Influence of Design Parameters on Vertical Motions of Trawler Hull Forms in Head Seas

8/18/2019 Influence of Design Parameters on Vertical Motions of Trawler Hull Forms in Head Seas

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M a r i n e T e c h n o l o g y , V o l . 3 4 , N o . 3 , J u l y 1 9 9 7 , p p . 1 8 1 - 1 9 6

I n f lu e n c e o f D e s i g n P a r a m e t e r s o n V e r t i ca l M o t i o n s o f

T r a w l e r H u l l F o r m s i n H e a d S e as

A b d i K i i k n e r 1 a nd M u h s i n A y d l n 2

The influence o f ship length, length to beam ratio, beam to draft ratio, prism atic coefficient,

non-dim ensional radius of gyration and Froud e numbe r upon s igni f icant ampli tude of coupled

heaving and pi tching mot ions of t rawler hul l form s fo r s ix di f ferent sea s tates has been s tudied.

For this purpose , 540 traw ler hul l form s have been generated fro m D oust traw ler series to

cover approp riate ranges o f the design parameters . Seakeeping behav ior of these form s has

been s tudied by us ing an es tablished ship mot ion com puter prog ram a nd regress ion m odels

of significa nt seakeeping events have been derived. Through this study, i t is believed that a

metho d has been prod uced for the seakeeping evaluat ion of t rawler form s dur ing the ear ly

des ign s tages , hence a l lowing fo r the des ign o f safer and mo re seakindly trawler des igns .

~ T R O D U C T I O N

T h e S u c c e s s o f a f is h i n g b o a t d e s i g n c a n b e

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

s e a w a y . T h i s i s d u e t o t h e f a c t t h a t t h e s h i p h a s t o

s u r v i v e i n e x t r e m e w e a t h e r , h a s t o c a r r y o u t h e r

m i s s i o n i n al l w e a t h e r c o n d i t i o n s b y m a i n t a i n i n g h e r

s p e e d a n d c o u r s e w i t h a m i n i m u m d i s c o m f o r t to h e r

c r e w . T h e r e f o r e a s tu d y o f s e a k e e p i n g b e h a v i o r o f a

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

r e s i s t a n c e , s t a b i l i t y a n d s t r e n g t h , a n d s h o u l d b e c a r r i e d

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

p r e s e n t t h e r e i s n o a v a i l a b l e m e t h o d t o b e u t i l i z e d f o r

t h is p u r p o s e e x c e p t f o r c o m m e r c i a l h u l l fo r m s ( s u c h a s

L o u k a k i s & C h r y s s o s t i m i d i s 1 9 7 5 ) b u t th e s e m e t h o d s

d o n o t p r o v i d e m e a n i n g f u l r e s u lt s f o r t r a w l e r h u l l

f o r m s . I t i s t h e p u r p o s e o f t h is p a p e r t o p u t f o r w a r d a

m e t h o d f o r t h is k i n d o f h u l l f o r m a n d h e n c e m a k e e a r l y

s e a k e e p i n g e v a l u a t i o n p o s s i b l e .

G e n e r a l l y i n ra n d o m s e a s , t h e b e h a v i o r o f a s h i p c a n

b e a n a l y z e d t h r o u g h t h e f o l l o w i n g s t e p w i s e e v a l u a t i o n s :

1 . S h ip m o t i o n s , v e r t i c a l a c c e l e r a t i o n s i n c l u d e d

2 . A d d e d r e s i s ta n c e a n d s p e e d r e d u c t i o n i n w a v e s

3 . R e l a t i v e m o t i o n s i n c l u d i n g d e c k w e t n e s s a n d

s l a m m i n g

4 . L o a d s a c t i n g o n s h i p ' s s t ru c t u r e

H e r e , a s a f i r s t s t e p f o r s u c h a n e v a l u a t i o n ,

s i g n i f ic a n t a m p l i t u d e s w i l l b e c o n s i d e r e d f r o m w h i c h

s h i p m o t i o n s i n c l u d i n g d e c k w e t n e s s a n d s l a m m i n g o f

a p a r t i c u l a r d e s i g n c a n b e d e r i v e d .

W h i l e t h e e f fe c t s o f s e a k e e p i n g b e h a v i o r c a n b e

c h a r a c t e r i z e d t h r o u g h t h e a b o v e f a c t o r s , c h a r a c t e r i z a t io n

o f s h i p d e s i g n f e a t u r e s w h i c h d e t e r m i n e h e r r e s p o n s e t o

w a v e s m a y b e c o n s i d e r e d u n d e r t h e f o l l o w i n g h e a d i n g s :

1 . M a i n s h i p d i m e n s i o n s , e s p e c i a l l y s h i p ' s l e n g t h

2 . S h i p f o r m

3 . W e i g h t d i s t r i b u t i o n

4 . S h i p s p e e d

5 . S e a s t a t e

S i n c e o u r m a i n c o n c e r n i s t h e t r a w l e r h u l l fo r m , a

s e r ie s o f 5 4 0 f o r m s h a s b e e n g e n e r a t e d f r o m D o u s t

t r a w l e r s e r i e s . A t y p i c a l g e o m e t r y o f th e s e r i e s is

i l l u s t r a t e d i n F i g u r e 1 . I n t e r m s o f s i g n i f i c a n t

p a r a m e t e r s , t h e ra n g e c o v e r e d i s g i v e n b e l o w :

L e n g t h i n t e r v a l . . . . . . . . . . . . . . . . . < 1 1 m - 4 5 m >

L e n g t h / b e a m i n te r v a l . . . . . . . . . . . . . . . . . . . . . . . < 4 . 4 - 5 . 8 >

B e a m / d r a f t i n te r v a l . . . . . . . . . . . . . . . . . . . . . . . < 1 . 9 - 2 . 7 >

B l o c k c o e f f ic i e n t in t e r v a l . . . . . . . . . . . < 0 . 4 8 9 0 - 0 . 5 6 7 5 >

W a t e r p l a n e a r e a c o e f fi c i en t i n t e rv a l . . < 0 . 6 6 2 5 - 0 . 7 5 0 0 >

P r i s m a t i c c o e f f i c i e n t i n t e rv a l . . . . < 0 . 5 9 0 0 - 0 . 6 5 0 0 >

k y y / L e n gt h i n t e r v a l . . . . . . . . . . . < 0 . 2 3 0 0 - 0 . 2 5 0 0 >

1

A s s o c i a te P ro fe s s o r, F a c u l t y o f N a v a l A rc h i t e c t u re a n d O c e a n E n g i n e e r i n g , Te c h n i c a l U n i v e r s i t y o f I s t a n b u l , I s ta n b u l , Tu rk e y .

z Research Ass is tant , Facul ty of Nava l Archi tec ture and Oce an Eng ineering, Tec hnica l Univers i ty of Is tanbul , Is tanbul , Turkey.

Manuscript rece ived a t SNAME headquarte rs July 12, 1996.

JU LY 1997 0025-3316/97 /3403-0181 $00.57 /0 MARINE TECHNO LOGY


2/16

tlur

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A.P

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I / / / / / I

I / I / / /t

r i l l / / J

2 4 G 6 12 14 16 18

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Figure 1 . Body p lan of a t rawler f i sh ing boat

T a b l e 1 . V al u es o f S W H ( m ) , A W L ( m ) a n d A W P (s ) i n t e r m s o f B e a u f o r t N u m b e r .

B e a u f o r t S i g n if i c an t A v e r a g e W a v e A v e r a g e

N u m b e r D e s c r i p t i on W a v e H e i g h t L e n g t h W a v e P e r i o d

( B N ) S W H ( m ) A W L ( m ) A W P ( s)

3 Gen t l e b r eeze 0 .3 0 5 6 .1 2 .4

4 M o d e r a t e b r e e z e 0 . 8 8 4 1 5 .9 3 . 9

5 F r e s h b r e e z e 2 . 1 0 3 3 0 . 0 5 . 4

6 S t r o n g b r e e z e 3 . 9 6 2 5 0 . 0 7 . 0

7 N e a r g a l e 7 . 0 1 0 7 9 . 0 8 . 7

8 Ga l e 1 1 .2 7 8 1 1 5 .0 1 0 .5

S eak eep in g b eh av io r o f th ese fo rm s an d h en ce

s ig n i f ican t am p l i t u d es o f co u p l ed h eav e an d p i t ch

m o t io n s h av e b een ca l cu l a t ed b y u t i l i z i n g t h e Wo l f so n

Un i t S h i p Mo t io n P ro g ram . Resu l t s o f t h ese

co m p u ta t i o n s h av e b een ev a lu a t ed , an d b y ad o p t i n g t h e

M o o r s a p p r o a c h ( M o o r & M u r d e y 1 9 6 8 ), a re g r e s s i o n

m o d e l u t i l i z i n g s i g n i f i can t p a ram ete r s h as b een

o b t a i n ed . T h ere fo re a m eth o d t o p red i c t s eak eep in g

b eh av io r o f a t r awle r h u l l f o rm t h ro u g h s i g n i f i can t

d es ig n p a ram ete r s h as b een o b t a in ed .

Th e sea co n d i t i o n s h av e b een d esc r i b ed wi th 6

d i f f e r en t sea s t a tes w h ich a r e g iv en i n Tab l e 1 i n te rm s

o f s i g n if i ca n t w a v e h e i g h t ( S W H ) , a v e r a g e w a v e l e n g th

( A W L ) a n d a v e r a g e w a v e p e r i o d ( A W P ) c h a n g in g w i t h

resp ec t t o Beau fo r t s ca l e o f win d fo rce .

E F F E C T O F M A IN D I M E N S IO N A N D D E S I G N

P A R A M E T E R S

Effect of Ship Length

S h ip l en g th h as an im p o r t an t e f f ec t o n b o th s i g n i f i can t

1 8 2 J U L Y 1 9 9 7 M A R I N E T E C H N O L O G Y


3/16

p i t c h a n d h e a v e a m p l i tu d e s . In g e n e ra l , a n in c re a s e in

l e n g th t e n d s to r e d u c e s ig n i f i c a n t p i t c h a mp l i tu d e in

a l m o s t e v e r y s e a s t at e . H o w e v e r , r e d u c t i o n i n

s ig n i f i c a n t h e a v e s e e ms to d i s a p p e a r fo r s e a s t a te s

h ig h e r th a n B N 4 . F ig u re s 2 a n d 3 i l l u s t r a t e th e r e s u l t s

o f a ty p ic a l h u l l fo rm fo r 0 , 5 , a n d 1 1 k n o t s fo rw a rd

speed .

E f f e c t o f L e n g t h t o B e a m a t i o

S tu d y in d ic a t e s, i n g e n e ra l , s ig n i f i c a n t p i t c h a mp l i tu d e

te n d s to in c re a s e w i th in c re a s in g L /B ra t io fo r l o w e r

s e a s t a t e s a n d th a t b o th h e a v e a n d p i t c h r e s p o n s e s s e e m

t o b e i n d e p e n d en t o f l e n g t h - t o - b e a m r a t i o f o r h i g h e r s e a

s t a t e s . A ty p ic a l r e s u l t fo r a t r a w le r fo rm fo r a fo rw a rd

s p e e d o f 9 k n o t s i s g iv e n in F ig . 4 .

E f f e c t o f B e a m t o D r a f t R a t i o

F o r s e a s t a t e s a b o v e B N 5 , b o th s ig n i f i c a n t h e a v e a n d

p i t c h a m p l i t u d e s t e n d t o d e c r e a s e w i t h i n c r e a s i n g B / T

ra t io . A l th o u g h re d u c t io n r a t io i s n o t v e ry s ig n i f i c a n t ,

t h i s t r e n d s e e ms to b e p e r s i s t e n t fo r d i f f e re n t fo rw a rd

s p e e d s . F o r lo w e r s e a s t a t e s , a c o n fu s e d p i c tu re

e me rg e s a n d r e s u l t s a re s t ro n g ly d e p e n d e n t o n th e

fo rw a rd s p e e d . T h i s s i t u a t io n i s s h o w n in F ig . 5 fo r a

t y p i c a l tr a w l e r f o r m f o r f o r w a r d s p e e d s o f 5 a n d 1 1

k n o t s .

E ffect o f Pr i sm a t i c C o ef f i c i en t

P r i s ma t i c c o e f f i c i e n t s e e ms to h a v e a p e r s i s t e n t

in f lu e n c e o n th e s ig n i f i c a n t p i t c h a mp l i tu d e fo r a lmo s t

e v e ry s e a s t a t e . A s C p in c re a s e s , s ig n i f i c a n t p i t c h t e n d s

to d e c re a s e . S ig n i f i c a n t h e a v e a m p l i tu d e o n th e o th e r

h a n d s e e m s t o d e c r e a s e w i t h i n c r e a s i n g p r i s m a t i c

c o e e f f i c i e n t fo r l o w e r s e a s t a t e ( i . e . B N < 5 ) . F o r

h ig h e r s e a s t a t e s s ig n i f i c a n t h e a v e a mp l i tu d e s e e ms to

b e i n d e p e n d e n t o f p r i s m a t i c c o e f f i c e n t v a l u e . F i g u r e 6

i l l u s t r a t e s th e s e t r e n d s .

