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D A V I D W . T A Y L O R N A V A L S H I P
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
Bethesda, Maryland 20084
VERTICAL PLANE MOTIONS OF SWATH SHIPS I N REGULAR WAVES By K.K. M c C r e i g h t and Ralph S t a h l Approved f o r P u b l i c Release: D i s t r i b u t i o n U n l i m i t e d
Ship Performance Department
D T N S R D C COMMANDER 00 T E C H N I C A L D I R E C T O R 01 O F F I C E R - I N - C H A R G E C A R D E R O C K S Y S T E M S D E V E L O P M E N T D E P A R T M E N T I! SHIP P E R F O R M A N C E D E P A R T M E N T 15 S T R U C T U R E S D E P A R T M E N T 1/ SHIP A C O U S T I C S D E P A R T M E N T 19 SHIP M A T E R I A L S E N G I N E E R I N G D E P A R T M E N T O F F I C E R - I N - C H A R G E ANNAPOLIS 04 A V I A T I O N AND S U R F A C E E F F E C T S D E P A R T M E N T Ki COMPUTATION, MATHEMATICS AND L O G I S T I C S D E P A R T M E N T 18 PROPULSION AND A U X I L I A R Y S Y S T E M S D E P A R T M E N T 27 C E N T R A L I N S T R U M E N T A T I O N D E P A R T M E N T 29
UNCLASSIFIED
S E C U R I T Y C L A S S I F I C A T I O N O F T H I S P A G E (When Date Entered)
R E P O R T D O C U M E N T A T I O N P A G E R E A D I N S T R U C T I O N S B E F O R E C O M P L E T I N G F O R M 1. R E P O R T N U M B E R DTNSRDC/SPD - 1076-01 2. G O V T A C C E S S I O N NO. 3. R E C I P I E N T ' S C A T A L O G N U M B E R «. T I T L E (and Subtitle)
V e r t i c a l Plane M o t i o n s o f SWATH Ships i n Regular Waves
5. T Y P E O F R E P O R T & P E R I O D C O V E R E D «. T I T L E (and Subtitle)
V e r t i c a l Plane M o t i o n s o f SWATH Ships i n
Regular Waves 6. P E R F O R M I N G O R G . R E P O R T N U M B E R 7. A U T H O R C s ;
K.K. McCREIGHT and RALPH STAHL
9. P E R F O R M I N G O R G A N I Z A T I O N N A M E AND A D D R E S S David T a y l o r Naval Ship R&D Center Ship Performance Department
Bethesda. M a r y l a n d 20084 10. P R O G R A M E L E M E N T , P R O J E C T , T A S K A R E A a WORK U N I T N U M B E R S 11. C O N T R O L L I N G O F F I C E N A M E A N D A D D R E S S 12. R E P O R T D A T E June 1983 11. C O N T R O L L I N G O F F I C E N A M E A N D A D D R E S S 13. N U M B E R O F P A G E S 108
U . M O N I T O R I N G A G E N C Y N A M E & f',DDRESS(ll dlllerent Irom Controlling Ollice) 15. S E C U R I T Y C L A S S , (ol thIa report) UNCLASSIFIED
U . M O N I T O R I N G A G E N C Y N A M E & f',DDRESS(ll dlllerent Irom Controlling Ollice)
15a, D E C L ASSI n c A T I O N / D O W N G R A D I N G S C H E D U L E
16. D I S T R I B U T I O N S T A T E M E N T Co/ (fi(s ReporO
Approved f o r P u b l i c Release: D i s t r i b u t i o n U n l i m i t e d
17. D I S T R I B U T I O N S T A T E M E N T (ol the abstract entered In Block 20, ll dlllerent Irom Report)
18. S U P P L E M E N T A R Y N O T E S
I 19. K E Y W O R D S (Continue on reverse aide ll necessary and Identlly by block number)
S m a l l - W a t e r p l a n e - Area, Twin H u l l S h i p s , Ship M o t i o n i n Waves
I 20. A B S T R A C T (Continue on reverae side II necessary and Identity by block number)
The v e r t i c a l p l a n e m o t i o n s o f SWATH s h i p s a r e t h e o r e t i c a l l y modeled. S t r i p t h e o r y i s used t o e v a l u a t e hydrodynamic f o r c e s . C o n t r i b u t i o n s due t o body l i f t c r o s s f l o w d r a g , and f i n l i f t dominate t h e damping c o e f f i c i e n t s . C o n s e q u e n t l y , t h e i r a c c u r a t e m o d e l i n g i s v i t a l t o t h e a c c u r a c y o f m o t i o n p r e d i c t i o n s ,
S E C U R I T Y C L A S S I F I C A T I O N O F T H I S P A G E (When Dale Entered)
have been u t i l i z e d i n t h i s development. C o r r e l a t i o n between p r e d i c t e d and e x p e r i m e n t a l r e s u l t s a r e p r e s e n t e d f o r hydrodynamic c o e f f i c i e n t s , e x c i t i n g f o r c e and moment, and r e s p o n s e s t o r e g u l a r waves.. The e x p r e s s i o n s d e v e l o p e d r e s u l t i n c o r r e l a t i o n w h i c h i s good and w h i c h i s n o t a b l y b e t t e r t h a n r e s u l t s r e p o r t e d p r e v i o u s l y .
TABLE OF CONTENTS Page LIST OF FIGURES ^ LIST OF TABLES . NOTATION AESTPACT I ADMINISTRATIVE INFORMATION ' . . . . l INTRODUCTION j EQUATIONS OF MOTION 2
HYDRODYNAMIC COEFFICIENTS AND EXCITING FORCES AND MOMENT 3
COMPARISON BETWEEN RESULTS FROM EXPERIMENT AND PREDICTION 4
ADDED MASS AND DAMPING 5 WAVE EXCITING HEAVE FORCE AND PITCH MOMENT 6
RESPONSES TO REGULAR WAVES 6
DISCUSSION 6
CONCLUSIONS AND RECOMMENDATIONS 9
ACKNOWLEDGEMENTS 9
REFERENCES 11
APPENDIX A - FREQUENCY DEPENDENT HYDRODYNAMIC COEFFICIENTS,
FORCES AND MOMENTS 74
AJ'PENDIX B - POTENTIAL FLOW COMPONENTS 83
APPENDIX C - VISCOUS COMPONENTS 87
LIST OF FIGURES
1 - Comparison between Experiment and P r e d i c t i o n f o r Added Mass and Damping C o e f f i c i e n t s o f t h e SWATH 6A (Bare H u l l ) f o r
Force and P i t c h E x c i t i n g Moment f o r t h e SWATH 6D 33
4 - Comparison between E x p e r i m e n t and P r e d i c t i o n o f Heave E x c i t i n g Force and P i t c h E x c i t i n g Moment f o r t h e SSP KAIMALINO i n
Head Waves •
6 - Comparison between E x p e r i m e n t and P r e d i c t i o n o f Regular Wave T r a n s f e r F u n c t i o n s f o r t h e SWATH 6B
7 - Comparison between E x p e r i m e n t and P r e d i c t i o n o f Regular Wave T r a n s f e r F u n c t i o n s f o r t h e SWATH 6C
8 - Comparison between Experiment and P r e d i c t i o n o f Regular Wave T r a n s f e r F u n c t i o n s f o r t h e SWATH 6D
a - Drag and I n e r t i a C o e f f i c i e n t s v e r s u s K e u l e g a n - C a r p e n t e r Number f o r C o n s t a n t V a l u e s o f t h e Frequency Parameter (From Reference 5)
10 - The Drag C o e f f i c i e n t o f F l a t P l a t e ( + ) , Diamond « » and C i r c u l a r ( O ) C y l i n d e r s a t Low KC (From Reference 6)
11 - E x p e r i m e n t - P r e d i c t i o n Comparison f o r Damping C o e f f i c i e n t w i t h No C o r r e c t i o n f o r C_, 12 - E x p e r i m e n t - P r e d i c t i o n Comparison f o r Damping C o e f f i c i e n t f o r Two-Dimensional C y l i n d e r s LIST OF TABLES 1 - F u l l - s c a l e P a r t i c u l a r s o f SWATH C o n f i g u r a t i o n s 2 - P a r t i c u l a r s o f S t a b i l i z i n g F i n s
3 - N o n d i m e n s i o n a l i z a t i o n F a c t o r s f o r Added Mass, Damping, Wave E x c i t i n g F o r c e , and Wave E x c i t i n g Moment
4 - R a t i o o f L i f t on A f t F i n t o L i f t on Forward F i n f o r V a r i o u s F i n S e p a r a t i o n s and O s c i l l a t i o n Frequency t o Speed R a t i o s
45
5 - Comparison between E x p e r i m e n t and P r e d i c t i o n o f R e g u l a r Wave
T r a n s f e r F u n c t i o n s f o r t h e SWATH 6A 51 56 61 66 80 96 97 14 15 16 82
NOTATION
A A m p l i t u d e o f i n c i d e n t wave
AR E f f e c t i v e a s p e c t r a t i o o f s t a b i l i z i n g f i n
