Propulsive efficiency and efficacy of a pumping sail

This study presents a framework to analyze the propulsive performance of a sail under oscillatory pumping motion, which should be modified from the analysis framework for conventional flapping wings. A new set of metrics, including the propulsive efficiency ηs and efficacy, which depend not only on the aerodynamic coefficient but also on kinematic conditions of the sailing vehicle, are proposed to characterize the propulsive performance of sail pumping. The necessity of the proposed metrics is illustrated by studying the propulsive performance of a two-dimensional airfoil under different heaving and kinematic conditions through computational fluid dynamic simulations. It was found that the sail pumping typically improves the propulsive performance by lift enhancement instead of drag reduction. Thus, the formation of leading-edge vortices may not be detrimental to the propulsive efficiency of a pumping sail, contrary to that for flapping wings. A propulsive efficiency greater than unity is achievable under certain sailing conditions because a sailing vehicle can extract energy from the wind.