E f f e c t o f L o n g i t u d i n a l R a d i u s o f G y r a t i o n

S in c e th e r a d iu s o f g y ra t io n r e f l e c t s t h e in f lu e n c e o f

w e ig h t d i s t r ib u t io n , a n y r e s t r i c t io n

on kyy/L

w i l l h a v e

a s ig n i f i c a n t e f f e c t o n th e o v e ra l l d e s ig n . R e s u l t s

in d ic a t e th a t a t B N 5 a n d a b o v e th e re i s a n e x p e c te d

a n d c o n s i s t e n t t r e n d . A c c o rd in g ly , a n y in c re a s e in

kyy/L

r e s u l t s in a n in c re a s e in th e s ig n i f i c a n t p i t c h a mp l i tu d e ,

i r r e s p e c ti v e o f t h e f o r w a r d s p e e d . H e a v e , o n t h e o t h e r

h a n d , d o e s n o t s e e m to b e s t ro n g ly in f lu e n c e d b y

kyy/L

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

t o a p p e a r . F o r l o w e r s e a s t a t e s , t h e b e h a v i o r o f

s ig n i f i c a n t p i t c h w i th r e s p e c t t o v a r i a t io n o f ky y /L

a p p e a r s t o b e r a t h e r c o m p l e x a n d s t r o n g l y d e p e n d e n t o n

th e fo rw a rd s p e e d . F ig u re 7 i l l u s t r a t e s th i s t y p e o f

b e h a v i o r f o r a t y p i c a l d e s i g n f o r t h r e e d i f f e r e n t s p e e d s .

E f f e c t o f F r o u d e N u m b e r

W i t h t h e e x c e p t i o n o f s e a s t a t e c o r r e s p o n d i n g t o B N

3 , s ig n i f i c a n t h e a v e a mp l i tu d e t e n d s to in c re a s e w i th

i n c r e a s in g F r o u d e n u m b e r a n d t h i s t r en d , a s e x p e c t e d ,

i s i n d e p e n d e n t o f al l th e o t h e r p a r a m e t e r s . F o r h i g h e r

s e a s t a t e s (B N > 5 ) s ig n i f i c a n t p i t c h a mp l i tu d e t e n d s to

i n c r e as e w i t h i n c r e a s in g F r o u d e n u m b e r , d i s p l a y i n g a

s a t u r a t io n t y p e b e h a v i o r . F o r l o w e r s ea s t at e s,

s i g n i fi c a n t p i t c h r e s p o n s e d i s p l a y s a c o n f u s e d b e h a v i o r

w i t h o u t a n y d e f i n i t e t e n d e n c y . T h i s s i t u a t io n i s s h o w n

i n F i g . 8 f o r t y p i c a l d e s i g n s w i t h v a r y i n g p r i s m a t i c

c o e f f i c i e n t s .

R e g r e s s i o n M o d e l o f H e a v e a n d P i t c h M o t i o n s

A s i s w e l l k n o w n , b o t h s i m p l e a n d m u l t i p le r e g r e s s i o n

a n a ly s e s h a v e fo c u s e d u p o n e s t a b l i s h in g a r e l a t io n s h ip

b e t w e e n d e p e n d e n t a n d i n d e p en d e n t v a r i a b l e s . F r o m t h e

p a r a m e t r i c a n a l y s is o f a sh i p h a v i n g h e a v e m o t i o n i n

h e a d s e a s, i t h a s b e e n o b s e r v e d t h a t t h e h e a v e

a m p l i t u d e h a s b e e n i n f l u en c e d b y 7 i n d e p e n d e n t

p a r a m e t e r s w h i c h d e f i n e t h e h u l l g e o m e t r y o f s h ip . T h e

v a l u e s o f t h e se p a r a m e t e r s a r e in n o n d i m e n s i o n a l f o r m

a n d g iv e n a s C w e , C B , L /B , T /L , L C B (p e rc e n ta g e o f

s h ip l e n g th ) ,

kyy/L

( r a d iu s o f g y r a t i o n ) a n d V / ~ g L .

T h e r e f o r e t h e m u l t i p l e r e g r e s s i o n m o d e l b e t w e e n t h e

d e p e n d e n t v a r i a b l e h e a v e a m p l i t u d e ( Z ) a n d t h e s e 7

i n d e p e n d e n t v a r i a b l e s c a n b e g i v e n i n t h e f o l l o w i n g

f o r m :

L T k~v

Z = a o + a I C w L + a 2 C B +a3-~ +a4T + a s L C B +a6-- -

V

+ a 7

( m e t e r ) (1)

T w e n t y l i n e a r e q u a t i o n s y s t e m s i n w h i c h e a c h h a s 8

u n k n o w n s a n d 2 7 e q u a t i o n s f o r e a ch m a i n s h i p l e n g t h

c a n b e o b t a i n e d a s f o l l o w s :

L l T l

Z 1= a 0 + a I C w L 1 + a 2 C B j + a 3 - + a 4 - + a 5 L C B 1

B l L l

+a6kVy +a v V~

L I g ~ l

L27 T27

Z , a + a C + a C + a + a

~7 = 0 i wL 27 z B27 3 - ~ - ~ 4 - - ff ~+ a5 L C B2 7

27 27

+ a 6 ~-2-~--------~7 av -- -- -- z- -- ( 2 )

C27

(?ex t cont inued on pag e 191)

J U L Y 1 9 9 7 M A R I N E T E C H N O L O G Y


4/16

0.75

0.60

0,4"5

0.30

0 .15

0 ,00

B N = 3

I

L /B=5 .1

SW H=0 .305 m

B / T = 2 . 3

AWL=6.1 m Cp=0.62

A W P = 2 .4 s k y y / L = 0 . 2 4

1 1 1 3 1 5 1 7 1 9

21 23 25 27 29 31 33 35 37 39 41 43 45

L (meter)

v

N

2 , 4 . 0

2.00

1.60

1 . 2 0

0.80

0.~-0

0.00

B N = 4 L / B = 5 . 1

I

SW H=0 .884 m B/T= 2 .3

AWL=I 5.9 m Cp=0.62

A W P = 3 .9 s k y y / L = 0 . 2 4

i . . . . . i . . ~ . i . . ~ . . . . . ~ . . L . . ~ . . .. . . .. . .. . :_ . . ~ . . . . .

11 13 1 5 1 7 1 9 21 23 25 27 29 31 33 35 37 39 41 43 45

o

N

3.75

3.00

2,25

1.50

0.75

0.00

B N = 5 L / B = 5 , 1

SW H=2 .103 m B/T=2 .3

AWL= 30.0 m Cp=0.62

A W P = 5 ,4 s k y y / L = 0 , 2 4

1 13 15 1 7 1 9 21 23 25 7 29 31 33 35 37 39 41 43 45

L meter

o

N

SW H=3 .962 m BIT= 2 .3

AWL=50.O m Cp=0.62

A W P = 7 ,0 s k y y / L = 0 . 2 4

5.00

4.00

3.00

2.00 '

i

1.00 ' I " ' I ' " I I I

• ~ - - . ~ , ~ - . . - c - - - : . . : - - - - - : . . . . . . . . . : - - . ~ . . . . ~ . . . . - . , . . ~ . .. ~

0 . 0 0 . . . . . . . . . . .

11 1 3 1 5 1 7 19 21 23 25 27 29 31 33 35 37 39 41 43 45

L meter

"o

N

6.00

.5.00

4 .00

3.(~0

2 .00

1.00

0.00

B N : 7

L / B = 5 , 1 I + v = 0 . n

SWH=7.01 0 m B/ 'T= 2.3

AWL= 79,B m Cp=0.62

A W P = 8 ,7 s k y y / L = 0 , 2 4

i i i i i l i

: [ - ~

" " " : . . . . . . . . 7 ' : " "~ . . . . " " . . . . . . . . . . Y ' " ' ' ' " " - " " ~

1 1 1 3 1 5 1 7 1 9

21 23 25 27 29 31 33 35 37 39 41 43 45

BN=8 l [ L /B=5 .1

SW H=I 1 .278 m B/T=2 .3

AWL=I 1 5.0 m Cp=O.62

A W P= 1 0 . 5 s k y y / L = 0 . 2 4

7.50

6.00

3.004"~0

1

bO

...'1 i i . . .I i i i i ' I

O.00

11 13 15 17 19 21 23 25 27 29 31 33 35 37 39 41 43 45

L (meter)

F i g , 2 T h e e f f e c t o f v a r y i n g s h i p l e n g t h o n h e a v e a n d p i t c h m o t i o n s

c o r r e s p o n d i n g t o 6 d i f f e r e n t B e a u f o r t N u m b e r s f o r z e r o s p e e d .

1 8 4 J U L Y 1 9 97 M A R I N E T E C H N O L O G Y


5/16

1 . 6 0

1 . 4 0

. 2 0

1 . 0 0

0 . 8 0

0 . 6 0

0 . 4 0

0 . 2 0

o . o o

S W H = 0 . 3 0 5 m B / T = 2 . 3

A W L = 6 , 1 m C p = 0 . 6 2

A W P = 2 A s k y y / L = 0 . 2 4

1 1 1 3 1 5 1 7 1 9 2 1 2 3 2 5 2 7 2 9 3 1 3 3 3 5 3 7 3 9 4 .1 4 3 4 5

L ( m e t e r )

v

o

E

N

B N = 4 L / B = 5 . 1

4 - V = 5 k n

S W H = 0 . 8 8 4 m B / T = 2 . 3 O V = l t k n

A W L = I 5 . 9 m C p = 0 . 6 2

A W P = 3 . 9 s k y y / L = 0 . 2 4

3 . 0 0 ~ 1

2 . 8 0

2 . 0 0

1 . 5 0

1 . 0 0

0 . 5 0 . . . . . : . . : : . : : . : . .

. . . . .

' - • " : - i ' ' ~ ' '

0 . 0 0 , i i , i i i i i i " i , , " , i I

1 1 1 3 1 5 1 7 1 9 2 1 2 3 2 5 2 7 2 9 3 1 3 3 3 5 3 7 3 9 4 1 4 3 4 5

"O

v

O

B N = 5 L / 8 = 5 . 1

4 - V = 5 k n

S W H = 2 . 1 0 3 m B / T = 2 . 3

o V = l 1 k n

A W L = 3 0 . O m C p = 0 . 6 2

A W P = 5 . 4 s k y y / L = 0 . 2 4

5 , 0 0

• : , : : : . : , . .

3 . 0 0 I ~

- ~ t

2 . 0 0 - i ~ i ~ }

• : : . . . . , , : : : • : , ,

1 . 0 0

. ' ~ I , l i I i i - - T T - 1 , -

1 1 1 3 1 5 1 7 1 9 2 1 2 . 3 2 5 2 7 2 9 3 1 3 , ] 3 5 3 7 3 9 4 1 4 3 4 5

o

N

8 N = 6 L / 8 = 5 . 1

+ V = 5 k n

S W H = 3 . 9 6 2 m 8 / T = 2 . 3

O V = 1 1 k n

A W L .= 5 0 . 0 m C p = 0 . 6 2

A W P = 7 . 0 s k y y / L = 0 . 2 4

6 . 0 0

5 . 0 0

4 . 0 0

3 . 0 0

2.0 0 . : : : . . . . . : : , .

• : : : . • . . . . : : .

1 .0 0 ~ ~ ~ ' - ~ { ~ "," ? : ~ , ~- - ,~ : - ~ - - - :

0 . 0 0

~ 1 1 5 J I , I , , I I , ~ i , i i

1 1 1 3 1 7 1 9 21 2 . 3 2 5 2 7 2 9 3 1 3 3 3 5 3 7 3 9 4 1 4 3 4 5

"o

E

v

N

7 . 5 0

6 . 0 0

4 . 5 0

3 . 0 0

1 . 5 0

0 . 0 0

N = 7 t / .= 5 . 1 I + V - 5 . n I

S W H = 7 . 0 1 0 m B / T = 2 . 3 O V = l k n

j A W L = 7 9 . 0 m C p = 0 . 6 2

L A W P = 8 . 7 _ _ ~ _ _ ~ _ ~

k y y / L = 0 , 2 4 -

; . . . . - 2 . : . J . " ~ " : . . : : r . [ . . . . [

1 3 1 5 1 7 1 9 2 1 2 3 2 5 2 7 2 9 . 3 1 3 3 3 5 5 7 , . 3 9 4 1 4 3 4 5

L ( m e t e r )

o

N

B N = 8 L / B = 5 . 1

4 - V = 5 k n

S W H = I 1 . 2 7 8 m B / T = 2 . 3

O V = I 1 k n

A W L = I 1 5 . 0 m C p = O . 6 2

A W P = 1 0 . 5 s k y y / L = 0 . 2 4

9 . 0 0

7 . 5 0

6 . 0 0 . .

4 . 5 0 " : ' " : " "

3 . 0 0

1 . 5 0 "

:'" " '~'"

: ' : . i

. . . . . . . . . : . . .

: • : . : . . . '

. . . . .

0 . 0 0 ' ~ ~ ~ ~ ~ ; i , ~ , , i ; ; ; , '

1 1 1 3 1 5 1 7 1 9 2 1 2 3 2 5 2 " 7 2 9 3 1 3 3 3 5 3 7 . 3 9 4 1 4 3 4 5

L ( m e t e r )

Fig. 3 T h e e f f e c t o f v a r y i n g s h i p le n g t h o n h e a v e a n d p i tc h m o t i o n s

c o r r e s p o n d i n g t o 6 d i f f e r e n t B e a u f o r t N u m b e r s f o r 5 e n d 1 1

k n o t s s h i p s p e e d s .



