Report No. 3^+6
LABORATORIUM VOOR
SCHEEPSBOUWKUNDE
T E C H N I S C H E H O G E S C H O O L DELFT
MEASURED AND CALCULATED SIDE EORCE OE A TEMPEST MODEL ; PERFORMANCE PREDICTION OE THE SHIP
by
G. Moeyes
C o n t e n t s
1 . I n t r o d u c t i o n "I
2 . E x p e r i m e n t s 2
2 . 1 . E x p e r i m e n t a l s e t - u p 2
2 . 2 . R e s u l t s 2
3 . C a l c u l a t i o n o f s i d e f o r c e , yaw moment and i n d u c e d r e s i s t a n c e h
k. F u l l s c a l e p e r f o r m a n c e T h.^. Speed downwind T h.2. P e r f o r m a n c e t o w i n d w a r d T 5 . References 9 T a b l e s F i g u r e s
1, I n t r o d u c t i o n
Upon r e q u e s t o f Dr. A d r i a n M i l l w a r d ( u n i v e r s i t y o f L i v e r p o o l , U.K.) t h e s i d e f o r c e , r e s i s t a n c e , yaw and h e e l moment o f a 1 m. w a t e r l i n e l e n g t h model o f t h e Tempest s a i l i n g b o a t have been measured i n t h e t o w i n g t a n k n r . 2
( 2 . 8 m w i d e , 1 . 2 5 m deep) o f t h e S h i p b u i l d i n g L a b o r a t o r y , U n i v e r s i t y o f T e c h n o l o g y , D e l f t .
The r e s u l t s s h o u l d be compared w i t h measurements o f t h e same q u a n t i t i e s i n an open-water c h a n n e l a t L i v e r p o o l t o i n v e s t i g a t e c o n f i n e d w a t e r i n f l u e n c e s . The a u t h o r has used t h e e x p e r i m e n t a l d a t a t o compare them w i t h c a l c u l a t e d v a l u e s and t o p r e d i c t t h e downwind and w i n d w a r d p e r f o r m a n c e o f t h e t r u e - s c a l e y a c h t .
2 . E x p e r i m e n t s
2 . 1 . E x p e r i m e n t a l s e t - u p
The model, w h i c h 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 I and f i g . 1 , has undergone two s e p e r a t e s e r i e s o f t e s t s .
I n t h e f i r s t one i t was r e s t r a i n e d i n h e e l and s u r g e , w h i l e d r i f t a n g l e s o f 0 ° , 2 ° , h° or 6 ° were p r e s c r i b e d . Because y a c h t s o f t h e Tempest c l a s s , can be k e p t u p r i g h t i n l i g h t and moderate winds by t h e crew i n t h e t r a p e z e i t was c o n s i d e r e d s u f f i c i e n t t o r e s t r i c t t h e h e e l a n g l e t o 0 ° ,
I n t w o p o i n t s , 0 . 6 m a p a r t i n l e n g t h , s i d e f o r c e s and h e e l moments ( w i t h r e s p e c t t o an a x i s 0 . 3 8 6 m above t h e w a t e r l i n e ) were measured w i t h s t r a i n gauge dynamometers. The yaw moments were o b t a i n e d by s u b t r a c t i n g t h e s i d e f o r c e s on f o r e and a f t dynamometer.
I n t h e second t e s t s e r i e s a l l (heavj) dynamometers were o m i t t e d and t h e model was towed by a r o p e c o n n e c t e d w i t h a dynamometer on t h e c a r r i a g e t o measure t h e r e s i s t a n c e . As t u r b u l e n c e s t i m u l a t o r s sand s t r i p s were f i t t e d v e r t i c a l on two p o s i t i o n s o f t h e f o r e s h i p and p a r a l l e l t o t h e l e a d i n g
edges o f k e e l and r u d d e r . A l l o t h e r c o n d i t i o n s were t h e same. The model speeds were 0 . 5 , 0 . 7 5 , 1 . 0 , 1 . 2 5 , 1 - 5 , 1 - 7 5 and 2 . 0 m/sec, w h i c h i s up t o about 1 0
k n o t s f u l l s c a l e .
