Roll damping due to lift effects on high speed monohulls

FAST'91

Roll Damping Due to Lift Effects on

High Speed Monohulls

A.B. A a l b e r s J . J . Blok M a r i t i m e Research I n s t i t u t e N e t h e r l a n d s (MARIN) THE NETHERLANDS ABSTRACT I n t h i s paper t h e c h a r a c t e r i s t i c s o f t h e r o l l b e h a v i o u r o f f a s t s h i p s w i l l be d i s c u s s e d and i l l u s t r a t e d . The a t t e n t i o n w i l l be f o c u s s e d on the i m p o r t a n t l i f t c o n t r i b u t i o n t o t h e r o l l damping and t h e r e s u l t s of t h e r o l l damping p r e d i c t i o n method o f t h e MARIN computer program ROLLDAMP.

V a l i d a t i o n r e s u l t s a r e g i v e n f o r t h e Royal N e t h e r l a n d s Navy M - f r i g a t e (model t e s t s and f u l l s c a l e t r i a l r e s u l t s ) , f o r a 36 m f a s t p a t r o l boat b u i l t by Singapore S h i p b u i l d i n g & E n g i n e e r i n g (model t e s t s ) and f o r t h e p a r e n t h u l l f o r m o f t h e Fast Displacement Ship s e r i e s (model t e s t s ) , j o i n t l y sponsored by t h e N e t h e r l a n d s , U n i t e d S t a t e s and A u s t r a l i a n N a v i e s .

1. INTRODUCTION

1.1 Fast Displacement Ship S e r i e s (FDS S e r i e s )

I n 1979, MARIN s t a r t e d an e x p e r i m e n t a l program on a s y s t e m a t i c s e r i e s of h i g h speed d i s p l a c e m e n t h u l l forms (FDS s e r i e s ) . T h i s s e r i e s was s t a r t e d i n t h e b e l i e f t h a t s i g n i f i c a n t improvement i n t h e performance of h i g h speed d i s p l a c e m e n t v e s s e l s was p o s s i b l e , e s p e c i a l l y w i t h r e -s p e c t t o t h e i r -seakeeping q u a l i t i e -s .

To s t a r t t h e s e r i e s , a p a r e n t h u l l f o r m had t o be s e l e c t e d and on ba-s i ba-s o f t h e i n f o r m a t i o n a v a i l a b l e i n t h e MARIN datababa-se a ba-s y ba-s t e m a t i c s u b s e r i e s o f t h r e e d i f f e r e n t f o r e b o d i e s and t h r e e d i f f e r e n t a f t b o d i e s

was d e s i g n e d . A l l c o m b i n a t i o n s were t e s t e d (BLOK and BEUKELHAN, 1 9 8 4 ) and t h e b e s t s h i p , a good b l e n d o f optimum calm w a t e r and seakeeping q u a l i t i e s , was s e l e c t e d t o be t h e p a r e n t h u l l f o r m o f t h e s e r i e s . An independent check was made f o r a l l models, u s i n g t h e B a l e s ' Seakeep-i n g I n d e x , r e s u l t Seakeep-i n g Seakeep-i n t h e same b e s t h u l l f o r m . Around t h e p a r e n t h u l l f o r m t h e 'magic cube' was c o n s t r u c t e d . The t h r e e axes o f t h e cube a r e L/B, B/T and Cg, see F i g u r e 1. The p a r e n t h u l l i s i n t h e c e n t r e o f t h e cube w i t h L/B = 8, B/T - 4 and - 0.4.

4 6 8 12 L/B

F i g u r e 1 'Magic cube' FDS-series.

A l l models i n d i c a t e d w i t h a d o t i n t h e cube have been t e s t e d i n calm w a t e r f o r t h e i r r e s i s t a n c e c h a r a c t e r i s t i c s up t o a speed o f F^^ - 1.4, u n l e s s t h e h u l l shape made i t n e c e s s a r y t o lower t h e speed l i m i t , e.g. f o r low L/B h u l l f o r m s . The e x p e r i m e n t s i n waves c o n s i s t e d o f d e t e r m i n i n g RAO's f o r p i t c h and heave, a c c e l e r a t i o n s and r e l a t i v e m o t i o n s i n head waves, w h i l e a l s o t h e r e s i s t a n c e i n c r e a s e due t o waves was measured. The speed range covered F^^ = 0.285, 0.43, 0.57, 0.855 and 1.14 and r e g u l a r waves as w e l l as l o w and h i g h i r r e g u l a r wave s p e c t r a were used f o r t h e model t e s t s .

Model t e s t s i n beam waves and r o l l decay t e s t s have been c a r r i e d o u t f o r t h e 5 models i n t h e Cg = 0.4 p l a n e o f t h e 'magic cube', i n t h e speed range up t o F^^ = 0.57. Since t h e r e s u l t s were so d i f f e r e n t f r o m what had been p r e d i c t e d u s i n g e x i s t i n g l i t e r a t u r e methods, a l a t e r

marked by t h e l a r g e d o t i n t h e cube. On b a s i s o f these r e s u l t s an i m proved e m p i r i c a l p r e d i c t i o n method f o r r o l l damping o f f a s t d i s p l a c e -ment h u l l forms c o u l d be developed.

