On the hydrodynamic forces acting on box type vessels and their motions

C)

1. Intreduction

The purpose of this paper is to establish

a practical ca1cu1aton method to estimate the motiou in waves of a box-type floating vessel

which is one of the typical floating offshore

structures.

In calculating the motion of a box-type

floating vessel with a small lcn.gth-td-beam

ratio (LfB) and a latge beam-to-draft ratio

I)

2

* Kawasaki heavy Industries, Ltd.

Aashi Ship Model Basin Co., Ltd.

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Tub O1578.FO5c733

On the Hydrodynamic Forces Acting on Box-Type

Vessels and Their Motions

Ryaji SAKATA", 1'Ie,it ber, Yosh'io YAMAGAM1', .3I';nber,

Hiroshi OxAloTo**, Member, Tctsuo II'EBudnt*, Mcnzber, Kiyoshi NEtA', iliembet

(Fïo» J.S.N.A. Kansai, Japan, No. ¡72, March ¡979. NO. ¡78, Scpk:thcr ¡930 a;d No. ¡83, Dcccmbr ¡98!)

Summary

lt sceni that a standard calculation method of motions for box-type vcsc]s. equivalent to Ordinary Strip Method for ships. has not been definitely established yet. In this paper, a ractic;d incttinì is presented for estimating their motions io 'raves u-it;l a high accuracy.

The adtinors have carried oùi forced ocil!a1ion tests. measurcmcnt of ta.e exciting force. and inolion tests in Lenin, head and oblique seas by use of box-type vcscls of small

length-to-bc-nm ratio (1./lì) which is supuocd to have 3-dinnensiontil cffcct, and macic 2climensio:nal and

3-ftmcrionai theoretical calcu)tions. The 3-dimensional calculation', gives accurate velues of ainnont all hydrodynarnic coeíñcients and wave exciting forces excluding damping terrì ei rolling, etc.. hut it has a disadvantage that CPU tinte s long. 'fhercfotc, as a practïca1 calcula-tion method of the mocalcula-tion, the authors have developed a Modified Strip Method (.\t.S.M.) on the basis of thc strip method of short I'U time, taking account of experintc:ital results and

3-dimcnional alu1ation results.

Tine M.S.M. is as follows:

Longitudinal strip niethioci is adopted as well as ordinary transverse strip method.

Strct Strip Method (or Salvcsen-uck-Faitixiscn Methcdl is introduced for estimating

'.eac exciting force.

31 Çcrectio', of 3-dimensional effect is made, based on expeiimental results and

'3-dimen-sional calculation results.

-1) Estimation method of cc!nlv damping for roll is mcdified, taking 3-dimensionni clic-ct and

hai1ow wa ter effect into consideration.

-(13Td), Ordinary Strip Method (O.S.M.), which

is the usual calculation method for ordin:nr> ships, gives inaccurate resuitsU. Therefc.rc,

it is necessary to review the hydrodynamic

coefficients and the wave exciting forces in the

equations of motions in order to develop an accurate calculation method of its motions.

lit this paper, a new niethoci to calculate

hydrodynamic coeffidents and wave exciting

forces of a box-type floating vessel on the

basis of theory and experiment, and to predict

its motions, is

presented. Tisis method is

practical one with high accuracy.

On the Hydrodynamic Forccs Acting on Box-TypeVessels and Their Motions

2 Forced oscillator

The subject device mounted on a towing

carriage is connected to the floating vcssel

and makes a forced periodic oscillation of the

floating vessel within a vertical plane by

changing its circular frequency and amplitude. Fig. I shows the sketch of the forced oscillator with the vessel.

The principal particulars of the forced oscil-lator are shown in Table 1.. (4e) in the Table

indicates the phase difference between the

combined motions which can be changed in

eyery 5°. The elevating device permits the

(,ed oscillator to be lowered a maximum of

Tablo I Pincipa1 particulars of forced o:,cilator

.,.. _._/ alç Dcrs:tcr Scoftn York I

/

ZForce

_X Fcrc

/2\/

_{_.____/-}

/

-

P;oc 5ntcr

-Me

r'ig. I ForccJ o,;cihlatcr

900 mm below the towing carriage when the

test is carried out for a shallow water

con-ditions.

3. Equation of motion

The equations of motions are equivalently

linearized and the insignificant coupling terms

are neglected.

Tue obtained equations of

motions are described as follows. (Equation of longitudinal motion) Coupled motions of heave, surge, and pitch

aj7Ö-i-airi+ai9C=Z fl

±azÖ±aeO

=X

r * ± (7mX

ai+aO±a3O=f

4c4 G

where z, X and O denote the displacenr.t of heave, surge and pitch. while Z, X and M the forces and moment of heave, surge and pit.h.

