Circumferential Lines and Express Service

In a number of large cities with both radial and circumferential urban rail service, there is a curious observation: there is express service on the radial lines, but not the circumferential ones. These cities include New York, Paris, and Berlin, and to some extent London and Seoul. Understanding why this is the case is useful in general: it highlights guidelines for urban public transport design that have implications even outside the distinction between radial and circumferential service. In brief, circumferential lines are used for shorter trips than radial lines, and in large cities connect many different spokes so that an express trip would either skip important stations or not save much time.

The situation

Berlin has three S-Bahn trunk lines: the Ringbahn, the east-west Stadtbahn, and the North-South Tunnel. The first two have four tracks. The last is a two-track tunnel, but has recently been supplemented with a parallel four-track North-South Main Line tunnel, used by regional and intercity trains.

The Stadtbahn has a straightforward local-express arrangement: the S-Bahn uses the local tracks at very high frequency, whereas the express tracks host less frequent regional trains making about half as many stops as well as a few intercity trains only making two stops. The north-south system likewise features very frequent local trains on the S-Bahn, and a combination of somewhat less frequent regional trains making a few stops on the main line and many intercity trains making fewer stops. In contrast, the Ringbahn has no systemic express service: the S-Bahn includes trains running on the entire Ring frequently as well as trains running along segments of it stopping at every station on the way, but the only express services are regional trains that only serve small slivers on their way somewhere else and only come once or twice an hour.

This arrangement is mirrored in other cities. In Paris, the entire Metro network except Line 14 is very local, with the shortest interstations and lowest average speeds among major world metro systems. For faster service, there is Line 14 as well as the RER system, tying the suburbs together with the city. Those lines are exclusively radial. The busiest single RER line, the RER A, was from the start designed as an express line parallel to Line 1, the Metro’s busiest, and the second busiest, the RER B, is to a large extent an express version of the Metro’s second busiest line, Line 4. However, there is no RER version of the next busiest local lines, the ring formed by Lines 2 and 6. For non-Metro circumferential service, the region went down the speed/cost tradeoff and built tramways, which have been a total success and have high ridership even though they’re slow.

In New York, the subway was built with four-track main lines from the start to enable express service. Five four-track lines run north-south in Manhattan, providing local and express service. Outside the Manhattan core, they branch and recombine into a number of three- and four-track lines in Brooklyn, Queens, and the Bronx. Not every radial line in New York has express service, but most do. In contrast, the circumferential Crosstown Line, carrying the G train, is entirely local.

In Seoul, most lines have no express service. However, Lines 1, 3, and 4 interline with longer-range commuter rail services, and Lines 1 and 4 have express trains on the commuter rail segments. They are all radial; the circumferential Line 2 has no express trains.

Finally, in London, the Underground has few express segments (all radial), but in addition to the Underground the city has or will soon have express commuter lines, including Thameslink and Crossrail. There are no plans for express service parallel to the Overground.

Is Tokyo really an exception?

Tokyo has express trains on many lines. On the JR East network, there are lines with four or six tracks all the way to Central Tokyo, with local and express service. The private railroads usually have local and express services on their own lines, which feed into the local Tokyo subway. But not all express services go through the primary city center: the Ikebukuro-Shibuya corridor has the four-track JR Yamanote Line, with both local services (called the Yamanote Line too, running as a ring to Tokyo Station) and express services (called the Saikyo or Shonan-Shinjuku Line, continuing north and south of the city); Tokyo Metro’s Fukutoshin Line, serving the same corridor, has a timed passing segment for express trains as well.

However, in three ways, the area around Ikebukuro, Shinjuku, and Shibuya behaves as a secondary city center rather than a circumferential corridor. The job density around all three stations is very high, for one. They have extensive retail as well, as the private railroads that terminated there before they interlined with the subway developed the areas to encourage more people to use their trains. This situation is also true of some secondary clusters elsewhere in Tokyo, like Tobu’s Asakusa terminal, but Asakusa is in a historically working-class area, whereas the Yamanote area was historically and still is wealthier, making it easier for it to attract corporate jobs.

Second, from the perspective of the transportation network, they are central enough that railroads that have the option to serve them do so, even at the expense of service to Central Tokyo. When the Fukutoshin Line opened, Tokyu shifted one of its two mainlines, the Toyoko Line, to connect to it and serve this secondary center, where it previously interlined with the Hibiya Line to Central Tokyo; Tokyu serves Central Tokyo via its other line, the Den-en-Toshi Line, which connects to the Hanzomon Line of the subway. JR East, too, prioritizes serving Shinjuku from the northern and southern suburbs: the Shonan-Shinjuku Line is a reverse-branch of core commuter rail lines both north and south, as direct fast service from the suburbs to Shibuya, Shinjuku, and Ikebukuro is important enough to JR East that it will sacrifice some reliability and capacity to Tokyo Station for it.

Third, as we will discuss below, the Yamanote Line has a special feature missing from circumferential corridors in Berlin and Paris: it has distinguished stations. A foreigner looking at satellite photos of land use and at a map of the region’s rail network without the stations labeled would have an easy time deciding where an express train on the line should stop: Ikebukuro, Shinjuku, and Shibuya eclipse other stations along the line, like Yoyogi and Takadanobaba. Moreover, since these three centers were established to some extent before the subway was built, the subway lines were routed to serve them; there are 11 subway lines coming from the east as well as the east-west Chuo Line, and of these, all but the Tozai and Chiyoda Lines intersect it at one of the three main stations.

Interstations and trip length

The optimal stop spacing depends on how long passenger trips are on the line: keeping all else equal, it is proportional to the square root of the average unlinked trip. The best formula is somewhat more delicate: widening the stop spacing encourages people to take longer trips as they become faster with fewer intermediate stops and discourages people from taking shorter ones as they become slower with longer walk distances to the station. However, to a first-order approximation, the square root rule remains valid.

The relevance is that not all lines have the same average trip length. Longer lines have longer trips than short lines. Moreover, circular lines have shorter average trips than straight lines of the same length, because people have no reason to ride the entire way. The Ringbahn is a 37-kilometer line on which trains take an hour to complete the circuit. But nobody has a reason to ride more than half the circle – they can just as well ride the shorter way in the other direction. Nor do passengers really have a reason to ride over exactly half the circle, because they can often take the Stadtbahn, North-South Tunnel, or U-Bahn and be at their destinations faster.

Circumferential lines are frequently used to connect to radial lines if the radial-radial connection in city center is inconvenient – maybe it’s missing entirely, maybe it’s congested, maybe it involves too much walking between platforms, maybe happens to be on the far side of city center. In all such cases, people are more likely to use the circumferential line for shorter trips than for longer ones: the more acute the angle, the more direct and thus more valuable the circle is for travel.

The relevance of this discussion to express service is that there’s more demand for express service in situations with longer optimum stop spacing. For example, the optimum stop spacing for the subway in New York based on current travel patterns is the same as that proposed for Second Avenue Subway, to within measurement error of parameters like walking speed; on the other trunk lines, the local trains have denser stop spacing and the express trains have wider stop spacing. On a line with very short optimum spacing, there is not much of a case for express service at all.

Distinguished stops versus isotropy

The formula for optimal stop spacing depends on the isotropy of travel demand. If origins and destinations are distributed uniformly along the line, then the optimal stop spacing is minimized: passengers are equally likely to live and work right on top of a station, which eliminates walk time, as they are to live and work exactly in the middle between two stations, which maximizes walk time. If the densities of origins and destinations are spiky around distinguished nodes, then the optimal stop spacing widens, because planners can place stations at key locations to minimize the number of passengers who have to walk longer. If origins are assumed to be perfectly isotropic but destinations are assumed to be perfectly clustered at such distinguished locations as city center, the optimum stop spacing is larger than if both are perfectly isotropic by a factor of \sqrt{2}.

Circumferential lines in large cities do not have isotropic demand. However, they have a great many distinguished stops, one at every intersection with a radial rail service. Out of 27 Ringbahn stops, 21 have a connection to the U-Bahn, a tramway, or a radial S-Bahn line. Express service would be pointless – the money would be better spent increasing local frequency, as ridership on short-hop trips like the Ringbahn’s is especially sensitive to wait time.

On the M2/M6 ring in Paris, there are 49 stops, of which 21 have connections to other Metro lines or the RER, one more doesn’t but really should (Rome, with a missed connection to an M14 extension), and one may connect to a future extension of M10. Express service is not completely pointless parallel to M2/M6, but still not too valuable. Even farther out, where the Paris region is building the M15 ring of Grand Paris Express, there are 35 stops in 69 kilometers of the main ring, practically all connecting to a radial line or located at a dense suburban city center.

The situation in New York is dicier, because the G train does have a distinguished stop location between Long Island City and Downtown Brooklyn, namely the connection to the L train at Bedford Avenue. However, the average trip length remains very short – the G misses so many transfers at both ends that end-to-end riders mostly stay on the radials and go through Manhattan, so the main use case is taking it a few stops to the connection to the L or to the Long Island City end.

Conclusion

A large urban rail network should be predominantly radial, with circumferential lines in dense areas providing additional connectivity between inner neighborhoods and decongesting the central transfer points. However, that the radial and circumferential lines are depicted together on the same metro or regional rail map does not mean that people use them in the same way. City center lies ideally on all radials but not on the circumferentials, so the tidal wave of morning commuters going from far away to the center is relevant only to the radials.

This difference between radials and circumferentials is not just about service planning, but also about infrastructure planning. Passengers make longer trips on radial lines, and disproportionately travel to one of not many distinguished central locations; this encourages longer stop spacing, which may include express service in the largest cities. On circumferential lines, they make shorter trips to one of many different connection points; this encourages shorter stop spacing and no express service, but rather higher local frequency whenever possible.

