The Seakeeping Characteristics of a Small Waterplane Area, Twin-Hull (SWATH) Ship

The Seakeeping Characteristics ai a Small

Waterplane Area, Twin-Hull (SWATH) Ship

Jairies A. Foin, Miircjarel D. Oohi and K a i h i y n K. tv'icCreighl

David W. Taylor Naval Ship llesea'ch c,nd Development Conler Boihesda. Maryland, U.S.A.

A B S T R A C T

T l i i s paper addresses tilt: r n o t i o i i n a S m a l l WaierplcTiti A r e o , T w i n - r i u l ! (SWATH) s h i u in a s c o v / a y , The ci)rii:.r!t s t a t u i o f f u l l scriie t r i a l s , m o ' i e l e x p e r i e n c e and p r o J ' c t i o n c - p c . l ; i i i t y is p r e s e r i i s d o n d t h e ( v / t l r o u ) i v T r i i c f a c t o r s c o n t r i h u f i n q t o Un- Q c n e i a ' i y l o w i i i r / i i o r i i a f SV/ATH ships Gie i d e n f i f i o d , . C o r r e l a t i o n bei'.veen I r o n s f e r f u n c t i o n s f r o m m o d i f i o d s t r i p t h e o r y pcedic-i ion.s. ur,d I M : I .scale r(;sa!t,s f o r SSP l<Ai.V..ALINO, a •SWATH s h i p , is g i v e n c i o n q w i t i i response s p e c t r a f r n m fuli scale i t i a i s i n c l u d i n y ; l i e o f f e c r o f a u t o i y i o t i c n ^ o t i o n c o n i r o i . C o m p a r i s o n s of n i o d i d a n d f u l l s c a l e m o t i o n s in Se;.i S t o i r s '( o n d 5 a r e s h o w n . P r e d i c t i o n s o f n a t u r a l periods a i e g i v e n as o f u n c t i o n o f speed and are c o m p a r e d to t r i a l r e s u l t s . T i i e design p h i l o s o p f i y f o r SV/ATH n a t u r a l periods is d a s c r i i j e d and f i t o d i c t i o n o t severest m o t i o n s t o be e c t e d in an e n c o u r d e r c d .seav/ey is m a d e by a 3loii.,,!cc!l c s t i i r i o t i n n l e e h n ' o u e . T h e o v e r a l l g o o d n i o t i o n s o;vd h o . b i t o b i l i t y c p o r c c t e r i s t i c s t o be e x p e c t e d o f b r - SW.'XTr! t y p e o f ship are sb.ov.Ti t o r a r a n g e o f speeds end headings l o tb.e s e a .

.'-•-i^fliiODUadON

Ttie a n a l y s i s o f rhe s e a k e e p i n g pe; f o r r r o n c e o f a n y ï i . i p design d e p e n d s on g o o d r h e o r e r i c a l p r e d i c t i o n s v a l i d a t e d tiy rnodei e x p e r i m e n t s and f u l l s c o l e i r i c i s . F o r

n^'w t y p e o f ship tbie depenciei'ce on e x p e r i m e n t a l d a t a is v n r , | lo b u i i d confici'-^nee in l i i e o n o i y i i c a i t o o l s a n d t o if'jin !ns:gi;t i n t o t i i c t i y d r c d y n a r n i c ph'.H'iomena u n i q i i e t o l ' i a t sf-iip t>'pe. In rliis paper a f u l i scale t r i a l o f a p i ' c i o l y p e is used t o .ricin c o n f i t i c n c e in on c n a i y t i c a l i;".erhod i h o t is the.n c p i i i i e d t o tb.e design p r o b l e m s of e x i f e m e v o l u s p r e d i c t i o n ond n m u i - o i p.eriods e s t i n i o ï i o n .

T h i s p a p e r has t w o p r i m a r y o b j e c t i v e . : . O n e is i o pre.se.nt t h e S M w o r i h i n e s s 1r:al d a t a on SSP K A i i V i A t J b l O • f l i c s h i p h y d ; o d y n o m i c s c o m m u n i t y v / i t l i o n ' f V ' e r p r e t a i i o n o f t h e shipbs m o t i o n be'^iayior. r i i s ofbioi' is

.'t..! n n n 5 i r a t e h o w t r i a l ; , m o d e l c-sperirnents a n d l i c a l p r e d i c t i o n s e n h a n c e r l i e d e v e l o p r . i r n t o f S l v . ; c o p i n g d e s i g n c o n s i d e r o i i o n s f o r .SVv'-\Tt 1 s h i p s .

2. THt:' g.A/ATH C O N C E P T

T h e SWATbl ship p r e s e n t s a u n i q n e chalb.'nge t o n a v a l a r c h i t e c t s and h y d i o d y n a n i i c i s t s , s i n c e i t s seai<eeping c h o r c c t e r i s l ies car, i)e d i c i o l e d by t h e d e s i g n e r t o a f o r g r e o t e r e x i e n t t h a n f o r c o n v e n f i o r ; a l i r i o n o i i u i l s . SVA\TH ships con o f f e r e x c e l l e n t moiio'-'s and su.>tai;-:ed speed c a p a b i l i t y in a s e a w a y . T h e ,SWATI"i concepif was d e r i v e d f r o m c o n v e n t i o n a l c a t a m a r a n s and o c e a n o i l - d r i l l i n g p l a i f o n n s . i t c o m b i n e s tb.c speed and i a r g e d e s k a r e a of the c o n v e n t i c n a l c u f a m a t e n w i t h fhe s e a k i n d l i n e s s end p l a t f o r m . s t a b i l i t y o f Hie d r i l l i n g r i g . A SV.'ATid s:-,;p c o n s i s i s o f i w o s i r e a m ü n e d s u n m e r g e d h u l l s t h a t a r e t o r p e d o d i b e in sbcpe c o n n e c t e d t o an a i j o v e w a t e r s t r u c t u r u l b o x b y one cr i w o t h i n s t r u t s on e a c h s i d e . P r o p e l l e r s l o c a t e d b e h i n d each h u i l p r o v i d e t h e p r o p u l s i v e f o r c e . C o n t r o l s u r f a c e s -on t h e s u b m e r g e d l o w e r l i u l ! e n h a n c e s f a b i l i t y and can be a c t i v a t e d to c o n t i o l t r i m a n d f u r t h e r r e d u c e m o t i o n s vvf;en t i i e ship is u n d e r w a y . A l y p i c o l S W A T H design v/ou!d h a v e o n l y 20 p e r c e n t o f t h e w a l e r p l o n e a r e a of a c o n v e n t i o n a i r n o n o l i i j l l . T h e r e d u c e d w a t e r p l a n e o r e a and r e d i s t r i b u t i o n o f o u o y e n t v o l u m e i n t o s i i b i r i e r g e d b u l l s r e d u c e tbie e x c i t o t i o n f o r c e s o f t t i e seav/ay ond i n c r e a s e t l i e n e t u r o l p e r i o d s o f m o l i o n of l l i e c r a f t . T h e r e l a t i v e l y i n f i e g u ' e n t o c c u n e n c e o f s t o r m v/aves v / i t h long p e r i o d s m a k e s i t possibl.i f o r snips w i t h e t i u o i l v l o n g n o t u r a i p e r i o d s t o a v o i d synch.ronous respoiise in t h e m o s t c o m m o , i l > ' o c c u r r i n g s c n v / a y s , T i i i s d e c o u p l i n g o f t b e ship f r o m w o v e e x c i t a t i e ; ) f o r c e s is t h e f u n d a m e n t a l idea b e h i n d t r i o SVv'ATH c o n c e p i . T h e r e d u c e d v / a t e r p i a n e a r e a also o l l o w s t h e SWATr i s i i i p l o be m o r e r e s p o n s i v e t c I h e f o r c e s g e n e r a t e d b y c o n t r o l s u i f o c e s t i i a n a c o n v e n t i o n a l s h i p . O f h e r p a r a m e i e r s >A/b!cIi s t r o n g l y i n f l i . i e n c e s e a k e e p i n g a r e l o n g i t u d i n a l m e t a c e n t r i c lieiglvt (CrMi_'), t r a n s v e r s e r n e t a c e n r r i c h e i g f i r (GM-|-), s e p a i a f i o n o f l o n g i t u d i n a l c e n t e r o f b u o y a n c y ond c e n t e r o f f l o l o f i o n ( l . C B - L C r ) , s l ï u t c o n f i g u r a t i o n o n d s i z e , e n d a r e a o n d p o s i t i o n of i h e c o i i t ; o l s u r ' f a c s s . T h e i n f l u e n c e of t l i e s e p a r a m e i e r s as r e f l e c t e d by t h o n a t u r a l p e r i o o s of a SVv'A'lH sliip v / i l i be discussed l a t e r .

T h e U.S. N a v y ' s dcvclapn-,e;if o f Ihe SVAMi-l c c n c e p J b e g a n in 1369 w i l h t h e desion o f SSP K A I M A L i b i O by 1 .