6/16

0 . 0 5

0. 04

I

0 . 0 3 I

o 0 . 0 2

~, 0.01

0.0C

N

B N = 3 [ L = 3 2 m [ ~

S W H = 0 . 3 0 5 m B / T = 2 . 7

A W L = 6 .1 m / C p = 0 . 6 5

/

A W P = 2 . 4 s / k y y / L = O . 2 3

. . . . . . . . . . . i . . . . . . . . . . . : . . . . . . . . . . . . . . i . . . . . . ' ' '

z

4.4 5.1 5.8

L / B

1 . 4 0

1 . 2 0

- o 1 . 0 0

0 . 8 0

0 . 6 0

. ~ o . 4 o

0 . 2 0

0 . 0 0

B N = 4 L = 3 2 m V = 9 k n

S W H = 0 . 8 8 4 m B / T = 2 . 7

A W L = 1 5 . 9 m C p = 0 . 6 5

A W P = 3 . 9

s k y y / t = 0 . 2 3

4.4

5.1

5.8

L / B

~, s.00

~,~ 2.50

o

2 . 0 0

1 . 5 o

1 o o

t,

0 . 5 0

N

0 . 0 0

4 . 4

8 N = 5

S W H = 2 . 1

0 3

m

A W L = 3 0 . 0 r n

A W P = 5 . 4 S

L = 3 2 m

8 / T = 2 . 7

C p = 0 , 6 5

k y y / L = 0 , 2 3

i [ :

e

i

. . . . . . . . . . . . . . . . o

i i i

5.1

5 . 8

L I B

4 . 5 0

4 . 0 0

" o 5 . 5 0

° " 3 . 0 0

2 . 5 0

2 , 0 0

1 . 5 0

1 , 0 0

v

0 . 5 0

0 . 0 0

4 . 4

B N = 6 L = 3 2 m / V = 9 k n

8 W H = 3 . 9 6 2 m

B / T = 2 . 7

l

W L = 5 0 . 0 m C p = 0 . 6 5

A W P = 7 . 0 s k y y / L = 0 . 2 3

. . . .. . . .. . . .. . . .. . . .. . . .. . . .. . . .. . . .. . . ~ . . . . . . . . i . . . . . . . . : : . . . .

i ~ ~ ......

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . i . . . . . . . . . . i . . . . . .

5 . 1 5 . 8

L / B

6 . 0 0

5.00

~o

O " 4 . 0 0

3 . 0 0

E 2 . 0 0

N 1 . 0 0

0 . 0 0

4 . 4

B N = 7

S W H = 7 . 0 1 0 m

A W L = 7 9 . 0 m

A W P = 8 . 7 s

L = 3 2 m

B / T = 2 . 7

C p = 0 . 6 5

k y y / L = 0 . 2 3

V = 9

k n

: . . . . . . . . . . i : ,

5.1

5 . 8

L / B

d 5 . 0 0 I

4 , 0 0 /

b 3 . 0 0 / '

N 2 . 0 0 •

4 . 4

B N = 8 1

S W H = I 1 . 2 7 8

m J

A W L = I 1 5 , 0 m J

A W P = I 0 . 5 s J

L = 3 2 m I I V g n I

B / T = 2 . 7 I I = I

C p = 0 . 6 5

k y y / L = 0 . 2 3

. . . . . . . . . ~ . . . : . . . . . . • . . . . . . . . . . ~ . . . . . . . . . i . . . . . . . . . . . . . .

............................. ............... ............................... ~ ..... .... ....

i i i i

5 . 1 5 . 8

L / a

Fig.

4 T h e e f f e c t o f L / B r a t i o v a r i a t i o n o n t h e s i g n i f i c a n t h e a v e a n d

p i t c h m o t i o n s c o r r e s p o n d i n g t o 6 d i f f e r e n t B e a u f o r t s c a l e o f

w i n d f o r c e .



7/16

0 . 1 0

0 . 0 8

0,06

0 , 0 4

0 . 0 2

0 , 0 0

t . 9

SW H =0 .30 5 m L /B =5 ,8

AW L =6 .1 m C p =0 .5 9

A W P = 2 . 4 s k y y / L = 0 . 2 5

. . . . . . . . . . . . . . . . . .

] [ . v s k o o j

V =

11

k n o t

i

i

2 . 3

2 , 7

B / T

~ - 2 . 0 0

~

1 . 6 0

1 . 2 0

-,

0 . 8 0 " "

" 0 . 4 0

E

~ " 0 . 0 0

1 . 9

BN-4 [ L-32 m I n o~ t

W H = 0 . 8 8 4 m L / B = 5 , 8 • V = 5 k n o t

AW L =I 5 .9 m J 0 p =0 .5 9 O V= 1

A~VP=3.9 s

L

k y y / L = 0 . 2 5

2 . 3 2 . 7

e p

W H = 2 . 1 0 3 m L / B = 5 , 8 • V = 5 k n o t

AW~_=30.0 m Cp=O.S9 O V= 11 knot

W P = 5 . ¢ s k y y / L = 0 . 2 5

4 ,5 C

e =

3 , 7 ~ ,

o

3 . 0 0

2 . 2 5

1 . 5 0

0 . 7 5

~ " 0 . 0 0

1 . 9

i

2 . 3 2 . 7

B / T

8 N - 7 L -3 2 m

5 W H = 7 . 0 10 m L / B = 5 . 8 • Y = 5 k n o t

4 W L =7 9 .0 m C p =0 .5 9

0

V = t ~

knot

AW 1 ==8-7 k yy /L = 0 .2 5

SW H =3 .g6 2 m L /E I=5 .B • V=5 k n o t

AW L =5 0 .0 m C p =0 .5 g 0 V= 1 k n o t

A W P = 7. O $ L ~ _ O = 0 . 2 5

~ 4 . 5 ( , :, . . . . . . .

k

, - E .

~" OOC ~ :

. 9 2 . 3

2 . 7

B / T

7 .0 C

~

6 .0 C

o 5 . 0 0

4 . 0 0

3.00

2.00

~

t . 0 0

~ " 0 . 0 0

. .. . . . . . . . . . . . . . - ½

L

1 . 9

2..3

2 . 7

B / T

8 . 0 0

7 . 0 0 ~

6 . 0 0

5 . 0 0

4 . 0 0

3 . 0 0

2 . 0 0

1 . 0 0

3 . 0 0

1 . 9

B N - 8 L - 3 2 m

SW H =I 1 .2 7 8 m L /B =5 .8 • V=5 k n o t

AW L =1 1 5 .0 m C p =0 .5 9 O V=1 1 k n o t

AW P=I 0 .5 • k yy /L =0 .2 5

; i - ~ . . . . . . . . . . . . . . . . . . . .

, i ,

2 . 3 2 , 7

B / T

F i g .

5 T h e e f f e c t o f B / T r a t i o v a r ia t i o n o n t h e s i g n i f i c a n t h e a v e a n d

p i t c h m o t i o n s c o r r e s p o n d i n g t o 6 d i f f e r e n t B e a u f o r t s c a l e o f

w i n d f o r c e f o r 5 a n d 1 1 k n o t s s h i p s p e e d s .

J U L Y 1 9 9 7 M A R I N E T E C H N O L O G Y 1 8 7


8/16

e N ~ [ ~ L ~ 2 m , [ . ~ B . .

9 W H = 0 . 3 0 5

m

B / T = 2 . 3

AWL= 6 . 1

m

I v = 5 k n o t • L / 8 = 5 . 1

AW I ~ = 2- 4 s k Y / / / L = 0 - 2 5

O

L / / B = 5 - 9

" 0 . 1 0

• 0 . 0 8

0 . 0 6

0 . 0 4

' 0 . 0 2

' O . O 0

0 . 5 9

0 . 6 2 0 . 6 5

C p

S W H = 0 . 8 8 4 m B , / T = 2 . 3 | 1 / ( ] = 5 . 1

A W L = I

5 9 m v=5

k n o t

A W P = 3 . g s k y y / L = 0 . 2 5

7 5 I :

. 5 0 .

. 2 5

. 0 0 •

. 7 5 -

. 5 0 •

. 2 5

. 0 0 k

0 . 5 9

. . . . . . . . . . . ~ . . . . ; . . . ~ . . . . . . .

0 . 6 2 0 . 6 5

C p

. 3 . 5 0

' 3 . 0 0

' 2 . 5 0

2 . 0 0

1 . 5 0

. 1 . 0 0

0 . 5 0

'

0 . 0 0

~ N . 5 ] L ~ 2 m [ . L , ~ - , ,

S W H = 2 . 1 0 3 m 8 , / 1 - = 2 .3

A W l _ = 30 . 0 m v = 5 k n o t • L / B = 5 . 1

A W P = 5 . 4 s k y y / l = 0 . 2 5 O L / B - 5 . B

i i . . . . . . . . . . .

0 . 5 9 0 . 6 2 0 . 6 5

C p

5 . 0 0

4 . 0 C

3 . 0 C

2 . 0 C

1 . OC

O. OC

0 . 5 9

~N., iL.~2m ] [. L,~=,..

S W H = 3 , g 6 2 m B , / T = 2 . 3

A V t L = 5 0 .0 m V = 5 k n o t • I / 8 = 5 . 1

A W P = 7 . 0 $ k y y / L = 0 . 2 5 O L / 8 = 5 . 8

. . . . . . . . . . . . . . . . . . . . . . . i . . . . . . . . . . . . . . i i . . . . . . . .

0 . 6 2 0 . 5 5

C p

B N - 7

]

L - 3 2 m

[ 4 - L J B - 4 . 4

S W H = 7 . 0 1 0 m B / ' T = 2 . 3 L / B = 5 . 1

A W L = 7 9 . 0 m v = 5 k n o t •

A W P = 8 . 7 k y y / L = 0 . 2 5

O

L / B = 5 . 8

7 . 0 0 , ,

6 . 0 0 L

, 1

, 5 . 0 0 . . . . . , . . . . . . . .. . . . . . .. . . . . . ; . . . . . . . . . . . . . . . . . . . . . . . . . . . .

4 . 0 0

3 . 0 0

2 . 0 0 ; . . . . . . . i . . . . . . . . . . . . . . . . . . .. . . ~

1 . 0 0

'

0 00

' ;

0 . 5 9

0 . 6 2

0 . 6 5

C p

7 . 5 0

6 , 0 0

4 . 5 0

3 . 0 0

1 . 5 0

O , O 0

B , 8 [ L ~ 2 m ] [ . ~ 8 . ,

S W H = I 1 . 2 7 8 r n 8, /* T =2 . 3 L / 9 = 5 . 1

A W l .= 1 1 5 . 0 r n v = 5 k n o t •

A W P = 1 0 . 5 = k y y / L = 0 . 2 5 0 L / 8 = 5 . 8

_ '.

~ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . i i . . .. .

; L ;

0 . 5 9 0 . 6 2

0 . 6 5

C p

F i g . 6 T h e e f f e c t o f C p v a r i a t i o n o n t h e s i g n i f i c a n t h e a v e a n d p i t c h

a m p l i t u d e s fo r 4 -. 4 ,5 . 1 a n d 5 .8 ( L / B ) r a t io s c o r r e s p o n d i n g

t o 6 d i f f e r e n t B e a u f o r t s c a l e o f w i n d f o r c e .



9/16

0 . 1 2

0 . 1 0

B N = 3 / L = 3 2 m • V = 0 k n

S W H = O . 3 0 5 m ] L / B = 4 . 4 0 V = 5 k n

A W L = 6 . 1 m B / T = 2 . 3 ÷ V = 1 1 k n

A W P = 2 . 4 s C p = 0 . 6 2

0 . 0 8 ' - : - : - - - -- : . . . . . . . . : - ' : : . . . . . . . . . . . . : . . . .

o 0 . 0 6 . . . . . ~ - : - - - - - - ~ - . . . . . . i . . . - i - - - - . : - - . . . . . . . . . i . . . . . .

0 . 0 4

0 . 0 2 ~ ~ ' ~ ' " " ~ - : i . . .. . .. . .. . .. . .. . .. . .. . ~ " : : : ' : . . . .

0 . 0 0

N 0 , 2 1 5 0 . 2 2 5 0 . 2 3 5 0 . 2 4 5 0 , 2 5 5 0 . 2 6 5 0 . 2 7 5 0 , 2 8 5

k ~ / L

B N - 4 L = 3 2 m

• V = O k n

S W H = 0 . 8 8 4 m L / B = 4 . 4 O V = 5 k n

A W L = 1 5 . 9 m B / T = 2 . 3 ÷ V = 1 1 k n

A W P = 3 . 9 s C p = 0 . 6 2

, : : . . . . . : ,

1 . 5 0

1 . 2 5

-o

1 . 0 0

0. 75 . . : : i : : : • i •

~

o50 : i i ; : i i J

~ o . 2 5 . L , . . . ~ i . . . . . . . . . . ~ i . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .~ . ~ ~ : : : . .

N 0.00 I i I i I i I i I ;

0 . 2 1 5 0 , 2 2 5 0 . 2 3 5 0 , 2 4 5 0 . 2 5 5 0 . 2 6 5 0 , 2 7 5 0 , 2 8 5

k w / L

B N = 5 L = 3 2 m

• V = 0 k n

5 W H = 2 , 1 0 3 m L / B = 4 . 4 O V = 5 k n

A W L = 3 0 , 0 m B / T = 2 . 3 + V = l 1 k n

A W P = 5 , 4 s C p = 0 . 6 2

3 . 5 0

3 o o I

: i : ~

2 , 5 0

o 2 ,0 0 : " ' : : . . . .

