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iEModel Experiments and TheoeticaI Calculations in Waves on a High Speed Container Ship with Trip!e Screws
By Fukuzo TASAI
Yasushi SUGIMURA
Mitsuhiro ABE Hiroyuki ARAKAWA
and Masanori KOBAYASHI
a-i mo
45 rj ij
l U 48 4 2
Roprirrted from
JOURNAL OF SEIBU ZUSEN KAI
(THE SOCIETY OF NAVAL ARCHITECTS OF WEST JAPAN) No. 45 FEBRUARY 1973
7CH1EF
Lab.
y. Scheepsbouwkunk
Technische Hogeschooi
3
(fii 47 <y io
<yjf4
) 73IEL
'-)'t:: L**
ill
iii
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*
lE **Model Experiments and Theoretical Calculations in Waves
on a High Speed Container Ship with Triple Screws
By Fukuzo TASAI
Yasushi SUGIMTJRA
Mitsuhiro ABE Hiroyuki ARAKAWA and Masanori KOBAYASHI
Summery
In this paper, motions, accelerations, deck pressures and resistance increase on high speed container ship with triple screws in waves were investigated. Model
experiments were conducted to be compared with the theoretical calculations, in regular head seas, in regular beam seas and in irregular beam seas.
Fleaving, pitching, swaying, yawing and rolling motions were computed by
solving the equations based on the Strip Method.
Especially, the equations of lateral motions were solved by taking into account the new non-linear effects on inertia, damping and restoring moments in rolling
motion, in which, inertia and damping moments were determined by using the
results of free rolling experiments. Following conclusions were obtained.
The calculated amplitudes of heaving and pitching motions, relative motions and vertical accelerations in head seas were in good agreement with model experi-mental ones, except the amplitude of vertical acceleration at stern.
In beam seas, the calculated amplitudes of rolling motion which were
computed by taking into consideration the new non-linear effects, coincided very satisfactorily with the model experimental ones.
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l 'y7Y't
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l:x0 n]O)
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(l=
M11dx , b2 = I NHdxb , CZZ=pgA,
jL0 JL0 (L1 (J. (L1 a20= Mflx),dx0, b20 = (Nj1x,VM)dx0, Coo = I (pg.2bxNHV)dxb, jL0 (L1 (Lf (L1 a00=I Msx°dxb, b00 = I N11xdx0 , = j(V°Mfl)dx--pgI,
JL0 JL0 L (Lf (L1 ao:=JMRxhdxb, b02L0 =JL0(N5x0VM11)dx0, CO2 = pg.2bx0dx0, (L1 F22=
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M11 zF N,1i&Lt0
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S,,' (3)
2.2.5Í
Fig. 2 4X0
G G 'I'È-c,
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Fig. 2
I
75 (4) wave X0(L1 rL!
a,, = Mdxb, b,, = I N,dxb, a,.. = a,,, = M,Xe,dXb,
JL6 )L0 = be,.,=J 1NSxbdxb, a, = a 'y = b,y=J'Ns(1wÒ)dx. a,,,, =j'M)%dxb. b,,,, =J1N0xdx. (Li (L1
a,
=a,,
= M$(l,RQG)x,dxh, b,,., = b,.fr= JLI N0(1,OG)x,dx,, (L1 (L1 a,..,= (15-2M0 0G 1$R+M,0G2)dX,, b = =WGM, F).,=JFdx.
=
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(6)
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Q)Y0. Y
c' Ey, , ?2.3.
t$iJQ)J
(6)t'j
=
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.'1--E40
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06
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M J,+(ça)
'I1.
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(13)
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t
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, Ya,,, ay,,,', Ya. 2.4. :7
- L
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5I
(14) L7Q), co Q)U(J,+(co))+b(co)'+W GZ'(ça)=Mri(ça)
f
M2(ço)ç,
=O
Photo 1.
