Windship Routeing

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 W I N D S H I P ROUTEING P r o f , i . r . J . A . S p a a n s R a p p o r t 6 5 4 - P ^ I 1 9 8 5 8 2 4 8 2 5

Delft University of Technology

Ship Hydromechanics Laboratory Mekelweg 2

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

W I N D T E C H ' 8 5 I N T E R N A T I O N A L SYMPOSIUM ON WINDSHIP TECHNOLOGY WINDSHIP ROUTEING b y P r o f . i r . J.A. S p a a n s D e l f t U n i v e r s i t y o f Technology Dept. M a r i n e Technology S e c t i o n H y d r o n a u t i c s D e l f t

1

-1. D e f i n i t i o n o f t h e p r o b l e m

Ship r o u t e i n g i s a p r o c e d u r e where an optimum t r a c k i s d e t e r m i n e d f o r a p a r t i c u l a r v e s s e l on a p a r t i c u l a r r u n , based on e x p e c t e d w e a t h e r , sea s t a t e and ocean c u r r e n t s .

O p t i m i s a t i o n can be p r e f o r m e d i n terms o f ( i ) minimum passage t i m e

( i i ) minimum f u e l c o n s u m p t i o n w i t h i n a s p e c i f i e d passage t i m e ( i i i ) minimum damage t o s h i p and/or ( d e c k ) c a r g o by t h e sea

( i v ) maximum c o m f o r t t o passengers

( v ) o r a c o m b i n a t i o n of t h e above c r i t e r i a .

For most commercial p u r p o s e s a c o m b i n a t i o n o f t h e c r i t e r i a ( i ) and ( i i i ) o r ( i i ) and ( i i i ) i s p r e f e r a b l e .

2. H i s t o r i c a l r e v i e w

For many c e n t u r i e s n a v i g a t o r s have g a t h e r e d c l i m a t o l o g i c a l and h y d r o g r a p h i c d a t a t o be used f o r l a t e r voyages.

The f i r s t p u b l i s h e d " S a i l i n g d i r e c t i o n s " now known, a r e t h e 1 3 t h c e n t u r y "Compasso de N a v i g a r e " f o r t h e M e d i t e r r a n e a n and t h e 15th c e n t u r y " A l Muhet" b i j I b n M a j i d f o r t h e N o r t h e r n I n d i a n Ocean and a d j a c e n t w a t e r s . T h i s famous A r a b i c n a v i g a t o r was Vasco da Gama's p i l o t on h i s f i r s t t r i p a c r o s s t h e

I n d i a n Ocean i n 1498.

P r i n c e Henry The N a v i g a t o r (1394-1460) promoted t h e s c i e n t i f i c approach t o n a v i g a t i o n and g a t h e r e d t h e b e s t c a r t o g r a p h e r s , a s t r o n o m e r s and o t h e r s c i e n t i s t s o f t h a t t i m e i n h i s n a u t i c a l c e n t r e i n Sagres P o r t u g a l . Shipmasters c o l l e c t e d i n f o r m a t i o n on t h e i r t r i p s and had a f t e r w a r d s t o r e p o r t i n Sagres where t h e i n f o r m a t i o n was g a t h e r e d and p r o c e s s e d i n t o c h a r t s and p i l o t b o o k s .

I n t h e 16th c e n t u r y t h e know-how o f t h e I b e r i a n s s p r e a d o v e r Europe, m a i n l y by t h e s t a n d a r d w o r k :

" A r t e de N a v i g a r " by Pedro de Medina V a l l a d o l i d 1545.

T h i s work was t r a n s l a t e d and p u b l i s h e d i n I t a l y , F r a n c e , H o l l a n d , E n g l a n d and Germany [ 1 ] . I n t h e 17th c e n t u r y D u t c h m a r i n e r s and c a r t o g r a p h e r s c o n t r i b u t e d c o n s i d e r -a b l y t o t h e -a r t o f n -a v i g -a t i o n , t h e i r c h -a r t s -and s -a i l i n g d i r e c t i o n s were o f w o r l d fame. Benjamin F r a n k l i n (1706-1790) p u b l i s h e d t h e f i r s t G u l f Stream c h a r t i n 1770. He g a t h e r e d h i s i n f o r m a t i o n m a i n l y f r o m t h e s h i p m a s t e r s o f "New E n g l a n d w h a l e r s " . The passage t i m e of t r a n s a t l a n t i c m a i l b o a t s was c o n s i d e r a b l y r e d u c e d by F r a n k l i n ' s c h a r t .

Matthew Maury (1806-1873) was t h e f o u n d e r o f M a r i t i m e m e t e o r o l o g y and

oceanography. He p u b l i s h e d t h e f i r s t " P i l o t C h a r t s " i n 1845, c o n t a i n i n g s e a s o n a l w i n d and c u r r e n t i n f o r m a t i o n . The average passage t i m e f r o m New Y o r k t o

C a l i f o r n i a r o u n d t h e H o r n f o r i n s t a n c e was reduced f r o m 183 days t o 139 days by u s i n g Maury's season c h a r t s {2'] .

A t t h e end o f t h e 1 9 t h c e n t u r y and i n t h e b e g i n n i n g o f t h e 2 0 t h c e n t u r y t h e "Deutsche Seewarte" p u b l i s h e d d e t a i l e d S a i l i n g d i r e c t i o n s ( S e g e l -handbücher) f o r s h i p m a s t e r s o f s a i l i n g v e s s e l s . F i g u r e 1 g i v e s t h e

average t i m e f r o n t s ( i s o c h r o n e s ) f o r s a i l i n g v e s s e l s o u t w a r d bound f r o m t h e L i z a r d as g i v e n i n [ 3 ] . The p e r f e c t voyage p l a n n i n g was c e r t a i n l y one o f t h e m a j o r reasons why t h e Germans, l i k e F e r d i n a n d L a e i s z ' f l y i n g P - l i n e , managed t o o p e r a t e s a i l i n g v e s s e l p r o f i t a b l y u n t i l f a r i n t o t h e 2 0 t h

c e n t u r y , when o t h e r s e a f a r i n g n a t i o n s had a l r e a d y t o t a l l y s w i t c h e d t o e n g i n e p r o p u l s i o n . (Only t h e F i n i s h s a i l i n g f l e e t o f G u s t a f E r i k s o n f r o m Mariehamn managed t o o p e r a t e square r i g g e d s a i l i n g v e s s e l s u n t i l t h e

second w o r l d w a r , w i t h cheap second-hand v e s s e l s , boyscrews and r e l a t i v e l y low wages). A h i s t o r i c a l l e s s o n i s t o be l e a r n t f r o m F e r d i n a n d L a e i s z : "The s h i p owner o p e r a t i n g w i t h o p t i m a l voyage p l a n n i n g w i l l s u r v i v e where o t h e r s have t o g i v e u p " I