A. . Added mass c o e f f i c i e n t f o r t h e i * ^ ^ mode due t o m o t i o n i n t h e j * ^ ^ mode ( j = 1 f o r s u r g e , j = 3 f o r heave, j = 5 f o r p i t c h ) A n P r o j e c t e d a r e a o f s t a b i l i z i n g f i n A o C h a r a c t e r i s t i c body a r e a A P P r o j e c t e d area o f body A w W a t e r p l a n e area a H o r i z o n t a l a x i s o f a t w o - d i m e n s i o n a l s e c t i o n a o V i s c o u s l i f t c o e f f i c i e n t
^33 S e c t i o n a l heave added mass c o e f f i c i e n t due t o heave m o t i o n
B S e c t i o n a l beam
Damping c o e f f i c i e n t f o r t h e i ^ ^ mode due t o m o t i o n i n t h e j ""^ mode
b V e r t i c a l a x i s o f a t w o - d i m e n s i o n a l s e c t i o n
^ 3 S e c t i o n a l heave damping c o e f f i c i e n t due t o heave m o t i o n
S Cross f l o w d r a g c o e f f i c i e n t SARPKAYA V a l u e s o f C^ o b t a i n e d by Sarpkaya li R e s t o r i n g c o e f f i c i e n t f o r t h e i ^ ^ mode due t o m o t i o n i n t h e j ""^ mode ^Lct ^ i f t c u r v e s l o p e w i t h r e s p e c t t o a n g l e o f a t t a c k f o r n^ n s t a b i l i z i n g f i n C_. C o r r e c t i o n t o C, Lz La n n
d T r a n s v e r s e d i m e n s i o n
d^ Center o f s u r g e f o r c e
d Average d e p t h s
D i s t a n c e between t h e mean w a t e r l i n e and t h e c e n t e r o f t h e l o w e r h u l l 1^ Fn Froude number U / ( g L ) ^ F^^'^ Wave e x c i t i n g f o r c e i n t h e i ^ ^ mode F V e r t i c a l f o r c e on a s l e n d e r m o d e r a t e l y i n c l i n e d body v GM^ L o n g i t u d i n a l m e t a c e n t r i c h e i g h t g A c c e l e r a t i o n due t o g r a v i t y i I m a g i n a r y u n i t ( ( - 1 ) ^ ) K e u l e g a n - C a r p e n t e r number (U^T/d) 2 k Wave number (= ë) k j ^ , Lamb's hydrodynamic c o e f f i c i e n t s L O v e r a l l s h i p l e n g t h X c o o r d i n a t e o f q u a r t e r c h o r d o f s t a b i l i z i n g f i n M Mass o f d i s p l a c e d volume
M' M' C o e f f i c i e n t s o f p i t c h moment due t o heave v e l o c i t y and p i t c h ^ v e l o c i t y
n^, n^ U n i t n o r m a l s
r H u l l r a d i u s
H o r i z o n t a l d i s t a n c e between s h i p ' s p l a n e o f symmetry and c e n t r o i d of s t a b i l i z i n g f i n Span o f n*^^ s t a b i l i z i n g f i n P e r i o d o f o s c i l l a t i o n T h i c k n e s s o f n^'^ s t a b i l i z i n g f i n D r a f t o f s t r u t Forward speed o f s h i p A m p l i t u d e o f h a r m o n i c a l l y v a r y i n g v e l o c i t y V e r t i c a l v e l o c i t y o f body r e l a t i v e t o t h e v e l o c i t y o f t h e f l u i d V e r t i c a l v e l o c i t y o f p o r t ( s t a r b o a r d ) l i f t i n g s u r f a c e r e l a t i v e t o t h e v e l o c i t y o f t h e f l u i d
C o e f f i c i e n t s o f v e r t i c a l f o r c e due t o heave v e l o c i t y and p i t c h v e l o c i t y Zl I + |z, I I s I p V e r t i c a l v e l o c i t y o f p o r t ( s t a r b o a r d ) h u l l r e l a t i v e t o t h e v e l o c i t y o f t h e f l u i d A n g l e o f i n c i d e n c e o f f l o w Used i n e v a l u a t i n g k^^ Heading o f t h e s h i p r e l a t i v e t o t h e i n c i d e n t wave (3 = 180 f o r head waves) 2 P e r i o d p a r a m e t e r (d /vT) Used i n e v a l u a t i n g Used i n e v a l u a t i n g a and 3 o o
p o s i t i o n i n t h e j ^ ^ mode
Mass d e n s i t y o f w a t e r
V e l o c i t y p o t e n t i a l
Wave e n c o u n t e r f r e q u e n c y
ABSTRACT
The v e r t i c a l p l a n e m o t i o n s o f SWATH s h i p s a r e t h e o r e t i -c a l l y modeled. S t r i p t h e o r y i s used t o e v a l u a t e hydrodynami-c f o r c e s . C o n t r i b u t i o n s due t o body l i f t , c r o s s f l o w d r a g , and f i n l i f t d o m i n a t e t h e damping c o e f f i c i e n t s . C o n s e q u e n t l y , t h e i r a c c u r a t e m o d e l i n g i s v i t a l t o t h e a c c u r a c y o f m o t i o n p r e d i c t i o n s . S e m i e m p i r i c a l methods d e v e l o p e d f o r e v a l u a t i n g t h e s e components a r e d e s c r i b e d . Data f o r o s c i l l a t i n g t w o -d i m e n s i o n a l c y l i n -d e r s , f l a t p l a t e s , an-d p a i r s o f f i n s as w e l l as s e m i e m p i r i c a l e x p r e s s i o n s f o r submarine hydrodynamic c o e f f i c i e n t s have been u t i l i z e d i n t h i s development. C o r r e l a -t i o n be-tween p r e d i c -t e d and e x p e r i m e n -t a l r e s u l -t s a r e p r e s e n -t e d f o r hydrodynamic c o e f f i c i e n t s , e x c i t i n g f o r c e and moment, and r e s p o n s e s t o r e g u l a r waves. The e x p r e s s i o n s developed r e s u l t i n c o r r e l a t i o n w h i c h i s good and w h i c h i s n o t a b l y b e t t e r t h a n r e s u l t s r e p o r t e d p r e v i o u s l y .
ADMINISTRATIVE INFORMATION
T h i s work was f u n d e d under t h e S h i p s , Subs and Boats Program Task Area SF 421-350-200, N62345. The f u n d i n g was a d m i n i s t e r e d by t h e E x p l o r a t o r y Development Programs O f f i c e , Code 1506, Ship Performance Department, David T a y l o r N a v a l S h i p Research and Development Center (DTNSRDC).
INTRODUCTION
The S m a l l W a t e r p l a n e Area Twin H u l l (SWATH) s h i p i s composed o f two h u l l s , each o f w h i c h has one o r two s u r f a c e p i e r c i n g s t r u t s c o n n e c t i n g them t o t h e above-w a t e r l i n e deck. T y p i c a l l y t h e l o above-w e r h u l l i s composed o f c i r c u l a r o r e l l i p t i c a l c r o s s - s e c t i o n s . Some h u l l s a r e s u b m a r i n e - l i k e i n shape and o t h e r s a r e composed of a s e r i e s o f c y l i n d e r s and c o n i c f r u s t u m s .
The m o t i o n s o f SWATH s h i p s a r e g r e a t l y d e t e r m i n e d by t h e s h i p ' s u n i q u e geome-t r y . S i n c e a l a r g e p o r geome-t i o n o f geome-t h e s h i p ' s buoyancy i s l o c a geome-t e d i n geome-t h e l o w e r h u l l s , t h e wave e x c i t i n g f o r c e s a r e r e l a t i v e l y s m a l l . The w a t e r p l a n e a r e a (A ) and l o n g i t u d i n a l m e t a c e n t r i c h e i g h t (CM^) a r e s m a l l i n comparison w i t h 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 . S i n c e t h e hea-ve and p i t c h n a t u r a l p e r i o d s a r e
i n v e r s e l y p r o p o r t i o n a l t o t h e square r o o t o f and GM^, r e s p e c t i v e l y , r e l a t i v e l y l o n g n a t u r a l p e r i o d s r e s u l t . Low r e s p o n s e s f o r o p e r a t i o n a t moderate speeds i n seaways o c c u r i n p a r t because most o f t h e energy o f a seaway t y p i c a l l y o c c u r s a t
c o n v e n t i o n a l s h i p s ^ * and SWATH s h i p s . ^ T w o - d i m e n s i o n a l t h e o r y assumes t h a t t h e r e i s no l o n g i t u d i n a l hydrodynamic i n t e r a c t i o n so t h a t hydrodynamic f o r c e s can be e v a l u a t e d by i n t e g r a t i n g t h e hydrodynamic c o n t r i b u t i o n s o f t w o - d i m e n s i o n a l s e c t i o n s
a l o n g t h e s h i p ' s l e n g t h .
