ZTr.. 147t 1.
Report of Committee 2b1
VÌare Loads, Llodel and Theory
Augist '1966
Committee Members Erof, 3', ]'ukuda
1rof. Ir. J. Gorritama, Chairman
G.J4 Goodrich rQf. E.V. Lewis
M. LØtveJ.t
Ix'. ,LP. Soejadi, Secretary
Contents:
ae
IntroducbioA. a
Model expormout and calculations to determine 3
wave beudin moments.
Theox'etiol dveloprnente nd detailed comparison 8
With model oeriments
¿, Prediction of lone terni distributions of wave loads 9
The presentation of model test results, 13
Research on wave loads In progress azid reoQmmenda
tions for future work.
6.1. LOcal wave loads 15
6,2. Distx'ibution of wave bending moment and shear force 1 over tho lenßth of the ship.
6.3. Influence of bulbous bow on bending momenta, 15
6,4e flendin moment transfer functions in oblique wavcs. 15
6.5. Refinement of bending moment caløulationa. 16
1!
.noduticm.
The study ot wave bade on. the 31iip tu a seswa? i9 0106017
related to ahip motion resoazc} ai4.tiozeore 8m1r.t7 in
appxoaeh to both probleinsic evident.
Due to a ve:y rapid increase GX the intez'et
t
zeno-meae aaaoolatecl with Bhip motions during the past 15 years,
expex'wenta1 seakoepin facilitlea now øzist in mair ohip mode1 basinB. Ixiatvumentatiou to cayout rnodei tests lai e8u1av
01' irrou1ar waves and even in. oblique waves i available and. tn some oases wcwe bending momente are measured sultanoously
with the model motions aa a matter of routine.
The more eecifio wave load research started with eyate' matie experiments; testa with aystematioa11 varied. ehip formo
were carried. out to Lind the relations between the main ship torn par*metra and the wave conditions on the One hand. and..
the wave bending moments on the other hand1 However, as in
the oase of ship motions, the number of important variables
is too large to arrive at sufflcsntly detailed £nLorrna14on in this way. uoh aysternatio model test series are uaeful to indiøat trends and to define the range of interest OX the
phenomena wider oonsideraton.
With the increasing insight in ship motions and wave liad problems a Olear tondenoy developed. to carry out model testa
with the speciLie aim to check the theoretical calculation of
wave loads on the ship in a seaway and in several oases a fairly good correlation between expàriment and calculation was repoted. The agreement sometimes i indeed remarkable
considering the rather extreme ùaumpttona concerning the
hydrodynamics of the pròbiam Yor mny applications the
osI-oulation 'of wave bending nonenta is already sufriciently accurate for the determination of trends1 However, a further
refinement of the thaz'y is necessary for practical ship eroae-eectiona, which nowadeys aómetimes have rather extrene
forme close cooperation of experiment and theory s
advisable for the further development of the wave bad re
aeach E
)
01ear171 computer calculations 1OI wave bending momenta aremuch juicker and oh,eper than correeppnding model teats and also the expeimeuta can now be designed. especiall' for the purpose of checking the theoiy and the relative ituortanoe of the sasumptiont being made1 Additioual model tests could bi made for those investigations where the theory is not
valid.. In general model tests should be used. mainly' to i.
provi the theory and to confirm the oaloulatione in oo'na specified eases.. Also model teats in waves where the ben-.
ding momants and shearing torce have not been recorded
may be of intereit in øonnection with investigations pri-. m.arily'directed towards wave loa4e, as øuob teatø can be applied to cheek sorne of the assumptions made in the oal»
cigations for bénding rnornents The z'eeearch on wave loads
which was published after thelast I,848.G. conference
confirms this view to a: great extent., A description of this material is given below.
2 Model .exor±menta and. ,calculatiora to determine wave
3waanad Joo (1) bave tested. a $erie Sixty ship model with blockoosffioient of .60 with. three different
weight distributions... he teste were carried out in regular
waves and the model was run in three different directions in relation to the waves.. The teste confirm what ii gene-.
rally
ound, i.e.. that the vertioa3. wave bending moments amidahip in head sise are leas for a weight distributwaoxz'esponding to a large. rad.iva of gyration than foi' smaller
radii of gyration.
