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On-Road Tire Tuning


Tires are the most important element in the quest to get a car to handle well. 
That's why they're the first to be discussed. Tires are 90% of a car's set-up, any time, anywhere. They're the first thing you should focus on, the first thing to get right, before you even start thinking about anything else. 
No other adjustment can compensate for bad tires; if you make a bad choice, you're basically screwed.

Your tires are the only link between the car and the ground. That link depends solely on the friction between the surface and the tire's contact patch, so let's have a look at how friction works first.

On-road tires

1.1. Friction

The formula for friction between two surfaces is side load = µ * weight. µ Is the coefficient of friction.
For a rubber tire, µ is definitely not constant; it varies with temperature, pressure and more importantly, amount of slip. This is represented in the next graph.

Graph: rubber friction
On the horizontal axis is the amount of slip, from 0%(no slip, the tire just rolls along) to 100% (Either the tire is standing still and the vehicle is moving, or the vehicle is standing still, but the tire is moving). On the vertical axis is the coefficient of friction. In the left part of the graph, slip within the tire is dominant, also known as tire squirm. This happens when the tire deforms under load, and the contact patch moves relative to the axle. This also causes slip angles to exist. In the right part, slip between the two surfaces is dominant; the tire starts to slide sideways a little. It is remarkable that µ reaches its maximum when there is a little slip, usually it's between 5% and 15%. That's because rubber interacts with the surface in a very special way.
In fact, the reason why the graph has such an odd shape is because it's a combination of things, there are two separate mechanisms involved: hysteresis and adhesion.

The first component, adhesion, is the phenomenon that the outermost atoms of the rubber molecules are in direct contact with the outer molecules of the surface. Rubber is a polymer, and its molecular structure resembles spaghetti of strings of atoms, the surface is most of the time crystalline, in which the atoms are more closely together. So when there is a speed difference between the two, the 'atom strings' in the rubber will be stretched. Some molecular bonds will break, and new ones will be formed. This process repeats itself as the one surface is dragged over the other. Obviously, breaking and stretching molecular bonds, and moving atoms around takes energy, and hence also a force. That is the adhesion force. It reaches its maximum when the speed difference is somewhere between 0,03 and 0,06 meters per second.

The second component, hysteresis, exists because rubber is being deformed. As the tire carcass is being distorted, in some areas the rubber gets compressed, and in other areas it gets stretched. For stretching to be possible, the atoms must move alongside each other, and as always, it's an irreversible process because of friction. The friction will make the tire heat up. Again, all this takes energy, and thus a force. That force is the hysteresis force, which is very similar to the adhesion force, only its size is determined by the internal friction in the rubber.

As the weight on the tire and the amount of slip vary, the proportion of the two components changes. For example, if there is more slip, the hysteresis component will be dominant over adhesion. If the rubber compound is very soft, and the temperature is high and the surface smooth, adhesion will be the dominant force.

Note that all the above is valid for very hard racing surfaces, like asphalt or really hard clay. If the surface is soft, it's the deformation of the surface that causes the friction force to exist: the spikes on the tires dig into the surface, and make grooves into it. In that case, the graph doesn't have a section that's curved down; µ always increases as the weight on the tire and the amount of slip increases. It's a totally different mechanism. That's also the reason why when an on-road car takes a turn, and transfers weight onto the outside tires, its cornering power decreases, while when an off-road car does the same thing, its cornering power increases. So it makes sense for on-road cars to have a high roll stiffness (think anti-roll bars), and for off-road cars to have a very low one.

