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Saving energy and enhancing performance are secular preoccupations shared byboth nature and human beings. In animal locomotion, flapping flyers or swimmersrely on the flexibility of their wings or body to passively increase theirefficiency using an appropriate cycle of storing and releasing elastic energy.Despite the convergence of many observations pointing out this feature, theunderlying mechanisms explaining how the elastic nature of the wings is relatedto propulsive efficiency remain unclear. Here we use an experiment with aself-propelled simplified insect model allowing to show how wing compliancegoverns the performance of flapping flyers. Reducing the description of theflapping wing to a forced oscillator model, we pinpoint different nonlineareffects that can account for the observed behavior ---in particular a set ofcubic nonlinearities coming from the clamped-free beam equation used to modelthe wing and a quadratic damping term representing the fluid drag associated tothe fast flapping motion. In contrast to what has been repeatedly suggested inthe literature, we show that flapping flyers optimize their performance not byespecially looking for resonance to achieve larger flapping amplitudes withless effort, but by tuning the temporal evolution of the wing shape (i.e. thephase dynamics in the oscillator model) to optimize the aerodynamics.

Rather than resonance, flapping wing flyers may play on aerodynamics to improve performance