3

-I n 1952 as f i r s t c o m m e r c i a l s h i p p i n g company t h e A m e r i c a n P r e s i d e n t L i n e s s t a r t e d t o recommend r o u t e s t o bypass t h e w o r s t storms f o r t h e L i n e ' s s h i p s o p e r a t i n g i n N o r t h P a c i f i c . A m e t e o r o l o g i s t was e n l i s t e d t o p r o v i d e f o r e c a s t s i n more d e t a i l t h a n government

p r e d i c t i o n s [ 4 ] . S i m u l t a n e o u s l y o t h e r s h i p p i n g companies were i n d e p e n d e n t -l y t h i n k i n g a -l o n g t h e same -l i n e s . By t h e end of t h e 1950's two A m e r i c a n c o n s u l t i n g f i r m s - Oceanroutes and P a c i f i c Weather A n a l y s i s , w h i c h l a t e r became Weather R o u t i n g I n c o r p o r a t e d - had been f o r m e d , l a t e r f o l l o w e d by Bendix M a r i n e Science S e r v i c e s . I n 1960 t h e Royal N e t h e r l a n d s M e t e o r o l o g i c a l I n s t i t u t e a t De B i l t was t h e f i r s t o f f i c e i n Europe t o p r o v i d e r o u t e i n g s e r v i c e s f o r t h e N o r t h A t l a n t i c , f o l l o w e d by B r a c k n e l i n t h e U.K. and t h e M a r i n e M e t e o r o l o g i c a l O f f i c e i n Hamburg. 3. C l i m a t o l o g i c a l r o u t e i n g Average v a l u e s o r f r e q u e n c y d i s t r i b u t i o n s o f w i n d s , sea s t a t e , i c e l i m i t s and ocean c u r r e n t s can be f o u n d i n c l i m a t o l o g i c a l a t l a s e s o r s p e c i a l season or m o n t h l y c h a r t s . The m a r i n e r can f i n d t h i s i n f o r m a t i o n i n c l u d i n g

recommended t r a c k s i n

- Ocean Passages f o r t h e W o r l d (B.A.) - P i l o t C h a r t s (USA)

- S a i l i n g d i r e c t i o n s and p i l o t books (B.A. and o t h e r s )

- C l i m a t o l o g i c a l a t l a s e s p u b l i s h e d by M e t e o r o l o g i c a l o r H y d r o g r a p h i c o f f i c e s .

"Ocean Passages" g i v e s recommended r o u t e s f o r s a i l i n g v e s s e l s , low powered v e s s e l s and powered v e s s e l s , see f i g u r e 2.

The " P i l o t C h a r t s " g i v e i n f o r m a t i o n o f ocean c u r r e n t s , i c e l i m i t s , w i n d d i s t r i b u t i o n and recommended t r a c k s , see f i g u r e 3. The B.A. P i l o t s g i v e a d d i t i o n a l i n f o r m a t i o n .

U s i n g c l i m a t o l o g i c a l d a t a f o r r o u t e i n g i s o n l y j u s t i f i e d i n areas where the w e a t h e r s i t u a t i o n i s s t a b l e l i k e t h e t r a d e w i n d and monsoon areas o u t s i d e t h e c y c l o n e season.

When c a r r i e d o u t on b o a r d , c l i m a t o l o g i c a l r o u t e i n g i s u s u a l l y done w i t h o u t r i g o r o u s computer programs. The s h i p m a s t e r a s s i s t e d by h i s n a v i g a t i n g o f f i c e r compares l o x o d r o m i c and g r e a t c i r c l e r o u t e s , t a k e s advantage o f c u r r e n t s , a v o i d s a r e a s w i t h a h i g h s t o r m f r e q u e n c y e s p e c i a l l y when

c o u n t e r w i n d s a r e e x p e c t e d , and a v o i d s areas w i t h low v i s i b i l i t y ; t h e i c e l i m i t s and t h e r e g u l a t i o n s of t h e l o a d - l i n e c o n v e n t i o n a r e t a k e n i n t o account when n e c e s s a r y . O f t e n t h e recommended r o u t e o r n e a r - b y one i s t a k e n as t h e b e s t as t h e s e r o u t e s a r e t h e r e s u l t of a g e - l o n g e x p e r i e n c e of m a r i n e r s . However, d i f f e r e n t t y p e s o f v e s s e l s i n o p e r a t i o n w i l l r e q u i r e d i f f e r e n t r o u t e s . For i n s t a n c e a f u l l y l o a d e d t a n k e r i s l e s s s u b j e c t t o damage by heavy seas t h a n a v e s s e l w i t h c a r g o on deck and c o n s e q u e n t l y the l a t t e r w i l l be r o u t e d on a t r a c k w i t h a l o w e r s t o r m f r e q u e n c y .

N a v i g a t o r s a r e t a u g h t a t n a u t i c a l c o l l e g e s how t o t a c k l e t h e s e p r o b l e m s . C a s e - s t u d i e s of d i f f e r e n t t y p e s of v e s s e l s and d i f f e r e n t r o u t e s a r e c a r r i e d out. I n t h e f o l l o w i n g s e c t i o n i t i s shown t h a t b e t t e r r e s u l t s can be

O O (t) [13 3 X> £u m cn fu OQ fü W O rt o

4. Weather r o u t e i n g i n g e n e r a l 4.1. G r a p h i c a l method

I n i t s i n f a n c y i n t h e 1950's t h e t a c t i c s o f w e a t h e r r o u t e i n g were o n l y aimed a t b y p a s s i n g s t o r m c e n t r e s o r t r o p i c a l s t o r m s t o reduce t h e damage t o s h i p and c a r g o .

I n 1957 R.W. James [ 5 ] i n t r o d u c e d a g r a p h i c method t o d e t e r m i n e a " l e a s t - t i m e - t r a c k " f o r an ocean passage. I n many r o u t e i n g o f f i c e s t h i s p r o c e d u r e i s s t i l l p r a c t i s e d . The s h i p ' s speed as f u n c t i o n o f t h e

s i g n i f i c a n t wave h e i g h t f o r f o u r d i f f e r e n t c o n d i t i o n s o f wave d i r e c t i o n s was used by James, as shown i n f i g u r e 4.

•0- S I G N I F I C A N T WAVE H E I G H T

F i g u r e 4. S h i p ' s speed as f u n c t i o n o f s e a s t a t e .

A t t h e R o y a l N e t h e r l a n d s M e t e o r o l o g i c a l I n s t i t u t e (KNMI) e m p i r i c a l d a t a a r e used t o p l o t t h e s h i p ' s speed i n a p o l a r d i a g r a m f o r d i f f e r e n t

7

-0°

180°

F i g u r e 5. P o l a r speed diagram.

