A Tire Doesn’t Work The Way You Think It Works

OK, I’m going to come out and say it: All tires should be flat! Air and a thin wall of rubber have no business holding up the weight of a car. Take the air out and you have a flat tire, take the rubber away and the wheel would sit on the ground. But somehow, putting them together gives you something that can hold a lot of weight.  How does a tire do that?

I learned the answer to this question many years ago from David Van Emberg, Executive Vice President of Original Equipment Sales at Michelin, and what he told me was not what I expected but made perfect sense once he explained it.

The Bicycle Model

Let’s start off with a simple example: a bicycle wheel with its three main components — the rim, the hub, and some number of spokes connecting them. For the moment, we will ignore the fact that a bicycle wheel also includes a tire. We will get back to that later.

The spokes connect the hub to the rim and keep it centered inside the rim by being tightened in a specific order by the wheel manufacturer. This puts each spoke in tension and allows the drive torque from the rear sprocket and the brake torque to transfer from the hub to the rim. The spokes also carry the weight of the bike and rider.

But now imagine a wheel where the number of spokes has been reduced to just four:

Would such a wheel work? In theory, yes. The hub is being constrained in all directions and if we now attach it to a bicycle, the wheel should still hold up the weight of the bike and rider.

But what if we make it even simpler by removing the spoke at the top:

What would happen now? If we attach this wheel to a bicycle, would it still hold up the same weight? Remember, the spokes of a bicycle wheel are made of very thin metal and are always in tension. In fact, you could replace them with strong wires and the wheel would still work the same. These spokes don’t do well in compression. Try to compress one and it will buckle very easily.

Putting weight on our three spoke wheel, we would expect it to quickly look like this:

But now, instead of removing the top spoke, what if we removed the bottom spoke?

If we now put weight on this wheel, the top spoke will be in tension and since spokes are very good at carrying load in tension, the hub would stay right where it is.

Of course this is all well and good as long as the wheel stays still. As soon as it starts to roll, the gap at the bottom will soon end up at the top and we will have the same situation we had before where the spoke that started out at the top is now the bottom spoke and will buckle. But this is one of the reasons why we have so many spokes. No matter how the wheel rolls, there will always be at least one spoke at or near the top to carry the weight.

The spokes have another very important job to do though. And that is to make sure the rim stays round. While a bicycle rim is made of steel or some other strong metal, it is fairly thin and narrow and isn’t infinitely strong or stiff. The weight of a rider will force the bottom part of the rim to try to flatten out against the road, just like the bottom part of a tire is flat against the road.

But in order for the rim to be flat against the road, it would need to get shorter in that area.

Compare the length of the red line representing the undeformed rim and the yellow line representing the flattened rim and you’ll see that the yellow line is slightly shorter. Since the rim is made of metal, it really doesn’t want to get shorter, so for the bottom to flatten out, the rim will need to bulge out somewhere else to maintain its length.

What happens in reality is that the rim doesn’t bulge out in any particular area, but instead increases in diameter everywhere except where it sits against the road. This means all the other spokes need to get just a little longer and since these spokes are very strong in tension, they don’t want to get longer and they limit how much the rim can bulge out. Limiting how much the rim can bulge out means it also limits how much extra length it can absorb and therefore how much flattening can happen at the bottom.

In this way, the tension in the spokes and the strength of the spokes make sure the rim stays round even when it is carrying weight.

Let’s Get Back To Car Tires

So how does this relate to a car tire? While I learned a lot from David Van Emberg, I wanted to know more, so I spoke (pun intended) with Jason Bokar, Original Equipment and Technical Sales Manager at Michelin. Prior to his current position, Jason led the Design School at Michelin where tire technology is taught. Needless to say, the guy knows a thing or two about tires and how they work. He provided me with an unpublished book called “Tire Mechanics: Membrane Theory” written by Timothy Payne, PhD at Michelin describing how tires work.

Jason uses this book in classes he teaches outside of Michelin as well and it is full of heavy theory about tires. There is a lot of very serious math in this book which I won’t try to describe here but you don’t actually need all those numbers to understand how this all works.

Tire Construction

Let’s start by looking at how a typical tire is constructed:

Image via: diagramtire (abbsrytire.com)

A tire is made up of a few key parts. These parts are common in all tires, regardless of who makes them or how they are made. There is the tread area on the outside, which is made of rubber, with a number of steel and synthetic belts and plies right underneath. There is another part which is hidden, and most people don’t even know it’s there but is critical to the way the tire works and that is the bead.

