Uncertainty in Accident Reconstruction Calculations

The problem of determining the uncertainty in the result of a formula evaluation is addressed. The origin of the uncertainty is the presence of variations in the input variables. Three popular techniques are discussed in the context of accident reconstruction. The first establishes upper and lower bounds through calculation of the largest and smallest possible values of the quantity being estimated for all combinations of the input variables. The second method uses differential calculus and places variations of the variables into a delta equation derived from the mathematical formula. The last method covers cases where statistical information about the input data is known. Approximate means and variances are developed for linear and nonlinear formulas. Examples are given for all of the methods such as calculation of speed from skid distance and calculation of stopping distance including perception-decision-reaction (PDR) time.