Different countries build rapid transit in radically different ways, and yet big cities in a number of different countries have converged on the same pattern: express service on the strongest radial corridors, local-only service on circumferential ones no matter how busy they are. There is a reason. Transportation planners in poorer cities that are just starting to build their rapid transit networks as well in mature cities that are adding to their existing service should take heed and design infrastructure accordingly.

The Case for a High Carbon Tax

Reading a bunch of people criticize green politics on the grounds that it imposes unreasonable reductions in living standards has clarified something for me. There’s extreme right criticism of Angela Merkel’s latest statement that climate protection is vital, accusing her of deindustrializing the country in the name of green-left ideology; from the left, Branko Milanovic, who has criticized the degrowth stream of environmentalism before, complained of people who “call for 50% reduction in income to combat climate change.” I think highly of Milanovic, both for his analysis of economic inequality and for his historical and social insights, but what he’s criticizing is actually a good example for why a high carbon tax does not actually mean a big reduction in income.

Take, as a starting point, the Stern Review‘s numbers. They were on the high side when the review was published in 2006, but a lot of the green consensus since then has converged toward them. As detailed on PDF-p. 20, the expected cost of unmitigated climate change is 20% of global GDP. The implication is that the optimal carbon tax today should be 20% of global GDP – we should be willing to reduce income by 20% now to avoid a permanent 20% reduction in income in the future. Global emissions intensity today is about PPP$2,400/t-CO2e ($127 trillion/53.5 billion t-CO2e), so the carbon tax should be $480/t, right?

But in reality, we should be willing to accept a much higher carbon tax. The reason is that the money raised by the carbon tax is not ejected into outer space. It circulates in the world economy. If a carbon tax is used to offset other taxes, or to pay for new government spending, then the same amount of money stimulates the economy. If it is used to reduce the deficit, then in the long run this stimulates some investment. The money is shifted rather than thrown away.

There is some cost to the carbon tax, but it is much lower than its face value. The cost is the economic loss from shifting consumption to carbon-free products, at the prices of a world in which greenhouse gases are not taxed at all. This is similar to the cost of a tax on cigarettes or alcohol or really any other product – the money is spent on less harmful activities.

The point is that the zero-carbon lifestyle that I advocate as the future is not one of penury. Evidently, so many people enjoy living in dense cities where cars are not necessary that those cities are very desirable. Cities like New York and London, which offer high-wage jobs and comfortable public transportation but aren’t building enough housing to accommodate the tens of millions of people who wish to take advantage of their opportunities, are very expensive to live in. The current zoning regimes in the US, and to some extent even in Europe, act as a negative carbon tax, making it harder to not emit greenhouse gases – this should be reversed, replaced with zoning liberalization and a positive carbon tax.

What’s more, the money saved by not having to drive goes to other forms of consumption. The proportion of income spent on transportation is lower in areas with good public transit than in ones without. Even taking subsidies into account, the operating and equipment costs of New York City Transit are about comparable to the depreciation cost of the cars that one would need to buy for New Yorkers to match the auto usage of the rest of the United States – and car purchases are just 40% of American auto spending, the rest going to fuel and spare parts. This saving is plugged into other kinds of local spending, such as going out to eat. In cities with more modern housing stock than New York this also includes better-accessorized housing. It may also include higher spending on consumer electronics.

What’s true is that not everyone wants to live that kind of future. Some people enjoy driving big cars and keeping the lights and temperature control in their large houses on even when they’re not at home. They will not be able to do so in any realistic green transition, and that’s a real cost. Some people even object to solar power and energy-efficient devices on culture war grounds, and they too will have to adapt to a culture they dislike, just as so many immigrants have. But the alternative lifestyle they will need to adapt to is one that so many comfortably middle-class people choose even at the current carbon cost of $0 that the imposition is not so onerous.

There are still remnants of people who define themselves by the environmental and health hazards of previous generations. Europeans and Japanese still smoke at pretty high rates, as do some subcultures in North America. We can expect that likewise, some people will keep driving at €2/liter fuel, at €3/liter, at €5/liter, and define themselves by not shifting to public transportation or even buying an electric car. But they will be marginal as the bulk of the population shifts to greener consumption, and if squeezing out the last remaining carbon emissions requires regulatory bans, not too many people will mind, just as people no longer mind restrictions on cigarette advertising.

So raise the fuel tax, early and often, and cut other taxes, and spend some of the difference on solar power and public transportation. And make it easy for people to move to big, dense cities by building more housing there. Maybe start worrying if the deadweight loss assuming there were no such thing as climate change grew beyond the cost of greenhouse gas emissions, but the carbon tax required to get there is such a large multiple of the cost of carbon emissions that by then the world would go zero-carbon. Do what you can to limit climate change to non-catastrophic levels, and keep raising carbon taxes and spending on alternatives to get there.

The Future is not Retro

One faction of urbanists that I’ve sometimes found myself clashing with is people who assume that a greener, less auto-centric future will look something like the traditional small towns of the past. Strong Towns is the best example I know of of this tendency, arguing against high-rise urban redevelopment and in favor of urbanism that looks like pre-freeway Midwestern main streets. But this retro attitude to the future happens everywhere, and recently I’ve had to argue about this with the generally pro-modern Cap’n Transit and his take about the future of vacations. Even the push for light rail in a number of cities has connections with nostalgia for old streetcars, to the point that some American cities build mixed-traffic streetcars, such as Portland.

The future was not retro in the 1950s

The best analogy for a zero-emissions future is ironically what it seeks to undo: the history of suburbanization. In retrospect, we can view midcentury suburbanization as a physical expansion of built-up areas at lower density, at automobile scale. But at the time, it was not always viewed this way. Socially, the suburbs were supposed to be a return to rural virtues. The American patrician reformers who advocated for them consciously wanted to get rid of ethnic urban neighborhoods and their alien cultures. The German Christian democratic push for regional road and rail connections has the same social origin, just without the ethnic dimension – cities were dens of iniquity and sin.

At the same time, the suburbs, that future of the middle of the 20th century, were completely different from the mythologized 19th century past, before cities like New York and Berlin had grown so big. Most obviously, they were linked to urban jobs; the social forces that pushed for them were aware of that in real time, and sought transportation links precisely in order to permit access to urban jobs in what they hoped would be rural living.

But a number of other key differences are visible – for one, those suburbs were near the big cities of the early 20th century, and not in areas with demographic decline. In the United States, the Great Plains and Appalachia kept depopulating and the Deep South except Atlanta kept demographically stagnating. The growth in that era of interregional convergence happened in suburbs around New York, Chicago, and other big then-industrial cities, and in parts of what would soon be called the Sunbelt, namely Southern California, Texas, and Florida. In Germany, this history is more complicated, as the stagnating region that traditionalists had hoped to repopulate was Prussia and Posen, which were given to Poland at the end of the war and ethnically cleansed of their German populations. However, we can still see postwar shifts within West Germany toward suburbs of big cities like Munich and Frankfurt, while the Ruhr stagnated.

The future of transit-oriented development is not retro

People who dislike the auto-oriented form of cities can easily romanticize how cities looked before mass motorization. They’d have uniform missing middle built form in most of the US and UK, or uniform mid-rise in New York and Continental Europe. American YIMBYs in particular easily slip into romanticizing missing middle density and asking to replace single-family housing with duplexes and triplexes rather than with anything more substantial.

If you want to see what 21st-century TOD looks like, go to the richer parts of East Asia, especially Tokyo, which builds much more housing than Hong Kong and Singapore. The density in Tokyo is anything but uniform. There are clusters of high-rise buildings next to train stations, and lower density further away, even small single-family houses fronting narrow streets far enough from train stations that it’s not economical to redevelop them. It offends nostalgic Westerners; the future often does.

In the context of a growing city like New York or London, what this means is that the suburbs can expect to look spiky. There’s no point in turning, say, everything within two kilometers of Cockfosters (or the Little Neck LIRR station) into mid-rise apartments or even rowhouses. What’s the point? There’s a lot more demand 100 meters from the station than two kilometers away, enough that people pay the construction cost premium for the 20th floor 100 meters from the stations in preference to the third floor two kilometers away. The same is true for Paris – there’s no solution for its growth needs other than high-rises near RER stations and key Metro stations in the city as well as the suburbs, like the existing social housing complexes but with less space between buildings. It may offend people who associate high-rises with either the poor or recent high-skill immigrants, but again, the future often offends traditionalists.

The future of transportation is not retro

In countries that do not rigidly prevent urban housing growth the way the US does, the trend toward reurbanization is clear. Germany’s big cities are growing while everything else is shrinking save some suburbs in the richest regions, such as around Munich. Rural France keeps depopulating.

In this context, the modes of transportation of the future are rapid transit and high-speed rail. Rapid transit is preferable to buses and surface trains in most cities, because it serves spiky development better – the stations are spaced farther apart, which is fine because population density is not isotropic and neither is job density, and larger cities need the longer range that comes with the higher average speed of the subway or regional train over that of the tramway.

High-speed rail is likewise preferable to an everywhere-to-everywhere low-speed rail network like that of Switzerland. In a country with very large metro areas spaced 500 km or so apart, like the US, France, or Germany, connecting those growing city centers is of crucial importance, while nearby cities of 100,000 are of diminishing importance. Moreover, very big cities can be connected by trains so frequent that untimed transfers are viable. Already under the Deutschlandtakt plan, there will be 2.5 trains between Berlin and Hanover every hour, and if average speeds between Berlin and the Rhine-Ruhr were increased to be in line with those of the TGVs, demand would fill 4-6 trains per hour, enough to facilitate untimed transfers from connecting lines going north and south of Hanover. The Northeast Corridor has even more latent demand, given the huge size of New York.

