A study on ship hydrodynamic forces in restricted water

I. INTRUIJUCTION

Willi t lie ut rease of sit i p size, some waterways oli cit once were coils idered uttlionitld

are now comparai ive iv shal low aitd'or narrow waterways. Tlii, iiiire,ase in ship size hits

iirouyht certain li ffiu:ui ty it uanettveriit ships, and s ¡ nu it atte oils i y put fo rwa rd a sto re important questititi il tile research of ship inaneuverabi iily he fore us.

To iuilv ship irtaueuverahi i ty in

restricted water, titi'

ittvestijiiliun into

uy-iroilytiamic forces act itij oit sui ii is otte of tite most import atti pro) iemt.The sore reti titi le way

to ileterirtirte tite itydroilyttatni u forces is to cotiduc t t lie niode i t es t. Fttj jito si ui i ed epe r unen la t iy tite hyiroilyttami e forces au t i ttj on ships nioviitti lit slitti tow water nrtd slitti iow citatntei by PMM test atti obi iqtte tow test [1). J n tite f i ciii of t iteore ti ca i cal cui a t i otis, si etnici body t licor)' atti i ow aspect -ra Ito witty titeory are oft ett use-il. Etiwa it roposeti a tite -oret icat model [2). 11e usciI tite ilotibte monte i

and assumed litai the ship toiler consiilerat iwt is steirde.r.11e aiso tisstttned iltat tite separate-ti free von ex sheet shed f rotti the hi t ye of tite sitip. hJtiui.ittq tite strip uutliwl, lite hytlrodynatttic talerai forces, litai is to say, sway forre tutti yaw ntotni'iit ai t ini ott tite ship travel iitq in a iii red iott iii: tjitcd _{to tite} loti rj i t iii i ta i ttx is were rai u ti i a teil by app i y i

A STtIIIV ON StilE

lIVltRUi)VNAMIC FORCES IN RESTRICTED WATER

mmff

Mimulweg 2,2628 CD Deift Td.O15-1eue?. Fax: 015.781838

tite law of f lu is,i motneit t tust. In stich k i titi of ca Ici-t Ial i on stole i, lite \'ari at i oit of tite ship foist atid tite separat ion tif tite botittdítiy layer cati be t ítkett ¡nti cous itie ra t i ott.

Three-dietensuoniti effects are iniportattt in shai tow water tite-re is a tendeticy for

lite fiuid

t o ft. utw sr ittt,td t lie tinily ettil s rat ftc r titani tinti er t lie h oily. A t itree-il i titu'ns i tutta t lese r¡iiii oit of tite luit. etttihies tite ititeractioitttffectslietweett titi' van i Outs sei ti (litS Of t ht' liii ii attil t lie etui

effects tu lie su i t uil iv treat t'i.

Tite hottndary e iemeit t nie thud is ti power fi-t i calcuilatioit method fuir solving tite pittetutiai fi ow itituti t arti i tra rs' litt ce - d¡ ntetts i i_tutu i h oil i es, So in this titille r t te h oittiit ¿t ty e i erneut t

me ihitd is usen! to i nves ligate t lie lift i tty

Pot eut lia i ft ow auioit t t tree-il intens i otta i sit ips i ti res t r i i; teil wit t er.

2 MATHEMATICAL MODEL ANtI CALCULATION PRINCIPLE 2. i BASIC ASSUMPTIONS

To caicttitite tite Itydrodyna'ntuc fonces acting oit tite sitip, fusI, tite assttitiitt iotts Listel hetow are niatie:

Tite fiutiii is ide-ai atti itucompressibie,

nutti tite mass forre is tueg 1cc lei.

Tite fiuiil moti oui is i moitit i onai atid

s t e ady.

i i i ) Tite Froutihe ututinher ¡ s re tali ve i)' small Zltetiçj Calli, Wttliait tittiversi ly of ttter Trautsportat ¡oit Enyineeritty Cit itia

Zittity X ¡ t'ti litt J Wuhan titi j ve rs it y of Wit ter Transpon tat ion Entijineening

[lutti

Wu Xiuitettg ?liiiiatt tittiversi ty of Water Trttnspot litt i tin Etty i neeri iij Cit i ita

¿iioiiiJ (ìuopilitJ ttittitatt Uit j vers i t)' of Water Trattsportat jott Eitijineerittij China

ABSTRACT

lJsittij hic huittilary eiemttit tnethiol, titis paper offers a method for caicutauiny tite

tilt itty potent ial flow auottt titree-dumertsioitai ships ntovung oIiiqueiy in confirteth waterways. Iti ottici to teprcsettt tite suai tow water effet: t, titi' yroitttiiiitrj eilen I ne fiuti and tite tttetitod uf ititaes iii-e tiseui. 'rute latter is extended to luciole tite _{sitiiiiuw chinutitei case.}

Frost the ctuniparisotl. tite tlteorelivai uaicuiation tesitits of titis patter tire

iii

sali-.fatory nijreetitcttt with tite existing experitnetttai resitits, attil closer to the expert-nieitittl lutti ilittit those (if sonic other tlteotetical ttiproacites.

