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We consider the propulsive performance of an unsteady heaving and pitchingfoil, experimentally studying an extensive parameter space of motionamplitudes, frequencies, and phase offsets between the heave and pitch motions.The phase offset $\phi$ between the heaving and pitching motions proves to be acritical parameter in determining the dynamics of the foil and its propulsiveperformance. To maximize thrust, the heave and pitch motions need to be nearlyin phase ($\phi=330^\circ$), but to maximize efficiency, the pitch motion needsto lag the heave motion ($\phi=270^\circ$), corresponding to slicing motionswith a minimal angle of attack. We also present scaling relations, developedfrom lift-based and added mass forces, which collapse our experimental data.Using the scaling relations as a guide, we find increases in performance whenfoil amplitudes (specifically pitch) increase while maintaining a modest angleof attack.

Scaling and performance of simultaneously heaving and pitching foils