16 h In e na ional Symposium on P ac ical Design o Ships and O he Floa ing S uc u es PRADS 2025
Ann A bo , MI, USA, Oc obe 19 h-23 d 2025
Seakeeping Calcula ion Wo k low o Hull Fo m Op imisa ion
Ruddy Ku nia*, Gaspa d Ducamp, and Joy Klinkenbe g
Ma i ime Resea ch Ins i u e Ne he lands (MARIN), Wageningen, The Ne he lands
Abs ac . This pape ocuses on a wo k low o seakeeping calcula ions o he hull o m op imisa ion
o a wind assis ed ship. The op imisa ion was pe o med o a bulk ca ie and a c uise ship. F om he
e e ence essels, hull a ian s o he bulk ca ie and he c uise ship we e gene a ed. A obus wo k low
was de eloped o pe o m au oma ic seakeeping calcula ions o each hull o m a ian . The calcula-
ions ocus on he mo ion Response Ampli ude Ope a o s (RAOs) and he su ge d i o ce Quad a ic
T ans e Func ions (QTFs). Be o e pe o ming he ull compu a ions o e he ship a ian s, alida ion
agains he model es s o he e e ence c uise ship wi h sail was conduc ed. Su oga e models o he
RAOs and QTFs we e de eloped o be used in he op imisa ion wo k low. Ve i ica ion o su oga e
models was pe o med agains he compu a ional esul s, easonably good esul s a e ob ained. Fu he -
mo e, e alua ion o he su oga e model esul s o e a sys ema ic a ia ion o design pa ame e s was
pe o med o s udy he ends o mo ion RAOs and d i o ce QTFs o e a design pa ame e a ia ion.
Finally, an op imised hull is e alua ed and compa ed o he e e ence hull.
Key wo ds: Seakeeping, op imisa ion, c uise ship, bulk ca ie , su oga e model
1. In oduc ion
In he OPTIWISE-EU p ojec amewo k, an ea ly-s age mul idisciplina y design ool was de eloped.
The ool is e e ed o as CREATOR which s ands o Compu a ional esul s-based Reg ession ship design
me hodology o Ea ly Assessmen o To al Ope a ional pe o mance including Rou ing. The CREATOR
wo k low is de eloped o he op imisa ion o a wind-assis ed ship. In he wo k low, CREATOR conside s
he ollowing aspec s: i) hull design and ca go capaci y, ii) p opulsion pe o mance in calm wa e , iii) ma-
noeu ing and i ) seakeeping pe o mances, ) ae odynamic pe o mance, and i) wea he ou ing ( oyage
simula ions).
M. Ga enaux, M. Ka ge and J. J. A. Scho . [2024] epo ed he CREATOR de elopmen and applied
he holis ic design and op imisa ion on a Newcas lemax bulk ca ie . They ound ha he e e ence ship has
he la ges powe sa ings pe on ca go*miles. A u he de ail op imisa ion was pe o med on he p opelle
design as desc ibed in [B. Schalk-Meije ink, E-J. Foe h, T. J. C. an Te swisga, 2025].
J. J. A. Scho ., P. G. Ba ena, R. Egge s [2025] applied he CREATOR op imisa ion wo k low o
an ea ly design o c uise ship wi h wind p opulsion. An op imised design was ob ained by conside ing
wo objec i es on he a e age equi ed sha powe o he ship wi h and wi hou wind p opulsion. Some
cons ain s we e applied co e ing he weigh dis ibu ion, he me acen ic ange o he ship s abili y and
he main pa icula s limi s. Pe o mance o each design candida es was e alua ed in oyage simula ions
wi h wea he e- ou ing.
This pape ocuses on he seakeeping calcula ion wo k low o he hull o m op imisa ions o he bulk
ca ie and he c uise ship as used in [M. Ga enaux, M. Ka ge and J. J. A. Scho ., 2024, J. J. A. Scho .,
P. G. Ba ena, R. Egge s, 2025]. Ve i ica ion and alida ion o he seakeeping calcula ions a e p esen ed.
Fu he mo e, seakeeping pe o mance e alua ion o he op imized hull is discussed.