For 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 and f o r c a t a m a r a n s , as w e l l , v e r t i c a l p l a n e m o t i o n s can be p r e d i c t e d a c c u r a t e l y u s i n g p o t e n t i a l f l o w t h e o r y . However, Lee^ r e c o g n i z e d t h a t f o r SWATH s h i p s v i s c o u s c o n t r i b u t i o n s t o t h e hydrodynamic damping c o e f f i c i e n t s a r e i m p o r t a n t . They can be d o m i n a n t , making t h e i r a c c u r a t e m o d e l i n g i m p o r t a n t . I n a t h e o r e t i c a l development Lee^ i n t r o d u c e d c o n t r i b u t i o n s
due t o l i f t and c r o s s f l o w d r a g o f t h e body and s t a b i l i z i n g f i n s . Hong i n t r o d u c e d p i t c h due t o surge and d e m o n s t r a t e d i t s i m p o r t a n c e i n m o d e l i n g l o w speed m o t i o n s . T h i s a p p r o a c h was g e n e r a l l y s u c c e s s f u l i n p r e d i c t i n g t h e v e r t i c a l p l a n e r e s p o n s e s of SWATH s h i p s . However, d i s c r e p a n c i e s between p r e d i c t e d and e x p e r i m e n t a l magni-t u d e s and u n c e r magni-t a i n magni-t y over magni-t h e a p p r o p r i a magni-t e v a l u e s o f c r o s s f l o w d r a g and l i f magni-t c o e f f i c i e n t s m o t i v a t e d t h e p r e s e n t s t u d y . The g o a l o f t h i s i n v e s t i g a t i o n i s t o
improve t h e q u a l i t y o f p r e d i c t i o n s and t o p r e d i c t v e r t i c a l p l a n e r e s p o n s e s o f a SWATH s h i p t o waves g i v e n o n l y t h e s h i p geometry, t h e l o c a t i o n o f t h e c e n t e r o f g r a v i t y , and t h e 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 ( g y r a d i u s ) .
EQUATIONS OF MOTION
For t h e p u r p o s e o f t h i s d e r i v a t i o n , a SWATH s h i p i s assumed t o be moving a t a c o n s t a n t speed a t a f i x e d a n g l e r e l a t i v e t o a s i n u s o i d a l wave t r a i n i n i n f i n i t e l y deep w a t e r . The wave a m p l i t u d e i s assumed t o be s m a l l so t h a t t h e r i g i d body m o t i o n s can be d e s c r i b e d u s i n g a l i n e a r model. The s h i p i s d e f i n e d i n a r i g h t
-handed c o o r d i n a t e system h a v i n g i t s o r i g i n a t t h e mean w a t e r l i n e a t t h e s h i p ' s 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 and c e n t e r l i n e . The z - o r d i n a t e i s p o s i t i v e upward.
The e q u a t i o n s o f m o t i o n o f t h e s h i p f o r t h e v e r t i c a l p l a n e a r e :
F^^^e-^-(M + A33)^'3 + B33C3 + C33?3 + A35^3 + B35?5 + C33C5 = F^^^e"
( I 5 + A,,)ï, + 6 5 3 ^ + C33?3 + A33C3 + B3353 + C33?3 5
where M i s t h e mass o f t h e d i s p l a c e d volume and I 3 i s t h e p i t c h mass moment o f
I n e r t i a . A _ , B _ , and C_ a r e t h e added mass, damping, and r e s t o r i n g c o e f f i c i e n t s i n t h e i * " ^ mode due t o a s i n u s o i d a l m o t i o n o f u n i t a m p l i t u d e i n t h e j ^ ^ mode. The
(e)
s u b s c r i p t 1 d e n o t e s s u r g e , 3 heave, and 5 p i t c h . F)^ i s t h e complex e x c i t i n g f o r c e o r moment and w i s t h e wave f r e q u e n c y o f e n c o u n t e r .
I n e v a l u a t i n g t h e c o e f f i c i e n t s , f o r c e s , and moments, s t r i p t h e o r y i s employed. T h i s i s a r e a s o n a b l e a s s u m p t i o n f o r t h e SWATH s h i p w i t h i t s s l e n d e r and g r a d u a l l y changing geometry over i t s l e n g t h .
The hydrodynamic c o e f f i c i e n t s and e x c i t i n g f o r c e s and moment a r e composed o f 2
p o t e n t i a l f l o w , c r o s s f l o w d r a g , and l i f t t e r m s . Lee's development i n c l u d e d c r o s s f l o w d r a g and l i f t terms f o r t h e body and t h e s t a b i l i z i n g f i n s . These components a f f e c t t h e damping and r e s t o r i n g c o e f f i c i e n t s and t h e e x c i t i n g f o r c e s and c o n s e q u e n t l y t h e m o t i o n s a t a l l speeds s i n c e t h e c r o s s f l o w d r a g t e r m s a r e
independent o f speed and t h e l i f t t e r m s a r e p r o p o r t i o n a l t o some power o f speed. I n t h i s i n v e s t i g a t i o n , new e x p r e s s i o n s e v o l v e d f o r t h e c r o s s f l o w d r a g c o e f f i -c i e n t s , t h e body l i f t t e r m s , and t h e f i n -c r o s s f l o w d r a g and l i f t -c u r v e s l o p e c o e f f i c i e n t s . F i n a l e x p r e s s i o n s f o r t h e hydrodynamic c o e f f i c i e n t s and t h e e x c i t i n g f o r c e s and moments a r e g i v e n i n Appendix A. D e t a i l s o f t h e development o f t h e s e e x p r e s s i o n s a r e g i v e n i n Appendices B and C. I t i s u s e f u l t o b r i e f l y summarize t h e r e s u l t s .
C u r r e n t l y , t h e p o t e n t i a l f l o w components o f t h e added mass and damping can be
4
e v a l u a t e d u t i l i z i n g e i t h e r t h e F r a n k Close F i t Technique o r t h e D a l z e l l Approxima-t i o n T e c h n i q u e . * When Approxima-t h e D a l z e l l A p p r o x i m a Approxima-t i o n Technique i s u Approxima-t i l i z e d , as i Approxima-t i s i n t h e r e s u l t s i n t h i s r e p o r t , t h e d i s t r i b u t i o n o f t h e p o t e n t i a l on t h e t w o
and heave e x c i t i n g f o r c e s and t h e p i t c h e x c i t i n g moment a r e d e v e l o p e d . T h i s
development i n c l u d e s an e x p r e s s i o n f o r an a p p r o x i m a t e d e p t h used i n t h e heave e x c i t i n g f o r c e and p i t c h e x c i t i n g moment and an e x p r e s s i o n f o r t h e c e n t e r o f surge w h i c h f a c i l i t a t e s I n c l u s i o n o f surge i n t h e e x c i t i n g moment.
I n Appendix C a development o f t h e c r o s s f l o w d r a g and l i f t terms and t h e c o r r e s p o n d i n g c o e f f i c i e n t s i s g i v e n . The c r o s s f l o w d r a g c o e f f i c i e n t s f o r t h e ^ body a r e e v a l u a t e d u s i n g e x p e r i m e n t a l v a l u e s f o r o s c i l l a t i n g c i r c u l a r c y l i n d e r s . A f a c t o r t o r e f l e c t t h e e f f e c t o f a s t r u t on t h e c r o s s f l o w d r a g c o e f f i c i e n t i s developed f r o m o s c i l l a t i o n d a t a f o r t w o - d i m e n s i o n a l SWATH s e c t i o n s . * The c r o s s f l o w d r a g c o e f f i c i e n t f o r t h e s t a b i l i z i n g f i n s i s e v a l u a t e d u s i n g e x p e r i m e n t a l d a t a f o r o s c i l l a t i n g p l a t e s . ^ S e m i e m p i r i c a l e x p r e s s i o n s f o r t h e v e r t i c a l p l a n e hydrodynamic c o e f f i c i e n t s o f submarines** s e r v e as a b a s i s f o r t h e development o f t h e SWATH body l i f t components. The l i f t c u r v e s l o p e o f t h e f i n s i s g i v e n and a c o r r e c t i o n i s made f o r t h e f r e q u e n c y dependent i n t e r f e r e n c e e f f e c t o f t h e f o r w a r d f i n on t h e l i f t o f t h e a f t f i n . ^ ' ^ For a p p r o p r i a t e c o n f i g u r a t i o n s , an a d d i t i o n a l c o r r e c t i o n i s made f o r t h e e f f e c t o f t h e h u l l wake on t h e l i f t o f t h e a f t f i n .
