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Analytical results on the role of flexibility in flapping propulsion

Published online by Cambridge University Press:  24 September 2014

M. Nicholas J. Moore
M. Nicholas J. Moore*
Affiliation:
Courant Institute of Mathematical Sciences, New York University, NY 10012, USA Department of Mathematics and Geophysical Fluid Dynamics Institute, Florida State University, FL 32306, USA
*
†Email addresses for correspondence: [email protected], [email protected]
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Abstract

Wing or fin flexibility can dramatically affect the performance of flying and swimming animals. Both laboratory experiments and numerical simulations have been used to study these effects, but analytical results are notably lacking. Here, we develop small-amplitude theory to model a flapping wing that pitches passively due to a combination of wing compliance, inertia and fluid forces. Remarkably, we obtain a class of exact solutions describing the wing’s emergent pitching motions, along with expressions for how thrust and efficiency are modified by compliance. The solutions recover a range of realistic behaviours and shed new light on how flexibility can aid performance, the importance of resonance, and the separate roles played by wing and fluid inertia. The simple robust estimates afforded by our theory may prove valuable even in situations where details of the flapping motion and wing geometry differ.

JFM classification

Biological Fluid Dynamics: Propulsion Biological Fluid Dynamics: Swimming/flying Vortex Flows: Vortex shedding
Type
Papers
Information
Journal of Fluid Mechanics , Volume 757 , 25 October 2014 , pp. 599 - 612
Copyright
© 2014 Cambridge University Press 

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