On the measurement of added mass and added moment of inertia for ship motions

(1)

2-13

IJF1

( 34

i 5

Hc7) 1.

IE

On the Measurement of Added Mass and Added Moment of Inertia for Ship Motions.

By Seizo Motora, Member Abstract

The Author has been conducting experiments _{to measure the added mass and added moment of} inertia of ship forms for the motions through six kinds of freedom, i. e., translations to z, y, -and z direction, and rotations about z, _{y, and z axis.}

In this paper the Author states about the results of measurement of added moment of inertia -about z axis, which were obtained by _{an impact method properely deviced for this purpose.}

Effect of the free sarface upon the added mass and diference between added masses for translation to one directionnd for oscilìatoy motion were also discussed in this paper.

4s

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[1]

7yJJ mi)

j

_{o)VjJ (m+mi)1}

_mi.

t, _27rV'mJk _{27ri/(m+ni')/k} _m'. 't

mv 7!-Ùj (m+m")v °)lJ:

_m". 'i

Gr-

1mv

_{_+(+m/tf)v20}

;ti-I,

U < t . UC4

[i]

_--t-c

I 2

7Utti

[2]. [3]

mo, m

(2)

(1>

m1i tU70

q) i=O Z q)=O

(2)

t

(.

±j-

,

t4)

f-t

R=K1+K2x

₍₃₎

(m+m1)±K1±+(k+K2)x=fcos wt

(4)

5 i-

'

Ut k

, t

3--2x

fc>

EOk

K2

(5)

kttZ*7

T=2nV(mi+,n)/k kUh.

T=2rV (m+mjK2/co2)/k

₍₆₎

k

U U'

,

ni[t (m+m

-ir

_(infl

+miK2Jc,2)? m1K2/,2=m'

₍₇₎

kU, m1 k m'

t7

iI_©t,

j5z kU-C

(8)

(1)

(9)

k

(2)

1kL-'0 [2], [3], [41,

_[510

ECLo-1irnm'=mi=rno± (10)

(2)

g

₍₈₎

t

o az Fig.1 (11) .

k t

[6]

11mm' p122=mo+ (OO =

m+2

k

(3)

o

o os

Hsec-Fíg.3 (a)

_J'>Jzi

_{Fig.3 (b}

_J'<Ji

-fli

1 277 model A ¡ ( o -0.5 15 25 Fig.2 yawing f. Jz' i,

_[3]

jsij t'0'j

Fig.1 _n' _t0 _base

T=O tJ )

2'J<

tI

t ini

U-C mo

k< t,

Fig.2 f

tI--Fig.1

ÍJJZ 5rjLtt'0 base

_d Jz' J _1Li ,

Ji

;iì,

< Fig.2 C

J'>Ji

_{Fig.3 (a)}

P<

LLJÍÇ

_<

_{°Yt9f Jzi}

tCOJit

Jz'

ht

, < Fig.2 _A

Jz,<Jz1

Fig.3 (b)

fl< i<

J'

5l Fig.2 _<

Ijj

_yawing

Fig. 4

Fig.4 0) (1)

jì

Fig.2 0)

A'B fi

(2) 5l B..0 f-

_{U (2) t5C (i)}

§ 2.

1LtÍ

Fig.5

f.

base

Fig.2 0) z

90)ffl

fij,

_{Gerritsma [7] jyi heaving} _{r$ pitching}

plot

_o)-,

_Ij,

íU-c0

4cQ) rolling

Jz>izi

(4)

ro1/' z-pìtchíny & heau;n.

baeri

Pli:

r1T

g:jr+

J-J/j j

J1/11 i:f7-/

Fig.5

T17

T/7

2iV,

)rv pitching 5P. 2 3 i: io- <, [1O] Q) *n

:

"2) i), m'

J'

,n 0.5

Ji

\\ _rolling

_Ot

I J2 cJ7 o 400 800 1200 1600 2Z) Fig. 6 /ra

Fig.4 IJ yawing

Fig.1

Table 1<-C).

2JLQ)l't ni

Zlt Ji

ni'

f

i, rolling yj J*,' IZ heaving, pitching ' O) rolling m'

J' -7c')

t-Ij ifli Ji

(5)

Fig. 6 Table 2

) I+J1

ki0

hì, test

AUC

ë0

-tj:

5

)o

(3)

t -:-C4:

, Jzi

Fig. 8 (a)

. ÑEC u.