'lite tjrottnd 'trig effect tutethod is sui titille for lintit regtultir Stil i rregti [tir hot tout shtnpes uf situ 110w ou t e rways so in (lii s sense it is more rea i i suc litait tite niet hod of i mages.

anti tite free surface is approximately considered as a rigid wall. For a ship moving i n sEa I ow wate r, titi' Ito t torn of witi eli i s

parallel to the free surface, titis assumption

results iii an equivalent _{problem involving}

tite _{flow pas t} a submerged double-body between

two parallel rigid walls

willi a distance of

double water hep 1h, as shown in figure 1.

Figure 1. Coordinate system attui flow model

iv) Tite separat ion I jite from ahi i-h the

separated vortex sheet sited is assumed to

he located

_{itt bilge keet.Tite surface of tite}

vortex

sheet is

assumed to ite

_infinitively

tiun and roll ed-up anti to lie a stream sur face,

across which the

_velocity

_{potent Ial} tiiscont¡nues auth _jmaps hut tite normal

velocity continues.

2.2 GOVERNING EQUATION

Arcorri i ng to tite pot en tini theory atti

from the as stimp t i otis listed nuove, one can

set up tite fol lowi ng govern i ng equat ioit aitd

boundary coud i li otis. Tite disturbance ve Ioc ity

potential must satisfy Laplace equation

[L] 2ttO (2 I)

and boundary coud i lions:

Body itotintiary cotti it ion

[B]

iiîonB

₍₂₂₎

Wall boundary conditi on

[W]

V.iro

on (2 3)

Free vortex layer condition

[F]

PP

w:nx (V1 -V ,i oit 1' (2 . 4)

Conii t i on at infinity

[.oj Vo

at ₍₂ 5)

y) End coud iIi on [K]

For a sii ¡p wit i cit is r nap lic al. ott in form

i t is oit able to get

titi' exact sottili

on tso titi'

metitoti of _{fitti te etemetttarv sotol iou is uscii}

here to yet

tite numerical sotutioit.

2. 3 THE CALCULATION UF TUE I NOUFFII VELOCITY AND IiVI)ROIYtNAM I C FORCES

To so Ive lite po t en il flow aboit t titi'

sit i p iii sitti liow water, lite key poi il is lo

re a lize lite wail hotniti a ry _{e otiti i ti on} (2 3),

lita t i s fl-l1. Titi' re a ri' Iwo ways to reti 117e;

orle is to

distribute

singularities

oit litt

bot nul of

tite waterway (lite so-cal lei'

_grouliliitg

e Ifet; t me tuoi ' ) lite o liter is t lie ute thou _of

i niriges.

(i) Tite grtittttuiiituj effect tite hoi

If w aol c represent tite body sit r face.

lo lt 0m _{wall of} the tea lerway attui free vo rt ex

layer rrspeitivesety,

atti if

ii is

lite exterior

tutti t ittirtutat vertor 0111 nf lite univ surface, tipper and lower wal Is anti lite free vortex laver

(uit0 lite

fittiui) titus y Greeit

t lien r Pm, litt' gv ici tI simIoI i oit s im ti fyitig

erittat iou (2 i) can he expressed as the

fol I owintj JJsB( ° _oP / )Is

--

_{r(p,f) ori r(p,g)} I ô 1 an r(p,g) on

¡JI

(O

' /

1-4ut _{an rip,g) a,?} (2.6)

r

itt rtjita ti oit qi veti tituve, i f we ilniose

- _{attui p i- ( ì}

_{-ii )}

an

lie fo Ilmvi mig _{e tilia}Iitilt I Ill Ir tilt lai mieti

rl--_JJ

ana _r(p,q)4. [Is

t

í( a

471 ît Y(PM

(2.7)

wite t e p attui ti uti' liii' s I r ettuj I its tif _{I lue}

s it fat e uli1itili' titi mutt tte re spi' I i t'i, p i

is tite slremi'jllt of lit'' fire vortex.

TItus, i I foIl itws I litt I litt' Iuotiv s tiritiro,

tite wail surface attui liii'

free vortex laver

cítti lit' exp resseui uy list riiuuil hug sottrces iitks nutui ti ipoIrs oit Iitrtrt.

ii) Tite nu'(itoti tIf mliii'.

o rl ittij lu Iiii' primi ittle tif i lita it'S,

lite f I tua fie Il tiuruti t I lit' lui it 11111V 1I itt

5itn Il ow au let w ¡lit i P1l lit ii i . t'gli ¡ Vim I ett t to

lita I rittiSeul

lv lite

citi lt _{imiti i}

tii i utile i lIti EJes

of litt' ship WI 1h respect Io litt'

free surface

ami tite Ito lt runt tif titi' stia t low wit terway. Si mil av ty, aliti I y i tu t lue flreen I lico rent q i ves

t he exp lessi titi tif lite ve ttir it y ¡tut eut lia t of

equations (2 '

i)--(2 '

a i

'

