Passive wing pitch reversal in insect flight

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Abstract
Wing pitch reversal, the rapid change of angle of attack near stroke transition, represents a difference between hovering with flapping wings and with a continuously rotating blade (e.g. helicopter flight). Although insects have the musculature to control the wing pitch during flight, we show here that aerodynamic and wing inertia forces are sufficient to pitch the wing without the aid of the muscles. We study the passive nature of wing pitching in several observed wing kinematics, including the wing motion of a tethered dragonfly,Libellula pulchella, hovering fruitfly, hovering hawkmoth and simplified dragonfly hovering kinematics. To determine whether the pitching is passive, we calculate rotational power about the torsion axis owing to aerodynamic and wing inertial forces. This is done using both direct numerical simulations and quasi-steady fluid force models. We find that, in all the cases studied here, the net rotational power is negative, signifying that the fluid force assists rather than resists the wing pitching. To further understand the generality of these results, we use the quasi-steady force model to analyse the effect of the components of the fluid forces at pitch reversal, and predict the conditions under which the wing pitch reversal is passive. These results suggest the pitching motion of the wings can be passive in insect flight.