r1,A// 7
0/
iL
ARCHIEF
17GfrL
s---32 5t
aep ouwune
re4rnhche HogescI
DeVft
IEm
**
Motions of Ship in Oblique Waves By Shin Tamiya, Member
Abstract
Assuming that the centre of gravity of a ship advances horizontally with a uniform velocity, the equations of general motions of the ship n oblique sine waves are obtained. From the
solution of the equations, we have found that the effect of the exciting moment and accordingly the angles of oscillations vary complicatedly with respect to the angle of encounter when the wave length is short or comparable with the length of the ship.
lt is also revealed that the interactions of rolling, pitching and yawing are small.
Making use of the results as to the motions in regular waves, the author has worked out an illustrative calculation of pitching and rolling angles in irregular seas and obtained some re-markable results which are, however, ordinarily experienced on board.
-t s
, X±1
, aJ
l}cD
5 l-tz¿ l/o
JC
Q)J*
E75 <
tLtt
UC©
) 7,?i (i , Linear superposition Qyt,i1L
Gx,,z
L i), X Zi-o
oG lt-
1*JJIIG
*, WK
< Ij, 4 sine wave7
LIfl
smith effect IiO
its
t{&cj 5.
1) K Drifting 'kOL1
I_, 1i-{&
1__
(1)
11o5
Fig. i XI Fig. 2 _U
A=Ï
W0KL0 2y0=WOL0 Q)v; i0if
Iy'b + (Im' I') =
IZZ'+ (IVl, - I')b = M
I'
z, y, z i b *' )(2)
(3)itT
7 (1)(I'
IWM') L- ?.ft U*t '
, í F JLì
e;'
I-FjLX,J)5Z,
O)Zr cos(k(XcosCZYsin «)+út}+d
HU-t
H 2ir I2irg '°v
« (Fig. 1) d0-X,Y,ZG-x,y,za)li, 6,
U-cx=Xvt+Y.q+Zq'
X= z + vty <pz.y=YX'p+ZO
(5)
Y=zq?+yzO
(6)
z = ZX. b Y OZ=x1'+yO+z
vGQ
C-t070G-x,z.ÏL
Zwr cos(k(x cos «y sin cx)+ (w+kv cos
( a ) rksin«sin{kxcos«+(w+kvcos«)t}G ay ew-6 COS CZ
¿..<o 8w
Fig. 2
i-b, b0, WL'iL''
W0L0 W1L1 ToC b1 ¿-co4çg-fjjb
ni S7X»)
pg(A+2y0[d])
(10)Kb<---Kb0(i
2 y<[d]
2 y0H(d)
A ,)
(li)
b1m---2y[7,d] \\
3 A I (4) (12)Lo_d=+[(Zw)W+w)LJ_d
r
cos(ky sin a)cos(kx cos cx+ct) x?bH=
-'
¿) xb1:,
7AU
dMX= pg(AX+2 y1[d]) Gm (-7e±d)dx
(1)(12)
[A5+2 y(,d)] Gm
A(KboKG)+-- Ys3iU
to
d'J\sQ
UUO
M = pg IJ[(Kbo_KG)
++
(70w-0)dx =Mxw_pgOf2[ ', Jdx = M0 4 GM O{I1, 1=1 2ys-x2dx=4Q)
X1 iii) i)Lt
(16)4=pgV it
r(8)cO
0w X 11G 74GMOii) 11-)Ì
M =f 2pg(AX+2 y1(id)}xdx 1,2 =JXjpgAxdx+pgJ 2y,(lwd)x.dx
Xj p1,2 XX=pgJ AXX dx+pgJ 2 y,r cos( y sin c)cos(kx cos +5t)x dx_pgJ 2 y, x2b dx
1'l XI
= MpgI '
(17)2
M=7pgJ LAz(KbOKG)+
X' s9JOwdx3.
M =Pgf {A1,+2 y,[d] } (O-7O)x dx
t X2 0My_7pgJ A1,'O,-xdx (19) 83
t_)'
-0,Jff
Zjt56D,
Jt-i
'Fk
2K1,,
O¿:i2
KXKy-5o
(13
4.. K.
