Impact characteristics of a vehicle population in low speed front to rear collisions

•Fundamental impact equations for low velocity rear end collisions.•Regression analysis of published staged low speed rear impact tests.•Mean and peak accelerations are linear functions of the collision closing speed.•The time to common velocity is independent of the collision closing speed.•The time to common velocity is a measure of the normalized vehicle stiffness.

Rear impact collisions are mostly low severity, but carry a very high societal cost due to reported symptoms of whiplash and related soft tissue injuries. Given the difficulty in physiological measurement of damage in whiplash patients, there is a significant need to assess rear impact severity on the basis of vehicle damage. This paper presents fundamental impact equations on the basis of an equivalent single vehicle to rigid barrier collision in order to predict relationships between impact speed, maximum dynamic crush, mean and peak acceleration, time to common velocity and vehicle stiffness. These are then applied in regression analysis of published staged low speed rear impact tests. The equivalent mean and peak accelerations are linear functions of the collision closing speed, while the time to common velocity is independent of the collision closing speed. Furthermore, the time to common velocity can be used as a surrogate measure of the normalized vehicle stiffness, which provides opportunity for future accident reconstruction.