They S1SQ cospar.ed the. test results with theoretical calculations based upon a strip theory (Vossers method) using Tasat's method tor deriving the values of added masa and damping, In these calculations the i.ntluence of Íorwad
speed on the coeftiients of the equations of motions is
neglected. Although the comparison shows that the oalou.-lated bending moaent variations have the same trend as the experimental reaults the absolute values of the øa3.ov.lationa
in quite a few cases, are not in agreement with the teat reeult
The Aiithort remark that a better correlation is to be eocted when the influence ot forward speed on the OOQ
icients of the
ecu*tiOna of motion and.the Smith ef.fect are taken intoaccount
Ivareon and Thoinseo (2) and 1varaón (3) tooted three models
in regular head. seas and oompare& the teat results with
theoretical calculations basad upon Iorvia-Kroukovsky'e strip
theory using Grim'8 öoeffloients foz added mass and damping..
The correlation between calculation and. nodel teat resulte le good although the calculted values ar eom.bat higher than the experimental x'eaulta
The model tests to detorAine wave loada on a T. tanker model
with different weight diBtributions and draughts reported
by' and ('p) were compared with theoretical
cai-oulationa based upon the same principles as in () and (3)
This comparison is reported by' tvett and Haalwu (5) and ehowe tu general good correlation, both for bending momente
amidebip and at uarter4enthe, as well sa for the shearing
forc. (eee Figure 1)., The teat results se weil as the cal-»: culationa ehow that concentration of weights amidehip resulta in relatively' high bending.moiuente ainidabip and that the
distribution of wave bending rnomenta and shearing torces aong
the hull girder is strongly influenced by the weight distr-bution in the abtp Due to the strong influence of changea
in might dietibutton upon the magnitude of wave loada a direct
and .correot evaluation of the influence ot reduction in draught can hardly be established, by' means of these mociteetal The
test results (4), however, indicate a small ednotion of the bending moments with reduction in drught4
otovtsiv (6) compared measured wave bending moments at the
seetion and at 8L quarter length from the st.r with
csj,tulations and found a reasonabló agreement.. One sodel way
a 'sy'am..trioal Vertical sided ship form and the other. was a
tanker' od..l Two load conditions,. giving a positiv. arid. a negátivi stili water bending.nment, and á range o orwar'd
A caiCULtjOfl 02' the dtstributioùoZ the wave boiidiug
nQmóut a1ou the 3eugth ot i ¡óntoon fo sour speee how
that the niazimu
v1aos are e1it1y toz'wur
or ' the mid. al:iip eotton L1 Lound experimentally br dDgeB (7),magiitwie ot t1i maxinu is pzactica3.1y the saine ae the
mtdhi section value.
The *me conc1uioue e touud tu (8) where: KOzkQV
ROtOVt5O! nveetigated a Cargo ship Lorm,
both by experiment aM oa1cu1aion. The aliip model wae divided at frame etattona amidships az4 at quaterlengthsd
The pazt at the tiiods;J. ware held tbethex, by a ßteel beam,
-£1tte4. with stra1n gaOe. In. these two Russian pulicUons
many Of the theoretical valuasin aeiral of the oases
on5i45r6d, are lower than the corresponding experimental válues. The details of the method which is used for the alcula'tona are not cOmp3.5t017 clear from this work partly becais x'e.
tez'enoe is made to other Ruaean literature whio} was not. available4
Uo (9) reported experimental resulte' of midship bendin'
moments for seven models of widely diUerent form representing
typical actual shipa with blookooe iient fro* O59 to O8Q,
ThÓ moments were measured. b strain gagea o two bare joiningthe halves of tho models.
