1 - Ship Structure Committee

SSC-246(SL-7-4).si “ THEORETICAL ESTIMATES OF WAVE LOADSI ON THE SL-7 CONTAINER SHIP INiREGULAR AND IRREGULAR SEASThis document has been approved forpublic release and sale; itsdistribution is unlimited.SHIP STRUCTURE COMMITTEE1974I

SSC-246(SL-7-4)Technical ReportonProjectSR-205,“ShipComputer Response”totheShipStructure CommitteeTHEORETICAL ESTIMATES OFWAVELOADSONTHESL-7CONTAINER SHIPINREGULARANDIRREGULAR SEASbyP.Kaplan,T.P.Sargent, andJ.CilmiOCEANICS, INC.underDepartment oftheNavyNavalShipEngineering CenterContract No.NOO024-70-C-5076Thisdomiw.thasbeenapprovedfor pubZicreleaseandsale; its distributionis unl-imited.U.S.CoastGuardHeadquartersWashington, D.C.1974

ABSTRACTThecomputer programSCORESforpredicting shipstructuralresponseinwavesisappliedtotheSL-7container ship.Theoperating conditions considered are2 displacements, 4 shipspeeds,21wavelengths, 19headingsand5 seastatesassumingbothlong–crested andshort–crested seas.These~esultsconstituteacompletedatabankfortheSL–7shipintheformofbothfrequency responses forregularwavesaswellasrmsandotherstatistical response measuresforirregular seas.Comparison ismadebetweenthecomputerandmodeltestsoftheSL-7inregularwavesinpredicting vertical, lateralandtorsional moments,andverticalandlateralshearsattwosectionsandheave,pitchandroll.Regionswherethetheoryandmodelexperiment donotagreehavebeenpointedoutandsomemeansofcorrection orextension ofthetheoryisdiscussed.-ii-

PageINTRODUCTION.......SHIPDESCRIPTIONANDLOADINGEXPERIMENTALDATA ..... . .. .. . ...COMPARISONOFTHEORYANDEXPERIMENTCONCLUDINGREMARKS........REFERENCES...........APPENDIX ........................................................................................................ ........121112242541-iii-

No.123456789101112131415TitleLTSTOFFIGURESPageLongitudinal Segmentation: SL–7Containership . . . . . 3Comparison BetweenTheoryandExperiment,Frame124HeaveandPhaseLag,0°Heading. . . . . . . 26Comparison BetweenTheoryandExperiment,Frame124HeaveandPhaseLag,180°Heading. . . . . . 26Comparison BetweenTheoryandExperiment,Pit;handPhaseLag,0°fielding.-. . . . . . . . . . . . 26Comparison BetweenTheoryandExperiment,PitchandPhaseLag,180° Heading. . . . . . . . . . . 26Comparison BetweenTheoryandExperiment,C.G.HeaveandPhaseLag, 180°Heading. . . . . . . . . 27Comparison BetweenTheoryandExperiment,RoliandPhaseLag,30°Heading. . . . . . . . . ..* 27Comparison BetweenTheoryandExperiment,RollandPhaseLag,60°Heading. . . . . ● *.** . . 27Comparison BetweenTheoryandExperiment,RollandPhaseLag,60°Heading. . . . . . . . . . . . 27Comparison BetweenTheoryandExperiment,MidshipVerticalWaveBendingMomentsandWavePhaseLag,0° Heading. . . . . . . .Comparison BetweenTheoryandExperiment,MidshipVerticalWaveBendingMomentsandWavePhaseLag,30°Heading. . . . . . .Comparison BetweenTheoryandExperiment,MidshipVerticalWaveBendingMomentsandWavePhaseLag,60°Heading. . . . . . .Comparison BetweenTheoryandExperiment,MidshipVerticalWaveBendingMomentsandWavePhaseLag,240°Heading. . . . . . .Comparison BetweenTheoryandExperiment,MidshipVerticalWaveBendingMomentsandWavePhaseLag,210”Heading. . . . . . .Comparison BetweenTheoryandExper

No. —1617181920212223242526272829TitleLISTOFFIGURESComparison BetweenTheoryandExperiment,MidshipVertical waveBendingMomentsandWavePhaseLag,0°Heading. . . . . . . . . . . .Comparison BetweenTheoryandExperiment,MidshipVerticalWaveBendingMomentsandWavePhaseLag,30°Heading. . . . . . . . . . .Comparison BetweenTheoryandExperiment,MidshipVertical WaveBendingMomentsandWavePhaseLag,60°Heading. . . . . . . . . . .Comparison BetweenTheoryandExperiment,MidshipVertical WaveBendingMomentsandWavePhaseLag,240°Heading. . . . . . . . . . .Comparison BetweenTheoryandExperiment,MidshipVerticalWaveBendingMomentsandWavePhaseLag,210°Heading. . . . . . . . . . .Comparison BetweenTheoryandExperiment,MidshipVerticalWaveBendingMomentsandWavePhaseLag,180°Heading. . . . . . . . . . .Comparison BetweenTheoryandExperiment,MidshipVerticalShearandPhaseLag,0°Heading.Comparison BetweenTheoryandExperiment,MidshipVerticalShearandPhaseLag,30°Heading.Comparison BetweenTheoryandExperiment,MidshipVerticalShearandPhaseLag,60°Heading.Comparison BetweenTheoryandExperiment,MidshipVerticalShearandPhaseLag,240°HeadingComparison BetweenTheoryandExperiment,MidshipVerticalShearandPhaseLag,210°Heading ..*Comparison BetweenTheoryandExperiment,MidshipVerticalShearandPhaseLag,180°Heading .*.● ✎ ✎● ✎ ✎●✎☛● ✎ ✎. . .. . .. . .. . .. . .. . .Comparison BetweenTheoryandExperiment,MidshipVerticalShearandPhaseLag,0°Heading. . . .Comparison BetweenTheoryandExperiment,MidshinVerticalShearandPhaseLaa.30°Headina. —L. _

No. .303132333435363738394041424344LISTOFFIGURESTitlePageComparison BetweenTheoryandExperiment,MidshipVerticalShearandPhaseLag,60°Heading. . . 33Comparison BetweenTheoryandExperiment,MidshipVerticalShearandPhaseLag,240°Heading. . . 33Comparison BetweenTheoryandExperiment,MidshipVerticalShearandPhaseLag,210°Heading. . . 33Comparison BetweenTheoryandExperiment,MidshipVerticalShearandPhaseLag,180°Heading. . . 33Comparison BetweenTheoryandExperiment,MidshipVerticalShearandPhaseLag,30°Heading. . . 34Comparison BetweenTheoryandExperiment,MidshipLateralShearandPhaseLag,60°Heading. . . . 34Comparison BetweenTheoryandExperiment,MidshipLateralShearandPhaseLag,240°Heading. . . 34Comparison BetweenTheoryandExperiment,MidshipLateralShearandPhaseLag,210°Heading. . . 34Comparison BetweenTheoryandExperiment,MidshipLateralShearandPhaseLag,30°Heading. . . . 35Comparison BetweenTheoryandExperiment,MidshipLateralShearandPhaseLag,60°Heading. . . . 35Comparison BetweenTheoryandExperiment,MidshipLateralShearandPhaseLag,240°Heading. . . 35Comparison BetweenTheoryandExperiment,MidshipLateralShearandPhaseLag,210°Heading. . ‘.35Comparison BetweenTheoryandExperiment,MidshipTorsional WaveBendingMomentsandPhaseLag,30°Heading. . . . . . . . . . . . . . . . . 36Comparison BetweenTheoryandExperiment,MidshipTorsional WaveBendingMomentsandPhaseLag,60QHeading. . . . . . . . . . . . . . . . . 36Comparison BetweenTheoryandExperiment,MidshipTorsional WaveBendingMomentsandPhaseLag,240°Heading. . . . . . . . . . . . . . . . 36-vi-

No.454647484950515253545556LISTOFFIGURESTitlePageComparison BetweenTheoryandExperiment,MidshipTorsional WaveBendingMomentsandPhaseLag,210°Heading. . . . . . . . . . . . . . . . 36Comparison BetweenTheoryandExperiment,MidshipTorsional WaveBendingMomentsandPhaseLag,30°Heading. . . . . . . . . . . . . . . . 37Comparison BetweenTheoryandExperiment,MidshipTorsional WaveBendingMomentsandPhaseLag,60°Heading. . . . . . . . . . . . . . . . 37Comparison BetweenTheoryandExperiment,MidshipTorsional WaveBendingMomentsandPhaseLag,240°Heading.. . . . . . . . . . . . . . . 37Comparison BetweenTheoryandExperiment,MidshipTorsional WaveBendingMomentsandPhaseLag,210°Heading. . . . . . . . . . . . . . . . 37Comparison BetweenTheoryandExperiment,MidshipLateralWaveBendingMomentsandPhaseLag,30°Heading. . . . . . . . . . . . . . . . 38Comparison BetweenTheoryandExperiment,MidshipLateralWaveBendingMomentsandPhaseLag,60°Heading. . . . . . . . . . . . . . . . 38Comparison BetweenTheoryandExperiment,MidshipLateralWaveBendingMomentsandPhaseLag,240°Heading.. . . . . . . . . . . . . . . 38Comparison BetweenTheoryandExperiment,MidshipLateralWaveBendingMomentsandPhaseLag,210°Heading.. . . . . . . . . . . . . . . 38Comparison BetweenTheoryandExperiment,MidshipLateralWaveBendingMomentsandPhaseLag,30°Heading. . . . . . . . . . . . . . . . 39Comparison BetweenTheoryandExperiment,MidshipLateralWaveBendingMomentsandPhaseLag,60°Heading. . . . . . . . . . . . . . . . 39Comparison BetweenTheoryandExperiment,MidshipLateralWaveBendingMomentsandPhaseLag,240°Heading. . . . . . . . . . . . . . . . 39-vii-

No.5758596061TitleLISTOFFZGUFJ3SComparison BetweenTheoryandExperiment,MidshipLateralWaveBendingMomentsandPhaseLag,210°Heading.. . . . . . . . . . . . - ●Comparison BetweenTheoryandExperiment,MidshipVerticalWaveBendingMomentsandWavePhaseLag,0°Heading,(A’33=0).. . . . . ● ● ● “Comparison BetweenTheoryandExperiment,MidshipVerticalWaveBendingMomentsandWavePhaseLag,60°Heading,(A’33=0) . ● ● - - . “ “ .Comparison BetweenTheoryandExperiment,MidshipVerticalShearandPhaseLag,60°Wading,(A’ 33=0)” ”. -” ”””. ””. .””9..” “...”Comparison BetweenTheoryandExperiment,MidshipVerticalShearandPhaseLag,0°Heading,(A’-lo=o). . . . . . ● . . . . . . . . . . . ., . . . .cPage3940404040LISTOFTABLESNo.TitlePageIIIIIIIVvVIVIIVIIIShipCharacteristics ...................... 4Estimated Weights, Centers &Gyradiifor“Heavy” LoadCondition .. 5Estimated Weights, Centers&Gyradiifor“Light” LoadCondition .. 6SummaryofModelBallast:“Heavy” Condition (ModelProperties .. 7ScaledtoFullSize).Sunwnary ofModelBallast:“Light” Condition (ModelProperties .. 8ScaledtoFullSize)WeightProperties oftheSL-7(Heavy) UsedintheComputer.... 9ProgramWeightProperties oftheSL-7(Light) YsedintheComputer....10ProgramComparison Between Theoretical andExperimental R.M.S.......17Responses inShort-Crested Seas-viii-