The seakeeping calcula ions we e pe o med using SEACAL, a 3D po en ial low panel sol e o ze o-
and o wa d-speed seakeeping calcula ions in he equency domain. SEACAL is de eloped a MARIN
unde Coope a i e Resea ch Ship amewo k (CRS 1) [MARIN, 2024a,b]. SEACAL sol es he bounda y
*Co espondence o: [email p o ec ed]
1Coope a i e Resea ch Ships (CRS) was s a ed in 1969 and ocuses on hyd odynamics, s uc u al and ela ed p oblems o all
kind o ship ypes om a undamen al, design and ope a ional pe spec i e. Today, he CRS consis s o 24 membe o ganiza ions and
companies ca ying ou a join wo k p og am. Mo e in o ma ion on h p://www.c ships.o g
1
alue p oblems o he double-body s eady po en ial, adia ion and di ac ion po en ials. Fo o wa d speed
cases, he eloci y po en ials a e ob ained om he sou ce dis ibu ion solu ions o he bounda y elemen
sol e wi h Rankine sou ce o e hull and ee-su ace domain. Fo ze o-speed o ela i ely low-speed cases,
G een- unc ion me hod is applied wi h he sou ce dis ibu ion only o e hull domain. A o wa d speeds,
he Rankine me hod sol es he ee su ace condi ion mo e accu a ely han he ze o-speed G een- unc ion
me hod. The d i o ces quad a ic ans e unc ions (QTFs) a e compu ed based on he di ec p essu e
in eg a ion me hod o he quad a ic pa and based on he Pinks e app oxima ion o he po en ial pa
[Pinks e , 1975].
A obus compu a ion wo k low was de eloped o pe o m au oma ic SEACAL calcula ions o each
hull- o m a ian s. SEACAL calcula ions we e pe o med o he bulk ca ie o e 50 hull a ian s in bal-
las and scan ling condi ions, while o he c uise ship o e 48 hull a ian s wi h ou me acen ic heigh s.
Ve i ica ion and alida ion o SEACAL esul s o he e e ence hulls we e pe o med be o e he ull com-
pu a ions o e hull a ian s. SEACAL esul s o he e e ence c uise ship wi h wind p opulsion we e
compa ed wi h model es s. The model es was pe o med a MARIN unde he OPTIWISE p ojec .
Su oga e models o mo ion Response Ampli ude Ope a o s (RAOs) and su ge d i o ce Quad a ic
T ans e Func ions (QTF) we e de eloped o be used in he CREATOR wo k low. The su oga e models
o he mo ion RAOs we e used o he wea he ou ing op imisa ion in he oyage simula ion. While, he
su oga e models o su ge d i o ce QTFs we e used o he ship powe ing op imisa ion ela ed o added
esis ance in wa es.
The su oga e models we e e i ied wi h he compu a ional esul s om SEACAL. Fu he mo e, e al-
ua ion o he su oga e model esul s o e a sys ema ic a ia ion o design pa ame e s was pe o med o
s udy he ends o mo ion RAOs and d i o ce QTFs.
This pape is o ganised as ollows. The design space is desc ibed in Sec ion 2.. Desc ip ion o he
compu a ional se up is p esen ed in Sec ion 3.. Su oga e modelling is desc ibed in Sec ion 4.. SEACAL
esul s a e p esen ed and discussed in Sec ion 5.. Finally, Sec ion 6. concludes his pape .
2. Design space
Main pa icula s o e e ence ships a e p esen ed in Table 1. o he bulk ca ie and he c uise ship.
Based on he e e ence hulls, 50 hull a ian s o he bulk ca ie and 48 hull a ian s o he c uise ship
we e gene a ed. The hull a ian s a e cha ac e ized wi h h ee design a iables o he bulk ca ie and i e
design a iables o he c uise ship. These a iables a e sys ema ically sampled using he La in Hype cube
Sampling (LHS) me hod McKay e al. [1979].
The design a iables o he c uise ship a e slende ness, block coe icien , ela i e LCB, beam- o-
d augh a io and displacemen , as shown in Table 2.. The LCB is de ined om amidship ela i e o he
leng h o e all subme ged LOS wi h posi i e alue being o wa d.
Table 3. shows he design space o he bulk ca ie consis ing o he ship b ead h (BW L), ela i e
longi udinal cen e o buoyancy (LCB) and he block coe icien (CB). The LCB is de ined om he
amidships ela i e o he ship leng h (Lpp) wi h posi i e being o wa d. The leng h o he ship a ian s is
ixed as he e e ence essel. These a ia ions lead o he ship displacemen a ia ion o (71.2,96.9) k on
o he ballas loading and (173.8,236.3) k on o he scan ling loading.
