Flexural Stiffness in Insect Wings: Effects of Wing Venation and Stiffness Distribution on Passive Bending

Abstract

American Entomologist • Spring 2005 During flight, insect wings bend and twist dramatically, and the instantaneous, threedimensional shape of wings may influence many aspects of flight performance. Insects have little control over this bending and twisting—wing deformations are largely passive and are controlled primarily by the architecture and material properties of the wing. However, our understanding of how insect wing design affects flexibility and passive wing deformation remains limited. Here, we discuss how insect wing venation affects overall bending stiffness, how stiffness varies throughout wings, and how these features of wing design affect passive bending. The pattern of supporting veins in insect wings varies widely among insect orders and families. Given the large phylogenetic changes in wing venation pattern (Fig. 1), one might expect insect wings to display large mechanical differences that would affect their deformability during flight. We examined the relationship between insect wing flexibility and venation by measuring flexural stiffness (EI) and quantifying venation pattern in 16 insect species from six orders. Flexural stiffness is a composite measure of the overall bending stiffness of a wing, combining the material properties of the wing (E, Young’s modulus) and the geometric distribution of this material (I, second moment of area). We measured overall EI of wings in the spanwise direction (from base to tip) and the chordwise direction (from leading to trailing edge) by performing static bending tests. We attached each wing at the base (or leading edge), applied a known force at the tip (or trailing edge), and measured the displacement of the wing. We then calculated EI with a simple beam equation (see Combes and Daniel 2003a). We also digitized the wing venation of each species and derived five measures of venation pattern (Combes and Daniel 2003a). To remove the effects of phylogeny, we calculated standardized independent contrasts of venation and stiffness measurements and examined the correlations between these contrasts. Our measurements show that EI is strongly correlated with wing size (Fig. 2), but the details of venation pattern do not appear to affect overall flexural stiffness (no significant correlations were found between contrasts of wing venation pattern and EI). The measurements also reveal a large anisotropy, or difference, between spanwise and chordwise flexural stiffness; spanwise EI is ≈1 to 2 orders of magnitude greater than chordwise EI in all species tested (Fig. 2). To determine how wing structure may contribute to this pattern of stiffness anisotropy, we created a simplified finite-element model of a Manduca (hawkmoth) wing. To create this model, a digitized Flexural Stiffness in Insect Wings: Effects of Wing Venation and Stiffness Distribution on Passive Bending