SHIPSTRUCTURECOMMITTEETheSHIPSTRUCTURECOMMITTEEisconstitutedtoprosecute.aresearchprogramtoimprovethehullstructuresofshipsbyanextensionof knowledgepertainingtodesign,materialsandmethodsoffabrication.RADMW.M.Benkert,USCGChief,OfficeofMerchantMarineSafetyU.S.CoastGuardHeadquartersCAPTJ.E.Rasmussen,USNMr.M.PitkinHead,ShipSystemsEngineeringAsst.AdministratorforandDesignDepartmentCommercialDevelopmentNavalShipEngineering~enterMaritimeAdministrationNavalShipSystemsCommandMr.K.MorlandCAPTL.L.Jackson,USNVicePresidentMaintenanceandRepairOfficerAmericanBureauofShippingMilitarySealiftCommandSHIPSTRUCTURESUBCOMMITTEETheSHIPSTRUCTURESUBCOMMITTEEontechnicalmattersbyprovidingtechnicalofgoalsandobjectivesoftheprogram,andresultsintermsofshipstructuraldesign,NAVALSHIPSYSTEMSCOMiVIANDMr.P.M.Palermo-MemberMr.J.il.O’Brien-ContractAdininistratorMr.G.Sorkin-MemberU.S.COASTGUARDLCDRE.A.Chazal-SecretaryCAPTD.J.Linde-MemberLCDRD,.L.Folsom-[4emberCDRW.M.Devlin-MemberMARITIMEADMINISTRATIONMr.J.Nachtsheim-ChairmanMr.F.Dashnaw-MemberMr.F.Seibold-MemberMr.R.K.Kiss-MemberMILITARYSEALIFTCOMMANDMr.T.W.Chapman-MemberMr.A.B.Stavovy-MemberMr.J.G.Tuttle-MemberNATIONALACADEPIYOFSCIENCESSHIPRESEARCHCOMMITTEEactsfortheShipStructureCommitteecoordinationfor the determinationbyevaluatingandinterpretingtheconstruction-andoperation.AMERICANBUREAUOFSHIPPINGMr.S.G.Stiansen-MemberMr.I.L.Stern-MemberSOCIETYOFNAVALARCHITECTSENGINEERSMr.A,B.Stavovy-LiaisonWELDINGRESEARCHCOUNCILMr.K.H.Koopman-LiaisonINTERNATIONALSHIPSTRUCTURESProf.J.H.Evans-Liaison&MARINEUs.CAPTUs.CAPTU.S.COASTGUARDACADEMYC.R.Thompson-LiaisonMERCHANTMARINEACADEMYW.M.Maclean-LiaisonNAVALACADEMYCONGRESS!lr.R.W.Rumke-LiaisonProf.J.E.Goldberg-LiaisonDr.R,Bhattacharyya-Liaison-ix-

NOTES-x-

INTRODUCTIONASpartofa continuing overallstudyof shipstructuralloads,workhasbeencarriedoutfora numberofyearsundersupportoftheShipStructure Committee[1]covering modeltests,theoretical analyses(including computer-program development) ,andfull-scale measurements. A particular programcoveringallofthesefacetsispresently underway withapplication totheSL-7container shipclass,whichrepresents thelargestandfastestshipofthattypepresently inoperationṪhisshipisexpectedtooperateathighspeedintheNorthAtlanticOcean.Theexistence ofa developed theoryfordetermining shipmotionsandloadsinobliquewaves[2],together withthecomputerprogram[3]baseduponthistheory,allowstheopportunity ofdetermining viacomputation thevariouswaveloadsthatactonthisship.At thesametime,resultsofextensive model-tanktestsofthisshipinregularwavesarealsoavailable[4],therebyallowingcomparisonbetweentheoryandexperiment. Inaddition,aprogramof full-scale measurements ontheoperatingvesselsthemselves isalsobeingcarriedout (see[5]). Thesesourcesafdataobtainedbydifferent meansallowanopportunitytoestablish correlation betweenvariousapproaches, sothatbettertoolsforloadprediction of futureshipscanbe established(aswellasprovidingdataforthisimportant typeof ship,asanendproductperse).Thesuccessful useofa theoretical prediction ofwaveloadsviacomputerisveryimportant forthisclassof shipsincethenumberofwave-induced structural loadings andthevariousconditions(orparameters)isquiteextensiveṬhisisduetotheimportance of thetorsional momentsandlateralshearforces,inaddition totheverticalandlateralbendingmoments,aswellasthedependence of thesequantities on theirparticular locationon theship.Combining theserequirements withthatof assessingthedependence uponallpossible wavedirections, aswellasshipspeed,indicates thelargenumberofvariations necessary fordetermining thecharacteristics of thevariousloadsaffecting acontainer ship.Theextentofthemodeltestsrepresented byallpossibleparametric valuesforoperation ofthisparticularship,aswellasconsideration of carrying outmodeltestsoffuturecontainer shipdesigns, pointsoutthebenefitsthatcanbeobtainedby application of anefficient computer programfordetermining thedifferent waveloadsforsuchships.Thepresentinvestigation isaimedatobtaining resultsfromcomputercomputations thatcanbedirectlycompared withthoseof themodeltestsin [4]inordertoobtaincorrelationbetweentheoryandexperiment, aswellastoindicatetheextentofanydeficiencies inthevariousmethodsofdetermining shiploadsandmotions.Inaddition, generalized responsedatais

tabulated forvariousoperating conditions oftheSL–7containershipunderdifferent static-weight distributions, differentspeeds,headings, andseastates.Thescopeofthecomputerstudyincludesallofthemodeltestconditions coveredin [4],aswellasanextendedrangeofshipoperating conditions. Theappendix presentsdataontheamplitudes andphasesofshipmotions(heave, pitchandroll)andloads(vertical andlateralbendingmomentsandshears,andtorsion),covering4 speeds,2 displacements, 19headings, and21wavelengths. Thisinformationcombined withwavespectrarepresenting 5 long–crested and5 short–crested irregular seastatesinordertoprovidestatistical measuresof responses inthoseseaconditions, whicharetabulated intheappendix.SHIPDESCRIPTION ANDLOADINGThespecifications oftheactualSL-7shipforpurposesofthepresentinvestigation arelistedbelowinTable1,withthedesignation of “heave”loadingcorresponding tonormalfullloadingintheNorthAtlantic,and“light”loadingcorresponding toinitialoadofoneSL–7container shipoperating inconjunctionwitha fleetofotherships.Theactualinformationthedis-tribution ofthestaticloadingisgiveninTables2and3,whichalsocontaininformationthesectionalverticalcentersandrollinertiathatarenotordinarily providedduringdesignstudies.Allofthisinformation isobtainedfrom[41, wherethetabulation waspreparedfortheshipintheformof 22loadingsegmentsṪherelations betweentheseloadingsegmentsontheship,theframenumbersandlines-plans stations(for20stationsalongLBP), andthesegments ofthemodeltestedin [4], aregiveninFigure1. Asdiscussed in [4], theverticalCGpositionoftheshipincludesthecorrection dueto freeliquideffectsonthetransverse metacentric height.Themodelusedinthetestsreportedin [4]didnotexactlyreproduce theconditions of loadingspecified inTables2 and3,butwasballasted toobtainvaluesascloseaspossibletothosevalues.Theresultsobtainedaregiven,in full-scale units,inTables4 and5,representing thecharacteristics forthethreemodelsegmentsinregardtothedegreeofmatchingobtained withthemodel.Inordertoapplythecomputer programof [3],itisnecessarytoestablisha distribution of loadingoverthe20stationsrepresenting theshipinregardtoweight,locationof sectionalCG,rollinertiaofeachsection,etc ṭhatwouldsatisfythemodelcharacteristics ifa propersimulation ofthemodelship,astested,istobemade.Thiswasdonebynumerical experimentation thatproducedresultsthatsatisfied thecharacteristics obtainedinthemodel,althoughtheprecisedistribution overthe20stations would-2-

~MoDELsEGmNT+8FT(r-iAfPl13I 22212019 1817 16 IS 14 12 11 10 9 8 7 6 5 4 3 2 1 (I / II-i1’030 4662 78 96112132142160178 194210226242258274290311 342II I IiO 19 18 1716 15 14 [ I I1312I11 10 9 ,I jj I54321o1 II I I 1 ! 1 I 1 I-~/4012345 67,9 10 11 12 13 1415 16 17 1819 2{)LOADINGSEGMENTS(SHIP)FRAMENO.COMPUTERSTATIONSPJZF. [4]STATIONS~ L*’Q*A. 946*6FE~T(’2855~8M)FIG.1 LONGITUDINAL SEGMENTATION: SL-7CONTAINERSHIP

notnecessarilybethesameasthatonthemodel.Sincethemodeldistributionover20stationsisnotknown,butthetotalresultsforeachmodelsegmentdomatch,thenon-uniquedistributionofloadingobtainedtorepresentthemodelisconsideredsufficientforthepresentpurposesofcomparisonofresultsforthesamecase.At thesametime,thedesignspecificationfortheship,aspresentedinTables2 and3,wereusedtoestablishtheloadingdistributionsforthefull-scaleshipthatwillbethebasereferenceconditionsforpredictionofresponsedataundervariousoperatingconditions,asgivenintheAppendixtothepresentreport.TheactualsectionaldistributionsusedinthecomputerprogramforthispurposearegivenbelowinTables6 and7.TABLEISHIPCHARACTERISTICSLength: Overall946.6Feet(288.518m.)Length: BetweenPerpendiculars880.5Feet(268.376m.)Breadth:MaximumLoadDesignation(forpurposesofthisstudy)LoadDesignation:SpecifiedDraftatLCFTrim,by sternLCGAftofmidshipVCGAbovebaselinemt-t CorrectedforfreeliquidsDisplacement105.5Feet(32.156m.)“HEAVY”NormalFU1lLoad(Departure)32.6ft.(9.95m.)0.14ft.(42mm.)38.6ft.(11.75m.)41.7ft.(12.70m.)3.30ft.(1.00m.)2.63ft.(0.80m-)47686L.T.(48400M.T.)“LIGHT”InitialPartLoad(Departure)29.1ft.(8.86m.)1.83ft.(.56m.)37.5ft.(11.42m.)39.8ft.(12.14m.)5.79ft.(1.76m.)5.32ft.(1.62m.)41367L.T.(41900M.T.)-4-