The future of travel is not retro

The transportation network both follows and shapes travel patterns. Rapid transit is symbiotic with spiky TOD, and high-speed rail is symbiotic with extensive intercity travel.

The implication is that the future of holidays, too, is not retro. Vacation trips between major cities will become easier if countries that are not France and Japan build a dense network of high-speed lines akin to what France has done over the last 40 years and what Japan has done over the last 60. Many of those cities have thriving tourism economies, and these can expect to expand if there are fast trains connecting them to other cities within 300-1,000 kilometers.

Sometimes, these high-speed lines could serve romanticized tourist destinations. Niagara Falls lies between New York and Toronto, and could see expansion of visits, including day trips from Toronto and Buffalo and overnight stays from New York. The Riviera will surely see more travel once the much-delayed LGV PACA puts Nice four hours away from Paris by train rather than five and a half. Even the Black Forest might see an expansion of travel if people connect from high-speed trains from the rest of Germany to regional trains at Freiburg, going from the Rhine Valley up to the mountains; but even then, I expect a future Germany’s domestic tourism to be increasingly urban, probably involving the Rhine waterfront as well as the historic cities along the river.

But for the most part, tourist destinations designed around driving, like most American national parks as well as state parks like the Catskills, will shrink in importance in a zero-carbon future. It does not matter if they used to have rail access, as Glacier National Park did; the tourism of the leisure class of the early 20th century is not the same as that of the middle class of the middle of the 21st. Grand Canyon and Yellowstone are not the only pretty places in the world or even in the United States; the Hudson Valley and the entire Pacific Coast are pretty too, and do not require either driving or taking a hypothetical train line that, on the list of the United States’ top transportation priorities, would not crack the top 100. This will offend people whose idea of environmentalism is based on the priorities of turn-of-the-century patrician conservationists, but environmental science has moved on and the nature of the biggest ecological crisis facing humanity has changed.

The non-retro future is pretty cool

The theme of the future is that, just as the Industrial Revolution involved urbanization and rural depopulation, urban development patterns this century involve growth in the big metro areas and decline elsewhere and in traditional small towns. This is fine. The status anxieties of Basil Fawlty types who either can’t or won’t adapt to a world that has little use for their prejudices are not a serious public concern.

Already, people lead full lives in big global cities like New York and London without any of the trappings of what passed for normality in the middle of the 20th century, like a detached house with a yard and no racial minorities or working-class people within sight. The rest will adapt to this reality, just as early 20th century urbanites adapted to the reality of suburbanization a generation later.

It’s not even an imposition. It’s opportunity. People can live in high-quality housing with access to extensive social as well as job networks, and travel to many different places with different languages, flora and fauna, vistas, architecture, food, and local retail. Even in the same language zone, Northern and Southern Germany look completely different from each other, as do Paris and Southern France, or New England and Washington. Then outside the cities there are enough places walking distance from a commuter rail line or on the way on a high-speed line between two cities that people can if they’d like go somewhere and spend time out of sight of other people. There’s so much to do in a regime of green prosperity; the world merely awaits the enactment of policies that encourage such a future in lieu of one dominated by small-minded local interests who define themselves by how much they can pollute.

Metro-North Doesn’t Know Best Industry Practices

Governor Ned Lamont’s plan for speeding up trains between New York, New Haven, and Hartford seems to have fallen by the wayside, but Metro-North and the Connecticut Department of Transportation are still planning for future investments. Several high-level officials met with the advocates from the Connecticut Commuter Rail Council, and the results are unimpressive – they have made false statements out of ignorance of not just best practices outside North America but also current federal regulations, including the recent FRA reform.

The meeting link is a video and does not have a searchable transcript, so I’m going to give approximate timestamps and ask that people bear with me. At several points, highly-paid officials make statements that are behind the times, unimaginative, or just plain incorrect. The offenders are Richard Andreski, the bureau chief of public transportation for CDOT, who according to Transparency.CT earns a total of $192,000 a year including fringe benefits, and Glen Hayden, Metro-North’s vice president of engineering, who according to See Through NY earns an annual base salary of $219,000.

20-25 minutes: there’s a discussion, starting a few minutes before this timestamp, about Metro-North’s future rolling stock procurement. In addition to 66 M8 electric multiple units (EMUs), the railroad is planning to buy 60 unpowered railcars. Grilled about why buy unpowered railcars rather than multiple units, such as diesel multiple units (DMUs), Andreski said a few questionable things. He acknowledged that multiple units accelerate faster than locomotive-hauled trains, but said that this was not needed on the lines in question, that is the unpowered Metro-North branch lines, Shore Line East, and the New Haven-Hartford line. In reality, the difference, on the order of 45 seconds per stop at a top speed of 120 km/h (55 seconds if the top speed is 144 km/h), and electrification both massively increases reliability and saves an additional 10 seconds per stop (or 30 if the top speed is 144).

More worryingly, Andreski talks about the need for flexibility and the installed base of diesel locomotives. He suggests unpowered cars are more compatible with what he calls the train of the future, which runs dual-mode. Dual-mode trains today are of low quality, and the innovation in the world focuses on single-mode electric trains, with a growing number of railroads electrifying as well as transitioning to multiple units. Metro-North itself is a predominantly EMU-based railroad – running more EMUs, especially on the already-wired Shore Line East, is more compatible with its existing infrastructure and maintenance regime than keeping low-performing diesel branches and running diesel under catenary on the trunk line.

1:14-1:17: Andreski states that the 60 unpowered single-level cars should cost about $250 million, slightly more than $4 million per car. When a reader of this blog noted that in the rest of the world, a 25-meter multiple-unit costs $2.5 million, Andreski responded, “this is not accurate.” The only trouble is, it is in fact accurate; follow links to contracts reported in Railway Gazette in the rolling stock cost section of this post. It is not clear whether Andreski is lying, ignorant, or in a way both, that is making a statement with reckless disregard for whether it is true.

Hayden then chimes in, talking about FRA regulations, saying that they’re different from American ones, so European and Asian prices differ from American ones, seemingly indifferent to the fact that he just threw Andreski under the bus – Andreski said that multiple-units do not cost $2.5 million per car and if a public contract says they do then it’s omitting some extra costs. The only problem is, FRA regulations were recently revised to be in line with European ones, with specific eye toward permitting European trains to run on American tracks with minimal modifications, measured in tens of thousands of dollars of extra cost per car. In a followup conversation off-video, Hayden reiterated that position to longtime reader Roger Senserrich – he had no idea FRA regulations had been revised.

Hayden’s response also includes accessibility requirements. Those, too, are an excuse, albeit a slightly defensible one: European intercity trains, which are what American tourists are most likely to have experience with, are generally inaccessible without the aid of conductors and manual boarding plates. However, regional trains are increasingly fully accessible, at a variety of floor heights, and it’s always easier to raise the floor height to match the high platforms of the Northeast Corridor than to lower it to match those of low-platform networks like Switzerland’s.

1:45: asked about why Metro-North does not run EMUs on the wired Shore Line East, a third official passes the buck to Amtrak, saying that Amtrak is demanding additional tests and the line is Amtrak’s rather than Metro-North’s property. This is puzzling, as 1990s’ Amtrak planned around electrification of commuter rail service east of New Haven, to the point of constructing its substations with room for expansion if the MBTA were ever interested in running electric service on the Providence Line. It’s possible that Amtrak today is stalling for the sake of stalling, never mind that commuter rail electrification would reduce the speed difference with its intercity trains and thus make them easier to schedule and thus more reliable. But it’s equally possible that CDOT is being unreasonable; at this point I would not trust either side of any Amtrak-commuter rail dispute.

Stuttgart 21’s Impending Capacity Problems and Timed Connections

The largest single transportation project in Germany today is a new underground main station for Stuttgart, dubbed Stuttgart 21. Built at a cost of €8.2 billion, it will soon replace Stuttgart’s surface terminal with a through-station, fed in four directions by separate tunnels. The project attracted considerable controversy at the beginning of this decade due to its cost overruns and surface disruption. It’s had a long-term effect on German politics as well: it catapulted the Green Party into its first ever premiership of a German state, and the Green minister-president of the state, Winfried Krestchmann, has remained very popular and played a role in mainstreaming the party and moving it in a more moderate direction.

But the interesting thing about Stuttgart 21 now is not the high cost, but a new problem: capacity. The new station will face capacity constraints worse than those of the surface station, particularly because Germany is transitioning toward timed connections (“Deutschlandtakt”) on the model of Switzerland. Since Stuttgart is closing the surface station and selling the land for redevelopment, a second underground station will need to be built just to add enough capacity. It’s a good example of how different models of train scheduling require radically different kinds of infrastructure, and how even when all the technical details are right, the big picture may still go wrong.

What is the Stuttgart 21 infrastructure?

The following diagram (via Wikipedia) shows what the project entails.

The existing tunnel, oriented in a northeast-southwest direction, is used exclusively by S-Bahn trains. Longer-distance regional trains (“RegionalBahn“) and intercity trains terminate on the surface, and if they continue onward, they must reverse direction.

The new tunnel infrastructure consists of four independent two-track tunnels, two coming in from the northwest and two from the southeast, with full through-service. In addition, an underground loop is to be constructed on the south in order to let trains from points south (Singen) enter Stuttgart via the Filder tunnel while serving the airport at Filder Station without reversing direction. The total double-track tunnel length is 30 kilometers.