The i n f l u e n c e of t h e s i g n i f i c a n t p e r i o d of s w e l l and sea on t h e s h i p ' s speed i s h a r d l y t a k e n i n t o a c c o u n t a t R o u t i n g O f f i c e s u n t i l now, a l t h o u g h t h e f u e l c o n s u m p t i o n i n t o n s p e r m i l e i s s i g n i f i c a n t l y h i g h e r i n a

s p e c i f i c i n t e r v a l o f wave p e r i o d s f o r a p a r t i c u l a r v e s s e l . F i g u r e 6 shows t h i s f o r a 23000 t o n s c o n t a i n e r v e s s e l a c c o r d i n g t o J o u r n e e [ 1 1 ] .

B e f o r e t h e computer t o o k o v e r , wave c h a r t s were hand-drawn u s i n g t h e i n f o r m a t i o n f r o m t h e w e a t h e r c h a r t s . The d i a g r a m o f f i g u r e 7 i s used by KNMI f o r t h i s p u r p o s e , g i v i n g t h e s i g n i f i c a n t wave h e i g h t and p e r i o d as f u n c t i o n o f w i n d speed, w i n d d u r a t i o n and w i n d f e t c h (= d i s t a n c e t o w i n d w a r d where t h e w i n d i s b u i l d i n g up t h e w a v e s ) .

^ s i g n i f i c a n t wave p e r i o d m seconds F i g u r e 6.

F i g u r e 7. S i g n i f i c a n t wave h e i g h t and p e r i o d as f u n c t i o n o f w i n d speed, w i n d d u r a t i o n and w i n d f e t c h .

-Nowadays, t h e enormous amounts of meteo d a t a a r e p r o c e s s e d by computers t o produce t h e a c t u a l and p r e d i c t e d w e a t h e r and wave c h a r t s . European M e t e o r o l o g i c a l o f f i c e s use a 6-day w e a t h e r p r e d i c t i o n f o r t h e N o r t h A t l a n t i c m a i n l y based on t h e d a t a f r o m t h e "European C e n t r e f o r Medium Range W e a t h e r f o r e c a s t s " i n Reading U.K. The wave c h a r t s a r e however m a n u a l l y c o r r e c t e d , on t h e b a s i s o f t h e wave i n f o r m a t i o n f r o m w e a t h e r r e p o r t s f r o m i n d i v i d u a l s h i p s , w h i c h r e p o r t s a r e t r a n s m i t t e d f r o m s e l e c t e d s h i p s w i t h 0600 h o u r s GMT i n t e r v a l . For t h e p r e d i c t i o n of t h e t r a c k t o be f o l l o w e d by a d e p r e s s i o n t h e 500 mb c h a r t s a r e used. The d i r e c t i o n o f a l i n e o f e q u a l a l t i t u d e o f t h e 500 mb p r e s s u r e l e v e l i s r o u g h l y f o l l o w e d by t h e c e n t r e o f a d e p r e s s i o n . I n f i g u r e 8 t h e a c t u a l and p r e d i c t e d 500 mb c h a r t s , t h e w e a t h e r c h a r t and t h e wave c h a r t f o r t h e a c t u a l s i t u a t i o n on 18 F e b r u a r y and f o r t h e s i t u a t i o n s

24 h, 48 h and 72 h t h e r e a f t e r a r e shown. I t can c l e a r l y be seen i n t h i s f i g u r e t h a t t h e a r e a w i t h t h e h i g h e s t waves does n o t c o i n c i d e w i t h t h e c e n t r e o f l o w e s t p r e s s u r e , b u t l i e s c o n s i d e r a b l y s o u t h - e a s t e r l y t o s o u t h e r l y o f f t h i s c e n t r e . The c h a r t s i n f i g u r e 8 f r o m t h e N e t h e r l a n d s M e t e o r o l o g i c a l o f f i c e show how a p a r t i c u l a r v e s s e l was r o u t e d o u t s i d e t h e a r e a o f h i g h e s t waves.

The g r a p h i c method o f d e t e r m i n i n g t h e l e a s t t i m e t r a c k t o t h e d e s t i n a t i o n i s shown i n f i g u r e 9. From t h e p o i n t o f d e p a r t u r e t h e d i s t a n c e c o v e r e d i n

12 h o u r s i s p l o t t e d i n a number o f d i r e c t i o n s . The e n v e l o p e o f t h e s e v e c t o r s i s t h e 12 h i s o c h o n e . The d i s t a n c e c o v e r e d i n 12 h o u r s i s d e t e r -m i n e d , t a k i n g i n t o a c c o u n t t h e s p e e d l o s s i n waves, see f i g u r e 4 and 5, and t h e wave c h a r t as g i v e n i n f i g u r e 8. From a number o f p o i n t s o f t h e

n

-12 h i s o c h r o n e a " l o c a l " 24 h i s o c h r o n e i s d e t e r m i n e d ; t h e e n v e l o p e o f t h e s e l o c a l i s o c h r o n e s i s t h e o v e r a l l 24 h i s o c h r o n e . As f a r as t h e w e a t h e r p r e d i c t i o n e x t e n d s t h i s p r o c e d u r e i s c o n t i n u e d as shown i n

f i g u r e 9.

From t h e d e s t i n a t i o n backwards a l i n e i s drawn p e r p e n d i c u l a r l y t o a l l i s o c h r o n e s . T h i s l i n e i s t a k e n as t h e " l e a s t t i m e t r a c k " . T h e o r e t i c a l l y t h i s i s n o t c o r r e c t ; i n each p o i n t o f t h e l e a s t t i m e t r a c k t h e p r o j e c t i o n of t h e d i s t a n c e t r a v e l l e d p e r u n i t o f t i m e on t h e p e r p e n d i c u l a r o f t h e i s o c h r o n e s h o u l d be m a x i m a l , as shown i n s e c t i o n 4.3. I n p r a c t i c e ,

however, t h i s manual method has p r o v e d t o be v e r y u s e f u l . Areas w i t h h i g h waves - e s p e c i a l l y head seas - a r e a v o i d e d because o f t h e i n h e r e n t speed

l o s s . The consequent advantage i s , t h a t l e s s damage t o s h i p and ( d e c k ) c a r g o w i l l be e x p e r i e n c e d , so s a f e t y and economy b e n e f i t s i m u l t a n e o u s l y . 4.2. P r a c t i c a l r e s u l t s Upon c o m p l e t i o n o f a r o u t e d voyage, r o u t e i n g o f f i c e s e v a l u a t e t h e recommendations g i v e n . W i t h t h e e x p e r i e n c e d w e a t h e r an e v a l u a t i o n r o u t e i s d e t e r m i n e d i n t h e same way as d e s c r i b e d i n s e c t i o n 4.1. I n t h e f o l l o w - u p r e p o r t w h i c h i s a l s o f o r w a r d e d t o t h e c l i e n t ,the t i m e p r o f i t s / l o s s e s o f t h e t r a c k f o l l o w e d i n r e g a r d t o t h e g r e a t c i r c l e t r a c k and t h e l o x o d r o m i c t r a c k a r e g i v e n and a l s o t h e t i m e l o s s o f t h e t r a c k f o l l o w e d i n r e g a r d t o t h e " e v a l u a t i o n t r a c k " i s p r o v i d e d .

