On the swaying, yawing and rolling motions of ships in oblique waves

(1)

Â

Pi-r/. J

/

*4C)C) Sway, Yaw, Roll

On the Swaying, Yawing and Rolling Motions

of Ships in Oblique Waves

By Fukuzo TASAT

w

32 ' FJ

7

Reprinted prom

JOURNAL OP SEIBU ZÖSEN KAI

(THE SOCIETY OF NAVAL ARCHITECTS OF WEST JAPAN)

No. 32 JULY ¡966

1!

".

(2)

*

)LI;Je

(j)

(I1i41{5

'-iii)

25

O Sway, Yaw, Roll ®i

( \

iL UI

On the Swaying. Yawing and Rolling Motions

of Ships in Oblique Waves

By Fukuzo TASAI

Abstract

In this paper, an approximate method for calculating the excitation sway force, yaw and roll moments acting on ships with speed in regular oblique waves has deen developed. Then, making use of the coupled linear differential equations of motion for three degrees of freedom in lateral plane, we investigated the coupling effect among sway, yaw

and roll motions of a ship with zero speed.

The calculated results show that in case of a ship with Cut up stern the coupling

effect between yaw and roll becomes large and the maximum amplitude of roll arises in quartering seas.

Ci

i:-c

Beam Sea Sway, Yaw. Roll Yaw IiII-L.

t. Sway

Roll o

tfpl:

_Í'-<t:0

'C C2J

Restrained body l< hydrodynamic

force

.IZU moment -3L.t: Sway, Roll

Roll Q)Ii. Froudc-Krilov

jl:<

iI!g/

Msl:'i\

iL- t:0

Beam Sea

_jtl.Ll.

'/'J

j(Ìli,

Restrained body theory )]}

t

, Froude-Krilov

, k MQYl'J'

, Sway, Yaw o

:1')L-l±,

lIEfTI

C3J

t&

?, kII

L.

O.Grijn.

(4J ¿T,

Lewis form section

'7)I4zlQ) Sway, Roll o ,tJ5Z7( , Sway o inertia force

i:

< Roll moment _{L. t:}

Roll moment

G0M 'j\Ji:, Roll moment Q(jI

Beam Sea

_{lit <, 45°}

L.tO

LIT, *Q) Froude-Krilov

i:

PQUt:70

)L

C5J l:jt,

oH Beam Sea

ITt<,

JÇL Roll

¿.

C6J

QcItQ Sway, Yaw, Roll

IL., 1l±,

'L

jfl2J'ii

(3)

26

Il.

Fig. i

-e, ILiI±,

ii

[l:i4L,C, f1j

xi'i'1,

01 1')11, 01

E'

J2Í44, G0xyz (G0

Rf')

Vìi, 0 (o G0z ¿

painted Load Water Line U,

olE'7'll

l:'lj1

'Jfe)a):{&

o Q) Subsurface Q)jIi, =hekCcos(k1 wi) (2.1)

fP.

h =ìy41iIiS,

k=w2Jg=27r/, X=

[]Q) orbital velocity

hsinxe_cos (kCcosx - ksiny - wet)

w0=w(1rcosx), r=wV/g

orbital acceleration

J2sinxeksin(hosx_ ke,sinxot)

(2-3)

lrJ\, e,

.

íw:

Strip method Il Ji pitch, heave

r

C7J

G,, x Sway force 1

Jl-ì'5Q),t -)ì:t0

F',70 F'i + ,n + N'

1'

ee (2.4)

(2 . 4) Q)

i JJ1±. Froude-Krilov

JPl:J < Jj.

2 tJj orbital acceleration

l:

< hydrodynamic

inertia force, 3 fftj orbital velocity ¿ < JJC , 4 ,.

m', N'

¿ strip

f1i( Sway 1J'- Z,,

v,j. V,, Q

1iiJ

(2-2). (23) ?y'

= Edsin (kxcos - wet)

(2.5) i,,=hWsinxe

cos(kxcosw,i)

IC d=o)2T/g. - T ±IîftQ)fl4(

OEuil C3J ,

(2.4) Q)cjlQ) F',,i,

F',2 F',,3

-1-Ed.

F',,1 pgS,,$,,,sinxe- 2

sin (kxcosw,1)

(26)

(F(T,. S,,, 1±

*T!Jj8it,

)

1± max. wave slope

- 1-Ed.

-F',,2 m'v =pgS ,.K',, - 9,,,sinxe- 2 Sfl (kxcos - w,t) (2- i) N',,hasinxe+ cos (kxcos - Wet) (2-8)

.

