{isTM*T IOi{ 0F $SlcB&ryillmry A$f,$ V&$,xg]&tIs]I,Jn? liI{YS{CAi-i Atrm UUFTERIffA{, MOBE[,$

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Tlie rnoc{errmirinq <pt the fLux of ship'$ researehimE - designinE - bui}"dj.ng acldthe n*cessrt,y o{ expem"ses reuluction i.n the early stages of des!.En and optirnizj,nqrequire the ut"i.lj"aation on a J"arqJe sca3.e of ttre semparters nhich, implieit.L]'o Gperatewith nnmeri-caJ. mo<ieLs of the behaviomr ot the ship "system".The preei.sion of thener;del.tlrq t:t Ltto *omplex hydrr:dyuarnic phenorneua, i"nvci"ved iu th* behaviour of thesitlp, consi.l{ereqt as a $vstern, defines i.n fireaL analysi.s the eonnectness in thetk:sdEmi"ree o"t tlee shi.p "syste&* a&d its optimiaation deqree.

In the sattle way, tlae irnpeissibilitv of model.linq aumerically certain extremelyi:r:n;p!,tlx .[]Tdre{i}Tt;3mir*1 pluer*omema mai.mLaj.ms imtCI up-to-dat*, j.& a EreaF- e.ritent, t}rettliJ rsati$n of the piilysical model"s, wtrlose results atre used di.rect.Ly, in ttreri+:srrtrj.nci'proeess and imdirec'Llv, for the eheckj.ng and vatidati_on of the nuEnericaLic.&'.l!, } mode,ts, corresponclin$ to them.

The Presemt paper offers a Eeneral aud compl.ete seheme of, the cheeki.mg-';a"!.i*at.iom. prsflsss o{ the physica}. aa$ numericaS, *iodel-s, appl"led in the shi-prese;rrcjlim{i a$"d des$.Emtlro irl ICEP&ON&V S.A" anttpwnataates the mcst importamt stageswfuj"ryfir, under praet,iaa.L e$pact, permit the est,imat.j.on of umeertaiat,y and thecimarntiticatierm of ttree srror mar-$in, affecting the normal" process of ship desj"Eninq"

There are pi:es*ntett ths fisncreLe conrparative ana3"yses of the result.s neqarding{i$e ;rmei tta* salila ship "system", these nesu}ts betnq ohtai"med by meams of twotl:t"ft*rent nurneri"eaL rnodeS.s, by model test$ {physica}. mode}} aud by sea triaLs oa thenetr"L ship.

i." ifypms $.[ mex"ei"mo used i-m mava]- &vdrmdyaarni.es am.d specifi* s&mrees of ernor

ftae process ot teg:hntcal areatj.on a$smmes th* represe*t.at:l"on j.n varj.ou$ weysslt l"fue $biectlv* reaLitv vhich oovill exj-st" as a physieaS. produet, at real sr:a].e.

Ac*ondi.ng to [Xl and [?] , the f irst aad the mort iarportaylt simulati.on LeveLis tfle "cone€Xltua3. model", defi.ned as the nnestal representat,iou of the physicalrealitY, hased on tfie exi.st.ing knovledqe and clbservati.ens at tire rea3. saatre (figurerai -

&'"s iiL [h* r.taval d*rrlaire it is nelt al-ways easy to observe the neanity, areequ;lil"y used the n'sca-18 ph],s:.sal mod&Ls" and the "aumetricatr models", hotfi assi.*lp-li..ti.*at,i*ns ot ttrhe reali.tv, umderLi_ni.$ry " certaim properties of the rea} orneql"ei:t,in$ o'i:frers, trnetrovarat for ttle pr.oblecil under consideratien.

I[fie s#a {e $hv.si"ca]. modeS.s perrnit the di"rect observati.on of tbe phenemema thes!:.ip *'rvsteil]" is suhrnit,ted"to" haviuq a repli.eative or deseri.pti.ve eharacter, whi.leLtne nmmer:ilaal relei,i$el.s perm"tt, Lhe es{imatiom o{ the syste*ltos e$oLution im time.domain,ltavinq a pnedictive cha::aryLer.

