Stable flapping flight in morphological space: Model, simulation, and explicit stability criteria

Understanding flight evolution requires quantifiable metrics. The complex flight dynamics and the vast morphological space insects have explored make it extremely challenging to define and understand what combinations of traits lead to these successful flyers. In this work, we constructed a mathematically tractable free-flight model, including the nonlinear wing-body coupling, to elucidate the effect of morphology on flight stability. Using this model to simulate almost a million different forms, we identified a region of passively stable upward flight, in addition to generic unstable flight. Analyzing the stability boundary in the 5D morphological and kinematic space, we found a set of explicit criteria that approximate the stability transitions, and expressed them in terms of two physically interpretable constraints. These two stability criteria provide a succinct metric for stability, quantifying the distance of an insect from the stable region directly from morphology, thus organizing a complex flight trait in a reduced and physically interpretable space. As such, they provide a framework for designing stable flapping-wing robots and for quantification of a critical phenotypic flight trait on top of the established phylogenetic relationships among insects.