The traction circle is way of thinking about the grip that a particular tire has on the road and how you can use it.
Visualize, if you will, a circle, with an x-axis and y-axis running through the center. The edges of the circle denote 100% utilization, the x-axis represents lateral grip (or cornering grip), the y-axis represents longitudinal grip (or braking/accelerating grip). This area in the circle represents the domain of your tire's grip. Points inside the circle are possible combinations of acceleration, braking, and turning; points outside cause the tire to lose grip and slide. If you're a real geek, you'll realize that this is a vector whose magnitude is always less than 1.
This traction circle is a way of teaching people the basics of tire grip, the essential limiting factor in performance driving. In the traction circle, you can be either turning left, turning right, accelerating, braking, or a combination of turning one way and accelerating and braking. Duh. The important thing the traction circle illustrates is that you can combine turning and speeding up or slowing down, but the less of one you do, the more of the other. This explains why you can't go through a hairpin at 100mph, but more importantly, it tells you why you can't go through a 51mph turn at 52. It also helps explain why turning strategies tend to tell you to brake, turn, accelerate rather than to brake through the turn, then accelerate through it.
It is also an important way of expressing driving cues. When a racer brakes at 80%, that 80% is not putting 80% of the pedal to the floor, nor is it a constant. The percentage depends on the overall size of the traction circle, which is the amount of grip available in the tire. If conditions change (such as cresting a hill or running over a bit of gravel), that 80% may become 110%, and the tire will slide. Of course, a racer's job is to always maximize available grip through a turn, so she would brake at 95% unless she was worried about weight transfers (which also affect available grip) or needed to turn.
Of course, the best strategy would be to follow very closely to the edge of the traction circle at all times so that one is not taken off guard by sudden changes, but you risk being passed by someone using 98% of their grip. Traction becomes an issue when following behind someone, as you will most likely be forced into the line they choose, so outbraking and pushing the car becomes the strategy to pass. However, because the difference between 100% and 95% is never more than a few seconds at the end of a race, it is more important to focus on cutting good lines and following the track than to focus on pushing the car.

From Wikipedia, the free encyclopedia

The Circle of forces or Traction circle is a useful way to think about the dynamic interaction between a vehicle's tire and the road surface. In the diagram below we are looking at the tire from above, so that the road surface lies in the x-y plane. The vehicle that the tire is attached to is
moving in the positive y direction.



Circle of Forces


In this example, the vehicle would be cornering to the right (i.e. the positive x direction points to the center of the corner). Note that the plane of rotation of the tire is at an angle to the actual direction that the tire is moving (the positive y direction). That angle is the slip angle.
A tire can generate horizontal force where it meets the road surface by the mechanism of slip. That force is represented in the diagram by the vector F. Note that in this example F is perpendicular to the plane of the tire. That is because the tire is rolling freely, with no torque applied to it by the vehicle's brakes or drive train. However, that is not always the case.
The magnitude of F is limited by the dashed circle, but it can be any combination of the components Fx and Fy that does not exceed the dashed circle. (For a real-world tire, the circle is likely to be closer to an ellipse, with the y axis slightly longer than the x axis.)
In the example, the tire is generating a component of force in the x direction (Fx) which, when transferred to the vehicle's chassis via the suspension system in combination with similar forces from the other tires, will cause the vehicle to turn to the right. Note that there is also a small component of force in the negative y direction (Fy). This represents drag that will, if not countered by some other force, cause the vehicle to decelerate. Drag of this kind is an unavoidable consequence of the mechanism of slip, by which the tire generates lateral force.
The diameter of the circle of forces, and therefore the maximum horizontal force that the tire can generate, is affected by many things, including the design of the tire and its condition (age and temperature, for example), the qualities of the road surface, and the vertical load on the tire.