2 . 2 . R e s u l t s
The measured s i d e f o r c e and h e e l i n g moment a r e g i v e n i n f i g u r e s 2 and 3 as a, f u n c t i o n o f d r i f t a n g l e . Because t h e p r e l i m i n a r y r e s u l t s showed t h e model n o t b e i n g l i n e d o u t c o r r e c t l y , t h e v a l u e s o f t h e d r i f t a n g l e i n f i g . 2 and 3
have been c o r r e c t e d .
The t o t a l s i d e f o r c e and t h e h e e l i n g moment appear t o be a l i n e a r f u n c t i o n o f t h e d r i f t a n g l e as c o u l d be e x p e c t e d owing t o t h e d o m i n a n t w i n g c h a r a c t e r i s t i c s o f k e e l and r u d d e r . A l s o a c c o r d i n g t o w i n g t h e o r y i t can be v / r i t t e n : F = y ( 2 . 2 . 1 ) M = C 2 3 ( 2 . 2 . 2 ) M V X m x 2
-and : \ - ( 2 . 2 . 3 ) z where : F = t o t a l s i d e f o r c e y M = h e e l i n g moment M = y a w i n g moment V = model speed m = d r i f t a n g l e
and C^^ have t e e n c a l c u l a t e d d i r e c t l y f r o m t h e diagrams i n f i g. 2 and 3
a n S a r e shown i n f i g u r e k. Because t h e measured M had v e r y s m a l l , and
1 2
t h e r e f o r e i n a c c u r a t e v a l u e s , t h e c o e f f i c i e n t C^^ ( f i g . h) has been o b t a i n e d f r o m t h e f a i r e d v a l u e s o f s i d e f o r c e f o r e and a f t .
The v e r y s l i g h t speed dependency o f t h e s i d e f o r c e c o e f f i c i e n t must be due t o t h e wave making i n f l u e n c e s o f t h e h u l l . I can be u n d e r s t o o d t h a t t h e s e i n f l u e n c e s have a g r e a t e r e f f e c t upon t h e c e n t r e o f e f f o r t o f t h e s i d e f o r c e , w h i c h i s d e m o n s t r a t e d by t h e speed dependency o f C^^^ and C^^'' i n f i g . k.
The c e n t r e o f e f f o r t w i t h r e s p e c t t o d r a u g h t and l e n g t h as a f u n c t i o n o f speed i s shown i n f i g . 5
The measured r e s i s t a n c e a t c e r t a i n d r i f t a n g l e s i s g i v e n i n f i g . 6 as a f u n c t i o n o f speed. The r e s i s t a n c e w i t h zero d r i f t a n g l e i s o b t a i n e d by f a i r i n g and 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 v e r s u s d r i f t a n g l e c u r v e s .
I t can be seen t h a t t h e model s t a r t s p l a n i n g a t a speed o f about 1 , 5 m/sec, w h i c h i s about 7 k n o t s f u l l s c a l e . P r o b a b l y t h e s e f e a t u r e s a r e q u i t e d i f f e r e n t i f t h e t r i m i s changed t y s h i f t i n g t h e crew i n t h e l o n g i t u d i n a l d i r e c t i o n . The s h i p r e s i s t a n c e , g i v e n i n t a b l e I I , has been c a l c u l a t e d w i t h t h e ITTC e x t r a p o l a t i o n method, t a k i n g i n t o a c c o u n t t h e d i f f e r e n t Reynolds numbers o f h u l l , k e e l and rudder.No c o r r e c t i o n i s a p p l i e d f o r t h e t u r b u l e n c e s t i m u l a t o r s . The r e s i s t a n c e i n kg p e r t o n h u l l d i s p l a c e m e n t i s compared i n t a b l e I I I w i t h such v a l u e s o f two s m a l l s e a g o i n g k e e l y a c h t s o f t h e d i s p l a c e m e n t t y p e , t h e S p i r i t 2 8 5 ] and a h a l f t o n n e r [ 6 ] .
