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 forelimbs of Caudipteryx, the most basal non-volant maniraptoran dinosaur with elongated 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 with incrementally larger wingspans. We compared them with what revealed through fossils in wing morphology. 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 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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Kinematics of wings from Caudipteryx to modern birds