A Simplified Mathematical Model of Pumped Hydrofoils

This paper presents a simplified mathematical model of pumped hydrofoil (PH)—a surfboard elevated above water surface and connected to tandem hydrofoils by strut. The PH is operated rider who stands on the produces swinging up-and-down motions resulting in forward propulsion device. In present paper, description vertical motion reduced linear oscillator excited an oscillating mass coupled with requirement that weight supported dynamic lift foil(s). inertial damping influence hydrofoil(s) accounted for expanding unsteady force foil(s) terms kinematic parameters. restoring term associated phenomenon automatic stabilization shallowly submerged hydrofoils. latter effect manifests itself when approaches free surface, its decreases, it moves away from increases. analytical solution pumping foil mass-spring type forced oscillations equation allows one calculate flapping and, thereafter, period-averaged thrust generated PH. speed has been estimated assumption device enters cruising mode becomes equal drag, comprising viscous, wave, induced drag components. under discussion relate main parameters system performance hopefully, provides further insight into phenomenon, design methodology, operation strategy. review part focuses two aspects problem: hydrodynamic behavior proximity their due oscillations.