(Equation of lateral motion) Couping motions of sway. roil and yaw

a*Ij±a*+a±a15tf+a4aw»X

S4JO..j

ay+a33y±a54çs±a53ç5+a3ç'

i rpfl f'

«ß2 +a*2Ú+a5+uG+as7±acs=L

1aM.1,

where y., and ç denote the displaceiuients o!

sway, roll and yaw, while Y, N and L the

force and moments of sway, roll and aw.

The non-linear tenu encountered in a amplitude motion or a rough sea will be

in-corporated into the equations of motion while observing the experimental results.

+ aizZ

4. Experiments

The experiments

vcre carried out in the

towing tank (length xwidth xdcpth=60 mx

6 mx 1.5 in) of the Kobe University of

Mer-cantile Marine.

In the forced oscillation tests, the floating

vessel is forcibly made a pure motion in a

still vater. The amplitude and phase lag of the hydrodynamic force are measured, fron 'vhch

the hydrodynamic cocfûcients of the uiutifl of equations are calculatedn. In tue meas-i3OCfl

± 90 mm WOY (Sue) M*. ± 70 mm

f?eIj (Pact') ± 30 dg

Freqjency 02 - 20 }!z

[)JrtTT*O c:ffcrcrT;at_{Torokrner Iyp} 3ch x 0OKg

no U*t DC. Motor 5.5 kw

EIeatc EcclriC Iotor '9C0mm Dc:.n

,,Wcni C'e3r Spne 1:

// I

r Sco?ch 'rrk u-F} S'.cT"Yc (Za)

LJ-g5..5_ --_--.-/J ZsFo " qj 3

100 Ryuji SAICATA, 'Voshio YAMAGAMI, Ilirosbi Oxsioto, Tetsuro LKEOIJCIII, Kiyoshi NEllA

Table 2 Model particulars

z

Wn,t, H,...25

- Y

"7

Fig. 2 Coordinate system and det':nition

urernent of th wave exciting forces, the wave exciting forces on the restricted floating ves-sel in waves are nicasureci by using a

dyna-mometer.

In the motion tcst in waves, the

motions of the floating vessel moored with

weak springs that hardly affect the motion,

are measured by the measuiing instrument for 6-degrees of Ircedom motion.

The coordinate system and the definition

of the notations arc presented in Fig. 2. The

model particulars and tile SCOC of tests arc

presented in Table 2.

The forced oscillation tests were carried out for all models. The motion tests in waves znid

the measurement of the wave exciting forces

were carried out with two types of model,

L/B=l.0 and 2.0. The notations in the TaUle

* ₊ : below the water line

Table 3 Conditions of the model tcsts

(4 Mean "atoe)

are as foJ lows.

0G: Ditancc from vater level to center

of gravity (positive is downward). K.rx,K1,y, K::: Radius uf gyration from tite

X, 7/ and z axes.

GIT, Gi1L: Distance froni gravity center

to lateral and longitudinal metacenters.

The conditions of model tests refercd in

this paper, L/L3=l.0, 13fd==5.0, water

depth-to-draft ratio (H/d)=9.-iO and 1.88, are

,pre-sented in Table 3. The forced roll tests were

carried out under tltre different rofl angles

because viscous effects are present in the iou

j

L (ai) 0.800 1.200 1.500 2.000 B (e) 0.800 0.600 0.462 0.360 d (e) 0.160 0.120 0.105 0.035 0.025 LIB 1.0 2.0 3.25 5.56 BId 5.0 5.0 4.4 13.2 14.0 E/d 9.40 1.88 12.50 1.88 14.29 1.90 62.84 8.00 Odd 0.506 0.000 0.095 -j.7j/, -2600 0.263 0.223

-0.263 0.298

-

-0.368 0.309 2.053 0.317 2.088 0.783

-itoic.n and w:':c excIting force tea r '0rcd o:cf8Ia1on teat Particulars' cf Mod Yaor Dealh H/d 9,LÛ!l ì3 Forced Oscitiction Test 'euve Zx/d '.1 Ç&, (,cd)

.L_.QÇ__..

0.125 "1 OÇ'25 O.CE57

{YL,

Roll 0J2.0

V.'ec:cj

_{ft./?d O.C5}

dampiig term.

5. Theoretical calculations

Theoretical calculations were executed in the

corresponding model test conditions men-tioned at the preceding Chapter 4. Three kinds of calculating methods, namely, the

2-demen-sional source distribution

method4, the

2-demensional rectangular region

method

(I-jima's method)'10

and the 3-diinehsioflal

source distribution method, 'ere used.

How-ever, in the 2-dimensional theoretical

calcu-latioìs, the difference between

above,

men-ti9ç1 two methods is very

small. So, the

rc-LJs by O.S.M. presented bere are those by

use of thc

2-dimensional lectangular rcgion.

