Publications

Measurements of the chord length (alpha M0.31) and diameter (alpha M0.35) of the femora, tibiae, humeri and radii from 32 species of mammals, ranging in approximate body mass from 0.020-3500 kg, support previous data which show that mammalian long bones scale close to geometric similarity. Scaling of peak stresses based on these measurements of limb bone geometry predicts that peak stress increases alpha M0.28, assuming that the forces acting on a bone are directly proportional to an animal's weight. Peak locomotory stresses measured in small and large quadrupeds contradict this scaling prediction, however, showing that the magnitude of peak bone stress is similar over a range of size. Consequently, a uniform safety factor is maintained. Bone curvature (alpha M-0.09) and limb bone angle relative to the direction of ground force (alpha M-0.07) exhibit a slight, but significant, decrease with increasing body mass. Duty factor measured at the animal's trot--gallop transition speed does not change significantly with body size. The moment arm ratio of ground force to muscular force exerted about a joint was found to decrease dramatically for horses as compared to ground squirrels and chipmunks. This six-fold decrease (alpha M-0.23) provides preliminary data which appear to explain, along with the decrease in bone curvature and angle, the similar magnitudes of peak bone stress developed during locomotion in different sized animals. The crouched posture adopted by small quadrupeds while running may allow greater changes in momentum (when accelerating or decelerating) or a decrease in the forces exerted on their limbs.

Measurements of the cross-sectional geometry and length of bones from animals of different sizes suggest that peak locomotory stresses might be as much as nine times greater in the limb bones of a 300 kg horse than those of a 0.10 kg chipmunk. To determine if the bones of larger animals are stronger than those of small animals, the bending strength of whole bone specimens from the limbs of small mammals and bipedal birds was measured and compared with published data for large mammalian cortical bone (horses and bovids). No significant difference (P greater than 0.2) was found in the failure stress of bone over a range in size from 0.05-700 kg (233 +/- 53 MN/m2 for small animals compared to 200 +/- 28 MN/m2 for large animals). This finding suggests that either the limb bones of small animals are much stronger than they need to be, or that other aspects of locomotion (e.g. duty factor and limb orientation relative to the direction of the ground force) act to decrease peak locomotory stresses in larger animals.