T-Table i t

i

Table 2 Y<Q

rolling

I>J1, J

J'

_{.j J1}

_{pitchingtj' heaving}

J'

YcO

J,1 § 3. z

_LO

(i)

a) yawing T(, T

_JIjUj,

Ta)2 1

I

5tJ'

5LZ0

Jz' Jo', Jo2

1jj

FO1j Je',

Jzi 5J 5

trt Jzi

(2)

3

Fig.7 c)<,

UUZ/

stopper

Stopper

r, weight o::/

W,e

(Iz+Jzi+2r2)o=2Wr

Fig. 7 - . E )Sj

ti-r

'is ,Js 'is Js

(E

rn,1

L'

(L1) fI

fI ()

mol Jy Jyl z fI E1

fI ()

in,' rn,1 E m o m01 ino' n:za

moo m01 in0' in02

z ifl0o rn,1 mo, rn,2

u1---.°

:.'l-E Lo L1

L'

_JolI Jo o L o L1 Jo,

L'

Jy2 L2

(6)

-à=V2g1G(1cosx)/,cp

_{) /3=T/2gL(1--cos/3)/Kp}

J2E 1r

jQ) impact O)t

()

g i g

i,

o Ö(o zijjg Iz±Jzi WKp21 (à)Ji

U- Iz±Ji J)R5

-L0

c, ,ß I&'. o '1

/

Fig.9 (a)

_{Fig.9 (b)}

()

Fig.8 (b)

i

ì1i

w

/ Iz

ICp

íW)

_i

(7)

C)2, c

&rJ' /3

t Fig.8 (b)

6 7 Oo Fig.9

iJc

Ij-Ct <,

9 jQ) Bo K--t,

C)h

, Table 3 C,Cp, C

Ut± [111

(Fig. 11)

KC1'

E Bo

U, Cut-up

::*< UQ),

&'j dead wood j-

¿KJ 1,

Cut-up C

§5.

jz1jí

§ 4

Ji o* Fig. 12

Fig. 16 (14 120

IILILIHiIIJvaiA

'-Iuu,-,i

WAVII

11111

iiij

L

Fig. 10 (a)

A0 § 4.

tJIj

(145.0mX19.50m><12.20m, d=8.03m, J=15,825t)

C 4 , LIB 3 1,700m Table 4K, --group

Fig. 10 (a),(b),(c),(d)

KUC0

Table4

Fig. 12 l Cb

JbK5

_In _{*ESKV Jzi/Iz}

21.0 m ((4 M 5.0IL ('I 20w' (M 30IL CI &0OL (M 10WL C'I J.5 WL SL I2.0WL - CM ,, 0 w'.. G. 30 W'.. 5°'WL SL Table 3 CM 'J

Fig 10 (b)

B0 ¡cm 4t) deg 90.0 90.0 90.2 61.2 61.6 deg 21.6 23.2 22.7 9.3 10.8 &orad/sce. 0.0576 0.0578 0.0581 0.0355 0.0354 I, kg-m2 2.79 2.83 2.82 2.84 2.85 1c-.J I,.kg-rn2 2.770 A H B C D E L,,1 . 1.700 d,,, 0.093 Cb 0.800 . 0.679 0.565 0.450 0.603

c

0.807 0.682 0.599 0.555 0.613 C 0.992 0.983 0.943 0.811 0.983 Ao A7 A11 B9 B7 B C0 D0 D7 D Eo B,,, 0.2280 0.1700 0.3400 0.2280 0.1700 0.3400 0.2280 0.2280 0.1700 0.3400 0.2280 LIB 7.456 10 5 7.456 10 5 7.456 7.456 10 5 7.456 Wkg 29.147 21.710 43.420 24.756 18.458 36.916 21.023 16.395 12.224 24.448 22.000 W/L3 5.933 4.419 8.838 5.039 3.757 7.514 4.279 3.337 2.488 4.976 4.478 Ikg-m3 3.32 2.45 4.65 2.65 2.06 3.38 2.30 2.07 1.43 2.35 2.17 scJL .198 .197 . .193 .192 .196 .178 .187 .209 .201 .183 .184 U" In Zt 0''t. 80 w 5.0 W'. 12 0°' w,. LW ('I 6.0 'IL CM 5.0 .n_

iIIi4W#J

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(8)

