A scaling law for the lift of hovering insects

Abstract

Insect hovering is one of the most fascinating acrobatic flight modes in nature, and its aerodynamics has been intensively studied, mainly through computational approaches. While the numerical analyses have revealed detailed vortical structures around flapping wings and resulting forces for specific hovering conditions, theoretical understanding of a simple unified mechanism enabling the insects to be airborne is still incomplete. Here, we construct a scaling law for the lift of hovering insects through relatively simple scaling arguments of the strength of the leading edge vortex and the momentum induced by the vortical structure. Comparison of our theory with the measurement data of 35 species of insects confirms that the scaling law captures the essential physics of lift generation of hovering insects. Our results offer a simple yet powerful guideline for biologists who seek the evolutionary direction of the shape and kinematics of insect wings, and for engineers who design flapping-based micro air vehicles.