8esi.eles ptlr* ph.oysieal and numerj"eal models are also used hybrj.d modets, i.e.nm.meri.cal" ruodels, based on rnathematieal descript,i"on of the physi.eaL phenomsrra, inwhieh are i.nt,r*duced experimentally measured data (as coefficients of equatio*s).

ilonsequ*m,t,ly, i.t inslde eaeh type of model is raiscd the problern of cliecki.nEttre pr'eclsaon {r:.t nroitr*.i-lialE} and uncertai.ntv anaLysis, betweeu the types o{ nrorl*}sc:f t-he same clegr*e, aJ"t beinq submi"tted to the abjestive reaLity, is raised the$r*b{em of, "parttal. validatisa"" whi}e rel"ated to this reality is raised ttre prmb}.enrof "g-Lof;a.[ va.l-idationoo.These procedrares of parti.atr- and stroba.l" rra]idati n offer

finally the level.of these morlels,rntervals.

of relianee on one ormaking precise the

another modelapplicability

and define the practieal. valuelimits and their confidence

\ -_..j- -;;* - --,r..! modet I

FI6URE 1a Different kinds of modets and stages oftheir validation

rn thi's eontext the obieetive of the uneertainty analysis both for theexperimental data and for the numerieal results is to buttd atr interval ofuncertaintv inside vhich mrst exist the "true value., (by definition unknovn), ritha eertain eonfidence level (usually g5t).Can be distingulshed tr*o categories oferrors: errors of preeision (aleatory or repeatable) and systematie (or fixed)errors ; the analysis of, uneertainty for each physical or numerieal modelled proeessimplyinq the detailed analysis of all source"-oi error, the estimation of error foreaeh of then and obtaining of the grobal uncertainty intervals.the buitdinq of the resultinq intervals of uncertaiuty coarplies vith thestaqes, proeeduren and calculation rethods, ninutely presentea in tJl ana tnl.As in the present paper re are interestea in ltre aspeet of the behaviour ofthe rhip "systen" as a rigid solid in irregular waves, tiist of all fron the Boi.ntof viev of the motiors, in the fig.lb is presented the general seheme, consideredcomplete bY the authors, tor checking-emparison-validation in the nunerieal(C.f.D. ) and experimental hydrodynanics

Aceording to this general flor diagran, the sourceseach type of model, are the following :

of error, specific fora) 3o; t[9- go_lgs].!-qauslx]-clllrolmjgl : fundamontal modelling errors, introdueedby the neqlected physical effeets and imposed by the impossibility of thesinultaneous mental representation of all the phenome[a, developing in ani !rit] theship "system".The systemic complexity of the ship irposes to ioeus the attentionboth on obrerving the unity and structural eonpatiiilily (designaling ttre so_eifieamain bloclrs of the systen, linked by nain generalized iiput/ooiput eoordinates) andon the sub-systens, rhieh must be espeeially studiea and vithout rhieh theeoneeptual representation looses its sense.b) fp-r*lbe,sqsarrcal*lQ.E.DJ nqdel :- errors of representation {}f the co[eeptual model by a continuous mathematical

model i

The obiective -physicat neatity- Futt

Con ceptual

Partiat validationNumericalmodel

Physi ca I

scate m odel

ERRORS OF CONIEPTUAL MODEL

(NE6LECTED PHISITAL EFECTS)

REPRESE NTATION

ERRO RS

DISCRETIZATION

E RRORS

PRO6 RAMMIN6

E RRORS

NUMERI CAL

INACCURACIES

DATA ANALYSIS OMPARISONS

E RRORS WITFI:

STR U CTURAL

ERRORS OF PHYSICAL AND

6EOMETRICAL MODEL

TESTIN6 ERRORS

(MEASUREMENT

POST-PROCESSING

ERRORS

DATA ANALYSIS STALE

E RROR S T F ECTS

MEASUREMENT ERRORS DATA ANALYSIS

ERRORS

vlEIRIrlFI

iltl0iNi

)

A

L

I

D

A

II

0

N

P

AR

TI

AL

ALI

D

ATI

0N

P

AR

TI

AL

C

0M

P

RI

S0Ns

V

ALI

D

AT

II

0N

A FLOW DIA6RAM FOR C.F D. AND EXPERIMENTALHYDRODYNAMICS VA LIDATION PROCESS

F U LL SCAL E REALITY( REAt S HIP )