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'-'-VI-a

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---i

t !qUiWi_

Fig. lo (c Co L. û4 05 06

Figli

0) C.CP.0

Q) A 07 08 ci, Fig. 12 ./ _ri 01 0 CM 0 0 «t. CM ¡50 «L CM 120wL CM .0 wt_ «3 0.2 0.1 o p

/

04 05 _0.7 0.8 c Fig.13 Ch

-L

Fig. 10 (d) Do

WtE .

'

b°)

0) Fig. 12

_=VJ1lW)

0),

0)i

o'

Ji

ij©

dead wood

Fig. 14 t LIB

5 #czi/L

, LIB k _{K t..c}

ULIB=oo

center plane

QL--F&°

Izi LQ)

1ri

L/B= 1

rt

Ji t0

LJB=1 O

Fig. 15 i7Jc{

Lid _s Fig. 15 .J 0), 50 Fig. 16

Cutup

5 E0 4 dead wood 8L CM 5.0«t.. CM ,o CM CM 6.0 w

(9)

û 02 01 l0 0.J O.! 0.f Fig. 17 6 8 'û "i' . . 07 0.F 0.9 tO S/L.A

Fig.16 Cutup

Cutup

_{Fig. 16}

j

§ 6 J2 c'

'J

J2

_Ji

0 'N

--Fig.14 LiB Fig.15

-

/ 1' cD

f

Jf

0J E, E A 07 o

(10)

Fig.18

-

2 :.' Fig. 17 lt Fig. 2

_{C t}

Stokes [12] s

[5]

_%Ñlt.

Fig. 17

9, V'T=1.3

U tU' 7a

J2

Fig. 17

-cD1-,

T=O Fig. 18 It 5 U

Jz t

#c2/L Fig. 13

Fig. 13 Fig. 18 Fig. 13 /5

']<,

Yo

JmT7

U < L LI]

fo-

U"CQ

5E

87 -UIQE T

86 4- ()

w*

r

J. 77

-rm-i *

285 -l

riJ p1J,jl

Vol.17, No.1-2, 3-4.

[5]

Weinblum G. Schiff und Haven 1951.

Gerritsma J. "Experimental Determination of Damping, Added Mass and Added Moment of Inertia of a Ship model mt. Ship. Progress. Vol. 4, No. 38.

Taylor J. L. "Some Hydrodynamical Inertia Coefficient" Philosophical Mag. 1930.

Lewis F. M. 'The Inertia of the Water Surrounding a Vibrating Body" TSNAME 1929.

11

104

-w* ri () p.67

(11)

o347lO

)1. 7Z--_L-- n

2-8

( 34 11

J:

2

On the measurement of added mass and added moment of inertia for ship motions. Part 2. Added mass Abstract for the longitudinal motions.)

By Seizo Motora Member Abstract

The Author describes in this paper the results of measurements of added mass for longitudinal

motions.

An impact method described in Part i was used for meauring device and the results

are compared with the theoretical values for a prolate spheroid after Lamb. It was found that the

ratio added mass to the mass of the ship mJm increases when Cb of the ship becomes large, as well as when LIB of the ship increases.

iJ U10

X

Ut-t

_. m

CO

§1.

'1 ;i5 ,_La

mzj

o 4.8%

n1 ±5%

m±mi

O. 2O. 4%

_oM

-l'i

'9, 7Ii (9IIO

h ¡

< Q) 3 ,,t

Ui0

--*

ocOh Fig.1 O) _<,

_{uIt '9}

'f

'i w

' Kp

b,

t1t à/gl(1cos) /Kp

(9

/r_/2gl(icos/3) /Kp

¡p impact g

(+)

w; K2

4+ß)cos2=w

(i)

ÌU q

Fig.i

(m+mi)uo

U..c

m--ni =

wpKin2lG

(i1/1cos +V1cos )cos

n

(12)

U51C

_U,

_{t0 )L}

tangent

Fig.2 Kr- <,

Wo stopper x U wo

°)Z,

5;L--Wo h

b:0

) h

±

WO uo°=woh±8E

2\

g,!

