Propulsive performance of a windsurf-inspired pitching foil

We study experimentally a symmetrical rigid foil performing pitching oscillations around a mean incidence angle (αm) with respect to an incoming flow in a hydrodynamic channel at a constant velocity where the Reynolds number based on the chord of the foil is Rec=ρU∞c/μ=14400. The problem is inspired by the pumping maneuver used by athletes on the new hydrofoil-based windsurf boards. In windsurfing, the pumping mode is used by athletes to produce unsteady propulsion. Because of the complex kinematics and the sail's position relative to the perceived wind, the sail produces thrust or drag, and lift. In sailing, the wind perceived by the sail is not parallel to the mean chord. Even if the sail is in a steady mode, it can propel the board by adjusting the mean incidence angle. Few studies investigate the impact of αm on the mean values of aerodynamic force. The goal of this study is to quantify the forces on this configuration by varying the pitching kinematics characterized by the Strouhal number (StA=fA/U∞, with f and A the frequency and amplitude of pumping, respectively, and U∞ the wind velocity perceived by the sail) from 0 to 0.27, and the mean incidence angle αm, from 0° to 30∘, of the foil. The force measurements show a high lift production and the delay of the stall angle according to StA which can be linked to previous studies about the generation of vortices at the trailing edge. A general trend of decrease is observed for the drag force coefficient in pitching compared to the static case. For the highest Strouhal numbers tested, the drag coefficient can become negative (thrust) in a range of αm up to 15∘ in specific cases. By using a sport-mimetic approach, we transform the measured lift and drag forces into propulsive and drifting forces, which are the decomposition of the aerodynamic force in the board frame. It is the reference frame in sailing to characterize and optimize physical parameters of the boat such as speed and trajectory. We investigate the impact of unsteady propulsion in upwind conditions. Doing so allows us to investigate race strategies because the generation of propulsion resulting from the drive force is linked to a sideways motion caused by the drift force. We also discuss the impact of using the pumping maneuver rather than the steady propulsion and show several behaviors that could help athletes with decision making.