Tests with two planing boat models in waves

LABORATORIUM VOOR

SCHEEPSBOUWKUNDE

T E C H N I S C H E H O G E S C H O O L DELFT

TESTS WITH TWO PLANING BOAT MODELS I N

WAVES-by

I r . J . J . van den Bosch

1 Contents 'I . Nomenclature . 2. L i s t o f f i g u r e s . 3. I n t r o d u c t i o n . k. Model d a t a . 5. SumiTiai-y o f t h e e x p e r i m e n t s . 5 . 1 . Calm w a t e r . 5.2. R e g u l a r head waves. 5 . 3 . I r r e g u l a r head seas. 6. D i s c u s s i o n o f t h e t e s t r e s u l t s . 6 . 1 . Calm w a t e r . 6 . 2 . R e g u l a r head waves. 6 . 3 . I r r e g u l a r head seas. 7. General c o n c l u s i o n s . 8. R e f e r e n c e s . 9. Appendix: Suimary o f t e s t r e s u l t s , i n c l u d i n g t h o s e w h i c h have been l e f t o u t o f t h e f i g u r e s . 9 . 1 . Calm w a t e r 9 . 2 . Regular vraves.

1. Nomenclature.

Area bounded by c h i n e s and t r a n s o m , p r o j e c t e d on a p l a n e t h r o u g h t h e s t r a i g h t p a r t o f t h e k e e l , a-j. V e r t i c a l a c c e l e r a t i o n f o r w a r d a t 0,1 L Q V e r t i c a l a c c e l e r a t i o n f o r w a r d a t 0 ,h L B r e a d t h over c h i n e s , a t any c r o s s s e c t i o n . a B " A B cm L Mean b r e a d t h o f area A . P B Maximum b r e a d t h over c h i n e s . C IflojX b Span o f p l a n i n g s u r f a c e , i . e . a c t u a l b r e a d t h o f p l a n i n g s u r f a c e , measured a t main spray p o i n t .

Froude number based on volume o f d i s p l a c e m e n t a t r e s t . G _{Center o f g r a v i t y ,}

g A c c e l e r a t i o n due t o g r a v i t y .

Real r a d i u s o f g y r a t i o n f o r p i t c h . L Length o f p r o j e c t e d a r e a A_^.

VJetted l e n g t h o f c h i n e , measured f r o m transom t o main spray p o i n t . Wetted l e n g t h - o f k e e l , measured f r o m t r a n s o m .

• 1 +1, ]_ _ c k

m 2 Mean w e t t e d l e n g t h , used f o r t h e c a l c u l a t i o n o f t h e Reynolds nimiber. R -y-j^ R e s i s t a n c e .

•D ^

^ ~ ^77" Reynolds number.

n V

S Wetted s u r f a c e , i n c o n t a c t w i t h " s o l i d " w a t e r . V Ship o r model speed.

Xp Center o f t h e p r o j e c t e d area A .

Yf^g(j^j') Frequency response f u n c t i o n f o r p i t c h .

^•z.r,{üd) Fi'equency responce f u n c t i o n f o r heave.

Heave a m p l i t u d e .

Rise o f c e n t e r o f g r a v i t y .

« Angle o f i n c i d e n c e , i . e . a n g l e between s t i l l w a t e r s u r f a c e and

3 D e a d r i s e a n g l e . A- Ship o r model w e i g h t . 0^ P i t c h a m p l i t u d e .

V K i n e m a t i c v i s c o s i t y ÜJ C i r c u l a r f r e q u e n c y . 0)^ C i r c u l a r f r e q u e n c y o f e n c o u n t e r . p Mass d e n s i t y o f w a t e r . C Wave a m p l i t u d e . a f; , Mean wave a m p l i t u d e o f h i g h e s t t h i r d p a r t a I / J V Volume o f d i s p l a c e m e n t a t r e s t .

F i g . 2 Wetted s u r f a c e and c e n t e r o f g r a v i t y r i s e i n calm w a t e r . F i g . 3 Angle o f a t t a c k and r e s i s t a n c e i n calm w a t e r .

F i g . k Sample o f m o t i o n r e c o r d i n g s f o r d i f f e r e n t wave h e i g h t s . F i g . 5 Some r e c o r d i n g s o f t h e v e r t i c a l a c c e l e r a t i o n s a t o,1 L. F i g . 6 The mean r e s i s t a n c e . F i g . 7 The mean a n g l e o f a t t a c k . F i g . 8 The mean r i s e o f t h e c e n t e r o f g r a v i t y . F i g . 9 The reduced p i t c h a m p l i t u d e s .

Fig.10 The reduced heave a m p l i t u d e s .

F i g .11 The v e r t i c a l a c c e l e r a t i o n s f o r v m r d a t 0 , 1 L. F i g ,12 Check o f t h e l i n e a r i t y o f t h e p i t c h a m p l i t u d e s . F i g .13 Check o f t h e l i n e a r i t y o f t h e heave a m p l i t u d e s . F i g . li+ Wave s p e c t r a . Fig.15 P i t c h - s p e c t r a . F i g. l 6 Heave s p e c t r a .

Fig,17 Comparison o f t h e p i t c h response i n r e g u l a r and i r r e g u l a r waves. F i g . 18, Compari.son o f t h e heave response i n r e g u l a r and i r r e g u l a r waves. Fig,19 Frequency o f occurence o f t h e peak a c c e l e r a t i o n s a t 0 , 1 L.

Fig.20 Comparison o f measured v a l u e s o f r e s i s t a n c e and a n g l e o f a t t a c k w i t h p u b l i s h e d d a t a .

Model 81+.

F i g .21 Comparison o f measured v a l u e s o f r e s i s t a n c e and a n g l e o f a t t a c k w i t h p u b l i s h e d d a t a .

on s t e a d y p l a n i n g s u r f a c e s , t h e r e i s s u r p r i s i n g l y l i t t l e t o he f o u n d on t h e s e a k e e p i n g b e h a v i o u r o f p l a n i n g c r a f t . For t h e use o f p l a n i n g b o a t s on open wate good sealteeping a b i l i t y i s one o f t h e f i r s t r e q u i r e m e n t s . The a b i l i t y t o r e a c h h i g h speeds i n waves i s l a r g e l y l i m i t e d by t h e o c c u r r e n c e o f h i g h v e r t i c a l a c c e l e r a t i o n s , w h i c h i n t u r n a r e dependent on t h e speed, t h e m o t i o n s o f t h e s h i p and t h e h u l l f r o m .

