Proceedings of the 5th Chesapeake Sailing Yacht Symposium, The Chesapeake Section of the Society of Naval Architects and Marine Engineers (summary)

5 JANUARY 17, 1981 T H E C H E S A P E A K E S E C T I O N O F T H E S O C I E T Y O F NAVAL A R C H I T E C T S AND MARINE E N G I N E E R S T H E C H E S A P E A K E B A Y Y A C H T R A C I N G A S S O C I A T I O N

U.S. NAVAL ACADEMY SAILING SQUADRON

T H E S O C I E T Y O F N A V A L A R C H I T E C T S A N D M A R I N E E N G I N E E R S One World T r a d e C e n t e r , S u i t e 1369, New Y o r k , N. Y . 10048 Paper 10 be presonWd • ! lh« C h e m p e s k » Selling Y e c h l Symposium. Annapolis. Marvland. January 17, 1961.

Design Development of a 4 0 m Sailing Yacht

I n p u b l i s h i n g the f i r s t e d i t i o n o f "Yacht A r c h i t e c t u r e " i n 1895 I was a b l e t o s t a t e t h a t t h e knowledge o f t h e s c i e n t i f i c p r i n c i p l e on which yacht designing i s based had been considerably extended since t h e p u b l i c a t i o n o f my l a r g e work e n t i t l e d "Yacht Designing" i n 1876. T h i s can a l s o be said o f t h e period between 1885 and 1897, and no doubt the present generation o f yachtsmen and those i n t e r e s t e d i n yachts have a much more exact knowledge of t h e science o f tfeval A r c h i t e c t u r e than t h e i r predecessors had, owing t o t h e i r having s t u d i e d the numerous works p u b l i s h e d on the s u b j e c t .

Yacht b u i l d i n g can be b e t t e r described by engravings than by w r i t i n g , and the p l a t e s and woodcuts which a r e g i v e n w i l l i n s t r u c t the amateur i n a l l the d e t a i l s o f c o n s t r u c t i o n according t o t h e p r a c t i c e o f t h e best b u i l d e r s .

Dixon Kemp Yacht A r c h i t e c t u r e , 1897

ABSTRACT

The development of the design of the 40 meter (131 foor) ketch A N T O N I A is followed from the com-mission to the beginning of construction. The require-ments of the client are reviewed against the final design. The scanti ings for the basic structure ore presented, along with their evolution. The progression of the rig from the original thoughts to the final version is presented. The stability andfloodable length curves are shown.

Lines, construction, sail plan, and accommoda-tions drawings are published, in addition to a c a l l for designers to resume a more constructive attitude towards publishing original design work for the advancement of the profession.

I N T R O D U C T I O N

Mony of us dream big dreams. A few men act to make their dreams come true. The commission to design the 40 meter ketch A N T O N I A is the result of one man's action in pursuing his dream.

THE C O M M I S S I O N

In the spring of 1980 I was approached about the possibility of designing a large sailing yacht. Two

design Ideas. As the client's thoughts evolved on what sort of boat he wanted, each of the boats were quite different.

A native of Brazil, he wanted to take advantage of the abundant and reasonably priced wood available there by building locally in wood. Initially, he had planned to build in the traditional method used in the commercial fishing vessels locally: carvel planking on

sown frames.

Then, on reading and studying John G u z z w e l l ' s book. Modern Hooden Yacht Construction, the client decided that cold-molded construction would be the best method. He also decided to hire John G u z z w e l l as a consultant on the construction, as well as for advice on the project in general, based on John's extensive offshore sailing experience.

John G u z z w e l l was then just commencing c o n -struction of 0 second vessel to my 37 foot pilothouse cutter design. I was given an opportunity to moke a proposal to the client, who was receptive to my ideas. Since John and I lived on neighboring islands, it would be easy for us to work together on the project.

He had already established a good working relation-ship over the post three years, during the building of the first of the 37 foot cutters. He also realized that the design and building of a sailing yacht of

T H E S O C I E T Y O F N A V A L A R C H I T E C T S A N D M A R I N E E N G I N E E R S O n e W o r l d T r a d e C e n t e r , S u i t e 1369, New Y o r k , N. Y . 10048 Papar lo be p r e s e r l e d at Ihe C h e s a p e a k e Sailing Yacht Symposium, Annapolis, Maryland, January 17. 1961.

Yacht Performance Analysis with Computers

Richard S. McCurdy, Consultant, Darien, CT.

A B S T R A C T

Advances i n computer t e c h n o l o g y c o n t i n u e to expand the everyday a p p l i c a t i o n o f e l e c -t r o n i c c a l c u l a -t i o n and programming. Wi-th e v e r y t h i n g from home computers to automotive d i a g n o s t i c d e v i c e s , hand-held Pong games, and c a l c u l a t o r w r i s t w a t c h e s now b e i n g b i g s e l l e r s , i t i s no s u r p r i s e t h a t computer-based marine I n s t r u m e n t s have i n c r e a s e d i n c a p a b i l i t y and p o p u l a r i t y . T h i s paper d e s c r i b e s some c u r r e n t developments i n e l e c t r o n i c s to e v a l u a t e the performance o f s a i l i n g y a c h t s , r a n g i n g from b a s i c d i g i t a l d i s p l a y s to f u l l - b l o w n s h o r e s i d e computers. NOmNCLATURE e wind angle o f f s e t

apparent wind speed ( c o r r e c t e d ) Vy^ apparent wind speed ( u n c o r r e c t e d

f o r upwash and h e e l ) V M G speedmadegood to windward o r l e e -ward; a l s o , V M G Vg boat speed V j t r u e wind speed k apparent wind a n g l e ( c o r r e c t e d )

/Sp^iff apparent wind a n g l e ( u n c o r r e c t e d f o r upwash and h e e l ) /3x t r u e wind a n g l e • j ^ upwash a n g l e heading on n e x t l e g or t a c k . ^ g heading of y a c h t O r heading of t r u e wind A leeway a n g l e (p h e e l a n g l e INTRODUCTION

