HYDRODYNAMIC ASPECTS OF SHIP
SAFETY
W. BeukeLman
Report No. 934-P
Transactions of the First International Conference in Commemoration of the 300-Th Anniversary of Creating Russian Fleet by Peter the Great, 7 - 14 June 1992, St. Petersburg, Russia.
Dalft University of Technology Ship Hydromechanics Laboratory Mekelweg 2
2628 CD Delft The Netherlands Phone 015 - 78 68 82
ST. PETERSBURG STATE U N I V E R S I T Y OF OCEAN T E C H N O L O G Y
TRANSACTIONS OF THE FIRST I N T E R N A T I O N A L
CONFERENCE IN C O M M E M O R A T I O N
OF THE 300-TH ANNIVERSARY OF CREATING
• RUSSIAN FLEET BY PETER THE GREAT
7 _ 1 4 J U N E 1 9 9 2
ST. PETERSBURG, RUSSIA 1992
T . . P E T E R S B U n O S T A T E U N I V E R S I T Y O F O C E A N T E C H N O L O G Y
C R F - 9 2
TRANSACTIONS OP THB FIRST INTERNATIONAL CONPBRBNCB
IN COMMEMORATION OP THB 900-TH ANNIVERSARY OP OREATINQ
RUSSIAN FLEET BY PETBR THB GREAT
7 - 1 4 J U N E 1 9 9 2
ST. PETERSBURG, RUSSIA
2
LIBRARY CATALOGING IN PUBLICATION DATA
Main e n t r y Qnder t i t l e s
Tt^ansactxons o f t h e F i r s t I n t e r n a t i o n a l Conference i n Connenoration o f t h e 300-th A n n i v e r s a r y o f c r e a t i n g K n s s i a n F l e e t hy P e t e r t h e g r e a t *
P a p e r s , presented a t t h e CRF-92, Conference on h i s t o r y o f s h i p h a i l d i n g , a p p l i e d hydrodynamics and t h e v o r l d ' s need f o r M r i n e t e c h n o l o g i s t s , S t . P e t e r s b u r g , 7-l< Jane 1992. 1. S c i e n c e - Techniques - Congresses, 2. H i s t o r y of s h i p b u i l d i n g , 3. H y d r o M c h a n l c s , I . P e t e r t h e G r e a t , 1€72-1725, I I . K b o l o d i l i n A.N. I I I . PUOT c o n f e r e n c e on t h e h i s t o r y o f s h i p b u i l d i n g and hydrodynonlcs <1992; 6 t . P e t e r s b u r g , B u s s i e ) . DDK €29.12 C o p y r i g h t <c) 1992 by POOT. A l l r i g h t s r e s e r v e d . No p a r t o f t h e a n t e r i a l p r o t e c t e d by t h i s copy r i g h t n o t i c e nay be reproduced o r u t i l i z e d i n any form o r by any m e a n s , e l e c t r o n i c o r mBChanical, w i t h o u t w r i t t e n p e r m i s s i o n from
t h e c o p y r i g h t owner.
The o p i n i o n s e x p r e s s e d i n t h i s book a r e t h o s e o f t h e i n d i v i d u a l a u t h o r s and not n e c e s s a r i l y t h o s e o f POOT o r t h e e d i t o r s .
5
ORGANIZERS
s t , P e t e r s b u r g S t a t e D n i v e r s l t y of Ocean Technology (POOT)
A s s o c i a t i o n P e t r o s c i e n c e (APS)
Orthodox T h e o l o g i c a l Acadeaty and Seminary, S t . P e t e r s b a r g
A s s o c i a t i o n Oceanotechnik (AOT)
Save Peace and Nature A s s o c i a t i o n (SPAN)
S c i e a t l f i c - T e c h n o l o g y S o c i e t y named a f t e r a c a d e m i c i a n A.N.Krylov (STS)
The c o n f e r e n c e has been o r g a n i x e d by t h e a d v i c e o f the I n t e r n a t i o n a l Working group,Leningrad, 21-25 May 1991
A d d r e s s i 190008, S t . P e t e r s b a r g , Lotsmnnaknya a t . , 3, PDOT T e l . I (812) 114 80 94, 114 80 18 ; r a x (812) 113 81 09 E d i t e d by P r o f . Alexander N. K h o l o d i l l n w i t h Dr. I r i n a M. D m i t r i e v a , K a t o l y A. X h o l o d l l i n a , E v g e n y i V. L a b a i n , Helen M. M i l a s h ( E n g l i s h language ) , Dr. V a a i l y l K. T r o o n l n ( Hydrcwwchanics ) , Dr. Andrey 6. Zakharov ( Photographs ) .