G . L a n g o f t h e N n v a l O c e a n S y s t e m s CenTer ( N O S C ) in C a l i f o r n i a and t h e M O D C A T p r c g r a m a t t h e D a v i d T a y l o r N a v a l Ship R e s e a r c h a n d D e v e l o p m e n t C e n t e r ( D T N S R D C ) . M O D C A T v/as r e n a i r i e d S W A T H ( S m a l l W a t e r p l a n e A r e a T w i n H u l l ) in l o d i f f e r e n t i a t e t h e c o n c e p t f r o m c c c i v e n l i o n a l c o t a m o r a n s . O v e r t l i c last t e n y e a r s progress has b e e n m a d e in tlie p r e d i c t i o n o f d r a g , s t a b i l i t y , m a n e u v e r i n g , m o t i o n s , a n d loads f o r S W A T H s h i p d e s i g n s , A s u m m a r y of t h i s w o r k is c o n t a i n e d in L a r n b a n d F e i n ( R e f . I ) . in p a r t i c u l a r t w o - d i m e n s i o n a l s t r i p t h e o r y has b e e n a p p l i e d to S W A T H ship m o t i o n s p r e d i c t i o n by L e e a n d C u r p f i e y ( R e f . 2). A c o m p u l e r p r o g r a m a p p l y i n g t h i s t h e o r y has s l i o w n good c o r r e l a t i o n w i t h m o d e l t e s t s f o r m o t i o n s , v / a v e e x c i t a t i o n f o r c e s a n d o s c i l l a t i o n c o e f f i c i e n t s . T h o p r e d i c t i o n s can be m a d e f o r r e g u l a r or i r r e g u l a r v/aves. T h i s t e c h n i q u e is r a t h e r t i m e - c o n s u m i n g so s i m p l i f i e d t e c l m i q u e s f o r e s t i m a t i n g t h e p o t e n t i a l f l o w added mass a n d d a m p i n g f o r t w o - d i m e n s i o n a l S W A T H s e c t i o n s hove been d e v e l o p e d by D a l z e l l ( R e f . 3) u n d L e e ( R e f . ' l ) . T h e s e p r o g r a m s c a n be used to s c r e e n a w i d e r a n g e of p o t e n t i a l designs in a s h o r t t i m e . SSi^ K A I M A L I N O w a s the f i r s t e x p e r i m e n t a l p r o i o i y p e f o r S W A T H s h i p s . T h e goal o f the U . S . N a v y ' s S W A T H p r o g r a m is l a r g e r p r o t o t y p e s t h o t con d e m o n s t r a t e t h e a d v a n t a g e s o f S W A T H .ships in r e l a t i o n to f-lava m i s s i o n s . T l i e M i t s u i S e m i - S u b m e r g e d C a t a m a r a n (SSC) M e s a - 8 0 ( R e f . 5) is a r e c e n t a d d i t i o n t o t h e f a m i l y o f SWATH p r o t o t y p e s . Its a t t r i b u t e s w i l l g r e a t i y a d v a n c e t h e d e v e l o p m e n t o f S W A T H t e e h n o i o g y , 3. SEM 1 - S U B M E R G Ë D P L A T F O R M (SSP) K A I M A L I N O 3.1 D e s c r i p t i o n S e m i - S u b m e r g e d P l a t f o r m (SSP) K A I M A L I N O is t h e f i r s t S W A T H ship b u i l t in t h e U n i t e d S t a t e s . D e s i g n e d by T . G . L a n g ( f ^ e f . 6), i t was i n t e n d e d as a w o r k b o a t f o r t h e f d a v a l O c e a n S y s i e m s C e n t e r ( N O S C ) H a v / a i i L a b o r a t o r y , i t has p r o v e n v a l u a b l e b o t h as a w o r k b o a t a n d as a p l a t f o r m f o r d e m o n s t r a t i n g t l i e s e a k e e p i n g a d v a n t a g e s o f t h e aVATbl c o n c e p t . C o n s t r u c t e d in 1973 by t b e C u r t i s B a y C o a s t G u a r d S|-iipyard in B a l t i m o r e , M a r y l a n d , t h e ship w a s m o d i f i e d a t D i l l i n g h a m S h i p y a r d in H a w a i i by t h e a d d i t i o n o f d i s p l a c e m e n t i n c r e a s i n g b u o y a n c y b l i s t e r s in 1975. T h e c u n e n t d i s p l a c e m e n t is 220 t o n n e s . T h e p a r t i c u l a r s o f SSP K / M M A L I N O a r e p r e s e n t e d in T a b l e I. O r i g i n a l d e s i g n v a l u e s and v a l u e s foi- t h e m o s t r e c e n t s e a k e e p i n g t r i a l s a r e g i v e n . T h e a d d i t i o n o f t h e b l i s t e r s is r e s p o n s i b l e for m o s t o f t h e c h a n g e s . A s s k e t c h e d in F i g u r e I , t h e sfiip c o n s i s t s o f two c y l i n d r i c a l lov/er h u l l s c o n n e c t e d to fhe u p p e r box by t w o s t r u t s p e r h u l l . B u o y o n c y b l i s t e r s o r e l o c a t e d on t h e i n b o a r d side o f e a c h h u l l , e x t e n d i n g v / i t h c o n s t a n t t h i c k n e s s f r o m a p p r o x i m a t e l y 7 to 16 m e t e r s a f t o f t h e nose a n d t e r m i n a t i n g a t 21 m e t e r s a f t o f t h e nose. T a p e r e d all m o v a b l e c o n t r o l f i n s ( c a l l e d c a n a r d s ) o r e l o c a t e d i n b o a r d j u s t o f t o f the noses. A c o n s l a n f c h o r d f l o p p e d h y d r o f o i l .spans t h e space b e t w e e n t h e h u l l s a f t o f a m i d s h i p s . F^udders a r e m o u n t e d in t h e p r o p e l l e r s l i p s t r e a m b e h i n d e a c h h u l l . T h e f o r w a r d s t r u t s i n c r e a s e in c h o r d and t h i c k n e s s f r o m a p o i n t j u s t b e i o v / t h e w a t e r l i n e t o t h e c o n n e c t i o n to the b o x , the oft s t r u t s a l s o i n c r e a s e in t h i c k n e s s as tlie box is a p p r o a c h e d . B o t h s t a r b o a r d s t r u t s a r e o u t f i t t e d w i t h s p r a y r a i l s a b o v e t h e w a t e r l i n e t h a t h e l p in d e f l e c t i n g s h e e t s o f w a t e r t h a t m i g h t c l i m b t h e s t r u t s in w a v e s . T h e a b o v e w a t e r b o x is f l a t b o t t o m e d e x c e p t f o r s l a n t e d , s h a p e d s e c t i o n s on t h e f o r w a r d e n d . T h e s e s e c t i o n s t e n d t o c u s h i o n s l a m s in h e a d s e a s . SSP K A I M A L d N O has n a t u r a l l y g o o d m o t i o n c h a r a c t e r i s t i c s in m a n y sea c o n d i t i o n s . A n a u t o m a t i c T a b l e 1 C l i a r a c t e r i s t i c s o f t h o S S P K A I A / I A L i r ' J O Original Design A s Tostod 1976 and 1979 Length, Undeiwater, m 24.8 24.8 Length, Overall, m 26.9 26.9 Displacement, M T S W 192.2 220.0 Draft, m .t.3 4.8

Beam, IViaximum Submerged, m 15.1 15.1

KG, Height of Center ot Cïravity

above Baseline, m 4.7 4.6

Diameter of Lower Hulls, m 1.98 1.E8

KB, Heiglit of CB above Baseline 1.75 1 . 6 5

G M l , m 4.42 3.84

G M j , m 2.01 1.01

Waterplane Area, 23.0 23.0

Longitudinal Distance CG Forward

of Aft Perpendicular, m 12.9 13.4

Longitudinal Distance C F Forward

of Aft Perpendicular, ni 13.5 13.5

Pitch Radius of Gyration, m 7.1 7.0

Roll Radius of Gyration, m 4.8 5.5

Aft Foil, Projected Area, m^ 25.1 25.1

Fnn/i/ard Canards, Total Area, m^ 7.1 7.1

F i g . 1 S k e t c h o f S S P KAil\;LAL!rslO S h o v / i n g i n s t r u m e n t L o c a t i o n s

m o t i o n c o n t r o l s y s t e m d e s i g n e d to r e d u c e m o t i o n s in all sea c o n d i t i o n s was d e s i g n e d and d o c u m e n t e d by H i g d o n ( R e f . 7). T h e s y s t e m uses t l i e f o r w a r d c a n a r d s e n d the s t e r n f o i l f l a p s t o m i n i m i z e p i t c h a n d r o l l m o t i o n s , r i e a v e is n o t r n i n i i n i z e d b u t i t c a n be c o n t r o l l e d so as to m i n i m i z e r e l a t i v e m o t i o n v / i t h r e s p e c t to t l i e v/ove in o r d e r to r e d u c e v / a t e r c o n t a c t s in l o w e n c o u n t e r f r e q u e n c y s i t u a t i o n s such as f o l l o w i n g seas. T h i s c o n t r o l m o d e r e l i e s on p r e s s u r e ( h e i g h t ) sensors l o c a t e d in the u n d e r w a t e r h u l l s in c o n j u n c t i o n w i t h m i n i m i i z e d i n e r t i a l p i t c h a n d r o l l . Pleading c o n t r o l is m a i n t a i n e d by the r u d d e r s k e y e d t o a yaw r a t e g y r o s c o p e . T h e ship has 153 k i l o w a t t s (20Ü h o r s e p o v / e r ) a v a i l a b l e f o r f i n and rudder a c t u a t i o n , v / h i c h scales up t o v a l u e s t h a t a r e u n a c c e p t a b l e for l a r g e r S W A T H d e s i g n s . H o v / e v e r , m o r e e f f i c i e n t a c t u a t o r s c o u l d p r o v i d e a c c e p t a b l e c o n t r o l d e f l e c t i o n

r a t e s f o r less p o w e r on l a r g e r ships as s h o w n by H i g d o n '^^'^'^SSP K A l M A L l I d O is o u t f i t t e d w i f h two 1660 k i l o w a t t (2230 h o r s e p o w e r ) a i r c r a f t t y p e gas t u r b i n e e n g i n e s in t h e inner box t l i o t d r i v e c o n t r o l l a b l e p i t c h p r o p e l l e r s t h r o u g h a c h a i n d r i v e s y s t e m . SSP K A I M A I J N O r e o c h e d 25 k n o t s in 1974 b e f o r e t h e b l i s t e r s w e r e a d d e d . C u r r e n t t o r q u e l i m i t a t i o n s on d r i v e t r a i n c o m p o n e n t s r e d u c e t h e t o p speed to a b o u l 18 k n o t s . SSP K A I M A L I t T O does n o t r e p r e s e n t c u r r e n t d e s i g n p h i l o s o p h y f o r SWATH s h i p s ; f o r e x a m p l e , t l i e f u l l span s i e r n f o i l is l a r g e r t h a n e i t h e r s t a b i l i t y or c o n t r o l r e q u i r e s . T h e s m a l l o v e r a l l size o f SSP K A I M A L I N O m a k e s her m o t i o n in h i g h sea s l a t e s w o r s e t h a n l a r g e r SWATH ships. In a d d i t i o n , her w a t e r p l a n e a r e a a n d m e t a c e n t r i c h e i g h t s r e s u l t in n a t u r a l m o t i o n p e r i o d s a t low speeds t h a t are n o t o p t i m u m f o r l a r g e r SWATH ship designs. These d i f f e r e n c e s o r e discussed in d e t a i l in L a m b and F e i n ( R e f . I) w i t h i n t h e c o n t e x t o f c u r r e n t SV/ATH design p r a c t i c e . N e v e r t h e l e s s SSP K A I M A L I N O does & -instrate t h e a d v a n t a g e s o f t l i e SWATH c o n c e p t . It ol p r o v i d e s a means f o r r e l a t i n g f u l l scale p e r f o r m a n c e t o t h e o r e t i c a l and e x p e r i m e n t a l m o d e l w o r k , ^ ffius v e r i f y i n g t h e design t o o l s that a p p l y to any S W A T H s h i p .

