Uncertainty in Calculations Using Lambourn's Critical Speed Procedure 2013-01-0779

Critical Speed Formula (CSF) belongs to the canon of tools used in reconstruction of vehicle accidents. It is used to calculate vehicle speed at the beginning of tire yaw marks and, together with the entire methodology of processing the information contained in the marks into the data, is often referred to as the Critical Speed Method (CSM). Its great practical importance as well as recurring doubts as to the reliability make it one of the best experimentally and theoretically studied methods. Although the CSF applies in fact to a point mass, it is used with reference to a vehicle, i.e., an increasingly complicated multi-body system. Accident reconstruction experts point out the particular usefulness of Lambourn's research concerning the CSM in respect to a passenger car. Because his method by virtue of solid research basis is extensively applied in practice, the paper is focused specifically on Lambourn's methodology in terms of analysis of uncertainty and influence of vehicle properties. Regarding the first problem, sensitivity and uncertainty due to the parameters of the CSM was analyzed. Regarding the latter one, simulation tests using programs of different degrees of complexity were performed, taking into account criteria which were not considered in experimental tests. It has also been shown that in the case of unknown braking deceleration and large curvature of yaw mark, it will be desirable to shorten the chord c during the measurement and adjust the m/c (where m denotes the middle coordinate) ratio to the range from 0.01 to 0.03. This will ensure the reduction of calculation uncertainty to a level not exceeding ± 10%, regardless of the torques applied to the wheels. The article presents the theoretical arguments supporting and extending Lambourn's thesis concerning error no greater than ± 10%, subject to the guidelines prescribed by Lambourn.