-A geoalm test Of one of the models showed iuoi,ificant dife
roncee due to 4imeneions when compared with ditferécoa be tween models of different forms" All of the mòdel were teated
ma very lare z'ange of wavé lenth ratió'e(up'tÒ AIL
3)anda range ot speeds The measured 'values of the dimensionless
midehip bending moment. are given in' numerical form after fairing
by a computer,. A remarkable. feature of the bendin moment curves
isa
paiD of peaks when plotted on a bass of wave length ratio.be bending moment. curves were-described atatiettca117 by.
expressions containing the 'waterline area coefficient, the
length over drauht ratio,tbe'lengthover breadth miao, the
radiva et ytion and the speed length ratio
flezult viiother normal ship forms tested in various establishments reo
The mea3ured bending momenta were compared with øalcu
lattons by Xorvin roukovsky's method as set forth by Jacobe et al.(1C). The reàulte are good and the double
ea isound
by the theory.Mania3 (li) carried out a series of teats to determine the wave bending moments in extremely high regular wavea
wo different weight distributions were used and the model was tested in bead end following eeae. The tests confirm the cono3ï9jofl that concentration of weight amidehip z'esulta in
an increaee of wave bending moments,
It is also conoludd that bogging and sagging wave bending momenta are genarally proportional to wave height up to a
height wave length ratio o 0,11 i.e, the steepest waves that
couldbe generated Ìophyeioal upper limit fìte wave
beMing mamenta was found in these testa.
Lsøy and Campbell (12) have tested two tanker models. -one with a bulbous bow and another without a bulb in regular waves and nave also measured the midship bending moments.
Apart from the bulbous bow there are otbe differences be tween the two models and. therefore the influeuce of the
bu]-bouw bow on the wave bending moments cannot be evaluated
directly from these teetB. The wave bending moments forth., model with the bulbous bow lere generally somewhat higher thàn for the other mode1 but the greater displacement may account for all or aonie part of the difference in bending moment re
corded,
Van L*mmere and Pangallla' (13) iùvoetigatedthe influ
eùoeof bulbous bGw on a 2L.000 DWTbùlearrier in ie.-ula waves. The tank wave spectrum used correaponded. tò a
Ñeumann spectrum form for wind fórce Beaufort 6, with a
significant wave height of 2.90 m and an average perLod or
seo. It is
onoluded in the repòrt that the 'bulboùbcw did not .afteet the wáve bending nòrzient adversely, thozmox'ethe wave bending moments n baflaat con4itiOn were lower
The ooìc1uons reached in the80 nVetiat1ön wexe
.
basecl'ou modë1test8 in oflewave Dpeotrum only uÉi thex'efore
ahould be rerded wth some reservatIon. It le of tuterost
to note that 1or the ballast condition the buiboua bow e1wws a lar6ei' increase in the 2iogging tiI1 water,bending moment with increaaiz*t epee1 than the cnventiona1 form,..bocau3e
the bulb re1ucee the atUl water bow wave.
. dgand
hibata(i4)ixwest4atedte erecta o
1eti spee' and course onmidsip wave bezding momentin
rOUheeas, Lor ßeometrJca11sirni1az destoyex ship rorme
avin 4tfforent lengths. . ...
Th.ia work io entirely based on calculations .acor4into tiie strip theory, modified. for the intluenoeof tOrwüds»oodand
using Thsai12 values for cross aectional damping and adceU ma8BÇ15);.Signitioant wave beightsand average periode
as given by 11 for the North Atlantic are used to formulate the energy apatrum.ot the sea weves 8hortcreetedesQf,Vthe seawaye simply introduced by (cosine)24 it was £oun
tiat.
the non-dtensiona3. amplitdee of the midship bending moment n
in head seas decrease considerably withincreasing ahi»
1enth; the affecta of ship speed are. small:
.;The amplit\dea of midship wave bending moment. in hed.
seas increase with increasing severity of the eeastate; in
short oreate head seas they are smaflor than n equivolent long created seas. Large decreasing. effects, on the ..miçhip.
