A calculation of turning motion in regular waves

(1)

1 NOV. 1g72

ARCHIEF

:ibljoiFieek van d

Qnderadefl F

-

zsbouwkunde

nische -ogeschcL

-DOCUMENIAIIE 1:

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DATUM:

DOC NTAHE

(bi

JE

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JE f,

A Calculation of Turning Motion in Regulär Waves.

By Shosuke INOUE

and

atsuya MURAHASHI

It C

..

.

r op j. jj

31 _U

fl412

Reprinted from

JOURNAL OF SEIBU ZÖSEN KAI

(THE SOCIETY OF NAVAL ARCHITECTS OF WEST JAPAN)

N0. 31 February 1966

Lab.

y.

Scheepsbouwkunde

Technische Hogeschool

(2)

a)3[J

Rydille1J Froude-Kryloff

yawing swaying force _steered

motions

-cß$)

LC0

,

1LU1 C2J lc.t 7

:

I

î!'1l:V

₇ _drifting force .

7, 1 :'

:lJtJ]j

(F*i401O

31 JßIiji:

77 TE k _lE

*

A Calculation of Turning Motion in Regular Waves.

By Shosuke INOUE

and Tatsuya MURAHASHI

Abstract

A ship progressing in waves performs heaving, pitching, rolling, yawing, swaying,

and drifting motion due to the dynamical forces of waves, and these motions affect the

manoeuvrability of the ship.

L. J. Rydill investigated the steered motion of _{a ship in regular waves using the linear}

theory, in consideration of the periodical lateral force and yawing moment as originally assumed by W.Froude. But a ship is drifted in direction of wave propagation due to the

phase

_{lag between the exciting force of waves and the ship motions as shown by}

Y. Watanabe.

In this paper the authors investigated the influence of drifting force on the course

keeping and the turning of the ship.

Main conclusions are as

follows:-A ship progressing in waves has a tendency to turn to the weatherside

due to the

drifting force, and the greater its deviation is, the less dynamical stability of the ship.

The effects

_{of the drifting force on the turning ship depends on the following}

equation,

E1 (Crn,r h,,0) CNZ - (Cm2 + hmwo + m1»0cr0) Cr12

> 0 radius of turning becomes larger when a ship turns to leeside

< 0

i, i, to weathersid'e

Nomenclature of this equatiòn shown in Table 1.

In generaly this is possitive at the course angle

_x

= 900

A locas of turning ship in relatively gentle waves is nearly

_{same as that of in calm}

(3)

-r

Fig I

+

tanker

çrQo

78

:%j

k*31

3Q)f'r-)1110

Ug C3J

l::

li heave

a;i'jh

a:.Jz

:

jJi drifting force ,f'J] U. :c'tj

roll -' heave

,:2i

k

íìii, Q)drifting force

riu,

i-'t:.

Y fit:0

)l't

:l1Q)

Table 2 i:if-0

50cm Q)4 f' 9 1

UfiQ)5. O

i- Ut:o

kQ)

I1 , 1-1iiJ

Ut0

A,B,

t:0 kQ) Q)fJ

Fig i, 2:-t0

t:t U: Cfi,l'Lt:'Jj±

orbital motion Q)171J

i±ì

C4J

C,

t±ìfl1Ut:0

Q)±<

tQ)jQ),

cJ- .kQ)t:

lIto li QIZ 9

'Q)L

90°

A, B:Q)J:

U,F. tBQ)

(4)

3)

y1J,

t4't

LI<

4)

:,

'i:z

79

Fig 2-2

(TankerB) III

ZQ)jj

orbital motion

:Q)

:Q)jfi-)5ffl: drifting force

{EIi<o C) driftimg force CS) l

Lt -,

C3)C4J j Froude - Krirov Q)

(6)

Q) dEifting force Q)E1E L,

Q) L ?IhIJ

7Lt:O

mi (8) ±,

(±TÇTh3:

L» L,

i ' H (3) Q)

J1LC,

(Q)

()