'JjEbli

p =

_,jg_kCcos(kcos - ksinw,t)

(2.9)

Lewis form section

two-dimmensional body l-'t (2

9) QI

,. , Froude-Krilo\

-F----Wave

Fig. i

(4)

Q)J:< Sway force

;4'tl

=pge3Ssinx S Sin (kxcosx -wJ)

{J1 L. S

= _KD

esin (ky3sinx)dz.,

y, z.

j Lewis form section contour Q)

O 'J(

(Fig.2),

(2.6)

ß±'hMft4-r 7

NIO

Lewis form section fffJj,

L.

tL.t.5 t:h, *d(nil±( 2 .10)

o

-J5, Beam Sea I:

l-). 2 itQ restrained

body I:4

j1jl-Cl,

_{Ut CS)}

t:t1-'

¿ l,

C8J

Xor/2,

wcw

tIi, kQ)c, 1EL<.

fLÑ':

't30

(2 .

4)

ç)4

-t,0

(2.4

Q)JJL, Roll moment t:-)1\-, V, xLb:<,

_ut:Uii))

restrained body :j

Roll Q)4tÇiJ moment o

(2.4)

M'3=M'5+M'52+M'03+M'04 _(2.12)

M'01 (Froude-Krilov Q)i))

Lewis form section l:ji4't

J-=COG9. S+ (P -R) TjpgS9sinsin (kxcOs

-U P-R

(ky3sinx)y4y.

ÇTe3sin

_{(ky.0sin) zsdzoJ} ₍₂₁₄₎

tjji:

(R-P)T/S=11

_(2.15)

M'01=

_{pgSisinx. S (Ö,,}

-li)

_sin_(kxcos

-(2.16)

=

F'51 (G0- ¡)

S(0G0-1) 4

.G,,M

(2.13) laf±7Q)[l:Jfl

05

Q)V1Q) Sway, Yaw, Roll

Z'30 o 60 75

('1s,

Z5)

27 (2-10) (2-11) (2.13)

z'

Fig. 2

L.OU, xh-0 or/2 i: 'íi-, fi Q)4jh, . Ed

0-1 02 03 04 05 06 07 o-g 10

Fig. 4

s H,.00 3:00 O 01 02 0-3 01 05 06 2 5d. Fig. 3 06 09 BO SO 3.9 20 1.0

(5)

Roll moment Q)Tfl ((9 J Q) p. 82O)

1

(2 .11), (2-14)

j, exact

'JJf,

H0=B/2T=4.O,

=S/BT=O. 8

JOQ) S, P-R

Fig. 3

Fig. 4 :,

X=or/2 Q)IQ) S, P-R

Table I,

Il :1

5l:P-Rl. H0

_'jflffJ-(

lÇ'r

H0jç

<

H03, 4

<. -c G0 Q)fi- H0

1)Q)J:1:, M'=pgS0,sinS- (0G0-11) Q)

G0 Q) t]I1Çr Ç.

(Fig. 5)

: (2.12) Q)2{, 3Q) moment l±(2J

tt:5l, i(Q)'LO

M'82:- F'2(OGo-1) (2.17) J4'Ü3 P' (0G0 - lu,) (2-18) 4:IÎl

Sway

Q)frl:-M'94--V4- {m'(Ö0-1,1)}j,,

l. l, 1± Sway force

moment lever

UtEH'f C8J Q)tlJ7,L0

5l,i}t: Sway force, Roll moment

Q)Q)7p, :fll:l

check t

)I1I,

x='/2 Q)l:, L134 (8]

ff). Q)íIlo

Table 1ff l:7i-.

Table 111

Bt (8J

Q)L6

izQ) IJ7.

Full ¿I

'l,lz

fine

4Ji

Q))(I

Sway

force Q) K'e", N'e-

EdQ);Q)trni:

< Q)l±

UiL

Sway force, Roll moment 1± E.<O.4

-)7, Sway force Q)

tt5t1 (10]

:Q)? correction

5Q)l

5 Fig. 5 (2.19) F

ft=i.2

o-=I O

H-

o =

os

O o.Z 0.f 0,6 0. O aZ 0.4 0.6 0. '

$ .0 o. ' o. 00 0740 o.6Ç6 ¡.0 0.9314 _0.869 _{o.8o j}

O-73'-o.161

.04

-'15 0.694 O.36'j .2324 -440 .404 1190 0,98

S tK'e' .9'91 2.126 .923 p371 o.qg 2.23251 .2.z37 2.0/i /55-o /303

(J 3t) .6 99 3.061 -704 j-170 0.838 2-23.0% 2.07/ /735 3.93/ _/023

- -0.Z65 -0.750 -0.835 -F6 I

-0./fl

-o409 -Q475 ...5

( 5) -o,148 -0.640 -0.637 -e410o -o/4/ -olaS -a201 -0/750

(P-r )e'/-r

-0.253 -0.238 -0.15'S 0./450 05/« o49 04-95 0.976

- Ç-)O4T 0,262 -0.2418 -0/87 J413 04190 o4157 o,365 0.297

0.03 6 0./Of 0/33 0.3/9 0.03'? 0/0-5/ 0/36 0/30

(6)

Cii.±,

fl:< Sway force, Roll moment

Strip method i,

Sway force, Yaw Roll moment

4tQ)

Sway force

F,. = W03sin (F,coso0i - F7sinw7t)

-

(2.20)