SEGMENTTABLE11EstimatedWeights,CentersandGyradiifor“Heavy”LoadCondition1234567 8 910111213141516171819202122TOTAL1. LongTonsWEIGHTI LCG2765.21847.71205.71613.41943.62379.22305.62610.83148.73343.73299.03179.23293.33039.82661.32898.72116.11678.31597.21244.5897.7691.347760.3(2240lb)421.25355.93297.07254.73214.75174.71134.7294.7254.7314.74-27.74-72.74-109.75-147.25-194.75-234.10-275.85-316.15-355.30-395.25-429.25–460.25-38.61VCG344.5033.4059.6747.9648.0844.4940.4638.3137.7536.6231.8331.0743.2745.6943.4844.7350.1350.5751.4850.0844.3651.9042.31K4 xx23.824.935.530.633.034.236.037.338.238.738.739.041.845.739.337.935.933.432.431.923.822.037.3K5 YY30.530.031.227.628.328.629.328.729.229.228.128.429.533.726.827.325.825.525.427.120.517.5215.1KG Zz22.022.931.120.323.224.426.428.729.430.231.731.731.936.632.331.629.927.626.124.918.518.8215.12. FeetForwardofMidship3. FeetAboveBaseline4. RollGyradius,Feet5. PitchGyradius,Feet6. YawGyradius,Feet-5-

TABLEIIIEstimatedWeiqhts,CentersandGyradiiSEGMENT1 2345678910111213141516171819202122TOTALfor“Li~ht””LoadCondition-WEIGHTJ777.41859.91217.91151.81379.21844.31990.62429.02547.52707.62714.92697.93284.93031.42726.32757.41631.31217.7982.5901.2889.3682.941422.81. LongTons(2240lb)LCG2421.25355.93297.07254.73214.75174.71134.7294.7254.7314.74-27.74-72.74-109.75-147.25-194.75–234.10-275.85-316.15-355.30-395.25-429.25-460.25-37.43VCG343.4032.8858.5247.3648.6744.9933.3635.8934.4233.8131.5431.4942.9745.3941.6542.0346.2147.1341.4740.7744.3652.0540.26K4 xx24.925.336.730.033.233.632.735.636.136.637.037.042.246.237.937.336.835.132.731.224.322.536.7K5 YY31.430.332.625.927.226.725.626.626.326.225.625.730.034.224.826.226.126.424.125.121.118.1214.8KG Zz21.822.831.021.725.125.725.928.529.430.431.731.631.936.732.331.831.029.428.427.018.618.9215.02* Feet ForwardofMidship3. FeetAboveBaseline4. RO1lGyradius,Feet5. PitchGyradius,Feet6. YawGyradius,Feet-6-

TABLEIVSummaryofModelBallast:“Heavy”Condition(ModelProperties ScaledtoFullSize)ModelSegments 123EntireModelShipLoading 1 through5 6 through10 11through22 1 through22SegmentsDesiredAchieved DesiredAchieved DesiredAchieved DesiredAchievedWeight, 7375.6 7380. 13788.0 13800. 26596.4 26600. 47760.0 47780.LongTonsLongitudinalCenter, 293.74 293.9 86.68 86.8 195.74 196.7 38.61 39.0ft.from fwd fwd fwd fwd aft aft aft aftVerticalCenter, 45.90 44.6 39.20 35.2 42.93 42.3 42.31 40.6ft.aboveRollGyradius, 31.38 28.2 37.23 35.6 38.72 37.8 37.31 36.0L I K ft● xxrPitchG ~adius, 74.61 72.4 63.82 68.4 126.31 123.821.5.09 215.0K~o 1YYYawGyradius, 72.15 65.1 63.38 66.7 126.80 119.3215.07 213.0KZz’ft.(Product ofInertia)/Mass, -268.72 248. 144.71 -48.2 -719.80 -408. -383.02 -342.K2 f~mzX2‘AngleofPrincipal -3.6 4.1 3.22 -0.9 -2.8 -1.8 -0.5 -0.4Axis,De~.Transverse Metacentric Height,~, ft.2.63 2.57FreeRollPeriod,seconds, Tr27.8ApparentRollGyradius = Tr~/1.108,Feet40.2(Apparent RollGyradius)~(Measured RollGyradius).1.11

TA3LEVSummaryofModelBallast:“Light”Condition(ModelProperties Scaledto FullSize)ModelSegments 123EntireModelShipLoadingSegments1 through5 6 through10 11through22 1 through22DesiredAchieved DesiredAchieved DesiredAchieved DesiredAchievedWeight,LongTons6386.2 6360. 11519.0 11520. 23517.7 23450. 41422.9 41330.LongitudinalCenter, 303.91 304.0 86.80 78.8 190.97 190.0 37.43 39.1ft.from fwd fwd fwd fwd aft aft aft aftVerticalCenter,ft.above45.07 45.4 36.10 32.8 40.99 40.8 40.26 39.3RO1lGyradius, 31.64 30.4 35.38 33.3 38,43 38.6 36.74 36.3+ Kxx‘ft.PitchGyradius, 74.69 78.2 61.66 59.2 122.99 121.3214.83 212.6K ft.YY‘YawGyradius, 72.39 66.2 62.42 58.7 123.86 112*2215.03 209.0K22Pft.(Product ofInertia)/Mass, -315.71~2X2f ft.zAngleofPrincipal -4.2AxisrDeg.432,7.0152.79 136.3.3 3.3Transverse Metacentric Height,~, ft.FreeRollPeriod,seconds, TApparentRollGyradius- TrGM/1.108, Feet(Apparent RollGyradius)/(Measured RollGyradius)-4!54. 16 -135.-1.9 -0.7.218.43 7.8-0.3 0.05.32 5.6020.042.81.18

TABLEVIWeightProperties of theSL-7(Heavy) usedintheComputer ProgramWeight,1 Verticalcenter2Station (lonqtons) ofgravity,ft.O (FP) 435.19 - 2.01161900.40 9.073421110.55 9.088431304.96 -15.541641625.78 -10.34965 1973.79 5.531667892323.47 - 4.56762709.73 3.35243024.64 4.26843420.21 5.0194103421.71 7,4784113206.49 10.8954123776.005 7,8594133526.57 2.5356142837.96 2.0016152893.305 1.8436162491.125 5.7896172056.03 7.9736.181758.175 8.8426191888.51 7.611620 (AP] 1075.395 - 6.8986Kxx‘ft.23.825.324.935.532.933.735.035.439.039.938.739.740.745.642.539.337.234.333.532.523.611. Theshipisdividedinto20segmentsof 44.025ft.lengths.Thewei~htateachstationisassumedtobeuniformlydistributed overthesegmentandcenteredatthestation.2. Theverticalcenterofgravityof eachelementismeasured,positivedownward, withrespectotheship’soverallVCG.-9-

TABLEVIIWeightProperties oftheSL–7(Light)usedintheComputer ProgramWeight,~ Verticalcenter2Station (lonqtons) ofgravity,ft.o1234567891011121314151617181920358.465866.421072.3051229.201273.111561.221931.512298.6552613.372827.7152804.372671.773479.653462.252830.202811.802117.151467.801158.8151514.621072.505- 3.29446,30567,2256- 9.8944-10.5944- 8.2844- 6.59445.30564.50565.90567.10568.60565.3056- 4.5944- 2.9944- 1.7944- 4.5944- 6.7944- 2.15447944- 9:2944K xx’‘t.24.9025.2625.3035.4033.5033.2033.6032.9235.0936.3336.8437.0038.6545.5042.5737.9036.9835.6434.1032.0023.001.2.Theshipisdividedinto20segments of 44.025ft.lengths.Theweightateachstationisassumedtobeuniformlydistributed overthesegmentandcenteredatthestation.Theverticalcenterofgravityofeachelementismeasured,positivedownward, withrespectotheship’soverallVCG.-1o-

EXPERIMENTAL DATATheexperimental dataobtainedinthemodeltestsin [4]included verticalandlateralbendingmoments,verticalandlateralshearforces,andtorsional moments,measuredatbothmidshipandattheforwardcutatFrame258. Measurements werealsomadeofthemotionsofheave,pitch,androll,aswellastherudderangle.Allresultsarepresented intransferfunctionform,i.e.lamplitude andphase,withtheamplitude referredtothewaveamplitude tested(response perunitwaveamplitude) andthephasereferredtothemidshipverticalbendingmoment.Pos–itivewaveelevation wasdefinedintheexperiments tobepositivedownward whichisoppositetotheconvention usedin [2]and[3],andresultsinsomecomplication inreconciling phasesbetweentheoryandexperiment.Therollextinction recordsinFigure4 of [4]forboththeheavyandthelightconfiguration, at 28kt.forwardspeed,wereanalyzedinordertoobtainvaluesof rolldampingfortheship.Resultsforthelightconfiguration weremorelinear(i.e.closerThemainregularwavetestswerecarriedoutovera speedrangeof 23-32kt.coveringallheadings(basedon symmetryconsiderations)between0° (following seas)and180°(headseas), in30°increments. Insufficient datawereobtained forbeamseastocharacterize theresponses forthatcase,duetoexperimentaldifficulties, andhenceno comparison betweentheoryandexperimentismadeforthatcase.Torsional momentsaremeasuredinthemodelexperiments aboutanaxislocated23.3ft. (fullscale)abovethebaselineinthecenterplane. Thisdata țogether withdataonthelateralshearforce(amplitude andphase),canbeusedtoobtainvaluesofthetorsional momentaboutanyotheraxislocatedatsomeverticaldistancerelativetothisreferenceȦn applicationofthisprocedure wouldbe toobtainthetorsional momentaboutthe“centeroftwist”or shearcenter,whichisnormallylocatedbelowthebaselineİnformation ofthisnaturecanbeobtainedfromthecomputer programcalculations aswell,butwillberestricted hereintothetestmeasurement reference conditionforpurposesof comparison oftheoryandexperiment.Certainspecialtestswerealsomade(inordertoisolatesomeeffects)thatarenotusuallymadeinthecourseofexperimentalstudiesinordertoassistincorrelatingtheoryandexperiment. Thesetestsincludedforcedrudderoscillations,withmeasurements of therollangle,lateralshearandbendingmoment,andtorsional moment(inregardtoamplitude andphaserelativetotherudderoscillation) inordertoisolatetheruddereffectson thosequantities. Anotherspecialtestprovidedrollextinctionrecords, whicharethebasicdatafrnmwhichlinearized rolldampingcoefficient estimates aremadeforuseinthecomputer program[3].-11-

