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Two methods for calculating speed from curved tire marks were investigated. The commonly used critical speed formula and a computer simulation program were evaluated based on their ability to reproduce the results of full-scale yaw tests. The effects of vehicle braking and friction coefficient were studied. Twenty-two yaw tests were conducted at speeds between 70 and 120 km/h. For half of the tests, about 30% braking was applied. Using the measured sliding coefficient of friction, both the critical speed formula and the computer simulations under-predicted the actual speed of the vehicle. Using the measured peak coefficient of friction, both methods over-estimated the actual speed. There was less variance in the computer simulation results. Braking tended to increase the speeds calculated by the critical speed formula.

Five collisions were staged in order to evaluate PC-Crash, a simulation program used for investigating motor vehicle collisions. Both vehicles were moving in all of the staged collisions at 1:1 or 2:1 speed ratios. Pre-impact speeds ranged from 19 to 56 km/h. Two separate methods were used to test the validity of the simulation program. Firstly, collision parameters were calculated from measured data, and used as input to the PC-Crash collision model. Secondly, the post-impact vehicle paths and rest positions were used to determine the pre-impact speeds. There was agreement between measured and simulated collision dynamics. Using the PC-Crash "Optimizer" to reconstruct the five collisions, the error in calculated pre-impact speeds of the ten vehicles ranged from-3.3 to +4.1 km/h. Vehicle speeds were determined based on post-impact rotation and paths, without detailed information on the braking from each wheel or the actual collision coefficient of restitution.

When vehicle collisions are reconstructed using a discrete kinetic time forward simulation program, many trials have to be performed to reach a point where the simulation results are close to the actual ones. The pre-impact speeds and directions of travel of each vehicle are the main variables that affect the post-impact motion of the vehicles. However, other factors, such as the exact resultant position where the impact forces are exchanged, the vehicle positions with respect to each other at impact, and the coefficient of restitution are important variables that also affect the results. When a number of impact parameters are unknown, a reconstruction can take a great deal of time. An optimizer tool in PC-Crash is designed to minimize reconstruction time and error by automatically varying a selected number of impact parameters, comparing the resulting simulation for each combination of parameters with the actual incident.

Without good-quality measurements taken at the time of an accident the analyst is faced with the need to extract measurement data from incident scene photographs. This paper discusses the history and development of the mathematical model for two-dimensional (2D) single exposure analytical photogrammetry, presents the software PC-Rect, and compares the analytical results obtained with PC-Rect to survey results. The sensitivity of the analytical results to the variation in such parameters as subject distance, camera height, digital photograph resolution, and bitmap density is discussed. The concept of using the directly rectified scanned photograph in the reconstruction task is introduced, and the utility of performing the dynamic simulation directly on the rectified photograph is discussed.

Knowledge about vehicle rolling resistance is required to calculate speed loss of accident vehicles during portions of their pre-impact and post-impact trajectory when they are not braking or sliding directly sideways. The accuracy of assumed rolling resistance values is most important in accidents with long post-impact roll out distances. Very little hard data are currently available1 and the accident reconstructionist must usually make estimates of drivetrain losses and normal and damaged tire rolling resistance to determine overall vehicle rolling resistance. In the first part of this study, the rolling resistances of various vehicles with different drive configurations are determined, based on accurate measurements made with a 5th wheel. In the second part, sensitivity analyses are done with PC-Crash2, a computer simulation program, to determine what effect the error in assumed rolling resistance has on speed calculations for various types of post-impact trajectories.

PC-Crash is a Windows™ - based accident reconstruction program developed in Graz, Austria by Dr. Hermann Steffan. PC-Crash collision analysis results are compared with previously published staged collision data. The program uses 2-D or 3-D vehicle geometry to model the pre-impact dynamics, impact engagement, and post-impact trajectories of multiple vehicles and multiple collisions. Steer angle, braking level, friction, and suspension properties at each wheel can be varied. Simulations can be visualized from any angle with the program's built-in 3-D animator. The staged collisions were reconstructed using PC-Crash and the trajectories were compared to actual measurements of the skid marks and rest positions. Vehicle speeds were compared to the PC-Crash predicted values.

The moments of inertia, in yaw, pitch, and roll, as well as the center of gravity height are necessary to successfully model the 3D dynamic behavior of vehicles before, during and after collision. A number of vehicle parameter estimation techniques have been developed and are currently in use in North America and Europe. Many parameters have been measured by NHTSA and others. The estimation techniques are compared to the available measured values, and recommendations are made for best estimating the parameters when measured values are not available. The sensitivity of 3D vehicle collision dynamics and trajectory simulation to variance in the moment of inertia is demonstrated.