F3=S2+S4S5+VS7

I

Yaw moment

Mpe = WøU)LsinX (Y7cosw7t Y8sinco)

Y=Yz+ Y4-+ VY

Roll moment

M =

Msinw)

M=F.bG0(M+M3+M5VM8)

M=F.0(M2+M4M5+ VIII7)

(2.20) - (2.22) Q)mJQ)

:

kcosx-=k

4c1)íQ) Sway, Yaw, Roll

-i

29

I 2

SS.sin(kix)dx/V0

S3 =

S7K'e-

sin (hz) dxl V0 S5 =5 N'7e- sin (kx) dx/m0w = _{sin (kx) dx/m0o} Y1

_{SwSxsin(kx)dx/V}

=SoKoCdxsin(k1x)dx/VoL

=5 e- x sin (hz) dx/m0oL Y7 = ( a7)e_+axsin (h1x) dx/mwL M =5Sw(RP)Tsin(b1X)dx/vo M3= l.sin(kix)dx/V0 1in(kTx)dx/ M7 = (m'lo) sin (h1x) dx/m0w

S2, M8

5 : even suffix Q)li, .,

(2.24) V0(f. m([-,7,0

IIL' G0 l:,ii

==.5=s7=Y2=Y4=Y6= Y8=M =M3=M5=M7=0

S Q) ?i 53(fQ) sin(k1x)

ftl: cos(k1x)

(2.25) (2.21) (2.22) (2.23) (221)

(7)

30

LLt1

(2.25)

Q) 9 -5

3Fig. i

Q)

x<9O° Q)1iJ

(k>0) ¿

x>900 Q)I4J

(k1<0)

S7, S Y1, Y3, M1

odd suffix

- Roll moment I:O Froude-KrilovJ11, (2.22) Q)M

M00=1 .ÓG0-M1 = S,S.Ó0+ (P-R)T}sin(k1x)dx/V0

M=S2- 0G0- M2=SS0G0+ (P-R)T}s(kx)dx/V0

M00 Q)lM0 Q)1fØ U'L M0 Q)

tIiU1O

Q) Beam Sea M0=O x=90° Q)Wj ) x=750 X=105° Q)7J

Mo='Mc2o+M /)jÇ ) .5

o C.Q)f. X=75° ¿ x05°

M0- L

3

90°

-x=75°

=1O5°

M0 Q)-

Roll moment Q)j

UL, (2-20),

(2.21),

(2.22)

'IJi

: V=0 -, S5, S, Y5, Y6, M5, M6

x=1O5° ¿, Sway force, Yaw moment, Roll moment Q)i2IC.?O

4'tl

N',e-+, N',e

llBÌ (8) Q)k', FC'l

H0 Q)1JN9i1UC

* <,

1f, Q)J)ft:

K'6e-+, K'6e

CÙic <'

:'L,

RollmomentQ))

U

L Roll 1f11Z 1f,

'j11°, Roll moment Q) x=90°

111

1f4O)Q) Sway, Yaw, Roll

V=0 Q), ìffQ)rI1Q) Sway, Yaw, Roll

Sway, Yaw, Roll ,

o

Ci)

m0(1 +K)+Ñ,i

ÑSÒ =F

(J+I)+ Ñp+m(X,). Ö+ ÑÓ+njCi j+ Ñq=M

(h+f)ö+Ñ0O+

m0K,1=

2 pSK'dx =m'dx, Ñ1=N'1dx

m0K1 =m'xdx, Ñ2SNXdx

= rn' (J0- l) dx,

iii,

= N',(0- 10.)dx,

k1132

I=n'x2dx Ñ=ÇN'x2dx

m0K ₌ Sm(ÖGo_1l)xdx.

Ñ=

L Yaw Q) mass moment of inertia

J, + I = Roll Q) virtual mass moment of inertia = Roll c) equivalent linear damping coefficient

11Fi...tit: F,1, M, Mge(V0

< ) ?)4jl\( (3.

'I -J (3-1) (3.2) J

(8)

ç?4&o)rk?) Sway, Yaw, Roll o)iÇ

31

(m0V±Ñ2)

(3.3)

=0. 20 without rudder, without screw o)Le-euwen o)llIiWI L t:* 1V

.5

: -11v ¿ Ñ

d

w=5

o) J+1,

:U Ñ ±j

20%o), f[o)f

Order

U10 i!- L:( 3

1 ) : m0V1 ',í1*l-c

LL (15)

<0.10J± jf

(3), Cli), C12J

1i*l'o

:J, f5

o) Sway, Yaw Q)

:4< hydrodynamic roll moment : [-

iíJ

¿±3& <,

Table iV

e

4l"1J

V=0 O)DpI:,

Roll l:t7 Sway

Yaw

bJ:, I,

o)-3

U7:

n-W.5

f0325 ,a=0.l'32

Leeuwen

fl-'r

g.? (.3

m(i+() (-%)

is.4 9.2 Leeuwn

_J-N-

(k7',,...0) 3. 3.2

;