1 . 5 0

1 .oo . ~ .~, i . i

i i i ' . . . . . ' ° ' i

0 . 5 0 ~

- :

N 0 . 0 0 ' ; i i i ~ ~ , , ; i i i ; '

0 . 2 1 5 0 . 2 2 5 0 . 2 3 5 0 , 2 4 5 0 , 2 5 5 0 , 2 6 5 0 . 2 7 5 0 . 2 8 5

B N = 6

L = 3 2

I

• V = O k n I

I

W H = 3 . 9 6 2 m L / B = 4 . 4 O V = 5 k n

i

A W L = 5 0 . 0 m B / T = 2 . 3 ÷ V = 1 1 k n i

I

A W P = 7 . 0 s

C p = 0 . 6 2

5 . 0 0

, 4 . 0 0

, : . . . . .

o 3.0 0 " " : ' : : : i i " : '

, . ~ ~ : ~ . ,

2 , 0 0

1 . 00 .... ~ - : - . : ' ~= . t : : :

. : : . . : ~ . . ,

N 0. 00 i I I i I i I i I i I

0 , 2 1 5 0 . 2 2 5 0 . 2 3 5 0 . 2 4 5 0 . 2 5 5 0 . 2 6 5 0 . 2 7 5 0 , 2 8 5

k L

L B N = 7 [ L = 3 2 m • V = 0 k n

S W H = 7 . 0 1

0

L / B = 4 . 4 O V = 5 k n

A W L = 7 9 , O m B / T = 2 . 3 ¢ V = 1 1 k n

A W P = 8 . 7 s C p = 0 . 6 2

6 . 0 0

5 . 0 0

o 4 . 0 0

3 . 0 0

2 . 0 0

1 . o o

N

0 . 0 0

0 . 2 1 5 0 , 2 2 5 0 . 2 3 5 0 . 2 4 5 0 , 2 5 5 0 , 2 6 5 0 , 2 7 5 0 . 2 8 5

~ r f / k

B N = 8 L = 3 2 m

•

V = 0 k n

S W H = 1 1 . 2 7 8 m L / B = 4 . 4 O V = 5 k n

A W L = I 1 5 . 0 m B / T = 2 , 3 ÷ V = l 1 k n

A W P = I 0 . 5 s C p = 0 . 6 2

8 . 0 0

~ o.oo~ ~ . . . . 1

; 5 .0o . . . . ~ ? . . . ~ . 1

" o o o ,l ° ° r " { : , . . . . . . . . .. . . ~ ~ . . .. . . . :, , , i i. : :......... : : 1

" 0 . 2 1 5 0 . 2 2 5 0 . 2 5 5 0 . 2 4 5 0 . 2 5 5 0 . 2 6 5 0 . 2 7 5 0 . 2 8 5

k / L

F i g . ? T h e e f f e c t o f ( k y y / L ) r a t i o v a r i a t i o n o n t h e s i g n i f i c a n t h e a v e

a n d p i t c h a m p l i t u d e s f o r 0 , 5 a n d 1 1 k n o t s s h i p s p e e d s

c o r r e s p o n d i n g t o 6 d i f f e r e n t B e a u f o r t s c a l e o f w i n d f a r c e .



10/16

B N = 3 L = 3 2 m • C p = 0 , 5 9

S W H = O . 3 0 5 m L / B = 4 . 4 [ ] C p = 0 , 6 2

A W L = 6 . 1 m B / T = 2 . 3 + C p = 0 . 6 5

A W P = 2 . 4 s k y y / L = 0 , 2 5

0 , 1 2

° " 0 . 0 8

0 . 0 6

0 . 0 4

E i : : : : : :: : :

N 0 . 0 0

0 . 0 0 0 . 0 4 0 . 0 8 0 . 1 2 0 . 1 6 0 . 2 0 0 , 2 4 0 . 2 8 0 , 3 2

F r o u d e N u m b e r

B N = 4 L = 3 2 m • C p = 0 ~ 5 9

S W H = 0 , 8 8 4 m L / B = 4 . 4 [ ] C p = 0 . 6 2

A W L = 1 5 . 9 m B / T = 2 . 3 ÷ C p = 0 . 6 5

A W P = 3 . 9 s k y y / L = 0 . 2 5

1 . 6 0

" o 1 . 2 0

0 . 8 0

0 . 4 0

N 0 . 0 0

0 . 0 0 0 . 0 4 0 . 0 8 0 . 1 2 0 . 1 6 0 . 2 0 0 . 2 4 0 . 2 8 0 . 3 2


B N = 5 L = 3 2 m • C p = 0 . 5 9

S W H = 2 . 1 0 3 m L / B = 4 . 4 u C p = 0 , 6 2

A W L = 3 0 . 0 m B / T = 2 . 3 + C p = 0 , 6 5

A W P = 5 , 4 s I k y y / L = 0 . 2 5

3 , :5 0

& O 0 ~ - 7 : ÷ ) " ~ 7

2 . 5 0 . .. . : . . . . . ; . . i . . . - - . . i . . . . i . . . . ~ . . . . : : ~ . : : .

o o . . ,~ - - ; , ' : " ' " ' ; " . . . . . . i . : :

1 . 5 0 . : . . . . . . .. . : . . . . . . . . . . . . . ; . . . . : - i . . . . i . . . . . . . : - - : - - : -

1 . 0 0

0 ,: 5 0 " ' - ~ " :' " ' " . • • " : " ~' " ? :

0 .0 0 i i ~ , ~ i i ; i , i i i

0 , 0 0 0 . 0 4 0 . 0 8 0 . 1 2 0 . 1 6 0 . 2 0 0 . 2 4 0 . 2 8 0 . 3 2


B N = 6 L = 3 2 m

• C p = 0 . 5 9

S W H = 3 . 9 6 2 m L / B = 4 . 4 u C p = 0 . 6 2

A W L = 5 0 . O m B / T = 2 . 3 + C p = 0 . 6 5

A W P = 7 . 0 s k y y / L = 0 . 2 5

5 . 0 0

2 0 0 i i ~ i

~ : ~

1 . 0 0 Z _ . _ ~ ~ " , : ' : ' ~ - " . ' : ' - r " " : : ' : : : i - ' : : ~ - ' : ' " " 7 " " T , - .

N 0 . 0 0 ; i i I } n ~ i , l ; I ; l

0 . 0 0 0 . 0 4 0 . 0 8 0 . 1 2 0 . 1 6 0 . 2 0 0 . 2 4 0 . 2 8 0 . 3 2


B N = 7 L = 3 2 m

• C p = 0 . 5 9

S W H ~ 7 , 0 1 0 m L / B = 4 . 4 o C p = 0 . 6 2

A W L = 7 9 , 0 m B / T = 2 . 3 + C p = 0 , 6 5

A W P = 8 . 7 s k y y / L = 0 . 2 5

7,0 0 . i ~ i : ' - i , : : '

, . 0 0 : : : :

5.00

o 4 .0 0 : :

" " :

:,

3 , 0 0

• . ; " i : : i : : . : .

2 . 0 0 E ' L [ ~ - - " - " - : - ' "~ - " k " " ; : - - 5 ~ " : ' " E " ~ ~ ~ ~ ' ' - - " : ' ? - - ' ~ i

1

.oo

. . ~ . ~ . . .

i i i :

0 . 0 0 ~

0.00 0.04 0.08 0.12 0,1 6 0.20 0.24 0,28 0.32


B N = 8 L = 3 2 m

• C p = 0 , 5 9

S W H = I 1 , 2 7 8 m L / B = 4 . 4 o C p = 0 . 6 2

A W L = l 1 5 . 0 m B / T = 2 . 3 ÷ C p = 0 , 6 5

A W P = I 0 . 5 s k y y / L = 0 . 2 5

7 . 5 0 , , ; , . , , : = . : ; : , . : - , . = - . :

~ ' 6 . 0 0 [

4 . 5 0

3 . 0 0

E

N 1 . 5 0

0 . 0 0

, , , , , , , L ; i , ~ , i ,

0 . 0 0 0 . 0 4 0 . 0 8 0 . 1 2 0 . 1 6 0 . 2 0 0 . 2 4 0 . 2 8 0 . 3 2


F i R . 8 T h e e f f e c t o f F r o u d e n u m b e r v a r i a t i o n o n t h e s i g n i f i c a n t

h e a v e a n d p i t c h a m p l i t u d e s f o r 0 . 5 9 , 0 . 62 a n d 0 . 6 5 C p

v a l u e s c o r r e s p o n d i n g t o 6 d i f f e r e n t B e a u f o r t s c a l e o f w i n d f o r c e

1 9 0



11/16

Th e r eg ress ion coe ff ic i ent s ( , a~, a 2 , a3 , a4 , as, a 6

a nd aT) a ppe a r i ng i n t he s e e q ua t i on s y s t e ms , a nd

m u l t i p l e c o r e l a t i o n c o e f f i c i e n t s a n d e s t i m a t e d s t a n d a r t

e r r o r v a lu e s c o r r e s p o n d i n g t o B e a u fo r t n u m b e r s

3 , 4 , 5 , 6 , 7 a n d 8 h a v e b e e n d e t e r m i n e d b y u s i n g m u l t i p l e

r e g r e s s i o n a n a l y s i s p r o g r a m s .

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

m o t i o n o f a sh i p c a n b e c o n s t r u c t e d i n a s im i l a r w a y a s

i n t h e h e a v e m o t i o n . H e n c e , t h e p o l y n o m i a l r e l a t i o n s h i p

b e t w e e n d e p e n d e n t v a r i a b l e Q ( p i t c h a m p l i t u d e ) a n d 8

i n d e p e n d e n t p a r a m e t e r s c a n b e e x p r e s s e d b y t h e

f o l l o w i n g m o d e l :

L L

Q = b0

+bjCwL+b2C

+b3-~ +b4-~

k V +bs~____L

(degree)

(3)

b 5 L C B + b6~ +b7-----

H e r e 2 7 e q u a t i o n s w i t h 9 u n k o w n s , t o t a l l y 2 0 e q u a t i o n

s y s t e m s , h a v e b e e n o b t a i n e d . S o l u t i o n o f t h e se e q u a t i o n

s y s t e m s b y u s i n g m u l t i p l e r e g r e s s i o n a n d c o r r e l a t i o n

a n a l y s i s f o r B e a u f o r t n u m b e r s 3 , 4 , 5 , 6 , 7 a n d 8 g i v e s t h e

r e g r e s s i on c oe f f i c i e n t s ( b 0 , b~ , b2, b3, b4 , bs, b6, b 7 a n d

b s) m u l t i p l e c o l e r a t i o n c o e f f i c i e n t s , a n d e s t i m a t e d

s t a nda r t e r r o r .

Results of M ultiple Regression and Corelation

Analysis

R e g r e s s i o n c o e f f i c i e n t s ( a 0 ,a l , a z . . . . a 7 a n d

b0 ,b~ ,b2 . . . . . b s ) f r om t he r e g r e s s i on a na l y s i s ha ve be e n

t e s te d f o r e a c h m a i n l e n g t h a n d s e a s ta t e , a n d h a v e b e e n

f o u n d v e r y r e li a b l e. T h e s e c o e f f i c i e n t s h a v e b e e n

t a b u l a t e d i n T a b l e 2 w i t h r e s p e c t t o t h e s h i p l e n g t h a n d

B e a u f o r t n u m b e r s . T o s e e t h e r e li a b i l it y o f t h e s e

c o e f f i c i e n ts , t h r e e g r o u p s o f s h i p s h a v i n g d i f f e r e n t

l e n g t h s h a v e b e e n t a k e n a s e x a m p l e s . I n t h e s e s a m p l e s ,

t h e c o m p u t e d v a l u e s f r o m r e g r e s s i o n e q u a t i o n s a n d t h e

r e s u lt s o b t a i n e d f r o m t h e W o l f s o n U n i t S hi p M o t i o n

C o m p u t e r P r o g r a m f o r th e t r a w l e r f i sh i n g bo a t s h a v e

b e e n s h o w n a s a s ca t t e r e d d i a g r a m i n F i g . 9 . A s is se e n

f r o m t h e d i a g r a m s t h e r es u l t s o b t a i n e d f r o m t h e

r e g r e s s i o n c o e f f i c i e n t s a r e v e r y r e li a b l e. A l s o , t h e

s i g n i f i c a n t h e a v e a n d p i t c h a m p l i t u d e s h a v e b e e n

d e t e r m i n e d b y a c o m p u t e r p r o g r a m u s i n g t he r e g r e ss i o n

r e s u lt s . T h e r e s u l ts o f t h i s p r o g r a m h a v e b e e n c o m p a r e d

w i t h t h e W o l f s o n U n i t p r o g r a m r e s u l t s a n d a r e

i l l u s t r a te d i n F i g . 10 .

