Abstract: The longitudinal dynamic flight stability of a hovering honeybee is studied by using the method of computational fluid dynamics to compute the aerodynamic derivatives and the techniques of eigenvalue and eigenvector analysis are employed for solving the equations of motion. The disturbed motion has three natural modes: an unstable oscillatory mode, a stable fast subsidence mode and a stable slow subsidence mode. The unstable oscillatory mode consists of pitching and horizontal moving oscillations with negligible vertical motion; and the coupling of nose-up pitching with forward horizontal motion (and nose-down pitching with backward horizontal motion) in this mode causes the instability. The stable fast subsidence mode consists of monotonic pitching and horizontal motions. The stable slow subsidence mode is mainly a monotonic descending (or ascending) motion. As a result of the unstable oscillatory mode, the hovering flight of the honeybee is dynamically unstable. However, the instability is 'slow' to the honeybee: the time for the initial disturbances to double (0.11 s) is more than 22 times the wingbeat period (5.1 ms). These results may explain why a honeybee can perform steady hovering and at the same time has good maneuverability: slowly growing disturbance can be easily suppressed by adjusting wing motion; and weak stability or instability is required for good maneuverability.

Key words: biomimetics, honeybee, hovering, dynamic stability, Navier-Stokes simulation, natural mode of motion