3.2 M o d e l E x p e r i m e n t s M o d e l e x p e r i m e n t s w e r e c o n d u c t e d a t D T N S R D C on G 1/7.8 scale m o d e l o f SSP K A I M A L I N O in 1971 as t h e design w a s b e i n g f i n a l i z e d . T h e o b j e c t i v e of t h e e x p e r i m e n t s v/as to e v a l u a t e t l i e d e s i g n and i d e n t i f y p r o b l e m a r e a s . Ttie 3.35 m e t e r (11 f o o t ) long m o d e l b u i l t üi D T N S R D C v/as o u t f i t t e d f o r d r a g , p r o p u l s i o n , s t a b i l i t y , s e a k e e p i n g , and s t r u c t u r a l m e a s u r e m e n t s . L x p e r i m e n t s w e r e c o n d u c t e d on C a r r i a g e 2 ( D T N S R D C ' s D e e p W a t e r S t r o i g h t l i n e B a s i n ) and in t h e s e a k e e p i n g t a n k o f i h e M a n e u v e r i n g and S e a k e e p i n g F a c i l i t y ( M A S K ) . F o r t h e seokeeping e x p e r i m e n t s t l i e m o d e l was s e l f - p r o p e l l e d and t e t h e r e d by p o w e r c a b l e s and s a f e t y lines t o t h e t o w i n g c a r r i a g e . P i t c h and roll a n g l e s w e r e m e a s u r e d by g y r o s c o p e s . R e l a t i v e b o w m o t i o n was o b t a i n e d f r o m on u l t r a s o n i c t r a n s d u c e r m o u n t e d on t h e b o w . A n o c c e l e r o m e t e r p l a c e d a t t h e f o r w o r d m o s t p o i n t o f t h e m o d e l m e a s u r e d bow v e r t i c a l a c c e l e r a t i o n . H e a d i n g w a s r - - ' n t a i n e d by s e r v o - c o n t r o l l e d r u d d e r s t h a t r e a c t e d t o Y and yov/ r a t e f e e d b a c k . P o w e r i n g w a s c o n t r o l l e d f r o m t h e c a r r i a g e and v a r i e d to k e e p s l o c k in t h e c a b l e s and s a f e t y l i n e s r e g a r d l e s s of t h e w a v e i n d u c e d s u r g e . Ttie a f i f o i l and canards w e i e f i x e d a t a n g l e s r e q u i r e d to g i v e level t r i m and d e s i g n s i n k a g e in c a l m w a t e r a t t h e speed under s t u d y . T h e i r r e g u l a r w a v e s w e r e p r o v i d e d by p n e u m a t i c w a v e m o k e r s d r i v e n by m a g n e t i c t a p e , f h e waves a p p r o x i m a t e d P i e r s o n - M o s k o w i t z sea s p e c t r a f o r Sea S t a t e s ') and 5. A l l h e a d i n g s v/ere i n v e s t i g a t e d o v e r a range o f speeds f r o m k.2 to 21 k n o t s f u l l s c a l e . T h e bov/ a c c e l e r a t i o n w a s h i g l i e s t in head seas w h i l e p i t c h m o t i o n was l a r g e s t in f o l l o w i n g s e a s . I^o s i g n i f i c a n t s l a m m i n g was n o t e d a t any h e a d i n g . T h e s e e a r l y r e s u l t s d i d n o t g i v e a c o m p l e t e p i c t u r e o f s e a k e e p i n g o f SSP K A I M A L I N O b u t t h e y did shov/ t h a t t h e r e w e r e no m a j o r p r o b l e m s . L a r g e m o t i o n s in s t e r n q u a r t e r i n g and f o l l o w i n g seas w e r e o f some c o n c e r n t h o u g h t h e y v/ere a s s o c i a t e d w i t i i l o n g p e r i o d s . T h e c o n c l u s i o n s o f t h e s e e x p e r i m e n t s v / e r e g e n e r a l l y v e r i f i e d by s u b s e q u e n t f u l l scale t r i a l s . ATsecond s e r i e s o f m o d e l e x p e r i m e n t s was c o n d u c t e d in 1973 as c o n s t r u c t i o n o f t h e ship v/as e n d i n g . T h e o b j e c t i v e v/as to i n v e s t i g a t e s y n e h r o n o u s c o n d i t i o n s v / h e r e the e n c o u n t e r p e r i o d in w a v e s c o r r e s p o n d e d to t i i e ship's • - i u r a l p e r i o d s . A 1.5 m e t e r long r a d i o - c o n t r o l l e d m o d e l d g n e d by HOSC w a s u t i l i z e d . T h i s m o d e l a l l o w e d f o r m o r e t i m e a t speed in i h e M A S K f a c i l i t y and c o u l d be r u n w i i f i o u t p o w e r f r o m t h e t o v / i n g c a r r i a g e . T h e m o d e l v/as i n s t r u m e n t e d t o m e a s u r e i m p a c t p r e s s u r e s , p ' t c l i , r o l l , r e l a t i v e b o w m o t i o n , a n d bow v e r t i c a l a c c e l e r a t i o n . T h e e x p e r i m e n t s c o n s i s t e d o f t h e d e t e r m i n a t i o n o f c a l m w a t e r n a t u r a l p e r i o d s a t z e r o speed, e v o l u a t i o n o f r e g u l a r w a v e responses and i n v e s t i g a t i o n s in a s e a w a y r e p r e s e n t i n g a f u l l scale m o d a l p e r i o d o f 9.5 seconds and s i g n i f i c a n t w a v e h e i g h t o f ' t m e t e r s .

T h e n a t u r a l p e r i o d s at z e r o speed w e r e 0.49 seconds f o r p i t c h , 8.06 seconds f o r heave and 15.7 seconds f o r r o l l i n f u l l s c a l e t e r m s . T h e r e g u l a r w a v e w o r k e m p h a s i z e d e n c o u n t e r f r e q u e n c i e s t h a t m i g h t e x c i t e s y n c h r o n o u s m o t i o n s . L a r g e s t m o t i o n s w e r e f o u n d in f o l l o v / m g seas w h e n ship speed w a s c l o s e t o t h e w a v e s p e e d . In t h a t case a l a r g e b o w d o w n s t a t i c t r i m o c c u r r e d due t o i h e a c t i o n o f t h e v/ave on t h e f u l l span a f t f o i l . T h i s c o n d i t i o n , w h i c h c o u l d lead t o t h e upper s t r u c t u r e b o w b e i n g b u r i e d in t h e w a v e and i h e p r o p e l l e r b r o a c h i n g , w a s l a t e r o b s e r v e d in f u l l s c a l e t r i a l s . In t h e i r r e g u l a r w a v e e x p e r i m e n t s s i g n i f i c a n t s l a m m i n g w a s e x p e r i e n c e d in head Sea S t a t e 6 a t soeeds a b o v e 10 k n o t s f u l l s c a l e . It s h o u l d be n o t e d t h a t all t h e s e m o d e l e x p e r i m e n t s v / e r e c o n d u c t e d w i t h c o n t r o l s f i x e d . S e v e r e m o t i o n s and i m p c c i s a t speed c o u l d be e x p e c t e d t o be a l l e v i a t e d by t h e use o f a u t o m a t i c c o n t r o l . 3.3 F u l l S c a l e T r i a l s SSP K A I M A L I N O has u n d e r g o n e e x i e n s i v e t r i a l s b e g i n n i n g in I97'4. T h e f i r s t series o t t r i a l s v/as c o n d u c t e d (as w e r e i h e m o d e l e x p e r i m e n t s ) on t l i e o r i g i n a l c o n f i g u r a t i o n . T h e s e w e r e c o m p l e t e d in 1975 ond i n c l u d e d i n v e s t i g a t i o n s of p o v / e r i n g , s t r u c t u r a l l o a d s , c o n t r o l r e s p o n s e , m a n e u v e r i n g , and s e a k e e p i r i q , i h e t r i a l c o n d i t i o n s v/ere l a t e r r e p e a t e d a f l e r SSP K A I M A L I N O was o u t f i t t e d w i t h b u o y a n c y b l i s t e r s . In a d d i t i o n , c o n t r o l s y s t e m e v a l u a t i o n t r i a l s , h e l i c o p t e r l a n d i n g t r i a l s , and c o m p a r i s o n i r i o l s w i t h t w o C o a s t G u a r d ships i i a v e b e e n c o n d u c t e d . T h e p o v / e r i n g r e s u l t s a r c d o c u m e n t e d by Stenson ( R e f . 9) a n d Woo and M.ouck ( R e f . 10). T h e m a n e u v e r i n g r e s u l t s a r e s u m m a r i z e d in L a r n b and F e i n ( R e f . 1). F i g u r e 2 is a p h o t o g r a p h o f SSP K A 1 M A I . . I N 0 u n d e r g o i n g t r i a l s . F i g . 2 SSP KAII'i/1ALir\!0 U n d e r g o i n g T r i a l s T h e f i r s t s e r i e s o f s e a k e e p i n g t r i a l s in 1975 v/as c o n d u c t e d in t h e K c i w i C h a n n e l b e t w e e n t h e islands o f O a h u and M o l o k o i (See F i g u r e 3 ) , M e a s u r e m e n t s v/ere m a d e o f t h e ship's r i g i d b o d y m o t i o n s ( p i t c h , r o l l , r e l a t i v e b o w m o t i o n ) , a c c e l e r a t i o n s ( s u r g e , s w a y , h e a v e , b o w

v e r t i c a l a n d p o r t v e r t i c a l ) , r a t e s {yaw, p i t c h , a n d r o l l ) , a n d i m p o c t o r e s s u r e s a t 20 l o c a t i o n s . T h e s e a w a y w a s m e a s u r e d by a f r e e f l o a t i n g buoy t h a t w a s d e p l o y e d by t h e chase b o a t . T h e b u o y c o n t a i n e d a d o u b l e i n t e g r o t m g o c c e l e r o m e t e r a n d t e l e m e t e r e d t h e w o v e h e i g h t s i g n a l b a c k t o t h e s h i p . T h e b u o y t e n d e d t o d r i f t and a t t i m e s w a s f a r e n o u g h f r o m t h e o p e r a t i n g a r e a t o m a k e t h e r e l e v a n c y o f s o m e o f t h e w a v e i r i e a s u r e r n e n t s q u e s t i o n a b l e . S i g n i f i c a n t w a v e h e i g h t was a b o u t 1.75 m e t e r s . T a b l e 2 S e a k e e p i n g T r i a l C o n d i t i o n s 160°V/ Niihau Trials Sites t 1975 Trial 2 1976 Trial 3 First 3 Days 4 Last Day -158^W Predominant ' North Wave Direclion

