Analysis of Simple Rollover Metrics

Both tilt table testing and the calculation of so-called Critical Sliding Velocity (CSV) have the goal of determining conditions wherein a vehicle can be tripped by sideways impact with an obstacle and roll exactly one-quarter turn. This paper first reviews the mechanics associated with each of these metrics, verifying that (i) the tangent of the measured tilt table angle can be expected to yield a metric less than but closely related to T/2h, and (ii) CSV calculations are by and large dependent only on the vehicle's calculated cg height h and the ratio T/2h. The paper then addresses what we view to be an important related issue: How well do the mechanics of these measures and/or calculations carry over to calculations related to incidents which include more than one-quarter turn? We approach this question by extending the derivation of the CSV calculation to compute initial sideways velocities V2 needed to initiate a tripped roll of more than one-quarter turn. Particular attention is paid to the mechanics of the second quarter-turn, examining boundary conditions that, depending on terrain, might be part of the continuing roll event. The calculated results indicate that CSV alone, and by implication h and T/2h alone, will not give a reliable feel for V2. Additional calculations indicate that the ratio of roof height to track width is a useful indicator of the ratio V2 to CSV.