COMPARISON BETWEEN RESULTS FROM EXPERIMENT AND PREDICTION
O s c i l l a t i o n , e x c i t a t i o n , and r e g u l a r wave d a t a a r e a v a i l a b l e f o r SWATH con-f i g u r a t i o n s denoted 6A, 6B, 6C, 6D, and SSP KAIMALINO. These r e s u l t s were used t o g u i d e t h e development o f t h e e x p r e s s i o n s i n t h i s r e p o r t . The f o u r c o n f i g u r a t i o n s i n t h e SWATH 6 s e r i e s employ t h e same l o w e r h u l l w h i c h i s a body o f r e v o l u -t i o n . The s -t r u -t s a r e d e s i g n e d so -t h a -t -t h e GM^ d i f f e r s f o r each s -t r u -t d e s i g n . C o n f i g u r a t i o n s 6A and 6B a r e s i n g l e s t r u t d e s i g n s , whereas 6C and 6D a r e t w i n
s t r u t d e s i g n s . P a r t i c u l a r s o f t h e c o n f i g u r a t i o n s and o f t h e l i f t i n g s u r f a c e s a r e
g i v e n i n T a b l e s 1 and 2.
C o r r e l a t i o n between e x p e r i m e n t and p r e d i c t i o n a r e g i v e n i n F i g u r e s 1 t h r o u g h 8. N o n d i m e n s i o n a l i z a t i o n f a c t o r s f o r added mass, damping, e x c i t i n g f o r c e , and
*As d e s c r i b e d by S t a h l i n a DTNSRDC r e p o r t w i t h l i m i t e d d i s t r i b u t i o n .
e x c i t i n g moment a r e g i v e n i n T a b l e 3. Open symbols a r e used f o r e x p e r i m e n t a l r e
-s u l t -s and -s o l i d -symbol-s a r e u-sed f o r p r e d i c t e d r e -s u l t -s u -s i n g t h e e x p r e -s -s i o n -s g i v e n 2
i n Appendix A. P r e d i c t e d r e s u l t s u s i n g Lee's e x p r e s s i o n s a r e g i v e n i n s o l i d l i n e on some o f t h e added mass and damping and a l l o f t h e r e g u l a r wave f i g u r e s . Hong's m o d i f i c a t i o n s a r e i n c l u d e d i n t h e r e g u l a r wave r e s u l t s .
I n s o l v i n g t h e c r o s s f l o w drag c o n t r i b u t i o n s , i t i s n e c e s s a r y t o know t h e m o t i o n o f t h e model r e l a t i v e t o t h e incoming wave. For r e g u l a r wave m o t i o n p r e -d i c t i o n s , t h i s component must be s o l v e -d i t e r a t i v e l y , u n t i l t h e responses o f t h e c r a f t converge; t h a t i s , t h e d i f f e r e n c e between t h e e s t i m a t e d and computed r e -sponses d i m i n i s h t o a c c e p t a b l e v a l u e s . However, i n t h e case o f f o r c e d o s c i l l a t i o n e x p e r i m e n t s , t h e m o t i o n o f t h e body i s known and t h e r e i s no i n c i d e n t wave. Con-v e r s e l y , f o r waCon-ve e x c i t i n g e x p e r i m e n t s , t h e body i s h e l d r i g i d and t h e m o t i o n o f t h e wave i s known. T h e r e f o r e , c a l c u l a t i o n o f t h e s e components i s s t r a i g h t f o r w a r d .
ADDED MASS AND DAMPING
Two s e t s o f d a t a f o r heave and p i t c h f o r c e d o s c i l l a t i o n t e s t s a r e a v a i l a b l e f o r t h e SWATH 6A. R e s u l t s f r o m a 1:51.2 s c a l e bare h u l l model f o r speeds c o r r e -sponding t o f u l l - s c a l e speeds o f 10, 20, and 35 k n o t s ^ ^ a r e p r e s e n t e d i n F i g u r e 1 a l o n g w i t h p r e d i c t e d r e s u l t s . R e s u l t s f r o m a 1:22.5 s c a l e model w i t h and w i t h o u t s t a b i l i z i n g f i n s f o r speeds c o r r e s p o n d i n g t o f u l l - s c a l e speeds o f 0, 20, and 28
12
k n o t s a r e p r e s e n t e d i n F i g u r e 2. I n c l u d e d a r e p r e d i c t e d r e s u l t s based on t h e e x p r e s s i o n s i n Appendix A and Lee's p r e d i c t e d r e s u l t s w h i c h were p r e s e n t e d i n R e f e r e n c e 12. These l a t t e r p r e d i c t e d r e s u l t s do n o t i n c l u d e t h e c r o s s f l o w d r a g c o n t r i b u t i o n s . I n c l u s i o n o f t h e s e t e r m s would i n c r e a s e t h e m a g n i t u d e s o f t h e damping t e r m s , most s i g n i f i c a n t l y a t z e r o speed.
I t i s u s e f u l t o compare e x p e r i m e n t a l r e s u l t s g i v e n i n F i g u r e l a (Fn = 0.38A) w i t h t h o s e i n F i g u r e 2e ( b a r e h u l l ) . I t i s expected t h a t t h e s e r e s u l t s s h o u l d be c l o s e i n v a l u e s i n c e t h e y a r e f o r i d e n t i c a l c o n d i t i o n s . Only t h e model s c a l e s d i f f e r . However, t h e r e s u l t s f o r A^^ g i v e n i n F i g u r e l a a r e s m a l l e r t h a n t h o s e g i v e n i n F i g u r e 2e. The d i f f e r e n c e i n r e s u l t s f o r A^^ i s p a r t i c u l a r l y i m p o r t a n t a t h i g h e r speeds as can be seen i n F i g u r e s l a and 2 1 . The p r e d i c t e d r e s u l t s a g r e e w e l l w i t h t h e measured r e s u l t s i n F i g u r e l a ; however, no e x p l a n a t i o n o f t h e
F e i n and Stahl"""^ c a r r i e d o u t e x p e r i m e n t s t o measure t h e surge and heave wave e x c i t i n g f o r c e s and t h e p i t c h e x c i t i n g moment. They i n v e s t i g a t e d f i v e speeds i n head and f o l l o w i n g seas f o r a 1 : 2 2 . 5 s c a l e model o f t h e SWATH 6D and f i v e speeds i n head waves f o r a 1 : 7 . 8 s c a l e model o f t h e SSP KAIMALINO. The d a t a g i v e n i n t h i s r e p o r t a r e p r e s e n t e d i n a d i f f e r e n t f o r m a t f r o m t h a t o f Reference 1 3 . To e l u c i d a t e t h e d a t a i n f o l l o w i n g seas, a l l d a t a have been p r e s e n t e d as a f u n c t i o n o f w a v e l e n g t h t o s h i p l e n g t h , r a t h e r t h a n e n c o u n t e r f r e q u e n c y . S i n c e t h e t h e o r y i s developed w i t h t h e p i t c h moment about t h e LCG a t t h e mean w a t e r l i n e , t h e measured p i t c h e x c i t i n g moment and surge e x c i t i n g f o r c e were used t o t r a n s f o r m t h e moment t o be about t h e LCG a t t h e mean
w a t e r l i n e , so t h a t t h e p r e d i c t e d and e x p e r i m e n t a l r e s u l t s were comparable. These r e s u l t s a r e g i v e n i n F i g u r e s 3 and 4.
RESPONSES TO REGULAR WAVES
K a l l i o ^ " ^ ' ^ ^ c a r r i e d o u t r e g u l a r wave e x p e r i m e n t s f o r t h e SWATH 6 s e r i e s . Heave, p i t c h , and r e l a t i v e bow m o t i o n responses as a f u n c t i o n o f w a v e l e n g t h t o
s h i p l e n g t h a r e g i v e n f o r f i v e r e l a t i v e wave headings f o r t h e 6A, 6B, and 6C and f o r head and f o l l o w i n g waves f o r t h e 6D. R e s u l t s a r e g i v e n i n F i g u r e s 5 t h r o u g h 8 Note t h a t two s e t s o f p r e d i c t e d r e s u l t s a r e g i v e n f o r a l l c o n d i t i o n s . One
2
s e t r e s u l t s f r o m t h e development i n t h i s r e p o r t and one r e s u l t s f r o m Lee's work
w i t h Hong's m o d i f i c a t i o n s i n c l u d e d .
DISCUSSION
I n i t i a l work by Lee i n d i c a t e d t h a t c o r r e l a t i o n between e x p e r i m e n t a l and p r e -d i c t e -d r e s u l t s a t z e r o spee-d f o r l o n g w a v e l e n g t h s was n o t s a t i s f a c t o r y . Hong's r e s u l t s d e m o n s t r a t e d t h e I m p o r t a n c e o f i n t r o d u c i n g t h e e f f e c t s o f surge and o f u s i n g t h e p r o p e r wave a m p l i t u d e i n e v a l u a t i n g t h e n o n l i n e a r t e r m s . The improved c o r r e l a t i o n t h a t r e s u l t s f r o m t h e i n c o r p o r a t i o n o f t h e e x p r e s s i o n s developed i n t h i s r e p o r t i s e v i d e n t l y due t o t h e method o f e v a l u a t i n g C^. P r e v i o u s l y , i t had been assumed t o be c o n s t a n t , whereas, f o r t w o - d i m e n s i o n a l s e c t i o n s ( o r s t a b i l i z i n g f i n s ) i t i s h e r e c o n s i d e r e d t o be a f u n c t i o n o f t h e m a j o r and m i n o r a x i s o f t h e
responses p r e d i c t e d t h r o u g h t h e p r e s e n t methodology a r e n o t a b l y c l o s e r t o t h e e x p e r i m e n t a l l y d e t e r m i n e d responses t h a n r e s u l t s f o u n d w i t h any o f t h e p r e v i o u s methods.