*

I2/3

H1-f 0,53 I J

f I

( n. 4. 3. J Ls.uwen

-ï:

(bs/n,)

27 .5L7 3,2

(s/n,)

25.2 44 Leeu w _- n, /3.5

4

/ffE/v.r,.n a.0'2 .z,o

1 ( M.c) .5 /5.0

Leeuwen _-N

(h4)

₂ _-2

o.e/

0./os

N7Z 1.3 33 5

Luwe'n _?DnVY,t

:z

,o.6o

4 *

YflOV'/

(k)

7.' Y.65

Yaw, Roll

±o

:

V=0 o), -j:i

(3.1)

VO o)j(o) Sway, Yaw

Ut.jM2,

3L

Rydill 111), IW (3),

(12) ,

moment , cQ) iLJflHii

fTÏtW (3) J±t.*L4i <-5U7

-,A.I. Raff (13J J:,(3

1) o)

Jo)*J V0

V0

(3 2)

V Sway, Yaw O)

11 Ut

: Lateral Bending

moment

1Ll (3)

J5ro) Sway, Yaw o)JijiL,

]tj]Jtf <, Pitch, Heave

Roll oui:

m(1+iC,)), (Jz+Iz)çi

o)t1

jIo)3l± 2nd

Order ILH6 (3) Raf f (13)

.5e,

(3. 1)

o)

< o) co)J o) circulation o) ¿131J: Superpose .5 (14),

o):I3--n±-Lv'0 VçO o)flio) Periodic Sway

J( Yaw o)

[UCJ, G. Van

Le-euwen C15J jL

tJ

(16)

Zlz -1

Leeuwen (15) o) 1!)U L

Todd 60 series C3=0.7O

±o)j

(9)

A. 79«i3

Fig. 6i: Body plan

L-24.54m, B=5.6m, D-=2.50m

tk4

Ltc.

12

W=184.5K.T, CB=O.584, d,,=2.06m, df=1.23m, d8=2.89m,

G0=-1.86m, G0M=O.62m, J=m0(0.

242Lp)2, T

6 Jr

2. equivalent

a=0. 32

C 9) Q) data 4of Li0

) T,8,=6.0 c3l-

F8, M8, M0.

fLt4,

Fy28

rfM0,lJ

=90°

MçeIlFig.7l:?st5i, 45°135°ft

f)t:0

3±12H'L

x=90° l:f3Ft-t:0 (3.1) 1l:,t

Roll Q)M Fig. 8 l:jfct0 Sway, Yaw

Fig. 8

IJi: x=90°

.Q)f)(li,

Ut(ff

1)c

Roll moment Q)xfJ'fj

G0l:ifl

2, 11ÌÎX I M I

.)çt'0

-J5m0K1. m0K

4J't:e1, Yaw Q) Roll i:

Roll maximum ¿ X=90°

Q)b'L.O

:

=n/2, T=6.0 'jQ)

Ij3(-1\, W4' C 8 J Q)

tttiûQ)fiLft JI4 C

(W1Q))

($

) Froude-Krilov

I F, I

298e 3281

I 2241m 243tm

(:)

IMI/9

1411m 154t.m

(i=1. 23) (7=1.34)

U(3)l Sway Q) inertia couple

(Lt: Roll moment

(4)

li

Lewis form section I(4

itfi (Table I.

() jbt: Froude-Krilov Q) Roll moment

M0 I =PgJSWCS. OG+ (P-R)TJdx. *Q)f1tú(l F08 , I M08 I

Q)l4l -tC WQ))7

10% over estimate

Ut

MI, IMI

(J'L

7>1.0

±Q) Trimmed condition Q)

it11'tl

7=0.727 (4)Q)fQ))J56%

I±Q)li 7

4C

3-.-4

wide section

)l, JQ)

B.

Profile

Fig. 9 i:1. Lpp=LWL=59. Orn, B=7. 1m. d=2. 33m, Trim=0, W=480K. T,

KG0=2. 707m,

0G0=-0.377m. G0M=0.736m. Z. a8=0.32 Yawing Q)J

VI 0.25L

To7.O

U, V=0

T0=7,

=76m Q)Q)ttt

G0 Q)) ) Q) Roll moment m(OG0-.,,) Q) X

Fig. 10 11

(ì1)

m0(1+k) =991.sec2/rn, Ñ0=Stscclm. m0Î.1 = 2541sec2

Ñ02=191sec, m0k4=21tsec2, Ñ5=4.7tscc,

J2+10=215931msec2, Ñ=12091msec, m0K0i= -4331.m.scc2,

Ñ0=-431msec. J.8+18=r4371.m.sec2. N08=801msec

m0K,m0K0.