I t i s a p p a r e n t t h a t t h e l i g h t Tempest g i v e s much h i g h e r v a l u e s , a l s o because i t s b r e a d t h t o d r a u g h t r a t i o and i t s w e t t e d a r e a t o d i s p l a c e m e n t r a t i o a r e f a r f r o m o p t i m a l f r o m a r e s i s t a n c e p o i n t o f v i e w .
-3 . C a l c u l a t i o n o f s i d e f o r c e , yaw moments and i n d u c e d r e s i s t a n c e
To p r e d i c t t h e s i d e f o r c e and yaw moment t h e method proposed hy G e r r i t s m a i n [ l ] f o r y a c h t s w i t h a f i n k e e l and r u d d e r c o n f i g u r a t i o n i s used. T h i s assumes t h e s i d e f o r c e g e n e r a t e d b y t h e h u l l t o be r e p r e s e n t e d by a v i r t u a l e x t e n s i o n o f k e e l and r u d d e r t o t h e s t i l l w a t e r l i n e ( f i g . 8 ) . Because t h e l i f t c o e f f i c i e n t a t s m a l l a n g l e s o f i n c i d e n c e i s a l i n e a r f u n c t i o n o f t h e d r i f t a n e l e , t h e s i d e f o r c e can be w r i t t e n as : ac y w m K \ 3 cy, / K R \ 8 a / SW
The yavj- moment i s :
2 r / ^ ^T \
= ^P..,.v_^ .1 LA, ~ 1 . X, + LA^ x^.C,
( 3 . 1 )
V - V " M s ^ "K ^ "^R s ^ ^ . ^ p - ^ s w r ^ ( 3 . 2 ;
where : = mass d e n s i t y o f waiter
LA = l a t e r a l a r e a o f extended k e e l o r r u d d e r 9 C L = s l o p e o f l i f t c o e f f i c i e n t v e r s u s a n g l e o f a t t a c k c u r v e 9a X - l o n g i t u d i n a l d i s t a n c e o f c e n t r e o f p r e s s u r e The s u f f i x K o r R denotes t o t h e k e e l o r r u d d e r r e s p e c t i v e l y . As t h e c e n t r e o f p r e s s u r e i s chooser a p o i n t a t t h e q u a r t e r - c h o r d l i n e o f k e e l o r r u d d e r a t a d i s t a n c e o f 0 . ^ 2 t i m e s t h e extended span under t h e w a t e r l i n e . The h e i g h t a r i s e s f r o m an e l l i p t i c a l l i f t d i s t r i b u t i o n . The c o e f f i c i e n t C i s a p p l i e d as a c o r r e c t i o n o f t h e a n g l e o f a t t a c k o f t h e bW r u d d e r . Due t o t h e v e l o c i t i e s i n d u c e d by t h e k e e l , t h e " s i d e - w a s h " , t h i s a n g l e i s n o t e q u a l t o t h e d r i f t a n g l e . A p p r o x i m a t e l y i s : C = 1 - - ' ^ ^ '^SW ^ TT.AR where : AR^ = e f f e c t i v e a s p e c t r a t i o . For t h e c a l c u l a t i o n o f t h e l i f t c u r v e s l o p e d i f f e r e n t t h e o r e t i c a l o r semi-e m p i r i c a l f o r m u l a semi-e a r semi-e a v a i l a b l semi-e . _ U _
