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### What is the Static Stability Factor?

Posted: Wed Jun 24, 2009 10:38 pm
A simplistic viewpoint is frequently encountered in which the so-called "static stability factor", or T/2H, is cited as the ultimate measure of the rollover resistance of a given vehicle design configuration. The static stability factor is, of course, derived on the basis of a rigid body, such as a block of wood or a brick. The analytical derivation of the factor assumes a purely lateral motion, without any rotation about a vertical axis (i.e., yawing), on a uniform high-friction surface. The total static weight is assumed to be supported by the leading edge of the rigid block at the point of incipient rollover.
rollover model.jpg (21.32 KiB) Viewed 9957 times
In an actual highway vehicle which is somehow made to operate at a large sideslip angle on a high-friction surface, the lateral acceleration achieved at the point of incipient rollover ranges (in G units) from approximately 70% to 90% of the calculated value of the static stability factor, depending on design details of the vehicle. Thus, individual vehicles with T/2H values of 1.20 and 0.94 respectively could have identical lateral acceleration values at incipient rollover, for the cited operating condition, if their design details produced the indicated extremes of performance:
(0.70)(1.20) = 0.84 (0.90)(0.94) = 0.84

The following is an excerpt from 1987 "Safety Issues Related to Mini-Cars from a Roadway Perspective",(11 megs!) Council, F.M., Reinfurt, D.W., McHenry, B.G. Pages 53-56, and Appendix E Details of the HVOSM runs

Vehicle parameters associated with rollover.
While other accident and HVOSM related efforts have examined issues related to roadway parameters, this specific HVOSM effort was designed to further examine vehicle parameters which might be related to increased rollover propensity. Past theory has suggested that a critical indicator of rollover propensity is the ratio of the half track width to the height of the center of gravity (T/2H).
The goal of this effort was to further examine this hypothesis and to search for other parameters which might be related to rollover propensity.
• This HVOSM effort involved repeated runs involving eight vehicles ranging in weight from 1699 to 4450 lb (0.77 to 2.02 Mg). While the initial goal was to input a steering maneuver which would put the vehicle in a near-rollover position and to then modify various parameters to determine which were critical, the method had to be modified due to the difficulty of obtaining such a state on a flat area with a normal coefficient of friction. As a substitute, the vehicles were run from the roadway onto a flat, high friction surface and placed in a yawed (nontracking) attitude. The nominal friction value for the test surface was then increased until a rollover occurred. The vehicle parameters were then studied as they changed with this change in critical rollover friction.

The results indicated that while both vehicle weight and T/2H are related to rollover, there are clearly some other vehicle parameters involved. This is most clearly shown by figures 3 and 4 below.
hsrcfig3.jpg (17.23 KiB) Viewed 9957 times
hsrcfig4.jpg (16.28 KiB) Viewed 9957 times
Here, vehicle weight and then T/2H values are plotted against the critical friction value resulting in rollover. If either weight or T/2H was a perfect indicator of rollover, then one would expect a fairly straight-line relationship with very little variability. However, as can be seen from the figures, there is some variability, with both vehicle weight and T/2H deviating from an increasing slope. More pertinent to this effort, the maximum variability is at the lower weight and T/2H values, values pertinent to smaller vehicles.

In a related set of runs, the center of gravity heights were changed in order to give all vehicles the same basic T/2H value. Simulation runs were then made to see if the critical friction factor remained constant. Results here also indicated that for the higher T/2H values (approximately 1.3) the critical friction coefficient for rollover was a constant function of the static stability factor (T/2h). However, for lower T/2H values of approximately 1.1, there was a great deal of deviation in the friction factors, again denoting the fact that T/2H is certainly not the only predictor of rollover potential.

Additional runs were made involving other vehicle parameters related to roll stiffness, radii of gyration about various axes, and suspension travel. Whereas these analyses indicated a general trend that would explain larger cars having greater resistance to rollover, there does not appear to be any single variable in itself that would indicate why certain vehicles roll at a friction coefficients which are 65 to 70 percent of their static stability factors while others roll at 90 percent of their static stability factors.
Thus, the test runs have indicated that while T/2H is certainly related to rollover propensity, it is not the sole indicator of the vehicle's propensity to roll. There exists an inherent resistance of vehicles to roll which must be a function of certain other vehicle parameters which are yet to be defined.
The results of these HVOSM analyses were then utilized in the development of research plans.