Effects of Mass and Stiffness Ratio Variation on Vehicle Speed Change and Closing Speed Calculations

In accident reconstruction, parameters such as the struck vehicle change in speed and the closing speed can usually be determined by means of conservation of energy and conservation of momentum approaches. While others have considered limiting cases of the effects of mass and stiffness on vehicle speed change and closing speed calculations, the full spectrum of variations in vehicle stiffness and mass ratios have not been rigorously evaluated.

This paper presents a discussion of the effects on the calculated vehicle speed change as a function of the variation of the mass and stiffness ratios. Closed form analytical solutions and graphical representations are derived and depicted for the situations in which the ratio of the barrier impact test masses equate to that of the ratio of the vehicle masses for the reconstructed situation in question and for the scenario in which they do not. Closed form solutions are provided for global maxima and minima for the non-dimensional multiplier of the barrier equivalent velocity (BEV) and restitution term (1+e) as functions of the non-dimensional vehicle mass and stiffness ratios. A practical example is provided demonstrating the application of these principles and findings. As demonstrated in a simplified example, the analytical tools provided in this paper are useful in performing reconstructions for two vehicle collisions in which significant ranges exist in the stiffness and mass parameters for one of the vehicles secondary to incomplete identification.