The non-linear term of orce acting upon turning ships

(1)

ARCN1E

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±

lE

The Non-linear Term of Force Acting upon Turning Ships

By Shosuke INOUE

ibliotheek van

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-ouwkunôe Ho. eschodlT

bCU MEN

rATIE.

D Ar UM:

ji.

/

32

-- I

417

Reprinted from JOURNAL 01 SEIBU ZÖSN KA

(THE SOCIETY OF NAVAL ARCHITECTS OF WEST JAPAN)

No. 32 JULY 1966

Lab.

v. Scheepsbouwkunde

Technische Hogeschool

Deift

Qrdera1de n

fISC

(2)

11X') :N;

,

N, N'r

Yp',

r)I11IE--7

I

)lillrti,

< 1j,

- - y Il:lfW,

j'ji:

d 9,

ltik Q±J

, Taylor

-'L

9, 3iJ1

-

jijj:

l't

jt--

UC, cross flow theo'

), Newton

i: ::jftI

I ±)L , Q)H

Q)d

D

tlE17

*-t:

l:IEQ0

) lCJ 2,

JJz 7

11 {

ß

{fi<iti

rjt9cr)-t:-1

t

pSU2/2,

pSLU2/2 &ljJl;j

-

N'= N?ß+Ñ,!r'+fÑ

f.L p,S,U,L

'L7JQ),

,

JL, f'=L(t/Ü7eo Yfi',

Yr', Nfl', N' 12

Ec59, fY, IN 12

¡3, f'

ìJ-,t

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The Non-linear Term of Force Acting upon Turning Ships

By Shosuke INOUE

Abtrat

The normal force and the- moment acting upon a ship whih turns by large helm

angle include the ionlinear terms of drift angle ß and angular velocity l- Experimental

results can be expressed as any funôtion of ß,

',

but that meañiñg is not sure. Theoretical investigations are based on low aspect ratio wing theory and cross flow heory (Newton's

resistance law), and the nonlinear term is appeared from cross flow theory. The most

important term is ß and the author calculated the term of ß using resistance coef. 2

fourteen years ago. In this paper resistance coef. is assumed as 2K2 and K2 is calculated

by turning trials of models and actual ships. K2 is as follows;

K2CO.25

The distance btwen pivoting pDint and centre of gravity is also researched by same

method and is nearly independent abDut ship type, bit inreasea to s.ne eaLeat with the

(3)

¶ 3.5 3.0 2.5 4 rr=Klrx(o. 367+0. 21X± 16d) N'p=1. 178J(O. 67+X/2)X ±

1- [KrX+K a

_2aßi

Y(ß)

6 Ñ'.=O.54x+ [K1

+Ka{Y(r') _N(r')}J

¿::;ii< :1*7 {LX

{9, rj '

1) .z,

ßrrlrc

96, ¿ E1ÚL íL c O. 8[1. 4570. 128(_)+(0. 466

-±4'L0 aY0'(ß)/aß eec.

Newton

r.j'B/L, 7t

O.5

(4)

a

27

8/L

0./0--o.,6

¡.250

0.7 1.1 1.0 I I I 0.5 0.6 0.7 O.& cw Fig. 2 C

L,t Fig. 1,2,3,4

IF, IN *. l&, Y'

I,

Q)fl' Newton

i(WiîV11 L11

19

ßr

1L2\

f1=K28 (1C2)C2 L I

... (3)

21 L2 \3 fNK2S(1'W2)C'W2 e-L) ßY.==hNßY

íìU C, L2

k4'L1IfC'J

?±tO

$2

2K2(2C-1)$2 ,, fN

Z. 2K2(2C_1)/L.$2

*-E t FìE&Q'FJ

K3 .7{fi j'.j:O. 64

<

j,3 K1

K1 1/2

1Qui1I;» O.8.O.9

K2 cross flow 2K2 ¿

L11j

Q)1pr2

R(1)(2)(3) 19 0(2 11.4 '.3 1.2

(5)

1.6

MS

a'y'

0. 5

r

0.10-0.15

1(2

14 '.3

12 1.I

J o 0.7Q 0.5

0.7

O. Fig. 3 L

cR(Nß'f-Yß')

A i (4)

N'r' Yß' Np'(m' - Y'r) +

-

_h) + f'

(mi' Yr) + h yN'r'}

A, CR, ¡RI

'L

ÏftU,

m,,' I pSL/2

5-t

iI± 2CBB/L

(ifl I,

jQ)

1± CR, r' kí', IQ)flii I1

iJz C,

L-C,

I:Kzz

¿ebt.0

7-:fl1v bl?

lEU

528' X 76'x 24. 5' 24m x 6. im x 2. 4m

X=0.2 C8=0.79

K=1

K1=0.80 f.