1.2 R o l l M o t i o n s o f Fast Ships

Fast s h i p s can be d i v i d e d i n two c a t e g o r i e s : d i s p l a c e m e n t s h i p s and s h i p s designed t o be p l a n i n g a t t h e i r o p e r a t i o n a l speed. For t h e p r e s e n t paper t h e f a s t d i s p l a c e m e n t t y p e s h i p i s c o n s i d e r e d , b e i n g a t y p e o f h u l l form f o r which a c o n t i n u o u s behaviour w i t h i n c r e a s i n g speed may be e x p e c t e d . T y p i c a l f o r these s h i p s i s t h e l o w b l o c k co-e f f i c i co-e n t , i . co-e . around Cg = 0.45, and t h co-e transom s t co-e r n .

For c o n v e n t i o n a l cargo s h i p s t h e p r e d i c t i o n o f t h e r o l l motions by means o f ( s t r i p t h e o r y ) computations can be c a r r i e d o u t u s i n g t h e e m p i r i c a l r o l l damping p r e d i c t i o n method o f IKEDA e t a l . ( 1 9 7 8 ) . The t h e o r y i s w e l l v a l i d a t e d f o r t h e low speed range and forms t h e b a s i s o f t h e MARIN program ROLLDAMP (VAN DER VEGT, 1 9 8 4 ) .

For h i g h speed, l o w Cg and, as we w i l l show l a t e r , f o r l a r g e B/T v a l -ues t h i s p r e d i c t i o n method has t o be m o d i f i e d . GRAHAM ( 1 9 8 6 ) and, r e c e n t l y , IKEDA ( 1 9 8 8 ) proposed m o d i f i c a t i o n s t o t h e r o l l damping c o n t r i b u t i o n s from eddy g e n e r a t i o n , b i l g e k e e l s and h u l l l i f t . I n t h e p r e s e n t paper t h e r e s u l t s o f a m o d i f i c a t i o n o f t h e r o l l damping p r e d i c t i o n s f o r h u l l l i f t , b i l g e k e e l s and eddy g e n e r a t i o n a r e p r e -s e n t e d , ba-sed on t h e r e c e n t FDS -s e r i e -s o f model t e -s t -s . 1.3 R o l l Damping I n t h e e m p i r i c a l t h e o r y o f IKEDA e t a l . ( 1 9 7 8 ) t h e r o l l damping o f a s h i p i s t h e c o m b i n a t i o n o f p o t e n t i a l damping o f t h e h u l l B^, f r i c t i o n Bp, eddy g e n e r a t i o n o f t h e h u l l B^,, h u l l l i f t damping B^^ and damping due t o b i l g e k e e l s Bgj^. SCHMIDTKE ( 1 9 7 8 ) added damping components due t o appendages, s e e k i n g a b e t t e r p r e d i c t i o n f o r f r i g a t e h u l l forms.

The r o l l decay t e s t s f o r t h e Cg = 0.4 plane o f F i g u r e 1 l e a d t o t h e c o n c l u s i o n t h a t t h e l i n e a r r o l l damping c o e f f i c i e n t i n c r e a s e s w i t h speed w h i l e t h e q u a d r a t i c c o e f f i c i e n t d e c r e a s e s . For t h e p a r e n t h u l l form ( F i g u r e 2 ) t h e damping c o e f f i c i e n t s and t h e r o l l response mea-sured i n r e g u l a r waves a r e g i v e n i n F i g u r e s 3 and 4. For models hav-i n g a r e l a t hav-i v e l y h hav-i g h GH, l hav-i k e t h e p a r e n t h u l l f o r m , t h e hav-i n c r e a s e o f the l i n e a r damping c o e f f i c i e n t w i t h speed appears t o be s m a l l , b u t

f o r l o w GM ( l o n g n a t u r a l r o l l p e r i o d ) i t i s v e r y l a r g e . T h e c o r r e l a -t i o n w i -t h -t h e e m p i r i c a l m e -t h o d o f I K E D A e -t a l . ( 1 9 7 8 ) w a s p o o r , s o t h a t i t w a s d e c i d e d t o c a r r y o u t a t h o r o u g h i n v e s t i g a t i o n o f r o l l d a m p i n g f o r t h e FDS s e r i e s b y m e a n s o f e x t e n s i v e r o l l o s c i l l a t i o n t e s t s a n d c o m p u t a t i o n s . F i g u r e 2 P a r e n t h u l l f o r m F D S , 0 Regular waves •„ = 0.143 — i _ _ " = 0.285 = 0.428 = 0.579 1 j/B/2g F i g u r e 3 M e a s u r e d r o l l r e s p o n s e f u n c t i o n o f p a r e n t h u l l f o r m F D S .

Without bilge keels With bilge keels

1 1 Quadratic ó —Ü — O (V O —A , —O l i O— • Lin ear O 0.2 0.4 0.6

F i g u r e 4 R o l l decay c o e f f i c i e n t s o f p a r e n t h u l l form FDS model t e s t s .