_{F=FasincrjFccosuet}

₍₁₎

F0=esmx f1o+O(f40+f5s+fn)}

F=smx {fi+ O(f4C+f5C+fGC)}

M=MsincrtM,coscrj

(2) M3=esinx {m3+O(m40+m50+m60)}

M0=esinx {,n0+e(m4+m5+m6)}

e :

O = O0sin(--8)

Q)tQQ)5i-..' IU7

t4-F

F1(Oscillation term)+F2 (Constant term) M= M1(Oscillation term)+M2(Constant term)

t

Q) F2, M2 , Drifting force Turning moment

F2 = --eSiflX e

f4C+f5C+f6C sine (5) (3) (4) M2 --4,sinX O {m43+m53+m60} cose

---:

ift L

argo A, tanker B l:

ttL;Lt7, Fig3

(5)

80

drifting force tanker

i:J-c

cargo ijs

:'

/ íYjj (Bld)

20 io

o

-

c_2 CR2.

- ___

tcink er

cQrgo

TUNIN6FACTOR

e=i

at X

90°

D4IñP/N6 COEF OF

ROLL/N5 ae=0.2

o

3°

60 qo 120

I'0

180

Fig

3 x=90° QFF

rôll QJJ

/ drifting force coefficient

1V

heave, sway, surge pitch, roll, yaw

'i U

::

JiThi±

ib U(

-'VC5

l,

tÍj2-:(

.5 -,

4't.0 k

tt5

'

*Q5Q)

Lt

13I4t/C

rE

-ct,

F4 o

I

Q) 1.

W

1N1V-J1 Fig44iu<, Wj: aJ £2

T]

M (Ûcosc

Uìsn a â) + M5Usina2

=

F

M (Usina + Ucos a ci) - MUcosa £2

=Fa (6)

iñ

=M

t: aÁ» 100

(6)

'1io

F,MQl1l:

cc £2

Q), k f'

:'t70 cc

£2

:

(6)

Q2. (CNam2+(mi._CNI

m5 z,, _/ _,, m5z,,

C)2

i 1 (01 = 2p1e r Q)

jj :

7, Cm Cm,, a + Cm,o) - ff.f (7) CA, = NI pSU2 Cm = Mi +pSL(P

t:-.0 .L IN 1M ± a (0

t:.iz

JJ±, ¿

a-t,

t

IJ1jj _{CNW CMW}

¿1

B]t

s

m,á + CNa

(m - CA,) W = CA,A, aR + CA,,,

V

Cm,a+zcoCmo,w

_CmuaRCm,

(8)

q1 9wsinXcos(ëes+'i)

Fig 4

wsinXSiflffcs + Cm2 (10)

.'=tan-1(1 ,,_CN1 Cma' /CNa Cmi

z,, _{m, z,,} _1/ m5z,,

(12)

(13)

81

kQ)-

P2= 2p1r2,c,,ö'0

_'0=p1iv;

_{(tuning factor)}

s=Ui/L,

W=L2/U,

₍₉₎ 2.

If

lir'z 5

¿?,

¿s t7J'

j

fJJ0 UtC,

'

IiLQ) [j .5

/d-

drifting force

Lt:1-,

:5-., *b±:::0

_{Rydille :t '}

_< _{U <}

_:j

IjJ}.-)j

CA,,. = CNI ®w Sin sin S + CR2 Cm,,, = Cmi

:-c

(8)

m c + GMa a - (Cmx

CN,,) ,= CHI ® SinXSfl

Cma a + z Cm,, o = - Cmi 9w Sjfl)COS S

w

+ 21

+ P2

= q esin x cos (ës +

)

p =

(_Ç"!s\

_i,,J

p

2 CN,.CmaCm,,(mxCN,,)

(7)

82

kU31

¿:;5 < ¿kQ) 5 q1

sinxc0s (ës+4ì)

n0=[(1_e2)2+ 4ice2J1"2 l coi = q1 9,,, sin sin (ff,s+c -'I'

¶'/'

