The seakeeping performance and steering properties of sailing yachts

R e p o r t No. 366

LABORATORIUM VOOR

SCHEEPSBOUWKUNDE

TECHNISCHE HOGESCHOOL DELFT

THE SEAKEEPING PERFORMANCE AND STEERING PROPERTIES OF S A I L I N G YACHTS b y J . G e r r i t s m a a n d G, Moeyes November 1972

THE SEAKEEPING PERFORMANCE AND STEERING PROPERTIES

OF SAILING YACHTS

by

J. G e r r i t s m a and G. Moeyes

C o n t e n t s . lo I n t r o d u c t i o n 2. The i n f l u e n c e o f d i s p l a c e m e n t on t h e s t i l l w a t e r p e r f o r m a n c e 3. The i n f l u e n c e o f d i s p l a c e m e n t and l o n g i t u d i n a l d i s t r i b u t i o n o f w e i g h t s on t h e windward performance i n a seaway 4. The s t e e r i n g performance

4.1. Forces and moments owing t o r u d d e r a n g l e 4.2. The f i x e d c o n t r o l s b e h a v i o u r

4.3. The b e h a v i o u r w i t h c o n t i n u o u s r u d d e r a c t i o n

5. C o n c l u s i o n

6. Acknowledgement

. I n t r o d u c t i o n

To a c e r t a i n e x t e n d t h e p e r f o r m a n c e o f a s a i l i n g y a c h t can be p r e d i c t e d w i t h t h e a i d o f s h i p model t e s t s i n a t o w i n g

t a n k . To e v a l u a t e t h e e x p e r i m e n t a l model r e s u l t s t h e p r o c e d u r e as p u b l i s h e d by Davidson [ l ] i s s t i l l used i n p r i n c i p l e , and t a n k p r e d i c t i o n s based on h i s method have proved t o be an e f f i c i e n t t o o l f o r t h e d e s i g n e r o f s a i l i n g y a c h t s .

P a r t i c u l a r l y i n t h e case o f l a r g e s e a g o i n g y a c h t s t h e r e d u c t i o n o f t h e r i s k o f f a i l u r e i s i m p o r t a n t and c e r t a i n l y f o r t h i s c l a s s o f v e s s e l s r o u t i n e t a n k t e s t s a r e more o r l e s s common p r a c t i c e .

Such t e s t s p r e d i c t t h e p e r f o r m a n c e f o r t h e windward and t h e r u n n i n g c o n d i t i o n s , assuming t h a t t h e r e a r e no seawaves. T h i s s i m p l i f i c a t i o n i s n o t r e a l i s t i c i n a l l cases, b u t i t i s

commonly assumed t h a t t h e y a c h t , w h i c h i s s u p e r i o r i n calm w a t e r compared w i t h an a l t e r n a t i v e d e s i g n , w i l l a l s o be t h e b e s t one i n a seaway. S i m i l a r a s s u m p t i o n s a r e u s u a l l y made i n t h e d e s i g n of^ s h i p s w i t h m e c h a n i c a l p r o p u l s i o n . The e f f e c t o f sea waves i s t a k e n i n t o a c c o u n t by u s i n g s t a t i s t i c a l power a l l o w a n c e s added t o t h e s t i l l w a t e r t a n k p r e d i c t i o n .

I n t h e l a s t decades model t e s t s i n waves have become an a d d i t i o n a l t o o l t o e v a l u a t e s h i p p e r f o r m a n c e i n a seaway, i n p a r t i c u l a r f o r s p e c i a l purpose s h i p s and f o r d e s i g n s w h i c h a r e o u t s i d e o f t h e range f o r w h i c h s u f f i c i e n t e m p i r i c a l

knowledge e x i s t s . I n a d d i t i o n t h e o r e t i c a l methods have been d e v e l o p e d t o c a l c u l a t e w i t h s u f f i c i e n t a c c u r a c y t h e o s c i l l a t o r y m o t i o n s o f a s h i p i n a g i v e n i r r e g u l a r seaway and r e c e n t l y a p r a c t i c a l method t o c a l c u l a t e t h e added r e s i s t a n c e i n waves became a v a i l a b l e .

Up t o now v e r y l i t t l e r e s e a r c h on t h e p e r f o r m a n c e o f s a i l i n g y a c h t s i n waves has been r e p o r t e d . Tank t e s t s i n waves a r e t i m e consuming and e x p e n s i v e ; c o n s e q u e n t l y i t i s n o t l i k e l y t h a t e x t e n s i v e i n v e s t i g a t i o n s o f t h i s s o r t w i l l be c a r r i e d o u t r e g u l a r l y f o r y a c h t d e s i g n s on a c o m m e r c i a l b a s i s . Oneof t h e v e r y few p u b l i c a t i o n s i n t h i s f i e l d was g i v e n by Spens e t a l 2 j .

Head waves as viell as o b l i q u e h e a d i n g s were c o n s i d e r e d and t h e i n f l u e n c e was d e t e r m i n e d , w h i c h t h e l o n g i t u d i n a l d i s t r i b u -t i o n o f -t h e w e i g h -t o f -t h e y a c h -t , c h a r a c -t e r i z e d by -t h e r a d i u s o f g y r a t i o n , has on t h e dynamic b e h a v i o u r i n waves.

The model e x p e r i m e n t s showed t h e advantage o f a s m a l l l o n g i -t u d i n a l r a d i u s o f g y r a -t i o n w i -t h r e s p e c -t -t o p i -t c h i n g m o -t i o n s and added r e s i s t a n c e . For s h o r t wave l e n g t h s a l a r g e r r a d i u s o f g y r a t i o n g i v e s s l i g h t l y b e t t e r r e s u l t s . As a f i r s t a p p r o x i -m a t i o n i t was shown t h a t t h e added r e s i s t a n c e i n waves v a r i e s as t h e squared wave h e i g h t , when wave l e n g t h and forv;ard speed a r e c o n s t a n t .

F i n a l l y t h e model e x p e r i m e n t s i n d i c a t e d t h a t t h e m o t i o n s and t h e added r e s i s t a n c e i n o b l i q u e waves can be e s t i m a t e d f r o m t e s t s i n head waves h a v i n g t h e same e f f e c t i v e wave l e n g t h and t h e same f r e q u e n c y o f e n c o u n t e r . I t was shown t h a t t h e r e s u l t s a r e n o t s e r i o u s l y a f f e c t e d by t h e i n c r e a s e o f t h e y a c h t ' s speed w h i c h i s n e c e s s a r y t o f u l f i l l t h e s e c o n d i t i o n s .

The agreement i s n o t e x a c t , b u t t h e method i s u s e f u l t o compare d i f f e r e n t d e s i g n s .

Seakeeping e x p e r i m e n t s c a r r i e d o u t i n D e l f t w i t h a model d e s i g n e as a h a l f t o n cup y a c h t showed a f a i r agreement w i t h t h e o r e t i c a l p r e d i c t i o n s o f t h e p i t c h i n g and h e a v i n g m o t i o n s [3_ . I n f a c t t h e r e s u l t s were b e t t e r t h a n e x p e c t e d , c o n s i d e r i n g t h e v e r y

"non l i n e a r " form o f t h e y a c h t and t h e use o f a l i n e a r s t r i p t h e o r y . D i f f e r e n c e s i n a m p l i t u d e s o c c u r a t l a r g e wave l e n g t h s , b u t i n t h e r e g i o n o f resonance w h i c h i s i m p o r t a n t w i t h r e g a r d t o added r e s i s t a n c e i n waves, t h e agreement i s v e r y s a t i s -f a c t o r y .

The e x p e r i m e n t a l a c c u r a c y o f t h e t e s t s i n t h e h e e l e d c o n d i t i o n may have s u f f e r e d f r o m l a r g e y a w i n g moments, b u t t h e r e s u l t s

seem t o i n d i c a t e t h a t m o t i o n s and r e s i s t a n c e f o r 20 degrees o f h e e l do n o t d i f f e r s u b s t a n t i a l l y f r o m t h e u p r i g h t c o n d i t i o n v a l u e s .

A t t h e t i m e t h a t t h e s e e x p e r i m e n t s were c a r r i e d o u t no s u i t a b l e method t o c a l c u l a t e t h e added r e s i s t a n c e i n waves was a v a i l a b l e , b u t t h e t e s t r e s u l t s c l e a r l y showed t h e i m p o r t a n c e o f t h e

added r e s i s t a n c e i n waves, w h i c h can e a s i l y d o u b l e t h e s t i l l w a t e r r e s i s t a n c e i n resonance c o n d i t i o n s , even i n v e r y moderate

sea c o n d i t i o n s .

The newly d e v e l o p e d method t o c a l c u l a t e t h e added r e s i s t a n c e o f s h i p s i n waves as r e p o r t e d i n [ 4 ] has p r o v e d t o g i v e r e l i a b l e r e s u l t s f o r a range o f s h i p t y p e s , i n c l u d i n g f a s t c o n t a i n e r s h i p s as w e l l as f u l l t a n k e r s . T h i s method was a l s o used t o a n a l y s e t h e seakeeping c h a r a c t e r i s t i c s o f t h e 1 2 m e t e r s

"Columbia" and " V a l i a n t " . The r e s u l t s were compared w i t h c o r r e s p o n d i n g model e x p e r i m e n t s , c a r r i e d o u t i n t h e D e l f t

S h i p b u i l d i n g L a b o r a t o r y , showing good agreement f o r t h e m o t i o n s as w e l l as f o r t h e added r e s i s t a n c e ; see f i g u r e 1.

The same methods were used t o a n a l y s e a s m a l l s y s t e m a t i c s e r i e s o f y a c h t d e s i g n s , w h i c h were t a n k t e s t e d t o d e v e l o p t h e success-f u l r a c e r " S t a n d success-f a s t " ( p u b l i s h e d as " A d m i r a l " i n [ s ] ) .