Table 1. Main pa icula s o he e e ence ships, bulk ca ie and c uise ship.
Pa icula Symbol Values Uni
Bulkca ie C uise
Leng h be ween pe pendicula s LP P 294.47 - m
Leng h o e all subme ged LOS -≈210 m
Mean d augh T18.5 ≈5.4 m
B ead h moulded on wa e line BW L 50 ≈25 m
2
Table 2. Design a iable o he c uise ship.
Design a iable Symbol Range Uni
Slende ness LOS
∇
1
3
(6,10)
Block coe icien CB(0.5,0.7)
Rela i e LCB LCB
Los (-5,3) %
Beam- o-d augh a io B/T (2.4,6)
Displacemen ∆(15,30) k on
Table 3. Design a iables o he bulk ca ie .
Design a iable Symbol Range Uni
B ead h moulded on wa e line BW L (40,50) m
Rela i e LCB ( wd AP)LCB/Lpp (2.4,3.69) %
Block coe icien CB(0.786,0.856) -
3. Compu a ional se up
This sec ion desc ibes SEACAL compu a ional condi ions and G asshoppe ©Rhino© o SEACAL
inpu gene a ion. The calcula ions we e pe o med wi h SEACAL 7.2.1.
3.1. Compu a ional condi ions
3.1.1. C uise ship
The ollowing condi ions a e applied o SEACAL compu a ions on he c uise ship. The wa e equency
anges om 0.05 o 2.4 ad/s, wa e di ec ion anges om 0 o 180 deg wi h s ep o 15 deg, ship speeds o
0, 6, 12, 15 and 17 kno s, me acen ic heigh s GMTo 1, 3, 5, and 8 m.
The choice o he maximum wa e equency is selec ed o be co espond o he minimum wa eleng h
equal o a hal o he minimum b ead h. F equency s eps a e selec ed o be ine in he peak equency and
coa se in he ail equencies, i.e. 0.02 ad/s in he equency in e al be ween 0.3 and 0.7 ad/s, 0.2 ad/s
in he equency in e al be ween 1.6 and 2.4 ad/s.
SEACAL wi h G een- unc ion me hod (wi hou ee su ace panels) is used o he compu a ions o he
ship sailing a speeds o 0 and 6 kno s. In hose compu a ions, he lid panels we e added o he hull mesh
o he i egula equencies emo al. Fo highe speeds, SEACAL compu es he Rankine sou ce o e he
hull panels and ee su ace panels.
O e 48 hull a ian s, see Table 2., ull compu a ions we e pe o med only wi h GMT= 3 m. Fo he
o he GMT alues, es a calcula ions we e pe o med by ecompu ing he added mass, damping coe i-
cien , exci a ion o ces, mo ion RAOs and d i o ces QTFs. The same sou ce dis ibu ion o e he panels,
as compu ed in he ull compu a ion, we e eused in he es a compu a ions.
The ship’s pa icula da a, CoG and adius o gy a ion we e upda ed ollowing he hull cha ac e is ics.
The adius gy a ion is compu ed as kxx = 0.424B−7.10−4B2,kyy =kzz = 0.266Lpp −3.1−5L2
pp. This
eg ession was de i ed om an exis ing da abase o simila ships. The inpu ile is hen upda ed in he
G asshoppe ©sc ip , as desc ibed in Sec ion 3.2..
3.1.2. Bulk ca ie
The ollowing condi ions a e applied o SEACAL compu a ion o he bulk ca ie . The wa e equency
anges om 0.05 o 1.6 ad/s, wa e di ec ion anges om 0 o 180 deg wi h s ep o 15 deg, ship speeds o
0, 8, 11 and 13 kno s o he scan ling loading and o 8, 12 and 16 kno s o he ballas loading.
3
Depending on he hull o m a ian s, he inpu ile is upda ed in he G asshoppe ©sc ip , Sec ion 3.2..
The adius o gy a ion was ob ained by a eg ession om an exis ing da abase, whe e kxx = 0.35B,
kyy =kzz = 0.25Lpp.
Mesh sensi i i y s udy was pe o med be o e unning he ull compu a ions. The ull compu a ions we e
hen pe o med o e 50 hull o m a ian s, o each o he wo loading condi ions.
