The dynamics of hovering flight in hummingbirds, insects and bats with implications for aerial robotics

We analyze the effects of morphology and wing kinematics on the performance of hovering flight. We present a simplified dynamical model with body translational and rotational degrees of freedom that incorporates the flapping, long-axis wing rotation and folding of the wing. To validate our simulation, we compare our results with direct measurements from hovering insects, hummingbirds and bats. Results show that long-axis wing rotation angle (a proxy for pronation) has a significant effect on energy efficiency. For a given wing rotation amplitude, the hovering system has a power-optimal flapping frequency for each stroke-plane orientation, and that frequency closely corresponds to the wingbeat frequencies observed in a diverse range of hummingbird species. We find that larger animals (with larger total mass and wing size), such as bats, require more power to maintain a stable hovering orbit and that hovering with a constant wingspan becomes increasingly impractical with increasing body size. We show, as an exemplar, that for a system of the size of a hovering bat, e.g. Glossophaga soricina, hovering with constant wingspan is dynamically possible, but is implausible and inefficient. For these conditions, hovering with varying wingspan, retracting the wing on the upstroke, is a more realistic hovering modality.