|In last month's article, we explained the physics
behind weight transfer. That is, we explained why braking shifts
weight to the front of the car, accelerating shifts weight to the
rear, and cornering shifts weight to the outside of a curve. Weight
transfer is a side-effect of the tires keeping the car from flipping
over during maneuvers. We found out that a one
braking maneuver in our 3200 pound example car causes 640 pounds to
transfer from the rear tires to the front tires. The explanations were
given directly in terms of Newton's fundamental laws of Nature.
This month, we investigate what causes tires to stay stuck and what
causes them to break away and slide. We will find out that you can
make a tire slide either by pushing too hard on it or by causing
weight to transfer off the tire by your control inputs of throttle,
brakes, and steering. Conversely, you can cause a sliding tire to
stick again by pushing less hard on it or by tranferring weight to it.
The rest of this article explains all this in term of (you guessed it)
This knowledge, coupled with a good `instinct' for weight transfer,
can help a driver predict the consequences of all his or her actions
and develop good instincts for staying out of trouble, getting out of
trouble when it comes, and driving consistently at ten tenths. It is
said of Tazio Nuvolari, one of the greatest racing drivers ever, that
he knew at all times while driving the weight on each of the four
tires to within a few pounds. He could think, while driving, how the
loads would change if he lifted off the throttle or turned the wheel a
little more, for example. His knowledge of the physics of racing
enabled him to make tiny, accurate adjustments to suit every
circumstance, and perhaps to make these adjustments better than his
competitors. Of course, he had a very fast brain and phenomenal
I am going to ask you to do a few physics ``lab'' experiments with
me to investigate tire adhesion. You can actually do them, or you can
just follow along in your imagination. First, get a tire and wheel off
your car. If you are a serious autocrosser, you probably have a few
loose sets in your garage. You can do the experiments with a heavy box
or some object that is easier to handle than a tire, but the numbers
you get won't apply directly to tires, although the principles we
investigate will apply.
Weigh yourself both holding the wheel and not holding it on a
bathroom scale. The difference is the weight of the tire and wheel
assembly. In my case, it is 50 pounds (it would be a lot less if I had
those $3000Jongbloed wheels! Any sponsors reading?). Now put the wheel
on the ground or on a table and push sideways with your hand against
the tire until it slides. When you push it, push down low near the
point where the tire touches the ground so it doesn't tip over.
The question is, how hard did you have to push to make the tire
slide? You can find out by putting the bathroom scale between your
hand and the tire when you push. This procedure doesn't give a very
accurate reading of the force you need to make the tire slide, but it
gives a rough estimate. In my case, on the concrete walkway in front
of my house, I had to push with 85 pounds of force (my neighbors don't
bother staring at me any more; they're used to my strange antics). On
my linoleum kitchen floor, I only had to push with 60 pounds (but my
wife does stare at me when I do this stuff in the house). What do
these numbers mean?
They mean that, on concrete, my tire gave me
gees of sideways resistance before sliding. On a linoleum race course
(ahem!), I would only be able to get .
We have directly experienced the physics of grip with our bare hands.
The fact that the tire resists sliding, up to a point, is called the grip
phenomenon. If you could view the interface between the ground
and the tire with a microscope, you would see complex interactions
between long-chain rubber molecules bending, stretching, and locking
into concrete molecules creating the grip. Tire researchers look into
the detailed workings of tires at these levels of detail.
Now, I'm not getting too excited about being able to achieve
cornering in an autocross. Before I performed this experiment, I
frankly expected to see a number below .
This rather unbelievable number of
would certainly not be attainable under driving conditions, but is
still a testimony to the rather unbelievable state of tire technology
nowadays. Thirty years ago, engineers believed that one
was theoretically impossible from a tire. This had all kinds of
consequences. It implied, for example, that dragsters could not
possibly go faster than 200 miles per hour in a quarter mile: you can
if you can keep
acceleration all the way down the track. Nowadays, drag racing safety
watchdogs are working hard to keep the cars under 300 mph; top fuel
dragsters launch at more than 3 gees.
For the second experiment, try weighing down your tire with some
ballast. I used a couple of dumbells slung through the center of the
wheel with rope to give me a total weight of 90 pounds. Now, I had to
push with 150 pounds of force to move the tire sideways on concrete.
Still about .
We observe the fundamental law of adhesion: the force required to
slide a tire is proportional to the weight supported by the tire. When
your tire is on the car, weighed down with the car, you cannot push it
sideways simply because you can't push hard enough.
The force required to slide a tire is called the adhesive limit
of the tire, or sometimes the stiction, which is a slang
combination of ``stick'' and ``friction.'' This law, in mathematical
is the force with which the tire resists sliding;
is the coefficient of static friction or coefficient of
is the weight or vertical load on the tire contact patch. Both
have the units of force (remember that weight is the force of
is just a number, a proportionality constant. This equation states
that the sideways force a tire can withstand before sliding is less
than or equal to
is the maximum sideways force the tire can withstand and is equal to
the stiction. We often like to speak of the sideways acceleration the
car can achieve, and we can convert the stiction force into
acceleration in gees by dividing by ,
the weight of the car.
can thus be measured in gees.
The coefficient of static friction is not exactly a constant. Under
driving conditions, many effects come into play that reduce the
stiction of a good autocross tire to somewhere around .
These effects are deflection of the tire, suspension movement,
temperature, inflation pressure, and so on. But the proportionality
law still holds reasonably true under these conditions. Now you can
see that if you are cornering, braking, or accelerating at the limit,
which means at the adhesive limit of the tires, any weight transfer
will cause the tires unloaded by the weight transfer to pass from
sticking into sliding.
Actually, the transition from sticking `mode' to sliding mode
should not be very abrupt in a well-designed tire. When one speaks of
a ``forgiving'' tire, one means a tire that breaks away slowly as it
gets more and more force or less and less weight, giving the driver
time to correct. Old, hard tires are, generally speaking, less
forgiving than new, soft tires. Low-profile tires are less forgiving
than high-profile tires. Slicks are less forgiving than DOT tires. But
these are very broad generalities and tires must be judged
individually, usually by getting some word-of-mouth recommendations or
just by trying them out in an autocross. Some tires are so unforgiving
that they break away virtually without warning, leading to driver
dramatics usually resulting in a spin. Forgiving tires are much easier
to control and much more fun to drive with.
``Driving by the seat of your pants'' means sensing the slight
changes in cornering, braking, and acceleration forces that signal
that one or more tires are about to slide. You can sense these change
literally in your seat, but you can also feel changes in steering
resistance and in the sounds the tires make. Generally, tires `squeak'
when they are nearing the limit, `squeal' at the limit, and `squall'
over the limit. I find tire sounds very informative and always listen
to them while driving.
So, to keep your tires stuck to the ground, be aware that
accelerating gives the front tires less stiction and the rear tires
more, that braking gives the front tire more stiction and the rear
tires less, and that cornering gives the inside tires less stiction
and the outside tires more. These facts are due to the combination of
weight transfer and the grip phenomenon. Finally, drive smoothly, that
is, translate your awareness into gentle control inputs that always
keep appropriate tires stuck at the right times. This is the essential
knowledge required for car control, and, of course, is much easier
said than done. Later articles will use the knowledge we have
accumulated so far to explain understeer, oversteer, and chassis