A harmonic model of hydrodynamic forces produced by a flapping fin

The hydrodynamic control laws of unsteady fins inspired by swimming and flying animals are considered. A controller based on cycle-averaged forces requires a bandwidth lower than the flapping frequency, with correspondingly slow reactions to disturbances or commands in order to avoid undesirable feedback from the oscillating fins. A harmonic model of the periodic thruster forces was empirically found using a mechanical fin flapping in roll and pitch in hover, in uniform flow, and under various kinematic conditions. A multi-fin vehicle could use this model to account for the dominant non-linearities and minimize undesirable motions through coordinated control of individual fins.