I n an a t t e m p t t o s i n g l e o u t t h e i n f l u e n c e o f one g e o m e t r i c a l p a r a m e t e r on t h e v e r t i c a l a c c e l e r a t i o n s , two models o f w h i c h o n l y t h e d e a d r i s e a n g l e s d i f f e r e d

were t e s t e d i n calm w a t e r and i n headwaves.

The f i r s t m o d e l , denoted as model Qh, was q u i t e s i m i l a r t o t h e "Clement" f o r m o f t h e S e r i e s - 62 (1j , t h e o t h e r , model 8 5 , was d e r i v e d f r o m t h e f i r s t by d o u b l i n g t h e a n g l e o f d e a d r i s e , k e e p i n g a l l o t h e r d i m e n s i o n s e q u a l a,s f a r as p o s s i b l e .

h. Model d a t a .

The f o r m o f h o t h models i s shown i n f i g u r e 1.

The main p a r t i c u l a r s a r e g i v e n i n t h e f o l l o w i n g t a b l e . c max cm L B c B c V A P X f o r w a r d o f t r a n s o m P G f o r w a r d o f t r a n s o m L V A V L 1/3 '273 cm L 1,500 m 0,^50 m 0,370 m 0,02731+ 3 m 0,5550 2 m 0,729 m = 1+8,6 p e r c e n t o f L 0 ,665 m - 1+1+ ,3 p e r c e n t o f L 0,301 m ^ , 9 8 6,11 ^,05 3,33 c max

The d e a d r i s e angle o f t h e p r i s m a t i c p a r t o f t h e p l a n i n g b o t t o m o f model 81+ was 12 d e g r e e s , t h a t o f model 85 was 2l+ degrees.

5- Summary o f t h e e x p e r i m e n t s .

5 . 1 . Calm w a t e r t e s t s .

The model was f r e e t o p i t c h and heave and r e s t r a i n e d f r o m o t h e r m o t i o n s . The r e s i s t a n c e dynomometer o f t h e s t r a i n - g a u g e t y p e was a t t a c h e d a t an a r b i t r a r y h e i g h t o f 0 , 1 l 6 m above t h e k e e l . P r e v i o u s e x p e r i e n c e has p r o v e d t h a t t h e h e i g h t o f t h e p o i n t o f a t t a c h m e n t has o n l y a v e r y s m a l l i n f l u e n c e on t h e e q u i l i b r i u m p o s i t i o n o f t h e model.

The f o l l o w i n g i t e m s were measured:

- t h e r e s i s t a n c e w i t h a s t r a i n gauge dynamometer - t h e t r i m a n g l e , w i t h a p o t e n t i o m e t e r

- t h e r i s e o f t h e c e n t e r o f g r a v i t y w i t h a p o t e n t i o m e t e r

- t h e f o r m and e x t e n t o f t h e w e t t e d s u r f a c e by u n d e r w a t e r photographs The r e s u l t s are summarized i n f i g u r e 2 .

5 . 2 . Regular head waves.

These e x p e r i m e n t s were c a r r i e d o u t f o r t h e speed range c o r r e s p o n d i n g t o 0,6 < F^^ < 3 . 2 , and t h e wave l e n g t h s c o r r e s p o n d i n g t o .

^ = 0,8 - ( 1, 0 ) - 1,2 - 1,6 - 2,0 - 2,5 and 3,0

The wave l e n g t h A = 0,8 L was used f o r model 81+, b u t t h e f r e q u e n c y o f

e n c o u n t e r \ras so c l o s e t o t h e n a t u r a l f r e q u e n c y o f a p a r t o f t h e s u s p e n s i o n system, t h a t f o r t h e t e s t s w i t h t h e n e x t model a somewhat l a r g e r wave

l e n g t h - was used.

For t h e l a r g e r p a r t o f t h e program a s t a n d a r d wave h e i g h t o f 0,06 m or ~r was u s e d , b u t f o r a few speeds and wave l e n g t h s t h e t e s t s were r e p e a t e d f o r wave h e i g h t s o f 0,0l+ m and 0,08 m t o g e t an i m p r e s s i o n o f t h e l i n e a r i t y o f t h e m o t i o n s . The speeds c o r r e s p o n d e d t o F „ = 1,2 2,0 -•f nV ' ' 2,9 o r 3,2 and t h e wave l e n g t h s t o ^ = 1,2 - 2,0 - 3,0 L The f o l l o w i n g i t e m s were d e t e r m i n e d : - t h e mean r e s i s t a n c e - t h e mean a n g l e o f a t t a c k - t h e mean r i s e o f t h e c e n t e r o f g r a v i t y - t h e p i t c h - a m p l i t u d e - t h e heave a m p l i t u d e - t h e v e r t i c a l a c c e l e r a t i o n f o r w a r d a t 0,1 L and a t 0,1+ L f r o m t h e f o r e s i d e o f L.

8

An a t t e m p t t o measure t h e phase-angle a t h i g h speed f a i l e d due t o v e n t i l a t i o n o f t h e wave p r o b e .

Some o f t h e r e s u l t s o f t h e measurements are p r e s e n t e d i n t h e f i g u r e s k to 13. I n t h e a p p e n d i x t h e o t h e r r e s u l t s a r e sutranarized.

5 . 3 . I r r e g u l a r head seas.

The e x p e r i m e n t s were c a r r i e d o u t a t c o n s t a n t speed c o r r e s p o n d i n g t o F =2 7 nV ' ' • The model s p e c t r a a r e shown i n f i g u r e l U , t r a n s f o r m e d f o r t h e f r e q u e n c y o f e n c o u n t e r .