=3qisinx

-1,,

Q) cargo A ø.4 tanker B Fn=O,1, L1v/L=2 0.3 Fig 5

r,J1

02 < 0. j

3.1 Drifting force

fP LtQ)liJ1J

0

Rolling

iìîiQ)

.5

joJ7[n: drifting fôrce

U

7 drifting force Ty turning moment * F2,M2

è

F2 = ®,.,,sin X {f4+f5+f6c} sinS M2 = '- 8,,sin m4,-f.rn52+m6,} cos S

'45ZtCN2Cm21r

F2 M2 CN2₌ Cm2 = i)

H1J

(11) CN2; Cm2 má+CÑ,,cr-(mX---CN)coÇN2

Cm,,a+izCm,w

Cm2 Cm,,CN2 CN,,Cm2 q2

¿+2pc+p2w=q2

COZ ,,,2=q1= ÇmCi CN,,Cm Cm,,CN2 CN,Cm2

P2 _ÇCmCm@!Z2CN)

A

a i:c a2 ¿gj<

a

C m'4 N2 (m2 - CNO,)Cm2 Cm,,Cv - ("ex - CN,)Cm2 2 _{CN,,Çrno,Cm,r(mx Cs,,)} (i U ¿

_C,,CCrn(fl2Czq,,)

(13') 180 X (5) (16) (19) (20) 0 60 120

(8)

83

UQ) drifting force iz

2ifl

CIICNZCN2CTh2

>0

_L=Tl:

<0

:

(21)

'LJZ

12 7 drifting force , f Cm20

: CR2

±'

JQ)CIE.

C7,a>0 .

:i17 ku-:îr3Q

drifting force

)l10

w,a

cfßMt

(22) X1 X2 _±

XiX2Pi±Vp_p2

(23) X1 ₂ w,a

Lt/E L

*)l:

J4i- L o=Ae11+A2e12+w2 arBel8+B2e128+ a2 (24)

:

AA2 B1B2 a w th i=A1X1e21±A2x2e (25)

Lt:C (24) (25)

(17)

if-j

a =cL (iX1 - Cmos)A1e21 +(iX2C)A2e + Cma2} : (26)

Lts=0ia=0=0

A1 +A2 +w2 0 A(i2Xi Cm,,,) +A2(izX2Cmo,)A2 +Ca2= 0 (27)

a2 ? 032

Cma2Co,z+Cm2

(28) (27)

A1izX;+A2iX2+Cm20

(29)

è1O

Lt-:3C

A1A2 X2

i

CmZ _A2=

X1

2 Cm2 (30) X1X2 XIXZ z XFX2

>iX

Cm20

LtcD

co=_-?__w2{e113_ ( X1 )e223}_±032 ₍₃₁₎ X2

¡X1 ¡<¡X2!

I'il

iPZ

¡l/>2i

1l1L

'j\

(9)

84

Ixi I

I: U-t

I&:

1-o

iQ)ttTh (1])

'I co

!e21+

e12s +cozj

4'J\,\ aS

Q)t

2, a2 Cm20 w,

a,

:O l w=H(s)c.'2 z=t(s)w2

H(s)=1±xx2{e1s_(-L)e12S}

s

_{_2(1)}

{e1ls_. (_.i_)2ea2s}

J(S)r=1+,'X{(X2 ,n7cm )13_2s}

3.0 tanker

/

cargo ----

/

/ 2.0 J(JJ - _¿

///

_/

_i(J)

10

///

I

U x=9O0

¡///

//

f/I

.2

cargo ship

tI&)'

00

li'25 tarker

Q)LEQ)I?

J-<7 ¿

Fig i

8 /p ;-1V)

.5 :Q)

l:1Uti10

Fig T

(ri)

2 - 4 5 6

Fig 61ìlQ)H(s)

E(s)

f(s)

1AF4SR CARdO WOOS 2 s-o

Fig 8

t:

1 o H(s) i(s) J(s)

i s

HIJJ

(02, a2 drifting force 2 1.0 Q) drifting force

Q)11

X lJz

:{0k7cUC, X

a,w, .8

Q) as Q)kRb1fr

(10)

tj-

<,

-:t: tanker B Q))j

cargo A t

32 j

Q)

ri

Q) !