tJt' N
N KK,=f'-hi
¿h1T (i
-%-[hlTJ2)=N2o (20)TCO h1T' N20),
O h7 'j<Jo
K7,St. Denis & Pierson
'57
52 K7, = N&..
=-- LB2po
s2(e)- kB7/.6 sinkBll)kBi1
x , 11 l y, 'z
LUjfl, a- t
C-=ë-L BkBj 'j',
sinkBi7 (23)¿-'-( (21)
j7
4kBp3i
N =+
L3B2pwee_25T[ (p+3) (2 p+3) (3 P+3)J :óII< K7,
ih2
kí5
JIKY
N v2Nçs I7,7, - 217,7,' - 2pgI Bv,2o (kB)e_25ECV.P(Cw) (24) L T2=2irfv2i
P(Cw) = Cw2/(3Cw) (25>t2-s I IIt (23)
BL3 C 1= 123-2C
(26> Q)- (1)(2)(3) 2i
1,'O ±2 K-+4GM-e= PU7J A(KboKG) ±-. y,8 dx (Izr' 17,7,')ps
I
- b+ pgl &=pgyfx22y, xcos(ky, sin c)cos(kx cos cs+w,t)dx+I,,'ç Izz'O.My_ypgf A X0w dx17,7,' .
< Q)3-'
Lt
U-EíLL
Ol-At,
.:::)ß1
<, t,
(G iÇ2)
KB--o (41) 0, ib2
I* '
5i, Oi¿,
- ' X (30)(31) It,ì
(mf)1L UIt O
ItAcC<
oPIt (33)-(35)
U ç-4 l'il- S2(w,a) i 0 O¿ o+do rro (2iX)2
S2(o,íx)doFig. 1 ¿T< ¿-tI
-c7)4
'ZZ'TVlI
(27) +2 h1+v10=m1 Sfl ()et
+2 k2+v22bm2 sin ot+ (28)
(pfli3 COS )et-0b (29)
2 ypgrkf 2 7pgrk.f
=
I'
m3 =-'s'i Izz,
(30)
f=sincxf1Az[KBKG+
]cos(kx coscx)dxfy=fxys cos(ky sinc)sin(kz cas c)dx (31)
fz=sinf'Axxsin(kxcosa)dx
(32)í LC
Om1(mf)isin(w5t+si)
(33) 1' m2Çmf)2 sin (øet +s2) (34) = m3(mf)s cas øt (35)LlJQ)
) 1 i=1, 2 (36)(nif)=
V(o2_v2)2+4 h20e2(37) (mf)a=-2hw 2 (38) =tan , i=1, (
0=Oo+Oi sin(úgt+ei) +02 sin(2 Cûet+512) (39)
b=b0+'1 sin(oj+es)+2 sin(2 ot+e)
(40)Iez'4S'Wçp 0e2
0o2I,
- -
2 I'
Pi cPi/Z_we272(4h2
cPI0i (41) 2 P22 Sifl Si ij 1O1 2. 2 V(v22_o2)2+(4 h2o)6.
101--7n 0.3 02 a' 00F S2o(w, )dw= [,ni(nof)i]2dw r 7pgf 2 4 n2H2i' j -
2 (mf)2dw_r '
72frYL7J
L (we2vi2)2+4 hj2O)e2 J a)dwSq,2(cò, x)dw= [m,(mf)o]'do,
-
r2 pgf - L 'oni' fH2(mf9)Odw fol2 = L (we°v22)2+4 ho°we2j.
S°(w, ) dc, ö 0. 866 [ f °°S02(w, c) dw] (45) - r '=0. 866 J dxJ Sq2(w, c)dw (46)Lo
o (43)(44) { j wt*
QJ1IJ)
5 cO0?5T (30)(32)
Jft. U0
(B(
rx1
A=A1_Tj)
Sl_L]
A ¿OL (30)(1)(32) Ft*kf,, =1SinCJ'[A(KB_KG) (1r) +-j (1_P)3] cos(kl cos c) d
0-I o 0,015-0.0! O.i05 30 0 (30') 30 0. 30 60 30 30 30 Fig. 4 A 4'
(rad)
Fig. 3 B m1, m2, m0 ('/sec') 'oC KG(rn) GM(n) T1(sec) Ta(sec) N20 BI! (kBC
f-.cos,-
sina
xJ1e(1_r)sin(
cos a)de(31') fz=Az12 Sjfl a
xf(1-)sin(kze cos a) dE
(32') A B C 80 8OGT U0SOOGT cc809000GT ¿94cT1: 26x55x25 2.00 .64 .711 78x9x5.5 3.50 .47 .653 1/25 i £i, £2 (deg) 140x19x10.5 8.00 .68 .694 o o o 0.3 0.2 0.02 Fig. 5 B (31') cosine C)Tlt cos(ky3sina) fÙ-z1 P 5W. q=1 o
LLLO 1i
U (® o) (W1,2)p1) U, Fig.3 1n,rn2,rn3 (B )Figs. 4-6 i. O,W1,1
1UO X o'
v=0 XC )./L=3.00
UI:.:0
A/L
1.5 jjr
f2,f,, ci(a1UC) /jk'
SincE, cosaUC< ,
fff7?Z< I:jt,
f,,sina
'iEU
a
a=0 °)< CJìt
ie, w,
UL dz
/J\ < , , kut A,B,C -9'7 A B,C U CwIJi-IIL4
Ut, Iiti
9.33(4.80 rn/sec) o)Jjfr 11 rn/sec C)Tl±UiJ.
