Evaluating Uncertainty in Accident Reconstruction with Finite Differences

The most effective allocation of accident investigation resources requires knowledge of the overall uncertainty in a set of calculations based on the uncertainty of each variable in real-world accident analyses. Many of the methods currently available are simplistic, mathematically intractable, or highly computation-intensive. This paper presents the Finite Difference method, a numeric approach to partial differentiation with error analysis that requires no high-level mathematical ability to apply, uses very little computation time, provides good results, and can be used with analysis packages of any complexity.

The Finite Difference method inherently incorporates an error treatment which provides investigators a basis to qualitatively rank from dominant to trivial the effects of uncertainty and errors in measured and estimated values. In this way, greater efforts in an accident investigation can be directed to the most influential of the measurements, while less effort need be expended on the values which have trivial effect on the analysis results. Three examples of uncertainty evaluation using the Finite Difference method in accident analyses are presented.