CONCEPTUAL MODEL PHYSICAL STALEMODE L

MODEL IESIS

ANALYTICALSOLUTION

DISCRETIZEDMATHEMATITAL MODEL TEST RESULT S

COMPUIER CODE FINAL EXPERIMENTALRESU LTS

FULL SCALE TRIALS

COMPUTATION

FU LL SCALE FINALRESULTS

ANALYTICAL RESULTS

OIHERNUMERICALRESULTS

EX PERIMENI,\LRESULTS

( BENCHMARKSINUMERICAL ( C.F. D. )

RE SU LTS

FIGURE 1b

- errors of diseretization, inposed by the replaeement of the continuous model(impossible or very difficult to solve uith analytieal methods) rith a di.scretized{numerical} nodel;errors of prograrwring, rhich appear during the proeess of creation of the

caleulation algorithm and of elaboration of the eomputer codei- numerical errors. speclfic to the adopted numerieal pethods and to the conputer

used tor the ealculations.e) r_ep. !-[e phy.sisr} "qg_al-e-,m$s] :- errors of qeometrical, kine*atic and dynmic rodelling. conbined vith errors ofphysical execution ;

- errors of experinentation (instrunental and human) i- errors of processing/post proeessing of the experinental results i- errors of tranrposition of the results from the model to the full scale ship

(directly linked rith the errors of nodelling and geaerated by the irpossihilityof sinrultaneous eonpliance rith certain inempatible criteria of sinilitude),

d) f.qr "th"e- fglMe. the 'lreal iLlo" :- emors of experimentation (irstrunental and hunan) i- errors of processing/post proeessing of the rerults.

2. tturerical rodelling (C.F.D.).Proeedures of cbactring and partial validatim

Having as a starting poiut paper [5], ve can assert, that the nain c]asses oftheories, usually applied tor the nodelling of the ship's motions are : the striptheory {in the classical variant Serrlttsna-Beukelnann or noderniaed variantsalvesen, fuek, Faltinsea) and 3-D theory (Zhao & Faltiusen), eaeh of then haviagits specifie nerits and linits.

ilalinq a profound aaalysis of the uneertainty on the specific of the numericalhydrodynamics applied in sea*eeping the list of the sources of €rrors can becompleted vith the folloving speeifie categories ;a ) llruglt*c.e.l"_er&:s -gqlgmleg_br 3

- the sortrce function (for ? D calculations) or the Green functions (for 3 I)calculations);

- problens of eonvergetrce for large aud complex equation systens, assoeiated to thematrixes of added mass and darping coeffieie[ts i

- irregular frequeacies on eonrputations of these hydrodFramic quantities ;- the number of "strip" under consideration and the number of polnts, describing

the shape ot each section (2I)) aud respeetively, the arnber and distribution ofthe panels. over the hulf (3DI ;

b) Phy-s"_i-c_il gmpr"qr.*gsgsg-e!_A1!- hv :- the effeets of the linear poteotial floy {the systen of non-statiotrary flaves,

generated by the hull's oseillation, interaction vith the stationary }ocalpotential around the ship, the three-dineasionality of the flor, etc.) i

- the etfects of the non-linear potential flov (the linearlzation of the conditionon the free surfaee, of the eondition on the hull aad the exciting foreeexpressions) i

- vlseous effeets i- the uncertainties in the rodellXng of the rave speetrum, sarpling choice of the

frequency domain of the irregular yaves and unproper rodelling of the vavespropagation.