toexponential decaywithtime)thantheheavycase,withtheheavyconfiguration beingprimarily dampedinnonlinear fashion.Theserecordswereanalyzed on thebasisof therolldampingbeingrepresented asa combination of linearandquadratic nonlineardamping,andthecoefficients foundforeachelemental term(see[61forillustration ofa similartypeofanalysis).Theseparatelinearandquadratic dampingvalueswerecombined, intermsoftheexpectedrangeofrollangles,toproducea finalestimateofequivalent linearolldampingfortheshipineachofthetwodisplacement conditions. ThesevalueswereLr=: = 0.10forthelightconfiguration, andgr= 0.09forthecheavyconfiguration, withtheassumption thatthesesamevaluesareapplicable overtheentirespeedrangeof 23-32kt.intheregularwavetestsof [4]. Theyareusedinthecomputer programalsoincarrying outcalculations forcomparing theoryandexperi–ment.COMPARISON OFTHEORYANDEXPERIMENTTheapplication ofthetheoryof [2]topredictheloadsandmotionsoftheSL–7shipisexpectedtoprovideanswersthataregenerally ingoodagreement withtheexperimental data.Thisisbaseduponthepreviousuccessful applications ofthetheoryin [2], theslenderfineformof theshipwhichisclosertotherequirements of a longslenderbodyforapplication ofstriptheory,andvariousother(unpublished) applications of thetheoryandprogramtodifferent shipforms.Whilethemajoraimofthisstudyisthedetermination ofwaveloads,informationon thecorrelation betweentheoryandexperiment forthemeasuredshipmotionsisalsousefulinproviding insightintothecapabilities ofthebasictheorysincethemotionsaresignificant elementsindetermining theloads.Themeasuredshipmotionsin [4]aretheheaveatFrame124(582.5ft.aftoftheforwardperpendicular) , thepitchAllofthecomparisons betweentheoryandexperiment aremadeusingthesignconventions, etc.of [4]sothattheexperimentalresultshownintheaccompanyingfiguresareduplicatedinthisreportfromthosein [4].Otherinformation presentedinthisreport,intheformof spectralresponseresultsgiveninTable8 andalsointheAppendix, whichrepresent thedatabankforSL-7responses asdetermined fromtheory,arepresented intermsoftheconventions[2]and[3].Alloftheconditionscoveredby theexperimenters in [4]~ whichisthenequivalenttoabout170-180different setsof frequency responses(bothamplitude andphase)havebeentheoretically evaluated withthedigitalcomputer program Ȯnlya limitednumberofplotsshowingrepresentative comparisons betweentheoryandexperiment arepresented inordertoillustrate theresults.-12-

angleandtherollangle.Tocomparethemeasuredheavewiththetheory,thepredicted heavewascombined withthepredicted pitchtogivetheresultant heaveatFrame124. TypicalheaveresultsareshowninFigures2 and3. Theagreement, unexpectedly, isnotgood.Ontheotherhand,typicalresultshowingtheverygoodpitchcomparison aredisplayed inFigures4 and5. Thislevelofagreement betweentheoryandexperim@n-L inpitchwasmaintained forallheadings, speeds,anddisplacements.Itthusdidnotseemreasonable thattheheaveatFrame124was beingcontaminatedbythepitch.Todemonstrate this,themeasuredheaveof Frame124wascombined withthemeasuredpitchtogivethemeasuredheaveattheshipCG inFigure6,towhichtheorywasagaincomparedȦgain,thetheoryandexperiment arenotinagreementṪtiscommonlyacceptedinthelimitof longwaves(A/L>>l) thattherati ofheaveamplitude tothewaveamplitude approaches l.0~whichisnotthecaseforthepresentheavemeasurements. Itisimpossible tobedefinitive inasmuchastheSL-7isoperating ina higherspeedregimethaninthespeedsusedinthevalidation of thetheory[2],butitappearspossiblethattheheavemeasurements areinerror.Thispossibilityhasbeenacknowledgedby theexperimenters, anditistheirbeliefthatifanexperimental errorexistsitwouldbe asystematic errorinheavealone.Thepossibility wasindicatedthata factoroftwo(2)couldariseina dialsettingsothatallmeasurements ofheavemightthenbemultiplied by a factorofone-half(0.5).Ifthiswerethecase,theagreement betweentheoryandexperiment wouldthenimprove.Typicalrollcomparisons areshowninFigures7 and8,andcanbe seentobepoor.Thismaybedueprimarily tothefactthatrolldampingisprobablynonlinear, andhenceitisnotproperlyrepresented inthepresentheoryof [2]and[3].Theseresultsarefortheheavyconfiguration wherethecombination oflinearandnonlinear rolldampingisreplacedbya probablytoolargeassumedequivalent lineardamping,asdiscussed inthepreceding sectionofthisreport.An illustration oftheresultsforthelightconfiguration, wheretherolldampingwasclosetolinear,isgiveninFigure9. Inthatcaseitcanbe seenthatbetteragreement betweentheoryandexperiment isobtained, therebyprovidingfurtherevidenceofthesignificance ofnonlinearrolldampingon shipresponseṪhelimitednumberof conditionstestedfordetermining rollresponses doesnotallowa completegeneralization oftheseresults,butonlypointstotheneedformorerefinedmethodsofpredicting rollmotionaswellasthevarioushipwaveloadsthataresignificantly influenced byroll.Thecomparison betweenth~theoryandexperiment inpre–dietingtheloadsontheSL-7areshowninFigures10-57.Thesefigureshowthevariation ofparticular waveloadsasfunctionsofwavelength, fordifferent speedsandheadings, artci forthetwo-13-

different displacement conditions. Thecomparisons giventherearepresented inthefollowing sequence; midshipverticalbendingmoment(Figures 10-21),midshipverticalshear~Figures 22-33) ,midshiplateralshear(Figures 34-41) , midshiptorsion(Figures42-49),andmidshiplateralbendingmoment(Figures 50-57).Onthewhole,thelackof consistent agreement isdisappointing,especially inviewof thegoodagreement shownin [2]aswellasinseveralsubsequent (butunpublished) applications ofthetheoryandprogramin [2]and[3].Tntheverticalplane,thetheoretical resultsareforthemostpartlowerthantheexperimentalresults.14nexaminationwasmadetoseeifthisdifferencewereduetotheinfluence ofhigherforwardspeed(l?roude Numbereffect) , asshownin [7]forthecaseofmotioninheadseas.Theequations usedin [7],whicharesimilartothosein [2], alsocontainsomeadditional termsinthecoefficient definitions thatcouldpossiblyinfluence thepredicted results Ṫhosesamecoefficient changeswereincorporated intotheprogramof [3]andcomputations repeatedfora fewdifferent cases.Theresultsobtained withtheothertheoretical modelwerealmostexactlythesameasthosefoundfromtheoriginaltheoryandprogramof [2]and[3].Thesituation inregardtothecomparison betweentheoryandexperiment becomesmoreevidentinthecaseof following andnearfollowing seas,wherethetheoryisconsidered tobe tentative duetothelowencounter frequencies. Thelimitation ofpresenttheoryisknownforthiscaseof lowencounter frequencies sincethebasicstriptheorytreatment isprimarily validforhigherencounter frequencies. Asmostoftheimportant applications ofshipmotionandloadpredictions havegenerally beenassociatedwithheadseaoperation, littleconcernwasdevotedtothefollowing(ornearfollowing)seaoperating conditions andhencethisbasiclimitation hasnotbeenemphasized in shipmotionliterature.Someinsightwasgainedintothecauseof thislackof agreementbydecomposingthemidshipverticalbendingmomentintoitsconstituent elementsỊtwasfoundthattheverticaladdedmasstermcontribution tothetotalbendingmomentismuchlargerinthecaseof following seasthaninheadseas,whichwasanunexpectedresultsincetheaddedmasstermenterstheequationsofmotionin association withanacceleration termandthefrequenciesaremuchlowerinfollowingseasthaninheadseas.Theexplanation isrelatedtothetheoretically infinitebehaviorofthetwo-dimensional verticaladdedmassasthefrequency approacheszero.Sincetheaddedmassshouldplaya minorroleforlowfrequencies,itwasdecidedtosettheaddedmassidentically to zerointheprogramandrepeathecalculations forthefollowing seas.TheresultshowninFigures58-61demonstrate thatdeletionoftheverticaladdedmasstermimprovestheagreement betweentheoryandexperiment. Thefactthattheverticalbendingmomentsandshearsareincreased withtheaddedmasstermdeletedisa resultofphasing Ṫheresultsforthemotionsofheaveandpitchwere“14-

notalteredsignificantly inthecomputations withthisverticaladdedmasstermmodification sincetheencounter frequencies forthosecaseswerelowandalsofarfromthenaturalresonance fre–quenciesforthosemodesofmotion.Similarcomputations werecarriedoutwiththeverticaladdedmasssetequaltoa constantvalue,withthatconstant valuecorresponding tothevalueatthelimitofinfinitefrequency, whichiseasilydetermined fromthesectionpropertiesİnthatcasealsotherewasanimprovementintheagreement betweentheoryandexperiment, althoughtheresultswerenotassatisfactory asinthecasewheretheverticaladdedmasswasidentically setequalto zero.As farasthecomparison betweentheoryandexperiment inthehorizontal planeisconcerned, thereisnoparticular knownlimitcondition thatisnotsatisfied whichwouldenableajudgement of consistency inthecomputedresultstobemade.Anydisagreement mightbe ascribed tothefactthatrolldampingisprobablynonlinear, anditsrepresentation withinthecomputerprogram(andtheory)isnotaltogether proper.Investigation wasmadein [4]oftheeffectoftheleewayanglechangecausedbytherudder,anditwasconcluded thatitseffectontheexperimentalresultswastoosmalltobeofanysignificance. Similarlytheinfluenceoftherudderon thewaveloadsinthehorizontal plane(lateral bendingmoment,lateralshear,andtorsional moment)wasnotlarg enoughto affectsignificantlytheexperimental valuesthatareusedforcomparison withtheory.TypicalresultsobtainedforthevariouslateralplanewaveloadsareshowninFigures34-57,whereitisseenthattheagreementtendstobe fairlygoodforthecaseof thelightloadingcon–ditionandnotasgoodfortheheavyloadingcondition.Certaincasesforthelightloadingalsoshowedlargedifferences betweentheoryandexperiment, andinallcaseswheretherewasa lackofagreement fortheloadsthesamesituation wasfoundtobetrueforthecaseofrollmotion.Theparticularly largedif–ferences occurredina regioncorresponding torollresonantresponse, whichisprimarily duetotheinfluence ofnonlinearityintherolldampingdiscussed previously. Thusit appearsthatanadequate prediction ofthevariouslateralplanewaveloadsishighlydependent upontheadequaterepresentation ofshiprollresponse withnonlinear rolldamping, whichisnottreatedinthepresentdevelopments in [2]and[3].Theinfluence ofrollingontorsion,forexample,hasbeenillustrated intheworkof [8]andsimilarly, theeffectofrollingonthelateralbendingmomentcomputation isshownin [9].Bothofthesecasesprovidefurtherverification ofthesignificant effectofproperollmotionrepresentation.Anothermethodof comparison betweentheoryandexperimentisbymeansofdetermining thermsvalueofparticular motionsandloadswhenassumingtheshiptobe invariousirregular seas.Theparticular seastatesconsidered arethosedescribed bythePierson-Moskowitz spectracoveringa rangeof significant wave-15-

