Dynamic flight stability of hovering model insects:theory versus simulation using equations of motion coupled with Navier-Stokes equations

In the present paper,the longitudinal dynamic flight stability properties of two model insects are predicted by an approximate theory and computed by numerical simulation.The theory is based on the averaged model(which assumes that the frequency of wingbeat is sufficiently higher than that of the body motion,so that the flapping wings' degrees of freedom relative to the body can be dropped and the wings can be replaced by wingbeat-cycle-average forces and moments);the simulation solves the complete equations of motion coupled with the Navier-Stokes equations.Comparison between the theory and the simulation provides a test to the validity of the assumptions in the theory.One of the insects is a model dronefly which has relatively high wingbeat frequency(164 Hz) and the other is a model hawkmoth which has relatively low wingbeat frequency(26 Hz).The results show that the averaged model is valid for the hawkmoth as well as for the dronefly.Since the wingbeat frequency of the hawkmoth is relatively low(the characteristic times of the natural modes of motion of the body divided by wingbeat period are relatively large) compared with many other insects,that the theory based on the averaged model is valid for the hawkmoth means that it could be valid for many insects.

Lateral dynamic flight stability of hovering insects: theory vs. numerical simulation

In the present paper, the lateral dynamic flight stability properties of two hovering model insects are predicted by an approximate theory based on the averaged model, and computed by numerical simulation that solves the complete equations of motion coupled with the Navier-Stokes equations. Comparison between the theoretical and simulational results provides a test to the validity of the assumptions made in the theory. One of the insects is a model dronefly which has relatively high wingbeat frequency (164 Hz) and the other is a model hawkmoth which has relatively low wingbeat frequency (26 Hz). The following conclusion has been drawn. The theory based on the averaged model works well for the lateral motion of the dronefly. For the hawkmoth, relatively large quantitative differences exist between theory and simulation. This is because the lateral non-dimensional eigenvalues of the hawkmoth are not very small compared with the non-dimensional flapping frequency (the largest lateral non-dimensional eigenvalue is only about 10% smaller than the non-dimensional flapping frequency). Nevertheless, the theory can still correctly predict variational trends of the dynamic properties of the hawkmoth's lateral motion.