Optimal Sail Angles to Drive Circular Motion

Abstract This study examines the optimisation of sail or airfoil angles to generate torque in circular motion, focussing on the interplay of lift and drag forces under constant wind conditions. Motivated by potential application to wind energy production and storage, the model considers a sail mounted on the surface of a rotating flywheel and identifies optimal sail orientations to maximise torque, highlighting dependence on the ratio of sail speed to wind speed. That is, when the sail travels slower than the wind speed, there are positions where the sail can utilise drag whilst travelling downwind; at higher speeds, this is not possible, and maximising lift whilst mitigating drag is crucial. We extend the model to a system with multiple evenly spaced sails, showing that increasing the sail count reduces torque variance, ensuring more stable energy production. Additionally, the analysis identifies a critical speed threshold above which the sails hinder rotation, acting only to decelerate the flywheel. Furthermore, sail placement can influence system performance, where the sail radius affects the torque generated and the optimal radius depends upon the rotational speed. These findings underscore the importance of precise control over sail parameters to enhance energy capture efficiency.