)ds r ru'p4) _r'p.g) ¿s dt

-

_{i C fJ(1i}

;j y'(p.i') 41L /'1--' /,14. O + (J-

)d+Jji._

' (2. 1) Fu3/7

where r'(p,q') denotes lite distance between lite image. poi n t

q' of the source point q (X0,

y, z0) and the field point

p (x,y,z) ,

its

expression is

r' (p, q')

L (x0>) 2

(YoY) 2 (z0+Zmil-z) 1/2

where

«, -i,

_{i, «,}

--Calco tat ion of tite iudced velocity

No mat ter whi ch one is used, the ground inj

effect

method or the method of images, tite

induced velocity potent ial can le regardel

as

a

combination of three parts - tite velocity

poteii t ial 4 _{i tiduced by surface sources,} tite

ve toc it V O t en lint 4 i nil nc eu i'v sur fac e

di Poles atti tite ve toc i ty po ten li a t r

induced by free vortices,

that is

(29)

Suits Ii litt ¡ng equation (2 9) into equaL i oui

(2

2) yields

11

(V

+V 4 V4 tiF) V;

1f field point p

is located un

tite ship

sturface,

from the expression of the velocity

induced hy tite surface sources, otte can gel

tite following eqtuation:

(V«+F)flVS-fl

- T/2

grounding effect method

+5

ii.

=

-\J -

17/2 method of iwages

_/1:__Jf5O5)[3(pq)115

Mt

-In eqitaliout (2 ii)) at L tite surface

integrals are to be interpreted

itt the sense

of principal value.

Herein let

-V0 (2 ₁₁₎

3n

Tints

for known a, equal ion (2

10) can lie solved.

Obviously

tite solution

of equation

(2 10) is ito t tutti que. To qe t lite titi i qiuc so lut i on, an nil i ti eon I cotti iti on getteraI ly

known as tite fu1 la couru t ion sitoutl'l be added. For tite cottt inni ty of lite

'ort icily,

tite

following formuLa lait be uscii:

(2 12) itere .0 + and t- detto te tite s t reng lits of

the surface dipoles at tipper

aiuti lower ¡tarIs

of tite bi Ige Line, respectively. Equal ion

(212) is equivalent to the Kuttia cottulitioti

imposed at

lite trailing eulge of

tite

foil

itt

wing theory.

From equal ions (2

_{ilJ)( 2}

12), p attui

r rait lue solveui fur liteimutre, lite Ittuhtrrui

vetority V at any point of the sitip surface

can be obtained.

Calculation of hytirodynantic forces

and itydrodyutamit ulerivatives

if T is

tue tutti t vector Initijeitt to lite

siti1, surface, hunt Ihn velutti y latiuju'utl tite sui sut fat nk1j veut liv

V1 :

(VV)

_{(2 13)}

Applying hlernotil Ii's equal iou lite

j st i jlitt li oit of lIte _{ulytuanii r} pressure _{Ott lue} sitiju surface cati lie oli taiuieui.

V

(2 14)

Ber nuise lite prs sti re I

j tri t.

j tilo lui'

luuuuiv. tite sway fturr attui 'aw uuutnncui I 'att lie

cii t'uil nl cui uy us i tug I lie fut Il tiwi ttg express i Otis. Fy: -.1

1a u l'i

M%:-_{.r .r} ( itvPÂ tu. l'y) i s _{(2 15)}

Duur i ttij niatueutve t i tug nuoti oit, tite luvuirouivttaniiu: forres ari itug ott lite ship runt

lue e.ji re s seul y Ta',Inr n..1' ait s i titis tuf I lu u

ntol ¡utu nuit! u oitlrui huuuiatnrlu'is utiuuuutl tite

iutiliat

equuiiihiriuuuti ,outulitiout of

_sltaitiltl

alun ai titoli out al r otts laut I

_fIerI.

11 (tut jv lite oit li gite moti oit i s u ini eu tini liete. I lieti lite

sway futre aiuti lii,' yaw ,tuuuuuiruih ail te

iii y uy _{(itt g i et Ii tig lut li j te u ut 'I e r I (ints)} Vmvv

N.N0v (2 Iii)

If

lIte

hifI

atugle is . lhucu lite

uuott-i]inuctusi outa I hvult o,lvuiatttir deriva I IVeS rail

(2.10) lu exprt'sst'ui l'y

p

N

N' _{(2 17)}

p VL ¡

: .NIINERAC 1h, REThi.T ,\Nil 1)1 1l t ON

3. h NIINER i i;A i. NETI1U1I

While applying tite qrotttitiiiug

effert

tite litnil Io ra luit Ial e lite hiyd r utdvttani ir forres

a1I itug oui lite siti1i. lun iuoiututinry cleiutent mntiittl di si:riiiu'ui altuuvc attuI

lIte tiiscrel izl ion

licor) air

urii Fi is 11v, I ut' .ii i u

sit tinte is

divi the'] iii lu iitui le ci r'unr'ti Is, i lieti eqtt ist retug ii

surface sotirres attui _{ti ¡potes are iHst riititteul}

nut carli el enicuil lite pujuti .1 retitlllt stur fare

dipoles

air

equtivalniul lui a vtirlex ritti).

