Tires and the COT

You all know Newton’s first law of motion (NASCAR version).

A race car going 130 mph down the frontstretch at Bristol is going to keep going 130 mph down the frontstretch at Bristol unless a force makes it do something different

In more science-y words, you can’t (thanks Josh) turn without a force that makes you turn. If you put a tennis ball on a string and whirl is around your head, the string keeps the ball turning in a circle. Race cars, obviously, don’t have strings. The thing that makes them turn are their tires.

Tires aren’t round, except when they’re stacked up horizontally in front of the hauler waiting to do their job. When a tire goes on a car, the part of the tire in contact with the ground is a flatish oblong shape called the contact patch.

When the car is sitting still, the contact patch is about the size of a man’s size 11 normal width shoe (or about 36 square inches). When the car is on the track, the contact patch size constantly changes, getting as small as 16 square inches per tire. Hold your hands up to ring a 4-inch by 4-inch area.

Think about how much force you need to change the motion of something like a 3600-lb car. To turn at Bristol going 130 mph takes a little more than two tons of force. What provides all that force are four surprisingly small patches of rubber in contact with the ground. The next time you get set to complain about Goodyear, think about what their tires are asked to do.

Goodyear provides basically different tires for different types of tracks. They’ll provide 25 different configurations of tires in 2009, and figuring out exactly what properties those tires need to have is why they have tire tests. Goodyear is constantly tweaking the tire properties – the type of rubber used for the tread, the strength of the sidewalls, the interior construction, etc. But there is now talk about making some more major changes in the tire to accomodate the heavier demands placed on the tires by the new car.

Regular readers of this blog know that the new car has a higher center of gravity, so more weight shifts to the right side of the car on left-hand turns, which places more load on the tires. The cars are set up to be more yawed. And still, the primary driver complaint you hear is that the cars won’t turn. So Goodyear is investigating make more major changes to the race tire.

Let’s start by looking at what we have now. The figure below shows (drawn to scale, even!) the current tire.

The tire has a bead diameter of 15 inches, which means that the wheel upon which the tire is mounted is a 15 inch diameter wheel. The outer diameter of the tire is 28.5 inches. Tire widths vary depending on the track, but most are between 10.8 inches and 11.8 inches.

Goodyear is talking about making a “taller” and “wider” tire, so let’s explore what options are open to them.

Dustin Longreports that the design of the tire is two inches taller (17 inches compared to 15 now) and 1.5 inches wider – and that it likely won’t be ready until 2011.

Wider Tires

Right now, it looks like Goodyear is considering a 1.5 inch wider tire, as shown above. Tires get their ability to make the car turn by friction between the tires and the track surface. The more friction, the more turning power. Friction, however, is a strange phenomenon. The frictional force between two surfaces doesn’t depend on the area in contact. So the assumption that a wider tire increases the frictional force is wrong.

What a wider tire does do, however, is change the fraction of the contact patch that is slipping relative to the fraction that is gripping. Consider two contact patches, both of which have the same area. The first one is 6 inches wide by 4 inches long. The second is 8 inches wide by 3 inches long. Both have a contact patch area of 28 24 square inches.

If you analyze the contact patch, the front edge grips while the area behind it is where slip happens. Slippage starts the same distance back from the leading edge of the contact patch. Let’s say for the sake of illustration that the first inch and a half of the contact patch is the gripping area. On the narrower contact patch, that’s 1.5 x 6 or 9 square inches, which makes that 9/24 or 37.5% of the contact patch area that is gripping. On our wider tire, we’ve got 1.5 x 8, which is 12 square inches of gripping area, which is 50% of the area of the tire. Since the contact patch areas are the same, you’re going to get more turning force from the wider tire since there’s a larger fraction of the contact patch gripping. For more details, I recommend Paul Haney’s excellent book “The Racing and High-Performance Tire”, which is available on his website. Haney is an excellent and very clear writer.

Increasing the tire width would definitely increase grip; however, that’s not the only consideration. The aspect ratio is the ratio of the sidewall height to the tire width. On commercial tires, that’s the number after the tire diameter. A 185/60R14 is a tire with a diameter width (thanks Ron!) of 185mm, an aspect ratio of 60%, and a wheel size of 14 inches.