heightsfrom10ft.to 50ft.,in stepsof 10fk. Thevaluesfromexperiment thatwereusedinthiscomputation weretheResponseAmplitude Operators(magnitude of frequency response) whichwerethensquared, multiplied withtheassumedwavespectra,andintegrated todetermine theappropriate rmsvaluebymeansof thetechnique of linearsuperposition [10].Extrapolation andinterpolationofthemeasuredatawereperformedwhennecessary, andinadditiona cosine–squared spreading lawwasappliedtopredictthestatistical responseforassumedshort–crested irregular seas.Sinceno experimental resultswerepresented in [4]forthecaseofbeamseas,onlytheresponses forheadandfollowing conditionsinshort-crested seasweredetermined. Allof thoseresultsusingtheexperimental datatoderivethestatistical measuresfordif–ferentseastatesareconsidered tobe the“measured” valuesrepresenting theexperimental results.Theintegration overtheheadinganglevariation fortheseshort-crested searesponses fortheexperimental datausedaspacingof 30°fortheheadinganglevariation~ whichisgenerallyconsidered tobe somewhatcoarse.Thetheoretical evaluations ofrmsresponses inshort-crested irregular seaswascarriedoutusing21wavelengthsand19different headingsof 10”spacingtodeter–minethoseresults Ȧllofthefinalrmsresultsfortherangeofspeeds,modelconfigurations, etc.forthetwobasicheadings, headandfollowing, inshort–crested irregular seasarepresented inTable8. Examination ofthevaluesinthisTableshowsthattheagreement betweenresultsfromtheoryandexperiment ismuchbetterfortheheadseaconditions thanforfollowing seas,whencon–sideringallcases.Th,isconclusion holdsforallofthevariousmeasuredquantities presented inTable8,coveringthemainresponses ofinterestṪheresultsforthefollowing seaconditionshowsomesignificantdifferences, fora numberofconditions,whichcanbe ascribedto theeffectofthedifficultiesencountered atlowfrequencies ofencounter fortheverticalplaneloadsandtheinfluence ofnonlinear dampingandpoorrollpredictioninregionsnearrollresonanceforlateralplaneresponses.Theseinfluences havebeendiscussed previously. However,inanumberofcases,thedifferences werenotassignificant whenconsidering rmsvaluesasinthecaseof frequency response, dueto thevariousaspectsof integration, smoothing, etc.overrangesof frequency andheading Ȧ possibleinfluence of themorecoarseheadingvariation andthelackof significant experimental dataforfrequency responseinwaveconditions forthelargerseastatesmayalsohavesomeinfluence affecting thecloseness ofthiscomparison.Althoughitisseenfromalloftheabovethatthepresentlydeveloped theoryandcomputer programin [2]and[3]havecertainlimitations forparticular operating conditions (e.g.followingseas,nonlinear rollinfluence~ etc.), theexistence oftheprogramdoesallowpredictions ofmotionsandloadsindifferent-16-

TABLEVIIIComparison BetweenTheoretical andExperimentalR.M.SṘesponses inShort-Crested Seas1.8321.4622.2012.221Heading= 0°Speed= 25kt.Significant WaveHeight,ft.10 20 30 40 50Pitch- Deg.Theory(Heavy) .1284 .558 999 1.369 1.679(Light) .1359 .5760 1:022 1.394 1.704Experiment (Heavy).1164 .556 .9926 1.284 1.464(Light).1254.5594 .9668 1.237 1.403VerticalBendingMoment(midship)-ft. tonsTheory(Heavy) 2.622E4 .8035E51.175E5 1.407E5 1.559E5(Light) 2.607E4 .773E5 1.122E5 1.339E5 1.482E5Experiment (Heavy) 4.2742E41.501E5 2.216E5 2.623E5 2.860E5(Light) 4.511E4 1.399E5 l.998E5 2.324E5 2.51E5LateralBendingMoment(midship)–ft. tonsTheory(Heavy) 2.139E44.195E4 5.243134 5.860134 .628E5(Light) 1.985E4 4.006E4 5.073E4 5.707E4 6.132E4Experiment (Heavy) 3.451E4 7.094E4 8.846E4 9.778E4 1.031E5(Light) 2.685E4 5.567E4 6.737E4 7.264E4 7.537E4LateralShear(midship)–tonsTheory(Heavy) 1.2471Z2 2.204E2 2.617E2 2.829E2 2.955E2(Light) 11.81Z1 2.046E2 2.415E2 2.602E2 2.711E2Experiment (Heavy) 1.3121Z2 3.057E2 3.945E2 4.398E2 4.650E2(Light) 7.707E1 l.794E2 2.248E2 2.455E2 2.563E2VerticalShear(midship)–tonsTheory(Heavy) 1.116E2 1.713E2 1.897E2 1.986E2 2.042E2(Light) 1.250E2 1.912E2 2.114E2 2.208E2 2.267E2Experiment (Heavy) 1.893E2 4.145E2 5.054E2 5.467E2 5.677E2(Light) 1.814E2 3.893E2 4.729E2 5.101E2 5.243E2Roll- Deg.Theory(Heavy) 5.324 7.875 9.634 10.854(Light) 3.791 5.149 5.939 6.441Experiment (HeaVy) 7.027 9.902 11.468 12.3595.118 6.470 7*111 7.450-17-

TABLEVIII(Continued)Comparison BetweenTheoretical andExperimentalR.M.SṘesponses inShort-Crested SeasHeading= 0°Speed= 25kt.Significant WaveHeight,ft.10 20 30 40 50Torsion(aboute.g.,lnidship)-ft. tonsTheory(Heavy) 3.524E3 9.979E314.505E31.753E4 1.963E4(Light) 3.651E3 8.802E311.597E313.145E314.085E3Experiment (Heavy) 1.834E3 6.495E3 9.373E3 1.091E4 1.178E4(Light) 2.056E3 5.266E3 6.793E3 7.519E3 7.902E3Heave(ate.g.)-ft.Theory(Heavy) .275 1.641 3.766 6.185 8.748(Light) .289 1.701 3.860 6.298 8.871Experiment (Heavy) 509 2.973 6.014 8.218 9.620(Light):511 2.976 6.016 8.220 9.622VerticalShear(Frame258)-tonsTheory(Heavy) 1.400E2 3.763E2 5.266E2 .618E3 .678E3(Light) 1.41OE2 3.693E2 5.124E2 5.124E2 .656E2Experiment (Heavy) 1.921E2 6.036E2 8.683E2 1.019E3 1.107E3(Light) 1.867E2 5.82E2 8.312E2 9.71OE2 1.052E3VerticalBendina‘Moment (Frame258)-ft.tonsTheory(Heavy) 1.949E4 4.541E4 .618E5 .719E5 785E5(Light) 1.947E4 4.409E4 5.920E4 6.849E4 1746E5Experiment (Heavy) 2.068E4 7.075E4 1.050E5 l.247E5 l.362E5(Light) 1.538E4 5.575E4 8.350E4 9.957E4 1.090E5LateralShear(Frame258)-tonsTheory(Heavy) 1.028E2 1.916E2 2.334E2 2.563E2 2.708E2(Light) . 948E2 1.774E2 2.167E2 2.382E2 2.518E2Experiment (Heavy) 1.289E2 2.563E2 3.089E2 3.343E2 3.481E2(Light) 1.051E2 2.11OE2 2.578E2 2.814E2 2.947E2LateralBendingMoment(Frame258)-ft.tonsTheory(Heavy) l.235E4 2.7E4 3.537E4 4.051E4 4.401E4(Light) 1.241E4 2.766E4 3.632E4 4.153E4 4.502E4Experiment (Heavy) 2.043114 4.678E4 5.711E4 6.155E4 6.381E4(Light) 1.308E4 3.336E4 4.267E4 4.698E4 4.924E4-18-

TABLEVII(Continued)Comparison BetweenTheoretical andExperimentalR.M.S.Responses inShort-Crested SeasHeading=0°Speed= 25kt.Significant WaveHeight,ft.10 20 30 40 50Torsion(aboute.g.,Frame258)-ft.tonsTheory(Heavy) 4.907E3 1.373E4 l.998E4 2.419E4 2.712E4(Light) 4.623E3 1.148E4 l.527E4 1.739E4 l.868E4Experiment (Heavy)4.513E3 l.572E4 2.234E4 2.587E4 2.786E4(Light)4.999E3 l.288E4 1.696E4 1.911E4 2.033E4-19-

ComparisonTABLEVIII(Continued)BetweenTheoretical andExperimentalR.M.S. Responses inShort-Crested SeasHeading= 0°Speed= 30kt.Significant WaveHeight,ft.10 20 30 40 50VerticalBendingMoment(midship)-ft. tonsTheory(Heavy) 2.158E4 .552E5 .784E5 .935E5 1.037E5(Light) 2.148E4 .535E5 .748E5 .885E5 .978E5Experiment (Heavy) 4.401E4 1.520E5 2.240E5 2.648E5 2.890E5(Light) 5.094E4 1.452E5 2.045E5 2.372E5 2.557E5LateralBendingMoment(midship)-ft. tonsTheory(Heavy) 1.924E4 3.948E4 5.086E4 5.800E4 6.301E4(Light ) 1.856E4 3.844E4 4.962E4 5.657E4 6.139E4Experiment (Heavy) 3.428E4 6.537E4 7.767E4 8.372E4 8.71E4(Light) 2.247E4 5.486E4 6.990E4 7.703E4 8.080E4Torsion(aboute.g.,midship)-ft. tonsTheory(Heavy) 3.948E310.218E314.199E3l.679E4 1.857E4(Light ) 4.071E3 8.471E310.691E311.921E312.681E3Experiment (Heavy) 2.288E3 6.860E3 9.766E3 1.139E4 1.232E4(Light) 2.791E3 6.127E3 7.704E3 8.455E3 8.85’2E3LateralBendinaMoment(Frame258)-ft. tonsTheory(Heavy) l.245E4 3.11OE4 4.145E4 4.696E4 5.013E4(Light) 1.325E4 2.948E4 3.896E4 4.486E4 4.890E4Experiment (Heavy) 2.037E4 5.059E4 6.253E4 6.764E4 7.023E4(Light) 1.363E4 4.249E4 5.601E4 6.233E4 6.564E4Torsion(aboute.g., Frame258)-ft. tonsTheory(Heavy) 1.871E3 417E4 .532E4 .603E4 .662E4(Light) 5.218E3 1:115E4 1.419E4 l.589E4 l.695E4Experiment (Heavy) 5.103E3 1.660E4 2.395E4 2.822E4 3.074E4(Light) 5.927E3 1.523E4 1.983E4 2.217E4 2.347E4VerticalBendinqMoment(Frame258)-ft. tonsTheory(Heavy)(Light) 3.695E4 8.959E411.127E41.214E5 l.272E5Experiment (Heavy)(Light) 1.712E4 5.887E4 8.738E4 1.038E5 1.133E5-20-