(All Trials) ?2°N •i- — ^ - - ^ 21°t ~ 1979 Trial 19/9 Trial 50 km F i g . 3 H a w a i i a n I s l a n d s T r i a l s L o c a t i o n s T r i a l s v / e r e c o n d u c t e d a t n o m i n a l speeds o f 16.5, 12.5 a n d 9.5 k n o t s . A v e r a g e speeds, s i g n i f i c a n t w a v e h e i g h t s , and t r i a l c o n d i t i o n s a r e l i s t e d in T a b l e 2. T h e c o n t r o l s y s t e m v/as not e m p l o y e d for t h e s e t r i a l s so c a n a r d s a n d t h e s t e r n f o i l w e r e f i x e d a t d e f l e c t i o n s d e s i g n a t e d for m e a n t r i m a t t h e g i v e n s p e e d . T h e t r i a l s p r o c e d u r e c o n s i s t e d o f a d j u s t i n g t l i e ship t o l e v e l f r i m a t z e r o speed a n d r e c o r d i n g d i s p l a c e m e n t . B e f o r e e a c h r u n Ihe ship w a s set on c o u r s e o t t h e d e s i r e d h e a d i n g t o fhe w a v e s as d e t e r m i n e d by a d e c k o b s e r v e r . A s w i t h a n y f u l l s c a l e t r i a l , t h e r e w a s s o m e d o u b t a b o u t t h e d i r e c t i o n a l i t y o f t h e seav/ay a l t h o u g h t h e d i r e c t i o n o f p r i m a r y e n e r g y w a s c a r e f u l l y o b s e r v e d . A t l e a s t 30 m i n u t e s o f d a t a w e r e t a k e n f o r each t r i a l c o n d i t i o n . M o c h a n g e s in p r o p u l s i o n or c o n t r o l d e f l e c t i o n w e r e p e r m i t t e d d u r i n g t h e d a t a c o l l e c t i o n p e r i o d . F e w i m p a c t s w e r e n o t e d , f h e o n l y case w h e r e d e c k w e t n e s s o c c u r r e d w a s in f o l l o w i n g seas w h e n t l i e w a v e speed a p p r o a c h e d the s h i p speed and a l a r g e a m p l i t u d e b u t g e n t l e b o w " p l o w - i n " o c c u r r e d . P r o p e l l e r b r o a c h i n g o c c u r r e d in s i m i l a r c o n d i t i o n s in g u a r t e r i n g seas. A s r e p o r t e d by K a l l i o ( R e f . 1 I ) , t h e d a t a w e r e i n a d e q u a t e f o r p o w e r s p e c t r a l a n a l y s i s ; n o w e v e r , s i g n i f i c a n t v a l u e s o f t h e m o t i o n s a n d a c c e l e r a t i o n s w e r e o b t a i n e d a t a l l h e a d i n g s . In N o v e i n b e r o f 1976 l o w speed t r i a l s v / e r e c o n d u c t e d by D T N S R D C o n SSP K A I M A L I N O t o o b t a i n b e n d i n g m o m e n t s in b e a m seas. In c o n j u n c t i o n w i t h t h a t e f f o r t , t h e m o t i o n s , bov/ v e r t i c a l a c c e l e r a t i o n , a n d seav/ay w e r e m e a s u r e d a t a l l h e a d i n g s a t t h e n o m i n a l speed o f 5 k n o t s . T h e s e r e s u l t s p r o v i d e d i n f o r m a t i o n a b o u t SSP K A I M A L I N O m o t i o n s in a h i g h Sea S t a t e 5 a t l o w s p e e d . T h e ship h a d b e e n m o d i f i e d p r i o r t o t h e s e e x p e r i m e n t s by t h e a d d i t i o n o f b u o y a n c y b l i s t e r s on the i n b o a r d lovver h u l l s . T h e ship w a s o p e r a t i n g o n o n l y one p r o p e l l e r d u r i n g t h e s e t r i a l s . P i t c h and r o l l w e r e m e a s u r e d a t t h e s t a b l e t a b l e ( l o c a t e d a b o u t 6 m e t e r s f o r w a r d o f t h e C G on t h e c e n t e r l i n e ) w h i l e b o w m o t i o n w a s d e t e r m i n e d f r o m a n u l t r a s o n i c h e i g h t sensor l o c a t e d 1.0 m e t e r f o r w a r d o f t h e b o w on t h e s h i p c e n t e r l i n e . B o w v e r t i c a l a c c e l e r a t i o n w a s m e a s u r e d as in t h e e a r l i e r t r i a l s in t h e p i l o t h o u s e . Wave s p e c t r a v / e r e a g a i n o b t a i n e d f r o m a f r e e f l o a t i n g b u o y a n d in t h e s e t r i a l s t h e b u o y v/as d e p l o y e d f r o m t h e ship and w a s v e r y n e a r t h e t r i a l l o c a t i o n n e a r O a h u I s l a n d .

Title Dato Location g , ^ , ^ Sea Significant Wuva Ht m r,'uiTil)er of Conditions Speeds Control Evaluated Seakcfiping Evalu.ilton 7/28/75 KAIWI STRAIT '1 1.8 6 9.8.12.8 no 7/31/75 KAIWI STRAIT •i 1.7 10 9.8,17 No Structural Evaluation 11/26/76 North-East of Oahu 5 3.fl 6 6 No Control Evaluation 1/21/79 South-East of Kauai 5 2.9 10 15.5 Yes 1/23/79 South-East of Kauai 4 2.5 4 0,10 Yos 1/25/79 South-East of Kauai 1 2.0 18 3.5,10,15.5 Yes 1/31/79 r-lorih-East of Oahu 5 3.2 19 7,10,15.5 Yes"

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S i g n i f i c a n t w a v e h e i g h t is g i v e n in T a b l e 2. T h e t r i a l s w e r e c o n d u c t e d w i t h o u t t h e use o f t h e c o n t r o l s y s t e m , as t h e speed v/as t o o lov/ for s u f f i c i e n t c o n t r o l e f f e c t i v e n e s s . S p e c t r a f r o m t h e s e t r i a l s w i l l be d i s c c s s e d in S e c t i o n 5. T h e m o s t r e c e n t s e a k e e p i n g t r i a l s w e r e c o n d u c t e d in J a n u a r y o f 1979 in o r d e r ro e x t e n d t h e r a n g e o f s e a k e e p i n g r e s u l t s , t o o b t a i n d a t a t t i a f c o u l d be used t o g e n e r a t e t r a n s f e r f u n c t i o n s , a n d t o q u a n t i f y t h e e f f e c t o f a u t o m a t i c c o n t r o l on the m o t i o n s of SSP K A I M A L I I ^ J O . These t r i a l s v / e r e c o n d u c t e d o f f K a u a i a n d O a h u as n o t e d in F i g u r e 3. Mea.surernents w e r e m a d e o f r i g i d body m o t i o n s , a c c e l e r a t i o n s and t h e s e a w a y . I m p a c t pressures a n d s t r a i n s w e r e r e c o r d e d b u t not a n a l y z e d s i n c e t h e r e w e r e f e w i m p o c t s . The t r o n s d u c e r l o c a t i o n s i n t h i s t r i a l a r e s h o w n in F i g u r e I . Waves w e r e a g a i n mea.sured by a f r e e f l o a t i n g b u o y in c l o s e p r o x i m i t y to t h e t r i a l a r e a . When n o t in t h e w a t e r the b u o y was a t t a c h e d fo the deck

a n d t h e r e b y p r o v i d e d a v e r t i c a l d i s p l a c e r n e n t m e a s u r e m e n t near t h e l o n g i t u d i n a l c e n t e r o f g r a v i t y ( C G ) t h a t w a s a l m o s t e q u i v a l e n t t o h e o v e .

In p r e p a r a t i o n f o r each p a r t i c u l a r r u n , t h e ship was s t e a d i e d on c o u r s e a t a p p r o x i m a t e l y t h e d e s i r e d s p e e d . T h e speed v a r i e d s l i g h t l y due t o w i n d ond v/uvo c o n d i t i o n s . T h e ship c o u r s e v/as set t o m a i n t a i n a h e a d i n g w h i c h w a s c o n s t a n t r e l a t i v e to t h e p r e d o m i n a n t seciv/oy as d e t e r m i n e d by o b s e r v a t i o n s . O n c e tine h e a d i n g and speed w e r e s e t , m a n u a l c o n t r o l s e t t i n g s w e r e m a d e or the c o n t r o l s y s t e m w a s t u r n e d o n , a n d t h e n t h e d a t a c o l l e c t i o n p o r t i o n o f a r u n began. C o l l e c t i o n t i m e w a s g o v e r n e d by t h e n e e d f o r . s u f f i c i e n t e n c o u n t e r s a t t h e g i v e n speed and h e a d i n g a n d v a r i e d f r o m 20 t o 50 m i n u t e s . N o chonges in m a n u a l c o n t r o l s u r f a c e d e f l e c t i o n or p r o p u l s i o n s e t t i n g s w e r e m a d e d u r i n g t h e r u n s . R e s u l t s f r o m t h e s e t r i a l s w i l l be d i s c u s s e d in f o r t h c o m i n g s e c t i o n s . In a d d i t i o n , SSP K A I M A L I N O p a r t i c i p a t e d in a t h r e e ship c o m p a r a t i v e t r i a l t h a t w a s c o n d u c t e d in M a y o f 1978. It is d o c u m e n t e d by W o o l o v e r a n d p e t e r s ( R e f . 12). SSP K A I M A L I N O v/as r u n a l o n g s i d e a 100 ton.no p a t r o l c r a f t .30 m e t e r s l o n g , a n d a 3000 t o n n e C o a s t G u a r d C u t t e r . T h e t r i a l s w e r e c o n d u c t e d in Sea S t a t e 3. E m p h a s i s v/as on h u m a n f a c t o r s a n d c o m p a r a t i v e r e l a t i o n s h i p s r a t h e r t h a n on a t « o l u t e d a t a . T h e r e s u l t s d e m o n s t r a t e t h a t SSP K A I M A L I N O has s u p e r i o r m o t i o n s t o a ship o f 10 t i m e s g r e a t e r d i s p l a c e m e n t tn t h e s a m e Sea S t a t e 3.