I n f i g u r e 10 t h e e v a l u a t i o n c h a r t i s shown f o r a p a r t i c u l a r case. The t r a c k a c t u a l l y f o l l o w e d shows t o be v e r y i r r e g u l a r . The a c t u a l l e a s t - t i m e t r a c k i s n o t shown i n t h e f i g u r e , b u t l i e s somewhat more t o t h e s o u t h . The t i m e p r o f i t i n t h i s case o f a 14 day voyage was a b o u t 2 days compared t o t h e g r e a t c i r c l e t r a c k and 3 days compared t o t h e l o x o d r o m i c t r a c k .

Average p r o f i t s a r e g i v e n i n r e p o r t s o f r o u t e i n g o f f i c e s l i k e [ 6 ] , [ 7 ] , [ 8 ] and [ 9 ] .

I n [ 9 ] t h e average r e s u l t s o f t h e D u t c h M e t e o r o l o g i c a l o f f i c e o f 1971¬ 1981 a r e p u b l i s h e d . The average t i m e p r o f i t i s d i f f e r e n t f o r 15 s e v e r a l g e o g r a p h i c a l r o u t e s and v a r i e s between 1 h o u r and 10 h o u r s .

For p e o p l e who a r e s u s p i c i o u s o f r o u t e i n g o f f i c e s p u b l i s h i n g t h e i r own r e s u l t s , r e f e r e n c e [ 8 ] i s recommended w h i c h s t a t e s t h a t t h e r e s u l t s p u b l i s h e d by KNMI a r e even somewhat c o n s e r v a t i v e .

I n [ 4 ] a S h e l l spokesman c o n f i r m s an average t i m e p r o f i t o f 4 h o u r s on an A t l a n t i c c r o s s i n g , w h i c h e q u a l s about 10 t o n s o f f u e l o r about $5000.- p e r t r a n s i t .

The p r i c e o f a r o u t e i n g a d v i c e f o r t h e N o r t h A t l a n t i c v a r i e s ; i n t h e N e t h e r l a n d s t h e charge i s about $200.- p l u s t e l e g r a m expenses. I n v i e w o f t h e i n c r e a s e d f u e l c o s t s , more s h i p o p e r a t o r s a r e u s i n g t h e s e r v i c e s o f r o u t e i n g o f f i c e s ,

ENHOUTE TIMES PER SELECTED ROUTES DECEMBER 197 9 1)AV3 MOVM'i 1 3 O -jó.) 14 O i j ; . 13 0 3 1 3 13 0 3 U I J I t o 3b* 10 o 3*0 9 0 2 ' t B/iU rHAMC l«JCO TO NOJIMA SAHI

SFO 'lOJ l^/Ti SPEED IN CALM - 20 0

1 3 -SELECTED ROUTES F i g u r e I I B , I n r e f e r e n c e [ 1 0 ] an i n t e r e s t i n g case s t u d y i s m e n t i o n e d , Oceanroutes I n c . r o u t e i n g o f f i c e s i m u l a t e d t h e passage o f t h e n o r t h P a c i f i c f r o m San F r a n c i s c o t o N o j i m a S a k i f o r t h e month of December f o r s e v e r a l y e a r s , where 8 d i f f e r e n t t r a c k s were compared, see f i g u r e 11 where t h e r e s u l t s f o r 1979 a r e shown. For each day d e p a r t u r e f r o m San F r a n c i s c o t h e e n r o u t e t i m e i s p l o t t e d v e r t i c a l l y f o r each of t h e 8 t r a c k s . D i f f e r e n c e s o f

about two and a h a l f days passage t i m e e x i s t on t h e 10th December and 2 1 s t o f December, b u t t h e c h o i c e o f t h e r o u t e i s r e v e r s e d i n b o t h cases I T h i s e x p e r i m e n t c l e a r l y p u t s a query a g a i n s t r o u t e i n g by P i l o t C h a r t s based s o l e l y on c l i m a t o l o g i c a l c o n s i d e r a t i o n s .

A p a r t f r o m t i m e / f u e l s a v i n g s , damage t o s h i p and c a r g o i s d i m i n i s h e d by a v o i d i n g h i g h ( h e a d ) s e a s . I n 1976 t h e Naval Weather S e r v i c e (USA) c o n t r a c t e d f o r a s t u d y c o v e r i n g 6 y e a r s of A t l a n t i c e x p e r i e n c e i n heavy w e a t h e r and i t s damage e f f e c t s . F i g u r e 12 summarizes t h e r e s u l t s . An a v e r a g e s h i p w i l l e x p e r i e n c e $1000.- per day damage t o s h i p and cargo when p r o c e e d i n g i n a s i g n i f i c a n t wave h e i g h t o f 6 m, whereas t h i s amounts t o $10,000.- p e r day f o r waves o f 8 m h e i g h t ; a d r a m a t i c increase.'

An e x p e r i m e n t c o n d u c t e d by Oceanroutes I n c . and m e n t i o n e d i n r e f e r e n c e [ 1 0 ] , was t h e a n a l y s i s o f t h e t r a n s m i t t e d w e a t h e r r e p o r t s o f J a n u a r y 1977 of 660 s h i p s e n r o u t e i n a t r a n s - P a c i f i c voyage o f w h i c h 39% were r o u t e d by a r o u t i n g o f f i c e . The f i g u r e 13 shows t h e r e s u l t , w h i c h i s a t f i r s t g l a n c e n o t v e r y d r a m a t i c . However t h e s t i n g i s i n t h e t a i l o f t h e d i s -t r i b u -t i o n , where i -t can be seen -t h a -t abou-t -t w i c e as many u n r o u -t e d s h i p s e n c o u n t e r s i g n i f i c a n t wave h e i g h t s o f more t h a n 6.5m t h a n r o u t e d s h i p s . The same graph i s made f o r s h i p s i n head seas i n f i g u r e 14 where t h e d i s t i n c t i o n between r o u t e d and u n r o u t e d s h i p s i s even c l e a r e r . On an average t h e sea h e i g h t was r e d u c e d by 14 p e r c e n t .

$ 100,000 i damage p e r day 10,000 tTT: 1 ,000 (1976) $ 100 30 I t (9,15) ra s i g n i f i c a n t w a v e h e i g h t F i g u r e 12.

