Presumption of hydrodynamic derivatives on ship manoeuvring in trimmed condition

(1)

24 APR. 1978

ARCHIEF

55 ,

lj J

53 $ 3

Reprinted from TRANSACTIONS OF

THE WEST-JAPAN SOCIETY OF

NAVAL ARCHITECTS No. 55 MARCH 1978

Lab.

y.

Scheepsbouwkunde

Technische Hogeschool

Dell t

I:

it

IE 1E W

Presumption of Hydrodynamic Derivatives on Ship Manoeuvring in Trimmed Condition

by Shosuke INOUE

Katsuro KIJIMA

Furnio MORIYAMA

(2)

i,

IE

,.E

iE.

W

Presumption of Hydrodynamic Derivatives on Ship Manoeuvring in Trimmed Condition

br 'Shosuke INOUE

Katsuro KIJIMA Fumio MORIYAMA

Súmmary''

To investigate the rnanoeuvring characteristics of ship, we have well known the available theories, in the use of slender body theory or low aspeèt ratio lifting surface theory, for predicting the hydrodynamic for'ce and moment acting on ship

hull. But we can't almost see the work which dealt .vith the hydrodynamic ones -acting On ship hull in trimmed cOndition. nôtwithstandingthe-manoeuvring chata-. cteristics of ship are greatly affected by her load condition. -

-In this paper, it was made clear the relations between hydrodynamic

deriva-tives on ship manoeuring and ship's load condition by the use of slender body theory. With these iiumerical results, we may coclude .that the hydrodynamic de-rivatives on ship manoeuvring are greatly affected bytrim quantity: ho*vefthere

are no influence of change of draft at a fixed trimmed condition. And the nu-merical results, we thay represent the following approximate formulae for

pre-dicting the hydrodynamic derivatives on ship manoeuvring in trimmed coñdition

-N'uß(t-) =

N'(0)(1_97.__)

-Nur(r) = N',(0)(1+0. 30_L_} . .

-where d,, and r represent the mean draft and trim quantity respectively,'

lß N'us(0)/Y(0).

*

**

(3)

128

tj0

4rO)M«*

j,

Ø4*

f,

±4ø

-

J 2tj,

E-C,

GØ 7f2>

e

2.

0)L,

/J\0

Fig. i

c,

5

Fig. i Coordinate System

[L] v2 = O [B] y.12=0

4r00f!o

[F]

*

=---

, ,

-U) X

(vtv]

-

_, = -,.3.

,

-[S] v.b=0, b=nX

-fiJZ.to ttL,

-< l'iL' V, al) p, l'iL' n' t., l''L' w, n,t l

t:+,

O)eto

--c (2)-45) o)T (i)

o)L'

Ltt70

2.1 "eS-?,

ø°

>' / . ,lL'l = U(x+i)+V(Y+z) (6)

t'L U:

X V: y (5) (i) }

(4)

Fig. 3 Reference Point on Body and Free Vortex t: t L, qi = R(f1), 2 = &1J2)y f = Colo gC_C1/2C2_C2/44 f2 = a1(C+1/C) W=a1C+az/C+a3/C (9) H0 = B/2d = (aj+ao+a3)/(a1a2+a3) = S/Bd = Ho,r/4. (a_as3a)/(ai+az+a3)2 d = }

Fig. 2 Conformal Mapping of Sectional Form (10)

C0 = a1aÇ+a2a+3a3a

C1 = a1aa2(a+aÇj-3a3aÇ

C2 = a1a'-3a3a (aÇ, a, a' -1(ai, a2, a3))

2.2 ( Fig. 3 l Jz-5l,

±ø

j P(x,r,ço),

'?)±a- Q(x',r',p')

-0

tLt i'JJ (F) Jz P v(P) P) (12) F 1-

i Oø

129 '1, 2

CtO)2,

Lewis Form Fig. 2

-0 -0

rp = (xx')i+ (rcosq'r'cosp')j+ (rsinr"sin ço')k rp0 = [(xxO2+r2+r'2-2ri'cos(')] 1/2

-* -, -*

i,

j, k

(x,y, z) t.

'

x-'0(L), y-*0(r), z-*0(r) (13)

x'-oO(L), y'-»O(Lß), z'-O(r) (14)

c0L-t,

=(ao,o,w)

,1 > 2, C,)3 (15)

21± (13), (14), (15) (12)

ø3} 5-tV-L x=X'

-T!

W-plane _C- plane (7)

(5)

130 55 -.