Vortex

ritigs aie

ti i:'lui liberi tun lite free

Vortex layer as wnl I .î' rn1ui nsi'ttl lIte suaI low

waler effeul,

hue rnrlhiuuil tuf _{iiistriitutlitiq}

s ¡ tigui tari lies oit litt' hut II tint tif lite uva le cuva)'

is tiseti.

Ile re iii sont" si uuu1u li f i tali 'n. aie tuai n liii ra liii lati ritt niouie I. lite sit

p su t laie is

iii vi rieti

tilo t riatiuluilar rInniruils uil i,uulit ruitis nutri p lauta t qn ari r i i a lernt uil euuiu'ut Is uil h lue renta i utile t.

Neglecting

_{the rolling-up, the separated}

_vortex

sheet s are replaced by the. horseshoe vort i ces. Tite

separai ion line is _{assumed to be approximately}

tinder the center _{keel with a distance li.}

shown in figure 2, 11:0.g5D (li-d_{rnttjii t).}

Figure 2. Simplified model of

tite separated vortex

After diseretization, we assume that

there are 2N elements on the surface of

t he double-body arid 2M e ieniett is on i he walls

including tite upper wall and lite _{lower watt).}

Bec alise of _{tite symmetry of}

tite buh I e-hody

and wal[s of tite wat erway willi _{respec t io}

tite

free surface,

ori by ita If of lite e temetti s

should he _cnnsi'ie.red irr tite _titmericat

calculation, that isMNeienents. if there

are K horseshoe vortices, lite

total nunber

of

tite equat uns is _{M+NK. Tite express i}

_{on of tite}

velocity induced by tite surface

_{sources is}

given by NI-M

>

(JIsJ[ds)

JI

iiI, 2,». NM (3._I)

wite re and , derrol e lite vectors o f _tite

source point j

attui i is _{image point}

j'

_to

tite

field pout t i respective [y, S _is

_{tite area of}

tite _jtir element.

Tite last equation _{can be expressed by}

A;

a

_{(3 2)}

j

:i

where ÄT is tite

_{infliteirce coefficient of}

_lite

surface sources.

4I(p

t

/3

)ds (itj)

ti

Tite st reug th of tite _{stir face. sources} (7

cati lie deterinitted by

a:- V0

(izi, 2.

.,NiM) _{(3 . 3)}

1f D, _{dettotes tite veloci Iv al i 1h control}

point ittilmiced by vortex ring wi_lit titi t strength at j tir element attui _{i Is image. il,, derrotes tite}

ve toc i t) at ilit cotti roi paint _{i urhuced by t he} horseshoe vortex willi tritit strettglit at _{j lit}

element arid its image, and i f we irrt rodtrce

(j:i, ..NiM)

C1: _{< .._}

(3 4) ii,, _{(j-NuMul,...,NIMIK)}

i:[, 2.»,

N4M.

licti from eqtat iou (2

ill)

it

r.

'.5.

CN,M. I CJt.Nf114

wiirte, B:-V

NuM

A:

_j:j

Au.n

_il,.,NuM

Front these I irtear equal i otis attui K aid it i ott al e qui ali ntis, p aiutI p r r n t

hie sol veti, atti li Put the i itiit'euh ve Ini-i lv \', j' r e s s it re 'hi st i lii _{Ii turi C,.,, I lic [1)11 i'uuiiyttauti ir} ile ii va ti ve s V ami N. r ut lu'. muli I a i tie1,

The calritIn li riti ji t i iii' i1 le fur liti' Ui tiro!

of images is itearlv

tite _{sanie, Except hat iviti je}

i'alctrlalittrj tite _{iiufluretuu'e eoeffii'irttls. we nutrst} t aLe tite itif i utpitreS nl i nages mvi lit

ru'spri' t to Ilie free stir fare anti _{lie io lt}

orn nf ihre waterway

all

oge tirer i itt o au i jotti

3. 2 MIMERi CAl. RESULTS ,\NbI Iiisi:uSS ¡ON

hhem'eiti, ajuiu lyitug liii' jr'ututmtiiimrrl effet: t

tute. tito! attui _{tite tu, i iiid of itliuqt's,}

tire h\'iit'iiuivttanii r fini p', tutu ttuuitiiu'uu I'. _{ail itiuj uni}

',itip. ntuuvimui 'nul rituel: al iii lfi'.rettl t'ali'.

