Overlapping Circles

I’ve been looking at a lot of big city metro maps recently while checking the construction cost database line by line, and I noticed a regrettable pattern in a number of megacities: they’re so big their metro networks have multiple circles in service or under construction, and instead of neat concentric circles they have overlaps.

What are overlapping circles?

Here is Moscow, for example. The map shows three circles: in blue is the Circle Line, or Line 5; in black is the Moscow Central Circle; and in red is the under-construction Big Circle Line, or Line 11.

The reason for this is that the Central Circle uses a legacy regional rail alignment. In isolation, with no legacy rail to speak of, circles tend to be more orderly, as in Beijing with its two concentric circles (Lines 2 and 10). However, if there is a legacy alignment, it may not be perfectly aligned with where, absent any legacy rail, it would make the most sense to place an orbital. This is the case above in Moscow: the Central Circle is close to the Circle Line in the south but abuts farther away in the north, and the Big Circle Line is built to be the opposite.

This is not unique to Moscow. Here is Tokyo:

The Oedo Line, in magenta, is a ring with a tail. The Yamanote Line, in light green, is a full ring, taller than it is wide so as to really be two north-south lines joined at both ends.

Why is this bad?

The point of a circumferential line is to provide public transit in the orthogonal direction to that of city center. This has any of the following uses:

  • To provide service on strong corridors that happen to be orthogonal to the direction of city center, such as Uptown Manhattan streets, Beijing ring roads, traces of former city walls in Paris, etc.
  • To connect strong near-center neighborhoods to one another, at a radius that balances the density close to the center with the greater need for a circumferential farther away to avoid the inconvenience of walking or taking  a two-seat ride on radial metro lines.
  • To connect outlying areas with strong near-center neighborhoods that lie on different lines.
  • To facilitate interchanges between different radial lines, especially ones that are close to each other, without too much backtracking and without overloading central transfer points.

This works best if the circumferential service is at approximately equal radius from the center. If it is not, then some segment of it may be partially radial, which means it will have all of the problems of radials (peakiness) and none of the benefits (service to city center). In extreme cases, an operational circle may literally pass through city center, as is the case for the Yamanote Line, or a nominal circumferential may pass close enough to count, as is the case for the East London line at Shoreditch, and then the problem is that one side of the region doesn’t get any circumferential service, that is Shitamachi and East London.

If there are multiple circles, then all of the above aspects get better if those circles are concentric, for the same reason. Having many circumferential lines closely parallel to each other can create a local grid in an especially large city; I proposed such a system for Lagos, which is both enormous and a tabula rasa.

Why does this keep happening?

The Moscow Central Circle and the Yamanote Line are both historic legacy commuter lines. Paris is in a similar situation, except the legacy is more recent and evolved over a generation: plans for a circumferential line beyond the M2/M6 ring go back generations, but nothing was done until recently, and the first effort in that direction was the early tramways. So there’s an incomplete ring formed by T1 and T2, another incomplete ring formed by T3, and the under construction M15 ring, the M15 ring intersects the T1/T2 ring because the T1/T2 alignments were based on where convenient surface roads or rights-of-way were available.

That this is so common in the largest cities in the world does not mean it is good. Sound prior planning should figure out locations for such circles in advance. In the case of Paris, there could have been the M2/M6 ring, and then the T3 ring beyond it (as a subway, not light rail) replacing the closely parallel Petite Ceinture, which is no longer useful since the radial Métro lines don’t have stops at the correct locations, and then the M15 ring, and then the orbital tramways of the Grande Ceinture. But I’m not going to use the incompetence tag if in the 1980s a city isn’t sure what its rail network will look like in the 2030s.

In a way, it’s like missed connections between metro lines. It comes from bad planning. It’s hard to avoid – the largest metro network without missed connections is Mexico City, which is unusually poor in radial lines, and even networks that have very few of these, like Paris, Beijing, and Seoul, keep building more. Overlapping circles are likewise present in Tokyo, Moscow, and soon Paris, and absent in only one city with multiple circles, the near-tabula rasa Beijing. However, planners should still aim to avoid this network awkwardness, figuring out network designs well in advance that create neat radials with city center meets and concentric circles for circumferential service.


  1. Jacob Manaker

    If Moscow built Line 11 to be mainline-rail compatible, they could swap the south-bank lines. Then they’d have two concentric circles, touching at Khoroshyovo and Andronovka. Do you know why they aren’t doing that?

    • Eric2

      That would be worse. Then each line would have a big zigzag in it. This way, each line is pretty straight.

    • Tonami Playman

      Line 11 is being built to Metro standard and will use rolling stock of 2.69m width and 3rd rail, while Central Circle is using rolling stock of 3.48m and Overhead 3KV DC so it will be expensive to build a swap. But if they have the will it can be done though I don’t know if the benefit would outweigh the costs.