One i s ; 3C, 8a 2 AR e (when t h e a n g l e o f a t t a c k i s e x p r e s s e d i n r a d i a n s ) . A n o t h e r e x p r e s s i o n , d e r i v e d f r o m t h e r e s u l t s o f numerous e x p e r i m e n t s [ 2_ w i t h w i n g s o f v a r i o u s s m a l l a s p e c t - r a t i o s , d i f f e r e n t t a p e r r a t i o s and sweep-back a n g l e s i s : 5 . 7 3 AR„ ( 3 . 5 ) ' 1 . 8+ c o s + h ' 1+ cos A
Some doubt may a r i s e c o n c e r n i n g t h e e x t e n s i o n o f t h e k e e l a t t h e b u l b s i d e i n o r d e r t o g i v e a good r e p r e s e n t a t i o n o f t h e l i f t c o n t r i b u t i o n o f t h e b u l b and i t s e f f e c t upon t h e l i f t d i s t r i b u t i o n o f t h e k e e l . However, t h e comnion - p r a c t i c e i n a e r o n a u t i c s i n c o n s i d e r i n g w i n g t a n k s o f p l a n e s i s f o l l o w e d by
I
v i r t u a l l y e x t e n d i n g t h e k e e l t o t h e b u l b a x i s ( f i g . B ) . The v a l u e s o f
and C ' f r o m ( 2 . 2 ,l ) and ( 2 . 2 . 3 ) have been c a l c u l a t e d a c c o r d i n g t o ( 3. l ) and
( 3 . 2 ) and a r e compared w i t h e x p e r i m e n t a l v a l u e s m t a b l e I V .
I t can be c o n c l u d e d t h a t G e r r i t s m a ' s method [ l ] g i v e s a good p r e d i c t i o n o f the s i d e f o r c e . The d i f f e r e n c e between t h e use o f (3. H ) and ( 3 . 5 ) i s so s m a l l t h a t one o f b o t h methods can n o t be f a v o u r e d i f s m a l l sweep-back a n g l e s a r e c o n c e r n e d .
The c a l c u l a t e d yaw moment c o e f f i c i e n t shows ( t a b l e I V ) t h a t t h e r e a l c e n t r e of e f f o r t o f t h e t o t a l s i d e f o r c e i s more f o r w a r d t h e n t h e p r e d i c t e d . The s i d e f o r c e o f t h e h u l l , i n t h e c a l c u l a t i o n r e p r e s e n t e d by a v i r t u a l e x t e n s i o n of k e e l and r u d d e r , i s i n r e a l i t y m o s t l y g e n e r a t e d b y t h e f o r e p a r t o f t h e h u l l because o f i t s wave-making p r o p e r t i e s . However, a d i f f e r e n c e o f 0 . 1 i n C^^ ' means a l o n g i t u d i n a l s h i f t o f t h e c e n t r e of e f f o r t o f about 0 . 0 2 9 m, w h i c h i s 3% o f t h e w a t e r l i n e l e n g t h . So t h e c a l c u l a t i o n g i v e s i n t h i s case a r e a s o n a b l e good p r e d i c t i o n o f t h e c e n t r e of e f f o r t ( s e e a l s o f i g . 5 f o r a c o m p a r i s o n o f c a l c u l a t i o n and e x p e r i m e n t ) . I t may be e x p e c t e d t h a t a deeper h u l l w i t h a l e s s t y p i c a l f i n k e e l and r u d d e r g e n e r a t e s a g r e a t e r p a r t o f t h e t o t a l s i d e f o r c e . T h e r e f o r e t h e yaw moment p r e d i c t i o n w i l l be w o r s e i n t h a t case.
