Chapter 2

Equation 3: Traction Circle

This given amount of traction is altered by adjusting car settings. Tire loads and camber are just a two of the things that can be changed to change the given amount of traction. The amount of traction is also altered by changes in tire compound, tire treads, track surfaces, etc. But it will always be a given amount of traction at any moment in time. The circle does not have to be perfectly round. The tire could have a little more side grip vs. forward grip, or vice versa. But the summing of "a" and "b" to get "c" will still look and be done as shown.

Figure 4: Traction Circle, example

Let's do another example. You are driving a two wheel drive car down a straight. The car is accelerating at the maximum force the tires will hold, hence the acceleration force extends to the circle. Question: How much steering can you apply? Answer: None. Whatever you do to the steering will make the tires break loose. Figure 5 shows "b" to be the maximum acceleration force, because it extends to the circle. The modified steering position is shown by line "a", it sums with "b" to make force "c", which is clearly outside of the circle. Therefore the tire slips. The car will spin nearly instantly.

Figure 5: Traction Circle, example

Equation 4: Cornering Power, each tire

That is it, in brief. Now, we will discuss it in more detail. Tire load can be adjusted by changing static weight or spring rates which will change the dynamic tire loads during cornering. Static cambers can be changed by changing the top suspension link length. Dynamic cambers change because of the suspension link positions on the frame and wheel hub. These are just a couple examples of ways to change loads and camber. Look at the Ct vs. Tire Load on Asphalt graph again. For each instantaneous tire load there is a corresponding Ct. As the tire load changes, the Ct changes. Ct also varies with tire camber, tire compound, the racing surface, ambient temperature, etc. Of these tire load, air pressure and tire camber are the most important because we can adjust them.

Changing the tire load (weight) on the tire changes the Ct (grip) of the tire; it changes the given amount of traction. The tire load can be changed by moving static weight in the car, cornering loads, acceleration transferring weight, braking transferring weight, etc. The camber can be changed statically by adjusting roll centers, suspension arm lengths, suspension ball joint play, etc. Camber also changes dynamically because of body-roll and bumps.

The Cambers and Tire loads are going to change, so we might as well understand how they are changing and make the best of the changes. Adjusting the tire load or camber is, in effect, adjusting the Ct (grip) of each tire, and thus the Cornering Power of the tire. By controlling these adjustments or changes we can achieve our desired handling characteristics.
 

Graph 2: Ct vs. Tire Load on Asphalt

The Ct vs. Tire Load on Asphalt is a graph of the front and rear car tire grip or Ct. The front tire is the one that peaks at 500 pounds and the rear tire is the one that peaks at 600 pounds. As you can see, there is a peak for each tire, that is, a maximum Ct at a specific tire load. Study the graph and put some values into Equation 4 and notice how the Cornering Power varies. It goes up or down depending on where you are in the graph. The Cornering Power changes with tire load.

Equation 5: Cornering Power, front or back

To prove this, pick a tire load your car might have while at rest. (In other words, pick a point on Graph 2 ). Now pretend your car is cornering. Weight changes from side to side. If the inside tire is 50 pounds lighter, the outside tire will be 50 pounds heavier. Weight transfers from side to side. Put these numbers into Equation 5 . Notice that the Cornering Power went down. No matter what values you pick on the Graph 2 the Cornering Power as described in Equation 5 is always reduced because of the changing tire loads. If any weight is transferred from side to side the Cornering Power is less than if no weight had transferred. This core concept is only one facet of setting the car's handling characteristics. There are others, but this is the main concept of race car handling. This math works this way because the Ct vs. Tire Load on Asphalt graph is not a straight line and is curved down.

Now you know how a change in tire loads affects the Cornering Power of one end of the car. The more load transferred at an end of the car, from side to side, means less and less Cornering Power at that end. Thus, to make the race car push, have the front tires have a lot more weight transferred from side to side than the back tires.

This math is ignoring aerodynamics, acceleration or braking load changes. These last few paragraphs still express the solid foundation of race car handling.

Also think about what happens in Equation 5 , when the car is accelerating or braking. We are talking about racing cars that lift 10% to 100% of their front weight off the front tires during hard acceleration. See the section called Finding Front Lift. This weight is transferred from the front to the back, so the given amount of traction at the back may actually be greater during acceleration. The Cornering Power may drop off greatly at the front of the car coming off the corners or while accelerating. But coming into the corners it may cause a lot of steering as the weight falls back on the front tires. It depends on the tires, surface, etc.

Figure 6: Negative Camber

Camber is a slight leaning of the wheels. In this picture the wheels are leaning in. This is negative camber. It is expressed in degrees. The Ct vs. Camber on Asphalt graph shows a typical plot of Ct vs. Camber. You can see that camber changes the Ct (traction) of the tires. Camber changes because of steering castor, suspension travel, and static adjustments. Suspension travel happens because of cornering body-roll, bumps, acceleration and braking. The suspension member lengths and mounting points can be adjusted, thus controlling the camber, thus controlling the car's handling characteristics. Or one may even consider a solid axle to control the camber.

Graph 3: Ct vs. Camber on Asphalt

By examining Equation 6 and the Graph 3 , you should see that the Cornering Power drops off very quickly as the camber comes into play. The Ct Camber is a coefficient of Ct TireLoad , which means it will only reduce the value of traction.

Equation 6: Cornering Power with Camber included

Suspension arm length and where they are mounted to the chassis determines how the wheel's camber will react to the body/chassis roll. The exact amount of change is not obvious. A way to predict how the camber will change because of suspension travel is to know where the roll centers are. See the Finding Roll Centers later in the document. Roll centers are imaginary points that the chassis/body rolls on. A ground level roll center has no camber changes because of bumps but camber varies directly with chassis/body roll. An example of this would be the equal length parallel arm suspension. Most race cars have close to parallel arms and near equal length arms.

Castor changes the Ct (grip) of the tires and therefore the car's handling characteristics. But it does so because castor becomes camber the more the tire is steered, therefore we'll only discuss camber. As the front tires are turned by the steering, they lean (camber) more. As far as side traction is concerned, camber and castor are the same.