Winglet keels in waves

T E C H N I S C H E H O G E S C H O O L D E L F T

AFDELING DER MARITIEME TECHNIEK

L A B O R A T O R I U M V O O R S C H E E P S H Y D R O M E C H A N I C A

WINGLET KEELS I N WAVES by P r o f . l r . J . G e r r i t s m a and

I r . J.A. Keuning

R e p o r t 6 9 3-P

November 19 85

Delft University of Technology

Ship Hydromechanics Laboratory Mel<elweg 2

2628 CD D E L F T The Netherlands Phone 0 1 5 - 7 8 6 8 8 2

R e c e n t l y t h e D e l f t U n i v e r s i t y o f Technology has r e p o r t e d e x p e r i m e n t s t o i n v e s t i g a t e t h e i n f l u e n c e o f d i f f e r e n t k e e l forms on t h e p e r = formance o f a s a i l i n g y a c h t . The s e r i e s o f k e e l s i n v e s t i g a t e d c o n s i s t e d o f a " p l a i n " deep d r a f t lOR t y p e k e e l , a s h a l l o w d r a f t k e e l , a k e e l c e n t r e b o a r d combina-t i o n , a s c h e e l k e e l , an e l l i p combina-t i c a l k e e l and combina-two k e e l s w i combina-t h wxng-l e t s The r e s u wxng-l t s o f t h e s e t e s t s have been r e p o r t e d i n Seahorse. R e c e n t l y t h i s p r o j e c t has been e x t e n d e d w i t h a s e r i e s o f t e s t s xn waves w i t h t h e " p l a i n " deep d r a f t k e e l and t h e two w i n g l e t k e e l s . The purpose o f t h e s e t e s t s has been t o i n v e s t i g a t e t h e i n f l u e n c e o f w i n g l e t s on t h e v e r t i c a l m o t i o n s (heave and p i t c h ) o f t h e y a c h t

i n waves and t h e e x t r a added r e s i s t a n c e i n waves, t h e w i n g l e t s a r e e x p e c t e d t o produce.

Based on t h e o r e t i c a l c o n s i d e r a t i o n s such an e f f e c t i s n o t t o be-e x p be-e c t be-e d f r o m t h be-e S c h be-e be-e l k be-e be-e l . C o n s be-e q u be-e n t l y t h i s t y p be-e o f k be-e be-e l has n o t been i n c l u d e d i n t h e e x p e r i m e n t s i n waves.

The geometry o f t h e t h r e e d i f f e r e n t k e e l s used i n t h i s i n v e s t i -g a t i o n s i s p r e s e n t e d i n t h e f i -g u r e 2.

The t h r e e d i f f e r e n t k e e l s have been c o n n e c t e d i n s u c c e s i o n t o one and t h e same h u l l , i . e . t h e model o f a 62' l o n g y a c h t d e s i g n e d by Jac de R i d d e r .

W i t h each k e e l - h u l l c o m b i n a t i o n a s e r i e s o f t e s t s i n r e g u l a r sx-n u s o i d a l waves have beesx-n c a r r i e d o u t , t h e l e sx-n g t h o f w h i c h have been v a r i e d between 0.7 5 t o 2.5 t i m e s t h e w a t e r l i n e l e n g t h and

t h e h e i g h t s have been between 0.35 and 0.50 m e t e r s ( f u l l s c a l e ) . Such wave c o n d i t i o n s w i l l n o t be e n c o u n t e r e d i n r e a l i s t i c sea con-d i t i o n s : t h e wave s u r f a c e a t sea i s h i g h l y i r r e g u l a r ancon-d t h e ave-r a g e h e i g h t o f t h e waves i n most cases w i l l be h i g h e ave-r . Howeveave-r t h e r e s u l t s o f t h e t e s t i n r e g u l a r waves c o u l d be used t o c a l c u l a t e t h e b e h a v i o u r o f t h e y a c h t i n a more r e a l i s t i c i r r e g u l a r sea, x f t h x s

sea i s a c c u r a t e l y d e s c r i b e d by means o f a so c a l l e d wave s p e c t r u m . These c a l c u l a t i o n - m e t h o d s a r e e x t e n s i v e l y t e s t e d and v e r i f i e d b o t h w i t h f u l l s c a l e e x p e r i m e n t s a t sea and, on model s c a l e , i n towxng t a n k s .