The most g e n e r a l c o n c e r n o f the r a c i n g s a i l o r ( o r s p e e d - c o n s c i o u s c r u i s e r ) i s t h e comparison of the y a c h t ' s speed i n g i v e n wind and s e a c o n d i t i o n s t o h e r p r e v i o u s perform-ance. U s u a l l y a y a c h t h a s a n a l o g o r d i g i t a l d i s p l a y s o f b o a t speed, wind speed, and wind d i r e c t i o n , and the owner o r crew n o r m a l l y take mental n o t e s o f normal s a i l i n g perform-ance, p a r t i c u l a r l y when on t h e wind. I f speed i s down, r e l a t i v e to r e c e n t o r longterm p e r -formance, the s a i l s a r e e y e b a l l e d f o r t r i m , or a p o s s i b l e s a i l change. C l e a r l y , such i n s t r u m e n t s do not c o n t r o l how the y a c h t i s

s a i l e d — t h a t remains i n the hands of humans. The i n f o r m a t i o n a v a i l a b l e on the i n s t r u m e n t s merely h e l p s t h e crew judge whether perform-ance i s s a t i s f a c t o r y and, i f n o t , s i g n a l s thera to l o o k around and f i g u r e out what i s wrong.

As t h e l e v e l of c o m p l e x i t y i n y a c h t i n s t r u m e n t a t i o n i n c r e a s e s , one should not be i n t i m a t e d i n t o t h i n k i n g t h a t the s a i l i n g s k i l l of yachtsmen i s b e i n g encroached upon. At t h i s t i m e , the most s o p h i s t i c a t e d of y a c h t computer systems i s t o t a l l y I n c a p a b l e o f e y e -b a l l i n g s a i l t r i m o r s t e e r i n g e f f i c i e n t l y i n a seaway. The purpose o£ computer-based i n s t r u m e n t systems i s to p r o v i d e more thorough r e p o r t c a r d s to t h e crew, w i t h more m e a n i n g f u l measures o f performance e v a l u a t i o n . The i n s t r u m e n t s i n d i c a t e how the y a c h t h a s been s a i l i n g r e c e n t l y , o r h a s s a i l e d a t some time i n the p a s t i n s i m i l a r c o n d i t i o n s . Based upon t h a t i n f o r m a t i o n , i t remains i n the f u l l judgment o f the s k i p p e r and crew to c o r r e c t t h e i r m i s t a k e s o r improve upon t h e i r p r e s e n t or p r e v i o u s b e s t performance' in" s a i l i n g the y a c h t . PART 1 H A N D - C A L C U L A T O R P E R F O R M A N C E A N A L Y S I S H a r d w a r e — T h e Hard Way The c o n s c i e n t i o u s r a c i n g s a i l o r keeps a log o f s a i l c o m b i n a t i o n s , l e a d p o s i t i o n s , boat speed, wind speed, wind a n g l e , and p e r -haps a few o t h e r p e r t i n e n t i t e m s . T h i s makes i t e a s i e r to reproduce s a i l t r i m s e t t i n g s i n g i v e n c o n d i t i o n s , and judge whether boat speed i s s a t i s f a c t o r y .

The wind r e f e r e n c e s I n t h i s c a s e a r e the a p p a r e n t r e a d i n g s s t r a i g h t o f f the m e t e r s . These v e r y l i k e l y c o n t a i n g r o s s e r r o r s of c a l i -b r a t i o n , -b u t a r e w o r t h w h i l e n e v e r t h e l e s s a s a b a s i s o f comparison f o r a p a r t i c u l a r y a c h t . Simple a s t h i s means I s , i t i s the o n l y means t h a t most o f t h e s a i l i n g w o r l d h a s had to e v a l u a t e i t s performance.

To take t h e n e x t s t e p one should under-stand t h e c o n c e p t s o f a p p a r e n t wind v e r s u s t r u e wind. The wind t h a t a person f e e l s on a moving v e h i c l e — b o a t , c a r , o r w h a t e v e r — i s c a l l e d apparent wind. I t i s the v e c t o r

T H E S O C I E T Y O F N A V A L A R C H I T E C T S A N D M A R I N E E N G I N E E R S O n e World T r a d e C e n t e r , S u i t e 1369, New Y o r k , N . Y . 10048 Paper Io be p i e s e n l c d at Itia C h e s a p e a k e Sailing Y a c h I Symposium, Annapolis, Maryland, January 17, 19S1.

Geometry of Sailmaking

It is the glory of geometry that from so few principles Jelchcd from without, it is able to accomplish so much."

Isaac Newton . n c Philosophiae Naturalis Principia Mathematica, Praetat

A B S T R A C T

The aerodynamic force developed by a sail depends on the sail's shape. The horizontal cross-sectional shape is of particular importance in determining saU performance. Two parameters for describing the shape are presented and three methods of measuring the shape are outlined. The current practice of using edge rounding and broadseaming is de-scribed and four solutions to the problem of creating faster shapes are presented. First, the pragmatic approach which uses an interative search for the fastest edge round and broadseam pattem is examined. Tiiree other approaches that model the sail as a mathematical surface and use geometry to compute the pattems are presented. Here the sail is treated as a stack of horizontal arcs with precisely defined shapes. In one method, a path excess equation is used to calculate the luff round for a mainsail. Another approach plots the geodesic paths on the sail's surface and computes the seam-by-seam broadseaming. Lastly, an integral method is em-ployed to find the broadseaming for a sail based on the Penguin mainsail. Measurements of the sail made by this method are presented and discussed.