Iii the 3-dimensional source distribution

method vc ernpluy the method by l7altinsen

and others. The surface of thevessel is

clivid-ed, following the Hess and

Smitht', into a

number of elements \vth flat

quadrangular;

the sources with uniform strength are

dis-tributed on each element; the velocity

po-tentials are represented by the distribution of sources; the pressures are

then obtained by

substituting the velocity potential into the

Bernoulli 's Equation; and the Imydroclynamic forces and moments are calculated by

integrat-ing this pressures throughout the surface of the vessel.

Tite wave exciting forces and

moments are derived h' use of the Haskind's relation from the radiatior. potential.

C. P. U. time of the 3-dimensional source

d

ibution method, with element number

On the Hydrodynamic Forces Acting onBox-Type Vessels and Their Motions 101

180 as indicated in Fig. 3, was about 68 seconds

per each frequency.

6. Ru1ts

jnumber of elements 180

Lospecl rolloofo ek'ment 1.0

Fig. 3 Subdivisorz in surface elements

Results of the forced oscillation tests, the measurement of the wave exciting force and

the theoretical calculations for the box-type

floating vessel with LJB=l.0 and

DJd=5.0

are presented in Fig.

4-17. In these figures,

the lateral axis indicates (=w?13/2g), and

longitudinal the hydrodynamic cocfhcjcnts and the wave exciting forces and moments in non-dimensional forms. The non-dimensional. co-efficients are defined in the folloving manner.

inertia term:

an au

heave -, Sway -, Roll -'

--pl'

pi7

a»

Coupling term (Roll-Sway)

Damping t cnn:

Heave -j --,

a12 /7

pv

2g Sway

;;'j;\'

7

a42 /13

Roll ---

_{pß\ 2g}

riI

Coupling term (Roll-Sway)

\\'ave cxcitiiig. force:

ZA YA

Heave

_pgLB'

Sway

NA

Roll

p9AL&

The phase lags of the. wave exciting forces

and moments are defined with respect to tiic

wave crest above the origin.

where

ti hydrodynamic coefficients

w: circular frequency p: mass density of water

displacement

g: acceleration of gravity

wave amplitude

From time results presented above, tl:e

fol-lowings became evident as concerns hie

O2 LlB'l.O Old 50 o s 1.

\

3 2 00

Fig. 4 Coefficient of virtual nss for heave

Fiar. 5 Coefficient of damping force for heave

o

O I 2 3 6

Os

Fig. 6 oefficieiit of virtual mass for sway

forces and moments on the box-type floattng

vessels.

(1) The 3-dimensional effects appear on the

sway inertia term, arid especially strong on

heave inertia, terni and the heaving force, and

Ryuji SÀiAr.t, Yoshio YA1xGAII, Iliroshi OKAM0ro, Tetsuro IIOIUCUI, Kiyoshi NEMA

- ---. 2-lass of the ship

LlBI.O OFd'S.O

O

--J--l83

----1----Fig. 7 Coefficient of dmng force for sway

L-' q a '----S--- -o

00 0

Fig. 9 Coefficient of damping moment for roll

the 3-dimensional source distribution method

explaincs the test

results better than

tite

O.S.M. Furthermore, tite effects tend to

become striking in a shallow vater conditins. These clearly suggest

the necessity of

the

2-'S 'S e 'S 'S ', 'S LIB!.0 d0.0 _C.' .&3JO ----L

-

'S

\

e _0.1 -S

"

. .

S-o

'N

-

S_{-.- e} 0 o O I 2 3 4 LID' 2.0 DId 5.0 F70-! 0102 6 [E ¿0 -n ---L'tIt.O 5Id-0 t e 6 s

.

'

L A

.

9LQ_1. 11,j---.-I-n _a L: o

Fig. 8 Coefficient of virtual rollmotneutof ircrbd

t.13 LO 0.1 0.0

L11 .J

ts

0/_,-'L

-4_O--Ç0lI: n"crnent of pvIti] of the ship

Fig. 10 Coefficient sway

ÇT4J7

- 06

On the Hydrodynarnic Forces Actiné on Box-Type Vessels and Their Motions 103

of coupling inertia of roll into

L'B'l.O B, O

1,_j

tdjp IL Ln

o

Fig II Coefñcient of coupling damping of roll into sway

L'E ''.0 5t5?' 5.0

02

i - 2 3 4

,-Fig. 12 Amplitude of heaving force

/

3dimensional theoretical calculation

-(2)

As concerns the sway damping, the

roll inertia, the coupling roll and sway incrtia ternis, the sway force and the rolling moment, it

is found that tue results by hIc O.S.M.

coincide fairly veil with the tcst results as

well as the iesults by hic 3-dimensioa method.

E. (de) o -90 -180 -210 Y. f1d 20 1.5 1.0 1 es I

/

s- -I 2 L'B'%.O Bld' 5.0 0.90'

Fig. 13 Phase lag of heaving force

1,0.1.0 Bld 5.0 00 [i.. C'____ --i I.