Hydrodynamic a s p e c t s o f S h i p S a f e t y I n t r o d u c t i o n Up t o now t h e m a j o r i t y o f t h e c o n s i d e r a t i o n s r e l a t e d t o s h i p s a f e t y i s d e v o t e d t o s t i l l w a t e r c o n d i t i o n w i t h s p e c i a l emphasis on s t a b i l i t y f o r t h e u p - r i g h t s i t u a t i o n a g a i n s t c a p s i z i n g . Nowaday i t m i g h t be c l e a r , t h a t dynamic i n f l u e n c e s s h o u l d n o t be n e g l e c t e d f o r s h i p s a f e t y e s p e c i a l l y t h e b e h a v i o u r i n a seaway [ 1 ] . A t f i r s t s p e c i a l a t t e n t i o n i s f o c u s e d a t t h e m a n o e u v r i n g a s p e c t s o f f a s t modern s h i p s i n c e r t a i n e n v i r o n m e n t a l c o n d i -t i o n s such as a f e r r y - b o a -t a -t h i g h speed i n r e s -t r i c -t e d w a -t e r . Seakeeping i n c l u d i n g m o t i o n i n d u c e d phenomena i s b r i e f l y c o n s i d e r e d . C h a o t i c b e h a v i o u r o f t h e t r a n s v e r s e s t a b i l i t y i n u l t i m a t e n o n - l i n e a r wave c o n d i t i o n s appears t o p l a y an i n c r e a s i n g l y i m p o r t a n t r o l e . S a f e t y r e q u i r e m e n t s f o r h i g h speed c r a f t h a r d l y e x i s t , b u t s h o u l d be d e v e l o p e d . The r o l e o f r e s e a r c h i n s t i t u t e s f o r s h i p s a f e t y as a u t h o r i z e d o r g a n i s a t i o n i s p u t f o r w a r d . M a n o e u v r a b i l i t y The s i t u a t i o n o f a f e r r y - b o a t l e a v i n g o r e n t e r i n g t h e h a r b o u r i s a r a t h e r c o m p l i c a t e d one t o a n a l y s e . Many hydrodynamic e l e m e n t s a r e p l a y i n g an i m p o r t a n t r o l e such as: t r i m / s i n k a g e , t h e bow wave, t h e e f f e c t o f b o t t o m and/or s i d e w a l l s o f a c h a n n e l and t h e p r e s e n c e o f waves.
