Last week, I wrote about which regional rail lines should run local and express trains and which should only run locals. I gave various guidelines, specific to that mode of transportation. The same question makes a lot of sense for subways (or elevated lines), and is especially important for large cities building new metro networks, typically in developing countries. The key difference is that subway trains almost always run so frequently that the only way to have local and express services is to build four-track mainlines, like in New York. So really, this is a question about when it’s useful to build four-track subways instead of two-track subways.

Costs

The cost of a four-track subway is higher than that of a two-track subway. However, the difference depends on the method of construction. Cut-and-cover four-track subways do not appear to be much more expensive than two-track subways; in the 1900s, New York had little to no cost premium over London or Paris. The First Subway’s underground segments, slightly less than half of which are four-track, cost $39 million per km in today’s money, compared with about $29 million per km in Paris in the same era (see sources in this post). The Metropolitan line in London cost about the same: £1.3 million for 6 km in the early 1860s, or about $30 million per km.

In contrast, boring four tracks appears to cost twice as much as boring two. It’s hard to find examples, since four-track bores are extremely rare; the examples I do know, such as the East River Tunnels and the tunnel carrying the Lexington Avenue Line under the Harlem River, are short. There are bound to be efficiencies in engineering and sitework reducing the cost of boring, just as there are with cut-and-cover, but the majority of the cost of tunneling is the boring and the systems. The majority of the rest is stations, and the local stations can be built for not much of a premium over stations on a two-track line, but the express stations require considerably more excavation.

What this means is that cities that build cut-and-cover should probably aim to build four tracks rather than two. In retrospect, Paris should have built Metro Line 1 with four tracks: the narrowest street segment, Rue de Rivoli, runs for 3 km and is about 20-23 meters wide, which can take four tracks if there are only local platforms, and everything else is at least 30 meters and could take four tracks and express platforms. The only express station under Rivoli would probably be Chatelet, where there is a wide square where the station footprint could expand.

The question of whether to use cut-and-cover today is a separate issue. It’s easier for the first few lines than for subsequent lines, which have to cross under the old lines. Nonetheless, it’s still in use, for example in China; the lack of express tracks on Chinese subways has led to criticism on some railfan forums, particularly by Japanese railfans, who are used to the fast express trains of the JRs through urban areas. But in India, the longest underground segment in Delhi, on the Yellow Line, appears to be bored, running deep under Old Delhi. The one potential pitfall is that bored tunnels, while generally more expensive to construct than cut-and-cover tunnels if wide streets are available, are nimbler, making it easier to build lines to high standards, with wide curves.

Benefits

The two obvious benefits of express subways are speed and capacity. New York averages a decent speed, just under 30 km/h, buoyed by express trains that average about 36 km/h. When frequency on both the local and express tracks is adequate, which it regrettably isn’t most of the time in New York, it’s possible to use cross-platform local/express transfers to improve trip times even for people on the local stations.

The capacity benefits are sometimes compromised by transfers. In New York, the express tracks are consistently more crowded than the local tracks on the main lines, and the Upper West Side in particular sees the city’s most overcrowded trains on the express tracks run alongside the second least crowded on the local tracks. However, on the East Side, the local and express trains under Lexington are both quite full. The number of passengers they carry would overwhelm any two-track line: to carry the same number of passengers on just two tracks at the current peak frequency, each train would need about 2,100 passengers, more per unit of train floor area than the most crowded Tokyo Metro lines.

There are also indirect effect of four-tracking. The most distant stations are presumably express-only, or, if not, passengers will transfer to an express train at the first opportunity. This means that adding local stops does not increase trip times for passengers far out, which in turn argues in favor of tighter stop spacing on local trains, to provide more coverage. Evidently, New York has one of the smallest interstations (on local trains) of any major metro network in the world, surpassed only by Paris, which built the Metro without regard for the suburbs. Second Avenue Subway, built with just two tracks, has wider stop spacing than other Manhattan north-south mainlines, missing 79th Street, with the planned phase 2 stopping at 106th instead of 103rd and 110th.

