Deciphering the flapping frequency allometry: unveiling the role of sustained body attitude in the aerodynamic scaling of normal hovering animals.

Hovering flight helps facilitate feeding, pollination, and courtship. Observed only in smaller flying animals, hover kinematic characteristics are diverse except for the decreasing flapping frequency with the animal size. Although studies have shown that these wing patterns enable distinct unsteady aerodynamic mechanisms, the role of flapping frequency scaling remains a source of disagreement. Here we show that negative allometry of the flapping frequency is required to sustain body attitude during hovering, consistent with experimental data of hovering animals, from fruit flies to hummingbirds, reported in the literature. The derived scaling model reveals that the lift coefficient and reduced frequency remain invariant with mass, enabling leading-edge vortex formation and wake-capture for a wide range of fliers to hover.