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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.

The algorithm used in the third version of the Calspan Reconstruction of Accident Speeds on the Highway (CRASH3) and planar impact mechanics are both used to calculate energy loss and velocity changes of vehicle collisions. They (intentionally) solve the vehicle collision problem using completely different approaches, however, they should produce comparable results. One of the differences is that CRASH3 uses a correction factor for estimating the collision energy loss due to tangential effects whereas planar impact mechanics uses a common velocity condition in the tangential direction. In this paper, a comparison is made between how CRASH3 computes the energy loss of a collision and how this same energy loss is determined by planar impact mechanics.

The tire-force ellipse and tire-force circle (more frequently referred to as the friction ellipse and the friction circle, respectively) have been used for many years to qualitatively illustrate the concept of tire-road force interaction, particularly the force-limiting behavior for combined braking and steering (combined tire forces). Equations of the tire-force circle/ellipse, or, more specifically, the force limit envelope, in its idealized form have also been used in the development of quantitative models of combined tire forces used in vehicle dynamic simulation software. Comparisons of this idealized tire-force circle/ellipse using a simple bilinear tire force model and using actual tire data show that it provides only a limited, simplified notion of combined tire forces due to its lack of dependence upon the slip angle and traction slip.