J. Duff, P.Eng., Ph.D.

E.C. Mikulcik, P.Eng., Ph.D.

For-Eng Consultants Ltd.

Using Newton’s Laws of Motion and the principle of the Conservation of Energy, this paper derives a theory that can accommodate co-axial impacts such as head-on collisions, low speed rear-end impacts, bumper test procedures, and perpendicular crashes into infinite barriers. The theory discusses the three fundamental factors that govern the intensity of an impact namely, the Approach Velocity, the Mass Effect, and Structural Aspects. The last factor is introduced through the concept of the Coefficient of Restitution, and the accommodation of infinite masses is explained through the use of the Mass Effect.

The theory produces a series of "equalities" in which the Collision Impulse is related in turn to Momentum change, Kinetic Energy loss, and a fundamental equation containing the three factors mentioned above. Consideration is also given to crush equivalencies between vehicles into rigid barrier and vehicle-to-vehicle collisions.

The paper includes sample calculations to illustrate the effect of changes to the various variables, and points out some shortcomings occasionally found in technical reports dealing with traffic accidents.

The simple theory is then extended to include a fourth parameter of concern in the field of impact analysis, i.e., the effect of external forces. These forces are normally applied through ground contact during vehicle-to-vehicle collisions. The paper illustrates how ground forces are introduced into the derivation of the impulse equations and how they modify the "equalities" derived earlier. Sample calculations are included to illustrate the effect of the inclusion of ground forces to help reconstructionists determine when they can be neglected, and when they should be included in a collision analysis.