Network effects

I have hammered repeatedly that metro systems need to avoid three pitfalls of network planning:

1. Tangential lines, starting as radial farther out but becoming circumferential closer in rather than staying radial and serving city center.
2. Reverse-branching: a common trunk in an outlying area splitting into branches in city center, the opposite of the more normal branching arrangement.
3. Missed connections, in which two lines intersect without a transfer.

It is easier to miss connections when the stop spacing is wider, because city centers are so small that line 1 can easily miss the road that line 6 will later run under. The Paris Metro has just one missed connection (M5/M14), and the city made a failed effort in the 1900s to bring Line 5 to what would be the transfer station, Gare de Lyon. New York has only two missed connections among the lines built from 1900 to the 1920s (Junius/Livonia on the 3/L, Bowling Green/Whitehall on the 4-5/RW), both of which are easy to fix; the city’s tens of misses come from a deliberate decision to avoid transfers in the lines built in the 1930s. Systems with wider stop spacing have more opportunities for missed connections, such as Tokyo, Shanghai, and Moscow.

Four-track mainlines short-circuit this problem doubly. First, fewer lines are required to provide the same coverage and capacity. On the eve of the Great Depression, New York had six subway mainlines, three with four tracks and three with two, and 2 billion annual riders. Even if a city insists that all transfer stations be express (which is the case in New York among lines built before the 1930s, though at one station express platforms were only retrofitted decades later), there are fewer potential intersections; at city center, even the express lines are unlikely to have very wide stop spacing.

Moreover, it’s fine to miss transfers on express lines. The reason missed connections are so bad is that the alternative option typically requires a three-seat ride. For example, the 1 passes between Columbus Circle-59th Street and 50th Street without a connection to the E train, leaving connecting passengers with one of two options: ride to Times Square and transfer there, which is both a detour and a very long walk between the platforms, or change to the B or D at 59th and then again to the E at 53rd; the latter option is the faster one, saving about 5 minutes of in-vehicle time and 3 minutes of transfer time.

But if one of the transfers is cross-platform, then a three-seat ride is less onerous. This is especially true if this transfer is local/express on a long shared trunk line, where the transfer stations usually don’t get as crowded as between two separate trunks. This means that it’s possible, if there is no better option, to have local-only transfers. Two of the top stations in New York, 53rd/Lex and Columbus Circle, are local-only transfers.

Scale

Small cities don’t need to think about express trains very much. Transit cities with about 2 million people in their metro areas, such as Vienna, Stockholm, Prague, Budapest, and Hamburg, make do with a handful of metro lines, sometimes supplemented by regional rail. But as they grow, the number of urban rail lines they need grows to the point that a coherent two-track network is too difficult, not to mention too slow. Paris manages to make do with the RER acting as the express layer, but outside India and Pakistan, cities that are just beginning to build their metro networks don’t have large legacy commuter rail networks to leverage for express service. In Africa between the Sahara and South Africa, nearly everything has to be built from scratch, and the same is true of Bangladesh and much of Southeast Asia and Latin America.

Moreover, in developing countries, a large number of cities either are megacities or can expect to grow to that size class soon. This is less true in Latin America, nearly all of which has at- or below-replacement birth rates, already high urbanization rates, and negative net migration (thus, the main case for four-track subways in Bogota hinges on the fact that the city has absurdly wide roads for cut-and-cover, not on future scale). However, in poor countries with high birth rates and low urbanization rates, cities can expect to increase their population many times over in the next few decades. Lagos and Dhaka are already huge, and midsize cities such as Nairobi, Kampala, Dar es Salaam, Addis Ababa, Khartoum, Accra, Abidjan, Douala, and Sanaa can expect to grow to that size class within a generation, as can midsize cities in countries with lower birth rates, such as Chittagong, Hanoi, and Ho Chi Minh City. In such cities, transportation planning should presume much greater scale than may seem warranted today.

A smaller-scale version of this principle can be found in cities that are growing rapidly due to immigration, especially Singapore but also Sydney, Melbourne, Toronto, Vancouver, and Stockholm. Such cities might want to consider infrastructure investments based not on their present-day population levels, but on those that they can expect after 30 more years of high migration rates. Vancouver and Stockholm are too small for express subways no matter what, and Toronto has already built its central spines with two tracks (and is upgrading its regional rail network to act as an express layer), but Singapore, Sydney, and Melbourne should all think about how to plan for the possibility that they will have 10 million people within 50 years.

