Chordwise wing flexibility may passively stabilize hovering insects

Insect wings are flexible, and the dynamically deforming wing shape influences the resulting aerodynamics and power consumption. However, the influence of wing flexibility on the flight dynamics of insects is unknown. Most stability studies in the literature consider rigid wings and conclude that the hover equilibrium condition is unstable. The rigid wings possess an unstable oscillatory mode mainly due to their pitch sensitivity to horizontal velocity perturbations. Here, we show that a flapping wing flyer with flexible wings exhibits stable hover equilibria. The free-flight insect flight dynamics are simulated at the fruit fly scale in the longitudinal plane. The chordwise wing flexibility is modelled as a linear beam. The two-dimensional Navier-Stokes equations are solved in a tight fluid-structure integration scheme. For a range of wing flexibilities similar to live insects, all eigenvalues of the system matrix about the hover equilibrium have negative real parts. Flexible wings appear to stabilize the unstable mode by passively deforming their wing shape in the presence of perturbations, generating significantly more horizontal velocity damping and pitch rate damping. These results suggest that insects may passively stabilize their hover flight via wing flexibility, which can inform designs of synthetic flapping wing robots.