Evolution of Vertebrate Flight: An Aerodynamic Model for the Transition from Gliding to Active Flight

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Abstract
I counter recent criticism against the arboreal theory of the evolution of flight in vertebrates. It has been stated, for instance, that incipient flapping during gliding would dramatically reduce life, and that the generation of vortex rings by wing strokes must be a principal problem for animals to solve in evolving powered flight. The criticism is mostly unfounded and lacks adequate explanations. My model, based on quasi-stationary aerodynamics, shows that sufficient lift and a net thrust can be produced even during very slight flapping in a gliding animal. The model is constructed so that the various flight variables always combine in such a way that the vertical lift force produced during one complete wing stroke in partially powered flight by a hypothetical animal always equals the weight of the animal. Given this constraint, the model then explores whether there is any net horizontal thrust beyond that needed to balance body drag. The outcome is that, given certain flight variables, a net thrust will always be generated during partially powered flight. Any such thrust can be used to make the flight path shallower than it is in equilibrium gliding for the same animal. This strongly supports the arboreal theory of the evolution of flight in birds, bats, and pterosaurs, which includes a gliding stage before powered flight originated. The transition between gliding and flapping also can be easily explained by the vortex theory. As it travels, a gliding animal leaves a continuous vortex sheet which rolls up into a pair of vortex tubes. Slight flapping might create undulating vortex tubes of essentially the same character. During more powerful flapping and with the upstroke being a recovery stroke, or with the air meeting the dorsal side of the wings on the upstroke, providing thrust and negative lift, the vortex tubes become interrupted and roll up into vortex rings. My aerodynamic model applies to the transition from gliding to powered flight, regardless of the evolutionary path of the gliding behavior.