One of the major difficulties in the safety design of motor vehicles is the variability of road accidents. This variability arises in part from the external accident conditions, such as the direction and velocity of impact, and also in part from the variation of the occupant, including such factors as size, weight, location and impact tolerance. The effect of such variability is to undermine the validity of a “typical accident” approach, in which a design is tested at a single speed with a single size of dummy and a single injury criterion.

Working from a statistical approach, using methods originating from statistical mechanics, this paper derives a quantitative measure of the injury probability, taken over the whole spectrum of road accidents. This gives an objective measure of injuries taken over the whole population of car occupants and accident situations, and therefore provides an assessment of the vehicle's impact injury potential which is more closely related to the road situations.

The paper also includes a solution of the related optimisation problem, that is the provision of the optimum force/deflection characteristic (within a given space) to minimise the injuries on the road.