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Influence of rotational inertia on turning performance of theropod dinosaurs: clues from humans with increased rotational inertia

David R. Carrier^*, Rebecca M. Walter and David V. Lee

Department of Biology, 201 South Biology Building, University of Utah, Salt Lake City, UT 84112, USA

View larger version (6K): [in a new window]   Fig. 1. Layout of the stepping-stone slalom course. The filled circles represent the location of the slalom poles, which were spaced 2 m apart. The larger gray circles represent the location of the cement stepping-stones.

View larger version (16K): [in a new window]   Fig. 2. Estimated rotational inertia versus body mass for carnosaur theropods based on a model of Allosaurus and of Homo sapiens.

View larger version (11K): [in a new window]   Fig. 3. (A) The angle turned in maximum-effort jump turns when turning with the control weight (open column) and when subjects turned with their rotational inertia increased by 9.2-fold (filled column) (N=5; P<0.0001, paired t-test). (B) The average running velocity in a slalom course of six 90° turns with the control weight (open column) and when the subjects ran with their rotational inertia increased by 9.2-fold (filled column) (N=9; P=0.0005, paired t-test). (C) The average running velocity in a slalom course of six 90° turns in which foot placement was restricted to three stepping-stones per turn (Fig. 1) when the subjects ran with the control weight (open column) and when the subjects ran with 9.2-fold increased rotational inertia (filled column) (N=8; P<0.00001, paired t-test). Values are means + S.E.M.

View larger version (10K): [in a new window]   Fig. 4. The percentage decrease in mass (open columns) and rotational inertia (filled columns) of the pre-caudal trunk, neck and head of Allosaurus fragilis that results from reductions in the mass of the head. Small changes in distal mass have large effects on rotational inertia.

View larger version (23K): [in a new window]   Fig. 5. Phylogeny of dinosaurs (Gauthier, 1986; Sereno, 1999; Holtz, 2000) showing the distribution of characters that are likely to have decreased rotational inertia. 1, pubes retroverted; 2, S-shaped neck; 3, cervical vertebrae pneumatized; 4, dorsal vertebrae pneumatized; 5, manus tridactyl; 6, forelimb reduced; 7, tail shortened; 8, manus didactyl; 9, head size reduced; 10, teeth lost; 11, body size reduced; 12, tail reduced, but more robust proximally. The functional significance of the characters is discussed in the text.

View larger version (25K): [in a new window]   Fig. 6. Hypothesized running postures of a juvenile Allosaurus. (A) A horizontal posture of trunk and tail may have been appropriate for prey capture but would have unnecessarily increased the rotational inertia during running. (B) To increase turning performance, theropod dinosaurs may have run with their trunk and tail arched in a jack-knife posture, their neck may have been sharply arched backwards to hold the head closer to the hindlimbs and they may have held their arms backwards along the sides of the body. The angle of the jack-knife posture would not have to have been as dramatic as illustrated in B to reduce rotational inertia significantly.