From such t e s t s i t may be c o n c l u d e d t h a t t h e b e h a v i o u r o f s h i p s and o t h e r f l o a t i n g o b j e c t s i n an i r r e g u l a r sea, w i t h a g i v e n wave spectrum can be p r e d i c t e d w i t h s u f f i c i e n t a c c u r r a c y u s i n g t h e s e t e c h n i q u e s .

D e s c r i b i n g t h e i r r e g u l a r sea w i t h a wave s p e c t r u m i t i s assumed t h a t t h e sea i s t h e r e s u l t o f t h e s u p e r p o s i t i o n o f many s i n u s o i -d a l wave components, each w i t h i t s own a m p l i t u -d e an-d l e n g t h . Un-der t h i s c o n d i t i o n t h e r e s u l t i n g m o t i o n s o f t h e s h i p may be c a l c u l a t e d by a d d i n g t h e r e a c t i o n s o f t h e s h i p t o each i n d i v i d u a l component. Hence t h e t e s t s i n r e g u l a r waves. See f i g u r e 3.

I n f i g u r e 4 t h e m o t i o n c h a r a c t e r i s t i c s o f t h e v e r t i c a l heave m o t i o n Z and p i t c h m o t i o n 6 a r e p r e s e n t e d f o r t h e " p l a i n " deep d r a f t lOR t y p e k e e l and t h e two w i n g l e t k e e l s . I n F i g u r e 1 a d e f i n i t i o n o f t h e v e r t i c a l m o t i o n heave and v e r t i c a l r o t a t i o n p i t c h a r e g i v e n . From t h e s e m o t i o n - c h a r a c t e r i s t i c s i t may be c o n c l u d e d t h a t , cons i d e r i n g t h e e x p e r i m e n t a l a c c u r r a c y , t h e p i t c h m o t i o n i cons n o t a f -f e c t e d by w i n g l e t s on k e e l s . T h i s appears t o be t r u e b o t h -f o r t h e "moderate'' w i n g l e t k e e l no 1 , as f o r t h e "extreme" w i n g l e t k e e l no 2. However t h e h e a v i n g m o t i o n i s i n f l u e n c e d t o some e x t e n t by t h e damping f o r c e w h i c h i s produced by t h e o s c i l l a t o r y m o t i o n o f t h e w i n g l e t s r e l a t i v e t o t h e s u r r o u n d i n g w a t e r . The t o t a l damping o f t h e k e e l w i t h w i n g l e t s i n c o m b i n a t i o n w i t h t h e h u l l i s s l i g h t l y l a r g e r t h a n t h a t f r o m t h e h u l l w i t h t h e " p l a i n " deep d r a f t k e e l and t h i s r e s u l t s i n a s l i g h t l y s m a l l e r v e r t i c a l m o t i o n o f t h e y a c h t . The d i f f e r e n c e s a r e s m a l l w i t h a maximum o f a b o u t 5%. The c h a r a c -t e r i s -t i c o f -t h e added r e s i s -t a n c e o f -t h e y a c h -t i n r e g u l a r waves i s p r e s e n t e d i n f i g u r e 5. From t h i s f i g u r e i t may be c o n c l u d e d t h a t t h e added r e s i s t a n c e i n waves o f t h e y a c h t w i t h t h e w i n g l e t k e e l s i s l a r g e r t h a n t h a t o f t h e y a c h t w i t h t h e " p l a i n " deep d r a f t k e e l . P a r t i c u l a r l y i n waves s h o r t e r t h a n 1.25 t i m e s t h e w a t e r l i n e l e n g t h t h e e x t r a added r e s i s t a n c e i s o f i n t e r e s t , b u t t h a t i s d i f f i c u l t t o c o n c e i v e f r o m t h i s f i g u r e s i n c e i t r e l a t e s t o t h e r e s u l t s i n r e g u l a r waves. T h e r e f o r e , u s i n g t h e added r e s i s t a n c e c h a r a c t e r i s t i c s as g i v e n i n F i g u r e 5 t h e added r e s i s t a n c e due t o waves, as w e l l as t h e average a m p l i t u d e s o f p i t c h and heave i n i r r e g u l a r waves have been c a l c u l a t e d , u s i n g t h e a f o r e m e n t i o n e d method.