2. EMPIRICAL MODEL FOR FDS ROLL DAMPING

2.1 Assumptions

W i t h r e s p e c t t o t h e r o l l damping o f f a s t s h i p s i t i s assumed t h a t t h e wave p o t e n t i a l damping i s w e l l p r e d i c t e d w i t h s t r i p t h e o r y . I n F i g -ures 5 and 6 r e s u l t s a r e shown f o r t h e p a r e n t h u l l form and t h e com-p u t e d com-p o t e n t i a l damcom-ping f o r F^^ = 0 i s q u i t e w e l l i n l i n e w i t h t h e o s c i l l a t i o n t e s t r e s u l t s a t v e r y low speed. I n t h e t w o - d i m e n s i o n a l p o t e n t i a l t h e o r y t h a t was used, t h e speed has no e f f e c t on t h e r o l l damping. T h i s i m p l i e s t h a t t h e speed dependent damping c o n t r i b u t i o n , which t h e o r e t i c a l l y f o l l o w s from a transom s t e r n c o n f i g u r a t i o n , has been i n c o r p o r a t e d i n t h e h u l l l i f t damping. The r o l l damping due t o appendages o t h e r t h a n b i l g e k e e l s has been e x c l u d e d s i n c e these were n o t p r e s e n t on t h e FDS model s e r i e s . A v a i l a b l e f u l l s c a l e t r i a l s data and model t e s t d a t a suggest t h a t b i l g e k e e l s have a f a r g r e a t e r e f -f e c t t h a n appendages and t h i s would seem t o be a -f a i r a s s u m p t i o n . The f r i c t i o n damping i s so s m a l l i n comparison t o t h e o t h e r c o n t r i b u t i o n s a t speed t h a t i t may be n e g l e c t e d .

The h u l l l i f t damping i n t h e e m p i r i c a l t h e o r y o f IKEDA e t a l . (1978) i s d e r i v e d from t h e l i f t on a v e r t i c a l p l a t e making r o l l m o t i o n s , an assumption t h a t may g i v e a reasonable p r e d i c t i o n f o r a c o n v e n t i o n a l h u l l w i t h l a r g e Cg and low B/T, i . e . a deep d r a f t . For t h e FDS h u l l forms i t i s n o t r e a l i s t i c s i n c e B/T i s r a t h e r l a r g e .

O s t r i p theory, = 0 Without bilge keels With bilge keels

" J 0 e 1 tests '^y^fff^ — = 0.428 = 0.285 = 0.143 o O O O 2 ^ 0 0 0.5 1.0 1.5 w/fe/2g F i g u r e 5 T o t a l r o l l damping c o e f f i c i e n t o f p a r e n t h u l l form FDS. o o ° o o A ai/B/2g = 0.9 o = 1.4 A ^ ^ A i 1 ^ _{o a g ^} 5 10 15 Section number 20 (bow)

The eddy damping o f t h e h u l l i s s m a l l f o r h u l l forms o f low C„ and round s e c t i o n s w i t h l a r g e b i l g e r a d i u s . A l t h o u g h t h e e f f e c t o f sec-t i o n shape i s p r e s e n sec-t i n sec-t h e I k e d a f o r m u l a sec-t i o n s , compusec-ted v a l u e s appeared t o g r e a t l y exceed t h e measured v a l u e s .

I n t h e b i l g e k e e l damping t h e e f f e c t o f two c o n t r i b u t i o n s i s d i s -cerned: b i l g e k e e l eddy g e n e r a t i o n and v o r t e x g e n e r a t e d p r e s s u r e i n t e r a c t i o n between b i l g e k e e l and h u l l . GRAHAM ( 1 9 8 6 ) m o d i f i e d these e x p r e s s i o n s t o f i n d a b e t t e r p r e d i c t i o n f o r f r i g a t e h u l l forms. I n the p r e s e n t i n v e s t i g a t i o n i t was assumed t h a t a t h i g h speed t h e p r e s -sure i n t e r a c t i o n w i l l d i s a p p e a r s i n c e t h e g e n e r a t e d v o r t i c e s w i l l d e v e l o p b e h i n d t h e h u l l . The consequence i s speed dependence i n t h e b i l g e k e e l damping, which was a l s o r e c o g n i z e d i n t h e d i s c u s s i o n o f Himeno t o t h e paper o f SCHMIDTKE ( 1 9 7 8 ) . Moreover, a t h i g h speed a s i z e a b l e l i f t e f f e c t on t h e b i l g e k e e l s may be e x p e c t e d .

Summarizing t h e above a s p e c t s , t h e r o l l damping f o r t h e f a s t d i s -placement s h i p s e r i e s i s proposed by t h e f o l l o w i n g f o r m :

= ^W<") + ^E'^s'^'^a) + + ^BKL^^s'") + BBKE<Vs'"'*a>

b e i n g t h e most i m p o r t a n t c o n t r i b u t i o n s and n e g l e c t i n g f r i c t i o n and appendage damping. The wave p o t e n t i a l and eddy damping a r e computed per s e c t i o n . The main v a r i a b l e s a r e f r e q u e n c y w, r o l l .amplitude and t h e s h i p speed .

s

On b a s i s o f t h e s y s t e m a t i c r o l l o s c i l l a t i o n t e s t s e r i e s o f t h e FDS models t h e dependency o f t h e damping c o n t r i b u t i o n s on t h e s e v a r i a b l e s c o u l d be e s t a b l i s h e d . Moreover, t h e wide h u l l f o r m parameter space makes i t p o s s i b l e t o e s t a b l i s h t h e dependency o f t h e l i f t c o n t r i b u -t i o n s on -t h e h u l l shape.

