  Scaling laws for the thrust production and energetics of self-propelled or
fixed-velocity three-dimensional rigid propulsors undergoing pitching motions
are presented. The scaling relations extend the two-dimensional scaling laws
presented in Moored & Quinn (2018) by accounting for the added mass of a
finite-span propulsor, the downwash/upwash effects from the trailing vortex
system of a propulsor, and the elliptical topology of shedding trailing-edge
vortices. The novel three-dimensional scaling laws are validated with
self-propelled inviscid simulations and fixed-velocity experiments over a range
of reduced frequencies, Strouhal numbers and aspect ratios relevant to
bio-inspired propulsion. The scaling laws elucidate the dominant flow physics
behind the thrust production and energetics of pitching bio-propulsors, and
they provide guidance for the design of bio-inspired propulsive systems.