I’ve discussed before the topic of missed connections on subway systems, both here and on City Metric. I’ve for the most part taken it for granted that on a rapid transit network, it’s important to ensure that whenever two lines intersect, they offer a transfer. This seems like common sense. The point of this post is not to argue for this principle, but to distinguish two different kinds of missed connections: city center misses, and outlying misses. Both are bad; if I had to say which is worse I’d say it’s the city center miss, but city center misses and outlying misses are bad for distinct reasons.

A useful principle is that every pair of rapid transit lines should intersect, unless one is a shuttle, or both are circumferential. If the city is so large that it has multiple circular lines at different radii (Beijing has two, and London vaguely has two as well depending on how one counts the Overground), then they shouldn’t intersect, but rapid transit networks should be radial, and every radial line should connect to every other line, with all radial-radial transfers ideally located within the center. City center misses weaken the network by making some radials not connect, or perhaps connect at an inconvenient spot. Outlying misses often permit more central transfers, and their problem is that they make it harder to transfer to the better or less crowded radial on the way to the center. London supplies a wealth of examples of the latter without the former.

What counts as a missed connection?

Fundamentally, the following picture is a missed subway connection:

The red and blue lines intersect without a transfer. Even if a few stations later there is a transfer, this is a miss. In contrast, the following picture is not a missed connection:

It might be faster for riders to transfer between the southern and western leg if there were a station at the exact physical intersection point, but as long as the next station on the red line has a transfer to the blue line it counts, even if the blue line has one (or more) stations in the middle. Washington supplies an example of this non-miss: it frustrates riders that there’s no connection between Farragut West and Farragut North, but at the next station south from the intersection on the Red Line, Metro Center, there is a transfer to the Blue and Orange Lines. London supplies another pair of examples: the Northern line and the Waterloo and City line appear to intersect the District line without a transfer, but their next station north from the physical intersection point, Bank, has an in-system transfer to Monument on the District.

There are still a few judgment calls in this system. One is what to do at the end of the line. In this case, I rule it a missed connection if the terminal clearly has an intersection without a transfer; if the terminal is roughly between the two stations on the through-line, it doesn’t count. Another is what to do about two lines that intersect twice in close succession, such as the Bakerloo and Hammersmith and City lines in London, and Metro Lines 4 and 10 in Paris. In such cases, I rule that, if there’s just one station on the wrong side (Paddington on Bakerloo, Mabillon on M10) then I rule it a single intersection and allow transfers at the next station over, by which standard London has a missed connection (Edgware Road has no Bakerloo/H&C transfer) and Paris doesn’t (Odeon has an M4/M10 transfer).

How many missed connections are there?

In Paris, there are three missed connections on the Metro there is one missed connection on the Metro (update: see comments below): M9/M12, M5/M14, M9/M14. As I discuss on City Metric, it’s no coincidence that two of these misses involve this miss involves Line 14, which has wide stop spacing. Narrow stop spacing makes it easier to connect within line-dense city centers, and Paris famously has the densest stop spacing of any major metro system. M9/M12 and M9/M14 morally should connect at Saint-Augustin and Saint-Lazare, but in fact there is no in-system transfer. M5/M14 should connect at Gare de Lyon, but when M5 was built it was not possible to get the line to the station underground and then have it cross the Seine above-ground, so instead it meets M1 at Bastille, while M14 doesn’t serve since it expresses from Gare de Lyon to Chatelet. A fourth missed connection is under construction: the extension of M14 to the north misses M2 at Rome, prioritizing long stop spacing over the connection to the M2/M6 circumferential.

