Modeling High-Speed Rail for Germany

I’ve used a ridership model to construct a proposal for American high-speed rail – but what about the country I live in? There’s an election this year and one of the contested issues is climate change, and with growing passenger rail advocacy, it’s not outside the realm of possibility that there will be a large federal investment in dedicated high-speed lines (“NBS”). So I think it’s useful to model what German intercity rail will look like if there is greater investment in NBSes, culminating in a nationwide network such that ICEs will spend nearly all the time on NBSes or occasionally heavily upgraded legacy lines (“ABS”) rather than on slower lines.

If anything, I’m more optimistic about this network on the 15-year horizon than about American high-speed rail. Germany is slowly building more lines, like Stuttgart-Ulm, with Ulm-Munich, Frankfurt-Mannheim, Hanover-Bielefeld, and Frankfurt-Fulda on the horizon. People are also studying the prospects of a more expansive map as part of Deutschlandtakt additions, but unfortunately many 200 km/h ABSes are considered good enough even if they’re in easy terrain for a 300 km/h NBS, like Berlin-Halle/Leipzig.

The model

The professional way to model ridership is to split the travel zone, in this case the entire country, into very small pieces. I’m instead going to use an approximation with metropolitan areas and divisions thereof. For an illustration of my model’s level of sophistication, see below:

He definitely doesn’t wear a mask on the subway. Credit: Annette Pendlebury.

The gravity model to use is approximately,

\mbox{Ridership} = \mbox{Pop}_{A}^{0.8}\cdot\mbox{Pop}_{B}^{0.8}/\mbox{distance}^{2}

The justification for the exponent 2 in the gravity model is that the elasticity of ridership with respect to trip times appears to be close to -2. The justification for the exponent 0.8 is that it empirically appears true when considering Japanese cities’ Shinkansen ridership to Tokyo; the reason for this is that metropolitan areas comprise many different subsections, and the ones farther from city center have longer effective trip time counting connection time to the train station, and larger metropolitan areas tend to have longer distance from the center to the edge.

In the linked paper, the elasticity remains -2 even at short distances. However, we’re going to assume a minimum distance below which the elasticity vanishes, to avoid predicting infinite ridership as distance goes to zero. If distance is expressed in km, the best-fit constant is 75,000, with populations and annual ridership both in millions, and then if there’s no minimum distance, the model predicts Frankfurt (with 4 million people) to Mannheim (2.8 million, 75 km away) has 92 million annual riders just between the two regions, which is utter nonsense. In Japan, ridership looks like the floor is 500 km. In Germany, I’m going to round this to 2.5 hours, and because in practice it’s a bit more than 500 km, I’m going to round the constant 0.3/2.5^2 down to 1.8. We thus get,

\mbox{Ridership} = 1.8\cdot\mbox{Pop}_{A}^{0.8}\cdot\mbox{Pop}_{B}^{0.8}/\mbox{max}\{2.5, \mbox{time}\}^{2}

The network

This is the current draft of what I think Germany should build:

Blue = existing NBS and ABS lines, red = NBSes to be built

This isn’t too different from past maps I made. Berlin-Hanover is 60 minutes on this map and not 75 as on previous maps; a nonstop Velaro Novo can do it in 60 minutes, and the projected ridership is high enough that a half-hourly stopping train for service to Wolfsburg is viable in addition to a core express service. The branch point in the Rhine-Ruhr is moved to Dortmund, which slightly slows down service to Cologne and requires more tunnels, but improves frequency to the system massively, since Dortmund is a connection point to regional trains. Göttingen-Erfurt is dropped – all it does is connect Hanover and Hamburg with Erfurt, which is very small, and speed up travel to Nuremberg and Munich by 30 minutes, which is interesting but not enough to justify 100 km of high-speed rail.

Frankfurt still has an awkward-looking loop, whose purpose is to permit trains from Mannheim to enter the central tunnel to be constructed from the east and then run through to Cologne. However, this may not be necessary – trains from Cologne to Mannheim could just as well skip Frankfurt Hbf, serving Frankfurt at the airport or at a new station to be constructed at Frankfurt Süd, analogous to Cologne-Deutz for north-south through-trains. The expected traffic level is so high that the hit to Cologne-Frankfurt frequency is not awful, and the network complexity added by the skip isn’t higher than that added by having Frankfurt-Mannheim trains enter the tunnel from both directions depending on onward destination.

The network trip times are expressed in multiples of 15 minutes, with some places where timed connections are desirable, such as Fulda between Berlin-Frankfurt and Hamburg-Munich trains. However, overall, the traffic density predicted by the model is so high that on the stronger lines, like Cologne-Frankfurt, the timetable would not look like an integrated timed transfer system but rather the more continuous rapid transit-style model seen in Japan.

The power of polycentricity

The 0.8 exponent in the formula for ridership means that if we get to divide a single metropolitan area into subregions, then its ridership will increase. This is only justifiable if trains serve all such subregions; if the trains only serve some subregions, then we have to subtract them out. When we analyze New York or Tokyo, we can’t just add up each part of the metropolitan area separately – if we do so we must remove unserved sections like Long Island or Chiba, and the effect turns out to be similar to just lumping the metro area together.

However, in the Rhine-Ruhr, trains do serve nearly all sections of the region. The shape of the network there is such that intercity trains will continue stopping at Dortmund, Bochum, Essen, Duisburg, Wuppertal, Dusseldorf, and Cologne, at a minimum. The only recognizable centers without stops are Bonn and Mönchengladbach, and Bonn is connected to Cologne by streetcar.

