New modelling of equations for Delta-V calculation in low-speed rear-end collisions between vehicles

OBJECTIVE: Rear-end vehicle collisions at low speeds are among the most common types of traffic accidents in Europe, often leading to whiplash injuries. Precise estimation of the change in velocity (Delta-V, DV) is essential for accident reconstruction, particularly when evaluating injury thresholds. Traditional momentum-based methods assume conservation of linear momentum and neglect energy losses, which may produce significant inaccuracies when the striking vehicle brakes before impact. This study aimed to evaluate the discrepancies between theoretical and empirical DV under braking conditions and to develop a practical correction methodology to enhance the accuracy of accident reconstructions. METHODS: ). Cross-validation techniques were employed to minimize bias given the relatively small dataset. RESULTS: for DV of struck vehicle). Application of the corrective regression models reduced DV errors to approximately 3%, representing an improvement in accuracy. CONCLUSIONS: This study confirms that braking in low-speed rear-end impacts disrupts momentum conservation, leading to systematic under- or over-estimation of DV using traditional methods. By incorporating vehicle mass and momentum differences into regression-based corrections, DV estimates can be substantially improved using minimal and easily obtainable parameters. The proposed workflow offers accident reconstructionists a practical, empirically validated method to enhance the reliability of DV calculations in braking scenarios. While results are robust across diverse makes and models, future research should expand to other impact types, such as lateral and oblique collisions.