A f t e r t h e d i s a s t e r w i t h t h e ' H e r a l d o f Free E n t e r p r i s e ' B i s h o p and P r i c e p r e s e n t e d a s t u d y e n t i t l e d 'On t h e dangers of t r i m by t h e bow' [2] i n w h i c h t h e y s u g g e s t e d t h a t l o s s o f d i r e c t i o n a l s t a b i l i t y p r e c e d e d l o s s o f h y d r o s t a t i c s t a b i l i t y . They p u t f o r w a r d as c o n d i t i o n f o r p o s i t i v e s t a b i l i t y :
pgVGM [Y^N;^ + (mU - Y3^)Nv] > 0 (1)
i n w h i c h p = d e n s i t y o f w a t e r V = volume o f d i s p l a c e m e n t o f s h i p GM = m e t a c e n t r i c h e i g h t Y-y, N^, Y-^, Nj^ a r e m a n o e u v r i n g c o e f f i c i e n t s I f GM i s p o s i t i v e t h e n : [Y^N^ + (mU - Y r ) N v ] > 0 (2) w h i c h may be w r i t t e n as: mUc(7) = [ Y^(7) N^(7) -Nv(7) ] + Y^(7) (3) 1
-w i t h = c r i t i c a l speed -w i t h r e s p e c t t o d i r e c t i o n a l s t a b i l i t y 7 T ^APP •FPP as t r i m f u n c t i o n ^m = d r a u g h t From t h i s B i s h o p and P r i c e [ 2 ] c o n c l u d e d t h a t t r i m by s t e r n i n c r e a s e s t h e c r i t i c a l speed above w h i c h i n s t a b i l i t y a p p e a r s . To i n v e s t i g a t e t h e i n f l u e n c e o f w a t e r d e p t h and t r i m on t h e d i r e c t i o n a l s t a b i l i t y o f a Ro-Ro f e r r y s h i p PMM t e s t s have been c a r r i e d o u t w i t h a model o f t h e ' H e r a l d o f Free E n t e r p r i s e ' a t t h e S h i p Hydromechanics L a b o r a t o r y o f t h e D e l f t U n i v e r s i t y o f Technology [ 3 , 4 ] . For a l l c o n d i t i o n s c o n s i d e r e d a n e g a t i v e d i r e c t i o n a l s t a b i l i -t y ( p o s i -t i v e r o o -t a) c o u l d be o b s e r v e d e s p e c i a l l y a -t h i g h f o r w a r d speeds. See F i g u r e 1 ' h = 1 2 . 5 m L = 1 2 6 . 1 m / B = 2 2 . 7 m CO
//
T = 5 . 6 9 m O jj//
h / T - 0 = A = = 2 . 2 Even k e e l t r i m b y t h e//
/ - bow 0 . 7 5 m -1 ^ 0.1 „ 0.2 1 1 1 1 1 1 1 6 10 14 18 1 F i g . l . S t a b i l i t y r o o t s o f a r o l l - o n - r o l l - o f f passenger f e r r y . [3,4] The i n f l u e n c e o f v a r i a t i o n o f w a t e r d e p t h on t h e d i r e c t i o n a l s t a b i l i t y i s g e n e r a l l y s m a l l . However t h e e f f e c t o f t r i m c o n d i t i o n i s more c l e a r showing a d e t e r i o r a t i o n f o r t h e case o f t r i m by t h e bow as shown i n F i g u r e 1 . R e s t r i c t i o n o f f o r w a r d speed dependent on t h e w a t e r d e p t h i s s t r o n g l y recommended. C a l c u l a t i o n o f t h e d i r e c t i o n a l s t a b i l i t y i s up t o now n o t p o s s i b l e i n a s a t i s f a c t o r y way because o f t h e laclc o fknow-l e d g e a b o u t v i s c o u s i n f know-l u e n c e w h i c h i s e s s e n t i a l t o d e t e r m i n e t h e m a n o e u v r i n g c o e f f i c i e n t s . F u r t h e r r e s e a r c h i s r e q u i r e d i n t h i s r e s p e c t . Seakeeping G e n e r a l
I t i s known t h a t s h i p m o t i o n s i n r e g u l a r and i r r e g u l a r waves may be p r e d i c t e d by computerprograms based upon 2 D ( s t r i p
t h e o r y ) o r 3 D ( d i f f r a c t i o n t h e o r y ) b o t h s t a r t i n g f r o m l i n e a -r i z e d p o t e n t i a l t h e o -r y .
A f t e r d e t e r m i n a t i o n o f t h e s h i p ' s response f u n c t i o n on r e g u l a r waves t h e b e h a v i o u r and o p e r a b i l i t y i n an i r r e g u l a r sea may be o b t a i n e d .
