Speed vs coverage: How do metro systems decide how to space their stops?

The Paris Metro: quite close to another station, this. Image: Getty.

The Paris Metro averages a stop every 600m. The Moscow Metro averages a stop every 1.7km. Most of the world's largest systems are in between, several clustering in the 1.2-1.3 km range, including the London Underground, the Tokyo subway, and the Mexico City Metro.

But why is this? How come metro builders in some cities chose to build stations three times as far apart as in others? And what about those cities that have no metro system, but are building one, such as Tel Aviv or Sydney? What should they do?

The basic tradeoff here is between speed and coverage. Wider stop spacing means fewer locations have a metro station, but the speed between the stations is higher. The Moscow Metro averages 41 km/h, while the Paris Metro only averages about 25km/h. Other systems are intermediate: in Tokyo the average speed is about 30km/h; in London 33km/h.

There are other factors determining average speed, so that newer lines are often fast for their stop spacing. But each additional station adds about 40-60 seconds of travel time, depending on top speed, track quality, and train acceleration capabilities. The tradeoff, then, is the question: are more stations worth the extra travel time?

Each metro-building tradition answers this question differently. In cities where the metro extends deep into suburbia, stop spacing is wide; Paris built the RER as a separate system, with express stop pattern, because the Metro was too slow to effectively serve the suburbs.

Moreover, different countries make different decisions based purely on tradition. Under Parisian influence, the Montreal and Lyon Metros have short stop spacing; under Moscow's influence the metro systems in the former Communist Bloc, from Eastern Europe to China and North Korea, usually average more than 1.5 km between stations. With neither influence, cities in developing countries that build new metros, such as in South Asia, seem to use the same stop spacing as London or Tokyo.

But there is more to the stop spacing decision than the speed versus coverage tradeoff. Large cities, which expect to build many metro lines, need to plan how those lines will intersect in their cores. The San Francisco urbanist Brian Stokle wrote about the related subject of line spacing: how cities space parallel metro lines in their central business districts. Using American examples, Stokle argues that the typical space for parallel lines is 500-700 meters; this also appears to be the average in Paris and in central London.

The upshot is that if two lines are parallel, spaced about half a kilometer apart, then a line that intersects them orthogonally had better have two stops half a kilometer apart, for transfers. For example, in the diagram below the red and blue lines are roughly parallel, and the black line is orthogonal to them.

This looks familiar. Image: author provided.

Metro planners aim to provide a transfer station at the intersection of every pair of lines. In practice, because most metro systems have denser line spacing than stop spacing, this is not always feasible. Metro systems that feed geographically small central business districts, such as central London or central Tokyo, end up with multiple missed connections; New York, where the subway was built by three separate companies, has more than twenty missed connections. But usually, there is only a small handful of missed connections, often just one or two.

A separate question is that of express lines. In New York, five of the nine subway trunk lines have four tracks, with local and express trains; in Seoul, Line 1 has four tracks as well. Thanks to the express lines, New York maintains very narrow stop spacing on the local lines.


But a more common situation is one in which every metro line has two tracks, with all trains making all stops, on which some lines are more express than others. In Paris, the RER A was built as an express version of Metro Line 1, and, decades later, Metro Line 14 was built with longer stop spacing as well, to relieve the central segment of the RER A.

This situation leads to missed connections. The RER A tries to make connections when it can, but still crosses a few lines without a transfer, or else it would be hardly any faster than Line 1.

London's equivalent, Crossrail, does the same: it misses some connections to north-south lines, because if it didn't, it wouldn't be faster than the Central line, simply because line spacing in Central London is so dense. Within the Paris Metro, excluding the RER, there are three missed connections, two involving Line 14; an under-construction extension of Line 14 misses yet another connection. In Asia, several cities, including Hong Kong, Beijing, and Delhi have express lines to the airport, with missed connections in every case.

But it's easier to build networks with long stop spacing in newer cities, purely because of how their business districts are laid out. In old industrialised cities like London, Paris, New York, and even Tokyo, there is a dominant CBD, a few square kilometers in area, and most metro lines enter it. In all of these cities, the CBDs for the most part predate the metro system.

In newer cities in developing countries, the CBDs look different, with multiple centers, sometimes purpose-built. This leads to longer line spacing, matching the wide stop spacing. On same-scale maps of their networks, Paris, London, and Tokyo all look like hard-to-follow blobs in their centers, whereas Chinese cities, especially Beijing, still look clear. In Beijing, the only missed connection today involves the airport express line.