Stuttgart 21’s station infrastructure will consist of eight tracks, four in each direction:

The two tracks facing each platform are generally paired with the same approach track, so that in case of service changes, passengers will not be inconvenienced by having to go to a different platform. The interlocking permits trains from each of the two eastern approaches to go to either of the western ones without conflict and vice versa, and the switches are constructed to modern standards, with none of the onerous speed restrictions of American station throats.

So what is the problem?

First of all, the four approach tunnels are not symmetric. The Feuerbach tunnel leads to Mannheim, Frankfurt, Würzburg, and points north, and the Filder tunnel leads to Ulm and points east, including Munich; both are planned to be heavily used by intercity trains. In contrast, the other two tunnels lead to nothing in particular. The Obertürkheim tunnel leads to the current line toward Ulm, but the under-construction high-speed line to Ulm feeds Filder instead, leaving Obertürkheim with just a handful of suburbs.

On the Deutschlandtakt diagram for Baden-Württemberg, every hour there are planned to be 12 trains entering Stuttgart from the Feuerbach tunnel, 10.5 from the Filder tunnel, 5.5 from the Bad Cannstatt tunnel, and 6 from the Obertürkheim tunnel. For the most part, they’re arranged to match the two busier approaches with each other – the track layout permits a pair of trains in either matching to cross with no at-grade conflict, but only if trains from Feuerbach match with Filder and trains from Bad Cannstatt match with Obertürkheim are both station tracks facing the same platform available without conflict.

A train every five minutes through a single approach tunnel feeding two station tracks is not normally a problem. The S-Bahn, depicted on the same map in black, runs 18 trains per hour in each direction through the tunnel; bigger cities, including Paris and Munich, run even more frequent trains on the RER or S-Bahn with just a single station platform per approach track, as on any metro network.

However, the high single-track, single-direction frequency is more suitable on urban rail than on intercity rail. On a metro, trains rarely have their own identity – they run on the same line as a closed system, perhaps with some branching – so if a train is delayed, it’s possible to space trains slightly further apart, so the nominal 30 trains per hour system ends up running 28 trains if need be. On an S-Bahn this is more complicated, but there is still generally a high degree of separation between the system and other trains, and it’s usually plausible to rearrange trains through the central tunnel. On intercity rail, trains have their own identity, so rearrangement is possible but more difficult if for example two trains on the same line, one express and one local, arrive in quick succession. As a result, one platform track per approach track is unsuitable – two is a minimum, and if more tracks are affordable then they should be built.

How do you intend to run the trains?

If the paradigm for intercity rail service is to imitate shorter-range regional trains, then through-tunnels are both easier and more desirable. A relatively closed system with very high frequency between a pair of stations calls for infrastructure that minimizes turnarounds and lets trains just run in the same sequence.

The Shinkansen works this way, leveraging three key features: its near-total isolation from the legacy train network, running on a different gauge; the very high demand for trains along individual corridors on specific city pairs; and the generally high punctuality of Japanese trains even on more complex systems. As it happens, Tokyo is a terminal, with trains going north and south but not through, as a legacy of the history of breaking up Japan National Railway before the Shinkansen reached Tokyo from the north, with different daughter companies running in each direction. However, Shin-Osaka is a through-station, fitting through-trains as well as terminating trains on just eight tracks.

In the developed world’s second busiest intercity rail network, that of Switzerland, the paradigm is different. In a country whose entire population is somewhat less than that of Tokyo without any of its suburbs, no single corridor is as strong as the Shinkansen corridors. Trains form a mesh with timed connections every hour, sometimes every half hour. Intercity trains are arranged to arrive at Zurich, Bern, and Basel a few minutes before the hour every 30 minutes and depart a few minutes later. In that case, more approach tracks and more platform tracks are needed. Conversely, the value of through-tracks is diminished, since passengers can transfer between trains more easily if they can walk between platforms without changing grade.

Infrastructure-timetable integration

Germany aims to integrate the infrastructure and timetable, as Switzerland does. However, Stuttgart 21 is a failure of such integration. The Deutschlandtakt service paradigm calls for many trains entering and leaving the station within the span of a few minutes. Today there are four effective approaches with two tracks each, same as under the Stuttgart 21 plan, but they are better-distributed.

The idea of Stuttgart 21, and similar proposals for Frankfurt and Munich, is solid provided that the intention is to run trains the Japanese way. It Stuttgart were designed to be the junction of two consistently high-intensity lines, then it would work without additional infrastructure. But it is not: its approach tunnels are supposed to support such design, but the service pattern will not look this way because of how the tunnels are placed relative to Germany’s population distribution. Even highly competent engineering can produce incompetent results if the details do not match the big picture.

Megaregions, Redux

Remember how ten years ago the American urbanist conversation was all about carving the country up into megaregions? The America 2050 project drew some lines connecting metro areas into regions, designed to imitate the Boston-Washington corridor in concept, and asserted that this would be the future of American growth. The concept seems to have dropped off the discourse, and for good reason, but it may be useful to have a second look. The Boston-Washington megalopolis is a genuine megaregion, and it’s useful to see which regions elsewhere in the world share its characteristics.

The key takeaway is that rich cities do not have to be in megaregions. The Northeast Corridor is a rich megaregion, and San Francisco, Los Angeles, and Chicago anchor smaller megaregions of their own; but in Europe, among the richest cities only Frankfurt and Amsterdam are in megaregions, while London, Paris, Hamburg, and Munich are not. Megaregions are areas of high population density and interlinked social networks. Their size may give them economic advantage, but it doesn’t have to; urbanists and urban geographers must avoid overselling their importance.

What is a megaregion?

The original Boston-Washington megalopolis was defined in the 1960s, as a linear region with continuous suburban sprawl. The core comes from New York and Philadelphia, which share some suburbs in Central Jersey, their regional rails meeting at Trenton. However, continuous sprawl goes north to New Haven, Hartford, and Springfield, with only a few tens of km of separation from Providence and Worcester on the way to Boston; and southwest to Baltimore and Washington, with suburbs spaced closely together along the I-95 corridor.

There are extensive academic connections. Academics are generally hypermobile, but form especially thick metropolitan connections. Living in Boston and reverse-commuting to Brown is normal, and people at Brown would sometimes go up to Harvard or MIT for seminars when sufficiently important or interesting people gave talks. Connections up and down the central part of the corridor are extensive as well, stretching from Yale down to Penn. There is a gap between New Haven and Providence, as Hartford and Springfield aren’t academic centers; perhaps for academics the megaregion only stretches from New Haven to Washington, but even so, at least two-thirds of the megaregion remains intact.

Socially, there are strong connections along the corridor as well. They’re rarely end-to-end, but people in fandom routinely go a state or two over for conventions, so conventions in Connecticut and Rhode Island draw from New York and Boston, conventions in New Jersey draw from Philadelphia and New Haven, and conventions in Maryland draw from Philadelphia and Northern Virginia. On some stretches, weekend trips are normal, like the Columbia students who’d go back to visit parents in suburban Philadelphia every weekend, or people in New York who dated people in New Haven and didn’t even really think of it as a long-distance relationship.

Which regions qualify as megaregions?

Outside the Northeast, it is difficult for me to judge the extent of social connections, with a few key exceptions. However, I can judge how continuous urbanization is and, using American survey data on commuting, whether two adjacent core urban areas share suburbs. In Europe, I do not have commuting data, but it is easy to look at regional rail maps and see when S-Bahn networks touch.

Asymmetric megaregions

In the United States, the three largest core metropolitan areas outside the Northeast – Los Angeles, Chicago, and San Francisco – all anchor megaregions. However, in all three cases, the big core metro area dominates the broader region. Los Angeles has continuous sprawl down the coast to San Diego, and the two metro areas’ commuter rail networks touch; Chicago similarly has continuous sprawl up to Milwaukee, and if Milwaukee bothered to run regional trains then they would probably go down to Kenosha and connect to Metra; the Bay Area’s high housing costs have driven many people to the San Joaquin Delta, most of the way to Sacramento, and the Amtrak route connecting San Jose and Oakland with Sacramento is largely planned as regional rail nowadays.

New York is of course much larger than the other core regions of the megalopolis, but its metro area has at most half the population of the region, and even that requires making the broadest assumptions on what counts as part of the metro area and the narrowest ones on what counts as part of the megalopolis. If metro New York excludes mostly economically independent areas like New Haven and Central Jersey, and the megalopolis includes some inland areas like Albany and Harrisburg, then New York is only one third of the megalopolis. In contrast, the five-county Los Angeles metro area has three quarters of Southern California’s population, the Bay Area has about two thirds of its megaregion’s population, and metro Chicago has about 85% of the combined population of Chicago and Milwaukee.

Suburb sharing in smaller megaregions

High population density and suburban sprawl can lead some core urban areas to share suburbs, forming a megaregion with much lower population than the megalopolis. Florida supplies at least one such example: out of 237,000 employed residents in Polk County, 26,000 commute to Orlando’s Orange County and 29,000 commute to Tampa’s Hillsborough County and St. Petersburg’s Pinellas County; the western parts of Polk County have a higher density of Tampa-bound commuters and the eastern parts have a higher density of Orlando-bound commuters, but there is a fair amount of mixing, as well as anywhere-to-anywhere commuting within the county. By all accounts, Orlando and Tampa should be placed into one megaregion.

South Florida is arguably a megaregion as well. It is treated as a metro area stretching from Miami or even Key West north to West Palm Beach, but its northern, central, and southern areas have distinct urban cores. Miami-Dade County has 982,000 employed residents, of whom only 28,000 work in Palm Beach County; in the other direction, 29,000 workers from Palm Beach commute to Miami-Dade out of 513,000. This megaregion stretches even further north – St. Lucie County has 13,000 out of 100,000 workers commuting to Palm Beach County – but there is a gap in both population density and commuting zones between Port St. Lucie and Space Coast. Socially, too, the people I know on Space Coast don’t have ties to South Florida, and barely have any to Orlando. So the bulk of Florida is really two linear megaregions, one north-south and one southwest-northeast, which may be close but do not merge.