3.2. G asshoppe ©Rhino© o SEACAL inpu gene a ion
A wo k low in G asshoppe ® Rhinoce os® has been de eloped o p o ide a consis en mesh ile and a
pa ame e inpu ile (.xml) o each hull o m. The wo k low s a s by eading a hull o m ile (.3dm), a
hyd os a ic ile (.lis) and a empla e o SEACAL inpu ile (.xml).
The main ship pa icula s a e aken om he hyd os a ic ile. The hyd os a ic ile is used o compu ing
he cen e o g a i y (CoG) posi ion. Longi udinal and ans e sal posi ion o CoG a e ob ained om
he cen e o buoyancy, he e ical posi ion (VCG) is ob ained om he KM alue and he GMTinpu .
In he bulk ca ie case, he VCG is di ec ly compu ed o be 50% o he dep h o he essel in ballas
condi ion and 55% in scan ling condi ion. A SEACAL inpu ile (.xml) is hen c ea ed con aining he
main pa icula s, CoG posi ion, adius o gy a ion, wa e di ec ions, wa e equencies, ship speeds and
o he nume ical se ing.
The main pa icula da a and he ship hull o m a e used o e-compu ing hyd os a ics in he G asshop-
pe ® and ob aining a wa e line cu e. This cu e is hen used o imming he hull o m o ge unde wa e
hull o m. The immed hull o m is spli in o se e al su aces, i.e. bow, mid-hull and s e n su aces. Those
su aces a e panelled and hen sa e o a . k ile.
In he G asshoppe ® Rhinoce os® wi h MARIN’s plugins, he Gen ool is used o c ea e uns uc u ed
mesh on he spli su aces. Fo each g id, a ixed g id size can be speci ied. So his app oach is sui able o
a la ge change in he hull o m a ian s.
A s a egy in de ining he g id size is needed so ha he mesh has a su icien o al panel o ob ain
an e icien compu a ion. The g id size a he mid ship is de ined as ∆x=λmin/9whe e he minimum
wa eleng h equals o he hal b ead h, λmin =B/2. A g id e inemen is applied o he bow and s e n
su aces. This app oach ixes he g id size o he hull a ian s wi h he same b ead h. This leads o ine
panels o mo e slende hulls o smalle b ead h hulls. Figu e 1. shows he meshes o he c uise ship
a ian s, ship 3 o he smalles displacemen , ship 33 o he la ges displacemen , ship 9 o he smalles
slende ness and ship 2 o he la ges slende ness. Figu e 2. shows he meshes o he bulk ca ie a ian s,
ship 34 o he minimum b ead h and ship 2 o he maximum b ead h.
Figu e 1. SEACAL meshes o he c uise ship a ian s: he la ges and smalles displacemen s a ian s, and he la ges
and smalles slende ness a ian s om he op o bo om plo s espec i ely.
4
Figu e 2. SEACAL meshes o he bulk ca ie a ian s: he smalles b ead h a ian , ship 34, and he la ges b ead h
a ian , ship 2, o he scan ling d a . F om op o bo om a e ship 34 (side iew), ship 2 (side iew), ship 34 ( op iew)
and ship 2 ( op iew), espec i ely.
4. Su oga e modelling
This sec ion discusses he me hodology o de eloping and e alua ing he su oga e models.
4.1. Su oga e model de elopmen
A sys ema ic app oach was applied in he de elopmen o su oga e models. A wide ange o models,
om simple whi e-box models, such as linea eg ession, o black-box models, such as neu al ne wo ks and
ensemble me hods (as hose implemen ed in Sciki -Lea n in [Ped egosa e al., 2011] and XGBoos [Chen
and Gues in, 2016]), was conside ed.
Be o e aining any model on he da ase , a se ies o p ep ocessing s eps was applied o make he inpu
da a as in o ma i e as possible. Se e al s a egies we e conside ed:
• No maliza ion 2, which scales he ea u es o a common ange and can imp o e he con e gence and
s abili y o many lea ning algo i hms.
• Polynomial ea u e combina ions 3, o allow models o lea n po en ially mo e complex, non-linea
ela ionships be ween a iables.