Taylor L order check (10)

-_resiri _{±'(rcosç' rcosç")] d /} r2±r*2_2rr*cos(_9)

z

Fig. 4 Flow Model

2L±d)l,

1èU±ltL.i

P)

t-cv0

(12) 2-<

7

l Fig. 4

JZ5,

(11)

¿j,

k3 (CC ,) (CC7')

.f3--tO

ftiL, k3

C, l

Fig. 5 t5&0I

2.3 Q)

JJa)M [S]

t:lC< )k

Lt0

'l

-n = (-ne, -n,, -n) n: « n,, n

»tt.0

ttLI

= A(U+u, V+v,w) u,v,w:x,y,z

-D10

We',

U»u, V+v, w

E-C, -. - -W- plane WI

Fig. 5 Conformal Mapping of Vòrtex

Location

(f6)

(6)

T'

(Np, N2) (19) , /J\

<tt

- N2n2

--ø-', (18),

(19)

-

-b*.N_0 (20) b*

tO)4,

(20)

=0

(21) C-Cs

t±'L f=Uf1+Vf2+f3, j1/i

C5 WJ C

(21)

3. -Q)t

Fig. 6 Reference Slab

-

*t;

f?IJ

Fig.-6

Y-ø4tL; *&)

<

d(x)_u4f ø(x,y,z)7zd1

_dx dx (22) 131 0

4''ik,

dt -p

5Ct-jJ (Y)

(N') Y PÜ[$øflsdl]

N =J

_ixdx =

PU[X5øfld1 ]_PuJ{føndi

. :J-t1,

§ ønds =

R[ §f(_idw]= R [ §f(_i)-dC]

.øReCf)U01+V02+03

[;fl1

b* (18) dx

I

(23) (24)

(7)

I32

Free Vortex Floe

0k. k-1,I ) Lewis Form Approximation (O _°2.03) l Sepootion Condition SB

t7iibfUl

PUkJ6J (k1,81 (24) L, (23) _{IÏÒJOt 5} Y

=

pU[₅ s1zydS] X XL/2

N= PUI{5 ø3flydS] _puJLIZ

_{5

(V02+03)n,dS}dx

2 X XLIZ LIZ X

(25),

jj

ßì

N I.PI Munk

OY) ¿

L

Lt:,

r _L, 7 fl(x)

ß(fl+-= ß+-

(26)

t:t.L, RlL1, V

tO

¿:<

U Vscosfi(x), V Vssinß(x) (27)

Decision of Vortex Strength

( ) 1 Decision of Flow ( Uf+Ùf,UL, ) Hydrodynooic Forres (Y,N ) L 4.

£«ftlit Fig. 7

5. *i

-: l,

-

5 t:

¿r keel

i'th L18

IQ) 'i

Fig. 8 lQ)

Fig. 7 Block Diagram of Numerical Calculation

Method of Hydrodynamic Forces Fig. 8 Free Vorteìin Transverse Section

ç

- _J

J-(25)

ShipForm Ship Motion

( B r

Potential Flow Free VorteI from Sow

(8)

I) 1:33

E1I h

lt-t,

h=S.d

(28)

tL d l:n71(

¿ttU

S=0.02-0.05

&Lt<0

(21);.t

i'tt ¿

-5 i;

M5

1E

tt7

O)P

.9,. .Bol1ay3

j

yo)TUZ

. .

-'

Vj

J-U-5.

LZI. Table i

Todd Series 60 4210W(Cb=Ó.6), 4212W(b=0.?), 4214 WB-4(Cb=0.8), LB-5(4214WB-4 '

L/B=5 cLftJ, Cb=0.8)

u7j(

60%, 70%Ø3*UtLt0

., ò5 Table i Todd Series 60 Q) 4210W(C6 =0.6), 4214W(C6 =9.$)

SR-i54,J

'(L=25m, C,=0.824)

t

l Y

F.ig 9-Fig. 24 ¿Ll?0

I'

r

y

0ø

LCbL,

r

®.

Cl; tr>0Ø

trim'by stern

l,

1.1) ne fG?.'

full?0

Y(r),Y(r),N',(r) iL2<-L,

N'ß(r)

LtI full tji' (4214WB-4 etc.)

iLI I- Y < .

