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First published online December 28, 2007
Journal of Experimental Biology 211, 234-238 (2008)
Published by The Company of Biologists 2008
doi: 10.1242/jeb.013797

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Research Article, Biomechanics of Flight

Aerodynamic efficiency of flapping flight: analysis of a two-stroke model

Z. Jane Wang

Theoretical and Applied Mechanics, Cornell University, Ithaca, NY 14853, USA

e-mail: jane.wang{at}cornell.edu

Accepted 22 October 2007

Summary

To seek the simplest efficient flapping wing motions and understand their relation to steady flight, a two-stroke model in the quasi-steady limit was analyzed. It was found that a family of two-stroke flapping motions have aerodynamic efficiency close to, but slightly lower than, the optimal steady flight. These two-stroke motions share two common features: the downstroke is a gliding motion and the upstroke has an angle of attack close to the optimal of the steady flight of the same wing. With the reduced number of parameters, the aerodynamic cost function in the parameter space can be visualized. This was examined for wings of different lift and drag characteristics at Reynolds numbers between 10² and 10⁶. The iso-surfaces of the cost function have a tube-like structure, implying that the solution is insensitive to a specific direction in the parameter space. Related questions in insect flight that motivated this work are discussed.

Key words: efficiency, aerodynamics, flapping wing, flight

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