TABLEV11I(Continued)ComparisonR.M.S ḄetweenTheoreticalResponses inShort-Cres-bedandExp~~imentalSeasHeading= 180”Speed = 25 kt.SignifiCai2t Wave Height,ft.10 20 30 40 50Pitch- Deg.Theory(Heavy)(Light).1961.19911.0771.0611.8461.8112.3942.3492.8012.750Experiment (Heavy).1904 1.00-7 1.714 2.157 2.423(Light) ●1904 1.007 1.714 2.157 2.423VerticalBendingMoment(midship)-ft. tonsTheory(Heavy)(Light )4.173x104 1.209x105 1.636x105 ~.8~lx105 2.015x1054.O93X1O4 1.IO4X1O5 I.454X105 1.644X105 1.71OX1O5Experiment (Heavy)(Light) 5.166x104’4.617x1041.416x1052.002x1052.316x1052.493x1051.590x1052.255x1052.623x1052.814x105LateralBendingMm.ent (midship]-ft. tonsTheory(Heavy) 2.486x104 5.717x104 7.333x104 8.170x104 8.656x104(Light) 2.376x104 5.30C9XIO* 6.~l~X~~4 7’.423x1047.827x104Experiment (Heavy) 3.175x104 6.388xlQ~ 7.646x10h S.207X104 8.496x104(Light) 2.639x104 5.325x10q’ 6.411x104 6.898x104 7.150x104LateralShear(midship)-tonsTheory(Heavy)(Light).7’95x102 1.313x102 lm493x102 1.572x102 1.614x102.756x102 1.215x102 I.375x102 I.445x102 1.484x102Experiment (Heavy) 1.075x102 1.807x102 2.033x102 2.124x102 2.169x102(Light) 1.024x102 1.666x102 I.858x102 1.935x102 1.972x102Vertical Shear (midship)-imnsTheory(Heavy)(Light)1.722x1024.617x1(326.005x1026.672x1027.672x1021.918x1025.121x1026.662x1027.410x1027.824x102Experiment (Heavy) 2.055x1024.240x1025.131x1025.548x102!5.770x102(Light) 2.055x1024.240x1025.131x1025.548x1025.770x102Theory(Heavy) I.481x103 2.962x103 3.641x103 4.052x103 4.422x103(Light) 1.670x103 3.028x103 3.867x103 5.064x103 6.604x103Experiment (Heavy)(Light) 1.970x1033.351x1033.795x1033.982x1034.077x1032.062x1033.515x1033.972x1034.161x1034.255x103-21-

TABLEVII(Continued)Comparison BetweenTheoretical andExperimentalR.M.S.Responses inShort-Crested SeasHeading= 180°Speed= 25kt.Significant WaveHeiaht.ft.10 20 30 40 50Heave(atc.g.)-ft.Theory(Heavy) .6059 3.491 6.440 9.167 11.828(Light) .6337 3.486 6.390 9.092 11.739Experiment (Heavy).9415 4.507 7.691 9.710 10.933(Light) ●9415 4.507 7.691 9.710 10.933VerticalShear(Fratne 258)-tonsTheory(Heavy) 1.729E2 4.976E2 .6886E3 .7971E3 .8642E3(Light) 1.668E2 4.506E2 6.124E2 .705E3 .763E3Experiment (Heavy) 2.344E2 7.313E2 1.048E3 1.218E3 1.314E3(Light) 2.213E2 6.877E2 9.853E2 1.146E3 1.236E3VerticalBendingMoment(Frame258)-ft.tonsTheory(Heavy) 1.696E4 4.638E4 5.935E4 .655E5 .689E5(Light) 1.875E4 5.462E4 7.123E4 7.891E4 8.302E4Experiment (Heavy) 2.046E4 6.277E4 9.020E4 1.051E5 1.134E5(Light ) 1.758E4 5.074E147.116E4 8.219E4 8.842E4LateralShear(Frame258)–tonsTheory(Heavy) .9404E21.999E2 2.506E2 2.765E2 2.915E2(Light)● 8981E21.867E2 2.313E2 2.537E2 2.664E2Experiment (Heavy) 1.166E2 2.205E2 2.546E2 2.685E2 2.754E2(Light) 1,.064E 2.072E2 2.406E2 2.542E2 2.609E2LateralBendingMoment(Frame258)–ft. tonsTheory(Heavy) 1.351E4 3.335E4 4.387E4 4.937E4 5.252E4(Light) 1.301E4 3.138E4 4.087E4 4.572E4 4.845E4Experiment (Heavy) ,J1.750E43.265E4 3.883E4 4.173E4 4.326E4(Light) 1.395E4 2.706E4 3.21OE4 3.435E4 3.551E4Torsion(aboute.g.Frame258)-ft.tonsTheory(Heavy) l.968E3 4.233E3 5.317E3 5.987E3 6.574E3(Light) l.893E3 3.838E3 5.133E3 5.878E3 9.028E3Experiment (Heavy)1.778E3 3.892E3 4.814E3 5.248E3 5.478E3(Light)l.524E3 3.662E3 4.632E2 5.090E3 5.332E3-22-

TABLEYIII(Continued)Comparison BetweenTheoretical andExperimentalR.M.S.Responses inShort-Crested SeasHeading= 180°Speed= 3(Ikt.Significant WaveHeight,ft.10 20 30 40 50VerticalBendingMoment(midship)-ft. tonsTheory(Heavy) 4.280E4 1.285E5 l.736E5 1.973E5 2.112E5(Light) 4.260E4 1.203E5 1.581E5 1.772E5 1.883E5Experiment (Heavy) 6.052E4 1.777E5 2.501E5 2.890E5 3.109E5(Light) 4.882E4 1.572E5 2.242E5 2.595E5 2.791E5Lateral“Bending Moment(midship)-ft. tonsTheory(Heavy) 2.357E4 5.448E4 7.034E4 7.866E4 8.350E4(Light) 2.257E4 5.051E4 6.429E4 7.132E4 7.531E4Experiment (Heavy) 3.043E4 6.196E4 7.507E4 8.108E4~ 8.421E4(Light) 2.571E4 5.225E4 6.308E4 6.795E4 7.047E4Torsion(aboute.g.,midship)-ft. tonsTheory(Heavy) 1.416E3 2.863E3 3.559E3 3.976E3 4.335E3(Light) 1.589E3 2.874E3 3.640E3 4.695E3 6.129E3Experiment (Heavy) 2.196E3 3.714E3 4.185E3 4.381E3 4.480E3(Light) 2.150E3 3.635E3 4.097E3 4.287E3 4.381E3Hea’ve(atc.g.)-ft..579 3.783 7.089 9.991 12.716Theory(Heavy)(Light) .609 3.755 6.979 9.837 12.542Experiment (Heavy).943 4.507 7.691 9.710 10.933(Light).943 4.507 7.691 9.710 10.933VerticalBendingMoment(Frame258)-ft. tonsTheory(Heavy)(Light) 1.970E4 6.429E4 8.718E4 9.806E410.392E4Experiment (Heavy)(Light) 1.976E4 5.678E4 7.859E4 9.027E4 9.685E4Torsion(aboute.g.Frame258)–ft. tonsTheory(Heavy)(Light) 1.795E3 3.771E3 5.033E3 6.589E3 8.574E3Experiment (Heavy)(Light) 1.555E3 3.831E3 4.857E3 5.336E3 5.588E3-23-

CONCLUDING REMARKSsea conditions, fordifferent speeds,headingsl loadings, etc.ofinterestforconventional surfaceships.On thatbasis”computationswerecarriedouttopresenta complete“databank”fortheSL-7shipintheformofbothfrequency responses forregularwavesaswellasrmsandotherstatistical response measuresforirregular seas.A1lof thisinformation ispresented intheAppendixtothisreport.Allofthepreceding resultsrepresent valuesobtainedfroma computer programrepresenting essentially thepresentstate-ofthe–artinshipmotionsandloadscomputation.Thetheoreticalbasisforthecomputations isa striptheoryrepresentation forfivedegreesof freedom(surgemotioneglected) ,whichiscon–sistentwithallotheravailable shipmotionanalysesapplicabletowaveresponses atarbitrary headingsandspeedsina seaway.Thelackof agreement betweentheoryandexperiment inparticularcaseshasbeenpointedout,andsomemeansof correction orextensionofthetheorytoallowitsapplicability tothesespecialconditions isalsodiscussedṪheparticular limitations oftheavailable theoryhavenotbeenemphasized inmanyprevioustudiesandonlymanifesthemselves inthiscasebecauseoftherangeofoperating conditions covered.Thecomputedresultsforheadandbowseas,aswellasanumberofresultsforthelightconfiguration in following seas(forlateralplaneresponses primarily) aresufficiently closetothemodeltestdatathata fairdegreeofreliability oftheirvaluescanbe acceptedṪhepredicted responses, instatisticalform,forthevariousloadsandmotionsofinterestfortheseconditions arethenusefulvaluesforcomparison withexperimentaldata.Theextentofutilityofthecalculated valuesforotheroperating conditions thatdidnotexhibitagreement withthemodeltestdataistherefore anunknownfactor.Howeverpossibleerrorsbetweenmeasuredresultsandpredicted valuesmaynotbe thatextremewhenconsidering realistic valuesobtainedduringfullscaletests,wherepreciseseastates,headingvariations,etc.arenotexactlyequivalent tothoseusedinthetheoreticalprediction. Thusa usefulsetofvaluesthatareanticipated fortheSL-7shipduringitsoperation inrealistic seawayscanbefoundby extracting theparticular valueslistedinthedatabankprovidedintheAppendixtothereport.Thesevaluescanbeusedforcorrelation betweenfull-scale measurements andtheoreticalpredictions, aswellasprovidea measureof theexpectedloadsforshipsof thistypeduringtheiroperation.-24-

1.2.3.4.5.6.7.8.9.10.REFERENCESHeller,S.R.Jr., Lytle,A.R.,NielsenrR.Jr.,andVasta,J.:“TwentyYearsofResearchUndertheShipStructureCommittee,” Trans.ASME,Vol.75,pp.332-384,1967.Kaplan,PaulandRaffrAlfred1.: “Evaluation andVerificationofComputerCalculationsofWave-Induced ShipStructural Loads,”ShipStructure Committee ReportNo.SSC-229,1972.Raff,A.I.: “Program SCORES--ShipStructural ResponseinWaves,!’ ShipStructure Committee ReportNo.SSC-230,1972.Kaplan,Paul,Sargent,T.P.,Raff,A.I.,Bentson,J.andBono,Placido:“AnInvestigation oftheRelative MotionsofACVLandingCraftandLargeAmphibious AssaultShips,”Oceanics, Inc.Rpt.No.72-90,February1972.Salvesen, N. andSmith,W.E.: “Comparison ofShip-MotionTheoryandExperiment forMarinerHullanda DestroyerHullwithBowModification,” NSRDCReportNo.3337~June1971.Grim,O.andSchenzle, P.: “Berechnung derTorsionsbelastungeinesSchiffesinSeegang,” Inst.furSchiffbau derUniversitat, Hamburg, BerichtNr 235amdNr 237,1969.Kaplan,P.: “Development ofMathematical ModelsforDescribing ShipStructural ResponseinWaves,”ShipStructure Committee ReportNo.SSC-193,January1969.St.Denis,M. andPierson, W.J.Jr.: “OntheMotionsofShipsinConfusedSeas,”Trans.SNAME,1953.Dalzell, J.I?.andChiocco, M.J.: “WaveLoadsina ModeloftheSL-7Containership RunningatObliqueHeadingsinRegularWaves,”DavidsonLaboratorr ReportNo.SIT-DL-1613,July 1972.(AlsoSSC-239, 1974ProgressReportQn Full–Scale DataandMeasurement onSL–7Container Ship,Teledyne Materials ResearchCompany,December1972.-25-