U 8E

UO t (2)

i: Wp K /21G

(V1cos +Vicos

)cos2

UO -m+1fli±wo/g

ip V g

(3)

(4)

wpK2pic

m+nii

-(woh +8E)lp2g IStPPr

Fg. 3

Wo

(Vi cos c±Vicos

j3)cos4-g 2.

2*7-9,

U0

i, impact U UO Ul=muoi on = U

(6)

U 10 _Q)J±J _Ei _1.0000 _1.0031

K:

7Jt-±C

stopper O1t

(5)

wo wo 0.4% -iIJr-t U PTht.c± s Fig. 3 .

t) h

o Fig.

i

Fig. 2

(13)

LIB base p. plot

Fig.4 Q)

<tb),

inzi/in 't LIB

5k <iZ)

Z) Lamb 0.,f 05

II*

_*U

:r-/ S201

rY S'--202

iZ)

Plot UZ)Ö,

LIB Z) dJB

Z))f U,

dcB

LUZ)t2 d/B 7ThUC

tZ)0

;- Z)0

Fig. 5 C0 base . Plot C0 Jc < tEZ)

4 5 6 7 Fig. 4 005 8 9 I0 17; :

;s--2'I

A

VA

d4

ppI.

§ 3. wo Q woh 5 Z)O

oft3 6E

uo Rf0 Rf0h

h.t, Weight Wo

w1/2Rfo

Blasius ' Cf

Uc Rf

5CZ) ¿, Swlwo

, 0.4% .

*t

ij+UIt:0

§4.

I] Bo

10 05),

10

Fig.6 B0

dIBL, d/Bhbij L-C

d/B=0.5 dIB=0.25 dJB

t d/B pZ)

0 0.5 117 al 8.5 c.p Fig. 5 Fig. 6 *

"-"

₉₉

(14)

8.7 055 Q45 05 8.55

Fig. 7

Fig.7 _d/B=const _ni

Fig.5 J

, C7 0.4,

0.5

0.9 Q)Joy- LIB

_LIB _base _. _Plot

Fig.7 Q) dr=const C

Para-meter

:::*

Fig. 6

n

ì d/B _{d/B=0. 75=const} _C) Fig. 7 _{d/B=const Q)} LIB dJB C) Q) rnj/m Q)t 5 _dIB base

Q)J

5

Q)d=const Q)wr0

)Q)LJB=const _LIB

Q)

Q)u:Q)

Lt

_{LIB, C,}

dIB n.j/n'i

plot L

_Q)It$

_{(dIB_=0.5)}

dIB=const

),

ft,

Cb0. 5

_{0.523) Q) Q)- L}

_'ni

Q) C _L

U Cb Q)tt

*Q)

Q) t _U, <

LL

tUQ)TL

,

Q)Q)'5

\

\\

\

N N _N 'N Key

'

'N

N

_N

L7;

Í*:à

5 6 _I _q 11 10 80 Q02 o

(15)

y

iffd

p3471O

* Fcos X-in +flizi F sin

rn+inj

h,

A

tani3

-

tanc X in+iflii

ht,

tO)j

On the measurement of added mass and added moment of inertia for ship motions.

(Part 3. Added mass for the transverse motions.)

¿

By Seizo Motora, Member

The Author describes in this paper the results of measurement of added mass for the transverse motions.

The Author employed an "athwartship accerelating method" which is grounded on the fact that, when a slender body like a ship is accerelated by a force making an angle c to the center plane of

the ship, the direction of accerelation does not coinside to that of the force, and let the angle of

accerelation to the center plane i3 there is a relation as follows

tance _1±i?J1

tanß

m±mzi

The results obtained by this method were satisfactory ones. It was found that myi/in decreases when. C value of a ship increases, that inyi/»i increases when a ship becomes more slender.

