Quick Note: U-Shaped Lines

Most subway lines are more or less straight, in the sense of going north-south, east-west, or something in between. However, some deviate from this ideal: for example, circular lines. Circular lines play their own special role in the subway network, and the rest of this post will concern itself only with radial lines. Among the radials, lines are even more common, but some lines are kinked, shaped like an L or a U. Here’s a diagram of a subway system with a prominently U-shaped line:

Alert readers will note the similarity between this diagram and my post from two days ago about the Washington Metro; the reason I’m writing this is that Alex Block proposed what is in effect the above diagram, with the Yellow Line going toward Union Station and then east along H Street.

This is a bad idea, for two reasons. The first is that people travel in lines, not in Us. Passengers going from the west end to the east end will almost certainly just take the blue line, whereas passengers going from the northwest to the northeast will probably drive rather than taking the red line. What the U-shaped layout does it put a one-seat ride on an origin-and-destination pair on which the subway is unlikely to be competitive no matter what, while the pairs on which the subway is more useful, such as northeast to southwest, require a transfer.

The second reason is that if there are U- and L-shaped lines, it’s easy to miss transfers if subsequent lines are built:

The purple line has no connection to the yellow line in this situation. Were the yellow and red line switched at their meeting point, this would not happen: the purple line would intersect each other subway line exactly once. But with a U-shaped red line and a yellow line that’s not especially straight, passengers between the purple and yellow lines have a three-seat ride. Since those lines are parallel, origin-and-destination pairs between the west end of the purple line and east end of the yellow line or vice versa require traveling straight through the CBD, a situation in which the subway is likely to be useful, if service quality is high. This would be perfect for a one-seat or two-seat ride, but unfortunately, the network makes this a three-seat ride.

The depicted purple line is not contrived. Washington-based readers should imagine the depicted purple line as combining the Columbia Pike with some northeast-pointing route under Rhode Island Avenue, maybe with an additional detour through Georgetown not shown on the diagram. This is if anything worse than what I’m showing, because the purple/red/blue transfer point is then Farragut, the most crowded station in the city, with already long walks between the two existing lines (there isn’t even an in-system transfer between them.). Thus the only direct connection between the western end of the purple line (i.e. Columbia Pike) and what would be the eastern end of the yellow line (i.e. H Street going east to Largo) requires transferring at the most crowded point, whereas usually planners should aim to encourage transfers away from the single busiest station.

When I created my Patreon page, I drew an image of a subway network with six radial lines and one circle as my avatar. You don’t need to be a contributor to see the picture: of note, each of the two radials intersects exactly once, and no two lines are tangent. If the twelve ends of six lines are thought of as the twelve hours on a clock, then the connections are 12-6, 1-7, 2-8, 3-9, 4-10, and 5-11. As far as possible, this is what subway networks should aspire to; everything else is a compromise. Whenever there is an opportunity to build a straight line instead of a U- or L-shaped lines, planners should take it, and the same applies to opportunities to convert U- or L-shaped lines to straight ones by switching lines at intersection points.


  1. SC

    How much do you expect ridership to grow on the Rockville/Bethesda section of the Red Line if it terminated at, say, Branch Avenue instead of Glenmont? It can be hard to finance major physical plant construction to change service without being able to justify that it would increase ridership.

    • Alon Levy

      What I’m proposing is to send the Red Line to Largo, not Branch Avenue. And I think of the resulting O&D pairs, Silver Spring-Alexandria is the strongest, much more so than Bethesda-Largo or (if there’s no swap) Alexandria-Largo.

      • Devin

        Useful question tho; if orange line service increases by ~40% (ie, ~10 trains/hr at peak) due to better utilization, what ridership gains should we expect?

        I don’t really have a good baseline for this but you might have thought about it in this or other contexts!

        • Devin

          (i guess this particular Q might have been more appropriate for the other thread sorry!)