L<0

Ñ'(r)

), N'(0) l

(25)

Table i Principal Particulars of Model

Ships -

N'(r) = (Munk moment)-

YCy) N'à(0)= (Münk moment) .Y(0) (30)

Y(r) =.Y(0) [+-._-]

(31)

PlLf*L, Th:',

øEJ3C? Xp

O)2to

(29) Todd Series 60 4210W 4212W 4214WB-4 Lt,, (m) 2. 500 2. 5Ò0 2. 500 B

(s)

0. 333 0. 357 0. 385 d

(s)

0.133 0.143 0.154 Cb 0. 600 b. 700 0. 800. C,, 0 706 0. 785 0. 871 C 0. 977 0. 986 0. 994 L/B 7. 500 7. 000 6. 500 Bld 2. 500 2. 500 2. 500 LId 18.75 17.50 16.25 k _(=2d,/L) 0. ib6. 0. r14 0. 123,

(9)

134 55

YÇ(r) = Y(0)

{i_o.8o__}

=

N'r(0)t1+Ô. 3O__}

ftL, lß=N'ß(0)/Y'(0)

Fig; 26Fig. 29

Lru0

t i

tLO /JL, Y,(r) Ltiç5

£UCLC, I-

'J Fig. 30Fig. 31

jLtV'70

J<5lc,

6.M

L

- 'J

Lt5,.

O) , I'

'jÇ,

i

4IL, 4i N

O)t,

' 'J)P57

cø

(34)

oè.tC,tt0

L±fto

t:,

Lt,

VJII

fif

l

tt,

4itl

-FACOM 230-75 . L (33) (34) Xp(t.) x(0)[1+1

i

(32) Munk

-,' 'H2 I'

N'ß(t.)1 _( Xp(0)(2+1'\( '(0

N'(0)

k

L )k3

Ø 5 l*

L*-

Fig. 25

Yt: xp(0)/j. ø1ffitL I(r)

L1*.

£±,

Q) N'ßCr)

Lt, Y(t.), Y(t.), N'r(r)

= Y(0)

(i+--.

_}

1 0.27 t.

(10)

135

e

4±* :"On the Tur-ning of Ships" 1956.

.

8*i

_i34

W. Bollay : "A Non-Linear Wing Theory and its Application to Rectangular Wing of Small Aspect Ratio", Z. A. M. M.. 1939.

(Î)

4t±t0

(i) JI'O) l L tØY L

Ú, ¿ l

Fig. 9, Fig. 11 d,.=O.5d

4thi5

Yß d,,=O.6d, O.7d

Yr _{'l2 dmO.5d}

løo

Pol*Ctto

tiEl

draft

Lt

iL

¿2lllA*A0 t3Q Fig. 9

Fig. 11

ivc

dm=O.5d

YB

ItL

Lt, U4It

Lt

DL0

Yr

Ltl

virtual massQ)Q)

ttt

*?

I

tØLttO

(11)

136 1.5 Vair) Ya(o 0.5 in Trimmed Condition 55 Vdm -0.6 -0.2 0 0.2 0.4 0.6 a

Fig. lo Static Derivatives of Yawing Moment in Trimmed Condition

T/dm

-0.4 -0.2 0 0.2 0.4 0

Fig. 13 Static Derivatives of Lateral Force

in Trimmed Condition

.T/dTTI -0.4 -0.2 0 0.2 0.4 0.6

-0.4 -0.2 0 0.2 0.4 0.6 0.8 T/dm

Fig. 11 Rotary Derivatives of Lateral Force

0.5

T _T/dm

-0.4 -0.2 0 0.2 0.4 0.6

in Trimmed Condition 1.5 0.5

r

'dm -0.4 -0.2 0 0.2 0.4 0.6 Nrs(i) Nr(O

Fig. 14 Static Derivatives of Yawing Moment Fig. 16 Rotary Derivatives of Yawing Moment in Trimmed Condition

Model Mean_Draft Aspect_Ratio Theory Experl_-ment ¿210W

0.5d

0.0543 --

o

0.Gd 0.0640

----

a

0.7d 0.0747

-

a

Model Mean_Draft Aspect_Ratio Theory Experi_-ment

¿210W

0.5 d 0.0543

-.-

o

0.6d 0.0640

----

£

0.7 d

0.0747 -

D

Model Mean_Draft Aspect_Ratio Theory 4212w 0.5 dO.6d 0.05720.0686

0.7d

0.0800

-Model Mean_Draft Aspect_Ratio Theory 4212W 0.5d 0.0572 0.6d 0.0686 0.7d

0.0800

-1.5 _NrsCr Nr.0 o A o 0.5 A o o 0.5 T _dm -0.4 -0.2 0 0.2 0.4 0.6

-0.4 -0.2 0 0.2 T

0.4 0.6 0.8 'dm

Fig. 12 Rotary Derivatives of Yawing Moment in Trimmed Condition

Vair)

