Flexural stiffness patterns of butterfly wings (Papilionoidea)

A flying insect generates aerodynamic forces through the active manipulation of the wing and the “passive” properties of deformability and wing shape. To investigate these “passive” properties, the flexural stiffness of dried forewings belonging to 10 butterfly species was compared to the butterflies’ gross morphological parameters to determine allometric relationships. The results show that flexural stiffness scales with wing loading to nearly the fourth power (pw 3.9) and is highly correlated with wing area cubed (S3.1). The generalized map of flexural stiffness along the wing span for Vanessa cardui has a reduction in stiffness near the distal tip and a large reduction near the base. The distal regions of the wings are stiffer against forces applied to the ventral side, while the basal region is much stiffer against forces applied dorsally. The null hypothesis of structural isometry as the explanation for flexural stiffness scaling is rejected. Instead, selection for a consistent dynamic wing geometry (angular deflection) in flight may be a major factor controlling general wing stiffness and deformability. Possible relationships to aerodynamic and flight habit factors are discussed. This study proposes a new approach to addressing the mechanics of insect flight and these preliminary results need to be tested using fresh wings and more thorough sampling.