Finally, crossing the Pond, Northern England features a megaregion out of core metro areas of similar size to those of Central Florida. Liverpool and Manchester are two historic cores and are formally two distinct metro areas, but are so interlinked they are arguably a single metro area, and are certainly a single multicore megaregion. There is contiguous suburban sprawl connecting the two cities with small gaps, and were British regional rail services better, their frequent urban rail networks would have touched. There are even some ties crossing the Pennines to Leeds; Britain has attempted to improve infrastructure between historic Lancashire and Yorkshire, using the language of megaregions to argue that this would boost the area’s economic profile.

Leapfrog urban connections

Western Germany and the Netherlands do not have contiguous sprawl in the same way that most developed countries do. On a satellite photo, the commuting zone of New York, Paris, Madrid, Toronto, or any other major city in their respective countries looks largely as a single blob of gray. The population density of this gray blob is higher in France than in the United States, but in both countries, a metropolitan area is made out of a single contiguous built-up area plus a handful of surrounding low-density exurbs.

In contrast, in Germany and the Netherlands there are undeveloped areas between adjacent cities. Most definitions of metropolitan agglomeration in Europe recognize that Cologne and Bonn are one metro area, but the two cities’ built-up areas barely touch and have farmland in between. The metro area of Frankfurt similarly contains multiple core cities with recognizable centers and some rural gaps between them, such as Darmstadt and Mainz. Urban areas with slightly bigger gaps do not necessarily fall into one metro area, but certainly comprise a single megaregion, including Germany’s largest, the Rhine-Ruhr with its roughly 11 million people and extensive internal S-Bahn connections.

Randstad is likewise a megaregion. The Netherlands zealously protects its high-yield farmland from urban sprawl, so suburbs are usually not contiguous with the cities they serve as bedroom communities for. There are agricultural gaps between Amsterdam, the cities of Flevoland, Utrecht, Rotterdam, and the Hague, and not too much commuting between the southern and northern edges of the combined region, and yet intermediate commuting and tight economic links mean it must be viewed as more than two or three disparate metro areas.

More controversially, I claim that the lower reaches of the Upper Rhine, from Frankfurt and Mainz up to Karlsruhe, form a single megaregion, and may even stretch farther up all the way into Basel. The gaps in urbanization between Frankfurt and Mannheim are not large – there is a city every few kilometers on both rail lines connecting the two cities. Moreover, the Frankfurt and Rhine-Neckar regions’ S-Bahns touch at Mainz, the Mainz-Mannheim line having recently been designated as S-Bahn quality and appearing on the regional schedules. The Rhine-Neckar S-Bahn in turn serves Karlsruhe. South of Karlsruhe the population density is high but less so, and the gaps between the cities are larger. But even without Baden south of Karlsruhe, the combined region has nearly 10 million people, and certainly has the highest GDP in Germany, as it is much richer than the Rhine-Ruhr.

Remember the Blue Banana?

In 1989, a group of French geographers led by Roger Brunet coined the term blue banana for a European megalopolis. As defined, it stretched from London or even Liverpool and Manchester in the north, across the Channel to the Low Countries, up the Rhine to Switzerland, and then across the Alps to Milan. The original definition deliberately omitted Paris from this zone, arguing that French urban geography was dominated by internal national links centered around the capital rather than the polycentrism of the Low Countries, western Germany, Switzerland, and Italy.

The last 30 years have not been kind to the Blue Banana. Much of Continental Europe was beset by a period of slow growth in the 1990s, sometimes called eurosclerosis; parts of it have slowly recovered in the 2000s and 2010s, most notably Germany, while others have stagnated, most notably Italy. In the 1990s, it was plausible to view Milan as more like Northern Europe than like Southern Italy. Today, it is no longer tenable. Before the 2008 crisis, Lombardy was as rich as Hamburg and southern Hesse and much richer than Stockholm and Copenhagen; today it is slightly behind Stockholm and slightly ahead of Copenhagen, and well behind Hamburg and southern Hesse.

The story of growth in the last generation has mostly been one of states, not regions. Northern Italy is much richer than Southern Italy, just as it has always been, but the entire country has equally stagnated. French growth has not been spectacular over this period, but it’s been better than Italian growth. Belgium, within the Blue Banana, has done better than France in the last generation, but not by much. In this entire period, the most notable subnational per capita income changes have been that London has pulled ahead while Northern England has stagnated, and that East Germany has grown faster than West Germany.

Megaregions and wealth

In the United States, the big megaregions have been loci of wealth, particularly the megalopolis. This has intensified in the current century. According to BEA data, since 2000, economic growth in the four core Northeast combined metro areas has exceeded the national average, gaining about 4 percentage points relative to the rest of the country in terms of both per capita income (from all sources) and net earnings (i.e. income from work). But even there, this is not the whole story, since Seattle, which is not in any megaregion, has had even faster growth.

Moreover, in Europe, there is no real correlation between megaregions and growth. The largest single megaregion in Europe, the Rhine-Ruhr, has slower economic growth than both the surging cities of southern Germany and the converging ones of the East. Paris and London are doing just fine as independent metro areas, Munich is still the richest city region in the EU, and Berlin is steadily converging to West German income levels.

Of course, no correlation and negative correlation are two different things. Just as the Rhine-Ruhr is slowly stagnating, the Frankfurt-Mannheim megaregion is growing, and Randstad has managed to recover from the recession alongside the rest of the Netherlands.

To the extent that there’s a link between megaregions and wealth, it’s that in developing countries, or even in midcentury America, poorer regions are mostly rural, and their cities tend to be small and less likely to interlink to form large metro areas. Thus, Eastern China has three megaregions with tens of millions of people each – Beijing-Tianjin, the Yangtze Delta, and the Pearl River Delta – underlying the wealth and urbanization of these regions; in contrast, the Indo-Gangetic Plain’s lower level of economic development means that even though population density from Bangladesh up the Ganges toward Delhi is as high as in southern Jiangsu, the cities are too small and too separated to form a Bangladeshi or West Bengali or Doabi megaregion.

But in a first-world context, the urbanization rate is about 100%. Even on-paper rural areas are within city regions and just happen to be small municipalities whose residents can drive in half an hour to a larger number of people than any premodern village pedestrian could interact with over a lifetime.

What this suggests is that the right way to think of first-world megaregions is not in terms of economic output, but in terms of density. In dense areas like the Netherlands, western Germany, England, and the Northeastern US, megaregions are likely to form out of links between adjacent cities. Not for nothing, the only part of the American Sunbelt where I’m comfortable describing metro areas as linking to form megaregions, Florida, also has the highest population density. The economies of Atlanta, Dallas, and Houston are a lot stronger than that of Central Florida, which is frankly a basket case, but cities in Texas and the Deep South are too far apart to function as megaregions.

Does high background density lead to higher incomes? Maybe. Strong urban networks really do allow for more economic specialization. But then these networks can be global, untethered from where one can travel by regional rail or urban highways. It’s an interesting question of economic geography, but on the level of a sanity check, some of the richest cities in Europe are doing just fine without the polycentric megaregional links going up and down the Rhine.

S-Bahn and RegionalBahn

The American rail activist term regional rail refers to any mainline rail service short of intercity, which lumps two distinct service patterns. In some German cities, these patterns are called S-Bahn and RegionalBahn, with S-Bahn referring to urban rail running on mainline tracks and RegionalBahn to longer-range service in the 50-100 km range and sometimes even beyond. It’s useful to distinguish the two whenever a city wishes to invest in its regional rail network, because the key infrastructure for the two patterns is different.

As with many this-or-that posts of mine, the distinction is not always clear in practice. For one, in smaller cities, systems that are labeled S-Bahns often work more like RegionalBahn, for example in Hanover. Moreover, some systems have hybrid features, like the Zurich S-Bahn – and what I’ve advocated in American contexts is a hybrid as well. That said, it’s worth understanding the two different ends of this spectrum to figure out what the priority for rail service should be in each given city.

S-Bahn as urban rail

The key feature of the S-Bahn (or the Paris RER) is that it has a trunk that acts like a conventional urban rapid transit line. There are 6-14 stations on the trunks in the examples to keep in mind, often spaced toward the high end for rapid transit so as to provide express service through city center, and all trains make all stops, running every 3-5 minutes all day. Even if the individual branches run on a clockface schedule, people do not use the trunk as a scheduled railroad but rather show up and go continuously.

Moreover, the network layout is usually complementary with existing urban rail. The Munich S-Bahn was built simultaneously with the U-Bahn, and there is only one missed connection between them, The Berlin S-Bahn and U-Bahn were built separately as patchworks, but they too have one true missed connection and one possible miss that depends on which side of the station one considers the crossing point to be on. The RER has more missed connections with the Metro, especially on the RER B, but the RER A’s station choice was designed to maximize connections to the most important lines while maintaining the desired express stop spacing.

Urban rail lines rarely terminate at city center, and the same is true for S-Bahn lines. In cities whose rail stations are terminals, such as Paris, Munich, Frankfurt, and Stuttgart, there are dedicated tunnels for through-service; London is building such a tunnel in Crossrail, and built one for Thameslink, which has the characteristics of a hybrid. In Japan, too, the first priority for through-running is the most local S-Bahn-like lines – when there were only six tracks between Tokyo and Ueno, the Yamanote and Keihin-Tohoku Lines ran through, as did the Shinkansen, whereas the longer-range regional lines terminated at the two ends until the recent through-line opened.