In Tokyo, there are many misses. I am not sure why this is, but judging by line layout, Tokyo Metro and Toei try to stick to major roads whenever possible, to avoid tunneling under private property, and this constrains the ability of newer lines to hit station locations on older lines. If I understand this map correctly, there are 19 missed connections: Ginza/Hibiya (Toranomon and Kasumigaseki should connect), Ginza/Mita, Ginza/Yurakucho, Ginza/Shinjuku, Marunouchi/Mita (Ginza and Hibiya should connect), Marunouchi/Yurakucho, Asakusa/Yurakucho, Asakusa/Hanzomon, Hibiya/Namboku, Hibiya/Yurakucho (Tsukiji and Shintomicho should connect), Hibiya/Hanzomon, Hibiya/Shinjuku, Hibiya/Oedo, Tozai/Oedo, Tozai/Fukutoshin, Mita/Oedo, Chiyoda/Oedo twice, and Oedo/Fukutoshin. Oedo is particularly notable for being a circumferential line that misses a large number of transfers.

In New York, there are even more misses. Here the culprit is clear: the two older layers of the subway, the IRT and BMT, have just two missed connections. One, 3/L at Junius Street and Livonia Avenue, is an outlying miss. The other is central: Bowling Green on the 4-5 and Whitehall on the R-W should connect. But the newer layer, the IND, was built to drive the IRT and BMT into bankruptcy through competition rather than to complement them, and has a brutal number of misses: ABCD/2-3, ACE/1-2-3, AC-F/2-3-4-5, AC-G/2-3-4-5-BQ-DNR, BD/NQRW, BDFM/NQRW, BD/JZ, E/1, E/F, M/NW, R/7, F/BD-NQ, F/NRW, F-Q/4-5-6, F/NW, G/7, G/JMZ. Counting individual track pairs, this is 46 misses, for a total of 48 including the two IRT/BMT misses; I’m excluding local-only transfers, such as Columbus Circle and 53rd/Lex, and counting the 42nd Street Shuttle as an express version of the 7, so it doesn’t miss the BDFM transfer.

Finally, London only has eight misses. In Central London there are three: the Metropolitan or Hammersmith and City line misses the Bakerloo line as discussed above, and also the Victoria line and Charing Cross branch of the Northern line at Euston. The other five are outlying: the Central line misses the Hammersmith and City line at Wood Lane/White City, and its branches miss the Piccadilly line’s Uxbridge branch three times; the fifth miss is Metropolitan/Bakerloo. But one more miss is under construction: the Battersea extension of the Northern line is going to intersect the Victoria line without a transfer.

The difference between the two kinds of miss

Many misses are located just a few stations away from a transfer. In New York, some misses are just a station away from a transfer, including the G/7 miss in Long Island City, the E/1 miss between 50th Street and 59th Street, and several more are a few stations away, such as the various BDFM/NQRW misses. In London, these include two of the three Central London transfers: there is an H&C/Bakerloo transfer at Baker Street and an H&C-Met/Victoria transfer at King’s Cross-St. Pancras. As a result, not counting the Waterloo and City line, only two trunk lines in the system do not have any transfer: the Charing Cross branch of the Northern line and the Metropolitan/H&C line.

On a radial network, if two lines don’t have any transfer, then the network is degraded, since passengers can’t easily connect. In New York, this is a huge problem: some station pairs even within the inner networks require two transfers, or even three counting a cross-platform local/express transfer. My interest in subway networks and how they function came about when I lived in Morningside Heights on the 1 and tried socializing with bloggers in Williamsburg near the JMZ.

In Paris the three misses are also a problem. Line 4 is the only with a transfer to every other main line. Line 9 intersects every other line, and Line 14 will when its northern extension opens, but both miss connections, requiring some passengers to take three-seat rides, in a city infamous for its labyrinthine transfer stations. Fundamentally, the problem is that the Paris Metro is less radial than it should be: some lines are laid out as grid routes, including Lines 3, 5, and 10; moreover, Lines 8, 9, 12, and 13 are radial but oriented toward a different center from Lines 1, 4, 7, and 11.

In London, in contrast, there is almost no pair of stations that require a three-seat ride. The Charing Cross branch of the Northern line doesn’t make any stop that passengers from the H&C or Met line can’t get to from another line with one interchange (Goodge Street is walking distance to Warren Street). A bigger problem is the lack of interchange to the Central line on the west, which makes the connections between the H&C stations on the west and some Central line stations awkward, but it’s still only a small number of stations on each line. So the problem in London is not network robustness.

