THE INFLUENCE OF A YACHTS HEELING STABILITY ON OPTIMUM SAIL DESIGN

This paper presents fundamental results concerning the optimum design of yacht sails and masts. The aerodynamics of a high aspect ratio sail in uniform flow is analysed using lifting line theory to maximise thr ust for a given sail area. The novel feature of this work is that thru st is optimised subject to the constraint that the aerodynamic heeling moment generated by the sail is balanced by the righting moment due t o hull buoyancy (and the weight of the keel). Initially, the heel angl e is therefore unknown, and determined as part of the solution process . Under the assumption;of small heel angle, the problem reduces to min imising a quadratic form in the Fourier coefficients for the circulati on distribution along the mast, and a simple analytic solution can be derived. It is found that if the mast is too high, the upper section i s unused, and as a consequence there is a theoretically ideal mast hei ght for a yacht of given heeling stability. Under the constraints of g iven sail area and heeling equilibrium it is found that no advantage i s to be gained by allowing reverse circulation near the top of the mas t. Various implications for yacht performance are discussed.