The objective of this study is to analytically model the fatality risk in frontal vehicle-to-vehicle crashes of the current vehicle fleet, and its sensitivity to vehicle mass change. A model is built upon an empirical risk ratio-mass ratio relationship from field data and a theoretical mass ratio-velocity change ratio relationship dictated by conservation of momentum. The fatality risk of each vehicle is averaged over the closing velocity distribution to arrive at the mean fatality risks. The risks of the two vehicles are summed and averaged over all possible crash partners to find the societal mean fatality risk associated with a subject vehicle of a given mass from a fleet specified by a mass distribution function.
Based on risk exponent and mass distribution from a recent fleet, the subject vehicle mean fatality risk is shown to increase, while at the same time that for the partner vehicles decreases, as the mass of the subject vehicle decreases. The societal mean fatality risk, the sum of these, incurs a penalty with respect to a fleet with complete mass equality. This penalty reaches its minimum (∼ 8% for the example fleet) for crashes with a subject vehicle whose mass is close to the fleet mean mass.
The sensitivity, i.e., the rate of change of the societal mean fatality risk with respect to the mass of the subject vehicle is assessed. Results from two sets of fully regression-based analyses, Kahane (2012) and Van Auken and Zellner (2013), are approximately compared with the current result. The general magnitudes of the results are comparable, but differences exist at a more detailed level. The subject vehicle-oriented societal mean fatality risk is averaged over all possible subject vehicle masses of a given fleet to obtain the overall mean fatality risk of the fleet. It is found to increase approximately linearly at a rate of about 0.8% for each 100 lb decrease in mass of all vehicles in the fleet.