Car size and injury risk: a model for injury risk in frontal collisions

Empirical studies have established that when pairs of similar cars collide, the relative injury risk between pairs of different size is inversely related to their mass ratio. Further empirical studies have shown that in frontal collisions between dissimilar cars, relative injury risk is inversely proportional to mass ratio raised to the power of n. The value of the exponent n increases with impact speed, with n approximately 1 at low speeds and n ranging from 2.81 to 3.74 for fatalities. In this paper a theory is derived which explains relative injury risk in terms of three parameters: length (or size) ratio, mass ratio and the ratio of collision energy absorption between the colliding vehicles. It is proposed that the ratio of collision energy absorption between colliding vehicles is a function of the structural collapse forces imposed at maximum dynamic crush. The theory shows that the fundamental factor in collisions between pairs of similar cars is size, i.e. length. For collisions between two dissimilar cars, Monte-Carlo simulations using generalised characterisations for the car population yield theoretical predictions that match empirical findings ranging from minor injuries (AISI +) to fatal (AIS6) injuries.