Growth constraints set an upper limit to theropod dinosaur body size

Despite nearly 200 years of scientific collecting and study, none of the extinct, bipedal, predatory, theropod dinosaurs have been reliably shown to exceed 12 m in length. Using digital 3D models of theropods with lengths spanning 80 cm to 12 m, their body masses were found to scale to the 3.5 power of body lengths. The lateral area of the pelvis and the cross-sectional area of the tail base of these animals corresponds to the cross-sectional areas of key muscle groups important for balance and locomotion, and both scale to the 2.4 power of body length. Body accelerations in the lateral and forward directions are, using F = ma, given by dividing muscle area (force proxy) by body mass. Plotting these acceleration estimates against body length shows them to decrease exponentially. The largest theropods with body lengths of 10-12 m have less than 10% of the acceleration capacity of the smaller forms. The distinct lack of fossil remains of theropods demonstrably longer than 12 m suggests that the theropod body plan had an upper size limit based on a minimum acceleration threshold. Rotational inertia of the theropod body was found to be proportional to body length raised to the 5.5 power, and with increasing length, the capacity for agility would rapidly diminish. The tight relationship between theropod pelvic area and body length allows for the estimation of body lengths of specimens lacking complete axial skeletons, and this is done for four, large, well-preserved pelves.