Open Collections

UBC Theses and Dissertations

UBC Theses Logo

UBC Theses and Dissertations

Experimental investigation of fishing vessel stability in a transverse seaway Rohling, Gerald Francis 1986

Your browser doesn't seem to have a PDF viewer, please download the PDF to view this item.

Item Metadata

Download

Media
831-UBC_1986_A7 R64.pdf [ 8.04MB ]
Metadata
JSON: 831-1.0096922.json
JSON-LD: 831-1.0096922-ld.json
RDF/XML (Pretty): 831-1.0096922-rdf.xml
RDF/JSON: 831-1.0096922-rdf.json
Turtle: 831-1.0096922-turtle.txt
N-Triples: 831-1.0096922-rdf-ntriples.txt
Original Record: 831-1.0096922-source.json
Full Text
831-1.0096922-fulltext.txt
Citation
831-1.0096922.ris

Full Text

EXPERIMENTAL INVESTIGATION OF F ISHING V E S S E L S T A B I L I T Y IN A TRANSVERSE SEAWAY By GERALD FRANCIS ROHLING B . S c . The U n i v e r s i t y o f C a l g a r y , 1982 A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF A P P L I E D SCIENCE i n THE FACULTY OF GRADUATE STUDIES DEPARTMENT OF MECHANICAL ENGINEERING We a c c e p t t h i s t h e s i s as c o n f o r m i n g t o t h e r e q u i r e d s t a n d a r d THE UNIVERSITY OF BRIT ISH COLUMBIA Sep tember 1986 © G e r a l d F r a n c i s R o h l i n g , 1986 I n p r e s e n t i n g t h i s t h e s i s i n p a r t i a l f u l f i l l m e n t o f t h e r e q u i r e m e n t s f o r a n a d v a n c e d d e g r e e a t t h e U n i v e r s i t y o f B r i t i s h C o l u m b i a , I a g r e e t h a t t h e L i b r a r y s h a l l make i t f r e e l y a v a i l a b l e f o r r e f e r e n c e and s t u d y . I f u r t h u r a g r e e t h a t p e r m i s s i o n f o r e x t e n s i v e c o p y i n g o f t h i s t h e s i s f o r s c h o l a r l y p u r p o s e s may be g r a n t e d b y t h e h e a d o f my d e p a r t m e n t o r b y h i s o r h e r r e p r e s e n t a t i v e s . I t i s u n d e r s t o o d t h a t c o p y i n g o r p u b l i c a t i o n o f t h i s t h e s i s f o r f i n a n c i a l g a i n s h a l l n o t be a l l o w e d w i t h o u t my w r i t t e n p e r m i s s i o n . D e p a r t m e n t o f M e c h a n i c a l E n g i n e e r i n g The U n i v e r s i t y o f B r i t i s h C o l u m b i a 2075 Wesbrook P l a c e V a n c o u v e r , B r i t i s h C o l u m b i a Canada V6T 1W5 D a t e : O c t o b e r 6 , 1986 ABSTRACT The continuing loss of l i f e at sea due to the capsizing of f i s h i n g vessels i n inclement weather requires the research and design communities to continue t h e i r search to f i n d methods for the prevention of further occurances. As part of t h i s i n v e s t i g a t i v e process t h i s thesis was prepared. To gain an i n i t i a l foothold on the dynamics of c a p s i z i n g the area of transverse seaways was considered for i t s c o n t r i b u t i o n to ca p s i z i n g through the impact of breaking waves on the side of the ship. Two model f i s h i n g vessels, b u i l t without bulwarks or superstructure, were prepared for t e s t i n g i n a 220 foot t e s t basin where, through the use of computer co n t r o l , a repeatable sea environment could be created. The models were equipped with adjustable displacements and centers of gravity to allow t e s t i n g of IMO s t a b i l i t y guidelines and the simulation of wind induced decreases i n general s t a b i l i t y . Tests were conducted i n s t i l l water, regular waves and breaking waves of the plunging j e t type. Motions, in c l u d i n g r o l l , p i t c h , heave, sway and yaw, were measured and stored on media for analysis by computer. Along with the e l e c t r o n i c monitoring of the vessel's motions a video tape was made of the tests to allow v i s u a l v e r i f i c a t i o n of motions at a l a t e r date. From the r e s u l t s of the tests i t was found that the si n g l e i i -c h i n e s e i n e r e x h i b i t e d g r e a t e r i n t a c t s t a b i l i t y i n a l l t r a n s v e r s e s e a c o n d i t i o n s t e s t e d t h a n d i d t h e w e s t c o a s t t r a w l e r . U n d e r no c i r c u m s t a n c e d i d t h e s i n g l e c h i n e s e i n e r c a p s i z e w h i l e , i n b r e a k i n g w a v e s , t h e t r a w l e r e x h i b i t e d r e p e a t e d c a p s i z i n g b e h a v i o u r when a t i t s h e a v i e s t d i s p l a c e m e n t and l o w e s t m e t a c e n t r i c h e i g h t . T h i s c a p s i z i n g i l l u s t r a t e s t h e n e e d f o r g r e a t e r s t a b i l i t y c h a r a c t e r i s i t i c s and i m p r o v e d s a f e t y c r i t e r i o n f o r b r e a k i n g waves s u r v i v a l o v e r t h a t r e q u i r e d i n r e g u l a r s e a s . i i i -TABLE OF CONTENTS A b s t r a c t i i C o n t e n t s i v L i s t o f T a b l e s v i i L i s t o f F i g u r e s v i i i N o m e n c l a t u r e x i i A c k n o w l e d g e m e n t s x v 1 .0 INTRODUCTION 1 1.1 HISTORY OF SAFETY REGULATIONS 1 2 . 0 MODEL D E S C R I P T I O N S 11 2 . 1 SINGLE CHINE SEINER 17 2 . 1 . 1 FULL SCALE SHIP DATA 17 2 . 1 . 2 SCALE MODEL DATA 21 2 . 2 WEST COAST TRAWLER 22 2 . 2 . 1 FULL SCALE SHIP DATA 22 2 . 2 . 2 SCALE MODEL DATA 28 3 . 0 DATA ACQUISIT ION 29 3 .1 SINGLE CHINE SEINER 29 3 . 1 . 1 AUTO PILOT 30 3 . 1 . 2 ACCELEROMETERS 30 3 . 1 . 3 VERTICAL GYRO 31 3 . 1 . 4 ANALOG TO D IG ITAL CONVERTER 31 3 . 1 . 5 LIGHT EMITTING DIODE DISPLAY 32 3 . 1 . 6 IBM P C j r . MICRO-COMPUTER 32 3 . 2 WEST COAST TRAWLER 33 4 . 0 TESTING 38 4 . 1 TEST F A C I L I T I E S 38 - i v 4 . 2 TESTING SEQUENCE 38 4 . 2 . 1 CALIBRATION 38 4 . 2 . 1 . 1 ROLL AND PITCH ANGLES 40 4 . 2 . 1 . 2 YAW 42 4 . 2 . 1 . 3 HEAVE AND SWAY ACCELERATIONS 42 4 . 2 . 1 . 4 WAVE HEIGHT 43 4 . 2 . 1 . 5 ZERO SETTINGS IN WATER 43 4 . 2 . 2 ROLL DECAY TESTS 44 4 . 2 . 3 REGULAR SEAWAY 45 4 . 2 . 4 BREAKING WAVES 47 5 . 0 ANALYSIS OF DATA 49 5 . 1 PRE-PROCESSING 49 5 . 1 . 1 SINGLE CHINE SEINER 49 5 . 1 . 2 WEST COAST TRAWLER 51 5 . 2 GENERAL PROCESSING 54 5 . 2 . 1 D . C . OFFSET REMOVAL 54 5 . 2 . 2 FOURIER F ILTERING 55 5 . 2 . 3 DECOUPLING THE MOTIONS 57 5 . 3 ROLL DECAY TESTS 59 5 . 3 . 1 ROLL EXTINCTION CURVES 59 5 . 3 . 2 V IRTUAL MASS MOMENTS OF INTERTIA 68 5 . 4 REGULAR SEAS RESPONSE 70 5 . 4 . 1 WAVEMAKER CHARACTERISTICS 70 5 . 4 . 2 ROLL RESPONSE AMPLITUDE OPERATORS 75 5 . 5 REGULAR SEAS S T A B I L I T Y FACTORS 77 5 . 6 BREAKING WAVE RESPONSE 93 5 . 7 BREAKING WAVES S T A B I L I T Y FACTORS 101 5 . 7 . 1 S T A B I L I T Y PARAMETER S ' 101 - v -5.7.2 STABILITY PARAMETER S* 102 6.0 RESULTS AND DISCUSSION I l l 6.1 FUNCTION OF METACENTRIC HEIGHT IN STABILITY 115 6.2 FUNCTION OF FREEBOARD IN STABILITY 117 6.3 EFFECTS OF SEVERE ACCELERATIONS ON SURVIVABILITY 118 7.0 CONCLUSIONS 120 REFERENCES 121 APPENDICES 123 A. SCHEMATICS 123 B. WEST COAST TRAWLER STABILITY REPORT 138 C. FOURIER SMOOTHING 152 D. BACKGROUND THEORY 162 - vi -LIST OF TABLES Table I IMO Work on S t a b i l i t y f o r Small Crafts 8 Table II Scaling Parameters 14 Table I I I Single Chine Seiner P r i n c i p l e Dimensions 17 Table IV Single Chine Seiner Metacentric Heights 21 Table V Single Chine Seiner Model C h a r a c t e r i s t i c s 21 Table VI West Coast Trawler P r i n c i p l e Dimensions 26 Table VII West Coast Trawler Metacentric Heights 27 Table VIII West Coast Trawler Model C h a r a c t e r i s t i c s 28 Table IX Relevant ASCII Characters Used 51 Table X F i l e Numbering Guide 52 Table XI E x t i n c t i o n C o e f f i c i e n t s f o r the Single Chine Seiner 61 Table XII E x t i n c t i o n C o e f f i c i e n t s f o r the West Coast Trawler 62 Table XIII V i r t u a l Mass Moments of I n e r t i a Single Chine Seiner 69 Table XIV V i r t u a l Mass moments of I n e r t i a West Coast Trawler 70 Table XV Breaking Wave Amplitudes 96 Table XVI Areas for Single Chine Seiner 106 Table XVII Areas f o r West Coast Trawler 107 Table XVIII Summary of S t a b i l i t y Requirements Compliance Single Chine Seiner 112 Table XIX Summary of S t a b i l i t y Requirements Compliance West Coast Trawler 113 Table XX S p e c i f i c a t i o n s of the V e r t i c a l Gyro 127 - v i i -LIST OF FIGURES Figure 1 Single Chine Seiner Layout 12 Figure 2 Single Chine Seiner Lines Drawing 13 Figure 3 Restoring Arm Curves for Single Chine Seiner 216.4 Tons Displacement 15 Figure 4 Restoring Arm Curves f o r Single Chine Seiner 249.6 Tons Displacement 16 Figure 5 West Coast Trawler Lines Plan 18 Figure 6 West Coast Trawler General Arrangement I 19 Figure 7 West Coast Trawler General Arrangement II 20 Figure 8 Restoring Arm Curve f o r West Coast Trawler 328.9 Tons Displacement 23 Figure 9 Restoring Arm Curves f o r West Coast Trawler 437.64 Tons Displacement 24 Figure 10 Restoring Arm Curves for West Coast Trawler 551.51 Tons Displacement 25 Figure 11 Test F a c i l i t i e s 39 Figure 12 C a l i b r a t i o n Rig 41 Figure 13 Processing Sequence Flow Chart 56 Figure 14 A c c e l e r a t i o n Vector Diagram 57 Figure 15 R o l l E x t i n c t i o n Curves f o r Single Chine Seiner 216.4 Tons Displacement 63 Figure 16 R o l l E x t i n c t i o n Curves f o r Single Chine Seiner 249.6 Tons Displacement 64 Figure 17 R o l l E x t i n c t i o n Curves f o r West Coast Trawler 328.9 Tons Displacement 65 Figure 18 R o l l E x t i n c t i o n Curves f o r West Coast Trawler - v i i i -437.64 Tons Displacement 66 Figure 19 R o l l E x t i n c t i o n Curves f or West Coast Trawler 551.51 Tons Displacement 67 Figure 20 Regular Seas Wave Amplitudes - Test Amplitude #1 .... 71 Figure 21 Regular Seas Wave Amplitudes - Test Amplitude #3 .... 72 Figure 22 Regular Seas Wave Amplitudes - Test Amplitude #4 .... 73 Figure 23 Regular Seas Wave Amplitudes - Test Amplitude #5 .... 74 Figure 24 R o l l Response Amplitude Operator Single Chine Seiner 216.4 Tons Displacement, GM = 0.2557 f t 78 Figure 25 R o l l Response Amplitude Operator Single Chine Seiner 216.4 Tons Displacement, GM = 1.1516 f t 79 Figure 26 R o l l Response Amplitude Operator Single Chine Seiner 216.4 Tons Displacement, GM = 2.1331 f t 80 Figure 27 R o l l Response Amplitude Operator Single Chine Seiner 249.6 Tons Displacement, GM = 0.2557 f t 81 Figure 28 R o l l Response Amplitude Operator Single Chine Seiner 249.6 Tons Displacement, GM = 0.5113 f t 82 Figure 29 R o l l Response Amplitude Operator Single Chine Seiner 249.6 Tons Displacement, GM = 1.1516 f t 83 Figure 30 R o l l Response Amplitude Operator Single Chine Seiner 249.6 Tons Displacement, GM = 2.1331 f t 84 - i x -Figure 31 R o l l Response Amplitude Operator West Coast Trawler 328.9 Tons Displacement, GM = 3.4154 f t . (bilge keels removed) 85 Figure 32 R o l l Response Amplitude Operator West Coast Trawler 328.9 Tons Displacement, GM = 3.4154 f t . (bil g e keels attached) 86 Figure 33 R o l l Response Amplitude Operator West Coast Trawler 437.64 Tons Displacement, GM -= 0.2953 f t 87 Figure 34 R o l l Response Amplitude Operator West Coast Trawler 437.64 Tons Displacement, GM = 1.7960 f t 88 Figure 35 R o l l Response Amplitude Operator West Coast Trawler 437.64 Tons Displacement, GM = 3.8238 f t . 89 Figure 36 R o l l Response Amplitude Operator West Coast Trawler 551.51 Tons Displacement, GM = 0.2953 f t 90 Figure 37 R o l l Response Amplitude Operator West Coast Trawler 551.51 Tons Displacement, GM •= 1.7960 f t 91 Figure 38 R o l l Response Amplitude Operator West Coast Trawler 551.51 Tons Displacement, GM = 4.1468 f t 92 Figure 39 Regular Seas S t a b i l i t y Factor Single Chine Seiner 94 - x -Figure 40 Regular Seas S t a b i l i t y Factor West Coast Trawler 95 Figure 41 Breaking Waves R o l l Response Single Chine Seiner 97 Figure 42 Breaking Waves R o l l Response West Coast Trawler 98 Figure 43 Breaking Waves Sway Response Single Chine Seiner 99 Figure 44 Breaking Waves Sway Response West Coast Trawler 100 Figure 45 Breaking Waves S t a b i l i t y Factor (S') Single Chine Seiner 103 Figure 46 Breaking Waves S t a b i l i t y Factor (S') West Coast Trawler 104 Figure 47 Breaking Waves S t a b i l i t y Factor (S ) Single Chine Seiner 108 Figure 48 Breaking Waves S t a b i l i t y Factor (S ) West Coast Trawler 109 Figure 49 Schematic of the V e r t i c a l Gyro 126 Figure 50 Data Telemetry System 129 Figure 51 Shipboard Instrumentation 130 Figure 52 T y p i c a l Time Domain Signal 154 Figure 53 T y p i c a l Frequency Domain Representation of Signal 155 Figure 54 The Dynamic Coordinate System 166 2 2 Figure 55 Wave Theory as a Function of H/gT and d/gT 178 Figure 56 V e l o c i t y P r o f i l e of a Breaking Wave 181 - x i -NOMENCLATURE Note: A b r i e f d e s c r i p t i o n i s given each term used i n t h i s t h e s i s . Following the de s c r i p t i o n i s a section number i n brackets, t h i s designates the section where the symbol i s defined i n f u l l or f i r s t mentioned. a : v i r t u a l mass moment of i n e r t i a about l o n g i t u d i n a l axis (§ D) a : A c c e l e r a t i o n (§ 2) A : regular seas wave amplitude (§ 5) b : Damping c o e f f i c i e n t (§ D) b^ : Damping c o e f f i c i e n t r e l a t e d to r o l l v e l o c i t y (§ D) b^ : Damping c o e f f i c i e n t r e l a t e d to r o l l v e l o c i t y squared (§ D) B : Center of Buoyancy (§ D) B : Beam of the ves s e l (§ 2) B(#) : Righting moment i n r o l l (§ 1) c() : Restoring moment as a function of time and r o l l angle (§ D) c^ : Restoring moment c o e f f i c i e n t ( f i r s t order) (§ D) c z : Restoring moment c o e f f i c i e n t ( t h i r d order) (§ D) c^ : Restoring moment c o e f f i c i e n t ( f i f t h order) (§ D) C : Block c o e f f i c i e n t (§ 2) b C : Midship s e c t i o n c o e f f i c i e n t (§ 2) m C : Waterplane area c o e f f i c i e n t (§ 2) wp d : Water depth (§ D) D : Depth of the ves s e l (§ 2) - x i i -F : F o r c e (§ 2) FB : E f f e c t i v e f r e e b o a r d (§ 2) g : A c c e l e r a t i o n due t o g r a v i t y (§ 1) G : C e n t e r o f G r a v i t y (§ D) G M : M e t a c e n t r i c h e i g h t (§ 1) G M : I n i t i a l m e t a c e n t r i c h e i g h t (§ 1) o GZ : R i g h t i n g arm (§ D) G Z 2 o q : R i g h t i n g arm a t an a n g l e o f i n c l i n a t i o n o f 20° (§ 1) GZ : Maximum r i g h t i n g arm ( § 1 ) max h : H e i g h t o f b r e a k i n g wave a t i m p a c t (§ 5) H : B r e a k i n g wave h e i g h t (§ D) I' : V i r t u a l mass moment o f i n e r t i a a b o u t t h e l o n g i t u d i n a l a x i s (§ D) k : Wave number (§ D) k : S p r i n g c o n s t a n t (§ 5) k : R a d i u s o f g y r a t i o n o f t he v e s s e l mass p l u s t h e added mass XX (§ D) K : B a s e l i n e (§ D) KB : D i s t a n c e f r o m t h e b a s e l i n e t o t h e c e n t e r o f b u o y a n c y (§ D) KG : D i s t a n c e f r o m t h e b a s e l i n e t o t h e c e n t e r o f g r a v i t y (§ D) L : wave l e n g t h (§ D) L : L e n g t h b e t w e e n p e r p e n d i c u l a r s (§ 2) BP m : Mass (§ 2) M : M e t a c e n t e r (§ D) M() : E x t e r n a l f o r c i n g f u n c t i o n (§ D) p : P r e s s u r e (§ 2) R : A v e r a g e r o l l a n g l e i n r e g u l a r s e a s (§ 5) - x i i i R : Maximum r o l l angle achieved i n a breaking wave (§ 5) S : S t a b i l i t y f a c t o r f o r regular seas (§ 6) S' : S t a b i l i t y f actor f or breaking waves - ve r s i o n 1 (§ 6) 5 : S t a b i l i t y f actor f or breaking waves - version 2 (§ 6) t : Time (§ D) T : Draft of the vessel (§ 3) T : Period of o s c i l l a t i o n (§ 5) T, : Natural period of o s c i l l a t i o n i n r o l l (§ 6) <t> V : V e l o c i t y (§ 3) a : Instantaneous wave slope (§ D) a' : Maximum e f f e c t i v e wave slope (§ D) M A : Displacement of the ves s e l (§ 1) A' : Added displacement of the ves s e l (§ D) : Total v i r t u a l displacement of vessel (§ D) 4> : R o l l angle r e l a t i v e to water surface (§ 1) 4>^ : Angle of downflooding (§ 1) <t> : Angle of heel f o r immersion of upper deck (§ 1) 4> : Angle of heel at maximum r i g h t i n g arm (§ 1) <j> : Mean r o l l angle over one cycle (§ D) m <f> : N t h r o l l i n a r o l l decay curve (§ D) n 4> : Angle of vanishing s t a b i l i t y (§ 1) V $ : Maximum r o l l angle i n regular seas (§ 6) A : Scaling f a c t o r (§ 3) n : E l e v a t i o n of the water surface (§ D) p : Water density (§ 3) 6 : Instantaneous angle of r o l l (§ 6) u> : Encounter wave frequency (§ D) e w : Natural frequency (§ D) x i v ACKNOWLEDGEMENTS F i r s t and f o r e m o s t I w o u l d l i k e t o t h a n k my s u p e r v i s o r , D r . S . M . C a l i s a l , f o r h i s p a t i e n t g u i d a n c e d u r i n g t h e p l a n n i n g , c o n s t r u c t i o n and e x e c u t i o n o f t h e s e e x p e r i m e n t s and t he w r i t i n g o f t h i s t h e s i s . The e x p e r i m e n t s t h e m s e l v e s w o u l d n e v e r h a v e b e e n p o s s i b l e w i t h o u t a c c e s s t o a t o w i n g t a n k and t h u s I w o u l d l i k e t o e x p r e s s my g r e a t a p p r e c i a t i o n t o G e r r y N . S t e n s g a a r d , Manager o f t h e Ocean E n g i n e e r i n g C e n t e r , f o r t h e u s e o f t h e f a c i l i t i e s a t B . C . R e s e a r c h . I n a d d i t i o n I w o u l d l i k e t o t h a n k George Roddan and G a r y N o v l e s k i o f t h e Ocean E n g i n e e r i n g C e n t e r f o r t h e i r a l w a y s e x c e l l e n t t e c h n i c a l a s s i s t a n c e d u r i n g t h e b u i l d i n g and t e s t i n g o f t h e m o d e l s . A number o f o t h e r p e o p l e l e n t i n v a l u a b l e a s s i s t a n c e d u r i n g t h e c o u r s e o f t h i s w o r k . I n p a r t i c u l a r I w o u l d l i k e t o t h a n k M a r c e l L e F r a n c o i s f o r t h e s o f t w a r e , and S t e v e n Thompson f o r t h e e l e c t r i c a l w o r k , i n t h e S e i n e r m o d e l . I a l s o w i s h t o t h a n k I r e n e B l a n k , A l e j a n d r o A l l i e v i , F a r s h i d N a m i r a n i a n , Dan M c G r e e r and G i r e e s h S a d a s i v a n , among o t h e r s , f o r t h e i r a s s i s t a n c e d u r i n g t h e t e s t i n g o f t h e m o d e l s . P o r t i o n s o f t h i s r e s e a r c h were f u n d e d b y t h e B . C . S c i e n c e C o u n c i l , t h e D e f e n s e R e s e a r c h E s t a b l i s h m e n t A t l a n t i c ( D . R . E . A . ) , and t h e N a t i o n a l R e s e a r c h C o u n c i l ( N . R . C . ) . T h e i r a s s i s t a n c e i s g r e a t l y a p p r e c i a t e d . - x v -1.0 INTRODUCTION 1.1 HISTORY OF SAFETY REGULATIONS The need f o r some type of guideline f o r the d e f i n i t i o n of ship safety i s nearly as o l d as water-borne c r a f t i t s e l f , the f i r s t formulation of a safety guideline was probably borne of experience and misfortune, i e : t r i a l and error. When an e a r l y t r a v e l l e r encountered a body of water he searched f o r some manner of conveyance to transport him and h i s supplies across. The e a r l i e s t of these c r a f t was supplied by nature and may have been ei t h e r logs or r a f t s . Rafts exhibited great s t a b i l i t y but when man decided to streamline t h i s c r a f t by reducing i t to a si n g l e l og i t was r a p i d l y r e a l i z e d that the former s t a b i l i t y had been s a c r i f i c e d , as anyone who has t r i e d standing on a f l o a t i n g log can t e s t i f y . Thinking of how to reduce t h i s problem the p o t e n t i a l s a i l o r attempted to lower h i s center of gra v i t y when he noticed that as his height reduced so d i d the rate at which he was rather unceremoniously dumped into the c h i l l y waters. With the help of tools newly developed he was able to hollow the log out, and s i t i n s i d e . This was a much more rewarding arrangement. Over the m i l l e n n i a t h i s rudimentary form of water-borne transp o r t a t i o n developed through the transformation of the si n g l e log c r a f t to a skin of material over a frame and from the motive forces of hands paddling i n the water to oars and s a i l s . S a i l i n g ships were found to be i n use i n Egypt as ea r l y as 3500 B.C. and - 1 -by 3000 B.C. [1] they were f r e e l y navigating the eastern Mediterranean, and probably also the Arabian Sea. The use of s a i l s once again presented a s t a b i l i t y problem which was overcome t h i s time by the s t o r i n g of b a l l a s t weight i n the lowest parts of the h u l l and l a t e r by the suspension of weights under the h u l l i n the form of a b a l l a s t e d keel. From the fourth millennium to the l a t e r Middle Ages the s t e e r i n g mechanisms of these ships remained v i r t u a l l y unchanged. Steering was s t i l l accomplished by the t r a i l i n g of a long oar behind the v e s s e l . In larger s a i l i n g ships the oar was attached to the stern and f i t t e d with a lever to garner greater mechanical advantage. L i t t l e was done to change t h i s system and g a l l e y slaves were used to a i d i n the steering of these vessels, a f a c t o r i n the maintaining of slavery i n vessels u n t i l the sixteenth century when, with the advent of naval a r t i l l e r y , i t was necessary to make room f o r cannons on ships crowded with g a l l e y slaves. In eighth-century China the v e r t i c a l rudder came into use and over time t h i s technology f i l t e r e d back to Europe. By the f i f t e e n t h century European shipping was growing by leaps and bounds as the new rudder allowed greater speeds by allowing the ship to s a i l c l o s e r to the wind. Speed was also increased by the c a r r y i n g of a much greater s a i l area. In 1492 the A t l a n t i c was crossed. A l l through t h i s period of expanding commerce the safety of vessels was more or le s s a matter of experience and good fortune. - 2 -A s a n examp le on J u l y 1 9 t h , 1 5 4 5 , t h e 120 f o o t , 700 t o n E n g l i s h b a t t l e s h i p Mary Rose s a n k i n P o r t s m o u t h h a r b o r a f t e r j u s t h o i s t i n g s a i l f o r b a t t l e a g a i n s t t h e i n v a d i n g F r e n c h [ 2 ] . The s u d d e n c a p s i z i n g and s i n k i n g o f t h e v e s s e l i s s t i l l v e i l e d i n c o n t r o v e r s y ( t h e F r e n c h N a v a l A u t h o r i t i e s c l a i m t h e y s a n k i t ) b u t i t i s known t h a t i t was i n a s e r i o u s b r e a c h o f s t a b i l i t y . A t t h e t i m e o f i t s s i n k i n g i t was 35 y e a r s o l d , o r i g i n a l l y b u i l t i n 1510 and named a f t e r K i n g H e n r y V I I I ' s s i s t e r M a r y T u d o r . B e c a u s e o f t h e wa r i t was b r o u g h t i n f o r r e f i t t i n g and rearmament w i t h t h e l a t e s t e q u i p m e n t . A t some p o i n t h e a v y b r o n z e g u n s , w h i c h r e p r e s e n t e d t h e l a t e s t i n m e t a l l u r g i c a l t e c h n o l o g y , were added -guns she h a d n o t b e e n o r i g i n a l l y d e s i g n e d t o c a r r y . I n a d d i t i o n she c a r r i e d 285 h e a v i l y a r m o r e d s o l d i e r s on d e c k , o v e r and above h e r r e g u l a r c r e w o f 415 men. T h i s r e f i t t i n g was c a l c u l a t e d t o add a n o t h e r 24 t o 25 t o n s t o Mary Rose's d i s p l a c e m e n t , a l l f a r above t h e w a t e r l i n e . A n o t h e r a d d i t i o n , h o i s t e d f r o m d e c k l e v e l t o a b o u t t e n f e e t i n t o t h e a i r a r o u n d t h e p e r i m e t e r o f t h e s h i p , was an a n t i - b o a r d i n g n e t . Ready f o r b a t t l e t h e s a i l s were h o i s t e d and t h e s a i l o r s w a i t e d f o r t h a t f i r s t g u s t o f w i n d t o c a r r y them i n t o b a t t l e . A s w e l l i n t h e w i n d f i l l e d t h e s a i l s and she s u r g e d f o r w a r d . S u d d e n l y , w i t h o u t w a r n i n g , t h e v e s s e l v e e r e d and w a t e r f l o o d e d i n t h r o u g h t h e open gun p o r t s . A s t h e s h o c k e d K i n g l o o k e d on t h e s h i p h e e l e d o v e r i n t o t h e w a t e r and c a p s i z e d , t o s i n k l i k e a s t o n e . A l l t h i s h a p p e n e d i n u n d e r a m i n u t e and o n l y 30 o f t h e e s t i m a t e d 700 c r e w members s u r v i v e d . - 3 -In the 1800's the advent of steam once again transformed the ships of the world. S t i l l powered by paddles, now i n the form of huge side mounted paddle wheels, they grew i n power and v e r s a t i l i t y . One of the f i r s t steamships, the Charlotte Dundas, b u i l t i n 1802, towed two 70-ton barges 19-j miles i n 6 hours along the Dalswinton Loch i n England against a headwind so strong no other v e s s e l dared s a i l i n i t . B r i t a i n followed the Americans into the b u i l d i n g of steam powered warships i n 1833. Steam was s t i l l considered inadequate, though, for long voyages u n t i l i n 1838 the Sirius crossed the A t l a n t i c i n less than 20 days, a record held only a few hours when i t was broken by the Great Western which made the same voyage i n 15 days. A f t e r the capsizing of the B r i t i s h warship Captain i n 1870, while on a routine mission [3], i t was decided that the dependence of the