The inertial and geometrical properties of helmets

The center of gravity (CG) and the principal mass moments of inertia about the CG of Army aviator, American football, and bicycle helmets were experimentally determined by a variation of the classic differential weighing and torsional pendulum techniques. In the course of these experiments, an innovative method for three-dimensional (3D) digitization was found. An electronic caliper, which measured length, was used with a computer algorithm to achieve 3D digitization. The results of the above measurements show that the weight of the helmet and the distances from the CG to the orthogonal coordinate axes intercepts with the outer shell surface were highly correlated with its principal mass moments of inertia. A set of regression equations was derived on theoretical considerations and served to unify the experimentally obtained data. Our results indicate that the principal mass moments of inertia of helmets vary linearly with its mass but nonlinearly with size and shape. For a helmet, given its weight and certain geometrical distances, the regression equations estimate the principal mass moments of inertia to within 5% of its experimentally-determined values. For the helmets studied in this series, a modified linear-regression relationship between the principal mass moments of inertia and its mass was found. This result is reasonable because the mass distribution of the current generation of helmets are set primarily by the head size and secondarily by helmet size, shape, and materials.