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

Maybe more than any other type of infrastructure, railways have a contingent of devoted enthusiasts. “Railfans” as they call themselves; Or should say “ourselves”? Maybe it's the nostalgia of an earlier era or the simple appeal of seeing enormous machinery up close. But railroads and the trains that ride along them are just plain fascinating. Train drivers are often known as engineers, but operating a locomotive is far from the only engineering involved in railways. In fact, building and maintaining a railroad is a big feat full of complexity. And I’d like to share some of that complexity with you, starting where the rubber meets the road, or in this case, where the steel meets the… other steel? It might sound like a simple topic, but don’t say that to the attendees of the annual Wheel Rail Interaction Conference. This stuff is complicated, so this is the first in a series of videos I’m doing on the engineering behind railways. Why do the rails of railroads have such a weird shape? The answer is pretty ingenious. I’m Grady and this is Practical Engineering. In today’s episode, wer’e talking about train wheels and rails.

Why do we build railroads anyway? They might seem self-evident now and even kind of elementary. But modern railroads are the result of hundreds of years of innovation. And like many kinds of innovation, the development of railroads was really just a series of solving problems. For example, how can we move upwards of 100 tons per vehicle without tearing up the road in the process? Well, instead of compacted gravel, asphalt, or concrete, we can build the road out of steel. But steel is expensive, so rather than a ribbon, we can save cost by using two narrow steel rails directly below the wheels. But wooden or rubber tires have a lot of rolling resistance because they deform under load, and that resistance adds up with each individual train car. So, we use steel for the wheels too. I built this model to show exactly how this works. My wheels are plastic and rails are aluminum, but I think you’ll still get the point. Steel wheels on steel rails are just so much more efficient than…[wheel falls off track]

Well, there is the problem of turning, too. Just because you put a rail below a wheel doesn’t mean it will follow the same path. You have to have some way for the rail to correct the direction of the wheel and keep it on track, literally. And, if you look at railway wheels, the answer is obvious: flanges. The wheels on railway vehicles all have them: a lip that projects below the rail to guide the wheel as it rolls along, keeping the position side to side. You could put flanges on the outside of wheels like this, but if a horizontal force like a hard turn caused one of the wheels to lift, the flange won’t help keep the wheel on track. We put flanges on the insides of wheels so they can keep a train from derailing even if one wheel lifts off the track. Let’s put some flanges on my wheels and try that demo again. [wheels bind up on track].

You can see we haven’t fully solved the problem. Unlike a wheel that has a tiny contact point with the rail, a flange is a big surface that creates a lot of friction around every curve. If you’ve heard that characteristic squeal of a train going around a corner, that’s the sound of flanges rubbing and grinding along the side of a rail. Rails on tight curves are often made of higher-grade hardened steel compared to straight portions of the track, and sometimes they’re even greased up to minimize friction between flanges and the edges of rails. But, there’s a bigger problem at play in this demonstration than simple friction.

Instead of independent wheels, most railway cars use solid axles attached to both wheels called a wheelset. They need that design to withstand the incredible loads each axle carries, but it poses a problem around bends. A solid axle means both wheels turn at the same rate, but the length of the outer portion of track in any given curve is longer than the inside of the curve. Two wheels of the same diameter spinning at the same rate will, kind of obviously, have to roll the same distance. Since there’s a mismatch between the distances the wheels need to travel, solid-axeled wheelsets with cylindrical wheels would always experience some degree of slipping around a turn. That would not only create a bunch of additional friction, but also keep the wheels from following the curved path, and a flange can only do so much.

The trick to railway wheels is something that’s not so obvious at first glance. The wheels are actually conical. The profile of the wheel is wider on the inside next to the flange, and gently narrows toward the outside of the wheel. A wheelset with conical wheels will naturally tend to self-center itself between two rails. On a straight section of track, a wheel that rides up higher on one rail will naturally fall back down, keeping the wheelset roughly centered on the road. In a sense, conical wheels want to stay on the tracks. There’s always a little bit of wobble (exaggerated here), so trains actually move down tracks in a sinusoidal side-to-side pattern that you can sometimes feel if you’re paying attention. Incidentally, that helps the wheels wear evenly. But where it really counts is on a curve.

The turning forces on a train cause it to tend toward the outside track. This shifts the wheels over as well. The outer wheel will ride on the thicker part of its tread nearest to the flange, while the inner wheel will ride toward its edge, which has a smaller circumference. This way, the effective diameter of each wheel changes in a curve and solves the slip problem that cylindrical wheels would face. Take a look at the way these conical wheels that I 3D printed behave as they make this corner. You can see the outside wheel rolling on the wider part, effectively increasing its diameter and thus distance traveled per rotation. Conversely, the inside wheel rides on the narrower part of the cone, and so it has a smaller diameter and travels a shorter distance per rotation.