COMPARISON BETWEEN THEORYAND EX~ERIMENTWN.%hWLITWE2.0-~ WM7 M6PUCZ?TXTa Em.umw (“.1$m>— ?mow (V-23KIS11.3-.,,000IIIFU\T MZ”L1Tv,!arrmxmm-i.●-m!wl D,spmtiC.urnlrom(V-25ms.#Utou lV-2S?39.,00o“-,“oc,01.9-.1 .4 .s .# 1.0 1.2 1.4 1.6 l.m 2.0WAVZlmK’111/smP LExrl’n.2 .1 .4 ., 1.U 1.Z 1., ,.* ~+, *.OUmt9010o 0 6rotI2-Frame124Heave&PhaseLag,.0°Heading*-’t=o H.:TL.,II —- [-= m.)8.‘.[8.Fig.3-Frame124Heave8PhaseLag,180°Heading●✎4.●.1-a.1‘,J,..,,ha -, , , ,Fig.4-P~tch&PhaseLag,O”Heading.1 .4 .a .m 1,* La 1.4 1.9 1.* 2.0●AR -m -kg.5-Pitch&PhaseLag,180°Heading

UWE Lwun’mUiw nrs?—;?0 mlumxl (v-n XT8.)— mmu1-7.$rm.)00oo1-.0 .0/+’(-1..Z‘,“x oL 1 I Le .4 .9 1.1 1.6 1.0wan -nmm -Fig.6-C.GOHeave& PhaseLag,180HeadingWwOlsrmctwwoCxmmmsr (V.2SKS.,— Tnrom (V-25T,IS.)1-”1.s 00 01.009.sI r I I t.1 .4 .$ .1 1.0 1.1 1.4 1.6 1., 2.0UAW La.crM/%Ml,LuimoI # I I 1 t I 1.a .4 .6 -m L.* X.a 1.* &.d l.m Z.oUAW uwm/sm7 ml-Fig.7- KO]I&PhaseLag,30°HeadingL01.5r’oo0 Em— (v-asmu..0.WAVEUN~/$U, lir!mmFig.8-Roll&PhaseLag,60°Heading2*.Fig.90-Roll&PhaseLag,60°Headingt~ ,70-‘F,,,.a .4 .6 .1 1.0 1.1 1.4 1.6 1.* Z*Waw -ml? mm--27-

20000I‘c--- ,, ,/\ ,+.--—...+ ~lwao -!...t L I I I 1.1 .4 .4 -m 1-0 1-1 1.4 1-* 1.9 ~.oxa?1AoFig.10-MidshipVertical WaveBendingMments&WavePhaseLag,08HeadingFig.11-MidshipVertical WaveBendingMoments&WavePhaseLag,30°Heading.-.. -m w-m a-m. )4000$30W08oo20000--- 0-..-.10000 \ ----I1.‘+uwt —m—I 1 1 I I 4.a -a .s -~ l-a 1.2 1.4 1.6 1.~ 1.*m —*W —.1 .4 .6 ., I.# 1.Z 1.4 1.6 1.* 2.0=* —=- -Inn-PUP —Fig.12-MidshipVertical WaveBendingFig.13-MidshipVerticalWaveBendingMoments&WavePhaseLag, Momnts&WavePhaseLag,60°Heading 240Heading8M*9O~d /-’ --..+-MI..I 1 I 1.1 .4 .6 .8 1.0 L-z 1.4 1.6 l.m z-m369119100o 0 0 01 1 Q,-28-

0!! Xmnlm!m[V.>sm.]m. .:.-%s n _ lilXORY(V-1!KS.)008:.-...- mm IV-30m.)30000400003000020000immo,.%‘.‘ .-------5Fig.14-MidshipVertical WaveBendingMoments&WavePhaseLag,210°Heading.6 .s L.o 1.1 a.4 1.4 l.m 1-.0-VI WSS1? q,>..Fig, 15-MidshipVerti641 WaveBendingMom~nts&WavePhaseLag,180HeadingS*U* -4s999rnu# -I3a00a!-nun -mom-I t I 1 ! 1 (.2 .4 .6 .9 1.0 1.2 1.4 1.6 l-m 2.0.Z .b- .6 .# 1.0 1.Z 1.4 1.9 L.@ 2.0mm I#mwmzm Llx7rlFig.16-MidshipVertical WaveBendingMoments&WavePhaseLag,0°Heading.1 .4Fig. 17-MidshipVertical WaveBendingMoments&WavePhaseLag,30°Heading-29-

VzXrrcu mKsT A-rwr,rz..Somo17..m!l,4a*mm--,mom ‘\,#’,\ L.?*9,9 \ \.,0\10**a \.. 0‘.~.- .I’k,,,,.1 .4 .s .* 1.* 1.1 1-s 1.s 1.s l.aJ,*tIFig.18-MidshipVertical WaveBendingFig.19-MidshipVerticalWaveBendingMoments&WavePhaseLag, Moments&WavePhaseLag,60°Heading —. 240°HeadingL:GVITDISI’IAC, ,.,&ro m?rmIl”Brr (“.25X2%.,n LxPcMMrNTIV-32Em.1WO1O—TImom w-l! a.)m.-rms n.. -.++mmrt[v-m Cj. )t– 0*WOOO\Q,/ \ o \ct. ,\10000 \100008‘.-%v10000❑ ~

\l -. ., eo Q.2 .4 .6 .* lea 1-2 1-’ ‘“mm -/su? -l.m 2.0MOtI 1 ,1I . . . . ,Fig.22-MidshipVertical Shear&PhaseLag,O0HeadingFig.1 1 # 1 I L , J.a .4 .6 .m l.a 1.1 1.4 1.* L.n ~-oUAn IJm6Tn/sm?mm23-MidshipVerti~al Sh?ar&PhaseLag,30 Heading—azmnrw-z~-.194rot t Q 1 t I I (.4 .* .a 1.0 1.1 1.4 1.9 1.0 1.0mm ~s=? UmTno00Fig.25’-MidshipVertic~l” Shear~PhaseLag,240Heading-31”

200— - m+2J C%, )1s0VmzLwrm/s”x,LulmFig.26-MidshipVertical Shear&PhaseLag,210° leadingI \TY!.->i $!, ?., X-.1,17X>.A\:;JTL1:~M1 I 1 r r # I 1.Z .4 .6 ., 1., 1.4 1.6 1., Z.OWm -wsMI=; =lmcmFig.27-Midshi~Vertical Shear&leadingo0o0\“ oFig.28-MidshipVertical Shear&PhaseLag,0°HeadingFig.29-Midship‘ferti~al SheariiPhhseLag,30 Heading-32-

IZooLIGHTDIS?IACEMENTo tx?rn[wml (v-x *T.+, Ucrr Olsmaccwm+o EQtnmti?ALw-asK’rs.)— TurOw {v-asm.>“bLLL___ (10 .>050-, 0.2 .4 .6 .a k-o 1.2 1.4 ~-~ l.~ 1.0KrJzLuOn/sm? Uvmn:Vz -SU?lAUHS*mmI‘LX[.1 .4 .6 1.* 1.6 I+a 1.0oL 1 0 t.2 .4 ,6 1.2 L.4 1.6 l-a 2.0&’- -mm LcnmFig.30-MidshipVerti~al Shear&PhaseLag,60 Heading..——.————,\Ti:;:., .:;~L!,rD.— mw [%-15m%. )# I 1.4 .6 .0 1.0 1.2 1+4 1.6 l.a 2.0ma ulcm/5M1*mmFig.31-Midship[ertical Shear&PhaseLag,240Heading—‘?MZOIY(V-25rrs.,I1s4-0I100-so--...000i“&__< oI , 1 I L.x .4 .6 .1 1.0 1.2 1.4 1.* 1.0 ~.0rev?.E+Hcrwsm? Lwrri+Fig.32-MidshipVertical Shear&PhaseLag,210°HeadjngFig.33-MidshipVertical Shear&PhaseLag,180°Heading-33-

2s0150=C.W D1-—0 La7rmx.mAL W-15 r.,,. )— Tumkt [*1Skm. )o—THmm’r(v-alm.]100osoI ! I I.4 .C 10 1 14n%lLtn&s/su? Alem -1 (1.6 1.* 2.0I # ,. , h1 I t.1 .4 .9 .0 1.0 1.4 1.s 1.1 2.0m- —Smx:=mmMO -c“270-k!31,0.‘----L-~u -I 1 1 I 1 # t 1.2 .4 .6 ., 1.0 1.2 1.4 L.6 l., z-amtz mcr8/8m1PuFx7rnFig.34-MidshipLateral Shear&PhaseLag,30°HeadingI I I # 1 # # I #.x .4 .9 .9 1.0 1.2 1.4 1.6 l,m 2.0WQ- Ummupm? mc’riFig.35-MidshipLateralShear&PhaseLag,60°HeadingaoaL.,!-PAL

01.,a5110:50o360LL I t 1.Z ,4 .* ., ,.0 ~.> ~,, ,:’ & ~:.WAVELEtlGm/2,, IrU!,c.f,,... .. .. . ...,-. ---Fig.38-MidshipLateral Shear&PhaseLag,30°HeadingFig.39-MidshipLateral Shear&PhaseLag,60°HeadingI—rn-t0m -omm W-23m.)154— THmkr W-2% .s.)n .u.a .4 ., .* 1.4 1.C 1., 2.0mn IA..SA1 L9mI I # I I 1 1.Z .4 .6 .1 l.g 1.2 1., L., ~.’, ~.:Um mGm/snlP WmnFig.40-MidshipLateralShear&PhaseLag,240°Heading0 0 0Fig.41-MidshipLateralShear&PhaseLag,210°Heading-35-0

. . . . - (v-,,H.,s=+aFig.42-MidshipTorsional WaveBendinMoments&PhaseLag,30 HeadingHum 0:-i-uz=urQ Wtmm W.*3 m.)— — (*15 l-m. )man -mm?“’t > 0I=m’m‘“Lp+ o Q.Z .4 A J 1-* 1.1 1-J ~.s ‘-* ‘.O00 \# 1 ! 0 I L.4 .4 .9 1.8 1.1 1.4 L* i., Z.oW- -1? mmFig.43-MidshipTorsional WaveBend-in Moments&PhaseLag,60a HeadingFig.44-MidshipTorsional WaveBend- Fig.45-MidshipTorsional WaveBendingoMoments&PhaseLag, ingMoments&PhaseLag,240Heading 210°Heading-36-