From t h e s e c a l c u l a t i o n s i t appeared t h a t t h e p i t c h m o t i o n i n i r r e -g u l a r waves i s n o t i n f l u e n c e d by t h e w i n -g l e t s on t h e k e e l .

However t h e r e i s a 2 t o 4% r e d u c t i o n o f t h e v e r t i c a l heave a m p l i -t u d e s f o r -t h e h u l l w i -t h -t h e more ex-treme w i n g l e -t k e e l no 2 and a 1 t o 2% r e d u c t i o n f o r t h e h u l l i n c o m b i n a t i o n w i t h w i n g l e t k e e l no 1, compared w i t h t h e h u l l w i t h t h e " p l a i n " deep d r a f t k e e l . The r e d u c t i o n o f t h e heave m o t i o n i n c r e a s e s w i t h i n c r e a s i n g wave h e i g h t .

I n T a b e l I added r e s i s t a n c e i n waves i s p r e s e n t e d f o r each o f t h e t h r e e h u l l - k e e l c o m b i n a t i o n s .

I n t h i s T a b l e t h e c o n s i d e r e d wave s p e c t r a o f t h e i r r e g u l a r sea, used i n t h e c a l c u l a t i o n s , a r e c h a r a c t e r i s e d by a k i n d o f average wave h e i g h t , c a l l e d t h e s i g n i f i c a n t wave h e i g h t and an average p e r i o d o f t h e waves T i .

The c a l c u l a t i o n s a r e based on t h e a s s u m p t i o n t h a t t h e y a c h t i s s a i l i n g i n head seas w i t h a speed o f 8 k n o t s . For s h i p l e n g t h s o t h e r t h a n t h e 62' l e n g t h o f t h e y a c h t under c o n s i d e r a t i o n i n t h i s s t u d y , t h i s speed must be m u l t i p l i e d w i t h t h e square r o o t o f t h e new w a t e r l i n e l e n g t h d e v i d e d by 62, i . e . V3O/62' f o r a 30' f e e t y a c h t .

T a b l e 1

Added r e s i s t a n c e i n waves kN

Hi/3 deep d r a f t Wing 1 Wing 2 m sec k e e l 0.5 4.0 0.37 0.40 0.44 1.0 4.5 1.04 1.15 1.24 1.5 4.9 1.77 1.97 2.14 2.0 5.3 2.46 2.68 2.92 2.5 5.8 2.72 3.04 3.30

From t h e T a b l e 1 i t i s o b v i o u s t h a t t h e added r e s i s t a n c e i n waves depends s t r o n g l y on t h e s i g n i f i c a n t wave h e i g h t and t h e average wave p e r i o d o f t h e sea. The added r e s i s t a n c e i n waves o f t h e w i n g l e t k e e l s , i s l a r g e r t h a n t h a t o f t h e deep d r a f t k e e l .

From t h e r e s u l t s o f t h e t o w i n g t a n k t e s t s w i t h t h e c o n s i d e r e d model i t i s known t h a t t h e r e s i s t a n c e o f t h e y a c h t i n a c l o s e -h a u l e d s i t u a t i o n , i n c l u d i n g t -h e e f f e c t s o f -h e e l a n g l e and l e e w a y , i s 3.77 kN. By a p p l y i n g t h i s v a l u e f o r a l l o f t h e t h r e e k e e l - h u l l c o m b i n a t i o n s t h e s m a l l d i f f e r e n c e s i n s t i l l w a t e r r e s i s t a n c e be-tween t h e t h r e e d i f f e r e n t c o m b i n a t i o n s a r e n e g l e c t e d {t. 5%) . W i t h t h e s e d a t a t h e d i f f e r e n c e s i n speed between t h e d i f f e r e n t c o m b i n a t i o n s c o u l d be e s t i m a t e d ; t h i s y i e l d s t h e f o l l o w i n g r e s u l t : when t h e y a c h t w i t h t h e deep d r a f t k e e l w i l l a t t a i n a speed o f

8 k n o t s i n a sea w i t h a s i g n i f i c a n t wave h e i g h t o f 2.5 m e t e r s , t h e y a c h t w i t h t h e v j i n g l e t k e e l no 1 w i l l r e a c h a speed o f o n l y 7.9 k n o t s and t h e y a c h t w i t h w i n g l e t k e e l no 2 o n l y a speed o f 7.8 k n o t s . A s p e e d l o s s o f 0.1 and 0.2 k n o t s r e s p e c t i v e l y .