The existenee of a such large range of sourees of error inposes, according tofig.lb, three cateqCIries of actions :r) ghe"-c}l!.s -a{_ :- the correetress ot the eontiuuous aad discretizeil rathenatical model trm the

point of vlev of the boundrry and initial condltions ;- the eoherenee and eoaslstsncy of the eonp[ter code tthe renoval of the progranming

errors and the eorreet pertornance of the eonaectiona betree$ rodulee) i.. the numerical inprecisions and i.nstabilities.These checking are perforned ou test data, rhich can be eompared to the exact

analytical results.lI ) cq"r3Bfl[]-i;q&g--[9- :

- the exaot analytical results ;- other numerieal results (asyrptotical forrulae) i- other calculation prograras, based on the sane prenises.rrr) The cheekiag and conparisons pernit the staiting of partiar validalion in thenumeriealhydrodynanie8,consirtingintheconfrontlngotmtainedresults to :- the behaviour of the coneeptual rodel in case of test data and of exact analytiealsolutions ;- the experirental rosults, existiag in the benehnarks ;- the experinental reaults, obtalned by rodel teots ;- the re$ults, obtained by neans nf other calculatlou prograf,s, reeognlzed as [ore

advaneod and more preciae.An exanple of partial validation of the !ll8$lll progran (sAnBvlL computor eodevariant), pernittiag the dsterninl*g of the ship's roiionr hy a variant of the striptheory, based oa the mltipol potentials Tasai-Porter and a eonforral tapping yith

nultiple coefficionte, ie. the eorparlsoa rith the rerults, obtalned by tire nrisstanspeeialists of TNII}{T saukt Fetersburg by using the ealeulatlon progran of theship's sotions in operation at CCI{I in Odetsa, this prograr belng basei on the sanephysical and lathematieal prenrises, but perfor*iag tho deseription of the rectionstorn and the calculation of the hydrodynartc coofticients by reane of prank closetit nethod (sources distributed over the rean yetted body of a cross-;ection). ThIsprogran, essentially identical yith that, elaborated by galveaen and Faltinsen (byadopting sranh's results) at the level of the year 1985, is currently used in thenaiority of the hydrodynarie laboratsrles aud hportalt elaaslfieation gocieil,eo(nanoly : 'l{orr(E{s" - Drll$ g.Ir.A., TRrAL' - T.H.D.Holland, "l{v-{lz* * Det fiorslreVeritas, l{orvay, '}IOnH-A8C,,-!ur€aE Veritas, franee, .glllpll0.'-f .T.L., Canada} and isunanimously considered as having the best perfomanees in the eathation of theseakeepinq charactoristies of the ships for noderate sea condltions.

The results, nutually transnitted betveen rcEplot{AV s.A. and rNrr}lr san[tPotersburg via RR3 Bucharest by r€aRs of the paper [6tr, are obtained for a contalnership of 8000 tdr. having the eharacteristics in the table l, in three regimes ofirregular sav€s, eharaeterized by the epectrun rBBC (tabte i), for three runningspeeds (0 ; I I(n aud 16 I(n) and tive relative anglos sbip-rave (0, {So, 90o, 135"and 1800).As analysis variable raa used tbe root-rean-square value of the proeess,eonsidered for a yave height equal to r r {at a eovering of 3t} aad, in irder totacilitate the cmparison, the synthesis diagrars, contaiaing tLe evolution of acertaln parar€ter depending on the relatlve angte 'g, ad tle af,ip'e speed *v.,, havein their ordiaate a percentage dtvision itron 0t to 100t, the value l00tcorresponding to the biggest abrolute value, ealeulated yith thl tyo program andwritten above the respectlve diagraa) and all the other values being ixpiessed aspercGntages of this naxinrn value.This vay of repreeentation has tro advantages :a) the ranges of values of eorresponding eurv.s have the same referene€ Eyster,permitting a direet and easy estiratlon of the retatiye percentage differeneobetween the tvo series of results ;bl the absolute {dinensional} values for a certaia corbinatioR sea csndition-heading

angle-speed are quietly deterninable calcutating the product betyeen thepercentag€, eorrespoading to the respectlve polnt talren out trm tbe diagrar,the maxinum value. rritten above it anil the vaves heiqht (3t) in yhieh the shipnavlgates?his vaY of, representatlon is also adequate for the irplerentation on theboard computers aeelating the captain to selCct the best shipplng roui" teipertnavigatiou systen), as it shovs very clearly the tendency of tnese eurvos dependingon the heading angle and shlp Bpeed.For illustration in fig.?a, b, c is represented the evolution of the pitehingangle'lh"-and-in fig.3a, b, e the evolution of the relative notior at ihe toreperpendieular (the signless eurves belng the Ronanian results aad tbose, rarked sithsigns the Russian results).The analysis of thase diagrams, the qualitative and quantitative co*parisonof the values and the calculatlon of tha systeaatic error pertit ur to foraulate the