I N T R O D U C T I O N

The problem of designing better and faster sails is extremely complex. Many factors including the motion of the yacht, turbulence of the wind and deformations in the riggmg, work to put a full solution to the problem beyond the range of present mathematics. In an effort to bring the problem down to manageable proportions, it is necessary to make a number of simplifying assumptions. Each assumption places a constraint on the wind and the yacht as well as the resultmg sail designs. As with any study, it is always hoped that the assumptions do not oversimplify the problem and severly limit the value of the solution or the conclusions.

The first step m designing sails with specific three-dimensional shapes is to select a convenient system for de-scribing the sail. Once this is done, a generalized mathema-tical formalism for building sails based on that or any de-scription must be devised. In tliis project, the sail has been described as a stack of horizontal arcs. I f this description is later found to be simpUstic or inadeuqate, then a new description can be substituted without changing the forma-lism. What remains to be considered then are the questions of determining a fast shape and how it is constructed.

In the past, saUmakers have been able to continually develop faster sails by using techniques which control the shape of the sail as seen by the wind. One technique, called

edge rounding, can have two purposes. It may be used to join the sail to its supporting mast or headstay and/or it may

be used to control the sail's shape. In the latter case, fabric is simply added to one of the supportmg edges of the sail in the form of a luff roach or a foot roach. When the sail is set, the added fabric permits the imier region of the sail to develop additional fullness. Another shaping teachnique, called broadseaming, consists of puttmg a slight taper in the seams between the sections of fabric that make up the sail. Unfortunately, the exact mechanism by which these tech-niques control the shape is not generally known. Althougli some lofts may have made theoretical or experimental ad-vances in this area, understandably their results have not been made public for proprietory reasons.

This project was intended to develop some under-standing of how these technqiues affect the shape and to give them some basis in mathematics. From this under-standing, it might be possible to devise a mathematical struc-ture which would allow the sailmaker to build sails with any three-dimensional shape. The choice of the shape miglit be based on aerodynamic analysis or past experience. In addi-tion, two mathematical models for simulating the sail were developed and used to determine tlie necessary edge round-ing and broadseamround-ing required to build sails under specific conditions.

It is hoped that this work will be of some value to sailors, sailmakers and others who are interested in sail de-signs. The paper is divided into several sections. It begins with a definition of shape parameters, followed by a descrip-tion of the shape measuring procedure used in this project and some comments on the two shaping techniques men-tioned above. The paper continues with the presentation of two mathematical models and three techniques for using them. In the concludmg section, one of these techniques is applied to a sail based on the Penguin mainsail.

D E S C R I B I N G T H E S H A P E

The aerodynamic force produced by a sail depends in part on the wind and the sail's shape. Although the three-dunensional flow pattem around the sail is complex, it can be approximated by assuming that the air divides at the lead-ing edge and then flows horizontally around the curved surface of the sail as shown in Figure 1. By this approach the three-dimensional sail surface can be modeled as a vertical

stack of inter-connected two-dimensional arcs. Each of the arcs has a particular shape and creates its own aerodynamic force. Together these arcs define the sail's shape and deter-mine its perforniance characteristics.

T H E S O C I E T Y O F N A V A L A R C H I T E C T S A N D M A R I N E E N G I N E E R S One World T r a d e C e n t e r , S u i t e 1369, New Y o r k , N. Y . 10048 Paper to he praaenled at ItiB Ctiosapeake Sailing Y a c h t Symposium. Annapolis, Maryland, Janijafy 17, 19fl1.

Sailing Yacht Capsizing

Olin J . Stephens, II. Karl L. Kirkman, Hydronautics, Inc., Laurel, MD. and Robert S. Peterson, NSRDC, Bethesda, MD.

VisN/ïw S E Q U E N C E P H O T O G R A P H S O F S A I L I N G Y A C H T C A P S I Z E ABSTRACT The 1979 P a s t n e t f o c u s e d a t t e n t i o n u p o n y a c h t c a p s i z e s a n d r e s u l t i n g damage and l o s s o f l i f e . A c l a s s i c a l s t a b i l i t y a n a l y s i s does n o t c l e a r l y r e v e a l some o f t h e c h a r a c t e r i s t i c s o f t h e m o d e r n r a c i n g y a c h t w h i c h may e x a c e r b a t e a c a p s i z i n g "tendency. A r e v i e w o f t h e m e c h a n i s m o f a s i n g l e - w a v e - i m p a c t c a p s i z e r e v e a l s i n a d e q u a c i e s i n s t a t i c m e t h o d s o f s t a b i l i t y a n a l y s i s and h i n t s a t a c o n n e c t i o n b e t w e e n r e c e n t d e s i g n t r e n d s and a n i n c r e a s e d f r e q u e n c y o f c a p s i z e . The p a p e r t r a c e s r e c e n t d e s i g n t r e n d s , r e l a t e s t h e s e t o c a p s i z i n g by a d e s c r i p t i o n o f t h e d y n a m i c m e c h a n i s m o f b r e a k i n g vfave i m p a c t , a n d o u t l i n e s t h e u n u s u a l o c e a n o g r a p h y o f t h e 1979 F a s t n e t v;hlch l e d t o a h e i g h t e n e d i n c i d e n c e o f c a p s i z e .

37

T H E S O C I E T Y O F N A V A L A R C H I T E C T S A N D M A R I N E E N G I N E E R S One World T r a d e C e n t e r , Suite 1369, New Y o r k , N. Y . 10048 Paper lo be presenletj at the C h e s a p e a k e Sailing YachI Symposium. Annapolis, Maryland, Januaiy 17, 1931.