2.2 L i f t Damping

C o n s i d e r i n g t h e round b i l g e h u l l forms o f t h e FDS s e r i e s , t h e i r f l o w l i n e s w i l l be smooth and s t r a i g h t , e x c e p t c l o s e t o t h e w a t e r l i n e . F i g u r e 2 shows some f l o w l i n e s f o r t h e p a r e n t h u l l f o r m . When t h e h u l l i s i n c l i n e d , t h e f l o w l i n e s w i l l s t i l l be smooth and t h e h y d r o -dynamic p r e s s u r e d i s t r i b u t i o n w i l l n o t show l a r g e v a r i a t i o n s . See F i g u r e 7, p r e s e n t i n g t h e r e s u l t s o f f l u i d f l o w c o m p u t a t i o n s o f t h e DAWSON computer program (RAVEN, 1 9 8 8 ) f o r s t a t i o n a r y f l o w .

Fn = 0.885 F i g u r e 7 Pressure d i s t r i b u t i o n f r o m s t a t i o n a r y f l o w c a l c u l a t i o n s f o r p a r e n t h u l l form FDS a t 10 deg h e e l i n g a n g l e . w/fe/2g 1.35 Computed 7 • Ü o Measured 0.5 1.0 F i g u r e 8 R o l l damping f r o m o s c i l l a t i o n t e s t s and c o m p u t a t i o n s f o r p a r e n t h u l l form FDS.

Under these c o n d i t i o n s i t i s a c c e p t a b l e t o a p p l y a m a t h e m a t i c a l de-s c r i p t i o n o f t h e r o l l damping a c c o r d i n g t o t h e t h e o r y f o r trimmed f l a t p l a t e s by SHUFORD ( 1 9 5 8 ) . T h i s t h e o r y r e s u l t s i n a l i f t damping which i s p r o p o r t i o n a l w i t h speed, as i s a l s o observed f o r t h e FDS s e

-r i e s , see F i g u -r e 8. I n t h i s f i g u -r e i t i s a l s o shown t h a t t h e damping of t h e p a r e n t h u l l f o r m i s v e r y s e n s i t i v e t o speed a t l o w f r e q u e n c y .

but h a r d l y so a t h i g h f r e q u e n c y . A t h i g h f r e q u e n c y i t i s p r a c t i c a l l y equal t o t h e wave p o t e n t i a l damping (see F i g u r e 5) w h i c h leads t o t h e c o n c l u s i o n t h a t t h e h u l l l i f t damping i s i m p o r t a n t a t low f r e q u e n c y . T h i s i s a g e n e r a l o b s e r v a t i o n f o r t h e whole s e r i e s , and s u p p o r t s t h e use o f t h e s t a t i o n a r y t h e o r y g i v e n by SHUFORD ( 1 9 5 8 ) .

An o u t l i n e o f t h e approach i s g i v e n below:

The l i f t damping Bj^ i s t h e r e s u l t o f t h e s m a l l i n c i d e n c e angle T o f the f l o w r e l a t i v e t o t h e k e e l t h a t i s i n t r o d u c e d by t h e r o l l v e l o c -i t y . T h -i s l -i f t a p p l -i e s a t a l e v e r arm w h -i c h depends on t h e beam o f the s h i p , and depends on t h e mean d e a d r i s e a n g l e p^,. A c c o r d i n g t o SHUFORD ( 1 9 5 8 ) t h e l i f t on a trimmed p l a t e w i t h t r i m a n g l e x i s g i v e n by: ( n e g l e c t i n g edge e f f e c t s f o r round b i l g e shapes)

F^ = 0.5 p C^, w i t h

= 0.5 n T c o s ^ T d - s i n p g ) / ( L / B + l )

- T ( l - s i n 3g,)/(L/B+l) f o r s m a l l v a l u e s o f T.

The s t a t i c component o f t h e l i f t f o r c e i s one o f t h e f o r c e s t h a t b a l ance t h e w e i g h t o f t h e s h i p . The r o l l induced l i f t f o r c e w i l l c o n t r i -bute t o t h e damping. W i t h B^'^ = l e v e r arm * r o l l induced l i f t , an e x p r e s s i o n r e s u l t s i n which t h e s e m i s t a t i c l i f t damping i s p r o p o r -t i o n a l -t o :

Bj^ = k p s Vg BV( L / B + 1 ) , w i t h

k = c o n s t a n t * (1 - s i n $„) S = w e t t e d a r e a .

The c o n s t a n t k and t h e f u n c t i o n d e s c r i b i n g t h e dependence on t h e f r e -quency have been d e t e r m i n e d f r o m t h e FDS o s c i l l a t i o n t e s t base, when we i n c l u d e t h i s h u l l l i f t damping i n t h e c o m p u t a t i o n o f r o l l angle i n waves we o b t a i n a f a i r l y a c c u r a t e p r e d i c t i o n as shown i n F i g u r e 9. I t has t o be r e a l i z e d t h a t a t t h e h u l l f o r m w i t h o u t b i l g e k e e l s t h e damping a t h i g h speed i s s o l e l y wave p o t e n t i a l damping and h u l l l i f t damping. The d i f f e r e n c e s between t h e measured and t h e computed damp-i n g damp-i n t h e h damp-i g h f r e q u e n c y range damp-i s m a damp-i n l y r e l a t e d t o t h e s l damp-i g h t l y t o o h i g h v a l u e o f t h e speed independent wave p o t e n t i a l damping.