O 5 10 15 20 25 30 (1,5) ( 3 , 0 ) ( 4 , 6 ) ( 6 , 1 ) ( 7 , 6 ) .(9,15) m

s i g n i f i c a n t wave h e i g h t (head seas)

17

-A n o t h e r n o t e w o r t h y r e s u l t i s m e n t i o n e d i n / l O / . -A Japanese a u t o m o b i l e s h i p p e r f o u n d t h a t a f t e r u s i n g r o u t e i n g recommendations f o r t r a n s - P a c i f i c voyages f r o m a r o u t e i n g o f f i c e , the average damage p e r a u t o m o b i l e s h i p p e d , dropped d r a m a t i c a l l y f r o m $ 2.95 t o $ 0.85 w h i c h i s a c o n s i d e r a b l e p r o f i t i n v i e w o f t h e 350,000 v e h i c l e s e x p o r t e d a n n u a l l y f r o m Japan t o t h e USA. 4.3. Computer methods

F i r s t o f a l l the p r e d i c t e d w e a t h e r d a t a are a v a i l a b l e i n d i g i t a l f o r m , as t h e p r e d i c t e d w e a t h e r c h a r t s a r e made by t h e computer. From t h e w e a t h e r c h a r t s , t h e a c t u a l and p r e d i c t e d wave c h a r t s a r e computed. A t t h e Royal N e t h e r l a n d s Weather I n s t i t u t e a computer program i s a v a i l a b l e t o produce

these wave c h a r t s f o r l i m i t e d g e o g r a p h i c a l a r e a s .

The second major i n p u t f o r the computer program i s t h e s h i p ' s speed i n sea c o n d i t i o n s w h i c h can g e n e r a l l y be d e s c r i b e d f o r a ( w i n d a s s i s t e d ) motor v e s s e l w i t h a g i v e n d r a u g h t , t r i m and h u l l c o n d i t i o n as V = f ( n , 1|J, H , T ,

0

, H , T ,

0

, V ,

0

) + S ( 1 ) s s s SW sw sw w w where: n = p r o p e l l e r r e v o l u t i o n s per m i n u t e lj; = v e s s e l h e a d i n g H = s i g n i f i c a n t wave h e i g h t o f sea s T = s i g n i f i c a n t p e r i o d o f sea s

0^ = average course o f sea waves H , T , 0 = p a r a m e t e r s f o r s w e l l sw sw sw V = w i n d speed w ^ 0 = w i n d d i r e c t i o n w c u r r e n t v e c t o r t V = speed o v e r t h e ground V = speed t h r o u g h t h e w a t e r

When m e t e o r o l o g i c a l and o c e a n o g r a p h i c a l d a t a a r e known as f u n c t i o n o f the p o s i t i o n and n i s c o n s t a n t , f o r m u l a ( 1 ) can be r e d u c e d t o

^7 = ? ( t , (j), X, ^)

where (j) = l a t i t u d e and A = l o n g i t u d e .

For a g i v e n s i t u a t i o n V (i|j) i s g i v e n by a speed p o l a r as shown i n f i g u r e 15, The speed p o l a r i n f i g u r e 15 a t r i g h t i s concave i n a g i v e n s e c t o r due t o an o b l i g a t o r y speed r e d u c t i o n when p r o c e e d i n g i n waves e n t e r i n g f r o m a b a f t t h e beam. By 'symmetric c r u i s i n g ' a h i g h e r average speed can be a t t a i n e d . I n a s t u d y by J.M.J. Journee o f D e l f t U n i v e r s i t y o f Technology / l l / , spon-s o r e d by t h e M i n i spon-s t r y o f Economic A f f a i r spon-s aspon-s p a r t o f a g e n e r a l 'energy s a v i n g ' p r o j e c t , m a t h e m a t i c a l models a r e g i v e n f o r t h e s h i p ' s speed and the f u e l c o n s u m p t i o n t a k i n g i n t o a c c o u n t t h e r e l e v a n t f a c t o r s .

To d e v e l o p a computer a l g o r i t h m , an o p t i m i s a t i o n c r i t e r i o n has t o be de-f i n e d . I n most programs t h e t r a n s i t t i m e i s m i n i m i z e d /12/, /13/, /14/ by c o m p u t i n g ((j). A, t ) f o r t h e voyage, k e e p i n g n c o n s t a n t . Only i n h i g h seas n w i l l be r e d u c e d t o a v o i d damage.

B a s i c a l l y two methods a r e i n use:

F i g u r e 15. Speed p o l a r s A s t a t e v e c t o r x ( t ) e r'^ and a c o n t r o l v e c t o r u ( t ) e R™ are d e f i n e d . The d i f f e r e n t i a l e q u a t i o n f o r x ( t ) i s g i v e n by X ( t ) = f ( x ( t ) , u ( t ) , t ) X ( 0 ) = X Q (3) X (T) = Xj f i n d X ( t ) and u ( t ) t o m i n i m i z e t h e o b j e c t f u n c t i o n a l T J = ƒ L ( x , u, t ) d t ( 4 ) 0

An a d j u n c t i v e v e c t o r p i s i n t r o d u c e d and when L (•) and f (•) a r e t w i c e c o n t i n u o u s l y d i f f e r e n t i a b l e f o r x, u and t , t h e p r o b l e m i s s o l v e d by s o l v i n g t h e s i m u l t a n e o u s e q u a t i o n s • X = f ( x , u, t ) p*" = L - p^ f (5) ^ X ^ X L - p*^ f = 0 u ^ u When t h e H a m i l t o n f u n c t i o n i s i n t r o d u c e d H = -L + p ' f ₍₆₎

19 -t h e s o l u -t i o n reads i = H P p = -H (7) H = 0 u I n t h e case o f minimum t i m e r o u t e i n g : T J = ƒ 1 d t 0 L = 1 H = -1 + p^ f = f ( x , ^, t ) (speed p o l a r ) X = p = -p f p^ f , = 0 X ( 0 ) = X Q X (T) = X j H ( X j , T) = 0 As J = p, and t h e i s o c h r o n e s as m e n t i o n e d i n s e c t i o n 4.1 a r e c o n t o u r s o f e q u a l J , t h e v e c t o r p i s t h e g r a d i e n t v e c t o r of J and i s p e r p e n d i c u l a r on a c o n t o u r l i n e . t t • A c c o r d i n g t o P o n t r y a g i n H = - l + p f = - l + p x has t o be m a x i m i z e d so t h e p r o j e c t i o n of t h e speed v e c t o r x on p has t o be m a x i m i z e d , as used i n s e c t i o n 4.1. I n f i g u r e 16 t h e t i m e f r o n t s f o r an A t l a n t i c t r a n s i t computed by t h e a l g o r i t h m o f B i j l s m a [ 1 3 ] are shown. When t h e r a t e o f decrease o f f u e l i s d e s c r i b e d by t h e e q u a t i o n X = f ( t , X, V, i,) (8)

f u n c t i o n s ijj ( t ) and v ( t ) have t o be d e t e r m i n e d m i n i m i z i n g T

J = ƒ f ( t , ^, X, V, i>) d t ( 9 )

0

I n [ 13] t h i s i s p o i n t e d o u t ; i t i s a s u b j e c t o f f u r t h e r r e s e a r c h a t KNMI.