1.2. The traction circle

Now that we know how friction works, and how it is usually maximal when there is a little slip, let's find out how it influences the car's handling.
Unless the tire's thread isn't symmetrical, friction is the same in all directions, and it also has a maximum value, which is also the same in all directions. This can be represented by the traction circle.

traction circle
The vertical component of the graph represents acceleration and deceleration, and the horizontal component represents turning left and right. The maximum amount of grip is represented by the edge of the circle, and the area of the circle represents the amount of grip of the tire on the road.
Naturally, the fastest way around a track is to use your tires to their very limit. So, to brake as fast as possible, you will need to take the tires to point C on the graph. If you brake too hard, and you exceed point c on the graph, you will skid, and your braking distance will increase. You might even lose control. The same thing goes for acceleration: if you exceed point a, you will experience a lot of wheelspin, and you'll accelerate slower. It's also possible to exceed the grip limits when cornering (points D(black) and B), and spin out.
But the hardest parts to judge aren't the axis lines, it's the parts in between. Point D for example (the green one) represents a situation where the car is turning right and accelerating. Note that D (green) is on the edge of the circle, yet the car isn't accelerating or turning at its maximum speed, it's somewhere in between. Let's say you are accelerating as fast as possible (point A), and you steer a little towards the left. On the graph, this means you're at a point left of a, which is outside the circle, so the tires will break loose, and the car won't turn (front wheel drive) or spin out (Rwd). Another interesting fact is that in order to get the most cornering power, there shouldn't be any power applied to the wheels. (Points B and D (black)) And conversely, in order to get the fastest possible acceleration or braking, no steering should be applied.

Keep in mind that the radius of the traction circle represents the maximum adhesion force, and this is proportional (well, kind of, as explained in the previous paragraph) to the vertical load on the tire. So, in brief: the size of the circle increases as more vertical pressure is exerted on the tire, and it decreases if there's less vertical pressure on it. The circle doesn't even exist when there's no pressure on the tire. It makes sense, because a tire that's hanging in the air can't resist any lateral force.

1.3. Slip angles

You might have wondered what exactly happens when you go beyond the traction circle, and how your car will react. Slip angles provide a clear way of describing this. 
A slip angle is the angle between where the tire is pointing and where it actually going. Each tire has its own slip angle. 
A tire that's not slipping has a slip angle of zero degrees. But 'slip' can be internal as well as external; the contact patch doesn't need to be slipping relative to the road, twisting of the tire's carcass is also a form of slipping.
This next drawing represents a car taking a turn at low speed. All four slip angles are zero.


Assuming the car has the correct Ackermann effect and no rear toe-in, the car can turn with none of the tires slipping. Note that the imaginary (well they're not so imaginary when I draw them out for you) lines through the four axles intersect at one point. That's the point the car is turning around. Sort of like the apex of the corner the car is taking. 
This is a typical situation when cornering speed is low, and all four tires have more or less the same weight on them.

But...unfortunately, things aren't always like you want them to be. One common condition is understeer. This happens when the front tires don't have enought weight on them, and they start to slip, hence creating a slip angle.

The slip angle of the front tires is the angle between the blue lines and the green lines. 
The car is not turning around the point you'd expect, or want it to turn. (where the blue lines intersect, point N) Instead, it's turning around the intersection point of the green lines(point U), which makes for a larger turning radius than expected. This is understeer: when the turning radius is bigger than you'd like it to be.
The opposite can also happen: the rear tires can have insufficient weight on them, and start to slip. this usually leads to a condition called oversteer, where the turning radius is smaller than you'd expect it to be.

Here, the rear tires have started to slip, creating  slip angles at the rear of the car. The inside front tire has also started to slip. This is because the car can't be turning around two separate points at the same time. in this case, the car is turning around point O, (whereas the driver would have expected it to be turning around point N.) When a car is cornering, the lines representing the slip angles always intersect at the point the car is rotating around. If they don't, the tire with the least amount of weight on it (in this case the inside front) will develop a slip angle.
Notice that the point which the car is rotating around (O) is now much closer to the center of the car, and more towards the front. The car will turn very sharply, much sharper and earlier than expected.
Plain over- and understeer are very common conditions, but in reality, all sorts of wacky things can happen. 
For example: you can power slide around the corner.

Although the front wheels are steered to the left, the car is turning to the right. (countersteering) The rear tires are sliding at an extreme angle. 
No need to say this requires some serious driving skill.