I J A O J I O N S R E S U L T S F O R SSP K A I M A L I N O The r e s u l t s o f s e a k e e p i n g e x p e r i m e n t s a r e d e s c r i b a b l e in s e v e r a l w a y s . One is in t h e f o r m of_ l l i e r a t i o o f s i g n i f i c a n t responses t o s i g n i f i c a n t v / a v e h e i g l i t . A s i g n i f i c a n t v a l u e is t h e o v e r a g e o f tfie o n e - t h i r d h i g h e s t values a n d m a y be o b t a i n e d f r o m a t i m e h i s t o r y o f t h e m o i i o n s or w a v e e x c u r s i o n s . A n o t h e r m e l h o d o f a n a l y s i s is t h e p o w e r s p e c t r a l d e n s i t y d i s t r i b u t i o n w h i c h r e l a t e s t h e e n e r g y o f the m o t i o n oi- w a v e t o t h e f r e q u e n c y . SSP K A I M A L l l x l O f u l l s c a l e t r i a l s s p e c t r a l d a t a a r e p r e s e n t e d in t h e n e x t s e c t i o n . A t h i r d m e t h o d of a n a l y s i s used in S e c t i o n 6.3 i n v o l v e s t h e t r a n s f e r f u n c f i o n s . "fhe t r a n s f e r f u n c t i o n s p r o v i d e t h e u n i t response of a m o t i o n t o a u n i t v/ave h e i g h t t h r o u g h o u t t l i e f r e q u e n c y r a n g e . The r a t i o s o f s i g n i f i c a n t responses t o s i g n i f i c a n t v/ave h e i g h t are p r e s e n t e d in F i g u r e s 4 t o 13 f o r t h e m o d e l and f u l l s c a l e s h i p . T h e d a t a w e r e o b t a i n e d i n Sea S t a l e s ' l a n d 5. T h e w a v e s p e c t r a f o r t h e m o d e l e x p e r i m e n t s v/ere d i f f e r e n t f r o m t h o s e in t h e f u l l s c a l e t r i a l s , T h e e f f e c t o f c o n t r o l a t h i g h speed is also i n c l u d e d p i t c h and r o l l i n F i g u r e s 10 t h r o u g h 13. F i g u r e s 4 t h r o u g h 7 show t h e e f f e c t o f speed on f r e e body m o t i o n s w i l h o u l a n y f o r m o f c o n l r o l in h e a d seas. T h e r e s u l t s show l i n e a r i t y t h r o u g h o u t t h e w a v e l i e i g h t ronge e x a m i n e d . C o n e i a t i o n b e t w e e n m o d e l a n d niW scale is g o o d f o r p i t c h t h r o u g h o u t t h e .speed r a n g e , i h e m o d e l r e s u l t s w e r e o b t a i n e d fromi t h e 1971 a n d 1973 e x p e r i m e n t s . F r o m a m a x i m u m a t z e r o s p e e d , p i t c h decreases t o a m i n i m u m n t 10 k n o t s , t h e n peaks at a b o u t 14 k n o t s . B e t w e e n 10 and 14 k n o t s t l i e v/ave d r a g h u m p o c c u r s . A t 10 k n o t s t h e s h i p is " c l i m b i n g " i t s . s e l f - g e n c r a l e d b o w w o v e and t h u s i t is h e a v i l y d a m p e d in p i t c h . A t 14 k n o t s t h e s l i i p - g e n e r o t e d w a v e is b e h i n d t h e ship ond m a y a c t in a d e s t a b i l i z i n g m a n n e r . T r i a l c o n d i t i o n s a f t e r t h e a d d i t i o n o f t l i e b u o y a n c y b l i s t e r s o r e i n d i c a t e d by s o l i d p o i n t s . T l i e d a t a w i t l i b u o y a n c y b l i s t e r s shov/ g o o d a g r e e m e n t w i t h t h e e a r i i e r d a t a v / h i c h i n d i c a t e s t h a t t h e b l i s t e r s , w h i c h o r e c e n t e r e d a t t h e l o n g i t u d i n a l C G , h a v e l i t t l e e f f e c l on p i t c h m o t i o n . F i g u r e 5 p r e s e n t s r o l l in h e a d seas. T h e m o d e l e x p e r i m e n t s v / h i c h v / e r e c o n d u c t e d in a u n i d i r e c t i o n a l head sea show m i n i m a l r o l l m o t i o n w h i l e t h e f u l l s c a l e t r i a l r e s u l t s shov/ s i g n i f i c a n t r o l l . T h i s m a y be a t t r i b u t e d l o t h e f a c t t h a t v/ave c o m p o n e n t s a r e p r e s e n t in t h e r e a l v i r o n m e n t f r o m o t h e r t h a n t h e d i r e c t i o n o f t h e . e d o r n i n o n t e n e r g y . T h e v e r t i c a l a c c e l e r a t i o n in F i g u r e 6 r e m a i n s r e l a t i v e l y c o n s t a n t w i l h s p e e d , s l i g h t l y i n c r e a s i n g a t t h e h i g h e r speeds. T h e i-atio o f s i g n i f i c a n t r e l a t i v e b o w m o t i o n t o s i g n i f i c a n t w o v e h e i g h t in F i g u r e 7 shows a l m o s t no speed e f f e c t . E x c e p t f o r a s i n g l e p o i n t near 16 k n o t s , t h e m o d e l d a t a a g r e e q u i t e w e l l w i t i i t h e f u l l s c a l e r e s u l t s . F i g u r e s 8 a n d 9 s h o w .speed d e p e n d e n c e o f t h e p i t c h and r o l l m o t i o n s in b e a m seas. P i t c h in b e a m seas a t speeds b e l o v / 5 k n o t s is s l i g h t l y h i g h e r f o r t h e f u l l s c a l e t r i a l s t l i a n f o r t h e m o d e l r e s u l t s . T h e d i f f e r e n c e is p r o b a b l y due t o u n c e r t a i n t i e s in h e a d i n g a n d v/ave d i r e c t i o n , b u t e v e n so i h e m o d e l d a t a do s h o w t h e p r e s e n c e o f p i t c h in b e a m seas. T h e p i t c h is j i r o b a b l y due t o the f o r e and a f t a s y m m e t r y of t h e s l i i p . I he l a r g e o f t f o i l e x c i t e s p i t c h as t h e s h i p r e s p o n d s t o t h e b e a m w a v e s , ond s i n c e t h e r e is no a r e a f o r v / a r d t o c a n c e l t h i s e f f e c t a riel p i t c h m o t i o n ensues. T h e m o d e l r o l l m o i i o n s a g r e e q u i t e w e l l v / i t i i t h e f u l l s c a l e o v e r the speed r a n g e in F i g u r e 9. A g a i n t h e b l i s t e r s s e e m t o h o v e l i t t l e e f f e c t on s i g n i f i c a n t r o l l . T h e peak in p i t c h a n d r o l l a t a b o u t 14 !;nots is a g a i n p r e s e n t in b e a m seas. R o l l f o l l o w s t h e same t r e n d w i t h s p e e d as p i t c h , d e c r e a s i n g t o a b o u t 10 ots and t h e n s h o w i n g on i n c r e a s e in t l i s v / a v e d r a g h u m p •-lime.

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1 Heading (deg) 180 Head F i g . 1 0 P i t c h M o t i o n f o r S S P K A l M A L i i - y O a t 1 0 i C n o t s T h e e f f e c t s o f a u t o m a t i c m o t i o n c o n t r o l a r e c l e a r l y d e m o n s t r a t e d i n F i g u r e s 10 t h r o u g t i 13 w h e r e t h e d a t a is p l o t t e d as a f u n c t i o n o f h e a d i n g . T h e f u l l s c a l e d a t a w e r e o b t a i n e d d u r i n g t h e c o n t r o l s y s t e m e v a l u a t i o n t r i a l s o f 1979. T h e m o d e l d a t a in F i g u r e s 10 a n d I I a r e f r o m e x p e r i m e n t s in Sea S t a t e s 5 a n d 6 ( w i t h o u t b l i s t e r s ) . T h e r e a r e no m o d e l d a t a w i t h a c t i v e c o n t r o l . A g r e e m e n t b e t w e e n m o d e l and f u l l s c a l e p i t c h m o t i o n is e x c e l l e n t a t a l l h e a d i n g s f o r 10 k n o t s . R o l l m a g n i t u d e is l o w f o r t h e m o d e l s in head and f o l l o w i n g seas b e c a u s e of the p u r e l y u n i d i r e c t i o n a l e n v i r o n m e n t in t h e t o w i n g t a n k b u t a g r e e s v / i t h t r i a l s q u i t e w e l l of t h e o t h e r h e a d i n g s . T h e e f f e c t o f m o t i o n c o n t r o l a t 10 k n o t s is s i g n i f i c a n t . M a x i m u m p i t c h m o t i o n w h i c h o c c u r s in q u a r t e r i n g seas is r e d u c e d t o a b o u t o n e - t h i i d i t s u n c o n t r o l l e d v a l u e . R o l l is I'educed by a p p r o x i m a t e l y o n e - h a l f a t a l l h e a d i n g s . T h e c o n t r o l e v a l u a t i o n t r i a l s r e s u l t s show a l a r g e r e d u c t i o n in s i g n i f i c a n i v a l u e s o f m o t i o n s a t 10 a n d 15.5 k n o t s a n d s o m e r e d u c t i o n a t 7 k n o t s . A t l o w e r speeds t h e c o n t r o l s u r f a c e e f f e c t i v e n e s s is n o t s u f f i c i e n t t o a f f e c t the m o t i o n s . F o l l o w i n g F i g . 11 R o i ! M o t i o n f o r S S P K A I M A L I N O a t 10 K n o t » F i g . F o l l o w i n g Heading (dog) 1 2 P i ^ c h M o t i o n f o r Ö-SP K A I M A U i M O a t 15.5 K n o t s V - 4 • 6

