## Introduction

THE RECONSTRUCTION OF HIGHWAY ACCIDENTS, which serves a number of purposes (e.g., law enforcement, statistical research, and litigation), has been accomplished to some extent since the early 1970’s by the use of computer programs.  Prior to that time, the analytical techniques (i.e., “hand” calculations) that were traditionally applied were predominantly “closed-form” calculations based on piecewise linear solutions of the equations of motion.  The accuracy of such calculations varied widely with the level of sophistication of the specific selected relationships and with the subjective interpretations of evidence included in the reconstruction.

In 1970, NHTSA sponsored a research project to develop a computer program that would achieve improved uniformity, as well as improvements in accuracy and detail, in the interpretation of physical evidence in highway accidents.  The resulting prototype computer program was the Simulation Model of Automobile Collisions (SMAC, Ref.1).

SMAC is a time-domain mathematical model in which the vehicles are represented by differential equations derived from Newtonian mechanics combined with empirical relationships for some components (e.g., crush properties,  tires) that are solved for successive time increments by digital integration.

Each vehicle is limited to the three degrees of freedom associated with plane motion (i.e., 2 translation, 1 rotation).  The tire forces are modeled by a non-dimensional side force function and the “friction circle” concept is included for the interaction between side and circumferential tire forces.  The collision force simulation is achieved by means of the modeling of each vehicle as a rigid mass surrounded by an isotropic, homogeneous periphery that exhibits elastic plastic behavior.

The SMAC computer model is an “open-form” of reconstruction procedure wherein the user specifies the dimensional, inertial,  crush and tire properties of the vehicles, the initial speeds, angles and driver-control inputs.  The program, through step-wise integration of the equations of motion, produces detailed time-histories of the vehicle trajectories including the collision responses.  The user compares the SMAC-predicted trajectories and collision deformations with the physical evidence to determine the degree of correlation.  Iterative runs can then be performed, varying initial speeds, heading angles and control inputs until an acceptable match of the physical evidence is achieved.

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Analytical Approach: Collision Routine