Effects of Stroke Deviation on Aerodynamic Force Production of a Flapping Wing

The effects of stroke deviation of a flapping model insect wing on its aerodynamic force production are studied by solving the Navier-Stokes equations. Stroke deviation of a flapping wing often takes the forms of various out-of-plane wing-tip trajectories that depend on the time variation of the stroke deviation angle. In the present paper, four typical wing-tip trajectories, referred to as cases A-D, were used to investigate the effect of stroke deviation by comparing the aerodynamic forces, flows, and power requirements of the flapping wings with and without stroke deviation. The stroke deviation has remarkable influences on the time course of the aerodynamic force of a flapping wing. The influences could be explained by two mechanisms: one is the added-rotation effect, which is introduced by the deviation angle of the wing; the other is the change in effective angle of attack of the wing, which is due to the angular speed of the deviation. In general, the stroke deviation only produces a small effect on the cycle-mean aerodynamic forces, because the changes due to stroke deviation could be roughly offset in a wingbeat cycle. The analysis of power requirements shows that stroke deviation will generally lead to an increase in energy consumption for insect flights, indicating that insects should have the tendency to maintain the flapping motion in a plane for hovering or low-speed flight, as is observed in nature.