Stability and agility trade-offs in spring-wing systems.

Flying insects are thought to achieve energy-efficient flapping flight by storing and releasing elastic energy in their muscles, tendons, and thorax. However, "spring-wing" flight systems consisting of elastic elements coupled to nonlinear, unsteady aerodynamic forces also present possible challenges to generating stable and responsive wing motions. The energetic efficiency from resonance in insect flight is measured by the Weis-Fogh number (N), which is the ratio of peak inertial force to aerodynamic force. In this paper, we present experiments and modeling to study how resonance efficiency (which increases with N) influences the control responsiveness and perturbation resistance of flapping wingbeats. In our first experiments, we provide a step change in the input forcing amplitude to a series-elastic spring-wing system and observe the response time of the wing amplitude increase. In our second experiments we provide an external fluid flow directed at the flapping wing and study the perturbed steady-state wing motion. We evaluate both experiments across Weis-Fogh numbers from 1 < N < 10. The results indicate that spring-wing systems designed for maximum energetic efficiency also experience trade-offs in agility and stability as the Weis-Fogh number increases. Our results demonstrate that energetic efficiency and wing maneuverability are in conflict in resonant spring-wing systems suggesting that mechanical resonance presents tradeoffs in insect flight control and stability.