A P P L I C A T I O N

T h e r e s u l t s o f th i s p r e s e n t s t u d y c o n t a i n i n g r e g r e s s i o n

c o e f f i c i e n t ta b l e s c a n p r o v i d e u s e f u l d e s i g n i n f o r m a t i o n

f o r t h e tr a w l e r s h u l l d e s i g n . T h e r e g r e s s i o n c o e f f i c i e n t s

a l l o w a q u i c k e v a l u a t i o n o f t h e s e a k e e p i n g ( s i g n i f i c a n t

h e a v e a n d p i t c h ) q u a l i t i e s o f a g i v e n t r a w l e r h u l l i n i ts

o p e r a t in g e n v i r o n m e n t . T o d e m o n s t r a t e t h e p r o c e d u r e ,

t h e 2 4 . 8 5 m l e n g t h o f t r a w l e r h u l l w a s s e l e c te d . T h e

i n t e r p o l a t io n i s s h o w n i n t h e f o l l o w i n g m a n n e r f o r t h e

h e a v e a n d p i t c h m o t i o n o f t h e t r a w l e r h u l l a t d ra f t

2 . 5 6 4 m , f o r B e a u f o r t n u m b e r 5 ( s i g n i fi c a n t w a v e

h e i g h t o f 2 . 1 0 3 m a n d w a v e p e r i o d o f 5 . 4 s ) a n d h u l l

s p e e d o f 8 k n o t s :

L = L e n g t h = 2 4 .8 5 m

B = B e a m = 4 . 8 7 3 m

T = D r a ft = 2 .5 6 4 m

C B = B l o c k C o e ff i ci e n t = 0 . 5 4 0 8

C w = W a t e r p l a n e C o e f fi c ie n t = 0 . 7 0 8 2

L . C . B . = - 0 . 3 3 9 ( ( -) A f t a n d L )

k y y = R a d i u s o f g y r a t i o n / L = 0 . 2 5

V = S h i p s p e e d = 8 k n o t s

T h e r e g r e s s i o n c o e f f i c i e n t s f o r t h e h e a v e m o t i o n o f

t h e t r a w l e r h u l l w e r e r e a d f r o m T a b l e 2 a s f o l l o w s :

F o r L = 2 4 m F o r L = 2 5 m

= - 0 . 0 6 8 6 a o = - 0 . 4 8 8 6

a 1

=

0 . 8 6 8 2 a~ = 4 . 0 4 0 9

a 2 = - 1 . 1 7 0 7 a 2 = - 4 . 5 7 5 7

a 3 = 0 . 0 1 3 7 a 3 = 0 . 0 1 4 9

a 4 = 2 . 3 7 2 1 a n = 2 . 3 9 1 4

a 5 = 0 . 0 2 6 9 a5 = 0 . 0 6 5 0

a 6 = 1 . 0076 a 6 = 1 . 2019

a 7 = 0 . 7 0 7 0 a 7 = 0 . 7 5 6 7

T h e s i g n i f i c a n t h e a v e a m p l i t u d e f o r t h e s e t w o f is h i n g

v e s s e l s c a n b e e v a l u a t e d f r o m t h e r e g r e s s i o n e q u a t i o n

as:

L T kyy V

+aT r-z-_

= a 0

+ a 1CWL

+ a 2 C B + a 3 -

+a4-~

+asLCB

a6--L--

~/gL

Z24 = - 0 . 0 6 8 6 + 0 . 8 6 8 2 x 0 . 7 0 8 2 - 1 . 1 7 0 7 x 0 . 5 4 0 8

+ 0 . 0 1 3 7 x (2 4 / 4 . 8 7 3 ) + 2 . 3 7 2 1 x ( 2 .5 6 4 / 2 4 )

+ 0 . 0 2 6 9 x ( - 0 . 3 3 9 x 1 0 0 /2 4 ) + 1 . 0 0 7 6 x 0 . 2 5

+ 0 . 7 0 7 0 x ( 8 x 0 .5 1 4 4 /~ / 9 .8 1 x 2 4 )

Z 24 = 0 . 6376 m

a n d

Z :5 = - 0 . 4 8 8 6 + 4 . 0 4 0 9 x 0 . 7 0 8 2 - 4 . 5 7 5 7 x 0 .5 4 0 8

+ 0 . 0 1 4 9 x ( 2 5 / 4 . 8 7 3 ) + 2 . 3 9 1 4 x ( 2 . 5 6 4 / 2 5 )

+ 0 . 0 6 5 0 x ( - 0 . 3 3 9 x 1 0 0 / 2 5 ) + 1 . 2 0 1 9 x 0 . 2 5

+ 0 . 7 5 6 7 x ( 8 x 0 . 5 1 4 4 / ~ / 9 . 8 1 x 2 5 )

Z 25= 0 . 6315 m

T h e i n t e r p o l a t i o n b e t w e e n 2 4 m a n d 2 5 m f o r 2 4 . 8 5

m i s g i v e n a s f o l l o w s :

( t ex t cont inued on pag e 196)

JULY 1997 MARINE TECHNOLOGY 191


12/16

T a b l e 2 . a R e g r e s s i o n c o e ff i c ie n t s o f h e a v e a n d p i t c h m o t i o n s f o r d i f f e r e n t B e a u f o r t n u m b e r s

Regr ess ion Coe f f i c ien ts o f Hea ve m ot ion Regr ess ion Coe f f i c ien ts o f P i t ch m ot ion

B N ao a l a2 a3 a4 a5 as a ; , bo b l b2 b3 b 4 b5 bs b7 I b8

3 0.1919-0.384 9i 0.2194 0.0115-0,0 489-0,0032 0,0072 -0.0809 4.9912.-,6.1678 3.5897 0.1693 0.0188-0,0 651-6. 6270-3 ,0950 1.6768

4 0.1140 -1.3092 1.3051 0.010 1 1.1859 -0.0097 0.502 2 0.231 ) 5,69 12 -7.7868 4.3019 0.1519 -0.0474-0,0972 0.9141 -0.7653 0.5428

5 0.4766 -2.0251 2.0960 0.00 85 1.323 4 -0.0180 0. 497 3[0 282 3 8.1220-16.755 3 13.1763 0.1990 -0.0643-0.216 5 2.6689 -0.3607 -0.1032

0.7583 -0.115 1 0.0707 0.0 060 1.2 225 0.00 50 0.4185 I 0.2747 7.8 587 -8.1197 3.7345 0.2318 -0.0718 -0.1214 4.2239 0.4 585 -1.4887

7 1.6 684 -1.3036 1.3771 0.00 52 1.1497 -0.0102 0.36 33 0.2595 9.7108-16 .3743 12 .3217 0.2731 -0.0785-0.237 3 5.5976 1.23 97 -2.9905

8 3.1983 -5.5258 5.9565 0.0064 1.095 1 -0.0630 0.3292 0.2308 14.894-62.173 0 61.7098 0.346 3 -0.0888-0.807 9 7.5881 2.981 3 -5.9829

3 0.1033 -0.1588 0.0454 0.0086 -0.1278 0.0000 0.10 61 -0.0689 2.7570 -0.6133 -1.6547 0.1 380 0.0250 -0.0049 -3.1874 -2.8380 1.3883

4 -0.2018 1.496 8 -1.7400 0.0109 1 .29 78 0.0247 0.4886 0.285: } 4.4138 -.3.7106 0.2636 0.1841 -0.0539-0.027 6 2.2573 -0.2144 -0.4349

5 -0.0200 2.5985 -2.9104 0.0088 1.4 315 0.0386i 0.4291 0.3 475 6.4564 -8.9299 5.1204 0.2 400 -0.0730 -0.0923 3.9229 0.0909 -0.9858

0.609811 1.387 4 -1.5698 0.0059 1.3 397 0.0230 0.3091 0.3463 7.3 416 -9.3656 5.3260 0.2 756 -0.0828 -0.1064 5.5119 0.5095 -1.8595

II

-3 7 1.4 142 1.3149 -1.4679 0.0039 1.243 5 0.0 215 0.2250 0.334~', 6.4365 8.30 38 -13.9941 0.3232 -0.0930 0.1055 6.7785 1.1637 -3.2383

8 2.2724 3.5470 -3.8514 0.0 027 1.126 7 0.048 5 0.1516 0.3096 13.3095 -45.8697 44.1674 0.3699 -0.1008 -0.5717 7.3049 1.7715 -4.6447

3 0.0746 0 .09 49 -0.2207 0.0071 -0.0883 0.0021 0.0300 -0.0600 2.475 2 -2.1413 0.8239 0.1047 0.0250 -0.0259 -3.5402 -3.6028 3.0749

4 -0.0469 -0.7585 0.6690 0 .01 34 1.5 599 0.00 01 0.7316 0.3426 3.7590 0. 9696 -4.8299 0.1425 -0.0452 0.0053 2.2832 -0.0077 -0.4824

~r~ 5 0.2358 -0.4909 0.39 41 0.010 6 1.68 47 0.0 040 0.6591 0.4117 4.5756 4.9 153 -9.8390 0.1931 -0.0622 0.0521 4.4708 0.77 74 -1.6904

~1 6 0.8424 -1.6253 1.65 93 0.00 77 1.604 8 -0.0113 0.5882 0.4083 5. 848 2 0.310 0 -5.1617 0.217 9 -0.0716-0.01 24 6.2839 1.622 9 -3.0685

-3 7 1.75 56 -2.5591 2.67 92 0.0053 1.504 3 -0.0232 0.4721 0.400 1 6.O816 8.6459 -12.2858 0.2515 -0.0808 0.0583 8.0210 2 .456 3 -4.5787

8 2.5624 -0.1000 0.0658 0.0035 1 .31 00 0.0048 0.4977 0.3815 7. 2180 2.63 64 -8.0796 0. 272 5 -0.0864 0.0154 9.5464 3. 714 4 -6.7557

:3 0.0 761 -0.1407 0.0540 0.0062 -0.0688 -0.0008 0.0600 -0.052:3 4.0400 -'18.0316 18.0182 0.0 907 0.0223 -0.2070 -3.7499 -2.6446 1.9736

= 4 -0.1178 0.2569 -0.4545 0.01 32 1.6055 0.0122 0.6033 0.36 35 1.9772 10.1215 -14.1359 0.1569 -0.0461 0.13 82 2.4884 1.9923 -3.3884

5 0.3075 -0.6913 0.5809 0.0096 1.717 6 0.0010 0.5017 0. 439 9 4.3040 3. 9267 -8.5922 0.2324 -0.0675 0.0485 4.9332 0.7 149 -1.8970

~1 6 0.9216 -1.7698 1 .7797 0.0 067 1.6604 -0.0130 0.3759 0.445;' 4.8290 7.3 460 -12.6092 0.2623 -0.0776 0.0 819 6.6 342 1.036 7 -2.5320

-3

7 1.4 897 0.3510 -0.4740 0. 0040 1. 5564 0.01 23 0.2831 0.435". 5.5426 10.6933 -16.5694 0.2993 -0.0873 0.115 2 8.1148 1.4152 -3.3931

8 2.4810 1.4143 -1.5950 0 .0021 1.4 063 0.0 244 0.2100 0.404 9 2.7635 43.7403-51.9709 0.3172 -0.0856 0.528 0 7.1495 3.9419 -7.2291

:3 0.0568 0.0 371 -0.1195 0.00 46 -0.0687 0.0 009 0.0039 -0.0438 0.31 43 8.27 61 -9.8437 0.0 732 0.0169 0. 0977 -1.7246-2. 6139 2.5468

= 4

-0.2843 0.754 5 -1.0056 0.01 54 1.8030 0.0205 O.9581 0.4115 4.10 14 -4.8959 1.5 756 0.1 351 -0.0458-0.06 58 2.5318 0.00 13 -0.3191

~¢ 5 0.1 652 -0.3171 0.1 712 0.0 117 1.92 66 0.00 82 0.7765 0.509 0 4.9413 -4 .1491 0.0860 0.18 72 -0.0618 -0.0580 5.358 1 1.491 6 -2.8584

~1 6 0.7 092 -0.8311 0.76 32 0.0086 1.88 42 0.0011 0.6844 0.5195 5.9461 -5.8959 1.62 21 0.208 7-0.0 721-0 .0861 7.265 5 2.3805 -4.2917

-3 7 1.7 212 -2.7452 2. 852 2 0.0060 1. 7865 -0.0235 0.5816 0.5090[ 6.6806 -3.9646 -0.8127 0. 236 9 -0.0821 -0.0683 9.1544 3.2658 -5.8595

8 2.3018 2 .19 73- 2.4 435 0.0037 1.6 220 0.0363 0.4700 0.4 724 8.6330 -'14.1920 10.01 40 0.2607 -0.0881 -0.1996 10.513C 3.9 377 -7.1769

3 0.1020 -0. 4255 0.3879 0.0041 '-0.0684 -0.0049 -0.0018 -0.0410 1.4 815 -3.5213 2.9606 0.0638 0.0137 -0.0460 -1.6296 -2.2847 2.2539

4 -0.9237 6.6750 -7.4137 0.0175 1. 9083 0.0956 0.9177 0.4 259 2.8 541 6 .3289 -10.4992 0.1359 -0.0467 0.0731 2.4126 -0.1574 0.0121

¢~ 5 -0.6058 6.53 08 -7.2066 0.0121 2.0211 0.0936 0.8137 0. 542 2 3.625 2 6.4650 -11.2985 0.1868 -0.0626 0.0720 5.5645 1. 616 7 -3.0778

~1 6 -0.2453 7.6 897 -8.4133 0.0091 1.9907 0.1 073 0.7176 0.5557 2.9293 20.3949~-26.641g 0.2081 -0.0736 0.2382 7.474 5 2.501 8 -4.5051

-3 7 0.6956 6.4 380 -7.0366 0 .00 63 1.8944 0.0 908 0.6124 0.5460 4.7920 12.0212 -18.01081 0.2339 -0.0837 0.1276 9.4335 3.4 256 -6.1198

8 2.3749 1.3636 -1.5534 0. 003 9 1.713 8 0.0266 0.5027 0.5085 5 .97 64 8.9395 -14.8816 0.2568 -0.0898 0.0858 10.803 6 4.0734 -7.4008

3 0.0600 -0.1087 0.0566 0.0034 -0.0693 -0.0011 0.0041 -0.03713 1.3943 -2.5515 2.1110 0.0485 0.0125 -0.0323 -2.1281 -2.1506 2.3176

