Carter, N., Beauchamp, G., and Rose, N., "Comparison of Calculated Speeds for a Yawing and Braking Vehicle to Full-Scale Vehicle Tests," SAE Technical Paper 2012-01-0620, 2012, doi:10.4271/2012-01-0620.
Accurately reconstructing the speed of a yawing and braking vehicle requires an estimate of the varying rates at which the vehicle decelerated. This paper explores the accuracy of several approaches to making this calculation. The first approach uses the Bakker-Nyborg-Pacejka (BNP) tire force model in conjunction with the Nicolas-Comstock-Brach (NCB) combined tire force equations to calculate a yawing and braking vehicle's deceleration rate. Application of this model in a crash reconstruction context will typically require the use of generic tire model parameters, and so, the research in this paper explored the accuracy of using such generic parameters. The paper then examines a simpler equation for calculating a yawing and braking vehicle's deceleration rate which was proposed by Martinez and Schlueter in a 1996 paper. It is demonstrated that this equation exhibits physically unrealistic behavior that precludes it from being used to accurately determine a vehicle's deceleration rate. Finally, the paper moves on to consider an equation that is attributed to the CRASH program in the 2010 edition of Traffic Crash Reconstruction by Lynn Fricke. This equation is nearly as simple as the Martinez and Schlueter equation, but its behavior is more reasonable.The BNP/NCB and the CRASH models are then used to calculate vehicle deceleration rates and speeds for two full-scale vehicle tests run by the authors, both involving yawing and braking vehicles. Braking levels for the vehicles in these tests were calculated using analysis of tire mark striations. The results of these speed calculations are compared to the measured speeds for each of those full-scale tests.