( i i ) The method o f " f o r w a r d dynamic programming"

I n t h e ocean a r e a u n d e r c o n s i d e r a t i o n a s e r i e s of g r i d p o i n t s i s a p p o i n t e d e q u a l l y d i s t r i b u t e d " a l o n g t r a c k " and " c r o s s t r a c k " a l o n g t h e g r e a t c i r c l e r o u t e , see f i g u r e 17. From t h e s t a r t i n g p o i n t t h e e n r o u t e t i m e t o t h e g r i d p o i n t s on t h e f i r s t c r o s s -t r a c k l i n e i s c a l c u l a -t e d w i -t h -t h e e x p e c -t e d w e a -t h e r and s h i p ' s p a r a m e t e r s .

C o m p u t e r piockiccd by means o f an incremental plotter using wave i n f o r m a t i o n over the period 17 ,(amiary-23 January 1970, fictitious ship's data a n d a 12-hour time step. The least-time track is indicated by the dashed line.

21

From each g r i d p o i n t on t h e f i r s t l i n e t h i s same p r o c e d u r e i s c a r r i e d o u t g i v i n g d i f f e r e n t times o f a r r i v a l a t t h e second c r o s s - t r a c k p o i n t s f o r d i f f e r e n t r o u t e s . The e a r l i e s t t i m e s o f a r r i v a l and r e s p e c t i v e r o u t e s a r e s t o r e d , o t h e r s a r e s k i p p e d . T h i s p r o c e d u r e i s c o n t i n u e d u n t i l t h e d e s t i n a t i o n i s reached. The r o u t e b e l o n g i n g t o the e a r l i e s t a r r i v a l t i m e i s t h e ' l e a s t - t i m e - t r a c k ' . I n f i g u r e 18 r o u t e s d e t e r m i n e d by t h i s method by Mayes /16/ a r e shown. The method was used by Mayes

i n s i m u l a t i o n programs o f s a i l i n g v e s s e l r o u t e i n g s .

The second method i s s i m p l e r , b u t a d i s a d v a n t a g e i s t h a t i n t e r p o l a t i o n i n t i m e f o r the meteo d a t a i s n e c e s s a r y t o compute the passage t i m e s between the g r i d p o i n t s , as m e t e o r o l o g i c a l d a t a are a v a i l a b l e f o r the s t a n d a r d 12 h GMT i n t e r v a l s .

I n / l l / a system i s d e s c r i b e d t o p r e s e n t t o the s h i p m a s t e r o f a motor v e s s e l c o n t i n u o u s i n f o r m a t i o n a b o u t t h e p e r f o r m a n c e o f t h e s h i p , t o f a c e h i m d i r e c t l y w i t h h i s f u e l management. Average f u e l c o n s u m p t i o n per h o u r , per m i l e and per kWh t o g e t h e r w i t h speed, power and rpm are p r i n t e d a f t e r each s e l e c t e d p e r i o d , f o r i n s t a n c e 20 m i n u t e s . A l s o i n f o r m a t i o n i s g i v e n a b o u t t h e e f f e c t on t h e s h i p ' s p e r f o r m a n c e by t h e degree o f f o u l i n g o f t h e s h i p ' s h u l l . An a l g o r i t h m i s d e v e l o p e d w h i c h s i m u l a t e s t h e s h i p ' s p e r -formance depending on t h e s h i p ' s h e a d i n g , the a c t u a l w e a t h e r and t h e w e a t h e r f o r e c a s t s . T h i s a l g o r i t h m i s used t o d e t e r m i n e t h e optimum speed

t o a r r i v e j u s t i n t i m e a t the d e s t i n a t i o n o r t o c a l c u l a t e t h e e x p e c t e d t i m e o f a r r i v a l a t a f i x e d e n g i n e s e t t i n g , rpm, e t c . The t o t a l d e v i c e i n -c l u d i n g the -computer was -c a l l e d 'energy -c l o -c k ' and i s -c o m m e r -c i a l l y f o r s a l e as a PERSUS (Performance S u r v e i l l a n c e System). The d e v i c e i s shown i n f i g u r e 19.

23 -C0>2.i;iKD CODES VOYAGE PLAirxTIKG 1 l i s t p o s i t i o n s 2 BTiter new p o s i t i o n H 3 d e l e t e p o s i t i o n s it i n s e r t p o s i t i o n s 5 change d a t a 6 c a l c u l a t e E.T.A T CFvlc\aate R.P.M. 8 e x i t module

P?J]3)ICTI0!; PLOT VOYAGE STOP MODULS = 7 ' 1 TBE n-TEBV^IL = li- 5 Ê

DRAUGKT roULIHG FUEL

RUB OUT 1 2 3 coïn F.KPH/vT RUB OUT coïn F.KPH/vT RUB OUT 0 v.. coïn F.KPH/vT F i g u r e 19.

5. Weather r o u t i n g o f s a i l i n g v e s s e l s

From the f o r e g o i n g c h a p t e r i t became c l e a r t h a t f o r o p t i m a l r o u t i n g knowledge o f t h e speed p o l a r i s o f prime i m p o r t a n c e .

For s a i l i n g v e s s e l s w i t h o u t motor a s s i s t a n c e t h i s p o l a r d i a g r a m i s p r i m a r -i l y dependent o f the w -i n d , b u t a l s o the speedloss by t h e s e a s t a t e s h o u l d be i n v o l v e d . M o s t l y the speed p o l a r s a r e g i v e n f o r a ' c o m p l e t e l y developed sea', w h i c h f o r i n s t a n c e means t h a t when s a i l i n g i n t h e l e e o f l a n d h i g h e r speeds a r e a t t a i n e d .

I n f i g u r e 20 t h e speed p o l a r s o f a 17,000 dwt Dynaship a r e g i v e n . T h i s s a i l i n g v e s s e l has a maximum s a i l area o f 103,000 f t ^ . F u r t h e r d e t a i l s o f t h i s v e s s e l a r e g i v e n by Wagner i n /17/. As a f u n c t i o n o f t h e t r u e w i n d a n g l e the speed t h r o u g h the w a t e r i s p l o t t e d f o r w i n d f o r c e s f r o m 1 t o 9 B e a u f o r t ; the w i n d speed i n k n o t s f o l l o w s f r o m the B e a u f o r t s c a l e v a l u e B f r o m V = 1.625 B / B. The minimum t r u e w i n d a n g l e when s a i l i n g c l o s e h a u l e d i s 50 . By 'symmetric c r u i s i n g ' a t B e a u f o r t 5, t h e speed made good i n t h e d i r e c t i o n o f t h e w i n d i s 5.5 k n , n o t t a k i n g i n t o a c c o u n t the t i m e l o s s

(speed l o s s ) by the t a c k i n g manoeuvres.

When s a i l i n g w i t h f o l l o w i n g w i n d s , symmetric c r u i s i n g i s a l s o more advan-tageous, as can be seen f r o m t h e speed p o l a r s .

