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.

 
 
 
 

The IPPC report on the melting ice caps makes for terrifying reading

A Greeland iceberg, 2007. Image: Getty.

Earlier this year, the Intergovernmental Panel on Climate Change (IPCC) – the UN body responsible for communicating the science of climate breakdown – released its long-awaited Special Report on the Ocean and Cryosphere in a Changing Climate.

Based on almost 7,000 peer-reviewed research articles, the report is a cutting-edge crash course in how human-caused climate breakdown is changing our ice and oceans and what it means for humanity and the living planet. In a nutshell, the news isn’t good.

Cryosphere in decline

Most of us rarely come into contact with the cryosphere, but it is a critical part of our climate system. The term refers to the frozen parts of our planet – the great ice sheets of Greenland and Antarctica, the icebergs that break off and drift in the oceans, the glaciers on our high mountain ranges, our winter snow, the ice on lakes and the polar oceans, and the frozen ground in much of the Arctic landscape called permafrost.

The cryosphere is shrinking. Snow cover is reducing, glaciers and ice sheets are melting and permafrost is thawing. We’ve known this for most of my 25-year career, but the report highlights that melting is accelerating, with potentially disastrous consequences for humanity and marine and high mountain ecosystems.

At the moment, we’re on track to lose more than half of all the permafrost by the end of the century. Thousands of roads and buildings sit on this frozen soil – and their foundations are slowly transitioning to mud. Permafrost also stores almost twice the amount of carbon as is present in the atmosphere. While increased plant growth may be able to offset some of the release of carbon from newly thawed soils, much will be released to the atmosphere, significantly accelerating the pace of global heating.

Sea ice is declining rapidly, and an ice-free Arctic ocean will become a regular summer occurrence as things stand. Indigenous peoples who live in the Arctic are already having to change how they hunt and travel, and some coastal communities are already planning for relocation. Populations of seals, walruses, polar bears, whales and other mammals and sea birds who depend on the ice may crash if sea ice is regularly absent. And as water in its bright-white solid form is much more effective at reflecting heat from the sun, its rapid loss is also accelerating global heating.

Glaciers are also melting. If emissions continue on their current trajectory, smaller glaciers will shrink by more than 80 per cent by the end of the century. This retreat will place increasing strain on the hundreds of millions of people globally who rely on glaciers for water, agriculture, and power. Dangerous landslides, avalanches, rockfalls and floods will become increasingly normal in mountain areas.


Rising oceans, rising problems

All this melting ice means that sea levels are rising. While seas rose globally by around 15cm during the 20th century, they’re now rising more than twice as fast –- and this rate is accelerating.

Thanks to research from myself and others, we now better understand how Antarctica and Greenland’s ice sheets interact with the oceans. As a result, the latest report has upgraded its long-term estimates for how much sea level is expected to rise. Uncertainties still remain, but we’re headed for a rise of between 60 and 110cm by 2100.

Of course, sea level isn’t static. Intense rainfall and cyclones – themselves exacerbated by climate breakdown – can cause water to surge metres above the normal level. The IPCC’s report is very clear: these extreme storm surges we used to expect once per century will now be expected every year by mid-century. In addition to rapidly curbing emissions, we must invest millions to protect at-risk coastal and low-lying areas from flooding and loss of life.

Ocean ecosystems

Up to now, the ocean has taken up more than 90 per cent of the excess heat in the global climate system. Warming to date has already reduced the mixing between water layers and, as a consequence, has reduced the supply of oxygen and nutrients for marine life. By 2100 the ocean will take up five to seven times more heat than it has done in the past 50 years if we don’t change our emissions trajectory. Marine heatwaves are also projected to be more intense, last longer and occur 50 times more often. To top it off, the ocean is becoming more acidic as it continues to absorb a proportion of the carbon dioxide we emit.

Collectively, these pressures place marine life across the globe under unprecedented threat. Some species may move to new waters, but others less able to adapt will decline or even die out. This could cause major problems for communities that depend on local seafood. As it stands, coral reefs – beautiful ecosystems that support thousands of species – will be nearly totally wiped out by the end of the century.

Between the lines

While the document makes some striking statements, it is actually relatively conservative with its conclusions – perhaps because it had to be approved by the 195 nations that ratify the IPCC’s reports. Right now, I would expect that sea level rise and ice melt will occur faster than the report predicts. Ten years ago, I might have said the opposite. But the latest science is painting an increasingly grave picture for the future of our oceans and cryosphere – particularly if we carry on with “business as usual”.

The difference between 1.5°C and 2°C of heating is especially important for the icy poles, which warm much faster than the global average. At 1.5°C of warming, the probability of an ice-free September in the Arctic ocean is one in 100. But at 2°C, we’d expect to see this happening about one-third of the time. Rising sea levels, ocean warming and acidification, melting glaciers, and permafrost also will also happen faster – and with it, the risks to humanity and the living planet increase. It’s up to us and the leaders we choose to stem the rising tide of climate and ecological breakdown.

Mark Brandon, Professor of Polar Oceanography, The Open University.

This article is republished from The Conversation under a Creative Commons license. Read the original article.