tolloring concluslo&f :a) tor the heading angles of practical interest, respactively B'=lg0c-135" (doninant

head vaves) and p-o"-45o (dominant tolloving yaves) the results are eategoricallyin the sane domaias, that reans that the partial nutual valldation of the tnocomputer programs can be considored satisfied ;b) tor the naves trom transverse direction U={5o-135" (especially at 90o} thedifferenees are sufficiently large, the f,.onanian eurvei having a nore abruptaspect, vith rore larked peaks, rshile the Russian curveg are .,snoother*.Theae differences ars dre to the tact that rhlle the tomanian eorputer prograiryorked vith unidirectional ISSC irregular vave*, having the vhole- energieoneentrated on their directisn of propegation, the f,ussian cmputer prograrrorked vith multidireetlonal vaves, having an energy spreading funetion of ttre

type " ;leostf ", that euphaslzed the degree of intercomelation of the

motions in real yayes and led to inportant seeondary responses.

3. liodel testr and tull seale reasure.onts. Bethation of uecertalnty aad globalvalidation

In aeeordanee vith the general validation sehene in fig.lb and vith theassertions in the previous ehapter, it results that the globat valiAatlon procedureean be perforned only in relation rlth the absolute obiective reatitf, in themeasure in vhieb it is knoyn and observable

The internediate stage of the nodel tests, affected by nany sources of error,permit in its turn only a partial validation either of the uuneiieat results or ofits orn experimental results in relation to the full scale measurenents.on the otherhand, even the results obtained by full scale experinents are *ffected by errors,introdueing'a eertain degree of uncertalnty.consequently, the global vitidationrepresentc tho direct colparison of the tman yalueo, possibly true ln their omconfidence interval, obtalned in different vays as the fereat sourees of errorbelong to the full seale experiments, thea€ are consldered referential, being also,qualltatlvely and quantitativoly, tbe ',nearest'. to the objective reality.

The estimation of uncertainty and the deternination of the confldenceintervals, aecording to the practieal proeedures, presented in detail ia [3I anit[{}, reguire the interactive porfomance of the full seale tests ard nodelr testein tLe basin for tro reasons :a) it must. be knoYl. reallstically and eritieally the F*e _qondfllon, uader r*hich thefull scale tests vere perforned (in fact, this ig-*the mostJn?ortant source oferror of the glolal. validation) and lnplicitly the ship,s behaviour ;b) this experinente nust be physieally and nunerically rodolled as aceurately aapossible (strictly observing the reeomendatlons given in paper [T],

""gaiaingthe neeessary rua length of the experlmental sampias, rhiel arsures a correet,statistie €rror estination).for exenplification are used the full scale tests perforred rith the samecontainer shtp in August 1988 for the determinatlon of the pitetring and rolling.angles of the ship and for the esthation of the ship,s anti-rolllng syetereffieieney'The testa uare perforred at the speed of 16 f,n, acaording io asenioetogonal sehene (u. 0n, 45o, 90", r3so and lg0o), the rlnd state being 4o-5oBand the sea state 3-4 D.fhe ehip'r load cradition yas the heavy brllast, orie, riththe eharacteristlcs in the table I and during the test rere situttaneously recordedthe pitching and rolllng angles, the rind speed aad direetion (inplieitfy thedominant Yavea direction), the ship's speed and directiqr.Iletails rlgarai"-g ih"performance of these tests are given in the palor tSl.As the exact values of the searaves characteristies rere not available (beeause sf the iaek of specialized buoysin the place and in the moment of the testa) yas used tLe ship's pitching as a"loyal" and relatively regular re$potrse value (in a ratbematicai sense), ha-vinq apronouneed charactor of linearity related to the yav6c height.For the deter3lnationof the real speetrum of Yaves, yere modelled ia the basin exactly the saseexperinental load condi'tions and ras determined the response tunctlon in the

tretluency domai.n tor pitching in regular head raves and applying the seeond relationl,lrener-ttruci.n. hy means of a Fourier B&( analyzer lras determined the demanded waveeneounter speetrum, dividing the pitching speetrum measured at the ship (the realpitehinu) by the square of the pitehinc response function (measured on the model andconsidered valid at the ship).?he calculatisas led to a signlficant height of the

sea yaves ot 2,834 m and a nodal period ?-6r31e , values used in both calculationprograms, being made at the same time, in the Russian program the spreading factorequal to *lrr in order to bring the yave speetra to the same unidirectionalexpression.

