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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.

Data from the RICSAC1 car crashes have been presented and analyzed in the original reports and in technical papers by others. Some issues dealt primarily with respect to the transformation of data from the accelerometer locations to the centers of gravity. Accelerometers were attached to the moving vehicles and so most results have been presented in moving coordinates. It appears that an additional step to transform the velocity changes and final velocities into inertial coordinates remains to be done. The initial and final inertial velocities and vehicle physical properties are used to compare the experimental data to the law of conservation of momentum. Some of the collisions lead to a loss in total system momentum, as expected. Some show a gain in system momentum which is not physically possible. An analysis of variance of this momentum data shows that the loss or gain of momentum is not systematically related to the type of collision.

Numerous algebraic formulas and mathematical models exist for the reconstruction of vehicle speed of a vehicle-pedestrian collision using pedestrian throw distance. Unfortunately a common occurrence is that the throw distance is not known because no evidence exists to locate the point of impact. When this is the case almost all formulas and models lose their utility. The model developed by Han and Brach published by SAE in 2001 is an exception because it can reconstruct vehicle speed based on the distance between the rest positions of the vehicle and pedestrian. The Han-Brach model is comprehensive and contains crash parameters such as pedestrian launch angle, height of the center of gravity of the pedestrian at launch, pedestrian-road surface friction, vehicle-road surface friction, road grade angle, etc. Such an approach provides versatility and allows variations of these variables to be taken into account for investigation of uncertainty.

A planar model for the mechanics of a vehicle-pedestrian collision is presented, analyzed and compared to experimental data. It takes into account the significant physical parameters of wrap and forward projection collisions and is suitable for solution using mathematics software or spreadsheets. Parameters related to the pedestrian and taken into account include horizontal distance traveled between primary and secondary impacts with the vehicle, launch angle, center-of-gravity height at launch, the relative forward speed of the pedestrian to the car at launch, distance from launch to a ground impact, distance from ground impact to rest and pedestrian-ground drag factor. Vehicle and roadway parameters include postimpact, constant-velocity vehicle travel distance, continued vehicle travel distance to rest with uniform deceleration and relative distance between rest positions of vehicle and pedestrian. The model is presented in two forms.