-Though t h e r e p r e s e n t a t i o n o f t h e h u l l m e n t i o n e d above was n o t e x p e c t e d t o g i v e good p r e d i c t i o n s o f t h e t o t a l i n d u c e d r e s i s t a n c e , t h i s c a l c u l a t i o n was c a r r i e d o u t as a d e m o n s t r a t i o n . From w i n g t h e o r y t h e i n d u c e d r e s i s t a n c e i s known as : 2 D. = i p ^ ^ . v ^ .LA.C^_ ( 3 . 6 ) 1 w i t h : ^ 2 - ^ ( 3 . 7 ) ^ i 2 . 8 AR e S u b s t i t u t i n g ( 3 . 7 ) i n ( 3 . 6 ) f i n a l l y g i v e s ( 2 . 2 i | ) , where can be e x p r e s s e d i n t h e c o n t r i b u t i o n s o f k e e l and r u d d e r , analogous t o ( 3. l ) and ( 3 . 2 ) . The v a l u e o f t h e c a l c u l a t e d i n d u c e d r e s i s t a n c e i s about 2 5 ^ o f t h e e x p e r i m e n t a l v a l u e
(see f i g . 7 ) . T h i s c l e a r l y i l l u s t r a t e s t h a t t h e h u l l g i v e s by f a r t h e most i n d u c e d r e s i s t a n c e , due t o i t s v e r y l o w aspect r a t i o and t h e r e f o r e v e r y i n e f f e c t i v e l i f t g e n e r a t i n g c a p a c i t i e s .
-h. F u l l s c a l e p e r f o r m a n c e
^ . 1 . Speed dovnwind
W i t h t h e a s s u m p t i o n t h a t s a i l i n g downwind under s p i n n a k e r t h e s h i p has no d r i f t , h e e l o r r u d d e r a n g l e , t h e speed can he c a l c u l a t e d w i t h an e s t i m a t e d e f f e c t i v e s a i l a r e a and s a i l e f f i c i e n c y f r o m t h e r e s i s t a n c e c u r v e . U s i n g a
. . 2 s a i l r e s i s t a n c e c o e f f i c i e n t o f 1 . 2 and an a r e a o f 32 m g i v e s f i g . 9, where
t h e speed a t t a i n a b l e a t a c e r t a i n t r u e w i n d v e l o c i t y i s shown. The i n f l u e n c e o f t h e p l a n i n g c a p a b i l i t i e s o f t h e h u l l i s e v i d e n t i n winds s t r o n g e r t h a n about 8 . 5 m/sec,
U.2. Performance t o w i n d w a r d
S a i l i n g t o windward t h e boat is k e p t u p r i g h t b\rthe crew. At g i v e n v a l u e s o f t h e r i g h t i n g moment t h e e q u i v a l e n t s i d e f o r c e can be c a l c u l a t e d f r o m t h e measurements i f t h e h e i g h t o f t h e c e n t r e o f e f f o r t o f t h e s a i l f o r c e i s e s t i m a t e d ( e . g . w i t h t h e method proposed by t h e Stevens I n s t i t u t e |^3 , and coimnonly used i n t h e S h i p b u i l d i n g L a b o r a t o r y a t D e l f t h ) . Because moment and s i d e f o r c e a r e a t t a i n e d a t c e r t a i n v a l u e s o f s h i p speed and d r i f t a n g l e t h e r e s i s t a n c e i n t h a t c o n d i t i o n can be f o u n d . Thus, c o m b i n a t i o n s o f s h i p speed, s i d e f o r c e and r e s i s t a n c e can be formed and b y u s i n g t h e G-imcrack s a i l c o e f f i c i e n t s and an e s t i m a t e d e f f e c t i v e s a i l a r e a t h e optimum speed made good t o w i n d w a r d can be c a l c u l a t e d 3 and k . The p r o c e d u r e above has been f o l l o w e d s t a r t i n g f r o m 2 5 , 5 0 , 7 5 , 1 0 0 and 1 2 5 ^ o f t h e maximum r i g h t i n g moment, w h i c h has been e s t i m a t e d as 26h kgm w i t h t h e crew i n t h e t r a p e z e and t h e
helmsman h i k i n g , b o t h w e i g h i n g 8 0 k g .
