# Basic Cornering Concept: Circle of Traction

## Circle of Traction & Skidpads

The Circle of Traction is a concept which chassis engineers use to determine how the available traction of the tires is being used. This is because there is only so much traction any given set of tires is capable of producing and it is distributed between cornering, braking and acceleration. Using this concept it is possible to determine how much traction is left for cornering once the forces of braking or acceleration are accounted for.

What Does it Mean?

The figure below shows a Circle of Traction. Where the tire actually touches the road / track is called the contact patch. It is the total available area for traction and varies with the tire size and suspension geometry. From the drawing the arrow in red represents a car accelerating in a left turn. It is the sum of the turning force and the acceleration force. The position of the arrow varies as the car negotiates a section of roadway or race track but one thing is constant; the available traction which remains invariable ignoring special conditions like down force from aerodynamic devices.

An example of this is a car is equally balanced and each tire has 750 lbs of load on them and the cornering efficiency is 100%. There is up to 750 lbs of traction per tire in which ever direction the driver turns or accelerates or brakes. Combine the maneuvers and there is less traction in other directions as shown by the dashed lines in the figure. The combined forces are subtractive. In the extreme case of either spinning the rear tires in acceleration or locking the brakes in hard braking there is no traction left for turning left or right. The car will either slide or the rear end will sway back and forth since there is no traction remaining to counter side forces.

## g Forces During Cornering

A car is subject to acceleration. If it is parked and at rest the force acting on its mass is the force of gravity through the vehicles center of gravity and the center of the earth with the car being attracted to the earth and the tires “pushing” on the earth and the earth “pushing” back with the same force. This is commonly called 1 g of acceleration, normal (90 degrees) to the earth’s surface. It is said that the car “weighs” 2000 lbs for example due to the g force (gravity) acting on the car. When the same car is in motion and turning a lateral acceleration force is developed. The force of gravity is still acting on the car but now the second cornering force becomes important and it is referenced to the earth’s acceleration for convenience so we call it g or lateral g stated in a fraction of or multiple g as in “My car is capable of .9g.”, meaning the lateral or side force when cornering is approaching 1 g of normal earth acceleration (gravity). This allows comparisons to be made as modifications are done to improve cornering lateral force.

## To Skid or Not to Skid?

The common method of determining lateral g force is to use a “skidpad”. This is a circle marked on a section of pavement of a known radius. The car is driven around the circle as fast a possible and timed to determine how much force is being developed. It is a very common test for both street cars and race cars and manufacturers usually publish the numbers as a reference to how well their design performed. It is a significant factor in how well a car will corner. The higher the g number the better the car is at cornering.

The most basic way of arriving at this number if you don’t have a g computer is to hand calculate the number. The formula is as follows:
Where:
T = The time in seconds required to turn 360 degrees.
g = Lateral acceleration expressed in earth normal acceleration (g).
Formula:
g = 1.225 x R
T2
Let’s look at an example:
You time your car as you make one 360 degree lap around the skidpad as fast as possible and it takes 13 sec. The skidpad has a 100 foot radius.

Sample:
g = 1.225 x 100
13 x 13
g = 122.5
169
g = .72

This g is equal to 72% of the normal earth gravity pushing laterally, sideways. As you make modifications to the car you repeat the process which gives you the ability to see by measurement what improvement has been achieved.