Responses o f SWATH c o n f i g u r a t i o n s t r a v e l i n g a t h i g h speed i n f o l l o w i n g waves has been a t o p i c o f i n t e r e s t . One p r o b l e m i n c o r r e l a t i o n f o r t h i s c o n d i t i o n i s t h a t i t i s d i f f i c u l t e x p e r i m e n t a l l y . As n o t e d by K a l l i o , " ' " ^ i n q u a r t e r i n g and f o l l o w i n g waves t h e r e was c o n s i d e r a b l e surge and c o n s e q u e n t l y t h e model s a f e t y
2
r e s t r a i n t l i n e s became t a u t . Lee r e p o r t e d e x t r e m e l y l a r g e p r e d i c t e d heave
responses f o r t h e 6A a t t h e w a v e l e n g t h c o r r e s p o n d i n g t o z e r o e n c o u n t e r f r e q u e n c y . * S i n c e t h e p o t e n t i a l f l o w t w o - d i m e n s i o n a l approach i s n o t v a l i d a t s m a l l e n c o u n t e r f r e q u e n c i e s , t h e o r e t i c a l work was u n d e r t a k e n t o overcome t h i s l i m i t a t i o n .
Hong ' a p p l i e d t o SWATH s h i p s u n i f i e d s l e n d e r body t h e o r y developed by Newman 18
and Sclavounos. R e s u l t s f r o m Hong's i m p l e m e n t a t i o n d i d n o t improve c o r r e l a t i o n and d i d n o t remove t h e s p i k e i n t h e 6A heave p r e d i c t i o n s . However, t h e r e s u l t s developed h e r e w h i c h f o c u s e d on t h e v i s c o u s components b u t r e t a i n e d t h e t w o -2 d i m e n s i o n a l p o t e n t i a l f l o w approach u t i l i z e d by Lee, do n o t i n c l u d e t h e s p i k e d r e s p o n s e . A l t h o u g h p i t c h i s o v e r p r e d i c t e d f o r t h e 6A and 6B, t h e s e r e s u l t s show g e n e r a l l y good c o r r e l a t i o n and s u p p o r t t h e h y p o t h e s i s t h a t t h e a b e r r a n t p r e d i c t i o n s f o r t h e 6A a r e n o t r e l a t e d t o t h e t w o - d i m e n s i o n a l p o t e n t i a l f l o w t h e o r y .
Since t h e p r e d i c t e d heave response s p i k e o c c u r s near z e r o e n c o u n t e r f r e q u e n c y , i t has been assumed t h a t t h e problems w i t h t h e p r e d i c t i o n s were due t o t w o
-d i m e n s i o n a l t h e o r y . However, F i g u r e 5e s u g g e s t s an a l t e r n a t i v e e x p l a n a t i o n . The 2
l a r g e heave r e s p o n s e r e p o r t e d by Lee o c c u r s near t h e w a v e l e n g t h w h i c h c o r r e s p o n d s t o z e r o e n c o u n t e r f r e q u e n c y ; however, t h i s a l s o o c c u r s i n t h e r e g i o n where t h e p i t c h response peaks. S i n c e heave and p i t c h a r e c o u p l e d , e r r o r s i n m o d e l i n g one
The r e g u l a r wave p r e d i c t i o n s w h i c h a r e a t t r i b u t e d t o Lee i n c l u d e a m o d i f i c a -t i o n w h i c h was an a -t -t e m p -t -t o remove -t h e s p i k e d b e h a v i o r . I n -t h e m o d i f i c a -t i o n when (JO i s l e s s t h a n 0.07 t h e p o t e n t i a l f l o w added mass and damping c o e f f i c i e n t s f o r each s e c t i o n have been assumed t o be e q u a l t o t h o s e f o r w = 0.07. G e n e r a l l y t h i s w i l l a l t e r p r e d i c t i o n s o n l y a t h i g h speeds i n f o l l o w i n g o r s t e r n seas. T h i s a p p r o x i m a -t i o n m e r e l y suppressed -t h e response. (See F i g u r e 5e.)
6A may be due t o i n a d e q u a c i e s i n t h e p i t c h p r e d i c t i o n s .
A n a l y s i s o f t h e r e l a t i v e i m p o r t a n c e o f v a r i o u s terms i n t h e p i t c h e q u a t i o n o f
m o t i o n I n d i c a t e s t h a t t h e t e r m C^^ may be dominant. For s i m p l i c i t y , c o n s i d e r t h e u n c o u p l e d p i t c h e q u a t i o n o f m o t i o n :
( I 5 + A55)53 + 853^5 + C35C3 = F3e-^^^
U t i l i z i n g t h e r e l a t i o n s h i p ^3 = ( 5 3 ^ + ±^^j)e~^^^, t h i s becomes
[-W ( I 3 + A33) + C^^IK^ + 633^3 = F3e
T w o - d i m e n s i o n a l t h e o r y i s n o t v a l i d a t s m a l l e n c o u n t e r f r e q u e n c i e s and A33 becomes 2
v e r y l a r g e i n t h i s r e g i o n . However, t h e presence o f w r e s u l t s i n a v e r y f o r t u n a t e 2
s i t u a t i o n f o r s m a l l (JO. That i s , when oo approaches z e r o , W A33 w i l l be s m a l l . The i m p o r t a n t t e r m i s C33. Whereas A33 and B33 a r e c a l c u l a t e d u s i n g two-dimen-s i o n a l t h e o r y , C33 i two-dimen-s n o t . C33 i two-dimen-s compotwo-dimen-sed o f a f i n l i f t t e r m , a body l i f t t e r m , and a t e r m w h i c h i s e s s e n t i a l l y GM^. Since t h e f i n l i f t t e r m w i l l be a p p r o x i m a t e l y e q u a l f o r a l l c o n f i g u r a t i o n s i n t h e SWATH 6 s e r i e s , i t can be n e g l e c t e d i n t h i s d i s c u s s i o n . I n a d d i t i o n , as c o n f i g u r e d i n t h i s r e p o r t , t h e body l i f t t e r m i s dependent on mass and p a r t i c u l a r s o f t h e l o w e r h u l l and w i l l be e q u a l f o r t h e 6A, 6B, and 6C c o n f i g u r a t i o n s . However, GM^ i n c r e a s e s s i g n i f i c a n t l y f r o m t h e f i r s t model i n t h e SWATH 6 s e r i e s t o t h e l a s t w i t h t h e 6A h a v i n g t h e s m a l l e s t and t h e
6D t h e l a r g e s t GM^. For s m a l l GM^ t h e l i f t t e r m s , and t h e body l i f t t e r m i n p a r t i c u l a r , w i l l be r e l a t i v e l y more i m p o r t a n t t h a n f o r a l a r g e GM^ c o n f i g u r a t i o n . T h i s argument i s c o n s i s t e n t w i t h t h e c o r r e l a t i o n w h i c h i n d i c a t e s t h a t t h e p r e -d i c t e -d heave s p i k e i n e a r l i e r work o c c u r r e -d f o r t h e 6A o n l y . Consequently, goo-d c o r r e l a t i o n between e x p e r i m e n t a l and p r e d i c t e d r e s u l t s f o r c o n f i g u r a t i o n s w i t h s m a l l GM/s w i l l be s t r o n g l y dependent on a c c u r a t e m o d e l i n g o f C33.
The body l i f t component used f o r t h e C33 development i s based on e x p e r i m e n t a l work on t h e 6A. T h i s i s an u n f o r t u n a t e l y s l i m d a t a base. I t i s expected t h a t
CONCLUSIONS AND RECOMMENDATIONS 2
1. Work by Lee has been used as t h e b a s i s f o r m o d e l i n g t h e v e r t i c a l p l a n e m o t i o n o f SWATH s h i p s . The g e n e r a l f o r m o f h i s work has been r e t a i n e d i n t h e p r e s e n t m o d e l i n g ; however, t h e e f f o r t r e p o r t e d h e r e has f o c u s e d on t h e v i s c o u s t e r m s . A l t e r n a t e s e m i e m p i r i c a l e x p r e s s i o n s f o r body l i f t t e r m s , c r o s s f l o w d r a g c o e f f i c i e n t s f o r t h e body and t h e f i n s , and l i f t c u r v e s l o p e c o e f f i c i e n t s f o r t h e f i n s have been d e v e l o p e d , and Improved c o r r e l a t i o n w i t h e x p e r i m e n t i s t h e r e s u l t .