-I /

_..

e 2 3 4

Fig. 14 Amplitude of swaying force

Fig. 15 Phase lag of SWZtVILIg force

The heave and roll damping terms

cannot be explained by the wave damping.

Therefore, a practical calculation method is required taking into the consideration of the

viscous effects appropriately based on

experi-ments.

Shallow water effects appear in heave,

roll, heaving force and roiling moment, and swy and swaying force in l'ange of mall (long wave lcngfli).

E s n - fr0 8 6 1. 2 o -2 -L -6 -8 i .4 o LIB' 1.0 Bld 5.0 LH (L_1LL A53 --o

(r

-

L.o o. slsp

I,,

-j,

2

J

104 Iyuji SsxtTA,Yoshio YAMAGAMI, Hiroshi OKA1oTo,TetsuroJ1<EBUCHT,Kiyoshi

Nct-L'B't.O U'd.SO '9O

¿ .. --.,--,.-.

00 2 4 19

Fig. 16 Amplitude of rolling moment

1' 1.0 9' 50 90'

o

Fig. 17 Phase lag of rolling moment

7. Practical calculation method

From the studies above mentioned, it be-came clear that almost all the hydrodynamic

coefficients and the wave exciting forces even in the oblique seas are accurately calculated by

3-dimensional source distribution method,

which is a strict solution, excluding a strong viscous effect term, such as the roll damping

term. However the CPU time required for

the calculation is about. 40 times that of

O.S.M., therefore there are problems in time and economy for the simulation calculation

or a great number of case studies to

deter-mine the principal particulars of the vessels.

On the other hand, the OS.M., which is

based on the 2-dimensional theoretical calcu-lation, has a short CPU time and convenicilce.

The problem nf this method, however, is in the accuracy of estimation. In other words,

when the O.S.M. is used for a box-type float-ing vessel with a large B/d, the approximation

of wave exciting forces and moments become

unreasonable, and the estimation

for roll

becomes inaccurate.

For instance, the roll

shown in Fig. 33 derives a great difference

among the results by the O.S.ìU., the

experi-ments and the 3-dimensional source clistribu-tion method.

Furthermore, in the OS\t. of

L/B= I .0

an unreasonable results

appears.

which the roll in beam seas does ilot coincide

with tue pitch in head seas. For example, the results of roll at the incident wave angle x=

750 should coincide with these of pitch at

_x=

15°.

However, as shown in Fig. 33, bat

results don't coincide each other. The r

amplitude ratio .4/kÁ is 2.4 at f reasona-ce

frequency and the pitch, without a

amplitude ratio OA/.'.( is 33.

So, a practical calculation itethod, named

the 3lodifìecl Strip Method Ç\LS.M.), was

devised to solve these proì)leI)ls. The metlieds adopted are as follows.

.(i) There are the sonrce clittibntion

meth-od and the lectanular regioil methmeth-od as the

2-dimensional theoretical calculation mthc .4,

but, we adopt the, latter in behalf of shoçtcc

CPU time. Then in order to remove

incon-sistency in the calculation results, which

occurs between the ldtera.l motton and

longitudinal motion in case of sinab LiD,

-only the strip method with lateral situ) which

dcvides the length as in O.S.M., but also the one with longitudinal strips are incorporat-d.

In the calculadon of wave cxciti;.z

forces which is

the primary cause for the

inaccuracy of motion calculation when Bid is large, the Strict Strir Method which the

boundary conditions are adjusted in a much stricter nianner, is adopted. Accurate wave exciting forces are obtained from this

calcula-tion method.

(With reference to the total

force acting upon the cross section, the value obtained by S.S.M. does coincide with that ot the S.T.F. Met hod». However, a difference in the pressure distribution is to be cncountcrcd

These 2-dimensional calculation rcsuh-are given a inìpIe 3-dimensional modiìcaticua

-hich uses the model test results an/I the

3-dimcntional theoretical calculation results'

references. lt is known that the

3-dimension-al effects of the ñiotions within a horizont3-dimension-al

plane are small and these within a perpendicu-lar plane appear remarkably, so the

3-dimen-sional modifications are conducted on the

heave, roll and the pitch.

A general outline of the M.S.M. mentioned

above is presented in Table 4. The notation

A and Ji with suffix in the Table are the

non-combined ternis of the added inertia coeffici-ents and damping coefficicoeffici-ents of each motion

mode, while F and M are the wave exciting forces and the moments. These coefficients and exciting forces may be obtained from the

Limensional potential theory.

The sumx

x, y, z, , O and ' are motion modes signifying

surge, sway, heave, roll, pitch and yaw,

ies-ectiie1y.