;H-t,

j:

iJ-t Lt-7:

t7

1faU1] (

:-c

S)

La

_:iL]-

_t70

CNRCNRS

C,,iCmS

FL Si

t7

'I

O<s

<Si o,3

_q2 + q_

P2 P2 P2 P2 CNn= CNR/SI q3= S = si Pa L

t:

0<s<s1 -r

85 CmR CmR/Si

qCm«2Nli+CÍ«mR

m i

q, Cm«CNR + CN«CmRm i« wrrKieas+K2e123+945 +)_(q2+q3_2Piq4) Pa P2'

Pa'

=K1('-'

_Cm\ei, + K2(1

q4ci«5

. Cm« I Cm« Cm« P2 Cm« / Co,«p2 (40)' (41) (42)

O<s(s1 -:

mYa+CN« a(mXCN«)w=CNRs±CN2 - C««a + tc - C CmR S+Cm2 (36)

Si <S -±

mYd+CR

a (mCN,,)o= CNR±CN2

Cma + id, Cm«w = Cmli :FCm2

(37) ¿ L ¿:t7:) o,

0<s (Si

i±

+Pao)= q2 + q, + q4s (38) s =

+2P+P2=

q2 + q, '(39)

(11)

86

P,31

--

--(q2 +q3 _2q4) _Çm

- (43) = 8, +

;2+q4-2q4)

]

X X2 2 P2 P2 P2 03

Ki=X2

-(qi+qs_2?-1q4)_

i

X1X2p2 Pi

i>2

z _P 3 s>s1 i

o=Kie213+K2e22s+_(q2+q5)

: (45) ---(q2+q3)-Cmn(si)FCrii2 (46) Cmi, C,,,,, ) C1,,.,p2 Cy,,,,

i e2is+K2le22s+ i (2+5)sJ

(47) X1 X2 P2 os

K'1

X2

{J_(qz+qs)_(si)}+

i ( Cm2+Cm(Si) X1X2 Pi X1X2 C,,,,,

K2=

X1 '{_J._(q2

+ q5) (s1)}

i

(Cm2+Cmn(Si)

Cmm+Cmo) X1X21 P2 X1-X2

z,

C,,,,, W3

''t'o 3Z.t:

LC

11b i" U:

,_CN,,(CRCrn2)+Cm,,(CNR±Cïq2)

-

-CCmCm,,(mx-CN.,,)

:IE,

Cm2 O

Cm)+CJqR

- CN,,CNR±Cm,(CNRCN2)<O (49)

c-

Cm,,

_c

Nr__4CNI+C N2 - - -50°

''

-

B:v'

tanker

Fig:-

:fi

350

R35

-JçIE1

]94'L,

3d' vafer

U2O°:Ut

2d' , d±ifting force iii) ..0 2 3 wai'eS

'o

CPt, ° : o Fig- 9 (44) (48) (50)

(12)

q (

Q-2Pr/q

G'T-<7:

4- C702=O

¿< (x9O°;

-7)

8 hm(CN2hm ChN) q Cy,,hm+Cm,,h (58) '1 (12J a0w0 7

)FJL

6a3o,

tt)

J2)

a) LC

a2,aw, ú,

_IJ<

kUC,

CN,(rnXCN,)o+hNao=CNac=CNft±CN2

CmCm,ó+ hmaoCmjFÇm2

(5)

:iw

Po2(Q1-q)w+(R-i-r)=O

(52)

p

h {hm(mXCN,,,)hNCm2} -CNh70 + Cm,hÑ

-c

ifl Crn,) Cm,.hm+hm(CNRhm CmflhN)

W mo

- -

-

-CN) + CITh.,hN

r

CNRhmCmRhN

- mli

mi '-'N,!nL + '-'m.,N

(r

r

CN2hm Cm2hN m2 m ¼, Cq,,hm+_Cmcky

IIQ)i q,

'

IC

Pco2Q@+R=O (53)

