# Visualizing Grip

It’s hard to overemphasize the importance of grip. Braking, cornering, accelerating: everything depends on grip. Understanding how rubber tires create grip is therefore really important for the racing driver. And yet, most drivers don’t know that much about it. Worse, they often have misconceptions that run against the facts.

• Amonton’s First Law: The force of friction is directly proportional to the applied load.
• Amonton’s Second Law: The force of friction is independent of the area of contact.
• Coulomb’s Law of Friction: Kinetic friction is independent of velocity.
• In addition, static friction is always greater than kinetic friction.

I don’t think many racers actually believe these laws. But should they?

The first law says that a 4000 lb car should stop in the same time as a 2000 lb car. Sure, it weighs twice as much, but it also experiences twice as much friction being twice as heavy. Theoretically, the weight of the car doesn’t matter. So why are there off ramps for trucks on long downhills?

The second law says that it doesn’t matter how wide your tires are. Skinny or fat, they have the same amount of grip. And what about grooves? The laws of friction say nothing about grooves. And yet, given a choice, racers would generally use a wider tire with no grooves. How exactly does width or grooves affect grip?

When considering how speed affects grip, most racers would point to aerodynamic downforce (or lift) rather than the rubber in their tires. Does speed actually affect grip? It turns out that it does, but not in the way you might expect.

If static friction was always greater than dynamic friction, why do race cars slide through corners? Doesn’t sliding produce less friction?

## 4 Really Important Graphs

In order to understand how tires work, you have to understand 4 graphs. In each of the graphs below, the coefficient of friction, μ, changes. Everything they teach you in introductory physics assumes that μ is constant. Maybe it is for metal blocks sliding against granite table tops at STP, but when it comes to tires, μ IS NOT A CONSTANT.

Graph A shows μ as a function of load (weight). When you double the amount of weight on a tire, it doesn’t give you double the grip. The coefficient of friction, μ, is lower at higher loadings. Is this why trucks need off ramps? Maybe a little, but actually no. It’s because their brakes overheat. However, it is why race cars are low, light, and have stiff suspensions. A low vehicle with stiff suspension doesn’t transfer much weight while cornering. As a result, the overall grip of the vehicle is high because none of the tires are getting too overloaded. Low weight also helps here, as do wider tires.

Graph B shows μ as a function of temperature. Every tire has an optimum temperature. Both cold and hot tires have less grip than one in the optimal range. If your tires are too wide, they may never get up to optimal temperature. For this reason, the optimal tire width isn’t necessarily the widest. TireRack did a great test where they tested a bunch of wheel and tire widths. The fastest tire wasn’t the widest. And when they went to a wet track, the fastest lap was an even narrower tire. One thing that contributes to heat is grooves. Squirming tread blocks are a major source of heat. As a result, grooved tires heat up more quickly than slicks. One reason for using slick tires is to spread the load better, but an even more important one is to prevent the rubber from overheating.

Graph C shows μ as a function of speed. The faster the car goes, the less time rubber has to interact with the road surface. Tires generate grip from molecular adhesion, mechanical keying, and hysteresis. At high speeds, there is less time for rubber to change shape. Under wet conditions, where adhesion no longer applies, grip is highly affected by speed.

Graph D shows μ as a function of slip angle. Every tire has an optimal slip angle. When a tire is twisted, which it always is to some degree, some parts of the contact patch are experiencing static friction while others are kinetic. This mixed state isn’t really addressed by any of the laws of friction.

## Visualizing Grip

The main point of this post is to give you a visual model of what is happening at the surface of your tire. With this model in mind, it might help you make sense of the conflicting information in the paddock or Internet.

Panel A represents a tire (squiggly line) pressing into the surface of a road (jagged line).

Panel B is what happens when you add load: the rubber goes deeper into the surface, creating more grip. But there’s only so far you can push the rubber in. This is why doubling the load on a tire doesn’t double its grip. Panel B could also be softer rubber or hotter rubber. In both cases, the rubber more easily conforms to the surface.

Panel C shows what happens at high speed. The rubber sliding across the road doesn’t have as much time to change shape, so it doesn’t deliver as much grip.

Panel D shows what happens when a tire overheats. The rubber comes apart, providing less contact with the surface. If the rubber gets hot enough, it may liquify or sublimate, creating a slippery layer between the surfaces.

This visual model isn’t perfect. For example, it doesn’t give any intuition about slip angle. However, maybe it does explain why Miatas are the best cars for rallycross. Seriously? Yes. If you look at the SCCA rallycross national championships over the last 10 years, Miatas have dominated the stock rear wheel drive class. You can literally bring any rear wheel drive car you want. There are no restrictions on power. And yet, Miatas are the dominant car. Why? Using our visual model, let’s imagine what is happening at the interface of dirt and rubber. Dirt is soft and will deform even more than the rubber. As a result, the two surfaces press into each other easily. The total amount of grip saturates very quickly, meaning heavy cars lose more grip than light cars. On dirt, you can only have so much acceleration before wheels spin, so low-powered cars aren’t really at a disadvantage. What’s the lightest RWD vehicle around? Miata. As you might imagine, light FWD cars also dominate the stock FWD class, but there’s a lot more options when it comes to buying a light FWD car.

## 5 thoughts on “Visualizing Grip”

1. I want to steal this article and add aero (and paragraph breaks), and post it in my site.

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2. Peter says:

Brilliant explanation, I didn’t think that way, the more rubber you have the more heat you can take.

However I noticed “The second law says that it doesn’t matter how wide your tires are. Skinny or fat, they have the same amount of grip.” The second law says about friction not grip. If I’m right than grip = friction + tyre properties (heat capacity, stiffness etc.) .

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1. The laws of friction don’t concern themselves with heat or any properties of rubber. Grip is effectively the same thing a μ.

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3. gordonforbes7 says:

I don’t think my comment posted properly and then I noticed that I can simply reply to the email so here is my comment regarding your excellent article. Which, by the way, was the best and most succinct explanation of grip I have ever read.