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.

 
 
 
 

Never mind Brexit: TfL just released new tube map showing an interchange at Camden Town!!!

Mmmmm tube-y goodness. Image: TfL.

Crossrail has just been given a £1bn bail out. This, according to the Financial TImes’s Jim Pickard, is on top of the £600m bailout in July and £300m loan in October.

That, even with the pound crashing as it is right now, is quite a lot of money. It’s bad, especially at a time when there is still seemingly not a penny available to make sure trains can actually run in the north.

But the world is quite depressing enough today, so let’s focus on something happier. On Saturday night – obviously peak time for cartographic news – Transport for London emailed me to let me know it would be updating the tube map, to show more street-level interchanges:

Connections between several pairs of stations that are near to each other, but have traditionally not been shown as interchanges, now appear on the map for the first time. These include:

  • Camden Road and Camden Town
  • Euston and Euston Square
  • Finchley Road and Finchley Road & Frognal
  • Kenton and Northwick Park
  • New Cross and New Cross Gate
  • Seven Sisters and South Tottenham
  • Swiss Cottage and South Hampstead

The stations shown meet a set of criteria that has been used to help determine which should be included. This criteria includes stations less than a 700m or a 10 minute walk apart, where there is an easy, well-lit, signposted walking route and where making the change opens up additional travel options.

The results are, well, this:

In addition, interchanges between stations have traditionally appeared on the Tube map as two solid lines, irrespective of whether they are internal or external (which means customers need to leave the station and then re-enter for the station or stop they need). This approach has now been updated and shows a clear distinction between the two types, with external interchanges now being depicted by a dashed line, linking the two stations or stops.

And lo, it came to pass:

I have slightly mixed feelings about this, in all honesty. On the positive side: I think generally showing useful street-level interchanges as A Good Thing. I’ve thought for years that Camden Road/Camden Town in particular was one worth highlighting, as it opens up a huge number of north-east travel options (Finchley to Hackney, say), and apps like CityMapper tell you to use it already.


And yet, now they’ve actually done it, I’m suddenly not sure. That interchange is pretty useful if you’re an able bodied person who doesn’t mind navigating crowds or crossing roads – but the map gives you no indication that it’s a harder interchange than, say, Wanstead Park to Forest Gate.

The new map also doesn’t tell you how far you’re going to be walking at street level. I can see the argument that a 400m walk shouldn’t disqualify something as an interchange – you can end up walking that far inside certain stations (Green Park, Bank/Monument), and the map shows them as interchanges. But the new version makes no effort to distinguish between 100m walks (West Hampstead) and 700m ones (Northwick Park-Kenton), which it probably should.

I’m also slightly baffled by some of the specific choices. Is Finchley Road-Finchley Road & Frognal really a useful interchange, when there’s an easier and more direct version, one stop up the line? No hang on West Hampstead isn’t on the Metropolitan line isn’t it? So that’s what it’s about.

Okay, a better one: if you’re switching from District to Central lines in the City, you’re generally better off alighting at Cannon Street, rather than Monument, for Bank – honestly, it’s a 90 second walk to the new entrance on Walbrook. Yet that one isn’t there. What gives?

The complete new tube map. The full version is on TfL’s website, here.

On balance, showing more possible interchanges on the map is a positive change. But it doesn’t negate the need for a fundamental rethink of how the tube map looks and what it is for. And it’s not, I fear, enough to distract from the Crossrail problem.

Jonn Elledge is the editor of CityMetric. He is on Twitter as @jonnelledge and on Facebook as JonnElledgeWrites.