ibujutirs _{life r-aluna} n'il _{(iii' '.i;ii iiuvr type}

_.ltit,

Tokyo Mn rut . _{Es so Osnba ' atti 'Series}

III

ti ve I y. l'lu' iii itri,i ¡un I iii tiros i orts _ruf

i unu

air' q ¡cet iii

tali'

h lite i alirtlat ion t'e.tr Ii.

ami' i _{unit u r' uil ' i 1h ih titi j}

rn's irI I s

oli laitupuf

_k'

_{expen'inti'tt Is oui}

smite oilier

liten-el ial

flppt'uraí lue. _{FnirIltriuiure, wi lb}

I lie alu cuí I lie nue lit uuul n f i niagr' s, liii' Iiieot'eliu;tl nin'tinu_iih cui Iiui _uaju.n' ¡s e,.Iruuulu'ul

lu i tu' luI e nui m'e r ritiuju le,., u u. e rif lu a llaiu

i btaituue I. liti' _{btvrlrouivuanui i ftit'i'es anti}

nituniettt

ai-tiri j tutu .it ips nov in_{j iu li grue t y al uil f fc reti I}

tua im' r ti cpb a tui il i fir t t'ui _{'hi nitric I ululi lus ame}

ca li-uil al erl fo t' ' la ririet' ' I \'1u e i it i p _attui

Tukyo Mitn' , nui r utinpa t cil wi lii _{line ex} si¡ng

exlteriunetrlal resirlls u. well,

TABI.E i

['r i tic pat iii nterts i omis of ca luit lati oit _{olij ec t s}

/

lt I

fol tows litai it-A1

(3. 5)

Mariner _{Tokyo Martr Esso Osaka}

Series 60

I.(nia) 2. 50!) 2. 111111 _{7.660 6, 096}

B(mm) 359.8 127.6 _{1,180 812,8}

I) uitm) _{lit,il Il II. 3}

1911.11 _{325. i}

Cri J 5flij _{0.8II (1.830}

0.6110 Jt NiM

p I

i,t r'r,ui,u B,M-API.F

Yv,i/ Y5..,

Y,j Y,.,

cxpnrbient [ti

uett,od of tinges

'' '-grounilhng effect tiethauh

1.5 ¿hl 2' hhi D D _{liess 171} i tnou [61 A Neuman IS] Nun [4] lIuto 3] S '-,_ 5 .5 '¿.0 2.5 Iii D

Figure 4. Tokyo Muru1 shat low water

effect

on derivalives Y5 and N5

Tite il i f fe reutce lue tween tite resti L t s o f I lie

il roittil i tig e f fec t nie I lttuii attui t lue resti ti s of t lue

inelluoti of ititages i s Sitial I as shiowut in f igtires nuit tables tjiveui tuiuove, Most of tite 'atuues of

\','

aun! N5' catcutated by both miethouls are slitti t t e r tiutntt t lie expe r inico I va t ucs. Bit I itt

extremely sitathow waler case, tite grouttutitutj

effect unelitoul gives tile

resuults closer to

lite exper ¡meut I a I vtu tites.

( i i ) CalculaI iou resiulls of tIte hvulrouis'ttttnui t forces itt situ how chatine t atttt

t lie i r rotitp nr i suit, willi lite expe ri meut lint restI its Ilerciut, lite tiit'Iltout

of images is used to

cut It-tul ti te tite !uyii roulyitttnii t: forres tic t Log on ships uutuvintj oli ii qtuety itt altaI how cittiuiuuet. Tite exlteriusett(aI data uscii for coittjtarisott are qtuol cii f root re fereitce [1] as wet t,

TaSte 6 outil titIle 7 give tite calcuttatiout

restii Is of tite iuvilrouiyutatni c tier ¡sot ives

V5' lttuui N5' tuf 'Mati tier' attui 'Tokyo bitt rut'

tul ui i f feu'e,t I wit Icr dcii t its tittul citatuuie t w i d lits, for conijiarisout, tite exlter.inteuutat resuLts tire

also given,

Fiijiire g attui finjuure 6 show tite curves of Yvjtw - Yvaaa attui Nana Nycc against tite

retal ive clitiutttet with 1h L-B (V-ciiatttiet wud lit, B-I retid lu of lite sil ¡p) for I liese two

slti1ts al reittt ive wtuter uleitllt hi Dai. 3

attui I. 2 respeu: t i ve (y ( H-water dep lit, lb uhritutujitt

of lite ship).

Frost these ligutres nuit tables, il

is clear

for a alti p unos i ng iii sito (tow cit aune I w i t It s atoe wtilei uieplht, ï/ ami N5' iiuucrease Wi lit lite

ilerrease of hie

t:htttitute( wiuitit, especialLy itt

e.tr'uiieLy shallow waler.

Froto lite lottuparisoit, tite ututcutat iOfl

resti Its are ini good auj reenteut t w i lit lite epe il lieti lit h I a Itt.

s. Ixperiniclit ill

1. _\\" - - - flic huit tu f _iinajes

3.