The suffix L arid B denote the

strip direction of the floating vessel, of which L, like in tue O.S:M., is the lateral strip divided

the length of the floating vessel, and B is the longitudinal strip divided the breadth. The

suffix FK signifies the Froudc-Kriloff force, while suffix D indicates the diffraction force. The .damping coefficient with

the suffix E

are the eddy damping, which will be ment ionecl

later, and are the term that cannot be derived

from the potential theory. Furtheremore, in

the modification for 3-dimensional effect on

combined ternis, although not presented in time

Table, only the combine terni of the surge

and pitch is a modification the same as that of the pitch. Time rtiodiflcation for 3-dimensional.

¿

'ct indicated here is determined on the

basis of the results of experiment and the 3-dimensional source distribution method thus far carried out. A more strict modification method, therefore, may be considered in the

future through further experiments and a

stricter calculation.

(4) TIte roll

damping, which cannot be

explained by a linear theory, is treated as tue non-linear roll damping that takes tite eddy damping, based on the experimental rcsults

into account.

-Tite roll damping

BV')

of box-type floating

vessel, on the assumption that it is made ill) almost entirely of tite wave making

coinpo-nent B1ç' and the eddy compocoinpo-nent may be presented as follows.

B(çf) aBiç+B2çi&

=Bi+--wABl)

Here, tite wave making damping coefficient B1 is

obtained from the potential theory.

The eddy damping coefficient B2 is derived from applying the modifications of

3-dimen-sional effect Cn and C, using tite relation

between the aspect ratio a/b of the fiat plate such as bottom and side val], and the drag

coefficient Cn showin in Fig. 18, and applying

the modification of shallow water effect C

which is derived on

ami ex perinierital basis

from tIme ratio of the floating vessel's breadth and the sea bottom clearance B/(H---d) shown in Fig. 19, into the 2-dimensional eddy

da:np-ing cocfficient B' obtained from appiicaion

of the Kirchhoffs dead vater model.

-

f__8

B2,= 1.2784 .

_'B'2

_/

_{3 OG\)}

1p5(--

+P5( i t \2d1

4lrsinn

I _{4+7! sin 2n '}

aa=tan

_KG 4ir sin j Ps=

_4±sins

,s=tan1

KG B/2

where 0G is positive in downward.

Therefore, the calculation formula foi eddy

damping coefficient is as follows.

B21= 1.2784 x p1(B)2 KGZ} 3 C(L/d) CB -Cn(2L/B) Cs -t., p, at bottom at side wall 3-dimensional effect shown in Fig. 18

Csw: SlÌahlo\v water effect shown in Fig. 19

Furthermore, because i.S.M. is a

calculat-ing method devised on time basis of the

exxri-mont results with the B/d=4l4 and II/?=

On the Hydrodynamic Forces Acting on Box-Type Vessels and Their Motins 105

at boltom at

as ID C

:

'\

2 4 b O 22 50 Ct -r,..,, s '.-.

Fig. 18 Coefficient of resistance for flat plate

2-40 conditions, it is necessary to mind that

the accuracy of this method is confirmed only within the scope of those particulars.

8. The evaluation of M.S.M.

The experimental and the theoretical

calcu-lation results are shown in Figs. 20-41, in

which our attention is placed on the

hydro-UtnS

6

dynamic coefficients, the wave exciting forces and the motions for a box-type floating vese1 with

L/B=l.0

and B/d=5.0 in an oblique

sea x=750

The notations used in

these figures are as follows.

=/Bj2íj

A: wave length

k=2/A: wave number

Rydrodynarnic coefficient

Wave exciting orcc

Added macs

or Inertia Damping

Surge AXB

Sway A _Byl Fyi,

Heave L2 L2 F L2

)L2 + 132 Az1 _{)L2 + B2} 51L ZIK + --- F,+ --- F200

Roll _{E-J- B} M$L

JL

Pitch

i- /I3 +

132 (1-,) ) A MO-K -f l- F

3 ) 132 52

)12f

4

1j

_-J Js I' -;:;çi n Yaw AL + A BL + B1 M,L + M1113

-106 Ryuji SxATA. Yoshio YAM\GAMf. Hii-ohiOKAMOTO,Tetsuro IKEnuciti, Kiyoshi NEMA

Table 4 Estimation of hydrodynamic coefficients and wave exciting (orces by M.S.M.

Io Is s

.1-a

c, Ez, c:

The phase differences of surge,

heave and pitch, based on the time that the wave crest passes the origin, and the phase

lag is designated as positive.

Hyfrofynaiuic cocifìcieni

'__5n the hydrodynarnic coefficieufs, it is il-lustratccl in ChtpLer 6 that the values caic.u-]atcd by O.S.M. arc comparatively close to

tue values of the experiment and the

3-di-mentional source distribution method, but a

3-climeitsional effect is clearly oppered on the

virtual mass of heave. 'fhereforc, appropriate

modifications of 3-dimensional effect need to

be carried out on the term which

the 3-di-mensional effect is the more remarkable. For

exam.ples, on the virtual mass of heave, the

results of

the model test,

the O.S.M., 3-dimensional source distribution method and the M.s.M. are presented in Fig. 20.