1.5 Ya(o)

D

(12)

"al?, 1.5 1.5 Nar Nnio 0.5 0.5 T -0.4 -0.2 0 0.2 0.4 0.6 m

a

T/dm

-0.4 -0.2 0 0.2 0.4 0.6

u

a

-0.4 -0.2 0 0.2 04 0. m

Fig. 18 Static Derivatives of Yawing Moment in Trimmed Condition

T/dm

-0.4 -0.2 0 0.2 0.4 0.6

Fig. 22 Static Derivatives of Yawing Moment in Trimmed Conditon

1.1) øø

-0.4 -0.2 0 0.2

0.5

1

-0.4 -0.2 0

r

p T

-0.4 -0.2 0 0.2

a

Vdm 0.4 0.6

-0.4 -0.2 0 0.2 0.4 0:6 'dm

7/dm

0.4 0.6

137

Model trlean_Draft Aspect_Ratio Theory Experi_-ment

4214WB -4 0.Sd 0.0616 s 0.6d 0.0739

----

a 0.7d 0.0862 u SR-IS'. 1.Od 0.1 465 X TANKER 0.0800 4

Model Mean_Draft Aspect_Ratio Theory Experi_-ment 4214WB 4 0.5 d 0.0616

-.-

s 0.6 d 0.0739 a Q.7 0.0862 u SR-154 I.Od 0.1465 x TANKER 0.0800 4

Model Mean_Draft Aspect_Ratio Theory

LB-5 0.5 d0.6d 0.06160.0739

0.7d 0.0862

Model Mean

Draft AspectRatio Theory LB-5 0.5d0.6d 0.06160.0739 0.7d 0.0862 1.5 Nrir> s s

Ni

a u 0.5 1.5 Nnr Nnco 1.5 Nr(r) Nrio 0.5 0.5 0.2 0.4 0.6 'dm

(13)

138

k55

-0.2 0 0.2 06 0.6 08

Fig. 26 Approximate Expression of Lateral Force Derivative in Trimmed Condition

.1.5 Nn

No

0.5

-u

0.50 -b-2 0 0.2 0.4. 0.6

Fig.- 25 Center of Pressure

dm

m u e

-0.2: 0:. 0-2 'O.Z 0.6 o:á.

Fig. 27 'Approxiüi'ate Eïpression of Yawing Mo-ment Derivative in Trimmêd Condition

a

u-T _T'dm

-0.2 0 0.2 0.4 0.6 0.8

Fig. 28 Approximate- Expression of Lateral Force Derivative in Trimmed Condition

1.5

Nrr-N rgO

.

o.

0.5 T -0.2.. 0 Q.2 .0.6 0.8

Fig. 29 Approximate Expression of Yàwing Moment. Derivative. iñ Trimmed

Condition . - -o. - . - Model Symbol Mean Dràf.t - . - . 4210W 0:5d' -. 0.7d CALCULATION ₄₂₁₄ _{-, 0.5d} WB-4 u 07d M do eI Mean Draft -Aspect

Ratio Experi-ment

4210W-0.5d 0.0543- o 0-6d 0.0640 . 0..7d 0.0747 o ¿2-14WB -4 0-Sd 0.06-16 e 0.6d 0.0739 a 0.7d 0-0862 SR-154 1.Od 0.1465 x TANKER 0O80O

Model Mean_Draft Aspect_Ratio _-mentExperi

4210W O.5d '0.0543 o 0.6d 0.0640 Q 7d ,-' 0.0747 a 4214WB 0.5d ' 0.0616 o 0.6d 0.0739 .0..7d 0.0862 .. SR-154 - .1.0d -0.1.463 '-'X TANKER .. . 0.0800 +

(14)

¿l(r)- AO)

-0.01

I) AO)?

L(r)-

(0) 0.01

Fig. 30 Course Stability Index on 4210W Model Ship

-0.02

I - - I I l

-0.4

-0.2. 0 0.2 0.4 0.6 0.8

Fig. 31 Course Stability Index on 4214WB-4 Model Ship

189

o e

M d

L

Mean

Draf,t

Aspect

Ratio

Th eory

Experi

-ment

4210W

0..5d

0.0543

--06d-

0.0640

----.

0.7d

0.0747

- o

M d

o e

L

Mean

Draft.

Aspect

Ratio

Th eor.y

-ment

Experi

4214W5

-4

0.5d

0.0616.

--

i

0.6d

0.0739

L.