)jf Ñ05

liçV'0

Restrained condition Sway force, Yaw )tij Roll moment

Fig. 11. 12 J3W 13 ljj

Sway

force

Yaw moment Q)ÌÍ

x=90° I:jU ((II

ÇJO IM58 I

Sway Q) inertia force i: jz

(4.1)

32

k32

(4)

IM0Ii®

1531m

(10)

Sway, Yaw, Roll coi-C

33

L. h- U Froucle-Krilov JJl:< moment lix=9O°

)fc 9

¿,

Fig. 13 Sway Q) inertia couple Ut: moment

(3. 1)

)]C Sway, Yaw, Roll

Fig.14, 15, 16 l:-

l:

- Fig. 14 Q) Sway Q)h'

ftjt

x=90°

Yaw

: Yaw ji(J ±1J135°

copeak

j45°

Q)peak

i)

Q, Sway, Roll c coupled moment : Ut Yaw moment

(4.2)

M=Ycost-i'8sinot

O

Q)AU ±:tktl, Y,, (:)j

m0K,xO

h,

Y, ):(j m,Rj

0U4'U

i YI »1

I O

Jtcm0KÖ 7k

< ÏÏii

m,K<0 -(t8bl:, M

Yaw ll'M 4 Q) peak <

Roll -9i p=O (dI) Yaw Sway, Roll Q) coupled equation

j-(±

Fig. 16 Q)iQ)

1,

fflJ(j

6O° Q)fJV(uIiï &

U (

'

o )(

(3 1)

O

t.

Fig. 16

, ii75°

'Iii ulliW

Flat i:

,

LU*Q)

Roll(:t1YawQ*,

7 Roll Swayco 1±, deck edge ¿ Froude-Krilov < 00

Z. x=90° Q)Q) 7=0.945

1I±Q4

7=0.823 ,

c.?.

Profile

Fig. 9 ):ft. L1,=115m, B=12m, d=4m, W=2,890t, Trim=0, G0M'=l.Olm.

T010( ¿ft'L, T,,=101ì Q)ILQ)4J (:-c-. flIL. a,=0.30, J,=m0(0.25L)2 ¿1U

t. Roll

)ji _.fIj

Fig. 17 (:ffc,

Sway, Yaw, Roll cofij

:--C4,

Ïii Q)!14I L

llt:,

c' 1,

Roll jiIi co

i c

(lJ U,

i:i

Oblique Ware 4) Sway, Yaw, Roll Q)

'>j

híthJil:

Ut, UU, -:coJ

tc

Q)I-

-(i)

IQ) Sway, Yaw, Roll l:

JIJhd

moment

V = O

I1fC Restrained body I:

Rull moment Q) Q) ,

N'e

Q)):<

V=0 Q)HQ) Sway, Yaw, Roll

(3.1)

V0 Q)Q) Sway,

Yaw Q)3lJj

Q)kL)± m,V

4-k

(3.2)

1-r4 Iik

-) 79r JJJJ ;jp

Roll a'Q)M±

¿

ji M0,. i <, 3Z Sway ¿ Yaw. Yaw Roll

Çj)(i. m,K1, mK,1

Ñ

/2b,

Sway, Yaw, Roll Q)4)dIlÇ[iIj

L x=90° l:EU

I'1 Yaw (1. Roll Q) inertia couple cot

:ij-kQ) Peak

L

(11)

Roll Q) peak

Yaw J(Lf. C6J

Roll Q) _peak

))lt(, Sway, \'nw

jiIj)j

f't-(, ':

peak

t

S

Q)Ijj'

Table 111 4iJ

. 5 :,

H0 lt7'Q) Froude-Krilov

Q) Roll

nb-ment

(6)

(3

1)

Oblique wave rQ)Ill(' moment,

moment

Roll Q)*!7 '.i

. ¿,

LM)-±4', U(U(

,,

Q)J(±, --li, 4Q)F]

Sway, Yaw Q) Roll

'3

'l7

74t

I3

(:,-'

Sway, Yaw, Roll Q)f'IJ)]

)'L7_

:,

)Q) Lines -' Q)Q)( UT t:fQ)±(i, EiIPQ)J,

tiU

<

L±i'

.±W:))j UJIf, atJ-'

(41.4.30)

i) W'

:

0Beam Sea 1:4j"

_30g,

_l± 45

(1965)

2J ffl4'

)Jri,

)I114Qf-3 J )IW C. Lincoln Crame : 'Steering Characteristics of Ships in Calm Water and Waves"

S.N.A.M.E., (1965)

4 J O. Grim, : "Das Rolimornent in Sebtaglaufender Welle" Schiff und Hafen, Heft 10, (1965)

5 J : p.570

D : "ta iQ) _4iij 131

JL( :

'

Q)j

Q),:-L'-"

31 1 (1953)

8 J FIl J ft, : "The Calculation of Hydrodynamic Forces and Moments acting on the

Two-Dimen'-sional Body" No.26 (1963)

9)

: "

b4:fr

'(Q)

Q)

i:l'-

« 49..

1OJ "Stripwise Calculation of Hydrodynamic Forces Due to Beam Seas" J. of Ship Research, June, (1964)

L. J. Rydill : "A Linear Theory for the Steered Motion of Ships in Waves" T. I. N. A. (1959)

)lJ

Q)[JJ1" Ç%5

116-.

