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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.

In the vast majority of impacts involving light vehicles, traditional impulse-momentum collision models can be used to analyze the mechanics of two colliding vehicles. However, these models cannot handle the multiple degrees of freedom associated with articulated (pin-connected) vehicles. In addition, collisions involving one or two articulated vehicles may not satisfy the basic assumptions of these traditional collisions models. In particular, the assumption that impulses of external forces (such as tire-road friction) are negligible compared to the impulse developed over the crash surface may not be valid. The large masses, long dimensions, the presence of the pinned joint, or all of these factors, may necessitate special considerations and more flexible model capabilities. This paper lists the assumptions that underlie the application of the principle of impulse and momentum to a planar collision between rigid bodies.

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.

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.

The force distributed over the contact patch between a tire and a road surface is typically modeled in component form for dynamic simulations. The two components in the plane of the contact patch are the braking, or traction force, and the steering, or side or cornering force. A third force distributed over the contacts patch is the normal force, perpendicular to the road surface. The two tangential components in the plane of the road are usually modeled separately since they depend primarily on independent parameters, wheel slip and sideslip. Mathematical expressions found in the literature for each component include exponential functions, piecewise linear functions and the Bakker-Nyborg-Pacejka equations, among others. Because braking and steering frequently occur simultaneously and their resultant tangential force is limited by friction, the two components must be properly combined for a full range of the wheel slip and sideslip parameters.

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.

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.

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.

Various vehicle dynamic simulation software programs have been developed for use in reconstructing accidents. Typically these are used to analyze and reconstruct preimpact and postimpact vehicle motion. These simulation programs range from proprietary programs to commercially available packages. While the basic theory behind these simulations is Newton's laws of motion, some component modeling techniques differ from one program to another. This is particularly true of the modeling of tire force mechanics. Since tire forces control the vehicle motion predicted by a simulation, the tire mechanics model is a critical feature in simulation use, performance and accuracy. This is particularly true for accident reconstruction applications where vehicle motions can occur over wide ranging kinematic wheel conditions. Therefore a thorough understanding of the nature of tire forces is a necessary aspect of the proper formulation and use of a vehicle dynamics program.

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).