R g . Following Heading (deg) 13 R o l l M o t i o n f o r S S P K A I i V l A L I I M O a t V3.5 K n o t s A t 15.5 k n o t s ( F i g u r e s 12 a n d 13) l o l i a n d p i t c l i a r e b o t h m a > d m u m in f o l l o w i n g seas. The c o n t r o l s y s t e m reduces s i g n i f i c a n t r o l l m o t i o n by 90 p e r c e n t a t i h i s speed in f o l l o w i n g seas and by a b o u t 70 p e r c e n t a t o t h e r headings, P i i c l i is r e d u c e d by o v e r 50 p e r c e n t a t a l l lieodings. T h e s e s i g n i f i c c n i v a l u e s d e m o n s t r a t e t h e e f f e c t i v e n e s s o f m o t i o n c o n t r o l . S i g n i f i c a n t v a l u e s are i m p o r t a n t in e s t a b l i s h i n g s e a k e e p i n g c r i i e r i a f o r designs since m o t i o n l i m i t s f o r w e a p o n s y s i e m s or a i r c r a f t o p e r a t i o n s o i e g e i i e r a l l y e x p r e s s e d in t e r m s of s i g n i f i c a n t responses. 5. D I S C U S S I O N O F F U L L S C A L E T R I A L S P E C T R A P o v / e r s p e c t r a l d e n s i t i e s as f u n c t i o n s o f e n c o u n t e r f i e q u e n c y w e r e o b t a i n e d by F o u r i e r a n a l y s i s o f t i i e m o t i o n s d a t a and a r e p r e s e n t e d f o r t h r e e speeds in Fil :s IA, 15 a n d 16. T h e response s p e c t r a in c o m o i n a t i o n v / i t h t h e w a v e s p e c t r a o f e n c o u n t e r p r o v i d e a good i n s i g h l i n t o t l i e s o u r c e s o f the m o t i o n s . T h e 5 knot speed d a t a w e r e o b t a i n e d in 1976 a n d t h e 10 a n d 15.5 k n o t speeds a r e f r o m t h e c o n t r o l e v a l u a t i o n t r i a l s o f 1979. F o r tha t w o t i i g h e r speeds, s p e c t r a w i f h a n d w i t h o u t a u t o m a t i c m o t i o n c o n t r o l a r e g i v e n . R e l a t i v e b o w m o t i o n (RB/y\) v/as m e a s u r e d in 1976 b u t n o t in 1979. V e r t i c a l m o t i o n near t h e C G w a s o b t a i n e d f o r m o s t c o n d i t i o n s in 1979 and is p r e s e n t e d in p l a c e o f f ^ B M f o r t h e i i i g h e r speeds. Wave s p e c t r a a r e p r e s e n t e d in F i g u r e s 17, 18 and 19 f o r e a c h t r i a l day f o r v / h i c h m o t i o n s p e c t r a w e r e o b t a i n e d . T i i e m o d a l peiTod o f t h e w a v e s p e c t r a is ' n a i c o i e d on e a c h m o t i o n s p e c t r u m by t h e s y m b o l T Q t o show t h e l o c a t i o n o f t h e m a x i m u m w o v e e n e r g y in t h e e n c o u n t e r f r e g u e n c y d o m a i n . The r e s u l t s f o r a 5 k n o t speed f r o m t h e 1976 t r i a l s in " fiigh Sea S t a t e 5 a p p e a r in F i g u r e R l . F o r e a c h h e a d i n g R B M , p i t c h and r o l l a r e p r e s e n t e d . T h e R B M d e p e n d s on P d c h , h e a v e and t h e e n c o u n t e r e d v/ave a t t h e b o w . A.t 'ligh f r e q u e n c i e s and lov/ speed SSP K A I M A L I N O t e n d s t o p l a t f o r m t h e w a v e s . T f i a t is, t h e s h i p t e n d s n o t t o '•-Mierienee m o t i o n as i t e n c o u n t e r s t h e w a v e s . S i n c e t h e '''BM s p e c t r u m r e a c h e s a m a x i m u m in t h e h i g h f r e q u e n c y J f l w h e r e p i t c h and r o l l a r e s m a l l , t h i s i n d i c a t e s t h a t '•5 r e l a t i v e m o t i o n m a y be due p r i m a r i l y f o h e a v e a n d t h e m o t i o n o f t h e s h o r t e r v / a v e s . A t l o w e r f r e q u e n c i e s c o n t o u r i n g o c c u r s as t h e s h i p f o l l o w s t h e v / a v e . T h i s leads t o l o w e r RBf/\ e n e r g y a t t h o s e f r e q u e n c i e s e v e n t h o u g h s i g n i f i c a n t p i t c h and r o l l e n e r g y mioy be p r e s e n t . In a l l cases t h e R B M peak e n e r g y o c c u r s a t f r e q u e n c i e s h i g h e r t h a n t h e v/ave m o d a l f r e q u e n c y ( i n d i c a t e d by T ^ o n t h e f i g u r e s ) . T h e RBfv^ is l a r g e s t in head and b o w seas a n d shov/s d o u b l e or s e c o n d a r y peaks o f t h e s e h e a d i n g s .

T h e p i t c h s p e c t r a a t 5 l<nofs a r e a l l s i n g l e p e a k e d a n d t h e peaks f e n d f o o c c u r a t oig = 0.65 r a d / s e c , w h i c h is c l o s e t o t h e e s t i m a t e d n a t u r a l f r e q u e n c y in p i t c h a t t h i s s p e e d , f ' o r head and bov/ seas t h e peak c o r r e s p o n d s t o t h e p e a k o f t h e e n c o u n t e r e d w o v e s p e c t r a i n d i c a t i n g c o n s i d e r a b l e e x c i t a t i o n near t h e n a t u r a l f r e q u e n c y f o r t h e s e h e a d i n g s . P i t c h response is m i n i m u m in b e a m seas as e x p e c t e d . T h e r o l l s p e c t r a o r e not as u n i f o r m as t h e p i t c h s p e c t r a and t e n d t o bc s o m e v / l i a t b r o a d e r . T h e p r i m a r y p e a k in t h e r o l l response o c c u r s o f t f i e peak in t h e w a v e s p e c t r a at a l ! headings v / i t h t h e e x c e p t i o n o f Iiead seas. A s e c o n d o r y p e a k is e v i d e n t a t 0.8 r a d / s e c in q u a r t e r i n g seas. T h e head sea t o l l s p e c t r u m is f l a t v / i i h s r n u i l peaks a b o v e and b e l o w t h e v/ave m o d a l f r e q u e n c y . T h e s p e c t r a f o r 10 k n o t s e r e c o n t a i n e d in F i g u r e 15. T h e s p e c t r a a r e p r e s e n l e d f o r v e r t i c a l m o t i o n n e a r f h e C G , p i t c h , and r o l l . T h e d a t a w e r e o b t a i n e d d u r i n g f h e c o n t r o l e v a l u a t i o n t r i a l s on J a n u a r y 2 5 , 1979, in a Sea S t a t e 4. T l i e r e s u l t s a r e p r e s e n t e d w i t h a n d w i t h o u t u t i l i z a t i o n of a u t o m a t i c c o n t r o l . T h e c o n t r o l l e d cases o r e i n d i c a t e d by t h e d c s h e d l i n e s . T h e c o n t r o l s y s t e m on SSP K A I M A L I N O is i n t e n d e d t o m i n i m i z e p i i c h a n d r o l l b u t not v e r t i c a l m o t i o n . T h e v e r t i c a l m o t i o n c o m p o n e n t due t o p i t c h a n d / o r r o l l is r e d u c e d in s o m e c a s e s , b u t h e a v e is sm.all in a l l c o n d i t i o n s , e v e n v / i t h o u t c o n t r o l . T h e v e r t i c a l m o t i o n peak c o r r e s p o n d s t o t h e w a v e m o d a l p e r i o d in a l l cases e x c e p t head seas. A s e c o n d a r y p e a k a t l o w e r f r e q u e n c y in h e a d and bov/ seas c o r r e s p o n d s t o a p e a k in f h e r o l l s p e c t r u m .

T h e p i t c h s p e c t r a at 10 k n o t s show m a x i m u m e n e r g y in q u a r t e r i n g seas. Wove m o d a l p e r i o d s c o r r e s p o n d t o p i t c h e n e r g y peaks in b e a m , q u a r t e r i n g a n d f o l l o w i n g seas. In head seas t h e p i t c h response is v e r y f l a t , w i t l i a s m a l l response o v e r a v/ide r a n g e of f r e q u e n c i e s . In b o w seas t h e r e is a s e c o n d a r y peak o l t h e m o d a l f r e q u e n c y o f f h e w a v e s a t a b o u t 0.85 r a d / s e c w h i l e t h e p r i m a r y peak is a t 0.72 r a d / s e c . In a l l c o n d i t i o n s t h e c o n t r o l s y s t e m g r e a t l y d e c r e a s e s f h e p i t c h r e s p o n s e . F o r e x a m p l e , in f o l l o w i n g seas t h e c o n t r o l s o r e l e a s t e f f e c t i v e b u t s t i l l r e d u c e t l i e peak v a l u e by o v e r 50 p e r c e n t . A t lov/ f r e q u e n c i e s in q u a r t e r i n g o n d f o l l o w i n g seas t h e c o n t r o l l e d response e x c e e d s f h e u n c o n t r o l l e d r e s p o n s e . T h e s e long p e r i o d m o t i o n s a r e o f t r i b u l o b l e t o t h e c o n t r o l s y s t e m ' s f e e d b a c k loop r e s p o n s e . T h e r o l l s p e c t r a a t 10 k n o t s f o r SSP K A 1 M A L 1 I 4 0 shov/ m a x i m u m response in I j e a m seas w i t h o i m o s t as g r e a t a r e s p o n s e in q u a r t e r i n g a n d b o w seas. C o n t r o l is e f f e c t i v e in r e d u c i n g r o l l m o t i o n s in a l l sea h e a d i n g s . In a l l cases t h e m a i n r o l l p e a k is a s s o c i a t e d w i t h t h e w a v e m o d a l p e r i o d a n d t l i e r e is a s e c o n d a r y peak a t u l o w e r f r e q u e n c y t h a t c a n be a t t r i b u t e d f o t h e n a t u r a l p e r i o d in r o l l . T h e l o w f r e q u e n c y peak is in t h e f r e q u e n c y r a n g e w h e r e m e a s u r e m e n t s o r e d o u b t f u l v / h i c h leads t o d i f f i c u l t i e s in f i x i n g i t s m a g n i t u d e . A t f i i r d pealc a t a h i g h e r f r e q u e n c y t h a n I h e w a v e p e a k is n o t e d f o r b o w a n d q u a r t e r i n g seas. I h i s is due t o a s i g n i f i c a n t c o m p o n e n t o f w a v e e n e r g y a t t h o s e f r e q u e n c i e s of e n c o u n t e r .