Kinetics in Small Boat Racing

ABSTRACT I n t h e e a r l y 1 9 6 0 s , new t e c h n i q u e s i n v o l v i n g b o d y movements a n d r a p i d , r e p e a t e d t r i m m i n g o f t h e s a i l s w e r e d e -v e l o p e d i n o r d e r t o s a i l a s m a l l b o a t f a s t e r t h a n e v e r b e f o r e . B e c a u s e t h e s e k i n e t i c t e c h n i q u e s d r o v e a b o a t m e a s u r -a b l y f -a s t e r , t h e i r use r -a p i d l y s p r e -a d f r o m c l a s s t o c l a s s a m o n g s t t h e t o p c o m p e t i t o r s . I n a n a t t e m p t t o t r y t o s t o p s m a l l b o a t s a i l i n g f r o m t u r n i n g i n t o a s t r i c t l y a t h l e t i c c o n t e s t , t h e I n t e r n a t i o n a l Y a c h t R a c i n g U n i o n i n -t r o d u c e d a r u l e i n 1965 g o v e r n i n g -t h e u s e o f k i n e t i c s . S i n c e t h e n , newer t e c h n i q u e s h a v e b e e n d e v e l o p e d t h a t a r e n o t c o v e r e d b y t h e p r e v i o u s r u l e . B e c a u s e t h e s e new m e t h o d s a r e s u b s t a n t i a l l y f a s t e r , many t o p c o m p e t i t o r s a r e i n c r e a s i n g t h e i r u s e o f t h e m . As t h e t o p s a i l o r s i n -c r e a s e t h e i r w i n n i n g m a r g i n s , t h e r e s t of t h e f l e e t i s o f t e n f o r c e d t o u s e k i n e t i c s i n o r d e r t o k e e p u p . As a r e s u l t o f t h e i r r a p i d l y s p r e a d i n g u s e , t h e lYRU h a s r e a d d r e s s e d i t s e l f t o t h i s p r o b l e m a n d h a s d r a f t e d a new p r o -p o s a l . H o -p e f u l l y , t h i s new r u l e , i f a d o p t e d , w i l l c l e a r l y d e f i n e when t h e p r e s e n t t e c h n i q u e s may b e u s e d a n d y e t s t i l l a l l o w f o r f u t u r e d e v e l o p m e n t s i n k i n e t i c t e c h n i q u e s . INTRODUCTION W i t h t h e i n c r e a s i n g p o p u l a r i t y o f s a i l i n g l i g h t d i s p l a c e m e n t a n d p l a n i n g h u l l s i n t h e e a r l y 1 9 6 0 s , new m e t h o d s w e r e d e v e l o p e d t o s a i l a s m a l l b o a t f a s t e r t h a n e v e r b e f o r e . Some o f t h e s e m e t h o d s w e r e p u m p i n g , r o c k i n g , s c u l l i n g , o o c h i n g a n d r o l l t a c k i n g . I n s t e a d y s t a t e c o n d i t i o n s , b y p u m p i n g t h e s a i l s on o n e o f t h e s e s m a l l b o a t s , i t i s v e r y e a s y t o d r i v e t h e h u l l f a s t e r t h a n i f t h e s a i l s w e r e t r i m m e d p r o p e r l y a n d t h e h u l l p u t i n t o e q u i l i b r i u m . By s t a r t i n g w i t h t h e s a i l s t r i m m e d w h e r e t h e r e was l i t t l e o r n o s e p a r a t e d f l o w ( p o i n t A, F i g u r e 1 ) , t h e n t u g g i n g r a p i d l y on t h e s h e e t s , i t w o u l d b e p o s s i b l e t o tem-p o r a r i l y i n c r e a s e t h e d r i v i n g f o r c e . I f t h e s a i l was t h e n h e l d a t t h i s new p o i n t ( p o i n t B, F i g u r e 1 ) , t h e n t h e f l o w w o u l d s e p a r a t e a n d t h e d r i v i n g f o r c e w o u l d f a l l o f f r a p i d l y ( p o i n t C, F i g u r e 1 ) . However, i f t h e s h e e t was e a s e d , a t t a c h e d f l o w w o u l d b e r e t a i n e d a n d t h e d r i v i n g f o r c e w o u l d r e t u r n t o p o i n t A. T h e r e f o r e , b y r e p e a t i n g t h i s t e c h n i q u e s a i l o r s a r e a b l e t o i n c r e a s e t h e d r i v i n g f o r c e s a n d t h u s t h e speed o f t h e i r h u l l s t h r o u g h t h e w a t e r ( F i g -u r e 2) . R o c k i n g a n d s c u l l i n g a r e t w o ^ c l o s e l y c o u p l e d t e c h n i q u e s . R o c k i n g seems t o w o r k b e c a u s e i t b r e a k s t h e s u r f a c e t e n s i o n s u r r o u n d i n g t h e h u l l , a l l o w i n g t h e b o a t t o l i f t o n t o a p l a n e s o o n e r . A l s o , i t moves b o t h t h e s a i l s and u n d e r w a t e r a p p e n d a g e s t h r o u g h l a r g e a r c s , i n c r e a s i n g t h e a p p a r e n t w i n d f o r t h e s a i l s a n d t h e l i f t on t h e a p p e n d -a g e s , t h u s i n c r e -a s i n g t h e d r i v i n g _ f o r c e . S c u l l i n g w o r k s m o s t e f f e c t i v e l y w i t h s w e p t b a c k r u d d e r s , a n d s i m i l a r l y c r e a t e s a d r i v i n g f o r c e b e c a u s e o f t h e d i s p l a c e d w a t e r b e i n g d r i v e n a f t . O o c h i n g i s a t e c h n i q u e u s e d m o s t o f t e n o f f t h e w i n d t o s t a r t a b o a t s u r f i n g o r p l a n i n g . By m o v i n g f o r w a r d o n t h e c r e s t o f a wave a n d t h e n a f t r a t h e r a b r u p t l y , t h e h u l l w i l l a c c e l -e r a t -e down t h -e f a c -e o f t h -e w a v -e . A l s o , b y c o u p l i n g a f e w t i m e l y r o c k s a n d pumps, t h e h u l l c a n s t a y on t h e wave f o r q u i t e some d i s t a n c e , i f i t i s t i m e d p r o p e r l y . R o l l t a c k i n g i s o n e o f t h e m o s t g r a c e f u l o f t h e s e e a r l y t e c h n i q u e s . By h e e l i n g t h e b o a t s l i g h t l y t o l e e w a r d t o c r e a t e w e a t h e r h e l m , f o l l o w e d b y t r i m -m i n g t h e -m a i n h a r d a n d r o l l i n g t h e h u l l t o w e a t h e r , t h e s a i l s w i l l h a r d l y l u f f i n t h e m i d d l e o f a t a c k . B e c a u s e t h e a c c e l e r a t i o n g a i n e d b y t h i s t e c h n i q u e r e s u l t s i n much l e s s d i s t a n c e l o s t t h a n i n a r e g u l a r t a c k , a s m a l l e r w i n d s h i f t c a n b e u s e d t o a t a c t i c a l a d v a n t a g e . H e r e was t h e b i r t h o f k i n e t i c p r o -p u l s i o n — b o d y movement a n d e n e r g y a i m e d a t d r i v i n g a s a i l b o a t f a s t e r t h a n the w i n d o r t h e waves w o u l d n o r m a l l y . U n t i l 1965, t h e o n l y r u l e g o v e r n i n g t h i s t y p e o f a c t i o n was R u l e 60 -¬ Means o f P r o p u l s i o n : A y a c h t s h a l l b e p r o p e l l e d o n l y b y t h e n a t u r a l a c t i o n o f t h e w i n d on t h e s a i l s , s p a r s a n d h u l l , a n d w a t e r on t h e h u l l .