The very first pneumatic tires had aspect ratios around 1, meaning that the width and the sidewall height were about equal. In 1984, 60% of commercially produced tires had aspect ratios of 80%.

Racing and other high-performance tires usually have lower aspect ratios, which means that the sidewall heights are closer to the tire width. If you think about turning, a lower aspect ratio means that there’re less flex in the sidewall, so you have better stability in turns. A larger aspect ratio gives you smooth handling, but a smaller aspect ratio gives you better responsiveness. Looking at a range from 10.8″ to 11.8″, the current aspect ratios would come out to be 57.2%-62.5%. Increasing the width by 1.5 inches without changing the height would change those values to 50.75-54.8%.

Decreasing aspect ratio increases the stresses in the belt cords, but decreases stresses in the carcass cords and bead wires, plus the stress distributions are more even across the tire. However, any irregularities in the road are transmitted more to the suspension system, which means the effect of bumps are magnified.

That’s important, as reported again by Dustin Long. He quotes Jimmie Johnson

From a feel standpoint, it seems like there’s less movement in the car where at Atlanta going through the bumps, not only is the car following the bumps and the interaction of the tire and the way it was compressing and cycling around, also had the car moving left to right, so as you’re going through those sensations it’s hard to tell if the car is loose or tight. Then you get to the center of the corner. At that point, usually your condition shows up but you’re left with the challenge of “Was I really loose getting in or is it just loose in the center.’ It just really confuses you and it takes away your confidence to carry speed in the cornera and affects your confidence in what changes you make to the car and really what is going on. It takes more time and is harder for the teams to find that magical setup to help that tire work right for you.

The tire plays a large part in the feel of the car. If the tire loses contact with the road because it’s following the bumps too well, that might throw even an expert driver like Johnson.

Lowering the aspect ratio reduces the average pressure of the contact area, as well as reduces the deflection of the tire, especially around turns. This could decrease tread wear. Lower aspect ratios also may allow the use of a softer tread compound because the stress distribution is more uniform.

Sounds good, huh? Unfortunately, there are a number of technical challenges in producing low-aspect-ratio tires. A problem called ‘reverse curvature’, which is the carcass cords curving inward instead of outward, can occur. This leads to pressure points and concentrated wear. The sidewall also must bear significantly more load in a low-aspect-ratio tire, which can lead to sidewall failure. A lot of strength has to be concentrated in a very short distance. The bead also must be constructed differently to provide greater support. The entire process of laying up the tire in the mold has to be done with greater precision, which means lower yields and higher requirements for quality control.

In the next post, we’ll look at what a ‘taller’ tire actually means and how the combination of taller and wider could mean changes for the new car.

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  1. You are a little incorrect on the tire size. A 185/60R14 tire is 185 millimeters (about 7.25 inches) WIDE and the sidewall height is 60% of the width mounted on a 14 inch wheel. A tire with a 185 mm height would only work on a go-cart, if that.
    A larger diameter wheel and corresponding tire wold give the benefit of allowing larger brakes, which would have better stopping power and also better wear characteristics.
    They could go with a larger wheel, lower aspect ratio and still get near the same over all diameter and revolutions per mile. or keep the apsect ration the same, more likely, and have a tire with much lower revs/mile which would effect the gearing of the cars.

  2. Good article, thank you for the information.
    Maybe I did not understand this:
    “The first one is 6 inches wide by 4 inches long. The second is 8 inches wide by 3 inches long. Both have a contact patch area of 28 square inches.”
    Isn’t it 24 square inches?

  3. Yep, Ron, you’re right about the numbers. Sloppiness on my part. A 7″ diameter tire would be a little tough to do much with.

  4. I’m clearly having a bad math day! Calculus and differential equations I can do, but arithmetic has always been an issue for me. Sigh… DLP

  5. Each tire has its own dimension and standards. Since the tire is the important factor for the safety of car, everyone should know about the factors concerning tires. There are various calculations in order to select a perfect tire for car based on their width and spacing.

  6. I seem to disagree I think you need to intentionally put a wear pattern of RF then RR into car. I have done this by simple simulation NASCAR 2009. The car is better on long runs. Using a softer front sway bar is better which you can with taller tires and Aerodynamic Bom Waves is the biggest limitation with COT. Who ever designed the front is trapped in the smoke cloud at Woodstock.

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