Car rollover collision with pit corner

Viba, Janis; Liberts, Gundars; Gonca, Vladimirs · 2009 · DOAJ

DOI: 10.3846/1648-4142.2009.24.76-82

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Summary

This paper presents a theoretical framework for analyzing the collision of a rigid body, specifically a car, with a "pit corner" obstacle, such as a road edge, ditch, or rock. The research is motivated by the need to accurately assess road accidents, particularly rollovers, which account for a significant portion of fatal crashes globally. The proposed theory aims to determine the motion parameters of a vehicle after impact, facilitating the reconstruction of accident scenarios and the estimation of initial vehicle velocities for insurance and forensic purposes. The methodology relies on the theorems of linear and angular momentum, incorporating two distinct restitution coefficients ($R_1$ and $R_2$) for the normal impulses from the two sides of the corner obstacle. The authors derive a system of eight equations to calculate the impulses, velocities, and angular velocities before and after the collision phases. Symbolic calculations are used to solve these equations, yielding formulas for the post-collision state based on initial conditions, mass, moment of inertia, and geometric coordinates. The model includes specific existence conditions to ensure the physical validity of the collision, requiring the contact point's velocity direction to transition from inside to outside the 90° sector of the pit corner. The study validates the theory through computer modeling of various collision scenarios, including side sliding without rotation, side sliding with rotation, and collision with rotation around an axis. Using a standard car model (mass 1500 kg, width 2 m, height 1.5 m) and varying restitution coefficients between 0 and 1, the authors calculate the remaining kinetic energy as a percentage of the initial energy. Results indicate that in regions where $0 \le R_1, R_2 \le 0.5$, the remaining kinetic energy ranges from approximately 21% to 56%, depending on the specific motion type. For instance, side sliding without rotation retains 27–45% of energy, while collision with rotation retains 21–41%. The paper also demonstrates how to calculate a series of collisions in a full rollover cycle, showing how cumulative energy loss allows for the backward calculation of initial velocity ($v_0$) and velocity at the start of the rollover ($v_1$) based on observed deformations and estimated restitution coefficients. The significance of this work lies in its application to accident reconstruction. By providing a mathematical tool to quantify energy loss during complex impacts with corner obstacles, the theory enables experts to estimate initial driving speeds and analyze the sequence of events in rollover accidents. The authors conclude that this approach is applicable not only to automotive safety but also to other fields involving impact analysis, such as technological processes, control systems, and sports mechanics. The inclusion of braking and sliding energy losses is noted as a necessary consideration for further refining the model's accuracy in real-world applications.

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• secondary collisions