Windsurf-mimetic study about unsteady propulsion

Abstract

We study experimentally a a three-dimensional reduced model of a sail shape performing pitching oscillations around a mean incidence angle ($\alpha_{m}$) with respect to an incoming flow in a hydrodynamic channel at a constant velocity where the Reynolds number based on the mean chord of the sail is Re$_{c} = \rho U_{\infty} c / \mu = 11900$. The problem is inspired by the "pumping" maneuver used by windsurf athletes. At the start of a race or in light winds, to get or keep the board in foiling mode, for example after a tack change, athletes use intermittent propulsion by "pumping" the sail, i.e. periodically changing the angle of incidence of the sail relative to the wind. The flapping or pitching parameters and position of the sail according to the flow (incidence angle) influence the aerodynamic forces acting on the sail by destabilising the flow and generating unsteady forces. We experimentally characterise the aerodynamic forces of the sail. We compare the sailing ($C_{drive}, \ C_{drift}$) and aerodynamic ($C_{drag}, \ C_{lift}$) coefficients between a static and an oscillating sail for different flapping parameters and different mean incidence angles of the sail and angles of attack of the boat. Thanks to the use of "pumping", we observe that it is possible to generate a drive force greater than the one generated without oscillation. Furthermore, "pumping" increases the range of mean incidence angle in which the drive force is positive. However, this increase inevitably comes with an increase in drift force, which is often detrimental. These data can be used to improve the Velocity Prediction Programme (VPP) associated with windsurfing and to help athletes optimise their "pumping".