4 -0.4478 2.293 3 -2.7390 0.02 10 1.971 2 0.O414 0.92 43 0.4328 3.2548 -1.2204 -2.2431 0 .120 5 -0.0460 -0.0253 3.0959 1.186 3 -2.3373

¢~ 5 -0.1421 2.51 71 -2.9114 O.0138 2.0877 0.0445 0.6875 0.5730 3 .81 87 -2.9951 -0.9488 0.1724 -0.0635 -0.0456 7.6071 3.6409 -6.6941

6 0.5149 1.3150 -1.5777 0.0088 2.O167 0.0274 0.4856 0.5818 3.4944 6.3 958 -11.4334 0.1957 -0.0753 0.0663 10.0181 4.7151 -8.4589

-3__3 7 1.2567 1.6264 -1.8753 0.0077 1.9 732 0.0320 0.4340 0.5 804 4.0786 9.0 788 -14.7019 0.2197 -0.0858 0.0924 12.261c 5.7639 -10.3313

8 2.4796 0.7 102 -O.8601 0.005 2 1.8 018 0.0192 0.3147 0.5415 6.3607 -4.7247 -0.0404 0.2414 -0.0924 -0.0825 13.934E 6.5371 -11.8253

3 0.0230 0 .0922 -0.1503 0.0032 I-0.0640 0 .00 15 0.0365 -0.0357 1.0883 -1.9 921 1.5 801 0.0540 0.0107 -0.0236 -2.17601-0.9530 0.2672

I=1 4 -O.1928 0.3721 -0.7869 0.0256 2.0206 0. 018 2 0.8996 0. 419 0 2.9530 1.7 736 -5.2613 O.1761 -0.0475 0.03 81 1.2733 1.3273 -2.5960

5 0.1857 -0.0 478-0.21 55 0.0 104 2.0738 0. 011 3 0.6667 0. 613 8 3.0313 8.0267 -12.81271 0.2252 -0.0675 0.1015 6.1984 1.3001 -2.9992

~1 6 0.6918 -0.0969-0. 1252 0.007 3 2.06 22 0.0101 0.5150 0.6357 4.36 95:3. 8637 -8.4819 0.2446 -0.0736 0.0521 6.4050 3.575 2 -6.5561

__3 7 1.542 6 -0.5176 0.3629 0.0044 1 .98 19 0.0039 0.3898 0.6317 5.2325 5.4373 -10.5 504 0.2751 -0.0841 0.0670 8.0639 4. 263 6 -7.7926

8 2.5 031 0.8761 -1.1 021 0.0024 1 .81 76 0.0199 0 .28 82 0.5916 5.8998 "7.8653 -13.3 534 0.2974 -0.0902 0.0933 9.1688 4.7590 -8.7880

3 0.0288 0.0877 -0.1397 0.0028 -0.0649 0.001 5-0. 000 3-0. 0334 0.4697 0.4 363 -1.0779 0 .0406 0.007 1 0.00 02 -0.0082-1.632 7 1.7306

I=1 4 0.2 430 -1. 499 5 1.1432 0.0316 2.1032 -0.0006 0.0033 0.4113 3.2035 0.84 79 -4.2502 0 .17 79 -0.0452 0.0288 0.0032 1. 6958 -3.2564

P.1 6 0.3 082 0.0535 -0.2617 0.0080 2.0118 0.01 35 0.0047 0.66 07 3.2935 9.49 39 -14.3618 0.2215 -0.0521 0.08 80 0.0163 6.1972 -10.5900

~1 6 0.8019 -0.31 11 0.1415 0.0 082 2.0834 0.0 074 0.0050 0.6842 5.0236 3.946 6 -8.8366 0.2499 -0.0588 0.0058 0.0221 7.7 604 -12.9685

-3

7 1.3 529 1.7203 -2.0036 0.0052 2.0087 0.03 16 0.0046 0.6771 5.5335 10.4 558 -16.2322 0.279 4 -0.0674 0.070 3 0.0271 9.6253 -16.0366

8 2.0084 5 .732 1 -6.2834 0.002 3 1.8 334 0.0799 0.0038 0.6307 10.1779-20.750E 17.2172 0.2 548 -0.06 64-0. 3249 0.0340 10.7765-18.1829

3 -0.1515 1.6600 -1.8285 0.0026 -0.0637 0.0208 0.0188 -0.0313 0.4101 0.5 161 -1.0005 0.0 325 0.00 91 0.0092 -O.3197 -1.5038 1.7609

I= 4 -0.4069 2.29 86 -2.9525 0.0333 1 .91 23 0.0 444 1.0761 0.3546 3.6349 -5.7824 2.8764 0.1611 -0.0458 -0.0496 1.6034 1.2 508 -2.2348

5 3.2665 .28.9984 30.9892 0.0098 2.1984 -0.3447 0. 874 2 0.6 538 3.7253 2.47 49 -6.8336 0.2163 -0.0630 0.0363 4.1262 3.1857 -6.0356

II 6 2.5539 .18.0394 19.2316 0.0071 2.2157 -0.2096 0.7713 0 .67 85 4.6814 2.8181 -7.6119 0.2395 -0.0736 0.0355 5.4335 4. 1061 -7.5561

-3 7 2.8630 -13.544g 14.4010 0.0047 2.2503 -0.1557 0.6894 0 .66 42 6.2 041 -0.6346 -4.3022 0.2603 -0.0840 -0.0156 6.3569 5 .6628 -10.2653

8 4.3 072 -16.6530 17.8084 0.0008 1.95 02 -0.1961 0.6374 0.6310 7.4 174 -3.3398 -1.5996 0.2849 -0.0906 -0.0490 7.6887 6.0071 -11.0344

1 9 2 J U L Y 1 9 9 7

MARINE TECHNOLOGY


13/16

Ta b le 2 . b Reg ress io n co ef f i c i en t s o f h ea ve a nd p i t ch m o t io ns fo r d i ff eren t B ea u fo rt num b ers

R e g r e s s i o n C o e f f i c i e n t s o f H e a v e m o t i o n R e c j r e ss i o n C o e f f i c i e n t s o f P i t c h m o t i o n

BN ao a l a2 a3 a4 as a~ a7 bo bt b2 133 134 b5 b ~ I07 bs

3 0 . 0470 -0 . 1184 0 . 0900 0 . 0023 -0 . 088 1 -0 . 0013 -0 . 0056 -0 . 0315 0 . 6629 -1 . 5218 1 . 2693 0 . 0307 0 . 0078 -0 . 0205 -0 . 8188 -1 . 2236 1 . 3200

4 -0 . 4993 3 . 3428 -4 . 1146 0 .0337 2 . 1044 0 . 0589 0 . 9870 0 . 3489 4 . 0218 -5 . 6562 2 . 5320 0 . 1638 -0 . 0436 -0 . 0689 1 . 4334 -1 . 6040 2 . 6325

5 -0 . 0686 0 . 8682 -1 . 1707 0 . 0137 2 . 37 21 0 . 0269 1 . 0076 0 . 7070 4 . 3724 -7 . 1454 3 . 5282 0 . 1778 -0 . 0525 -0 . 0912 6 . 5541 2 . 6804 -5 . 1087

6 0 . 3993 1 . 08 24 -1 . 3 63 0 0 .0105 2 . 3818 0 . 0290 0 .8957 0 . 7316 5 . 1083 -4 . 1399 0 . 1654 0 . 1748 -0 . 0707 -0 . 0504 7 . 52 11 3 . 3906 -6 .0698

7 1 . 3403 -0 . 1904 0 . 0444 0 . 0076 2 . 3188 0 . 0122 0 . 7770 0 . 7314 10 . 3 355 -45 . 48 41 43 . 9737 0 . 2135 -0 . 0852 -0 . 5628 10 . 7 567 5 . 1559 -9 . 3266

8 3 . 1684 -6 .5162 6 .8795 0 . 0059 2 . 1274 -0 . 0680 0 . 6097 0 . 6853 7 . 17 71 -6 .2379 1 . 8652 0 . 2088 -0 . 0887 -0 . 0816 10 . 9 367 5 . 1869 -9 . 2757

3 0 . 0364 -0 . 0507 0 .0215 0 . 0020 -0 . 0668 -0 . 0005 -0 . 0049 -0 . 0295 0 .4437 -0 . 1596 -0 . 14 31 0 . 0268 0 . 0072 -0 . 0039 -0 . 7180 -1 . 1043 1 . 2201

4 0 . 4177 -5 . 1354 4 . 9 85 8 0 . 0 35 8 1 . 9502 -0 . 0444 1 . 1084 0 . 3300 3 . 1123 2 . 7044 -6 . 4390 0A 701 -0 . 0 41 1 0 . 0356 0 . 9732 -1 . 8360 2 .9190

l ur } 5 - 0 . 4886 4 . 0409 -4 . 5 75 7 0 . 0149 2 . 3914 0 . 0650 1 . 2019 0 . 7567 3 . 6052 -1 . 6802 -2 . 3163 0 . 1698 -0 . 0529 -0 . 0144 6 . 8609 3 . 3163 -6 . 2864

6 0 . 0757 3 . 6 62 1 -4 . 1368 0 . 0110 2 . 4934 0 . 0618 0 . 9853 0 . 7688 4 . 9006 -5 29 29 1 . 1553 0 . 1863 -0 . 0737 -0 . 0617 8 .7418 4 . 2544 -7 . 8339

7 1 . 2878 0 . 1424 -0 . 32 61 0 . 0079 2 . 4039 0 . 0169 0 . 8105 0 . 7692 6 . 0296 -7 . 2217 2 . 8028 0 . 2075 -0 . 0856 -0 . 0875 10 . 982( : 5 . 4 97 0-1 0 . 0 32 2

8 2 . 7 3 6 0 -2 . 7 4 99 2 . 8 20 9 0 . 0 0 5 0 2 . 2 1 7 5 -0 . 0 2 0 5 0 . 6 6 9 6 0 . 7 2 4 5 6 . 7 9 7 1 -6 . 5 2 03 1 . 8 2 0 3 0 . 2 2 3 2 -0 . 0 9 30 - 0 .0 8 1 0 1 2 . 5 7 3 6 6 . 3 2 5 9 - 1 1 . 5 8 6 1

3 0 . 0 2 3 1 0 . 0 0 0 0 - 0 . 0 2 4 9 0 . 0 0 1 5 -0 . 0 5 86 0 . 0 0 0 0 0 . 0 0 0 8 - 0 . 0 2 56 0 . 4 5 7 1 0 . 0 0 00 - 0 . 2 4 0 1 0 . 0 1 9 6 0 . 0 8 5 9 - 0 .0 8 0 7 - 0 .9 1 2 2 - 1 .2 4 0 7 1 . 7 0 0 2

4 0 . 0169 0 . 0800 -0 .6265 0 .0399 1 . 6810 0 . 0167 0 . 6704 0 . 2397 1 . 9377 0 . 0008 -3 . 4255 0 .1187 -0 . 0378 -0 . 0059 3 . 9874 5 . 0294 -11 . 6284

5 0 . 0334 0 . 0000 -0 . 2812 0 . 0160 2 . 6050 0 . 0190 0 . 8788 0 . 8086 2 . 9057 0 . 0008 -4 . 1 28 1 0 . 1758 -0 . 05 51 -0 . 0052 8 .3199 3 . 7921 -7 . 7421

~ 1 6 0 . 5 3 35 0 . O 0 0 0 4 3 . 2 4 2 8 O . O 1 3 1 2 . 6 2 2 2 0 . 0 1 8 1 0 . 7 2 6 1 0 . 8 34 3 3 . 4 8 3 0 O . O O 0 0 - 4 .4 1 9 2 O . 1 9 O O - 0 .0 7 3 5 - 0 .O O 5 1 1 0 . 6 8 2 2 5 . 7 1 7 6 - 1 1 .1 4 7 2

, - : 7 1 . 3374 0 . 0000 -0 . 2004 0 . 0099 2 . 5808 0 . 0170 0 . 5874 0 . 8418 4 . 3064 0 . 0 (X) 0 -4 . 8536 0 . 2138 -0 . 0860 -0 . 0069 13 . 2 45£ 7 . 0879 -13 . 6530

8 2 . 4 6 72 0 . 0 0 0 0 - 0 .1 6 0 2 0 .0 0 7 0 2 . 3 9 5 8 0 . 0 1 5 0 0 . 4 4 1 9 0 . 7 9 5 1 5 . 0 7 5 2 0 . 0 0 00 - 5 . 0 8 2 1 0 . 2 3 0 6 - 0 .0 9 3 8 -0 . 0 0 84 1 5 . 0 9 7 2 8 . 0 3 8 4 - 1 6 .4 6 0 1

3 0 . 01 61 0 . 0226 -0 .0422 0 . 0012 -0 . 053 1 0 . 0004 -0 .0014 -0 . 02 11 0 . 3197 -0 . 4425 0 . 2669 0 . 0160 0 . 0045 -0 . 0067 -0 . 4100 -0 . 8294 1 . 0393

4 -0 . 0326 1 .4215 -2 . 2399 0 . 0425 1 . 2902 0 . 0322 0 . 5535 0 . 1145 3 . 5270 -2 . 4595 -0 . 5245 0 . 2096 -0 . 0257 -0 . 0245 -1 . 9039 -0 . 9 48 1-0 . 86 16

