T - - - - - U I. . . . U2 - - +- - Y2 Z r / / / /FIG.B5.3 .3T( S) 4 84 I.O Q5 M.TAKAGI e t al .i- - AoB o Cl E 2AMPLITUDES OF ROLL % : 45~, 2r~A:OO46m - - ~ -o- .......J~ ~( Z ~ A ~ I ~ IIT I23T ( S ) 4 FI G. B6 . l I.O s~ 0 5I.O v ,Q5 0 0 K, P - . - L I. . . . L 2- - M, Q . . . . . N- - . o . - -AMPLITUDES OF ROLL % =457 2z:,A=OO46m ~prI/ I23T ( S ) 4 Ft G. B 6 . 2/~VIPUTUDES O FR O L L% =45, 2r~A=O.O46m - - S- - - - - - T . . w U Io Uv2 . . . . . W . . . . . . . X YI- - - ~- - - Y2Z I 3 T ( S ) 4FuG.B o . 3Me t hods f or cal cul at i ngs emi - s ubmer s i bl ewavemot i on85 L oQ5 - - AAMPLITUDESOF ROLL oB9(,-90,-2~A=OO46m o ~ " ~ " -. . . . . Z,a, J" ~ " - / / 2 i T ( S )4FIG.BT, 1 1.0 e l0 5C 1 . 00.5 o 6AMPLITUDES OFROLL % : 90 , 2~,A :OO46m - - - LI. . . . L 2 , _ _ . . - - - - o - - ,..:~ ~ZB 2.5T ( S ) 4 FIo. B7. 2 IAMPLITUDES OFROll 9(, =90~, 2BA=OO46m ~ S_ _ m Tt3 Ul o o. . . . U2 --'o'-"Y2. l " , ' " l - - / I~ ' ~ I I II 2 .3 T ( S ) 4FIG.B7. 3 86M.TAKAOt e t a l .1 . 0,..gQ5 06 AMPLITUDES OF PITCH 9(, =0,2z;A =0.04.6m o ~+ __. . ~_.J 5T ( S ) 4FI6.B8.1 1 .0Q 5 ,1.0 Q5 % i iAMPLITUDES OFPITCH 7,, =01 2~A =0.046 m K- - ~ - - Z B- - - - - L I. . . . L 2I 2 .5T ( S ) 4Fi6.B8.2 AMPLITUDES OF PITCH 1(,= ~ 2~A=OO4.6m sJl U|o ~~ ~- - - : - - } 2I 2 5 T ( S ) 4FIG,B8.3 Methods for calculatingsemi-submersiblewave motion87 I.C Q~ lii 'AMPLITUDES OF PITCH Z: 45 , 2~A : 0046m - - AoB ,~Cl 61 G2 . . . . . . Z y , I25T (S)4 FK}.B9. l 1.0 (:P 0.5 00 1.0 (:D Q5 i AMPLITUDES OF PITCH % =45~, 2~A :O046m - - ~ - - K LI L2 - - MN . . . . . . . 0 -.,w~--Qp~ ~R ~ZB - . J , 23T(S)4 FIG. B9.2 I AMPLITUDES OF PITCH % : 45 , 2c~A:OO46m I - - S- - - - - - T - - . - - UI . . . . U2 oV _ - 1 i _ - w . . . ~~ 125T(S)4 FIG. B9.3 88M.TAKAGI e t al .O2 O. - - A "~" BAMPLITUDESOF YAW/ _ - - - : : _c ~ , , ~ : 4 5,2 ~ : o . 0 4 6 r n / [25T( S) 4 FIG.BI0.1 0.2 0.1 Oo - - ~ - - KAMPLITUDESOF YAW - - . - - L I. . . . L2~,: 4 5 2 ~ A = O O 4 6 m- - M- - o - . ZB~ _ . ~ - - - - ~ - . . . . . . . . . .I25r ( s ) 4 FI6.BIO.2 O2 -..#. OI o 6i iAMPLITUDESOF YAW %=4sTS,2~A :0.046 m/ ~: : : uL/ B 7/ / / - I25T ( S ) 4 Fic.BI0.3 Met hodsforcalculatingsemi -submersi bl ewavemot i on AP P E NDI XC C AL C UL AT I ONR E S UL T S OF P HAS E S( T = 1 - 1 0 s e c , =45 ) 89 9O 0 -90 -180 PHASES OF SURGE 1C =45~, 2BA:O.O46m I''''' ( s ' ) '5TIO A - - - " - - I , ZA- - - +C2I D. . . . . . d FIG.Cl . 