Uader these eonditions, the four series of results nere reBresented in one andthe same sytrthesis diagram (fig.4) in vhich, besides the tvo curves, obtalnednumerically (CFD) ras also represented the absolute experimental eurve, reeorded atthe full scale, respeetively the senl-experinental curve, obtained in the end of theyear l98B by model tests and transposed to the real ship, each of then vith itsconfidence interval.

For transverse yaves do not exist experimontal points for pitching, being,effectively recorded only rolling, rhat means that the disturbing vave Yas a fulldeveloped sea, being more like a unidirectional vave thar like a rnultidireetionalone and produeing very reduced or non-existent seeondary responses.Arryvay, for thefour heading angles for vhich exists the possibility of comparison can be remarkeda good grouping of the mean values, especially in head vaves.The analysis of thesevalues anil of the confidenee intervals, both ln relative and absolute setrse, led tothe validation table 3, aceording to vhieh the global validation can be consideredas satisfactory, both the tendencies of evolutlon of the caleulated values relatedto the measured ones and the existenee domains of the solutions, i.e. the confidenceintervals are in full eoneordanee.

4. Conclusions

a) The complexity of the phenomena and proeesses to rhich the ship "systen' isexposed in irregular vaves inposes its research by means of different klnds ofmodels-eonceptual, physical, aumerieal (CfD), between rhich nust be performedpartial and global validation ;

b) Before their perfornanee for eaeh model is neeessary a serious analysis of thesources of errors, their quantification, the determination of the sensitivityto errors and the determination of the final eonfidenee intervals, resultinq fromthe uncertainty analysis ;

c) The complete general scheme of validation in the nunerical (C.f,D. ) andexperimental hydrodynamics (flg.Ib) clearly lndicates the signiticance of the"cheeking" and "comparison" ntltions and their connection vith the "partial" and"global validations" i

d) The numerical and experinental results, obtained for a container ship of 8000tdv,indicate that the numerical nodels rhich vere used are partlally and globallyvalidated ln a satisfactory Yay ;

e) The insuffi.clency of the data, obtained at full seale, re$arding the behaviourof the ship "system" in irregular vaves imposes in the future the focusingof the attention on the performanee of seakeeping tests as eomplete anil preciseas possible.

5. Ieferenees

lll G.VAN OORTIIIERSSBN, "Predicting the hydrodynamic performarce in ship design :

tests or computations ?

CFD and CAD in Ship Design. I{ageningen, The Netherlands, 25-26 September 1990,pp. 233-245

121 I.NOVAC, "Cercetari asupra oscilatiilor generale ale navelor si stabillreapararetrilbr sistemelor de anortizare pasive", Teza de doctorat, Galati,Romanla, 1991, Op.7-22

t3l "Report of the banel on validation procedures", Proceedings of the 19th

TABLE

DENOMINATION

LENGTH BETWEENPERPENDICULARS

CONF.

PROJ E CT

BREADTH

H EI 6HT

DRAUGTH ( FORE )

MEASURED

ON BOARD3,852

DRAU6TH ( AFT ) 6, 318

DRAU6TH (MEDiUM )