The bead is a thick braided steel wire that sits very close to the wheel and is very strong. The bead wire is why you need a tire installation machine to install tires on rims. It’s not easy to just do it with a set of tire spoons like you would with a bicycle tire.

The last major part of a tire is the sidewall, which connects the tread and belts to the bead. The sidewall contains a series of radial plies, sometimes called “cords”, which wrap around one bead wire and run all the way over to the other bead wire. These cords are very strong, and they give the sidewall a lot of strength in tension.

Comparing this construction to our bicycle wheel example, we see that the tread and belts underneath them are analogous to the rim while the bead wire, which sits tightly around the wheel, is analogous to the hub. The sidewall must therefore act like the spokes, right? But does it?

The sidewall of a tire is not very good at carrying load in compression. This is obvious by the fact that when we let the air out of a tire, it goes flat. The sidewall just buckles under the weight of the car, just like a bicycle spoke would if we try to push on it. But if we pull on it, the cords inside will prevent the sidewall from stretching, just like the spokes of our bicycle wheel.

But what about the rim? Our bicycle rim was pretty strong just by itself, but the tread area of a car tire is quite flexible. In fact, take the air out of a car tire and you can deform the tread and steel belts with your hands. Clearly this part of a car tire isn’t very stiff. The one aspect where our bicycle rim and a car’s tread area of a tire ARE similar is in the fact that both want to stay the same length.

The metal of a bicycle rim doesn’t want to stretch or compress and neither do the steel belts of a tire. This means that if any part of a tire sits flat against the road, there must be another part of it that is bulging out just like in our bicycle example. Let’s look at the case of a flat tire. Obviously, a flat tire has a large area at the bottom that is flat against the road so a lot of the tread must have gotten pushed upward and outward to account for the difference in length between the tire when it was round and the tire now that a large part of it is flat. With all the air gone, this isn’t really a problem since the sidewall is flexible enough that it allows the tread area to bulge out to compensate for the fact that part of the tread is flat.

But that doesn’t do us much good if we want to drive our car, does it? How do we get our tire to act more like a bicycle wheel so it can carry the weight of the car?

To Explain This, Let’s Start With A Flat Tire, And Add Air

This is where the real difference comes in. A bicycle wheel doesn’t need compressed air to support weight, but a tire does. Now, I know many of you will be shouting at your screen that a bicycle wheel also has a tire that needs compressed air, and you are absolutely right. But bear with me for a little longer and I’ll explain.

As you can see in this image, with no air pressure, the weight of the car has pushed the wheel down, buckling the sidewall, and making the bottom of the tire go into a flat shape against the road surface. What is not clear in this image is that this flattening has caused the entire tire to grow in diameter slightly in order to absorb the extra length of the part of the tread that is now flat. Here’s what I mean — notice how the flat tire has a larger diameter in this little sketch:

This image shows the concept in an exaggerated way, but you get the point. The yellow line and the red line are both the same length, but because the red line has been flattened at the bottom, the extra length had to go somewhere so the entire circle has grown slightly. The difference in radius between the yellow and red circles is called the “counter deflection” because the tire is deflecting in the opposite direction from the deflection happening at the bottom.

I’ve drawn it in a simplistic way above, but this diagram from Payne’s book shows it in more detail:

Image via: Michelin North America, Inc.

This diagram also shows that there is a transition area where the undeformed tire (at the top) transitions to the flat of the contact area. The tire doesn’t instantly go from round to flat.

But there is something else happening inside the tire sidewall that is not visible from outside. The cords that are running from the tread area to the bead wire normally run in a purely radial direction, shown here as yellow arrows representing an undeformed tire:

But as we set the tire down on the ground and the bottom part of the circle gets flattened out, the tread gets pushed upwards and these cords have to follow along. This means they get skewed and are no longer radial:

The green and red arrows denote the cords after the tire has been deflected and you can see how they are skewed relative to their original position denoted by the yellow arrows. This phenomenon is known as “de-radialization” since the majority of the tire cords are now no longer in a purely radial position. You can also see how the de-radialization is worst near the point where the tread transitions from round to flat and slowly gets less as you go up the tire until you get to the top where the cords are still exactly radial.

Now, let’s start adding air into our tire and see what happens. As the pressure builds up, the air starts pushing outward on all parts of the tire. It tries to force the tread back into the round shape it normally has, but more importantly, it pushes outward on the sidewall, putting the cords into more and more tension. As the tension in the cords grows, they don’t want to be skewed anymore. Imagine pulling on a string at an angle:

The string wants to straighten out. The same thing happens with the cords. They want to straighten out and go back to their original radial position. But they can only do this by pulling the tread back down, reversing the process that previously allowed the flattened part of the tire to push the extra tread upwards. This forces the flat part at the bottom of the tire to get smaller and smaller.