        • Alon Levy

          So, Orange and Silver Line frequency today is 7.5 tph peak, 5 off-peak. With unbranching, it should be easy to get up to 15 tph peak, and then off-peak frequency depends on how much you value base frequency but probably 8 is absolute minimum, and 10 is better. 7.5 tph vs. 15 has meaningful impact on ridership, but I’m not sure how much; naively the worst-case scenario for travel time is a 4-minute difference, so it could be like a 4-minute improvement in travel time, which is pretty substantial on an urban subway (Vienna-Farragut is 31 minutes). Off-peak the impact is of course much larger.

  2. newtonmarunner

    Thanks, Alon, for this.

    I assume NYC is a special case for the “L” shaped rule. Otherwise, if L shaped lines are prohibited (e.g., E) some of those Queens-Manhattan trunk lines would end up in Jerz. …

    For DC, I’d like to do east-west (E-W) and north-south (N-S) lines with the E-W line starting in NoVA going through C St. hitting Federal Triangle, Archives, 3rd and C, and somewhere on new mythical Red Line up to NE DC and the N-S line from SE DC hitting (maybe Navy Yard), Federal Center SW, 3rd and C, Judiciary Sq., McPherson Sq. and Columbia Heights, continuing on 14th St. What are your thoughts on that? Too much stress on the Orange Line getting to Farragut and Foggy Bottom from the eastern side?

    • Alon Levy

      New York should have built the east-west lines across Manhattan to New Jersey (Hudson County and Newark were big even in 1900), without any awkward Queens-Manhattan-Brooklyn patterns. But between the branching (which makes it hard to break lines without breaking transfers) and the sheer number of routes, I think fixing the problem is too difficult.

      • newtonmarunner

        Except back in 1900-1910, iirc, FiDi — not Midtown — was thought to be NYC’s CBD. So Queens to FiDi was thought to be a radial line at the time the subway was being built. Obviously now with 10.5-11 trunk lines (depending on how you count Flushing) in Midtown and 40-60 percent of that in FiDi, things have changed: Midtown is the CBD while FiDi is a secondary destination. None of this could have been predicted, though.

        I agree that getting rid of the L shaped lines in NYC — with NYC’s massive branching and express subway lines — would be incredibly difficult to do. You’d have to start with eliminating the unconventional interlining, which alone would politically take 20 years to do (even though allowing conventional branching only would increase headways on all tracks — and therefore capacity — by 20-50 percent). See DeKalb as an example. And add 5-9 line regional rail for more paths to job clusters. Then you could take the Queens-Manhattan tunnels to Jerz (though you could do 42nd St. right now). But I could see the political outcry of Queens residents having to give up some of their 1-seat rides to parts of Midtown and have 3-seat rides to Fidi (though with one having a cross-platform transfer) for Jerz to get subway coverage. …

      • SC

        East-west lines to New Jersey WERE built under the Hudson River as the Hudson & Manhattan Railroad, which is now operated as the PATH system. The reason why fewer tunnels were built under the Hudson River to New Jersey, then and now, was that construction under the river was difficult and expensive; construction of the H&M tunnels underneath the river had stopped for three decades after dozens of deaths before tunneling technology had improved enough to complete the tunnels in 1907. By then, the first north-south IRT subway line had opened to much greater success and demand, hence why more north-south subway lines were built.

        • Alon Levy

          They were built from Jersey to Manhattan, but then turned around rather than going east to Brooklyn and Queens. This is not about construction difficulty – the East River is almost as wide as the Hudson, and hosts 4 subway tunnels to Queens and 6 to Brooklyn.

          • SC

            The East River is about half as wide as the Hudson, and it has fewer bureaucratic and logistical hurdles to clear for construction (for instance, only one municipality is involved). As much as you can plot an “ideal” design, you can’t actually build anything without clearing the bureaucratic and logistical hurdles. And no, those bureaucratic and logistical issues cannot be solved by advocacy alone.

  3. Ikram

    The design you suggest sounds like the standard model for Soviet subway systems (and CIS, post Soviet). Three lines forming a triangle in the city centre. A circle line where warranted (only moscow).

