Kinematic control of aerodynamic forces on an inclined flapping wing with asymmetric strokes

In the present study, we conduct an experiment using a one-paired dynamically scaled model of an insect wing, to investigate how asymmetric strokes with different wing kinematic parameters are used to control the aerodynamics of a dragonfly-like inclined flapping wing in still fluid. The kinematic parameters considered are the angles of attack during the mid-downstroke (α(md)) and mid-upstroke (α(mu)), and the duration (Δτ) and time of initiation (τ(p)) of the pitching rotation. The present dragonfly-like inclined flapping wing has the aerodynamic mechanism of unsteady force generation similar to those of other insect wings in a horizontal stroke plane, but the detailed effect of the wing kinematics on the force control is different due to the asymmetric use of the angle of attack during the up- and downstrokes. For example, high α(md) and low α(mu) produces larger vertical force with less aerodynamic power, and low α(md) and high α(mu) is recommended for horizontal force (thrust) production. The pitching rotation also affects the aerodynamics of a flapping wing, but its dynamic rotational effect is much weaker than the effect from the kinematic change in the angle of attack caused by the pitching rotation. Thus, the influences of the duration and timing of pitching rotation for the present inclined flapping wing are found to be very different from those for a horizontal flapping wing. That is, for the inclined flapping motion, the advanced and delayed rotations produce smaller vertical forces than the symmetric one and the effect of pitching duration is very small. On the other hand, for a specific range of pitching rotation timing, delayed rotation requires less aerodynamic power than the symmetric rotation. As for the horizontal force, delayed rotation with low α(md) and high α(mu) is recommended for long-duration flight owing to its high efficiency, and advanced rotation should be employed for hovering flight for nearly zero horizontal force. The present study suggests that manipulating the angle of attack during a flapping cycle is the most effective way to control the aerodynamic forces and corresponding power expenditure for a dragonfly-like inclined flapping wing.