Steel on steel

Last night I missed the last train at Dresden-Neustadt. Not by much, but enough. The next one was three hours away. The station emptied out, the last trams on Schlesischer Platz rattled off and did not come back, and after that the only sounds were the wind moving through that big arched hall and the occasional freight train sliding through without stopping. I had a bench, a platform, and nothing to do except look at the rails.

If you have never stood close to a rail, it is worth doing once. It is a strip of steel about as wide as your palm, polished to a mirror where the wheels touch it. And the wheel touching it is also steel, and the bit of it actually in contact with the rail is about the size of a fingernail. A four-hundred-tonne train is standing on a few dozen fingernails.

I thought about that for a while. Then, because three hours is a long time, about the rest of it. This post is the rest of it. It is longer than usual and has things you can push and drag, because I found that half of what I know about trains only made sense once I could see the numbers move. If you are one of my parents' friends and this looks like homework, I promise it is not. There is no test. There is a game at the end, though, and if you would rather just play that, skip straight to it.

One bad idea that turned out to be brilliant

The thing about steel on steel is that it is slippery. Not ice slippery, but far slipperier than a tyre on a road. Engineers measure this with a number called the rolling resistance coefficient, which just means how hard you have to push to keep the thing rolling. For a car tyre on tarmac it is a bit over one percent of the weight. For a steel wheel on a steel rail it is about a tenth of that.

That sounds like a small difference and it really is not. Drag the slider and see.

That is the whole reason trains exist. Not the engines, not the tracks, not the timetables. It is that if you make the wheel and the road both out of steel, the same push goes eight times further. A freight train can move a tonne of goods well over a hundred kilometres on a single litre of diesel. That is why you can put a container on a train in Hamburg and get it to Munich for a few euros, and why your parcel is cheaper than the coffee you drink while waiting for it.

So the nineteenth century looked at this and said brilliant, let's build ten thousand kilometres of it, and they did, and then they discovered the problem, which is the same fact read the other way round.

The same fact, read backwards

If steel on steel barely resists rolling, it also barely resists sliding. Which means it barely resists stopping.

When a car brakes, the tyres grip the road and the road pulls the car to a halt. A decent car on a dry road can pull nearly a full g of braking. A train's wheels have nothing to grip. The best they can manage, pressed as hard as the brakes can press them, is about a tenth of that. And the train weighs a thousand times more.

Set that to 300 and look at the number. Three kilometres, to stop one train. If the driver of an ICE, the white Intercity-Express that is Germany's fast train, sees something on the line at full speed, there is nothing to be done except brake and wait. Three kilometres is a minute of waiting. Someone has died in that minute, in every country with fast trains, more than once.

You would think the answer is better brakes, and people have tried. The ICE 3 has a brake that does not touch the rail at all. It hangs magnets a few millimetres above the steel and drags on it electrically, like the brakes on a rollercoaster. It helps, but it does not change the basic fact, which is that the wheel can only push against the rail as hard as the rail lets it, and the rail does not let it push very hard.

Hills

The same slipperiness shows up when the track goes up.

A car will drive up a twenty percent gradient without complaint, which means it climbs twenty metres for every hundred it goes forward, about as steep as a road ever gets. A train's wheels will start spinning on a slope so gentle you would not notice it walking. Try it. Pick a train, pick the weather, and tilt the track.

Two things fall out of this that I found genuinely surprising.

The first is that being heavier does not help. You would think a heavy locomotive grips better, and it does, but it also has more weight to drag uphill, and the two cancel exactly. What matters is what fraction of the train's weight sits on wheels that are actually powered. A freight train is a locomotive pulling twenty dead wagons, so almost none of it is. That is why freight lines are so flat, and why the Alps were a wall for a hundred years. An ICE has motors under half its coaches, which is a big part of why it can go places a locomotive-hauled train cannot.

The second is leaves. Every autumn, trains across northern Europe run late because of leaves on the line, and every autumn people laugh at the excuse. It is not an excuse. Sitting there in the middle of September with the trees still full, I was thinking, give it a month. Wet leaves get crushed into a slick black paste that cuts the grip to a fifth of normal. Trains that could climb a hill in July cannot climb it in October, and trains that could stop in a kilometre need two. Railways across Europe run trains every autumn that do nothing but blast the rails with water and sand to scrape it off.

Why there are signals, and why they are where they are

So now put those two facts together. A train at speed cannot stop within the distance its driver can see, and it cannot swerve. The only way to make that safe is to make sure there is never anything in front of it, ever, and to tell it to slow down long before it could possibly see why.

The way that was solved, in the 1840s, is still how most of the railway works. You cut the line into blocks and you make one rule, which is one train per block, no exceptions. At the start of each block there is a signal. If the block ahead has a train in it the signal is red and you stop. That is genuinely the whole system.

From the bench I could see one signal at the end of the platform. Every time a freight train slid through it went red behind it, and then, a long minute later, back to green, and once you know what that minute is you cannot stop watching for it.