r e s t o r i n g moment on the angle of heel, not j u s t on i t s upright p o s i t i o n , as described by the r e l a t i o n s h i p ; B(^) - gAGM^ (1.001) where: g = a c c e l e r a t i o n due to g r a v i t y A = displacement GM «= metacentric height 4> = r o l l angle was important and should be considered. This marked the s t a r t i n g point f o r the p r e s c r i b i n g of minimum values f o r r i g h t i n g moments. - 4 -In h i s 1939 doctoral thesis Rahola made a proposal f o r the s t a b i l i t y requirements of small ships based on those of Benjamin (1913) and P i e r r o t t e t (1935). This proposal was developed through a survey of successful and unsuccessful ships of that time based on casualty reports. From t h i s he drew up the following conclusions [4]: (a) the values of the arms of s t a t i c a l s t a b i l i t y must be: i ) at l e a s t 0.14m at an angle of 20° and, i i ) at l e a s t 0.20m at an angle of 30°; (b) the " c r i t i c a l angle" of heel i s meant the angle of heel at which the curve of arms of s t a t i c a l s t a b i l i t y reaches i t s maximum value. These requirements are re f e r r e d to as the Rahola s t a b i l i t y c r i t e r i a . A recent i n v e s t i g a t i o n of Raholas work has shown that the sample s i z e used f o r the development of the c r i t e r i a was not s t a t i s t i c a l l y s i g n i f i c a n t . Nevertheless, t h i s c r i t e r i o n i s the basis f o r many of the nat i o n a l regulations or recommendations incl u d i n g the Intergovernmental Maritime consultative Organization (IMO) recommendations f o r small passenger ships, f i s h i n g vessels and, more recently, supply ships. During the early years of IMO (then known as IMCO) analysis of i n t a c t s t a b i l i t y casualty records f o r both cargo ships and f i s h i n g vessels were c a r r i e d out by delegations from countries such as Germany, Poland and France with proposals put f o r t h f o r - 5 -s t a b i l i t y criterion by Poland, USSR, Denmark, Germany, France, Sweden and others. For these i n i t i a l studies 7 parameters were chosen for investigation to find which should be used for establishing s t a b i l i t y guidelines. These parameters were: (i) [GM ] i n i t i a l metacentric height o ( i i ) [<f> ] angle of heel at maximum righting arm m ( i i i ) [<f> ] angle of vanishing s t a b i l i t y (iv) [GZ ] maximum righting arm max (v) [GZ 2 Q 0] righting arm at an angle of inclination of 20° (vi) [<£f ] angle of downflooding (vii) [<f> ] angle of heel for immersion of edge of upper deck Upon receipt of a l l the reports and recommendations four of the above parameters were chosen for further study by the various delegations at IMO: (i) [GZ ] maximum righting arm max ( i i ) ] angle of vanishing s t a b i l i t y ( i i i ) [<f> ] angle of heel at maximum righting arm m (iv) [GM ] i n i t i a l metacentric height o From the results of these studies a number of st a b i l i t y parameters were f i n a l l y selected and numerical values assigned to form the present day IMO recommended c r i t e r i a . IMO criterion as recommended for fishing vessels: - 6 -A. The area under the GZ curve up to an angle of heel of 30° must be greater than 0.055 meter-radians. B. The area under the GZ curve up to an angle of heel of 40°, or the angle of downflooding <j>^ i f less than 40°, must be greater than 0.09 meter-radians. C. The area under the GZ curve between 30° and 40° of heel, or between 30° and d> i f less than 40°, must be f greater than 0.03 meter-radians. D. The maximum r i g h t i n g arm beyond 30° of heel must be greater than 0.2 meters. E. The angle of heel where the r i g h t i n g arm i s a maximum must be greater than 30°. F. The i n i t i a l metacentric height, GM , must be o greater than 0.35 meters. In some nationa l regulations, the s o - c a l l e d weather c r i t e r i o n i s used, which includes the influence of wind induced heeling moments on the area under the s t i l l water r i g h t i n g lever curve. In add i t i o n a water-on-deck c r i t e r i o n has also been added to some c r i t e r i o n as small c r a f t capsizings have been a t t r i b u t e d to t h i s phenomenon. - 7 -S i t u a t i o n Cargo Vessels Fi s h i n g Vessels 1. Steady wind and wind gusts with severe r o l l i n g C a l c u l a t i o n proced-ure worked out 1983 General procedure given i n T.C. C o e f f i c i e n t s under consideration 2.Following waves - loss of stab, on c r e s t - broaching C a l c u l a t i o n proced-ure under study. C r i t e r i a proposal by GDR. No c a l c u l a t i o n proc-edure a v a i l a b l e -under study As for cargo vessels C r i t e r i a not yet proposed As for cargo vessels C r i t e r i a not yet proposed 3. Breaking waves from side No c a l c u l a t i o n proc-edure a v a i l a b l e -under study No c a l c u l a t i o n procedure a v a i l a b l e but under study. C r i t e r i a proposal by Norway (<£v> 80°) 4.Forces from f i s h i n g gear — C a l c u l a t i o n procedure a v a i l a b l e but not under study. C r i t e r i a proposal by U.S.S.R. 5.Water on deck No C a l c u l a t i o n proc-edure a v a i l a b l e -under study C a l c u l a t i o n procedure given i n p r i n c i p l e i n T.C - under study 6.Icing Under observation C a l c u l a t i o n procedure i n T.C. - under obser-v a t i o n 7.Flooding P r o b a b i l i s t i c concept recommended. Damage cont r o l plan concept worked out 1983 - under study. Not under study. Table I - IMO work on S t a b i l i t y f o r Small Crafts From Intact and Damaged S t a b i l i t y of Small Crafts with Emphasis on Design by Emil A a l l Dahle, and Gunnar Edvin N i s j a , U n i v e r s i t y of Trondheim, 1984. (T.C. = Torremolinos Convention) [5] The present trend i n IMO i s to supplement the minimum GZ requirements with fu n c t i o n a l requirements based on the operating - 8 -conditions expected during the vessels l i f e t i m e . A summary of the status of the IMO's "Sub-Committee on Stability, Load Lines and Fishing Vessel Safety" i s shown i n Table I. S t a b i l i t y c r i t e r i o n f o r the s t a b i l i t y of f i s h i n g vessels when subjected to breaking waves from the side i s s t i l l under study as i l l u s t r a t e d by Table I. Up to the present time the only a d d i t i o n a l c r i t e r i o n put into r e g u l a t i o n expressly to counteract the e f f e c t s of breaking wave capsizing i s to require a minimum angle f o r vanishing s t a b i l i t y of 80°. F i s h i n g vessels o f f e r a rather unique problem to the designer i n that i t w i l l be operated over a large range of displacement and weight d i s t r i b u t i o n s thus creating the added inconvenience of not being able to design for a c e r t a i n operating c o n d i t i o n as with most other c r a f t . Despite the best e f f o r t s of a large number of research and governing bodies there i s s t i l l a r e c u r r i n g i l l u s t r a t i o n of the inadequacies of the f i s h i n g f l e e t with regards to safety by the repeated accounts of ships l o s t at sea. Fis h i n g being one of the most dangerous occupations, surpassing even such notably hazardous occupations as coal mining. Because of these continuing losses, many occurring i n heavy weather, there i s a push to more accurately define the mechanisms involved i n a capsizing due to breaking waves taken on the beam. With t h i s i n mind a program for the i n v e s t i g a t i o n of f i s h i n g - 9 -v e s s e l dynamics was s t a r t e d at the U n i v e r s i t y of B r i t i s h Columbia Department of Mechanical Engineering. This program involves the dynamical response t e s t i n g of scale model f i s h i n g vessels i n a c o n t r o l l e d environment with an emphasis on determining unstable operating conditions. - 10 -2.0 MODEL DESCRIPTIONS Two fishing vessel designs were studied for this research. The f i r s t design was of a single chine fishing seiner designed for Cleaver and Walkingshaw of Vancouver by B.C. Research Ocean Engineering Center staff and represents the typical form of the vessel. The second design tested was of a fishing trawler designed by Peter S. Hatfield Ltd. of Vancouver. This design represents the latest design technology for this class of fishing vessel. The single chine design has not, as of the date of this thesis, been buil t and thus remains only a design consideration. The trawler, on the other hand, has been built and in now currently operating off the West Coast. Both of the models were manufactured of wood by F.M. Pattern Works of Vancouver according to the original lines drawings of the respective Naval Architecture firms. The models were of the hul l design only and thus excluded any bulwarks, deck fixtures or superstructure. To determine the size of the model required a manner of being able to scale relevant properties is required. The method of determining the scaling factors is through a non-dimensionalizing procedure called the Buckingham Pi Theorem. This theorem allows the selection of what appear to be a l l the relevant parameters and then applying the theorems principles to obtain non-dimensionalized sets of these parameters. A table of the resulting scaling parameters is shown in Table I I . - 11 -c l e a v e r & w a l k l n g e h a w J t d . n a v a l a r c h i t e c t * : 1 W I. V - 12 -- 13 -To make the table easier to understand the r e l a t i o n s shown use two basic r a t i o s determined from the non-dimensionalizing procedure, these are; A, the r a t i o of the ship length to the model length and c, the r a t i o of ship water density to model water density. TABLE II SCALING PARAMETERS Parameter F u l l Scale Model Length L L/A Density P p/c Time t t / A 1 / 2 Mass m m/cA3 V e l o c i t y V V/A 1 / 2 A c c e l e r a t i o n a a Force F F/cA 3 Moment M M/cA* Pressure P. p/cA Frequency w wA1'2 The s c a l i n g f o r length i s the same f o r a l l the other dimensions of the model, i e : r = i r - r - A ( 2 - 0 0 1 ) - 14 -4.5 RESTORING ARM CURVES SINGLE CHINE SEINER 216.4 TONS DISPLACEMENT 20 40 60 80 100 120 ANGLE OF HEEL (degrees) 140 Figure 3. Restoring Arm Curves for Single Chine Seiner 216.4 Tons Displacement - 15 -RESTORING ARM CURVES SINGLE CHINE SEINER 249.6 TONS DISPLACEMENT 20 40 60 80 100 120 ANGLE OF HEEL (degrees) 140 Figure 4. Restoring Arm Curves for Single Chine Seiner 249.6 Tons Displacement - 16 -2.1 S INGLE CHINE SEINER 2.1.1 F U L L SCALE SHIP DATA The f u l l s c a l e d i m e n s i o n s o f t h e s e i n e r a r e s u m m a r i z e d i n T a b l e I I I w h i l e a g e n e r a l a r r a n g e m e n t p l a n and t h e l i n e s d r a w i n g c a n be f o u n d i n F i g s . 4 and 5 r e s p e c t i v e l y . TABLE I I I SINGLE CHINE SEINER P R I N C I P L E DIMENSIONS LIGHT HEAVY L e n g t h O v e r a l l (LOA) 7 7 . 0 f t . 7 7 . 0 f t . L e n g t h B e t w e e n P e r p e n d i c u l a r s ( L ^ ) . . . . 6 9 . 9 f t . 6 9 . 9 f t . Beam (B) 2 3 . 0 f t . 2 3 . 0 f t . D e p t h (D) 1 5 . 0 f t . 1 5 . 0 f t . D r a f t (T) 9 . 5 f t . 1 0 . 5 f t . D i s p l a c e m e n t (A) 2 1 6 . 4 t o n s 2 4 9 . 6 t o n s B l o c k C o e f f i c i e n t (C ) 0 . 5 0 0 0 . 5 3 1 M i d s h i p S e c t i o n C o e f f i c i e n t (C ) 0 . 7 5 6 0 . 7 7 5 m W a t e r p l a n e A r e a C o e f f i c i e n t (C ) 0 . 8 5 0 0 . 8 6 2 wp KM 1 3 . 0 7 8 f t . 1 2 . 8 1 8 f t . The m e t a c e n t r i c h e i g h t s u s e d i n t h e t e s t i n g were d e t e r m i n e d f r o m a r e v i e w o f e x i s t i n g v e s s e l s o f s i m i l a r d e s i g n and d i s p l a c e m e n t . From t h i s s u r v e y i t was f o u n d t h a t m e t a c e n t r i c h e i g h t s o f f r o m 1% t o 10% o f t h e beam v a l u e w o u l d be a p p r o p r i a t e . - 17 -Figure 6. West Coast Trawler General Arrangement I w*m D I C K Figure 7. West Coast Trawler General Arrangement II The a c t u a l v a l u e s u s e d a r e shown i n T a b l e IV and t h e r i g h t i n g arm c u r v e s f o r t h e two d i s p l a c e m e n t s t e s t e d a r e shown i n F i g s . 6 and 7 . TABLE I V SINGLE CHINE SEINER METACENTRIC HEIGHT TABLE LIGHT HEAVY % B GM # 1 0. .2557 f t . 0 . .2557 f t . 1. .11 GM # 2 N / A 0. .5113 f t . 2, .22 GM # 3 1. .1516 f t . 1. .1516 f t . 5. .00 GM # 4 2 . .1331 f t . 2 . ,1331 f t . 9. .27 2 . 1 . 2 SCALE MODEL DATA The mode l o f t h e s e i n e r was b u i l t on a s c a l e o f 1 3 : 1 . The d i m e n s i o n s o f t h e mode l a r e g i v e n b e l o w i n T a b l e V . The mode l was b u i l t w i t h o u t b u l w a r k s o r s u p e r s t r u c t u r e . TABLE V SINGLE CHINE SEINER SHIP MODEL CHARACTERISTICS L i g h t Heavy L e n g t h O v e r a l l (LOA) 5 . 9 2 3 f t . 5 . 9 2 3 f t . L e n g t h B e t w e e n P e r p e n d i c u l a r s (L ) 5 . 3 8 1 f t . 5 . 3 8 1 f t . bp Beam (B) 1 .769 f t . 1 .769 f t . D e p t h (D) 1 .154 f t . 1 .154 f t . - 21 -D r a f t (T) 0 . 7 3 0 f t . 0 . 8 0 8 f t . D i s p l a c e m e n t (A) 2 2 0 . 6 l b s . 2 5 4 . 5 l b s B l o c k C o e f f i c i e n t (C ) b 0 . 5 0 0 0 . 5 3 1 M i d s h i p S e c t i o n C o e f f i c i e n t (C ) m 0 . 7 5 6 0 . 7 7 5 W a t e r p l a n e C o e f f i c i e n t (C ) wp 0 . 8 5 0 0 . 8 6 2 KM 1 .006 f t . 0 . 9 8 6 f t . GM # 1 0 . 2 3 6 " o r (1 .11% B) GM # 2 0 . 4 7 2 " o r (2 .22% B) GM # 3 1 . 0 6 3 " o r (5 .00% B) GM # 4 1 . 9 6 9 " o r (9 .27% B) 2.2 WEST COAST TRAWLER  2.2.1 FULL SCALE SHIP DATA The t r a w l e r f o r m t e s t e d was t a k e n f r o m l i n e s d r a w i n g s o f a n e x i s t i n g f i s h i n g v e s s e l . I t was t h e r e f o r e p o s s i b l e t o o b t a i n t h e a c t u a l f u l l s c a l e o p e r a t i n g c o n f i g u r a t i o n s f r o m t h e i n c l i n i n g e x p e r i m e n t s done as p e r C a n a d i a n C o a s t G u a r d S a f e t y r e g u l a t i o n s . The s t a b i l i t y b o o k l e t p r e p a r e d f r o m t h e e x p e r i m e n t s i s shown i n A p p e n d i x C . A b r i e f s y n o p s i s o f t h e p e r t i n e n t d a t a c a n be f o u n d i n T a b l e V I . - 22 -4.5 3.5H 3H 2 CC 2.5 < i 2 o co LU tr 1.5 H 0.5 H RESTORING ARM CURVE WEST COAST TRAWLER 328.9 TONS DISPLACEMENT Legend A GM = 3.4/ 54 f t . 20 40 60 80 100 ANGLE OF HEEL (degrees) 120 140 I Figure 8. Restoring Arm Curve for West Coast Trawler 328.9 Tons Displacement - 23 -RESTORING ARM CURVES WEST COAST TRAWLER 437.64 TONS DISPLACEMENT 40 60 80 100 ANGLE OF HEEL (degrees) 140 Figure 9. Restoring Arm Curves for West Coast Trawler 437.64 Tons Displacement - 24 -4.5 < (D Z tr o H CO UJ 3.5 3 1.5-0.5-RESTORING ARM CURVES WEST COAST TRAWLER 551.51 TONS DISPLACEMENT Legend A GM = 4.1468 ft. X GM = /.796 /t. • CA/ = 0.2953Jt. * * * \ \ \ \ \ \ \ \ \ \ \ / 4 / / \ \ \ \ \ \ i » \ \ \ I \ D 20 40 60 80 100 120 140 ANGLE OF HEEL (degrees) Figure 10. Restoring Arm Curves for West Coast Trawler 551.51 Tons Displacement - 25 -TABLE V I WEST COAST TRAWLER P R I N C I P L E DIMENSIONS LIGHT MEDIUM HEAVY L e n g t h O v e r a l l (LOA) 1 0 7 . 0 f t . 1 0 7 . 0 f t . 1 0 7 . 0 f t . L e n g t h B e t w e e n P e r p e n d i c u l a r s ( L ) 9 9 . 7 5 f t . 9 9 . 7 5 f t . 9 9 . 7 5 f t . Beam (B) 2 9 . 2 0 f t . 2 9 . 2 0 f t . 2 9 . 2 0 f t . D e p t h (D) 2 8 . 5 0 f t . 2 8 . 5 0 f t . 2 8 . 5 0 f t . D r a f t (T) 9 . 6 0 f t . 1 1 . 3 2 f t . 1 3 . 0 1 f t . D i s p l a c e m e n t (A) 3 2 8 . 9 0 t o n s 4 3 7 . 6 4 t o n s 5 5 1 . 5 1 t o n s B l o c k C o e f f i c i e n t ( C . ) . . . 0 . 3 3 7 9 0 . 3 8 2 3 0 . 4 2 4 0 D M i d s h i p S e c t i o n C o e f f i c i e n t (C ) 0 . 5 9 7 6 0 . 6 3 7 4 0 . 6 7 3 0 m W a t e r p l a n e A r e a C o e f f i c i e n t (C ) 0 . 7 4 3 3 0 . 7 8 5 1 0 . 8 1 2 0 wp KM 1 6 . 1 8 3 f t . 1 5 . 7 6 3 f t . 1 5 . 5 0 0 f t . The m e t a c e n t r i c h e i g h t s were n o t d e t e r m i n e d as a p e r c e n t a g e o f t h e beam b u t were t a k e n f r o m t h e a c t u a l m e a s u r e d v a l u e s o b t a i n e d d u r i n g t h e i n c l i n i n g e x p e r i m e n t . F o r c o m p a r i s o n p u r p o s e s t h e m e t a c e n t r i c h e i g h t s shown i n T a b l e V I I a r e a l s o g i v e n as t h e p e r c e n t a g e o f t h e beam. I n a d d i t i o n t h e r i g h t i n g arm c u r v e s c a l c u l a t e d f o r t h e c o n f i g u r a t i o n s t e s t e d a r e shown i n F i g s . 1 1 , 12 and 1 3 . - 26 -TABLE V I I WEST COAST TRAWLER METACENTRIC HEIGHTS LIGHT MEDIUM HEAVY % B GM # 1 N / A 0 . 2 9 5 3 f t . 0 . 2 9 5 3 f t . 1 .01 GM # 2 N / A 1 .7960 f t . 1 .7960 f t . 6 . 1 5 GM # 3 3 . 4 1 5 4 * f t . N / A N / A 1 1 . 7 0 GM # 4 N /A 3 . 8 2 3 8 ^ f t . N / A 1 3 . 1 0 GM # 5 N /A N / A 4 . 1 4 6 8 * f t . 1 4 . 2 0 d e s i g n GM v a l u e s . GM # 1 was c h o s e n as a n a r b i t r a r y w o r s t c a s e s c e n a r i o . T h i s GM r e p r e s e n t e d t h e s m a l l e s t GM v a l u e e x p e c t e d i n o p e r a t i o n u n d e r t h e most a d v e r s e l o a d i n g c o n d i t i o n s . GM # 2 i s t h e minimum a l l o w a b l e d e s i g n GM as d e f i n e d b y t h e I n t e r g o v e r n m e n t a l M a r i t i m e C o n s u l t a t i v e O r g a n i z a t i o n s a f e t y r e g u l a t i o n s r e g a r d i n g f i s h i n g v e s s e l s [ 6 ] . The minimum v a l u e c a n be f o u n d t h r o u g h t h e r e l a t i o n s h i p , GM = 0.53 + (2 x B x (GM + GM )) (2.002) MIN 1 2 GM - 0.075 - 0.37 x + 0.82 x [ ? | ] 2 (2.003) GM = -0.014 x fjh (2.004) where B = maximum beam ( m e t e r s ) FB —: e f f e c t i v e f r e e b o a r d ( m e t e r s ) T = d r a f t o f v e s s e l ( m e t e r s ) - 27 -The r e s u l t s are expressed i n meters. 2.2.2 SCALE MODEL DATA The model of the trawler was b u i l t to a scale of 15:1. Following the configurations set above the following dimensions for the model were derived. TABLE VIII WEST COAST TRAWLER MODEL PARAMETERS Light Medium Heavy Length O v e r a l l (LOA) 7.1 f t . 7.1 : f t . 7.1 f t . Length Between Perpendiculars (L ) bp 6.65 f t . 6.65 f t . 6.65 f t . Beam (B) 1.95 f t . 1.95 f t . 1.95 f t . Depth (D) 1.90 f t . 1.90 f t . 1.90 f t . Draft (T) 0.64 f t . 0.75 f t . 0.87 f t . Displacement (A) ( i n tons) 221.4 294. < 6 371.0 Block C o e f f i c i e n t (C ) b 0.3379 0.3823 0.4240 Midship Section C o e f f i c i e n t (C ) m 0.5976 0.6374 0.6730 Waterplane Area C o e f f i c i e n t (C ) wp 0.7433 0.7851 0.8120 KM 1.08 f t . 1.05 f t . 1.03 f t . GM # 1 N/A 0.02 f t . 0.02 f t . GM # 2 N/A 0.12 f t . 0.12 f t . GM # 3 0.23 f t . N/A N/A GM # 4 N/A 0.25 f t . N/A GM # 5 N/A N/A 0.28 f t . - 28 -3 . 0 DATA ACQUISITION To accurately monitor and record the motions of the models during the t e s t i n g program a suitable system had to be developed. Over the year and a h a l f that was required to t e s t the two models the type of system used changed dramatically. The f i r s t model tested, the sing l e chine seiner, had a f u l l y s e l f contained system on board. That i s , a l l the equipment from sensors to data storage were a l l contained within the v e s s e l . With the second model the e l e c t r o n i c s had undergone a complete reworking with the purchase of a remote data telemetry system which allowed the removal of a large part of the on-board equipment to shore. Each of the systems used w i l l be described separately but the emphasis w i l l be on the second system as i t was assembled and developed under the supervision of the author. The e a r l i e r system, used i n the sing l e chine model, was already constructed and operational when the model was received and therefore was used without a l t e r a t i o n . A more complete d e s c r i p t i o n of the e a r l i e r e l e c t r o n i c s system can be found i n a thesis being w r i t t e n by Alejandro A l l i e v i of the Department of Mechanical Engineering, U n i v e r s i t y of B r i t i s h Columbia, e n t i t l e d "Experimental and Numerical Analysis of a Fishing Vessel's Motions and Stability in a Longitudinal Seaway". 3 . 1 SINGLE CHINE SEINER Motions necessary to define the f u l l range of ship - 29 -displacements included r o l l , p i t c h , heave, sway, surge and yaw. Each of these displacements or rotations were measured by appropriate mechanisms and the information relayed to an a n a l o g - t o - d i g i t a l converter which sampled the data signals and fed the b i t stream into the s e r i a l port of an IBM PCjr home computer. This binary information was c o l l e c t e d i n a memory buff e r u n t i l a preset l e v e l was reached and then t r a n s f e r r e d as a block to an analog tape recorder for subsequent r e t r i e v a l and a n a l y s i s . A schematic of the e l e c t r o n i c s can be found i n F i g . 51 showing the major components and t h e i r connections. Following i s b r i e f d e s c r i p t i o n of the components involved i n the system. 3.1.1 AUTO PILOT To measure the yaw of the model an autopilot/compass system developed by Wagner Engineering of North Vancouver was i n s t a l l e d . This system i s i d e n t i c a l to those found on many l e i s u r e c r a f t throughout North America. The system represents the l a t e s t i n technology f o r the company and has high frequency response c h a r a c t e r i s t i c s i d e a l f o r use i n model t e s t i n g . Power required for the operation of the device was 12 VDC and t h i s was supplied by the on-board b a t t e r i e s of the model. 3.1.2 ACCELEROMETERS To measure the displacements i n the heave and sway d i r e c t i o n s the model was instrumented with l i n e a r accelerometers oriented - 30 -a l o n g t h e h e a v e and sway a x i s o f t h e m o d e l . The a c c e l e r o m e t e r s were S c h a e v i t z ± 2 . 0 g . s e r v o t y p e v e r s i o n s w i t h a r e q u i r e m e n t o f ± 1 3 . 0 V o l t s D . C . e x c i t a t i o n . The e x c i t a t i o n was s u p p l i e d b y two s e t s o f 12 V . D . C . b a t t e r i e s e a c h w i r e d i n s e r i e s w i t h t h e i r own 1 .5 V . D . C . s u p p l e m e n t a l s u p p l y t o p r o v i d e a p p r o x i m a t e l y ± 1 3 . 0 V . D . C . . 3 . 1 . 3 VERTICAL GYRO The m o t i o n s o f t h e mode l i n r o t a t i o n a b o u t two o f i t s p r i n c i p l e a x i s were o f p r i m a r y i m p o r t a n c e i n t h i s r e s e a r c h w o r k . To p r o v i d e d i r e c t measurement o f t h i s r o t a t i o n a Humphry V G 2 4 - 0 8 2 5 - 1 d u a l a x i s v e r t i c a l g y r o was i n s t a l l e d t o measu re b o t h r o l l and p i t c h . O u t p u t o f t h e two a x i s was p r o v i d e d b y p o t e n t i o m e t e r s mounted on t h e s h a f t s o f t h e i n t e r n a l cage m e c h a n i s m . E x c i t a t i o n was p r o v i d e d t o e a c h o f t h e s e p o t e n t i o m e t e r s b y i n d e p e n d e n t 9 V . D . C . b a t t e r i e s . 3 . 1 . 4 ANALOG TO D IG ITAL CONVERTER To t r a n s f o r m t h e a n a l o g s i g n a l s p r o d u c e d b y t h e v a r i o u s s e n s o r s c o r r e s p o n d i n g t o t h e a s s o c i a t e d m e a s u r e d q u a n t i t i e s i t was n e c e s s a r y t o i n s t a l l a d e v i c e c a p a b l e o f c o n v e r t i n g t h e s e v a l u e s . The u n i t u s e d was an ADC-1 w h i c h i s c a p a b l e o f s a m p l i n g a t a r a t e o f 70 s a m p l e s p e r s e c o n d . The c h a n n e l s a r e s a m p l e d c o n c u r r e n t l y and t h e n f e d i n t o t h e s e r i a l p o r t o f t h e P C j r , m i c r o - c o m p u t e r i n s e r i e s . Power f o r t h e u n i t was s u p p l i e d b y t h e 12 VDC b a t t e r y on b o a r d . - 31 -I n a d d i t i o n t o r e c e i v i n g d a t a t h e u n i t was a l s o c a p a b l e o f c o n v e r t i n g d i g i t a l v a l u e s r e a d f r o m t h e s e r i a l p o r t and c o n v e r t i n g t h e s e i n t o a n a l o g v o l t a g e s . T h i s was u s e d t o power t h e L.E.D. d i s p l a y on b o a r d t h e m o d e l . 3.1.5 L IGHT EMITTING DIODE DISPLAY To be a b l e t o c o n v e y a t a l l t i m e s t h e s t a t u s o f t h e e l e c t r o n i c s s y s t e m a b o a r d t h e mode l i t was n e c e s s a r y f o r some t y p e o f d i s p l a y . B e c a u s e t h e r e was no p o s s i b l e method o f u s i n g a m o n i t o r t o d i s p l a y t h e compu te r s t a t u s a s e t o f l i g h t e m i t t i n g d i o d e s ( L . E . D . ' s ) was i n s t a l l e d . The l i g h t s were i l l u m i n a t e d a c c o r d i n g t o t h e s t a t u s b e i n g i n d i c a t e d . The s t a t u s v a l u e s w e r e : i ) s y s t e m r e a d y t o r e c o r d , i i ) s y s t e m r e c o r d i n g , i i i ) s y s t e m w r i t i n g d a t a t o t a p e and i v ) s y s t e m r e s e t t i n g . One f u r t h e r c o n d i t i o n was p o r t r a y e d c o i n c i d e n t a l l y , t h i s c o n d i t i o n was o f e l e c t r i c a l m a l f u n c t i o n c a u s e d b y i n s u f f i c i e n t e l e c t r i c a l power and was i n d i c a t e d b y any number o f l i g h t s b e i n g l i t i n an a r b i t r a r y p a t t e r n . 