  2. Eric2

    I don’t see the issue. No grid is perfect, and overlapping rings like can also be part of a near-grid. Looking at the planned line 11 in Moscow (in dashed blue), there is no segment where it really qualifies as radial rather than circumferential. (By the way, interesting to see in that picture how the metro ends right at Moscow municipal boundaries, like NYC.)

    From a geometric perspective, it is possible to tesselate an area with either squares or equilateral triangles. Roads usually cover a region in squares in order to simply intersection design, but this reasoning does not apply to metro lines, where the “intersections” are pedestrian-only. A metro network is just as effective if the region is divided into triangles. Overlapping rings plus radials is one case where triangles tend to form in the network (a dense network of radials in the core is another such case). This is more effective, not less, in in providing for trips from anywhere to anywhere. In the final analysis, every region has significant geographic irregularities in land use and trip demand, and usually this will outweigh considerations of pure symmetry.

  3. Herbert

    Many cities built a circle line primarily for freight. That’s the origin of the Nuremberg Ringbahn and the outer ring in Berlin. The outer ring in Berlin has the added awkwardness of being inside city limits in the old east but bypassing them in the west because that was its purpose pre 1989. It is thus perhaps not surprising that most proposals for a second S-Bahn ring in Berlin go nowhere…

    Nuremberg has a ring bus (lines 35 and 65 which convert into one another at their nominal endpoints) along B4R which imho would work better as a tram, but Nuremberg is unreasonably tram hostile. Hamburg has weird circles in its heavy rail network which make no sense whatsoever. Copenhagen is building a ring tram through some of its “fingers” and there is the idea of building a second Öresund crossing at Helsingborg/Helsingor Which would then create a Malmö H-H Copenhagen ring… In Munich one of the alternative proposals to the second S-Bahn trunk was a ring https://de.m.wikipedia.org/wiki/M%C3%BCnchner_Ringbahn Which still has some local support and might be the easiest way to cut the travel time to the airport to non ridiculous levels…

    • Eric2

      It is really mind boggling how pretty much every city in the world, no matter how good at transit in general, manages to get some simple things completely wrong. Like unnecessary missed transfers. Or loopy lines from nowhere to nowhere.

      • Frederick

        It’s because a city is a growing organism. Why would a system built a century ago perfectly matches the demands of a century later?

  4. Tonami Playman

    I see an opportunity for Delhi to have two concentric circles, but it seems it will involve too much modification and costing too much. Looking at the Delhi metro map, They are in the process of completing the first circle closing the Pink line loop.

    The Magenta line could serve as an outer circle by taking over the southern Blue line branch after Botanical garden station. It would involve building a new 1.9km viaduct diverging from the current Magenta line alignment after AMITY Chowk following the northern boundary of Botanical garden park in order to approach Botanical garden station from the west and taking over the Blue line east of the station. It would continue through to Electronic city proceeding to make a second loop across northern Delhi.

    Then build a new 5km viaduct going through Dadri main rd and Jain rd linking the Blue line Botanical garden station to the Noida Sec 76 station on the Noida metro Aqua line. But then I realized that the Blue line is Broad gauge while both Magenta line and Aqua line are Standard gauge. If the gauges were not a hindrance, they would still need to extend the Aqua line platforms from 140m to 190m, but that seems like less of a hassle compared to fixing the gauge issue.

    • Eric2

      Platform length is not a hindrance at all, because in a city of Delhi’s size all platforms will eventually need to be long.

      In general Delhi Metro does lots of suboptimal planning though. Lines do a lot of meandering, which makes the trip speed inherently slow. There are at least 5 stub lines that end on the outskirts rather than reaching the city center. Lots of lines have L shapes which, in addition to the stub lines, means a ridiculously high number of transfers are necessary, and makes it difficult to propose sensible extensions (as you just found out). And of course Delhi’s land use and metro fare policies are horrible, but those are not really the subject of this post.

      (On the plus side, they are building a lot, they are building elevated which makes costs reasonable, and they have few if any missed transfers.)

  5. fbfree

    I don’t really see what’s wrong with the design in Moscow.
    1) Peakiness is a problem for radials that reach the city center. That’s not really the case here.
    2) Having connections between the two radial lines provides additional coverage for two-seat rides that concentric rings wouldn’t provide. This is not a problem for the inner ring, which would have no stations not at or near a radial connection, but it is a problem for outer rings which may have significant intermediate stops.
    3) This maintains consistency in the length of the ring lines, improving reliability vs. having a line be significantly longer than the other.
    This design also works well if the connection point can be at significant secondary nodes in the region.

    • Matthew Hutton

      The other thing is that the Tokyo loops make sense. Having a conventional rail connection in the Shingawa to Tokyo to Ueno corridor joins up most of Tokyo’s main stations for long distance travel – although nowdays mostly you’d just change at Tokyo main station to be fair.

      One of the big reasons Paris is shit to change trains at is the massively slow walking times at Gare d Nord and Gare d Montparnasse to get to the metro/RER.

  6. Pingback: The Limit of Circles in the Suburbs | Pedestrian Observations

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