Abstract
The dynamic, three-dimensional shape of flapping insect wings may influence many aspects of flight performance. Insect wing deformations during flight are largely passive, and are controlled primarily by the architecture and material properties of the wing. Although many details of wing structure are well understood, the distribution of flexural stiffness in insect wings and its effects on wing bending are unknown. In this study, we developed a method of estimating spatial variation in flexural stiffness in both the spanwise and chordwise direction of insect wings. We measured displacement along the wing in response to a point force, and modeled flexural stiffness variation as a simple mathematical function capable of approximating this measured displacement. We used this method to estimate flexural stiffness variation in the hawkmoth Manduca sexta, and the dragonfly Aeshna multicolor. In both species, flexural stiffness declines sharply from the wing base to the tip, and from the leading edge to the trailing edge; this variation can be approximated by an exponential decline. The wings of M. sexta also display dorsal/ventral asymmetry in flexural stiffness and significant differences between males and females. Finite element models based on M. sexta forewings demonstrate that the measured spatial variation in flexural stiffness preserves rigidity in proximal regions of the wing, while transferring bending to the edges, where aerodynamic force production is most sensitive to subtle changes in shape.
Highlights
During flapping flight, insect wings accelerate masses of air, generating the forces necessary to support the insect’s weight and to perform complex maneuvers
We developed a method of approximating spatial variation in flexural stiffness along two axes of the wing
We attached a fresh wing at either the wing base or leading edge, and applied a point force to the wing with a pin attached to a force beam, using a small drop of cyanoacrylate glue to prevent the pin from slipping off the wing tip or trailing edge
Summary
Insect wings accelerate masses of air, generating the forces necessary to support the insect’s weight and to perform complex maneuvers. These ultralight airfoils (generally only 0.5–5% of body mass; Ellington, 1984b) must withstand the forces imposed upon them by the surrounding air, as well as the inertial forces caused by accelerating and decelerating their own mass up to several hundred times per second Insect wings perform these roles extremely successfully, despite the fact that they are largely passive structures, with no muscular control past the wing base (Wootton, 1992). Some aspects of wing flexibility have been mimicked in models by altering the relative positions of wing regions (Liu et al, 1998; Vest and Katz, 1996) or by modeling deformations as harmonic waves (Combes and Daniel, 2001; Daniel, 1987; Wu, 1971) These approaches provide unique insights into the mechanisms of force generation during flight, but often neglect one or more critical components of wing deflection (e.g. spanwise bending, chordwise bending or torsion), which can have large effects on aerodynamic force production (Batchelor, 1967). Models of insect flight that incorporate passive wing flexibility (in which shape changes are driven by forces imposed upon the wing rather than being specified in advance) are exceedingly rare (e.g. Smith, 1996)
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