5 - 0 .0 2 6 8 0 . 68 7 0 - 1 . 0 5 5 3 0 . 0 1 2 5 2 . 6 5 2 2 0 . 0 2 6 1 0 .9 0 4 8 0 . 8 7 3 1 3 . 3 4 1 2 - 1 .5 4 9 5 - 2 . 2 8 13 0 . 1 9 7 0 - 0 . 0 6 3 0 - 0 . 0 1 8 1 5 . 9 1 9 0 3 . 6 1 2 3 - 7 .2 6 5 2

6 0 . 4940 0 . 6535 -0 . 99 31 0 . 0097 2 . 6577 0 . 0253 0 . 6999 0 . 8976 5 . 2256 -12 .0227 8 . 7 97 1 0 . 2157 -0 . 0740 -0 . 1483 7 . 9978 4 . 3719 -8 . 3917

7 1 . 1 4 42 2 . 0 3 6 0 -2 . 4 4 03 0 . 00 6 4 2 . 6 4 4 5 0 . 0 4 1 5 0 . 5 6 6 7 0 . 9 1 3 6 1 2 . 4 3 7 0 - 6 4 . 2 5 7 5 6 4 . 2 2 12 0 .2 6 6 4 -0 . 0 8 5 0 - 0 .7 8 7 3 8 . 9 7 7 7 4 . 0 8 4 5 - 6 . 1 4 3 5

8 2 . 4122 0 . 6948 -0 . 9488 0 . 0037 2 . 4729 0 . 0233 0 . 4345 0 . 8 68 1 10 . 8 060 -40 . 66 47 38 . 5428 0 . 2846 -0 . 0925 -0 . 4980 10 . 3 735 4 . 5818 -9 . 0318

3 0 . 0167 -0 . 0288 0 . 92 08 0. 00 07 -0 . 03 91 -0 . 0003 -0 . 0056 -0 . 0159 0 . 5854 -3 . 4646 3 . 6158 0 . 0008 0 . 0043 -0 . 0436 -0 . 4987 -0 . 5564 0 . 7328

4 0 . 1191 0 . 4137 -1 . 0693 0 . 0377 0 . 9622 0 . 0180 0 . 3572 0 . 0382 2 . 3587 -1 . 1658 -1 . 2294 0 .1747 -0 .0113 -0 . 0054 -0 . 7810 0 . 5197 -4 . 1926

5

- 0 . 0 30 1 0 . 2503 -0 . 6329 0 . 0137 2 . 8929 0 . 0228 1 . 0093 0 . 9824 2 . 7886 1 . 4628 -5 . 5030 0 . 2049 -0 . 0658 0 . 0281 6 . 0527 4 . 0482 -8 . 3764

~11 0 . 5168 0 . 1162 -0 . 45421 0 . 0104 2 . 8648 0 . 0204 0 .7750 0 . 9980 2 . 3864 13 . 9909-19 . 3311 0 . 2198 -0 . 0 74 1 0 . 1806 7 . 55 81 4 . 5823 -9 . 1007

= ,,1 7 0 . 9874 3 . 1 42 1 -3 . 6 65 6 0 . 0070 2 . 8742 0 . 0572 0 . 6248 1 . 9254 5 .5634 -2 . 9946 -1 . 7839 0 . 2582 -0 . 0 85 1 -0 . 0282 9 .1725 4 . 5264 -9 . 0795

8 1 . 9 3 23 4 . 7 9 2 5 -5 . 3 9 22 0 . 0 0 4 1 2 . 7 0 7 1 0 . 0 7 5 9 0 . 4 7 8 3 0 . 9 8 1 3 5 . 6 3 2 0 4 . 9 9 00 - 1 0 .6 6 1 1 0 . 2 7 6 1 - 0 .0 9 3 4 0 . 0 6 8 2 1 0 . 6 6 5 E 4 . 9 7 7 8 - 9 . 8 5 5 3

3 0 . 0073 0 . 0173 -0 .0248 0 . 0005 -0 .0298 0 . 0002 -0 . 0037 -0 . 0124 0 . 1008 -0 . 0436 -0 .0234 0 . 0066 0 . 0 ( ;25 -0 . 0014 -0 . 0763 -0 . 5589 0 . 8820

I ~ 4 - 0 . 5 58 1 6 . 0320 -7 . 0759 0 . 0356 0 . 8806 0 . 0825 0 . 4506 0 . 0254 1 . 9259 -0 . 3357 -1 . 94 61 0 . 1704 -0 . 0064 0 . 0235 -0 . 1345 -0 . 3437 -2 . 6581

5 - 0 .1 1 3 5 - 0 . 1 4 9 1 - 0 . 2 0 3 9 0 . 0 1 3 2 3 . 1 2 7 1 0 . 0 2 0 4 1 . 4 0 2 0 1 . 0 7 6 1 3 . 3 3 0 9 - 3 .1 6 3 9 - 0 .5 4 6 8 0 . 1 9 1 3 - 0 . 0 8 6 1 - 0 .0 3 6 0 5 . 2 3 3 9 4 . 9 9 4 5 - 1 0 . 5 1 4 2

6 0 . 5 0 8 6 - 0 .7 9 2 9 0 . 5 2 2 8 0 . 0 0 9 1 3 . 0 3 8 0 0 . 0 1 1 1 1 . 1 2 6 6 1 . 08 4 7 3 .8 1 6 9 2 . 0 5 8 1 - 6 .5 4 7 3 0 .2 1 0 4 - 0 .0 7 3 6 0 . 0 3 2 0 6 . 2 0 9 2 5 . 9 0 4 3 - 1 2 . 2 3 1 9

7 1 . 2640 -0 . 5 t1 0 0 . 2658 0 . 0059 3 . 0782 0 . 01 41 1 . 0276 1 . 1206 5 . 0957 0 . 2655 i - 5 . 1263 0 . 2343 -0 . 0867 0 . 0072 7 . 8374 7 . 3495 -15 . 0225

8 2 . 5112 -I . 6571 1 . 5494 0 . 0 03 1 2 . 9232 -0 .0018 0 . 89 31 1 .0792 6 . 1495 -0 . 7044 -4 . 3540 0 .2478 -0 . 09 51 -0 . 0072 9 . 1200 8 . 3673 -17 . 0003

3 0 . 0037 0 . 0117 -0 . 0158 0 .0003 -0 . 0219 0 . 00 01 O . (XT23 -0 . 0094 0 .0590 -0 . 0 27 1 -0 . 0889 0 . 0047 0 , 0022 -0 . 0007 -0 . 1004 -0 . 3129 0 . 4754

4 0 . 2706 -1 . 0782 0 . 6837 0 . 0260 0 . 5022 -0 .0055 0 . 2645 -0 .0127 3 . 9785 -12 . 1295 10 . 6976 0 . 1583 0 . 0081 -0 . 1518 -2 . 8522 -4 . 5673 6 . 3 421

o ~ 5 0 . 0 3 9 5 - 3 .0 8 2 8 2 . 9 0 8 9 0 .0 2 1 4 3 .5 5 2 3 - 0 . 0 1 1 1 1 . 7 8 3 6 1 . 2 1 3 1 3 . 7 8 7 3 - 9 . 9 2 9 1 i 6 . 9 3 0 9 i 0 . 1 4 0 8 - 0 . 0 6 3 9 - 0 .1 0 8 8 6 .7 4 2 9 4 . 4 4 7 2 - 9 .2 2 4 0

~ 1 6 0 . 5 7 47 -2 . 3 5 15 2 . 1 7 1 6 0 . 0 1 3 6 3 . 3 3 6 2 - 0 .0 0 3 5 1 .3 3 7 9 1 . 2 1 6 9 3 . 9 0 3 1 - 3 .5 4 0 6 -0 . 1 8 12 0 .1 5 4 3 - 0 .0 7 2 2 - 0 .0 2 9 0 8 . 6 64 9 4 . 9 8 0 0 - 9 .8 6 7 8

7 1 . 7 0 6 3 - 5 .4 6 8 4 5 . 5 69 8 0 . 0 1 0 8 3 . 4 0 1 9 - 0 . 0 4 3 5 1 .2 0 4 9 1 . 2 5 86 5 . 6 1 0 1 - 1 0 . 2 0 3 1 6 . 5 3 49 0 . 1 6 6 9 -0 . 0 8 5 0 - 0 .1 1 4 4 1 0 . 8 3 7 1 6 . 3 5 9 8 - 1 2 . 4 9 7 1

8 2 . 8 1 1 3 - 5. 1 6 6 3 5 .2 9 6 3 0 . 0 0 7 2 3 . 2 3 7 7 - 0 .0 4 1 9 1 . 0 2 4 1 1 . 2 1 5 9 6 . 2 3 4 5 - 8 . 2 0 3 1 4 . 1 3 2 4 1 0 . 1 7 6 7 - 0 . 0 9 4 2 -0 . 0 9 03 1 2 . 6 1 7 5 7 . 4 3 0 4 - 1 4 .5 5 2 4

I I

3 0 . 0043 -0 . 0060 00 08 2 0 . 0003 -0 . 0180 -00001 -0 . 0017 -0 . 0088 0 . 0472 -0 .05333 0 . 04 83 0 . 0 02 8 0 . 0013 -0 , 0014 -0 . 0335 -0 . 3120 0 . 5524

¢1 4 0 . 1522 -0 . 2776 -0 . 1 06 90 . 02 32 0 , 3287 0 . 0030 0 .2976 0 . 0245 2 . 1764 -3 . 6847 2 . 0459 0 . 1394 0 .0110 -0 . 0336 -1 . 56 61 -2 . 1804 0 . 9153

5 -0 . 6482 1 . 6569 -2 . 4114 0 . 0322 4 . 0502 0 .0503 2 . 4041 1 . 3989 2 . 5354 4 . 3262 -6 .8658 0 . 1988 -0 . 0898 0 . 0512 5 . 4155 3 . 54 63 -7 . 96 08

6 0 . 2444 0 . 9560 -1 .4232 0 .0097 3 . 3895 0 . 0363 1 . 2950 1 . 2830 2 . 9793 6 . 6046 .11 . 354£ 0 . 1995 -0 . 0737 0 . 0915 6 . 5154 6 . 4030 -13 . 9163

7 0 . 9608 1 . 5834 -2 . 06 01 0 . 0066 2 . 4 84 1 0 . 0438 1 . 1817 1 . 3374 3 . 5927 10 . 9248 i - 16 .541~ 0 . 2235 -0 . 08 71 0 . 1426 8 . 1775 7 . 8913 -16 . 9331

8 2 . 0867 1 . 5 51 2 -1 . 9875 0 . 0035 3 . 3472 0 . 0 41 6 1 . 0374 1 . 3019 4 . 2647 13 . 2039 19 . 2943 0 . 2364 -0 . 0964 0 . 1689 9 . 5793 9 . 0122 -19 . 1757

3 0 . 0053 -0 . 0165 0 . 0177 0 . 0002 -0 .0135 -0 . 0002 -0 . 0043 -0 . 0065 0 . 0427 -0 . 1210 0 . 1235 0 . 0018 0 . 0009 -0 . 0020 -0 . 04 91 -0 . 2119 0 . 3889

4 0 . 1440 -0 .4733 0 .1767 0 . 0186 0 . 2973 -0 . 00 01 0 . 2674 -0 .0233 1 . 7240 - 2 . 9 87 1 1 . 8525 0 . 0970 0 . 0169 -0 . 0333 -2 . 03 01 -1 . 3506 -0 . 4733

u~ 5 0 . 2232 -4 . 80 41 4 . 3970 0 . 0350 4 . 0212 -0 . 0247 2 . 0454 1 . 3848 2 .4372 - 0 . 7 28 8-3 . 40 95 0 . 2077 -0 . 0754 -0 . 0022 8 . 1803 2 . 4403 -6 . 3072

~ 1 3 . 6 3 0 7 0 . 0 2 0 E 1 . 0 5 7 0 1 . 4 2 52 3 . 9 3 7 6 - 7 .1 7 2 6 3 . 3 0 84 0 . 2 1 6 6 - 0 .0 8 3 2 - 0 . 0 6 5 1 1 0 . 6 0 9 8 2 . 3 1 9 0 ; - 5 . 0 8 0 2

0. 4424 -0 . 5164

0. 0799 0 . 0121

= -~ 7 1 . 52 46 -3 . 0 87 1 2 . 8738 0 . 0088 3 . 74 41 -0 . 011 : 0 . 9108 1 . 4975 4 . 6556 -4 . 4045 -0 . 2834 0 . 2461 -0 . 0987 -0 . 0304 13 . 1 88 5 2 . 6845 -5 . 6157

8 2 . 7317 -3 .7899 3 .6952 0 . 0052 3 . 6215 -0 .022 , 0 . 7269 1 . 4679 6 . 9828 -17 . 5 339 13. 4 647 0 . 26 41 -0 . 1104 -0 . 1928 15 . 3 901 2 . 9142 -5 . 8030



14/16

0.40

0 . 3 5

E 0 . 3 0

B N = #

L = I 9 m S W H = 0 . 8 8 4 m o R e g r e s s i o n . . .

+ W o l f s o n U n i t . . .

A W P = 3 . 9 s

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o J 5 . . . . . . . : . . . , , , ÷ . , . . . . e . . . . . i . , . , , . ~ . . . . . . . . . . . . . . . b . = . . . . , . . . . . . . . . . . . . . . . . . . . . . . . . . -

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3 5 7 9 1 1 1 3 1 5 1 7 1 9 2 1 2 3 2 5 2 7

S h i p N u m b e r

j B N = 4

L = I g m S W H = 0 . 8 8 4 m o R e g r e s s i o n . . .

