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Linear analysis and corresponding vehicle tests have been used since the late 1950's to help understand the directional response of automobiles and commercial vehicles. This work is now well accepted, and linear terms such as understeer gradient and response time are descriptors routinely used to characterize vehicle performance in the linear range. This paper assesses the use of various levels of complexity in linear models. It verifies that, for steady state measures such as understeer gradient, all important effects can be handled quasistatically and a two degree of freedom model is adequate. The paper then illustrates situations in which the roll degree of freedom can be important for transient calculations, and assesses the changes in calculated transient results deriving from the addition to the model of time lags in lateral tire force buildup.

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.