# Moscow: Questioning the Circle Line

Frequent commenter Alon Levy found a glossy English-language PDF (part 1, part 2) from Moscow’s Metro, showing off the latest stations and performance statistics. He has a question about the Circle Line:

The circular line is not well-patronized by local standards. It ranks 6th out of 11 in ridership. Its problem, I think, is that its radius is too small; it was built as a reliever for the central radial/radial transfer points, but is not as useful by itself. This is different from the Yamanote and Oedo Lines and especially Seoul’s Line 2, which are really multiple lines joined together as a circle.

Do you think my explanation here is correct? Or could there be other factors why some circular lines work better than others?

First things first:  ranking 6th out of 11 in ridership is a meaningless statistic.  All that matters is ridership per unit of service (e.g. per train hour) if you want to evaluate the use of the service itself.  You can also talk about ridership per route km or per station if you want to evaluate the use of the infrastructure.  Ridership figures mean something only when compared to some unit of investment, or when compared to the same service in a different time period.  Transit lines are of vastly different sizes and scales, so the ridership on a transit line means nothing when compared directly to any other transit line.

As usual, you can find lots of cool maps of the Moscow Metro with a touch of Googling.  I like this one.  But the short answer to Alon’s question is this:  Wikipedia gives the circumference of the Circle Line as 19.3 km.  Let’s imagine for simplicity that the line really is an exact circle, and look at the geometry.

A circumference of 19.3 km gives us a diameter of 6.1 km.  So the longest one-way trip you could want to make on the Circle line is 6.1 km linear distance away, though via the Circle Line it’s 9.15 km (half the circumference).  Many of those trips, though, are served more directly by one of the many radial lines, most of which flow through across the city.

So note one geometric challenge of any circle line:  Nobody will ever want to ride more than half of it, because if you ride more than halfway around the circle, the trip would have been shorter if you’d ridden the line the other way.  By contrast, all of the radial lines of the Moscow Metro are useful for long trips as well as short ones.

This is actually a corollary of an even more basic piece of transit geometry, which is that if you imagine an area of even density, the transit line that will cover the largest area with the smallest number of line-km is a straight line, not a curved or bending line.  A straight line also has the unique feature of being the shortest path between any two points on the line, whereas a curved line is always longer than the shortest path.

So the Circle Line will never be ridden more than 9.1 km.  When it is ridden 9.1 km, it will be for the purpose of going a linear distance of only 6.1 km.  That suggests to me that with some armwaving, the dominant tripmaking on the Circle line is probably trips of 3-6 km.  (Less than 3 km, your trip is often faster via surface transit, or even by walking, because of access time at subway stations.)

That’s pretty short, a lot shorter than the average trip on most systems, and I bet it’s a lot shorter than the average trip on Moscow’s radial subway lines.

So yes, successful circle lines (like London’s and Tokyo’s, and the one that Montréal is planning) are much larger than Moscow’s, so that even a trip around 1/4 to 1/3 of the arc of the circle is a fairly long corridor, usually 10 or more stations, which is the most direct link between all of those stations. On Moscow’s 11-station Circle Line, 5 stations is halfway around the loop, so you’re likely to be using the line to go only 2-4 stations.  That’s a pretty limited market for a single direction of a subway line.

And remember, this basic geometry is true of circular surface transit too, whether bus or rail or tram, though surface transit requires less access time than subways and therefore can be useful for shorter trips, thus justifying smaller circles.

### 16 Responses to Moscow: Questioning the Circle Line

1. Brent September 2, 2010 at 9:09 pm #

Interestingly, circle lines (a.k.a. ring roads, beltways, etc.) are much more common for highways than for transit infrastructure, and I believe that relates to a number of critical differences between driving / highway operations and transit ridership.
A highway beltway is commonly used to provide a shorter trip, either because it is actually a shorter distance, or because it provides additional capacity around an area where congestion has slowed travel speeds.
A transit circular route is less likely to result in a shorter travel time. For one thing, for many trips you incur a transfer penalty (which is generally not a factor for road users). Secondly, subway routes don’t generally tend to have the same increase in delay in congested conditions that automobiles do (and have a much higher capacity), so there’s little opportunity for time savings in bypassing busy areas. If anything, busier lines result in higher frequencies and shorter waiting times.
A third factor might be that transit trips generally tend to be more core-oriented, as opposed to “through” highway trips that would be more predisposed to avoid the core if possible.

2. Alon Levy September 2, 2010 at 9:31 pm #

I forgot to mention something else in my email: Moscow Metro has very long interstations – 1.7 km on average, versus 1.1-1.3 in Tokyo, Seoul, and London. This means that the station access time issue is a bigger problem in Moscow. I think your way of thinking about it, in terms of number of stations, is the best.

