Swimming in the Air: The Power of Drag at Miniature Scales

At the very edge of powered flight exist miniature insects with typical characteristic wing lengths of less than 1 mm. At such small scales, this domain of flight is characterized by Reynolds numbers ($Re$) of the order of 10 or less where the effects of air viscosity are significant. One distinguishable feature of miniature-scale flight is that of "drag-based" flapping kinematics, which are as closely related to the motions of swimming as they are to flying. The exact reason why miniature insects use drag-based kinematics, rather than the classical lift-based approach used by non-miniature insects, is not obvious. Hence, in this study, we investigate the above ambiguity via a quasi-steady aerodynamic approach. It is found that, for a stroke whose translational profile is symmetric about the half-period, pure-drag-based kinematics cannot be more aerodynamically effective or efficient than pure-lift-based kinematics. In fact, in almost all of the cases considered, lift-based flight is actually more advantageous than drag-based flight when half-strokes are symmetric. However, pure-drag-based kinematics become more favorable when we begin to consider flapping half-strokes that are asymmetric about the half period. When the asymmetry between the down- and up-stroke periods is increased, it is found that a force imbalance arises, via which viscous drag can be used to counteract the gravitational force. As such, the present study suggests that the reason why miniature insects do not use the conventional lift-based approach for flight, is a matter of taking advantage of their highly viscous environment, which allows for augmentation of both effectiveness and aerodynamic efficiency in hovering flight.