Drag the slider up and watch what happens behind the first train. It stops for a few extra seconds at the station, and the train behind it hits a red and stops, and the one behind that hits a red and stops, and the whole line ends up standing still one block apart. Nobody did anything wrong. The system did exactly what it was built to do.

That animation is why DB is late. Not the only reason, but the mechanism. The German network is old and dense and very full. When one train loses three minutes, the trains behind it cannot overtake, cannot close up, cannot do anything except wait for their block to clear. Every announcement that says "Verspätung aus vorheriger Fahrt" is that slider being nudged somewhere you cannot see, an hour ago, two hundred kilometres away.

There is one more piece. Because the train cannot stop within sight of a red signal, there has to be a warning before it. On German lines that warning, the Vorsignal, stands exactly one thousand metres before the real signal. Why one thousand? Because that is what a train doing 160 km/h needs. It is baked into the rules.

Next time you are on a train, any train, watch the signals go past. You will see a yellow one, and a little later a red one, always in that order, always about a kilometre apart, and now you know why. I have not been able to stop noticing it since.

Which raises a question. What about trains that go faster than 160?

Switching

Before I get there, the other thing I was looking at from the platform was the points. Weichen, in German. The bits where one track becomes two.

There was a set right at the end of the platform, under a lamp, and I realised I had never really looked at how they work. Click on this one.

Two thin tapered blades, and the whole thing hinges on which of them is pressed against the rail. Move them a few centimetres and the train goes to Berlin instead of Leipzig. That is the entire mechanism. It is also, if you think about it, a bit alarming that something that heavy and that fast is steered by a piece of steel the width of a knife blade.

They freeze, of course. Water gets in, ice forms, the blade will not move, and until someone comes with a blowtorch or the heater kicks in, nothing can cross it. That is the Weichenstörung. Most of the big German junctions have electric heating under the points now, which is why winter is less bad than it used to be.

The train you take to Berlin

The ICE is where all of this piles up, because it is the fastest thing that has to live with every one of these rules.

It runs on electricity from the wire overhead, which in Germany is fifteen thousand volts at 16.7 hertz, not the 50 hertz coming out of your wall. Early electric motors could not cope with 50, so a hundred years ago the railway built its own power grid at a third of the frequency, and it was never worth ripping out. There are power stations in Germany that make electricity for trains and nothing else. And almost none of that electricity goes where you would think.

At walking pace nearly all the effort goes into the wheels. By 300 km/h, nine-tenths of it is going into shoving air out of the way. Air resistance rises with the square of speed and the power needed rises with the cube, and that curve is the reason almost nobody runs faster than 300 in regular service. Going from 300 to 400 would cost more than double the power for a third more speed. The French have done 575, once, for a record, with a train stripped to the bone and the voltage in the wire turned up. It is not a commuter service.

It is also why the ICE looks the way it does, because the nose is not styling. The Japanese famously redesigned theirs after an engineer noticed a kingfisher entering water without a splash. At high speed a train enters a tunnel the same way, and the pressure wave it pushes ahead of it used to come out the far end with a bang you could hear from hundreds of metres away. The doors and windows are sealed for a related reason, because at 300 passing another train in a tunnel is a pressure slap that would pop your ears. You feel a little of it anyway. Now you know what it is.

And when it brakes, the motors run backwards and turn into generators, and the energy goes back up the arm on the roof into the wire for the next train to use. A train slowing into Berlin is powering one leaving it.

The game

Which brings me back to the one-thousand-metre question, and this is the part I most wanted to build.

You are the driver and there is a red signal ahead. The distant signal, the warning, is a thousand metres before it, as the rules say. You are doing 160. When you see the warning, brake.

Now do it at 200, and then at 300.

You cannot, and it is not that you were slow. At 300 km/h a train needs three kilometres, and the warning is at one, so by the time you can see the warning you have already lost. No driver could do it. Which is why, above 160 km/h in Germany, there are no signals beside the track at all. The train talks to the line, through a cable between the rails on older routes and by radio on newer ones, and the signals appear on a screen in the cab, telling the driver to brake for a red that is still three or four kilometres away, out of sight around a bend. On the newest lines the driver mostly watches, because the train already knows.

Steel on steel is slippery, so trains are cheap, so we built thousands of kilometres of them, so they cannot stop, so we invented blocks and signals and a thousand-metre warning, so they could not go faster than 160, so we took the signals off the track and put them in the cab. A hundred and eighty years of engineering, all downstream of one decision somebody made about what to build a wheel out of.

Somewhere around the second hour I ran out of train facts and just sat there, colder than I had planned for. The first train came at some point after that, and it was late, and by then I did not mind. Verspätung aus vorheriger Fahrt.

If any of the numbers in here are wrong, tell me in the comments and I will fix them. And if you have a thing you find yourself thinking about on platforms at night, I would like to know what it is.