The relationship between mass and acceleration for impacts on padded surfaces

It is shown analytically that when an object impacts a deformable surface, the acceleration it experiences is inversely proportional to its mass. This is because acceleration is reduced by deformation of the surface, and more massive objects deform the surface more. Since head injury is thought to depend more on acceleration than applied force, this result implies that children may be at greater risk than adults when striking a padded surface. To test the theoretical prediction, 2.69 and 7.40 kg missiles were dropped 31.8 cm onto three deformable surfaces: dry sod, moist sod, and an artificial playing surface. Impact force was measured with a force plate, and divided by missile mass to obtain acceleration. For each test surface, the smaller mass produced a larger acceleration than the larger mass, confirming the theoretical result. Additionally, load-deformation characteristics of the three surfaces were measured, and the results used to predict the effects of mass on acceleration during impact. The predicted results agreed well with the experimental data for the artificial surface (2.3% difference) and moist sod (5.7% difference), but less well for dry sod (21% difference).