The f o l l o w i n g measurements were c a r r i e d o u t : - t h e wave h e i g h t

- t h e p i t c h m o t i o n - t h e heave m o t i o n

- t h e v e r t i c a l a c c e l e r a t i o n s a t 0,1 L and 0,1+ L

The f o r m o f t h e h i g h e s t wave h e i g h t s p e c t r u m c o r r e s p o n d s r a t h e r r o u g h l y t o a h o r t h Sea s p e c t r u m a t t h e windspeed o f a good B e a u f o r t h; f o r a s h i p w i t h a d i s p l a c e m e n t o f about k3 t s , t h e l e n g t h o f t h e s h i p w o u l d be L,„l8 m and t h e speed a p p r o x i m a t e l y 30 k n . The " s i g n i f i c a n t " wave h e i g h t w o u l d amount t o 1,25 m.

From t h e wave h e i g h t s p e c t r u m amd t h e m o t i o n s p e c t r a , shown i n t h e f i g u r e s 15 and 16, t h e m o d u l i o f t h e f r e q u e n c y - r e s p o n s e - f u n c t i o n s f o r p i t c h and heave were d e t e r m i n e d . There a r e p r e s e n t e d i n t h e f i g u r e s IT and 18. The f r e q u e n c y o f o c c u r r e n c e o f t h e v e r t i c a l a c c e l e r a t i o n s i s shown i n f i g u r e I 9 .

6. D i s c u s s i o n o f t h e t e s t r e s u l t s .

6 . 1 . Calm v/ater

As t h e h u l l f o r m o f model Qk c l o s e l y r e s e m h l e d t h e "Clement" f o r m , t h e t r i m and r e s i s t a n c e s h o u l d a l s o f i t i n w i t h t h e S e r i e s - 62. T h i s

happened n o t t o he t h e case as i s shown i n f i g u r e 20. Close e x a m i n a t i o n o f t h e h u l l a f t e r t h e t e s t s r e v e a l e d t h a t because o f w a r p i n g o f t h e h u l l m a t e r i a l a s l i g h t c o n v e x i t y had d e v e l o p e d o f t h e a f t e r p a r t o f t h e b o t t o m . T h i s

can be t h e e x p l a n a t i o n o f t h e d i s c r e p a n c y .

The r e s i s t a n c e and angles o f i n c i d e n c e c a l c u l a t e d w i t h t h e a p p r o x i m a t i v e method d e v e l o p e d by S a v i t s k y (2) f r o m t e s t s w i t h p l a n i n g p r i s m s , a r e shown i n t h e f i g u r e s 20 and 2 1 . For model 85 t h e agreement i s r e a s o n a b l e ^ t h e s l i g h t l y d i f f e r e n t a n g l e o f i n c i d e n c e can be e x p l a i n e d by t h e f a c t t h a t t h e breadth- o f t h e p l a n i n g h u l l a t t h e t r a n s o m i s c o n s i d e r a b l y s m a l l e r f o r t h e model t h a n f o r t h e p r i s m a t i c forms . For low speeds t h e method f a i l s , because t h e a c t u a l model can n o t be c o n s i d e r e d any l o n g e r as a p r i s m , when t h e convex f o r w a r d b o t t o m p a r t s e n t e r t h e w a t e r .

I t i s r e m a r k a b l e t h a t t h e r e s i s t a n c e o f t h e deep - V model i s o n l y s l i g h t l y more t h a n t h a t o f i t s f l a t t e r c o u n t e r p a r t . When e x t r a p o l a t i n g t h e r e s i s t a n c e s t o s h i p v a l u e s , t h e s e d i f f e r e n c e s become even s m a l l e r because o f t h e l a r g e r w e t t e d s u r f a c e o f t h e deep - V m o d e l , and t h e decrease o f t h e f r i c t i o n a l r e s i s t a n c e c o e f f i c i e n t w i t h - t i r e i n c r e a s e o f Reynolds number.

P r o b a b l y t h e t r i m a n g l e s o f t h e model Qh 8.re t o o l a r g e f o r l e a s t r e s i s t a n c e .

6 . 2 . R e g u l a r head waves.

The q u e s t i o n o f l i n e a r i t y i s i m p o r t a n t , o r r a t h e r i t i s i m p o r t a n t t o know i f t e s t s i n i r r e g u l a r waves w i l l g i v e r e s u l t s w h i c h w i l l p r e d i c t t h e t r u e o r d e r o f q u a l i t y o f t w o m o d e l s , t h a t i s t o s a y , when model A appears t o be b e t t e r th-an model B i n r e g u l a r waves, t h e same s h o u l d f o l l o w f r o m t e s t s i n i r r e g u l a r waves w i t h a s u f f i c i e n t l y w i d e f r e q u e n c y r a n g e . T h i s f o l l o w s a u t o m a t i c a l l y when t h e m o t i o n s can be d e s c r i b e d by a s e t o f l i n e e r d i f f e r e n -t i a l e q u a -t i o n s . I -t seems even p r o b a b l e -t h a -t q u i -t e a l o -t o f n o n - l i n e a r i -t y can be i n t r o d u c e d b e f o r e t h i s w i l l i n v a l i d a t e t h e c o m p a r i s o n .

The f i r s t i m p r e s s i o n o f th-e l i n e a r i t y can be had f r o m t h e r e c o r d i n g s o f t h e m o t i o n s and t h e a c c e l e r a t i o n s , as shown i n t h e f i g u r e s k and 5- When l o o k i n g

a t t h e r e c o r d e d a c c e l e r a t i o n s o f model Qk, w i t h t h e s t e e p r i s e when t h e bovf h i t s t h e w a t e r s u r f a c e , i t i s seen t h a t t h i s e v i d e n t n o n - l i n e a r i t y appears t o have a r e l a t i v e l y s m a l l i n f l u e n c e on t h e s i n e - c h a r a c t e r o f t h e p i t c h m o t i o n .