These methods may be used f o r a l l s h i p t y p e s and c o n d i t i o n s w i t h a r e s t r i c t i o n f o r : 1. t h e r e l a t i v e m o t i o n a t h i g h f o r w a r d speed. 2. cases w i t h s t r o n g v i s c o u s damping i e . b a r g e s , r o l l i n g and s h a l l o w w a t e r . 3. n o n - l i n e a r m o t i o n s m o s t l y i n t r o d u c e d by h i g h waves. 2
Here a l s o s h o u l d be m e n t i o n e d a g r o w i n g emphasis on t h e dynam.ic c o n d i t i o n o f t h e damaged s h i p . I m p o r t a n t r o l l i n g m o t i o n s due t o sudden w a t e r i n g r e s s may o c c u r and s h o u l d be c o n s i d e r e d i n t h e f u t u r e . M o t i o n i n d u c e d phenomena L o o k i n g a t t h e m o t i o n i n d u c e d phenomena i t s h o u l d be r e a l i s e d t h a t f o r t h e s h i p s a f e t y i t i s i m p o r t a n t t o c o n s i d e r n o t o n l y u l t i m a t e c o n d i t i o n s b u t a l s o t h e c o m f o r t o f p a s s e n g e r s and crew ( r e s p o n s i b l e f o r s h i p h a n d l i n g ) and t h e p o s s i b i l i t y o f damage o f s h i p o r c a r g o . The phenomena a c c o u n t e d f o r i n t h i s r e s p e c t a r e v e r t i c a l and l a t e r a l a c c e l e r a t i o n s , deck wetness and slamming ( i m p a c t p r e s s u r e s ) . I f c r i t e r i a f o r t h e s e phenomena a r e known o p e r a b i l i t y p r e d i c t i o n s may be c a r r i e d o u t . Such r o o t mean s q u a r e c r i t e r i a a r e p r e s e n t e d i n t a b l e 1 f r o m [5] f o r t h e r o l l a n g l e , t h e v e r t i c a l and l a t e r a l a c c e l e r a t i o n s as p e r c e n t a g e o f t h e a c c e l e r a t i o n o f g r a v i t y g. T a b l e 1 : C r i t e r i a w i t h r e g a r d t o a c c e l e r a t i o n and r o l l [ 5 ] .
Root Mean Square C r i t e r i o n D e s c r i p t i o n V e r t . a c c . L a t . acc. R o l l
0.20 g 0.10 g 6 .0° L i g h t manual work
0.15 g 0.07 g 4 .0° Heavy manual work
0.10 g 0.05 g 3 .0° I n t e l l e c t u a l work 0.05 g 0.04 g 2.5° T r a n s i t p a s s e n g e r s 0.02 g 0.03 g 2 .0° C r u i s e l i n e r Deck wetness t a k e s p l a c e i f a t a s t a t i o n on b o a r d t h e r e l a -t i v e m o -t i o n exceeds -t h e l o c a l f r e e - b o a r d . Ochi's c r i t e r i a f o r slamming a r e : 1. f o r e s h i p a t about 0 . I L a f t e r FPP emerges f r o m t h e w a t e r 2. v e r t i c a l speed w i t h r e s p e c t t o t h e w a t e r s u r f a c e exceeds a c r i t i c a l v a l u e V^j- = 0.09 /gL\
Slamming and deck wetness c r i t e r i a o f t e n used a r e r e s p e c t i v e -l y 3 and 5% o f t h e wave e n c o u n t e r s .
The c r i t i c a l slamming p r o b a b i l i t y a g a i n s t s h i p l e n g t h f o r merchant s h i p s i s shown i n F i g u r e 2 f r o m [ 5 ] .
For some cases i e . modern h i g h speed c r a f t t h i s c r i t e r i u m based on t h e v e r t i c a l v e l o c i t y o n l y i s n o t s u f f i c i e n t . Recent r e s e a r c h on wedges h i t t i n g t h e w a t e r s u r f a c e shows t h a t t h e f o r w a r d speed a l s o has a s t r o n g i n f l u e n c e on t h e i m p a c t p r e s s u -r e w h i l e t h e h i g h e s t p -r e s s u -r e s c o u l d o n l y be o b s e r v e d a t a n g l e s o f about 1 t o 2 degrees between h u l l and w a t e r s u r f a c e . P r e d i c t i o n o f t h e s e p r e s s u r e s shows p r o p o r t i o n a l i t y t o t h e squared v e r t i c a l and f o r w a r d speed as shown b y Beukelman and Radev i n [ 6 ] .