Comp. Meas, A _0.14 0 0.28 • _0.43 0,57

\

1 0 1.0 2.0 aj/fe/2g

F i g u r e 9 R o l l response i n beam waves o f p a r e n t h u l l f o r m FDS.

2.3 Eddy Damping

I n t h e e m p i r i c a l t h e o r y o f IKEDA e t a l . ( 1 9 7 8 ) t h e eddy damping o f the h u l l i s d e s c r i b e d as a f u n c t i o n o f t h e s e c t i o n a l shape. For con-v e n t i o n a l h u l l forms t h e agreement has been w e l l con-v a l i d a t e d . Howecon-ver, f o r t h e f a s t d i s p l a c e m e n t type s h i p s w i t h ( g e n e r a l l y ) a transom s t e r n , t h e l o c a l B/T r a t i o may be q u i t e h i g h . I n t h e f o r m u l a t i o n s (IKEDA e t a l . , 1978 and VAN DER VEGT, 1 9 8 4 ) t h e s e c t i o n a l eddy damp-i n g c o e f f damp-i c damp-i e n t damp-i s p r o p o r t damp-i o n a l t o T^, w, C^^ and a speed f u n c t damp-i o n F(V ) . The speed f u n c t i o n d e s c r i b e s a q u a d r a t i c r e d u c t i o n o f t h e eddy damping w i t h speed. The c o e f f i c i e n t C^^ depends on h u l l f o r m and sec-t i o n a l B/T and s e c sec-t i o n a l area c o e f f i c i e n sec-t a. Hence:

B^' = c o n s t a n t * p t'' w cJi, C„ F(V^)

I n F i g u r e 10 i s shown t h a t Cj^ tends t o become e x t r e m e l y l a r g e f o r l a r g e B/T and f o r s m a l l a t h e v a l u e o f Cj^ may become n e g a t i v e . These are c o n d i t i o n s t h a t w i l l n o t occur f o r a c o n v e n t i o n a l h u l l f o r m , b u t

f o r FDS w i t h l o w Cg and wide, s h a l low s e c t i o n s a f t i t causes a p r o b -lem. A s i m p l e m o d i f i c a t i o n t o t h e f o r m u l a t i o n s has been a p p l i e d t o extend t h e v a l i d i t y o f t h e eddy damping c a l c u l a t i o n scheme. 2.4 B i l g e Keel Damping ( L i f t ) C o n s i d e r i n g t h e b i l g e k e e l s as l i f -t i n g s u r f a c e s , -t h e SHUFORD ( 1 9 5 8 ) f o r m u l a t i o n f o r t h e l i f t on a trimmed f l a t p l a t e may a g a i n be used. A c c o r d i n g t o SCHMIDTKE ( 1 9 7 8 ) t h e r e i s a c l e a r dependence o f t h e b i l g e k e e l damping t o t h e i r submer-gence d e p t h , which i s expressed as a p r o p o r t i o n a l i t y t o s i n r , i n which r i s t h e angle e n c l o s e d by

the w a t e r l i n e and t h e l i n e connect-i n g t h e c e n t r e o f g r a v connect-i t y and t h e b i l g e k e e l , see F i g u r e 2. Simple g e o m e t r i c c o n s i d e r a t i o n s l e a d t o a b i l g e k e e l l i f t damping g i v e n by: C J 01 •4-O) O O 500 a . E ro -o >. -o -D LÜ Sectional B/T 4' 4 FDS Ikeda et a l .

1

—V

0 0.5 0.75 1.0 Sectional area c o e f f i c i e n t a F i g u r e 10 Eddy damping h u l l . ^BKL ^ c o n s t a n t * " ^BK ^S ' s i n r cos Y = d i s t a n c e from c e n t r e o f g r a v i t y t o b i l g e k e e l . For t h e a p p l i c a t i o n t o t h e FDS s e r i e s t h e e x p r e s s i o n f o r t h e b i l g e k e e l area Sgj^ has been f u r t h e r d e t a i l e d and t h e p r o p o r t i o n a l i t y c o n s t a n t has been d e t e r m i n e d from t h e f i t .

2.5 B i l g e Keel Damping (Eddy)

The b i l g e k e e l eddy damping has been o b t a i n e d by a d a p t i n g t h e ex-p r e s s i o n s g i v e n by SCHMIDTKE ( 1 9 7 8 ) and GRAHAM ( 1 9 8 6 ) . Whereas Schmidtke's e x p r e s s i o n s y i e l d t h e t o t a l b i l g e k e e l damping, t h e p r e s e n t work r e q u i r e s an e x p r e s s i o n f o r t h e eddy damping o n l y . The r e l a t i v e l y l a r g e b i l g e r a d i u s o f t h e f a s t h u l l forms ( a s s o c i a t e d w i t h s m a l l m i d s h i p s e c t i o n a l area c o e f f i c i e n t ) a l l o w s f u r t h e r s i m p l i f i c a

-t i o n s , so -t h a -t an e x p r e s s i o n r e s u l -t s f o r -t h e s e c -t i o n a l b i l g e k e e l damping o f t h e f o r m :

^BKE' ^ c o n s t a n t * p r ^ w .f.^ b^^^ F" , w i t h

2 /, -.0.6 F" = - r cos Y ^ g bgj^/o) (J.^ rJ F(Vg)

I t has t o be r e a l i z e d t h a t t h e b i l g e k e e l eddy damping does n o t p l a y an i m p o r t a n t r o l e due t o i t s speed dependence. The dependence on b i l g e k e e l h e i g h t b^j^ i s s l i g h t l y s t r o n g e r t h a n l i n e a r .