It is also o f i n t e r e s t t o p o i n t out t h a t in b e a m seas a t 10 k n o t s t h e w a v e m o d a l p e r i o d v/as a p i ) r o x i m a t e l y t f i e s o m e as t h e n a t u r a l p e r i o d s o f h e a v e a n d p i t c h , c a u s i n g s u b s t a n t i a l response in t l i e s e m o d e s . T h e n a t u r a l p e r i o d in r o l l o f t h e ship a t t h i s speed is a b o u t 21 s e c o n d s or Z i n rn Z rn O ^ Ü Z z Y - 4 - 7

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f 0 1 2 3 Frequency, co (rad/sec) Fig. 1 7 VA/avG S p e c t r u m f o r 5 K n o t M o t i o n S p e c t r a O 1 2 Frequency, to (rad/sec) F i g . 10 W a v e S p e c t r u m f o r 10 K n o t f V l o t i o n S p e c t r a 1 2 3 Frequency, cu (rad/sec) F i g . 19 W a v e S p e c t r u m f o r 1Ö.5 K n o t M o t i o n S p e c t r a a p p r o x i m a t e l y t v / i c e it.s pitci-i p e r i o d . A l t h o u g h l i t t l e wove e n e r g y e x i s t s at f h e r o i l n a t u r a l f r e q u e n c y , s o m e small r o l l m o t i o n does a p p e a r . H o v / e v e r t h e p r i m e response in r o l l o c c u r s v / i l i i i n l!ic s o m e f i e q u e n c y r e g i m e as p i t c h v / h i c h lias l a r g e e x c i t a t i o n a t i t s n a t u r a l f r e o u e n c y . T h i s b e h a v i o r is e x h i b i t e d in b o w a n d qil .'ring seas as v / e l l . T h u s , at least f o r t h i s s p e e d , iliere a p p e o r s l o be s i g n i f i c a n i c o u p l i n g b e t w e e n the t h r e e modes ( p i t c h , h e a v e and r o l l ) o f m o t i o n . T h e response s p e c t r a a t 15.5 k n o t s o b t a i n e d in a Sea State 5 (on J a n u a r y 2 1 , 1979) d u r i n g t h e c o n t r o l e v a l u a t i o n t r i a l a r e g i v e n in F i g u r e 16. R e s p o n s e of v e r t i c a l m o l i o n near t h e C G , p i t c h and r o l l a r c i n c l u d e d , though v e r t i c a l m o t i o n was n o i a v a i l a b l e f o r t h e h e a d and f o i i o w i n g sea c a s e s . A m o n g i l i e cases o v a i l a b l e , v e r t i c o l m o t i o n r e s p o n s e is g r e a t e s t in q u a r t e r i n g s e a s . C o n t r o l o f p i t c h a n d r o l l has l i t t l e e f f e c t o n t h e v e r t i c o l m o t i o n e x c e p i in c | u a r t e r i n g seas. In o i l coses t h e p r i m a r y p e a k s for v e r t i c a l m o t i o n c o r r e s p o n d i o t h e f r e q u e n c y o f m a x i m u m w a v e e n e r g y . A s e c o n d a r y p e a k in q u a r t e r i n g seas a t oig = 0.72 r a d / s e c m a y r e s u l t f r o m i h e f a c t t h a t Ihere is s i g n i f i c a n t w a v e e n e r g y neor t h e h e a v e and p i t c h n o t u r a i p e r i o a s .

P i t c h r e s p o n s e is m o r e t h a n on o r d e r of m a g n i t u d e larger in f o l l o v / i n g and q i j o r i e r i n g seas t h a n in h e a d , b o w or b e a m seas. P i l c i i r e s p o n s e is p r i m a r i l y v / o v e i n d u c e d in l>eum, q u a r t e r i n g a n d f o i i o w i n g seas, a n d in f o l l o w i n g seas ihe e n c o u n t e r e d v/ove s p e c t r u m has c o n s i d e r a b l e e n e r g y near i h e n a t u r a l p i t c h p e r i o d a t i h e 15.5 k n o t s p e e d . T h e Icirge responses in q u a r t e r i n g e n d f o l l o w i n g seas o c c u r a t lov scjuencies w h e r e t h e w a v e s t r a v e l a t speeds c l o s e t o the ^,iip s p e e d . T h e l a r g e s t e r n c o n t r o l f o i l in t h e SSP c o n induce l a r g e m o t i o n s under s u c l i c o n d i t i o n s . In b o w seas pircfi response is f l a t o v e r a b r o a d r a n g e w i t l i t h e m o s t energy a t = O.A r a d / s e c . T h e head sea p i t c h r e s p o n s e specirum, is d i s t i n c t i v e in t h a t t h e r e is l i t t l e response, o f liie w o v e m o d a l p e r i o d b u t i n s t e a d peak v a l u e s of r e s p o n s e occur a t e n c o u n t e r f r e q u e n c i e s o f O.A a n d 1.8 r a d / s e c . Tlie higti f r e q u e n c y p e a k is i n a r e g i o n v / h e r e t h e r e is ' d i l a p i t c h r e s p o n s e f o r a n y o t h e r h e a d i n g . A c t i v e - o n t r o l s i g n i f i c a n t l y d e c r e a s e s t h e p i t c l i r e s p o n s e f o r a l l headings. R o l l s p e c t r a a t 15.5 k n o t s e x h i b i t w a v e m o d a l p e r i o d induced r o l l i n g f o r a l l sea f i e o d i n g s . A l s o t f i e r e is a • c c o n d a r y p e a k i n h e o d , i i o w and b e a m seas of a l o w e r ' r e q u e n c y o f e n c o u n t e r v / l i i c h is a p p r o x i r n a f e i y 0 . 3 5 •ad/sec, c l o s e t o t h e e s t i m a t e d r o l l n a t u i ' a l f r e q u e n c y . In ' o l l o w i n g seas i h i s s a m e f r e q u e n c y is c l o s e t o t l i e i n o d o l i'<-'i'iod o f t h e e n c o u n t e r e d w a v e s , r e s u l i i n g in an a m o u n t '•'f r o l l r e s p o n s e g r e a t e r t h a n i h e r o l l r e s p o n s e in b e a m J^Qs and o n l y s l i g h t l y less t f i a n t h e r o l l in q u o r f e r i n g s e a s . • o n t r o l o f r o l l m o t i o n is v e r y e f f e c t i v e a t a l l h e a d i n g s as ' ' ' n t r o l l e d r e s p o n s e s a t e a l m o s t i n s i g n i f i c a n i c o m p a r e d t o j ' l s u n c o n i r o l l e d c a s e s . In p a r t i c u l a r , t h e s e v e r e r o l l i n g in 'ng seas is v i r t u a l l y e l i m i n a t e d b y t h e c o n t r o l F i g u r e s 17, 18 a n d 19 g i v e t h e v/ave s p e c t r a in t h e v / a y e f r e q u e n c y d o m a i n f o r e a c h o f t h e t h r e e days o n w h i c h t l i e d a t a in t h e response s p e c t r a w e r e o b t a i n e d . T h e r e is v e r y l i t t l e w a v e e n e r g y i i e l o v / o j g = 0.3 r a d / s e c w h i c h causes d i f f i c u l t i e s in d e f i n i n g lov/ f r e q u e n c y e f f e c t s in f h e m o t i o n s p e c t r a . .Each w a v e s p e c t r u m is s i n g l e p e a k e d t h o u g h t h e r e a r e s o m e i n d i c o f i o n s o f s e c o n d a i y h u m p s . T h e s i g n i f i c o n i w a v e h e i g h t s f o r t h e s e s p e c t r a o r e g i v e n in T a b l e 2. O v e r a l l , t h e .seakeeping t r i a l s o f SSP K A I M A L I N O d e m o n s t r a t e d t l i a t t h e s h i p c o u l d o p e r a t e o v e r l i s f u l l speed r a n g e in v/ave c o n d i t i o n s up t o o h i g h Sea S t a t e 5. E x c e s s i v e s l a m m i n g v/as n o t e n c o u n t e r e d a t a n y h e a d i n g e i t h e r v / i t h or w i t h o u t a u t o m a t i c m o t i o n c o n t r o l . S l a m m i n g a t 15.5 k n o t s in a head Sea S t a t e 5 v/as v i r t u a l l y e l i m i n a t e d by t r i m m i n g t h e ship bov/ up t v / o d e g r e e s . T h e ship's t e n d e n c y t o h e a v e ( f o l l o w i n g t h e w a v e s ) l i e l [ ) e d in m o d e r a t i n g t t i e i m p a c t s . A t no l i m e d i d i l i e ship s l o w d o w n due l o sea c o n d i t i o n s e v e n t h o u g h t l i e a v e r a g e m a g n i t u d e o f i l i e o n e - t e n t h h i g h e s t v / a v e s ( d o u b l e a m p l i i u d e ) w a s m o r e i h o n t w i c e t h e c l e a r a n c e h e i g h t o f 1.8 m e t e r s . D u r i n g i l i e Sea S t a t e 5 t r i a l s on J a n u a r y 2 1 , 1979, t h e a v e r a g e o f t h e o n e - t e n t h h i g h e s t w a v e s v/os 3.65 m e t e r s w h i c h is 15 p e r c e n t o f t h e l e n g t h o f Ihe s h i p . O n t h a t doy SSP K A I M A L I I J O o p e r a l e d t o r o v e r 10 h o u r s a t speeds a r o u n d 15.5 k n o t s a t a v a r i e t y o f h e a d i n g s v / i t h no d e g r a d a t i o n o f c r e w or s h i p p e r f o r m i a n c e . 6 . C O M P A R I S O N W I T H T H E O R E T I C A L M O T I O N P R E D I C T I O ! -6.1 S W A T H Ship P r e d i c t i o n M e i l i o d o l o q y C o n f i d e n c e in t h e a b i l i t y of t h e o r y t o p r e d i c t t r e n d s and g e n e r a l m a g n i t u d e s of m o t i o n is p a r t i c i j l a r l y i m p o r t a n t f o r i h e S W A T H ship d e s i g n e r s i n c e t h e SW/\TFI c o n c e p t l o c k s t h e e x t e n s i v e e x p e r i e n c e in d e s i g n a v a i l a b l e t o t h e m o n o h u l l d e s i g n e r . W h i l e m o d e l e x p e r i m e n t s a r e r e q u i r e d b e f o r e a d e s i g n is f i n a l i z e d , t h e o r e t i c a l p r e d i c t i o n s m u s t be used t o a n a l y z e t h e m o t i o n o~' p o t e n t i a l c o n f i g u r a t i o n s a t an e a r l y s t a g e o f d e s i g n . T h e d e v e l o p m e n t of t h e t h e o r y used a t DTNSRL')C t o d e s c r i b e i h e i n o t i o n s o f SWATH ships is p r e s e n t e d by L e e a n d C u r p h e y ( R e f . 2 ) . S t r i p t h e o r y p r o v i d e s five basis t o r t h i s d e v e l o p m e n t . T h a t is, i t is a s s u m e d t h a i t h e f i o w c l one t r a n s v e r s e t w o - d i m e n s i o n a l s e c t i o n o f f h e s l i i p Is i n d e p e n d e n t o f t h e f l o w ot o n o i h e r s e c t i o n , T i i i s a p p r o a c h has been used s u c c e s s f u l l y t o p r e d i c t i h e m o t i o n s 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 ships; h o w e v e r , SWATI-i ships d i f f e r f r o m c o n v e n t i o n a l d i s p l a c e m e n i ships in s i g n i f i c a n t v / o y s , c r e a t i n g a m o r e c o m p l e x p r o b l e m . F o r e x a m p l e , t h e i n i e r a c f i o n e f f e c t s r e s u l t i n g f r o m t l i e closeness of t h e t w o h u l l s m u s t be d e s c r i b e d . T h e r e l a t i v e i ) - s m a l l w a t e r p l a n e a r e a o f S W A T H ships i m p l i e s a s m a l l h e a v e V - 4 - 1]