bending moment cannot be expected for course angles below Q degreee.as compared with the head oa case.1
In long crested essa a reduction Öf 50% Óanebe expooted for acourse angle of 60 degreeø
-ordenstrm (16) investigated the influence of beading ou the
transfer funCtions L'or midship bending moments. or ecual eì'feótive wave lengths h found from ezperimeüts carried out
in N8MB and Davidøon Laboratory that the influence of heading
Løtveit a1iowet in unpub1isled work that. the ana
of the wave enezgy hae xmzoh less influeuoe on.the
bending mornent than the srsaing function of. the tzanefe t1unction,
3. heoreticLeie1oDmenta
4!t.ed. comaieonitth
model eøie.
iarnan;etalmaì (17) showed the valtdit7 of
the modified atri theory by . ooniparing measured distibu-'
tions Of th hydrodynmio orceealon the length
of a.
oecillating Blip model in still water with oalou1ations
.It *peared that tbe iffect Of forward speed n the diètrt
.
bttiOne of d*impin forces is very important ad aven nega-Uve values of th, 90 degrees out of phase oros lectional.fODoee, which were meaeured with a eegentedmodel, could be
ecpiai.nød y theory1
Tbis esesreh. i primaz'ily concerned with ship motions
ut:
the importance of a reliable prediotio cf crae sectional..,torces. fo the calculation of wave bending momenta i evident..
A eiilar
,.whioh. will be reportód in the near Suture,. was Sound tar the .dieibution. of exciting wave forces alomgthe ship length:,: . . .
Zn thesa caloui.ationa as in m9n of the cited bending moment calulatioñe.the CrOes eection*i VI1iIeS for .
duiing
ad. added. mása are deterined by sicg Taeat*e methode In
tiL,Ìtod which tavery aimilar to Gri'a method, the croas
sections of the ship are approximated. bybhree coefficient
trans-£UrmaUon of unit ofrcle POr nori*aI shilike seCtions
this tairl
rough aroxitntition gives goo4 reeultø incompa-rison with eporiwents. on oscillating cylinders, but.
differ-enOe* are expected tor instance for .sectionshaving .anextreme
bulbous Lorm.. . ... .
(18) computed the reipoñaeoperatorsofship motions
and vertical wave bending moments in regular waves for two
ship £orm of the 3eries 60 having 0,60 and 04'O
block-coefficient for zero forward speed, ? 0.10 and 0.20, a range of headings, wave length ratio's. and several loading conditions,
These very extensive caloulti,ons areb.ased on Y1ataibe's
modifie4 st'ip theory, taking into, account the effects Of iward speed, andTasai's croes s tional válue for damping
and. added nase4
4. Prediction of lon term dietributiona of wave loads.
In the A1eport of Committee i on nvizonmental Conditions
1964. a procedure for practical computation of long term stress diatributiøne ia deacrib.. The bending momnt. response
operator as a function of speeds, 'frequency añd heading is
assumed to' be known and. stastioadata of' st ificant wave heights, wave dlreàtion8' and averase wave periodS tàr the
oonsidsredz,oute are given,
,
The beñding moment response ope1ator Can be determinedby model teste Or'caZou.attofls as er tnstanòe decribed'by
ida(1),
.Nordenetrrn (23)usesa similar method to oaloulaté the. long term distribution6 of wave induced ship motioø and loads. bia method is based on the assumption that the square root of twice the ship response variance
(Vi)
is
proportional to the significant wave height when
the average apparent wave period T is oonstant,
It is assumed that the wave spectra are completeiy deecribed. by the aignificant wave height and the avezage apparent wave
period. ..
It te then possible to describe the response in ay' specified
weather conditions by meansof the "energy operator V1
/
w)1/ as a function ofA wave spectrum
3, (w),
can be written in the formt w1/3r (,w), and therefore the
energy operator can be obtained from this f ormulatioEL of the spectrum and a known transfer function as a function of
1
10
Ptiblia ted data ou visuatly etirnatedwaveheihtaR and
periods Ç wore aflalyee( and it wa round that the ions
term diatribution of cambe: d.e8oribed by a .Ieibuli
dt.tribttiou .funotion when T lies wit1in email intezitals,
The relations between the visually esti.mated parameters
(H
and T,) and tñ tet láátre C(4 ,,)/3
ndwere obtained from data on viausi and instrumental obser
vation; 1ven, by Qartwright.