3.1.6 IBM P C j r . MICRO-COMPUTER To a c t as c e n t r a l c o n t r o l t o t h e e n t i r e e l e c t r i c a l d a t a a c q u i s i t i o n s y s t e m an IBM P c j r m i c r o - c o m p u t e r was i n s t a l l e d . T h i s c o m p u t e r was c h o s e n b e c a u s e o f i t s compac t s i z e and r e l a t i v e l y i n e x p e n s i v e c o s t p r o p o r t i o n a l t o i t s c o m p u t i n g p o w e r , b e c a u s e i t was c a p a b l e o f b e i n g c o n t r o l l e d w i t h a w i r e l e s s i n f r a r e d l i n k - 32 -k e y b o a r d and t h i r d l y , b e c a u s e i t was c o m p a t i b l e w i t h s t a n d a r d IBM d e s k t o p c o m p u t e r s a l l o w i n g us t o d e m u l t i p l e x t h e c a s s e t t e d a t a e a s i l y a n d c o n v e n i e n t l y . B e c a u s e t h e compu te r was o r i g i n a l l y d e s i g n e d t o o p e r a t e on AC power t h e i n t e r n a l power t r a n s f o r m e r o f t h e u n i t h a d t o be m o d i f i e d s u c h t h a t i t c o u l d f u n c t i o n w i t h a 24 VDC power s u p p l y . B e c a u s e t h e i n t e r n a l c i r c u i t r y r e q u i r e d o n l y 12 VDC and 5 VDC s u p p l i e s t h i s p o s e d no g r e a t p r o b l e m . 3.2 WEST COAST TRAWLER E x p e r i e n c e w i t h t h e s i n g l e c h i n e s e i n e r , as w e l l as l i s t e n i n g t o r e p o r t s o f e a r l i e r a t t e m p t s a t d a t a c o l l e c t i o n w i t h p r e v i o u s m o d e l s i n t h e d e p a r t m e n t i n d i c a t e d t h a t a n u p g r a d i n g o f t h e e q u i p m e n t u s e d i n t h e s e n s i n g , c o l l e c t i n g and s t o r i n g o f t h e d a t a was i n o r d e r . I t was t h u s d e c i d e d t h a t , s t a r t i n g w i t h t h e t r a w l e r m o d e l , a new e l e c t r o n i c s s y s t e m w o u l d be d e v e l o p e d . W i t h t h i s i n m i n d a s t u d y was made o f t h e i m p o r t a n t a s p e c t s o f t h e t e s t i n g p r o g r a m and how t h e y may a f f e c t t h e t y p e o f s y s t e m we w o u l d r e q u i r e . The m a j o r p o i n t p o i n t o f c o n s i d e r a t i o n was a p l a n n e d s e t o f e x p e r i m e n t s t o be done o u t d o o r s i n f r e e r u n n i n g t r i a l s . B e c a u s e o f t h i s no d i r e c t l i n k b e t w e e n t h e mode l and any o t h e r u n i t was a c c e p t a b l e as u m b i l i c a l c o r d s , b e s i d e s b e i n g awkward a n d cumbersome a l s o a d v e r s e l y a f f e c t e d t h e t r u e d y n a m i c a l r e s p o n s e o f t h e v e s s e l . The c o r d a c t i n g as b o t h e x t r a mass and a damper on t h e t r u e m o t i o n s o f t h e mode l due t o d r a g and i n e r t i a . - 33 -Another f a c t o r found to be very important was the matter of weight. In previous t e s t s , i n c l u d i n g the si n g l e chine seiner, i t was found to be impossible to i n s t a l l a l l the required b a t t e r i e s , motors, servos, sensors, converters and recorders and s t i l l r e t a i n a displacement le s s than the design l i g h t ship condition. In p a r a l l e l to t h i s was the problem of space, with a l l the equipment required to be c a r r i e d on board space became a premium and optimum placement of e l e c t r o n i c s could not always be accommodated. With t h i s i n mind i t was decided that as much e l e c t r o n i c s as possible was to be l e f t on shore. Free running tests required external c o n t r o l of the model and thus, j u s t as i n e a r l i e r configurations, a remote c o n t r o l system using components found i n hobbyist applications was i n s t a l l e d to c o n t r o l p r o p e l l e r speed and d i r e c t i o n as well as to c o n t r o l the rudder angle. A l l controls were b u i l t as proportional controls with a high degree of r e s o l u t i o n . To power the v e s s e l a 24 VDC high torque e l e c t r i c motor was i n s t a l l e d running through a 5:1 reduction gearbox. Voltage to the motor was supplied by two 12 VDC b a t t e r i e s through a regulator connected to the radio c o n t r o l receiver. The r e c e i v e r was powered i n turn by i t s own 6 VDC rechargeable battery supply. Powering of the v e s s e l now decided, the next step was to allow measurement of the appropriate v e s s e l displacements. I n s t a l l a t i o n of a v e r t i c a l axis gyro, compass and l i n e a r accelerometers was next. E x c i t a t i o n was required for these sensors 34 -and thus a means of reducing the number and v a r i e t y of b a t t e r i e s was searched f o r . In the end a s i g n a l conditioner b u i l t by Terrascience of Vancouver was selected. The s i g n a l conditioner played many r o l e s i n the v e s s e l . I t required a s i n g l e power source providing anywhere from 10 to 40 VDC and can supply from eight d i f f e r e n t channels e i t h e r v a r i a b l e (0 to 10 VDC) or f i x e d (±13 VDC) e x c i t a t i o n s . For the accelerometers f i x e d ± 13 VDC e x c i t a t i o n were required and thus the f i x e d output was selected which i s f a c t o r y preset at exactly ±13 VDC. For the compass/autopilot a supply i n the range of 12 VDC was required. This was beyond the scope of the s i g n a l conditioner but was equal to the input voltage to the conditioner so the supply was derived from the terminal s t r i p supplying voltages to the i n t e r n a l e l e c t r o n i c s . Also along the same l i n e s was the v e r t i c a l gyro. This piece of equipment required 28 VDC to operate but was proven to work with reduced voltages without appreciable degradation i n q u a l i t y . Since the motor powering the model required 24 VDC there was already a good source a v a i l a b l e . Tapping into the terminal s t r i p we were able to provide s u f f i c i e n t voltage f o r the gyros operation. This reduced to two the number of b a t t e r i e s required to operate the model. In contrast the s i n g l e chine seiner required 10 b a t t e r i e s ranging i n s i z e from 1.5 VDC to 12 VDC. With the reduction i n the number of b a t t e r i e s recharging the system was a simple operation r e q u i r i n g only the i s o l a t i o n of the b a t t e r i e s from the e l e c t r o n i c s , a matter of throwing two surface mounted switches, and connecting the charger jumper wires i n - 35 -parallel to the two batteries. Other sensors mounted i n the model included a rudder angle sensor installed for later testing in following seas. The rudder angle was measured by a potentiometer mounted above and mechanically connected to the rudder shaft. Excitation for the potentiometer was supplied by the signal conditioner. Having installed a l l the sensing equipment a means of collecting and storing the data was s t i l l required. The signal conditioner acted as a main clearing centre for a l l the shipboard data. Each sensor was assigned a channel in the conditioner which each contained a circ u i t for f i l t e r i n g and amplifying the signal. Low pass f i l t e r s were installed to eliminate any noise picked up by the wiring from sources such as electric motors or fluorescent lighting. Gains were selected such that each channel would provide a ±10 VDC f u l l scale output. This made a l l the data channels uniform and easier to handle. To keep the amount of electronics to a minimum i t was decided that this was the maximum we wanted to carry on board the model, save one. To get the data from the model to shore some form of transmission was required. After a market search a telemetry system was found that seemed to f i t the b i l l . This system, produced by Sigma Data of Surrey, B.C., allowed the simultaneous transmission of up to eight channels from a remote source to a receiver up to three miles away. - 36 -The t e l e m e t r y s y s t e m r e q u i r e d o n l y t h a t a t r a n s m i t t e r and a n t e n n a be p l a c e d i n t h e m o d e l . No o t h e r e l e c t r o n i c s was r e q u i r e d . To p r o v i d e t h e ±5 VDC i n p u t t h e t e l e m e t r y s y s t e m was d e s i g n e d t o accommodate t h e o u t p u t o f t h e s i g n a l c o n d i t i o n e r was s t e p p e d down t h r o u g h t h e u s e o f a v o l t a g e d i v i d e r . The s i g n a l s were a l l f e d i n t o t h e t e l e m e t r y s y s t e m t r a n s m i t t e r w h i c h a s s i g n e d t o e a c h c h a n n e l a u n i q u e f r e q u e n c y i n t h e a u d i o b a n d . The a m p l i t u d e o f e a c h o f t h e s e f r e q u e n c i e s was m o d u l a t e d i n p r o p o r t i o n t o t h e v o l t a g e o f t h e i n p u t s i g n a l . A +5 VDC o f f s e t was added t o a l l t h e i n p u t s i g n a l s so t h a t t h e y r e a d f r o m 0 t o 10 VDC t o f a c i l i t a t e t h i s c o n v e r s i o n . Once t h e c o n v e r s i o n was c o m p l e t e t h e a u d i o s i g n a l s were summed and a t t a c h e d t o a UHF c a r r i e r f r e q u e n c y p r o v i d e d b y t h e UHF r a d i o t r a n s m i t t e r b u i l t i n t o t h e s y s t e m . T h i s s i g n a l was t h e n f e d t o a n i n t e r n a l g r o u n d p l a n e o m n i - d i r e c t i o n a l a n t e n n a c a p a b l e o f b r o a d c a s t i n g f r o m n e a r l y any o r i e n t a t i o n m a k i n g i t s u i t a b l e f o r a mode l w h i c h may, a t t i m e s , be r e q u i r e d t o b r o a d c a s t f r o m a n g l e s o f r o l l e x c e e d i n g 90 d e g r e e s ; o r t o t a l l y i n v e r t e d . Power f o r t h e t r a n s m i t t e r was s u p p l i e d b y one o f t h e s i n g l e 12 VDC l e a d a c i d b a t t e r i e s . A more c o m p l e t e d e s c r i p t i o n o f t h e e l e c t r o n i c s , i n c l u d i n g s c h e m a t i c s and s p e c i f i c a t i o n s c a n be f o u n d i n A p p e n d i x A . - 37 -4.0 TESTING 4.1 TEST FACILITIES To allow the t e s t i n g of the model i n a known repeatable wave environment a t e s t basin was required. The Ocean Engineering Center of B.C. Research provided access to the towing tank at t h e i r f a c i l i t y f o r the several months required f o r the s t a b i l i t y t e s t i n g . The towing tank i n the Ocean Engineering Center i s 220 feet i n length, 12 fee t i n width and 8 feet i n depth. I t i s equipped with a programmable h y d r a u l i c a l l y operated wavemaker s i t u a t e d at one end of the tank and a preparation tank at the other. A movable beach can be r a i s e d to block the towing tank t e s t s e c t i o n from the preparation tank. A schematic of the t e s t i n g f a c i l i t i e s i s shown i n F i g . 11. 4.2 TESTING SEQUENCE A large amount of data was created during the t e s t i n g program. This data gathering can be divided into three main groups or sections: s t i l l water response, regular seaway response and breaking wave response. This section w i l l present the methods used to obtain the data. 4.2.1 CALIBRATION - 38 -JANUARY 9, 1986 UNIVERSITY OF BRITISH COLUMBIA TEST FACILITIES BEAM SEAS ROLL RESPONSE DRAWN BY" GERRY RDHLING To be able to accurately measure the response of the models the instruments on the model had to c a l i b r a t e d so that the motions of the model would be c o r r e c t l y represented. To do t h i s a c a l i b r a t i o n r i g was devised. This r i g , i l l u s t r a t e d i n Figure 12, allows the model, outside of the tank, to be rotated to any selected angle and the voltages output by the various sensors recorded. B r i e f l y described here w i l l be how each sensor was c a l i b r a t e d f o r i t s respective sense. 4.2.1.1 ROLL AND PITCH ANGLES The model was placed on the c a l i b r a t i o n r i g such that i t was constrained to rotate only about an axis perpendicular to the centerplane of the model f o r r o l l and p a r a l l e l to the centerplane for p i t c h . The instrumentation was then turned on and the equipment allowed to reach operating speed and temperature. Once the equipment was ready the boat was placed with the design waterline p a r a l l e l to the h o r i z o n t a l . The voltage output by the gyroscope was measured and the o f f s e t i n the Signal Conditioner adjusted such that the voltage received and displayed by the shore u n i t was zero. This value was then noted f o r zero degrees r o l l or p i t c h . The model was then rotated 10 degrees i n the clockwise d i r e c t i o n and f i x e d . A reading was made of the voltage output by the shore u n i t and noted. This was repeated up to about 40 degrees of r o l l or p i t c h (the l i m i t s of the r i g with a 300 pound model attached) and then repeated f o r the counter-clockwise d i r e c t i o n . A - 40 -JANUARY 10, 1986 UNIVERSITY DF BRITISH COLUMBIA CALIBRATION RIG BREAKING WAVE RESPONSE TESTS DRAWN BY* GERRY ROHLING f u l l c a l i b r a t i o n f i l e was then completed. In these cases the r e s u l t s were l i n e a r hence a s t r a i g h t l i n e was f i t t e d to the data and the slope and intercept determined. 4.2.1.2 YAW The model was placed on a large table equipped with wheels and s i t u a t e d away from any strong magnetic sources. The equipment was turned on and allowed to reach operating temperature. The model was then rotated so that the bow of the model pointed due north according to the on-board compass. The a u t o p i l o t was then zeroed at true north. The output of the aut o p i l o t to the shore u n i t should read zero at t h i s point and the s i g n a l conditioner o f f s e t was adjusted to produce the zero reading. With the zero point noted the model was rotated 15 degrees and the output of the a u t o - p i l o t noted. The model was then rotated another 15 degrees and again the output noted. This was repeated every 15 degrees u n t i l the model had completed a yaw of 90 degrees. The model was then brought back to true north, the zero checked f o r r e p e a t a b i l i t y and then the same procedure was done i n the other d i r e c t i o n to give a c a l i b r a t i o n range of ± 90°. The c a l i b r a t i o n was l i n e a r within t h i s range so a slope-intercept was determined. 4.2.1.3 HEAVE AND SWAY ACCELEROMETERS The procedure f o r heave and sway c a l i b r a t i o n follows very - 42 -c l o s e l y the procedure f o r r o l l . Instead of noting j u s t the r o l l angle and then taking the ac c e l e r a t i o n readings the component of the g r a v i t a t i o n a l vector acting upon the s e n s i t i v e axis of the accelerometers was recorded and the c a l i b r a t i o n done against t h i s a c c e l e r a t i o n . These values were also l i n e a r and provided a slope and intercept. 4.2.1.4 WAVE HEIGHT The wave height was measured using a two-wire resistance wave probe suspended from a footbridge spanning the towing tank j u s t "upstream" from the model's l o c a t i o n i n the tank. (See F i g . 11 [Test F a c i l i t i e s ] ) The tank was allowed to s e t t l e such that the surface was smooth and then the wave probe was adjusted such that i t s center p o s i t i o n was at the waters surface. The voltage output was recorded. The wave probe was then r a i s e d i n steps of one inch ( s i g n i f y i n g a drop i n the water surface) and the output voltage at each step recorded up to 5 inches. The probe was then brought back to zero, the voltage output re-checked, and then the procedure was repeated with the wave probe being immersed i n the water i n one inch steps. The output was found to be l i n e a r so a slope and interc e p t was determined. 4.2.1.5 ZERO SETTINGS IN WATER Despite having zeroed every instrument on the c a l i b r a t i o n r i g there i s s t i l l the p o s s i b i l i t y of instrument d r i f t due to temperature, battery voltage and l o c a l geo-magnetic f l u c t u a t i o n s . - 43 -Because of this possible change in instrument zero before the start of each series of test runs the model was placed in the tank, instruments running, and allowed to settle to the desired rest position. Once the model was motionless the data acquisition was started to record a f i l e of the voltage values output by the instruments. This f i l e was then saved along with the data f i l e s collected in that set and used to remove any residual DC offset. 4.2.2 ROLL DECAY TESTS To gather data on the damping of the hull form, the natural frequencies of the various configurations tested and the in-water r o l l moments of inertia a r o l l decay test was deemed necessary. While the model was held at some arbitrary angle the water surface in the tank was allowed to settle down such that there were no perceptible waves present. When the surface had become sufficiently calm the model was released and allowed to oscillate unhindered. Upon release of the model data collection was initiated. In addition to the electronic data collection a stopwatch was used to measure the time required for 10 f u l l cycles of o s c i l l a t i o n to occur. A video record of the r o l l decay test was made for future reference. A quick calculation was then made to determine the approximate value of the natural frequency through the relation, - 44 -10 (4.001) T n 10 where: T time f o r 10 o s c i l l a t i o n s 10 and to = natural frequency (Hz . ) This process was repeated three times and the average value of the natural frequency measured was recorded f o r use i n the regular seas segment of the t e s t as the center value of the frequency range to be tested. Each r o l l decay t e s t was repeated three times, each one s t a r t i n g at a larger i n i t i a l r o l l angle than the one before. I t was attempted to have the l a s t r o l l decay measured to s t a r t at the vanishing angle of s t a b i l i t y . Care had to be taken during t h i s f i n a l t e s t as the model was j u s t as l i k e l y to i n i t i a t e r o l l i n the caps i z i n g d i r e c t i o n s as the r e s t o r i n g d i r e c t i o n . Occasionally the motion had to be arrested and r e s t a r t e d i f the model showed a tendency toward capsizing. 4 . 2 . 3 REGULAR SEAWAY This s e c t i o n of the t e s t matrix allowed the measurement of the response of the ves s e l to a r e g u l a r l y repeating wave f o r c i n g function of a pre-determined frequency and amplitude. This t e s t i n g of the response i n a very narrow-banded spectrum allowed the i n d i v i d u a l measurement of points on the response amplitude operator curves. From the r o l l decay tests conducted e a r l i e r i t - 45 -was known what the r o l l n a tural frequency was and thus the t e s t frequencies chosen were arranged such that the natural frequency of the configuration being tested would f a l l halfway between the lowest frequency tested and the highest frequency. Due to l i m i t s i n the range of frequencies that the wavemaker could produce, t y p i c a l l y i n the range of 0.2 Hz. to 1.5 Hz., i t was not always possible to centre the natural frequency within the band of frequencies selected. For example, the natural frequency for the trawler i n i t s smallest metacentric height c o n f i g u r a t i o n t y p i c a l l y f e l l i n at approximately 0.21 Hz. with many at lower frequencies. This precluded us from being able to p i c k any frequencies lower than the natural frequency and thus we unfortunately were only able to produce the upper h a l f of the response amplitude operator. For each regular wave te s t the model was placed transversely i n the tank and allowed to s e t t l e down to a s t i l l water condition. The computer c o n t r o l l i n g the wavemaker was then fed the parameters for the wave desired, i e : the frequency and the amplitude, and the wavemaker started. When the waves reached the model the c o n t r o l l i n e s holding the vessels p o s i t i o n were relaxed and the model allowed to move f r e e l y . The data a c q u i s i t i o n and the video recording are then s t a r t e d and the subsequent motion of the model recorded. Occasionally the model would s t a r t to veer o f f from i t s beam on p o s i t i o n to the waves and had to be brought back into l i n e . - 46 -This was done by applying a very gentle tension to the required c o n t r o l l i n e . This was not done unless the v e s s e l had deviated considerably from beam-on, i f the yaw experienced by the model was only a few degrees the ves s e l was normally l e f t alone. The other occasion that may prompt con t r o l l i n e use was i f the model, due the act i o n of the larger waves, was destined to be thrown against one of the walls of the tes t tank. For the preservation of the model t h i s was not allowed to happen and much more severe c o n t r o l was allowed. When t h i s occurred i t was noted i n the records f o r future reference. Tests were done at each of three amplitudes f o r each of the frequencies chosen. The amplitudes were i n terms of voltages and were 33%, 66% and 100% of the wavemakers f u l l scale allowable d r i v i n g voltage. The frequencies that were picked included one frequency computed to be at the natural r o l l frequency of the ve s s e l . Frequency steps were us u a l l y on the order of 0.1 Hz.. 4.2.4 BREAKING WAVES The l a s t part of the t e s t i n g matrix, and the most important from an i n v e s t i g a t i v e point of view, was the measuring of the response of the ves s e l to the impact of a breaking wave. In these tests the wavemaker con t r o l was reprogrammed to allow the cre a t i o n of a breaking wave through the a c t i o n of a c o n t r o l l e d frequency sweep. That i s , a range of frequencies were - 47 produced s t a r t i n g at slower moving high frequency waves and ending with f a s t e r moving low frequency waves. At some point, a distance from the wavemaker, the wave crests produced would synchronize and the r e s u l t i n g s i n g l e wave would be of a magnitude s u f f i c i e n t to become unstable and break. Each of the tests was s t a r t e d with the wavemaker run so that the point of wave breaking could be determined. With t h i s knowledge the model was placed across the tank at a point where the j e t of the breaking wave would be f u l l y formed and be of i t s greatest v e l o c i t y . The wavemaker was r e s t a r t e d and the c o n t r o l l i n e s holding the p o s i t i o n of the boat released. The breaking wave created was preceded by a trough and followed by a smaller trough as i s t y p i c a l of plunging j e t type waves. The ship would r o l l i nto the trough and, depending on the s i z e of the wave, e i t h e r s t a r t to swing back into a v e r t i c a l p o s i t i o n or receive the impacted while s t i l l r o t a t i n g into the wave. The r o l l response of the v e s s e l was measured from the time the wave f i r s t s t a r t e d to form t i l l a f t e r i t had been s a t i s f a c t o r i l y determined that e i t h e r the model had capsized or was i n no danger of becoming unstable. This t e s t was repeated several times at each amplitude and at l e a s t three d i f f e r e n t amplitudes were tested. The co n t r o l l i n e s were not used i n any of the t e s t i n g runs unless i t was obvious that p h y s i c a l harm would come to the model, such as impacting the walls of the tank, from the actions of the wave. - 48 -5.0 ANALYSIS OF DATA 5.1 PRE-PROCESSING The data obtained from the t e s t i n g was i n a number of formats. The motion data from the single chine seiner tests was i n a compressed binary format on standard audio cassettes while i t ' s wave data was i n compressed binary format on 8 inch floppy disks. The trawler had a l l i t s data stored i n a multiplexed binary format on 8 inch f l o p p i e s . To make the data accessible to the user i t had to be tr a n s l a t e d into standard ASCII character f i l e s so i t could be manipulated by conventional software means on a v a r i e t y of computers, most importantly, the VAX VMS 11/750 of the Department of Mechanical Engineering at the U n i v e r s i t y of B r i t i s h Columbia. In t h i s s ection the procedures required to produce the f i n a l , processing ready, data f i l e s w i l l be discussed. This discussion w i l l be broken down into two separate parts; Single Chine Seiner and Trawler as the procedure required f o r the Single Chine Seiner d i f f e r s considerably from the Trawler methods. Once the data i s i n ASCII format f i l e s the discussion w i l l revert back to a single path of analysis as there i s no further d i f f e r e n c e i n the procedure (except f o r a differ e n c e i n the f i l e numbering scheme). 