:u(52)tt-coo, 0)0'

_Q±VQ2_4FR

₅₄ W ₎

,Q+q±1/(Q.-q)2_4P(R+r)

- (55) 2F

St)

---

(56)

Lz

':JI L'J

2Qq+q2_4p1/Q2_4P

iJ Lc'j

&3U LC

=:=-[Q2

_{i+

t'}J- ú+ p[q

(51) 0)

Ut

E-:lit7

(51) ¿

(13)

88

U t: C

Cm

-

r1_ Q-P

'»L;

VQ24PJ

P<O,, q>O,

C .J m>O

4-:3r-r7, C

J (CiV,hm+Cm,hN)>O

(Q_-'P ) (CN,h,m+Cm,JZN) =CCmX+ Cm,Y+hmZJ

(Q2 - 4PR)(Czq,,hm + Cm,hN)2= C -CrnJC Cm,Y+ hmZJZ + 4hmYCCmRX+ Cm,YJ

= C CmX+ Cm,Y+ IZJ2 + 4hmYCRX+ 4CmXCm,Y

Ut:)C C

J iEÑ

hniYCmRX+Cm,,,XCmrY

f X=CivjZm+Cm,hN

Y= (mi- CN,)hCm,hN

Z= Ciq jhm - CmRhN

q/p(O XYjO

i:-r

E

CCmRhm

E>O

w-ç R-'j

q CN,hm+Cm)ZNN2

<o

¿ /7

T:ii-

¿

:a

Cmø <O

Ez3ç'j:

CE70

b)

(iivL:)

a u,

st8a,

Ut:

, m11+m12a-n128ø = C,2 (62)

--m2a+fl2th+fl22o,=

Crn2 m11=my nIz=?nZ-CN-hNaO mIZ=CN+hNú,O+mXaQwO

n2lz

fl22 _-Cm,+hmao CN2, Cm2 ±ì1iì

)

LF1 X

S

U9i'U'L

H)Kz

< )5'

Drifting force

Q)U7Z,

4- (62) Ú (63)

2pi=

n21 n11 Cm,hm _C Cm " Chm + CmrhN N2 - q mfn22-m22nl2 _q' -rnl2Cm2+'n22CÑ2 2 2 m11n21 -. (59) (58')

(14)

:èj3iti:

=441 'e '+ A2'e2'3

)l,,

X2'rPi'±Vp'p2

Sc,,2q2' m,2Cml+m2CN2 P2' fllZfl22 -fl22fll 2 :Q) z

t<f7o

U-C

8w2'>O'L,Q)J1

è 'L

IM,,IZ

E' =m22CN2 -ml2Cm2 (Cm,, - hmwo)CN2 - (CN,, + IZN(»o +mzaowo)Cm2 (67)

X9O°Q)è

Cm20

7&

E= Cm,,

:Q) E'

,

Q)Irlè<

Q)ftk H'(s) r(s) J'(s)

è =

H'(s)w2'

=1'(s)6w2'

ètt è

137,,

<

ll'(s) J'(s)

!!

<1

cargo A è tanker B :CQ li'(s) I'(s) J'(s)

FiglO z-r,,

: drifting force ' s

è1LQ)1O

t/t

Fig 3 Q)

_CÑ2X

)Y

I]l:,H1x=9O°

Q)X=90°*45°Q)C,k

Fig 11 Q,t

:

j:E

Thè'0 Lt:

X=45°

CN20, O°

Cjqz=Cis2max

èi

135°

j

CN2=O

è

C,,,2

CN2 thJ1è

_{X Q)L'1'U± S Q)b} _{L <,}

Q)t

x=-wos

(degree: (70) '21

Fig lo

jLJ1Q) H'(s) I'(s) J'(s) 89

è'o

P'

¿(s) 3.0 2.0 1.0 + CN2

Fig li

11Q) drifting force

(68)

tc)

Xi,

X2 Q)1l: X,',

X2' Jfli

H(s) ¡(s) f(s)

(15)

(73) (4)

