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For several staged collisions, results obtained with closed form reconstruction calculations and with a computerized step-by-step procedure are compared with measured responses. A refined, closed-form reconstruction procedure is defined, derivations of the analytical relationships are outlined and detailed results of sample applications are presented. Closed form calculation procedures for estimating impact conditions became a topic of interest in relation to the development of an automatic starting routine for iterative applications of the Simulation Model of Automobile Collisions (SMAC) computer program. The accuracy of initial estimates of speeds determines the total number of iterative adjustments of SMAC that are required to achieve an acceptable overall match of the evidence. Since a high degree of success was achieved in the refinement of such calculation procedures, the end product, by itself, is considered to be a valuable aid to accident investigations.

The trajectory solution procedures of the original CRASH program included both the SPIN routine and an exploratory trajectory simulation option to approximate and refine the linear and angular velocities at separation. The resulting separation speeds were then used to determine the impact speeds by means of application of the principle of conservation of linear momentum. This paper presents a detailed review of the logic, rationale and limitations of the trajectory solution procedures of the original CRASH program and discusses a number of refinements including: incorporation of the principle of conservation of angular momentum, approximations of the effects of changes during collision in the positions and orientations of the two vehicles and of the effects of external forces and moments that act on the two-body system during the collision, and adaptations of optimization techniques for error reduction and convergence in iterative solutions.

A brief description and history of the SMAC computer program, including its relationship to CRASH, is presented. The rationale for a continued interest in the SMAC approach to reconstruction is discussed. Modifications and refinements that have contributed to the current capabilities of SMAC-87 are briefly described, representative results of applications are presented and planned future developments are defined.