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 tyres keeping the
car from flipping over during manoeuvres. We found out that a one G
braking manoeuvre in our 3200 pound example car causes 640 pounds to transfer
from the rear tyres to the front tyres. The explanations were given directly in
terms of Newton's fundamental laws of Nature.
This month, we investigate what causes tyres to stay stuck and what causes
them to break away and slide. We will find out that you can make a tyre slide
either by pushing too hard on it or by causing weight to transfer off the tyre
by your control inputs of throttle, brakes, and steering. Conversely, you can
cause a sliding tyre to stick again by pushing less hard on it or by
transferring weight to it. The rest of this article explains all this in term of
(you guessed it) physics.
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 tyres 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 reflexes, too.
I am going to ask you to do a few physics "lab" experiments with me to
investigate tyre adhesion. You can actually do them, or you can just follow
along in your imagination. First, get a tyre 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 tyre, but the numbers you get won't apply directly to tyres, 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 tyre and wheel assembly. In my case, it is
50 pounds (it would be a lot less if I had those $3000 Jongbloed wheels! Any
sponsors reading?). Now put the wheel on the ground or on a table and push
sideways with your hand against the tyre until it slides. When you push it, push
down low near the point where the tyre touches the ground so it doesn't tip
over.
The question is, how hard did you have to push to make the tyre slide? You
can find out by putting the bathroom scale between your hand and the tyre when
you push. This procedure doesn't give a very accurate reading of the force you
need to make the tyre 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
neighbours 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 tyre gave me 85 / 50 = 1.70 gees of sideways
resistance before sliding. On a linoleum race course (ahem!), I would only be
able to get 60 / 50 = 1.20G. We have directly experienced the
physics of grip with our bare hands. The fact that the tyre resists sliding, up
to a point, is called the grip phenomenon. If you could view the
interface between the ground and the tyre with a microscope, you would see
complex interactions between long-chain rubber molecules bending, stretching,
and locking into concrete molecules creating the grip. Tyre researchers look
into the detailed workings of tyres at these levels of detail.
Now, I'm not getting too excited about being able to achieve 1.70G
cornering in an autocross. Before I performed this experiment, I frankly
expected to see a number below 1G. This rather unbelievable number
of 1.70G would certainly not be attainable under driving
conditions, but is still a testimony to the rather unbelievable state of tyre
technology nowadays. Thirty years ago, engineers believed that one G
was theoretically impossible from a tyre. 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 go
= 198.48 mph if you
can keep 1G 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 tyre with some ballast. I
used a couple of dumbbells slung through the centre 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 tyre sideways on concrete. Still about 1.70G. We
observe the fundamental law of adhesion: the force required to slide a tyre is
proportional to the weight supported by the tyre. When your tyre 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 tyre is called the adhesive limit of
the tyre, or sometimes the stiction, which is a slang combination of
"stick" and "friction." This law, in mathematical form, is
where F is the force with which the tyre resists sliding;
µ is the coefficient of static friction or coefficient
of adhesion; and W is the weight or vertical load on the tyre
contact patch. Both F and W have the units of force
(remember that weight is the force of gravity), so µ is just a
number, a proportionality constant. This equation states that the sideways force
a tyre can withstand before sliding is less than or equal to µ
times W. Thus, µW is the maximum sideways force the
tyre 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 W, the weight of the car
µ 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 tyre to somewhere around 1.10G. These effects are
deflection of the tyre, 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 tyres, any weight
transfer will cause the tyres 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 tyre. When one speaks of a "forgiving" tyre, one
means a tyre that breaks away slowly as it gets more and more force or less and
less weight, giving the driver time to correct. Old, hard tyres are, generally
speaking, less forgiving than new, soft tyres. Low-profile tyres are less
forgiving than high-profile tyres. Slicks are less forgiving than DOT tyres. But
these are very broad generalities and tyres must be judged individually, usually
by getting some word-of-mouth recommendations or just by trying them out in an
autocross. Some tyres are so unforgiving that they break away virtually without
warning, leading to driver dramatics usually resulting in a spin. Forgiving
tyres 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 tyres
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 tyres make.
Generally, tyres 'squeak' when they are nearing the limit, 'squeal' at the
limit, and 'squall' over the limit. I find tyre sounds very informative and
always listen to them while driving.
So, to keep your tyres stuck to the ground, be aware that accelerating gives
the front tyres less stiction and the rear tyres more, that braking gives the
front tyre more stiction and the rear tyres less, and that cornering gives the
inside tyres less stiction and the outside tyres 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 tyres 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 set-up.
= 198.48 mph if you
can keep 1G 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.
