Axial propulsion with flapping and rotating wings, a comparison of potential efficiency

Interest in biological locomotion and what advantages the principles governing it might offer in the design of manmade vehicles prompts one to consider the power requirements of flapping relative to rotary propulsion. The amount of work performed on the fluid surrounding a thrusting surface (wing or blade) is reflected in the kinetic energy of the wake. Consideration of the energy in the wake is sufficient to define absolute minimum limitations on the power requirement to generate a particular thrust. This work applies wake solutions to compare the minimum inviscid propulsive power requirement of wings flapping and in rotation at wing loading conditions reflective of hover through a state of lightly-loaded cruise. It is demonstrated that hovering flapping flight is less efficient than rotary wing propulsion except for the most extreme flap amplitude strokes (Theta > 160 degrees) if operating at large wake wavelength. In cruise, a larger range of flap amplitude kinematics (Theta > 140 degrees) can be aerodynamically more energy efficient for wake wavelengths reflective of biological propulsion. These results imply, based on the observed wing kinematics of continuous steady flight, that flapping propulsion in animals is unlikely to be more efficient than rotary propulsion.