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g = gravity, 32.2
H = c.g. height above
µ = mu, coefficient
SF = rollover safety
T = wheel track or
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
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
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
For the maximum practical SF, the ideal car will look like the one in
above, low and wide
SUV vehicles, as presently
configured, are not consistent with acceptable SF
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