3. VALIDATION

3 .1 Parent H u l l Form FDS

For t h e p a r e n t h u l l form o f t h e FDS s e r i e s t h e outcome o f t h e r o l l damping p r e d i c t i o n model d e s c r i b e d above i s p r e s e n t e d i n F i g u r e 8 and g i v e s a good agreement w i t h t h e measurements. Since t h e f o r m u l a t i o n s were tuned on t h e FDS s e r i e s database t h i s s h o u l d n o t come as a s u r -p r i s e . I n F i g u r e 9 t h e r o l l RAO's as -p r e d i c t e d f r o m s t r i -p t h e o r y c o m p u t a t i o n s , u s i n g t h e FDS ROLLDAMP code are compared w i t h measured r o l l responses from r e g u l a r beam wave t e s t s . The agreement a t t h e f r e q u e n c i e s up t o and i n c l u d i n g t h e n a t u r a l r o l l f r e q u e n c y i s v e r y good, c o n f i r m i n g t h e a c c u r a c y o f t h e p r e d i c t i o n model. A t t h e h i g h e s t f r e q u e n c i e s t h e agreement d e t e r i o r a t e s , assumedly due t o t h e i n a c c u -r a t e wave e x c i t a t i o n s f-rom s t -r i p t h e o -r y i n t h i s f -r e q u e n c y -range. Note t h a t t h e n a t u r a l r o l l f r e q u e n c y o f t h e p a r e n t h u l l f o r m as t e s t e d i s r a t h e r h i g h , and t h a t i n many p r a c t i c a l s i t u a t i o n s t h e n a t u r a l r o l l f r e q u e n c y w i l l be l o w e r . I t i s a l s o c l e a r l y shown t h a t f o r t h i s h i g h n a t u r a l r o l l f r e q u e n c y t h e speed dependence o f t h e r o l l response i s r e l a t i v e l y s m a l l .

3.2 Fast P a t r o l Boat o f 36 m

A s m a l l s c a l e body p l a n o f t h e s h i p i s g i v e n i n F i g u r e 11 and t h e r e -s u l t -s o f t h e r o l l damping mea-surement-s (by mean-s o f r o l l decay t e -s t -s ) w i t h and w i t h o u t b i l g e k e e l s i s compared w i t h t h e computed v a l u e s f r o m t h e FDS ROLLDAMP code i n F i g u r e 1 2 . For t h i s s h i p , w i t h r e l a -t i v e l y a l o w e r n a -t u r a l r o l l f r e q u e n c y -t h a n -t h e p a r e n -t h u l l f o r m o f the FDS s e r i e s , t h e speed e f f e c t on t h e damping i s pronounced. The agreement w i t h t h e p r e d i c t e d v a l u e s i s v e r y good. I t has t o be r e a l

-i z e d t h a t t h e c e n t r e o f g r a v -i t y o f t h e s h -i p l -i e s -i n t h e w a t e r p l a n e , so t h a t s w a y r o l l c o u p l i n g e f f e c t s a r e n e g l i g i b l e . Due t o t h e s i z e a b l e b i l g e k e e l s t h e i r e f f e c t i s c l e a r l y shown. The component b r e a k -down i n T a b l e 1 shows t h a t a t h i g h speed t h e i r r e l a t i v e magnitude remains l i m i t e d though.

F i g u r e 11 Fast P a t r o l Boat ( C o u r t e s y SSE).

Computed Measured

• With bilge keels o Without bilge keels

Table 1

R o l l damping c o n t r i b u t i o n s

M-- f r i g a t e 36 m Fast P a t r o l C r a f t C o n t r i b u t i o n

Speed Speed Speed Speed Speed

12 kn 17 kn 23 kn 20 kn 35 kn P o t e n t i a l 8.5% 8.5% 8.5% 19.9% 1 2 . 5 % H u l l f r i c t i o n 0.8% 0.9% 0.8% 0.5% 0.3% H u l l l i f t 36.3% 51.4% 61.0% 64.4% 70.7% B i l g e eddy 36.2% 20.2% 10.3% 0.5% 0.3% B i l g e k e e l l i f t 10.4% 14.7% 17.2% 14.7% 16.2% B i l g e k e e l eddy 7.8% 4.3% 2.2% 0.0% 0.0% T o t a l computed 100.0% 100.0% 100.0% 100.0% 100.0% e x c l . c o u p l i n g w i t h sway

3.3 Royal N e t h e r l a n d s Navy F r i g a t e ' K a r e l Doorman'

Very r e c e n t l y a s e r i e s o f f u l l s c a l e t r i a l s was conducted on board o f t h e brand-new RNN f r i g a t e K a r e l Doorman, w h i c h i s t h e l e a d s h i p o f a c l a s s o f e i g h t M type 3000 tonnes m u l t i - p u r p o s e f r i g a t e s c u r r e n t l y under c o n s t r u c t i o n f o r t h e N e t h e r l a n d s Navy.