2. C o r r e l a t i o n o f added mass and damping c o e f f i c i e n t s and t h e e x c i t i n g f o r c e and moment a r e g e n e r a l l y good. Zero speed r e s p o n s e c o r r e l a t i o n i s comparable t o
3 2 or b e t t e r t h a n r e s u l t s based on Hong's m o d i f i c a t i o n s t o Lee's work. H i g h speed c o r r e l a t i o n i s good and i s n o t a b l y b e t t e r t h a n p r e v i o u s r e s u l t s shown by Hong."'"^ F o l l o w i n g sea r e s u l t s no l o n g e r d i s p l a y t h e a b e r r a n t b e h a v i o r w h i c h o c c u r r e d i n
2 17
Lee's and Hong's SWATH 6A r e s u l t s .
3. The t w o - d i m e n s i o n a l p o t e n t i a l f l o w t h e o r y i s c e r t a i n l y adequate f o r t h e p r e d i c t i o n o f s h i p m o t i o n s o f SWATH s h i p s s i m i l a r t o t h e 6 s e r i e s .
4. F u r t h e r e x p e r i m e n t a l work would f a c i l i t a t e r e f i n e m e n t o f t h e v i s c o u s e x p r e s s i o n s d e v e l o p e d h e r e and would expand t h e r e g i o n s o f c o n f i d e n c e . The f o l l o w -ing i n v e s t i g a t i o n s a r e recommended: a. E x p e r i m e n t a l i n v e s t i g a t i o n o f C^ f o r SWATH s e c t i o n s and f o r c i r c u l a r c y l i n d e r s a t v e r y l o w would be u s e f u l . b. E x p e r i m e n t a l I n v e s t i g a t i o n o f t h e e f f e c t o f f i n - f i n i n t e r f e r e n c e f o r a d d i t i o n a l c o n f i g u r a t i o n s , i n c l u d i n g ones where t h e a f t f i n i s l a r g e r t h a n t h e f o r w a r d f i n would be u s e f u l . c. E x p e r i m e n t s o f t r u e f r e e - t o - s u r g e c o n d i t i o n s u s i n g r a d i o - c o n t r o l l e d models i n f o l l o w i n g waves would a i d i n t h e assessment o f p r e d i c t i o n
t e c h n i q u e s .
d. E x p e r i m e n t a l i n v e s t i g a t i o n o f C^^ f o r e x i s t i n g models, i n c l u d i n g t h e 6B, 6C, and 6D, would make i t p o s s i b l e t o d e f i n e t h e body l i f t component of C33 more p r e c i s e l y and t o improve t h e r e l i a b i l i t y o f p r e d i c t i o n o f r e s p o n s e s i n f o l l o w i n g seas a t h i g h speeds.
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C o e f f i c i e n t s o f a 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 Model," Report
DTNSRDC/SPD-744-01 (Jan 1977).
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-ments on Two SWATH C o n f i g u r a t i o n s , " Report DTNSRDC/SPD-0928-01 (Jun 1980).
14. K a l l i o , J.A., " S e a w o r t h i n e s s C h a r a c t e r i s t i c s o f a 2900 Ton S m a l l
Water-p l a n e Area Twin H u l l (SWATH), ReWater-port DTNSRDC/SPD-620-03 (SeWater-p 1976).
15. K a l l i o , J.A., "SWATH 6D Model E x p e r i m e n t s i n R e g u l a r Head and F o l l o w i n g Waves W i t h and W i t h o u t F l o o d a b l e S t r u t s , " Report DTNSRDC/SPD-0914-01 (Feb 1980).
16. Hong, Y.S., " P r e d i c t i o n o f M o t i o n s o f SWATH S h i p s i n F o l l o w i n g Seas,"
Report DTNSRDC/SPD-81-039 (Nov 1981).
17. Hong, Y.S., " P r e d i c t e d M o t i o n s o f High-Speed SWATH S h i p s i n Head and
F o l l o w i n g Seas," Report DTNSRDC/SPD-82-036 ( J u l 1982).
18. Newman, J.N. and P. S c l a v o u n o s , "The U n i f i e d Theory o f Ship M o t i o n , "
P r o c e e d i n g s o f t h e T h i r t e e n t h Symposium on N a v a l Hydrodynamics, Tokyo, Japan
(Oct 1980).
19. Lee, CM,, " A p p r o x i m a t e E v a l u a t i o n o f Added Mass and Damping C o e f f i c i e n t s
of Two-Dimensional SWATH S e c t i o n s , " Report DTNSRDC/SPD-78-084 (Oct 1978),
20. K o r v i n - K r o u k o v s k y , B,V, and W,R. Jacobs, " P i t c h i n g and Heaving M o t i o n s o f a Ship i n Regular Waves," T r a n s a c t i o n s o f t h e 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 , V o l . 65 ( 1 9 5 7 ) .
2 1 . Newman, J.N., " M a r i n e Hydrodynamics," The MIT P r e s s , Cambridge,
Massachu-s e t t Massachu-s ( 1 9 7 7 ) , pp. 362-371.
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P r e s s ( 1 9 6 0 ) , pp. 414-421.
23. Keulegan, G.H. and L.H. C a r p e n t e r , "Forces on C y l i n d e r s and P l a t e s i n
an O s c i l l a t i n g F l u i d , " J o u r n a l o f Research o f t h e N a t i o n a l Bureau o f S t a n d a r d s ,
25. P i t t s , W.C, J.N. N i e l s e n , and C E . K a a t t a r i , " L i f t and Center o f P r e s
-s u r e o f W i n g - B o d y - T a i l C o m b i n a t i o n -s a t Sub-sonic, T r a n -s o n i c , and S u p e r -s o n i c Speed-s," NACA Report 1307 ( 1 9 5 7 ) .
P a r t i c u l a r 6a' 6B1 60^ 6D2 3 SSP L e n g t h o v e r a l l , m 73.15 73.15 73.15 73.15 26.40 D i s t a n c e between c e n t e r l i n e s , m 22.86 22.86 22.86 26.80 12.19 D r a f t , m 8.13 8.13 8.13 8.13 4.66 D i s p l a c e m e n t , m e t r i c t o n 2,946 2,946 2,946 2,946 2,946 L o n g i t u d i n a l CG, a f t o f nose, m 35.45 35.14 34.72 36.10 13.46 V e r t i c a l c e n t e r o f g r a v i t y (KG), m 10.36 10.36 10.36 9.00 4.28 L o n g i t u d i n a l m e t a c e n t r i c h e i g h t , m 6.10 11.60 13.70 26.40 5.03 As g i v e n i n R e f e r e n c e 14. As g i v e n i n R e f e r e n c e 15. As g i v e n i n R e f e r e n c e 13.
TABLE 2 - PARTICULARS OF STABILIZING FINS Conf i g u r a t i o n 6B1 6D2 SSP ' 3 4 Forward F i n , Each Chord, m 2 59 2.16 2.16 2.59 1.95 Span, m 3 11 2.59 2.59 3.11 1.83 L o c a t i o n , ^ m 17 15 17.15 17.15 17.15 2.82 A f t F i n Chord, m 4 48 3.73 3.73 4.48 2.38 Span, m 5 36 4.48 4.48 5.36 10.55 L o c a t i o n , ^ m 62 24 62.24 62.24 62.24 20.59 As g i v e n i n R e f e r e n c e 14, As g i v e n i n R e f e r e n c e 15. As g i v e n i n R e f e r e n c e 13. A f t f i n spans between t h e h u l l s .