The t h r e e p r e l i m i n a r y d e s i g n s have t h e same w a t e r l i n e l e n g t h , b r e a d t h and r a t i n g , b u t t h e d i s p l a c e m e n t s v a r y c o n s i d e r a b l y . The i n v e s t i g a t i o n was c a r r i e d o u t t o a n a l y s e t h e i n f l u e n c e o f d i s p l a c e m e n t and l o n g i t u d i n a l r a d i u s o f g y r a t i o n on t h e w i n d -ward p e r f o r m a n c e i n seawaves.

The p e r f o r m a n c e o f a s a i l i n g y a c h t i s n o t o n l y c h a r a c t e r i z e d by i t s speed and b e h a v i o u r i n s t i l l w a t e r and i n waves, b u t a l s o by t h e way i t s t e e r s . T h i s f a c t has drawn t h e a t t e n t i o n , when w i t h t h e advent o f t h e modern f a s t c r u i s e r - r a c e r s

problems o f c o n t r o l l a b i l i t y i n r u n n i n g c o n d i t i o n s were r e -p o r t e d i n many cases. One o f t h e f e a t u r e s o f t h e s e y a c h t s i s t h e s h o r t f i n k e e l w i t h s e p a r a t e d r u d d e r , w h i c h i n v i t e d many c r u i s i n g s k i p p e r s t o c o n s i d e r s h o r t k e e l y a c h t s as unmanageable and t h e r e f o r e u n s a f e . As w i l l be i l l u s t r a t e d l a t e r i n t h i s paper, t h i s o p i n i o n i s p r o b a b l y n o t c o r r e c t .

i n r o u g h w i n d and sea c o n d i t i o n s t h a n b e f o r e . The l a r g e r f o r c e s w h i c h w i l l be e x e r t e d i n t h e s e c o n d i t i o n s can n o t always be c o n t r o l l e d .

The f i r s t way t o meet t h e c o n t r o l l a b i l i t y problems i s t o g i v e t h e crew d e v i c e s w h i c h can c o u n t e r a c t t h e l a r g e r a c t i n g f o r c e s . As f a r as i t concerns c o u r s e k e e p i n g t h i s method

c o u l d be c a l l e d : t o i n c r e a s e t h e " s t e e r i n g power" o f t h e s h i p . To s e r v e t h i s purpose f o r example a more e f f e c t i v e r u d d e r can be made, by u s i n g more r u d d e r a r e a , a b e t t e r f o r m and by

g i v i n g i t a b e t t e r l o c a t i o n , w e l l a f t and w i t h o u t s l o t s between t h e t o p o f t h e r u d d e r and t h e h u l l . Spens e t a l [ 2 i n c l u d e d t h i s approach i n t h e i r paper; t h e y measured t h e f o r c e s and moments on a y a c h t model as a f u n c t i o n o f r u d d e r a n g l e .

I n t h e D e l f t S h i p b u i l d i n g L a b o r a t o r y measuring f o r c e s and moments owing t o r u d d e r a n g l e has been a p a r t o f a more e x t e n d e d t e s t program w i t h t h e h a l f t o n cup model and t h e two 1 2 meter y a c h t s .

A n o t h e r approach o f t h e s t e e r i n g problem i s t o d e s i g n t h e y a c h t and i t s c o n t r o l s (helm o r s t e e r i n g w h e e l , l e n g t h o f helm, p o s i t i o n o f k i n g p o s t i n t h e r u d d e r , e t c . ) i n such a way t h a t t h e helmsman, as " o p e r a t o r " o f t h e "system" y a c h t

spends t h e l e a s t amount o f energy and a t t e n t i o n t o t h i n g s w h i c h do n o t c o n t r i b u t e t o h i s o n l y purpose: " o p t i m a l s t e e r i n g o f t h e s h i p " . O p t i m a l c o u l d t h e n be i n t e r p r e t e d as c o v e r i n g i n t h e s h o r t e s t t i m e a t r a c k between two g i v e n p o i n t s . T h i s method can be c a l l e d i m p r o v i n g t h e " s t e e r i n g c o m p l i a n c e " o f t h e s h i p and i t s c o n t r o l s . S t e e r i n g power and c o m p l i a n c e t o g e t h e r f o r m t h e s t e e r i n g q u a l i t i e s o f a y a c h t . F i g u r e 11 shows s c h e m a t i c a l l y t h e c o n t r o l system o f a s t e e r e d y a c h t .

The i n p u t c o n s i s t s o f a r u d d e r a n g l e and a d i s t u r b a n c e due t o w i n d and waves, b o t h r e s u l t i n g i n a t u r n i n g moment and a s i d e f o r c e .

The o u t p u t i s t h e s h i p s c o u r s e .

There i s no m u t u a l i n f l u e n c e between i n p u t and o u t p u t , f o r w h i c h we say t h a t t h e u n s t e e r e d y a c h t i s an open l o o p system.

The open l o o p system has s e v e r a l t i m e s been t h e s u b j e c t o f i n v e s t i g a t i o n . Spens e t a l [ 2 ] d e t e r m i n e d t h e dynamic p r o p e r -t i e s o f a yawing and swaying y a c h -t h u l l w i -t h o u -t s a i l s , p a r -t l y by e x p e r i m e n t , p a r t l y by c a l c u l a t i o n ; see f i g u r e 1 2 .

I n D e l f t an e x t e n s i v e o s c i l l a t i o n t e s t program has been c a r r i e d out w i t h t h e models o f t h e h a l f t o n cup y a c h t [3 and t h e two 12 meter y a c h t s as w e l l as w i t h t h e 13 meter w a t e r l i n e y a w l "Stormy". The measured f o r c e s , p r o p o r t i o n a l t o sway, r o l l and yaw a m p l i t u d e s , v e l o c i t i e s and a c c e l e r a t i o n s d e t e r m i n e t h e l i n e a r i z e d e q i a t i o n s o f m o t i o n . I n one o f t h e n e x t c h a p t e r s

more a t t e n t i o n w i l l be p a i d t o t h e appearance and c h a r a c t e r i s t i c s o f t h e e q u a t i o n s o f m o t i o n o f t h e open l o o p c o n t r o l system.

I f a helmsman i s asked t o s t e e r t h e s h i p he w i l l compare t h e a c t u a l c o u r s e w i t h t h e d e s i r e d c o u r s e and s e t t h e helm a c c o r d i n g t o t h e c o u r s e d e v i a t i o n . A d d i t i o n a l i n f o r m a t i o n f o r h i s r e a c t i o n can be t h e r a t e o f t u r n o r yaw v e l o c i t y , i n c l i n a t i o n , helm

a n g l e , s a i l b e h a v i o u r e t c . Whether he uses a l l s o u r c e s o f i n f o r m a t i o n o r o n l y t h e c o u r s e d e v i a t i o n , and t o what d e g r e e , depends upon t h e man and t h e p r o p e r t i e s o f t h e system he has t o s t e e r . Because o f t h e feed-back o f t h e a c t u a l c o u r s e t o t h e helmsman t h e whole system o f y a c h t and helmsman i s c a l l e d a c l o s e d l o o p system.

I t i s g e n e r a l l y assumed t h a t c o u r s e d e v i a t i o n and yaw r a t e have a s i g n i f i c a n t i n f l u e n c e upon t h e helmsmans b e h a v i o u r . For a f i r s t a p p r o x i m a t e a n a l y s i s o f t h e helmsmans i n p u t and o u t p u t , however, a l i n e a r r e l a t i o n between c o u r s e d e v i a t i o n and r u d d e r a n g l e may be assumed.

I n one o f t h e n e x t c h a p t e r s t h e response o f a y a c h t t o r u d d e r a n g l e w i l l be c o n s i d e r e d as a base f o r f u r t h e r r e s e a r c h on t h e s t e e r i n g p e r f o r m a n c e o f t h e helmsman o f a s a i l i n g y a c h t .

2 . The i n f l u e n c e o f d i s p l a c e m e n t on t h e s t i l l w a t e r p e r f o r m a n c e .

The l i n e s o f t h e t h r e e d e s i g n s , w h i c h a r e t h e s u b j e c t o f t h e p r e s e n t a n a l y s i s a r e shown i n f i g u r e 2 and t h e c o r r e s p o n d i n g main p a r t i c u l a r s a r e g i v e n i n T a b l e 1 .

Table 1

Main p a r t i c u l a r s o f t h e d e s i g n s no. I , I I and I I I

I I I I I I

Length of design waterline

wl m 1 0 . 0 0 1 0 . 0 0 1 0 . 0 0 maximum breadth B m 3.66 3.66 3.66 draught m 2 . 1 5 2 . 1 5 2 . 1 5 displacement A kg 8 2 0 7 9 7 5 9 1 1 4 4 3 displacement of h u l l _AH kg 7 6 8 0 9 2 1 1 1 0 6 7 0 centre of buoancy a f t ^ L , wl m 0.26 0.26 0.34

centre of gravity under DWL m 0.25 0.39 0.52

prismatic c o e f f i c i e n t of h u l l 0.566 0 . 5 7 2 0 . 5 6 6 e f f e c t i v e s a i l area wl H 2 m 66 7 1 7 5 length displacement r a t i o wl H 5.07 4.77 4.54 r a t i n g wl H f t 33.6 33.6 3 3 . 6 W i t h r e s p e c t t o t h e main d i m e n s i o n s i t i s i m p o r t a n t t o remark t h a t a l a r g e r d i s p l a c e m e n t a t c o n s t a n t l e n g t h , b r e a d t h and d r a u g h t r e s u l t s i n a l o w e r a s p e c t r a t i o n f i n k e e l because o f t h e l a r g e r d e p t h o f t h e h u l l .

The windward p e r f o r m a n c e o f t h e t h r e e d e s i g n s i n calm w a t e r i s g i v e n i n Table 2 , as t h e speed made good V v e r s u s t h r e e s t a n d a r d v a l u e s o f t h e t r u e w i n d speed V, .

tw Table 2

Speed made good ( a l l speeds i n m e t e r s p e r second)

V, tw V mg V, tw I I I I I I 3 . 5 1 . 9 0 1 . 8 7 1 . 8 8 7 . 0 2 . 7 3 2 . 6 8 2 . 6 9 1 0 . 0 2 . 9 7 2 . 9 3 2 . 9 4

7.