T H E S O C I E T Y O F N A V A L A R C H I T E C T S A N D M A R I N E E N G I N E E R S O n e World T r a d e C e n t e r , Suite 1369, New Y o r k , N . Y . 10048 p . p . , 10 bo prosonteO .1 lh» C h o s a p o a k . Sailing Y a c h I Symposium. Annapolis, M.iylancl, January 17. 1981,

RED HERRING, High Performance Cruising Ketch

ABSTRACT The d e s i g n , c o n s t r u c t : i o n a n d p e r -f o r m a n c e o -f a n a r r o w , -f a s t c r u i s i n g 55 f o o t cat; k e t c h i s d i s c u s s e d . S t a b i l i t y i s p r o v i d e d by b a l l a s t o n a l o n g b l a d e t h a t c a n be t i l t e d l a t e r a l l y a n d a l s o l i f t e d t o a c h i e v e s h o a l d r a f t . A p a r a -m e t r i c d e s i g n p r o c e d u r e a n d a g r a p h i c a l p e r f o r m a n c e m e t h o d i s p r e s e n t e d , INTRODUCTION T h i s p r o j e c t ; h a s i t ' s b e g i n n i n g s e v e r a l y e a r s ago when Mr, W. Van A l a n C l a r k , J r . f i r s t d i s c u s s e d h i s i d e a s on c r u i s i n g b o a t s w i t h me, r e m a r k i n g u p o n t h e e a s e w i t h w h i c h l o n g s l e n d e r h u l l s move t h r o u g h t h e w a t e r . He f e l t t h a t a l i g h t w e i g h t , n a r r o w b o a t , w i t h s i m p l e a c c o m m o d a t i o n s , c o u l d be d e s i g n e d t h a t c o u l d make f a s t c o a s t a l p a s s a g e s u n d e r s a i l a n d power. S t a b i l i t y c o u l d be p r o v i d e d b y a b u l b k e e l t h a t c o u l d be l i f t -ed f o r " g u n k h o l i n g " a n d t i l t e d s i d e w a y s f o r i n c r e a s e d s a i l i n g s t a b i l i t y when n e c e s s a r y . We e x c h a n g e d n o t e s , s k e t c h e s and c a l c u l a t i o n s o v e r s e v e r a l y e a r s , c u l -m i n a t i n g , i n t h e s p r i n g o f 1979 w i t h t h e d e c i s i o n t o go a h e a d and b u i l d a y a c h t t o t r y o u t t h e c o n c e p t . A f t e r s e v e r a l i t e r a t i o n s o f c r i t i c a l p a r a m e t e r d e t e r -m i n a t i o n s , a s e t was s e l e c t e d t h a t we f e l t w o u l d b e s t s a t i s f y t h e r e q u i r e m e n t s . A 5 f o o t s a i l i n g m o d e l was made a n d t e s t -e d , f o r b a l a n c -e a n d s a i l i n g a b i l i t y , s t a t i c t r i m and l a t e r a l s t a b i l i t y , s t r a i g h t t o w i n g a n d t o w i n g u n d e r s i m u -l a t e d s a i -l i n g c o n d i t i o n s . The r e s u -l t s w e r e p r o m i s i n g , i n d i c a t i n g t h e p o s s i -b i l i t y o f u p w i n d s p e e d s o f m o r e t h a n 8 k n o t s , a n d r e a c h i n g s p e e d s o v e r 16 k n o t s . A f t e r a f e w m o d i f i c a t i o n s , p l a n s w e r e d r a w n up f o r t h e f u l l s i z e c r a f t . E r i c G o e t z , o f B r i s t o l , R . I . , who h a s b u i l t a number o f h i g h p e r f o r m a n c e wooden y a c h t s , was s e l e c t e d as t h e b u i l d e r . The b o a t was l a u n c h e d o n O c t o b e r 25, 1980. PARAMETRIC STUDY The p e r f o r m a n c e o f a s a i l i n g c r a f t i s d e t e r m i n e d b y t h e n a t u r a l f o r c e s o f w i n d , w a t e r and g r a v i t y i n r e s p o n s e t o t t s s t a b i l i t y , d i s p l a c e m e n t , w e t t e d s u r -f a c e , s a i l a r e a , e t c . The a r t o -f d e s i g n and c o n s t r u c t i o n h a s b e e n h i g h l y r e f i n e d i n t h e a r e a o f r a c i n g c o m p e t i t i o