Here you can see how the inflated tire has much less skew in the cords and a much smaller flat portion on the ground as a result. The tension in the cords simply doesn’t allow the tread to get pushed up and outward like it was in the deflated tire. You may also notice that the difference in radius between the yellow and red circles is much less. The counter deflection has been greatly reduced by the addition of air pressure.

What’s happening is that the air pressure is forcing the tread of the tire to form a hoop, and the cords in the sidewall to straighten out. And just like the hub in a bicycle wheel is held up by tension in the upper spokes, a car wheel is held up by tension in the sidewall at the top of the tire. The wheel is literally “hanging” inside the hoop formed by the tread. The sidewall at the bottom has no ability to support the weight of the wheel, and air pressure doesn’t change that. All the air is doing is creating that hoop and putting tension into the cords.

Keep in mind though, as the tire rotates, each cord is changing from a purely radial position to a de-radialized position. Back and forth, back and forth, with every rotation of the tire. The cords are squirming around inside the sidewall as they are forced to change position, and this causes heat to build up. Keeping the right amount of air pressure in your tires keeps this to a minimum and extend the life of your tires. Heat is the enemy of tires, so you can see why keeping this squirming around to a minimum is so important.

Load Capacity

But there is another function of the tension in the cords. The tension in the cords that results from the air pressure is directly related to the amount of load the tire can carry. Since the weight of the car is held up by tension in the cords at the top of the tire, the cords must be strong enough to handle that load. That’s not a very difficult thing to do since the cords are actually very strong. But as the tire rotates, a particular cord will move from being on the bottom of the tire, to being on the side, to being on the top, to being on the other side, to being on the bottom again. Over and over. Only when the cord is at the top of the tire is it under tension. Everywhere else, it is loose. And on the bottom, it is being squashed. This constant change from tension, to relaxed, to squashed, will eventually cause the cord to break, just like a piece of metal does when you bend it back and forth enough times. It’s called fatigue. Air pressure solves this problem by putting the cords into tension right from the start.

Imagine if we stretch a wire between two walls so that there is 100 lbs. of tension in the wire.

If we now want to increase the tension in the wire, we could pull on it close to where it attaches to one of the walls, but we would first have to overcome the 100 lbs. tension that is already in the wire.

If we pulled on it with a force less than 100 lbs. the wire would still remain in tension.

The same thing happens in the cords of the tire. The air pressure puts them under a certain amount of tension, and as long as the weight of the car does not exceed that tension, then the total tension in the cords will not change even as each one rotates from the bottom of the tire to the sides and to the top. This keeps the cords from fatiguing since the tension never changes. It also shows another reason why it is so important to keep your tires inflated properly. Low air pressure means the tension in the cords is less, and now the weight of the car could cause the tension to fluctuate and result in failure due to fatigue.

Tire Stiffness

As we increased the air pressure inside the tire, the amount of deflection at the bottom became less and less. Clearly, a flat, or underinflated tire, has a lot more deflection at the bottom than a properly inflated one. Since the weight of the vehicle doesn’t change as we add air, in order for the tire deflection to reduce, the stiffness of the tire must be increasing.

If we follow along in Payne’s book and go through all the math that describes how a tire works, we will eventually get to the equation for tire stiffness which is:

Kz = 0.685 x √P x √W x √K_λ

Where Kz is the tire stiffness, P is the air pressure, W is the tire width, and K_λ is the counter deflection stiffness. This may look daunting, but don’t worry about all these other parameters, just look at P. As you can see, as we increase air pressure, P, the tire stiffness, Kz, also increases. This makes sense, since, as we saw earlier, adding air to a tire reduces the deflection and since the vehicle didn’t get heavier, in order for the deflection to go down, the tire stiffness must have increased.

Air Pressure is Key

So, after all the math and fancy theory, your tires, at their core, aren’t sitting on a cushion of air, they really work just like a bicycle wheel, with the car’s rim acting like the bicycle wheel hub, the tire sidewall acting like the bicycle spokes and the tire tread acting like the bicycle wheel rim.

I know there is a lot to unpack here and the math behind it is absolutely crazy. But if there is one lesson to learned from all this, it is the importance of keeping the right air pressure in your tires. It is critical to making the sidewall behave like bicycle spokes, and that is the key to how a tire supports the weight of your car.

Your tires, and your wallet, will thank you.

Top graphic base image: Vredestein Tires