U, Ut.C1 'JI» 1

h <,

inyj h

niyi _LIB

tt) d/B h

_tO

Cl

:i

rzz, I iJJ

bnI mti

5,

Utlt

7c _h

, »h

J

_h . Fig.1

(U<')

c

F*.7h

X

(3)

tance h. tan,

m±nii h m±m,i

_m.i

I1iM

invi

2-9

( 34 11

UWT

ci:

:°) 3

(16)

174

Fig.l

Fig.2 my Fig. 2

±T

rolling _weight

9. -

stopper V3-, ₅

<C<o

stopper

©*V Fig.3 a)b)

tano h tan3

Table i

t (3)

S e cZ

iu

(3)

Fig.3 a) t Table

i O) ct=16.4° O) -a-,

b) t c=57.6°

O)IO

7/,Y/'//// 7/ '

j // /// /

Table i B0

ti

iO6 Fig. 3 Fig. 4 /J\

_<C

_{tan 4tan i3} ₌₃ o D

¿5

O)i Fig. 4 O)

h U, rolling

_IE5

:t stopper

weight w stopper oscillograph

_{o h-}

_h (m+my±

+m)o=w

₍₄₎

2 m+my

1O

8m tan a m+nz. m-1-2n m--i1i1 m1/rn

-tan P rn+m m In 16.4° 1.880 22.2° 1.890 36.2° 1.885 43.5° 1.898 57.6° 1.888 82.5° 1.910 1.891 1.040 1.967 0.967

(17)

¡.5

±2%

Table 2 cT

<

o

22 LIB

Fig. 6 it Table 2 LIB base l

Plot U© LIB

_t

< i

rn4rn

lt--i,

U<t1EW

Fig. 6

Fig. 5

oscillogram OIJy5 Fig. 5

_T1

r2

±5%

5 :1 . -± ir

,j

,t

rr 77Z 21 ì.'i i Fig. 7 Ç.;o Co' o-q X t-s .1'f Bo Table 2

tan a/tan P (m+m,,t/m (on+m01)/m 7r/7n

A0 1.732 1.0503 1.873 0.873 A1 2.092 1.0448 2.186 1.186 Arr TI. 524 B0 1.696 Br 2.250 1.0336 2.330 1.330 1.610 co 1.975 D0 2.092 1.0234 2.141 1.141 Dr 2.543 Dir 1.757 q q to 81 8.7

(18)

176 05 t g.

t3

106 H

d/B -

LIB tíU°fU

íLt, dIL

t

-< 7

23 Cb

Fig.7 C C1 75 nijj/m

24 d/B

Fig.6 t d

LIB d/B b0) LIB m-3-, dIB d/B A0, B0, D0 d/BP.

UcL dIB myi/m

- Fig. 8 Fig.6 d 1L

d/B

-.25 .30 .35 .04 4.5 .55 .60 Fig. 9 /

/

z

/

//

/ /

/

/ /

/

/ /

/

/ /

A/ /

/

.4

/

/ / /

/ //,

_'

/ / /

// / /

// /

_'

/

//

/ p //

_/

/ 1/

i,,

_/

/

//

_/

'i I, id lé -d/c° _A

_/

- '2:-O/\.

/

1.4

r,

4

t!

TAÌ1P

:4I1

û.5 ü.3 n'

Fig.7 i

Cbr0.4-O.9

_{Plot Ut°),}

Fig.8

Fig.9

_{d/L=const 0):*}

,

i:0)

LIB=7. 45(yJ(D

Fig. 8 _{) d/B}

1IE

_d/B=corist

0) _- ₎ _o

O- I q _¡I _Li,

(19)

Fig.9 _L/B,CO3dJB m,ifm

d*Q

5

d/B base dJL=const 2

d/B=const LIB

25 01E

Fig.9 d/B=const=0.5 plot

_mt

_d/B

=const

ìIE

_d/B=const _LIB 7

niyijm -t LIB < t

*:

1O

40) C0=O.5l4, dIB=O.5

_{dIB=const :::f} Fig.9

OE0) dIBrconst

:-,T,

< tç myj

7o

26

I1 m

)Hi

dead Wood mjj Eo Fig. 10 Fig. 10 nv,i

it dead wood

i

. m

--t

8AA

fli0/j myj

(5)

tcJ U 6ni,i t m

6A

27

myi 'i.' G. G O myixOG m +mn GG

Oj7, -5 E0

5 dead wood O,G,G'

