A two-dimensional aerodynamic model of freely flying insects

Possible free flights of insects by a single flapping motion were studied. It is well-known that insects utilize vortices generated by flapping, by which they generate larger lift than that evaluated by the ordinary aerodynamic theory. However, the effect of the motion of the center of mass (CM) of the insect on its flight has not been clarified. To clarify the effect, numerical simulation was performed for a simple model considering the coupling between the vertical CM motion and the separation vortices generated by flapping wing. As a result, it is shown that the flapping flight has the following interesting features. First, despite a single flapping motion, the model exhibits two types of flapping flight: a steady flight in which the CM velocity oscillates and a wandering flight in which the CM velocity varies irregularly. These two types of flights are selected by the initial conditions even when all the parameters are the same. Second, at a certain critical parameter value, the steady flight loses its stability and undergoes an abrupt transition to the wandering flight. Interestingly, at this critical value, the steady flight can be regarded as hovering. The possible flights are analyzed in terms of bifurcation, and the bifurcation structure is qualitatively explained based on a simple assumption. These results suggest the significance of the effect of CM motion.