SKELETAL DESIGN, LOCOMOTION, AND SCALING IN MAMMALS

Peak stresses acting in the bones of mammals are predicted to increase seven-fold with a 1000-fold increase in body mass ((alpha)M(,b)('0.28)), if the forces acting on the bones increase in proportion to an animal's body weight. This is a direct consequence of the geometric scaling of limb bones over nearly the entire size range of mammals (shrew to elephant): length (alpha)M(,b)('0.35), diameter (alpha)M(,b)('0.36), cross-sectional area (alpha)M(,b)('0.72), and second moment of area (alpha)M(,b)('1.43). To maintain a uniform safety factor (ratio of fractures stress to peak functional stress) over a range in size, the material strength of bone would have to increase similar to the predicted increase in peak stress with increasing size. This hypothesis was tested by measuring the bending strength of small mammal (and avian) bone and comparing the results to published data available for large mammal bone. No significant difference was found, however, over a range in size from chipmunks to cattle (ultimate bending stress ranged from 200-250 MN/m('2)). Moreover, peak stresses calculated to be acting in the limb bones of horses compared to those acting in the bones of chipmunks and ground squirrels during high-speed locomotion were fairly similar in magnitude (range: 30-100 MN/m('2)); so that a safety factor of 3-5 is maintained over this range in size. The variance of these data with that predicted by the scaling of limb bone geometry, indicates that the forces acting on a bone do not increase in direct proportion to an animal's body weight.

Three schemes are proposed which may serve to reduce the forces acting on the bones of larger animals: (1) increased duty factor (D(,f)) of the limb, (2) decrease bone curvature ((zeta)), and (3) reduction of the angle ((alpha)) of a bone to the direction of ground force. Data obtained for animals ranging in size from 0.010-300 kg show that D(,f) (measured at the trot-gallop transition or top speed) does not change significantly with size ((alpha)M(,b)('-0.01)), whereas (zeta)((alpha)M(,b)('-0.09)) and (alpha)((alpha)M(,b)('-0.07)) decrease slightly. The exponents for (zeta) and (alpha) are significantly different from zero but only account for 50% of the reduction in stress due to bending. Compressive stress is not affected by these parameters.