Using the p o l a r d i a g r a m o f t h e Dynaship t h e l e a s t t i m e t r a c k f o r a t r a n s -A t l a n t i c passage was d e t e r m i n e d a t our Department, making use o f t h e a c t u a l w e a t h e r c h a r t s o f t h i s a r e a d u r i n g a week i n November 1980. From t h e w e a t h e r c h a r t s as produced by the R o y a l N e t h e r l a n d s Weather I n s t i t u t e , c h a r t s were d e r i v e d w i t h l i n e s o f e q u a l w i n d speed, see f i g u r e 21 and 22; the w i n d d i r e c t i o n s are g i v e n by v e c t o r s .

From t h i s i n f o r m a t i o n t h e speed p o l a r i n any p o i n t a l o n g t h e t r a c k i s known a t 12 h o u r i n t e r v a l s . W i t h the same method as d e s c r i b e d i n s e c t i o n 4.1, the subsequent t i m e f r o n t s o f 12 h o u r i n t e r v a l s are d e t e r m i n e d . I n f i g u r e 23 the time f r o n t s are shown w i t h the l e a s t t i m e t r a c k and t h e g r e a t c i r c l e t r a c k .

Some r e s u l t s o f t h i s s i m u l a t i o n :

- g r e a t c i r c l e d i s t a n c e f r o m Bishop Rock (49°30' N 006°30' W) t o Cape Race (46 40' N 52 40' W) i s 1829 n.m.; the g r e a t c i r c l e course o f d e p a r t u r e i s 282°; the v e r t e x l a t i t u d e i s 50°40.5' N;

- passage t i m e a l o n g the l e a s t t i m e t r a c k i s 10 p e r i o d s o f 12 h o u r s , see f i g u r e 23;

- d e p a r t u r e course i s 310 ;

- d i s t a n c e a l o n g the l e a s t t i m e t r a c k i s 2034 n.m.; - h i g h e s t l a t i t u d e a l o n g the l e a s t t i m e t r a c k i s 56 N; - average speed a l o n g t h e l e a s t t i m e t r a c k was 17 k n ;

- a l o n g the g r e a t c i r c l e , the v e s s e l w o u l d have been 8.25 days under way a v e r a g i n g 9.24 k n . (Prölls p r e d i c t e d i n /17/ an average e c o n o m i c a l speed of over 9 k n o t s I ) . I n t a b l e 5.1 t h e t r a v e l l e d d i s t a n c e per p e r i o d o f 12 h o u r i s n o t e d b o t h f o r g r e a t c i r c l e and l e a s t t i m e t r a c k . E s p e c i a l l y n o t e w o r t h y i s the much s m a l l e r s t a n d a r d d e v i a t i o n i n t r a v e l l e d d i s t a n c e per p e r i o d , r e s u l t i n g i n b e t t e r p r e d i c t i o n o f ETA.

I n r e a l i t y t h e r e s u l t s w i l l be l e s s s p e c t a c u l a r because one has t o work w i t h p r e d i c t e d w e a t h e r c h a r t s whereas i n t h i s s i m u l a t i o n t h e s u c c e s s i v e

a c t u a l w e a t h e r c h a r t s have been used. The r e l a t i o n between r o u t i n g r e s u l t s f r o m p r e d i c t e d and f r o m a c t u a l w e a t h e r c h a r t s w i l l be a r e s e a r c h p r o j e c t i n our Department i n D e l f t i n t h e coming t i m e .

25

-F i g u r e 20. Dynaship p e r f o r m a n c e . P o l a r d i a g r a m .

F i g u r e 23. L e a s t t i m e t r a c k and g r e a t c i r c l e t r a c k o f r o u t e d s a i l i n g v e s s e l .

29 -P e r i o d number 2 3 5 6

7

8

9

1 0 1 1 1 2 1 3 1 4 1 3 1 6 a T r a v e l l e d d i s t a n c e L e a s t t i m e 20/4

192

17k

225

20lf

195

213

1(S6

246

193

2 0 3 A -2 0 3 , 4

2 0 , 5 8

Normed d i s t a n c e a G r e a t c i r c l e L e a s t t i m e

168

90

75

89

120

82

58

62

180

1 1

/-i.

60

138

110

85

216

153

1800

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o ; 8 5 5 5

1,1062

1,0029

0,9587

1,0472

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152094

0 , 9 5 3 ?

1 0 1

0,1012

G r e a t c i r c l e

1j4933

0,8000

0,6667

0,7911

1,0667

0,7289

0,5156

0,5511

1 6 0 0 0

1 ,0133

0,5333

1,2267

0,9778

0,7556

1,9200

1,3600

1 6 1

0,4178

T a b l e 5 . 1 . 6. Weather r o u t i n g o f w i n d a s s i s t e d m o t o r v e s s e l s

T h i s i s a r e s e a r c h p r o j e c t i n o u r Department where we have j u s t s t a r t e d on /18/ and i t appears t o us t h a t l a r g e s a v i n g s o f f u e l can be o b t a i n e d when u s i n g o p t i m i z a t i o n programs as p o i n t e d o u t i n s e c t i o n 4.3.

The p r o b l e m i s now t o d e f i n e one u n i q u e speed p o l a r f o r a g i v e n w i n d speed and d i r e c t i o n , as t h e r e i s one e x t r a p a r a m e t e r : t h e p r o p u l s i o n power. L e t c h e r /19/ has p u b l i s h e d on t h i s i s s u e b e f o r e . To s i m p l i f y m a t t e r s we assume t h e g r o s s income p e r voyage a f i x e d amount. F u r t h e r we assume t h a t t h e d a i l y expense f o r t h e v e s s e l i s a f i x e d amount p l u s an amount t h a t i n -creases w i t h t h e p e r c e n t a g e o f p r o p u l s i o n power, see f i g u r e 24 t h e c i r c l e s on t h e l e f t .

An e s t i m a t e i s made o f t h e t o t a l t r a v e l l e d d i s t a n c e f o r t h e passage and t h e r e f o r e t h e g r o s s income p e r t r a v e l l e d m i l e i s known. \n\en t h e speed

p o l a r s f o r d i f f e r e n t p e r c e n t a g e s o f p r o p u l s i o n power a r e known, e i t h e r f r o m model s t u d i e s o r f r o m measurements on b o a r d o f t h e v e s s e l , t h e gross income p e r hour s a i l i n g i s known, see t h e p o l a r f i g u r e s i n f i g u r e 24 on t h e r i g h t . S u b s t r a c t i n g t h e d a i l y c o s t and p r o p u l s i o n c o s t p o l a r s f r o m t h e g r o s s income p o l a r s w i l l g i v e t h e n e t income p o l a r s p e r h o u r s a i l i n g . The e n v e l o p e c u r v e o f t h e s e n e t income p o l a r s w i l l r e s u l t i n f i g u r e 25 where t h e o p t i m a l m o t o r p r o p u l s i o n p e r c e n t a g e i s now u n i q u e l y d e f i n e d as f u n c t i o n o f t h e t r u e w i n d a n g l e and as a consequence t h e r e i s a u n i q u e speed p o l a r f o r a g i v e n w i n d s i t u a t i o n , see f i g u r e 26.

true wind angle \ ^

symmetric cruising

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symmetric cruising

F i g u r e 2A. 'Income p o l a r s '

motor

propulsion

power

(2 engines)

1 0 0 %

7 5 %

5 0 %

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1 ^ \ 1 \ 1 1

\ !