The most ideal metro network looks radial, with a circular line or two. Every pair of radial lines should intersect, once, with a transfer station, and every radial should intersect every circle twice, again with transfers. Ideally interchange stations should only involve two lines at a time, to avoid clogging the most popular locations. The diagram above is a good example of a coherent network with three lines. Unfortunately, the interaction of line spacing and stop spacing makes the ideal network difficult to construct. It's also unlikely that the street network is perfectly aligned for this; for example, cities with street grids, like Beijing or Philadelphia, can't easily build lines diagonally to the grid.

 

The ideal network? At least, if you ignore the chaos of that central station. Image: CityMetric.

This means that the only way to guarantee easy connections between metro lines in most large cities is to build very short stop spacing, as in Paris. Unfortunately, this imposes a sharp limit on train speed - and it's precisely the largest cities that have the most need for speed, since their suburbs usually stretch farther out of city center than those of smaller cities.

Metro construction is full of compromises. Cities that are building new systems, especially in the developed world, are likely to have so much sprawl, from decades of growing without a metro, that they need long stop spacing to serve the suburbs effectively. But they also are likely to have an organic central business district with many close-in dense neighborhoods, which would benefit from short stop spacing; they also have everywhere-to-everywhere commutes, as all modern cities do, which makes good interchanges between lines a must. Something has to give, and each city needs to figure out how, in its particular situation, to choose the optimal point in the speed-coverage tradeoff.

 
 
 
 

There isn’t a war on the motorist. We should start one

These bloody people. Image: Getty.

When should you use the horn on a car? It’s not, and anyone who has been on a road in the UK in living memory will be surprised to hear this, when you are inconvenienced by traffic flow. Nor is it when you are annoyed that you have been very slightly inconvenienced by another driver refusing to break the law in a manner that is objectively dangerous, but which you perceive to be to your advantage.

According to the Highway Code:

“A horn should only be used when warning someone of any danger due to another vehicle or any other kind of danger.”

Let’s be frank: neither you nor I nor anyone we have ever met has ever heard a horn used in such a manner. Even those of us who live in or near places where horns perpetually ring out due to the entitled sociopathy of most drivers. Especially those of us who live in or near such places.

Several roads I frequently find myself pushing a pram up and down in north London are two way traffic, but allow parking on both sides. This being London that means that, in practice, they’re single track road which cars can enter from both ends.

And this being London that means, in practice, that on multiple occasions every day, men – it is literally always men – glower at each other from behind the steering wheels of needlessly big cars, banging their horns in fury that circumstances have, usually through the fault of neither of them, meant they are facing each other on a de facto single track road and now one of them is going to have to reverse for a metre or so.

This, of course, is an unacceptable surrender as far as the drivers’ ego is concerned, and a stalemate seemingly as protracted as the cold war and certainly nosier usually emerges. Occasionally someone will climb out of their beloved vehicle and shout and their opponent in person, which at least has the advantages of being quieter.

I mentioned all this to a friend recently, who suggested that maybe use of car horns should be formally restricted in certain circumstances.

Ha ha ha. Hah.

The Highway Code goes on to say -

“It is illegal to use a horn on a moving vehicle on a restricted road, a road that has street lights and a 30 mph limit, between the times of 11:30 p.m. and 07:00 a.m.”

Is there any UK legal provision more absolutely and comprehensively ignored by those to whom it applies? It might as well not be there. And you can bet that every single person who flouts it considers themselves law abiding. Rather than the perpetual criminal that they in point of fact are.


In the 25 years since I learned to drive I have used a car horn exactly no times, despite having lived in London for more than 20 of them. This is because I have never had occasion to use it appropriately. Neither has anyone else, of course, they’ve just used it inappropriately. Repeatedly.

So here’s my proposal for massively improving all UK  suburban and urban environments at a stroke: ban horns in all new cars and introduce massive, punitive, crippling, life-destroying fines for people caught using them on their old one.

There has never been a war on motorists, despite the persecution fantasies of the kind of middle aged man who thinks owning a book by Jeremy Clarkson is a substitute for a personality. There should be. Let’s start one. Now.

Phase 2 will be mandatory life sentences for people who don’t understand that a green traffic light doesn’t automatically mean you have right of way just because you’re in a car.

Do write in with your suggestions for Phase 3.