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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.

The Critical Speed Formula is used in the field of accident reconstruction for the estimation of the speed of a vehicle that has been given a sudden unidirectional steer maneuver by the driver and when the tires develop a high enough sideslip to leave curved visible marks on the pavement. This and other uses of the formula are investigated in this paper. Reconstructions are done using computerized dynamic simulations of a turn maneuver for 3 different, driver forward control modes: braking, coasting and accelerating. The experimental results of Shelton (Accident Reconstruction Journal, 1995) are analyzed statistically and are compared to the results of the simulations. Results show that the Critical Speed Formula can give reasonably accurate results but that the accuracy varies with several factors. One is where along the trajectory measurements are made to estimate the tire mark curvature.

Many investigators have used the equations of impulse, momentum and energy to analyze the changes in velocities when two vehicles collide. The equations generally include the classical coefficient of restitution which is used as a measure of energy loss. These equations and the coefficient are based upon large forces and short-duration contact between the two bodies. In all real collisions contact is over a surface, and in many vehicle collisions, momentary or permanent interlocking of deformed parts occurs over this surface. This causes a moment to develop whose impulse can significantly affect the dynamics; most authors neglect or ignore this moment (1, 2, 3, 4, 5)*. In this paper, the equations of impact of two vehicles are derived including the moment impulse. An impact moment coefficient is defined. The value of this coefficient determines the extent to which a moment is developed between the two vehicles during impact. Two examples are presented.

Little experimental data have been reported in the crash reconstruction literature regarding high-speed sideswipe collisions. The Insurance Institute for Highway Safety (IIHS) conducted a series of high-speed, small overlap, vehicle-to-barrier and vehicle-to-vehicle crash tests for which the majority resulted in sideswipe collisions. A sideswipe collision is defined in this paper as a crash with non-zero, final relative tangential velocity over the vehicle-to-barrier or vehicle-to-vehicle contact surface; that is, sliding continues throughout the contact duration. Using analysis of video from 50 IIHS small overlap crash tests, each test was modeled using planar impact mechanics to determine which were classified as sideswipes and which were not. The test data were further evaluated to understand the nature of high-speed, small overlap, sideswipe collisions and establish appropriate parameter ranges that can aid in the process of accident reconstruction.

Many accident reconstructions rely on the use of friction factors for the analysis of vehicle speeds. Measurement of the friction factor, or coefficient of friction, at the accident site is usually an important step in achieving a more accurate estimate of the friction factor at the time of the accident. Over the years several on site test methodologies have emerged within the accident reconstruction community. However, little has been published which compares the data and results from the different methods. This paper presents a comparison of some methodologies. A g-analyst1 accelerometer, a VC•20002 accelerometer, and a bumper chalk gun3/radar gun4 are compared for locked wheel friction values under different speed and road surface conditions. Data from the two on board systems are recorded simultaneously. Measurements are made for several stops at each of the speeds and two road surface conditions.

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.

Reconstruction methods typically are based upon impact velocity changes computed by one of two approaches. These are damage based or crush measurement techniques and impulse and momentum equation solutions. Crush measurement techniques have an analytical foundation based to a large extent on point mass collision theory, limited primarily to collisions of vehicles with a common final velocity at the contact surface. Impulse and momentum methods can treat a full, 2-dimensional collision with arbitrary restitution and friction coefficients. As such their analytical foundation is much broader than damage based or crush measurement methods. The energy loss relationship and the tangential correction factor form an important part of the crush measurement methods. These two relationships are derived in a more general fashion than has been available. These two approaches are compared in this paper. The comparison focuses on the ability to accurately calculate energy loss.

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.

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.

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.

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.

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.

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 paper describes, lists and demonstrates the features of a computer program which permits animation of a plan view of a vehicle's trajectory on a video monitor. Page-flip animation in the Microsoft QuickBasic 4.5 language for MS DOS compatible computers is used. The program accepts and uses a sequential data file, defined by the user, of vehicle positions and orientations over uniform time intervals. Following animation, the program allows selection of an arbitrary sequence of some or all of the vehicle's positions on the monitor for transfer to a hard copy. The computer program is being distributed for public use as a utility program. A short review of the use of computerized animation software in legal environments is presented.

The problem of determining the uncertainty in the result of a formula evaluation is addressed. The origin of the uncertainty is the presence of variations in the input variables. Three popular techniques are discussed in the context of accident reconstruction. The first establishes upper and lower bounds through calculation of the largest and smallest possible values of the quantity being estimated for all combinations of the input variables. The second method uses differential calculus and places variations of the variables into a delta equation derived from the mathematical formula. The last method covers cases where statistical information about the input data is known. Approximate means and variances are developed for linear and nonlinear formulas. Examples are given for all of the methods such as calculation of speed from skid distance and calculation of stopping distance including perception-decision-reaction (PDR) time.

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).