The difference between an S-Bahn and a subway is merely that the subway is self-contained, whereas the S-Bahn connects to suburban branches. In Tokyo even this distinction is blurred, as most subway lines connect to commuter rail lines at their ends, often branching out.

RegionalBahn as intercity rail

Many regional lines descend from intercity lines that retooled to serve local traffic. Nearly every trunk line entering London from the north was built as a long-range intercity line, most commuter rail mainlines in New York are inner segments of lines that go to other cities or used to (even the LIRR was originally built to go to Boston, with a ferry connection), and so on.

In Germany, it’s quite common for such lines to maintain an intercity characteristic. The metropolitan layout of Germany is different from that of the English-speaking world or France. Single-core metro regions are rather small, except for Berlin. Instead, there are networks of independent metropolitan cores, of which the largest, the Rhine-Ruhr, forms an urban complex almost as large as the built-up areas of Paris and London. Even nominally single-core metro regions often have significant independent centers with long separate histories. I blogged about the Rhine-Neckar six months ago as one such example; Frankfurt is another, as the city is ringed by old cities including Darmstadt and Mainz.

But this is not a purely German situation. Caltrain connects what used to be two independent urban areas in San Francisco and San Jose, and many outer ends of Northeastern American commuter lines are sizable cities, such as New Haven, Trenton, Providence, and Worcester.

The intercity characteristic of such lines means that there is less need to make them into useful urban rail; going express within the city is more justifiable if people are traveling from 100 km away, and through-running is a lower priority. Frequency can be lower as well, since the impact of frequency is less if the in-vehicle travel time is longer; an hourly or half-hourly takt can work.

S-Bahn and RegionalBahn combinations

The S-Bahn and RegionalBahn concepts are distinct in history and service plan, but they do not have to be distinct in branding. In Paris, the distinction between Transilien and the RER is about whether there is through-running, and thus some lines that are RegionalBahn-like are branded as RER, for example the entire RER C. Moreover, with future extension plans, the RER brand will eventually take over increasingly long-distance regional service, for example going east to Meaux. Building additional tunnels to relieve the worst bottlenecks in the city’s transport network could open the door to connecting every Transilien line to the RER.

Zurich maintains separate brands for the S-Bahn and longer-distance regional trains, but as in Paris, the distinction is largely about whether trains terminate on the surface or run through either of the tunnels underneath Hauptbahnhof. Individual S-Bahn branches run every half hour, making extensive use of interlining to provide high frequency to urban stations like Oerlikon, and many of these branches go quite far out of the city. It’s not the same as the RER A and B or most of the Berlin S-Bahn, with their 10- and 15-minute branch frequencies and focus on the city and innermost suburbs.

But perhaps the best example of a regional rail network that really takes on lines of both types is that of Tokyo. In branding, the JR East network is considered a single Kanto-area commuter rail network, without distinctions between shorter- and longer-range lines. And yet, the rapid transit services running on the Yamanote, Keihin-Tohoku, and Chuo-Sobu Lines are not the same as the highly-branched network of faster, longer-range lines like Chuo Rapid, Yokosuka, Sobu Rapid, and so on.

The upshot is that cities do not need to neatly separate their commuter rail networks into two separate brands as Berlin does. The distinction is not one of branding for passengers, but one of planning: should a specific piece of infrastructure be S-Bahn or RegionalBahn?

Highest and best use for infrastructure

Ordinarily, the two sides of the spectrum – an S-Bahn stopping every kilometer within the city, and a RegionalBahn connecting Berlin with Magdeburg or New York with New Haven – are so different that there’s no real tradeoff between them, just as there is no tradeoff between building subways and light rail in a city and building intercity rail. However, they have one key characteristic leading to conflict: they run on mainline track. This means that transportation planners have to decide whether to use existing mainline tracks for S-Bahn or RegionalBahn service.

Using different language, I talked about this dilemma in Boston’s context in 2012. The situation of Boston is instructive even in other cities, even outside the United States, purely because its commuter rail service is so bad that it can almost be viewed as blank slate service on existing infrastructure. On each of the different lines in Boston, it’s worth asking what the highest and best use for the line is. This really boils down to two questions:

  1. Would the line fill a service need for intra-urban travel?
  2. Does the line connect to important outlying destinations for which high speed would be especially beneficial?

In Boston, the answer to question 1 is for the most part no. Thirty to forty years ago the answer would have been yes for a number of lines, but since then the state has built subway lines in the same rights-of-way, ignorant of the development of the S-Bahn concept across the Pond. The biggest exceptions are the Fairmount Line through Dorchester and the inner Fitchburg Line through suburbs of Cambridge toward Brandeis.

On the Fairmount Line the answer to question 2 is negative as well, as the line terminates within Boston, which helps explain why the state is trying to invest in making it a useful S-Bahn with more stops, just without electrification, high frequency, fare integration, or through-service north of Downtown Boston. But on the Fitchburg Line the answer to question 2 is positive, as there is quite a lot of demand from suburbs farther northwest and a decent anchor in Fitchburg itself.

The opposite situation to that of Fairmount is that of the Providence Line. Downtown Providence is the largest job center served by the MBTA outside Boston; the city ranks third in New England in number of jobs, behind Boston and Cambridge and ahead of Worcester and Hartford. Fast service between Providence and Boston is obligatory. However, Providence benefits from lying on the Northeast Corridor, which can provide such service if the regional trains are somewhat slower; this is the main justification for adding a handful of infill stops on the Providence Line.

In New York, the situation is the most complicated, befitting the city’s large size and constrained location. On most lines, the answers to both questions is yes: there is an urban rail service need, either because there is no subway service (as in New Jersey) or because there is subway service and it’s overcrowded (as on the 4/5 trains paralleling the Metro-North trunk and on the Queens Boulevard trains paralleling the LIRR trunk); but at the same time, there are key stations located quite far from the dense city, which can be either suburban centers 40 km out or, in the case of New Haven, an independent city more than 100 km out.

Normally, in a situation like New York’s, the solution should be to interline the local lines and keep the express lines at surface terminals; London is implementing this approach line by line with the Crossrail concept. Unfortunately, New York’s surface terminals are all outside Manhattan, with the exception of Grand Central. Penn Station has the infrastructure for through-running because already in the 1880s and 90s, the ferry transfers out of New Jersey and Brooklyn were onerous, so the Pennsylvania Railroad invested in building a Manhattan station fed by east-west tunnels.

I call for complete through-running in New York, sometimes with the exception of East Side Access, because of the island geography, which makes terminating at the equivalent of Gare du Nord or Gare de Lyon too inconvenient. In other cities, I might come to different conclusions – for example, I don’t think through-running intercity trains in Chicago is a priority. But in New York, this is the only way to guarantee good regional rail service; anything else would involve short- and long-range trains getting in each other’s way at Penn Station.

The High-Speed Rail Germany Needs

I’ve argued in two previous posts that Germany needs to build a complete high-speed rail network, akin to what China, Japan, France, South Korea, and Spain have built. Here is the network that Germany should build in more detail:

The red lines denote high-speed lines, some legacy 250-280 km/h lines but most built to support 300-320 km/h, that are justifiable within the context of domestic travel. Some of these already exist, such as the Frankfurt-Cologne line and the majority of the Berlin-Munich line; Berlin-Hamburg is a legacy line upgraded to 230, currently tied with Frankfurt-Cologne for fastest average speed between two major cities in Germany. A handful of red lines are key legacy connections, i.e. Dresden-Leipzig and Dortmund-Duisburg. Some more detail on the red lines is available in Google Maps.

The blue lines denote high-speed lines, generally built to 300, that only make sense in an international context. The lines in France are the LGV Est and its short low-speed branch across the border to Saarbrücken. In Belgium the line preexists as well as HSL 3 and HSL 4, but is quite slow, averaging only 140 km/h from Brussels to Aachen thanks to a combination of a slow segment to Leuven and a speed-restricted western approach to Liege. In the Netherlands, Switzerland, Czechia, Austria, and Poland the lines are completely speculative, though in Czechia a high-speed line from Prague to Dresden is under study.

Update 8/19: here is another map of the same network, color-coded differently – red is proposed lines (most by me, a few officially), yellow is lines under construction, blue is existing lines, black is low-speed connections. Note that outside Berlin’s northern approaches, urban approaches are not colored black even if they’re slow.

Trip times

To compute trip times, I dusted off my train performance calculator, linked here. The parameters I used are those planned for the next-generation Velaro (“Velaro Novo“), i.e. a power-to-weight ratio of 20.7 kW/t and an initial acceleration rate of 0.65 m/s^2; the quadratic air resistance term is 0.000012, as any higher term would make it impossible to reach speeds already achieved in tests. On curves, the lateral acceleration in the horizontal plane is set at 2.09 m/s^2 on passenger-priority lines, mirroring what is achieved on Frankfurt-Cologne, and 1.7 elsewhere, accounting for lower superelevation.

These are aggressive assumptions and before running the code, I did not expect Berlin-Munich to be so fast. With intermediate stops at Erfurt, Nuremberg, and maybe also Ingolstadt, this city pair could be connected in 2.5 hours minus a few minutes for interchange time at the terminals. In general, all trip times printed on the map are a few minutes slower than what is achievable even with some schedule padding, corresponding to dwell times at major through-stations plus interchange at terminals. The upshot is that among the largest metro areas in Germany, the longest trips are Hamburg-Stuttgart at 3:30 minus change and Hamburg-Munich at 3:15 minus change; nothing else is longer than 3 hours.

