## Derivation Of The Havelockcastles Equation

In a series of papers published in the Proceedings of the Royal Society between 1909 and 1932, T. H. Havelock examined the problem of wave resistance from a basic point of view. His method was to replace the hull by a collection of fluid sources in the forward part and sinks in the stern part. The strength of these sources and sinks is specified such that the resulting flow about them is just equivalent to the flow about the actual hull. If is the surface elevation above the unperturbed...

## High speed References

1 Buhler, Vance, Fiberglass Sandwich Standard Details. Bequia, St. Vincent, W. I., 1976. 2 Cannell, D. and J. Leather, Modern Developments in Yacht Design. New York Dodd, Mead, and Co., 1976. Chapter 7. 3 Gougeon, Jan, Joe, and Meade, West System. Gougeon Brothers, Inc., 1973. 4 Gougeon, Jan, Joe, and Meade, Graphite Fibers. Gougeon Brothers, Inc., 1975. 5 Johannsen, T. J., One-off Airex Fibre glass Sandwich Construction. Buffalo, N.Y. Chemacryl, Inc., 1973. 6 Mahinske, E. B, CFRS, 85 A, 28...

## Hulls And Outriggers

The primary purpose of a boat hull is to provide a vertical buoyant force in opposition to the weight of the boat and accommodation for the crew and cargo. The motion of the hull through the water gives rise to a resistive drag R that constitutes by far the largest part of the hydrodynamic drag . Therefore a knowledge of the nature of this resistance as a means to minimizing it is of prime importance to the design of really fast sailing boats. The parameters that enter into the description of a...

## Structural Design

We have seen that our quest for higher sailing speeds is in large degree a matter of eliminating 4fat We cannot afford to make everything excessively robust as one would for a Thames barge. Structural design must be carefully considered in order that stress points can be identified and allowed for without overbuilding. The strain field of a sloop-rigged monohull craft is indicated in Fig. 3-1 where tensions have been labelled with a T and compression strain by a C. The need for a very stiff...

## References

1 Castles, Walter, AY RS 83B, 13 (1976) and private communications. 2 Havelock, T. H., Proc. Roy. Soc A, 138, 339 (1932). 3 Hogner, E., tr czi ur Matematik, tsironomi, oc i Fysik, 17, (1923). 4 Kelsall, Derek and John Shuttleworth, M ultihull International, 111, 67 (1977). 5 Lunde, J. K., Society of Naval Architects and Marine Engineers (1951). 6 Mason, P. A., Proceedings of the Sixth AIAA Sailing Symposium, Los 7 Peters, A. S., Communications of Pure and Applied Mathematics, 2, 123 8 Weinblum,...

## Contents

1 The Physics of Fast Sailing 1 4 Sails and Lateral Stability 37 5 Lateral Plane and Rudders 49 6 Hydrofoil Applications 60 7 Safety and Seakeeping 78 8 Performance Prediction 84 12 An Overall View 118 Appendices A Derivation of the Havelock-Castles equation 121 B Hull Resistance for Semicircular Sections 124 The origins of man's use of wind-driven water craft are lost in antiquity. With the coming of the industrial revolution in the nineteenth century and the availability of cheap fuels, sail...

## Asymmetrical Racing Hulls Catamaran

Represents a zero-order approximation for the wave resistance. This is not good enough for our purposes, however. An exact theory was given by Havelock in 1932. A simplified, but still quite general form of Havelock's equation has been found by Castles for hulls with lateral and longitudinal symmetry. A discussion of the physical basis of Havelock's theory and Castle's equations for single or multiple hulls is given in Appendix A. Castles' equation for a single hull is The quantity 5 is the...

## VrJ

Provides an approximation to IV r f r K 10 knots as calculated from the IOMR equations to within less than five percent. Thus Eq. (8-21) provides a useful tool with which to compare the performance potential of various designs. Now let us consider a simplified version of the heeling equation, 8K approximately valid at the point where the windward hull lifts out yW h ipA VA2AsCy). (8-22) PERFOR- Again we use Eq. (8-4) to eliminate V . We obtain prediction VB2 + 2Vb Vt cos y + VT2 - v2 0 (8-23)...

