An Analytical Assessment of the Critical Speed Formula

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. Another factor is the forward control mode; the accuracy is the highest when the vehicle accelerates through the turn and is the lowest for braking. The experimental data is also used to determine the statistical uncertainty of speed estimation.