1 -9( -18C PHASES OF SURGE % :45~, 2z~A:OO46m I I I I I5 ~ K- - - - - LI , L 2 , M , N , O , R- - - 0 - - -~ Z BF I G , C1.2 + ( s ) i c90M,TAKAGIet al.180 90 -90 -180 PHASES OF SURGE 9(, : 45, 2~A =O046m T. . . . . . . . . . . . . . . . ./5T ( S ); - . . .. , . , . ~ - . - - a . . . - - ~. . . . . . - ~ o - - c ~ . - - - e - - - . q ~ . . ~ - . . . .- - S . . . . . W . . . . T ' 2 U I ' Y I ' Y 2 . . . . . . ZX V FIG.C1.3 18C 9(: - 9 0-180 PHASESOFSWAY 7(, : 45 , 2roA= 004.6m I I i 5T (S) --A---D oB- - - - GI,G2 . . . . . . d . . . . . 7A FiG.C2.1 Methods forcalculating semi-submersible wavemotion91 1 8 C9 ( ]- 9 C - 18C PHASESOFSWAY %.=45,2 g A : Q O 4 6 m'' '' T ( S i ' 5I C~ KFIo.C2.2 - - . - - LI,L2,M,O,P,Q.R.ZB . . . . . N 0 _ c ~-18C PHASES OF SWAY ,,'X.= 4 52~A=O.O,~m rrs. . . . . w FIG. C2,3 "tl L~ m tl,I iI/ -~ pOO 7"- -(.J1 __ --~-. 0.1> .... "1' ii .o~ m 3 J I L~ J tl~ 3 CrY- (Jl- N ~l~Ig -UO ! l O --- o + .0: ol -'I~ -- I I ii -71- --- ~t, ...... rl-i -to 3 m ~:IiIJ fill > > Me t hods forcal cul at i ngs emi - s ubmer s i bl ewavemot i on93 18C 9O 0 - 9 0- 1 8 0P H A S E S O F R O L L , J"~:45, 2~, : o ~ m /, 4,:+z~,:,,/ I / J"$/',I ~ / ! ! ! i I. . . . . z,,J / f - - - qFIG. C4. l i 8 090 0 -9( - 1 8 (P H A S E S O F R O L L ~ I / / ~% =45, 2 ~ a= 0 . 0 4 6 m /! ~ / ~: / - - - t . I I 'FIG.C4. 2 94M.TAKAGI e t al .0- 9 0-180 IP H A S E SO FR O L L i ~ t ~ X .I C : 4 ~ 2 ~ , : 0 . 0 4 6 m i A / i \I , , : T ( S i ~ " \ / ' " ~ [ / ] "/ " - - - S . . . . . W , ~- - - T . . . . . . X ! m l- - - - U - - ~ - Y , ,- - ,,f \ i \ovz? /Fio.C4.3 18C 9O -90 -180 PH ASESoO FP IT C H ~ ~C: 4 5 , 2 ~ A: 0 . 0 4 6 m ~ j X ~ , I"A- - ~ - - 7 ~ h r - ; ~ T ~ ,t ~ , . . , - - 4 - - - 4 ~ . - f - - - - 4. G 2 , ' I / ' l } , J o /- - - - u , ' I A / I 1 / ~ 2 i , ; . . / ~ ,; : : - 8 ~ 5 T , ( s ) / [ , I , ~ , , ' q- : - ~ , , ' > " , , ! I V ! ' , , 1.~ ~ - , ~ ~ . ~ _ ~ L ......~: - . . . . . . L ~ -Io FiG.C5.1 Methodsforcalculating semi-submersible wavemotion95 1 8 0~90 0 -90 PHASES OFPFFCH 9(, =45*, 2~A :0.046m K --.--LI ....L2 M . . . . . N i. . . . . . 0', -..,-..p5 . . . . Q .--o-.-R ~Z~ FIG.C5.2 i(~)fi!IIx",~< CO 9O 0PHASES~ P,~C,\\7 .45;2..oo4m\ \ II , ~ / " "UI..... -X-' ~""Y2~\I u2- - ~Y, z- \ \ \] FIG.C5.3 96M.TAKAGI et al .2~ 03 180 9C 0 -90 F " ~ . . o- - A=! oo~ = - - - - ~ - - - - - ~. . . . ZA5T(S)I0 PHASES OFYAW % =45~ 2z;A =004.6m FIG.C6.1 27(1 C ,O180 90 o [ -90 5 F I 6 . C 6 . 2PHASESOFYAW 'X, =45 2z;A =QO4.6m ~ K- - - - - L I. . . . L 2. . . . ~ Q. . . . . . . . 0 ~ R- ' ~ZB T ( S ) I 0Met hodsforcalculatingsemi - submer si bl c wavemot i on97 270' 180 90 0 -90 PHASES OF YAW ~ SoV . . . . . W Z N I",, I"" N N N F I G . C6. 3