K=I

_K2=O.85 _K2=o.90

241 0. 291 0.233 0.500 0. 597 0. 507 0. 537

(6)

a

'L

a/L

O./0.--0.í

0. 4 0.7

U tk

2, 3 I 2

(3°)

0.85 C.6 C.1 C.7 - T.8

F

L 6. 00 3. 44 4. 50b 4. 500 2. 655 B ,, d m 0. 857 0. 368 6.487 0. 225 0. 617 0. 247 0. 702 0. 270 0. 527 0. 254 O O O 0 0.058 AR/Ld 1/60 1/66.8 1/60 1/67.2 CB 0.61 0. 71 0. 70 0. 81 0. 527 R 12.0 13.4 6.1 6.0 7.5 7.6 6.0 5.9 3.5 2.2 CR 2.00 1.86 2.25

-

2.00 1.94 1.45 1.47 2.48 4.03 K2 0.32 0. 39 0. 39

-

0. .9 0. 49 0. 56 0. 54 0. 33 0. 35

i.

I I I 0.5 0.6

0.7

0.9 Fig. 4 1ff

KØ1

0.7 0(4 s 0.5 0.5

03

(7)

(35°)

K2 base Fig. 5

Q)

K2

/CB1tUC

j cross flow Utl± 2K2

i fl9)1i1

/

Coa-oireB Q)2K21:*,

2K2=10-0.25--C0.99,B/do2.3 t12K20.74

Fig.5ft

tanker 'j tu[I , kQ) Reynold' No.

Q)15

p, frk

Q) 7fIE 1: 7

iV Pivoting point

' ¿ÍJ1<

CR

AR[N+ (,nz'-Y'r)_J

s

1'rYs'Nß'(mx'- Yr') ±C-

+ ¡zyNß'}

(5)

J 4

ß/r'

± RI3/L ± pivoting point ]t!1

10°, 20°, 30°, 35°,

40°1:--t1ffaK2

C(5) ß/r' < C1 C2 C3 T T2 T3 L m 122 138 145 197 213 213

B m

17.4 18. 8 19.6 26.4 30.5 30.5 d 3.885 3.963 4.62 10.58 11.365 11.303 1 3.440 3.785 4.33 0 0 0 A8/Ld i/32. 4 1/28.3 1/33.8 1/75.8 1/75.6 1/75.2 C8 0.673 0.655 0.613 0. 779 0. 78 0. 78

ti

R m

200 190 215 225 278 330 500

-

297 278 289 241 CR 1.4 1.60 1.80 1,88 1.57 1.61 1. 54

-

1.53 1. 10 1.57 1. 7i K2 0. 33 0. 33 0. 34 0. 39 0. 37 0.42 0. 22

-

0. 42 0. 3S 0.42 0. 32 T4 _T5 _T6 _T3 _T3

_F

L 192. 5 224 224 172 183 48

B m

26. 52 35. 4 35. 4 24. 8 28. 0 8. 3 d m 10.327 6.840 12.06 8. 15 10.0 3.28 'r 0 3.80 0 0 0 1.76 A8/Ld 1/72.0 1/42.0 1/74.1 1/57.8 1/76.1

1/8

C8 0. 783 0. 765 0. 816 0. 76 0. 83 -0. 487 th

ti

R im 3Q8 306 325 315 299 233 245 284 280 240 56 54 CR 1.31 1.41 1.46 1.43 1.93 1.89 1.59 1.50 1.30 1.45 1.52 1.52 K2 0. 44 0. 47 0.49 0. 48 0. 60 0. 41 0.46 0. 56 0. 59 0. 50 0.24 0. 23

(8)

j. o

0.5 F

-s

F

C

CISC

c

Fig 5

C

t4ÖDEL

ACTUAL SHIP

flSHI

BOAT

C

CARøS11

T TANNER

1 -r

T

-r

T

s-r.

-r-r

r

-rST

'ST

7-r.

o

0.5

0.6

0.7

0.8

(9)

f3,

or

I

Fig. 6

)MODEL=

ACTUAL S1!.IP

T 7

c.øc

P

FISHING BOAT

C

CA Rû SHIP

T

TANKER

ca

I t

0.5

0.6

C )

F

C

(10)

ß/r'.

C5 base Fig. 6 C5=O.6, 0.7,

C,

pivoting point ls70,

l:{ < 'L? CjQ) pivoting point Q)1

:-,-c?JfiUK2, pivoting point Q1LCB base

't7. 5l:L,tz0

Lt

)t:

Jci&

)2Jk

Wi

,

S. moue: "On the turning of ships." Memófrs of the faculty of engineering Kyushu uiversity 1956

JTE : _)i33fl-r

j)

2 -1950

irw, -Jç: 5

(k Q)') (kQ) 2)

T3Ii962

Q)f

I06!-1960 loo 200 300 35 40° C. T.8 Q) Q) ) f4) 0. 32 0.45 0. 32 0.45 0. 32 0.44 O.:32 0.44 0. 315 0.44