In accident reconstruction, the distance a pedestrian has been projected by an impact may be used to provide an estimate of the speed of the striking vehicle. With tyre marks becoming less common, as ABS braking is introduced, the method is gaining in importance.
Speed estimation from throw distance rests on an empirical basis of field studies, which relate the distance projected to the speed of the vehicle. However field studies by themselves provide no understanding of the physical process. That understanding is important in the consideration of the effects of site characteristics, such as gradient or coefficient of friction.
The paper presents the equation of motion for an idealised particle, travelling over a surface where the upward reaction from the surface varies from moment to moment, including times when the particle is airborne and the reaction is zero. A simple formula is derived linking the minimum initial speed, the coefficient of friction and the total distance travelled:-
A series of tests was carried out to check this relationship experimentally. A dummy was projected on an airborne trajectory and the distance travelled was measured. It was found that whilst there were differences from the simple formula, those differences were small. For most practical purposes the simple formula provides a speed estimate of sufficient accuracy.
This speed estimate is for the minimum speed at which the pedestrian must have been projected. The average speed will be slightly higher and the speed of the striking vehicle higher again. Comparison with the results of field studies suggests that these effects add on some 20% or so.