Scaling of long bone fracture strength with animal mass

Most long bone fractures are the result of bending and/or torsional loading. To allometrically relate bone torsional and bending strength to animal mass (M), we define the bone strength index SB = J/dl where J = midshaft cross section polar moment of inertia, d = diameter, and l = length. In geometrically similar scaling, one would expect SB alpha M2/3. In this study, long bone geometric parameters were measured for 12 species of Artiodactyls. The relationships determined for length and diameter are similar to those reported by previous investigators (l alpha d3/4, l alpha M1/4). For the Artiodactyls studied, we found that SB alpha M0.82. Data previously collected by Biewener on a wide range of mammals (non-Artiodactyls) showed different scaling characteristics (l alpha d0.89, l alpha M0.31). However, our analysis of his data suggests roughly similar scaling of the torsional and bending strength index, SB alpha M0.77. It therefore appears that, in spite of differences in scaling of length and external diameter, the bending and torsional strengths scale similarly across a broad range of animals.