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First published online July 23, 2003

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Into thin air: contributions of aerodynamic and inertial-elastic forces to wing bending in the hawkmoth Manduca sexta

S. A. Combes^* and T. L. Daniel

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

View larger version (16K): [in a new window]   Fig. 1. Apparatus used to visualize Manduca sexta wing bending in normal air and helium. (A) Each wing was marked with dots of reflective paint at the wing tip (wt), leading edge (ld) and trailing edge (tr) and filmed from orthogonal views while flapping around the dorsal-ventral axis of the wing hinge (the y-axis). After filming, air was repeatedly removed from the box and replaced with helium until the box was filled with>95% helium. Wings were then filmed while flapping at the same amplitude and frequency. (B) Coordinates of the marked points were digitized and converted into angular position (), with the origin at the wing base and position (viewed from the leading edge) measured from the center of rotation.

View larger version (30K): [in a new window]   Fig. 2. Finite element model based on a Manduca sexta wing. The model approximates the planform geometry, vein configuration and spatial variation in flexural stiffness of a real wing. Declining material stiffness (E) of membrane and vein elements results in an exponential decline in flexural stiffness (EI), as measured in Manduca wings (Combes, 2002; Combes and Daniel, 2003b). Each color represents a different value of material stiffness, which varies from 4.7x107 Nm-2 to 4.5x109 Nm-2 in membrane elements, and from 1.9x1011 Nm-2 to 1.8x1013 Nm-2 in vein elements. The wing was rotated at its base around the y-axis, and bending was analyzed by tracking the positions of nodes at the wing tip (wt), leading edge (ld) and trailing edge (tr).

View larger version (35K): [in a new window]   Fig. 3. (Ai-Ci) Angular position and bending at the wing tip (A), leading edge (B) and trailing edge (C) of a Manduca wing flapped in normal air versus helium. The time base of 0.5 Hz control sequences (slow rotation) was adjusted to match 26 Hz experiments for comparison. At each of the wing locations, angular position during the control sequence (slow rotation; black line) was subtracted from position during the 26 Hz sequences in normal air or helium (green or orange lines) to quantify temporal patterns of wing bending (blue or red lines). (Aii-Cii) Amplitude coefficients from Fourier analyses of wing bending in normal air and helium are shown on the right, with the driving frequency of 26 Hz indicated by asterisks.

View larger version (31K): [in a new window]   Fig. 4. (Ai-Ci) Angular position and bending at the wing tip (A), leading edge (B) and trailing edge (C) of a finite element model based on a Manduca wing. Wing bending was calculated as in Fig. 3, by finding the difference between the angular position of a stiff wing (black line; analogous to the 0.5 Hz control sequence in real wings) and that of a flexible model wing, with or without mass damping (green or orange lines). (Aii-Cii) Amplitude coefficients from Fourier analyses of wing bending in the damped versus undamped model are shown on the right, with the driving frequency of 26 Hz indicated by asterisks.