\\

_{- ji OStili} Iilj e f fcc t i' t 2. 4 I. I. (t _{.5 2.11} ¿ n hiess fl ¡hi N5i N5.., 6. t huuiuue [61 Ncwinau SI 5 K,utu _li 4. 15,%,, j j i 3. 2. _t

*

-.=--t 5 2.11 ¿'SIC! Ii

Figure 3. Mariner type ship: shallow water

effect on derivatives Y5 attui N5

(i)

Ca Icu lati ott resu lt s t) f t lie hyd

roulyna-sic forces

itt sinnt tow water titi] titei r uom1ttuison

w i hit I lie cxiii r i tue ut u t ri s i t I

Ca ti- ut tu ti oit re s tif Is fo t' 'Ma ritter' anti Tokio Ma rit' tire t i s t el i ti t titi t e i tinti t ib te 3

respectively. Tite experinietittit

results

cottiiticted by Fitj mo [i] atti lite restiI Is of

s (eitler holy (lietiry rata ta

lei! by '¿bao [1] are

ijiven itt tite sattie tables for cotti1ittrisoit. Figure 'J atti fiijttre .1 show the curves of

cat cut at ed tutu exp eri nett (at re sii I Is of Ye Y5:0 ajiti for these Iwo ships. Tite resti Its

catcu'tateui uy Kaut _[1] . Newniait _[g] . lottie [6]

liess [7] tini 7h so ti re s Itowu itt tite se

fi tjttres as we lt for t-ottipttri soti,

TaIt te .1 attuI I alu te g i ve tite ca Icit tali oit

resttl ta fur 'Esso Osttka' attil

'Series

tjU'

tite correstottiiing experitttettltil resut Is are

quoted frost refereutces [Il] tutu ]tj[

As showti lit tab t e 2 tinI t ab t e 3, os t of

tite t- tilt; tu tali litt re s nil s j i Veli uy liii ti seit I

pin1r are closer (o

(he exjterittiviital values

litait litose given by referetuue [3], esiteritti h)'

for Y' va tites itt e. t retut' ty aliti 110w Wit te r. Il

is r t cttr t ita t I lii' resti Its ca t i ni, ti I cui uy Zitao

are loo staat I.

F i unti f i gti te 3 attuI fi Il tire 1. nios t of tite

u a I i-lt t a I i ttit tes ti I I s it f Y vii.' a ut,1 N511 / N5«5

g i vett y lires eti I tui' I tul a re t us er to tite

experititettliul resulta litait Ihtuisu theoretical (y

&-aututttIih uy Knit. Ncnsiitit, ittoite. liess atol Zltao, Also fiotti hauute atiul figures

g i veti ahoye, i t fti 1h ows t litt I tite cat rit lati oit

results

ujivett by itresetit palier tire 'lose to

t lie exp" ti nett tti h '(alti iii h ott h y litt h lie lute

ship forttta itut titstj for tite luth I sitip fouttti,

7.

6.

Time experimental resut ts cor respond to the Fronde imonter F.:ij. 09115.

TABLE 3

ilvdrouhvnami r 1er iva ti ves for Tokvo Mamit ' in sia i tow on t er

2.5 1.119 1.5 ¡.2.1 211.0 21.0 25.9 30. 77. I 13.7 iIi.Ii 21.5 ¿9.1 51.5 11.5 11.3 21.9 32.2 17.3 11.4 17.1) 211.11 211.5

it.:t

5.1)3 7.78

Ii.)

15.0 21.9 5. IR 5.70 0.39 lU. 4 !J.0 4. 15 5. lilt 0.95 12.1' 23.2 5.51 (i. 51) 1. (Ill 111.5 1(1.2

Tite experinteitta L resti t ts correspond to tite Froutle niunher fr:tI. 0675

For 11. tite experiment at result s rorresporlul I n tite Froinle uttirmIc,

Fr:O. 071!. For i!,IJ!. 5 antI ilD1. 2. tIte _{experiniciltilt jesuits corre.puuuul} lui

the Fronde. numluer F:0. 0138.

TABLE 5

1ivuiriyuamic derivatives for 'series 10'

itt sua! tow waler

Tite experiineitlat resol Is iorri'spotmi] _{to tite Froumie ,tiuml,nr F,fl. I 2.}

11,11

-Y

/ 10)

from experiniciut

fron' tite groutnulitug effect metitod from lie metitori of images

from Zhtao's catculatiot

X IIJ )

from experimetut

from lite groutitil ing. effect me hou from tite me tuoi of i nages

from Zitao's catculntiott

11,0 11.01) 13. fun 9.61 2.5 15.1)1) 11.115 ¡1.82 2.0 25,111) 11.25 211.119 1.5 115.1111 ¿II, ¡2 III. Il) 13. III 12.111 12.111 1.2 SlIttO 75, ¡9 60.32 19.1111 l'i. 1111 11.71 -Y

X i0)

from experiunemit

from tite groutni ing e fferl front tite. nie tito! of images

melito'!

