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First published online December 14, 2005
Journal of Experimental Biology 209, 32-42 (2006)
Published by The Company of Biologists 2006
doi: 10.1242/jeb.01957

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Induced airflow in flying insects I. A theoretical model of the induced flow

Sanjay P. Sane

Department of Biology, University of Washington, Seattle, WA 98195, USA

View larger version (18K): [in a new window]   Fig. 1. The Induced Flow Model. (A) Blade element model. A schematic of the flapping wings of an insect. The grey strips show one of the elements of the blade element model, with the sectional circulation around it. (B) Momentum Flux Model. Extension of the near-field model in A to the far-field. The regions around the flying insect are divided into far-field inflow (P), near-field (Q), and far-field outflow (R). In this figure, i and far represent the near-field outflow and far-field outflow based on standard actuator disk theory.

View larger version (15K): [in a new window]   Fig. 2. Beta function fits to wing morphology. Filled blue circles show actual data points measured for () in (A) Drosophila melanogaster (fly) wing and (B) Manduca sexta (moth) wing. The black curves are Beta functions generated by the Eqn 40 for Drosophila melanogaster (A) and Eqn 46 for Manduca sexta wing (B).

View larger version (23K): [in a new window]   Fig. 3. Circulation along the wing span. (A) Circulation as a function of non-dimensional spanwise position for the case example of a Drosophila wing. The red curve shows the functional form of chord length as a function of non-dimensional spanwise position, and the green curve shows the functional form of circulation for a revolving propellor blade with a varying lift coefficient that varies linearly from base to tip. The black curve depicts the final functional form of the circulation on an insect wind obtained by multiplying the values generating the red and blue curves. (B). Comparison of the theoretically derived circulation variation with an experimentally derived distribution of circulation from DPIV data in a model Drosophila wing from Birch et al. (2004).