5.1.1 SINGLE CHINE SEINER Upon completion of the t e s t i n g f o r the day a number of audio cassettes and an 8 inch floppy disk remained containing the - 49 -m e a s u r e d v a l u e s f o r t h e d a y . The a u d i o c a s s e t t e s h e l d t h e i n f o r m a t i o n f o r t h e m o t i o n s o f t h e v e s s e l i n f i l e s c o r r e s p o n d i n g t o t h e s e q u e n t i a l n u m b e r i n g s y s t e m o f t h e d a t a a c q u i s i t i o n p r o g r a m . The d a t a i n t h e c a s s e t t e f i l e s was i n a m u l t i p l e x e d b i n a r y f o r m a t . T h i s h a d t o be d e m u l t i p l e x e d and t r a n s l a t e d i n t o u s a b l e A S C I I f i l e s . To do t h i s a p r o g r a m was w r i t t e n t o r e a d t h e d a t a i n f r o m t h e c a s s e t t e t h r o u g h t h e c a s s e t t e i n t e r f a c e p o r t o f a IBM PC c o m p u t e r where i t was d e m u l t i p l e x e d and t r a n s l a t e d i n t o A S C I I c h a r a c t e r s and t h e n w r i t t e n t o 5 . 2 5 " f l o p p y d i s k f i l e s o f t h e same f i l e name. The f i l e names were t h e same as g i v e n b y t h e d a t a a c q u i s i t i o n p r o g r a m and s t a r t e d a t A and went t o Z , o c c a s i o n a l l y t h e number o f t e s t s e x c e e d e d 26 i n w h i c h c a s e t h e s u b s e q u e n t c h a r a c t e r s i n t h e s t a n d a r d A S C I I t a b l e shown i n T a b l e I X were u s e d . To d i f f e r e n t i a t e w h i c h f i l e c o n t a i n e d t h e d a t a on t h e r o l l a n g l e v e r s u s t h e d a t a on t h e h e a v e a c c e l e r a t i o n , e t c . , i t was r e q u i r e d t o append a number t o t h e f i l e s . A summary o f t h e m o t i o n s and t h e i r a s s o c i a t e d f i l e number s u f f i x e s c a n be f o u n d i n T a b l e X . A f t e r t h e d a t a was a l l t r a n s f e r r e d o n t o 5 . 2 5 " f l o p p y d i s k s t h e d i s k s were t a k e n t o t h e D e p a r t m e n t o f M e c h a n i c a l E n g i n e e r i n g where a n IBM P C , u s i n g PCKERMIT t e r m i n a l e m u l a t i o n s o f t w a r e , was c o n n e c t e d t o t h e VAX 1 1 / 7 5 0 . E a c h d i s k i n t u r n was p l a c e d i n t h e IBM PC d r i v e and u s i n g s t a n d a r d KERMIT d a t a t r a n s f e r p r o t o c o l , s e n t v i a t h e t e r m i n a l c o n n e c t i o n t o f i l e s on t h e V A X . The f i l e s , l a b e l l e d w i t h f i l e n a m e e x t e n s i o n s .DAT, now on t h e V A X , c o u l d be a c c e s s e d b y t h e p rog rams r e s i d e n t on t h e c o m p u t e r . 50 -TABLE IX RELEVANT ASCII CHARACTERS USED ASCII CODE CHARACTER ASCII CODE CHARACTER 097 a 116 t 098 b 117 u 099 c 118 V 100 d 119 w 101 e 120 X 102 f 121 y 103 g 122 z 104 h 123 { 105 i 124 1 106 J 125 } 107 k 126 ~ 108 1 127 109 m 128 Q 110 n 129 u 111 o 130 e 112 P 131 a 113 q 132 a 114 r 133 a 115 s 134 a The data c o l l e c t e d from the wave probe, r e s i d i n g on the 8 inch floppy disk, was processed by a separate procedure. Because t h i s procedure i s the same as for the data c o l l e c t e d f o r the Trawler t e s t i n g i t w i l l not be explained here. 5.1.2 WEST COAST TRAWLER With the replacement of the o l d data a c q u i s i t i o n system with the new telemetry system i t was possible to c o l l e c t a l l the data on one device and thus make the l a t e r handling of the data f a r easie r . The ship motions and wave data were a l l c o l l e c t e d simultaneously by the Mine 11 computer mounted on the towing carriage of the tank at B.C. Research. This data, upon completion - 51 -o f a s e r i e s o f t e s t s , was i n m u l t i p l e x e d b i n a r y f o r m a t on 8" f l o p p y d i s k s . To g e t t h i s d a t a t r a n s f e r r e d t o t h e VAX 1 1 / 7 5 0 was o n l y a m a t t e r o f m o u n t i n g t h e d i s k s i n t h e 8" d r i v e s o f t h e VAX and s p e c i f y i n g an RT11 f o r e i g n d i s k f o r m a t s p e c i f i c a t i o n i n t h e command s t r i n g o f t h e d i s k r e a d command b e f o r e r e a d i n g . The d i s k was r e a d i n b u l k b y t h e VAX 1 1 / 7 5 0 and u n i q u e f i l e s c r e a t e d i n i t s memory a c c o r d i n g t o t h e o r i g i n a l d i s k f i l e names . These f i l e s were t h e n renamed b y t h e a u t h o r b y a d d i n g 100 t o t h e f i l e - n u m b e r s t o d i f f e r e n t i a t e t h e s e f i l e s f o r m t h e f i l e s c r e a t e d b y t h e s i n g l e c h i n e s e i n e r t e s t i n g . TABLE X F I L E NUMBERING GUIDE CHANNEL NUMBER MOTION SINGLE CHINE SEINER WEST COAST TRAWLER WAVE HT. 1 0 YAW 9 1 RUDDER 10 2 SWAY 14 3 P ITCH 12 4 HEAVE 13 5 ROLL 11 6 The d a t a f i l e s , t h o u g h on t h e V A X , were s t i l l i n c o m p r e s s e d b i n a r y f o r m a t and h a d s t i l l t o be d e m u l t i p l e x e d . To do t h i s t h e y - 52 -were r u n t h r o u g h a p r o g r a m c a l l e d ADMUX w h i c h d e m u l t i p l e x e d t h e i n p u t f i l e s and c r e a t e d a s e r i e s o f o u t p u t f i l e s , e a c h c o r r e s p o n d i n g t o an i n d i v i d u a l m o t i o n o r e n v i r o n m e n t p a r a m e t e r m e a s u r e d . The n u m b e r i n g scheme o f t h e o u t p u t f i l e s c a n be f o u n d i n T a b l e X . The d a t a o b t a i n e d f r o m t h e s i n g l e c h i n e d a t a h a d a l r e a d y b e e n p r o v i d e d i n u n i t s u s a b l e b y t h e p r o c e s s i n g r o u t i n e s , n a m e l y , t h e y 2 were i n s u c h u n i t s as i n c h e s , m e t e r s / s e c , and d e g r e e s . The d a t a d e r i v e d f r o m t h e West C o a s t T r a w l e r t e s t s was p r o v i d e d i n e l e c t r i c a l u n i t s c o r r e s p o n d i n g t o t h e s i g n a l s m e a s u r e d f r o m t h e s e n s i n g e q u i p m e n t . The c a l i b r a t i o n o f t h e s e n s i n g e q u i p m e n t o f t h e West C o a s t T r a w l e r h a d b e e n done and t h e f i l e s c o n t a i n i n g t h e c a l i b r a t i o n v a l u e s r e s i d e d on t h e V A X . The c o n v e r s i o n o f t h e f i l e s c r e a t e d b y ADMUX f o r t h e West C o a s t T r a w l e r i n t o u s a b l e u n i t s was done b y a s e r i e s o f p r o g r a m s e n t i t l e d HEAVE, SWAY, ROLLANGLE, WAVE and YAW. E a c h o f t h e s e p r o g r a m s c o n v e r t e d i t s own f i l e t y p e f r o m t h e v o l t a g e v a l u e s o r i g i n a l l y p r o v i d e d i n t o t h e a c t u a l p h y s i c a l q u a n t i t i e s r e q u i r e d . The f i l e n a m e e x t e n s i o n s o f t h e new f i l e s c r e a t e d were .UNT i n s t e a d o f .DAT t o r e f l e c t t h i s c h a n g e . B e c a u s e o f a n e r r o r i n t h e i n i t i a l c a l i b r a t i o n o f t h e d a t a a c q u i s i t i o n p r o g r a m t h e v o l t a g e v a l u e s m e a s u r e d were a l l i n v e r t e d ^"The p r o g r a m s u s e d i n t h e c o u r s e o f t h i s r e s e a r c h a r e a l l m e n t i o n e d i n h i g h l i g h t s . The number o f p r o g r a m s u s e d p r e c l u d e d l i s t i n g t h e s o u r c e code as i t w o u l d h a v e made t h i s t h e s i s a r a t h e r u n w i e l d l y i t e m . - 53 -r e s u l t i n g i n s u r p r i s i n g v a l u e s b e i n g o b s e r v e d i n t h e l a t e r a n a l y s i s . T h i s was an e a s y p r o b l e m t o c o r r e c t and was a c c o m p l i s h e d b y f e e d i n g a l l f i l e s c r e a t e d i n t h e 101 and 102 s e r i e s o f t e s t s t h r o u g h t h e p r o g r a m CAL IB w h i c h i n v e r t e d e a c h o f t h e v o l t a g e v a l u e s r e c o r d e d a g a i n . 5.2 GENERAL PROCESSING The d a t a was now r e a d y f o r p r o c e s s i n g . F o r t h e d a t a t o be m e a n i n g f u l i n l a t e r a n a l y s i s i t h a d t o be c o n d i t i o n e d t o p r o v i d e d a t a a c c e p t a b l e f o r f u r t h e r p r o c e s s i n g and i n t e r p r e t a t i o n . T h i s p r o c e d u r e i n v o l v e d c o r r e c t i n g f o r any d e f i c i e n c i e s i n t h e o r i g i n a l d a t a c o l l e c t i n g p r o c e d u r e ( d e s c r i b e d i n s e c t i o n 5 . 1 ) , r e m o v i n g t h e DC o f f s e t s f o u n d i n t h e f i l e s , f i l t e r i n g o u t t h e e x t r a n e o u s n o i s e p r o d u c e d and d e c o u p l i n g t h e m o t i o n s o f t h e v e s s e l so t h a t e a c h f i l e c o n t a i n e d o n l y t h e v a l u e s a s s o c i a t e d w i t h t h a t u n i q u e d i s p l a c e m e n t v e c t o r . A f l o w c h a r t o u t l i n i n g t h e p r o c e d u r e f o l l o w e d t o p r o c e s s t h e d a t a c a n be f o u n d i n F i g . 1 3 . 5.2.1 D . C . OFFSET REMOVAL The f i r s t manner o f b u s i n e s s was t o e l i m i n a t e t h e DC o f f s e t s f r o m t h e d a t a . T h i s was a c c o m p l i s h e d b y two m e t h o d s . The f i r s t method was t o remove t h e DC o f f s e t c r e a t e d b y t h e s i g n a l s f r o m t h e b o a t . T h i s was done be s u b t r a c t i n g f r o m t h e r e c o r d s t h e n u l l v a l u e s r e c o r d e d i n t h e NULL F I L E c r e a t e d a t t h e b e g i n n i n g o f e a c h t e s t s e q u e n c e . T h i s v a l u e c o r r e s p o n d e d t o t h e s t i l l w a t e r r e a d i n g o f t h e i n s t r u m e n t s when t h e v e s s e l h a d no t r i m ( o u t s i d e o f t he - 54 -t r i m due t o t h e w e i g h t c o n d i t i o n ) , no h e a v e , no sway and no r o l l i n g m o t i o n s c o u p l e d w i t h no h e e l . I f t h e r e was a r e s i d u a l DC o f f s e t i n t h e d a t a , as was t h e c a s e w i t h t h e f i l e s c r e a t e d l a t e r i n t h e t e s t day due t o d r i f t o f t h e e l e c t r o n i c s and t h e s e n s i n g e q u i p m e n t , t h i s was removed w i t h a n a v e r a g i n g DC o f f s e t t y p e o f m a n i p u l a t i o n . T h i s was done t h r o u g h t h e u s e o f t h e p r o g r a m DCRMV. T h i s p r o v i d e d us w i t h a f a i r l y good s e t o f d a t a f i l e s . The e x c e p t i o n s t o t h i s were t h o s e f i l e s t h a t were e x c e s s i v e l y n o i s y o r c o r r u p t i n o t h e r m a n n e r s . To p r o v i d e us w i t h a c l e a n e r s i g n a l a f i l t e r was r e q u i r e d t o p r o v i d e a b e t t e r f o o t h o l d f o r t h e r e s i d u a l DC o f f s e t r e m o v a l p r o g r a m . 5.2.2 FOURIER F ILTERING F i l t e r i n g o f t h e d a t a was a c c o m p l i s h e d w i t h t h e u s e o f a n u m e r i c a l f i l t e r p a t t e r n e d a f t e r t h e s t a n d a r d F a s t F o u r i e r T r a n s f o r m (FFT) . The f i l t e r u s e d i s an a d a p t a t i o n o f t h e FFT b y A u b a n e l and Oldham [7] f o r u s e on p e r s o n a l c o m p u t e r s where r e q u i r e m e n t s o f e f f i c i e n c y and f l e x i b i l i t y a r e p a r a m o u n t . T h i s p r o g r a m was f o u n d t o be v e r y a p p r o p r i a t e f o r my u s e b e c a u s e i t a l l o w s a f i l t e r i n g f a c t o r t o be s p e c i f i e d w h i c h a c t s somewhat l i k e t h e v a l u e o f t h e h i g h end f r e q u e n c y o f a l o w - p a s s f i l t e r , d e p e n d i n g on t h e number o f d a t a p o i n t s . A more c o m p l e t e d e s c r i p t i o n o f t h e p rog rams t h e o r y c a n be f o u n d i n A p p e n d i x C . - 55 -"3 H" c: co P R O C E S S I N G S E Q U E N C E cn TJ O o fl> in D iQ CO fD iQ C fD 3 O fD o 01 file.DAT file.DAT i REMOVE THE ERRONEOUS VOLTAGE VALUES IN THE FIRST TWO RUNS DUE TO BAD CALIBRATION FILES * • file. NEW CONVERT VOLTAGE VALUES TO THE ACTUAL PHYSICAL UNITS USING NULL RECORDS AND THE UNEAR CALIBRATION TEST RESULTS ^ fiie.UNT i SMOOTH THE DATA USING A FAST FOURIER TRANSFORM METHOD WITH END EFFECT REMOVAL BY LINEAR SUBTRACTION OF AVERAGE START AND END VALUES flie.FOU i DECOUPLE THE SWAY AND HEAVE VALUES FROM EACH OTHER AS WELL AS REMOVING THE GRAVITY EFFECTS INDUCED BY THE ROLL MOTION OF THE MODEL file.TRU A subroutine was created from the program a f t e r conversion of i t s o r i g i n a l source code, by the author, from BASIC to FORTRAN. This subroutine, named SMOOTH, was then c a l l e d by another program, named F I L T E R , to f i l t e r out any high frequency (above approximately 5 Hz.) noise form the data. These new f i l e s output by the f i l t e r i n g program were appended with the extension .FOU. 5.2.3 DECOUPLING THE MOTIONS The data contained i n the Heave and Sway f i l e s do not represent the actual accelerations of the model i n the d i r e c t i o n s of the world coordinate system. They contain contributions from the perpendicular a c c e l e r a t i o n as well as the a c c e l e r a t i o n due to gr a v i t y because of the influence of the r o l l motion of the v e s s e l . MHEAVE GRAVITY Figure 14. A c c e l e r a t i o n vector diagram To remove t h i s e f f e c t the sway and heave f i l e s had to be decoupled from each other through the r o l l angle f i l e . This was - 57 -done by a vector addition/subtraction of those components not required. From F i g . 13 the following equations can be derived to produce actual a c c e l e r a t i o n values f or the v e s s e l . l e t t i n g nheave and nsway be the actual accelerations, and l e t t i n g heave and sway be the accelerations measured by the sensors we get; heave = nheave cos(0) + nsway sin(0) - g cos(0) (5.001) sway = nsway cos(0) - nheave sin(0) + g sin(0) (5.002) or, s o l v i n g f o r the actual values; nheave cos(0) = heave - nsway sin(0) + g cos(0) (5.003) nsway cos(0) •» sway + nheave sin(0) - g sin(0) (5.004) s u b s t i t u t i n g f o r nsway i n (5.003) and nheave i n (5.004) we get; nheave cos(0) = heave - sway + nheave sin(g) - g sin(fl) cos(0) sin(0) + g cos(0) (5.005) nsway cos(0) = sway + heave - nsway sin(0) +g c o s ( 6 ) cos(0) sin(0) - g sin(0) (5.006) s i m p l i f y i n g , and bringing l i k e terms to the same side, we a r r i v e at; - 58 -i . /n . ^ 2 / / i w h e a v e sway s i n ( 0 ) ,, 2,„. nheave (1 + t a n ( 5 ) ) * + g (1 + t a n (5) c o s ( 0 ) c o s 2 ( « ) (5.007) / i . 2 / / i w sway . heave s i n ( 0 ) nsway (1 + t a n (8)) = z — + (5.008) cos(0) COS (5) k n o w i n g (1 + t a n 2 ( 0 ) ) = l / c o s 2 ( 0 ) we a r r i v e , f i n a l l y , a t t h e r e l a t i o n ; nheave = h e a v e c o s ( 0 ) - sway s i n ( 0 ) + g ( 5 . 0 0 9 ) nsway = heave s i n ( 0 ) + sway c o s ( 0 ) ( 5 . 0 1 0 ) The p r o g r a m s t h a t i m p l e m e n t e d t h i s d e c o u p l i n g a r e named, f o r sway and h e a v e , NSWAY and NHEAVE r e s p e c t i v e l y . 5 . 3 ROLL DECAY TESTS 5 . 3 . 1 ROLL EXTINCTION CURVES The e x t i n c t i o n c u r v e s , as d e f i n e d b y t h e e q u a t i o n : &4> = a<f> + h4>2 + c<j>3 (5.011) m m m w h e r e : A<j> = <j> - <f> n - l n and <f> = (<f> + <j> ) / 2 m n - l n were d e t e r m i n e d b y g o i n g t h r o u g h e a c h r o l l d e c a y t e s t ' s r o l l f i l e - 59 -and compiling a l i s t of the maximum r o l l angles measured i n degrees. P a i r i n g each set of consecutive r o l l angles (one p o s i t i v e and one negative to make a complete r o l l cycle) the mean r o l l angle of the absolute values was computed along with the change i n r o l l angle. These values were tabulated separately f o r p l o t t i n g the change i n r o l l angle as a function of the mean r o l l angle. The points were then smoothed to provide a curve without i n f l e c t i o n points. Three sets of data points were removed from each curve, one at the low end of the amplitude scale, one at about the middle, and one at the high end of the curve. These points were then plugged into the e x t i n c t i o n c o e f f i c i e n t matrix to obtain the c o e f f i c i e n t s of e x t i n c t i o n using Cramers Rule of Determinants [8], i n the ea r l y stages, and l a t e r , a s o l u t i o n was obtained through ® the use of a IBM PC a p p l i c a t i o n package e n t i t l e d TK! SOLVER . The e x t i n c t i o n curves can be found i n Figures 15 through 19. In add i t i o n the actual c o e f f i c i e n t s of e x t i n c t i o n are presented i n tables XI and XII. - 60 -TABLE XI EXTINCTION COEFFICIENTS FOR THE SINGLE CHINE SEINER DISPLACEMENT G.M. EXTINCTION COEFFICIENTS (kg) (mm) 100.27 6.0 a - 0. 19538 b = 0. 00117 c • 0 00007 100.27 27.0 a - o. 07389 b - o. 01294 c =-0. 00005 100.27 50.0 a = 0 06093 b o 03283 c =-0 00053 115.68 6.0 a = 0 07463 b - o 01334 c =-0 00022 115.68 12.0 a - 0 23214 b =-0 00389 c = 0 00028 115.68 27.0 a - 0 .23474 b = 0 .01767 c =-0 .00013 115.68 50.0 a = 0 .29632 b = 0 .01220 c =-0 .00009 - 61 -TABLE XII EXTINCTION COEFFICIENTS FOR THE WEST COAST TRAWLER DISPLACEMENT (kg.) G.M. (mm) EXTINCTION COEFFICIENTS 101.15 69.3 a — 0 29856 b - 0 03660 c =-0 00054 101.15 69.0 a =-0 15169 b - 0 03835 c =-0 00070 133.36 106.0 a - 0 06900 b = 0 03140 c =-0 00067 133.36 36.0 a - 0 24350 b =-0 01379 c = 0 00079 133.36 6.0 a = -0 33179 b - o 07830 c =-0 00233 168.15 81.6 a = -0 20816 b - 0 03765 c =-0 00053 168.15 36.0 a =-0 19111 b - 0 03400 c = -0 00046 168.15 6.0 a =-0 23880 b = 0 .05520 c =-0 00087 - 62 -ROLL EXTINCTION CURVES SINGLE CHINE SEINER 216.4 TONS DISPLACEMENT Legend GM = 2.1331 ft. GM = 1.1516 ft. GM = 0.2557 ft. / / / / S / / t ' r t / * / t / * / * / x / * / 4* y * * * / / y' S ^0, V / ' ' s 1 1 1 1 1 10 20 30 40 50 MEAN ROLL ANGLE (degrees) igure 15. R o l l Extinction Curves for Single Chine Se 216.4 Tons Displacement 30-1 25-o» 0) T3 20 o I-o I- 15-I-X UJ O CC 10-ROLL EXTINCTION CURVES SINGLE CHINE SEINER 249.6 TONS DISPLACEMENT Legend cm = 2J331 ft. GM = 0.6//3 fl. CM = 0.2557 ft. 10 20 30 40 MEAN ROLL ANGLE (degrees) 50 F i g u r e 16. R o l l E x t i n c t i o n C u r v e s f o r S i n g l e C h i n e S e i n e r 2 4 9 . 6 T o n s D i s p l a c e m e n t - 64 -ROLL EXTINCTION CURVES WEST COAST TRAWLER 328.9 TONS DISPLACEMENT 3 0 2 5 -co 0 »-0) •o 2 0 O I- 15 o z I-X LU 10 o 5 -Legend Without Bilge Keels With Bilge Keels / / / / / * * / ' x" y X • x^ / X • x / X /• X * / > / / / X / X • X y X / X y X * X * > • _/ * s / / 10 2 0 3 0 4 0 MEAN ROLL ANGLE (degrees) 5 0 Figure 17. R o l l Extinction Curves for West Coast Trawler 328.9 Tons Displacement - 65 -ROLL EXTINCTION CURVES WEST COAST TRAWLER 437.64 TONS DISPLACEMENT MEAN ROLL ANGLE (degrees) Figure 18. R o l l Extinction Curves for West Coast Trawler 437.64 Tons Displacement 3 0 2 5 co o © D ) © •o g H O 2 0 -1 5 X LU -I 1 0 O CC 5 -ROLL EXTINCTION CURVES WEST COAST TRAWLER 551.51 TONS DISPLACEMENT Legend GM = 4.1468 ft. GM = 1.7960 ft. GM = 0.2953 ft. / / / / / */ *s / *y ty */ *y / / / / y */ y / f 0 1 0 2 0 3 0 4 0 5 0 MEAN ROLL ANGLE (degrees) Figure 19. R o l l Extinction Curves for West Coast Trawler 551.51 Tons Displacement - 67 -5.3.2 MOMENT OF INERTIA The v i r t u a l mass moment of i n e r t i a of the ves s e l i n s t i l l water, assuming no damping, can be determined through the use of small angle l i n e a r v i b r a t i o n theory. For an undamped sing l e degree of freedom system the natural frequency of v i b r a t i o n can be expressed as, (5.012) where: k = spring constant m = mass I f we then solve f o r the mass, and include the added mass i n the mass term such that m — m + m' — I' , as the ves s e l i s X X a c c e l e r a t i n g i n water, we obtain, V = w2 • k (5.013) xx n Substituting, f o r small angles, the r e s t o r i n g moment i n r o l l we get, V = / ^ ) • A • GM (5.014) XX [_ Z 7 T J Knowing the natural period of o s c i l l a t i o n f o r the model - 68 -configurations tested the v i r t u a l mass moments of i n e r t i a are cal c u l a t e d . The r e s u l t s are shown i n Tables XIII and XIV f o r the model scale. TABLE XIII VIRTUAL MASS MOMENTS OF INERTIA SINGLE CHINE SEINER (seconds) I' XX 2 (kgomos ) CONFIGURATION A = 216.4 T GM - 0.2557 f t 4.8309 0.3547 A - 216.4 T GM - 1.1516 f t 2.6525 0.4455 A - 216.4 T GM = 2.1331 f t 1.7699 0.3967 A - 249.6 T GM - 0.2557 f t 4.5045 0.3546 A - 249.6 T GM = 0.5113 f t 3.3784 0.4322 A = 249.6 T GM - 1.1516 f t 2.3148 0.4212 A - 249.6 T GM - 2.1331 f t 1.7361 0.4653 - 69 -TABLE X I V VIRTUAL MASS MOMENTS OF INERTIA WEST COAST TRAWLER ( s e c o n d s ) I' XX 2 (kgomas ) CONFIGURATION A = 3 2 8 . 9 T GM - 3 . 4 1 5 4 f t 1 .5256 0 . 4 1 4 9 A = 3 2 8 . 9 T GM = 3 . 4 1 5 4 f t 1 .5149 0 . 4 0 9 1 A = 4 3 7 . 6 T GM = 0 . 2 9 5 3 f t 6 . 1576 0 . 7 7 1 6 A - 4 3 7 . 6 T GM = 1 .7960 f t 2 . 2 9 2 0 0 . 6 5 0 3 A = 4 3 7 . 6 T GM = 3 .8238 f t 1 .3165 0 . 4 5 6 8 A = 5 5 1 . 5 T GM = 0 . 2 9 5 3 f t 4 . 7 1 7 0 0 . 5 7 0 1 A = 5 5 1 . 5 T GM = 1 .7960 f t 1 .9916 0 . 6 1 8 3 A = 5 5 1 . 5 1 T GM - 4 . 1 4 6 8 f t 1 .3280 0 . 6 3 4 9 5 . 4 REGULAR SEAS RESPONSE  5 . 4 . 1 WAVEMAKER CHARACTERISTICS A c o m p i l a t i o n was made o f a l l t h e r e g u l a r wave h e i g h t measuremen ts f r o m b o t h t h e s i n g l e c h i n e s e i n e r and t r a w l e r t e s t s . These v a l u e s were s o r t e d a c c o r d i n g t o f r e q u e n c y and wave maker a m p l i t u d e s e t t i n g . A h i s t o g r a m was d e v e l o p e d f r o m t h i s d a t a w h i c h h a d a s t e p s i z e o f 0 . 0 5 H z . E a c h h i s t o g r a m h a d i t s mean and - 70 -REGULAR SEAS WAVE AMPLITUDES TEST AMPLITUDE #1 0.16 0.14 0.12-eo .2 0 . 1 0 E UJ Q 0.08-0.04-0.02-0.00 L e g e n d • Measured Values Mean t • • t r t # • o E UJ o z < 0.0 6 0 1 2 3 4 5 WAVE FREQUENCY (rad/sec.) Figure 20. Regular Seas Wave Amplitudes - Test Amplitude #1 - 71 -R E G U L A R S E A S W A V E A M P L I T U D E S T E S T A M P L I T U D E #3 0.16 0.14-0.12 <2 0.10-co © E ui Q 3 Q. < 0.08 0.06 0.04 0.02 0.00 L e g e n d # Measured Values Mean • • A • 7 J / * * • • I • • •7 •• e E u z < 0.0 6 0 1 2 3 4 5 WAVE FREQUENCY (rad/sec.) F i g u r e 21. Regular Seas Wave Amplitudes - Te s t Amplitude #3 - 72 -R E G U L A R S E A S W A V E A M P L I T U D E S T E S T A M P L I T U D E #4 0.16 0.14 0.12 (0 ® 0.10 E UJ 0.08 0.04-0.02-0.00 — • • • • L e g e n d • Measured Values Mean 1 I 1 I 1 t> 6.0 r E ui o rr 0.0 0 1 2 3 4 5 6 WAVE FREQUENCY (rad/sec.) Figure 22. Regular Seas Wave Amplitudes - Test Amplitude #4 - 73 -REGULAR SEAS WAVE AMPLITUDES TEST AMPLITUDE #5 0.16-1 : : : : : 1 WAVE FREQUENCY (rad/sec.) Figure 23. Regular Seas Wave Amplitudes - Test Amplitude #5 - 74 -variance c a l c u l a t e d f o r the points l y i n g within i t s bounds [9] The mean f o r each histogram containing data points was then associated with the center frequency of that histogram. Histograms containing no data points were neglected. A p l o t was then made of the mean wave amplitude as a function of frequency f o r each of the f i v e wave amplitude s e t t i n g s . The variance i s also p l o t t e d on the same graph to show the r e p e a t a b i l i t y of the wave amplitudes. The r e s u l t s can be seen i n Figures 20 through 23. The r i s e i n the variance i s very small over the range of wave frequencies tested except f o r te s t amplitude #5 (Fig. 23) where there i s a sudden jump i n the variance curve. This can be a t t r i b u t e d to the decay i n the s t r u c t u r a l i n t e g r i t y of the wavemaker. The mounting b o l t s connecting the hydraulic actuator to i t s base came a d r i f t allowing a large percentage of the excursion of the hydraulic ram to be taken up by the mountings instead of the panel. This was remedied a f t e r discovery and only a few records are affected. The amplitude response of the wavemaker over the range of frequencies tested showed a considerable inconsistency. The wavemaker has an optimum range of operation where maximum wave height can be obtained, at lower frequencies the wavemaker cannot execute a paddle excursion s u f f i c i e n t to maintain wave amplitudes while at high frequencies the hydraulics cannot respond quickly enough to reach f u l l excursion at the d r i v i n g voltage peak. 5.4.2 ROLL RESPONSE AMPLITUDE OPERATORS From the r o l l and wave amplitude records the r o l l response amplitude operators could be determined. To accurately determine the r o l l angle and wave amplitude values the respective f i l e s were fed into a Fast Fourier transform routine that broke the signals down into t h e i r component frequencies. These spectrums were stored i n separate f i l e s and from these f i l e s the amplitudes were scanned f o r the l a r g e s t value recorded. The la r g e s t value, because of the p r i o r f i l t e r i n g , could be confidently assumed to be associated with the desired motion or displacement. The associated frequency was also output and i f the frequency was not within 5 percent of the t e s t frequency i t was discarded and the search repeated. These amplitudes were pr i n t e d out along with the response amplitude operator f o r the given (measured) wave frequency of that f i l e set. The r o l l response amplitude operators were determined through the use of the following r e l a t i o n s h i p [10], ROLL (5.015) where: $ = r o l l angle g = a c c e l e r a t i o n due to g r a v i t y co wave encounter frequency A = wave amplitude - 76 -The r o l l response amplitude operator data was created i n much the same manner as the wave amplitude p l o t s . A l l the values were sorted according to frequency and a mean and variance were computed f o r each d i v i s i o n of the histogram used. These can be seen i n Figures 24 through 38. The variance i s much more pronounced i n the p l o t s of the r o l l R.A .O. as i t i l l u s t r a t e s the n o n - l i n e a r i t i e s introduced i n large angle r o l l due to resonance and large amplitude waves. 