3. Joseph E September 2, 2010 at 10:31 pm #

“Ridership figures mean something only when compared to some unit of investment, or when compared to the same service in a different time period.” Good point, Jarrett
For Moscow, we can compare the Circle Line (12 stations, 19.3 km) to the system as a whole (182 stations, 301 km). The Circle Line had 8.4 percent of total system ridership, on average, in 2006, according the the linked document (see page 24): http://www.mosmetro.ru/files/490452881469473dab5b7d/2006en-1.pdf
This 8.4% of ridership compares to 6.6% of total system stations, and 6.4% of total station kms (miles). So the average circle line station has above-average patronage, and each km of track is used more than average. I think that is pretty good performance for a line that mainly connects other lines.
Perhaps having the Circle Line at such a short radius (3 or 4 km) from the center of the city makes it close enough to be in the high-density area of employment and residence, increasing ridership compared to what you might expect. I would imagine that central-city stations on the radial lines would be even busier, but I’m not sure if that information is available.

4. ant6n September 2, 2010 at 10:31 pm #

More successful circle lines: Madrid’s circle line (23.5km, 28stops) is one of the busiest in the system. Berlins circle line (37.5km/27stops) is also very successful (400k daily riders), and one of the backbones of the system.
It seems ring lines, if sufficiently large, can be really useful. It sometimes seems that you don’t give these lines enough credit.
On a side note, I disagree that one should measure the success in passengers per train-km. That would mean that you just have to run fewer trains on your line to make them more succesful, by forcing everybody in the same vehicle. I think there exist different metrics, and they all have to be understood in context.

5. anonymouse September 2, 2010 at 11:03 pm #

When the Circle Line was being planned, Moscow was a much smaller city, so it was a rather more useful idea when it was built in the early 50s. It was also designed to link almost all of Moscow’s rail terminals (it hits 7 of the 9, and provides access to all suburban mainlines). But yes, geometry does work against it: it’s only faster to go via the circle if the transfer in the city center will have you double back, so most trips would be short (only 1/4 circle). The other case where it’s useful is when there’s no direct connection between a pair of lines. Anyway, success is relative: every weekday, it carries just slightly fewer passengers than the entire Washington Metro.

6. GD September 3, 2010 at 2:51 am #

another way to provide circular service is to have two lines do the job. If you look at this map of Vienna’s subway service at
you will see how the green U4 line creates two circles – one with purple U2, and one with brown U6. These two circles run more or less alongside two ring-like roads – the Ring delineating Vienna’s historic center, and the “Gürtel” (i.e. “belt”-street) bordering the inner districts.
As in the case of Moscow, the subway’s layout mirrors the historical development of the city’s shape, and has arguably not quite caught up yet. Transdanubia is something of an afterthought, only served by parts of U6, U1 (red), and–soon–U2. Yet connections between the transdanubian parts of the subway system are few and not too frequent — it’s all focused on shuttling people across the danube, and into the center.

7. Peter Parker September 3, 2010 at 3:17 am #

I’m not sure of Moscow’s density patterns as one moves from the CBD, but if it’s like many cities I suppose there’s a trade off between (i) higher density, (ii) shorter line length, (iii) greater car traffic volumes (which would favour a closer-in line), versus (iv) time saved for cross-suburban trips and (v) accommodation for suburban growth, which would favour a line with a larger radius.
As a comparison, Melbourne’s first and busiest orbital SmartBus route (903) is an average 10-20 km from the city (Melbourne is lopsided towards the east). The second one (902) is 20-25km out on average, while the third (to start in a few weeks) averages 25 – 35km out. Average speeds are likely to be highest on the most outer route, but the trip generators are generally a bit further apart.
PS: Welcome to Melbourne, and note that you will be catching up with Chris and Scott (amongst others)!

8. Tom West September 3, 2010 at 6:21 am #

Brent’s comparison between subway/transit oribital lines and highway oribital roads is an interesting one. I think the main difference is that oribital transit liens are generally aimed at those travelling *within* the city, just not via the centre, while orbital roads are aimed more at those travelling *around* the city (hence why they often have “bypass” in their name).
In any transit system, trips with origin and destination both outside the main city and on opposite sides are rare, so transit routes tend not to be aligned that way. Actually, it’s a vicious circle, with lack of trips causing a lack of service, which causes a lack of service.
Roads can support cross-city trips, because once you build a road, the capacity is always there, so you can use the road in the counter-peak direction: counter-peak direction capacity in the AM peak is the same as peak direction capacity in the PM peak.
By contrast, transit capacity is based on vehicles, so counter-peak direction capacity in the AM peak is generally less than peak direction capacity in the PM peak.
If one considers passenger rail systems, even if counter-peak service is provided, it generally requires a connection in the city centre – sometimes with more than one station involved (Boston and Glasgow spring to mind). Even where through trains are available (e.g. Toronto’s Lakeshore lines and London’s Thameslink services), most routes still terminate in the city centre.