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- - c r u i s m q \

' symm.

\ i c r u i s i n q "

engines

\

1 ' • " • ^ "11

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31

-F i g u r e 26. P o l a r diagrams f o r speed, f u e l c o s t and n e t income per h o u r , as f u n c t i o n o f t r u e w i n d a n g l e f o r a g i v e n w i n d speed.

W i t h t h i s speed p o l a r t h e maximum n e t income r o u t e i s d e t e r m i n e d w i t h t h e method d e s c r i b e d i n s e c t i o n 4; s i m u l t a n e o u s l y t h e f u e l expenses a r e

ac-cumulated, r e s u l t i n g i n :

- p r e d i c t e d maximum income r o u t e ; - t o t a l f u e l c o s t a l o n g t h e r o u t e .

The r e s e a r c h program 'wind a s s i s t e d v e s s e l s ' o f t h e s e c t i o n H y d r o n a u t i c s w i l l cover t h e f o l l o w i n g subprograms i n t h e coming t i m e :

( i ) d e v e l o p i n g computer programs f o r 'maximum n e t income r o u t e i n g ' ; ( i i ) d e v e l o p i n g 'performance programs' f o r w i n d a s s i s t e d motor v e s s e l s ; ( i i i ) i n v e s t i g a t e t h e s e n s i t i v i t y f o r 'assumed d i s t a n c e ' i n r o u t e i n g r e s u l t s ; ( i v ) s i m u l a t i o n o f ocean passages w i t h ' r e a l w e a t h e r ' ( h i n d c a s t i n g ) w i t h d i f f e r e n t t y p e s o f w i n d a s s i s t e d motor v e s s e l s t o f i n d t h e b e s t d e s i g n ; ( v ) i n v e s t i g a t e d e g r a d a t i o n i n r o u t e i n g r e s u l t s when u s i n g 'expected w e a t h e r ( f o r e c a s t i n g ) ' i n s t e a d o f ' r e a l w e a t h e r ( h i n d c a s t i n g ) ' . We a r e i n t e r e s t e d t o do t h i s r e s e a r c h i n c o o p e r a t i o n w i t h o t h e r s and we are s p e c i f i c a l l y i n t e r e s t e d t o t e s t e x i s t i n g o r p l a n n e d w i n d a s s i s t e d v e s s e l s i n o u r r o u t e i n g programs. References / ] / E r n s t Crone. C o r n e l i s Douwes z i j n l e v e n en z i j n w e r k . T j e e n k W i l l i n k , Haarlem, 1941. Ill A m e r i c a n P r a c t i c a l N a v i g a t o r . O r i g i n a l l y by N a t h a n i e l B o w d i t c h . Defense Mapping Agency, USA, 1977.

/3/ Segelhandbuch für den A t l a n t i s c h e n Ozean. Deutsche Seewarte.

L. F r e d e r i c h s e n & Co., Hamburg, 1910. /4/ Dodging t h e w e a t h e r . Q u a r t e r l y J o u r n a l o f t h e American Bureau o f S h i p p i n g . August 1982. /5/ R.W. James. The p r e s e n t s t a t e o f s h i p s r o u t i n g . I n t e r o c e a n '70 i n t e r n a t i o n a l c o n f e r e n c e . /6/ G.C. K o r e v a a r . E x p e r i e n c e s and r e s u l t s o f t h e s h i p r o u t i n g o f t h e R o y a l N e t h e r l a n d s M e t e o r o l o g i c a l I n s t i t u t e , S c i e n t i f i c r e p o r t 76-9, KNMI, De B i l t , 1976. HI R e s u l t s o f M a r i n e and I s t h m i a n l i n e s w e a t h e r r o u t e d c r o s s i n g 1961-1963. Weather R o u t i n g I n c o r p o r a t e d , New Y o r k . /8/ R e p o r t on t h e r e s u l t s o f w e a t h e r r o u t i n g N o r t h A t l a n t i c t r a f f i c by t h e R o y a l N e t h e r l a n d s M e t e o r o l o g i c a l I n s t i t u t e . S h e l l I n t e r n a t i o n a l M a r i n e L t d . , MRP/22, J u l y 1966.

33

-/9/ D. Heyboer,

KNMI R o u t e r i n g ( D u t c h ) , NTT-De Zee, 1981, no. 11. / l O / W.G. C o n s t a n t i n e .

Weather r o u t i n g f o r s a f e t y and economy.

Ship o p e r a t i o n and s a f e t y c o n f e r e n c e , Southampton, A p r i l 1981. / I 1/ J.M.J. J o u r n e e .

F u e l s a v i n g by s u r v e i l l a n c e and s i m u l a t i o n o f s h i p ' s p e r f o r m a n c e ( i n D u t c h ) .

NTT-De Zee, November 1982. /12/ C. de W i t .

O p t i m a l m e t e o r o l o g i c a l s h i p r o u t i n g .

N e d e r l a n d s S c h e e p s s t u d i e c e n t r u m TNO, r e p o r t no. 142 S, August 1970. /13/ S.J. B i j l s m a . On m i n i m a l - t i m e s h i p r o u t i n g . Royal N e t h e r l a n d s M e t e o r o l o g i c a l I n s t i t u t e , r e p o r t no. 94 ( 1 9 7 5 ) . /14/ G. F r a n k e l , H. Chen ( M I T ) . O p t i m i z a t i o n o f s h i p r o u t i n g . P r e p a r e d f o r N a t i o n a l M a r i t i m e Research C e n t e r . K i n g s P o i n t , New Y o r k , 1978. /15/ L.S. P o n t r y a g i n . M a t h e m a t i c a l Theory o f o p t i m a l p r o c e s s e s . I n t e r s c i e n c e P u b l i s h e r s I n c . , New Y o r k , 1962. /16/ James H. Mayes. S a i l i n g s h i p w e a t h e r r o u t i n g . Symposium on w i n d p r o p u l s i o n o f c o m m e r c i a l s h i p s , London, 1980. / I 7/ B. Wagner. C a l c u l a t i o n o f t h e speed o f t r a v e l o f s a i l i n g v e s s e l s . J a h r b u c h d e r S c h i f f b a u t e c h n i s c h e n G e s e l l s c h a f t 6 1 . S p r i n g e r V e r l a g , 1967. /18/ 0. S t e i n e r t . P r o j e c t p r o p o s a l ' R o u t i n g o f w i n d a s s i s t e d v e s s e l s ' ( i n D u t c h ) . Dept. o f M a r i n e T e c h n o l o g y , S e c t i o n H y d r o n a u t i c s , August 1984. /19/ J.S. L e t c h e r .

O p t i m a l p e r f o r m a n c e o f s h i p s under combined power and s a i l .