Predicting the pedestrian pre-impact speed from the pedestrian projection distance and vehicle damage measurements

Abstract

Methods to estimate the pre-impact pedestrian speed from limited post-accident measurements are required both for biomechanics research and for legal applications following vehicle–pedestrian collisions, but none is currently available. Such a method is presented in this paper. A constant-inertial-property pedestrian model based on the conservation of momentum is first shown to predict satisfactorily the transverse offset of a pedestrian between the primary and secondary impacts in wrap-trajectory vehicle–pedestrian collisions and is then used in a Monte Carlo environment to predict the pedestrian pre-impact speed distribution utilizing an estimate of the vehicle speed based on the pedestrian projection distance, the ratio of the longitudinal offset to the transverse offset for the pedestrian primary and secondary contact locations on the vehicle (indicated by the primary and secondary vehicle damage locations) and, where available, information on the pedestrian gait stance at impact (derived from the injury location on the head). Separate analysis of recently published Fourier relationships between the transverse offset and the contact location on the head derived from modelling with Mathematical Dynamic Models (MADYMO) software is used to show that the gait stance is related to the location on the head of head injuries from the vehicle contact, and that contact locations significantly anterior or posterior of the coronal plane are predominant. Results from the constant-inertial-property pedestrian model show that significant differences occur between the ratio of the transverse offset to the longitudinal offset with the struck leg leading and the corresponding ratio with the struck leg lagging. The special case of nominally zero transverse offset between the primary and secondary damage locations from the contacts of the pedestrian with the vehicle is considered, and pedestrian speed confidence limits for accident reconstruction purposes are provided. Regression equations relating the pedestrian speed to the pedestrian projection distance and the ratio of the transverse offset to the longitudinal offset of the damage location on the vehicle are presented. These provide the first means to predict the pedestrian speed from limited post-accident damage locations on the vehicle and the pedestrian projection distance.