In o de o compa e he models in a sys ema ic and ai manne , 5- old c oss- alida ion was employed
4. As illus a ed in Figu e 3., his echnique spli s he da ase in o i e subse s. A each i e a ion, one subse
is held ou o model e alua ion, while he emaining ou a e used o aining. This p ocess is epea ed
i e imes so ha each subse se es as he es se once. Al hough mo e compu a ionally expensi e, his
app oach o e s wo majo ad an ages:
2Sciki -lea n on s anda diza ion
3Sciki -lea n on polynomial ea u es
4Sciki -lea n on c oss- alida ion
5
• I helps o mi iga e o a leas de ec o e i ing by ensu ing ha he model is e alua ed on unseen da a
du ing each i e a ion.
• I enables a mo e obus compa ison be ween di e en models by educing he a iance associa ed
wi h a single ain/ es spli .
Figu e 3. Illus a ion o 5- old c oss- alida ion. The da ase is spli in o i e equal pa s ( olds), and he model is ained
i e imes, each ime using a di e en old as he es se (in g een) while he emaining ou olds a e used o aining
(in blue). This app oach ensu es ha e e y da a poin is used o bo h aining and e alua ion, p o iding a mo e obus
assessmen o model pe o mance.
All combina ions o models, p ep ocessing s a egies, and c oss- alida ion con igu a ions we e hen sys-
ema ically e alua ed o iden i y he bes -pe o ming models. Each con igu a ion was assessed using s an-
da d pe o mance me ics—such as mean squa ed e o (MSE), R² sco e, o o he s depending on he p ob-
lem o mula ion. This quan i a i e e alua ion allowed us o objec i ely compa e he di e en app oaches
and selec hose o e ing he bes balance be ween accu acy, obus ness, and compu a ional e iciency.
Sepa a e models we e ained o each indi idual componen o o ce and mo ion ans e unc ions, in
o de o educe he complexi y o he lea ning ask. This app oach also allowed us o iden i y and selec he
mos sui able model o each ou pu , gi ing us he lexibili y o ocus on he mos challenging cases when
needed.
4.2. Su oga e model e alua ion
In he case o he bulk ca ie , he mos e ec i e models we e ensemble me hods. In pa icula , al-
go i hms such as Random Fo es and Ex a T ees Reg esso demons a ed s ong p edic i e capabili ies,
likely due o hei obus ness o noise, abili y o model non-linea ela ionships, and limi ed equi emen
o hype pa ame e uning. These ee-based ensembles a e pa icula ly well-sui ed o abula da ase s wi h
mode a e dimensionali y and pe o m well e en wi h ela i ely small aining se s.
Howe e , when applied o he c uise ship case, hese ensemble models p o ed insu icien , especially
o p edic ing oll mo ion. We a ibu e his o wo main ac o s:
• The oll esponse is inhe en ly complex and non-linea , which makes i di icul o cap u e wi h
ensemble me hods ha end o model a iable in e ac ions in a ela i ely igid and piecewise manne .
• The aining da ase o he c uise ship exhibi ed g ea e a iabili y in e m o design pa ame e s while
s ill being ela i ely limi ed in size.
To add ess his, a ully connec ed neu al ne wo k was used, whose s uc u e and pa ame e s a e lis ed
in Table 4.. The a ionale behind his choice is he lexibili y and adap abili y o neu al ne wo ks, which
can app oxima e complex, non-linea mappings be ween inpu s and ou pu s, p o ided ha he a chi ec u e
is well- uned and egula ized. In his con ex , he neu al ne wo k ou pe o med he ensemble me hods and
deli e ed signi ican ly be e esul s o he c uise ship case, pa icula ly in p edic ing oll.
6
Table 4. Neu al ne wo k a chi ec u e and aining pa ame e s.
Pa ame e Value
Ne wo k size [64,64]
Ac i a ion ReLU
Op imize Adam
Lea ning a e 1e-3
N . o epochs 500
5. Resul s and analysis
This sec ion p esen s SEACAL compu a ional and su oga e model esul s and analysis. The esul s a e
p esen ed o he c uise ship and bulk ca ie .
5.1. C uise ship
5.1.1. SEACAL esul s o he e e ence ship
Be o e pe o ming he ull compu a ions o e ship hull a ian s, compa ison be ween SEACAL and
model es we e pe o med o he e e ence ship. The compu a ional esul s we e compa ed o he model
es wi h sail. Fo he compa ison agains he model es wi h sail, he oll RAO om SEACAL we e uned
o he model es .
Figu e 4. shows he mo ion RAOs o he ship sailing a 12 kno s in s e n-qua e ing seas in 17 kno s
T ue Wind Speed (TWS) and 90 deg T ue Wind Angle (TWA). A easonably good ag eemen in he mo ion
RAOs be ween SEACAL and he model es is achie ed.