5.5 REGULAR SEAS STABIL ITY FACTORS The response of the vessels tested to the influence of a r e g u l a r l y repeating wave function i s described well by the cre a t i o n of r o l l response amplitude operators. This does not ne c e s s a r i l y help, though, i n describing the safety of the ves s e l i n a c e r t a i n seaway as we cannot t e l l how near the v e s s e l i s to i t ' s point of capsizing. To better get a grip on the "safety" of the v e s s e l a parameter was required that could quantify t h i s response i n such a manner that zones of safe operation could be defined. The key parameters considered e s s e n t i a l f o r the quantifying of the vessels s t a b i l i t y were the following, > A, the amplitude of the r e g u l a r l y repeating sea the vessel i s operating i n > R, the average maximum r o l l angle achieved by - 77 -ROLL RESPONSE AMPLITUDE OPERATOR SINGLE CHINE SEINER 216.4 TONS DISPLACEMENT GM = 0.2557 ft. 350 300 250 200 150 100 50 0 L e g e n d # Measured Values Mean 1 r—m »—fw w | | r-0 0.5 1 1.5 2 2.5 ENCOUNTER FREQUENCY (rad/sec.) Figure 24. R o l l Response Amplitude Operator Single Chine Seiner 216.4 Tons Displacement, GM = 0.2557 f t . - 78 -ROLL RESPONSE AMPLITUDE OPERATOR SINGLE CHINE SEINER 216.4 TONS DISPLACEMENT GM = 1.1516 ft. 700 600-500-o < CC 400 O 300 CC 200 L e g e n d # Measured Values Mean \ A : #\ 1 0 0 0 0 0 6 0 0 0 0 o z < rr \ 0.5 1 1.5 2 2.5 ENCOUNTER FREQUENCY (rad/sec.) Figure 25. R o l l Response Amplitude Operator Single Chine Seiner 216.4 Tons Displacement, GM = 1.1516 f t . - 79 -ROLL RESPONSE AMPLITUDE OPERATOR SINGLE CHINE SEINER 216.4 TONS DISPLACEMENT GM = 2.1331 ft. 30 25 20 15 10 5 L e g e n d • Measured Values Mean i • • I A • \ \ • 1 1 1 1 i r 0 0.5 1 1.5 2 2.5 ENCOUNTER FREQUENCY (rad/sec.) Figure 26. R o l l Response Amplitude Operator Single Chine Seiner 216.4 Tons Displacement, GM = 2.1331 f t . ROLL RESPONSE AMPLITUDE OPERATOR SINGLE CHINE SEINER 249.6 TONS DISPLACEMENT GM = 0.2557 ft. 120-1 100-80 60 40 20 0 L e g e n d # Measured Values Mean • I 1 1 y ww | w w—iv 1 r 0 0.5 1 1.5 2 2.5 ENCOUNTER FREQUENCY (rad/sec.) Figure 27. R o l l Response Amplitude Operator Single Chine Seiner 249.6 Tons Displacement, GM = 0.2557 f t . ROLL RESPONSE AMPLITUDE OPERATOR SINGLE CHINE SEINER 249.6 TONS DISPLACEMENT GM = 0.5113 ft. 200 150 100 50 L e g e n d Measured Values Mean 10< 0.5 1 1.5 2 ENCOUNTER FREQUENCY (rad/sec.) 2.5 Figure 28. R o l l Response Amplitude Operator Single Chine Seiner 249.6 Tons Displacement, GM = 0.5113 f t . - 82 -ROLL RESPONSE AMPLITUDE OPERATOR SINGLE CHINE SEINER 249.6 TONS DISPLACEMENT GM = 1.1516 ft. 120 100 80 60 40 20 0 L e g e n d # Measured Values Mean • + «—m i 1 r » — » 1 1 r 0 0.5 1 1.5 2 2.5 ENCOUNTER FREQUENCY (rad/sec.) Figure 29. R o l l Response Amplitude Operator Single Chine Seiner 249.6 Tons Displacement, GM = 1.1516 f t . ROLL RESPONSE AMPLITUDE OPERATOR SINGLE CHINE SEINER 249.6 TONS DISPLACEMENT GM = 2.1331 ft. 30 25-20-o • < cc o cc 15-10-L e g e n d # Measured Values Mean 4 w 4 L * 60 z < 2 •o 0.5 1 1.5 2 ENCOUNTER FREQUENCY (rad/sec.) 2.5 Figure 30. Roll Response Amplitude Operator Single Chine Seiner 249.6 Tons Displacement, GM = 2.1331 f t . - 84 -ROLL RESPONSE AMPLITUDE OPERATOR WEST COAST TRAWLER 328.9 TONS DISPLACEMENT GM = 3.4154 ft. (bilge keels removed) 0.5 1 1.5 2 ENCOUNTER FREQUENCY (rad/sec.) Figure 31. R o l l Response Amplitude Operator West Coast Trawler 328.9 Tons Displacement, GM = 3.4154 f t . (bilge keels removed) •- 85 -ROLL RESPONSE AMPLITUDE OPERATOR WEST COAST TRAWLER 328.9 TONS DISPLACEMENT GM = 3.4154 ft. (bilge keels attached) 20 - i 15 o • < cc o cc L e g e n d • Measured Values Mean < I • • 4 l\ / : \ J « 3 0 20 10 2.5 0 0.5 1 1.5 2 ENCOUNTER FREQUENCY (rad/sec.) Figure 32. R o l l Response Amplitude Operator West Coast Trawler 328.9 Tons Displacement, GM = 3.4154 f t . (bilge keels attached) - 86 -• ROLL RESPONSE AMPLITUDE OPERATOR WEST COAST TRAWLER 437.64 TONS DISPLACEMENT GM = 0.2953 ft. 70-1 : : ! : 1 ENCOUNTER FREQUENCY (rad/sec.) Figure 33. R o l l Response Amplitude Operator West Coast Trawler 437.64 Tons Displacement, GM = 0.2953 f t . - 87 -ROLL RESPONSE AMPLITUDE OPERATOR WEST COAST TRAWLER 437.64 TONS DISPLACEMENT GM = 1.7960 ft. 80 70-60-50 • o < * 40 30-20-10 L e g e n d # Measured Values Mean • /•\ % \ J A 4 < •A '\-% 1 0 0 0 Ui (J z BOO < 2.5 ) 0.5 1 1.5 2 ENCOUNTER FREQUENCY (rad/sec.) Figure 34. Rol l Response Amplitude Operator West Coast Trawler 437.64 Tons Displacement, GM = 1.7960 f t - 88 -ROLL RESPONSE AMPLITUDE OPERATOR WEST COAST TRAWLER 437.64 TONS DISPLACEMENT GM = 3.8238 ft. L e g e n d # Measured Values Mean ENCOUNTER FREQUENCY (rad/sec.) Figure 35. R o l l Response Amplitude Operator West Coast Trawler 437.64 Tons Displacement, GM = 3.8238 f t . - 89 -ROLL RESPONSE AMPLITUDE OPERATOR WEST COAST TRAWLER 551.51 TONS DISPLACEMENT GM = 0.2953 ft. L e g e n d # Measured Values Mean • m A • i i — - — 1 1 r 0 0.5 1 1.5 2 ENCOUNTER FREQUENCY (rad/sec.) Figure 36. R o l l Response Amplitude Operator West Coast Trawler 551.51 Tons Displacement, GM = 0.2953 f - 90 -ROLL RESPONSE AMPLITUDE OPERATOR WEST COAST TRAWLER 551.51 TONS DISPLACEMENT GM = 1.7960 ft. o < • cc o cc - — L e g e n d • Measured Values Mean • A • / \ J # 1 • * \ 4 > /\\ 4 0 0 O z 2 0 0 < tr. % 2.5 0 0.5 1 1.5 2 ENCOUNTER FREQUENCY (rad/sec.) Figure 37. Roll Response Amplitude Operator West Coast Trawler 551.51 Tons Displacement, GM = 1.7960 f t . - 91 -ROLL RESPONSE AMPLITUDE OPERATOR WEST COAST TRAWLER 551.51 TONS DISPLACEMENT GM = 4.1468 ft. 10-1 8 6 4 2 • L e g e n d • Measured Values Mean • • /• \ /• \ / # \ / # • ENCOUNTER FREQUENCY (rad/sec.) Figure 38. R o l l Response Amplitude Operator West Coast Trawler 551.51 Tons Displacement, GM = 4.1468 f - 92 -t h e v e s s e l w h i l e o p e r a t i n g i n t h i s s e a > A r e a , t h e a r e a under t h e GZ c u r v e f o r the c o n f i g u r a t i o n o f t h e v e s s e l under c o n s i d e r a t i o n These t h r e e v a l u e s c o u l d be combined i n t o a r a t i o o f t h e e n e r g i e s w i t h i n t h e o p e r a t i n g e n v i r o n m e n t and t h e ene r g y i n h e r e n t w i t h i n t h e v e s s e l . Thus a s t a b i l i t y f a c t o r , c a l l e d S, c o u l d be d e f i n e d , as f o l l o w s [ 2 6 ] , A • R S = (5.016) A r e a P l o t s o f t h e s t a b i l i t y p a r a m e t e r s S as a f u n c t i o n o f t h e beam to w a v e l e n g t h r a t i o c a n be f o u n d i n F i g u r e s 39 and 40 f o r t h e s i n g l e c h i n e s e i n e r and t h e west c o a s t t r a w l e r r e s p e c t i v e l y . Each p l o t r e p r e s e n t s t h e t o t a l r e s p o n s e d a t a o f t h e h u l l i n r e g u l a r s e a s . 5.6 BREAKING WAVE RESPONSE A n a l y s i s o f the b r e a k i n g wave r e s p o n s e s t a r t e d w i t h a c o m p i l a t i o n o f t h e maximum r o l l , sway and heave v a l u e s e x p e r i e n c e d d u r i n g each t e s t r u n o v e r t h e e n t i r e t e s t i n g s e r i e s . T h i s c o m p i l a t i o n was done t h r o u g h t h e use o f the program BREAKER w h i c h i n s p e c t e d t h e maxima and minima o f each d i s p l a c e m e n t c u r v e , f o u n d t h e l a r g e s t v a l u e , and o u t p u t t h e maximum v a l u e , a l o n g w i t h i t s c o r r e s p o n d i n g e v e n t t i m e t o a f i l e a s s o c i a t e d w i t h each t e s t 93 REGULAR SEAS STABILITY FACTOR SINGLE CHINE SEINER Legend O 216.4 tons, CM=0.2S57 ft. • 216.4 Tons, CM=1.1S16 ft. V 216.4 tons. GM=2.13SI ft. O 249.6 7bns, CM=0.2S57 ft. 4- 249.6 7bn«, CM=0.51I3 ft. A 249.6 tons, CM=1.l5t6 ft. O 249.6 tone. CM=2.1331 ft. O O O 0.6 B/L 0.8 1.2 Figure 39. Regular Seas S t a b i l i t y Factor Single Chine Seiner - 94 -REGULAR SEAS STABILITY FACTOR WEST COAST TRAWLER 0.09 0.08-0.07 Legend S28S0 Ibn», 32B.90 Tbns, 437.64 Jbn«, 437.64 Jbn«, 437.64 7bn», 55/.5Z Tbns. 55/5* n>n«. 55/.S7 Ibn«, CM=3.4tS4 ft. [a] CM=3.4I54 ft. [b] , CM-3.B238 ft. , CM=t.7960 ft. . Cit=0.2953 ft. CM=4J468 ft. CM=I.7960 ft. CU=OJ2953 ft. 0.06-0.05-o 0.04-0.03-0.3 B/L 0.4 0.5 0.6 Figure 40. Regular Seas S t a b i l i t y Factor West Coast Trawler - 95 -c o n f i g u r a t i o n . These f i l e s were l a t e r p r i n t e d o u t f o r a n a l y s i s w h i c h i n c l u d e d i n s p e c t i o n o f t h e maxima e v e n t t i m i n g t o e n s u r e t h a t t h e e v e n t r e c o r d e d c o r r e s p o n d e d t o t h e o n s e t o f t h e b r e a k i n g wave and n o t some o t h e r e x t e r n a l e v e n t . T h i s was e s p e c i a l l y i m p o r t a n t f o r t h e f i l e s w h i c h c o n t a i n e d m u l t i p l e t e s t i n g r e s u l t s f r o m t h e S i n g l e C h i n e S e i n e r s e r i e s as t h e d r a g b a c k was a l s o i n c l u d e d i n t h e d a t a f i l e and h a d t o be f i l t e r e d o u t b y t r a p p i n g t h e t i m e s p a n t h e m a x i m a / m i n i m a s e a r c h was t o o p e r a t e i n . TABLE XV BREAKING WAVE AMPLITUDES BREAKING WAVE AMPLITUDE BREAKING WAVE NUMBER SINGLE CHINE SEINER WEST COAST TRAWLER 2 3 . 6 3 m e t e r s 4 . 1 9 m e t e r s 3 3 . 82 m e t e r s 4 . 4 0 m e t e r s 4 3 .99 m e t e r s 4 . 6 0 m e t e r s 5 4 . 1 6 m e t e r s 4 . 8 0 m e t e r s A p l o t o f t h e maximum sway a c c e l e r a t i o n v a l u e s as a f u n c t i o n o f t h e b r e a k i n g wave h e i g h t number i s made f o r e a c h c o n f i g u r a t i o n t e s t e d . These p l o t s c a n be f o u n d i n F i g u r e s 41 and 42 f o r t h e s i n g l e c h i n e s e i n e r and t h e w e s t c o a s t t r a w l e r r e s p e c t i v e l y . The maximum r o l l a n g l e s e x p e r i e n c e d due t o t h e i m p a c t o f t h e b r e a k i n g wave a r e shown i n F i g . 43 f o r t h e s i n g l e c h i n e s e i n e r and F i g . 44 f o r t h e w e s t c o a s t t r a w l e r . - 96 -BREAKING WAVES ROLL RESPONSE SINGLE CHINE SEINER 200 oH 1 1 1 1 1 0 1 2 3 4 5 6 BREAKING WAVE NUMBER Figure 41. Breaking Waves Ro l l Response Single Chine Seiner - 97 -BREAKING WAVES ROLL RESPONSE WEST COAST TRAWLER Legend 328.90 tons, 32830 Ibne, 437.64 Rmt, 437.64 Jbn», 437.64 tons, 5S1.5I ftma. 561.51 Ibnt, X 55/.5»Jbn«, CH=S.41S4 ft. [a] CM=3.4tS4 ft. [&] , CM=3.B238 ft. , CH=t.7980 ft. , CM=0.29SS ft. CM=4J468 ft. GM=I.?960 ft. CM=0J1953 ft. X O r 0 1 2 3 4 5 BREAKING WAVE NUMBER Figure 42. Breaking Waves Ro l l Response West Coast Trawler 6 - 98 -BREAKING WAVES SWAY RESPONSE SINGLE CHINE SEINER Legend O 216.4 tons, CM=0.2557 ft. • 216.4 Tbns, CM=1.1S16 ft. V 216.4 Tbns, CM=2.1331 ft. O 249.6 Tbns, CM=0.25S7 ft. + 249.6 Tbm,CM=0.5113 ft. A 249.6 7bn», CM-1.1S16 ft. O 249.6 7bns, CM=2.1331 ft. 1 I I I I I I 0 1 2 3 4 5 6 BREAKING WAVE NUMBER Figure 4 3 . Breaking Waves Sway Response Single Chine Seiner - 99 -BREAKING WAVES SWAY RESPONSE WEST COAST TRAWLER 12 CM : 1 0 CO r - 8 6 4-2-Legend 328.90 Tbns, 328.90 Tbns, 437.84 Tbns. 437.84 Tbns, Tbns, 551.51 Tbns. 551.51 Tbns, X 55/.5» 7bn«, CH=3.4I64 ft. a CM=3.4I64 fl. b Cti-3.8238 ft. , CM=1.7980 ft. , CM=0.2953 ft. CM-4.1468 ft. CM=1.7960 ft. CM=GJ953 ft. X X O-f 1 1 1 1 1 0 1 2 3 4 5 6 BREAKING WAVE NUMBER F i g u r e 44. B r e a k i n g Waves Sway Response West Coast T r a w l e r - 1 0 0 -5.7 BREAKING WAVE STABILITY FACTORS 5.7.1 STABILITY PARAMETER S' The s t a b i l i t y of the vessels i n breaking waves i s considered to be a function of a number of parameters but i t i s generally considered that the following parameters are the most important: > R, the r o l l amplitude achieved by the v e s s e l upon wave impact > h, the height of the breaking wave when i t s t r i k e s the ves s e l > Area, the area under the GZ curve f o r the configuration of the ves s e l under consideration. Using the above parameters a basic energy balance can be made with the area under the GZ curve being proportional to the energy required to r o l l the ves s e l to the angle of vanishing s t a b i l i t y and the height of the breaking wave proportional to the energy inherent i n the breaking wave. The r o l l angle attained by the model i s then an i n d i c a t i o n of the amount of energy t r a n s f e r r e d to the v e s s e l by the breaking wave. Relating these energies i n a r a t i o the following s t a b i l i t y parameter i s derived, S' - R ' h (5.017) Area - 101 -where the parameters R, h and Area are as defined i n the di s c u s s i o n above. A p l o t of the s t a b i l i t y parameter, S' , for each v e s s e l tested as a function of the beam to wave height r a t i o can be found i n Figures 45 and 46. 5.7.2 STABILITY PARAMETER S* I t became apparent from an i n v e s t i g a t i o n of the s t a b i l i t y parameter that there was not a good c o r r e l a t i o n between the s t a b i l i t y of the v e s s e l and i t s S' f a c t o r . Thus, a f t e r an i n v e s t i g a t i o n of the data, i t was discovered that no p r o v i s i o n had been made to account for the r o l l response amplitude operator of the v e s s e l . This curve gives an excellent i n d i c a t i o n of the bandwidth of the v e s s e l ( i e : that frequency range over which the ve s s e l exhibited a r o l l response) and hence the amount of energy i t can absorb from a spectrum. I f the impulse of the breaking wave i s assumed to contain a l l frequencies then that v e s s e l which c a r r i e s the l a r g e r r o l l response amplitude operator area w i l l t h e o r e t i c a l l y absorb more of the a v a i l a b l e energy i n the breaking wave. With t h i s information i n hand a new s t a b i l i t y parameter was developed through non-dimensionalizing those f a c t o r s most i n f l u e n t i a l i n the capsizing of the v e s s e l . These were: - 102 -BREAKING WAVES STABILITY FACTOR SINGLE CHINE SEINER 60 50 CC o I-o LL LU CC Q. CO 40-30 -20-10 T 4 Legend O 249.6 Tbns, CM=0.2SS? ft. • 249.6 Tbns, CM=0.S1I3 ft. V 249.6 7bns, CM=t.lSt6 ft. O 249.6 Tbns, CM=2J331 ft. 4 216.4 Tbns, CU=0.25S7 ft. A 216.4 Tbns. CM=t.1SI6 ft. O 216.4 Tbns, CU-Z.1331 ft. . T f . . + o o o 4.5 5.5 6 6.5 B / f F i g u r e 45. Breaking Waves S t a b i l i t y F a c t o r (S') S i n g l e Chine Seiner - 103 -B R E A K I N G W A V E S S T A B I L I T Y F A C T O R W E S T C O A S T T R A W L E R cc o i-o 900 800-700-600-500-LU ? 400-CC CL m 300 200 100 i 0 Legend 328.90 Tbns, 328.90 Tbns, 437.84 Tbns, 437.84 Tbns, 437.84 Tbns, 6SI.S1 Tbns, SSI.SI Tbns, 651.51 Tbns, Gil=3.4tS4 ft. Clt=3.4t54 ft. , CU-3.B238 ft. , CM=t.7960 ft. . CH=0.29S3 ft. CU-4.U68 ft. Clt=t.7960 ft. CM=0J1953 ft. CAPSIZING REGION NO CAPSIZING REGION 10 X X X —I— 15 B/f 20 25 30 Figure 46. Breaking Waves S t a b i l i t y Factor (SM West Coast Trawler - 104 -> <f> , t h e maximum r o l l a n g l e a c h i e v e d ( r a d i a n s ) max > (j> , t h e a n g l e o f v a n i s h i n g s t a b i l i t y ( r a d i a n s ) > H , t h e b r e a k i n g wave h e i g h t ( m e t e r s ) > A , t h e a r e a u n d e r t h e a p p r o p r i a t e r o l l R . A . O . c u r v e RAO R R R ( s e c o n d s *) > A , t h e a r e a u n d e r t h e a p p r o p r i a t e r i g h t i n g arm c u r v e GZ ( m e t e r s ) > A t , t h e d u r a t i o n o f i m p a c t o f t h e b r e a k i n g wave ( s e c o n d s ) The r e s u l t i n g e x p r e s s i o n f o r S b e c o m e s ; RAO GZ A t ( 5 . 0 1 8 ) The d u r a t i o n o f i m p a c t o f t h e b r e a k i n g wave was d i f f i c u l t t o measure and t h u s an e s t i m a t e was made o f t h e t i m e d u r a t i o n . T h i s e s t i m a t e i s b a s e d on v a l u e s m e a s u r e d f o r t h e d u r a t i o n o f i m p a c t b y D a h l e [11] and B a l i t s k a j a [ 1 2 ] . B o t h a u t h o r s r e a c h e d an e s t i m a t e o f 0 . 1 s e c o n d s d u r a t i o n f o r i m p a c t on t h e mode l s c a l e . T h i s v a l u e was u s e d h e r e a l s o , s c a l e d a p p r o p r i a t e l y . A n o t h e r d i f f i c u l t y was i n t h e m e a s u r i n g o f t h e a r e a s u n d e r t h e r o l l r e s p o n s e a m p l i t u d e o p e r a t o r c u r v e s . Due t o t h e l i m i t a t i o n s o f t h e t a n k i t was n o t p o s s i b l e t o e x t e n d t e s t f r e q u e n c i e s down t o o r b e l o w t h e n a t u r a l f r e q u e n c i e s o f t h e s m a l l e r m e t a c e n t r i c h e i g h t c o n f i g u r a t i o n s o f t h e m o d e l s . When t h e R . A . O . c u r v e was i n c o m p l e t e a n e x t r a p o l a t i o n was done f r o m t h o s e c u r v e s w h i c h were f u l l y f o r m e d a d j u s t i n g f o r t h e changes i n - 105 -metacentric height and resonance c h a r a c t e r i s t i c s . TABLE XVI AREAS FOR SINGLE CHINE SEINER CONFIGURATION A G Z A R A O A = 216.4 Tons GM = 0.2557 f t 11.634 ft-deg. 167.95 -1 sec. A = 216.4 Tons GM - 1.1516 f t 36.536 ft-deg. 50.86 -1 sec. A = 216.4 Tons GM = 2.1331 f t 79.714 ft-deg. 4.70 -1 sec. A = 249.6 Tons GM - 0.2557 f t 11.481 ft-deg. 17.52 -1 sec. A -= 249.6 Tons GM = 0.5113 f t 17.708 ft-deg. 5.60 -1 sec. A = 249.6 Tons GM = 1.1516 f t 37.669 ft-deg. 6.84 -1 sec. A = 249.6 Tons GM - 2.1331 f t 85.220 ft-deg. 2.70 -1 sec. The s t a b i l i t y parameter S was c a l c u l a t e d from these areas using the breaking wave amplitudes shown i n Table XV. The r e s u l t s are shown i n Figures 47 and 48 f o r the Single Chine Seiner and the West Coast Trawler r e s p e c t i v e l y . The capsizing events f o r the * trawler are at 4> /4> — 3 and an S value of 600. Though only one max v c a p s i z i n g symbol appears on the fig u r e i t i s i n actual f a c t a * number of capsizing events. The S value and the <f> /<f> value f o r max v each of the capsizings, due to the nature of the parameters, are i d e n t i c a l and thus p l o t as one point. - 106 -TABLE XVII AREAS FOR WEST COAST TRAWLER CONFIGURATION A GZ A RAO A = 328.9 Tons WITHOUT KEELS 194.04 ft-deg. 4.21 - 1 sec. A = 328.9 Tons WITH KEELS 194.04 ft-deg. 3.39 - 1 sec. A = 437.6 Tons GM = 3.8238 f t 278.04 ft-deg. 2.78 - 1 sec. A = 437.6 Tons GM - 1.7960 f t 142.59 ft-deg. 7.95 - 1 sec. A = 437.6 Tons GM = 0.2953 f t 60.50 ft-deg. 3.85 - 1 sec. A = 551.5 Tons GM = 4.1468 f t 227.96 ft-deg. 3.04 - 1 sec. A = 551.5 Tons GM = 1.7960 f t 81.304 ft-deg. 10.06 - 1 sec. A = 551.5 Tons GM = 0.2953 f t 16.259 ft-deg. 4.37 - 1 sec. I t i s i n t e r e s t i n g to note that the S values c a l c u l a t e d f o r the Single Chine Seiner are, on average, much larger than that f o r the West Coast Trawler. This can be a t t r i b u t e d to the difference i n scale of the two models tested. The Single Chine Seiner was tested at a scale of 1:13 while the West Coast Trawler was tested at a scale of 1:15. Both models were roughly the same s i z e and operating i n i d e n t i c a l environments. When the parameters are extended to f u l l scale numerical differences appear that cause the S values f o r the seiner to be much greater. The areas under the GZ curves f or the seiner, on average, are - 107 -B R E A K I N G W A V E S S * STABILITY F A C T O R S INGLE CHINE SEINER 4 0 0 0 0 3 5 0 0 0 -3 0 0 0 0 -25000-1 CC O h-O 2 0 0 0 0 * to 1 5 0 0 0 -1 0 0 0 0 -5 0 0 0 Legend O 216.4 Tbna, CM=0.2SS7 ft. • 216.4 Tbns, GU=1.1S16 ft. V 216.4 Tbna, GM=2.1331 ft. O 249.6 Tbna, CM=0.2S57 ft. + 249.6 Tbna, CM=0.S113 ft. A 249.6 Tbna. CM=1.1516 ft. O 249.6 Tbns, CM=2.I33I ft. 0 0.2 0.4 0.6 0.8 1 1.2 Maximum Roll/Vanishing Angle of Stability F i g u r e 47. B r e a k i n g Waves S t a b i l i t y F a c t o r ( S * ) S i n g l e C h i n e S e i n e r - 108 -BREAKING WAVES S* STABILITY FACTOR WEST COAST TRAWLER 1000 800 tr o o if * CO 600 400-200 Legend 3Z8.90 Jbn», 328.90 7bn«, 437.84 Tbns, 437.84 Tbns, 437.84 Tbns, SSI.SI Tbns. 55/.5Z Tbns. SSI.SI Tbns. Gtt=3.4154 ft.[a] CM=3.4IS4 /t.[6] , Ck-3.8238 ft. , 01=1.7960 ft. , GH=0.29S3 ft. CM=4J468 fl. CM=I.7960 ft. CM=0J9S3 fl. X X X XK X O 0 1 2 3 4 Maximum Roll/Vanishing Angle of Stability Figure 48. Breaking Waves S t a b i l i t y Factor (S*) West Coast Trawler - 109 -smaller than f o r the trawler. The duration of wave impact, using 0.1 seconds model scale for both, scales up to a smaller impact duration on the seiner at f u l l scale and the area under the respective r o l l response amplitude operator curves i s generally smaller f o r the seiner. * Inspecting the equation f o r S (5.018) i t can be seen that a l l these s c a l i n g differences cause the f a c t o r to grow. To allow * d i r e c t numerical comparison of the S parameters between d i f f e r e n t vessels would require an adjustment for the type of v e s s e l as the * seiner operated s a f e l y at large S (seiner) values while the * trawler capsized at much smaller S (trawler) values. A comparison of the S' and S values p l o t t e d shows that the S parameter gives a better representation of the behaviour of the two vessels. As an example F i g . 45 shows the seiner, with a displacement of 216 tons and metacentric heights of 0.2557 f t . and 2.1331 f t . , to be more unstable than other configurations (highest S' values). F i g . 47 gives a better i l l u s t r a t i o n of t h i s tendency * with the S values. S i m i l a r l y with the trawler. From F i g . 46 the lower metacentric height configurations show larger S' values and from F i g . 48 there i s a much more marked d i f f e r e n t i a t i o n between these configurations and the higher metacentric heights tested. - 110 -6 . 0 RESULTS AND DISCUSSION The two m o d e l s t e s t e d e x h i b i t e d s t a b l e r e s p o n s e s i n mos t o f t h e t e s t i n g p r o g r a m , w i t h t h e e x c e p t i o n o f one c o n f i g u r a t i o n o f t h e w e s t c o a s t t r a w l e r i n b r e a k i n g w a v e s , r e g a r d l e s s o f t h e c o n f i g u r a t i o n o f t h e m o d e l . To i l l u s t r a t e how s e v e r e l y some o f t h e c o n f i g u r a t i o n s v i o l a t e d e x i s t i n g s t a b i l i t y r e q u i r e m e n t s t a b l e s l i s t i n g t h e v e s s e l c o n f i g u r a t i o n s and m a r k i n g t h e s t a b i l i t y c r i t e r i a v i o l a t i o n s made were drawn u p . To r e c a p t h e s t a b i l i t y c r i t e r i o n o f c o n c e r n i n t h i s t e s t i n g t h e y a r e l i s t e d h e r e , w i t h an a l p h a b e t i c c o d i n g . T h e s e l e t t e r s c o r r e s p o n d t o t h e s t a b i l i t y c r i t e r i a l e t t e r s f o u n d i n T a b l e s XV and XVI. A . The a r e a u n d e r t h e GZ c u r v e up t o an a n g l e o f h e e l o f 30° must be g r e a t e r t h a n 0 . 0 5 5 m e t e r - r a d i a n s . B. The a r e a u n d e r t h e GZ c u r v e up t o an a n g l e o f h e e l o f 40° must be g r e a t e r t h a n 0 . 0 9 m e t e r - r a d i a n s . C . The a r e a u n d e r t h e GZ c u r v e b e t w e e n 30° and 40° o f h e e l must be g r e a t e r t h a n 0 . 0 3 m e t e r - r a d i a n s . D. The maximum r i g h t i n g arm b e y o n d 30° o f h e e l must be g r e a t e r t h a n 0 . 2 m e t e r s . E . The a n g l e o f h e e l where t h e r i g h t i n g arm i s a maximum mus t be g r e a t e r t h a n 30° . F . The i n i t i a l m e t a c e n t r i c h e i g h t must be g r e a t e r t h a n 0 . 