A. 1. Raf f : The Dynamic Calculation of Lateral Bending Moments on Ships in Obligue Waves" TRG Report 147, (1964)

W4" : "Obligue Wave Q)Q) Sway, Yaw, Roll

(I )

_"

M (25) (1965)

G. Van. Leeuwen : "The Lateral Damping and Added Mass of a Horizontally Oscillating Shi model" TNO Report No. 65S, (1964)

jE6 "On the measurement of the Stability Derivatives by mcan3 (f forced yawing Technique" 118 ii

(12)

79 . 9 191 * 40

4'IQ)

Sway, Yaw, Roll

Q)-»-Fig. 8 04 03 02 0.1 My,

/w

L,,210 l'w,60 se 1w '6 Tw5 Osec Tw6 0 sec Tw6 Osec 35 15 30 05 60 7 90 05 120 35 150 155 190 Z degree) Fig. 6

Fig. 7

15 30 45 50 75 90 105 120 135 150 165 180 X (degree)

(13)

36

H

7

AP 19 17 15 13 -1 5 -. 900 800 .- 700 u. AP 19 17 15 13 60 500 400 200 200 100 Subchaser 59m Dest royer 115m Fig. 9 20 19 1817

1513

iI 9

7 .FP

-Ic 9 7 5 3 Fig. lo Swayln9 Force Fig.

il

9 7 5 3 LWL F-P 180 LWI

ï

h 30 45 60 75 90 105 120 135 150 165 X degree)

(14)

E 500 0 400 300 200 loo Rolling Momerrt Yawrng Moment 60 75 90 105 120 X (degree) Fig. 13 135' i'b IMee 0.'t) FieI/

IiI/

)Froude-KritoVs Theory) 08 07 06

1::

03 02 Ql Cos)ot-rl Swaying Motion . Sin (ro I - f)) 79 5 30 45 60 75 90 05 120 135 150 165 153 X (degree) _{Fig. 14} o Yawing Motion -1 15 30 45 60 75 90 105 120 (35 150 155 160 Fig. 15 5 30 45 50 75 90 105 20 135 150 65 80 X (degree) Fig. 12 00 03 J? 01

(15)

38 7 5 5 1. 3 2

Rotting Motion t Subchaser )

JI

O=-80Sntwt-Ee')

By Coupled Euotions o Sway, Yaw, Roll

By Coupled Equations of Sway, Roll

-.- Froude - Kril ov's Theory

Fig. 16

Rotting Motion t Destroyer t

9= O,Sin),I-E)

-.-- By Coupled Equations of Sway. Roll

o--- By Coupled Equations of Sway, Yaw, Roll

X degree) Fig. 11 1/.0' 1200 100° 80 ou 40 20 11.0 120 100 80 20 O 135 60 90 105 120 150

- X (deqrie)

75 15 30 1.5 165 180 180 165 15 30 45 60 75 gg 105 120 135 150 L) co uu 40

(16)

Table I-1

S

(z

?c°)

Table I -2

H0= 0.2 _H.= 0.4-0 0.1 0.2 4.14. 0.6 .0 _'0 0.1 0.2 o.4- 0.6 .0 0 1.0 0.9590 0.9/0 0.128 075" Q.632' .0 0.959 o.9o1 0.2241 07419 OL.6Z0 0. .o o. 90.4 o. 9,« 0.937 076g 0.652 . o. o.913 0.9341 0.763 o.637 0.1 lo o.959 0.920 0.2417 0.702 46'l/

l

o'96o _0.1/? 0.1415' 0777 0.660 07 o 0.762 0.927 0.959 o.779 a6?3 i. o 0. 96z 0.925' 0.856 0.793 0.682

0.6 . 0.965' 0.9341 0.6,71 0.116 0.7/9 '0 o.766 0.933 O,ß'70 0.9/I 0707

0.5 l'O o. 972 0.999 0.99/ 3,6,41/ Q.75'3 . o 0.970 3.9410 o,96 0.133 0.733

H0-o.8

0 0.1 0.2 0.4 0.6 l.a 0 0.1 0.2 0.41. 0.6

/0

û I. o 0. 953 0.706' 0. 9/9 0.737 0576 I. 0 0. 952 3.909 0.3/2 0.725' 0.547 lo o.9s6 0.9/2 0.130 0.73« 0.6/9 -o o.956 q9io o,j241 0.71,..o 0.512 O I o o.957 0.9/I 0.6,4/ 0.770 0.6412 .o 0.958 0.9/7 0.136 o7S7 6I7

0 7 o o 96Z 92'5Z 0.13-3 0. 716 0665 1.0 0.962 0.923 0. 60.8 0.776 od«/ 0.6 .0 0.968 0.93. ₀₉₆₇ 0.805 0.67 / o

a,5

0.927 0.16 / 0.75« 0.667 0.5 o _0,97z _0.9.37 0.990 3.823 0.7/8 .0 a.967 o.?37 0.6,75 0.1/3 H0 .0 H0 1.2 0 0.1 0.2 0.9 0,6 .0 0 0.1 0.2 0.4 0.6

