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Automobile accident reconstruction and vehicle collision analysis techniques generally separate vehicle collisions into three different phases: pre-impact, impact and post-impact. This paper will concern itself exclusively with the modeling of the impact phase, typically defined as the time the vehicles are in contact. Historically, two different modeling techniques have been applied to the impact of vehicles. Both of these techniques employ the impulse-momentum formulation of Newton's Second Law. The first relies exclusively on this principle coupled with friction and restitution to completely model the impact. The second method combines impulse-momentum with a relationship between crush geometry and energy loss to model the impact. Both methods ultimately produce the change in velocity. ΔV, and other pertinent information about a collision.

This paper presents a reconstruction technique in which nonlinear optimization is used in combination with an impact model to quickly and efficiently find a solution to a given set of parameters and conditions to reconstruct a collision. These parameters and conditions correspond to known or prescribed collision information (generally from the physical evidence) and can be incorporated into the optimized collision reconstruction technique in a variety of ways including as a prescribed value, through the use of a constraint, as part of a quality function, or possibly as a combination of these means. This reconstruction technique provides a proper, effective, and efficient means to incorporate data collected by Event Data Recorders (EDR) into a crash reconstruction. The technique is presented in this paper using the Planar Impact Mechanics (PIM) collision model in combination with the Solver utility in Microsoft Excel.

In this third edition of Vehicle Accident Analysis & Reconstruction Methods, Raymond M. Brach and R. Matthew Brach have expanded and updated their essential work for professionals in the field of accident reconstruction. Most accidents can be reconstructed effectively using calculations and investigative and experimental data: the authors present the latest scientific, engineering, and mathematical reconstruction methods, providing a firm scientific foundation for practitioners. Accidents that cannot be reconstructed using the methods in this book are rare. In recent decades, the field of crash reconstruction has been transformed through the use of technology. The advent of event data records (EDRs) on vehicles signaled the era of modern crash reconstruction, which utilizes the same physical evidence that was previously available as well as electronic data that are measured/captured before, during, and after the collision.