0,,- ]%.. .+ ---- ---I I t 1 0 4\ .4 .S .9 1.9 1.2 1.4 1.6 1.* 1.9I t t t 11.* .4 .4 .9 1.- 1.1 1.4 1.6 1.1 L*- -/ntr -Fig.46-MidshipTorsional WaveBend- Fig.47-MidshipTorsional WaveBendingMoments&PhaseLag,60°in Moments30iHeading &PhaseLag,HeadingULrr OuP—0 Iuzum ($-23m.)— -m [-25 m.)o =&UIK!lT (V-2$m9+)— mww (V-15m.)m.”“to--m-F** ‘1n4 -.m .1 03z“ -L,.00Fig.48-MidshipTorsional WaveBendingMoments&PhaseLag,240°Heading1 I L.a .4 .6 ,* 1.0 1.1 1.’ L.* 1., Z.oWa# —/sum —Fig.49-MidshipTorsional WaveBendingMoments&PhaseLag,210°Heading-37-

IM,.,amoo“tmm ●:sr-lrrMad. . ..- — (v-mKm.) Imvl mls?LuHrlmo Ix?cuxwr(v-x m?!.)o mrumil’f1-10 KTS.1— - W-H m.)---- - (-30m.)4 .4 .6 .# 1.0I I 1 1 11.1 1.4 1.6 1.9 2.0u- ~z? -o00Fig.50-;;;ids;;~ Lateral WaveBending&PhaseLag,30°HeadingFig.51-MidshipLateral WaveBendingMoments&PhaseLag,60°Heading●UIT DMr-RIo Urcum IV.11m.)n m— [V-3*X-IS.)— — (WISxm.)-.—-~ -M my.,.1. -.--!’Emu (-3s m.)Fig.52-Midship LateralMoments &Phase WaveBending Fig53-Midship LateralLag,240° Moments &Phase WaveBeningLag,210 iHeadingHeading-38-

IR..mxa40000 ~3;000tn mtmtmmr (V-30R?s.)— nlma? W-25 n%. )0oo,.Fig. 56-MidshipLateral WaveBendingMoments&PhaseLag,240°HeadingoI Q, q o 0 t t.,x .4 .6 ., 1., J.z 1.4 i., 1., X.Omm -mu —Fig.57-MidshipLateral WaveBendingMoments&PhaseLag,210°HeadingFig.54-MidshipLateral.,-WaveBending Fig.55-Midship Lateral WaveBending10000~,.-.Moments&PhaseLag,30° Moments &PhaseLag,60°Heading1>,. I‘0000 %?=..400008swam.,.AMU -\,.low\Imoo.,-39-

500004000030000mo*O10009,, F,, ..,y- ... ..?\y ,.., :1.: ,.,. L1.JI : P,,-,,-,,00150lado\r“33-050Fig.60-MidshipVertical Shear&PhaseLag,60°Heading, (A’33=0)Wl,vem7{GTl,/s,,IPLtilc’n+-.IO#w ‘.-40-Fig. 61-MidshipVerticalShearPhaseLag,0°Heading,(A’33=0)

APPENDIXThisappendixcontainsa typicalsetofcomputer printoutsthatconstitutesthecom-puter databankfortheSL–7ship.Theinformation presented includes thefrequency responses(amplitude andphase)foralloftheshipmotionsandloadsconsidered inthisstudy.Thisinformation corresponds tooperating conditions covering4 speeds~viz.25kt.~ 27.5kt.,30kt.,and32.5kt.(denoted as 42.2ft./see., 46.42ft./see.,50.64ft./see.and54.86ft./see. inthetabulations) , 2 displacements(Heavy,at 47,760TonsandLight,41,422.9 Tons),for19headingsat10°intervals fromfollowing seastoheadseas,for21regularwavelengths thatcoverthespectral energybandsextending from10-50ft.significant waveheight.Inadditiontothefrequency responseinformation forregularwaves,statistical responses arealsopresented fortheSL-7shipatthesamespeedsanddisplacements for5 long-crestedirregular seasandalso5 short–crested irregular seas,withsignificant waveheightsof 10ft.,20ft.~30ft.~ 40ft.and50 ft. Thewavespectracorresponding to thesesignificantheightsarethoseof thePierson-Moskowitz family.Inadditiontothemotionsandloads,verticalandlateralaccelerations weredetermined at fourpointson theship.Thelocation ofthefirstpairofpointsis 166.252ft.aftoftheforwardperpendicular, 65.259ft.up fromkhekeel,and3.333ft.portandstarboard ofthecenterline. Thelocation ofthesecondpairofpointsis445.502ft.aftoftheforwardperpendicular,37.027ft.upfromthekeel,and0.9583ft.portandstarboard ofthecenterline. ThSSe locations correspond toparticular pointsontheinstrumented SL-7shipwhereaccelerQmetersarelocated,therebypresenting information thatcanbecorrelated withfull-scale measurements.Alloftheresponses are given in units of feet,longtons,andsecondsṪheinformationthetorsionalmomentcorrespondstotheevaluation ofthisquantityabout the centerofgravitylocationȦllofthecomputations wereca~~~edoutforthefull-scale shipwhosecharacteristics arepresented inTables1-3.-41-

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UNCLASSIFIEDsecurity classltlcatlOnIDOCUMENTCONTROL DATA- R&D(Securityc!nssificdion oft!tle,bodyof abstract andindexind annotationmusf be anteredwhen the overatlreportia claas)fled)ORIGINATING ACTIVITY (Corporateauthor) 1241. REpo RT SECURITY CLASSIFICATIONOceanics,Inc.Technical Industrial ParkPlainview, NewYork11803UNCLASSIFIED2b. GRouPTheoretical Estimates ofWaveLoadsontheSL–7Container ShipinRegular andIrregular SeasDESCRIPTIVE MOTE$G%Ie ofreporta~djnc~us;ve da$es)FinalReportAu THoR(5I (Fl,st name,middle Jnitfal, last name)PaulKaplan; Theodore P.Sargent and~ohnCilmiREPORT DATE 7a. TOTAL MO. OF PAGE$ 7b. MO. OF REFSApril1973 62 10NOO024-70-C-5076,. PROJECT MO.Project SerialNo.SF35422306.Task2022,SR174I. COhlTR&CT OR GRhFJT MO. 9ti.0RlGlt4ATORnS REPORT NUMBER(SIReportNo.73-96m.OTHER REPORT F20(sl(Any othernumberathat may bo assi@edth~areport)L),D15TRIBUTIOM STATEMENT,1.SUPPLEMENTARY MOTE$12. SPONSORINGMILITARY ACTIVITYI NavalShipSystemsCommandThecomputer programSCORESforpredicting shipstructuralresponse inwavesisapplied totheSL-7container ship.Theoperating conditions considered are2 displacements, 4 shipspeeds, 21wavelengths, 19headings and5 seastatesassumingbothlong-crested andshort-crested seas.Theseresults constitutea complete databankfortheSL-7shipintheformofbothfrequency responses forregular wavesaswellasrmsandotherstatistical response measures forirregular seas.Comparison ismadebetween thecomputer andmodeltestsoftheSL-7inrequ~ar wavesinpredicting vertical, lateral andtorsional moments; andvertical andlateral shearsattwosectionsandheave,pitcharm$~11. Regions wherethetheoryandmodelexperiment donotad%~whave~~-e~~ pqin~ed outandsomemeansofcorrection orextena$’tin ofthet~~~$yisdiscussed.)D:;:;.,1473UNCLASSIFIEDSecurity Classification

UNC~ASSI~lEDSecurity Classificationk 14,KEY WORDSCOMPUTERSROLELINK AWTROLELINK BWTROLELINKcw-f.MATHEMATICALPKIDELSSHIPHULLSST~UCTUR.AL ANALYSTSWAVEsCONTAINERSHIPb US.GOVERNMENT PRINUNG OFFICE:lgl~ 626-719/125UNCLASSIFIED—SecurityClassification—./

~HIV RESEARCHCOMMITTEEMaritimeTransportationResearchBoardNationalAcademyof Sciences-NationalResearchCounci1The Ship Research Cormnittee has technical cognizance of the interagencyShip Structure Committee’s research program:PROF. J. E. GoldberJ, Chairman, School of Civil Engineering, i%rdue UniversityPROF. R. W. CLOUGH, Prof. of (XV{L Engineering, Un

SHIP STRUCTURE COMMITTEE PUBLICATIONSThese documents are distributed by the National TechniealInformation Service, SpringfieZd, Va. 22151. These documentshave been announced in the Clearinghouse JournalU.S. Government Research & Development Reports (USGRDR)under the indicated AD numbers.SSC-237, Computer Progrwns for the Digitizing and Using of Library Tapes ofShip Stress and Environment Data by A. E. Johnson, Jr. ,J. A. Flaherty, and 1. J. Walters. 1973. AD 768863.SSC-238, Design and Installation of a Ship Response Instrumentation SystemAboard the SL.7 Class Contain ership S. S. SEA-LAND McLEAN byR. A. Fain. 1973. AD 780090.SSC-239, Wave Loads in a Model of the SL-7 Containership Running at ObliqueHeadings in Regu2ar Waves by J. F. Dalzel1 and M. J. Chiocco. 1973.AD 780065.SSC-240, Load Criteria for Ship Structural Design by E. V. Lewis, R. van Hooff,D. Hoffman, R. 8. Zubaly, and W. M. Maclean. 1973. AD 767389.SSC-241, ThermoeZastic Model Studies of Cryogenic Tanker Structures byH. Becker and A. Colao. 1973. AD 771217.SSC-242, Fast Fracture Resistance and Crack Arrest in Structural Steels byG. T. Hahn, R. G. Hoahland, M. F. Kanninen, A. R. Rosenfield andR. Sejnoha. 1973. AD 775018.SSC-243, Structural Analysis of SL-7 Containership Under Combined Loadingof Vertical, Lateral and Torsional Moments Using Finite ElementTechniques by A. M. Elbatouti , D. Liu, and H, Y, Jan. 1974.SSC-244, Fracture-Control Guidelines for Welded Steel Ship Hulls byS. T. Rolfe, D. M. Rhea, and B. O. Kuzrnanovic. 1974.SSC-245, A Gu{de for Inspection of High-Strength Steel Weldnrentsby The WeldFlaw Evaluation Committee. 1974. (Not yet published).SL-7 PUBLICATIONS TO DATESL-7-1, (SSC-238) - Design and Installation of a Ship Response InstrumentationSystem Aboard the SL-7 Class Containership S.S. SEA-LAND MeLEAN byR. A. Fain. 1973. AD 780090.SL-7-2, (SSC-239) - Wave Loads in a Model of the SL-7 Containezwhip Funningat 0b2ique Headinge in Re@@ Waves by J. F. Dalzel1 and M. J. Chiocco.1973. AD 780065.SL-7-3, ( SSC-243 ) - Structural Analysis of SL-7 Containership Under Combinedtiading of Vertical, Lateral and Torsional Moments Using FiniteE7.ementTechniques by A. M. Elbatouti , D. Liu, and H. Y. Jan. 1974SL-7-4, (SSC-246), Theoretical Estimates of Wave Load. on the SL-7 ContainerShip in Regular and Irregular Seas by P. Kaplan, T. P. Sargent, andJ. Cilmi. 1974.