/0

IO I 0 0.93-1 0.90 / 0.203 0707 0.531 I 0 0.9417 t 892 0.77/ 0.4412 0.398 ¡.0 0.7.413 o.9o1 0.8/7 0728 0.3-60 _-0 0952 0,00 0.717 8 0.4130 0.3

lo

0.937 o. 9/S o. 73o 07416 ô.594 I. 94 0.901 0.103 0.49/ 0.414 3

0.7 ¡.0 0.96 / o.9?/ o 8413 o.744 0.4/3 .0 0.13-9 0.9/3 0.8/9 0.7/41 a.4191 0.6 ¡.0 o.95' o927 0. 959 0.712 .o 0.942 0.92, a 933 0.734 0.535 3.5 I 0 0.967 0.1341 0865 Jo. ¡cl 0.468 . o 0.943- 0.967 0.1416 o.73-y 0376

H,- ¡.4

H- .6

0 0.1 0.2 0.4 0.6 ¡.0 0 0.J 0.2 0.4- 0.4 ¡.0

l'O 1.0 0.949 0.815 0.783 0.668 0./MO? .0 3.9419 0. 9512 _3.77/ 0.6412 0.3519

O.f o 0,953 0,903 o7?8 0.690 0.478 .o 0.952 0.90a 0.717 0.462 0.430

0.8 lo 0957 09/0 0.9/3 0.7/2 43-08 ¡.0 0.954 0.102 0.903 o.69/ 0416$

07 ¡0 '0.960 0.9/7 o.927 0.733 0.5410 l.a o.959 0.7/5 0.9/8 0.7/9 0.998

0.6 1.0 0.953 0.924 0.8410 0.733 0473 .0 0162 0.92/ 0833 0.734 0235' 0.5' 1.0 0.956 0.730 0 954e 0.7741 0.607 .0 o.945' 0.927 0.946 0.73-i 0.576

Ho-20

O 0.1 0.Z

41o.

¡O 01 0.2 0.4 0.4 ¡-0

lO 1.0 0.9417 0.2841 0.742 0.588 0.Z95 I 0 0.93? 0.23-5 0.6417 0.41/8 0.042

0.f ¡.0 0.951 0.892 0.760 0,6/5 0.322

lo

o.9413 0.966 0.672 0.4152 0.079

0.8

lo

o.7541 o.9oI 0.779 0.642 0.365 ¡.0 0.9411 0.971

06'

.990 0./IS

0.7 g. o 0.958 0.909 0 71.6 0.669 04105 . o 0.953 o.989 0.722 0.530 0/64

0.6 ,0 0.961 0.9/6 0.8/3 0.697 0.452 . o.956

oft

075v o.5'74 0.233

0.5' _¡o 3.963 0.922 0.127 0.726 03-04 .0 o.7S 0.908 4.790 0.630 0322 H0-4o û 0.1 . ¡0 ¡.0 0,927 0.8/8 0.529 0.230 -0/'« 0.1 i. 0 o 9341 3.63/ 0.54/ 0.267 -o09.. 0.8 ¡'0 0 9410 0.844 0572 03/5' -003-7 07 i. 0 0.9415 _abo 0.627 0.347' -0.0/2 0.6

lo

O 950 0.273- 0,67/ 0.4135' 0.056 0.5' io 0.755 0.199 0.720 0.0.20 4./SS

F'k' Sway, Yaw, Roll

39

(17)

40

F-R

(Z='O°)

Table 1f-1

F-R

(Xo')

Table 11-2

H=0.2 H, o.-0 0.1 0.2 0.4 0.6 .0 0 0.1 0.2 0.4- ai, -o 1.0 -0.4720 -0.4433 -04'/65 -0.3677 -0.32540 -02560 -0.«367 _.fL/o9 -0.3969 -43421 0.3036 _7379

0.9 _{0,44i.5 -440/77 -o3937 -t33429 -g3o99 -o2447 -o400,'o -(U777} ;559 -o.;/3' -O.2o7 -0.22/Ç

o.f -4412f -03295 -43672 -0.3267 -0/.5 -C.2334 -0.3629 -03227 -02970 -'0.a5S8 -02027

0.7 -0,3760 -03554 -03363 -o.30/Z -0,2703 -0.2107 -0.3/96 -0.30/-9 -oes -o,24-'37 -0.2263 -0/106

0.6 -0.3303 -0,3/32 '0.2979 -0.2627 -0.2433 -0.Z0Q/ -0.26"/ -0.2533 -23f6 -0.2/36' -4/9/2 -01.732

0. -077/s -42593 0,21/?0 -02292 '.O.,ZOá'Z -0,/757 -0.2037 0.l924 '4/P4 -0/637 -0/462 -û.//740