It is

found that the calculation results, obtained

by simple modification of 3-dimensional effect

of the M.S.L, as shown in Table 4, are close

io the results of the experiment and the

3-dimensional source distribution method.

he eddy damping coefficients of roll are presented in Figs. 21 and 22. They are ob-tained by substracting the roll dampings of wave making from the total roll dampings.

It can be observed from Fig. 21 that the

2-dimensional eddy damping is larger than the

experimental value and that it matches the

experimental result fairly well when makes

the modification of 3-dimensional effect. Fig.

22 shows tue roll dan))i1lg of the same model

in a shallow water depth (II/d=l.88).

The

modification of shallow water effect with one

of the 3-dimeiisioial effect makes the fairly

well results as compared with the experimental

results.

it is thus found that the calculated

1J6.'O /S.O

Fig. 20 Virtual mass for heave

.o.

-,-\_--Fig. 21 Eddy damping moment for roll

Fig. 22 Eddy damping moment for roll

results of tuìe eddy dampings suggested in

Chapter 7-(4) show a close identity with the

experimental results. Further, as indicated in

Fig. 23, a fairly good agreement is obtained by

the addition of the eddy damping and tue

wave making damping, although -the

calcula-tion results of only tile 2-dimensional or the

3-dimensional dampings for wave making are different from experiment values.

XA? 4, ZA, ÇA, 04, çA: The amplitudes of

surge; sway, heave, roll, pitch and yaw.

Pv

LF-LO BId.5O

Hid 9h

The coordinate is taken on the right hand

system, and

the bow and the upward

directions arc designated as positive.

s n o Col Iol n 3-Dn'.

-Ç!!

_ktSJ.l

XA, YA, ZA,NA,MA,L4: The amplitudes of surging force, swaying force, heaving force,

rolling moment,

pitching moment, and

yawing moment.

-2

Mo p!.!yrP!

8.2 TVave exciting force

Both the experimental and the

theoretial

alculation results of the wave exciting forces

-

are presentcd in Figs. 24'29.

The wave

exciting forces are ti e values defined tue

O-point as center.

On the roiling moment in Fig. 24, the calcu-lation values by O.S.M. differ greatly from the

experimental values, and the difference

of

pitching moment in x= 15° from rolling

mo-mcnt in x=75 is also

observed, though both ought to coincide.

On the other hand, the

results of the 3-dimensional source

distribu-tion method and the

(llore, it is the

same as S.S.M.)

clearly coincide with the

cxprimental results.

On the

results by

O.S.M. in the Fig. 25 the pitching moments

similarly does not coincide with the others, while the results of the 3-dimensional source distribution method,

the M.S.M. and the

experimental show a

fair well agreement.

The same can be said about the yawing

mo-ment in Fig. 26, and the

values by O.S.M.

can not easily

approach zero asymptotically even when the becomes below 2.0. This

will subsequently cause the generation

of a

difference in motion, which will be mentioned later.

On the heaving forces in Fig. 27 the results

by O.S.M. show a slight difference from tjmc

others in the trend, and the results by S.S.?IE.

of the strict 2-dimensional strip method arc

showing, as a whole, a somewhat largervalue, because the 3-dimensional effect is not taken

Q Io o 179' lO 974' 50 Hsd.9. X ¡

Ít

Calos'OMd OSM.

/

/'

. _5..._.. '5 1.') Q'U. Q.lSh. .,,l.

Fig. 24 Amplitude of rolling moment

11857.0 814'S.O Htd.9. X. .7S L l27l.'OO I o--- _,._ .,-.--==o

Fig. 25 Arnpiitn':lc of pitch moment

Fig. 26 Amplitude of yawing moinetit

into account. However, the results of the

3-dimensional source distribution met h

od and

the M.S.M. match the experimental results very well. On the surgingand swaying forces

in the Figs. 28 and 29,

the experimental

f k -ç.. fr J

10-T

_n LÎ8l0 8/4.50 /d. L8 _N. g4!-'

aìi

Ls''

-O :5l?S ----1.LS,.t. 1 s A

Fig. 23 Damping moment for roll

103 Ryuji SAcATA, Yoshio YAJAGAMr,Fliroshi OK.MoTO, Tetsuro 1winucflf,

Niyoshi NEMA LIB''0 9Ij'SO t_0 Hld.9.o. -x

7

-

t 0.5 s o

-o

4

Fig. 27 Amplitude of heaving force

LIB'l.0 BId'5.O 815.94 E r1'rr' CatJC!S

-:

:R

A O

,-2 3 4

Fig. 28 Amplitude of surging force

O LIBI.O BSdSO lild9L % 75

-m.-LIB'l.O BIS S50 HId,9.L % 35 c C.C-,-.--A 0 2 3 4

b-Fig. 29 Amplitude of swaying force

Fig. 30 Amplitude of surging response

z' LI0 .0 BId 5.0 4 % ,Th t1u. 2 o

Fig. 31 Amplitu.:lc of svaving respoflsc

lO 5 LIB'1.0 BIS 9.0 814.9.4 % 75 I.5 O 3 L

Fig. 32 Amplitude of heaving response

results and the results of the three kinds

of jheoretical calculation al! nost coincide.