n . Mea-s u r e m e n t r u l e Mea-s do n o t n e c e Mea-s Mea-s a r i l y d e v e l o p g r e a t e r p e r f o r m a n c e , b u t t e n d t o make d e s i g n e r s t h i n k i n t e r m s o f p e r f o r m a n c e r e l a t i v e t o r a t i n g . D e s i g n r e f i n e m e n t s a r e now a t s u c h a l e v e l t h a t d i f f e r e n c e s i n y a c h t s , t h a t c o v e r a r e l a t i v e l y s m a l l d e s i p n s p e c t r u m , c a n o n l y be d e t e r m i n e d on t h e r a c e c o u r s e . The RED HERRING c o n c e p t d e v i a t e d so f a r f r o m p r e s e n t r a c -i n g p r a c t -i c e t h a t -i t a l l o w e d a b r o a d e r and more i n e x a c t s t u d y o f t h e c o n t r o l l -i n g p a r a m e t e r s and no c o n s -i d e r a t -i o n h a d t o b e g i v e n t o a n y r a t i n g m e a s u r e m e n t s y s t e m s . We know t h a t l i g h t w i n d p e r f o r m a n c e demands a g o o d s a i l a r e a t o w e t t e d s u r -f a c e r a t i o and t h a t h e a v y w i n d p e r -f o r m a c e demands a g o o d maximum s a i l f o r c e t o d i s p l a c e m e n t r a t i o . S t a b i l i t y comes w i t h beam and b a l l a s t b o t h o f w h i c h b r i n g p e n a l t i e s o f w e t t e d s u r f a c e a n d a h i g h d i s p l a c e m e n t t o l e n g t h r a t i o s . A g a i n l a r g e s a i l a r e a s i m p l y h i g h h e e l i n g mom e n t s w h i c h r e d u c e momaximomumom s p e e d p o -t e n -t i a l , p a r -t i c u l a r l y u p w i n d . I -t i s p o s s i b l e t o s t a r t w i t h a s t a n d a r d known d e s i g n a n d t h e n s e l e c t t h e n e c e s s a r y de-p a r t u r e s f r o m t h e n o r m s u c h as e x t r a s a i l o r e x t r a d r a f t e t c . , t o o b t a i n t h e d e s i r e d e f f e c t . T h i s i s i n e s s e n c e t h e m e t h o d u s e d u n d e r t h e o l d CCA r u l e . How-e v How-e r i t was f How-e l t t h a t t h How-e d How-e p a r t u r How-e s f o r t h e RED HERRING c o n c e p t w e r e t o o r a d i c a l t o make u s e o f s u c h a m e t h o d f o r e s t i m a t i n g p e r f o r m a n c e . I n i t s p l a c e a p a r a m e t r i c d e s i g n s e l e c t o r was d e v e l o p e d w h i c h c o u l d g i v e a r o u g h a p p r o x i m a t i o n , u s i n g s e v e r a l s i m p l i f y i n g a s s u m p t i o n s and d e s i g n p r o p o r t i o n a l i t i e s , o f t h e e x p e c t e d p e r f o r m a n c e s p e c t r u m . Q u i c k i t e r a t i o n s a r e p o s s i b l e a n d c a n l e a d t h e d e s i g n e r t o t h e d e f i n i t i o n o f a p a r t i -c u l a r -c r a f t . A f t e r t h e d e s i g n has b e e n d e v e l o p e d , more p r e c i s e c l a c u l a t i o n s c a n be made t o g i v e c l o s e r p r e d i c t i o n s . The p a r a m e t r i c s e l e c t o r i s shown i n F i g . 1 w h e r e d i m e n s i o n s can b e e n t e r e d i n a f l o w c h a r t a n d d e s i r e d p e r f o r m a n c e p a r a m e t e r s s e l e c t e d t o t a i l o r a y a c h t t o h a v e p a r t i -c u l a r -c h a r a -c t e r i s t i -c s . An e x p l a n a t i o n o f e a c h b o x i s shown i n T a b l e 1 . As t h e

67

THE S O C I E T Y O F N A V A L A R C H I T E C T S A N D M A R I N E E N G I N E E R S O n e World Trade Center, Suite 1369, New Y o r k , N. Y . 10048 p . p e , 10 be presenlod .1 Ihe C h o l a p e . k s Sailing Y a c h t Symposium, Annapolis, Maryland, January 17, 1981.