(79) (80)

s=s,

t7&

(-4,

4, o)e2'i + (A,, A, o)e1'2i +

0

2

(n2X", + z22) (A, A,0)e2'1-+ (n21X'2+n22) (A A,0)e'2,

±

2n22?$1q2ar=G (81)

AtAo(1 es,

) A2 =A22(i_-

e8

) (82)

sz

Qz :UC

cargo Atnker B :-*- Fig 12

r'tV) tanker

Fig 11

_{853U x=45° Q),}

S0

kU CÑ2CR2nuix//4WO ¿:to ¿

CN2 ±

.s0-s,

± C2C2s

s1-s2

ij CN2=-N2(s-2s,)

CN2 = O S4-S5 CN2= S5-S6

Ç2=N2(S-s6)

s5-s7 CÑ2=O O) .so-sl +2p,&+p28cQ=q2Qs m22

-45° -CÑ2(5-s4) q2o} S1S2"57

-71) (72) (73) (74) (75) (76) (77) (78) (79) (80)

q20= mnCN2

&»20

.__zí q20

;_' P2' P2'

DJtJJ{Li s=0, &o=0 a=O

A'

'2'

2p' q2_

i

q20

X,-X2 P2 P2

X1X2 P2

A20

'

2P'q2o

i

q20 - X', X'2 P'2- _P'2 - X'2 _P'2 SI-s2

±2p,8th+P'2wq2o(2sis)

8(021 =(2s)+?2_

8a=

_m22{n21X'i+ n22)A,ie1'; + (n2X'2-t- fl22)A2,2'2

- 21 -9--+ZO

(2s, s)+ 024

(16)

91

G)&t<,

h:--t,

Fig (13)

Q)TnkQ)lllJ

< / 'i <

U

X900

5

t

drifting force

5 ftt

:JJU,

Q)&

¿ k ¿JL

tt

o

e

0.S L.O 1.5 45 So 60 70 80 100

05 Fig. .12-1

(cargo A) 45 50 60 70 80 9ó o 42ò X

Fig 12-2

%& (tanker B)

2.0 2.5

30

(17)

92 WA VE

.7

tanker

(

et

at

W00.Ç30

E')'

O

Figl3

LEl:-t:

:,

L,

-itE L

t:

< < <

LAC,

Z:

drifting forcet0

L-c:

J)lQ)

roll -J ,

Q)lt

driftnig force

-,t drifting force

tlT::,

--

roll

drifting force :-Jç <

t

5,

f' t,

ifLi

E' = (Cm,, h,0) CN2 - (C,,,,, + h00+ fl,oao)Cm2

>0

liJ-4

<0 tJi:

:ft1

x='90°

E'O

oll

yaw, sway Q);j:

L. J, Rydille: "A linear theory for the steered motion of ships in waves" Trans, I, N, A, 1958

flimfìE,

r

:IQ1Jfi

i1

2fl9

_J

A/

49- 1932

(18)

L : B : d : d' : a i4zt ₅

i:

_-r

7

-93

Yoshihiro Watanabe "Some construction to the theory of rolling" _{Trans, I. N. A 1938}

Kyoji Suehiro ,,On the drift of ships caused by rolling among waves "Trans. I. N. A 1924

A. Krilov "A general theory of the oscillation of a ship on waves." Ti-ans, .N, A, 1898

Hajime Mamo ,,The drift of a body floating on waves" Journal of ship reseazch 1960

rBeam Sea lj

30

Shosuke moue "On the turning of ships" The Memoirs of the Faculty of Engineering Kyushu

Univ. vol XVI No.2

Kenneth S..M. Davidson and L. I. Schiff "Turning and course-keeping gualities" TSNArVIE₁₉₄₆

J R. Paulling, OJ, Sibul, 13th M A T T C 1962

484-: Yawing

V94-Table i Nomencleture ship length ship breadth draft

modifed draft for an imagined ship d

distance of G below L.W.L.