78 k
(16) I1co (J+ (ç)-Mr1(ço))
(()M2())
47}(MO GZ'(ç') GZ'(ço)=GZ(çô)w.gm/W.sinj:j.'I, w.gm
i7
)7JKCi,1
5 ç4J T,'(ç,)
,)M2(ço))
T'(,)
W GZ'(ç',,,,)=
- N'(ç)aA
T (ç)
L, N'() =
L' -
l c»j N'1Ù-i±t:
ftoj
,Lt: N'(p,), T,/(ç)
(17), (18)(J'+Mrt('a)), ((ç)M2(ç,))
) WGZ'(ç,)
*6
-af
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47IKÌ'57
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-LT
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84,000 BHF261y
')5--, --Lro
4 m 7t5 7
3í}k 2 O) 1jKj7 C7)±
midship
1]oyr' ')L'7
Photo I .f34j
79'fable!.
Principal Particulars
IjEja.
1Ib±j*c!,
flIJ,JiJr ljo
i-tt:,,
*tt
7',f,23I
k*rIcl0t-fttc,,
-t' 'LI),fkJJ('! (80 mX8 mX3. 5 m)
1LfO
3.2. 2 L=U.32.J,
H 2(= 2C/1)=1/501/30IJ1)L,
' l74-- V
F,,=
0.2, 0.25, 0.275, 0.30 L L, Ii IJiE1 2/L=0.62'--6.6,-arj A(= T,,,,/T,,,)=0.6-2. O , H/2=1/200-1/80
L, 2gIJJ-
Pierson MoskowitzL--- i-
3TirJl'T6lt
1) r4aO»,l', ±T$)
ET*8( (F. P., station 1/2)
ETOÌ (station 9%, 1/2) (F. P. station 9%) -.ìL', 7-.h 2) JO) ji'JJC1f±Ti),
IjJ:fl,
Fig. 3-6
ItO
*62Î{3'Ll, F.P. station 1/2 (Fig. 4, 5)IJK&t
I) -1ilJLt,,
/ 'Tr ElmIUPMS5
-ir- Lt,,
Photo 2, 3
Actual Model
Length between perpendiculars L» (m) 252.00 4.000
Breadth B (m) 32.20 0.511
Draft cf (m) 11.00 0.175
Volume of displacement J (m3) 51128.0 0.20447
Blook coefficient C,, 0.5728 0. 5728
Prismatic coefficient C,, 0.5892 0. 5892
Midship section area coefficient G,, 0.9722 0.9722
Waterplane area coefficient C,, 0.7851 0. 7851
Longitudinal center of Buoyancy from M. S. 1» (m) 6.56 0. 104(aft)
Longitudinal radius of gyration K» 0. 25 0.25 Lp,,,
Transverse radius of gyration K,,,, 0. 379 B 0. 3792 B
Test value
Pitching period T,, (sec) 7.30 0.92
Heaving period T,, (sec) 8. 10 1.02
Rolling period T,, (sec) 20. 0 2. 520
Center of gravity above keel line KG (m) 13. 30 0.211
80 45
Section F P
AP Y2
S Potentiometer for Surge H, Potentiometer for Heave
P; Potentiometer for Pitch
P;P2, P3 Pressure gage
Ar, As, Accelerometer
9,2
P, P2P3 Pressure gage
AF Accelerometer
R Relative bow motion sensor
EP Fig. 4 Fig. 3 Square Station /2 91/2 FR T, Thrust dynamometer Q ; Torgue dynamometer
N Counter of number of revolution
M; D.0 Motor
R ; Reletive bow motion sensor
Accelerometer
R Rettive Motion Sensor
3 * 3tOY
S
Potentiometer for surge and Sway
H
Potentiometer for Heave
Y
Potentiometer for Yaw
P
Potentiometer for Pitch
R ;
Potentiometer for RoH
G ;
Center
of gravity of the Model
J ;
Vertical
gyroscope
Fig. 6
Photo 2. 2tL = 1.25, F = 0.275
82
kj45
lo Eop Col rr,ple screw Single screw I-IS) F,' is-Fig. 7 I'±l
Cornporison with Single ScrewI Fn 0275
0 15 - At Photo 3. 1/L = 1.25, F,, = 0. 275 4. 4.1. 4.1.1.