Mathematical Hull Design for Sailing Yachts

ABSTRACT M a t h e m a t i c a l r e p r e s e n t a t i o n s o f h u l l s u r f a c e shape have l a r g e l y s u p -p l a n t e d g r a -p h i c a l f a i r i n g a n d l o f t i n g o f l i n e s i n t h e s h i p b u i l d i n g a n d a i r -c r a f t i n d u s t r i e s , b u t have h a d l i t t l e a p p l i c a t i o n s o f a r t o s m a l l c r a f t . P a s t m e t h o d s o f h u l l d e s i g n a r e s u r -v e y e d t o p u t m a t h e m a t i c a l d e s i g n i n t o h i s t o r i c a l p e r s p e c t i v e a n d p o i n t u p i t s many a d v a n t a g e s . The b a s i c c o n c e p t s o f a n a l y t i c g e o m e t r y o f s u r f a c e s n e e d e d f o r y a c h t h u l l d e s i g n a r e b r i e f l y i n t r o d u c e d w i t h r e f e r e n c e s . S e v e r a l s p e c i a l a s p e c t s o f t h e g e o m e t r y o f y a c h t h u l l s , a r i s i n g f r o m c o n s i d e r a -t i o n s o f a e s -t h e -t i c s , h y d r o d y n a m i c s , and c o n s t r u c t i o n m e t h o d s a r e d i s c u s s e d and c a s t i n t o a n a l y t i c f o r m f o r i n c l u s i o n i n a h u l l d e s i g n scheme. The p a p e r e x p l a i n s i n d e t a i l a p a r t i c u l a r r e p r e s e n t a t i o n s y s t e m c a l l e d F A I R L I N E / I , s i m p l e e n o u g h t o f i t i n t o t h e p r o g r a m a n d memory l i m i t a t i o n s o f a T I - 5 9 c a l c u l a t o r , y e t e x t r e m e l y v e r s a t i l e . A p r o g r a m l i s t i n g and s e v e r a l e x a m p l e h u l l d e s i g n s c r e a t e d w i t h t h i s p r o g r a m a r e p r e s e n t e d . N O M E N C L A T U R E ( N u m b e r E 3 i n p a r e n t h e s e s r e f e r t o e q u a t i o n s i n t e x t w h e r e s y m b o l s a r e d e f i n e d . ) a x - p o s i t i o n o f S t a t i o n 0 ( 2 ) b s t a t i o n s p a c i n g ( 2 ) B - s p l i n e b a s i s f u n c t i o n s B F , D F beam a n d d e p t h s t r e t c h i n g f a c t o r s ( d i r a e n s i o n l e s s ) o, d c o n s t a n t s s p e c i f y i n g p l a n e ( 3 ) f ( x ) f r e e b o a r d t o s h e e r l i n e F. b a s i s f u n c t i o n s f o r l i n e a r ^ c u r v e f i t t i n g ( 9 ) h ( x ) h a l f - b r e a d t h t o s h e e r l i n e L l e n g t h o v e r a l l n s t a t i o n number N n u m b e r o f b a s i s f u n c t i o n s r c o d e d f o r m o f m a s t e r s t a . v e r t e x s s t r e t c h e d l o n g i t u d i n a l c o o r d i n a t e ( d i r a e n s i o n l e s s ) S l o n g i t u d i n a l s t r e t c h i n g c o n s t a n t ( d i m e n s i o n l e s s ) t p a r a m e t e r o n s t a t i o n c u r v e ( 1 0 ) X, y, z C a r t e s i a n c o o r d i n a t e s a. c o e f f i c i e n t s o f l i n e a r c u r v e f i t ( 9 ) s t r e t c h i n g f a c t o r s ( I 3 ) e t i l t o f c u t t i n g p l a n e ( 3 ) cf> a n g l e o f h e e l

INTRODUCTION -- HISTORICAL PERSPECTIVE D e s i g n and s p e c i f i c a t i o n o f t h e com-p l e x c u r v e d s u r f a c e s o f a s h i com-p h u l l i s one o f t h e c e n t r a l p r o b l e m s o f n a v a l a r c h i t e c t u r e . S i n c e t h e e a r l i e s t t i m e s , w a t e r c r a f t h a v e , f o r good f u n c t i o n a l r e a s o n s , b e e n among t h e m o s t c o m p l e x -s h a p e d u t i l i t a r i a n o b j e c t -s c r e a t e d b y man. Of t h e v a r i e t y o f means w h i c h have e v o l v e d o v e r t h e c e n t u r i e s t o c r e a t e t h e s e s h a p e s , m o s t a r e s t i l l i n l i m i t e d u s e t o d a y . B e f o r e e n t e r i n g i n t o t h e l a t e s t r e v o l u t i o n i n s h i p s u r f a c e d e s i g n , we w i l l s u r v e y p a s t m e t h o d s b r i e f l y , w i t h m e n t i o n o f t h e i r a d v a n t a g e s a n d d i s a d v a n t a g e s . O r d i n a r i l y t w o d i s t i n c t p h a s e s o c c u r b e t w e e n t h e n a v a l a r c h i t e c t ' s i n i t i a l c o n c e p t i o n o f a h u l l f o r m a n d t h e r e a l i z a t i o n o f t h a t h u l l f o r m as a t h r e e - d i m e n s i o n a l s t r u c t u r e 1 d e s i g n a n d c o n s t r u c t i o n . U n l e s s t h e d e s i g n e r a n d b u i l d e r a r e t h e same p e r s o n , t h e e s s e n t i a l l i n k b e t w e e n t h e s e p h a s e s i s a s e t o f p l a n s ; e v e n when t h e b u i l d e r i s t h e d e s i g n e r he w i l l u s u a l l y f i n d i t h i g h l y a d v a n t a g e o u s t o f i r s t p r e p a r e f a i r l y c o m p l e t e p l a n s so as t o w o r k o u t as many d e t a i l s as p o s s i b l e b e f o r e c o m m i t t i n g a n y m a t e r i a l s . The p l a n s r e p r e s e n t i n g t h e h u l l t a k e t w o f o r m s1 ( 1 ) t h e l i n e s p l a n , a d r a w i n g s h o w i n g o r t h o g r a p h i c v i e w s o f t h e h u l l a n d i t s i n t e r s e c t i o n s w i t h c e r t a i n p l a n e sj a n d ( 2 ) t h e o f f s e t t a b l e , a t a b u l a r p r e s e n t a t i o n o f many o f t h e d i m e n s i o n s d e p i c t e d o n t h e l i n e s p l a n . The f i r s t s t a g e i n c o n s t r u c t i o n i s o r d i n a r i l y

T H E S O C I E T Y O F N A V A L A R C H I T E C T S AND M A R I N E E N G I N E E R S O n e World T r a d e C e n t e r , Suite 1369, New Y o r k , N . Y . 10048 Paper lo be presented at the Chosapeatte Sailing Yacht S / m p o s l u m , Annapolis, Maryland, January 17, 1931.

A Design Guide for Estimating Speed

Made Good fora Sailing Yacht

Deborah W. Berman, Webb Institute of Naval Architecture, Glen Cove, NY.