GM

area of the water plane

S # the centre vertical plane

C5 block ccefficient

C : water plane area coefficient

C : midship area coefficient

W : displacement of ship

y

volume of ship

k : aspect ratio of a pair of centre vertical planes =

U : ship speed

s, y, z coordinate axis fixed in the ship, origin at the centre of gravity G, z, lengthwise y. transverse, z, downward

t : time

s ship number progressing in the unit time i, =

tu

wave length wave height

maximum surface wave slope

'y : effective wave slope coefficient

c frequency of wave

frequency of encounter

Ce non-dimensional frequency of encounter = crL/U

x ship's course relative to the direction of advance of waves

o : rolling angle

anguler deviàtion from course

(19)

94

a0 : drift angle at steady turning

-:

rdder angle

£2 : anguler velòcity of turning of ship

non dimensinnal anguler velocity of ship

N N at stead' turning

phase lag, between wave and rolling, of ship

N

hydrodynamic lateral forvce

M

i, turning morneit

F1, F2 lateral force due to waves

M1, M2 turniñg marnent due to waves

m, m

coefficieat of virtual mass of ship

i

i'

virtual moment of inertia arourd the virtical axis passing G

CÑ Cm

} derivertives with respect to a and (O of the hydrodynTamic force and moment on

the ship

CNN, Çmo,

CNR, CmR coefficient of normal force and moment due to rudder CNt, CN2 coefficient of lateral force due to waves

Cmi, Cm2 i, turning moment di.ie to waves

Table 2 Principal particulers of model ships

Cargo ship A Length 1.000 m Breadth 0. 175 m Draft 0.077 m Displacement 9. 70 kg Cb 0.712 Cw 0.840 Cg 0.985 GM 0.Ö12 m 0G 0. 0122m

d'----d

0.0660m

Cw Tr (rolling) 1.20 sec CN

0598

Cg

0.178 Cm 0.191 Cm,

0.085

rn 0.261 0.486 1g 0. 0308 Tanker B 1.000 rn 0.289 m

0.114m

25.90 kg

0.786 0.885 0. 974

0.024 m

0.0151 in 0. 1012 m 1.34 sec 0. 705 0. 262 0.289

0. 118

0. 480 0. 886 0.0580

(20)

a-c = a- + -_cr2coSX

95.

Drifting Force

drifting force

jQ C3J'vc

j4 _drifting force _U

biíth:

yawing - pitching

rolling angle drifting force

t-

¡* rolling

:jt UC'J'

è

drifting force L-(83)

Fig 14

e

a- L U=a-(1_a-COsX)=V+22rflcosX

(84)

n=L/L

F =

Q)AB

f1:

Lw/sinx - O ¿

p() )f)-4

(85)

LQ P i:

fj\{$

dv :f'j7)J

'

=

pge81 sinx{[sin(-sinx +cosx a-J)J+-sinx[xucos(sinx+cos

yusin(sinx+

cosx - a-ct)J-4sinx[sin(sin + cosx

o-t)

+ ìcos(-sinx+-cosxa-4Jdv

...

(86)

Ut:{iJ<jj F IL

-rcc

?Lx

F= _Psinx{cPsct[j e

sin(-sinx±-cos)dv

x (co4sinx -i-

cos) dv _tinx.ÇS .Ç e 8csin(sinx+

cos dv

-

sinx

tos(*x+cJ

r

(21)

96

_isÇ Ç Ç e°cos(sinx+

:ficosx)dv;sinxÇ

S Sve fl(TSirX+ cosX)dV e

_sinxÇÇÇe '

+ sinx

e"'

sin

(sinX

fcosx)dv)

v)Q)

V

L.W.L. LT

V0 Q-5

L.W.L. Q)vtQ)

/o

cos(sin

± cosx)=cos(-sinX)cos(-frosx)

-

sin(.sinx)sin(cosX)

sin(six+

V3

L, f

j

-d Ç ÇÇ3e R

sin(sinx+cosx)dv

R

_{cos(-irix--.cosx)dVo}

F-):t7

Fr pg'WslnxL{f18+f23 +133 + 0(143+153 +f63)}sino3 +f2 +f3c+ 0(f4C +f53 +f63)cosu3i 123

crc

_'Lcinx

cos(cosx)

= e cos(- -sinx) dv i

jjj

R lic Vo

sin(-cos)

Izo

=sinX

123 R Vo Isc _X5 e R

cos(sinx)

s'nxÇ _!ojnX 33 R ÇÇ0

sincos

f

r1 =

_sin(sinx)d

dv 14e Eo -i cos(-cosx)

i

(C

R. r

=sinxlll

e R _JiJV0 _3flZ

f63)

_1.