9. Tom West September 3, 2010 at 6:23 am #

Technical issue: clicking on the map to bring up a larger version produces a window without scrollbars, so you can’t see the bottom of the map.

10. Sean September 3, 2010 at 10:11 am #

Alan Levy commented: I think, is that its radius is too small; it was built as a reliever for the central radial/radial transfer points, but is not as useful by itself.
But the role of relieving the central portion of the network could justify the line all on it’s own. To measure the success of the line, you’d have to measure not just the ridership of the line itself but also the additional rides that were made possible on the central portion of the network.

11. EngineerScotty September 3, 2010 at 10:16 am #

One thing interesting about the line–it doesn’t appear to have any stops other than at transfer points to other lines. And most of the major through lines in the system have a transfer point somewhere downtown (the exception appears to be the dark and light green lines). For many trips between one radial line to another–is it more convenient to just go downtown and transfer once, or to transfer to the circle line and then to the line you are trying to reach?

12. Zoltán September 3, 2010 at 1:14 pm #

On largely radial networks, it’s nearly always quicker to interchange in the centre of the city, as the radials tend to have the best frequency, and crucially, because it involves one interchange instead of two. While this is true for metro systems, it is a particular problem for bus networks, with their lower frequency and in some cases greater transfer penalty.
The one exception to this is when the orbital route (be it a full or partial circle) links a number of important custom generators, and therefore a single interchange to the orbital will take you to your destination. For example, the very successful 550 orbital route in Helsinki and Espoo, runs well-loaded buses every 5-10 minutes, and manages this because it serves a number of important district centres and employment areas, and does so at the cost of being very far from a perfect circle.
On the opposite extreme, the 8/9 outer ring buses in Leeds sticks to the outer ring road for more or less its full length, and apart from two large shopping centres that happen to be on that ring road, largely serves only desolate bus stops a few yards from those of intersecting bus routes and low density suburbia, and runs empty buses every hour.
So the prerequisite of a successful orbital route should be that it serves a lot of custom generators directly, as it won’t be much use purely on the merit of interchanges. I would guess that the Moscow Metro’s circular line serves some useful places by itself in order to get that 8.4% of total system usage quoted by Joseph E. When designing orbital routes, it is therefore less about abstract notions of the correct radius, and more about the best way to link radial routes to important origins and destinations outside of the centre of a city.

13. Peter Parker September 3, 2010 at 3:54 pm #

Zoltan – a very good point – transit seems to work best if it can cater for a variety of purposes. Hence the circle bus routes in Melbourne and Perth (which both run to a 15 min weekday/30 min weekend frequency) follow this principle and are extremely successful.

14. Jarrett at HumanTransit.org September 3, 2010 at 4:25 pm #

Peter.  Yes, and Brisbane's Great Circle bus line would do well also, if they'd run it a little more frequently.   Sydney also has a very successful half-circle frequent bus line, the 400.

15. Anandakos February 9, 2011 at 7:14 am #

“So the prerequisite of a successful orbital route should be that it serves a lot of custom generators directly”.
Zoltan’s point is true of ANY transit line, radial or circular. Even though it costs more, transit should penetrate the core of activity centers. Anything else is a waste of the public money.

16. Viz August 20, 2011 at 12:11 pm #

Its not exactly a prerequisite if it is planned together with urban activity developments. In the case of Madrid, the circular line joined some pre-existing points of attraction, such as the uni campus and several non-central commercial areas (population density in Madrid is high all over, so there are many commercial streets far from the CBD) but other points like bus and train stations were created along with it.
An orbital line is a useful tool to connect all lines to points like transport hubs which are better located at the start of motorways and not in the central core in European cities.
Also, the line borders the outside of what could be considered the ‘inner city’ (although like I said density remains high outside). In this outer line is where a lot of the not-so-cost-efficient activity takes place: the inner city becomes more commercial towards the centre as land prices increase and only direct commercial activity is worth the cost; so offices, hospitals, sports facilities or council and government branches are in many cases located towards the inner-city’s outer border, where land is not so highly priced yet location is still advantageously central, and there are also wider roads, more parking space, etc.
Some of these activity areas already existed and others developed after, but the existence of the line helped them all grow.
Also, some of the intermediate stops along the line provide metro stations for residential areas, especially in the South, which would otherwise have no service as the distance between radial lines increases as you move further from the center.
The circular line has proved so useful in aiding the constitution of an activity net (as opposed to activity happening only in unrelated radial corridors) that as the city has grown many have expressed the desire that a further outer arc should be created for the same purpose.
As a final point of note, the commuter rail system in the Madrid metropolitan area has another loop on the West and a lasso on the East. Also, 5 large suburban cities in the South of the metropolitan area have a circular metro line connecting them, besides the metro and train lines connecting them to Madrid.