The r e s u l t i n g optimum speed-made-good v e r s u s t r u e w i n d v e l o c i t y c u r v e ( f i g .1 0 )
has a more s t r a i g h t l i n e c h a r a c t e r t h e n t h e same, n e a r l y p a r a b o l i c , c u r v e s o f b i g g e r ocean y a c h t s , f o r t h e s a i l e f f i c i e n c y o f t h e l a t t e r one decreases w i t h i n c r e a s i n g w i n d speed because o f i t s h e e l i n g .
I t must be n o t e d t h a t t h e p r e d i c t e d speed-made-good i s n o t v e r y a c c u r a t e because i n some cases r e s i s t a n c e and s i d e f o r c e had t o be e x t r a p o l a t e d beyond t h e
speed range c o n s i d e r e d i n t h e e x p e r i m e n t s .
To compare t h e p e r f o r m a n c e o f t h e d i n g h y t y p e Tempest k e e l b o a t a t a w i n d speed o f 3. 5 m/sec w i t h t h e S p i r i t 2 8 [ 5 ] and t h e h a l f t o n n e r [ 6 ] t a b l e V has been c o m p i l e d .
-Though t h e way o f s a i l i n g a Tempest w i t h o u t h e e l c o n t r i b u t e s t o a b e t t e r s a i l e f f i c i e n c y t h e " d i m e n s i o n l e s s p e r f o r m a n c e " o f t h i s b o a t i s n o t b e t t e r t h e n t h e one o f i t s b i g g e r s i s t e r s o f t h e d i s p l a c e m e n t t y p e , A p r o b a b l e r e a s o n i s t h e , w i t h r e s p e c t t o t h e h u l l d i s p l a c e m e n t , h i g h r e s i s t a n c e o f t h e s h a l l o w d r a u g h t Tempest. However, i t may be u n d e r s t o o d t h a t s a i l i n g i n a r u n a t h i g h e r w i n d v e l o c i t i e s t h e Tempest i s b y f a r t h e b e t t e r , t h a n k s t o i t s p l a n i n g a b i l i t i e s .
-5. R e f e r e n c e s
1. 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 T h i r d AIAA Symposium on S a i l i n g , Redondo Beach, G a l . , 1 9 7 1 2 . L. F o l g e r W h i c k e r , D. Eng, L.E. E e h l n e r E r e e - s t r e a m c h a r a c t e r i s t i c s o f a f a m i l y o f l o w - a s p e c t - r a t i o , a l l movable c o n t r o l s u r f a c e s f o r a p p l i c a t i o n t o s h i p d e s i g n D a v i d T a y l o r Model B a s i n , r e p o r t 9 3 3 - dec. 1 9 5 8 3 . P.G. Spens S a i l b o a t t e s t t e c h n i q u e Stevens I n s t i t u t e o f T e c h n o l o g y , Hoboken, N.J. T e c h n i c a l Memorandum No. 1 2 U, o c t. 1 9 6 6 h. G. Moeyes