8.3 Motion of floating vessc/ Figs. 30-4-1,

where the motion

center is

The experimental results and the thcorcti- O-point.

-cal -calculation results of motion for tue box- On the surging response in Fig. 30, only the

type floating vessel in waves are presented in tendency of tlì

calculation result l.y 05M.

On the HydrodynamiC Forces Acting on Box-Type Vessels and Their Motions 109

2

(Th

6

o

i 2

3

10 5 3 2 1.5

Fig. 33 Amplitude of rolling response

rA

o 10 5 3 2 LS IO 5 3 2 i.5 2 3 IlBl.O Bld 5.0 Ht..5.4 75

- 3.Cn.

05M

j

M. o .53

Fig. 34 Amplitude of pitching response

Fig. 35 Amplitude of yawing response

E2 Ei S 0 i R ro 5. 3 1 1.5 Ecìnirrenj._J Cz :Coe CS'. Phase of surging response

Fig. 37 Phase of heaving respolse

3

Fig. 38 Phase of pitching response

LIS.I.0 SId SO

Uld,g.n % 75'

Tr:

!iii:

differs from the others, and the results of .the

experiments, the 3-dimensional source dist

ri-bution method and the M.S.M. match very

do coincide, but a difference is seen in the peak well. On the swaying response in Fig. 31, the value. The results of other three are in ci3e

tendency of the calculation results by O.S.M. agreement with each other.

On the heavn

-180 o ro Fig. 36 s 3 2 I 80

110 Ryuji S&KAT., YoshioYAMAG SMI, Hiroshi Ox..xoTo, Tetsuro IKEBLJCBI, Kiyoshi NELA

LIB I.0_Bld 5.0 ID f f i5 I X/I k5

2

I'

Hld.S.i % 7S 2 3

n

On the Hydrodynamic Forces Acting_{on Box-Type Vessels and Their Motions}

_iii

Fig. 40 Airìplitucle of heavingresponse

response in the Fig. 32, a peak is not _{seen in} the calculation

_{results by O.S.M., but the}

results of the other three have _peaks

respec-tiv î, _{and almost coincide v.-ith each}

other.

the rolling response in Fig. 33, the re-suits by OS.M., the same as the wave excit-ing forces, differ greatly from

_{those of the}

experiments. _{Furthermore, they also differ}

from the Pitching

response in the x= 150,

though both should by

_{nature be the same.}

On the results by O.S.M. _{the peak is not seen}

in the pitching

_{response, and the peak value} of the roll, in spite of the same eddy damping is used in the estimation as the other

theoreti-cal caicu!atjors is 1.5 times those

of the

expel-irnerits. _{Here, also the results of other}

three are quite in accord.

_{O;i the pitching}

response in the Fig. 34, the pak is not

ob-served in the results by O.S.M., showing _the

OE k3 2 Fig. 39 1 2 S\ \z

\\

CI

Amplitude of surging response

LIS' 1.0 BId 5.0 75' L.o,inI o 2 3 IO 5 3 LS A/I o I 2 3 tOS 3 2 LS . A/I

Fig. 41 Amplitude of pitchingresponse

difference from the experimental results, _while

the results of other three

are almost all in

accord. On the yawing 1.esponse in the _Fig.

35, the calculation results by O.S.1. show a

difference from those of the other three when

b is less than 2.0, and this shows _{a existence}

of yawing response even in a sufficiently long wave length conditions. _{This difference will} create a problem whìcii the box-type floatin vessel is moored and exposed in long _period

waves.

-Then we -efer to the phase

_{difference of}

motion. In mooring problems el aL, it is

noces-sai-y to accurately calculate the displacement

and the acceleration

_{at any points of the}

floating vesseh.

For this reason, the calculation ofeach phase

difference of motion becomes one of the most

important factors.

_{Some examples of the}

phase difference of motions are presented ¡1] Figs. 36-38.

_{¡n the phase difference, the}

tendency of the results by 0S.M. differs _from

the other too, while those of the three are

almost in accord.

On the motion of the

same floating vessel

in a shallow water depth

_{(HId= 1.88) the}

results of the experiments and _{the theoretical} calculations are Presented in _{Figs. 39-41.}

These show that the calculated _{results by the} O.S.M., the saroe _{as in a (heel) water depth,} do not Provide adequately accurate results in

a shallow vatcr depth. _{I lowever, it also}

shows that the results of

_{the 3-dimensional}

LID' 1.0 Bld. 5.0

I1,d.I.oq -X E. omm, ,m t C etC u'e t. C O II-i-. 25 -- 3.Dmn.