    I haven’t seen any commentary by you on the Soviet model, but it seems you wound up in the same spot, by accident or design .

    • Untangled

      That triangle thing you speak of can also be found in Prague and Budapest. I’m not so sure about others but there could be more. Alon’s map for me doesn’t look like them to me though.

      It looks a bit like Vienna U-Bahn map to me for some reason though. I can’t pinpoint why. Vienna does have a U-ish line and another that looks like it’s ready for a U-shaped extension.

    • Eric

      That’s not Soviet-specific, it’s logical for anywhere. When you have 2 lines, they cross in the city center. When you have 3 lines, they also all go to the city center. But rather than intersecting at one station, they intersect at 3 separate stations. That has 2 benefits: more downtown area has access to multiple subway lines, and the transfer volume is split across 2 stations for each line, minimizing delays.

      Most Western systems have a too complicated history to get this shape (less top-down planning than in Eastern Europe), or else they have many more than 3 lines. However, newly planned mid-sized Western systems do have similar structure. Munich for example has a 3 line triangle, with each line having 2 branches, and some of the branches crossing each other in the outskirts. Washington DC itself is a 3 line triangle – Metro Center, Gallery Place, L’Infant – but the Yellow and Blue Line branches, rather than crossing in Virginia, are interlined in Virginia.

      • Ikram

        It may be a logical design, but seems more common in the Eastern block systems.

        For example, several newer metro or light metro systems in Canada ( Calgary, edmonton, ottawa), — none of them have a three line triangle system planned. In contrast, similar sized cities in Russia (Samara, Kazan, Yekaterinburg) have a triangle in mind, even if they are only starting with one line.

        If its so logical, why don’t we see it more?

        • Alon Levy

          Vancouver is eventually getting there with the UBC extension, Singapore has this system (ignore the North-South Line’s bend to the west to hit Jurong East and just focus on the NS/EW/NE lines), Boston’s first three lines have this system, and Washington and Milan’s first three lines more or less already have it. If you allow all three lines to meet at the same station (as the first three lines in Moscow do!) then add Stockholm.

          Oh, and I forgot: Prague has this system, too; it’s Eastern bloc, but the plans predate communism.

          • Untangled

            Vancouver’s one will look like one big triangle, usually, it’s contained within a smaller, more central area.

            I think Delhi Metro has a triangle too at Rajiv Chowk-Mandi House-Central Secretariat, though that one looks a bit funny on a geographically accurate map. I guess the Kashmere Gate-Rajiv Chowk-Mandi House one is also technically a triangle, but a bigger one. Two triangles right next to each other, not bad.

        • SC

          This blog harps so much on circumferential lines, but it’s interesting that a triangular system is pretty much a circle made of three points around the city center.

  4. Diego Beghin

    Barcelona also has weirdly shaped lines. Line 3 makes a U-turn in Drassanes, Line 5 U-turns at La Sagrera, and Line 4 makes an incomplete circle around the Eastern part of the city. It’s also common for two lines to meet tangentially. It’s true that Barcelona has a tricky geography with hills which get in the way of straight metro lines.

    They appear to be solving these problems by building new lines, when lines 9 and 10 are complete, they’ll provide a direct east-west service in the north between La Sagrera and the main university campus.

    • Diego Beghin

      As for DC, the red line is baffling. Was there really no compelling destination in Maryland to send line to? Or was more of a funding/political issue?

      • Eric

        From what I remember, the initial plans were different, and yes it was funding/politics that led to things being constructed the way they are.

      • Alon Levy

        What I read on the internets is that when the Washington Metro was first planned, they had four outer ends in mind, corresponding to the outer ends of the Red and Blue Lines; they had the two lines meeting at Metro Center and Farragut, but didn’t make much of an effort to have lines cross properly since the point was to get people from the suburbs to city center. The final decision came because it was easier to build the lines the way they currently are at Farragut than to cross them. They don’t even have a transfer at Farragut because building one would’ve required moving the statue and the relevant government agency flipped.