IC>C1H ITtf ft Iml
F i g . 2 The slamming c r i t e -r i a dependent on s h i p l e n g t h . [ 5 ]
Chaos and c a p s i z i n g
The most dangerous s i t u a t i o n f o r a s h i p a r i s e s when t r a v e l l -i n g -i n q u a r t e r -i n g and f o l l o w -i n g seas. N o n - l -i n e a r l a r g e a m p l i t u d e r o l l i n g i s m o s t l y i n t r o d u c e d f o r t h a t case a t sub-h a r m o n i c , sub-harmonic and u l t r a - sub-h a r m o n i c r o l l o s c i l l a t i o n s as shown i n F i g u r e 3.
Because o f n o n - l i n e a r i t y t h e r o l l response c u r v e w i l l show a bended c h a r a c t e r l e a d i n g t o m u l t i - v a l u e d responses f o r one f r e q u e n c y as d e m o n s t r a t e d i n F i g u r e 4. 0-1 a< 0 3 10 2.0 JO u / W , CO n o n n i b t M n v t t r f t q u i n c y F i g . 3. R o l l i n g a m p l i t u d e cpg_ o f F i g . 4. T y p i c a l response t h e s t e a d y - s t a t e p s c i l l a - c u r v e . [ 8 ] t i o n s v e r s u s t u n i n g r a t i o w / w q i n a l l resonance r e g i o n s . [ 7 ]
T h i s may l e a d t o bounded and s t a b l e m o t i o n s c a l l e d an a t t r a c t o r . A l l t r a j e c t o r i e s t e n d i n g t o w a r d s an a t t r a c t o r a r e d e f i n e d as s a f e b a s i n o r domain o f a t t r a c t i o n . Near resonance t h e r e i s a r e g i o n r e p r e s e n t i n g u n s t a b l e s t e a d y s t a t e response w i t h jumps t o resonance a t a c y c l i c f o l d b i f u r c a t i o n ( s a d d l e -node) . The t r a j e c t o r i e s a r e p r e s e n t e d i n a phase space d i a g r a m showing t h e r o l l a n g l e ( d i s p l a c e m e n t ) and t h e a n g u l a r v e l o c i t y ( r e p r e s e n t i n g t h e energy) as shown i n F i g u r e 5 f r o m Rainey and Thompson [ 9 ] . The shaded a r e a i s t h e s a f e b a s i n .
homocliriie tinKrnr.r • m ( K ) l h i K M i m l a r r
OJi OA O.C O J 1.0
normaJIiwl forcing niagnilu<l«, ƒ — F/F'
,^ig.6. Safe b a s i n a r e a as f u n c t i o n o f wave h e i g h t . [ 9 ] F i g . 5 . T r a j e c t o r i e s i n phase space f o r a s h i p i n s t i l l w a t e r . Shaded a r e a i s t h e s a f e b a s i n . [ 9 ] E r o s i o n o f t h e s a f e b a s i n by i n c r e a s i n g wave f o r c e i s shown i n • F i g u r e 6. For t h i s r e a s o n Rainey and Thompson s u g g e s t t o s u b j e c t a s h i p model t o a t r a i n o f r e g u l a r t r a n s i e n t waves w i t h i n c r e a s i n g wave h e i g h t s . The c r i t i c a l wave h e i g h t o r wave s t e e p n e s s i s p l o t t e d a g a i n s t t h e wave p e r i o d r e s u l t i n g
WAVE S T E E r N E S S
Ztio Heel 10- H M I
i n t h e T r a n s i e n t Capsize Diagram as shown i n F i g u r e 7. [ 9 ] T h i s i s p r e s e n t e d as an a t t r a c -t i v e and f a s -t p r o c e d u r e i n ana-l y s i n g t h e p o s s i b i ana-l i t y o f a c a p s i z e . I t i s a l s o p o s s i b l e t o o b t a i n t h i s T r a n s i e n t Capsize Diagram b y computer s i m u l a t i o n . I n t a c t s t a b i l i t y o f h i g h speed c r a f t V a r i o u s t y p e s o f advanced h i g h speed v e h i c l e s a r e a c h i e v i n g t h e i r h i g h speed b y means o f s p e c i a l d e s i g n f e a t u r e s o r dev i c e s as dynamic l i f t o r f a n -g e n e r a t e d l i f t . The most com-monly used s h i p t y p e s a r e shown i n F i g u r e 8. [10] BEAM SEAS Q U A R T E R I N G SEAS WAVE PERIOD (Mt) F i g . 