I n t h e f i g u r e s 12 and 13 t h e r a t i o s between t h e m o t i o n a m p l i t u d e s and t h e wave h e i g h t a r e g i v e n f o r d i f f e r e n t v/ave h e i g h t s . O b v i o u s l y t h e o n l y non-l i n e a r i t i e s o f some i m p o r t a n c e o c c u r a t t h e h i g h e s t speed and t h e non-l a r g e s t wave l e n g t h . T h i s c o n c e r n s t h e a m p l i t u d e s , n o t h i n g i s known about t h e phases The r e d u c e d p i t c h a m p l i t u d e s o f model öh t e n d t o i n c r e a s e w i t h t h e wave h-eight, w h i l e t h e r e v e r s e i s t r u e f o r model 85.

The mean a n g l e o f a t t a c k and t h e mean r i s e o f t h e c e n t e r o f g r a v i t y w h i c h t o g e t h e r d e t e r m i n e t h o mean a t t i t u d e o f t h e m o d e l , a r e p r e s e n t e d i n t h e f i g u r e s 7 and 8. E v i d e n t l y e s p e c i a l l y model Qk comes much h i g h e r o u t o f t h e w a t e r i n waves t h a n i n smooth w a t e r . T h i s i n d i c a t e s tha,t t h e m o t i o n i s n o t s t r i c t l y l i n e a r .

The r e s u l t s o f t h e r e s i s t a n c e measurements were r e m a r k a b l e i n t h e case o f model Qh. For a number o f wave l e n g t h s t h e mean r e s i s t a n c e appeared t o be s m a l l e r t h a n t h e smooth w a t e r r e s i s t a n c e i n a speed range around F^^^=3. T h i s c o u l d n o t be e x p l a i n e d , b u t t h e i m p r e s s i o n e x i s t e d t h a t t h e phase r e l a t i o n s between t h e m o t i o n s and t h e wave were r e s p o n s i b l e f o r t h e phenomenon

The r e d u c e d a m p l i t u d e s o f p i t c h . a,nd heave a r e p r e s e n t e d i n t h e f i g u r e s 9 and 10. The m o t i o n s o f model 85 appear t o be l e s s t h a n t h o s e o f model Qk fox a l l wave l e n g t h s i n t h e h i g h speed range above F^^ = 2

The v e r t i c a l a c c e l e r a t i o n s f o r w a r d , p r e s e n t e d i n f i g u r e 11 d i f f e r m a r k e d l y f o r b o t h m o d e l s , as \ras a l l r e a d y a p p a r e n t f r o m t h e r e c o r d i n g s

shown i n f i g u r e 5- The s u p e r i o r i t y o f model 85 h o l d s f o r a l l speeds and wave l e n g t h s t e s t e d .

I r r e g u l a r head seas.

The measurements o f t h e wave h e i g h t and t h e m o t i o n s , and t h e subsequent a n a l y s e s o f t h e wave h e i g h t s p e c t r u m and t h e m o t i o n s p e c t r a , y e a l d e d t h e f r e q u e n c y - a m p l i t u d e - r e s p o n s e s o f p i t c h and heave. T h i s has been done on t h e a s s u m p t i o n t h a t t h e m o t i o n s would be s u f f i c i e n t l y l i n e a r t o j u s t i f y t h i s p r o c e d u r e . The r e s u l t s f o r two d i f f e r e n t wave s p e c t r a a r e shown i n the- f i g u r e s I T and l 8 . The s p e c t r a a r e shown i n t h e f i g u r e s Ik t o l 6 . U n f o r t u n a t e l y t h e r e c o r d i n g o f t h e p i t c h m o t i o n o f model Qk i n t h e l o w e r v i a v e s p e c t r u m appeared t o have been s p o i l e d by an i n s t r u m e n t a l f a i l u r e . T h i s i s t h e r e a s o n why th-ese r e s u l t s have been o m i t t e d f r o m t h e f i g u r e .

The comparison o f t h e responses f o r r e g u l a r and i r r e g u l a r waves r e v e a l s t h a t f o r t h e h i g h f r e q u e n c y f l a n k o f t h e c u r v e s t h e agreement i s r e a s o n a b l e . The t e n d e n c y o f t h e c u r v e s f o r r e g u l a r waves t o r i s e a t t h e t o p above

t h o s e f o r i r r e g u l a r waves, has n o t been e x p l a i n e d . The g e n e r a l o r d e r has n o t been a f f e c t e d by t h i s .

The a n a l y s e s o f t h e i r r e g u l a r m o t i o n s shows v e r y c o n s i s t e n t r e s u l t s f o r t h e two d i f f e r e n t wave h e i g h t s p e c t r a and t h e r e l a t i v e q u a l i t i e s o f t h e m o d e l s , as h-ave been f o u n d f r o m t h e t e s t s i n r e g u l a r waves, a r e t r u l y r e p r o d u c e d . The a c c e l e r a t i o n s e x p e r i e n c e d by t h e f l a t model a r e n o t as s t r i h - i n g as t h o s e w h i c h have been o b s e r v e d i n r e g u l a r waves, b u t t h e d i f f e r e n c e between t h e t w o models i s s t i l l c o n s i d e r a b l e , as i s shown i n t h e f r e q u e n c y o f o c c u r r e n c e d i s t r i b u t i o n s i n f i g u r e 19.

12

7. G e n e r a l c o n c l u s i o n s .

The i n c r e a s e o f t h e d e a d r i s e a n g l e r e s u l t s i n a c o n s i d e r a b l e g a i n i n s e a k e e p i n g a b i l i t y a t t h e c o s t o f some power The decrease o f t h e v e r t i c a l a c c e l e r a t i o n s i s p a r t l y a d i r e c t outcome o f t h e l a r g e r d e a d r i s e , p a r t l y an i n d i r e c t consequence o f t h e i n f l u e n c e o f t h e h u l l f o r m on t h e mean a t t i t u d e o f t h e b o a t and on t h e m o t i o n s . Model 85 s i t s l o w e r i n t h e w a t e r t h a n model Qh, i t s t r i m a n g l e i s l e s s ,

and i t s m o t i o n s , i n p a r t i c u l a r p i t c h a r e l e s s , f e a t u r e s w h i c h t e n d t o s o f t e n t h e impact i n waves. V i s u a l o b s e r v a t i o n s gave t h e i m p r e s s i o n tha,t a l s o t h e phase o f t h e m o t i o n s w i t h r e s p e c t t o t h e waves was d i f f e r e n t and t h i s a l s o c o u l d have

c o n t r i b u t e d t o t h e e v i d e n t l y b e t t e r p e r f o r m a n c e o f t h e deep - V model. T h i s r a t h e r complex r e l a t i o n between d e a d r i s e a n g l e and s e a k i n d l i n e s s c a u t i o n s one a g a i n s t g e n e r a l i z a t i o n .

