This study seeks to better quantify the parameters that drove the evolution of flight from non-volant winged dinosaurs to modern birds. In order to explore this issue, we used fossil data to model the feathered forelimb of Caudipteryx, the most basal non-volant maniraptoran dinosaur with elongate pennaceous feathers that could be described as forming proto-wings. In order to quantify the limiting flight factors, we created three hypothetical wing profiles for Caudipteryx representing incrementally larger wingspans, which we compared to the actual wing morphology as what revealed through fossils. These four models were analyzed under varying air speed, wing beat amplitude, and wing beat frequency to determine lift, thrust potential and metabolic requirements. We tested these models using theoretical equations in order to mathematically describe the evolutionary changes observed during the evolution of modern birds from a winged terrestrial theropod like Caudipteryx. Caudipteryx could not fly, but this research indicates that with a large enough wing span Caudipteryx-like animal could have flown, the morphology of the shoulder girdle would not actually accommodate the necessary flapping angle and metabolic demands would be much too high to be functional. The results of these analyses mathematically confirm that during the evolution of energetically efficient powered flight in derived maniraptorans, body weight had to decrease and wing area/wing profile needed to increase together with the flapping angle and surface area for the attachment of the flight muscles. This study quantifies the morphological changes that we observe in the pennaraptoran fossil record in the overall decrease in body size in paravians, the increased wing surface area in Archaeopteryx relative to Caudipteryx, and changes observed in the morphology of the thoracic girdle, namely the orientation of the glenoid and the enlargement of the sternum.
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