3L
'
5n4j-t {. CQ)
OAL4)CO L.., X (43) S2(w,a) O 4iIÍLL0 (Fig. 7(a)) S2(o,. a) =C0 cos2(3-a). C0=1. 16 m2-sec À/L=0.75 LOO 1.50 2.00 3.00 A 31.5 39.2 55.1 80.4 131.6 C2 88.2 111.0 145.4 160.8 171.8 B 0 37.6 142.5 171.3 175.2 177.4 e.. 129.1 153.2 169.3 174.2 177.6 C 1 13.4 15.4 21.6 35.3
-e2 137.8 156.0 169.8 174.4 -86 .71 .78 2.28 3.27 7.00 0.38 1.00 0.80 6.00 6.96 15.40 0 3.58 4.02 6.50 .0320 .00876 .01334 3 OES 0.4 0.2 0.t LxBXD(m) 7J( d(m) C C7,aol 8. oé-' 60 Fig. 6 C Q)M41 S i=O.55Ú)w2=1.1O:dJ:.:J o (ùi,e)2 212m, 53m Q):Q) 3ff, 0. 75 C0 12. Q) S -
'
- )L- Q) X- Neumann Spectrum j312. 2.83m, ;c' );L'Q) 'c-:l2. 116m C70
ø°°0.751.75 Q)PM-e 6 7 8 .9 10 ¡.1 i-2Fig. 7 (a) l'il'
.3. /3 u-cit 00, 90°, 1800 .2. LxBXDXP7jZ=68.50X11.00X7.50X4.0O Cb=060, Cp0. 638, Cw0. 69, KG4. 03, GM=0. 90, T1=9. 00 T2=4. 95, N200. 015 (ìi m, sec) U f I
Q)27j.Fig.7(b)
(1.633 itjO
Q) 116m, 2.83m . 't 3& Fig 7 (b)'
Q)- Ii
Q)UÌ0 Neumann Q)
Spe-4LQ)1
(OSl+JiiJ)
ctrum ¿Q)MJ U
t
Q)tQ)It°f )
l&Uc,
-2.RN
Magnification factor
5t
lt*.ti'5, 1955
i
(Fig. 7(b)Q]) -Çt
1Q)lOt
I)
] ;Q) Q)1JÒ
c, K- U C1tL/2
(2
)2S2(a, c1) =C' cos($c), C'O. 01,
/3=0, j-,
I UC it 0. 020, 0. 133, 0. 155 {R U,(g
c)Q)fl
C'Q)jPQ)
,l4 o=0-2.O
t
'1,b2t Q)fj1,
83 83 83 lEI 83 .0043 .0167 .0186 .0070 .0273 .0304 0 .276 0 .0137 .0098 .0077 .0223 .0160 .0126 .0514 0 .0262 °I° tO 48 838' 424883 li)8648 8301148484883 radiani;4 57
,
J/lF i
/j\ < 1:,z
Ctcost,
'oy
±Tri U-l2,
rt'i <;i.
1i, 4l*to0
r.o1z:,
ttt: Neumann, ìsijèò
Magnification factor
c'jj 5-jj
r (43)(45) ¿ ' 5S2[] =f:s, x]dx
)J-C,'cSø[o]t*
S2(w,)l'<
IJLCl,
<too
*ClK U'
O)-tt f'fL t---
-'i-co-cj,
j-'-7
i) Manley St. Denis and Wjlland J. Pierson: "On the Motions of Ship in Confused Seas," TSNAME. 1953 (30')(31')(32')
55c. Figs. 8,9,10 0)
i, t/,3IJj
f=l sin
¿[A(KB_KG)bi (C5, t)+-f/'2(Cw t)] Bi2 (kBC .fy=cosi,
2.S1fl).s(Cwt)
Fig. 8lo. = Al2 sin cx (Cr, t) t=klcosa o 2 3 Fig. 9 Fig. lo 3 -z