. .
It Was thus possible to obtain the long termdistzibution 01 .i when Tv. lie. within small intervale rorn the
energy operator R and the oorresondtng ].ong term
tribution of
Thé total 1cn$ term di&tributio ot was obtained by summation ror ali uaiueewee shown that long term.distributiona calculated in. this way ccin be described by another Weibuli diatribution
Th lanted long term distributton is finally obtained
in s eimp]e way fom the lon teràibu1l ditibition
6f i as shown in
(aLf). The calculated long term diatribuionsagree satitatilyìithfufl scale teint
The metbo4 of calculation was analysed in eoedetail In (23) and the influence o',tbe foUow*g ta6tori anong
others on the calculated largeat expected reapQuee
2.. tazilcex' was inveatIate&;
t)The tranafer function as a function oÍ beactinp angle
b) the ve..enevgy ...A
o) The reIctionehip be then
Ç '
and d The relationship between andIt was found that the function describing the influence
of beading. bas a great influence ontho esl
further research is needed in order to establish the proper fnctiona1 rei tionóbipa .
s
The' ai1
apradiig of the wa'ïe enODy haø De1cttviy 1oasInfluence nd cUxe*tjona1jtr fuDct7tons of the fo
ga
practieaU7 b. sem Ñault fÓr'
24'l
4The reLation between nd Md aotiea11 no
Influence bu the' ,relatton betweöu IL
'u4 6w1/3
great importano..' '
'''
Thece Gonc1usion are valid tor the abip WbIQh ta consIdered
in (23)
!v!&
reox't that in hitherto utib1iahe work a large
i.uence c
the z'élatioa betweéñ Ç and for other' lengtha of ohip is fouM..' Bowo4ei' tb.è r'latton between,Ev aucl
hae te saine influence for all
1the of
ship and does theréfore not change the relation between the
largeat oxeeted r'.ponee and length of ab.ip.
Lei' (is) reports three main obøtaoleß to the development
1. Wave $peotXa ave: no been available to &cctately dòsor*e
erere eor'e.thatar'e rare but rnake aain.tfioant
contribution ttbe long. ,ter'in d&tibU.tiOUw
The redictiou
long term ditributione reuir'ec the
de-int.on of the variance (or' øtandrd deviation) à'
bendin.monient within individual weather categorio, as well ae the mean value,
3e COmparison btWen pred.iot.d dttribu.ti6n3. ús tboi Obe
tinodfro'4tiAl.egale ahistrees statttios
ediZieult by' the,. tact 5hLr 4ata uauaU inoludo wind
velocity r'ath thanwave fightá.,.
Progrese hue recently been made on sU three of thso pointe at Webb Institutó of Naval Ârchiteeture .connocton with
!ea1
tor the America Bureau o 6hippixg1Twelve extreme wave.spec.tra recorded by a Toker meter on
North £tlantjo weather ehipe were used to correct the ily
of seaspeotra, in log-.slope form,.previouely ueed at Webb for predicting long term distrbutjona of wave loads, The
averae.aignifioant wave height of the 12 extreme eoords
WeB 48,2 feet and the highest was 54,7 feet. Conaiderablé variation in average bending moment can b !cP00t
in
individual observations at sea. The maiD cause is obviously
the variation in the sea conditions and hence the
sectra
It the weather is Classified by wind Bpeòd, the oea apéctrum
Óafl vary greatly in both. shape and ares, depending on the
stage 0± development of the sea and presence ox' absence of
awei.Uutitivea'tb.er is oleeittOd by wave hoight, tho only
variation. will bo
spectrum sp'
.
OomtoD (20) demonstrated by analysis of predicted spectra
.Gf Wave bending momenti that the lon tezn di3tribition
Were easentialty the sáne when obtained, in either of the
t03.lówin8 ways.
