Optimizing Spanwise Lift Distributions Yacht Sails Using Extended Lifting Line Analysis

This paper discusses how to maximize the drive force produced by an upwind sail. It aims to provide a better understanding of the behavior of this force as a function of the heel angle of the yacht and the wind speed. It also discusses the corresponding optimal spanwise loading distributions. An extended lifting line code, based on Weissinger's method, is developed to analyze the performance of an isolated mainsail in upwind conditions. It is extended to account for the heel angle of the yacht via effective angle theory, and an image sail is used to model the influence of the sea surface. Profile drag is modeled using experimental data. The extended lifting line code is validated against wind-tunnel measurements and data from the literature. A second code is then used to optimize the spanwise loading on a mainsail such that the drive force is maximized. Constraints are implemented to ensure positive circulation over the entire span and to limit the sectional loading to realistic values. Finally, the extended lifting line code is inverted to calculate the twist distribution necessary to produce the desired, optimized loading distribution for a given sail planform. The calculated twist distribution is found to be realistic and achievable.