±TIB
Fig. 7. 8 ET
4tMm iîtlli
0.8< A/L< 1.2J)C
JF4. W482
Lt
*ø
KThC, 1/L312 tJc
ff1'j]--112)0)HB, L/B=6.810-,
Heocing Aniplitode "f £ 20 20 0 Pitching Amplitude - AIL Fig. 8 5 20CarhporiSofl with Single Screw I Fn = 0.275
Fig. 9 i F,=0.275 Fig. 10 i
®jFez=0.275
lo
N
ca
1°
100
J
1i»5
JL* F,, =0. 275 Fig. 9, 10 Fig. 9 1;1.3 Ü'I} 1 FthlQ) hL
UV0
Fig. 10 Fig. 11, 12 a**-4.1.2. ,t O±FJJOs G
X5 Q)ilL
*L Z,
Z, = Z0X0OC = Z,.000S(Cû,t±E,) , Z, , F. P. station 1/2 Fig. 13, 14dynamic swell up
<LV'0 Fig. 14 Q
station 1/2*fli
t'Jl
2/L< 0.9 Relotve Motion at F P Fr Eap Cal 0000 0250 0275 0300 3 4fj 1.0 15 - A/i. Fig. 13 F. P. \ «z' 05 20 IORelaEve MotIon at StatIon .,
05 IO
-
ISFig. 14
stationl/2 )Cl 7,
83
Deg) Phase og of Pitching
200
/,'/
loo/«
lì,, ¡I;,, 7/" Fo 0200 0250 0275 Cal 0300 5 5 'L 20/
PSaso ag ot HeavIng 000 Fo Cal 0 200 0 250 0275 0300 00.--200 -200F0=0.275 F. P. Fig. 15
Fig. 16
Ï( A. P.
A/L< 0.9 /L >0.9 - 3
JLt i
Vig. 17, 18 station 9,4
1,/2 llJ
station 91/a<L
station 1/2 0.75< /L< 1.25 CompariSon with Single Screw C Fo = 0275Exp Cal Triple Screw
-Single ncr---(NB)
-g5 ' :l(U i45
Fig. 19 Station
JTjJO
ioi±, F0=0.275
275
Vertical 400elerotlon at Station 1/2
Fn Enp Cxl 0200 0250 0275 0300 A/L
Fig. 15
F. P. ¿$c 1
4tjI Fig. 16 A. P. &cD 1 T,152Fig. 20 Station 1/2
iiit, F=0.275
o 40 n.j o Io o Fr 0200 0250 0275 0300 Vertical 4008lerxt,on Exp Col .5 -- -- --. .5 os or /. StatiOn g I/O\.\
o \\'.\.
o 40 0.2 -.5 o 30 20 IO 5 2:0 A L Fig. 17 Station 9 2Coreporison with Single Screw CFn 0275
50 inkl Exp Triple Col 5 Screw c Single Screw c 03 (NB) 030 20 ¡ 20 IO os o IS 20 o
Comperison with Singlo Scrow Fn 0
Triple screw 2.0 S! ng le scr ew "j .5- (H B) I-0 ro 00 0 lo IS 20 - O5 1.0 15 ax
Fig. 18 Station 1/2 Z, Ii1Z
Comparison with Single Screw C En - 0 275 t
Exp Col Triple Screw Sirgle screw (NB) 4
î;
DJ±.k, F0°0.275C)Hi) F=0.275
0tU Fig. 8
<JrU
F: l(
F,, = 0.275 o-Wc 14Ijy Fig. 19,
20 lo- Station 9½
1Î4Ç 3 iIü station 1/2 3 ìJ
t
4.1.3. 4h
Fig. 21 oJjtjjf
4T/Çog°.H2)iJi, A/L
LCO :0)t
24h subcarriage 0T I)
>' 7'Q) :5JyJK
0.150t:
4R/(ßg2 H2) 9)10) Ç44 11)
oJ44 Fig. 22 ioj
jjc))
A/Laft
Increorerif 0f Thrust Resistance Increment ( Fn 0 275
85
0 0200
i' 2---- 0250 S . --- 0275/1 \\
. 0300 / / r-. ii ¡a///
/
. 4.1.4.±T&h <7JKE
Fig. 4 i Lt F.P., 9V0 -'(LtJ±)
l7jKTE3[jL,
7fl7JÇ ..J(5o),
F,, 2/L, H/A C<l Fig. 23-270O
30 z 20
/
2 so.j' /
j'
¡P S'S COnSoner )VLl25, IOd-I2967/
/
//
/
Priron'd ' X S /e P5ine,,n/ S S ;5O-'
7
_., ,,. P riscan/O.,.