        • newtonmarunner

          I think the environmentalists objected to a Farragut transfer because of some historic trees that would have had to have been destroyed.

          WMATA was modeled after BART — a hybrid local subway/regional rail system. Back in the olden days, the buses would take people directly from South Fairlington (in Arlington) where my dad grew up directly to the CBD. Traffic wasn’t bad back then, so this wasn’t a horrible ride. Now everybody in NoVA on Metrobuses is dropped off at the Pentagon. [For a lot of military families, this isn’t too bad, and many when I was growing up made NoVA — particularly off 236/Braddock Road in Annandale (where I grew up) — their home.]

          I’ll stop there.

        • newtonmarunner

          Forgot, Metro to Dulles was part of the original dream. Now doing it will result in a disaster. Either the project will (1) have ridiculous capital and operating costs per rider as nobody will take it (given how long and expensive the commute will be) or (2) exacerbate the Orange Crush as commuters won’t even be able to board as far out as East Falls Church.

  5. rewenzo

    I assume this criticism of U lines doesn’t extend to Toronto’s Line 1. It’s a literal U – shape, but if the Yonge and University lines kept going down Yonge and University they’d hit the lake in a couple of blocks. So really, they’re just two parallel radial lines that go all the way downtown with through service at Union.

  6. Alex B.

    Thanks for addressing this, Alon.

    I’m sold on the idea that a U-shaped line is less than ideal when planning. And in the situation for Washington, I’d get your proposal for rectifying the situation if you were starting from scratch. However, what I’m curious about is weighing the benefits of changing (at great cost and with great disruption) an existing service instead of just adding to the network.

    In your proposal for DC, you seemed to go to great lengths to minimize cost and minimize tunneling, yet shifting the Red Line to run under H Street NE would be extraordinarily disruptive and costly (as opposed to just leaving the Red Line as-is and building a new east-west line under H Street with a transfer to the Red Line). What’s the tipping point for that tradeoff between the costs and benefits?

    • newtonmarunner

      Then the question comes to where would you put the H St. Line to the West (and the East)? How will this new H St. line connect to the rest of the system? How will the new H St. Line connect to the new Green and Yellow lines (assuming it still takes over the Blue Line east of the Anacostia River)? If you’re not using legacy tracks (e.g., the Red and Blue Lines as Alon does), then you’re going to be laying down even more concrete — and having to tunnel either by Farragut or by L’Enfant, in order to connect to the rest of the system — which will be even more expensive than a simply H St. tunnel that uses Red (west side) and Blue line (east side) legacy tracks, and may not even connect with the rest of the system (read: doing less). Alon’s plan is doing the most with the least amount of resources.

      • Alon Levy

        What he’s counterproposing is the same as my plan but without switching the Red and Yellow Lines at Union Station. So, no touching the Red Line, and a Yellow Line tunnel from L’Enfant to Union Station and thence under H Street to the Largo branch. This means tunneling under the Union Station tracks, but that’s necessary either way. The savings in what Alex is proposing come from not having to build turnouts on the Red Line, to break it apart (but one of the two sets of turnouts is probably doable above ground…).

        • Alex B.

          Yes, Alon – that’s it.

          You’ve sold me on the problems with the U-shaped Red Line. But correcting that issue now would be extremely costly, and I’m curious what the breaking point is for when doing so would be worth it. The Red Line’s routing is a sunk cost at this point.

          This is admittedly a bit of a rhetorical question; but the nature of adding turnouts to tunnels that were never designed for that seems both costly and disruptive.

          • Alon Levy

            I don’t have a cost breakdown, but I know it was done frequently in the past. Toronto did it when it established the two-line system, replacing the old Y (consisting of both halves of the Bloor-Danforth line and Yonge-University, before the Spadina extension was built). Paris did it frequently on the Left Bank in the 1930s as it grew the network, and purely on the level of sanity checking, construction costs here were pretty low then.

