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First published online October 21, 2004
Journal of Experimental Biology 207, 4147-4155 (2004)
Published by The Company of Biologists 2004
doi: 10.1242/jeb.01239

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The role of drag in insect hovering

Z. Jane Wang

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

View larger version (17K): [in a new window]   Fig. 1. Hovering motions studied in this paper. (A) The chord position (solid line with a black circle) and the coordinates, (B) generic asymmetric strokes along an inclined stroke plane, (C) normal hovering along a parabolic stroke plane and (D) normal hovering along a figure of eight. The strokes in C and D can be decomposed into pairs of asymmetric strokes described in B. The numbers next to the chords indicate the time sequence and also identify the corresponding segments in the decomposition.

View larger version (45K): [in a new window]   Fig. 2. Comparison of idealized normal hovering along a horizontal stroke plane (A) and dragonfly hovering along an inclined stroke plane (B). (i) Wing motion and averaged lift and drag, (ii) instantaneous vertical (CV) and horizontal (CH) force coefficients (solid line, net force; broken line, lift contribution; dotted line with circles, drag contribution), (iii) snapshots of vorticity (red, counterclockwise rotation; blue, clockwise rotation) and velocity fields (red vectors) during the fourth period, and (iv) time-averaged velocity field over one period (blue vectors). The maximum translational velocity (Umax) serves as a reference velocity scale. The broken square corresponds to the region shown in iii.

View larger version (97K): [in a new window]   Fig. 3. Vorticity field in four cases, ß=75°, 63°, 48° and 30°. In each case, 10 snapshots equally spaced over one period are shown (red, counterclockwise rotation; blue, clockwise rotation). The elliptic wing is in white. The stroke plane is horizontal for graphing purposes. The direction of gravity (g) relative the stroke plane is shown at the top left.

View larger version (24K): [in a new window]   Fig. 4. Instantaneous vertical (CV) and horizontal (CH) force coefficients in the cases of ß=75°, 63°, 48°, 30° and 4°. t is dimensionless (normalized by the flapping period).

View larger version (16K): [in a new window]   Fig. 5. Comparison of the averaged vertical (V) and horizontal (H) force coefficients and specific power (P) as a function of ß. P is scaled by a factor of 1/10 to fit in the graph.

View larger version (11K): [in a new window]   Fig. 6. Reducing specific power by eliminating half of a stroke.