DAMPING, WAVE EXCITING FORCE, AND WAVE EXCITING MOMENT V a r i a b l e Nond imen s i o n a 1 l z a t i o n F a c t o r ^33 M A A ML 2 ML ^33 M ( g / L ) ^ / ^ B33, B53 1/2 M ( g L ) ' ^ ^ ^ 5 M L ( g L ) ^ / ^ F ( e ) MgA/L F ( e ) MgA where A g Wave a m p l i t u d e A c c e l e r a t i o n due t o g r a v i t y L O v e r a l l s h i p l e n g t h M = Mass o f D i s p l a c e d volume
F i g u r e 1 - Comparison between Experiment and P r e d i c t i o n f o r Added Mass and Damping C o e f f i c i e n t s o f t h e SWATH 6A (Bare H u l l )
f o r V a r i o u s Speeds . o o ( u r . l U FiadicClm 0.113 O m O.IM a n o.ni A A Q • O Ö O Ö (.0' 0.192 O • O.Ut • • 0.672 A A A A • 04,A 2.0 3.0
bp«rla«ot ro (tot .11) Fr»llctloi. 0,192 O • 0.672 A • 0 11 • • ° o n o o • O O O • ° 8 * 6 6 O 2.0 -5.0 bparüient Pa (taf. 11) Pradtctloo 0.192 O • o.3at • • 0.672 A A Ü O • A
° •
• O»33 F i g u r e 1 ( C o n t i n u e d ) 4 * O 4 • • • • O 1,0 O O Exptrlflcnt
ro (tof. 11) rtoJ lotion
0.192 O e O.Mt • • 0.672 A A r/J o ' o O OÜ' ^53 O" • A • • • O," * * * n A bporlamc ro (Hot. 11) rtoJletloo 0.192 O • 0.38« • • 0.672 A A O 'o» O • • • • • I '. 1 ÜJ' F i g u r e l c - Damping C o e f f i c i e n t s B^^ and B^^
n (Uf.11) 0.19! O 0.314 • 0.672 A A ê a" A A A o • • • • • • FD (l.f.11) Fradiction 0.192 O
•
o.3at n • • 0.672 A A * 4 A A A A A A .A A ^ A A A A A A A a a a • • D% • • n" • Ü • IJ • • Q ° • 1 O *o • • 0 • • 1 0 O O O 2.0 F i g u r e I d - Damping C o e f f i c i e n t s B^^ and B^^F i g u r e 2 - Comparison between Experiment and P r e d i c t i o n o f Added Mass and Damping C o e f f i c i e n t s f o r t h e SWATH 6A
1.4 1.2 1.0 .0 .6 l a r a HaU Q ^ Aft ria A ( )
rod aad Aft riaa A I I A .8 1.0 1.2 1.4 1.6 1. 2.0 2.2 2.4 . 2 h ' 5 3 - . 2 - . 3 J L J \ I _ L .8 1.0 1.2 1.4 1.6 1.8 2.0 2.2 2,4
' 5 5 .16 .14 .12 .10 .08 .06 .04 .2 h ' 3 5 -.2 - . 3 C o . t U u r . t t o » ( H I . 1?) f t ^ i l c t l o . ( U . . H I .1 2 ) b r « Dull O M t Fill • rod •nd Alt F l m A „ CP o o O o .8 1.0 1.2 1.4 1.6 1.8 2.0 2.2 2.4 CJ ' J L J L J L .8 1.0 1.2 1.4 1.6 1,8 2.0 2.2 2.4 to'
F i g u r e 2 ( C o n t i n u e d ) '33 2.0 1.5 1.0 0.5 - 1 . 0 ^53 - . 2 h . I x p a r l M i t r r a d l c t l o n C o . t l i a r i t l i . « ( I . t. 1 2 ) F r « l l e t l . i i ( U i . Mt. 1 2 ) I l K HuU O M t r l n a f i
Fud aild M t Fin* A A
O O
J I I L J L
1.0 1.2 1.4 1.6 1.8 2.0 2.2 2.4
' 5 5 .4 .2 - . 4 ITcJiction C l l t u r . t l o n ' ( » . t . 12) f r . d l c t l . n < U . . tot.12) Uca Hull O 9 ~ * l t Fin O i !
Fwd and Aft Flna A A
J L J I L
.8 1. 0 1.2 1.4 1.6 1.8 2.0 2.2 2.4
«35
8 1.0 1.2 1.4 1.6 1.8 2.0 2.2 2.4
F i g u r e 2 ( C o n t i n u e d ) 1.4 1.2 1.0 l l . b p a r l M o t P r x l l c t l o n i : o . l l g i . r . t l o « {Ul. 12) r r» i l c t l o . i ( U i . tot. 1 2 ) •aca Hull O • » f t riB a Ü
Fud and Ut riaa A A
••• •
.8 1.0 1.2 1.4 1.6 1.8 2.0 2.2 2.4 . 2 h ' 5 3 -.1 - . 2 O O J L J L 1.0 1.2 1.4 1.6 1.8 2.0 2.2 2.4C o ü H i u r . t l o . . (»«<• 12) F i . d l c t l o . < L . . , U t. 1 2 ) M t Fit) Fud «nd A f t F l n i O a A O r; • É A • • É J L J L 8 1.0 1.2 1.4 1.6 1.8 2.0 2.2 2.4 0 1.2 1.4 1.6 1.8 2.0 2.2 2.4
F i g u r e 2 ( C o n t i n u e d ) 2.5 2.U 1.5 1.0 G.5 b p a r l n o t Pradlctlon C o B l l t u r . t t o » ( U f . 1 ? ) f t i d l e t l o . ( U « . »«f. 12) b r a Hull Q • * f t ria O S /\ ^ ^^'^ *" ^ ^ " ? ° T f f ^ O O 9 « J L J L O .8 1.0 1.2 1.4 1.6 1.8 2.0 2.2 2.4 .6 ^53 -.2 - . 4 -.6 • ^ • • • • • • • • D J L .8 1.0 1.2 1.4 1.6 1.8 2.0 2.2 2.4 F i g u r e 2g - Damping C o e f f i c i e n t s B^^ and B^^ f o r Fn = 0,384
.6 ' 5 5 .2 CxparlMnt Prediction C o o t i i u r . t i o » (».<• 12) P r t d i e t i o n ( U . . b l . 12) b r a Hull O O Aft r i n a s
Fud and Aft FUa A A
" t ) * U * c» CP • n « n O f Q J I L .8 1.0 1.2 1.4 1.6 1.8 2.0 CO-2.2 2.4 1.2 1.0 .8 " 3 5 J L J L •°.B T o 1.2 . 1.4 1.6 1.8 2.0 2.2 2.4
F i g u r e 2 ( C o n t i n u e d ) 1.4 1.2 1.0 a! 33 .6 C i p a r l x n t Ptadlctlon C o o f l . u r . t l o n (»•<. 12) f r i d l c t l i i n ( U t . Ul. 12) S«r« Piull O • Aft Fin • g Fi«l tnd Alt Fln« A A — . A A A A A A A A • n ° • O D D , J L .8 1.0 1.2 1.4 1.6 1.8 2,0 2.2 2.4 O J ' a; .4 .3 53 -.1 ^ ^ f ^ ^ o ^ o O O O J I J _ L L .8 1.0 1.2 1.4 1.6 1.8 2.0 2.2 2.4 a)
.16 .14 .12 ' 5 5 .10 .08 .06 .04 Ü O O J \ \ L 8 1.0 1.2 1.4 1.6 1.8 2.0 2.2 2,4 ' 3 5 - . 2 - . 4 - . 6 - . 8 - 1 . 0 .8 / • / Sai< null ' a / ^ ' Fud .Dd Alt F i n . C o . f l . u . . t l o . ( t V t. 1 2 ) F H d U t l o a i u . . fMi.nx 1.0 1.2 1.4 1.6 1.8 2.0 2.2 2.4
F i g u r e 2 ( C o n t i n u e d ) 33 3.0 2.5 2.0 1.5 1.0 .B .6 .4 '53 - . 2 . b i x r l a m t Fradlctlon C o o t U u r i t U n ( l i t . 12) rr«<Hctlon ( U i . Ut. 1 2 ) b r . Hull O » f t Pin • • Pud .nd Ut Pla. A ,1 • m • 5 - 5 ^ ° o o 1.0 1.2 1.4 1.6 1.8 2.0 2.2 2.4 « P « o » o » • o . Q W o ^ 0 . 0 0 © J L J L •8 1.0 1.2 1.4 1.6 1.8 2,0 2.2 2.4 F i g u r e 2k - Damping C o e f f i c i e n t s B^^ and B^^ f o r Fn = 0.538
'55 C « . t l l u t . t U n (»««• 12) < U . . » . f. l 2 ) b r * Hull O 9 Ait r i n • • Fvd md Alt Flna A A Ptcdletlon c O « ( y » C » — O J L J . L .8 1.0 1.2 1.4 1.6 1.8 2.0 2.2 2.4 to' ' 3 5 1.2 1.0 Ö.8 0.6 O./} 0.2 J ^ \ L .8 1.0 1.2 1.4 1.6 1.8 2.0 2.2 2.4 co F i g u r e 2£ - Damping C o e f f i c i e n t s B^^ and B^^ f o r Fn = 0.538
F i g u r e 3 - Comparison between Experiment and P r e d i c t i o n o f Heave E x c i t i n g Force and P i t c h E x c i t i n g Moment
