Optimal pitching axis location of flapping wings for efficient hovering flight

Flapping wings can pitch passively about their pitching axes due to their flexibility, inertia, and aerodynamic loads. A shift in the pitching axis location can dynamically alter the aerodynamic loads, which in turn changes the passive pitching motion and the flight efficiency. Therefore, it is of great interest to investigate the optimal pitching axis for flapping wings to maximize the power efficiency during hovering flight. In this study, flapping wings are modeled as rigid plates with non-uniform mass distribution. The wing flexibility is represented by a linearly torsional spring at the wing root. A predictive quasi-steady aerodynamic model is used to evaluate the lift generated by such wings. Two extreme power consumption scenarios are modeled for hovering flight, i.e. the power consumed by a drive system with and without the capacity of kinetic energy recovery. For wings with different shapes, the optimal pitching axis location is found such that the cycle-averaged power consumption during hovering flight is minimized. Optimization results show that the optimal pitching axis is located between the leading edge and the mid-chord line, which shows close resemblance to insect wings. An optimal pitching axis can save up to 33% of power during hovering flight when compared to traditional wings used by most of flapping wing micro air vehicles (FWMAVs). Traditional wings typically use the straight leading edge as the pitching axis. With the optimized pitching axis, flapping wings show higher pitching amplitudes and start the pitching reversals in advance of the sweeping reversals. These phenomena lead to higher lift-to-drag ratios and, thus, explain the lower power consumption. In addition, the optimized pitching axis provides the drive system higher potential to recycle energy during the deceleration phases as compared to their counterparts. This observation underlines the particular importance of the wing pitching axis location for energy-efficient FWMAVs when using kinetic energy recovery drive systems.