_{), m=22.00kg}

_inyj=0.797m

dead wood _{(Fig. 11}

dead wood _{A=l72.2cm2 dead wood}

3 C=7O.84cm Eo Q){Ij _A=1262cm2 _m=22.00kg. Fig. il * ₈₇ lEi Fig. 10

(6)

E1 E. 07 0.8 aq 1.0

X.

d 12 1.0 08 14 02

(20)

m=O.16Orn '

575,

tm-- ,

:/

_IH-J

Fig. 12 ©T

<O

Fig. 12 _.Tz+Jzi G' o) GG'=6. 00 cm

(6)

ffI1I Ö

'=6. 00

OGxmyi±8in01 m+niyi +Òfli

J) OG=12.26cm

¿:i:Z0

u

(dead wood) X C F.?p. 12 8ni1 lfl?/j o - 3CX3A OG=

8.50cm

A+8A

0G (ll) = 12. 26 cm

b) , dead wood C 11. 85 cm m,i + 8m?11

0G (jJ) =12. 26 cm

b)

flQ)

dead wood 5 ), dead wood

(21)

Zt

35t11O

* cos ot (1) (2) -E:

-

:::*

-u-

-On the Measurement of Added Mass and Added Moment of Inertia for ship Motions (Part 4. Pitching motion)

By Seizo Motora, Member Abstract

In this paper, the author states about the results of measurement of added moment of inertia and damping coefficieut about y axis, i. e. for pitching motion.

A forced oscillation method same as was used by Golovato was employed for measuring device, and 14 series models varying C1 and LIB are used.

As the added moment of inertia and the damping of pitching motion vary with the frequency of the motion, values of them corresponding to the natural pitching frequency are choosen as the typical values when discussing the effect of ship forms.

A chart from which additional moment of enertia and damping coefficent of ships having arbitrary Cb, LIB and d/B can be obtained is proposed in this paper.

§1 I

1---

J

4) Jo,--

_{) 9,} _{Lï7ao ;E1i}

-' Fig.1

4)L'7 9

FK-ll g0 tP

Ij/r M

Fig. 1

(2)

2-16

(n 35

5

JJFI

J

_f1J1HJE

-

4 -'

"

(22)

-I:

:5

i:Ut

<

9 Oscillogram o)

}jt

¿líJ

it0

Fig.3

Ij-0

Ub)O

F UiE',

§3 210 o1O',

M, s

Fig. 4 o) <) base pr plot F

J'

Np Fig.4 Fig.5 Bo 5.4cm

idL--'

O)

CO)

F 5 F .

U0

Fig. 2 Mcos s Iy+Jy' ₂ (WGM

₎

Msin s

N=

Dw U 1' lu ,

t7 IC:j-j 9,

Jul §2 5 5, U, Fig. 4 U1c

o.12oo)rl

F t F UC Canti-lever _Eo) Oscillograph F

'1»o)í'i° IF disc zo

E Fig. 3 Fig. 5 7- '7

(3)

Fig.2

O)F<

set U

1 B0 ;

(23)

(Ky'/L -)

Nr'

NpVg.L

Fig. 6

WL2 W.W2 Fig.5

'jL)

_Fig.6 _K01/L J 7 Fig.6

/j\) 9,

,i w I Fig. 7 2

,/

Fig.7t

B0

¿"

_\\

L=145m bare plot mag-nification factor cO o . 2 Fig. 8

K'/L

N'

' w

BMt KY'IL

-i

N'

_*o

N'

w

K'/L

base

plot '5

Fig.8 <

),

(1)

tit?i, (2), (3), (4),

(2) (4)

Ah-J <,

t (1)'(4)

O) _{magnification factor} _145m

J

40km O))j

Neumann

Spectrum

IEi1Q

to)

_<t7

(1)

(2)

₍₃₎

₍₄₎

, 1. 297° 1. 066° 1. 092° 1. 102° j

K'/L

J:

N' Ê W' base

plot

íCUto

L/4

UHUt

L.42_

WLK/L

(5). (L-fliC, '( 2 .3 'o (1' +E -3 'F r?, øf/L/3JP ,

(6)

(d .CL /5 J Io .05 o CZ 42 Z 0f 44f 4 J

(24)

C0

§4 ± J *

..

