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Page Nomenclature
g = gravity, 32.2 ft/sec-sec
H = c.g. height above datum, in.
µ = mu, coefficient of friction
SF = rollover safety factor, %
T = wheel track or track, in.
Tipover formulae variables
Now it is time to investigate c.g. height, H further, its relationship mathematically to wheel track, T and all the other factors that don't count. To start, examine the next illustration below.
Fig. 4
Sometimes in life common sense runs opposite to reality. The only two variables that enter the equations for sliding vs. tipping evaluation are show in the above line drawing, Fig.4. They are c.g. height, H and track, T. That's it! Everything else you think might have some effect does not. Weight, for instance cancels out in the derivation of dynamic vehicular calculations. Loading the car, however affects stability, not due to the weight itself but on its distribution and the resultant effect it has on H. Tires and tread design don't make much difference either, if properly rated and inflated. In fact, if better gripping tires were possible, a lot more cars would roll over because the equations assume a coefficient of sliding friction (µ) of 0.75. A higher value of friction would more easily "trip" the car, mathematically speaking. You need not worry about the nuances of (µ).
Rules of thumb
Before going to the equations, it might be useful to state some rules-of-thumb that may help you eyeball a vehicle for stability, without having to first derive the two dimensions required:
Maximum reaction forces available on a flat, smooth, concrete surface is assumed for the equations to be 0.75g. Where g=32.2 ft/sec-sec.
SF must be high enough to prevent tipping under rare, but conceivable, conditions of 1.0 g or better. It is recognized that unusual conditions occasionally occur that may raise effective µ as in the case of rolling over a soft surface, or encountering road irregularities.
The limiting dimension of T is the 80 inch width maximum for autos.
The limiting factor of H is the mathematical limits established by maximum T and acceptable values of SF.
Whatever is the empty vehicle H, it will get higher when the car is loaded. Typical increases are 2 to 3 inches at maximum load. It is possible to calculate the adverse change in c.g.
Vehicles where T is less than, or equal to 1.5 times H have SF values less than 0% up to 0% and are unstable and unsafe. They are sure to tip when pushed to the maximum available reaction force on turns. A vehicle where SF = 0% theoretically would balance perfectly on the outside wheels on a maximum performance turn.
When T is more than 1.5 times H, vehicles become increasingly stable as T becomes larger or H becomes smaller. It is twice as effective to reduce H than to increase T. Eventually, T maximizes out due to the vehicle width limit. At that point, increasing H merely diminishes SF.
When T is 2 times H, (T = 2H), a vehicle is stable and has an SF of 33+% which is minimally acceptable for sale to the public for passenger use.
For the maximum practical SF, the ideal car will look like the one in Fig. 4 above, low and wide
SUV vehicles, as presently configured, are not consistent with acceptable SF values.