Het meten van de z e i l p r e s t a t i e s van j a c h t e n door m i d d e l van modelproeven S h i p b u i l d i n g L a b o r a t o r y , U n i v e r s i t y o f T e c h n o l o g y , D e l f t , r e p o r t no. 2 8 6 , dec. 1 9 7 0 5 . Z e i l p r e s t a t i e s v a j i de S p i r i t 2 8 S h i p b u i l d i n g L a b o r a t o r y , U n i v e r s i t y o f T e c h n o l o g y , D e l f t r e p o r t no. 3 1 5 , j u l y 1 9 7 1 6 . G. Moeyes De z e i l p r e s t a t i e s van een h a l f - t o n s - j a c h t S h i p b u i l d i n g L a b o r a t o r y , U n i v e r s i t y o f T e c h n o l o g y , D e l f t r e p o r t no. 2 9 1 , dec. 1 9 7 0 . 9
-TABLE I P a r t i c u l a r s o f s h i p and inodel Symbol D e s c r i p t i o n u n i t s s h i p model (1 ) ^OA l e n g t h over a l l m 6.TO 1 . 1 1 7 ^DWL l e n g t h on d e s i g n w a t e r l i n e m. 5 . 8 7 0 . 9 7 8 ^DWL b r e a d t h on d e s i g n w a t e r l i n e m 1.1+1+ O. 2 U O T H d r a u g h t o f h u l l o n l y m 0 . 2 2 0 . 0 3 6 T t o t a l d r a u g h t m 1 . 1 0 0 . 1 8 3 d i s p l a c e m e n t o f h u l l o n l y 1 0 0 0 k g 0 . 5 ^ 2 A t o t a l d i s p l a c e m e n t 1OOOkg 0 . 5 8 0 2 . 6 8 5 k g LCB^ l e n g t h c e n t r e o f buoancy o f h u l l o n l y , b e h i n d m i d d l e o f w a t e r l i n e l e n g t h m 0 . 0 9 S t o t a l w e t t e d a r e a m 2 5 . 9 0 LDW/A^ ' n l e n g t h - h u l l d i s p l a c e m e n t r a t i o 7 . 2 1 ^DWL/^H b r e a d t h - d r a u g h t r a t i o 6 . 5 5 ^^\/^DWL r e l a t i v e p o s i t o n c e n t r e o f buoancy % - 1 . 5 p r i s m a t i c c o e f f i c i e n t 0 . 5 7 S ^ b SA , ed e f f e c t i v e w i n d w a r d s a i l a r e a e f f e c t i v e downwind s a i l a r e a 2 m 2 m 1 8 . 7 ^ + 3 1 . 9 7 ( 1) model s c a l e 1 : 6
TABLE I I : S h i p r e s i s t a n c e V s m/s ec V s k n o t s ^T s kg n R /A k g / t o n 0 . 9 8 0 1 . 9 1 2. 1 0 . 1 2 6 3 . 9 1 . 2 2 5 2 . 3 8 3 . 6 0 . 1 5 7 6 , 6 1 . U 7 0 2 . 8 6 5 . 3 0 . 1 8 9 9 . 8 1 . 7 1 5 3.33 7 . ^ 0 . 2 2 0 1 3 . 7 1 . 9 6 0 3 . 8 1 1 0 . 0 0 , 2 5 2 1 8 . 5 2 . 2 0 5 I+ . 2 9 1 3 . 1 0 . 2 8 3 2 I + . 2 2 . 1 + i i 9 H. 7 6 1 7 . 2 0 . 3 1 5 31 . 7 2 . 6 9 I + 5 . 2 1 + 2 2 . 3 O.3I+6 1+1 .1 2 . 9 3 9 5 . 7 1 2 9 . 2 0 . 3 7 8 5 3 . 9 3 . 1 8 H 6 . 1 9 3 8 .U 0 , 1 + 0 9 7 0 . 8 3 . 1 + 2 9 6 . 6 7 ^ 9 . 5 0.1+1+1 9 1 . 3 3 . 6 7 1 + 7 . 1I+ 6 0 . 2 0 , 1 + 7 2 111.1 3 . 9 1 9 7 . 6 2 7 0 . 0 0 , 501+ 1 2 9 . 2 h.^6h 8 . 0 9 7 9 . 5 0 . 5 3 5 1 U 6 . 7 1+.1+09 8 . 5 7 8 9 . 2 0 . 5 6 7 1 6 ^ . 6 l+ . 6 5 ^ 9 . 0 5 9 8 . 8 0 . 5 9 8 1 8 2 . 3 I+ . 8 9 9 9 . 5 2 1 0 8 . 3 0 . 6 3 0 1 9 9 . 8
( 1 ) The Froude number has been based on an " e f f e c t i v e " l e n g t h f r o m f o r e p e r p e n d i c u l a r t o t r a n s o m o f 6. 17 m.
