Humeral bone strength and flight in eumaniraptoran dinosaurs

Flight requires that the animal be able to generate sufficient lift and thrust to support its weight in air. This requires that the humerus have a sufficiently strong section modulus to withstand the applied stresses. In order to study the possibility of flight in extinct dinosaurs, the humeral section modulus of 17 species of extant volant birds with masses ranging from 5.8 grams in Regulus calendula to 8.959 kg in Cygnus olor has been measured. The humeral section modulus is related to the mass of the animal via a power law with an exponent of 1.14 (standard deviation 0.02). The humeral section modulus is evaluated for 19 extinct dinosaurs from Dromaeosauridae, Troodontidae and Avialae. Comparing to the data for extant volant birds allows for the determination of those dinosaurs whose humeri were too weak to support powered flight. All five species of Avialae are found to have had humeri sufficiently strong for flight. Four dromaeosaurids (Microraptor gui, Graciliraptor lujiahunensis, Buitreraptor gonzalezorum, and Changyuraptor yangi) and one troodontid (Jianianhualong tengi) are also found to have had humeri that were strong enough for flight. This is a necessary, but not necessarily sufficient, condition for flight.