The t e s t s i n i r r e g u l a r waves showed t h a t a c e r t a i n degree o f n o n - l i n e a r i t y does n o t appear t o i n v a l i d a t e t h e q u a l i t a t i v e c o n c l u s i o n s w h i c h can be drawn vrhen comparing t h e b e h a v i o u r o f one model w i t h t h a t o f t h e o t h e r , under t h e same c o n d i t i o n s . Of c o u r s e more evidence s h o u l d be p r o v i d e d b e f o r e si;ch a s t a t e m e n t can be g e n e r a l i z e d .

I t seems a d v i s a b l e t o r e p e a t t h e e x p e r i m e n t s i n i r r e g u l a r waves a t a h i g h e r speed b u t up t i l l now t h i s i s n o t w i t h i n t h e r e a c h o f t h e f a c i l i t i e s o f t h e model t a n k i n D e l f t .

8. R e f e r e n c e s

-( 1 ) Clement, E.P. and B l o u n t , D.L.,

' R e s i s t a n c e T e s t s o f a S y s t e m a t i c S e r i e s o f P l a n i n g H u l l Forms". T r a n s a c t i o n s o f The S o c i e t y o f N a v a l 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 . Vol.71 1963 p. h9^

(2) S a v i t s k y , D .

"Hydrodynamic D e s i g n o f P l a n i n g H u l l s " . Marine Technology V o l. 1 no. 1 October I96I+.

9 . 1 . Calm w a t e r Model Qh _{V = 1 ,052 X 10 m /sec.} -6 2 V R 0: ₁ m s m/sec k g . d e g r . 111 2 m/sec cm m m 1 1 ,10 0,11+ - 0 , 7 8 1,1+6 0,637 1 ,72 2,01 1,15 - 1 ,30 1,1+3 0,637 2,03 3,10 3,53 - 1 ,39 1,1+0 0,631 2,22 3,30 U, 2 6 - 1 ,03 1 ,38 0,627 2,H7 3,hO 1| , ^ 2 -oM 1 ,35 0,615 2 , 6 1 3,50 ^ , 5 1 -0,2l+ 1 ,33 0,6ol+ 2,85 3,60 h,lh 0 ,00 1 ,29 0,580 3,03 3,80 5,01 +0 ,2l+ 1 ,2l+ 0,552 3,33 1|, 10 6,11 + 0 , 9 3 1,1i+ 0,1+73 3,76 h,30 7,00 +2,23 1 ,oi+ 0 ,1+1 1 3,91 h,31 6,88 +2,52 1 ,01 0,398 3,U7 14,21 6,31 + 1 ,28 1 ,10 0,1+1+6 hM hM 6,1+7 + 3,70 0,92 0,359 5,13 h,35 5,93 +l+,30 0,89 0,31+5 5 , 6 2 hM 5,H8 +^,73 0, 8 1 + 0,327 5,88 h,6h _5,25 +l+,89 0,80 0,315 3,2H i+,05 5,55 +0 ,62 1,17 0 ,1+96 1,89 2,66 2,32- -1,1+8 1,1+1 0,635 0,99 0 , 3 1 - 0 , 1 5 ^0 ,1+2 1,50 0 ,610

Model 85 V = 1,052 X 10" m / s e c . V R 1 m s 0 m/sec kg degr. cm m d m 1 ,00 0,36 -0 ,22 - 0 , 3 8 1 ,50 0,628 1 ,1+9 1 ,32 - 0 , 5 0 - 0 , 8 2 1 ,^7 0,61+1 3,09 14,27 3M 0 ,00 1 ,31 0,622 1+ ,01 H,50 5,18 + 1,66 1 ,16 0,1+98 5,10 ^,81+ 5 ,22 + 3,22 1 ,03 0,^53 2,52 3,69 3,58 - 0 , 6 8 1 ,38 0,621+ 5,60 5,1H 5,10 +3,60 1 ,00 0,1+32 3,52 ^ , 5 9 l+,32 + 0 , 7 2 1,25 0,612 5,56 5,11 5,10 +3,60 1 ,00 0,1+33 2,09 3,11+ 2,72 -1 ,1+0 1 ,1+3 0 ,61+0 k,hQ h,62 5 ,36 + 2 , 5 ^ 1 ,10 0,488 6,01 5,3h U,8o + 1+ ,00 0,98 0,1+19

