Racing without Friction

Daytona is an enormous, sweeping track. Two-and-a-half miles, 31-degree banking and corner radii of a thousand feet. The infield by itself is 180 acres. If you’ve ever been there (or Talladega), it really does take your breath away when you first enter. Now, bigger tracks (or rather, tracks with bigger turns) automatically mean higher speeds.

There’s a formula for this that tells you how much force you need to make a car turn under specific conditions.

The way to think about this is that it is harder to turn (i.e. you need more force)

• when you have a heavy car
• when you’re going fast
• when you’re trying to make a tight turn

So when you compare a thousand foot turn radius like at a superspeedway with the 250-foot turn radius of Bristol, it’s four times easier to turn at Daytona if all other things are held equal.

The equation above is the equation for centripetal force, which is the force that makes a car turn. The centripetal force tends to confuse people because of its direction. The centripetal force points toward the center if the car is moving in a circle. The way I think of it is if you swing a tennis ball around on a string in a horizontal circle over your head, the thing that keeps it going in a circle is the string – producing a force toward the center.

Well, it’s the exact same thing for a car, except instead of a string, you have tires. The force needed to turn a NASCAR stock car at 130 mph at Bristol is about six tons. Yep, tons.

Because Daytona is so much larger, you need about four times less force to turn at the same speed.

But why stop at 130 mph?

When Daytona was being planned in the fifties, Bill France knew he wanted high banks. Why?

Speed.

That’s right, banking equals speed, too. Here’s why. Look at the car on a flat track first. I’ve drawn it so the car is moving away from you and it’s turning left (of course).

 

The force the track exerts on the car is always perpendicular to the track surface. So none of the force of the track on the car is in the direction that helps the car turn. All of the turning force has to come from the interaction between the tires and the track. If you don’t have enough friction, then you’re going to slide out toward the wall.

Banking helps us turn. Let’s give our track a little banking and see why.

 

Two things change. First, the friction between the tires and the track have also tilted. That means you’re not getting the full force from the tires that you did before; however, the force of the track on the car has also shifted direction.

Now the track is helping the car turn. The higher the banking, the more help the car gets from the track.

If you’ve never been on a track, it’s almost hard to appreciate banking. Here’s me filming for our Science of Speed webvideo series at Texas Motor Speedway. I had this great pair of boots I had planned to wear for this shoot, but it turns out you really can’t wear heels on 24 degrees of banking.

And no, the car is not moving. I am adventurous, but I am not (usually) stupid.

 

Turning on Ice

So one of the questions I sometimes get asks how important friction is in turning corners. So let’s play Einstein here…

Einstein thought up all kinds of very strange and mathematically intense ideas about how the universe – space and time, specifically, work. He couldn’t actually do experiments to test all of his ideas. (Plus, he was a theorist and it’s usually best not to trust them with anything more potentially dangerous than a sharp pencil.)

So he did what are called gedanken experiments. Gedanken is the German verb for ‘to think’. These are thought experiments – but they sound much more impressive if you call them gedanken experiments.

We’re going to imagine that a highly localized ice storm hits Daytona. So localized, in fact, that it just hits turns 3 and 4 of the Daytona International Speedway. It covers them with ice. What happens to the car hurtling in there?

There’s an equation – and if you’re the kind of person who breaks into a cold sweat at the sight of a radical (that’s a square root), then just grab your chair tight for a moment. (If you want to see the details, I suggest the wonderful Hyperphysics site.)

 

All this says is that it is possible to bank a track highly enough that you can take the turn without ANY FRICTION AT ALL.

So if we plug in the numbers for Daytona… we find that, in the absence of friction, you could go 139 mph around the turn.This shouldn’t be all that surprising – after all, Daytona could be viewed as an overgrown luge or bobsled track, right? Those tracks have very high banks because there’s a minimal amount of steering going on.

Being the mathematically OCD person I am, I graphed the maximum speed as a function of banking degree.

Remember that we not only have friction, we have lots of it from the tires interacting with the track – that’s why the cars go much faster than in our frictionless case here.

Interestingly, if a car doesn’t go fast enough around a banked turn, it will actually slide down the track.

This presents a major problem when you’re repaving a very banked track because, as a rule, heavy machinery doesn’t move very quickly. The video below shows the 2010 Daytona repaving (pictures, but mostly video).

You’ll see that the paving trucks are actually being held in place by other equipment because otherwise, they would slide (or worse, tumble), right down the track. And that would make for some pretty sloppy surfaces to race on.