  Flying insects are thought to achieve energy-efficient flapping flight by
storing and releasing elastic energy in their muscles, tendons, and thorax.
However, flight systems consisting elastic elements coupled to nonlinear,
unsteady aerodynamic forces also present possible challenges to generating
steady and responsive wing motions. In previous work, we examined the resonance
properties of a dynamically-scaled robophysical system consisting of a rigid
wing actuated by a motor in series with a spring, which we call a spring-wing
system \cite{Lynch2021-ri}. In this paper, we seek to better understand the
effects of perturbations on resonant systems via a non-dimensional parameter,
the Weis-Fogh number. We drive a spring-wing system at a fixed resonant
frequency and study the response to an internal control perturbation and an
external aerodynamic perturbation with varying Weis-Fogh number. In our first
experiments, we provide a step change in the input forcing amplitude and study
the wing motion response. 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 results across the Weis-Fogh number, which describes
the ratio of inertial and aerodynamic forces and the potential energetic
benefits of elastic resonance. The results suggest 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.
