Efficient self-propelled locomotion by an elastically supported rigid foil actuated by a torque

Unsteady Propulsion of a Two-Dimensional Flapping Thin Airfoil in a Pulsating Stream

“…It oscillates around a mean value with an amplitude usually much smaller than the mean, and a frequency that typically doubles the flapping frequency. For instance, for a small flapping amplitude (airfoil chord length ratio, say, ϵ ≪ 1), the cruising velocity oscillations amplitude has been found to be of the order of ϵ 2∕3 times the mean velocity for a simple aquatic locomotion model [11], and of the order of ϵ 2 for a simple ornithopter flight model [10]. The frequency doubling is nicely illustrated by the ability of a sinusoidally plunging airfoil to produce thrust by the Knoller-Betz effect [12].…”

“…Most aerodynamic models come from studies that consider the oscillating foil in a flow with constant freestream velocity. However, the cruising velocity of animals, or robotic vehicles, that use flapping wings or fins to propel themselves is not constant [3,[7][8][9][10][11]. It oscillates around a mean value with an amplitude usually much smaller than the mean, and a frequency that typically doubles the flapping frequency.…”