          • Fbfree

            Hi Alon,
            In Toronto, the change from Y service to 2 lines did not require any changes in the track layout. The Y service included a Bloor-Danforth service from the start, and the tracks were appropriately laid. There may have been some need to rework the tunnels for the Spadina subway extension, but that work was from the end of a line, and probably involved extending by an existing bell mouth.

        • newtonmarunner

          That seems bad to be since then the Blue/Yellow would have an akward path from Alexandria to Largo vía Pentagon, L’Enfant, Green or Orange, Union Station, H St., and Benning — and the financial cost would be virtually the same as your plan w/ linear paths but with added akward paths to deal with in the future.

          Then 40 years from now we’ll be talking about how to break up the Alexandria/H St/SE DC Line in order to make the network more useful. Many will give their high and mighty speech’s on their imaginary soapbox about a certain part of the region’s ties to a certain job cluster, and that we can’t possibly do that.

          As a NoVA native, I get that Alon is breaking up major ties across the region (including in NoVA) with two-seat rides in order to add more service, reliability, coverage. I think all of the alternatives are worse: they all involve too little service or too weak connections or both (and too much money, too). Alon has the least bad option to fix Metrorail, and leave room for its expansion.

          The reality is that cities evolve with the subway. With six tracks (three trunk lines) at L’Enfant (under Alon’s plan), many newer employers will likely choose to locate by the world’s ugliest station area over Farragut and Foggy Bottom. The same is true if there are four tracks at Archives and six at Gallery Place. The result is the job growth at Farragut probably won’t be as high as in L’Enfant, Archives, or some of the other places I mentioned.

          • Alex B.

            I’m really not asking about the network benefits. Again, if this were the proposal from the start, I’d be on board.

            My concerns are specifically about the actual costs and disruptions. Like it or not, the Red Line was planned the way it was planned. Dramatically changing that plan has some serious costs. The note about Toronto above squares with my understanding as well – they eventually planned on the service changes and doing so did not require a massive reconfiguration of existing underground infrastructure.

          • newtonmarunner

            Of all the plans I’ve seen, Alon’s plan is without a doubt financially the cheapest. He’s the only plan I know that doesn’t tunnel under the Potomac. [WMATA’s plan goes under the Potomac twice, and still strips away Alexandria’s one-seat ride to L’Enfant/Archives/Gallery Pl.]

            Infrastructure is a long-term investment. That is how we must think of it. If you see breaking up the rump Red Line as a 60-100 year investment (of which a relief line could provide for an easier two-seat ride to Farragut and Foggy Bottom, though I think going through Mt. Vernon in Arlandria and Washington St. in Old Town, which has greater ties to Farragut and the West End, is preferable to Columbia Pike, which has greater ties to the Pentagon and L’Enfant), as I do, the costs of disruption for better, more useful transit seem pretty minimal.

          • newtonmarunner

            But what use would having the Yellow take over the Red and the Red go to H St. have for today? It would retain the rump Blue Line’s current one-seat ride to Metro Center and Farragut on the Red Line, effectively relieving the Orange Line East of Farragut of its increased load from handling Alexandria/S. Arlington transfers @ L’Enfant to Farragut and Foggy Bottom (as Alexandria/S. Arlington will now have to get to Farragut/West from the east). Otherwise, more on the Largo Branch would likely transfer in SE DC to the Orange for Metro Center/Farragut, leaving a greater load to the Orange Line, which has SE DC (Green and Orange) as well as the Alexandria side of the new Yellow Line. The Red Line to Farragut/Metro Center would have NE DC’s Green, new Yellow, and H St/Largo. That’s the use of breaking up the Red Line today the way Alon has it. [Fwiw, I’d further break up the rump Red in a relief line by sending the Green fully down 14th St. taking over the Red (the Anacostia Line’s natural northen habitat), and have the relief line go up 18th St. from Farragut to Adams Morgan, then Columbia, then take over the rump Green, and have the current rump Red go to Takoma Transit Center vía New Hampshire.]

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