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CO H e 5 3 2 0 S W A T H 6C =• «- M o d e l — — T h e o r y F i g . 0 200 400 W a v e L e n g t h (m) 20 H e a v e T r a n s f e r F u n c t i o n f o r S W A T H 6C a t Z e r o S p e e d i n B e a m S e a s a. Ë < 200 400 W a v e Length (m) F i g . 2 1 H e a v e T r a n s f e r F u n c t i o n f o r S W A T H 6C a t 20 K n o t s i n B e a m S e a s SV-/ATI-I 6C — M o d e l Ttiooi-y 200 400 W a v o Length (rn) (300 F i g . 2 2 F i s i a t i v e B o w i V i o t i o n T r a n s f e r F u n c t i o n f o r S W A T H 8C a t Z e r o S p e e d i n B e a m S e a s •a Q. E < F i g . 0 200 400 W a v e L e n g t h (m) 23 H e l a t i v e R o w I V i o t i o n T r a n s f e r F u n c t i o n f o r S W A T i ' i 6 G a t 2.0 K n o t s i n B e a m S e a s r e s t o r i n g f o r c e . C o n s e q u e n t l y , v i s c o u s d a m p i n g e f f e c t s w h i c h m a y be i g n o r e d in m o d e l l i n g t h e v e r t i c a l plane m o t i o n s of c o n v e n t i o n a l d i s p l a c e m e n t ships b e c o m e r e l a t i v e l y i m p o r t a n t f o r SV/ATH ships. T h e e f f e c t of f o r w a r d speed on t h e v/ave t r a i n is not m o d e l l e d f o r e i t h e r SVV'ATH or c a n v e n t i o n o l s h i p s . F o r t h e SWATH s h i p f h e wai<e c r e a t e d by a s t r u t w i l l a f f e c t t h e f l o w at s e c t i o n s a f t o f i t . It c o n be e x p e c t e d t h a t t h i s e f f e c t w i l l be g r e a t e r f o r ships v / i t h t w o s t r u t s per h u l l t h a n f o r ships w i t h one long s t r u t and t h a t slender s t r u t s w i l l g e n e r a t e less wal<e t l i a n t h i c k e r ones.

C o r r e l a t i o n o f t h e o r y v / i t h m o d e l e x p e r i m e n t s has s h o w n g e n e r a l l y g o o d a g r e e m e n t f o r a r a n g e o f speeds end h e a d i n g s . A s e r i e s o f e x p e r i m e n t s f o r t h e S W A T H 6 series v/as c a r r i e d o u t f^y K a l l i o ( R e f . 13). T h e s e w e r e m o d e l s f o r a 2900 t o n n e , 73 m e t e r design w i t h v a r i o u s G M L ' s . T h e c o n f i g u r a t i o n s , d e n o t e d / \ , B , and G , hod t h e same l o w e r h u l l s b u t d i f f e r e n t s t r u t c o n f i g u r a t i o n s . T h e 6 A and f h e 6B a r e s i n g l e s t r u t c o n f i g u r a t i o n s w h e r e a s Ihe 6 G is u t w i n s t r u t c o n f i g u r a t i o n . C o r r e l a t i o n b e t w e e n t h e o r y and m o d e l e x p e r i m e n t s is g e n e r a l l y g o o d ; h o w e v e r , c e r t a i n p r o b l e m s e m e r g e . Z e r o speed p r e d i c t i o n s are s o m e w h a t i n c o n s i s t e n t in q u a l i t y . T h i s is p r o b a b l y due l o p r o b l e m s in t h e g e n e r a l m o d e l l i n g o f t h e n o n l i n e a r v i s c c u s d a m p i n g . A t h i g h e r .speed, b e h a v i o r is w e l l d e s c r i b e d but f o r some c o n d i t i o n s s o m e d i s c r e p a n c i e s in m a g n i t u d e e x i s t . Com,parisons o f K a l l i o ' s m o d e l e x p e r i m e n t s arid p r e d i c t i o n s f o r t h e 6 C c o n f i g u r a t i o n s a r e pi-esented in F i g u r e s 20 t o 23 f o r z e r o a n d 20 k n o t s in b e a m seas, f i e o v e and r e l a t i v e b o w m o t i m response per u n i t v/ave a m p l i t u d e a r e g i v e n as o f u n c t i o n of w o v e l e n g t h . M zero speed t h e peak v a l u e o f h e a v e is v/ell p r e d i c t e d t h o u g h it is p r e d i c t e d t o o c c u r a t a s l i g h t l y g r e a t e r w a v e length t h a n f o u n d in t h e m e a s u r e m e n t s . T h e d i s c r e p a n c y in heave afso s e e m s t o be r e f l e c t e d in t h e r e l a t i v e bow m o t i o n p r e d i c t i o n s . The c o r r e l a t i o n f o r 20 k n o t s is v e r y good as s h o w n i n F i g u r e s 20 a n d 2 2 . 6.2 E x c i t a t i o n F o r c e C o m p a r i s o n s f o r SSP K A I M A L I N O T h e g o o d c o r r e l a t i o n v / i t h m o d e l scale t r a n s f e r f u n c t i o n s for SWATH 6 C i m p l i e s t h a t p r e d i c t i o n s f o r SSP K A I M A L I N O , a l s o a t w i n s t r u t d e s i g n , s h o u l d ba r e a s o n a b l e . U r i f o r t u n o f e l y , t h e r e a r e no m o d e ! scale t r a n s f e r f u n c f i o n s a v a i l a b l e f o r SSP K A I M A L I N O w i t h v / h i c h to ,mal';e t h e o r e t i c a l c o m p a r i s o n s . F l o v / e v c r , morJel s c a l e r e s u l t s do e x i s t f o r t h e v/ave e x c i t i n g h e a v e force a n d p i t c h m o m e n t . S i n c e f i i e y are on i m p o r t a n t e l e m e n t in m o t i o n p r e d i c t i o n , t h e y g i v e some i n d i c a t i o n o f the r e l e v a n c y o f t h e m o t i o n p r e d i c t i o n s f o r SSP K A i M A L I N O , T h e f o r c e s and m o m e n t s on t h e rnodei in head seas were o b t a i n e d as p a r t of on e x p e r i m e n t a l p r o g r a m d o c u t r i e n t e d by F e i n and S t o h l ( R e f . RO. T h e m o d e l d i d n o t have b l i s t e r s , w h e r e a s the p r e d i c t i o n s i n c l u d e t h e e f f e c t of b l i s t e r s . T h e b l i s t e r s w e r e s h o w n t o have s m a l l e f f e c t on t h e head sea m o t i o n in F i g u r e s h a n d 5; e v e n though m o t i o n s a r e t h e s a m e , e x c i t i n g f o r c e s a r e n o t necessarily t l i e s a m e . T h e n o n d i m e n s i o n a l h e a v e f o r c e (F3o(e)) a n d phase («3) v / i t h r e s p e c t t o t h e v/ave ore g i v e n in t e r m s o f n o n d i m e n s i o n a l e n c o u n t e r f r e q u e n c y . T h e n c n d i m e n s i o i i -a l i z -a i i o n f o r e n c o u n t e r f r e q u e n c y is:

N/17

( t ) w h e r e L. is t h e e n c o u n t e r f r e q u e n c y i n r a d / s e c , is n o m i n a l l e n g t h in m e t e r s a n d is g r a v i t a t i o n a l c o n s t a n t in m/.sec2. 4 - 12