'
I :Weather, classified on the basis of wind, with a wit
vari-aion in wave apeo trl areaa as wall' as hapea-bence a
large variance o! banding moment,'
2. Weather claesified on the basis of aigzìifiont wave beih.t With variátion in wave speotra due to he dii1erenoes ônly - hence, a small vartauoe of bending moment.
1owever, in naking prediction o1n model teet, it 1j8 ¡flfl
eaaier' to muke use o method '2.
Band (iebb I tituta)::ehQwed in an unpublished mexaorunduni
that a sirnp1 reltionsbLD xiat3. among thø variances Qtt
bending moment vs wave eigbt
wave height vs wind
enàing moment va wind.
This relation which permit model predictona to be rolatd
to wind concLitions is
cr o- + taie e2
wheie:
cl la the variance of ehip
reeponee relativo to wine(non dimensional),
al .13.the variance, of ahip reoponse zeative to WVB
(non dimensional)
ii the vazinaco' of wave heikit (ainhticnt) 're'ative
to iin
(:e.t),
''
taD2 e2 is the slope of the curve o 3hip response
vaitze, ¿werae a
i/IO hthot età.) vs elgniieíint
wave beiht. .
The above relatIonship san be shown to be true for wave
bending' mömente arid eatimnationo of Q, tan @ and can
be ¿nade on the basis of model teste and/or øalculation arid wave'wind statistica and/or measurements, This permits the determination of long term distributions on the basis of
wind velocity foz"diÑct ornparicon with Lull eale data..
.. Theresentatiori of model teat resulta.
LU esultò from zödel teste in waves should be presented in a 'form which is áa convenient as posaible t6r further calw
culattons, for instance the calculation o! lone term dietrl butions baeed upon ode1 '.tests reaulti arid wave statistics
It will
thea be very oovenient to have the teat resulte preoented as transfer functions or other formo of presentation which are eaatly convertedjntó transfer Lunotiona.
Tizo value of the experimental resulta from tests in irregular
waves i very limited if. only the significant values '(r,m,s. or .1/3 bilzest etc.) or only cumulative distributions of the
variables ràcorded in one or. two ideal sea 'spectra are iven, It is then impossible from auch data to Lind the transfer
functions of the variable. In such Oases the responee apectra
should be iveri to enable the determination of the transfer function. It should be noted that Moor (9) states that ouch transfer fianotions are poorly defined. Further InveottatIons
It would be advantagous to compare aU. reault from model teste with some standard wave bending moment
lation.. Although etifl used b7 designers the conventional
static calculation is not always ideal f'or auch öoniparieon
purposee Por instance the rátio ot the actual bonding moment
and the conventiönal statto bendizg moment is net oontant for a particular ship when the weight distribution is
changed (see (*)).
Another' aiternati're would be the comparison
with strip the'
ory calculations UGsvor, no uniformity exists In this rea." pact and amull ditferenoes in the euat*.on of motion coeffi-ciente for instance cause diîerenoea in the final result. As long as the calculation methode are steadily' improving and no standard procedure has been. developed it is hardly possible to ae euch calculations as a standard. for
com-parieoA. It seems very a4vteable to describe the methods
-4wbicieulattone are based in sufficient detail to
avoid confusion in this reapect, Also the weight diatri.' bution along the length of the ship should. be definedexplioitlr and not only by. its momenta with respect t the
main Croea.'sectionp
It is found advant9geoua to give the reoults in the feria
of non'.dimeneional coefficients or .n dimensional loads di..'
rectly'.A presentation where the resulte are converted to
"effeGtive wave height" should be treated 4oarefully' as this presentation can resulbin. mi,eundez'etanding, because the
"ffeetive wave height" is uot. the earns or bending moments.
at other crosasectione, hearing foro.s,pttch,
acoeleratioe etc,.
6. Re., o. wave load.s. ro. ea nd ra
6.1. Local wave load
Research to itweatigats the transverse, load aotin on the
midship section et a ship. model in regular bead waves will be carried out by soda (Ship 1eeeaçch Institute, Tokyo). The
pressure acting on.the hull at the midship eection et a T.2
tanker model will be measured in a rarìe et wave lengthn
Terazawa (Osaka University) announced the calculation et ship motions and pressure distribution due to waves on the
aurtaoe ot the hull tor 17 ship orma,
6.2 Distribution otwae bending moment and. shear force Óver
the length
8bi.
