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Page Nomenclature
c.g. = center of gravity
SF = rollover safety factor, %
Dynamic c.g. shift
Now it is time to get this car in motion, because that's what this is all about. So, the diagram below reveals new, important information.
Fig. 2The vehicle shown in Fig. 2 is in counter-clockwise curvilinear motion now on a curve of 100 foot radius. It is traveling at a velocity of 31.9 mph and coasting. By having the car coast a lot of variables are eliminated from the equations because a vehicle under propulsion will exhibit different characteristics depending upon whether it has a front axle drive or rear axle drive. The amazing difference in this diagram is that the c.g. has "moved". This movement is called dynamic c.g. shift and is evaluated by vector geometry. It has moved from the centerline outward, away from the center of the circle it is traveling around. The amount it has moved is 19 inches. I tell you this so you will be assured that engineers can calculate these things. In fact, I calculated the above example and everything to follow. Nothing here appears in any published work; it is all original.
There is no mystery why the c.g. moves. It moves because of something called centrifugal force. Centrifugal force acts on the c.g., but only when the car follows the circumference of the 100 foot radius circle. You can demonstrate centrifugal force easily. Here are two ways to do it: First, take a small lead fishing sinker and tie a string to it. Then whip it around in a circle. The sinker will fly out and place tension on the string. You will feel it's "pull". This pull, called centripetal force, is caused by the opposite, but equal, centrifugal force acting at the c.g. of the sinker. The second way is to hang the lead sinker from your rear view mirror and take a drive. Make a normal corner turn at a constant speed. Observe that for the 90 degrees of the turn, the sinker will deflect from vertical and stay there in place as long as the vehicle maintains a constant angular velocity. It is though an invisible hand has grasped the sinker and moved it. Centrifugal force is a force of nature that we can observe but not really explain. It is sort of like gravity, an artificial gravity. The centrifugal force varies. It increases very rapidly with speed (velocity squared) and inversely proportional to the radius (meaning, the smaller the circle, the more centrifugal force). The most important thing to remember about c.g. movement is that it must never meet or cross over the tipover lines that join the front and rear wheels.
To further demonstrate the power of math, I will tell you that the left side wheels of the car are lighter and the right side wheels are heavier. The left front wheel now weighs in at only 287 lbs., the right front 1403 lbs., left rear only 155 lbs, and the right rear 755 lbs. The car is really heavy on the right side now, because of centrifugal force acting dynamically on the c.g.. I will make a most important point now: The amount of c.g. movement not only depends on the centrifugal force itself but also on the height above the surface (datum) of the c.g. The height of the c.g. is the third dimension of the c.g. (along with the other two dimensions, lateral and longitudinal previously discussed) and will be further considered due to its tremendous importance.
Dynamic c.g. shift and safety factor
Even though the left wheels are light and the right ones are heavy, this car is perfectly stable! In fact, the c.g. has not finished moving yet! If the velocity of this car is boosted up to 33.5 mph the c.g. will move out another 2 inches, to within 7.8 inches of that notorious tipover line. The wheels will be lighter yet, and yet this car remains perfectly controllable. That is why I have labeled this diagram as SAFE. Later the calculations will show this car to have a calculated 38% rollover safety factor, SF.
If you are alarmed about the c.g. approaching the tipover lines, you may be interested in knowing that this behavior profiled is for a low slung compact car; you will soon see that SUVs don't do so well. Their values of SF are universally lower.
One additional note is that the tires on this vehicle are rated for 1201 lbs. each. The loading is fine at rest, but in a hard turn, when the tires are really stressed due to turning forces, they are overloaded as well. In a maximum performance turn at 33.5 mph, the outside front tire is overloaded by 260 lbs. Perhaps the auto maker should take note.
