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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.

Residual damage caused during a collision has been related through the use of crush energy models and impact mechanics directly to the collision energy loss and vehicle velocity changes, ΔV1 and ΔV2. The simplest and most popular form of this crush energy relationship is a linear one and has been exploited for the purpose of accident reconstruction in the well known CRASH3 crush energy algorithm. Nonlinear forms of the relationship between residual crush and collision energy also have been developed. Speed reconstruction models that use the CRASH3 algorithm use point mass impact mechanics, a concept of equivalent mass, visual estimation of the Principle Direction of Force (PDOF) and a tangential correction factor to relate total crush energy to the collision ΔV values. Most algorithms also are based on an assumption of a common velocity at the contact area between the vehicles.

This research investigates the uncertainty in the calculation of the change in velocity, ΔV, and the crush energy, EC, due to variations in the computed values of crush stiffness coefficients, A and B (d₀ and d₁), and due to variations in the measurements of the residual crush, Ci, i = 1,...6, using the CRASH3 damage algorithm. An understanding of the nature of such uncertainties is of particular importance as both the ΔV and EC are frequently used as inputs to reconstruction methods and become variations in the reconstruction process. These variations lead to uncertainties in the results of the reconstruction which are generally the preimpact speed of one or both of the vehicles involved in the collision. This paper consists of three parts. The first investigates the uncertainty associated with the calculation of the stiffness coefficients A and B (d₀ and d₁).

A mathematical model is developed which permits calculation of velocity changes of vehicles involved in a collision where one or both vehicles are articulated. This includes any single vehicle pulling a trailer (such as an automobile towing a recreational vehicle) or tractor, semitrailers. The equations of the model are based upon direct application of Newton's laws of impulse and momentum. Typically made assumptions (such as the insignificance of external impulses) are discussed and analyzed. Examples of the model's application are provided including the impact of tractor, semitrailers into rigid barriers.

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.