For r u n n i n g c o n d i t i o n s t h e r e s i s t a n c e R f o r z e r o a n g l e o f h e e l and no d r i f t i s o f i n t e r e s t . F i g u r e 3 shows t h e t h r e e r e s i s t a n c e c u r v e s on a base o f f o r w a r d speed.

Design I I I has t h e l o w e s t r e s i s t a n c e per t o n d i s p l a c e m e n t , b u t t h e r u n n i n g speeds a r e a l m o s t e q u a l f o r t h e t h r e e d e s i g n s , e x c e p t t h e l i g h t e s t v e r s i o n I , w h i c h i s s l i g t h l y b e t t e r f o r windspeeds e x c e e d i n g 7 m/s. Based on t h e S t i l l w a t e r p e r -formance t h e c o n c l u s i o n i s t h a t d e s i g n I i s t o be p r e f e r r e d . A l t h o u g h t h e d i f f e r e n c e s between t h e t h r e e d e s i g n s were measurable, t h e p e r f o r m a n c e s a r e v e r y c l o s e t o each o t h e r . C o n s i d e r i n g t h a t t h e I.O.R. 1970 r a t i n g f o r t h e t h r e e y a c h t s i s e q u a l , t h i s means t h a t t h e r a t i n g f o r m u l a works v e r y w e l l i n t h e c o n s i d e r e d case. ( 3. The i n f l u e n c e o f d i s p l a c e m e n t and l o n g i t u d i n a l d i s t r i b u t i o n o f w e i g h t s on t h e windward p e r f o r m a n c e i n a seaway.

The added r e s i s t a n c e o f a y a c h t i n sea waves i s m a i n l y caused by t h e h e a v i n g and p i t c h i n g m o t i o n s . Heave i s d e f i n e d as t h e v e r t i c a l o s c i l l a t o r y m o t i o n o f t h e c e n t r e o f g r a v i t y o f t h e v e s s e l , whereas p i t c h i n g i s t h e r o t a t i o n a l o s c i l l a t o r y m o t i o n w i t h r e g a r d t o an a t h w a r t s h i p ' s a x i s .

The n a t u r a l p e r i o d s o f heave and p i t c h a r e v e r y i m p o r t a n t f o r t h e b e h a v i o u r o f a y a c h t i n waves. I f one o f t h e s e m o t i o n p e r i o d s i s e q u a l t o t h e p e r i o d o f wave e n c o u n t e r , v i o l e n t m o t i o n s may r e s u l t . I n such r e s o n a n t c o n d i t i o n s a l a r g e i n -c r e a s e o f t h e r e s i s t a n -c e i s o b s e r v e d and a -c o r r e s p o n d i n g l o s s o f speed o c c u r s . R e f e r r i n g t o f i g u r e 1, t h e maximum o f t h e added r e s i s t a n c e c u r v e i s near t o resonance o f t h e h e a v i n g and p i t c h i n g m o t i o n s . I n t h e s e c o n d i t i o n s t h e i m m e r s i o n o f t h e bow o f t h e y a c h t i s l a r g e due t o t h e u n f a v o u r a b l e phase o f t h e bow m o t i o n w i t h r e s p e c t t o t h e wave.

I t s h o u l d be remarked t h a t i n resonance c o n d i t i o n s t h e abso-l u t e m o t i o n a m p abso-l i t u d e s a r e n o t n e c e s s a r i abso-l y a maximum. I n v e r y l o n g waves t h e m o t i o n a m p l i t u d e s can be v e r y l a r g e , b u t as t h e y a c h t more o r l e s s f o l l o w s t h e wave c o n t o u r s , t h e r e l a t i v e m o t i o n w i t h r e s p e c t t o t h e wave and t h e added r e s i s t a n c e a r e v e r y s m a l l .

For t h e e s t i m a t i o n o f t h e n a t u r a l p i t c h i n g p e r i o d t h e t o t a l mass moment o f i n e r t i a o f t h e y a c h t has t o be known. T h i s c o n s i s t s o f t h e r e a l mass moment o f i n e r t i a and a h y d r o -dynamic a d d i t i o n , w h i c h can be c a l c u l a t e d w i t h s u f f i c i e n t

a c c u r a c y . W i t h t h e a i d o f a f u l l s c a l e o s c i l l a t i o n e x p e r i m e n t the t o t a l i n e r t i a can be d e t e r m i n e d and hence t h e r e a l mass moment o f i n e r t i a can be e s t i m a t e d .

F u l l s c a l e o s c i l l a t i o n t e s t s w i t h " S t a n d f a s t " , w h i c h was

f o r c e d o s c i l l a t e d i n a p i t c h i n g m o t i o n made by hand e x c i t a t i o n i n calm w a t e r , r e s u l t e d i n a n a t u r a l p i t c h i n g p e r i o d

Tg = 2.4 seconds.

W i t h c a l c u l a t e d v a l u e s f o r t h e hydrodynamic mass moment o f i n e r t i a A, t h e p i t c h damping c o e f f i c i e n t N„„, t h e r e a l mass 0 a moment o f i n e r t i a o f t h e y a c h t I ^ ^ , c o u l d be d e t e r m i n e d w i t h t h e measured p i t c h i n g p e r i o d : T„ = 2TTV " - ^ ^ 1 I +A (3.1.) yy where: A - t h e d i s p l a c e m e n t GM^ - t h e l o n g i t u d i n a l m e t a c e n t r i c h e i g h t The r a d i u s o f g y r a t i o n k^^ f o r p i t c h i n g f o l l o w s f r o m : k V yy Ï — ^ (3.2.) where: g - t h e a c c e l e r a t i o n due t o g r a v i t y For t h e " S t a n d f a s t " t h e r e s u l t i n g r a d i u s o f g y r a t i o n i s 25% of t h e o v e r a l l l e n g t h o f t h e y a c h t .

I t i s assumed t h a t t h i s v a l u e may be used f o r s i m i l a r y a c h t s of a p p r o x i m a t e l y t h e same d i m e n s i o n s .

The n a t u r a l p e r i o d o f h e a v i n g cannot be d e t e r m i n e d f r o m f u l l s c a l e e x p e r i m e n t s , because i t i s n o t p o s s i b l e t o o s c i l l a t e a y a c h t m a n u a l l y i n a pure v e r t i c a l m o t i o n . However i n t h i s case t h e c a l c u l a t i o n o f t h e mass o f t h e y a c h t i s v e r y s i m p l e and t h e hydrodynamic a d d i t i o n t o t h e r e a l mass can be de-t e r m i n e d w i de-t h s u f f i c i e n de-t a c c u r a c y .

The n a t u r a l p e r i o d f o r heave T f o l l o w s from; 2 T, = 2 T r \ / J A ^ (3.3.) a 3 where: Ö - t h e s p e c i f i c w e i g h t o f w a t e r A ^ j _ - t h e w a t e r p l a n e area a - t h e hydrodynamic mass f o r v e r t i c a l m o t i o n For t h e " S t a n d f a s t " a n a t u r a l h e a v i n g p e r i o d T = 2 . 2 seconds was f o u n d . I n b o t h c a l c u l a t i o n s t h e i n f l u e n c e o f t h e r e l a t i v e l y h i g h damping was t a k e n i n t o a c c o u n t .

I t may be o f i n t e r e s t t o know t h a t t h e added mass moment o f i n e r t i a f o r t h e c o n s i d e r e d y a c h t i s 69% o f t h e r e a l i n e r t i a , and t h e added mass i s 185% o f t h e mass o f d i s p l a c e m e n t .

I n comparison w i t h merchant s h i p s t h e damping o f p i t c h and heave i s f a i r l y l a r g e , w h i c h i s p r o b a b l y owing t o t h e r e l a -t i v e l y h i g h beam/draugh-t r a -t i o o f -t h e h u l l .

C o n s i d e r i n g t h e r a d i u s o f g y r a t i o n f o u n d w i t h t h e " S t a n d f a s t " e x p e r i m e n t , t h r e e v a l u e s were chosen f o r t h e p r e s e n t a n a l y s i s of t h e t h r e e y a c h t d e s i g n s .

The p i t c h i n g and h e a v i n g m o t i o n s , as w e l l as t h e added r e -s i -s t a n c e i n wave-s were c a l c u l a t e d f o r : k = 0 . 2 3 , 0.25 and 0.27 o f t h e o v e r a l l l e n g t h s o f t h e d e s i g n s .

When a y a c h t i s p r o g r e s s i n g i n bow o r head waves t h e p i t c h i n g and h e a v i n g m o t i o n s g e n e r a t e damping waves w h i c h a r e super-imposed on t h e i n c i d e n t wave system. These damping waves c a r r y energy away f r o m t h e y a c h t and t h e added r e s i s t a n c e w h i c h

r e s u l t s can be found by e q u a l i z i n g t h e work done by t h e

r e s i s t a n t f o r c e and t h e r a d i a t e d damping wave e n e r g y . A p r a c t i c ; method f o l l o w i n g t h i s p r o c e d u r e i s g i v e n i n [ 4 ] , where t h e

s t r i p t h e o r y i s used t o e s t i m a t e t h e energy d i s s i p a t i o n o f each c r o s s s e c t i o n o f t h e v e s s e l .