These speed d i f f e r e n c e s become l a r g e r i n t h e s i t i u a t i o n t h a t t h e y a c h t i s s a i l i n g w i t h l e s s f o r w a r d speed i n t h e same sea, because t h e s t i l l w a t e r r e s i s t a n c e decreases w h i l e t h e added r e s i s t a n c e due t o t h e waves remains a l m o s t unchanged f o r speeds between 6 and 8 k n o t s . I n t h e s e s i t u a t i o n s t h e l o s s o f speed o f t h e k e e l w i t h w i n g l e t s compared t o t h e " p l a i n " deep d r a f t k e e l s t r o n g l y i n

-c r e a s e s ; i . e . t o 0.2 and 0.4 k n o t s a t 7 k n o t s and t o 0.4 and 0.6 k n o t s a t 6 k n o t s r e s p e c t i v e l y .

The l a r g e r added r e s i s t a n c e i n waves o f t h e w i n g l e t k e e l i s m a i n l y due t o t h r e e d i f f e r e n t a s p e c t s .

The w i n g s produce i n d u c e d r e s i s t a n c e due t o t h e f a c t t h a t t h e y a c h t p e r f o r m s o s c i l l a t o r y heave and p i t c h m o t i o n s . I n t h e seaway t h e wings go up and down i n t h e s u r r o u n d i n g w a t e r t h e r e f o r e p r o d u c i n g l i f t w h i c h i s accompanied by t h e p r o d u c t i o n o f i n d u c e d r e s i s t a n c e . T h i s i n d u c e d r e s i s t a n c e i n c r e a s e s t h e o v e r a l l r e s i s t a n c e o f t h e h u l l - w i n g l e t k e e l c o m b i n a t i o n s when compared w i t h t h e " p l a i n " deep d r a f t k e e l .

Secondly as r e s u l t e d f r o m a n a l y s i n g t h e heave m o t i o n c h a r a c t e r i s -t i c s -t h e wings -t e n d -t o dampen -t h e heave m o -t i o n s -t o some e x -t e n -t . T h i s r e s u l t s i n an i n c r e a s e o f t h e r e l a t i v e v e r t i c a l m o t i o n be-tween t h e h u l l and t h e s u r r o u n d i n g w a t e r w h i c h t h e r e f o r e p r o d u c e s more r a d i a t e d damping waves. T h i s r e s u l t s a l s o i n an i n c r e a s e o f

F i n a l l y t h e r e i s a l s o a p o s s i b l e p o s i t i v e e f f e c t o f t h e w i n g l e t s on t h e r e s i s t a n c e o w i n g t o t h e phenomena t h a t an o s c i l l a t i n g w i n g

(due t o t h e m o t i o n s o f t h e y a c h t ) i n an o s c i l l a t i n g f l u i d (due t o the o r b i t a l v e l o c i t y o f t h e w a t e r p a r t i c l e s i n t h e waves) can p r o -duce a p o s i t i v e t h r u s t dependent on, among o t h e r s , t h e phase be-tween t h e two o s c i l l a t i n g m o t i o n s .

The r e s u l t i n g added r e s i s t a n c e i n waves such as p r e s e n t e d i n f i g u r e 5 i s t h e sum o f t h e s e t h r e e combined e f f e c t s .

I t may be c o n c l u d e d t h a t t h e o v e r a l l e f f e c t o f w i n g l e t s on t h e added r e s i s t a n c e i n waves has n o t been b e n i f i c i a l i n t h e two cases w h i c h have been i n v e s t i g a t e d .

An o t h e r a s p e c t o f t h e i n c r e a s e i n damping i s t h e r e s u l t i n g change i n t h e dynamic p r o p e r t i e s o f t h e y a c h t , i n p a r t i c u l a r t h e v e r t i c a l m o t i o n s i n waves.