Sî::
S-20 0200 6250 ã2I5 odoc EXP Original MaruO Modified Morso Fig.23 Fig.24< ?!i/JK)3E, A/L=1.0, H/A = 1/29.6 Cill <j4<, A/L=1.25,H/A=1/29.6
.''LIOO EP 95 1/'.1/296 Contasse, 'rnao/d ID O S P5nsean/d D .5 4 Pmeon/d r- LIt S 0200 0250 0275 0300 Fn SI 20 IO 05 Io IS 20 O IS 25
Fig. 21 4ffi Jj fl Jj Fig. 22 F,, =0.275
¡0 60 50 40 30 LO O
86 60 70 6.0 40 30 20 I.0 0/L'150. H/A./3O2 F P gV2 Contalnon P6'd O A P,necrVd A Pmean/d [l C U 00 70 = 60 50
::
20 454:. 1/
/4/
//
//
j
'r
,-77
/
,/
---p
6' s'LQ25 HA' /386 F P 9 , Contone, PJd Q A Pi., mean/O A .5 L Pmean/d O = to '/1.I2S H,&'/43î
50 0230 0200 0300 0275 0300 En Fig. 27-/*lgl0
<3ìJ', 2/L=1.50, H/2=1/38.6
10'20 4 P5755, 1/331ï () '
P113, )4Ï P0a.LL5
Fig. 23, 24, 25 I0I H/1==1/30 aj 1/L=1.0, 1.25 JZ 1.50 2/L =1.0 F02/L=1.25 s,jrj 1.50
Z0
DI± Fig. 13
1/L<,1.i <¿, 1/L>1.1
JLrV0
:, H/A Fig. 26, 27, 24
4.2.
Fig. 28
L'Ct: N
7JKi ' t0'
Y YOY0 Fig. 28 upper limit dtrJ lower limit.o
je1=35owgl<
Fig. 29L'C0
O)Z
),t24Jt:0
O-0- ----
-'-0250 0275 osäö Fig.26 A/L=1.25, H/2=1/43. I 7,0 Pm./d F.P0 9',5 Conton,r 60 P,n,an/d A A -Pmean/d O O U 0200 0250 0275 0300 EnFig.25 e2:
--fljiei3.4
)j(E, A/L=rl.50, 11/2=
1/30. 2
2,0
2. 2o
tì 3 *11:2
1 2 015 alo 005 O iS m (degree o without A R.T e with ART. 30a)
(12)N(g) 1I
Fig. 28 11iAl5, b ) (11) (O T,(ço0) 1 Fig. 29c)
GZ(çu0) ¿I Fig. 30(17) N'(g0) I12, Fig. 28 Q upper limit lower limit
(16) O)
T'(ça)
Fig. 29GZ'(g0) ICI Fig. 30
87
io 5
-ee ¶Pns ( detree
Fig. 28 N ci) t *1 ûi
Fig. 30 ? AOL 111 ith 11th
Fig. 29 -*11i(t
88
05
5-Fig. 31 1)t
Roling Amplitude ( without A R T
Experiment
-. - Theory LineO,) -lw/A /100 Theory Non Linear) Theory Non Linecr)
Hw/t Corresponding to Exp
Exporitn'Oflt
-. - Theory )Lineor) Nw/h.. /l00
Thoory(Non Linear) Theory)
Nw/A Corresponding to Eop
05 0 i5 20
Fig. 32
*®IIHM
Fig. 31
41ftij4C)
ji'
II'
Fig. 31
rft:4
<3i:
Oo
(1/100) LCit0
©
ku&_)d;/
N 1iU Fig. 28 a,
Tç,0, WGM.ço
ut, H/A1/100 LLt:-,i
Fig. 31, 32 rf®
V0) ©
:,
® ¿ ®E H/A
t-®o)
Fig. 33
t:±2. 4
i-[-j
t1ri upper, lower Fig. 28
N{' upper limit, lower limit
itL7 t'4, H/A I
ktil
Lt: )1t:0upper limit C
°7o kIji,
}.® ® 2. 2. 3
3-'
it:,
Fig. 32 H/A H/A OS lo 20 A =6
N 2-'
4
3. 89
Rolling fmpMude t with R.T
Experiment Upper L0We ColcuIction o o IO IS A w I2ig. 34 o 05 .0 15 20 A = T0 Fig. 33
7JK-Lt:L
C,Ì-'
LC1 tQ)
®M-05
CQ)7' L» L, / <, t:ò5, L <,IC
K C, L f1]ltC,
LCA' i
jlV'C7j 5
E,'kl: *G)
i45
71 Fig. 84lc-0 M1J<
CC.