f o r t h e SWATH 6D 4 0 O O 3 O • O O O
• •
2 (J 9 E x p e r i m e n t O O Fn ( R e f . 1 3 ) P r e d i c t i o n 0 0.0 O•
O • 0.077 O•
1 - O O 0.192 O•
O 0 0.384 • • <;> 0.538 A • O 0 1 1 1 1 1 1 1 1 2 3 /, 5 6 7WAVELENGTH TO SHIP LENGTH
(DEGREES) 180
-
•O* %) • ^ O 90-O 0
•
• «O • • • o • ^ O -90 O 180 1 1 1 1 1 I 1 1 2 3 A 5 6 7WAVELENGTH TO SHIP LENGTH
Vn 0.0 0.077 0.192 0.384 0.538 E x p e r l j n e n t ( R e f . 1 3 ) O O O a A P r e d i c t i o n .5 3 4 WAVELENGTH TO SHIP LENGTH
18(1 h 9 0 (OEGRF.ES) -90 -180 O O 3 4 WAVELENGTH TO SHIP LENGTH
F i g u r e 3 ( C o n t i n u e d ) , 0 » , 0 » u O < o l O O < _) O Fn E x p e r i m e n t ( R e f . 1 3 ) P r e d i c t i o n <>• O 0.0 O
•
om o 0.077 0.192 Ü O•
i 1 I *•
O 1 0.384 0.538 < i;i A i • A 1 2 3 4 5 6 7 WAVELENGTH TO SHIP LENGTH180 90 (DECREES) • O -180 h O 4-3 4
WAVELENGTH TO SHIP LENGTH
E x p e r i m e n t .9 Fn ( R e f . 1 3 ) P r e d i c t i o n 0.0 0
•
.8 0.077 O•
0.192 O 0 .7 0.384 n • 0.538 A • .6 0 • .5 O ^ È O O Q t .4 ( ) O O O ^ 8• te
Ê O O .3-%
.2 .1 • 1 1 1 0 0 1 2 3 1, 5 6WAVELENGTH TO SHIP LENGTH
(DEGREES) "
-90
-180
O
3 4 WAVELENGTH TO SHIP LENGTH
F i g u r e 3 ( C o n t i n u e d ) 4 3 1 0 -A • • B • • A A iJ A A A • • U A U • A E x p e r i m e n t A ( P Fn ( R e f . 1 3 ) P r e d i c t i o n (.1 A A A A 0.0 0.077 O O
•
•
• n 0.192 O • 1 Ü L l A 1 0.384 0.538 I • A 1 • • 1WAVELENGTH TO SHIP LENGTH
(DEGREES)
3 4 5 WAVELENGTH TO SHIP LENGTH
1.0 E x p e r i m e n t A Fu ( R e f . 1 3 ) P r e d i c t i o n 0.0 O
•
A 0.077 O ( ) 0.192 O O 0.384 • n ^ A 0.538 A /\ A A • • " 3 4 WAVELENGTH TO SHIP LENGTH"5 (•1VXKEES)
UAVELENCTH TO SHIP LENGTH
F i g u r e 3 ( C o n t i n u e d ) It A •O O •
•
• 3 0 () • O 0 O F' 2 0 O c9 o° o • V O O Fn 0.0 0.077 E x p e r i m e n t ( R e f . 1 3 ) O O P r e d i c t i o n • • 1 O O Ü C) O O 0.192 0.384 0.538 O L i A • • • 0 1 1 1 1 1 1 1 1 2 3WAVELENGTH TO SHIP LENGTH
5 5 7 180 0 90 O "3 (DEGREES) ° • O •o • O » • O • O 0 • O -90 -180 C ^ 0 8 p 1 1 , 1 1 2 3 A 5 6 7
WAVELENGTH TO SHIP LENGTH
.9 Fn E x p e r i m e n t ( R e f . 1 3 ) P r e d i c t l o n .8 U.U 0.077 O O
•
•
.7 0.192 0.384 0 n • • .6 0.538 A A . 5 .4 .3 O ö O Li•
O & O ri O•
O O * • O •• •
O•
.2 • o » . 1 0 ( 9 O 1 1 1 1 1 . 1 0 0 1 2 3 4 5 6 7WAVELENGTH TO SHIP LENGTH
WAVELENGTH TO SHIP LENGTH
F i g u r e 3 ( C o n t i n u e d ) ^3 0 ( O O
• •
O O l _ O O O O * O O O i)0 O f a 0.0 0.077 0.192 0.384 0.538 J E x p e r i m e n t ( R e f . 1 3 ) O O O 11 O P r e d l e t t o n 180 F «3 (DEGREES) 90 h 0\--90 -180 O Oo& t &WAVELENGTH TO SHIP LENGTH
WAVELENGTH TO SHIP LENGTH
"5 .9 • • O o • O O O • o • O O O I O <> • „ t O "0 O Kn 0 . 0 0.077 0.192 0.384 0.538 E x p e r i m e n t ( R e f . 1 3 ) O O O n A O O P r e d i e t l o n O O O O
WAVELENGTH TO SHIP LENGTH
1 8 0
(DEGREES)
3 4 WAVELENGTH TO SHIP LENGTH
F i g u r e 3 ( C o n t i n u e d ) F- 2 O A A A -a A • A • 0.0 0.077 0.192 0.384 0.538 E x p e r i m e n t ( R e f . 1 3 ) O t ) <> • A P r e d i c t i o n ( ) O 3 4 WAVELENGTH TO SHIP LENGTH
(DEGREES)
3 4 5 WAVELENGTH TO SHIP LENGTH
.9 .7 .6 .2 A (^ 9 a A A o n AA A • I • A 1 O ft Fn E x p e r i m e n t ( R e f . 1 3 ) F r e d i c t i o n 0.0 O
•
0.077 O 0.192 O 0 0.384 • n 0.538 A A A^ |A 4 5 WAVELENGTH TO SHIP LENGTHCDI'GREES) "
-3 "4 WAVELENGTH TO SHIP LENGTH
F i g u r e 4 - Comparison between Experiment and P r e d i c t i o n o f Heave E x c i t i n g Force and P i t c h E x c i t i n g Moment f o r t h e
SSP KAIMALINO i n Head Waves
2 E x p e r Iment Fu ( R e f . 13) P r e d I c t l o n 0.0 O
•
- 0.095 • 0.222 • 0.317 O 0.491 O•
(J•
O O • O O O O O O _ O O O O f> O•
O O 1 1 1 L • 0 1 2 3 4 5 6 7WAVELENGTH TO SHIP LENGTH
03 (DEGREES) 180 90 0 90 180 -O 0 0 O O i 3 4 5 WAVELENGTH TO SHIP LENGTH
05 2 E x p e r i m e n t Fn ( R e f . 13) P r e d i c t i o n 0.0 0
•
0.095 • • 0.222 L l • 0.317 0•
0.491 0•
i. 0 „ • 0 0 0 0 0• • • •
• • •
e 0 0 ° 0 0 0 0 n 0 1_ 1 1 1 u I 2 3 4 5 6 7WAVELENGTH TO SHIP LENGTH
180
-0 ° 0 0 0 0 ° 90 • 0 o o o 0 0 0 0 0 {'•\
• • • • •
0 -90 = \J 180 Ü 1 1 1_ 1 1 1 2 3 4 5 6 7WAVELENGTH TO SHIP LENGTH
F i g u r e 4 ( C o n t i n u e d ) • A A A • • A A A Fu 0.0 0.095 0.222 0.317 0.491 E x p e r i m e n t ( R e f . ' 1 3 ) O A • <> O A P r e d i c t i o n <:> A
O
o
L 3 4 5 WAVELENGTH TO SHIP LENGTH180 90 (DEGREES) 0 -90 -180 ° ^ °A
1
A 1 1 1 1 ' 1 3 4 5 WAVELENGTH TO SHIP LENGTHF' I A A A A
^ 1
3 4 5 WAVELENGTH TO SHIP LENGTHE x p e r i m e n t Fn ( R e f . 13) P r e d i c t i o n 0.0 O 0.095 A A 0.222 11 U 0.317 O <> 0.491 O O a A 180 h 90 h "5 (DEGREES) ^ -90 -180 A . A A A A A ^ '^Ag • • o D • A ! * * e A A 1? A A • a
1 1
3 4 5 WAVELENGTH TO SHIP LENGTHF i g u r e 4 ( C o n t i n u e d ) O O O
• %
• O O O O O O O O F". 0.0 0.095 0.222 0.317 0.491 3 4 5 WAVELENGTH TO SHIP LENGTHO E x p e r i m e n t ( R e f . 1 3 ) O O P r e d i c t i o n «3 (DEGREES) O
HAVELENGTll TO SHIP LENGTH
F- 1 E x p e r i m e n t O Fn ( R e f . 1 3 ) P r e d i c t i o n 0.0 0
•
( ) 0.095 A O U 0.222 • 1: i 0 * 0 0 0 0 • 0 ó ó 8 0 0.317 0.491 0 0 ó 0 \> (.;-• O * -L 3 4 5 WAVELENGTH TO SHIP LENGTH<^5 (DEGREES)
3 4 5 WAVELENGTH TO SHIP LENGTH
F i g u r e 5 - Comparison between E x p e r i m e n t and P r e d i c t i o n o f Regular Wave T r a n s f e r F u n c t i o n s f o r t h e SWATH 6A
E x p e r i m e n t ( R e f . 1 4 ) O
P r e d i c t i o n #
HEAD SEAS 0 KNOTS P r e d i c t i o n ( L e e ) •
