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 behind the rise of the ornamental restaurant toilet?

Toilets at Sketch restaurant, London. Image: Nik Stanbridge/Flickr.

A few weeks ago, I found myself in the toilets of a zeitgeisty new Italian restaurant in east London called Gloria. As with so many contemporary restaurant toilets, those in question were an aesthetic extension of the establishment’s soul. The inventive menu was matched by two-way mirrored toilet doors.

The setup was this: cubicle occupants could see out while the unisex crowd milling around the taps could check their outfits on the exterior mirrors. All fun and games, I thought. But then I found myself mid toilet with a guy peering into my door to change his contact lens. Either he had spectacularly bad manners or he was unaware of the two-way door thing. (Let’s hope it’s the latter.)

Gloria’s toilets aren’t unique in their attempt to be distinctive. The loos at nearby Mr Fogg’s Maritime Club & Distillery are adorned with specimen boards of dead spiders. Meanwhile, Edinburgh’s The Sun Inn invites patrons to pee in buckets, and trumpets double as urinals in The Bell Inn in East Sussex. Men can wee into the vista if they’re dining in the Shard. And Sketch’s ovum shaped loos are the stuff of urban legend.

Further afield, transparent doors become frosted only after they’re locked at Brussels’ Belga Queen. In Otto’s Bierhalle in Toronto, diners can press a button to activate their own private rave. And the toilets in Robot Restaurant in Tokyo have gold-plated interiors and dancing robots.

What’s behind this trend? Are quirky toilets just a bit of fun – or an unnecessary complication to the simple act of going for a wee and checking you don’t have tomato sauce on your chin?

Yotam Ottolenghi’s London flagship restaurant Nopi crops up often in conversations about restaurant bathrooms. A hall of mirrors glitters enticingly ahead of loo-bound diners. “The bathroom needs to be the nicest part [of] the whole place because that’s where you’re on your own,” says Alex Meitlis, the designer behind the space.

But no one is truly alone in 2019. If surveys are to be believed, nearly 65 per cent of millennials take their phone to the bathroom with them. Mike Gibson, who edits the London food and drink magazine Foodism agrees that the bathroom selfie – searches for which, incidentally, yield over 1.5m results on Instagram – is part of the reason that contemporary lavatory design is so attention seeking.


“Any new venue that's opening will be super aware that there's probably not an inch of their restaurant that won't be photographed or filmed at some point”, he says. But bathrooms like Nopi’s predate this trend. Indeed, Meitlis believes he has created a haven from the smartphone obsession; Nopi’s mirrors are angled in such a way that means you have to seek out your reflection. “You can choose whether to look for yourself in the mirror or not.”

Another driving force is the increasingly competitive restaurant landscape. “It’s almost like there’s some sort of ever-escalating competition going on amongst new openings, which makes every visit a faintly terrifying experience”, says food writer and New Statesman contributor Felicity Cloake. Gibson agrees. “Restaurants want an edge wherever possible, and design definitely comes into that.”

So novelty bathrooms get you noticed, promote social media engagement and entertain diners who are momentarily without the distraction of company. (Although, it must be said, quirky bathrooms tend to make the loo trip a more sociable experience; a Gloria spokesperson described the restaurant’s toilets as somewhere you can “have a good laugh and meet people along the way.”)

Nevertheless, I’m not the only one who finds bathroom surprises disconcerting.  One TripAdvisor user thought the Belga Queen loos were “scary”. And a friend reports that her wonderment at the Nopi bathroom was laced with mirror maze induced nausea – and mild panic when she realised she didn’t know the way out. Should restaurants save the thrills for the food?

“I think it's important not to be too snarky about these things – restaurants are meant to playful,” says Gibson. Cloake agrees that novelty is fine, but adds: “my favourite are places like Zelman Meats in Soho that have somewhere in the dining room where you can easily wash your hands before sitting down and tucking in.”

So perhaps we should leave toilets unadorned and instead ramp up the ornamentation elsewhere. Until then, I’ll be erecting a makeshift curtain in all mirrored toilets I encounter in future. An extreme reaction, you might say. But, as I wish I could have told the rogue contact lens inserter, it’s not nice to pry into someone else’s business.