The stopping pattern should be uniform. That is, every 320 km/h train between Berlin and Munich should stop exactly at Berlin Südkreuz, Erfurt, Nuremberg, and maybe Ingolstadt. If these trains skip Ingolstadt, it’s fine to run some 250 km/h trains part of the way, for example between Munich and Nuremberg and then northwest on legacy track to Würzburg and Frankfurt, with the Ingolstadt station added back. Similarly, from Hamburg south, every train should stop at Hanover, Göttingen, Kassel, and Fulda.

In certain cases, the stopping pattern should be decided based on whether trains can make a schedule in an exact number of quarter-hours. That is, if it turns out that Munich-Nuremberg with an intermediate stop in Ingolstadt takes around 42 minutes then the Ingolstadt stop should be kept; but if it takes 46 minutes, then Ingolstadt should be skipped, and instead of running in the depicted alignment, the line should stay near the Autobahn and bypass the city in order to be able to make it in less than 45 minutes. I think Ingolstadt can still be kept, but one place where the map is likely to be too optimistic is Stuttgart-Munich; Ulm may need to be skipped on the fastest trains, and slower trains should pick up extra stops so as to be 15 minutes slower.

Frequency and service planning

Today, the frequency on the major city pairs is hourly. Under the above map, it should be half-hourly, since the faster trip times will induce more ridership. As a sanity check, TGVs connect Paris with each of Lyon’s two stations hourly off-peak and twice an hour at the peak. Paris is somewhat larger than the entire Rhine-Ruhr, Lyon somewhat smaller than Stuttgart or Munich and somewhat larger than the Rhine-Neckar. But the ICE runs somewhat smaller trains and has lower occupancy as it runs trains on a consistent schedule all day, so matching the peak schedule on the TGV is defensible.

The upshot is that Berlin can probably be connected every 30 minutes to each of Hamburg, Munich, Frankfurt, Cologne, Düsseldorf, and the Ruhr proper. Frankfurt-Munich is likely to be every 30 minutes, as are Hamburg-Frankfurt and Hamburg-Munich. To further improve network connectivity, the schedule at Erfurt should be set in such a way that Hamburg-Munich and Berlin-Frankfurt trains are timed with a cross-platform transfer, regardless of the pulse anywhere else. A few connections to smaller cities should be hourly, like Berlin-Bremen (with a timed transfer at Hanover to Hamburg-Frankfurt or Hamburg-Munich), Leipzig-Munich, Leipzig-Frankfurt, and Frankfurt-Basel.

The loop track around Frankfurt is based on a real plan for mainline through-tracks at the station, currently in the early stages of construction. The near-Autobahn loop is not included, but such a connection, if done at-grade, could provide value by letting trains from Munich enter the station from the east and then continue northwest toward Cologne without reversing direction.

If the international connections are built as planned, then additional hourly and even more frequent connections can be attractive. Zurich-Stuttgart might well even support a train every half hour, going all the way to Frankfurt and thence to either Cologne or Berlin. Similarly, Berlin-Frankfurt-Paris could plausibly fill an hourly train if Frankfurt-Paris is cut to 2:30 via Saarbrücken, and maybe even if it takes three hours via Karlsruhe.

The one exception to this interconnected mesh is Fulda-Würzburg. The Hanover-Würzburg line was built as a single 280 km/h spine through West Germany with low-speed branches down to Frankfurt and Munich. Unfortunately, completing the Würzburg-Nuremberg segment has little value: Munich-Frankfurt would be almost as fast via Stuttgart, and Hamburg-Munich would be half an hour faster via Erfurt with not much more construction difficulty on Göttingen-Erfurt. Fulda-Würzburg should thus be a shuttle with timed transfers at Fulda, potentially continuing further south at lower speed to serve smaller markets in Bavaria.

Cost

The domestic network depicted on the map is 1,300 km long, not counting existing or under-construction lines. Some lines require tunneling, like Erfurt-Fulda-Frankfurt, but most do not; the heaviest lifting has already been done, including between Erfurt and Nuremberg and around Stuttgart for Stuttgart 21 and the under-construction high-speed line to Ulm. I doubt 100 km of tunnel are necessary for this network; for comparison, Hanover-Würzburg alone has 120 km of tunnel, as the line has very wide curve radii to support both high-speed passenger rail and low-speed freight without too much superelevation. The cost should be on the order of 30-40 billion euros.

The international network is more complex. Berlin-Prague is easy on the German side and even across the border, and the only real problems are on the Czech side, especially as Czech planners insist on serving Usti on the way with a city center station. But Stuttgart-Zurich is a world of pain, and Frankfurt-Saarbrücken may require some tunneling through rolling terrain as well, especially around Saarbrücken itself.

Even with the international lines added in, the German share of the cost should not be too onerous. Getting everything in less than 50 billion euros should not be hard, even with some compromises with local NIMBYs. Even on an aggressive schedule aiming for completion by 2030, it’s affordable in a country where the budget surplus in 2018 was €58 billion across all levels of government and where there are signs of impending recession rather than inflation.

With its mesh of medium-size cities all over the country following plausible lines, Germany is well-placed to have the largest high-speed rail network in Europe. It has the ability to combine the precise scheduling and connections of Switzerland and the Netherlands with the high point-to-point speeds of France and Spain, creating a system that obsoletes domestic flights and competes well with cars and intercity buses. The government can implement this; all it takes is the political will to invest in a green future.

Why I Write About Rail Costs, not the Cost of Other Things

I’ve been asked from time to time, Alon, you write about comparative rail costs all the time, but what about roads? Sometimes the question expresses curiosity about whether roads display the same American construction cost premium as urban rail does; sometimes it expresses frustration that The Discourse doesn’t complain about road costs. Regardless of why people ask, I’d like to explain my reasoning in depth, especially now that serious people are asking why this is the focus of my comparative research.

There’s an easy answer and a hard answer. The easy answer is that I’m a railfan. I got into this because I was living in Morningside Heights and taking the subway to social events in Brooklyn and Queens, which involved 3- and sometimes 4-seat rides. It got me interested in coverage gaps and subway extensions, which got me interested in the construction costs of such extensions.

But that’s not really it. From my original purpose of comparing a few urban infill subways in large global cities I got into operating costs, and high-speed rail, and light rail, and electrification, and even road tunnels (here is my comparison of urban road tunnel projects). What’s more, other people have looked at comparative costs, and even without sharing my not-knowing-how-to-drive origin story, they don’t compare individual road projects much. The Brookings study about the Interstates looked at the entire cost of the US Interstate program rather than teasing it out project by project.

What’s really going on is that subways are megaprojects. Megaprojects are visible, and I don’t just mean physically – they’re widely discussed in the media and politics, and cost overruns invite intense criticism by the opposition and by investigative reporters. Everybody in New York knows about Second Avenue Subway, and everybody in New Jersey knows about the Gateway tunnel, and everybody in London knows about Crossrail.

The upshot is that megaproject cost estimates are just more reliable than those of anything else. What I mean is not that cost overruns are unlikely. Rather, what I mean is that cost overruns are difficult to hide, unless the agency goes the Canadian route of fluffing the budget with very high contingencies. The current budget for Grand Paris Express is around €35 billion, up from €25 billion when it was first announced. If it actually ends up at €36 billion and not €35 billion then it may be possible to scrounge extra funds from a few sources sub rosa, but not if it ends up at €45 billion.

The largest source of wasteful spending in the world is the American military. It has a budget of $700 billion a year, debated largely behind the scenes, with boisterous generals and their lackeys ready to publicly defend every $600 toilet seat and every procurement item in the district of any member of Congress who dares object. There is a shroud of secrecy around everything that can be justified as national security. There is no exit threat – the military can’t be shut down the way an underperforming state railroad can be privatized. Hidden costs are rampant, and as far as I understand, they are on the order of a few billion dollars at a time.

I bring up American military waste not to justify civilian waste on infrastructure, but to compare which costs can be plausibly hidden. If the US military can miss a few billion dollars, the transport planners of Ile-de-France can miss tens to hundreds of millions of euros on a 15-year, 200-kilometer project. Those of Madrid can probably miss an amount of money on the same order of magnitude as those of Paris. The low construction costs in Madrid have been plugged into additional construction, giving Madrid Europe’s third longest metro network after London and Moscow; those hundreds of kilometers built in the last 25 years could not have cost the same as in France, let alone the US, because this would have been too big of a difference, and the media would have noticed.

The same situation equally occurs for road megaprojects, such as tunnels or big urban reconstruction projects, such as the lane additions in Los Angeles. But it does not occur for run-of-the-mill road widening outside urban areas or for small projects to increase the capacity of a junction from a cloverleaf to a four-level interchange. These are not sufficiently visible for me to be able to trust that there is full cost accounting in the trade and popular press.

I’m happy to compare the costs of road tunnels between different cities; the few examples I have found paint the same picture as the subway cost comparison. But above-ground road construction is harder, just because “above-ground” can mean anything from a complex viaduct-over-viaduct to simple at-grade construction. Even then, ancillary costs like unnecessary street reconstruction may be bundled into the overall budget, and since above-ground construction isn’t so expensive, these extras may be a sizable fraction of the cost.

For a similar reason, I don’t look at airports so much: they’re just harder to compare. I do not know how big the Berlin-Brandenburg disaster is compared with other airports under construction, so I do not know how much it should cost; I don’t even know what the equivalent metric of cost per km or cost per new station excavated is. In contrast, to take another well-known German infrastructure disaster, Stuttgart21 has a definite tunnel length – 30 kilometers, as well as another 25 above ground – so I can compare with other regional rail projects and say that actually the cost of Stuttgart21 (€6.5 billion) is not so high relative to how much urban mainline rail tunneling costs elsewhere in the world.