3 5 m e t e r s . G . The v a n i s h i n g a n g l e o f s t a b i l i t y must be g r e a t e r t h a n - 1 1 1 -80° • TABLE XVIII SUMMARY OF STABILITY REQUIREMENTS COMPLIANCE SINGLE CHINE SEINER STABILITY REQUIREMENT CONFIGURATION A B C D E F G A = 216.4 T GM = 0.2557 f t • • • • • • • A = 216.4 T GM - 1.1516 f t • • • • • • • A = 216.4 T GM = 2.1331 f t • • • • • • • A = 249.6 T GM - 0.2557 f t • • • • • • • A - 249.6 T GM = 0.5113 f t • • • • • • • A = 249.6 T GM = 1.1516 f t • • • • • • A - 249.6 T GM = 2.1331 f t • • • • • • • • : does not meet c r i t e r i o n • : meets c r i t e r i o n 112 -TABLE XIX SUMMARY OF STABILITY REQUIREMENTS COMPLIANCE WEST COAST TRAWLER STABILITY REQUIREMENT CONFIGURATION A B C D E F G A - 328.9 T GM = 3.4154 f t • • • • • • • A - 437.6 T GM = 0.2953 f t • • • • • • • A - 437.6 T GM - 1.7960 f t • • • • • • • A = 437.6 T GM = 3.8238 f t • • • • • • • A - 551.5 T GM = 0.2953 f t • • • • • • • A - 551.5 T GM = 1.7960 f t • • • • • • • A = 551.5 T GM = 4.1468 f t • • • • • • • • : does not meet c r i t e r i o n • : meets c r i t e r i o n The West Coast Trawler more r e a d i l y met the s t a b i l i t y requirements as the i n i t i a l area under the GZ curve f o r the greatest GM value was much greater than that f o r the Single Chine Seiner. From Table XIX i t can be seen that there are only two configurations that a c t u a l l y do v i o l a t e some of the s t a b i l i t y requirements. These two are the 437.6 tons displacement c o n f i g u r a t i o n with a metacentric height of 0.2953 feet that only v i o l a t e d the i n i t i a l metacentric height requirement and the conf i g u r a t i o n that capsized: 551.51 tons displacement with a metacentric height also of 0.2953 feet. The configuration that - 113 -capsized v i o l a t e d not only the minimum i n i t i a l metacentric height requirement but also v i o l a t e d every other requirement save the requirement f o r having the peak of the GZ curve beyond 30° of heel. The design configurations meet, as i s to be expected, a l l the s t a b i l i t y requirements including the minimum vanishing angle of s t a b i l i t y . The Single Chine Seiner, on the other hand, much more r e a d i l y v i o l a t e d the s t a b i l i t y requirements. The only two configurations that met a l l the s t a b i l i t y requirements were the 216.4 and the 249.6 tons displacement configurations, both with a metacentric height of 2.1331 feet. A l l other configurations tested v i o l a t e d one or more of the s t a b i l i t y requirements. When the Single Chine Seiner's metacentric height was reduced from the l e v e l s that f u l f i l l e d a l l the s t a b i l i t y requirements the f i r s t c r i t e r i o n to be v i o l a t e d was the minimum vanishing angle of s t a b i l i t y . This was followed c l o s e l y by the v i o l a t i o n of a l l minimum area requirements. The only s t a b i l i t y requirement that was not v i o l a t e d was, again, the requirement of the peak GZ value being beyond 30° of heel. With t h i s knowledge i t i s i n t e r e s t i n g to discover that the v e s s e l which showed the most dangerous breaking wave response, the West Coast Trawler, was also the vessel that most r e a d i l y met the s t a b i l i t y requirements as set f o r t h by IMO and others. This i l l u s t r a t e s the need for ensuring that vessels which o r i g i n a l l y meet a l l s t a b i l i t y requirements remain i n compliance throughout - 114 -t h e i r working l i f e . 6.1 FUNCTION OF METACENTRIC HEIGHT IN STABILITY As the metacentric height was reduced, f o r a given displacement, both vessels exhibited greater r o l l response amplitudes to regular wave for c i n g , as can be seen by the much greater r o l l R.A.O. peak values i n Figures 24 through 39. The reduction of metacentric height d i d not n e c e s s a r i l y imply that the ve s s e l was on the verge of capsizing as the smallest metacentric height tested, 0.2557 f t . , was found on the si n g l e chine seiner which d i d not, at any time, e x h i b i t capsizing tendencies. As the metacentric height decreased the areas under the GZ curves f o r the respective configurations also reduced. In addi t i o n the vanishing angle of s t a b i l i t y became smaller. Because of t h i s reduction i n area under the GZ curves, and the increased r o l l angles a t t r i b u t e d to lower metacentric height values, the * s t a b i l i t y parameters S, S' and S a l l grow i n r e l a t i o n . The S, S' and S parameters are then ind i c a t o r s of the energy content within the v e s s e l configuration. With some knowledge of the type of environment a ve s s e l i s to operate i n the s t a b i l i t y parameters S and S' could be used i n conjunction with the most severe sea spectra from that environment to determine a minimum requirement f o r the area under the GZ curve. - 115 -Balancing the energy within the sea spectra to the energy required to capsize the vessel (known from model tests) a resulting minimum value for the area under the GZ curve could be arrived at. This method, for a regular seaway, can be described as follows: l e t S be the maximum value of the parameter S corresponding to the limit of ship st a b i l i t y for a given class of ships (in this case single chine seiners). Then, as the ship load condition is considered fixed, the denominator of the fraction defining S can be considered to be known. The numerator of S has yet two unknowns to be determined for a given sea state. While average wave amplitude and average r o l l amplitude are inter-related, they can be determined for a given sea spectrum. Experimental testing of a model, as was done here, w i l l give s t a t i s t i c a l l y averaged r o l l motions. Under these conditions a ship that can operate satisfactorily would be expected to have a minimum dynamic st a b i l i t y (area under the general s t a b i l i t y diagram) in a given sea spectrum to: (6 .001) where: m area under the o sea spectrum m = area under the o r r o l l spectrum - 116 -K = constant If K is a universal constant for a given class of ships, regulatory agencies can specify a dynamic s t a b i l i t y for the expected average wave conditions. These rules, while s t i l l related to the existence of a wave spectrum, would be more flexible and would require s t a b i l i t y depending on the s t a t i s t i c a l prediction of environmental conditions. After the values of m and m are obtained, the minimum area o or required under the general s t a b i l i t y diagram can be estimated for the specified environmental conditions the ship would operate in. If an ITTC wave spectrum with a significant wave height of 11 feet and a value of 5 for the parameter S is assumed, a proposed approximate value of K is 0 . 8 . With the st a b i l i t y parameter S the method would be altered to include the area under the r o l l response amplitude operator as well as the area under the general st a b i l i t y diagram. 6.2 FUNCTION OF FREEBOARD IN STABILITY The only capsizing of the West Coast Trawler in breaking waves occurred when the vessel was in i t s greatest displacement and hence in i t s minimum freeboard configuration. From this i t would appear that the amount of freeboard, in i t s e l f , does not account for the capsizing. - 117 -What does become a p p a r e n t i s t h a t , f r o m an i n v e s t i g a t i o n o f t h e sway a c c e l e r a t i o n s r e c o r d e d , t h e f r e e b o a r d does h a v e a m e a s u r a b l e e f f e c t on t h e amount o f sway a c c e l e r a t i o n e x p e r i e n c e d b y t h e v e s s e l . As t h e f r e e b o a r d i s i n c r e a s e d t h e m e a s u r e d sway a c c e l e r a t i o n s a l s o i n c r e a s e d . T h i s t r e n d was t r u e so l o n g as t h e b r e a k i n g waves were s m a l l e r i n a m p l i t u d e t h a n t h e f r e e b o a r d o f t h e v e s s e l . I f t h e j e t o f t h e b r e a k i n g wave was a b l e t o p a s s u n h i n d e r e d o v e r t h e d e c k o f t h e v e s s e l t h e r e c o r d e d sway a c c e l e r a t i o n s b e g a n t o d r o p . The l a r g e s t a m p l i t u d e b r e a k i n g wave u s e d i n t h e t e s t s was g r e a t e r t h a n any o f t h e f r e e b o a r d s t e s t e d as c a n be s e e n b y t h e c o n s i s t e n t t r e n d b y a l l c o n f i g u r a t i o n s t o a r e d u c e d sway a c c e l e r a t i o n a t t h e l a r g e s t b r e a k i n g wave , b r e a k i n g wave number 5 . 6 . 3 EFFECTS OF SEVERE ACCELERATIONS ON SURVIVABIL ITY A c c e l e r a t i o n s e x p e r i e n c e d b y t h e two v e s s e l s i n b r e a k i n g 2 waves were b o t h a v e r a g i n g on t h e o r d e r o f 3 m / s e c . I n some 2 i n s t a n c e s , w i t h t h e West C o a s t T r a w l e r , up t o 5 m / s e c a c c e l e r a t i o n s we re m e a s u r e d . T h i s i s r e m a r k a b l e as i t i m p l i e s a g r e a t d e a l o f f o r c e i s b e i n g e x e r t e d on a l l f i x t u r e s i n t h e b o a t h u l l as w e l l as p r o v i d i n g a n o p p o r t u n i t y f o r an a p p r e c i a b l e f r e e s u r f a c e e f f e c t ^ . I f e i t h e r t h e f i s h h o l d s o r t h e f u e l t a n k s h o l d a The f r e e s u r f a c e e f f e c t i s t h e r o l l moment i n d u c e d b y t h e s l o s h i n g o f a f l u i d t o one s i d e w i t h i n a c o n t a i n e r . C a l c u l a t i o n s i n d i c a t e t h a t f o r a 5 m / s e c sway a c c e l e r a t i o n and no r o l l t h e r e w o u l d be a s l o p e change o f t h e f l u i d s u r f a c e o f 26 d e g r e e s . - 118 -s i g n i f i c a n t amount of f l u i d or catch and there i s room f o r i t to s h i f t there i s the p o s s i b i l i t y of great heeling moments being produced. Heave accelerations, though measured, are not shown as the values determined f e l l as a random function of the vessels configuration. The heave accelerations were i n the range of 1 2 2 m/sec to 3 m/sec when impacted by a breaking wave. - 119 -7.0 CONCLUSIONS The s t a b i l i t y r e q u i r e m e n t s o f t h e IMO and v a r i o u s o t h e r g o v e r n m e n t a l r e g u l a t o r y b o d i e s , i f me t , p r e v e n t e d t h e v e s s e l , w i t h o u t b u l w a r k s o r s u p e r s t r u c t u r e , f r o m d e v e l o p i n g h a z a r d o u s m o t i o n c h a r a c t e r i s t i c s i n r o l l . When t h e s t a b i l i t y r e q u i r e m e n t s were v i o l a t e d , and t h e n o n l y i f t h e y were s e v e r e l y v i o l a t e d , d i d any mode l t e s t e d show a t e n d e n c y t o c a p s i z e . W i t h t h i s i n m i n d i t w o u l d a p p e a r t h a t t h e mos t p r a g m a t i c a p p r o a c h w o u l d be t o e n s u r e t h a t v e s s e l s o p e r a t i n g a t s e a meet a l l t h e p r e s e n t IMO s t a b i l i t y r e q u i r e m e n t s . The s t a b i l i t y r e q u i r e m e n t of <j> > 80° p r o p o s e d b y Norway f o r s u r v i v a b i l i t y i n b r e a k i n g waves a p p e a r s t o be a d e q u a t e f o r t h e s i z e s o f b r e a k i n g waves t e s t e d i n t h i s p r o g r a m t o d a t e . No mode l was k n o c k e d t o an i n i t i a l r o l l a n g l e g r e a t e r t h a n 80° i n t h e p r o g r a m , n o t e v e n f o r t h e v e s s e l t h a t c a p s i z e d . The v a n i s h i n g a n g l e o f s t a b i l i t y f o r t h i s c o n f i g u r a t i o n was a l i t t l e o v e r 60° a n d , f r o m v i s u a l i n v e s t i g a t i o n o f t h e c a p s i z i n g e v e n t , t h e b r e a k i n g wave t h a t c a u s e d t h e v e s s e l t o c a p s i z e was o n l y a b l e t o c r e a t e a h e e l o f s l i g h t l y o v e r t h i s v a l u e . S c a l c u l a t i o n s show t h a t i n a d d i t i o n t o t h e n e e d f o r a l a r g e v a l u e o f <f> t h e a r e a u n d e r t h e r e s t o r i n g arm c u r v e s h o u l d be o f V s u f f i c i e n t m a g n i t u d e t o a b s o r b t h e e n e r g y o f t h e b r e a k i n g wave . A measu re o f t h e m e t a c e n t r i c h e i g h t does n o t a l w a y s i n d i c a t e a v e s s e l c a r r i e s t h i s minimum r e q u i r e m e n t . - 120 -REFERENCES [I] L i l l e y , S., Men, Machines and History, Lawrence & Wishart, London, England, 1965. [2] Rule, M. , The Search f o r MARY ROSE, National Geographic Magazine, National Geographic Society, Washington, D.C., May, 1983, pp. 654 - 675. [3] Hocking, CA. , F.L.A. , Dictionary of Disasters During the Steam Age 1842 - 1962, Vol I., Lloyds Register of Shipping, London, England, 1969. [4] M o r r a l l , A, Intact Ship S t a b i l i t y C r i t e r i a , Proceedings of Small Ships Sur v i v a l Seminar, Ship and Marine Technology Requirements Board, Department of Industry, London, England, 1979. [5] Dahle, E.A., and N i s j a , G.E., Intact and Damaged S t a b i l i t y of Small Crafts with Emphasis on Design, U n i v e r s i t y of Trondheim, 1984. [6] Inter-Governmental Maritime Consultative Organization, Code of Safety f o r Fishermen and Fishing Vessels, Part B, Safety and Health Requirements for the Construction and Equipment of F i s h i n g Vessels, London, 1977. [7] Aubanel, E.E. and Oldham, K.B., Fourier Smoothing Without the Fast Fourier Transform, BYTE Magazine, February 1985, McGraw-Hill Inc., Peterborough, NH., pp. 207 to 218. [8] Thomas Jr.,G.B., Calculus and A n a l y t i c Geometry, Addison-Wesley Publishing Company, Reading, Mass., 1968. [9] Walpole, R.E., and Myers, R.H., P r o b a b i l i t y and S t a t i s t i c s f o r Engineers and S c i e n t i s t s , Second E d i t i o n , Macmillan Publishing Co., Inc., New York, N.Y., 1978. [10] Bhattacharyya, R., Dynamics of Marine Vehicles, John Wiley & Sons, New York, N.Y., 1978. [II] Dahle, A.D. and Kjaerland, 0., The Capsizing of M/S HELLAND-HANSEN, The i n v e s t i g a t i o n and recommendations f o r preventing s i m i l a r accidents, Proceedings of The Royal I n s t i t u t i o n of Naval A r c h i t e c t s , London, England, 1979. [12] B a l i t s k a j a , E.O., Results of Experimental Investigation f o r Capsizing i n Breaking Waves, Un i v e r s i t y of Michigan, College of Engineering, No. 048, March 1970. [13] Terrascience Signal Conditioner Reference Manual, Terrascience Ltd., Vancouver, B.C., 1985. [14] Bhattacharyya, R., Dynamics of Marine Vehicles, John Wiley & Sons, New York, N.Y., 1978. - 121 -[ 1 5 ] Himeno, Y. , P r e d i c t i o n of Ship R o l l Damping - State of the Art, Department of Naval Architecture and Marine Engineering, College of Engineering, The U n i v e r s i t y of Michigan, Ann Arbor MI, 1 9 8 1 . [ 1 6 ] Ibid. [ 1 7 ] Ibid. [ 1 8 ] Sarpkaya, T and Isaacson, M. , Mechanics of Wave Forces on Offshore Structures, Van Nostrand Reinhold Company Inc., New York, NY, 1 9 8 1 . [ 1 9 ] Ibid. [ 2 0 ] Dahle, A.D. and Kjarland, 0 . , The Capsizing of M/S HELLAND-HANSEN, The i n v e s t i g a t i o n and recommendations f o r preventing s i m i l a r accidents, Proceedings of The Royal I n s t i t u t i o n of Naval A r c h i t e c t s , London, England, 1 9 7 9 . [ 2 1 ] LeBlond, P.H. and Mysak, L.A., Waves i n the Ocean, E l s e v i e r S c i e n t i f i c Publishing Company, Amsterdam, The Netherlands, 1 9 7 8 . [ 2 2 ] Pizer, S.M. and Wallace, L.V., To Compute Numerically. Concepts and Strategies, L i t t l e , Brown Computer Systems Series, L i t t l e , Brown & Company, Ltd., Boston, Ma., 1 9 8 3 . [ 2 3 ] Doebelin, E . O . , Measurement Systems, A p p l i c a t i o n and Design, McGraw-Hill Book Company, New York, N.Y., 1 9 7 5 . [ 2 4 ] Burden, R.L., Faires, J.D. and Reynolds, A.C., Numerical Analysis, Second E d i t i o n , Prindle, Weber & Schmidt, Boston, Ma., 1 9 8 1 . [ 2 5 ] Tse, F.S., Morse, I.E., and Hinkle, R.T., Mechanical Vibrations, Theory and Applications, Second E d i t i o n , A l l y n and Bacon, Inc., Boston, Mass., 1 9 7 8 . [ 2 6 ] A l l i e v i , A.G., C a l i s a l , S.M., Rohling, G.F., Motions and S t a b i l i t y of a Fis h i n g Vessel i n Transverse and Longitudinal Seaways, STAR Symposium, Society of Naval A r c h i t e c t s and Marine Engineers, New York, N.Y., 1 9 8 6 . 122 APPENDIX A SCHEMATICS OF THE ELECTRONIC SYSTEMS - 123 -APPENDIX A . SCHEMATICS OF THE ELECTRONIC SYSTEMS The e l e c t r o n i c s u s e d i n t h e t e s t i n g o f t h e two v e s s e l d i f f e r e d c o n s i d e r a b l y . B e c a u s e t h e e l e c t r o n i c s u s e d i n t h e s i n g l e c h i n e s e i n e r were n o t d e v e l o p e d b y m y s e l f I w i l l r e f r a i n h e r e f r o m p r e s e n t i n g more t h a n a c u r s o r y o v e r - v i e w o f t h e e l e c t r o n i c s . A b l o c k d i a g r a m i s shown i l l u s t r a t i n g t h e l a y o u t o f t h e componen ts and t h e power s u p p l i e s . The West C o a s t T r a w l e r b e n e f i t e d f r o m a c o m p l e t e r e d e s i g n o f t h e d a t a a c q u i s i t i o n s y s t e m . A s u r v e y was c o n d u c t e d o f t h e methods u s e d b y o t h e r s i n t h e s h i p mode l t e s t i n g i n d u s t r y t o h e l p e v a l u a t e what does and d o e s n ' t w o r k . From t h i s s u r v e y i t was g l e a n e d t h a t a r e m o t e l y c o n t r o l l e d v e s s e l w i t h a f u l l y s e l f c o n t a i n e d d a t a t r a n s m i s s i o n s y s t e m w o u l d n o t o n l y be f e a s i b l e b u t d e s i r a b l e . E s p e c i a l l y when c o n s i d e r i n g we were g o i n g t o c o n d u c t o u t d o o r s e a t r i a l s o f t h e m o d e l . A b l o c k d i a g r a m was d rawn up i n d i c a t i n g t h e components we w o u l d l i k e t o i n c o r p o r a t e i n t h e d a t a a c q u i s i t i o n s y s t e m . T h i s i n c l u d e d t h e t y p e s and number o f s e n s o r s r e q u i r e d , t h e means o f p o w e r i n g t h e s e n s o r s and g a t h e r i n g t h e i r o u t p u t , and f i n a l l y a means o f r e l a y i n g t h i s i n f o r m a t i o n t o a d a t a s t o r a g e u n i t w h i c h w o u l d h o l d t h e i n f o r m a t i o n r e c e i v e d f o r l a t e r r e t r i e v a l f o r p r o c e s s i n g . - 124 -A . l VERTICAL GYRO The l i s t of sensors required was e a s i l y f i l l e d as most of the desired equipment was already a v a i l a b l e f o r the sing l e chine seiner t e s t s . One piece of equipment that was not a v a i l a b l e was the u n i t to measure r o l l and p i t c h of the v e s s e l . An o l d m i l i t a r y s t y l e v e r t i c a l gyro was av a i l a b l e from previous tests but t h i s u n i t was found to be both bulky and poor i n q u a l i t y . The output was f a r n o i s i e r than s p e c i f i c a t i o n s permitted. The search f o r a replacement f i n a l l y netted us the Humphry v e r t i c a l gyro described here. A f t e r consultation with the suppliers of gyroscopes to the a i r c r a f t industry i t had been s e t t l e d on Humphry as a supplier of the gyro. Their range of gyros and t h e i r reputation i n the industry gave some reassurance that the piece would be r e l i a b l e and robust. This was l a t e r proven to be somewhat misleading as we found that the marine te s t environment, even with a l l the extra precautions taken, proved to be a very h o s t i l e one f o r the gyro. D e t e r i o r a t i o n of the p i c k - o f f q u a l i t y due to high humidity and shock loadings became a problem l a t e r i n the tes t program, culminating i n the returning of the un i t to the service department for an overhaul and the r e p e t i t i o n of a small set of experiments found to have been too badly a f f e c t e d by the malfunction to be usable. The model selected was a VG24-0825-1 v e r t i c a l gyro with a range of +/- 60° i n p i t c h and +/- 90° i n r o l l . The frequency - 125 -•rH - 126 -1 - 127 -r e s p o n s e o f t h e u n i t was a d e q u a t e f o r t h e a n t i c i p a t e d t e s t r a n g e . A summary i f i t s r e l e v a n t s t a t i s t i c s c a n be f o u n d i n T a b l e X V I I and a b l u e p r i n t o f t h e d i m e n s i o n s o f t h e g y r o s c o p e c a n be f o u n d i n F i g . 4 8 . A . 2 L INEAR ACCELEROMETERS The measurement o f t h e a c c e l e r a t i o n s o f t h e v e s s e l i n h e a v e and sway r e q u i r e d t h e i n s t a l l a t i o n o f two l i n e a r s e r v o - s t y l e a c c e l e r o m e t e r s . The a c c e l e r o m e t e r s u s e d a r e t h e same as h a v e b e e n u s e d f o r many y e a r s b y t h e s t a f f o f B . C . R e s e a r c h Ocean E n g i n e e r i n g C e n t e r f o r t h e m e a s u r i n g o f t e s t v e s s e l a c c e l e r a t i o n s . The u n i t s u s e d were S c h a e v i t z mode l l i n e a r a c c e l e r o m e t e r s w i t h a r a n g e o f +/ - 2 . 0 g . A . 3 AUTO-PILOT/COMPASS SYSTEM The n e e d f o r some means t o measure t h e yaw o f t h e v e s s e l , p l u s p r o v i d e some a d d i t i o n a l c o n t r o l i n t h e r u n n i n g o f t h e mode l i n open w a t e r s l e d us t o d e c i d e on t h e i n c l u s i o n o f an a u t o - p i l o t u n i t . T h i s u n i t w o u l d a l l o w us t o b o t h measu re t h e yaw as a d e v i a t i o n f r o m a s e t d i r e c t i o n on t he compass and i n c o r p o r a t e a n a u t o p i l o t s y s t e m i n t h e c o n t r o l o f t h e h e a d i n g o f t h e v e s s e l t o h e l p k e e p u n i n t e n t i o n a l l y l a r g e a n g l e r u d d e r m o t i o n s f r o m b e i n g i n t r o d u c e d i n a n a t t e m p t t o m a i n t a i n a d e s i r e d c o u r s e h e a d i n g . A l o c a l s e a r c h o f s u p p l i e r s i n t h e Lower M a i n l a n d u l t i m a t e l y l e d us t o t h e d o o r s o f Wagner E n g i n e e r i n g . The e n g i n e e r s a t t h i s - 128 -EASTWARD HO MDDEL WAVE PROBE DEMODULATOR RECEIVER STORAGE DECEHBER 10, 1985 UNIVERSITY OF BRITISH COLUMBIA DATA TELEMETRY SYSTEM EASTWARD HQ MODEL SCHEMATICS  DRAVN IY» GERRY ROHUNG Figure 51. Shipboard Instrumentation - 130 -f i r m were most h e l p f u l and understanding of our needs and were able to suggest a new a u t o - p i l o t u n i t they had f i n i s h e d developing f o r small r e c r e a t i o n a l c r a f t which would s a t i s f y both our needs fo r l i g h t weight and quick response. Because of our need for such a u n i t and the i n t e r e s t shown i n our t e s t i n g Wagner Engineering donated an e n t i r e a u t o p i l o t u n i t , minus hydraulics, to our t e s t program. A . 4 R U D D E R A N G L E S E N S O R Other sensors were i n s t a l l e d i n the v e s s e l , notably a sensor for determining the rudder angle at any given time. This was not required f o r the beam seas t e s t i n g that comprise t h i s thesis but was i n s t a l l e d f o r the following seas tests a n t i c i p a t e d f o r the v e s s e l i n the summer of 1986. The sensor consisted p r i m a r i l y of a potentiometer mounted above, and secured to, the rudder shaft. A. 5 S I G N A L C O N D I T I O N E R The information presented by the various sensors on board the ship had to be relayed through a c e n t r a l processing point p r i o r to entering the data telemetry system to b r i n g the signals to the same standards i n regards to amplitude and o f f s e t . In addition, a number of units required a very stable e x c i t a t i o n to ensure accurate motion sensing. The s i g n a l conditioner used i s an ST41B dual channel board mounted, along with three i d e n t i c a l boards i n a u n i t equipped with - 131 -a power supply designed to operate from a 10 to 40 VDC power supply. The s i g n a l conditioner was supplied by Terrascience of Vancouver. P r i n c i p l e features of the uni t , plus i t s s p e c i f i c a t i o n s , are shown below. Independently v a r i a b l e regulated e x c i t a t i o n f o r each channel (2 to 10 V d.c.) - Independent regulated p o s i t i v e and negative e x c i t a t i o n per dual channel u n i t (+/- 13 V d.c.) - Independent switch selectable gain (1 to 1000) f o r each channel - Pr o v i s i o n f o r bridge completion components to accept 1/4, 1/2 or f u l l bridge inputs to each channel - Four pole Butterworth low pass f i l t e r on each channel - A l l supplies and outputs f u l l y short c i r c u i t protected. SPECIFICATIONS  E x c i t a t i o n Plug selectable e x c i t a t i o n of either; 1) separate 2 - 10 V d.c. (60 mA maximum load) per channel or 2) s i n g l e +/- 13 V d.c. (+/- 60 mA maximum load) per dual channel Line Regulation - 132 -2 -10 V dc +/- 13 V dc less than 0.02% f o r +/" 10% input change less than 0.2% for +/- 10% input change Load Regulation les s than 0.05% for 5 mA to 60 mA load v a r i a t i o n l e s s than 0.2% for 5 mA to 30 mA load v a r i a t i o n Ripple e i t h e r source le s s than 1 mV peak to peak DC - 100 Hz. Amplifier Input - true d i f f e r e n t i a l instrumentation a m p l i f i e r greater than 10 megaohms impedanc Maximum common mode input +/- 15 V dc - no damage Maximum d i f f e r e n t i a l input +/- 30 V dc - no damage Common mode r e j e c t i o n better than 90 dB DC - 60 Hz Gain - switch selectable as follows: LEGEND: X: closed 0: open GAIN Sl/1 Sl/2 Sl/3 S3/1 S3/2 X 1 0 0 0 0 0 X 2 0 0 0 X 0 X 5 0 0 0 X X - 133 -2 - 10 V dc +/- 13 V dc X 10 X 0 0 0 0 X 20 X 0 0 X 0 X 50 X 0 0 X X X 100 X X 0 0 0 X 200 X X X 0 0 X 500 X X 0 X X X1000 X X X X X Switches kept open: Sl/4 Switches kept closed: S3/3 and S3/4 BRIDGE COMPLETION Sl/4, S2/4 p.c. mounted switches that connect the p o s i t i v e a m p l i f i e r input (S+) to a bridge network for use i n 1/4 and 1/2 bridge a p p l i c a t i o n . Note J3, J4 jumper need to be i n place f o r 1/4 and 1/2 bridge a p p l i c a t i o n s . BALANCE RANGE S3/3, S4/3 pc mounted switches that when closed double the balance range of the SET BALANCE co n t r o l (authors note: at the expense of a s l i g h t loss i n precision) BALANCE OFF S3/4, S4/4 p.c. mounted switches that when opened disconnect the SET BALANCE control from the am p l i f i e r . SELECT EXCITATION SOURCE J l a p.c. mounted male header which on odd channel numbers only allows the s e l e c t i o n of e i t h e r v a r i a b l e e x c i t a t i o n (2 to 10 V dc) or f i x e d e x c i t a t i o n of +/-13 V dc. set as follows: - 134 -connect a to b for v a r i a b l e e x c i t a t i o n (2 to 10 V dc) connect b to c f o r f i x e d e x c i t a t i o n (+/- 13 V dc) Connectors: Inputs are Bendix PT02A 12-10S m i l i t a r y s t y l e connectors p i n connections are as follows: PIN # FUNCTION A S- si g n a l negative B P+ e x c i t a t i o n p o s i t i v e C P- e x c i t a t i o n negative D S+ si g n a l p o s i t i v e E N.C. F SHIELD cable s h i e l d G 1/4 B quarter bridge H N.C. J N.C. K V- e x c i t a t i o n negative (odd channels numbers only) Outputs are standard BNC ( i s o l a t e d from chassis) connectors Power Supply Requirements: This v e r s i o n of the s i g n a l conditioner comes with transformer option number 01 which requires 10.6 to 40 V dc supply and provides a regulated +/- 15 V dc to the boards, p i n connections are as follows: FUNCTION PIN # D.C. INPUT AC INPUT - 135 -A p o s i t i v e l i v e B common neutral C chassis chassis Signal Conditioner Board Dimensions: Size: 250 mm X 170 mm X 110 mm Weight: 3.2 kg. Further information can be found i n the owners manual supplied by the manufacturer [13]. A.6 TRANSMITTER/MODULATOR The signals passed through the s i g n a l conditioner are fed into the modulator-transmitter f o r transmission to the remote r e c e i v i n g s t a t i o n . The input range of the transmitter was +/- 5 V dc thus, i f the output of the s i g n a l conditioner was expected to exceed t h i s value a voltage d i v i d e r was i n s t a l l e d i n - l i n e with the si g n a l conditioner feed to ensure no saturation of the input to the modulator-transmitter would occur. The function of the transmitter can be described as follows; the incoming signals are a l l voltage s h i f t e d 5 v o l t s to render the +/- 5 V dc s i g n a l into a 0 to 10 V dc s i g n a l . Each of the incoming sig n a l s are then assigned a unique frequency i n the audio band. This frequency i s then modulated proportional to the amplitude of the incoming s i g n a l . The i n d i v i d u a l audio frequencies are then summed and attached to a UHF radio wave c a r r i e r wave for - 136 -transmission from an omni-directional antenna mounted within the model. A.7 RECEIVER The radio s i g n a l sent from the model i s intercepted by the onshore r e c e i v e r which removes the c a r r i e r wave from the radio s i g n a l and sends the remaining audio s i g n a l out a standard c o a x i a l l i n k . A.8 DEMULTIPLEXER/DEMODULATOR This u n i t takes the audio s i g n a l and s e l e c t i v e l y f i l t e r s each respective frequency to create 8 channels of data. These frequencies are then demodulated to regain t h e i r 0 to 10 V dc range. A -5 V dc o f f s e t i s again applied to the data and the output i s 8 channels of +/- 5 V dc data. A . 