Driver injury and fatality risk in two-car crashes versus mass ratio inferred using Newtonian mechanics

Abstract

This paper aims at explaining the results of a recent empirical study that found that when cars of unequal mass crash into each other, the ratio of driver fatality risk in the lighter car to risk in the heavier car (the fatality risk ratio) increased as a power function of the ratio of the mass of the heavier car to that of the lighter car (the mass ratio). The present study uses two sources of information to examine the relationship between these same quantities: first, calculations based on Newtonian mechanics, which show that when two cars crash head-on into each other, the ratio of their changes in speed (delta- v) is inversely proportional to mass ratio; second, National Accident Sampling System data, which show how delta- v affects driver injury risk. The study is performed for fatalities and severe injuries and for unbelted and belted drivers. Combining the two sources of information gives the result that fatality risk ratio increases as a power function of mass ratio, the same functional form found in the empirical study. Because the study is rooted in Newtonian mechanics, it clearly and directly identifies physical mechanisms involved and leads to the conclusion that mass, as such, causes large differences in driver injury and fatality risk when cars of unequal mass crash into each other.