An Integrated Model of Rolling and Sliding in Rollover Crashes

Rollover crashes are often difficult to reconstruct in detail because of their chaotic nature. Historically, vehicle speeds in rollover crashes have been calculated using a simple slide-to-stop formula with empirically derived drag factors. Roll rates are typically calculated in an average sense over the entire rollover or a segment of it in which vehicle roll angles are known at various positions. A unified model to describe the translational and rotational vehicle dynamics throughout the rollover sequence is lacking. We propose a pseudo-cylindrical model of a rolling vehicle in which the rotational and translational dynamics are coupled to each other based on the average frictional forces developed during ground contacts. We describe the model as pseudo-cylindrical because vertical motion is ignored but the ground reaction force is not constrained to act directly underneath the center of gravity of the vehicle. The tumbling phase of a rollover is modeled in three distinct phases: an initial brief airborne phase between roll initiation and the first ground contact, an early phase in which relative sliding between the perimeter of the vehicle and the ground causes the roll rate to increase, and a later phase in which the vehicle rolls without sliding and the roll rate decreases. In the early phase, the average vehicle deceleration is higher and is governed by sliding friction. In the later phase, the average vehicle deceleration is lower and is governed by geometric factors. Model predictions were fit to data from 12 well-documented rollover crashes in order to derive empirical values for the model parameters. In 11 out of the 12 rollovers studied, the model predictions matched the actual results with good accuracy. The results validate the underlying physical principles of the model and provide data that can be used to apply the model to real world rollovers. The proposed model provides a physical basis for understanding vehicle dynamics in rollovers and may be used in certain cases to improve the accuracy of a rollover reconstruction.