The added r e s i s t a n c e i n waves R f o l l o w s f r o m LTe I h'\^ dx^ dt (3.4.) 0 0 where: L - w a t e r l i n e l e n g t h A - wave l e n g t h i - t i m e b' - c r o s s - s e c t i o n a l damping c o e f f i c i e n t c o r r e c t e d f o r t h e f o r w a r d speed V - r e l a t i v e v e r t i c a l v e l o c i t y o f t h e w a t e r w i t h r e s p e c t t o a c r o s s - s e c t i o n - p e r i o d o f wave e n c o u n t e r Xj^ - l e n g t h o r d i n a t e o f y a c h t ' s h u l l The v e r t i c a l r e l a t i v e m o t i o n V i s c a l c u l a t e d by v e c t o r i a l summation o f t h e h e a v i n g m o t i o n , t h e v e r t i c a l m o t i o n due t o p i t c h i n g and t h e v e r t i c a l m o t i o n o f t h e wave. The s t r i p t h e o r y g i v e s r e l i a b l e r e s u l t s i n t h e case o f merchant s h i p f o r m s , when compared w i t h model e x p e r i m e n t s [ 4 j . A l s o f o r s a i l i n g y a c h t s a r e a s o n a b l e c o r r e l a t i o n w i t h model e x p e r i m e n t s i s

f o u n d , as a l r e a d y shown i n f i g u r e 1.

For t h e t h r e e y a c h t d e s i g n s t h e m o t i o n s and t h e added r e s i s -t a n c e i n a range o f wave c o n d i -t i o n s were c a l c u l a -t e d f o r -t h e t h r e e v a l u e s o f t h e r a d i u s o f g y r a t i o n a l r e a d y m e n t i o n e d . The c a l c u l a t i o n s were c a r r i e d o u t f o r z e r o h e e l i n g a n g l e and head waves were assumed. I t i s a d m i t t e d t h a t t h i s i s a s i m p l i -f i c a t i o n , b u t n o t a c o m p l e t e l y u n r e a l i s t i c one, as shown i n t h e i n t r o d u c t i o n .

A l s o , i t s h o u l d be m e n t i o n e d t h a t an e x t e n s i o n t o o b l i q u e headings and t h e i n c l u s i o n o f a h e e l i n g a n g l e o f f e r s no d i f f i -c u l t i e s i n p r i n -c i p l e , b u t f o r e-conomi-c reasons t h e e x i s t i n g computer programs had t o be used.

The i r r e g u l a r waves, as used i n t h e a n a l y s i s , c o r r e s p o n d t o

t h e s p e c t r a l d e n s i t y f o r m u l a t i o n as g i v e n by P i e r s o n - M o s k o v i t c h , b u t t h e i r r e l a t i o n between w i n d speed and wave spectrum i s n o t used. The seaway i s c h a r a c t e r i z e d by t h e s i g n i f i c a n t wave h e i g h t o n l y and t h e w i n d speeds a r e chosen i n d e p e n d e n t o f t h e c o n s i d e r e d moderate sea c o n d i t i o n s .

I t i s p o s s i b l e t h a t s a i l i n g y a c h t s o p e r a t e i n sea c o n d i t i o n s w h i c h d i f f e r f r o m t h o s e g i v e n by t h e s t a n d a r d sea s p e c t r a . However, a l s o i n such cases h i g h e r energy c o n t e n t s and t h u s h i g h e r wave h e i g h t s c o r r e s p o n d t o l o n g e r wave l e n g t h s , when we c o n s i d e r t h e h i g h f r e q u e n c y range o f t h e sea s p e c t r u m w h i c h i s i m p o r t a n t f o r s m a l l v e s s e l s . T h i s f e a t u r e a p p l i e s t o ocean wave s p e c t r a as w e l l as t o c o a s t a l wave s p e c t r a , and w i l l p r o v e t o be i m p o r t a n t f o r t h e a n a l y s i s o f t h e t h r e e y a c h t d e s i g n s .

F i g u r e 4 shows f o u r ocean wave s p e c t r a a c c o r d i n g t o t h e Person M o s k o v i t c h f o r m u l a t i o n and added wave r e s i s t a n c e o p e r a t o r s f o r t h r e e r a d i i o f g y r a t i o n f o r d e s i g n I , w i t h a f o r w a r d speed o f 6.74 k n o t s i n head waves.

M u l t i p l i c a t i o n o f t h e wave s p e c t r a l d e n s i t i e s w i t h t h e c o r r e s -p o n d i n g added wave r e s i s t a n c e o -p e r a t o r s r e s u l t s i n t h e t h r e e c u r v e s i n f i g u r e 5, where o n l y one sea s p e c t r u m i s shown as an example. The area under t h e s e c u r v e s i s p r o p o r t i o n a l t o t h e added r e s i s t a n c e i n waves. F i g u r e 5 shows t h a t an i m -p o r t a n t r e a s o n f o r t h e d i f f e r e n c e s i n added r e s i s t a n c e i s t h e s h i f t o f t h e added r e s i s t a n c e o p e r a t o r s t o lower wave f r e q u e n c i e s , because i n t h i s r e g i o n o f l o n g e r wave l e n g t h s t h e wave h e i g h t and t h u s t h e wave s p e c t r a l d e n s i t i e s i n c r e a s e . I t i s c l e a r l y shown t h a t l a r g e r d i s p l a c e m e n t s and w e i g h t s d i s t r i b u t e d more t o w a r d s t h e ends o f t h e y a c h t , b o t h r e s u l t i n h i g h e r added r e s i s t a n c e . The f a v o u r a b l e e f f e c t o f t h e l a r g e r r a d i u s o f g y r a t i o n i n s m a l l wave l e n g t h s i s v e r y s m a l l and does n o t c o u n t e r b a l a n c e t h e f o r m e r e f f e c t . T h e r e f o r e a s m a l l r a d i u s o f g y r a t i o n i s a d v i s a b l e as t h e b e s t average s o l u t i o n . A condensed p l o t o f a l l t h e added r e s i s t a n c e v a l u e s f o r t h e t h r e e y a c h t d e s i g n s i n a range o f i r r e g u l a r wave c o n d i t i o n s , i s shown i n f i g u r e 6 a g a i n f o r a speed o f 6.74 k n o t s c o r r e s -p o n d i n g t o a Froude number F^ - 0.35. For c o m p a r i s o n p u r p o s e s t h e s t i l l w a t e r r e s i s t a n c e i s g i v e n f o r each o f t h e t h r e e c o n s i d e r e d h u l l f o r m s . The i r r e g u l a r seaway i s c h a r a c t e r i z e d by t h e s i g n i f i c a n t wave h e i g h t , w h i c h i s d e f i n e d as t h e average o f t h e one t h i r d h i g h e s t waves and c o r r e l a t e s w e l l enough w i t h t h e e s t i m a t i o n f r o m v i s u a l

I n Table 3 t h e added r e s i s t a n c e i s g i v e n as a p e r c e n t a g e o f the c o r r e s p o n d i n g s t i l l v/ater v a l u e s f o r a speed o f 6.74 k n o t s and a r a d i u s o f g y r a t i o n k_,, = 0.25 L y y oa T a b l e 3 Added r e s i s t a n c e i n waves r e l a t e d t o t h e s t i l l w a t e r r e s i s t a n c e , w i t h V = 6.74 k n . and k = 0.25 L^^ wave h e i g h t m I I I I I I 2.90 82% 79% 76% 2.15 66% 64% 61% 1.70 52% 51% 48% 1. 10 26% 25% 24% T a b l e 3 shows t h a t t h e l i g h t e s t y a c h t I has t h e l a r g e s t r e s i s t a n c e i n c r e a s e p e r c e n t a g e , when r e f e r r e d t o t h e s t i l l w a t e r u p r i g h t c o n d i t i o n , a l t h o u g h i t has t h e s m a l l e s t a b s o l u t e r e s i s t a n c e i n c r e a s e . However, t h e d i f f e r e n c e s between t h e t h r e e d e s i g n s a r e r e l a t i v e l y s m a l l , c o n s i d e r i n g t h e assumptions h a v i n g been made i n t h e c a l c u l a t i o n s .

When s a i l i n g t o windward w i t h a speed o f 6.74 k n o t s , t h e s t i l l w a t e r r e s i s t a n c e i s i n c r e a s e d due t o d r i f t and h e e l i n g a n g l e by a p p r o x i m a t e l y 59%, 66% and 74% f o r d e s i g n I , I I and I I I r e s p e c t i v e l y . The l a r g e r i n d u c e d r e s i s t a n c e o f t h e l a r g e d i s p l a c e m e n t y a c h t s i s caused by t h e l e s s e f f i c i e n t f i n k e e l s because o f t h e l o w e r a s p e c t r a t i o . The n e t r e s u l t i s a b e t t e r windward p e r f o r m a n c e i n waves o f t h e l i g h t d i s p l a c e m e n t y a c h t , p r o v i d e d t h a t t h e s i m p l e a d d i t i o n o f i n d u c e d r e s i s t a n c e and added wave r e s i s -t a n c e i s p e r m i s s i b l e .

C o n c e n t r a t i o n o f w e i g h t s i n t h e mid p o r t i o n o f t h e y a c h t ' s h u l l i s o f advantage: i n a l l cases t h e added r e s i s t a n c e i s

13.

The e f f e c t o f t h e added r e s i s t a n c e on t h e speed made good o f t h e t h r e e d e s i g n s i s shown i n f i g u r e 7 f o r t h r e e s t a n d a r d v a l u e s o f t h e t r u e windspeed, r e s p e c t i v e l y V^^ = 3.5, 7.0 and 10.0 meters p e r second and a range o f s i g n i f i c a n t wave h e i g h t s . Here a g a i n t h e added wave r e s i s t a n c e was added t o t h e t o t a l s t i l l w a t e r r e s i s t a n c e , now i n t h e h e e l e d c o n d i t i o n w i t h a d r i f t a n g l e .

For t h e speed made good c a l c u l a t i o n t h e "Gimcrack" c o e f f i c i e n t s were used f o r t h e s a i l f o r c e s [ l ] . They were m o d i f i e d by a p r o c e d u r e d e s c r i b e d i n 6] t o cope w i t h t h e l a r g e r r e s i s t a n c e -s i d e f o r c e r a t i o ' -s due t o t h e wave-s.