For the exact same reason, when I look at above-ground urban rail I try to separate out truly at-grade light rail from elevated lines. The only times I try to do a deep dive are when these projects encroach on the cost range of subways, like the Boston Green Line Extension. Elsewhere, ancillary costs can be substantial, as with the Nice tramway: 70% of the budget was the tramway itself and 30% was stormwater drainage, rebuilding a public plaza, tree planting, and other extras. Extras introduce an error term into comparisons that are harder to ignore when the cost is $50 million per kilometer than when it is $300 million per kilometer.

Road costs remain a powerful sanity check. All of the reasons I (and others) believe are behind the American construction cost premium are equally applicable to roads and urban rail. So far, looking at road tunnels confirms the subway pattern, but there just aren’t a lot of road tunnels built around the world – they’re expensive for the capacity they provide. And if it’s possible to carefully tease out above-ground road megaproject costs then a comparison is welcome as well. But they are unlikely to form the backbone of any comparison.

Metro tunnels, for all the handwringing about special circumstances, are pretty consistent. Some places have easier rock and some have harder rock, but usually this will be noted in the trade and popular press; the most fundamental quantities, length and the number of stations, are if anything easier to find than the headline costs; ancillary extra costs are usually not significant, and when they are, they tend to be bundled into quantifiable metrics like station size and depth. The only big difference in reporting regimes is that some places (like Spain) bundle together infrastructure and rolling stock costs whereas most don’t.

The main approach to project-level comparison of infrastructure costs across countries has to be about urban rail, because that’s by far what’s most common across the world. The error bars around ex post costs are small enough that even a relatively restricted sample is suggestive of the real global effect as I’m learning when adding more and more projects to my database (currently about 130 projects totaling 2,000 km). This is the most comparable list of public infrastructure projects, and what we may learn about why various American urban rail lines cost so much and why Spanish and Korean and Nordic ones cost so little is likely to generalize.

Why You Should Complete High-Speed Lines

Some countries build complete high-speed rail networks, on which one can travel between cities almost entirely at high speed, such as France, Japan, and China. Others build partial networks, mixing low- and high-speed travel, such as Germany. The planning lingo in the latter is “strategic bypass” or “strategic connection.” And yet, there is nothing strategic about most mixed lines. If a line between two cities is partly high-speed and partly low-speed, it is usually strategic to complete the high-speed line and provide fast travel – the benefits will exceed those of having built the original high-speed partial segment. Since Germany’s rail network largely consists of such mixed lines, the benefits of transitioning to full high-speed rail here are large.

The arguments I’m about to present are not entirely new. To some extent, I discussed an analog years ago when arguing that in the presence of a complete high-speed line, the benefits of building further extensions are large; this post is a generalization of what I wrote in 2013. Then, a few months ago, I blogged about positive and negative interactions. I didn’t discuss high-speed rail, but the effect of travel time on ridership is such that different segments of the same line positively interact.

The upshot is that once the basics of a high-speed rail networks are in place, the benefit-cost ratio of further extensions is high. In a country with no such network, the first line or segments may look daunting, such as India or the UK, but once it’s there, the economics of the rest tend to fall into place. It takes a while for returns to diminish below the point of economic viability.

A toy model

Take a low-speed rail line:

Now build a high-speed line parallel to half of it and connect it with the remaining half:

You will have reduced trip time from 4 hours to 3 hours. This has substantial benefits in ridership and convenience. But then you can go all the way and make the entire line fast:

Are there diminishing returns?

No.

The benefits of reducing travel time per unit of absolute amount of time saved always increase in speed; they never decrease. The gravity model holds that ridership follows an inverse square law in total cost, including ticket fare and the passengers’ value of time, which time includes access and egress time. Reducing in-vehicle travel time by a fixed amount, say an hour, increases ridership more if the initial travel time is already lower.

This is on top of reductions in operating costs coming from higher speed. Trains on high-speed track consume less electricity than on legacy track, because they cruise at a constant speed, and because head-end power demand scales with time rather than distance traveled. Crew wages per kilometer are lower on faster trains. And the cost of rolling stock procurement and maintenance is spread across a longer distance if the same train is run more kilometers per year. In the toy model, there are actually increasing returns coming from rolling stock costs: upgrading half the line to high speed requires running an expensive high-speed train on the entire line, whereas completing the high-speed line does not require increasing the cost per unit of rolling stock.

Diminishing returns do occur, but only in the context of an increase in top speed, not in that of speeding up slow segments to match the top speed of faster segments. In that context, benefits do diminish and costs do rise, but that is not the same as completing high-speed lines.

As the maximum speed is increased from 160 to 200 km/h, the train speeds up from 22.5 seconds per kilometer to 18. To provide the same increase further, that is to reduce the time taken to traverse a kilometer by a further 4.5 seconds to 13.5, the speed must increase to 266.67 km/h. To provide the same 4.5-second increase once more, the speed must increase to 400. Curve radius is proportional to the square of speed, so these increases in speed must be accompanied by much more exacting track geometry. Tunnels may well be unavoidable at the higher speeds in topography that could accommodate 200-250 entirely at-grade.

What’s more, operating costs rise too as top speed increases. The electricity consumption on a 300 km/h cruise is lower than on a legacy line on which trains transition back and forth between 200 and 100 and all speeds in between, but the electricity consumption on a 350 km/h cruise is definitely higher than on a 250 km/h cruise.

However, what is relevant to the decision of what standards to build a line to is not relevant to the decision of how far to extend this standard. Once a 300 km/h segment has been built, with a dedicated fleet of trains that cost €30 million per 200-meter set, the returns to upgrading the entire segment the train runs on are higher than those of just building the initial segment.

Can some strategic segments be easier to build than others?

Yes, but only in one specific situation: that of an urban area. The toy model says nothing of construction costs – in effect, it assumes the cost of making the first 200 km fast is the same as that of making the next 200 km fast. In reality, different areas may have different construction challenges, making some parts easier to build than others.

However, if the construction challenge is mountainous topography, then the higher cost of mountain tunnels balance out the greater benefit of fast trains across mountains. The reason is that in practice, legacy rail lines are faster in flat terrain than in the mountains, where past construction compromises led to sharp curves.

This situation is different in urban areas. In urban areas as in the mountains, costs are higher – land acquisition is difficult, and tunnels may be required in areas where the alternative is buying out entire city blocks. But unlike in the mountains, the existing rail line may well be reasonably straight, permitting average speeds in the 120 km/h area rather than the 70 km/h area. In that case, it may be advisable to postpone construction until later, or even keep the legacy alignment.

One example is the Ruhr area. The tracks between Dortmund and Duisburg are not high-speed rail – the fastest trains do the trip in about 34 minutes, an average speed of about 95 km/h. Speeding them up by a few minutes is feasible, but going much below 30 minutes is not. Thus, even if there is a 300 km/h line from Dortmund to points east, the returns to the same speedup between Dortmund and Duisburg are low. (Besides which, Dortmund is the largest city in the Ruhr, and the second largest, Essen, in the middle between Dortmund and Duisburg.)

Another is Connecticut. East of New Haven, there is relatively little urban development, and constructing a 300-360 km/h line roughly along the right-of-way of I-95 poses few challenges. West of New Haven, such construction would require extensive tunneling and elevated construction – and the legacy line is actually somewhat less curvy, it’s just slower because of poor timetable coordination between Amtrak’s intercity trains and Metro-North’s regional trains. While the returns to building 250-300 km/h bypasses around the line’s slowest points in southwestern Connecticut remain high enough to justify the project, they’re lower than those in southeastern Connecticut.

The situation in Germany

On the following map, black denotes legacy lines and red denotes purpose-built 300 km/h high-speed lines:

The longer red segment, through Erfurt, is the more challenging one, including long tunnels through the mountains between Thuringia and Bavaria. The complexity and cost of construction led to extensive media controversy. In particular, the choice of the route through Erfurt came about due to Thuringia’s demands that it serve its capital rather than smaller cities; DB’s preference would have been to build a more direct Leipzig-Nuremberg route, which would have had shorter tunnels as the mountains in eastern Thuringia are lower and thinner.

Since then, a lot of water has passed under the bridge. The route opened at the end of 2017 and cut travel time from 6 hours to 4, bypassing the slowest mountain segment, and is considered a success now. In the North German Plain, the trains mostly cruise at 200 km/h, and trains traverse the 163.6 km between Berlin and Halle in 1:09-1:11, an average speed of 140 km/h.

Nonetheless, the benefits of painting the entire map red, roughly from the city limits of Berlin to those of Munich, are considerable. The North German Plain’s flat topography enables trains to average 140 km/h, but also means that building a high-speed line would be cheap – around 137 km of new-build line would be needed, all at-grade, at a cost of about €2.5 billion, which would cut about half an hour from the trip time. In Bavaria, the topography is rougher and consequently the legacy trains’ average speed is lower, but nonetheless, high-speed rail can be built with cut-and-fill, using 4% grades as on the Cologne-Frankfurt line.

I’m uncertain about the exact travel time benefits of such a high-speed line. I put a route through my train performance calculator and got about 2.5 hours with intermediate stops at Südkreuz, Erfurt, Nuremberg, and possibly Ingolstadt (skipping Ingolstadt saves 3 minutes plus the dwell time), using the performance characteristics of the next-generation Velaro. But I’m worried that my speed zones are too aggressive and that the schedule should perhaps accommodate TGVs coming from Paris via Frankfurt, so I won’t commit to 2:30; however, 2:45-2:50 should be doable, even with some unforeseen political compromises.

But even with less optimistic assumptions about trip times, Germany should do it. If it was justifiable to spend €10 billion on reducing trip times from 6 hours to just under 4, it should be justifiable to spend around half that amount on reducing trip times by another hour and change.