Model Qh V m/sec R cc degr. ^a z a e a ""0,41 V m/sec kg cc degr. cm. cm. cm., d e g r . _g g A = 1,20 m. A/L = 0 , 8 3,03 3,53 1 ,00 1,98 H,58 5,03 5,59 k,^9 0,63 3,17 4,78 4,93 H,96 5,o6 6,76 - 0 , 2 0 2,4o 6,60 6,32 5,78 +0 ,20 + 1 ,76 -o,4o - 1 , 5 0 + 4,32 +4,92 +5,36 2,25 2,36 2,45 2 ,42 2 ,61 2, 0 8 2,34 0,31 0,46 0,26 0 , 3 2 0,50 0 ,4o 0,48 0,45 0,75 0,71 0,39 0 ,60 0,48 0,4o 0,64 1 ,53 0,16 0,22 3,64 3,97 4,32 0,33 0,86 0,07 0,14 1,63 1 ,77 2,19 A = 1 30 ra. A/L _{- 1,2} 1 ,03 2,00 2,96 U,12 5,07 1,50 2 , ^ 9 3,56 H,58 5,56 2 , 0 1 3,59 5,04 2,06 3,52 5,05 1 ,02 3,31 4,50 5,4o 3,51 1,51 3,72 5,21 5,24 4 , 0 2 3,21 4,75 3,67 5,16 5,50 0,80 3,44 5,38 7,44 6,82 0,58 4,88 7,38 7,18 6,30¬ 3,04 6,78 6,20 4,00 6 , 9 6 6 , 4 2 0,00 - 1 ,40 0 ,00 + 3,60 +4,90 -^0,78 - 0 , 4 2 +2,00 + 4 , 4 2 +5,18 - 1 , 5 4 +2,06 +4,56 -1 ,56 + 1 ,88 +4,68 3,09 3,29 2,76 2,65 3,10 3,15 3,30 2 , 7 6 2,79 2,45 2,00 2,09 1 ,80 3,74 3,30 3,33 1,92 0 , 4 i 0,57 1 ,03 1 ,02 1 ,12 0 ,42 0,98 1 ,01 o; 9 9 0 ,21 0,75 Q,75 0,45 1,20 1 ,25 3,86 1,14 1 ,24 1 ,4o 1,16 1 ,99 1 ,00 1 ,47 1 ,23 1,10 0,69 1 ,05 0,88 1,34 1 ,93 1 ,36 0,42 0,19 0,67 3,36 6,92 0,29 0,47 1 ,70 4,60. 5,95 0 , i 4 3 ,08 2,48 0,28 3,7^ 7,41 0,17 0 , 1 1 0,33 1 ,55 3,92 0 , 1 2 0 , 1 9 0,95 1,98 2 , 9 4 0,00 0,51 J ,13 0 , 1 1 3, 4 3 3,77

Model Qk V m/sec. R k g . degr. cm crn z a cm 0 a degr. g ' ' O , 4 L g X = 2,4o m. A/ L _{= 1,6} 1 ,00 0,81 0 ,26 - 0 , 2 2 3,00 2,48 4,90 0,36 0,23 1,98 3,19 3,26 - 1 ,4o 2,95 2,05 2,70 0,30 0,20 3,00 4,45 5,20 +0,24 3,10 1,17 2,14 0,64 0 ,28 k ,00 5,16 7,56 + 3,60 2,92 1,76 2,11 2,21 1 ,21 5,07 3,66 6,68 +5,18 3,05 1 ,68 1 ,81 6,80 2,81 5,63 4,21 5,80 +5,48 3,08 1,57 1,59 8,99 4,03 kM h,ö9 7,16 +4,6o 3,00 1,70 1,90 4,53 1 ,82 2,55 3,89 5,78 - 0 , 4 8 3,00 1 ,14 2,04 0,44 0 ,20 1 ,50 1 ,56 o,6o - 0 , 7 2 3,00 3,22 4,20 0,44 0,31 3,47 5,03 7,22 + 1 ,72 2,6o 1 ,46 2 ,00 1 ,25 0,63 1 ,02 1,99 2,99 4,01 5,07 5,55 4,58 2,56 1 ,46 3,48 2,03 3,55 5,00 2 ,00 3,54 5,12 A 0,62 3,18 4,24 4,42 4,94 5,08 4,71 3,98 1 ,42 4,31 3,24 4,74 4,85 3,51 5,14 5,75 = 3,00 0,18 3,20 4 , 8 0 . 6,86 6 ,20 5,86 6,62 4,62 0 ,42 6,24 3,18 6,6o 6,00 3,02 5,78 6 ,22 m. -0,30 - 1 ,40 + 0,12 + 3,20 +4,62 +5,14 +4,28 - 0 , 3 8 - 0 , 6 6 + 1 ,50 - 1 , 4 o + 1 ,00 +4,82 •^1,16 + 1 ,82 + 3,16 A/ L 3,06 2,96 3,01 2,70 2,80 2,99 3,00 3,00 2,95 2,65 2 ,21 2,50 2,18 4,00 3,89 3,80 = 2,0 2,6o 3,13 1 ,91 2,36 2 ,24 2,15 2,35 2 ,24 2,91 2,07 2,50 1 ,80 1,90 4,41 2,79 2,90 4 ,20 3,35 2,79 2,86 2,46 2,29 2,71 3,00 4,30 2,68 2,52 2,14 2,00 4,52 3,56 3,11 0,38 0,58 1 ,66 6,37 7,31 3,89 0,37 0,38 0,96 0,27 0,71 2,72 0,51 1 ,71 9,38 0,27 0 ,26 0,94 2,31 2,93 1 ,6o 0,23 0 ,22 0,49 0,18 0,36 1 ,20 0,32 0,91 3,96

