CONTENTS page Back one
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,
The 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
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.
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