Lateral dynamic flight stability of a model bumblebee in hovering and forward flight

The lateral dynamic flight stability of a model bumblebee in hovering and forward flight is studied, using the method of computational fluid dynamics to compute the stability derivatives and the techniques of eigenvalue and eigenvector analysis for solving the equations of motion. The lateral motion of the model bumblebee is unstable at hovering and low flight speed (advance ratio J=0, 0.13), and becomes neutral or weakly stable at medium and high flight speeds (J=0.31-0.57). The instability at hovering and low speed is mainly caused by a positive roll-moment derivative with respect to the side-slip velocity, which is due to the effect of changing the axial velocity of the leading-edge-vortex (LEV) (i.e. the 'lateral wind' due to the side motion of the insect increases the axial velocity of the LEV on one wing and decreases that on the other wing). As flight speed increases, because the mean position of the wings moves more and more backward, the effect of 'changing-LEV-axial-velocity' becomes weaker and weaker and the roll-moment derivative decreases first and then changes its sign to become negative, resulting in the neutrally or weakly stable motion at medium and high flight speeds.