M.SM.

o

source distribution method and the M.S.M.

are

iñ close agreement with those of the

experiments.

9. Conclusion

Three types of model tests, namely, the

forced oscillation tests, the measurements of

wave exciting force and the motion tests

in waves, and calculations by the O.S.M.,

the M.S.M. and the 3-dimensional source

dis-tribution method were carried out, in order

to develop a practical and accurate method

to calculate the motions for 3-dimensional box-type floating vessels. An summarized

conclusion is given below.

When the

motions of

a bo-type

floating vessel with small LIB and large B/d are calculated, the required CPU time by the

O.S.M. is short, but the accuracy of the calcu-lation is not so good.

Almost all, hydrodynamic coefficients ami wave exciting forces, excepting roll damp-in terms, can be accurately calculated by the

3-dimensional source distribution method.

And the motions can be estimated with heigh

accuracy by taking the damping term into

accobut. The disadvantage, however, is in

the long CPU time, and its practical use is

questionable.

The Modified Strip Method with short. CPU time vas developed as a practical calcu-lation method.

By this M.S.\l., the CPU

time is appropriate and the result is suffici-ently accurate; The roll can be accurately

calculated by taking into account tile eddy

damping with time _{3-dimensional effect and}

the shallow water effect on the basis of the

experimental data. 10. Acknowledgement

Our I meartiest _{acknowledgement and} ap-preciation are extended to Prof. T. Matsuki and all concerned at the Kobe University of

Mercantile Marine, through their kind

coopera-tion and assistance.

112 _{Ryuji SAXArA, Yoshio YAMAGAMI, Iliroslii OAnoTo, Tctstiro IKEucdnr, Kiyoshi NEMA}

Rcfcrencs

I) _{H. J. MIGLIORE and P. PALO-.Analy sis of Barg}

Motion Using Strip and Three Diinensoia

Theories, OTC, Vol. 3, No. 3558. pp. 1765-177

April-May (1979)

H. Fujii and T. TAIAHASnI: 3kasurcrncnt

the Derivatives of Sway. Van- and Roll 1otir

by ti-io Forced Oscillation Technique, Jour. c

Soc. Naval Arch. of Japaji. \l. 130, pp. i31 HO, Deceinbar (1971), (in Japanese)

N. Muoi, R. SAldATA and Y. YAMAGAM!: C: the Analysis of Measured Output from Mc Test--À new Estimating Mcti:ocl cf ca Sine Periodic Wave Components Disturbed 5

Noise. Jour.

or Nansaj Soc. Naval .\r.:' Japan, No. 172. pp. 1-3. March (1979), (in Jara

nesc)

i -1). T. Trecucrmi: \Vavc Induced Forced and M

j tians in Shal1ov \Vater, Jo':r. of Nansai S

Naval Arch. Japan. No. 161, pp. 77-37, Ju.:

-. (1976), (in Japanese)

5 T. Iji:.i, Y. T.nucimr and Y. YuMURA: Scat -J tering of Surface \Vaves and the Mutionìs of

Rectanti1ar Body by \Vavcs in Finite Wa' n Depth, Proc. of Japan Soc. Civil Eng., No 2 d

pp. 33-43, June (1972). (in Japanese)

0. M. FALTINSEN and F. C. SlicuaLsEN:

Mo-tions of Large Structures in Waves at Zro

Froude Number, International Svrnposin

the Dynamics of Marine Vhj1cs and Str

irr Waves, pp. 91-106, ApriI (1974)

S. M. Ti-aam, K. S.iTo r.

Gizze; l-[vdrodynamnic P1Cssures on a -.

strained Ship in Oblique Waves, Jour. cf S:

Naval Arch. of Japan, No. 133. pp. 85-100, J:i

(1973). (in Japancsc)

N: SALVaSEN, E. o. Tecx anti O. M. FALTINSE

Ship Motions and Sea Load, TSNAME, Vol. .

(1970)

S. YAMAS1ErTA anti T. I(A'rAclmsl: The Rcsaa'

of a Systematic Series of Tests on flo1iin 5Ioaa

of a Box-Shaped Floating Structure of Shal!.j7

Draft, Trans. of \\Test_Japaa Soc. Naval .-\rc.., No. 60, pp. 77-86, Aug. (1980) (in Japanese)

.C. C. Mar and J. L. BLACK; Scattering ei Surface \Vaves by Rectan3ular Obstacles in Vater of Finite Depth, J. Fluid Mccli. Vol. 3.

499-511 (1969)

J. I.. hass and A. M. O. SniTir: Calculation . f

Non-Lifting l'otential Flow about .rLe:ratY Three-Dirmicirsional Bodies, J. Ship iResearcC Vol. 8 No. 2, September, (1964)