Scaling laws for the performance of rigid propulsors intended for underwater locomotion

Scaling laws are presented for the propulsive performance of rigid foils undergoing oscillatory motion in water. Water tunnel experiments on a nominally two-dimensional foil show that the scaling laws provide an excellent description of the data for thrust, power, and efficiency. The scaling laws are then extended to account for the effects of non-sinusoidal motions by using a parameter based on the maximum velocity of the trailing edge, which describes the experiments on non-sinusoidal gaits described by Jacobi elliptic functions reasonably well. Lastly, intermittent motions are considered. The thrust and power is shown to scale linearly with the duty cycle, and scaling laws for the energetics are presented. Intermittent motions are generally energetically advantageous over continuous motions, unless metabolic energy losses are sufficiently high.