Propulsive performance of a windsurf-inspired pitching foil

Abstract: We study experimentally a symmetrical rigid foil 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 according to the chord of the foil is, $Re_{c} = \rho U_{\infty} c / \mu = 14400$. The problem is inspired from the pumping maneuver used by athletes on the new hydrofoil-based windsurf boards. The goal of the study is to quantify the forces on this configuration by varying the pitching kinematics characterized by the Strouhal number ($St_{A} = fA/U_{\infty}$), from 0 to 0.27, and the mean incidence angle $\alpha_{m}$, from 0 to 30$<sup>{\circ}$, of the foil. The force measurements show a high lift production and the delay of the stall angle according to $St_A$ 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 compare to the static case. For the highest Strouhal numbers tested, drag coefficient can become negative (thrust) in a range of $\alpha_{m}$ up to 15$<sup>{\circ}$ in specific case. We present the various impacts of the amplitude of beating and the frequency of pitching on the aerodynamic forces for small mean incidence angle and high mean incidence angle (above the static stall angle). By using a sport-mimetic approach, we transform the measured lift $&amp;$ drag forces into a propulsive and drifting force. Doing so allows us to investigate race strategies. We investigate the generation of propulsion in upwind conditions.