The main p a r t i c u l a r s o f t h i s s h i p a r e l i s t e d i n Table 2. The s h i p i s f i t t e d w i t h a Rudder R o l l S t a b i l i z a t i o n system o f n o v e l d e s i g n . T h i s system combines t h e s t e e r i n g and t h e r o l l s t a b i l i z a t i o n i n one system t h u s o b v i a t i n g t h e need f o r a s e p a r a t e s e t o f a n t i - r o l l i n g f i n s . For t h i s added t a s k t h e r u d d e r s and t h e i r d r i v i n g gear have t o be o f im-p r o v e d and s t r o n g e r d e s i g n t h a n i s common on a s h i im-p , t o a l l o w t h e c o n t i n u o u s m o t i o n r e q u i r e d t o p r o v i d e r o l l damping i n t h e wave f r e -quency band. Table 2 Main p a r t i c u l a r s o f M - f r i g a t e ' K a r e l Doorman' D e s c r i p t i o n U n i t Magnitude Length B r e a d t h D r a f t Displacement m m m tonnes 112.70 13.10 4.28 3210.00

For t h e f u l l s c a l e r o l l i n g t r i a l s i n calm w a t e r t h i s rudder system l a y o u t i s a d m i r a b l y s u i t e d t o e x c i t e t h e s h i p i n r o l l i n g even up t o c o n s i d e r a b l e a n g l e s .

The s e r i e s o f t r i a l s t h a t we a r e concerned w i t h here were r o l l ex-t i n c ex-t i o n ex-t r i a l s a ex-t speed i n calm w a ex-t e r . The rudders would be moved back and f o r t h a t the n a t u r a l r o l l p e r i o d , t h e r e b y g r a d u a l l y w o r k i n g up t h e r o l l angle up t o v a l u e s as h i g h as 17 degrees. The rudders were t h e n p u t amidships and the r e s u l t i n g e x t i n c t i o n o f the r o l l an-g l e was r e c o r d e d . The t r i a l s were c a r r i e d out a t t h r e e sea speeds, 12, 17, and 23 k n o t s , as measured by the s h i p ' s l o g .

Ship Model . • ^—^^^^^—~ " N7 kn 0 kn F i g u r e 13 R o l l decrement curves f o r M - f r i g a t e .

From t h e t i m e h i s t o r y p l o t s t h e a m p l i t u d e decrement p l o t s were made as shown i n F i g u r e 13 from which the damping c o e f f i c i e n t was ob-t a i n e d . The e x p e r i m e n ob-t a l r e s u l ob-t s as shown i n F i g u r e 14 show ob-t h a ob-t ob-the damping c o e f f i c i e n t depends upon the s h i p speed. As shown i n F i g u r e 13 t h e i n c r e a s e i n speed r e s u l t s i n an i n c r e a s e i n l i n e a r r o l l damping c o e f f i c i e n t and a decrease i n q u a d r a t i c damping c o e f f i c i e n t . Both model t e s t s and f u l l s c a l e t e s t s t e n d t o s u p p o r t t h i s . T h i s f i n d i n g agrees w i t h t h e r e s u l t s o f the FDS d a t a f i l e s and i s m a i n l y t o be a t t r i b u t e d t o the i n c r e a s e i n h u l l l i f t damping w i t h speed, as

i s shown i n F i g u r e 5. The damping c o e f f i c i e n t was a l s o computed w i t h the use o f t h e program ROLLDAMP and t h e v a l u e s a r e compared i n F i g u r e 14.

O v e r a l l t h e c o r r e l a t i o n between f u l l s c a l e t r i a l s r e s u l t s and model t e s t s i s q u i t e good. To o b t a i n more i n s i g h t i n t o t h e c o m p o s i t i o n o f the r o l l damping as computed by t h e program ROLLDAMP we show t h e breakdown i n Table 1. I t i s shown i n t h i s t a b l e t h a t t h e most impor-t a n impor-t c o n impor-t r i b u impor-t i o n s a r e due impor-t o h u l l l i f impor-t and b i l g e k e e l l i f impor-t . As shown i n F i g u r e 14 t h e c o m p u t a t i o n s on b a s i s o f t h e program ROLLDAMP under-e s t i m a t under-e t h under-e t o t a l damping c o under-e f f i c i under-e n t . Thunder-e main runder-eason i s t h a t t h under-e COG d i d n o t c o i n c i d e w i t h t h e o r i g i n i n t h e w a t e r p l a n e , so t h a t a c o n s i d e r a b l e r o l l - s w a y c o u p l i n g i s bound t o be p r e s e n t i n t h e model and f u l l s c a l e t r i a l s r e s u l t s .

• Fun scale t r i a l s

A Model tests

o Computation ( e x c l . coupling with sway)

V Computation ( i n c l . coupling with sway)

7 V ^ y ^ • • 0 n 1 1 1 1 1 1 12 15 17 20 23 25 (knots) I I I I I I 0.1 0.2 0.3 0.4 0.5 F i g u r e 14 R o l l damping c o e f f i c i e n t o f M - f r i g a t e .

To o b t a i n data t o judge t h i s i n f l u e n c e computer timedomain s i m u l a -t i o n s were made u s i n g -t h e program FREDYN. T h i s program employs a f u l l y n o n - l i n e a r d e s c r i p t i o n o f t h e m o t i o n s and was r u n t o produce t h e r o l l decay t i m e h i s t o r i e s i n c l u d i n g t h e e f f e c t o f sway c o u p l i n g . The r e s u l t s a r e a l s o shown i n F i g u r e 14 and a r e seen t o c o i n c i d e f a i r l y w e l l w i t h t h e measured d a t a .