X 1O) front experinucittfrom lite grouu,mulitty effect from tite method tuf ituua'Jes

metituui 5.10 5.23 i 1.51 7.21) 7.1111 1.59 8.111 8. Ii 9.tIli TABLE 2

i[vdrodvtianir

derivatives

for 'Mariner' in shalLow water

11,-D _{2.5 ¡.93 ¡.5 1.21}

from expe.riniettt _{1.10 15.1)1) 18.711} 211.01) 91,. 911

iU)

from tite grounding effect n'climi Ill. ii 12. II 15.27

_ii.

I '10 _12.79

from the method of images ii. 711 12. '10 11. II 25. 70 _{55. lull}

from Zi,ao's calcitlatioti 9.107 Ii. f9 13.31 17.76 27.13

front experiment _{3.53 .1.52 1.25 11. (i7 12.50}

-N ( X 10) from t lie g mutti i ng e f fec t nie hort 3.22 I. ¡2 .1. 115 ('.61

IlS?

fron' time ne titod of _inniges

from Zliao' s ratc,tiat io,! 3.31,_3.77 1.1121. 10 5.6.) q. Is 7. I?

i 3. í,ti II. ¡2

TABLE .1

liydrodynantic derivatives for 'Esso Osaka' iii shallow water

ii/li _{1.5 1.2}

from experiment 211. 19 I?. 95 126. 911

Y( >iU)

front I ito _{groniuti jig el 1cc t mel hod ¡3.113 11.19 111.116}

from tite method of images ¡4.85 13. IO 1lJ. 7(1

from experiment 7.81 21.111 .1'). 75

-N

X ¡0)

front tite (jrottiiIinj effect method 5.01 IS. 24 12.12

The e:\perilnentat restiE Es torresputil to the FrutiJe minitier F.:0. 0675

lite e.periiuviital results íürrespoiitl to the Froude ituetirer F:0.

11905

TABLE 7

lfvili'udviiaiiiiu derivai ives for Tukyo Main' iii shal low i iiJriiiiei

Figure 5. Mariner type ship,

finite width effect

_{Figure 6. Tokyo Maru}

_{finite width effect}

oit derivatives Yv and N (11/0:1.3) _{on derivai ives Y and Nv (1L'0I. 2)}

It'll ¡.2 1.5 1.9

N-B _{6.12 1.59 3.136 6.12 4.59 3.06 6.12 .1.59 3.06}

¡0)

u epiitoftut

70 1 91 7 112 6 12 ¿ 16 6 19 6 29 ¿ ¿9 6 ¿9 5

froui caluttlatiun 31.5 911.7 100.6 31.6 36.2 -10.1 26.1 27.6 311.9

N,( -

Ill')

frout e:.pet iiiiit 2)11 33.8 48.1

tl.:t

Itt.? 20.1. 11.8 12.6 12.9

frout (a1i.ulttiOit 12.3 3-1.2 39.8 13.7 11.5 16.5 9.70 10.2 11.7 2.2 LO

.4

1.0 2.0 L 6 1.2 0.8 YvI(wI Yv.

\

\

N N

N

2.0 1.6 1.2 0.8 2.0 1.6 1.2 0. YVHW/

N

N

experiment calculai ion [1] experiment Ii)

----calculaI ion

-N1/

2. 3. 4. 5. 6. Wi B I 2

N/ N

i

\

_N 3. i

4.

. L W1B 2. 3 _{1. 5.} 6. Wiß 8

3.

_4.

5

6

tlyilrohiiairii TAIlLE derivai ives 114) L fur 'Mariner 1.3

iii shat low channel

LS 1.9

5.56 4.17 2.78 5.56 4.17 2.78 5.56 4.17 2.78

l[i)

fr(Jill expe ri nie itt 57.0 73.7 91.7 _II). I 35.6 -11.6 ¿0.3 21.8 23.2

fi nit t ¡r linEal i _{14.5 -18.2 511. L 20.9 31.1 38.0 18.? 20.1 25.6}

1U) f i-nit e.\I) i IIiliCti t 2.5 11.2 IO. 1 _{0.50 9.91 12. I 5.88 6. 67 7. 21}

CONCLUSIONS

From

lie discLsiolI iii the ire'ius section,

the fol towiiifJ coTtc1usi()II an l'e Ijawn.

1. For the SIIilItU\V watur ase, tilL' resuLts

ca I Cu L & t ed

I'

t lie roiititt i uj e f fec t we t tod aie : lose to t Ituse ca t sii t a cil li) t lii' ni I toil

of ittiayes. Altlrotirjit tite CI>U titile of tite jroitdirty effeet melito'! is Loityer titan

llttt of

the utetliod of intayes, tue yroitttii ¡ny effect me t hoi i 5511 t íd e foi. Io t t _{re y ti a r} arid

i rretju lar iotliotit titi liattk sirajtes of tite waterways; so irr titis sense,

il

is itore real i s ti e. In ai: t tít I i a letta t _{on i t} ran [re uscii

to reitlare tite method of iruirijes.