F i g u r e 7 shows t h a t t h e l i g h t e s t y a c h t has t h e h i g h e s t speed made good, when t h e assumptions h a v i n g been made a r e e x c e p t e d . The l o w e s t speed made good v a l u e s i m p l y some e x t r a p o l a t i o n o f t h e e x p e r i m e n t a l d a t a and may n o t be v e r y r e l i a b l e . As a m a t t e r o f i n t e r e s t t h e t r u e wind a n g l e o f d e s i g n I i s g i v e n i n f i g u r e 8 f o r t h e same s t a n d a r d windspeeds on a base o f wave h e i g h t .

F i n a l l y t h e s i g n i f i c a n t heave and p i t c h a m p l i t u d e s were c a l c u l a t e d f o r t h e c o n s i d e r e d sea c o n d i t i o n s . The r e s u l t s a r e summarized i n f i g u r e s 9 and 10. A p p a r e n t l y t h e r e i s l i t t l e i n f l u e n c e o f t h e y a c h t ' s d i s p l a c e m e n t on heave, b u t t h e l a r g e d i s p l a c e m e n t h u l l has t h e l a r g e s t p i t c h i n g m o t i o n s .

4. The s t e e r i n g p e r f o r m a n c e .

4.1. Forces and moments e x e r t e d by t h e r u d d e r

I n T a b l e 4 some e x p e r i m e n t a l l y d e t e r m i n e d f o r c e s and moments owing t o r u d d e r a n g l e have been c o l l e c t e d .

T a b l e 4 Ship X 10^ N, X 10^ 0 model 2811-1 (Spens [2] ) model 2811-2 (spens [2] ) h a l f t o n y a c h t Columbia 1344 1921 3079 3280 - 485 - 700 - 1563 - 800

I n t h i s t a b l e i s t h e s i d e f o r c e d i v i d e d by pV L (p i s mass d e n s i t y o f w a t e r , V i s s h i p speed, L i s w a t e r l i n e l e n g t h ) 2 3 i s t h e t u r n i n g moment d i v i d e d by pV L . A l l v a l u e s a r e d i m e n s i o n l e s s i n o r d e r t o compare y a c h t s o f d i f f e r e n t s i z e a t d i f f e r e n t speed. From t h e s t e e r i n g p o i n t o f v i e w t h e t u r n i n g moment i s t h e most i m p o r t a n t . T a b l e 4 shows t h a t t h e models c o n s i d e r e d by Spens [ 2 ] , see f i g u r e 12, have a v e r y poor r u d d e r a c t i o n , though t h e r u d d e r s e p a r a t e d f r o m t h e k e e l (model 2811-2) was an improvement o f t h e o r i g i n a l c o n f i g u r a t i o n (model 2811-1). T h i s one had t h e r e p u t a t i o n t o have bad s t e e r i n g p r o p e r t i e s . The 12 meter "Columbia", f i g u r e 14, w i t h i t s combined l o n g k e e l and r u d d e r , g e n e r a t e s a l a r g e s i d e f o r c e owing t o t h e i n f l u e n c e o f a r u d d e r a n g l e upon t h e f l o w p a t t e r n around t h e whole k e e l . The r u d d e r a c t s as a v / i n g - f l a p .

However, due t o t h e f o r w a r d p o s i t i o n o f t h e r u d d e r and because o f t h e f a c t t h a t t h e k e e l t a k e s p a r t i n t h e a d d i t i o n a l s i d e f o r c e g e n e r a t i o n , t h e t u r n i n g e f f e c t i v e n e s s i s about h a l f t h a t o f t h e h a l f t o n model, see f i g u r e 13. The r u d d e r o f t h i s l a s t y a c h t , s e p a r a t e d f r o m t h e k e e l and l o c a t e d w e l l a f t i s f r o m a l l c o n s i d e r e d cases by f a r t h e b e s t s t e e r i n g d e v i c e . The c h a r a c t e r i s t i c s o f t h e " V a l i a n t " a r e o f i n t e r e s t . The t u r n i n g moment v e r s u s r u d d e r a n g l e p l o t o f t h e "Columbia", f i g u r e 15, shows a n o r m a l amount o f l i n e a r i t y . The t u r n i n g moment on t h e " V a l i a n t " however, i s n o t o n l y much s m a l l e r b u t i s a l s o s t r o n g l y n o n - l i n e a r , see f i g u r e 15. Due t o f l o w

s e p a r a t i o n a t t h e b l u n t a f t e r b o d y , t h e s m a l l r u d d e r a c t s f u l l y i n t h e wake o f t h e s h i p . A t s m a l l r u d d e r a n g l e s

a l m o s t no t u r n i n g moment i s p r o d u c e d . Even a t u r n i n g moment i n t h e wrong d i r e c t i o n has been o b s e r v e d , b o t h i n t h e t o w i n g t a n k and i n p r a c t i c e . The w i d t h o f t h e l o o p i s a b o u t 25 d e g r e e s . I f t h e helmsman o f " V a l i a n t " g i v e s a r u d d e r a n g l e s m a l l e r t h a n a b o u t 10 d e g r e e s , t h e s h i p c o u l d t u r n t o w a r d s t h e o p p o s i t e d i r e c t i o n t h a n i t i s supposed t o do. D u r i n g s t a n d a r d y a c h t p e r f o r m a n c e t e s t s i n D e l f t , t h e same f l o w s e p a r a t i o n phenomena have been o b s e r v e d on s e v e r a l modern ocean r a c e r s w i t h v e r y f u l l a f t e r b o d i e s . Both t h e windward p e r f o r m a n c e and t h e t u r n i n g p r o p e r t i e s c o u l d be improved i n t h o s e cases by f a i r i n g t h e b u t t o c k l i n e s . Yacht

d e s i g n e r s , when i n c r e a s i n g t h e p r i s m a t i c c o e f f i c i e n t and s h i f t i n g t h e c e n t r e o f buoancy more a f t , s h o u l d be aware o f t h e a d v e r s e e f f e c t s o f t o o steep b u t t o c k l i n e s .

15.

4.2. The f i x e d c o n t r o l s b e h a v i o u r .

S t a t i c r o t a t i n g arm and dynamic o s c i l l a t i o n t e s t s w i t h s h i p models a r e used t o d e t e r m i n e t h e e q u a t i o n s o f m o t i o n , f r o m w h i c h t h e f i x e d c o n t r o l s b e h a v i o u r can be d e r i v e d .

F o l l o w i n g t h e methods used i n t h e m a n o e u v r a b i l i t y r e s e a r c h o f merchant s h i p s Spens and o t h e r s d e s c r i b e d t h e moving y a c h t w i t h f i x e d r u d d e r by t h e l i n e a r coupled e q u a t i o n s o f m o t i o n i n sway and yaw, n e g l e c t i n g t h e r o l l m o t i o n :

M. = o where: V - t h e sway v e l o c i t y V - t h e sway a c c e l e r a t i o n (p - t h e yaw r a t e ^ - t h e yaw a n g u l a r a c c e l e r a t i o n m - t h e mass y^,Yo,etc - d e r i v a t i v e s o f t h e sway f o r c e N ,N- ate - d e r i v a t i v e s o f t h e yaw moment

(4.2.1.) The s o l u t i o n o f t h e two e q u a t i o n s g i v e s t h e s t a b i l i t y r o o t s w h i c h d e t e r m i n e t h e b e h a v i o u r o f t h e s h i p a f t e r an i n i t i a l d i s t u r b a n c e f r o m t h e e q u i l i b r i u m c o n d i t i o n , w h i l e t h e r u d d e r ( c o n t r o l ) i s f i x e d . I f a l l r o o t s a r e r e a l and n e g a t i v e , t h e s h i p w i l l , a f t e r an i n i t i a l d i s t u r b a n c e , come t o a s t r a i g h t p a t h a g a i n , see f i g u r e 16 a. I t i s c a l l e d : f i x e d c o n t r o l s s t a b l e o r i t i s s a i d t o have a p o s i t i v e f i x e d c o n t r o l s s t a b i l i t y . I f one o f t h e r o o t s i s p o s i t i v e t h e s h i p i s u l t i -m a t i v e l y g o i n g t o t u r n around a c i r c l e , s t i l l w i t h t h e r u d d e r f i x e d i n t h e c e n t r e p o s i t i o n , and i s c a l l e d t o be f i x e d c o n t r o l s u n s t a b l e . I f t h e r o o t s a r e complex t h e f i x e d c o n t r o l s b e h a v i o u r o f t h e s h i p i s o s c i l l a t o r y , see f i g u r e 16b. The o s c i l l a t i o n i s damped and t h e s h i p i s f i x e d c o n t r o l s s t a b l e i f t h e r e a l p a r t s o f t h e complex r o o t s a r e n e g a t i v e . I n t h e case o f p o s i t i v e r e a l p a r t s t h e o s c i l l a t i o n i s undamped, w h i c h means a f i x e d c o n t r o l s u n s t a b i l i t y .

I n t h e f i r s t r e p o r t s about m a n o e u v r a b i l i t y on s a i l i n g y a c h t s 2 ] , [ 3 ] t h e c o n c l u s i o n s c o n c e r n i n g t h e c o n t r o l l a b i l i t y were based upon t h e s t a b i l i t y r o o t s o f t h e c o u p l e d sway-yaw e q u a t i o n s ( 4 . 2 . 1 . ) . These r o o t s a r e m e n t i o n e d i n t a b l e 5. Table 5 D i m e n s i o n l e s s s t a b i l i t y r o o t s o f t h e c o u p l e d sway-yaw e q u a t i o n s o f m o t i o n Ship ^ 1 ^2 mDdel 2811-1 (Spens [ 2 ] )

-

0.45 - 2.51 model 2811-2 (Spens [ 2 ] )

-

1.66 -i 0.53 i model 2988 (Spens [2] ) - 1.37 - 2.94 h a l f ton yacht, = 0.243 (1) [3]

_-

2.60 H 2.87 i half ton yacht, F^ = 0.468

_-

1.37 •1 2.82 i Stormy w i t h o r i g i n a l bulb keel

-

2.32 + 2.95 i Stormy w i t h f i n keel

_-

2.06 •i 2.89 i Columbia, F = 0.168 n

-

1.60 •1 0.34 i F = 0.251 n = _1.53 '1 _{0.33 i} F = 0.335 n 1.47 -! 0.44 i Valiant, F =0.163 n

-

0.33 - 3.03 " F = 0.244 n 0.25 - 2.91 F = 0.325 n - 0.58 - 3.88 (1) Froude number i s : = where: V = s h i p speed i n m/s g = a c c e l e r a t i o n o f g r a v i t y i n m/s' L = w a t e r l i n e l e n g t h i n m The r e a l p a r t s o f a l l r o o t s a r e n e g a t i v e , w h i c h means t h a t a l l s h i p s have a f i x e d c o n t r o l s s t a b i l i t y i f t h e y a r e c o n s i d e r e d t o p e r f o r m o n l y swaying and y a w i n g m o t i o n s .