Rather, the problem in London is severe capacity limitations on some lines. Without good outlying interchanges, passengers who want to get between two lines need to ride all the way to the center. Most likely, passengers between the Piccadilly and Central line branches to the west end up driving, as car ownership in West London is relatively high. Passengers without a car have to instead overload the Central line trunk.

The same problem applies to misses that are strictly speaking not missed connections because the two lines do not actually intersect. In Paris, this occurs on Line 7, which swings by the Opera but doesn’t go far enough west to meet Lines 12 and 13. In London, the best example is Hammersmith station: the H&C and District lines have separate stations without an interchange, but they do not intersect since it’s the terminus of the H&C line and therefore I don’t count it as a miss. But morally it’s an outlying miss, preventing District line riders from changing to the H&C line to reach key destinations like Euston, King’s Cross, and Moorgate without overloading the Victoria or Northern line.

In New York this problem is much less acute. The only outlying misses are the 3/L and the ABCD/2-3; the 3/L connects two very low-ridership tails, so the only serious miss is on the Upper West Side. There, passengers originating in Harlem can walk to either line, since the two trunks are two long blocks apart, and passengers originating in Washington Heights can transfer from the A-C to the 1 at 168th Street; at the other end, passengers bound for Midtown can transfer at Columbus Circle, using the underfull 1 rather than the overcrowded 2 and 3.

The role of circumferential lines

Outlying transfers are useful in distributing passengers better to avoid capacity crunches, but they are incidental. They occur when formerly competing suburban lines get shoehorned into the same subway network, or when two straight roads intersect, as in Queens. But the task of distributing passengers between radial lines remains important and requires good connections between as many pairs of radials as possible.

The usual solution to this is a circumferential line. In Moscow, there are several missed connections in the center (Lines 3/6, 3/7, 6/9) and one more planned (8/9), but the Circle Line helps tie in nearly all the radii together, with just one missed connection (to Line 10 to the north) and one more under construction (to Line 8 to the west). The point of the Circle Line is to allow riders to connect between two outlying legs without congesting the center. This is especially important in the context of Moscow, where there are only a handful of interchange stations in the center, most of which connect more than two lines.

In London, the Overground is supposed to play this role. However, the connections between the Underground and Overground are weak. From Highbury and Islington clockwise, the Overground misses connections to the Central line, the Victoria line, the main line of the District line, the Piccadilly line, the Hammersmith and City line, both branches of the Northern line, and the Piccadilly line (it also misses the Metropolitan line, but that’s on a four-track stretch where it is express and local service is provided by the Jubilee line, with which there is a transfer). Much of this is an unforced error, since the Underground lines are often above-ground this far out, and stations could be moved to be better located for transfers.

In New York, the only circumferential line is the G train, which has uniquely bad transfers, legacy of the IND’s unwillingness to build a system working together with the older subways. Triboro RX (in the original version, not the more recent version) would play this role better: with very little tunneling, it could connect to every subway line going counterclockwise from the R in Bay Ridge to the B-D and 4 at Yankee Stadium. On the way, it would connect to some major intermediate centers, including Brooklyn College and Jackson Heights, but the point is not just to connect to these destinations in the circumferential direction but also to facilitate transfers between different lines.

Going forward, cities with large metro network should aim to construct transfers where feasible. In New York there are perennial proposals to connect the 3 and L trains; these should be implemented. In London, the missed outlying transfers involve above-ground stations, which can be moved. The most important miss, White City/Wood Lane, is already indicated as an interchange on the map, but does not to my understanding have an in-system transfer; this should be fixed.

Moreover, it is especially important to have transfers from the radial lines to the circumferential ones. These improve network connectivity by allowing passengers to change direction (from radial to circumferential, e.g. from east-west to north-south within Queens), but also help passengers avoid congested city centers like outlying radial-radial transfers. Where circumferential lines don’t exist, they should be constructed, including Triboro in New York and Line 15 in Paris; where they do, it’s important to ensure they don’t miss connections the way the Overground does.