Front-to-rear crashes between vehicles at speeds well below 20 mph account for a surprisingly large number of significant injuries, usually classified as Whiplash Associated Disorders (WAD). Although an efficient model or process that relates the vehicle-to-vehicle collision conditions and parameters to the level and characteristics of injury is desirable, the complexity of the problem makes such an overall crash-to-injury model impractical. Instead, this paper develops and explores a reasonably effective model of the vehicle-to-vehicle impact that determines the forward/rearward accelerations, velocities and the contact force as functions of time for both the striking and struck vehicles. Tire drag due to braking is included to allow the assessment of its effects.
Each vehicle is given a single degree of freedom consisting of translation of the center of gravity in the direction of vehicle heading. It is assumed that vehicles are centrally aligned and that suspension effects are negligible. The contact force is modeled using nonlinear spring and damping elements each with a coefficient and exponent. The coefficients and exponents are parameters of the model and are varied to obtain realistic contact pulse shapes, durations and velocity changes. Tire drag is modeled using Coulomb friction with equal static and dynamic coefficients.
Data from experimental collisions typically is found to include high-frequency variations due to conditions such as initial bumper misalignments as well as short-duration, local structural conditions (such as spot weld failures, buckling and failure of brackets, etc.). At least some of the high-frequency content is due to structural conditions near the accelerometers. The model is developed to match the overall acceleration pulse shape and magnitude and not reproduce the high-frequency variations. By selecting stiffness and damping coefficients to match contact duration and coefficient of restitution, the model can be used to determine peak accelerations and ΔV's for the purpose of accident reconstruction and for occupant motion studies.