17.

I n p r i n c i p l e freedom i n r o l l has t o be c o n s i d e r e d t o o .

Owing t o t h e r e l a t i v e l y l a r g e v e r t i c a l d i s t a n c e between t h e l a t e r a l c e n t r e o f k e e l and r u d d e r and t h e c e n t r e o f g r a v i t y , a sway o r yaw m o t i o n i n t r o d u c e s a r o l l i n g moment, w h i l e a r o l l m o t i o n g i v e s sway f o r c e s and yaw moments. T h i s h y d r o d y n a m i c c o u p l i n g i n sway, r o l l and yaw c a n n o t be n e g l e c t e d and must be e x p r e s s e d i n t h e e q u a t i o n s o f m o t i o n , w h i c h a r e : (4.2.2.) N^.v + N^.v + N^.cj) + N^.<i) + M^-.^' + N^,^ + ( N ^ . - I , J . ( ^ - = o J where: ( i n a d d i t i o n t o t h e l i s t o f symbols a f t e r (4.2.1.) (j) - t h e r o l l a m p l i t u d e é> - t h e r o l l a n g u l a r v e l o c i t y <t>' - t h e r o l l a n g u l a r a c c e l e r a t i o n '^v'^v'^'-'^ ~ d e r i v a t i v e s o f t h e r o l l moment

I n D e l f t a t e c h n i q u e has been d e v e l o p e d t o measure t h e sway f o r c e , r o l l moment and yaw moment when t h e y a c h t , model p e r f o r m s f o r c e d harmonic o s c i l l a t i o n s i n one o f t h e s e

modes o f m o t i o n .

Compared w i t h t h e r o o t s o f t h e b a s i c sway-yaw system ( T a b l e 5) the c a l c u l a t e d s t a b i l i t y r o o t s o f t h e c o u p l e d s w a y - r o l l - y a w system ( T a b l e 6) show t h a t t h e c o u p l i n g w i t h r o l l has a

d e s t a b i l i z i n g i n f l u e n c e . I n some cases t h e system d e s c r i b e d i n t h i s way i s even u n s t a b l e . Table 6 D i m e n s i o n l e s s s t a b i l i t y r o o t s o f t h e c o u p l e d s w a y - r o l l - y a w e q u a t i o n s o f m o t i o n Ship h a l f ton yacht,F = 0.243 " F"= 0.486 Columbia II Valiant F"= F"= 0.168 0.251 0.335 F^= 0.163 ^= 0.244 54 62 60 53 49 0.32 0.24 0.53 + 1 + i + 2.99 3.14 0.34 0.33 0.40 3.04 2.94 3.88 0.53 0.22 0.11 0.10 0.20 0.39 0.51 0.43 -I¬ T + + + + 5.62 2.52 7.46 5.08 3.81 8,39 5.45 3.97

For s a i l i n g y a c h t s i t i s n e c e s s a r y t o make a n o t h e r e x t e n s i o n t o t h e e q u a t i o n s ( 4 . 2 . 2 . ) . Every m o t i o n changes magnitude and d i r e c t i o n o f t h e a p p a r e n t w i n d , w h i c h has i t s i n f l u e n c e on t h e s a i l f o r c e .

By u s i n g i n t h e downwind c o n d i t i o n t h e s i m p l e c o n c e p t o f a m a i n s a i l and s p i n n a k e r w h i c h blows i n t h e a p p a r e n t w i n d d i r e c t i o n and g i v e s o n l y f o r c e s because o f i t s d r a g p r o p e r -t i e s , -t h e changes i n s a i l f o r c e can be c a l c u l a -t e d . Because o f i t s m u t u a l independence hydrodynamic and aerodynamic f o r c e s can be added t o f o r m a new s e t o f e q u a t i o n s o f m o t i o n .

They a r e s i m i l a r t o t h e system shown i n ( 4 . 2 . 2 . ) , e x c e p t f o r a d d i t i o n a l terms dependent upon t h e course d e v i a t i o n . These f o l l o w f r o m t h e dependency o f t h e aerodynamic f o r c e s on t h e w i n d d i r e c t i o n and cause t h e appearance o f a f i f t h s t a b i l i t y r o o t (see t a b l e 7 ) .

Table 7

D i m e n s i o n l e s s s t a b i l i t y r o o t s o f t h e c o u p l e d s w a y - r o l l - y a w e q u a t i o n s o f m o t i o n i n c l u d i n g aerodynamic f o r c e s

Ship _S3

half ton yacht, F^=0.243 F =0.486 n F =0.168 n F =0.251 n Columbia II II Valiant F^=0.335 F =0.163 n F =0.244 n F =0.325 n 2.50 + 2.98 i 2.27 + 1.35 i 1.61 + 0.36 i 1.56 + 0.35 i 1.60 + 0.48 i 0.38 0.37 0.74 - 3.08 - 3.01 - 3.97 1.54 + 5.55 i 1.72 + 3.22 i 1.13 + 7.38 i 1.19 + 4.94 i 1.61 + 3.37 i 1.78 + 8.19 i 1.91 + 5.08 i 1.76 + 3.59 i - 0.02 0.32 - 0.02 - 0.01 0.04 0.04 0.09 0.16 I t can be seen f r o m t h e v a l u e o f t h i s r o o t t h a t t h e e x t e n s i o n o f t h e system w i t h aerodynamic f o r c e s has a f u r t h e r d e s t a b i l i z i n g i n f l u e n c e i n most o f t h e cases.

The i n f l u e n c e o f t h e way i n w h i c h t h e moving system i s des-c r i b e d ( des-c o u p l e d sway-yaw, des-c o u p l e d s w a y - r o l l - y a w w i t h o u t s a i l s or c o u p l e d s w a y - r o l l - y a w w i t h s a i l s ) , on t h e p r e d i c t e d c o n t r o l s f i x e d b e h a v i o u r o f t h e h a l f t o n y a c h t i s d e m o n s t r a t e d i n

f i g u r e 17 f o r a f i n a l l y s t a b l e c o n d i t i o n and i n f i g u r e 18 f o r a f i n a l l y u n s t a b l e c o n d i t i o n .

The most r e a l i s t i c d e s c r i p t i o n o f t h e m o t i o n o f a s a i l i n g y a c h t i s t h e c o u p l e d s w a y - r o l l - y a w e q u a t i o n s o f m o t i o n , i n c l u d i n g hydrodynamic and aerodynamic f o r c e s .

B e f o r e c o n t i n u i n g t h i s paper a t t e n t i o n w i l l be p a i d t o t h e s i g n i f i c a n c e o f t h e s t a b i l i t y r o o t s , t o r e a l i s e what t h e f i x e d c o n t r o l s : b e h a v i o u r means i n t h e process o f s t e e r i n g a s a i l i n g y a c h t .

The helmsman o f a b i g merchant s h i p , l i k e a s u p e r t a n k e r , w i l l n o t c o n t i n u o u s l y r e a c t t o any c o u r s e d e v i a t i o n , b u t o n l y

change t h e r u d d e r a n g l e i f t h e c o u r s e d e v i a t i o n has surpassed a c e r t a i n t h r e s h o l d . From t h e n o n , t h e r u d d e r w i l l be k e p t i n t h e same p o s i t i o n u n t i l t h e t h r e s h o l d i s r e a c h e d i n t h e o t h e r d i r e c t i o n . I f t h e s h i p , because o f i t s mass, i s r e a c t i n g v e r y s l o w l y , t h e p e r i o d between two s u c c e s s i v e r u d d e r a c t i o n s w i l l be l o n g . C o n s e q u e n t l y t h e p a t h and m o t i o n s o f a l a r g e heavy s h i p w i l l m o s t l y be governed by i t s c o n t r o l s f i x e d b e h a v i o u r ( w i t h i n i t i a l c o n d i t i o n s ) , expressed i n t h e degree o f s t a b i l i t y .

Small s h i p s l i k e s a i l i n g y a c h t s , because o f t h e i r much s m a l l e r mass, r e a c t much f a s t e r and c o n s e q u e n t l y t h e t i m e d e l a y

between a r u d d e r a c t i o n and i t s r e c o g n i s a b l e e f f e c t i s v e r y s m a l l . The helmsman i s f o r c e d t o p e r f o r m a n e a r l y c o n t i n u o u s r u d d e r a c t i o n t o n e u t r a l i z e t h e e f f e c t s o f d i s t u r b a n c e s and h i s own e a r l i e r r u d d e r a c t i o n . Thus, t h e a n a l y s i s o f t h e s t e e r i n g and m a n o e u v r i n g a b i l i t i e s s h o u l d be e x t e n d e d t o i n c l u d e t h e helmsman's p e r f o r m a n c e . I t i s p r o b a b l e t h a t t h e k i n d o f s t e e r i n g d e v i c e , wheel o r helm, i n f l u e n c e s t h e s t e e r i n g t a c t i c s , w h i c h s h o u l d be i n -c l u d e d i n t h e a n a l y s i s . The a b s o l u t e v a l u e s o f t h e s t a b i l i t y r o o t s d e t e r m i n e t h e t i m e c o n s t a n t s o f t h e system. As l o n g as t h e s e have t h e same o r d e r o f m a g n i t u d e as t h e t i m e c o n s t a n t s o f human b e i n g s , w h i c h i s n e a r l y always t r u e f o r s a i l i n g y a c h t s , t h e system can be s t e e r e d , w h e t h e r i t has a p o s i t i v e c o n t r o l s f i x e d s t a b i l i t y o r n o t . I t can o n l y be s a i d t h a t a v e r y u n s t a b l e system w i l l p r o b a b l y be much more d i f f i c u l t t o s t e e r t h a n a s t a b l e , n e u t r a l o r o n l y s l i g h t l y u n s t a b l e one.