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, A W P = 3 . 9 s " "

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+ . 5 o I " ' " " ' L ' i i { . . . . . . . ; . . . . . . . } . . . - . . i . . . :. . . 4 . . . . . . . i . . . . . . . i . . . . . . . : : . . . . . . i ;

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] S h i p N u m b e r

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B N = 5

L = 2 4 m S W H = 2 . 1 0 , 5 m o R e g r e s s i o n . . .

+ W o l f s o n U n i t . . .

A W P = 5 A s

:. . : :.. . . ~ + : . , + =

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S h i p N u m b e r

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+ W o l f s o n U n i t . . .

A W P = 5 . 4 s

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S h i p N u m b e r

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0.50

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B N = 6

L = 3 5 m S W H = 5 . 9 6 2 m o ~ , e , _ j r e s s , o n

+ W o l f s o n U n i t . . .

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S h i o N u m b e r

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L = 3 5 m S W H = . 3 . 9 6 2 m o R e g r e s s i o n . . .

A W P = 7 . 0 s + W o l f s o n U n i t . . .

i 5 . 0 0 F

. . . . . . . . . . . . . . . . . . . . . . .

~ 4 . 00 p . . ~ . . . " . . . . . . e . . . . . . . . . . . . . . . . . . . . . " . . . . . . ~ . . . . . ~ , . e . . , , ~ . . . . . . . . . . L : . . o , . . : . . . ¥ .

t . ' ' : :

~ . o o + 1 : 4 . . . . i~ r - i - - - i - : :: . i . . . . ;. . . . . .~ i : ~ i .. . . ; i . . . i . . . . ; .i : 4 . . .

2 . 0 0 t - - . . . . . . . . . : -- -- :-

. . . . . . . . . . . . . . . . . . . . . . . . . . .

~ . . . : . - - : . . . . .

1 3 5 7 9 1 1 1 3 1 5 1 7 1 9 2 1 2 3 2 5

S h i p N u m b e r

F i g . 9 T h e c o m p u t e d v a l u e s o f t h e s i g n i f i c a n t h e a v e a n d p i t c h

a m p l i t u d e s f r o m b o t h W o l f s o n U n i t S h i p M o t i o n p r o g r a m

a n d R e g r e s s i o n e q u a t i o n f o r 1 9 , 2 4 - a n d . . 5 5 m s h i p l e n g t h s .



15/16

0 . 4 0

v E 0 .30

N

0.20

0 . 1 0

0.00

5

L = I 5 m B N = 4

L / B = 5 , 1 0 S W H = 0 . 8 8 4 m : R e g r e s s i o n . . .

W o l f s o n U n i t . . .

B / T = 1 . 9 0 A W P = 3 . 9 s

: ~ : • : ; - : .

. . . . . . ~ . . . . . . . i . . . . . . . i . . . . . . . . ~ . . . . . . . . . . . . . . i . . . . . . ~ . . . . . . . i . . . .. . . ~ . . . . . . . . . . . . . . . , . . . . . . .

. . . . . . . . . . . . . . . i . . . . . . . . . . . . . . . i . . . . . . . . . . . . . . . . i . . . . . . ~ . . . . . . . i . . . . . . . . . . . . . . i . . . . . . . . . . . .

. , . i . i

6 7 8 9 1 0 1 1

S h i p S p e e d ( k n o t )

L = I 5 m B N = 4

R e g r e s s i o n

L / 8 = 5 . 1 0 S W H = 0 . 8 8 4 m

W o l f s o n U n i t . . .

B / / T = I . 9 0 A W P = 3 , 9 s

~ 2 . 8 o ~ . ; : . . . . . . ' . ; . . 1 2 . ' . . ; . ' . i . . . . i . . ; . ' . . . . ' . ' . L . . _ ~ . . ' z i ~ .

~

2 . 4 0

2 . 0 0 . . . . . . , . . . . . . . . . . . . . . ~ . . . . . . . ~ . . . . . . . , . . . . . . . ~ . . . . . . ~ . . . . . . . . . . . . . . . . . . . . . . . . ~ .. . . . . . . . . . . .

. . . . .. . ~ . . . . ~ . . . . .. i , , , " , . .~ , , , . ,~ , , ; . . . . .

1 . 2 0 . . .. . .

- : . . . . . . : . . . . . . : . . . . . . . ~ . . . . . : . . . . . " . . . . . : . . . . . " . . . . : . . . . .. . " . . . . . . . : . . . . . .

0 . 8 0 . : _ : _ : _ : . . i , . : : : /_ : . . . , . , i . . .. . . . i , : : _ , : L : , . . : . i L , : : i , : , L . i : : _ : : : i , . : : . . . : _ : :

0 . 4 0 . . . . . . . : .. . . . . . ~ . . . . . . : . . . . . . . i . . . . . . : . . . . . . . i . . . . . : . . . . . . i . . . . . . . : . . . . . . . i . . . . . . . . . . . . .

. . . . . . . . . . . . . . . ~ . . . . . . ~ . . . . ~ . . . . . . . . : . . . . , , : . . . . . . , : . . . .

0 . 0 0 . . . . . . .

: '

:

'

:

'

:

'

:

'

5 6 7 8 9 10 11

Sh i p S peed ( k no t )

L = 2 7 m B N = 5

L / 8 = 4 . 4 0 5 W H = Z . 1 0 5 m • R e g r e s s i o n . . .

a W o l f s o n U n ; t . . .

B / T = 1 . 9 0 A W P = 5 . 4 s

o . ~ o i : : i : :

~ ' 0 . 6 0 . , .

. . : . i . . . : ~ :

0 . 3 0 . . . . . . ~ . . . . . . . : . . . . . . . ~ . . . . . . . : . . . . . . . ~ . . . . . . . . . . . . . : . . . . . . . . . . . . . . . i . . . . . . . . . . . . .

i ~ i : i :~ : " " i "

. . . . . . . . . . ~ , , , : . . . . i . . . : . . . . . ; . . . . . ; . . . . ; . . . . ~ . . . . i , , . ;

" ~ i i : i " : : : :

0 . 0 0 I i I i ; i I i

5 6 7 9 10 11

Sh i p

S p e e d

(knot )

L = 2 7 m B N = 5

R e g r e s s i o n . . .

" " ~ ' ' ~ u / ¢ ~ = , + . , + u S W H = 2 , 1 0 3 m & W o l f s o n U n i t . . ,

B / T = 1 . 9 0 A W P = 5 . 4 s

4 . o

: ~ : ~ . : :

3 . 0 . . . . . . . . " . . . . . . . . . . . . . . . . . . . . . . . . ~ . . . . . . . ' . . . . . . . ~ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ~ . . . . . . . . . . . .

. . . . . . . . ; . i . . . ~ : . ~ . . : : . . . . . - . . . . ; . , . - . . . . :, . . . - . .

I 2 . o . . . . . . . . . . . . . . . . . i . . i . . . . . . . . . i . . . . . . . . ~ . . . . . . . . . . . i . . . . . : . . . . .

~ . o . . . . . . . . . . . . . . . . . . . . . . . i . . . . . . . . ; . . . . . . . : . . . . . . . . . . . . i . . . . . . . . i . . . . . . . : . . . . . . . . ~ . . . . . . i . . . . . .

0 .0 i ~ i i i I i I 1 i

5 6 7 8 9 10 11

Ship Spe ed (knot )

L = 3 8 m B N = 6

• R e g r e s s i o n . . .

L / 8 = 5 . 8 0 S W H = 3 . 9 6 2 m a W o l f s o n U n l t . . .

B / T = 2 . 3 0 A W P = 7 . 0 s

, ~ , 1 . 2 5 . .

. . . . . . . . .. . . . . . . . " . . . . . ; . . . . . . . : . . . . . . ~ . . . . . . . . . . .. . . ~ . . . . . . ~ . . . , , , i . ~

0 . 7 5 . . . . . . . < . . . . . . . ~ . . . . . . . . . . . . . ~ . . . . . . . . . . . . . ~

0 . 5 0 . . . . . . . ~ . . . . . . . ; . . . . . . . . . . . . . . . . ~ . . . . . . : . . . . . . ~ . . .. . . ~ . . . .. . . ~ . . . . . . . . . . . . . . . ~ . . . . . . . . . . . . . .

0 . 2 5 . . . . .. . . , : :: : . . . .

0 . 0 0

,

i i

,

; ; ;

5 6 7 8 9 10 1

S h i p S p e e d ( k n o t )

, 4 , 5 0

3 . 7 5

t ~ 3 . o o

2 . 2 5

L = 3 8 r n B N = 6

• R e g r e s s i o n

L / B = 5 8 0 S W H = 3 9 6 2 m - " ' "

• ' " z ~ W o l f s o n U n i t

B / T = 2 . 3 0 A W P = 7 . 0 s " ' "

. . . . .. . : . . . . . .. . ~ . . . . .. ; . - _ ~ ~ ~

. . . . . . . . . . . . . . . . ~ . . . . . . . . . . . . . . . . . . . i . . . . . . . . . . . . . . . ; . . . . . . . - . . . . . . . ; . . . . . . . : . . . . . . . : . . . . . .

. 50 . . . . . . . , . . . . . . . ~ . . . . . . ~ . . . . . . . :: . . . . . . . . . . . . . . . : . . . . . . . . . . . . . . . . ~ . . . . . . . . - . . . . . . . . . . . . . . . . . . . . . . . .

: ~ i - = -

0 .7 5 . . . . . . . . . . . . . . . i . . . . . . . i . . . . . . . ~ . . . . . . : . . . . . . . . . . . . . . . . . . . . . . . i . . . . . . . : . . . . . . . , . . . . . . . ~ . . . . .

0.00 i

~, ; , , i

5 5 7 8 9 1 1

S h ~ p S p e e d ( k n o t )

F J ~ . t O T h e c o m p u t e d v a l u e s o f t h e

s igni f icant

h e a v e a n d

pitch

a m p l i t u d e s f r o m b o t h W o l f s o n U n i t S h l p M o t i o n p r o g r a m

a n d R e g r e s s i o n e q u a t i o n w i t h t h e v a r i a t i o n o f s h i p s p e e d s

f o r 1 5 , 2 7 a n d 2 7 m s h i p l e n g t h s .



16/16

Z2485 Z24 (24.85 24)(Z2s Z24

0.6376 (24.85 24)(0.6315 0.6376) 0.6324 m

Wo l f s o n U n i t r e s u l t i s

0.632 m

The significant pitch amplitude can be obtained in a

similar manner from the regression equation.

For L= 24 m For L=2 5 m

b 0 = 4.372 4 bo = 3.6052

bj =- . 1454 bl = -1.6802

b e = 3.5282 b2 =- 2. 31 63

b 3 = 0.1778 b 3 = 0.1698

b~ = -0.0625 b 4 = -0.0629

b s = -0.0912 b 5 = -0.0144

b 6 = 6.5541 b6 = 6.8609

b 7 = 2.6804 b 7 = 3.3163

b 8 = -5.1087 b 8 = -6.2864

Q b o blCwL b~CB b3L b 4 L b s L C B b

6-T

bv V--~- b V2

g L 8 g-£

Q24 4.3724 7.1454×0.7082 3.5282x0.5408 0.1778

x(24/4.873) 0.0625x(24/2.564) 0.0912×( 0.339

× 100/2.4) 6.554 1×0. 25 2.68 04x( 8 x0.514 4/

9.81x24 ) 5.1087x(8x0.5144)/(9.81x24)

Q24 3'62949°

and

Q25 3.6052 1.6802x0.7082 2.31x0.5408 0.1698

x(25/4.873) 0.0629x(25/2.564) 0.0144x( 0.339

x 100/25) 6.86 09x0 .25 3.3163 x(8 x0.5144)/

9.81 x25 ) 6.2864×(8x0. 5144)2/(9.81 x25)

Q25 3 59229°

The interpolation between 24 m and 25 m for 24.85

m is as follows:

Q 2 4 . 8 5 Q 2 4 (24.85 24)(Q25 Q 2 4 ) 3.62949 0.85

x(3. 5922 9 3.62949) 3.59787 °

Wo l f s o n U n i t r e s u l t i s 3.598 °

The results of the computation o f ship motions in head

seas correlate very well with the Wolfson Unit

Computer Program results.

CONCLUSION

It is believed that through the study in this paper a

significant gap in trawler design has been filled and a

methodology (inclusive of prediction method) has been

offered to designers for the evaluation of seakeeping

behavior of their designs during the early stages of the

design process.

In this way operational safety can be improved

significantly. It is intended that other significant

seakeeping events will be studied and published in a

similar way to enrich the seakeeping design tools of

trawler designers.

R E F E R E N C E S

1 Doust, D. J. , Optimized Trawler Forms Trans.

N.E.C.I.E.S., 1962.

2 Loukakis, T.A. and Chryssostomidis, C.,

Seakeeping Standard Series for Cruiser-Stern Ships

Trans. SNAME, Vol. 83, 1975.

3 Moor, D.I. , Effects on Performance in Still Water

and Waves of Some Geometric Changes to the Form of

a Large Twin-Screw Ship Trans. S.N.A .M. E., Vol.

78, 1978.

4 Moor, D.1. and Murdey, D.C. , Motions and

Propulsion of Single Screw Models in Head Seas

Trans. R.I.N.A., Vol. 110, 1968.

5 Odabasl, A.Y. and Hearn, G.E., Seakeeping

Theories: What is the choice? North-East Coast

Institution of Engineers and Shipbuilders, Advance

copy, Nov., 1977.

Documents

Influence of Design Parameters on Vertical Motions of Trawler Hull Forms in Head Seas