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Snively E, O'Brien H, Henderson DM, Mallison H, Surring LA, Burns ME, Holtz, Jr. TR, Russell AP, Witmer LM, Currie PJ, Hartman SA, Cotton JR.2018. Lower rotational inertia and larger leg muscles indicate more rapid turns in tyrannosaurids than in other large theropods. PeerJ Preprints6:e27021v1https://doi.org/10.7287/peerj.preprints.27021v1
Synopsis: Tyrannosaurid dinosaurs had larger than predicted preserved leg muscle attachments and low rotational inertia relative to their body mass, indicating that they could turn more quickly than other large theropods. Methods: To compare turning capability in theropods, we regressed agility estimates against body mass, incorporating superellipse-based modeled mass, centers of mass, and rotational inertia (mass moment of inertia). Muscle force relative to body mass is a direct correlate of agility in humans, and torque gives potential angular acceleration. Agility scores therefore include rotational inertia values divided by proxies for (1) muscle force (ilium area and estimates of m. caudofemoralis longus cross-section), and (2) musculoskeletal torque. Phylogenetic ANCOVA (phylANCOVA) allow assessment of differences in agility between tyrannosaurids and non-tyrannosaurid theropods (accounting for both ontogeny and phylogeny). We applied conditional error probabilities a(p) to stringently test the null hypothesis of equal agility. Results: Tyrannosaurids consistently have agility index magnitudes twice those of allosauroids and some other theropods of equivalent mass, turning the body with both legs planted or pivoting over a stance leg. PhylANCOVA demonstrates definitively greater agilities in tyrannosaurids, and phylogeny explains nearly all covariance. Mass property results are consistent with those of other studies based on skeletal mounts, and between different figure-based methods (our main mathematical slicing procedures, lofted 3D computer models, and simplified graphical double integration). Implications: The capacity for relatively rapid turns in tyrannosaurids is ecologically intriguing in light of their monopolization of large (>400 kg), toothed dinosaurian predator niches in their habitats.
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Spreadsheet for mass property calculations: Tarbosaurus bataar ZPAL MgD-I/4
This spreadsheet includes all equations necessary for calculating mass properties from lateral and coronal reconstructions. Contact author Eric Snively (firstname.lastname@example.org) for instructions.
Figure for digitizing Tarbosaurus bataar (ZPAL MgD I/4), after Paul (2010) and Hurum and Sabath (2003).
This image was used for digitizing outlines and calculating mass properties of Tarbosaurus bataar (ZPAL MgD I/4). The skull is tilted down in lateral view, and shortened in dorsal view to match the length. See text for details. The tail is restores as moderately wide, after Persons and Currie (2011).
This spreadsheet has all variables and equations for calculating rotational inertia of the body and swing leg pivoting above a stance foot, for all specimens. The animal has just pushed off with its swing leg, whose center of mass is now ventrolateral to the acetabulum.