The t i m e c o n s t a n t s a r e v e r y c l e a r l y v i s u a l i s e d i n Bode-d i a g r a m s , w h i c h w i l l be Bode-d i s c u s s e Bode-d i n t h e n e x t c h a p t e r . Not much i s known about t h e i n f l u e n c e o f t h e shape o f t h e Bode-diagram upon t h e helmsman's p e r f o r m a n c e , t h a t i s t o say upon t h e " s t e e r i n g c o m p l i a n c e " o f t h e s h i p and i t s c o n t r o l s . A t l a s t i t must be n o t e d t h a t l o n g k e e l y a c h t s do n o t have the b e t t e r c o n t r o l s f i x e d s t a b i l i t y b e l i e v e d by many s a i l o r s . 4.3. The b e h a v i o u r w i t h a c o n t i n u o u s r u d d e r a c t i o n . I f t h e r u d d e r a n g l e v a r i a t i o n i s assumed t o be c o n t i n u o u s i t can be c o n s i d e r e d as t h e sum o f an i n f i n i t e number o f p u r e s i n e s , a l l w i t h t h e i r own a m p l i t u d e and f r e q u e n c y , see f i g u r e 19. Because t h e s t e e r e d y a c h t ( t h e open l o o p system i n f i g u r e 11) i s assumed t o be l i n e a r , t h e t o t a l response t o t h e i r r e g u l a r r u d d e r a n g l e i s e q u a l t o t h e sum o f t h e

responses t o each s i n u s o i d a l component. T h i s response component i s a l s o a pure s i n e . L e t us c o n s i d e r one o f t h e components

w i t h a c i r c u l a r f r e q u e n c y C J . The r u d d e r a n g l e component, w i t h a m p l i t u d e 5 , i s

a

5 ( t ) r 5in (ui) ( 4 . 3 . 1 . )

A f t e r a d d i n g t h e f o r c e s and moments due t o t h i s r u d d e r a n g l e t o t h e e q u a t i o n s o f m o t i o n , t h e c o u r s e d e v i a t i o n Cj; can be o b t a i n e d as:

(p(è) = If^ ( w t + £^) (4.3.2.)

where: (^^ - t h e course d e v i a t i o n a m p l i t u d e

- t h e phase a n g l e between r u d d e r a n g l e and c o u r s e d e v i a t i o n

t - a t i m e p a r a m e t e r

W i t h a g i v e n r u d d e r a n g l e a m p l i t u d e t h e r e s u l t i n g c o u r s e d e v i a t i o n a m p l i t u d e s and phases can be c a l c u l a t e d f o r a range o f c i r c u l a r f r e q u e n c i e s U).

21 , I n c o n t r o l e n g i n e e r i n g t h e p l o t o f t h e a m p l i f i c a t i o n f a c t o r or response a m p l i t u d e o p e r a t o r , d e f i n e d as (i) , v e r s u s i a a c i r c u l a r f r e q u e n c y U , i s c a l l e d t h e Bode-diagram o f t h e system. B"'ollowing t h e method o f t h e p r e c e d i n g c h a p t e r t o c o n s t r u c t the e q u a t i o n s o f m o t i o n , t h e Bode-diagram can be c a l c u l a t e d f o r t h e y a c h t c o n s i d e r e d as a system p e r f o r m i n g c o u p l e d sway-yaw m o t i o n s ( a c c o r d i n g t o (4.2.1.) extended w i t h r u d d e r f o r c e s ) , p e r f o r m i n g c o u p l e d s w a y - r o l l - y a w m o t i o n s w i t h o u t s a i l s ( a c c o r d i n g t o (4.2.2.) e x t e n d e d w i t h r u d d e r f o r c e s ) or p e r f o r m i n g c o u p l e d s w a y - r o l l - y a w m o t i o n s w i t h s a i l s . T h i s has been done f o r t h e h a l f t o n y a c h t a t a speed o f 4 k n o t s , see f i g u r e 20, and 8 k n o t s , see f i g u r e 2 1 , and f o r t h e "Columbia" a t a speed o f 4 k n o t s , see f i g u r e 22.

The f r e q u e n c y range o f i n t e r e s t c o n s i s t s o f t h o s e f r e q u e n c i e s w h i c h f o r m a s i g n i f i c a n t c o n t r i b u t i o n i n t h e helmsman's

i r r e g u l a r r u d d e r a c t i o n , say between U) - 0.2 and CO = 4 ( p e r i o d s between 1^ and 30 s e c o n d s ) .

A comparison o f t h e Bode-diagrams i n t h i s range shows t h a t t h e r e i s o n l y a s l i g h t d i f f e r e n c e i n t h e response t o a s i n u s o i d a l r u d d e r a c t i o n i f o n l y c o u p l e d sway and yaw

m o t i o n s a r e c o n s i d e r e d , o r i f t h e d e s c r i p t i o n o f t h e system i s extended w i t h a c o u p l e d r o l l m o t i o n and aerodynamic

f o r c e s .

We a r r i v e a t t h e same c o n c l u s i o n when t h e g e n e r a l response f u n c t i o n i s d e r i v e d f r o m t h e e q u a t i o n s o f m o t i o n as:

sway-yaw coupling w i t h r o l l

coupling . (4.3.3.)

Ul CJ^ u^

course sway-yaw coupling coupling w i t h r o l l

From an o r d e r o f magnitude a n a l y s i s o f t h e d e r i v a t i v e s i t can be c o n c l u d e d t h a t t h e terms due t o t h e added c o u p l i n g w i t h r o l l n e a r l y c a n c e l each o t h e r . B e s i d e s , t h e t i m e c o n s t a n t , due t o t h e i n c l u s i o n o f t h e s a i l f o r c e s , i s g e n e r a l l y so l a r g e t h a t ( r ^ . s + l ) can be a p p r o x i m a t e d by .S. So, a u s e f u l r e p r e s e n t a t i o n o f t h e response f u n c t i o n i s g i v e n b y : cp T j s + 1 (4.3.4.) w i t h : T-^tJK^

The response f u n c t i o n o f t h e system, r e g a r d e d as a h u l l p e r f o r m i n g o n l y c o u p l e d sway and yaw m o t i o n s has e x a c t l y

t h e same f o r m as ( 4 . 3 . 3 . ) , w h i l e t h e v a l u e s o f t h e p a r a m e t e r s a r e n e a r l y e q u a l .

Thus, i n c o n s i d e r i n g t h e response o f t h e s a i l i n g y a c h t t o a c o n t i n u o u s r u d d e r a c t i o n by t h e helmsman, t h e t o t a l system o f t h e swaying, r o l l i n g and yawing h u l l w i t h s a i l s can s u c c e s s f u l l y be s i m p l i f i e d t o t h e swaying and yawing h u l l o n l y .

The p a r a m e t e r s i n t h e s i m p l i f i e d response f u n c t i o n , can be d e t e r m i n e d w i t h f o r c e d o s c i l l a t i o n t e s t s , w h i c h has been s t a n d a r d i z e d i n some t o w i n g t a n k s f o r m a n o e u v r a b i l i t y r e s e a r c h o f merchant s h i p s .

As we have f i n i s h e d t h e p r e c e d i n g c h a p t e r w i t h a judgement o f t h e i m p o r t a n c e o f t h e c o n t r o l s f i x e d b e h a v i o u r , we have t o do t h e same here f o r t h e b e h a v i o u r due t o a c o n t i n u o u s r u d d e r a c t i o n .

23.

Every tendency o f t h e y a c h t t o d e v i a t e f r o m i t s c o u r s e , o r even t o b r o a c h , w i l l be i n t r o d u c e d by d i s t u r b a n c e s due t o w i n d and waves. Because o f t h e f a s t response o f t h e s h i p

t o d i s t u r b a n c e s , t h e helmsman n e a r l y i m m e d i a t e l y r e c o g n i s e s t h i s tendency and t r i e s t o n e u t r a l i z e i t w i t h a r u d d e r a c t i o n , w h i c h i n h i s t u r n has a q u i c k response. I f t h e s t e e r i n g power o f a y a c h t i s t r a n s l a t e d as t h e power t o n e u t r a -l i z e d i s t u r b i n g i n f -l u e n c e s , i t i s b e s t expressed by the response a m p l i t u d e o p e r a t o r , o r a m p l i f i c a t i o n r a t i o

o f c o u r s e d e v i a t i o n and r u d d e r a n g l e . The h i g h e r t h e response a m p l i t u d e o p e r a t o r , t h e b e t t e r t h e s t e e r i n g power.