V m/sec. R kg CC d e g r . cm . a cm z a cm 0 a degr. g g X = 3,75 m. A/L = 2,5 1,0h _0,47 0 -0,30 3,00 2,75 3,30 0,15 0,11 2 ,00 _2,99 3,12 -1 ,36 _2,95 3,6o 2,91 0,26 0,23 3,96 _4,59 6,72 +2,70 2 , 5 8 3,30 3,4o 1,23 0,67 5,54 4 ,22 5,50 +5,40 _{2,75 3,23 3,05 5,96 2,65} 5,o4 3,88 6,02 +4,80 _2,59 3,38 3,33 5,12 2,22 3,07 4 , 2 1 5,98 +0 ,42 2 , 6 2 3,06 3,15 o,4o 0,28 4,57 ^ , 7 7 6,36 +4,44 3,00 3,33 3,26 2,57 1,30 5,07 3,92 5,98 + 4 , 9 2 2,6o _3,35 3,28 4 , 7 3 1 ,95 4,66 4,74 6,30 +4,56 2,80 3,43 3,28 2,98 1,47 2,55 3,65 4,48 -0 ,30 3,00 3,21 2,94 0 ,23 0,25 1,50 _{1 ,37} 0 ,o6 - 0 , 9 4 _{2 , 9 1} 2,86 3,23 0,15 0,17 4,89 4,78 6,10 +4,86 2,40 3,53 3,25 3,50 1 ,71 A = 4,50 m. A/L = 3,0 1 ,02 _0,39 - 0 , 0 8 -0 ,36 3,06 2 , 8 2 2,80 0,10 0,09 1,98 2,97 3,10 - 1 , 4 4 3,00 3,4o 2 ,62 0,19 0,17 2,98 4 ,01 5,00 +0,28 2,76 3,52 2,80 0 ,26 0 ,22 4 ,03 4 , 6 1 6,80 + 3,30 +4 ,4o 2,65 4,00 3,44 _0,79 0 ,43 4,58 4,62 6,20 + 3,30 +4 ,4o 2 , 9 8 4,32 3,80 1 ,53 0,80 5,07 4,88 5,74 +4,80 2,60 4,53 3,96 3,00 1 ,52 5,62 5,12 4,90 +5,32 2,85 4,54 3,97 6,72 3,11 3,54 4,47 6 ,60 + 1 ,68 2,70 3,70 3,24 0,45 0,32 1 ,53 1,45 0,16 - 0 , 9 4 3,10 2,96 2,76 0,13 0,14 2,54 3,64 4 , 5 6 - 0 , 2 6 _{3,15 3,55} 2,52 0 ,20 0,23 2,02 3,18 3,24 -1 ,38 3,99 4,42 3,39 0,29 0,19 3,56 4 , 8 4 6,20 + 1 ,96 3,80 _4,99 4,26 1 ,00 0,32 5,02 5,44 4 J 4 +5,20 3,61 5,90 4,74 5,30 2,48 2,02 3,11 3,00 - 1 , 4 8 2,29 2,60 1 ,90 0,15 0,19 3,51 ^ , 5 7 6,46 + 1,60 2 , 1 1 2,75 2,39 0,32 0 ,20 5,01 4 , 7 4 5,80 +4,66 2 , 1 1 3,60 3,28 1 ,67 0,78

Model 85 V m/sec . R k g . cc degr. a z a e a ^ 0 , 4 L V m/sec . R k g . cc degr. cm. cm. cm. degr. g g A 1 ,50 m. A / L = 1,0 1 ,56 3,02 k,ok 4,99 5,47 3,50 4,52 2,07 2 , 5 1 1 ,60 5,01 5,14 5,14 5,29 5,o4 5,11 3,37 3,74 - 0 , 2 0 4,16 6,08 6 ,06 5,74 4,76 5,90 2,66 3,50 - 0 , 5 9 - 0 , 4 4 + 1 ,90 +3,4o +4,08 + 0 , 3 4 +2,80 - 1 , 7 8 - 0 , 9 2 3,35 2,83 2,88 2,65 2,85 2,69 2,82 3,00 3,21 0 , 4 1 0,38 0,45 O , 4 T 0,45 0 , 3 4 o , 4 o 0,13 0 , 2 4 0,74 0,49 0,63 0,69 0,55 0,48 0,60 0,40 o,4o 0,13 0 ,42 0,87 1,19 1,49 0,56 0,96 0 ,18 0,38 0,07 0,24 0,48 0 , 6 2 0,78 0,29 0,4o 0,07 0,18 A = 1,^ iO m. A / L = 1,2 1 ,02 2,17 3,13 3,53 4,43 5,21 2,48 4,00 5,57 2 , 3 1 3,48 5,49 2,04 3,47 5,50 0,96 3,73 4,50 4,67 5,87 5,78 3,90 5,48 5,75 3,90 4,63 5,99 3,23 4 , 9 1 5,38 0,30 2,96 3,70 4,50 5,80 5,68 3,50 5,68 5,64 3,42 4,68 5,60 2,50 4,48 5,76 -0 ,06 -1 ,38 - 0 , 4 2 +0,38 +2,50 + 3 , 3 2 - 1 ,06 + 1 ,78 + 3,80 - 0 , 9 8 +0 ,28 + 3 , 8 4 - 1 ,68 +0 ,44 + 3 , 8 2 3,12 3,10 2,66 3,00 2,56 2,37 2,65 2,85 2,52 3,82 3,44 3,50 2,00 2,09 1 ,95 1 ,83 0,22 0,39 0,45 0,66 0,55 0,20 0,60 0 , 6 0 0 , 2 1 0,64 0 , 8 1 0,15 0 , 3 1 0,44 3,73 0,89 0,64 0,73 0,90 0,77 0,70 0,95 0 , 7 8 1,07 0,96 1 ,00 0,54 0,52 0,55 0,39 0,17 0,39 0,52 1 ,02 1 ,08 0,27 0 , 8 1 1 ,35 0,32 0,72 1 ,95 0 ,06 0,38 0,86 0,20 0,10 0 , 2 4 0,32 0,58 0,61 o , i 4 0,45 0,80 0,19 o,4o 1,05 0,00 0,17 0,46

m/sec. k g . degr. cm. a cm. a cm a degr. g ^ O , 4 L g A = 2,40 m. A / L = 1,6 1 ,02 0,85 - 0 , 0 6 - 0 , 4 2 2,85 2,12 4,68 0,38 0,18 2,03 3,55 3,12 - 1 ,bO 3,00 1 ,92 2,59 0,43 0,24 2,49 4,14 3,92 - 0 , 9 8 3,16 1,10 1,94 0,48 0,19 3,Oh 4,74 4,00 - 0 , 5 0 2,98 0,88 1,60 0,56 0,23 3,53 5,03 4,84 +0 ,20 3,05 0,96 1 ,35 0,65 0,32 4,08 5,00 6,00 + 1 ,86 2,80 1,15 1,43 0,96 0,45 4,46 4,91 5,60 +2,54 2,63 1 ,20 1 ,39 0,99 0,51 5,48 5,13 5,50 - + 3,82 2,80 1 ,72 1,32 1,49 0,77 5,01 ^,97 5,68 + 3,22 2,77 1 ,24 1,33 1,29 0,69 A = 3,00 m. A / L = 2,0 1 ,02 0,63 - 0 , 1 8 - 0 , 2 2 3,00 2,44 3,97 0,27 0 , l 4 2,00 3,26 2,42 -1 ,16 3,07 3,33 3,45 0 , 4 2 0,32 2,94 4,53 3,10 - 0 , 3 2 2 , 9 2 1 ,90 2 ,61 0,48 0 ,26 4,05 5,34 5,00 + 1,56 2,70 1 ,71 1,99 0,54 0,39 5,07 5 ,01 5,14 + 3,22 2,60 1,84 1,91 1,13 0,33 5,62 5,26 4,98 + 3,78 2,70 1,74 1,77 1 ,34