EPILOGUE The r o l l d a m p i n g s u b j e c t s a d d r e s s e d i n t h i s p a p e r a r e n o t e n t i r e l y new. A c e n t u r y ago t h e a b o l i s h m e n t o f s a i l p o w e r h a s s t r i p p e d t h e s h i p s o f a i r d a m p i n g due t o t h e l a r g e s a i l a r e a , as a c o n s e q u e n c e o f w h i c h t h e r o l l i n g o f s e a g o i n g s h i p s became a p r o b l e m . W i l l i a m F r o u d e was one o f t h e f i r s t t o t a c k l e t h i s p r o b l e m . The b e n e f i c i a l e f f e c t t h a t s p e e d h a s o n r o l l d a m p i n g , hence on r e d u c -i n g t h e r o l l a n g l e s h a s a l r e a d y b e e n r e c o g n -i z e d b y S -i r W -i l l -i a m W h -i t e i n 1895 when r e p o r t i n g u p o n h i s f u l l s c a l e t r i a l s o n t h e b a t t l e s h i p 'HMS R e v e n g e ' . A l s o t h e i m p o r t a n c e o f b i l g e k e e l s was b r o u g h t t o l i g h t q u i t e some t i m e ago i n t h e 1 9 3 0 ' s when t h e b a t t l e s h i p 'USS M a r y l a n d ' v e r y n e a r l y r o l l e d o v e r when r i d i n g a t a n c h o r o n a l o n g s w e l l t h a t g o t h e r t o t h e p o i n t o f 30 d e g r e e s r o l l a n g l e w h e r e t h e d e c k became awash. I n t h e n i c k o f t i m e s h e c o u l d p a r t h e r m o o r i n g s a n d g e t u n d e r w a y b e f o r e d i s a s t e r s t r u c k a n d t h e p r e s e n c e o f b i l g e k e e l s a n d t h e i r c o n s i d e r -a b l e r o l l d -a m p i n g i s g e n e r -a l l y t h o u g h t t o h -a v e s -a v e d t h e s h i p .

The p r e s e n t p a p e r i s meant t o i n v e s t i g a t e t h e same r o l l d a m p i n g s u b -j e c t . Y e t o n b a s i s o f s y s t e m a t i c m o d e l e x p e r i m e n t s , b a c k e d - u p b y f u l l s c a l e t r i a l s we h a v e b e e n a b l e t o more t h o r o u g h l y u n d e r s t a n d t h e com-p o s i t i o n o f r o l l d a m com-p i n g a n d come u com-p w i t h a com-p r e d i c t i o n m e t h o d t h a t shows g r e a t p r o s p e c t f o r p r e s e n t - d a y h i g h s p e e d h u l l f o r m s a n d s h i p t y p e s , n o t a b l y f r i g a t e s . REFERENCES

BLOK, J . J , a n d BEUKELMAN, W. ( 1 9 8 4 ) The h i g h s p e e d d i s p l a c e m e n t s h i p s y s t e m a t i c s e r i e s h u l l f o r m s - S e a k e e p i n g c h a r a c t e r i s t i c s , SNAME. GRAHAM, R. ( 1 9 8 6 ) SHIPM03, i m p r o v e d v i s c o u s r o l l d a m p i n g p r e d i c t i o n s f o r t h e SHIPMO c o m p u t e r p r o g r a m . T e c h n i c a l Memorandum 8 6 / 2 1 2 , DREA, IKEDA, Y, ( 1 9 8 8 ) E f f e c t o f f o r w a r d s p e e d o n r o l l d a m p i n g o f a h i g h s p e e d c r a f t , E n g l i s h t r a n s l a t i o n b y T.U. B e r l i n 1990 o f p a p e r i n J o u r n a l o f K a n s a i Soc. o f Nav. A r c h , J a p a n , V o l . 2 0 8 .

IKEDA, Y., HIMENO, Y. a n d TANAKA, N. ( 1 9 7 8 ) A p r e d i c t i o n m e t h o d f o r s h i p r o l l d a m p i n g . U n i v e r s i t y o f Osaka P r e f e c t u r e , D e p t . o f Nav. A r c h . R e p o r t 00405.

RAVEN, H.C. (1988) V a r i a t i o n on a theme by DAWSON. 1 7 t h ONR Sympo-sium.

SCHMIDTKE, R.T. ( 1 9 7 8 ) Ship sway, r o l l and yaw motions i n o b l i q u e seas. SNAME.

SHUFORD J r . , C.L. ( 1 9 5 8 ) A t h e o r e t i c a l and e x p e r i m e n t a l s t u d y o f p l a n i n g s u r f a c e s i n c l u d i n g e f f e c t s o f c r o s s - s e c t i o n and p l a n f o r m . Report 1355, N a t i o n a l A d v i s o r y Committee f o r A e r o n a u t i c s . L a n g l e y A e r o n a u t i c a l Lab.

VAN DER VEGT, J.J.W. ( 1 9 8 4 ) S l i n g e r g e d r a g van Schepen. K I V I Zeegangs-dag ( i n D u t c h ) .