1o)
4j '] K J A *1.01t [i*O)ii PL LJ..5L1L,
--:w) 6 4 390
k45
05
Swoyrq Arpht1dO wThOi A R T. ) Swoyrq Anpltde
With A R T Io o Fig.35 Fig. 36
Iffi9
1.3 05 20 30 40 IS ¡ o. OS,Fig. 37 i
*hFF6i
Fig. 38JFig
LUt: 5c0
Q)OtLI yC (8) 0)
0)1 Fig. 35, 36 7JK i:¿:AEô tLVo
Fig. 37, 380)T Lth
TMlVj
*:y4
5.gu: Ti
<, JFffi,
4t = 0.1i' 7M
j/t:0
Hamming window'31 Vt:0 Fig.40, 41, Fig. 39
Lii
'
Mco
o*Ej:
$0)U
5t0
t:, . ÇO1 i 7K±1tJ
jf3 3.2, o=5.8 k, Fig. 39 72 Fig. 34 ej Col £,p--j5
'=2. O,
Ç01/39.° ¿.,
co (thO) 2jiJjJz
o Power Spectrum of o-Irregular Wave Tw = .69 sec H 104 mm (Jg E gJ
o
ii
liii III
Iiii
r Iii
i000 200 400 600 800 1000 200 rad/sec 10 -o O JO IX-
-
0-00 O o 00 o o 000 2 00 Fig.39 A ut o correlog rom (without A R T 200 400 500 800 000 sec Power Spectrum without A R.T 400 600 rad/secFig. 40 io)9
I' 91III
I iIii il
j jIi
I 2 00 IO('0 80092 A u to corre cg rom
(with AR.T
Power Spectrum with ART. 2 00 400 600 a oc IO 00 IO 00 rad/secFig. 41 jf4øE
I. 6.I)J,
t7Qi*wo
±Ti Lt
Lt:0 dynamic swell up<&L,
O.75<1/L< 1.2 ft1Ok
Lt0
oj aIL¿ ¿s5 11 jfl L C I
Thi]
t
Liilov' A/L
i1c$,0fLz ,
tttt:0
*BE H/a=1/3O oj±, /L= 1.0
<4), 1/L= 1.25, 1.50 -4o)j
1I6JLt:0
¿li, 2/L= 1.0,
1.25 1.50
i±l
3A L t:': t
114 ?*0)7
oQ1Jz,
93 7)
CJ
/J\ <,*i5Z)
2t:0 t:t
L.,FU!
.5to)) L1 L4.
'l t) 1th
11 t:,j-m,
{iJa)lf''4
v'tt
t:i
z.5ZljJa
t oqI-()
<L±f
rJi'o$
t:)tJ ) o
1) F6 7K1Z.);
' ' 4e;', i,
o 44$U
7
ffli; '1l
ETj
;4illJ-, 1959
"Beam Sea (4}lj",
Jj
fv'z",
105k30!-, 1965
4) Tasai, F.; "Hydrodynamic Force and Moment Produced by Swaying and Rolling Oscillations
of Cylinders on the Free Surface", Vol. IX, No. 35, 1961.
5)
kTJ; "Multihull Ship'
Jl-vZ',
Appendix 1, 1970 6) "Some Contributions to the Theory of Rolling and its Related Problem", )jjI1939 7)
i; '
141, 1971 8) 9)'o-f
",($1)",
k 43 r, 1972tXiL 101f, 1957
10) 1.1) ;rf; 'g", ftlC
(2)",
108e, 1960i144$7)
12) F61, 17fz5,
JIIì,
?i5F6'",
I3í)k, 4i, 1971
A;
13)
14) WPl{U;