It really is kind of ingenious. Most vehicles have a differential gearbox to deal with this challenge of navigating curves; train cars just use some clever geometry. But that’s not the end of the story. You might even be thinking, “Richard Feynman already taught me this in the 80s… It’s nothing new.” But there’s more engineering involved in how train wheels and rails interact, including the interesting shape of modern rails. Think about that taper angle first. One standard in the US uses a 1:20 ratio. For the main part of the wheel, that means the outside diameter is roughly a quarter inch or 6 millimeters less than the inside diameter, and that difference has a big effect on the allowable radius of curves in a railroad. A steeper cone can navigate sharper curves, since there’s a bigger difference in the circumference from the inside to outside. You can see my wheelset can’t navigate this s-curve, despite the exaggerated conicity.

This challenge is partly solved with trucks, called bogies in the UK. You can kind of think of trucks as big rollerskates under each end of a train car. The trucks can rotate relative to the rest of the car, and they usually have some pretty serious springs and suspension systems to keep a smooth ride rolling. Most trucks keep the wheel sets parallel, but some can even allow them to ride radially with each curve.

However, even with trucks or bogies, wheels can overshoot their optimal orientation on the tracks. When the simple sinusoidal motion created by the tapered wheels is amplified by the speed of the car, the oscillation can violently slam the trucks side-to-side on the rails. This is called hunting behavior. The violent motion can even cause a train to derail. It’s worst with empty cars, and usually only happens at higher speeds, so a lot of engineering goes into developing wheel profiles and truck designs that raise the hunting onset speed so that it doesn’t limit how fast a train can go. That’s a lot of innovation on the wheel side, but what about the rails?

Just like all parts of a railroad, the rails themselves have evolved over time. Turns out there are a lot of shapes they can take and still serve the same basic function, but modern railway rails are shaped that way for a reason. Weight is equivalent to cost for big steel structures, so there’s nothing on these rails that isn’t absolutely necessary. In a sense, rails are I-beams, a shape that is well-known for its strength and something we see in plenty of other heavy load bearing steel structures. But there’s more to it than that. The bottom part of the rail, called the foot, distributes enormous loads, converting the extreme contact pressure of a steel wheel into something that can be withstood by a wooden or concrete tie. The web elevates the train above the ground, giving clearance for the flanges of the wheels and keeping everything clear of small debris that might end up on the tracks.

The head of the rail with where the action happens. This thick rounded section of steel takes an awful lot of abuse over its life, and thus experiences the bulk of the wear. An old rail section, especially on the high side of a curve, looks remarkably different than a newly forged rail. Here’s why: Theoretically, the speed of a spinning wheel exactly matches the speed of the rail at a mathematically precise point. But trains don’t care about math. For one, even steel wheels on steel rails deform a little bit as they roll. Rather than a single point, there is a small contact patch between the two. That tiny area, roughly the size of a small coin, carries all the weight of the train into the rail. But, because the contact patch is spread across the tapered wheel, the wheel is turning at many different speeds on the same piece of rail. Only the center of the contact patch actually moves at the exact speed of the train. This results in a small amount of grinding as the train moves along, slowly wearing down both the wheel and the rail. Eventually they start to conform to each other, and that’s mostly a bad thing.

Wheels can wear down to get a vertical face that wants to climb up the rail or a hollow profile with a quote-unquote “second flange” that takes the wrong direction at a switch. Most rail wheels have some amount of hollow to them, which changes how conical they actually are. Some wheels are even designed to be taken off and machined back into spec to extend their life. The best way to reduce this wear is to use hardened materials and reduce the size of the contact patch by curving the top of the rail so that the wheel only touches a tiny part of it as it rolls by. After that, it’s just a decision about how much wear you want before needing to replace the rail. The more metal you include in the rail head, the more it will cost, but the longer it will last. In fact, not all rails are equal. The lightest rails are used on straight sections and small commuter service lines. The largest rails are used on curves and heavy-haul freight tracks. Once they get worn down on the main line, they often get reinstalled for a second life in a yard or a siding where they can still bear train cars and locomotives at slow speeds.

So, rails are shaped in the funny way for a reason: they’re bulbous both to reduce the size of the contact patch and provide enough steel to wear away before needing to be replaced. And the shape of rails and wheels is still a topic of research and innovation. Just in the past few years, the standard profile of North American freight train wheels was updated to the new AAR-2A standard. Just a tiny change in the shape of the wheel was tested to have 40% less wear than the previous spec. That means trains will start seeing better steering, lower friction, better fuel consumption, and longer lasting infrastructure.

In many ways, railroads might seem like old technology, a solved problem that doesn’t need more engineering. But it’s just not true. Modern railroad companies use sophisticated software, like the Train Energy and Dynamics Simulator, to keep track of all the complexities involved in how wheels and rails interact. Simulators can let you adjust factors like train makeup, different track conditions, operating conditions, suspensions, and more to characterize how trains will handle and how much energy they’ll use. That’s the topic of the next video in this series, so stay tuned if you want to learn more.

In the 19th century, railway engineering was all about how to build railroads, finding routes through difficult terrain and efficient forms of construction. Modern rail engineering is all about getting the most out of the system. It might not look like much when you see a train passing by, but a huge amount of research, testing, and engineering went into the shape of those rails and wheels and we’re still improving them today.