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.

 
 
 
 

What’s up with Wakanda’s trains? On public transport in Black Panther

The Black Panther promotional poster. Image: Marvel/Disney.

Black Panther is one of the best reviewed superhero films of all time. It’s instantly become a cultural touchstone for black representation in movies, while shining a positive light on a continent almost totally ignored by Hollywood. But never mind all that – what about the trains?

The film takes place in the fictional African country of Wakanda, a small, technologically advanced nation whose power comes from its main natural resource: huge supplies of a magical metal called vibranium. As is often the case in sci-fi, “technologically advanced” here means “full of skyscrapers and trains”. In other words, perfect Citymetric territory.

Here’s a mostly spoiler-free guide to Black Panther’s urbanism and transport.

City planning

It’s to the credit of Black Panther’s crew that there’s anything to talk about here at all. Fictional cities in previous Marvel films, such as Asgard from the Thor films or Xandar from Guardians of the Galaxy, don’t feel like real places at all, but collections of random monuments joined together by unwalkably-wide and sterile open spaces.

Wakanda’s capital, the Golden City, seems to have distinct districts and suburbs with a variety of traditional and modern styles, arranged roughly how you’d expect a capital to be – skyscrapers in the centre, high-rise apartments around it, and what look like industrial buildings on its waterfront. In other words, it’s a believable city.

It’s almost a real city. Image: Marvel/Disney

We only really see one area close-up: Steptown, which according to designer Ruth Carter is the city’s hipster district. How the Golden City ended up with a bohemian area is never explained. In many cities, these formed where immigrants, artists and students arrived to take advantage of lower rents, but this seems unlikely with Wakanda’s stable economy and zero migration. Did the Golden City gentrify?

Urban transport

When we get out and about, things get a bit weirder. The narrow pedestrianised sand-paved street is crowded and lined with market stalls on both sides, yet a futuristic tram runs right down the middle. The tram’s resemblance to the chunky San Francisco BART trains is not a coincidence – director Ryan Coogler is from Oakland.

Steptown Streetcar, with a hyperloop train passing overhead. Image: Marvel/Disney.

People have to dodge around the tram, and the street is far too narrow for a second tram to pass the other way. This could be a single-track shuttle (like the former Southport Pier Tram), a one-way loop (like the Detroit People Mover) or a diversion through narrow streets (like the Dublin Luas Cross City extension). But no matter what, it’s a slow and inefficient way to get people around a major city. Hopefully there’s an underground station lurking somewhere out of shot.


Over the street runs a *shudder* hyperloop. If you’re concerned that Elon Musk’s scheme has made its way to Wakanda, don’t worry – this train bears no resemblance to Musk’s design. Rather, it’s a flying train that levitates between hoops in the open air. It travels very fast – too fast for urban transport, since it crosses a whole neighbourhood in a couple of seconds – and it doesn’t seem to have many stops, even at logical interchange points where the lines cross. Its main purpose is probably to bring people from outlying suburbs into the centre quickly.

There’s one other urban transport system seen in the film: as befitting a major riverside city, it has a ferry or waterbus system. We get a good look at the barges carrying tribal leaders to the ceremonial waterfalls, but overhead shots show other boats on the more mundane business of shuttling people up and down the river.

Transport outside the city

Unfortunately there’s less to say here. Away from the city, we only see people riding horses, following cattle-drawn sleds, or simply walking long distances. This is understandable given Wakanda’s masquerading as a developing country, but it makes the country very urban centric. Perhaps that’s why the Jabari hate the other tribes so much – poor transport investment means the only way to reach them is a narrow, winding mountain pass.

The one exception is in freight transport. Wakanda has a ridiculously developed maglev network for transporting vibranium ore. This actually follows a pattern seen in a lot of real African countries: take a look at a map of the continent and you’ll see most railways run to the coast.

Image: Bucksy/Wikimedia Commons.

These are primarily freight railways built to transport resources from mines and plantations to ports, with passenger transport an afterthought.

A high-speed maglev seems like overkill for carrying ore, especially as the film goes out of its way to point out that vibranium is too unstable to take on high-speed trains without careful safety precautions. Nevertheless, the scene where Shuri and Ross geek out about these maglevs might just be the single most relatable in any Marvel movie.

A very extravagant freight line. Image: Marvel/Disney.

Perhaps this all makes sense though. Wakanda is still an absolute monarchy, and without democratic input its king is naturally going to choose exciting hyperloop and maglev projects over boring local and regional transport links.

Here’s hoping the next Black Panther film sees T’Challa reforming Wakanda’s government, and then getting really stuck into double-track improvements to the Steptown Streetcar.

Stephen Jorgenson-Murray tweets as @stejormur.

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