-'

i-Q)

< o Cb01 Fig.9 <, C < ic L/4 L/B=5, Cb=0.8

ntiF

lJCbQ/J\

O) O) -

/

IJ\ _<

j

Fig. 10

< C

'-J

Uto

B/LO)

Fig. 11 p'-

'

BIL

Ut0

Fig. 12 < B/L

IiU--o

(d/B)

O)J

Ky'JL t Fig. 13 < d/B Fig.14

< d/B b0

l

2s1) ¿

0.3 02 û 0 03 02 0/5 0/0 8.05 o 0.13 0.1 1103

/,

04 05 8.6 07 12!

--

¿if 0.1 02 5/, C. -0.600 C, -0.29? C, 0 150 /

4441

f t

I,

//

u

/ /

/1

--,i'

/

/I/

,/ ,

-'I

I, ,05/

-11/

_

Fig. 11 Fig. 12 97 29 00 û S

Fig. 9

Fig. 10 0.1 02

(25)

0. 025 f230 .625 888 645 626 " Fig. 15 :1 o.,., oi ois ¿'0 .5.2.5 628 0.35 8iû o...j 0.55 Fig. 16 EEOD Cb, LIB, d/B

IU) Cb,L/B,d/B 11J

K00/L

Np' ODJ5 chart

_{Fig. 15}

Fig.16Qh<0OD't2,

frame line

frame line U

frame line _F0( _V , _V _), _F1(U,-U), _F11 Key' i 1,

--5

Fig. 13 _{Fig. 14} Pitching _Pitching OD 4 .5 6 5, L/ 022 022 0dû ₀₄₅ ¿'5 iL 5 5 q 8 -J 15

(26)

¿11

U-Gerritsma(4) òì C5=0. 6 h Fig. 18 h <t.c ,

-'j

rJC0

02 0.1 0.I 02 _Q7L Fig. 20 B. 0i z-o.J

5-(V,-U) O) 3j (5J-t

Co=0. 756)

K'/L 0J

N'

Fig. 17 0)

h <O)

* c7) )T _< _<, 5

)O

(6)

oj

U'

4

0))

, h h pitching t'j h

/ F,

h h P-. Brard(°)

Jf

4 Vw = g

__o i-:ì.i1

V

h0)h <

iI: z --t

N'

Fig.20 O)h<t0 Fig.20

A0

j'-h A j'-h'[

K7L

9 h A < ? h 7o F. 0 (7-7) zu-q3

;,

\(

,,i//lil/ / L -- 0.40 : '

w Tsec V critical_(m/sec) _{(L=145m h}V/VgL 0.5 12.57 4.90 .130 1 6.28 2.45 .0652 1.5 4.18 1.634 .0433 2 3.14 1.225 .0325 4 1.57 .612 .0162 o J CO' Fig. 17 4 1 5 /0 Ii '5

--Fig. 18 0! 0? 03 Fig. 19 , w=8, 9 10

base l. plot Ut

h h

5UCL-. UU1 Gerritsma

O)1'

j

h

ì-c-

pitch-ing

K'/L

n' o 95 0.4 03 4 0.1 02 0. 01 8 0 03 D? Di 0.8,5 -4-o

(27)

§5 tiE.>

K'/L

Jpn

j: .226 .174 .160 .154

4b <

Jt5ìk

<, U

- -

z-'

1---'

z-/

¿5

9,

¿* LQ

LT

J:U-'

105 LU

:J-- ¡J± 77

Brard, R. Introduction à l'étude theorique du tangage en marhe. ATMA, 1948 ((4)-#) Gerritsma J. Experimental determination of damping, added mass, and added moment of inertia of a ship model. Tnt. Ship. Progress. Vol. 4, 1957

'7 ,

UU3t

<- U.-c

LW', 'ù:*.7

0Fig.21VB0

' Fig.22 Fig.22

I

linear _'j -o 0 ig Fig. 22

(1)

(2)

(3)

JQ)1 2, 2 J: (1) (2)

k-i s«'

N'=. 0825'--.. 1032 .0927 Fig. 21 N' =. 0940

'J0

, 3 nQ) case

/

(28)

§1 'i

me'

)

4 ',

UO rod

U

Tb

even keel nTU0

rod

Ijj

disc

i. h YtC Zcoswt

Z=JT

w=J

(m+mt)2+N,+o-AwZ=Fcos (wt±s)

dU N5=E

AW

F=

e=O)b h*

(1), (2) 5:

i

(

F cos \

m+mz'=---

_w-.