7 . T r a n s i e n t Capsize Diagram f o r a t y p i -cal s h i p . [ 9 ] P U N I N G H y O R O F O I L ACV <J Ö SES SWATH ACV SES SWATH A i r Cushion V e h i c l e S u r f a c e E f f e c t S h i p S m a l l W a t e r p l a n e Area Twin H u l l . F i g . 8 . Types o f Advanced M a r i n e V e h i c l e s . [ 1 0 ] A t l o w speeds t h e h u l l b o r n e o r d i s p l a c e m e n t mode s h o u l d be c o n s i d e r e d s e p e r a t e l y f o r s t a b i l i t y . A l t h o u g h t h e r e q u i r e -ments a r e s i m u l a r t o t h o s e o f c o n v e n t i o n a l d i s p l a c e m e n t s h i p s p e c u l a r q u a l i t i e s o f t h e s e s h i p t y p e s s h o u l d be a c c o u n t e d f o r such as low f r e e b o a r d , e n t r a p p e d a i r e t c . A t h i g h speeds t h e s t a b i l i t y c h a r a c t e r i s t i c s a r e q u i t e d i f f e -r e n t f -r o m t h e d i s p l a c e m e n t c o n d i t i o n . The i n f l u e n c e o f t h e l i f t d e v i c e s , t r a n s o m f l a p s and a i r p r e s s u r e i s v e r y s e n s i -t i v e e s p e c i a l l y i n wave c o n d i -t i o n s . L o n g i -t u d i n a l s -t a b i l i -t y e x p r e s s e d as deck d i v i n g p r o b a b i l i t y i s a v e r y s e r i o u s p r o b l e m i n f o l l o w i n g and q u a r t e r i n g seas.
Model t e s t i n g i s t h e o n l y way up t o now t o o b t a i n s e c u r i t y f o r r e q u i r e d c o n d i t i o n s . I t w i l l be c l e a r t h a t i t i s h a r d l y p o s s i b l e t o d e s i g n s a f e t y r u l e s f o r a l l t h o s e s h i p t y p e s i n d i f f e r e n t s i t u a t i o n s . IMO-recommendations f o r t r a n s v e r s e s t a b i l i t y a r e r e l a t e d t o h y d r o f o i l s o n l y . C o n c l u s i o n s and recommendations I n v i e w o f t h e n e c e s s i t y t o c o n s i d e r t h e dynamic b e h a v i o u r f o r s h i p s a f e t y , w h i c h i s even more s t r e s s e d f o r modern h i g h speed c r a f t a n d t h e i m p o s s i b l i t y t o d e s i g n r u l e s and c r i t e r i a f o r a l l s h i p t y p e s i n dangerous and dynamic s i t u a t i o n s , i t i s a d v i s e d t o r e q u i r e f o r each s h i p ( t y p e ) a c e r t i f i c a t e f r o m a u t h o r i z e d r e s e a r c h i n s t i t u t e s o r o r g a n i s a t i o n s . These i n s t i t u t e s o r o r g a n i s a t i o n s s h o u l d w i t h r e s p e c t t o s h i p s a f e t y c o n s i d e r f o r d e f i n e d c o n d i t i o n s : t h e d i r e c t i o n a l s t a b i l i t y t h e p r o b a b i l i t y o f s h i p p i n g w a t e r and slamming 5
- t h e degree o f d e g r a d a t i o n o f t h e p e r f o r m a n c e o f crew and passengers - t h e m o t i o n s and s t a b i l i t y d u r i n g w a t e r i n g r e s s - t h e b e h a v i o u r i n a t r a i n o f t r a n s i e n t f o l l o w i n g waves r e s u l t i n g i n a T r a n s i e n t Capsize Diagram. Research s h o u l d be aimed a t t h e s e m e n t i o n e d s u b j e c t s . R e f e r e n c e s [1 ] Beukelman, W., ( 1 9 9 2 ) , 'Hydrodynamic a s p e c t s o f M a r i n e S a f e t y ' , F i r s t J o i n t Conference on M a r i n e S a f e t y and E n v i r o n m e n t , S h i p Pro-d u c t i o n , D e l f t U n i v e r s i t y o f Technology, The N e t h e r l a n Pro-d s
[2 ] B i s h o p , R.E.D. and W,G. P r i c e , ( 1 9 8 8 ) ,
'On t h e dangers o f T r i m by Bow', E v e n i n g M e e t i n g , London and J o i n t E v e n i n g M e e t i n g , Glasgow, The Royal I n s t i t u -t i o n o f Naval A r c h i -t e c -t s (RINA).
