A re-parameterisation of the Power Model of the relationship between the speed of traffic and the number of accidents and accident victims

This paper presents a re-analysis of the Power Model of the relationship between the mean speed of traffic and road safety. Past evaluations of the model, most recently in 2009, have broadly speaking supported it. However, the most recent evaluation of the model indicated that the relationship between speed and road safety depends not only on the relative change in speed, as suggested by the Power Model, but also on initial speed. This implies that the exponent describing, for example, a 25% reduction in speed will not be the same when speed changes from 100 km/h to 75 km/h as it will when speed changes from 20 km/h to 15 km/h. This paper reports an analysis leading to a re-parameterisation of the Power Model in terms of continuously varying exponents which depend on initial speed. The re-parameterisation was accomplished by fitting exponential functions to data points in which changes in speed and accidents were sorted in groups of 10 km/h according to initial speed, starting with data points referring to the highest initial speeds. The exponential functions fitted the data extremely well and imply that the effect on accidents of a given relative change in speed is largest when initial speed is highest.