To i n v e s t i g a t e t h e s e a s e r i e s o f so c a l l e d f o r c e d o s c i l l a t i o n t e s t s have been c a r r i e d o u t i n t h e t o w i n g t a n k . I n t h e s e t e s t s t h e model i s c o n n e c t e d t o a P l a n a r M o t i o n Mechanism w h i c h f o r c e s t h e y a c h t t o p e r f o r m harmonic o s c i l l a t o r y m o t i o n s o f d i f f e r e n t f r e q u e n c i e s and a m p l i t u d e s . The model has been f o r c e d t o o s c i l l a t e b o t h i n t h e heave

and i n t h e p i t c h mode.

From t h e r e s u l t s o f t h e s e t e s t s i t appeared t h a t w i n g l e t s m a i n l y i n f l u e n c e t h e dynamic p r o p e r t i e s i n t h e heave mode: t h e damping i n c r e a s e s as does t h e mass o f t h e w a t e r w h i c h i s f o r c e d by t h e y a c h t t o f o l l o w i t s m o t i o n (added mass).

Thereby t h e t o t a l v e r t i c a l mass o f t h e y a c h t i s i n c r e a s e d and com-b i n e d w i t h t h e e n l a r g e d damping t h i s may r e s u l t i n t h e f e e l i n g on board o f t h e y a c h t as i f i t were l a r g e r t h a n t h e a c t u a l s i z e , w h i c h seems t o be t h e e x p e r i e n c e o f p e o p l e who have been s a i l i n g on

i ( F i g u r e 1. R e g u l a r waves. X wave l e n g t h , F i g u r e 1. . — G wave a m o l i t u d e a " • L

X

— wave h e i g h t >v wave p r o f i l e , ^ / ^ d i r e c t i o n o f p r o p a g a t i o n heave m o t i o n p i t c h m o t i o n v e r t i c a l up and down m o t i o n o f t h e y a c h t . Z = a m p l i t u d e o f m o t i o n a. r o t a t i o n o f t h e y a c h t around an a x i s t h r o u g h t h e c e n t r e o f g r a v i t y . 6 - a m p l i t u d e o f p i t c h a n g l e

v/lng k e e l I I ^- - ° -<

A Hum of many simple siiio w a v e s makes a sea.

By a d d i n g a l a r g e number o f r e g u l a r s i n u s o i d a l waves each w i t h i t s own wave l e n g t h and a m p l i t u d e and comming f r o m d i f f e r e n t d i r e c t i o n s t h e p i c t u r e o f t h e r e a l sea a r i s e s as we know i t f r o m o u r v i s u a l o b s e r v a t i o n s . I n v e r s e l y we can s p l i t up t h e i r r e g u l a r sea i n a l t h e s e d i f f e r e n t components. I f t h e r e a c t i o n o f t h e s h i p on a l l t h e s e p a r a t e comp o n e n t s i s known t h e n t h e t o t a l r e a c t i o n o f t h e s h i comp on t h e i r r e -g u l a r sea i s t h e sum o f a l l t h e s e s e p a r a t e r e a c t i o n s . T h i s i s known as t h e l i n e a r s u p e r p o s i t i o n t e c h n i q u e . I t t h e r e f o r e i s s u f f i c i e n t t o measure t h e r e a c t i o n o f t h e s h i p on r e g u l a r waves

O 0.5 1./X ^ 1.0 1.5 wave l e n g t h 30m I5ni lOm

F i g u r e 4a I n t h i s f i g u r e t h e v e r t i c a l m o t i o n o f t h e y a c h t f o r each o f t h e t h r e e k e e l s (heave m o t i o n ) i s p r e s e n t e d f o r d i f f e r e n t l e n g t h s o f t h e s i n u s o i d a l waves when t h e y a c h t i s a d v a n c i n g a t 8 k n o t s . On t h e h o r i z o n t a l a x i s t h e l e n g t h o f t h e s h i p d e v i d e d by t h e wave l e n g t h i s p r e s e n t e d as w e l l as t h e a c t u a l wave l e n g t h f o r t h e s h i p under c o n s i d e r a t i o n . On t h e v e r t i c a l a x i s t h e a m p l i t u d e o f t h e r e s u l t i n g heave m o t i o n d e v i d e d by t h e wave h e i g h t i s p r e -s e n t e d . Being n o n d i m e n s i o n a l i n t h i s way t h e f i g u r e i s a p p l i c a b l e t o y a c h t s o f d i f f e r e n t s i z e s . From t h e f i g u r e i t may be c o n c l u d e d t h a t i n v e r y l o n g waves t h e y a c h t f o l l o w s t h e waves, i . e . za/^a e q u a l s 1 , and f o r v e r y s h o r t waves t h e y a c h t does n o t respond t o t h e waves, i . e . ^ ^ / L a goes t o z e r o . I n between t h o s e s i t u a t i o n s t h e y a c h t s w i t h t h e d i f f e r e n t k e e l s respond i n c o r r e s p o n d e n c e w i t h t h e l i n e