BISPLACEM ENT 7 9 45,4

TORRETTED METACENTRIC

H EI GHT 1,7 66

TRANSVERSE 6YRADIUS IN

ROLL DIRECTION 0,410

LONGITUDINAL 6YRADIUS IN

PITC H DIRECTIO N0,253

NATURAL ROLL PERIOO

SHIP SPEEDMEASUREDON BOARD

TABLE 2

ISSC WAVE SPECTRUM

C HARAC TERI STI CSSYMBOL MU 508 70 B 908

SI6NIFICANT WAVE

HEl6HTH 1t3 m 2 I 7

M ODAL PERIOD T s lr,4 6,3 8,9

DIMENSIONLESS

MEAN PERIOD Z=TE 1...1,5 1,5.. .2 >2DIMENSIONLESS

MEAN WAVE LENGTH Y' - 0,25 0,25 .. .0,5 >0,5

WAVE

DESIRIPTIONSHORT M EDIUM LO NG

TABLE 3

Item-------_8ELATIVE sH tP- WAVE

DENoMtNATtoNNTtoNS 1800 135 0 900 450 0o

1Pitch measured on boardlship triats): \; 3,63o. 3,130 2,97o 3,220

2 Uncertainty interva[ : ! 2 ohr0,0730 !0,0620 r 0,057 0 r0,0640

3Pitch measured in model tests;

l? ( transposed )ger/s' 3,1+2o 3,10 0 3,570

It Uncertainly interval: t 4./" ! 0,1500 !0,1370 t0,1240 r 0,1434

5Pith f rom C.F. D. russianresutts, L€ 3,90o 3,620 3,05 o 3,45o

6 Uncentainty interval z ! 7 oh !0,2730 I 0,2530 !0,213 !0,21+2o

7Pith f rom C.E D. romanianresu Its : rt?e. 3,92" 3,530 2,9 60 3,380

I Uncerlainty interva[ : !Bo/o 0,305 0 0,2820 0,2370 0,27 00

9 Bias ernor, (rLi - \E I 0,120 0,29o 0,230 0, 35o

10Re la tive bias e rpop( 4 -:q/[t r tY, 100 .r" 3,2 oA 8,49"/o 7,1+2oh 9,8 o/o

11 Bias error: tli - rUF I 0,27 0 0,49o 0,19 o 0,25 o

12Re [a live bias error ;(tI-n€)/rLIx 1oo.h 6,920/" 13,510/o 5,9 oA 6,67 "

13 Bias error: tr{-rtil 0,19 0 0,40 0,09 00 ,160

1L iiElft,7,},',.'i'oi ," 4,g7oA 11,33'h 3,0 4"/o 4,73oA

15 Bias ePror, I l!- ,tlt 0,15 o 0,20 0,0 5o 0,120

16Retative bias €tpor:l:n{ - rtl I t rt?, 1oo .h 3,85o4 5,52Vo 1,64oA 3/+8Y"

17 Bias ernop : t r(-rtl, I 0, 070 0,110 0,14 0,19 o

18Relative bias error :

l\!-:[Ftt:|Gx 100./. 1,g3oh 3,12o/o 4,73"h 5,62o/"

19 Bias error , (ef- nf t 0,09o 0,0 go 0,09o 0,07o

20Relative bias err or :

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t81

fTTC, vol.l, lladrid, $pain, 16-22 $eptember, 1990, pp.5T?_604"The Ouarity contror Group',, proeeedings of ttre-loiorril; vol.r, sanFrancisco, caritornia, u.s.A., rg-25 septeiber, 1993, pp.zs-ior

o'FAtTrNsEN, T.svENsEN, "rncorporation of seakeeping'theories in cAD.,, cFD andcAD ir ship Design, sageninqen, The Nethertanas , 25-26 $eptember r9g0, pp.l4?-I64A'I'ttAKsrMAD'Ir' o.A.osrPoV "Calculul earacteristlcilor de navigabilitate sirezistenta strueturala pentru nava portcontainer de fabricatie romaneasca facutconform programului de eereetare tehnico-stiintlfiea intre m{rrHr tunss) siRegistrul Naval Roman - ICEPROHAV S.A. (Romania), Leningrad, l9g9 (Catcule invaluri neregulate), pp .L7-24R'D'PIERCE, "Run [.,ength and $tatistieal Error Estimation for seakeeping Testsand Trials',, proeeedings of the 23rhA.T.T.c.. Ig93, u.s.A., p;.if_Oer'NovAc, "Anallea comparativa a calitatilor ile navigabiritati-ale unuiporteontainer obtinute prin ineercari pe modele si ta natura (iI", BuletinTehnic RN[, nr.lsl, Iggl, Bucuresti, pp.l-tf