ABSTRACT

T h i s s t u d y d e v e l o p s a s i m p l i f i e d c o m p a r a t i v e p r o c e d u r e f o r use i n p r e l i m i n a r y y a c h t d e s i g n t o p r e d i c t E q u i l i b r i u m s i d e f o r c e , r e s i s t a n c e , leeway a n g l e and speed made good t o w i n d w a r d f o r a canoe h u l l s a i l i n g y a c h t w i t h i n s p e c i f i c f o r m p a r a m e t e r s on any o f f i v e s t a n d a r d s e r i e s k e e l s .

These f o r c e s , a n g l e s and speeds a r e p r e d i c t e d f o r any y a c h t h u l l r e s e m b l i n g one o f n i n e models - r a n g i n g f r o m l i g h t t o medium-heavy l e n g t h t o d i s p l a c e m e n t r a t i o (190 t o 351) -o f t h e D e l f t S y s t e m a t i c S e r i e s f -o r w h i c h t h e r e i s n u m e r i c a l d a t a . The f o r c e s a r e c a l c u l a t e d at speed t o l e n g t h r a t i o o f 1.3 and h e e l a n g l e o f 30° t o e n a b l e t h e d e s i g n e r t o make u s e o f e x i s t i n g c o m p a r a t i v e s a i l p l a n and r i g g i n g d a t a . The f i v e k e e l s o f v a r y i n g a s p e c t and a r e a r a t i o , s p a n n i n g c u r r e n t d e s i g n p r a c t i c e , a r e p a r t o f a m a t r i x d e v e l o p e d a t t h e D a v i d s o n l a b o r a t o r y . I n t h i s p a p e r , a canoe y a c h t h u l l f o r m s i m i l a r t o M o d e l T o f t h e D e l f t S e r i e s i s t a n k t e s t e d on 3 S t a n d a r d S e r i e s k e e l s and compared t o r e s u l t s o b t a i n e d f r o m t e s t i n g a 5.5 m h u l l , w h i c h i s s i m i l a r t o M o d e l 8, on t h e same k e e l s . A p r e d i c t i o n p r o c e d u r e I s d e v e l o p e d and c h e c k e d a g a i n s t t e s t r e s u l t s . A few E q u a t i o n s , s e l e c t e d v a l u e s f r o m i n c l u d e d t a b u l a t i o n s , a c a l c u l a t o r , p e n c i l and p a p e r w i l l y i e l d q u a n t i t a t i v e i n f o r m a t i o n f o r t h e y a c h t d e s i g n e r i n t h e s e l e c t i o n o f a k e e l f o r t h e h u l l o f a s a i l i n g y a c h t . L I S T OF SYMBOLS A r e a AF. A, b c C G . CEH r a t i o A^ / L w l ,^^2 / S, g e o m e t r i c a s p e c t r a t i o o f k e e l L a t e r a l a r e a o f k e e l , s q u a r e f e e t a p p a r e n t w i n d a n g l e , a n g l e b e t w e e n VS a n d VA d e p t h o f k e e l b e l o w canoe b o d y , f e e t mean c h o r d l e n g t h o f k e e l , f e e t beam t o d r a f t o f canoe h u l l r a t i o c e n t e r o f g r a v i t y s i d e f o r c e c o e f f i c i e n t c e n t e r o f e f f o r t , h e i g h t above L w l , f e e t CLR c e n t e r o f l a t e r a l r e s i s t a n c e p e r c e n t o f L w l a f t f o r w a r d end o f L w l C c e n t e r l l n e L C p r i s m a t i c c o e f f i c i e n t P C r e s i s t a n c e c o e f f i c i e n t R d c e n t e r o f e f f e c t o f h e e l i n g f o r c e b e l o w L w l , f e e t b / L w l d e p t h r a t i o e, f a n g l e s b e t w e e n s h i p ' s head and r e s u l t -ant w i n d f o r c e on t h e s a i l s

y a n g l e between s h i p ' s head and t r u e w i n d , (VT) A d i s p l a c e m e n t s h i p m, n s l o p e o f r e s i s t a n c e a n d s i d e f o r c e l i n e s V d i s p l a c e d volume .OIL' d i s p l a c e m e n t canoe h u l l - l e n g t h r a t i o L / ^ 1 / 3 s l e n d e r n e s s r a t i o w i t h r e s p e c t t o j\_ sweep a n g l e f( h e e l o r r o l l a n g l e , d e g r e e s n s h i p s i d e f o r c e ( l b s ) measured i n h o r i z o n t a l p l a n e a t r i g h t a n g l e t o VS, HS h m o d e l v a l u e s i d e f o r c e , I h s . K r i g h t i n g moment, f t - l b , v e r t i c a l C G . a t L w l K s i d e f o r c e c o e f f i c i e n t , speed i n k n o t s H r e s i s t a n c e c o e f f i c i e n t , s p e e d i n k n o t s L / B l e n g t h t o beam r a t i o L w l w a t e r l i n e l e n g t h o f canoe b o d y , f e e t X l e e w a y a n g l e o r yaw; may a l s o d e n o t e s c a l e r a t i o b e t w e e n m o d e l and s h i p

NS yaw moment, f t - l b measured i n p l a n e a b o u t m i d s e c t i o n , p o s i t i v e bow w i n d -w a r d R s h i p r e s i s t a n c e , l b s r m o d e l r e s i s t a n c e , l b s . RM r i g h t i n g moment o f y a c h t SA s a i l a r e a , s q u a r e f t . U n b a l a n c e arm d i s t a n c e b e t w e e n t o t a l w a t e r f o r c e a n d t o t a l s a i l f o r c e , f t . o r ^ L w l VA a p p a r e n t w i n d , k n o t s , v e c t o r sum VS and VT VMG speed-made-good-to-windward, k n o t s , component o f VS i n t r u e w i n d d i r e c t i o n V s h i p ' s speed, f t . p e r s e c . V s h i p ' s s p e e d , k n o t s K

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