Meeting Abstract
In hovering flight, which has evolved independently in insects, birds, and bats, animals can maintain a stable position in space while feeding on resources such as pollen and nectar. Here, we quantitatively model and simulate the hovering mechanisms observed in insects, hummingbirds and bats. We have developed a reduced-order dynamical model consisting of a rigid body (trunk), with three degrees of freedom (2 translational and 1 rotational), and two wings, each with two rotational degrees of freedom (elevation/depression and pronation/supination) and a folding/unfolding degree of freedom to modulate wingspan. The wings can be effectively massless (e.g., insect and hummingbird wings) or relatively massive (e.g., bat wings). We estimate aerodynamic forces using a quasi-steady blade element formulation. Based on extensive simulations, we outline a range of kinematic motion without wing folding that defines a necessary condition for hovering, and we validate this region with experimental data from insects and hummingbirds. We show that modulating pronation angle is critical for producing efficient hovering, and that this result is compatible with the recorded hummingbird wing motions. Our simulations also predict an optimal wingbeat frequency that produces a local minimum for power consumption. By mapping observations from nine hummingbird species, we show that their wingbeat frequency is consistently near the optimum flapping frequency. For bats, which possess relatively heavy articulated wings, we show that wing folding and unfolding is critical for permitting hovering and for maintaining a reasonable degree of power consumption. Comparisons with biological data show good agreement with our model predictions.