:For checking the validity of the modified strip theory
tortIie caloulationofshearstreas and bending momenta the
couipa'iaouot their dtstrïbution over thò length or a ship
mo.lin regular wavea and' tie resulte eta calculation is
etz'emely importnt. :
A report to:
ùe of the "Wetber Reporter" will becómpletéd in the near tutuÑ by Gòodrio (PL) and possibi' a aiáÌlaranälyais will be made or the tbee 8eriea ship forms
which were tested by de Doeo.,..
6.. Influence of bulbous bow on tendin momenta.
.' The model
teat
roterred'to 'ndcte;tht,tbe
inf],ueo.eof n bulbous bow on wave kendi .moente e prob.bly loss,, ra
flounced then might have ben expected when taking.into aocount the, long lever for thextra.diep,lacement due to the bulb, but
it iafelt that further oontiraiation of this conclusion ia
re-u1re4 before it can be generally accepted.
6,, endinmÖnienttrnfer function
in óblique wavee.To make relietic pi'ediottone of the long terni distribution
of wave loads Lt is necessary tÓ'kncw the transfer tunctio for lateral bending momenta as well as for vertical bending moments in oblique waves,
Carefully conducted model test should be carried out to check
the modified strip theory used in these oases.
16. 6.5. Retnement of
endinioment oalcu1atios.
A further refinement of the bending moment calculation
is the use of p1s (22) method for the .eyaluation
ofcroas sectional ya1u08 for damping and added masa..
Srnttb (21) programmed a multi coefficient transforaation
of the unit circle for ahiplike sections, including
'verextreme bulbous forma, and arrived at a close fit for these aectiona.The calculatiöu will be compáred. with experiments
on heaving cylinders to cbee the theory.
Tb
influence osueh close fit calculations
on the bending momente should be compared. with model
eerimente,. In
paitióular thó distributlónof th&benaing'momentóver the
length of tizo ship is'af intereatin this
case.Confirmation oZ auch more refined methods allow the
investigation of detafl'problem., such as.the inflen
ofbeam-draft ratio variations on the bending moment., : 66. Standard. wave aeotra,
lt isneoeasarto formulate a atndardtamiIy
ofwave spectra, represening observed aea states realistically
in order te make COmparable sböt term and long term prs
terenoe.
3waan VA and Jooeefl, V.i,A,:"he Influence of Weit
DiStribution ou Wave endin Moments".
Internat. ShipbProgx. 12 (1965): 13k, pp 389.407.
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£rek och Berknad. Vrden ter, Parts Upptrdande i
aeßelbundna Va6or'..
Chaluiere ?ekn. B akoLa. Inst. Skeppsbygnadetekric.
Rap. 3ept. 196
Ivareaon, A: "Olika Prkeppafornera Invekan pa artygs
Iankeppapaknningaz'; Essultat av Modelf'òrek 3. regel-. bundna Vagor"1
..Qhalers Tekn. Bgskola lust, 8keppsbynadstek.
RaI». June 196..
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termtne Jcve Loada on a T-2 Tanker"
Det. Norake Toritas, Fubi, No. 42. (196k) 22 p.
(5)LØtveit, M. and BaslwK.: "Comparison btwean
Calcu-lAted. and. Measured Wave endiu Mothente, Sheain PODOf B
and. Pitching Motion for a T-2 Tanker MoAel in Regular 2
Waves"
Dot Noreko Veritaa Rep. No, 6k3k-8.
Rostovtaev, D.M,: 'Wave Bending Moment in the Pore Fart
of a $hip". (In Russian), Trans. Leningrad 3bipb.
Zst,
No, 39 (1962) p. 69. (8 pp.).
DOeS 3.Oh. da: "Experimental Determination of Bending
Momenta for Three Modela of Different Puliness in
Regular ave&'.
