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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.

Designed for the experienced practitioner, this new book aims to help reconstruction specialists with problems they may encounter in everyday analysis. The authors demonstrate how to take the physics behind accidents out of the idealized world and into practical situations. Real-world examples are used to illustrate the methods, clarify important concepts, and provide practical applications to those working in the field. Thoroughly revised, this new edition builds on the original exploration of accident analysis, reconstruction, and vehicle design. Enhanced with new material and improved chapters on key topics, an expanded glossary of automotive terms, and a bibliography at the end of the book providing further reading suggestions make this an essential resource reference for engineers involved in litigation, forensic investigation, automotive safety, and crash reconstruction.

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.

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.

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.

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.

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.

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.

Equations of motion are derived for a two axle, 4 wheeled vehicle pulling a one axle, 2 wheeled trailer. Linear and nonlinear tire side force models are discussed. Examples of computer solutions of the equations are presented for both single vehicle motion and articulated vehicle motion. A comparison of tractor semitrailer maneuvers with experimental data shows good results.

A new method is described and illustrated which solves the planar, two vehicle collision reconstruction problem. The method, called LESCOR (LEast Square Collision Reconstruction), determines the initial velocity components when given: (1) final velocity components, (2) vehicle physical data, (3) damage geometry, (4) collision geometry and (5) the impact coefficients (restitution and friction). A novel feature is that if the impact coefficients are unknown but some of the initial velocity data is known (such as zero initial yaw rates and vehicle headings), the method will find the remaining initial velocities and the unknown coefficients. Using a six equation impact model and the method of least squares, LESCOR calculates any combination of 6 or less unknown initial velocity components and impact coefficients. Five example collision reconstructions are presented based on RICSAC collisions and a field example.