# Where the Car Hits the Road......Tires

March 9, 2018

Introduction

As Sim Racers we often focus on tuning suspensions, dampers, gearing ratios, and the differentials. All of these adjustments mean nothing if we cannot transfer that performance to the road. Tires more than not become an afterthought, tires can arguably be considered the most important component of the car. Tires transfer the work performed by our engine to the road, however not all energy transfers occur without loss, In the case of the car, the transfer of energy is limited by how much grip our tires have. It is absolutely crucial that we setup our tires correctly so that we can maximize the energy transfer from the car to the road.

To understand how we can accomplish this we need to understand a few concepts about grip.

The Traction Circle

All tires have whats called the maximum frictional force, this is a property of the tire. Each tire can be different and is based on several variables such as tire compound, tread, etc.  The equation for frictional force is a function of two variables, the coefficient of friction (property of the tire), and the normal force (weight of the car). The equation is given below,

Next, we need to break our maximum frictional force into its respective components, that is the Force in the Y axis, and Force in the X axis. Notice we do not break the equation into the Z axis, this is because the Frictional Force already considers this Axis. We get the equation below,

If we take our coordinate system, the Y axis is in the direction of acceleration, and the X axis is in the direction of cornering the equation now becomes,

Some of you may have noticed, this equation takes the form of a circle. If we were to draw this equation as a circle we would arrive at something that looks like the diagram below,

On the diagram above, the red line is equal to our maximum frictional force. Using this circle we can easily identify design points. Lets consider the following two cases.

Where do I receive my maximum grip for acceleration?

To calculate the question above we want to figure out what our maximum grip is for acceleration, that is to say where is Faccel at its maximum? From trigonometry we know that COS is at its minimum at 90 degrees and SIN is at its maximum at 90  Degrees. If we plug 90 into the equation above for theta, we get the result below,

This means our acceleration force is equal to our maximum frictional force, in laminar terms, we will achieve our maximum acceleration. If we think about this in terms of car handling, it makes sense, it means we will achieve our maximum frictional force when our car is traveling in a straight line (no cornering component).

Where do I receive my maximum grip for cornering?

Similar to the previous section, we need to ask ourselves at what theta is our Fcorner at its maximum? We know that COS is at a maximum at 0 degrees, and SIN is at its minimum at 0 degrees. If we plug 0 into we get the result below,

This means our cornering force is equal to our maximum frictional force when our acceleration component is equal to 0, that is to say we will be using all of our grip when we are not accelerating or decelerating in the turn.

How can I use the traction circle when driving?

From our analysis above we know that our maximum acceleration occurs when are not turning, and our maximum cornering grip occurs when we are not accelerating or decelerating. To use this in a practical sense, it means our inputs need to be proportional and smooth. To drive at the limit of grip, we must drive on the outer edges of the circle. To do this, we must brake hard before we turn, as we turn we want our acceleration to become close to zero. If we are able to smoothly transition from hard braking to neutral acceleration we will achieve our maximum grip. On corner exit, we want to smoothly advance the throttle as we lessen our steering input.

Tire Geometry

Tire Pressure

Now that we know how grip works, lets consider the tire shape itself,  when inflating a tire, we want the tire to have the ideal shape, if we over inflate the tire, the tire patch will be narrow, if we under inflate only the edges of the tire will be in contact with the ground. In the ideal inflation our tire will have have uniform contact with the ground. To illustrate this concept refer to the diagram below,

Tire Chamber

The above diagram only considers the tire while straight and level (not in cornering), in cornering the tire will be at an angle with the ground, reducing our contact patch size. To increase our contact size in a corner, we can place the wheel at an angle, this is called Camber, negative camber is when the top of the tire is closer to the car chassis. There is positive camber, but positive camber is hardly ever used (some in oval tracks). To illustrate the effects of camber lets consider the diagram below,

From the picture above, we can see that 0 camber is ideal when we are not cornering, and some camber is ideal when we are cornering. Because of this, we must find the balance between too much camber and too little camber.

Tuning the Tire

When it comes to tire tuning one of the most important parameters we look at is temperature. The following are typical guidelines you can follow,

1) The average temperature of the tire needs to be close to our optimum tire temperature.

2) The outside of the tire needs to be approximately 10 C cooler than the inside of our tire (this is affected my camber).

3) The middle section of the tire should be the average of the outside of the tire and the inside of the tire (this is affected by tire pressure).

PC2Tuner

PC2Tuner has a built in tire analysis tool. After performing 2 or 3 laps in the game, the user inputs the tire temperatures given from the telemetry HUD. The tool will then tell the user if the tire needs to be inflated more, if the tire is too cold,  or if the tire needs more camber.

PC2Tuner is available for \$10 at the following link:

https://www.racingsimtools.com/product-page/pc2tuner

An example of the program is shown below.

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