9 MINC COMPUTER The data a c q u i s i t i o n was done with the use of a MINC 11 mini-computer running B.C. RESEARCH data a c q u i s i t i o n software. The output of the demodulator/demultiplexer as well as the feed from the wave probe were fed into the input s t r i p of the computer where i t was sampled and stored on 8 inch floppy disk f o r subsequent a n a l y s i s . - 137 -APPENDIX B WEST COAST TRAWLER STABILITY REPORT - 138 -STABILITY REPORT M.V. "EASTWARD HO" •NELSON BROS. FISHERIES INCLINING EXPERIMENT ' I n a c c o r d a n c e w i t h O w n e r s i n s t r u c t i o n s a n d C.S.I, r e g u l a t i o n s , t h e s u b j e c t v e s s e l was i n c l i n e d when n e a r i n g c o m p l e t i o n a t t h e B u i l d e r ' s y a r d . T h e f o l l o w i n g c o n d i t i o n s e x i s t e d a t t h e t i m e o f t h e i n c l i n i n g e x p e r i m e n t : L o c a t i o n : D a t e : R e p r e s e n t a t i v e s : T o t a l men o n b o a r d : W i n d a n d t i d e : W a t e r D e n s i t y : B i l g e s : C o n d i t i o n o f t a n k s : F u e l o i l - F w d . <fc. P S - A f t P S D a y T a n k F r e s h w a t e r - A f t P S H y d r a u l i c O i l T a n k F w d . L u b e O i l T a n k F w d . H y d r a u l i c R e s e r v o i r T a n k s P & S I n c l i n i n g w e i g h t s u s e d : D i s t a n c e w e i g h t s m o v e d : P e n d u l u m p o s i t i o n P e n d u l u m l e n g t h S t a r S h i p y a r d ( M e r c e r ' s ) L t d . New W e s t m i n s t e r , B . C . J u n e 4 , 1969 M r . B . S m i t h - C . S . I . K r . G. M e r c e r - B u i l d e r M r . P . S . H a t f i e l d S e v e n C a l m , n o c u r r e n t F r e s h Pumped d r y 1650 g a l . - 1700 g a l . c a p . P r e s s e d F u l l - 2700 g a l . c a p . P r e s s e d F u l l - 2700 g a l . c a p . P r e s s e d F u l l - 4400 g a l . c a p . P r e s s e d F u l l - 4400 g a l . c a p . O p e r a t i n g l e v e l - 1 5 0 g a l . c a p . P r e s s e d F u l l - 2100 g a l . c a p . P r e s s e d F u l l - 2100 g a l . c a p . 100 g a l s . - 260 g a l . c a p . 175 g a l s . - 260 g a l . c a p . O p e r a t i n g l e v e l 4 © 1000 l b s . ( t o t a l 4000 . l b s . ) 2 7 ' - 0 " S h a f t t u n n e l 9 9 " - 139 -D r a f t s o f v e s s e l as I n c l i n e d : Fwd. A f t P S P s Mean D r a f t Minimum f r e e b o a r d as i n c l i n e d : ' P 5 Mean Trim as i n c l i n e d : Displacement o f v e s s e l as i n c l i n e d : Record o f d e f l e c t i o n s : B'-3" 8'-3" l l ' - l l " ll»-7" 10'-O" S h i f t 1 2 3 4 5 6 7 8 D i r e c t i o n P t o S P t o S 5 t o P S to P S t o P S t o P P t o S P t o S 14/16 14/16 14/16 14/16 13/16 14/16 14/16 13/16 47" 51" 49" 6" by s t e r n 345.5 L. Tons (S.W.) D e f l e c t i o n 0.8750 0.8750 0.8750 0.8750 0.8125 0.8750 0.8750 0.8125 6.875 Mean d e f l e c t i o n 6.875/8 - 0.859" GM as i n c l i n e d : GM - w x d x 1 - .447 x 27 x 99 - 4.06 f e e t d i s p . x a 345.5 x .B59 LCG & KG as i n c l i n e d : From H y d r o s t a t i c Curves at 345.5 L. Tons (S.W.) Th e r e f o r e KM GM KG 15.97 f e e t 4.06 f e e t - 11.91 f e e t MCT 1" -LCB LEVER -Th e r e f o r e LGG 30.05 f t . tons 3.90 f e e t a f t 6 x 30.05 - .52 f e e t 345.5 4.42 f e e t a f t " 140 -a o J 0 J UJ u. O O o r I V5 0 o I o o r w "an o o w 0 iL 0 2 S rt) id 1 t IL u c si e f t 1 4 1L 4 0 j t t o T 0 a + o o t j t 3 * * 0 o A a o o ii o 6 6 \ j ? N •<»• 1 0 w in ifl j CD n M d> •5 ro V o I \ a. * t t IL i» IL •t L ! 0 0 o M 0 0 /-0 o 0 0 u 0 o (0 0 0 il v z 1 : t i i • i ! i i 0 J 0 I p» •i 2 vi •i 2 w 2 2 to z "* w' z 1 41 : I T E M — — VJT. U.T&nS M O M E ( J T W I O M E N T . V C S S . E L A % U4C*_lMe-C» 3 4 - 5 . S O 4-US.OO •'.4.42 l5-L--".00 .*"£A.U_I>J.G O E L 5 W \ . Ol«C-iE • to l.s-B •-- .TO T ( £ > J - S C t> e-\ > M kOivte t. OO n.-s n i s • i.oo •¥ ~) . C O .S". oo i en."so .* z i o . o o S e w e r t4.<e?r CM '1»i-(=»TT=OfE.M ... • • SYSfe Is*. DO i - Z . I 4 - 4-P itei<si<e- .Ki«=*r t K i L>vi>j-ierrTe . - J l ' S 11.CO 5 4 4 - 5 •*• W l.co u.oo 11- CO -t-4-0£ - tA-.co - I M C L J M < * J C _ oTs> : C-} 1 4 7 5 •» Z.fcS - V . T l LDIU . v_ •:. *st=-r. F*S :" C-0." - 5 V -fp \Z.OO . - -to(. OO - ISSiP-OO ~ r v s o • pis J - J - 2.P.--0 I.Uo - is-s-.feo -n.tfo + 3 5 6 .B© 7 camera. (.-J fe. 2.C-L.SO . - W . T P - t r . n r 15 i r - ZS"7.-*0 -. T O T A L S •JS07 •r 11" . 5 5 t-XcxJ DRftPT AFT "3'- a* © . S^s" p-r. 6 ' -L C F ( AxFT « c JSS rr . 5UW -L C Q ( — v...... 1 . i~> rr. K M ,t»p -—r. L C T 3 . . . 3 • ( 6 *T. K G fed 1 • 8 9 " T . G M .. . 5 3 0 1 F T . T - . J S FR"£. &ORPA.C& • — WVCT- 1A . 0 0 r T . T»u< Ar • oo rr. TRIM £«y H E A D ) 1\ • 57 I N C H K . ' H E E L . CO' «so-. * £ C C D 7071 l.t>DC C M & > N » © 2. D P 34-4. :. - - "t-V - l . l Z - «..c4-(£>5 I T U (.11 t.ro • * 2 - - .04-- 142 -~e ~ t * ie S T • « n * » ; r r E M r — V J T . L - . T O M S M O M E U T M O M E U T . UJCHT -&HtT» w e n .t<» J T R 6 & H . W A T « .. APT : » i s tine • *s-|. " F U E L " O I U ":r' :.' rwe> *»4i .so I S S . 6 o - S S B . e o ~ ."- : : . c e w T s n . . .&.£<• LSO Aono - "M.-ic - . UCD • C K I = 4 0 <;eFP«e.t5','.. .7..*. ..... ~ "t -PO 10.0P t-O-OO -2».0£> - Z .»" . OD "STOnuEfc i ; : _ : •; •:. Z..OP \1.DD -2.7.00 - tf"4- OO — — - -- —• • • • - - . •• ........ •• • • . .. .... , ." --T o T A L t | 32-B 4- D < S". UCs * I C 7 see. s o i-.Tou D R f c F T A F T .<<?'-» T * A . P = " r F T . D R ^ F T F W D •3'- — L C F . ( A F T ") rr. L C S . ( — ) rr. IU I-T. L C B . C — ) " - 3 . . - 7 S - rr K G . 2 4 P T . _ _ ; i -.as. P T . C M . 5 t 7 r r . T R I M W O M E U T . __ :.. . 5 « 5 • Sc: FT*£ji. & 0 R P A . C 6 t l F T -—.- :a«-~i5~ rt-Tcvi . fct» F T . T R I M V." V » o ^ 6 " . H E E L . I S " s o " C O * - & I K 4 © •ires .ffOOP .7071 I.COO C M & Z . P S > Z.UU " - - . X . O -t.e^ - • S T B c z . : f R i c ^ m K i G U E v / e f t ) • s s r i . u s l.fel ."71 - . I t - 143 -- J T E . M . V T . L . T O K S ! K G M O M E W T \ _ C C . DEPARTURE .TO. SRAJViDS : 41-97 tC^ta. 59 4CE ~ : _ •.• -. .. . a v i s . VL SO 500-65 '. " - — " " . . . . . . . . . . : . . . . . • -— i:- ;; —_ . . . . . : . . . . . • - • ' • - • • . — . "-v.: . . . . . . . . . _ — .. .... !. J: — — . . . . — . . — •• • — — ' ; - •• • — - •• ' . . . . . . . . . .. . . . . . . ... •j - _ _ • — — 7 . . . . . •• *~- - - * . . . . . . . . . •j-.:... . ... . • . . . • .. -~:r — . - -- . . . . . . •• . . . . . . _ . . . . . . ? • — . . . - ' ' . T O T A L . * S5I •.»& 4516- S\ D i S P u A C E . K E . U T 251 • 16 l . T M t A F T 7/4" .MEAtJ .- t»F*A,P"T S R W T f="»J o L C F . ; ( A P T tfy - "7-91 rj- M I N I M U M PReE&OARD LCG . -• ( — ) t S 4 rr K M . . . r>4 - C — ) 3.^ 8 *T- K G • . . 11- © t o " ."' ' B » G a.- »4 F T G M X • T R I M t/OMEkJT . . . 751 • 4B FTToJ F R £ £ &GRFA.CE. 0 • n tv\t"r* C M c o n s w E t T c o a •37 T R I M C*1 M * * . © } /J I'x. 0.4-65 ujctfS HEEL. * 0 » G O * I B ' _s»i»-4 . e . $930 1'0000 C M E>ih4 e !"."' 0-74 l-4< 1-49 X - « 7 M€»o ~ " ~ " + et>\ - Oli -0-95 - I « S - 0. -6 2 1 -oe 0-44 - O O b - a e t J - 1 44 -I frRgiVAL ikT 6QOJMP6 (n&i LIQUIDS « . s toa ts , wo c * g & o ) 4 8 - ie •*7 <*1 «** I T E M NrVT. U.TOKS.' K G M O M E N T 280-39 I 3507-It VI-16 * . 3fci-99 .FRESH owkTEtt. " ... _ ' . AFT 1 4 - 0 5 13 i o 164-05 .50 (.0 710-^0 F U E L O I L " 15-36 7-16 n o - o o -17-35 - 7i>4> • SO CENTRE 4 - 7 0 5-90 2 7 - 7 0 -34•'30 . no to CREvO ft." fcFFlCTS" i -09 OD-00 *XO .00 2&.00 ITORfc* 1-50 1 7 0 0 75-50 -27.00 ± 0 - 5 0 " O T A L t 3>7 -01 12-23 3&T4-- 51 rlfco * 54,9- 90. Ci\£.?=>i_ACG.»-'\E>-lT 31-7 • O X L.Tetfs 5 R 6 F T A F T I C -M E A . g . O R A . F T . 4© FT. E s « A P * T F " W O £>-L C F . : ( A F T « • ) 7 . 17 (FT. M.'MiMyyi r " R £ E . E » O A , U O A ' •9" L C G . « . 6O » T K M IG»- I S FT. L C B . - < — > 3 • fcl * T . K G I-2- 13 F T B.G. 1 • 62 rr. »wo. G M 3- 95 . FT . T K l S r l w\c»Me>JT .. 576. • 96 rr. •hit. E.URt=ACe. O •20 FT. a 7 • 75 FT .TMJ . O K A t o r t w E C T a e » 3- 75. F T . T R I M 2.0 •75 Mcaii H E E L . I S " • S O ' JE>IKI e> . 1536 . SfffO •7<s7/ C M & i w ' e o n i«e 2 - 6 . 5 3 1 5 3 1 5 4 0-64 . -'0-10 - ( . 0 2 -1-67 - v e t - V * 4 GTL ' fRlGrfTtKlG l_CVew) ( • 4 . 3 KM - 0.O9 - 145 -T A A L F L O A D c p w ' P i T i P N : Q&o'/p L . I B U H I > * - 4 & T C * < « » , sr>% C A R G O ) ~e I K ie * T • tx. «« *s ' I T E M " ~ " •WT. u.Te><s K G M O M E U T L e a . L I G H T . S H I P ">S07 . 1 4 . * 5<ol - 9 9 - F t f c e f c H W A T E R : A F T 9 . "S7 11.80 M O W •>-"Fotc:". oa~ *.'"~ fc.SD -n-io - 17S\ * o — - , — — . . o o s i T K e . 3 . 15> 4 . 75 ( 4 6 4 . -ace© — 1 it . OO "_ej£t=w 4 - ~ c r r & i . T W ; . ..-'.—ir.."- ''... : 1. DO i0 . 0O to. oo - r.S".o: - » ~ . 0 0 "«ToFte.s»'. V..'. ..... . . .""i :i.Q© n.oo n.oo -Z70O r7 . o o . t A R C O .. I S t . S O 7 .SS 9 7 4 - 0 0 i - l l . S O — . — - ' • .. . . . . . . . . . . — • •• • • " " ~~ •" — . , . ' . - — . .; " - " • . T O T A L * 4 - 5 7 . & 4 I0.7fc> *r-HO .11. = > R A F T A F T M E A W D R A . F T It . 3 2 . FT . D W A F T F » I D I C F ( A F T ti V 6 i 7 !T P T . M l M I M W M F R E E B O A K O a'-»c?/4* L E G ( } '."ruv.*f" F T . K M IS". foO FT". L C "& < • — ) :T:.VI:.:-4.- ee»: F T . K G I P . 7<o r r . B .G . £f»>C>.} . .-0.-3.A. F T . G M 4 - S r 4 . r r . T R l K * fcrtOMEJJT _ . ' . : 1CS -1 . ~. Fr.ToJ F F r & E . t O R P A C E v J . O S FT . M E T \ * ss> F T - T M G M C O W W E C . T t » 3 . V I FT -T R I M H E E L . 4 S * G O * i s ' . S S P e O • 707« .«5>4.S9 ( .000 C M S»\*>» © ' R 1 * 0 5 . J D 3 e-i - - 3 4 — .9>t - Z .V< - 3 . S S • '9*S> <~17 ( - 4 7 • B-7 .16 - 146 -I T>^.vA,vrr\i^<s P R O M C I ^ O O N I P ^ , : ( e » s % u g o i a s ^STOKE^ ; F J H . CABCO' • * • • • • • *e "' • i * ie • er M> «*I •*> : r r E M ~ ~ <WT. U . T O K S KG M O M E U T U1G M O M E H T . L.IG*-IT. S H I P fZ.SsO 3S07- 2-4. • 129 _PP4£&M . W A T E R . ... A F T . est. 11.tc 7b.10 ••S0.34 *• » * o . s o " f u E i _ - : o t L " : " . . FWD •7. n fr.ZS -17.OD - i t i .<lO . . C O M T E K . . t. 4.SO S>. B S - S . S T S - . 77 " C R C O 4 "epFlECTS ". :„ .„ ." . . ' . .. . 1.00 10.00 Z.O.OO - IS.OO — Zi'.OO • TO n o o II. -Zleo .£A.«.«© _ Z t t T D D » 7 o Z S 7 P . OO •*- a o 4&.oo . . — — — — -,"„ 1. „ ''. '.... „ . — — - _ ; • • •;• -• - - — •.— •• "-- • .'. :.' . T O T A L t 5S-2. . O l 11.06 6.2.3*.% 1 D l £ . P u A , C E M E » J T <SC» 3 ,OI C.Tcwt D R A F T A F T —u l. .MEA.KI 1 3 ,-K.S rr. B R K F T F w d - " I f . L C F ( A F T # ) 6 .r»£> FT. MlM l M U M * P R £ E B * A n o 1 ' -L C G . ... ( — ) — • C a t . . . r r . K M IS". 3.6 FT. L f & . < — ) S- .-7&: P T . K G ' ' U . ©e I T . .. . ;• 0 . 4 . 5 , . T . G M . 4 - ' 3 o F T -T R M V \ 0 * * E > J T . 3 . 5 " & • ' 3 ^T.-roMS FRce. £,uFtr=/vee. • 1 4 - PT. M C T G M C.OP5«EC.Ti£B lt> F T . T R I N A H E E l . " " IS" ^ 0 ° 4 5 " GO* 7 5 " ..£>tKi . e . t i » 6 6 .S0OO .-7071 .•Stele O (. OOO c M &«Ni e lofc z 3-foo 4-.it> M t o " " "' " '. . - .1*. -.LB - Z O l -z.es - 3 . S 3 GZ. fRiGfcrnKlG 1.40 (-74, M i .<*3 - 147 -T f c g e i V A l *>T PORT f t p * / L'tfOlOt <> «5TORE5, FULL CARGO]). " 8 " . 4 8 - - " ' • si.- -•-«*,. ... 4 1 « E S . I I T E M VJT. L . . T O K & ! KG M O M E t J T l_ce> M O w i E M T "~" • 260-39 12-50 S501-2C * 1-26 •t-.34,1-99 _FRESW VWtTER, : i f T' < • ee U.30 .. .' 2 1 -25 + 5 0 0 0 • 9 4 - 0 0 roti. CIL F-WD RfcS. 2.05 6>-10 a - 5 o - \ 4 r f c O - 54-42 — — . — . .. C l U T R F . ... 0 - f e 3 4 - 5 5 •a. 14 -3530 - ...22-24 " c e e v J •rtFFECTST.l"^ . < .00 . 20 -00 -25-oo - . .15 DO STORES - • • • • • 0-10 n « ? 3-40 -27 00 -•" " 5-40 CARGO.. .. " 2 6 5 - 0 0 9 - 7 0 2570- O O + 11-50 +. 3046-00 " ' -•• r- '-' —- _ _ ... . ~:— '.~z::~. — . : . " ~ :. '. • "" ' r . . . . — . . . . . . . . . • • • T O T A L , 5 5 1 . 1 5 I M 5 «i<37 • (5 D l & P L 551 • (5 L.T.NS D R A F T A F T U ' - 9 " N ^ E £ A K 1 . t 3 F * A . f = ' T 1 3 • O 1 FT. S>T={Ai=-T F="vJ O u'- iVe L C F ( A F T « " ) e 6fo FT. M<sl lMUtv\ F R £ E E * A T ! D L C G : • ( — V £> 2 0 fT. K M 15-5& FT. L C " & - < — ) *> e>7 F T K G H-15 rr. o 5 3 FT. »tT G M 4.11 FT. 7"KtMt . . 2 9 2 I 1 » T . T . K * E - U R F A C E . 0 :o6 rr. 3 9 • 7 6 r r . T ^ i GK ^ I t O I ' l W E C T e o 4- 13 r r . T R I M £&V STERAD 7 ; 3 4 iNcms. H E E L . . ~ . . • - :»s» 2.0" 4 5 * G O * 1 5 " • s o ' . 1565 . seso • l o l l • .9659 (•oooo C M Ealtvt © 1-07 2-o7 2- 92 3-36 3-99 4-i3 MS»o " - 0 1 6 - O 6V4 - » M 4 - 1-97 -2-64. -3 -54 G7_ . (R tGr fT i tJG U2s/ev) 0-69 . t-43 • TS 1-61 I - \l 0- 59 - 148 -:PQRT fcfTgg DlSCU^ggt, vmvt ICE (\0% LlgJlDS » STOgtS, VlO C^RSO^ ; ( T E M VT. U.TO K S) K G M O M E U T .LIGHTSHIP ".: ; ~ " 11-50 3S01--Z4. * 1 -16 + .".3<cl -99 . .FEE SW WATER..." ..." kFT II.W 7J "25 f SO'&o •» "34 • 00 "FUEL OIL " ~—\: . FvjD. P^ s. .. a -06 6-10 ..II-50 - Ifc- So - -34-47 CENTRE . •. .... . 0-4.1 41S 7-74 -15-lo -•: 11 -IA " c i u w v EFFECTS —"•• -: i r ™ . " : . _ : : T : . : l-oo 00-00 10-00 -15-00 -•....25 -co . - ; : o.ao 17 00 . 3 ,4© -1700 - 5 -40 17 50 — ic& . _ : : • _ — r . . . .. • : — - - • - • - - — - ... . " : • . _ _ r ' ". - - _ " V" ... — • — ' - - _•- • -•'• .... -• * " • T O T A L S 30B--4-I i3'ie 4- \ '10 3<Z>«. •9} 0 1 £.F> « A C E « \ E > J T 3 o B • 4-t L.-tow* D ^ f e F T A F T 9' . . M E A S I . O W . F T s • as FT. 5 R A ! » T F W D L C F .- ( A F T tf ) £> • V7 »T. MIMIWIDM F R e C L B ^ A ^ O L C G : •...(.-• V 1 • xo r r . K M . . . •. 16- •22. rr. L G B . 3-51 FT. K G 13- 19 r r B . G 1.31 rr. FWD. G M a-t?3 FT 7 1 2 - 4 3 rr.-swt F R i t 6 U R F A . C & 0- OB fr. M \ C _ T - 47- ©8 r r TOKS G M cont ra E C T i S . ' O 1 95 fT. T R l M t_ev U E M ? ) 26-1© >MCMf« H E E L . - • I S " | 3>0P - U S ' G O * « > 0 " . i » 6 < 5 . Z9SO •lei I 1 •DOOO C M £> IN I © 9 7 6 1-49 I M i -55 S - 6 5 1-95 M & o ' - M l -1 -04 - 7 - 6 7 cr (RicurtKjG u e v e * : ) o-to . I-V7 - C 01 - 149 -. JOT " STE.Rkl T R K W L E R J..MV.' EASTWARD MO* ^ o ^ ^ ' ^ E 1 (MpS) CURVES ~ ' < T O V E , H W F l E L D 4 C O M P , \ U Y U T C " W O r V T v J V A U C O O V E K B . C . APPENDIX C FOURIER SMOOTHING - 152 -C l FOURIER SMOOTHING The smoothing technique used i n the processing of the experimental data to eliminate high frequency noise from the signa l s was developed by E r i c E. Aubanel and Keith B. Oldham of Trent U n i v e r s i t y , Peterborough, Ontario. The technique they developed smooths data obtained at regular i n t e r v a l s and containing any number of data points. The discussion that follows i s based p r i m a r i l y on an a r t i c l e they published i n the February 1985 issue of BYTE magazine. The d i s c u s s i o n w i l l be broken into two parts. F i r s t , a l i t t l e explanation of the Fourier transformation i s given with how the high frequencies can be removed and, secondly, an explanation of the algorithm used for the smoothing technique. C . l . l THE FOURIER TRANSFORM Fourier transformation of a number of data points produced i n the time domain remaps the energy contained within the s i g n a l into the frequency domain. As an example, i f the input s i g n a l to be transformed was a pure sinusoid with a frequency of 1.0 Hz. and an amplitude of 10.0 units the frequency domain representation would be a si n g l e spike at 1.0 Hz. with an amplitude of 10.0 u n i t s . I f there was a second s i g n a l , l e t ' s say a 5 Hz. sine wave of amplitude 20.0 u n i t s , superimposed upon the o r i g i n a l 1.0 Hz. si g n a l we would have what i s shown i n F i g . 52 as the time domain - 153 -s i g n a l . When t h i s i s transformed into the frequency domain the r e s u l t i n g map becomes what i s shown i n F i g . 53. TYPICAL REPEATING FUNCTION 40 T : ! -40 H 1 "1 : 1 1 0 1 2 3 4 TIME (seconds) Figure 52 T y p i c a l Time Domain Signal From the i l l u s t r a t i o n i n F i g . 53 i t can e a s i l y be seen that the removal of high frequency components becomes almost a t r i v i a l matter i n v o l v i n g the truncation of the components on the frequency axis beyond some chosen c u t - o f f point and then transforming the r e s u l t i n g waveform back into the time domain. This remaping to the time domain i s c a l l e d Fourier inversion. - 154 -The performing of a Fourier transform on a serie s of r e a l TYPICAL FREQUENCY DOMAIN REPRESENTATION OF REPEATING FUNCTION 40 30 111 Q • 20-| Q_ < 10 2 4 6 8 FREQUENCY (Hertz) 10 Figure 53 T y p i c a l Frequency Domain Representation of Signal data points, x^ , produces two sets of transforms: N-1 1 v f 2jrjk>, N ! X J c o s(-iH N-1 k =0,1,2 N-1 (C.001) k =0,1,2 N-1 (C.002) J-o The el i m i n a t i o n of high frequency components from the frequency domain can be represented as a m u l t i p l i c a t i o n , - 155 -(C.003) by a function, f ^ , which i s c a l l e d the d i g i t a l f i l t e r function. The f i l t e r f unction can take any number of forms. The most obvious type of f i l t e r f unction i s the rectangular f i l t e r which cuts o f f a l l transforms f o r k>E. The problem with using t h i s form of f i l t e r i n g i s that i t can lead to f a l s e accentuations of frequencies corresponding to transform points near where the f i l t e r begins. The method proposed i n the paper was to use a quadratic f i l t e r function which produces a gradual attenuation of the frequencies at the high end. The f i l t e r f unction can be represented as the mathematical function; f k = 1-(|] k-1,2,3 E - l 0 k=E,E+l,. . . (C.004) The smaller the chosen value of E, the greater the high frequency attenuation. The c l o s e r E i s to (~~~) t n e l e s s a f f e c t e d the inverted s i g n a l . To reduce the amount of computational work required the two equations f o r the Fourier transforms can be inspected for terms that repeat and that are equal to zero. With t h i s reduction i n terms the two equations become: N-1 R j = o (C.005) - 156 -\ = ~lr + I r I xj c o s C ^ ) k = 1 - 2 E - 1 (c-006> N-l \ = ~4 I X j s i n C ^ 3 k=l,2,...,E-l (C.007) j - i E - 1 \ - \ + 2 l f A ( c - 0 0 8 ) E- 1 k= 1 j - l , 2 , . . . , N - l (C.009) where X j i s the high-frequency-stripped analog of x^. The term f o r I i s zero because the sine of 0 i s 0. The f a c t o r of 2 found i n o equations (C.008) and (C.009) i s there because of the r e s t r i c t i o n of E being less than or equal to ^ and by taking advantage of the symmetries (R^ ^ = R^, 1^ ^ = -1^) already noted. This s i m p l i f i c a t i o n s t i l l leaves a considerable amount of number crunching to be done. I t was because of t h i s that a further reduction i n computation was developed using an algorithm c a l l e d the Fast Fourier Transform (FFT). This approach to the problem applies the properties of sines and cosines such that the number of computations i s s i g n i f i c a n t l y reduced. S i m i l a r l y , t h i s allows a reduction i n the number of m u l t i p l i c a t i o n s required, r e p l a c i n g a large number of them with additions instead. The storage space required f o r transform and i n v e r s i o n i s greatly reduced as the new - 157 -numbers computed can over write the o r i g i n a l values. On the negative side of the FFT coin the algorithm requires that the number of data points to be processed be a power of 2. This r e s t r i c t i o n requires the user to us u a l l y "pad" the input data by adding a number of zero data points to the end of h i s record to meet the power of 2 requirement. This method i s c a l l e d " z e r o - f i l l i n g " . Besides creating a d d i t i o n a l demands on memory a l l o c a t i o n the add i t i o n of zeros to the end can cause undesired high frequencies to be added to the s i g n a l due to possible d i s c o n t i n u i t i e s between the r e a l data and the zero l i n e extension. Also working against the use of the FFT f o r smoothing purposes i s that i t i s an inherently square method, i e : i t requires the computation of 2N outputs from 2N inputs. Thus, i t cannot e x p l o i t the advantages of being able to produce E outputs from N inputs. With a l l these factors involved i n the use of the FFT f o r data smoothing the process was taken one step further by Aubanel and Oldham to produce the algorithm used f o r the smoothing of the data i n t h i s t h e s i s . Further reductions i n computation could be r e a l i z e d by inspection of equations (C.006), (C.007) and (C.009). I t can be seen that a l l of these equations are of the form; M + V s i n m |-27rml-> (C.010) m=l - 158 -where G, m, U^, Vm,M and 1 are appropriately interpreted. To evaluate expression (C.010) the sum was s p l i t into odd-m and even-m terms, M or M-1 _ r« T T r27r(m+l)l 2TT1^ i . r27r(m+l)l 27rl>, G = ) U c o s f — - —i-=—J + V s i n — V T - j H m = l , 3 M or M-1 /-27rml-v cos [— 3^ + V ,Y U m m = 2 , 4 m . r27rml-N 5 1 nl—N~J (C.011) and the arguments of the trigonometric terms are modified i n the odd-m moeity. A d d i t i o n a l formulas were added to expand the modified functions and the m i s then replaced by 2m-1 i n the f i r s t summation and by 2m i n the second. A f t e r c o l l e c t i n g terms i t was found that, I n t - M + l 2 r G - I » 2 , . I - ( T ) - V I ! 1 < T ) « 2 . " " ( T r ) m=l , 2 U 0 S i n f % i ) + V 9 c o s f ^ + V 2m-1 *- N J 2m-1 N •> m . f4fnil>, : l n l — N ~ J (C.012) I f M i s odd, equation (C.012) c a l l s f o r the values of V^ +^ and U"M+1' which were not present i n equation (C.011); the authors in t e r p r e t e d these terms as zero. A comparison of t h i s method with the e a r l i e r FFT form shows there are two extra terms to compute but the number of summed - 159 -t e r m s h a s b e e n c o n d e n s e d b y a f a c t o r o f two . I f t h i s c o n d e n s a t i o n p r o c e d u r e i s r e p e a t e d P t i m e s , where P=Int{log2(2M- l)} , t h e n a s i n g l e (m=l) t e r m , G = n e w e s t U c o e f f i c i e n t c o + n e w e s t V c o e f f i c i e n t s i n (C.013) r e m a i n s f r o m w h i c h G c a n be compu ted . The u s e o f t h i s p r o c e d u r e r e d u c e s t h e number o f s i n e s and c o s i n e s n e e d e d t o be computed f r o m M t o P + l e a c h . C . l . 2 FOURIER INVERSION To r e c r e a t e t h e t i m e doma in d a t a t h e f r e q u e n c y components a r e summed t o g e t h e r as powers o f s i n e s and c o s i n e s , w i t h t h e i r a s s o c i a t e d p h a s e s , t o p r o d u c e t h e t i m e doma in c u r v e . The o p e r a t i o n c a n be w r i t t e n as f o l l o w s : C . l . 