ÇÇÇ R

=sinx

e 16c J

JJJv0

e

cos-sinx

csin(sin

r1

0cos(cos)d

s1n(sin)d

-co r1 çeo e Sin(-cosX)d sin(-sin x)dL -co dv (.-cosx) dv

cos(_cosx)

sin(sx)

dv

cos(sinx) 1cos(cosx)

ç (87) (88) (89) (90) (91)

(22)

94) M3 = fis i

r

fie iL sin x + O (m3

cosk2fl

sink2!

+

+ in63)) ini, cos k2 =pgÇ fi in13 JL sin k, 143 r

=pgl

sink2

,n4, _r

sink,

=pg

f43 cosk2 ,n4c

_iL

I cosk2 /5, r

=pgf5

sink2 'n53 ='pgr sink2

153 iL

cosk2

i in53 iL

cosk2

f6, r

pg% _f6

sink2 I in5, r ₍ sink,L

=pg% 4f6. 1

d-163)

iL

cosk2

m63 _iL

Lcosk,J

E 1 _{Q) J%}

t 7 -

97

v0/R Q) order

U1-

x3/R,

y3/R aJ

F 1 order

JJ

heave swag roll

j:j L-c'j

{&t

123f2c=O,

f=f=O

(92)

y., even keel Q) ,

sin (cos)

y.,

Lj:J UC-h5-)

<

íUQ)±'i'0 UC strip

ffl

-c:

. y. midship wall sidéd

ij(:

E,

i, :Q)Ç ¿f

t7'2,

In,, Inc 1±

:a)

:

1

LIb'L70

t.

sin=k1,

_-cosx=k2

(93) Í1 < ¿

x,,

i

L'J'

, COSk1 E

i _.-(k1E)2+

sink1 E

k1 E ---(k1E)+

Ck1_ i

y.

E lQ) ¿,

waterline ,

j: Rankine Q)

mean draft d'=CbfCe

Ut:C,

U

j.

:{-c

t:t U,

:5: a(OG) AC<.t70

f

2d'0e'k {i -

k1d' +

(kd')2} {i_. i(

f4

f

E0eak {i_jk d'+ --(k1 d')2} {(k E0)2_(ki E0)4} (95)

16 2d'E0eak[{-dki

- --(dk

)2} --s- {d k1 ---(d k)2}J (i_--(k1 E)3}

F = F3sinut - F3cosa-3t (96)

F, = 6, sin

{f, + 9(143 + f5, + 158)) F3 = 6, sin x {fi + 9 (f4, + I5c + fC)}

M = M, SlflU8t M3 cosa3t (97)

(23)

98 Lo 0.8 o. é

4

e. Z o

Fig 15-1

o qo 60.

Fi2 15-2

Fig 15-3

Fig

15--9 j: 15--90'sinG,-t--8')

Utcl'C,

lJQ)E. 'J lU

F

(Oscillatiòn Term) +constx 0'0«f4+f5+f6)sin6+(J+fsg+f63)cos6}

(98)

M=i (Oscillation Térm) +const x 9'0{(m4± +sn6)sin6 + (m4 + m52 +m6)cos8}

i7

drifting force

ri turning moment ?'L

F2=--e sin x

9' U4è+f5c+f6 SiT) 6

M2W Sin %

cos 6

cargo A, tanker B

W,WL Ii

LtQY

f, ñz

U

Fig 15, 16, l:fft0

i

(24)

0.1 0. i .01 .03 77165 s/aX .02

'ç,

60 30

Fig 16-3

99 .ò3 .à2 .5