Wing kinematics in a hovering dronefly minimize power expenditure

When an insect hovers or performs constant-speed flight, its wings flap at certain amplitude, frequency, angle of attack, etc., and the flight is balanced (vertical force equals to the weight, and horizontal force and pitch moment are zero). It is possible that when some other sets of values of wing kinematical parameters are used, the force and moment balance conditions can still be satisfied. Does the wing kinematics used by a constant-speed flying insect minimize the power expenditure? In this study, whether the wing kinematics used by a freely hovering dronefly minimizes its energy expenditure was investigated. First, the power consumption using the set of values of wing kinematical parameters that was actually employed by the insect was computed. Then, the kinematical parameters were changed while keeping the equilibrium flight conditions satisfied, and the power consumption was recalculated. It was found that wing kinematical parameters used by the freely hovering dronefly are very close to that minimize its energy consumption, and they can ensure the margin of controllability from hovering to maneuvers. That is, slight change of wing kinematical parameters did not cause significant change of the specific power (maintained a relatively small value).