H,-o6

0 O-I aZ 0.4 0.6 .0 0 0.1 aZ 0-4 0.6 1.0

.0 -43739 -03537 -0.3349 -0.2927 -0.26540 -'0.2070 -0.2232 -0.27/3 -02575 -02356 -0.2/1/ -0/645 0,9 _-(3277 -43097 -0.2920 -0.26/0 -0.2322 -a/92/ -o.o.46 '-02/42 -0.2043 -0/242 -o.//60 -0/2.93

0.9 -0.2795 -42633 -a2495 -02201 -0/999 -0/536 -0.1626 _{-4/525 -0/46o -0/.223' -0,/39 -ao177} 0.7 -02.047 -0.2//I -o/99/ -0/745 -4/535 -o/Il 7 -ao9/ 0 -00243 I-0,4736 -00/440 I -J7 -0.036 0 0.6 0,/6/9 -0/506 "4/376 0/204 "0/037 '-40767 -80078 -000/2 00003 0.0/3) o.o/99 0.0278

0E -o9ô3 -00727 -o.o63 _L-° =0.0372 °/96 0.0 797 I 4/34 0/093 0.1/26 4/15/ o./i3

.0

O °-1 0.2,. 0.4- 0./ I-o Q o.: 0.2, 0.4 0,6 lo

I. O -0/350 0/640 -0./6/0 -0/53/

-ao269

-0,/4/6 "0/1 '9 -0.0/93 -0.0347 -0.0/0/9 -043-35 -ao3-85 -0.05/i

0.9 -00923 -0.09/7 -409/0 -oaf/a -a.0661J 0.0704 a.0504 0.D'/4'z 0.o3/3 0.0/95 40052

O. 9 -00/24 -0.0/23 -0 012/ -co/IS -00//O -0.0093 01716 0 /607 0/999 0/297 0.1//I 0.0792

0.7 0.0779 40773 o.0746 0.0707 0.0/oS 0.2002 0,279/ 02673- 0.2446 0.2/94 0/773 0.6 0,/905 0/900 0/909 0/034 01744 0,/527 o.433o 0.423f 04.'3f 0.3190 0.5717 0.3579 0.2927 0. 0.333f 03334 0.3307 0321,10 03/09 0.276/ 0 42241 o.6 /40 0.305-0 0.5447 o.46/1 H.- /.6 O 0-1 J 0.2 0.4 - d.6 l-O 0 0I I 0.Z 0.4. 0.6 I O .0 0/522 0/290 0/000 0.06/2 0.0368 0.0/23 0.3460 0.2929 0.2526 0,/9/0 0/400 0.0769 0.9 0.26/I 0.2356 0.2/06 4/62/ 0,/330 0.01/2 0.4047 o 4040/7 j0.1Loo6 0,3254 0.2607 0573-2 0.40730 0.1,0/38

o/SIl

027/I 0.0 0.3000 0.3640 43399 0,2936 0,2493 0/7/2 o.6598 s.1/O 0,536/ o.6-/4'3 04907 6*422 03907 02966 0.1221 0726/ 07479 6656 05723 040/6 0.6 0.720f 0.70/0 0.6797 0.3292 45709 0.904.00 ,.o530 1.02/50.905-8 0.90/3 '09036 0.5035 0.5 c.9652 0.9492 0.92 91 0.2700 02/23 435/8 / 36/f /3360 /.3,Q30 /2/75- /1097 42456 l-f.- 2.o l-l.-3.o

o 0.1 02 0.4 o.. 1.0 o o.i o.z ' o.4- 0.6

I. 0 0.9295 47377 '0.6525 0.5023 0,3793 0.2037 2.4748 2.239/ /9760 /4647 1.0073 0.33-4 / 09 1.0176 69324 0.8484 0.6275 0S'9a4 42992 2,2705 2.6227 2.36/7 /0/37 /2374 0,1/333 0.0 /2326 1.1604 /0783 0.9094 '0.7400 0.40398 3.323Z 3.0723 28365 22/22 /3/93 05511 0.7 /.5o79 1.93/6 /3584 /192? 499/4 o.6o5/ 3,0909 3.6830 3.50235 2.7933 2.0627 0,7236' 0.6 /.05/j,/.7898 /7/5-0 /5335 /3/27 09455 46227 4.4947 4/8746 3.4976 2.6679 09779 0. 2.3/20 2.2000 22090 2.0330 /7797 ¡/95/ 56935 3-48/9 5.2329 44797 34906 ¡.365/ l-L-4.o

i

O 0.1 i ß.Z 0.4 0.6 .7 1.0 49272 43/98 3.7436 2.5422 1.4356 4/61/0 0.9 5465/ 40977o 43882 3.0661 1,7920 0.1370 0,9 3.3433 5.7902 5/774 3.72°? 2.2/66 0/2/I 0-7 7.2237' 6.7197 1 ¿.i/í 4559? 2.780/ c,//96 o6 95/78 9.1/SO 79197 3.5922 0.19Z7 0.5 ,o,.Oo6f 7.9483 7.2973 7.2237 ' 4,6397 0.2/00