The effects of wing inertial forces and mean stroke angle on the pitch dynamics of hovering insects

This paper discusses the wing inertial effects and the important role of the mean stroke angle on the pitch dynamics of hovering insects. The paper also presents a dynamic model appropriate for averaging and discusses the pitch stability results derived from the model. The model is used to predict the body angle of five insect species during hover, which are in good agreement with the available experimental results from different literature. The results suggest that the wing inertial forces have a considerable effect on pitch dynamics of insect flight and should not be ignored in dynamic analysis of hovering insects. The results also suggest that the body of hovering insects can not be vibrationally stabilized in a non-vertical orientation. Instead, the pitch angle of a hovering insect's body is mainly due to a balance of the moment of the insect's weight and the aerodynamic moment due to flapping kinematics with a nonzero mean stroke angle. Experiments with a flapping wing device confirm this results. To clearly explain the used model and clarify the difference between vibrational and non-vibrational stabilization, first this paper discusses the vibrational control of a three-degree-of-freedom force-input pendulum with its pivot moving in a vertical plane.