[Note that this article is a transcript of the video embedded above.]

Formula 1 is, by many accounts, the pinnacle of car racing. F1 cars are among the fastest in the world, particularly around the tight corners of the various paved tracks across the globe. Drivers can experience accelerations of 4 to 5 lateral gs around each lap. That’s tough on a human body, but think about the car! 5 times gravity is about 50 meters per second… per second, and an F1 car weighs 800 kilograms (or 1800 pounds). If you do a little quick recreational math, that comes out to a force between the car and the track of more than 4 tons. And all that force is transferred through four little contact patches below the tires.

Traction is one of the most important parts of F1 racing and the biggest limitation of how fast the cars can go. Cornering and braking at such extreme speeds requires a lot of force, and all of it has to come from the friction where the rubber meets the road. Pirelli put thousands of hours of testing and simulations into the current design. Nearly a hundred prototypes were whittled down to 8 compounds: two wet tires and six slicks of various levels of hardness that offer teams a balance between grip and durability during a race.

And yet, when you look at another of the most extreme vehicles on earth you see something completely different. A single modern diesel freight locomotive can deliver upwards of 50 tons of forward force (called tractive effort) into the rails, but it’s somehow able to do that through the tiny contact patches between two smooth and rigid surfaces. It’s just slick on slick. It seems impossible, but it turns out there’s a lot of engineering between those steel wheels and steel rails. And I’ve set up a couple of demonstrations in the garage to show how this works. I’m Grady, and this is Practical Engineering. In today’s episode, we’re talking about why locomotives don’t need tires.

In a previous episode of this series on railway engineering, I talked about how hard it is to pull a train based on the various aspects of grade, speed, and curves. I even tried to pull a train car myself. The whole point of locomotives is to overcome that resistance, to take all the force required to pull the train and deliver it to the tracks to keep the whole thing rolling. Most modern freight locomotives use a diesel-electric drive. The engine powers a generator, which powers electric traction motors that drive the wheels. There are a lot of benefits to this arrangement, including not needing a super complicated gearbox to couple the engine and wheels. But, even with electric traction motors, locomotives are still limited by the power rating of those motors, and power is the product of force and velocity. So if you graph the speed of a locomotive against the force it can exert on a train, you get this inverse relationship. But, this isn’t quite right. Of course, there are physical and mechanical limits on how fast a train can go, so the graph gets cut off there, but there’s another limitation that governs tractive effort on the slow side. Even if the motors could generate more force at slow speeds (and they usually can), the friction between the rails and wheels limits how much of that force can be mobilized (called the adhesion limit).

The graph makes it clear why this is such a major challenge for a railroad: you can’t even use the full power of the engine because you’re limited by the friction at the wheels. It’s why dragsters do a burnout before the race: to warm up the tires for more friction. I was reading this Federal Railroad Administration report, and I love that it called friction the “last frontier” of vehicle/track interaction; it’s just so important to nearly every aspect of railway engineering. The lack of friction is really the reason railways work in the first place: it means the rolling resistance of enormous loads can be overcome by relatively tiny locomotives. But, of course, some friction is necessary so that trains can accelerate and brake without slipping and sliding on the rails. There are alternatives, like the cog railways that carry trains up steep mountains, but most freight and passenger trains use simple “adhesion” for traction; just the steel-on-steel friction and nothing else. The area that’s physically touching between a wheel and rail, called the contact patch, is roughly the size of a US dime: maybe 2 to 3 square centimeters or half of a square inch. Imagine gluing a dime to the wall and then hanging two average sized cars from it. That’s a loose approximation of the traction force below each wheel of a locomotive; it’s a lot of friction!

Incredibly, friction really boils down to two numbers, one that’s simple (weight, or more generally, the normal force between the two surfaces), and a coefficient that’s a little more complicated. Let me show you what I mean. I have a little demonstration set up here in the garage. It’s just a sled attached to a spring scale. I can add a weight to the sled, and then slide different materials underneath. The reading on the scale is the kinetic friction between the materials. Even if the weight stays the same, the force changes because every material interacts differently with the steel sled, and this can get super complicated: asperity interlocking, cold welding, modified adhesion theory, interfacial layers, et cetera. I’m not going to get into all that, but it’s important to engineers who think about these problems. All that complexity gets boiled down into a single, empirical value called the coefficient of friction. Double the coefficient; double the friction. And the same is true of the normal force. If I double the weight on the sled, I get roughly double the reading on the scale for each of the materials I pulled underneath it.

In some ways, it really is that straightforward. You have two knobs to manage tractive effort: the weight of the locomotive and the friction coefficient. But you don’t always have a lot of control over that second knob. Environmental contaminants like oil, grease, rust, rain, and leaves lower the coefficient of friction, making it harder to keep the wheels stuck to the track. So you kind of just have the one knob to turn. Very generally, the math looks like this: You look at the steepest section of track where the highest tractive effort is required and divide that force by the “dispatchable adhesion,” a complicated-sounding term which is really just the friction coefficient that you can count on for the specific locomotive and operating conditions. Maybe it’s 30% for a modern locomotive on dry rail or 18% for an older model on a frosty winter morning. Now you have the total weight needed to develop that tractive effort. For longer and heavier trains, you can’t just use a single massive locomotive, because there are limits to the weight you can put on a single wheel before the tracks fail or you damage a bridge. That’s why many large freight trains use two, three, four, or more locomotives together.