[3 ] Beukelman, W., ( 1 9 9 0 ) ,
'The i n f l u e n c e o f t r i m on t h e d i r e c t i o n a l s t a b i l i t y o f a Ro-Ro s h i p i n s h a l l o w w a t e r ' . R e p o r t 854-E, S h i p Hydro-mechanics L a b o r a t o r y , D e l f t U n i v e r s i t y o f Technology and p r e s e n t e d i n D u t c h a t a Symposium about t h e ' S a f e t y o f Ro-Ro S h i p s ' , TU D e l f t , The N e t h e r l a n d s .
[4 ] G e r r i t s m a , J . , ( 1 9 9 1 ) ,
'Forced o s c i l l a t i o n e x p e r i m e n t s ' , Proc. o f a Royal Soc. D i s c u s s i o n M e e t i n g on 'The Dynamics o f S h i p s ' , London. [5 ] K a r p p i n e n , Tuomo, (19 8 7 ) ,
' C r i t e r i a f o r s e a k e e p i n g p e r f o r m a n c e p r e d i c t i o n s ' , T e c h n i c a l Research C e n t r e o f F i n l a n d , S h i p Lab., nstm 87 [6 ] Beukelman, W. and D. Radev, ( 1 9 9 1 ) ,
'Slamming s i m u l a t i o n on p e n e t r a t i n g wedges a t f o r w a r d speed'. I n t . Symposium on Hydro- and Aerodynamics i n M a r i n e Eng., HADMAR'91, Varna, B u l g a r i a .
[7 ] F r a n c e s c u t t o , A., ( 1 9 9 1 ) ,
'On t h e n o n - l i n e a r m o t i o n s o f s h i p s and s t r u c t u r e s i n n a r r o w band sea'. P r o c e e d i n g s o f an I n t . U n i o n o f Theo-r e t i c a l and A p p l i e d Mechanics M e m o Theo-r i a l Symposium on t h e Dynamics o f M a r i n e V e h i c l e s and S t r u c t u r e s i n Waves, B r u n e l l U n i v e r s i t y , UK.
[8 ] S o l i m a n , Mohamed S., ( 1 9 9 1 ) ,
'An a n a l y s i s o f S h i p S t a b i l i t y based on t r a n s i e n t m o t i o n s ' , F o u r t h I n t . Conference on S t a b i l i t y o f Ships and Ocean V e h i c l e s (STAB'90), N a p l e s , I t a l y .
[9 ] Rainey, R.C.T. and J.M.T. Thompson, ( 1 9 9 1 ) ,
'The T r a n s i e n t Capsize Diagram A new method o f q u a n t i -f y i n g s t a b i l i t y i n waves', J . o -f S h i p Research, V o l . 3 5 . [10] Book: P r i n c i p l e s o f N a v a l A r c h i t e c t u r e f r o m : The S o c i e t y o f N a v a l A r c h i t e c t s and M a r i n e E n g i n e e r s , New York, USA.