¿ . Front t lie ronrtpar i sont w i lit t lie ep eii riít'it lit! r e stilt s atid

lit

t irrte ri tít t res tilts taicuitticii uy _{/.hai). NeOn} nl _al., it slintulil ite ttoleii titat tite rturnerirrl restiI is of tite Icil roiiyriaitr je le r i Vt ti ves of sii ips titov i uy

till! i titre I s' i it sita Il ow wit t e r 'a li: trial el! liv tire t heore li r:a i noie t di si ri ieri in p resert I ¡ti1te r are iii sa lis fac tury ítij rechten t w i tir tite exper iirtett ta t Vit lires. No t only t lic j tonni i ny effect ittlitoil litti írtsu the method of Ìtflít9?S

can offer the utitrrierilll results closer to lie exper intentai drtr litait titose of sottte other

tlieore t I ra! t'j roai;ltes their ti orteil nillOVe, esirec ial ly iii eA t rentre ty sita I low Wirt er.

For tite 5hti tow citaritie i case tite caturtlatititi resttl Is offered y present Itítper are in ijntiii arjreetniettt ni lin lire exist inij

expe r j nitert la t i a lit.

3. Front tite exire r ititeui t a t atti ca Leu la ted lesi! its, it full uns lint t line sway Irtre anti yaw ritottienl ait ittij oli lite sltip irr shaLlow water are lartjer litan that itt deep waler. The shallower t lic na ter i eji t it, t lie la r yti r tite va t tie s aitil lhe iirireiriettlstr n'. Titis is a Is;; I itic for lite shaLlow rlutintet lit',? Beside

this, with tite

riecrense of the i tarnte! nil lii, tine ityiirodvrrannic

forces increase Ii fol tows tit;it lii;' lryilroiiynnairric fori; es au ti rty oil titi' sit I' i it ne s li I

liii

water rire, very di ffe.rettt f rttirt t Itose in uttliuttitiled waler, so tiraI liii' tnrrnentveralii lily of litt' ship

tends to lie very rtittrlt affected 'y tite fini te water deplit arid wid lit.

t. It is feasible to caLcittale tite ky! rociyinatrni i: _{forces ai: t i iij} uni lire sit i1t rlroviriij nib li que Ly i ri restrict eri water by t lie niet Itud

yivein in luis paper, ínl thuttijit foi lire prnut leal 3lnirpose lite accuracy of tire calculaI ioni nie thou shoti il lie improve!.

REFERENCES

(t) Fitjirnii. iii., "Experimental Stitches irin Skip Iarioeuvríili i lily iti Rest rie lei at eis--Part I, Inn tenia ti annI t Sit ipliti i Id i ny Pronjress, Vo t. I , No. 168 . i9&0 pv. ¿79-313!

Ftnwa, T., "llyilrodyriannnir: Forces Actiiinj on a Ship inn Oh t iqine Tunintuj, '' Jotnr. Suc. Na'.

Ar;'iti t Jnpunrt, \'ttt. 13.1 , l'i?). Pli. J35 Ii? Than \'uari.',ie. ''Cali tlatiott of Siri1t Mainnetiv ii ntuj Mo li ous in Stia tt ow Na le i, St'hti ffsti'i hulk, \'ttl. 33. No. 3, 1986 p. 1)1 - 11)4

4) Kan, M. and llariaoka, T. , "Arr nil ys i s for tire Effen:t uf Shallow Water ripou Turniiunij, Jour.Soc,Nav,Archi t. Japan, Wnt. 115, 196.1 pp. iJ

() Newtnnirt,J.N., "l.aterat Molion of a Slender

Burly lue tweeir Twn Para [tel Wa t Ls, " J oinr. of Ftniiii Mein., Vot.39 1969 _{PP. 97115}

intuir e,S. anici Mnirayintrrn, K., "Citicnntat joli of Tnt rit i ttuj Sit ip Be ri 'a ti ves irr Slur tIow Wir t e r, Trains. 1Yes tJ ap;nn Soc. Na', Arch i t, Nu. 3?, 1969 Pv. 73-85

lIess, F,, "Rtnduier Effect ivenness and Cotrrse-Keepiity Stabi lily irr Surit tow Wirier: A Theoretical Model," innterinaliortal Skipbntittiiny Proyress. Vor. 2.1, No. 276 , 1 9'i7 _{pit. 2136-221}

Ertrj;'nte, . and Miller, Jr., "Status Report

ont ir Mode t-FinI I _{Scale Correlation Study Based} ou tite 'Esso Osaka' lulartetiverinty [hita," _{Proc. of}

HIlt ATTI; Vol. ¿ , 1980 _{Pp. 1237-12h?}

Loeser D.J., "Ilelerrniniat ion of Marneu'cring Propert je, in Skat tow Waler by linnprrlse Techniques, Juutr, of Ship Researcit, Vol. 26,No._{1, 1902 pp.1-15}