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The critical curve speed formula used for estimating vehicle speed from yaw marks depends on the tire-to-road friction and the mark’s radius of curvature. This paper quantifies uncertainty in the radius when it is determined by fitting a circular arc to three or more points. A Monte Carlo analysis was used to generate points on a circular arc given three parameters: number of points n, arc angle θ, and point measurement error σ. For each iteration, circular fits were performed using three techniques. The results show that uncertainty in radius is reduced for increasing arc length, decreasing point measurement error, and increasing number of points used in the curve fit. Radius uncertainty is linear if the ratio of the standard deviation in point measurement error (σ) to the curve’s middle ordinate (m) is less than 0.1. The ratio σ/m should be less than 0.018 for a radius found using a 3-point circular fit to be within 5% of the actual value 95% of the time.

Accident reconstructionists rarely have complete data with which to determine vehicle speed, and so the true value must be bracketed within a range. Previous work has shown the effect of friction uncertainty in determining speed from tire marks left by a vehicle in yaw. The goal of the current study was to assess improvements in the accuracy of vehicle speed estimated from yaw marks using progressively more scene and vehicle information. Data for this analysis came from staged S-turn maneuvers that in some cases led to rollover of sport utility vehicles. Initial speeds were first calculated using the critical curve speed (CCS) formula on the yaw marks from the first portion of the S-maneuver. Then computer simulations were performed with progressively more input data: i) the complete tire marks from the whole S-maneuver, ii) measured vehicle mass, iii) measured suspension stiffness and damping, and iv) measured steering history.

Modern vehicles record dynamic data from a number of on-board sensors for events that could precede a crash. These data can be used to reconstruct the behavior of a vehicle, although the accuracy of these reconstructions has not yet been quantified. Here, we evaluated various methods of reconstructing the vehicle kinematics of a 2017 and a 2018 Toyota Corolla based on Vehicle Control History (VCH) data from overlapping events generated by the pre-collision system (PCS), sudden braking (SB) and anti-lock brake (ABS) activation. The vehicles were driven towards a stationary target at 32-64 km/h (20-40 mph) and then after the pre-collision alarm sounded the vehicle was steered sharply right or left and braked rapidly to rest. VCH data for PCS event were recorded at 2 Hz and for the sudden braking and ABS activation events at 6.7 Hz.