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.

 
 
 
 

Transport for London’s fare zones secretly go up to 15

Some of these stations are in zones 10 to 12. Ooooh. Image: TfL.

The British capital, as every true-blooded Londoner knows, is divided into six concentric zones, from zone 1 in the centre to zone 6 in the green belt-hugging outer suburbs.

These are officially fare zones, which Transport for London (TfL) uses to determine the cost of your tube or rail journey. Unofficially, though, they’ve sort of become more than that, and like postcodes double as a sort of status symbol, a marker of how London-y a district actually is.

If you’re the sort of Londoner who’s also interested in transport nerdery, or who has spent any time studying the tube map, you’ll probably know that there are three more zones on the fringes of the capital. These, numbered 7 to 9, are used to set and collect fares at non-London stations where the Oyster card still works. But they differ from the first six, in that they aren’t concentric rings, but random patches, reflecting not distance from London but pre-existing and faintly arbitrary fares. Thus it is that at some points (on the Overground to Cheshunt, say) trains leaving zone 6 will visit zone 7. But at others they jump to 8 (on the train to Dartford) or 9 (on TfL rail to Brentwood), or skip them altogether.

Anyway: it turns out that, although they’re keeping it fairly quiet, the zones don’t stop at 9 either. They go all the way up to 15.

So I learned this week from the hero who runs the South East Rail Group Twitter feed, when they (well, let’s be honest: he) tweeted me this:

The choice of numbers is quite odd in its way. Purfleet, a small Thames-side village in Essex, is not only barely a mile from the London border, it’s actually inside the M25. Yet it’s all the way out in the notional zone 10. What gives?

TfL’s Ticketing + Revenue Update is a surprisingly jazzy internal newsletter about, well, you can probably guess. The September/October 2018 edition, published on WhatDoTheyKnow.com following a freedom of information request, contains a helpful explanation of what’s going on. The expansion of the Oyster card system

“has seen [Pay As You Go fare] acceptance extended to Grays, Hertford East, Shenfield, Dartford and Swanley. These expansions have been identified by additional zones mainly for PAYG caping and charging purposes.

“Although these additional zones appear on our staff PAYG map, they are no generally advertised to customers, as there is the risk of potentially confusing users or leading them to think that these ones function in exactly the same way as Zones 1-6.”


Fair enough: maps should make life less, not more, confusing, so labelling Shenfield et al. as “special fares apply” rather than zone whatever makes some sense. But why don’t these outer zone fares work the same way as the proper London ones?

“One of the reasons that the fare structure becomes much more complicated when you travel to stations beyond the Zone 6 boundary is that the various Train Operating Companies (TOCs) are responsible for setting the fares to and from their stations outside London. This means that they do not have to follow the standard TfL zonal fares and can mean that stations that are notionally indicated as being in the same fare zone for capping purposes may actually have very different charges for journeys to/from London."

In other words, these fares have been designed to fit in with pre-existing TOC charges. Greater Anglia would get a bit miffed if TfL unilaterally decided that Shenfield was zone 8, thus costing the TOC a whole pile of revenue. So it gets a higher, largely notional fare zone to reflect fares. It’s a mess. No wonder TfL doesn't tell us about them.

These “ghost zones”, as the South East Rail Group terms them, will actually be extending yet further. Zone 15 is reserved for some of the western-most Elizabeth line stations out to Reading, when that finally joins the system. Although whether the residents of zone 12 will one day follow in the venerable London tradition of looking down on the residents of zones 13-15 remains to be seen.

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