Safety and the car size effect: A fundamental explanation

In this paper the passive safety of cars is examined in the context of the influence of car size and mass on the relative safety of cars. The fundamental relationships of Newtonian mechanics are used to derive a generalized equation for the relative safety of cars of different sizes when involved in frontal collisions. Further equations are derived for collisions between cars of similar size and for single vehicle crashes. These are combined with overall injury criteria to give a series of predicted Relative Injury Risk relationships. Theory shows that in collisions between cars of similar size and in single vehicle accidents the fundamental parameter which determines Relative Injury Risk is the size, i.e. the length, of the car, whereas in collisions between dissimilar sized cars the fundamental parameters are the masses and the structural energy absorption properties of the cars. The predictions from the theoretical models are compared with the results of field evaluations of Relative Injury Risk to car occupants carried out in the USA and in Europe for car to car and single vehicle collisions. There is a high level of correlation between the theory and the field evaluations of Relative Injury Risk. Finally the overall structural crush behaviour of cars is reviewed and ways of further improving the overall passive safety of cars are proposed.