One of the most overlooked and least understood part of the car is the common tire (tyre).
There are a couple basic principles to the tire. The first of which most people understand, the more force you have on a wheel the greater frictional force (traction) it can put out. The second lesser known principle of equal importance, is that the more stressed a tire is the less efficient it is.
For example if I push down with 1000lbs on a given tire, I may only be able to get 1000lbs of frictional force out of it. This force may be used either in braking, accelerating, and/or in turning.
Now what logic would normally guide us into thinking is that if we somehow managed to get 2000lbs of down force on that same tire we would then be able to get 2000lbs of traction out of it. That assumption is close, but not entirely correct. At 2000lbs of down force that same tire may be only able to get 1800lbs of traction.
This loss of traction is due to the tire deforming and "stretching" as it moves. Knowing this, it is much easier to see why fat tires produce more grip then skinny tires. Larger tires are simply able to spread the weight out better and operate under less stress.
Next up, the traction circle.
The traction circle dictates how much force a tire is able to put out while accelerating, braking, and/or turning.
It is broken down into a graph where the y-axis represents the traction available for braking and accelerating, and the x-axis represents the traction available for turning (see picture below). Everywhere inside the circle is what that tire is capable of producing.
Say the same tire has the 1000lbs pushing it down, then using trig we can figure out how much of a combined loading it is capable of. For example, if we use 500lbs of turning traction and 500lbs of accelerating traction then we get sqrt(500^2+500^2)=707.1 lbs of combined effort. That means we are only using just over 70% of the total traction!
At maximum traction, 1000 lbs = sqrt(707.1^2+707.1^2)=1000 lbs. Or, with 707.1 lbs of acceleration and turning traction we are pushing the tire to it's limit.
This is an interesting conclusion! The traction circle tells us that if we are in a corner and we don't take it as hard as possible, we can then use a lot more force to accelerate and or brake.
Professional race car drivers know of this and try to keep their car as close to the edge of this circle as possible for as long as possible, after all the more force you can put down, the faster you will go.
If you have any questions feel free to ask, this is only a tiny step into a deeper subject of tires and traction.