A three-dimensional inverse method for the design of sails

Abstract

This paper investigates an inverse process for the design of yacht sails. The method is described and then applied to the design of optimal sails for a specific yacht. The proposed inverse method generates the three-dimensional shapes of a headsail and mainsail from prescribed loading (i.e. differential pressure) distributions, accounts for the effect of the sea surface, and also simulates the twist and shear of the incoming flow. The uncoupled iterative routine solves a sequence of analysis steps so that the sail shapes are deformed in such a way that their updated loading distributions converge to the specified target distributions. During each iteration equations derived from two-dimensional Thin Aerofoil Theory, calculate a geometry correction from the difference between the current and target loading distributions. This correction is applied to the sail geometry, and a vortex lattice method code calculates the updated three-dimensional differential pressure distributions, which are again compared to the target distributions. Usually only five iterations are required to converge to sail shapes that have the target loading distributions. The inverse method has been validated by inverting the traditional way of analysing sails, i.e. a set of sails with known geometry has been analysed and the loading distributions on the headsail and mainsail were calculated. These distributions were then used as an input for the inverse code. It was found that the difference in camber between the original sails and the calculated geometry is less than 0.01% of camber at the mid-span of the sails. The second part of the paper presents two methods for the design of optimal sails for a yacht. One of the methods uses the more traditional analysis approach, while the other employs the inverse method described in this paper. The optimisation is performed for a Transpac 52 yacht in 12 knots (6.5 m/s) of true wind speed to obtain the best velocity made good. Results from both methods are presented and discussed and it is found that the results in terms of boat speed are similar although the trims differ slightly. However, the new inverse method is approximately nine times faster than the traditional analysis approach.