Figu e 4. Compa ison o he mo ion RAOs be ween SEACAL (dashed-line) and he model es da a (+) o he ship
sailing a 12 kno s in s e n-qua e ing seas (30 deg) and in wind condi ions o 17 kno s TWS and 90 deg TWA.
7
5.1.2. SEACAL esul s o he ship a ian s
Figu e 5. shows he mo ion RAOs o e 48 hull a ian s. The esul shows a clea a ia ion o mo ion
RAOs, pa icula ly in he hea e, oll and pi ch RAOs. This la ge a ia ion in he mo ion RAOs ep esen
a la ge a ia ion in he pa icula s o he hull a ian s. Fu he mo e, a la ge a ia ion is also shown in he
su ge d i o ce QTFs, see Figu e 6.. The peak QTF magni ude a ies om 100kN/m2 o 400kN/m2.
La ge a ia ion in he design a iables makes i di icul o s udy ends o RAOs and QTFs om he
compu a ional esul s. The ends can be s udied in a la e sec ion om e alua ion o su oga e models ha
ha e been de eloped om hese da ase .
Figu e 5. Mo ion RAOs esul s o e 48 hull a ian s a 12 kno s. F om op o bo om plo s a e su ge, hea e and pi ch
in head seas, 180 deg ee heading (le column) and sway, oll and yaw in s e n qua e ing seas, 45 deg ee heading ( igh
column).
Figu e 6. Su ge d i o ce Quad a ic T ans e Func ions (QTFs) o e 48 hull a ian s a 12 kno s in head seas (180
deg ee heading)
8
5.1.3. Ve i ica ion o su oga e models
Su oga e models ha e been de eloped wi h he model aining o e 48 ships. The e e ence ship was
no included in he aining. In his sec ion, he esul s o he su oga e models a e compa ed o he SEACAL
da a o he e e ence ship.
Figu e 7. shows he oll mo ions RAOs and su ge d i o ce QTFs o he e e ence ship sailing a 12
kno s. The con ou RAOs a e qui e well econs uc ed by he su oga e models wi h some disc epancies in
he magni ude. Fu he imp o emen o he su oga e model p edic ion migh be needed bu he p edic ed
end o e ship a ia ion con ibu es mo e in he hull o m op imisa ion p ocess as discussed in he nex
sec ion.
Figu e 7. Compa ison be ween SEACAL (le ) and he su oga e model (middle) o he oll mo ions RAO ( op) and
su ge d i o ce QTF (bo om). The di e ences a e shown a he igh column.
5.1.4. Su oga e model esul s o a sys ema ic a ia ion o he design pa ame e s
The densi y plo s o e a sys ema ic a ia ion o design pa ame e while keeping cons an o he o he
pa ame e s, a e shown in Figu e 8. o he hea e and oll RAOs, and he su ge d i o ce QTFs. The d i
o ce QTFs a e shown o he ship sailing a 12 kno s in head seas (180 deg) while he mo ion RAOs a he
same speed in beam seas (90 deg).
The hea e RAO o e he displacemen a ia ion shows ha he na u al equency is shi ed o a lowe
equency o inc easing displacemen . The end o e ela i e LCB is simila as he end o e he displace-
men bu o a lesse ex end. Con e sely, he slende ness a ia ion shi s he na u al equency o a highe
equency o mo e slende ships. The end is simila as in he a ia ion o e CB.
The oll RAOs o e he a ia ion o B/T o displacemen show a simila end. The peak equency is
shi ed o he lowe equency o inc easing B/T o displacemen . I is clea ha a la ge ship wi h la ge
displacemen o la ge B/T gi es a smalle esponse in he oll RAO. Con e sely, he inc easing slende ness
o CB inc eases oll RAO. The oll RAO shows small a ia ion o e he a ia ion o ela i e LCB .
The su ge d i o ce QTF o e he a ia ion o displacemen shows ha he peak equency is shi ed
o he lowe equencies o he ship wi h a la ge displacemen . The ends o e he a ia ion o B/T o
ela i e LCB a e simila , he magni ude a he peak is la ge o a la ge alue o B/T o o a mo e o wa d
LCB posi ion. The peak QTF does no change o e he CB a ia ion. The d i o ce magni ude dec eases
o a mo e slende ship.
9
