Stability 6

Page Nomenclature
g = gravity, 32.2 ft/sec-sec	H = height of c.g. above datum, in.
µ = mu = coefficient of friction	SF = rollover safety factor, %
SUV = sport utility vehicle	T = wheel track, in.

It is now useful to further discuss the concept of safety factor, SF. Safety factor, in engineering, refers to the number of times better the specifications are to be assigned to a part, than those specifications that part needs to minimally do the job assigned. A bolt, for example may have to carry a load of 1000 pounds, but one may be fitted strong enough to handle 3000 pounds. The bolt is then said to have a safety factor of 3. Safety factor therefore makes a part more reliable.

I wish I could say it was possible to have a rollover safety factor of 3, but it isn't. The physics of the problem tell us that, given the dimensional restraint of 80 inch vehicle width and practical minimum ground clearance, about all that can be done with cars is a SF less than or equal to 75%. It will be seen by calculation that SF is far less, possibly inadequate, for most SUVs.

You may skip this paragraph, if desired. Explaining safety factor is best done not by description, but by vector analysis. Achieving 75% is not easy and I don't know if any Big Three cars can approach it. To give 75% some meaning, this really translates into 1.75 x µ. And that turns out to equal 1.3 g. If a car could somehow be able to boost its grip on the road, that is, increase µ from 0.75 to 1.3, it would be able to overspeed through a curve fast enough to generate 1.3 g centrifugal force and not tip. But since µ is fixed at a maximum of about 0.75, the car will surely slide, not tip. Even though the car itself could take more centrifugal force, the tire-to-road, friction gives up and the car slides. This is what we want. Mathematically speaking, V sub t is greater than or equal to V sub s, where V = velocity, t is tipover and s is sliding. The reason for this explanation is to satisfy those who need to be assured that the formulae are rational and that they have merit. SF is not an imaginary concept; it has real world value because it accurately predicts whether a vehicle will tip or remain upright when it is mishandled.

The safety factor equations will yield anything from a negative SF, 0, to a positive SF. Units of SF are expressed in %. A table will follow below the formulae to help evaluate results of calculations.

To help with the calculations, actual examples will be used, with values substituted. The first example will be in detail. The others, abbreviated. All are important to show the effect of changing the magnitude of critical dimensions, even by relatively small values.

Only two measurements plugged into a simple algebraic equation are needed to determine whether or not any vehicle will tip over or slide in a situation which exceeds the physical limits of land vehicles. The same equation will yield a "safety factor" value which then can be compared with other vehicles under consideration as well as judge whether or not the anti-upsetting properties of the vehicle is sufficient to be considered safe for passenger car use.

Note: trucks used for cargo are in a different category; professional truck drivers realize the inherent limitations of necessarily top-heavy vehicles to suit a commercial purpose; truck drivers are expected to drive much more conservatively than drivers of regular passenger cars. The rule that a vehicle be very tipover resistant applies only to those cars, SUV's, and pickup trucks that are intended for and sold for passenger car use.

You need to obtain two dimensions for the vehicle under investigation. See Fig. 5 above. The first measurement is designated: Wheel track, T and the second is loaded vehicle center of gravity height, H. Heretofore, no consideration was given to c.g. with respect to whether or not the vehicle was at curb weight or maximum gross weight. From hereon, all calculations involving SF must use H as calculated at maximum gross weight. The reason for this will be obvious later as it will be shown that H increases with load.

Getting T is easy. It will be found in the general specifications of the owner's manual, in the shop service manual for the car or on an internet file. It is also simple to just take a steel tape measure and measure from tire-to-tire at the outside of the tread and subtract the width of one tread to establish the center-to-center distance. The other dimension, H is going to be more difficult to get, but it can be done. Amazingly, H is not in any public source that I can determine, despite its crucial importance. It is not in the manuals. Manuals sometimes show a c.g. longitudinally for placing a car on a hoist safely, but H is not dimensioned and often placed at some ridiculous, arbitrary place on the drawings. The dealer will not have the information either. Its my understanding that the Federal Agency, D.O.T. had to take their own c.g measurements. Measuring H is difficult and requires very elaborate equipment. If you are interested in a General Motors car, try going thru the chain of command starting at the dealer, progressing to customer service and then to engineering archives. Do not accept the answer that the manufacturer doesn't know. General Motors, for instance, uses two giant pendulums to swing the car under study. From the intervals of the oscillations, complex calculations will yield H to within 1%. Remember, if you do get H from the factory it represents vehicle empty (curb) weight H, not the vehicle loaded weight H needed. It will be shown later how to convert from H sub curb weight to H sub maximum gross weight, the value needed to substitute into the equations.

Let's now look at a practical example. I will start by evaluating a compact station wagon.

Case 1
Compact Station Wagon (Front Wheel Drive)

Weight, curb 2600 lbs.
Load, max 1050 lbs.
Wheel track, T = 57.6 in.
Empty c.g. height, H = 25.0 in.

The first step is to recalculate the c.g. to determine its new height after the vehicle is loaded to its maximum weight as specified by the manufacturer. It should be noted that many, if not all proving tests done by testing agencies fail to load the test vehicle. If Consumer's Reports tester had loaded the controversial Suzuki, there would have been no question at all as to its propensity to tip over in hard "S" turns onto the fitted outrigger safety device. Calculating loaded vehicle H, is not difficult if the curb weight and empty vehicle H is known. Click_here to see the method and calculations. Don't worry, you will be able to return to this spot.

You now know the new H is 28 in. to be used in the equations.

Substituting the know values into equation (1):

SF% = (67 x 57.6/28) - 100, which reduces to

137.83 - 100 = 37.83, rounded off to

38%

The second equation (2) works as well. Any small difference is some rounding off taken in the derivation of (1) above. This formula is exact. I suggest you use a scientific calculator which allow you to insert all the parentheses. Be sure to follow the exact format as in the illustration. Substituting into (2), the key strokes are:

100 x ((57.6 - (1.5 x 28) = / (1.5 x 28)) =

37 (percent)

Please note that the / symbol above refers to the "division" key!