-

Zj

Fsin

Na -wZ h

h0

*

(i)

2--17

(W*P 35 5

>/

)5

&'--,

W..

)L

-On the Measurement of Added Mass and Added Moment of Inertia for ship Motions. (Part 5. Heaving motion)

By Seizo Motora. Member Abstract

A forced oscillation method same as was used in the case of pitching was employed. The effects of ship forms upon additional mass and damping force are discussed about the values corresponding to the ship's natural frequency.

It was found that the ratio

additional mass to ship's own mass increases when Cb and B/L

increases, that damping coefficent decreases when Cb increases and increases when BIL increases. Charts of added mass coefficent and damping coefficent same as for pitching motion are also proposed

(29)

t1ir niz'

Q)< J1

Oscillogram <

§2 2-14

Oscillogram F, ,

w

)UC Fig.1 )< plot UC)tt, (3)

_'-Jz

ni+m2' Nt1. Fig.2 _base .

plot U0

2 -I I0 5 :'

Thut-- b.U10

mz'/m N,1.t=N,1/L7W h

(4)

w'=WVB/g

j U

Bo _Fig.3 i .-1_. 5_- L.6') .0 o .,

U*HJ<

m0'/ni N11.' §3

t

!i

(i) CcO%4J

Cb hk

m'/m .0 _/ ¿Q ₂ .1 w, -I

Y /

p, o -Fig. i _{Fig. 2} Fig. 3 sn'/in Fig.4

k

< i _{N,,/ o)(} _{Fig. 5} _{< C} Cb

-J

C

_c

(

i

B/L

Fig.6, Fig.7

_{<, inz'/in,Ni1.'} _BIL

d/B _{Fig. 8, Fig. 9} _< _cl/B

_J1-Z

_{rn/m, o) N'}

o)i- fl251/fli

N,1.' O>ff

4 j î. 20 i',-.5 0.1 /.1

(30)

75 8.5 o 1.0 05 o. OS 4 3 al C.1 Fig. 4 _{Fig. 5}

4

2

/

/ .

-o.o -a---Fig. 6 _{Fig. 7} Fig. 8 _{Fig. 9} Cb,L/B,d/B _N,,'

_{57 Chart}

Fig. 10 _{U Fig. 11}

(5)

frame line

frame line _C1 _{frame line}

Fo(VV), Fj(UU), Fn(VU)

Fig.12,13 _{Fig. 10, Fig. 11}

(_{. O)}\

_IJ))/

_Jj5

_.i'5ß 0) _Fig.

14(a)(b), (C)

m/m, N' I:

0 05 _0l ₀₂ 88 Io 0.5 _od ₀₇ 004 Of 07 09 2 I .1.25 "Ja ,33 0,1.1 .1.15 _0.25

0.J0 /J5 osa adj osa

(31)

2.0 ¡B 1.6 ¡4 12 Lo 8. O. o..' 0. /8 ¡ I.

/8.

0.25 8.38 835 0gO 0.15 050 0.55 8.60 Fig. 10 7 8

/01/5/I

0.25 0.30 0.35 0.12 0.15 0.50 0.55 Fig. 11

CÍL7S <,

4 m'Jrn A.1

N,'

*Ct'

5

(7)

2Ui'

1b Cbû.7 Key

--.

_dLC 0.8 YB, Cb

- -

t. 4 5- 7 011 6

(32)

2

(a)

2

(b)

t Fig. 12 Fig. 13 w. Fig. 15 C0

strip method 'J

o _o., ¿12 0.3 o (û' -

2=w'2

D. w'base ) Fig.15 2 plot

2L

Fig.1O chart Fig. 15 3 O. o _0/ 012

ui

3

tt Fig.

Fig. 14 6 ,nz'Jno B/L linear .

*J 50

) 3kZ < fI

i.

iB/L 1lt 9k

< tL'ïF

strip method

to

K)<

5

t; 'KW»UI0

(V-V) o û. ¡ 02 0.3