But, that friction coefficient isn’t set in stone. You do have some control there. Even since the days of steam locomotives, sandboxes have been used to drop sand on the tracks to increase the friction between wheels and rails. If you look closely, you can sometimes see the pipes that deliver sand in front of the wheels. Some railways use air, water jets, chemical mixtures, and even lasers to clean the rails, carry away moisture, or just generally increase control over wheel/rail friction. And there’s another way to turn that knob that’s a little tricky to understand, because there’s really not a hard line between a wheel sticking to a rail through friction and a wheel sliding on it from not enough. Actually, all locomotive wheels under traction exist somewhere in between the two! Let me show you what I mean.

Even though both locomotive wheels and rails are made from hardened steel, that doesn’t mean they’re infinitely stiff. Everything deforms to some extent. But, it would be pretty tough to show the deformation of a steel-on-steel surface under hundreds of thousands of pounds in a garage demonstration, so I have the next best thing: a rug and a circular brush that spins on a shaft. This brush simulates a locomotive wheel, and right now, it can spin freely. So, when I pull the rug underneath it, nothing unexpected happens. There’s essentially no traction here. The force between the brush and the rug (representing a wheel on a rail) is negligible, and there’s no slip. The brush turns at the same rate as the rug moves. But I can change that.

I have a little homemade shaft brake made from a camera clamp, and I can tighten the clamp to essentially lock up the rotation of the brush. Now when I pull the rug under the wheel, it’s noticeably more difficult. The brush is applying a strong traction force to the surface, and also, it’s completely slipping. The relative movement between the wheel and the rail is basically infinite, since the wheel isn’t moving at all. Again, maybe this isn’t too surprising of a result. What’s interesting, I think, is what happens in between these two conditions. If I loosen the clamp so that the brush can rotate with some resistance and pull the rug through again, watch what happens.

The bristles deform as the brush rolls along. They’re applying a traction force, even as the brush rolls. If you look closely, the bristles stick to the rug at the front, but at a point within the contact area, they lose that connection to the rug and slip backwards. And this is exactly what happens to locomotive wheels as well. The surface layer of the wheel is stretched forward by the rail, but toward the back of the contact area, there’s not enough adhesion, and they separate as the elastic stress is released. The stick and the slip happen simultaneously. What’s fascinating about this behavior is that the locomotive wheels actually spin faster than the locomotive is moving along the rails, an effect called creep. And the brush makes it obvious why. The bristles in contact with the rug are flexing, making that part of the wheel rim essentially longer. So the wheel has to turn faster to make up for the difference, or in this demo (since the brush is static), the rug has to travel a greater distance for the same amount of rotation. I can make this clearer with a bit of tape.

With the brake off and no traction, I can pull the rug through and mark the length the rug traveled for half a rotation of the brush. Now, with the brake on, I can pull the rug through again. And you see that the rug traveled a longer distance, even though the brush rotated the same amount as before. If we graph the behavior of a wheel across these various conditions, you get something like this. With no traction, there’s no slip, and so there’s also no creep. But as traction goes up, a bigger part of the contact patch is slipping, and so its relative motion to the track, its creep, goes up. Eventually you reach a point where the entire contact patch slips, and the traction force levels off. You can spin and spin, but you’ll never develop more force.

Of course, that graph is a theoretical situation under ideal conditions. Your intuitions might be saying that a wheel that’s fully sliding on the rail has less traction than one that has at least some stick, and you’d mostly be right. For lots of materials, the “dynamic” friction coefficient when something is sliding, like my little sled demo, is less than the coefficient of friction when there’s no relative movement. That gives rise to this effect called stick-slip, where you get oscillation between sliding and sticking. A violin bow is a great example: the friction from the hairs in the bow stick, then slide, along the string, causing it to vibrate and create beautiful music.

On a locomotive, it’s less desirable. Stick-slip can lead to corrugation of the rail and unwanted noise. It was a notorious problem for steam locomotives because the traction force at the wheel rim was always fluctuating. But the other effect this difference in static versus dynamic friction creates is that the traction versus creep curve in the real world often looks more like this. There’s a maximum in there, and if you go past it toward greater slip, you get a lot less traction.

And that’s the trick many modern locomotives take advantage of. Sophisticated creep control systems can monitor each wheel individually and vary the tractive force to try and stay at the peak of that curve. Eeking out a few more percentage points on the friction coefficient means you can take better advantage of your power, and sometimes even use fewer locomotives than would otherwise be required, saving fuel, cost, and wear and tear.

All that complexity, and you still might be wondering, why all the trouble when you could just use a different material with a higher friction coefficient, like the rubber tires on cars? And the answer is just that everything comes with a tradeoff. Some passenger rail vehicles do use rubber tires, and some locomotives have steel “tires” that can be removed and replaced. But I think those F1 tires are a perfect analogy. You generally use the soft sticky ones when you want to gain track position and switch to the harder, more durable tires to maintain position without losing too much time in the pits. But pit stops for freight trains are pretty expensive. If you keep following that logic to more and more durable tires that can carry multiple tons of weight across hundreds of thousands of miles, you just end up with a steel wheel on a steel rail, and you find other ways to get the traction that you need.