TABLE I I I Comparison o f s h i p r e s i s t a n c e p e r t o n h u l l d i s p l a c e m e n t . F ( 1 ) n R /A T ' H s k g / t o n Tempest S p i r i t 2 8 h a l f t o n n e r 0 . 1 5 5 . 7 2 2 . 1 6 1 . 9 9 0 . 2 0 1 0 . 7 0 l+.OO 3 . 6 0 0 . 2 5 1 8 . 0 8 6 . 3 6 6 . 0 1 0.30 2 7 . 8 6 9 . 8 2 9 . 5 8 0 . 3 5 1 + 2 . 8 0 1 5 . 7 0 1 5 . 2 3 0.1+0 6 5. 3 1 31 . 3 3 3 3 . 5 5
( 1 ) Froude numher has heen based upon an e f f e c t i v e l e n g t h f r o m f o r e p e r p e n d i c u l a r t o t r a n s o m o f 6 . 1 7 m. Tempest S p i r i t h a l f t o n n e r = 6 . 1 7 m = 6 . 9 0 m = 7 . 0 0 m
TABLE I V : C a l c u l a t e d and e x p e r i m e n t a l v a l u e s o f C„^ and C,,'' . y 2 c a l c u l a t e d ^ e x p e r i m e n t a l ( 1 ) ( 2 ) 3.51+ 3.1+0 3.1+0 a 3. 5 5 y c ^ - 0. 0 7 -0.10 0.03 a 0. 1 5 ( 1 ) ( 2 ) 3C L a c c o r d i n g t o ( 3 . 1 + ) w i t h "^L a c c o r d i n g t o ( 3 . 5 ) 3a w i t h 3a 30, y y V m M M
TABLE V :
Comparison o f s h i p p e r f o r m a n c e t o windward and downwind.
True w i n d speed Q u a n t i t y Tempest S p i r i t 2 8 h a l f t o n n e r 3 . 5 m/sec. 0.22k ' 0 . 1 7 6 i d ) 0 . 2 8 9 0 l+ . 8 ° 0 . 2 3 0 0 . 1 9 1 O.26I+ 9 . 6 ° 3 . 6 ° 0 . 2 2 2 0 . 1 7 6 0 . 2 3 5 8 . 7 ° 2 . 6 ° 3 . 5 m/sec. ^d'^^sLj^^L 0.22k ' 0 . 1 7 6 i d ) 0 . 2 8 9 0 l+ . 8 ° 0 . 2 3 0 0 . 1 9 1 O.26I+ 9 . 6 ° 3 . 6 ° 0 . 2 2 2 0 . 1 7 6 0 . 2 3 5 8 . 7 ° 2 . 6 ° 3 . 5 m/sec. V^'^^^DWL 0.22k ' 0 . 1 7 6 i d ) 0 . 2 8 9 0 l+ . 8 ° 0 . 2 3 0 0 . 1 9 1 O.26I+ 9 . 6 ° 3 . 6 ° 0 . 2 2 2 0 . 1 7 6 0 . 2 3 5 8 . 7 ° 2 . 6 ° 3 . 5 m/sec. ^s^'^S^DWL 0.22k ' 0 . 1 7 6 i d ) 0 . 2 8 9 0 l+ . 8 ° 0 . 2 3 0 0 . 1 9 1 O.26I+ 9 . 6 ° 3 . 6 ° 0 . 2 2 2 0 . 1 7 6 0 . 2 3 5 8 . 7 ° 2 . 6 ° 7 . 0 m/sec. O.UOl 0 . 3 9 6 0 . 3 8 0 7 . 0 m/sec. ^d^^sLp^^^ O.UOl 0 . 3 9 6 0 . 3 8 0 speed downwind speed-made-good s h i p speed on o p t i m a l c o u r s e t o w i n d w a r d h e e l a n g l e d r i f t a n g l e