T h i s c r i t e r i o n must m a i n l y be a p p l i e d i n t h e f r e q u e n c y range of t h e s i g n i f i c a n t d i s t u r b a n c e s w h i c h i s , d e p e n d i n g upon t h e s h i p s s i z e , r o u g h l y e s t i m a t e d , f r o m U»0.5 t o about OJ» 6,

( p e r i o d s f r o m 1 t o 12 seconds, c o r r e s p o n d i n g w i t h s t e r n waves f r o m 4 t o 60 meters l e n g t h o r w i t h w i n d g u s t s ) . Because t h e v a l u e o f t i m e c o n s t a n t s , deduced f r o m t h e s t a b i l i t y r o o t s , a f f e c t s a l s o t h e f o r m o f t h e Bodediagrams, t h e s e r e l a -t i v e l y s i m p l e f i g u r e s c o n -t a i n a l l i n f o r m a -t i o n n e c e s s a r y -t o j u d g e t h e s t e e r i n g q u a l i t i e s o f a y a c h t . Unless more r e s e a r c h w i l l be done c o n c e r n i n g t h e i n f l u e n c e o f system c h a r a c t e r i s t i c s

(Bode-diagram) upon t h e helmsman's b e h a v i o u r , t h e i n t e r p r e t a t i o n w i l l be d i f f i c u l t f r o m t h e h a n d l i n g p o i n t o f v i e w .

5. C o n c l u s i o n .

5.1. On seakeeping.

I t may be c o n c l u d e d t h a t a r e d u c t i o n o f t h e l o n g i t u d i n a l

r a d i u s o f g y r a t i o n i s f a v o u r a b l e f o r t h e windward performance o f a y a c h t . I f a w e i g h t o f 1% o f a y a c h t ' s d i s p l a c e m e n t i s s h i f t e d f r o m a m i d s h i p s towards one o f t h e ends, a 25%

r a d i u s o f g y r a t i o n w i l l i n c r e a s e t o 25.5%, w i t h a c o r r e s -p o n d i n g t o t a l r e s i s t a n c e i n c r e a s e o f about 1 % . A more d r a s t i c change o f t h e l o n g i t u d i n a l w e i g h t d i s t r i b u t i o n has o f c o u r s e a l a r g e r e f f e c t on t h e y a c h t ' s r e s i s t a n c e i n waves. When c o n s t a n t d r a u g h t i s c o n s i d e r e d i n a d e s i g n , l a r g e d i s p l a c e m e n t y a c h t s have l e s s e f f i c i e n t f i n k e e l s , due t o t h e f a c t t h a t t h e deeper h u l l reduces t h e span o f t h e f i n . A l t h o u g h t h e l a r g e d i s p l a c e m e n t y a c h t has t h e l o w e s t r e s i s -t a n c e p e r -t o n d i s p l a c e m e n -t i n -t h e u p r i g h -t c o n d i -t i o n and a s m a l l advantage w i t h r e s p e c t t o t h e added r e s i s t a n c e i n waves p e r c e n t a g e w i s e , t h e l e s s e f f i c i e n t f i n k e e l seems t o be t h e cause o f a l e s s f a v o u r a b l e windward p e r f o r m a n c e , when compared w i t h l i g h t e r d i s p l a c e m e n t h u l l s . Large d i s p l a c e m e n t y a c h t s have a s l i g h t l y l a r g e r p i t c h i n g m o t i o n i n seawaves. I t may a l s o be c o n c l u d e d t h a t model e x p e r i m e n t s i n t h e s t i l l w a t e r c o n d i t i o n r e m a i n a m e a n i n g f u l l t o o l f o r t h e d e s i g n e r o f s a i l i n g y a c h t s . 5.2. On s t e e r i n g .

The " s t e e r i n g power" o f a y a c h t can be i n c r e a s e d by u s i n g a w e l l s i t u a t e d s e p a r a t e d f i n k e e l and r u d d e r .

The r e a l i s t i c c o u p l i n g o f r o l l w i t h sway and yaw and t h e i n c l u s i o n o f aerodynamic f o r c e s i n t h e e q u a t i o n s o f m o t i o n

o f a y a c h t , s a i l i n g o f f t h e w i n d , has a d e s t a b i l i z i n g i n f l u e n c e on t h e c o n t r o l s f i x e d s t a b i l i t y . However, i n most cases, t h e c o n t r o l s f i x e d b e h a v i o u r and s t a b i l i t y have no d i r e c t i n

25,

The f a s t r e a c t i o n o f a y a c h t f o r c e s t h e helmsman t o a

c o n t i n u o u s r u d d e r a c t i o n . The Bode-diagram, f r o m w h i c h t h e response t o such an a c t i o n can be d e r i v e d d i r e c t l y , c o n t a i n s the necessary i n f o r m a t i o n t o j u d g e t h e s t e e r i n g q u a l i t i e s . The a s s u m p t i o n o f l i n e a r i t y , w h i c h must be made f o r con-s t r u c t i n g t h e Bode-diagram, i con-s v a l i d u n l e con-s con-s uncommon h u l l or r u d d e r forms o r b a d l y l o c a t e d r u d d e r s a r e concerned. I n d e r i v i n g t h e Bode-diagram t h e r e a l i t y o f t h e c o u p l e d s w a y i n g , r o l l i n g and yawing y a c h t w i t h s a i l s (on a downwind c o u r s e ) can s u c c e s s f u l l y be s i m p l i f i e d by c o n s i d e r i n g t h e c o u p l e d swaying and yawing h u l l o n l y .

Research on t h e s t e e r i n g b e h a v i o u r o f t h e helmsman o f a s a i l i n g y a c h t i s necessary i n o r d e r t o c o n s i d e r a l l a s p e c t s o f i t s c o n t r o l l a b i l i t y .

6. Acknowledgement.

The a u t h o r s a r e i n d e b t e d t o Sparkman and Stephens

who k i n d l y p r o v i d e d d e t a i l e d i n f o r m a t i o n o f "Columbia" and " V a l i a n t " , t o Frans Maas and E.G. van de S t a d t who p u t t h e d e s i g n s o f r e s p e c t i v e l y t h e s y s t e m a t i c

s e r i e s and t h e "Stormy" t o t h e i r d i s p o s a l .

The m o t i o n and added r e s i s t a n c e t e s t s o f "Columbia" and " V a l i a n t " were c a r r i e d o u t by J o o s t van Santen.

27.

f e r e n c e s .

K. Davidson

E x p e r i m e n t a l s t u d i e s o f t h e s a i l i n g y a c h t

The S o c i e t y o f Naval A r c h i t e c t s and Marine E n g i n e e r s 1937

P.G. Spens, P. de S a i x and P.W. Brown

Some f u r t h e r e x p e r i m e n t a l s t u d i e s o f t h e s a i l i n g y a c h t The S o c i e t y o f Naval A r c h i t e c t s and M a r i n e E n g i n e e r s 1967 J. G e r r i t s m a

Course k e e p i n g q u a l i t i e s and m o t i o n s i n waves o f a s a i l i n g y a c h t

P r o c e e d i n g s o f t h e t h i r d AIAA Symposium on t h e Aero/ hydrodynamics o f s a i l i n g C a l i f o r n i a 1971 J. G e r r i t s m a and W. Beukelman A n a l y s i s o f t h e r e s i s t a n c e i n c r e a s e i n waves o f a f a s t c a r g o s h i p I n t e r n a t i o n a l S h i p b u i l d i n g P r o g r e s s 1972 Y a c h t i n g World A n n u a l 1972 London I l i f f e books P.G. Spens S a i l b o a t t e s t t e c h n i q u e

Davidson L a b o r a t o r y , Stevens I n s t i t u t e o f Technology T e c h n i c a l Memorandum no. 124, 1958

CO

100 50 30 20 15 10 75

Wave length • nn.

Design I V=6.74 knots Wave height = 230m. radius of gyration 0.27 LQ;^ 1 1 1 1 1 1 Design X 0 — V=6.74 knots

radius of gyration Q27 LQ^—y Wave height = 250m.

0 --\— 11

_V

" A W )— 11 / J > ^ 1 ₁

\ /^^'

hi 1 [ • 0 1 2 3 1, _{5 6 '} .1 I I I l l l l I 100 50 40 30 25 20 radius of gyration 0 2 7 LQ^ 40 30 20 10: Design M V= 6.74 knots Wave heights230m Circular'^frequency óf encounter — J — I I I M i l . . . I I I 100 50 40 30 25 20 15 Wave length — 10 9 - rad/s. J L

V=6.74 knots.

Still water resistance 136 kg.

wave height 25 m. J L 0 0.23 025 1.1m. 0.27 150 100 50 V= 6.74 knots.

Still water resistance 154 l<g. wave height 2.9 m. 0 023 0.25 1.1m. 0.27 Radius of gyration •-OA

Fig.6: Added resistance in w a v e s .

V= 6.74 knots.

Still water resistance 180 kg.

1 2

Significant wave height — > • m.

Desired

+ /

course

V

Course ^

deviation

Helmsman

Helm

angle

Feed back

Fig. 11: Block diagram of the steered yacht.

Disturbances

Closed loop system

_Open loop system

Fig.16a: Fixed control behaviour of ship with real stability

roots.

unstable /

initial disturbance is exerted

Fig. 16b: Fixed control behaviour of ship with connplex

stability roots.

5 O

L i O

H coupled sway-yaw description.

-O coupled sway - roll-yaw description without sails.

^ coupled sway-roll-yaw description with sails.

3 0

M

A

2 0 1 0

c

1 0 h 2 0 3 0 4 0

4 O

3 O

H coupled sway-yaw description.

-O coupled sway - roll-yaw description without sails.

-A

coupled s w a y - r o l l - y a w description with sails.

2 0 1 0 0 1 0 2 0 3 0 4 0 5 0

I l l l l l l i l l l l l l l l l l l l l l l l l l l I I 11 l l l l

0.01 0.1 1 10 100

(JÜ •

O) •

+ 180

+90

O

1 l l l l l l i l 1 I I I I I I I I 1 1 1 | l I I M 1 l l l l l 1 1 I I 1 1 ₁ 1 l l l l l l i l 1 1 1 1 l l l l l 1 I I I l l l l l 1 1 1

1

1 I I I

0.01 0.1 1 10 100

0) >

i

Wind

Waves

Yacht

geometry and

dynamics

J L

Disturbing course deviation

Rudder

geometry and

dynamics

Disturbing force on helm

Desired

course

Rudder

geometry

Force on helm

Helmsman

Helm angle

Yacht

dynamics

r

Actual course