Dynamic flight stability of a model hoverfly in inclined-stroke-plane hovering

Most hovering insects flap their wings in a horizontal plane, called “normal hovering”. But some of the best hoverers, e.g. true hoverflies, hover with an inclined stroke plane. In the present paper, the longitudinal dynamic flight stability of a model hoverfly in inclined-stroke-plane hovering was studied. Computational fluid dynamics was used to compute the aerodynamic derivatives and the eigenvalue and eigenvector analysis was used to solve the equations of motion. The primary findings are as follows. (1) For inclined-stroke-plane hovering, the same three natural modes of motion as those for normal hovering were identified: one unstable oscillatory mode, one stable fast subsidence mode, and one stable slow subsidence mode. The unstable oscillatory mode and the fast subsidence mode mainly have horizontal translation and pitch rotation, and the slow subsidence mode mainly has vertical translation. (2) Because of the existence of the unstable oscillatory mode, inclined-stroke-plane hovering flight is not stable. (3) Although there are large differences in stroke plane and body orientations between the inclined- stroke-plane hovering and normal hovering, the relative position between the mean center of pressure and center of mass for these two cases is not very different, resulting in similar stability derivatives, hence similar dynamic stability properties for these two types of hovering.