## Lateral Plane And Rudders

In order to enjoy a condition of stationary equilibrium, the underwater parts of a sailing boat arrange themselves at an angle A, known as the leeway angle, to the vector Vb such that the keel and hull generate a hydrodynamic force Fh equal and opposite to the aerodynamic force Fa . In this chapter we shall be concerned to find the means whereby this hydrodynamic force can be generated so as to keep the hydrodynamic drag angle Sh at a minimum. In Fig. 5-1 we show the underwater portion of a...

## High Speed Sailing

A Study of High-Performance Multihull Yacht Design IX > 1)1), MLAD& COMPANY NliW YORK Published in the United States of America by Dodd, Mead & Company, Inc., 1979 Copyright 1979 by Joseph Norwood, Jr. All rights reserved No part of this work may be reproduced in any form without permission in writing from the publisher Library of Congress Catalog Card Number 79-87640 Designed by Jonathan Sharp Printed in Great Britain

## Trimarans

Trimarans have certain natural advantages over catamarans. Let us examine them. In Fig. 10-la we show a schematic trimaran with the cross-hatched area showing the lateral weight concentration. In some designs the outriggers are also used for accommodation, however we do not consider these charter-type vessels as high-speed craft. Figure 10-lb, c, & d shows three variations of the weight distribution in catamarans. Small catamarans carry all their weight on deck and not in the hulls see (b)...

## The Physics Of Fast Sailing

Sailing boats exploit the discontinuity in fluid flow that exists at the air water interface in order to propel themselves. We may consider the water to be at rest and describe the velocity of the wind by a vector VT. The magnitude of this vector is equal to the wind speed with respect to the water and the direction of the vector coincides with the wind direction. Under the influence of the wind, the boat moves at a speed VH in a direction given by the vector B. Motion of any object through...

## An Overall View

On any course save dead downwind, the speed of a sailing boat with respect to the true wind speed is determined by J, the angle between the velocity vector of the boat and the apparent wind vector. The smaller , the faster the boat. The course theorem Eq. 1-5 shows us that can be thought of as the sum of two angles, the aerodynamic and hydrodynamic drag angles, which in turn depend on the lift-to-drag ratio of the above water and below water parts of the boat respectively. The problem to be...

## FBL Fxb FyL

If the Bruce foils are to have fixed dihedral angles, I have spent some time contemplating the engineering possibilities of having r i K 11-5 Forces and lor que in plan variable dihedral angles and, in the end, I rejected the idea as impractical for small craft then In order to solve these equations we need one more relation. Looking at Fig. 6-1 we see that over a reasonably broad range of foil-borne speeds, one may approximate Fx R by Solving Eqs. ll-l - ll-8 , we find for , the longitudinal...

## Safety And Seakeeping

In this chapter we shall be primarily concerned with the problem of multihulPs extreme initial stability and the consequent high com-at sea. Other grave situations may occur, of course. Multihulls may be dismasted in situations where a monohull would not owing to the multihulls extreme initial stability and the consequent high com-pressional loading on the mast owing to gusts. Multihull rudders and boards are similarly more prone to breakage than monohull rudders as a result of the considerably...

## Hydrofoil Applications

The tendency to view hydrofoils only as a means to lift the hull or hulls clear of the sea is conditioned by the fact that hydrofoils have been applied mainly to engine-powered craft which are subject to a less complex set of forces than sailing craft. In Fig. 6-1, to obtain a quantitative feeling for the problem, we have plotted the vertical lift-to-drag ratio weight-to-resistance of a typical multihull craft as a function of VJ L using Eq. 1-8 . Also shown is a curve labelled hydrofoils,...

## Dihedral Lift Foil

Where K is the windward depressing force and y is its lateral distance from the centre of effort of the Bruce foils. In the limit of large K W, Eq. 6-9 approaches which represents a bounded increase in the drag angle SH. Thus the attainable value of VB VT decreases, however given enough wind, the sail-carrying power is so increased that the actual top speed is higher than before. Such righting moment enhancement by either the water scoop or hydrofoil technique should be contemplated for a speed...

## Sails And Lateral Stability

The force FA generated by the sails is given by the expression where pA is the mass density of air at sea level under standard conditions pA 2.38 103 slug ft3 , VA is the apparent wind speed, As is the sail area, and CA is a numerical coefficient. As we saw in Chapt. 1, this force can be decomposed into a lift force A The lift coefficient CL is known to be an approximately linear function of the angle of attack a up to the point of stall, and to depend in addition on the aspect ratio A of the...