-5,52 5,14 4,96 +3,62 2,39 1,77 1,77 1,29 0,79 ^,55 5,05 5,4o +2,60 2,60 1,85 1,95 1,12 0,54 3,48 _5,15 3,84 +0,04 2,86 1,64 2,07 0,69 0,27 2,44 3,99 3,48 - 1 ,00 2,96 2,60 3,01 0,50 0,19 2,03 3,53 2,52 - 1 ,22 3,76 4,21 4,30 0,48 0,34 3,52 5,49 3,28 +0,10 3,52 1 ,82 2,51 0,65 0,32 5,03 5,31 5,00 + 3,26 3,23 2,18 2 ,24 1 ,51 0,85 2,03 3,35 2,56 - 1 , 5 4 2,38 2,69 2,79 0,28 0,26 3,54 5,15 4,00 +0 ,24 2,09 1 ,19 1,65 0,38 0,23 5,00 5,11 5,36 + 3 , 1 2 2,07 1,50 1,55 0,80 0,46

Model 85 V R cc _c z G a a , m/sec k g . d e g r . G a a a f O , 4 L m/sec cm. cm. cm. degr. g g A = _{3,75 m.} A / L _{= 2,5} 1 ,03 0,48 - 0 , 3 0 - 0 , 2 6 2,96 2,90 3,35 0,16 0,11 2,03 3,21 2,40 - 1 ,30 2 , 9 8 3,60 3,21 0,32 0 ,24 2,52 3,98 3,44 - 0 , 6 4 3,00 3,52 3,06 0,32 0,27 3,00 4 , 6 1 3,38 - 0 , 0 8 3,08 3,20 3,08 0 , 4 l 0,28 3,50 5,35 3,66 +0,13 2,65 2,66 2,82 0,46 0 , 2 8 4,05 5,63 4,52 + 1 ,56 2,72 2,53 2,57 0,60 0,36 h,5h _5,47 +2,64 2 ,60 2,86 2 , 6 1 0,82 0,44 5,05 5,43 5,60 +3,36 2,80 2 , 8 2 _2,55 1,08 0 ,60 5,56 5,74 5,44 +3,76 2,68 2,84 2,53 1 ,31 0,75 A = 4 , 5 0 m. A / L _{= 3,0} 1 ,05 0,47 - 0 , 3 2 - 0 , 4 o 2,95 2,79 2,60 0,00 0,10 2 ,02 3,20 2,34 - 1 , 6 0 3,00 3,26 2,70 0,16 0,15 2,46 3,89 3,64 - 0 , 5 6 3,00 3,60 2,52 0 ,20 0,18 2,99 4 , 5 1 3,24 - o , 4 o 2,82 3,56 2 , 7 0 0,2T 0,21 4,01 5,41 4,80 + 1,50 3,00 3,54 2 , 9 0 0,43 0,28 3,48 5,28 3,52 + 0 , 1 2 3,00 3 , 4 l 2,90 0,33 0 ,24 4,43 5,38 5,32 + 2 , 5 2 2,67 3,69 2,95 0,58 0,36 5,02 5,63 5,56 +3,28 2,60 3,78 3,00 0,83 0,45 5,53 6,03 5,30 + 3,74 2,75 3,90 3,12 1 ,08 0,54 2,00 3,11 1,50 - 1 , 6 0 4,20 4,4o 3,75 0,25 0,18 3,52 5,47 3,36 +0,18 3,98 4,55 3,73 0,44 0,29 5,53 6,74 4 , 9 2 +3,68 3,87 -4,63 3,65 1,57 0,75 5,56 5,87 5,20 + 3,96 2,20 3,10 2,48 0,78 0,46 2,01 3,14 2,24 ^ 1 , 6 4 2,40 2,50 2 , 1 0 0,11 0 ,08 3,55 5,25 3,70 +0,36 2 , 2 1 2,63 2,26 0,23 0,19

• O X/L=2.0

A A

X/L=3.0

MOD.84

Fn

=18.8

3

L / 2 C = 3 0

cl

L / 2 ^ =18.8

L / 2 d = 3 7 . 5

—

L / 2 ^ =20

I

31

^ = 1 . 2

F i g . 13: Check of t h e l i n e a r i t y o f t h e V heave a m p l i t u d e s

Uk

O

+

+

+

0

1 0

1

0

Fnn=2.7

. IRREGULAR WAVES ^^^'^

V +J l | / 9 r = U A

- ^ 3 1 / 3 i

O

_{1 0}

F i g . 17: Comparison o f t h e p i t c h response i n r e g u l a r and i r r e g u l a r waves

1.5

Z^LO

0.5

0

MOD 84 REGULAR WAVES

Fny=2.7 ° )

IRREGULAR WAVES]

L/2£ai/3 =

:25.2

— —

L/2£ai/3 =

:25.2

+

0

_{1 0}

1.5

lYz^(cOe)

1.0

a 0.5

0

MOD.85

REGULAR WAVES

Fny=2.7

^ j l R R E G U L A R WAVES {

1

L/2Cai/3 =

:25.2

1

L/2Cai/3 =

:25.2

+

<^

++

\ O O

0

₁₀

18: Comparison o f t h e heave r e s p o n s e i n r e g u l a r and i r r e g u l a r waves

m / s e c 2

F i g , 20: Comparison o f measured v a l u e s o f r e s i s t a n c e and a n g l e o f a t t a c k w i t h p u b l i s h e d d a t a . Model Qh

0.20

R

0.18

0.16

O.U

0.12

0 . 1 ^

MOC

).85

M EASUREI

SAVITSK :Y

^,

Fn

F i g . 2 1 : Comparison o f measured v a l u e s o f r e s i s t a n c e and a n g l e o f a t t a c k w i t h p u b l i s h e d d a t a . Model 85