Scaling Laws of Bio-Inspired Propulsion*

Aquatic animals oscillate their fins in combined heaving and pitching motions in order to swim fast and efficiently.  To date there still are not accurate scaling laws to describe the physics of swimming.  Here we focus on pitch-dominated swimmers and we develop scaling laws to predict the thrust and power of both two and three-dimensional propulsors pitching about their leading edge.  Additionally, extensive two- and three-dimensional potential flow simulations as well as experiments show excellent collapse of the data for the thrust and power by using the developed scaling terms.  The scaling laws are further extended to the cost of transport (CoT).  These scaling relations offer the first mechanistic rationale for the scaling of swimming energetics observed in biology.  Specifically, the CoT is shown to scale predominately with the added mass power.  This suggests that the CoT of organisms using unsteady propulsion will scale with their mass as CoT ~ m^-1/3, which is indeed consistent with existing biological data. Finally, these scaling relations offer a framework that can be extended to combined heaving and pitching motions and intermittent swimming.