3 OPERATION OF THE ALGORITHM The d a t a t h a t i s t o be smoothed i s s t o r e d i n an a r r a y named X ( J ) ,J=1 N , where N i s t h e number o f p o i n t s i n t h e i n p u t w a v e f o r m . The number o f i t e r a t i o n s t h a t t h e r o u t i n e h a s gone N-l N - l (C.014) - 160 -t h r o u g h , Q, i s s e t t o z e r o . From a n a v e r a g e o f t h e f i r s t t e n p o i n t s and t h e l a s t t e n p o i n t s a s t r a i g h t l i n e i s s u b t r a c t e d f r o m t h e d a t a t o e l i m i n a t e t h e p o s s i b l e end e f f e c t s o f i n t r o d u c i n g u n w a n t e d h i g h f r e q u e n c y i n f o r m a t i o n i n t o t h e d a t a . The amount o f s m o o t h i n g t o be done i s d e t e r m i n e d b y t h e s p e c i f i c a t i o n o f t h e s m o o t h i n g f a c t o r , E . T h i s f a c t o r must be an i n t e g e r g r e a t e r t h a n 1 and l e s s t h a n o r e q u a l t o ^ . The f i r s t t r a n s f o r m c a l c u l a t e d i s R , f o l l o w e d b y t h e e v a l u a t i o n o f R and o J k I f o r k=Q t o E - l . A f t e r t h i s t h e f i r s t i n v e r s e t r a n s f o r m i s k p e r f o r m e d . T h i s i s t o c a l c u l a t e d t h e v a l u e o f X q u s i n g t h e q u a d r a t i c f i l t e r f u n c t i o n and R^. F o l l o w i n g t h i s t h e r e s t o f t h e new v a l u e s , x ^ , j = l N , a r e computed i n t u r n u s i n g R^, 1^  and t h e q u a d r a t i c f i l t e r f u n c t i o n , f A l l t h e t r a n s f o r m e d d a t a v a l u e s , r e p r e s e n t i n g t h e smoothed d a t a , a r e s t o r e d i n a r r a y X1(J),J=1 N . The i t e r a t i o n c o u n t e r , Q , i s s e t t o Q+l and a n o t h e r p a s s i s p e r f o r m e d i f t h e s m o o t h i n g was i n s u f f i c i e n t . W i t h t h e new p a s s t h e d e g r e e o f s m o o t h i n g s p e c i f i e d b y E c a n be c h a n g e d . Once t h e d a t a i s smoothed t o s a t i s f a c t i o n t h e s t r a i g h t l i n e removed a t t h e s t a r t o f t h e p r o c e s s i s added b a c k i n t o t h e d a t a f o r f i n a l o u t p u t . - 161 -APPENDIX D BACKGROUND THEORY - 162 -D.O BACKGROUND THEORY D.l SOME BASIC DEFINITIONS To be able to better understand the c h a r a c t e r i s t i c s of a ves s e l i n a marine environment some means was necessary to describe the pertinent aspects of the vessels design and motion. In t h i s s e c t i o n the notation used w i l l be explained and some background given to the basic equations of motion and how the parameters computed r e l a t e to the ships motion. D . l . l DISPLACEMENT Displacement i s the measure of the weight of water corresponding to the volume of the ves s e l below the surface of the water. This value i s equal to the weight of the ves s e l when i t i s suspended from a scale i n a i r . The standard symbol used f o r displacement i s A. D.1.2 TRIM Trim i s the l o n g i t u d i n a l i n c l i n a t i o n of the v e s s e l . This may be expressed as the angle between the baseline of the ship and the waterplane. Usually the trim i s expressed as the differe n c e between fore and a f t d r a f t s . D.l.3 DRAFT - 163 -Draft is the measure of the lowest point of the vessel from the surface of the water. Draft values quoted for a vessel are usually given for the fore and aft sections of the vessel as the trim is not always 0 degrees from the design trim. For the sake of comparison most drafts, when compared, are either the average of the fore and aft drafts or the largest draft measured along the length of the vessel. There are two types of draft measures quoted. These are the molded draft and the keel draft. The molded draft is measured from the waterline down to the molded baseline. The keel draft is measured from the waterline to the lowest point on the keel. The second is usually the one operators of the vessel w i l l quote when asked the draft of their vessel. D.l.4 BASELINE The baseline is a design aid used by the naval architect to define the datum elevation of the vessel and from which a l l elevations are measured. This line does not necessarily have to coincide with the lowest point of the hull as any arbitrary plane is just as adequate. The baseline is usually placed such that i t intersects the centerpoint of the vessel at i t s lowest point. This line is referred to in nomenclature as K. D.1.5 CENTER OF GRAVITY The center of gravity is a point from which a mass of - 164 -equivalent magnitude to the vessel could be placed to produce identical moments about a l l three exclusive axis. The position of this center of gravity is usually along the longitudinal axis of the vessel (provided i t has no heel) and is measured in the other two planes as the distance from the center-line of the hull longitudinally and i t s height from the baseline. This point is normally marked with the symbol G. D.1.6 CENTER OF BUOYANCY The center of buoyancy of a vessel is the point within the vessel that a l l the hydrostatic buoyancy forces appear to be acting. This position is normally denoted by the symbol B. D.1.7 METACENTER The metacenter is a point located above the baseline where, at some angle 6<f>, the vector representing the buoyant force on the hull intersects the line drawn perpendicular to the plane of the baseline through the center of gravity. The symbol for the metacenter is the letter M. D.1.8 KM KM refers to the distance from the baseline, K, to the metacenter, M. This value is a function of the displacement and draft of the vessel. - 165 -D.l.9 KG KG r e f e r s to the distance of the center of gravity, G, from the baseline, K. This v a r i e s with the v e r t i c a l p o s i t i o n of the center of gravit y . D.l.10 GM GM i s c a l l e d the metacentric height and i s equal to KM minus D.l.11 GZ GZ i s also named the r i g h t i n g arm and i s the distance between the center of gravity, G, and the vector produced by the buoyant force a c t i n g on the h u l l at an angle 8<f>. KG. y FIXED COORDINATE SYSTEM y k MOVING COORDINATE SYSTEM Figure 54. The Dynamic Coordinate System - 166 -D.2 THE DYNAMIC COORDINATE SYSTEM To represent the motions of the vessel mathematically two sets of coordinate systems had to be developed. These are illustrated in Fig. 54. D.2.1 WORLD COORDINATES The world coordinates are fixed in space externally to the vessel. These coordinates give the absolute displacements of the vessel with reference to i t s surroundings. The reference frame is assumed to be fixed in space. Normally this reference frame, though fixed in space, i s , for the study of ship motions, allowed to exist in one point relative to the surface of the Earth as i t is unnecessary to include the Earths rotation. D.2.2 LOCAL COORDINATES The local coordinates are fixed to the vessel and usually have their intersection, 0, as the location of the center of gravity, G, of the vessel. The z axis runs longitudinally through the h u l l parallel to the center line of the vessel. The x-axis extends horizontally from the center of gravity and the y-axis rises v e r t i c a l l y from the center of gravity. D.3 EQUATIONS OF MOTION - 167 -D.3.1 Equation of R o l l Motion (Uncoupled) The motion of a ship i n a transverse seaway can be described by a r e l a t i o n s h i p of the r o l l angle of the ship, the r e s t o r i n g moments and the e x c i t i n g forces. For small r o l l angles a s i m p l i f y i n g approach of l i n e a r equations of motion i s usu a l l y considered s u f f i c i e n t and produces acceptable r e s u l t s . When the r o l l motions of the ship become large the n o n - l i n e a r i t i e s involved i n the motions can become very important. These n o n - l i n e a r i t i e s could eventually magnify some small v a r i a t i o n i n e x c i t a t i o n to the point where r e s t o r i n g moments are not only i n s u f f i c i e n t but may a c t u a l l y contribute to the capsizing of the v e s s e l . To develop the non-linear equation of r o l l motion (uncoupled) we f i r s t s t a r t with the standard l i n e a r form of the equation of motion. This equation i s of the form, it a<f> + b<j> + c<f> <= 0 (D.001) or, I' H + hp. + AGity - 0 d t 2 d t (D.002) where a v i r t u a l mass moment of i n e r t i a about the lo n g i t u d i n a l axis = I' -[(A+A')/g]k2 XX A = displacement of the v e s s e l - 168 -A' /g= added mass of the ves s e l f o r r o l l i n g k = radius of gyration of the vess e l mass plus added mass term f o r the r o l l i n g motion b = damping c o e f f i c i e n t GM = metacentric height (transverse) (j> = angle of r o l l ( i n s t i l l water) i f the v e s s e l i s not i n s t i l l water the angle of r o l l considered above i s r e l a t i v e to the instantaneous surface of the water. That i s , the di f f e r e n c e i n angles between the r o l l angle of the ves s e l and the angle de f i n i n g the slope of the water surface, a. I f the damping and i n e r t i a terms are assumed to be functions of <f> alone then the equation of motion can be expressed as, I' <f> + h<f> + AGM(^-a) = 0 (D.003) XX or A k 2 A k 2 A k 2 1 XX 1 XX 1 XX where A = A + A' l In many cases the waveform def i n i n g the surface of the water can be expressed as a simple sinusoid of the form, - 169 -a = a 'sinw t M e (D.005) where maximum e f f e c t i v e wave slope encounter wave e frequency Su b s t i t u t i n g these assumptions into the the equation f o r simple l i n e a r motion (D.004) we obtain the general equation of l i n e a r r o l l i n g i n a si n u s o i d a l seaway. A f t e r s i m p l i f i c a t i o n of c o e f f i c i e n t s we obtain, which i s a l i n e a r second order d i f f e r e n t i a l equation that can be solved using conventional techniques f o r an exact s o l u t i o n . This r e l a t i o n s h i p i s only adequate, though, f o r r o l l angles of les s than around 8 degrees [14]. Non-linear r o l l i n g can be caused by a number of fa c t o r s , these are divided into two primary categories; those that a f f e c t the r o l l damping of the ve s s e l and those that a f f e c t the r e s t o r i n g moment of the v e s s e l . These n o n - l i n e a r i t i e s can be expressed as, where a represents the v i r t u a l mass moment of i n e r t i a as a <j> + 2ixf> + u> <f> = a' u> sinw t (D.006) (D.007) 170 -function of the encounter frequency and b^ and b^ are damping coefficients related to the r o l l velocity and r o l l velocity squared, respectively. The absolute value of one of the terms in the velocity squared r o l l damping is included to retain the sign of the force such that i t is always opposing the r o l l motion. The c(<j>,t) term is the restoring moment term and this is a function of •both the instantaneous r o l l angle and time. It can be expressed as the series expansion, c(*,t) - c^t)* + c 3 ( t ) ^ 3 + c 5 ( t ) « 4 5 + . . . ( D . 0 0 8 ) The last term in the non-linear r o l l motion equation is M(w ,t) which varies with both the encounter frequency and elapsed e time. D.3.1.1 Non-Linear Damping Coefficients Returning to the single degree of freedom equation of motion, AA + B . ( ^ ) + CA - M.(wt) ( D . 0 0 9 ) <p <P <P <P The damping moment can be expressed as a series expansion of <f> and |^| in the form B ^ = B <f> + B <f>\(t>\ t B / + . . . ( D . 0 1 0 ) which is the non-linear representation as described earlier. To - 1 7 1 obtain values of the non-linear damping c o e f f i c i e n t s from t e s t i n g the most popular technique i s to conduct f r e e - r o l l t e s t s . In the f r e e - r o l l tests the model i s r o l l e d to a c e r t a i n angle and then released. The motion i n i t i a t e d i s such that there i s no sway or yaw as these would a f f e c t the values of the damping obtained. The heave and p i t c h motions, on the other hand, are allowed i n so much as they are a part of the r o l l i n g process of the model as i t attempts to maintain a constant displacement and trimming moment at a l l r o l l angles. The p i t c h and heave are to be r e s u l t s of the natural hydrostatics of the ve s s e l and not of the i n i t i a l motion. I f we denote by <f> the absolute value of the r o l l angle at any given time corresponding to the n t h extreme r o l l value we can develop a r e l a t i o n s h i p of t h i s angle to the mean r o l l angle. This r e l a t i o n s h i p i s r e f e r r e d to as curves of e x t i n c t i o n . Following the work of Froude and Baker [15], a t h i r d order polynomial can be used to represent the curve of e x t i n c t i o n as follows, A<f> = a<f> + b<f>2 + of? (D.011) m m where the angle of r o l l i s given i n degrees. and the values of and <f> are given by: A^ = <t> - <f> (D.012) n-l n and )/2- (D.013) m n-l n The c o e f f i c i e n t s of polynomial (D.011), a, b and c, are - 172 -c a l l e d the c o e f f i c i e n t s of e x t i n c t i o n . The r e l a t i o n s h i p between these c o e f f i c i e n t s of e x t i n c t i o n and the damping c o e f f i c i e n t s shown i n equation (D.010) can be derived by i n t e g r a t i n g the equation of motion shown i n (D.009), without the external-force term, over the time f or a h a l f r o l l cycle to complete. The energy d i s s i p a t e d due to damping i s then equated to the work done by the r e s t o r i n g moment. This r e s u l t can be expressed i n the form, 9 B + f-w <f> B + | w 2 ^ 2 B l 3rr n m 2 4 n m 3 (D.014) Comparing t h i s r e l a t i o n s h i p to that shown i n (D.011) and r e l a t i n g terms the e x t i n c t i o n c o e f f i c i e n t s can be expressed i n terms of the damping c o e f f i c i e n t s as follows: a = f ^ B i (D.015) 9 2 b - w m § B 2 < D - 0 1 6 > 9 3 j ^ B (D.017) 8(180) <f> For the above r e l a t i o n s h i p s to hold the c o e f f i c i e n t s B , and B 3 must remain independent of the r o l l angle. From other i n v e s t i g a t i o n s [16] i t has been found that the the value of B 2 i s a function of the r o l l amplitude and that the e f f e c t s of b i l g e keels are expressed p r i m a r i l y i n B2. Only that part of B 2 that remains constant i s proportional to b. The part of B 2 that i s in v e r s e l y proportional to the r o l l amplitude i s apparently - 173 -t r a n s f e r r e d to c o e f f i c i e n t a, and that part of B that i s proportional to the r o l l amplitude i s found i n c o e f f i c i e n t c. Thus i t can be seen that to be able to give a true representation of the r o l l damping f o r a l l angles of r o l l a continuous function cannot adequately define the value as the c o e f f i c i e n t s of the r e l a t i o n s h i p vary over the range of r o l l angles achieved. Thus i t has been suggested that equivalent l i n e a r damping c o e f f i c i e n t s be developed of the form, a - a + b^ + c<j>2 = £ B (D.018) e m^ m^ 2 C, e v ' Using the expression for r o l l e x t i n c t i o n developed by B e r t i n [17], Ad, = tty 2 (deg.) (D.019) we can take the c o e f f i c i e n t N as a form of an equivalent non-linear damping c o e f f i c i e n t . This term has been c a l l e d the " N - c o e f f i c i e n t " . Rewriting i n terms of the e x t i n c t i o n c o e f f i c i e n t s we get: N = + b + cd, (deg.) (D.020) 0 m m where N depends strongly on the mean r o l l angle, ^ , and i s u s u a l l y given i n terms of the <f>^ value such as N^Q, etc where the subscript corresponds to the value of <f>^. - 174 -D.3.1.2 Non-Linear Restoring Moments The r e s t o r i n g moment f o r a water-borne v e s s e l i s a function of i t s displacement, i t s geometry, the p o s i t i o n of i t s center of gr a v i t y and the angle of r o l l . For small angle theory the r e s t o r i n g moment can be assumed to be l i n e a r , l i k e the t y p i c a l c o i l spring where the r e s i s t i n g force i s proportional to the change i n length of the spring. For angles of r o l l l e s s than about 8° t h i s approximation i s adequate. From inspection of a t y p i c a l r i g h t i n g arm curve^ i t can be seen that the slope of the curve at small angles can be represented by a s t r a i g h t l i n e . I f t h i s l i n e i s extended u n t i l i t reaches the i n t e r s e c t i o n with the <j> = 1 radian l i n e the corresponding value on the GZ scale i s equivalent to the metacentric height of the ve s s e l . Thus, as was b r i e f l y mentioned i n the introduction, small angle r e s t o r i n g moments can be represented by the function: M = AGM<£ (D.021) When the r o l l angles become large i t i s very important to consider non-linear c o e f f i c i e n t s as the r e s t o r i n g moment a c t u a l l y decreases a f t e r the ves s e l has r o l l e d beyond i t s c r i t i c a l angle. The r e s t o r i n g moment should then be a function such as: Righting arm curves f o r the models tested are shown i n chapter 3 - 175 -M = AGZ(^) (D.022) The values for GZ(^) can be readily found through the use of available computer routines for ship design or by hand following the procedures outlined in the Principles of Naval Architecture published by The Society of Naval Architects and Marine Engineers. D.4 WAVE DYNAMICS The types of waves found in the ocean depend upon wind, temperature, geographic and atmospheric conditions. This does not lend i t s e l f easily to modeling. To be able to gain some insight into the response of vessels to these wave conditions a number of simplifications, or approximations, are made. The f i r s t approximation is that the waves found in the ocean can be represented by the summation of a number of discrete regular wave trains of varying frequency, amplitude and phase at various angles of incidence to each other. This is defined as a sea spectrum and a number of methods have been devised by Oceanographers to both measure these in the f i e l d and to represent them numerically through mathematical relationships. Beyond this there is also the problem of wave shape, though the sea spectrum is defined as a summation of a number of regular sinusoidal waves i t is not always possible to create these waves in a test environment. Because the wave forms are a function of their environment they change as the depth they are in varies in - 176 -relation to the wavelength of that wave frequency. Waves can thus deviate from the regular sinusoidal form and become more trochoidal, ie: fl a t t e r troughs and sharper peaks, u n t i l the point where the wave slope at the peak is sufficiently steep that collapsing of the crests occurs. D.4.1 Regular Waves Regular waves are defined as equidistant and a l l travelling at simplest approximation to a regular product of linear wave theory. The wave i s : those waves whose crests are the same phase velocity. The wave is the sinusoidal wave, a relationship for a sinusoidal n = A cos(kx-wt) (D.025) where: r/ = elevation of water surface at time, t, and distance x A = amplitude of the wave form k = wave number — 2n/L a) = wave frequency (radians) The existence of sinusoidal waves depends on both i t s frequency and the water depth. Figure 55 illustrates the regions of existence of the various wave types. Typically the region of linear waves is where the depth of the water is much greater than the wave height, as is the wavelength, ie: d > L > n. The zone demarcated by the crosshatching represents the range of wave types used during the testing computed from their wavelengths, - 177 -amplitudes and the known depth of the tank. D.4.2 Non-Linear Waves The non-linear waves types are numerous, examples include Stokes I l n d order, Stokes Vth order, Cnoidal, Hyperbolic and Trochoidal wave theories. [18] These theories are a l l expansions of the wave theory from i t s l i n e a r approximations to include higher order terms. 0.0000510.001 0.002 0.005 0.01 0.02 005 0.1 0.2 d Figure 55. Wave theory as a function of H/gT2 and d/gT 2 - 178 -From the fig u r e of wave types as a function of the wave length and water depth we can see that each wave theory has a unique area of a p p l i c a t i o n where i t best describes the wave environment. There i s some overlap of the theories i n parts of the wave type spectrum. D.4.3 Breaking Waves When an i n d i v i d u a l wave exceeds the hydrostatic and hydrodynamic l i m i t s the wave f a l l s apart. This i s known as wave breaking. There are a number of d i f f e r e n t s t y l e s of breaking waves; they include the s p i l l i n g breaker, the plunging j e t , the c o l l a p s i n g breaker,and the surging breaker. Breaking waves can be expected when the wave height to wave length r a t i o becomes a c e r t a i n r a t i o as a function of the water depth. This r a t i o , put f o r t h by Miche (1944) [19], can be expressed as, - - 0.142 tanh(kd) (D.026) L where: H — wave height L = wave length k «= wave number d = water depth This only provides an i n d i c a t o r of the conditions required - 179 -f o r a breaker to form. I f the water becomes s u f f i c i e n t l y shallow almost any waveform w i l l break. The type of breaking wave to expect when a wave t r a i n encounters a beach can be computed through the parameter B .Galvin (1968), which i s expressed as: 8 = H /(L m2) (D.027) o o where: H /L — deep water wave o o slope m = beach slope with the d i f f e r e n t types of breakers designated by: B > 5 : s p i l l i n g breaker 5 > B > 0.1 : plunging breaker B « 0.1 : c o l l a p s i n g breaker B < 0.1 : surging breaker. D.4.4 Energy Content of Waves The waves, as they progress, trans f e r energy to t h e i r surroundings. Regular waves d i s s i p a t e energy at a regular and c o n t r o l l e d rate while a breaking wave expends much greater energy over a shorter period of time. D.4.4.1 Regular Waves The energy f l u x P, which i s the average rate of tr a n s f e r of energy per u n i t width across a plane perpendicular to the d i r e c t i o n of wave propagation, can be expressed by i n t e g r a t i n g - 180 -over the depth and taking the time average of the instantaneous rate at which work is done and the kinetic and potential energy transfer across this plane. This can be expressed as; [P + 2 P 2 2 (u + w ) + pgz] u dz (D.028) -d which, for steady, progressive waves, reduces to: P = pc u 2 dz (D.029) H / I / y / [ 0 V_ 1 V E L O C I T Y P R O F I L E C ' Figure 56. Velocity prof i le of a breaking wave D.4.4.2 Breaking Waves - 181 -The energy transmitted from a breaking wave i s a function of the amplitude of the wave and the point of impact of the wave as well as the time from i n i t i a l breaking that the wave s t r i k e s the object. A t y p i c a l v e l o c i t y p r o f i l e of a breaking wave i s shown i n Fi g . 56 [20] . From t h i s p r o f i l e i t can be seen that a great deal of the energy tr a n s f e r r e d by a breaking wave i s contained within the high v e l o c i t y j e t of water at i t s cr e s t . The t r a n s f e r of energy to a ves s e l on impact with a breaking wave can be expressed through an energy balance. The energies involved can be broken into four main components, these are: : the energy d i s s i p a t e d by damping max ( B J + B | £ |? )d4 44 V 1 1 (D.030) where: B = non-linear V damping B = l i n e a r damping 44 $ •= r o l l v e l o c i t y E : the energy transferred E = 2 -— 2 1 M dt 2 0 2 I' XX from the wave slope (D.031) - 182 -where: M = moment induced 2 by wave slope I' «= vir t u a l mass X X moment of inertia At = duration of 2 the energy transferred from the jet exposure to the wave .At M dt 3 2 I' ( D . 0 3 2 ) where: M = moment induced 3 by plunging jet I' = vir t u a l mass X X moment of inertia At = duration of 3 exposure to the j et the energy content of the heeled vessel - 183 -E •= A 4 9 , max GZ cty o The balance then becomes: E = E + E = E + E 2 3 1 4 (D.033) where: GZ •= righting arm A = displacement <f> = max angle of max inclination (D.030) - 1 8 4 -

Cite

Citation Scheme:

        

Citations by CSL (citeproc-js)

Usage Statistics

Share

Embed

Customize your widget with the following options, then copy and paste the code below into the HTML of your page to embed this item in your website.
                        
                            <div id="ubcOpenCollectionsWidgetDisplay">
                            <script id="ubcOpenCollectionsWidget"
                            src="{[{embed.src}]}"
                            data-item="{[{embed.item}]}"
                            data-collection="{[{embed.collection}]}"
                            data-metadata="{[{embed.showMetadata}]}"
                            data-width="{[{embed.width}]}"
                            async >
                            </script>
                            </div>
                        
                    
IIIF logo Our image viewer uses the IIIF 2.0 standard. To load this item in other compatible viewers, use this url:
https://iiif.library.ubc.ca/presentation/dsp.831.1-0096922/manifest

Comment

Related Items