Internat, $bipb. rzogr. 1960.
Kozlakov, V.V., RØStCVtBOV, DM. and Qarbuz, V..8.
"Experimental Studies of sending Momenta Occu.ng in
Ships of the 1ibyshevges Olasa in Regular Waves".
(In Ruoian). Trama, Leningrad Shipb. met. No. k3
?5oox, D.I.: "Longitudinal sending Momente on JIodelù in
tteád 8aaa'. Traneactione Royal 800iety of Naval
Arohitocto, 1966.. V
Jacob3, 71.R., Dalzell, .,F. and Lalangao, P.:"Guido to Computational irooedure for Analytical valuation of 8hip Bending Moments in Regular Waves",
Davidson Laboratory, Report No 791 1960.
niar, NM. "Investigation of eudingMoinentawitbii
the lLtdahip Ralf Length of a Mariner
Model in xtre
Wavesu. DvUeon Lab. Rep, No. 1016 (1964)
Laekey., LV.. and OainpbeU., G4R.; "The Design of Hull
torme fox Super rankers and Bulk Carriers1t.
Mar, echol. 3 (196S); , pp. 23-41..
Lammeren, W.P.A.. van and Pangalila, P.V.A.: "Research on Bulboua Bow Ships", Part lIB: "Behaviour of a 2a0OO Ton D.Vi... Bulk Carrier wth a Large Bulbous Bow in a 8eaway. Studiecenerum. TNO Sobeepsb, en 1avigatie»RoUand. Rep.
No. 723 (196) June, 11 pp.
ukud.a, J. and Shibata, J, "The Effects of Ship Length1
Speed and Course on Midship Bending Moment, laiiaing and.
Bow S mergence in Rough ¿3eaa". Memoires of the
aot. of
Eng., Fushu Unverait7 Vol. ffl,No. 21966,.
Tasai, "On the .Danping and Added MaSS of Ships Neaving .aid Pttdhing", fleport of flesearoh Xnst, for Applied ..L'recba-flioe,..uthuunivex'sity1960.
NordenotrØm, N,z "Calculation of Wave Induced Motion and
Loada". Progrese Iepot No. i. .Det. Norøke Vertas Ñeport
so.. 6510S.
Gex'rttsma, J and B*.tkoln, Li "The DistrbuMton Of the
H.ydrodrnamic Forces.on. a ieav.ing arid Pitching Ship VIodol
in Still Wtez"
Internat. 3hipb. Progr.. 1964..(18) Fukuda, J,: Conputer rograxnm Results for Response
Operatore of Ship Motions and Vertical WavÓ Bending Moments in Regular Waves on Uerohant 8hipe of .60 «and.7O Blookcoefticient".
Fact. of Eng. FU3hu University, Japan 1966,
(19):LWi, E.V.:, "Prediction of' Lonß Term Distzbuttons àt W&ve røas", Ifornal Note Webb inst of Tecbnology
1966.
Ompton, R,U.: "An Investigation of Wave Induced .1iip
Bendino liomentS in Typical 8ea Spectra".
14.8, Thesis, Web. Znst, of Teclnology 1964,
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Arbitrary Ship Foms" Eeport 148 (in preparation),
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Porter, .W.L., "PessureDietributions,'Added.Mass ana Damping Coefficient for Cylinders Oscillating in a Free $uiSaCe.
University of California, 1960.
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A pilot study with the oonputer prora N 40, Det
Norake 'Vorita'ÑeeaÑh epartment repOrt no. 66-'ll-S 1966,.
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3hip Dosign C1me'a L iverøity of Teobnoloy
Gothenburg, 1965e.
(W&S 6219)
(W&S 6199)
Figure 1.
Comparison of computedand measured bending moments in regular waves
from reference [5J)
.016
LOADING CONDITION VII .012
/
s-.000 e a .016 .01 .006 004 CM .../ ò A A .016 .01 .006 CH .004 & MIDSHIP FORWARD AFT MODELTESTS *UTEDVALUES
° ' / L -1.75
--.01 004 O