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From t h e f i g u r e i t i s o b v i o u s t h a t t h e heave m o t i o n i s somewhat i n f l u e n c e d by t h e w i n g l e t s . The a m p l i t u d e o f t h e heave m o t i o n s o f t h e y a c h t w i t h t h e w i n g l e t k e e l s i s s m a l l e r i n t h e wave l e n g t h range f o r m 1.0 t o 2.0 t i m e s t h e s h i p l e n g t h .

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wave 0.5 L/A. 1.0 l e n g t h 30m I5m 1.5 lOm f i g u r e 4b I n t h i s f i g u r e t h e r o t a t i o n a m p l i t u d e o f t h e y a c h t ( p i t c h ) , de-v i d e d by t h e wade-ve h e i g h t and some constants,, i s p r e s e n t e d f o r d i f f e r e n t wave l e n g t h s o f t h e r e g u l a r s i n u s o i d a l waves, measured w i t h a c o n s t a n t f o r w a r d speed o f 8 k n o t s i n head waves.

The p i t c h m o t i o n a m p l i t u d e d e c r e a s e s t o z e r o when s a i l i n g i n v e r y l o n g o r v e r y s h o r t waves. I n t h e wave l e n g t h r a n g e o f 1.0 t o 2.0 t i m e s t h e l e n g t h o f t h e y a c h t t h e p i t c h m o t i o n i s q u i t e c o n s i d e -r a b l e . As may be o b s e r v e d f r o m t h e f i g u r e t h e d i f f e r e n c e s between t h e t h r e e d i f f e r e n t h u l l - k e e l c o m b i n a t i o n s a r e v e r y s m a l l . I t may be c o n c l u d e d t h a t t h e p i t c h m o t i o n i s n o t a f f e c t e d by t h e a d d i t i o n o f w i n g l e t s on t h e k e e l .

in > -P O 4-> 0 :^ 0) Ü ai -P •H U) 0) i-l 0) fO F i g u r e 5 8 kn deep d r a f t k e e l wing k e e l I w i n g k e e l I I 0 0.5 L/A wave l e n g t h 30m

The added r e s i s t a n c e o f t h e y a c h t when s a i l i n g w i t h a c o n s t a n t speed o f 8 k n o t s i n r e g u l a r waves i s p r e s e n t e d i n t h i s f i g u r e , f o r d i f f e r e n t wave l e n g t h s . When s a i l i n g i n waves l a r g e r t h a n 2.5 t i m e s t h e s h i p l e n g t h t h i s added r e s i s t a n c e i s m i n i m a l . W i t h d e c r e a s i n g wave l e n g t h t h e added r e s i s t a n c e i n c r e a s e s w i t h a peak v a l u e a t r o u n d and about a wave o f 1.5 t i m e s t h e s h i p l e n g t h . The p r e s e n t a t i o n o f t h e added r e s i s t a n c e i s made n o n d i m e n s i o n a l by d e v i d i n g i t by t h e wave a m p l i t u d e squared and some c o n s t a n t s , so t h e r e s u l t s a r e a p p l i c a b l e t o s i m i l a r y a c h t forms o f o t h e r s i z e s as w e l l . From t h e f i g u r e t h e h i g h e r added r e s i s t a n c e o f t h e w i n g l e t k e e l s i s o b v i o u s i n p a r t i c u l a r f o r t h e s h o r t e r waves. The r e s i s t a n c e i n -c r e a s e s w i t h t h e s i z e o f t h e w i n g l e t s . S i n c e t h e s e s h o r t waves a r e a l w a y s p r e s e n t i n t h e s p e c t r u m o f a wind g e n e r a t e d sea, t h e r e s i s t a n c e o f t h e h u l l w i t h t h e k e e l w i t h w i n g l e t s can be c o n s i d e r a b l y h i g h e r t h a n f o r t h e " p l a i n " deep k e e l ,