Stability Criteria for Flapping Flight

The vastness of the morphological and dynamical space explored by nature's flying animals makes it extremely challenging to identify the specific criteria required for successful flyers. Here, we construct an efficient flapping flight model capable of exploring this large flight space, thus providing a new tool for understanding the basic design principles of flapping flight. Our model contains the essential physics for simulating free flight, including the full nonlinear wing-body coupling. The first surprise of our simulations is the discovery of a region of passively stable upward flight. This stable region is bounded by a non-trivial hypersurface in a five-dimensional parameter space. Analyzing the bounds of the wing beat frequency range leads us to analytic approximations of this stability boundary in terms of two dynamically interpretable dimensionless parameters. We test these stability criteria with extensive simulations in the five-dimensional parameter space. The analytic form of the criteria make it possible to predict flight stability based purely on morphological parameters. They also offer basic guidelines for designing stable robotic flyers.