Dividing cities and counties that are in the Rhine-Ruhr metropolitan region into the influence zones of the seven cities with stops based on what is the closest, we get Dortmund with 1.8 million, Bochum with 0.5, Essen 2, Duisburg 1, Wuppertal 0.9, Dusseldorf 2.3 (2 if we subtract out Mönchengladbach), and Cologne 2.9. Adding them up with exponents 0.8 is equivalent to considering a monocentric metropolitan core of 18.1 million; if we subtract out Mönchengladbach, it’s 17.6 million. This is enormous – larger than Paris and London, where only one high-speed rail stop is possible per train.

This also means we need to separately consider domestic and international traffic. Randstad is polycentric as well, and at a minimum there should be stops at Utrecht (1 million), Amsterdam (2.5), and Rotterdam (3.5), which means the region acts like a monocentric region of 9 million. The upshot is that if there were a 300 km/h train connecting Utrecht with Dusseldorf and Cologne with onward connections at both ends, and fares were st at domestic ICE rates and not Thalys rates, the connection between the two conurbations alone would generate about 17 million passengers a year. Of course, the model thinks all trip times up to 2.5 hours are equivalent, and the most distant city pair, Rotterdam-Dortmund, would be perhaps 1:45, but onward connections to German cities like Mannheim, Stuttgart, and Hanover are all 2:30 or longer with a 300 km/h Dutch line, and so there are benefits to constructing such a line over running at lower speed within the Netherlands.

To the extent the Frankfurt-Mannheim region can be thought of as a polycentric megaregion, the same is true there. Frankfurt, by which I mean Hesse-Darmstadt minus Bergstrasse, is 3.7 million people; Mainz is 0.6; the Rhine-Neckar (including Bergstrasse) is 2.4 million; Karlsruhe is 1.1 million; Stuttgart is 2.5 million. The model thinks that these regions combined generate 25 million annual trips to the Rhine-Ruhr.


  1. Benjamin Turon

    The German rail system is pretty amazing and I’ve been reading up on it lately. I wish there was more information on it in English, including the average kph for city pairs. I do have several books on HSR from the 1980s till today that do cover the basics of DB’s efforts, and YouTube videos and Google Maps can be pretty informative as well. Cab videos are particularly fascinating, watching a few trips including Nürnberg – München. With the Empire Corridor EIS delayed again by another year (going on year twelve, DEIS released in Spring 2014) I’ve been looking over the five alternatives, and a smarter version of ALT 125 seems the best when taking in consideration the state’s Climate Act with its zero-carbon mandate for transport. When looking at the Empire Corridor one could think of upgrading the Hudson Line — including the AC overhead electrification excluded in ALT 125 — as a “ABS” and then building to Buffalo a “NBS” as laid out in ALT 125, except by electrifying the entire corridor you can have a speed of 160-to-220 mph on the new tracks west of Schenectady. That could travel times NYC-Buffalo to about 5 hours, 2hrs NYC-Albany and 3hrs Albany-Buffalo. Leaving a new dedicated-HSR line NYC-Albany for a later stage avoids the tens of billions in construction costs that led NYSDOT to reject preliminary ALT 160 and 220, and I rather invest $15 billion for real high speed rail than $6 billion for a upgraded Amtrak service on the existing CSX right-of-way. The goal should be to use intercity rail to merge the state into one mega-region and you need real HSR to do that, and Germany seems to offer a good case study on how to do that by leveraging existing infrastructure.

    ICE 1 Nürnberg – München

    New York’s high-speed rail project faces lengthy new delay

    • adirondacker12800

      West of Little Falls building a 125 mph railroad is really stupid. It’s flat. There is straight ROW. And it’s flat. All the way to Denver. The Turboliners toyed with making it in 2 between Albany and Manhattan. 2 hours is something Bulgarians could be proud of.

      • Benjamin Turon

        The Empire Corridor to Hoffmans west of Schenectady is 169 miles of Metro-North and Amtrak track which is primarily used by passenger trains, while west of Hoffmans you have CSX owned right-of-way, the freight railroad having a 90-mph speed limit (see Virginia DC-Richmond) and being opposed to electrification. Thus it makes sense to fully upgrade the Hudson Line “ABS-style” and then build to Buffalo a new line “NBS-style”. I would imagine that electrification would drop travel times NYC-Hoffmans (acceleration and tilt) so that NYC-Albany would fall below 2 hours, giving you a “Brightline” average speed of 70-mph or greater. Combined that with a 160-mph new line and with a a 100-mph average speed you could get NYC-Buffalo in about 5 hours, which is Hamburg-Munich (5h 31min) by DB’s ICE. I suppose NYC-Toronto could be Hamburg-Zurich (7h 35min). Obviously a big issue with the EIS is that its undertaken primarily by consultants and DOT employees/officials with little knowledge of modern intercity rail, as evidence by the failure to electrify the Hudson Line in ALT 125 so you could go 160 on the proposed new line west of Albany.

        • adirondacker12800

          There’s one of the problems. 160 is decades old service speed. It’s 300 kph or 186mph, or more these days. In practice the fastest you can go through a grade crossing is 110. In the regulations if you want to go 126 you need to grade separate. The cost difference between grade separating for 111 versus 222 in the flat places west of Little Falls is effectively zero.

          The scope in the bookcases full of studies collecting dust is too constrained. The I-87 congestion study has evaporated from the NYSDOT’s web site. South of Albany was out of the scope so they assumed it would remain slow. Boston and Philadelphia weren’t even mentioned. If they make it really fast between Albany and Buffalo it makes it really fast between New York and Toronto or Boston and Toronto too. Really fast between Albany and Montreal makes it really fast between Boston and Montreal or Philadelphia and Montreal. Someone needs to think in terms of Northeast-Midwest-half of Canada. Not Rome to Amsterdam. New York not the Netherlands to Italy.

          • Matthew Hutton

            I’m sure we have grade crossings with 200km/h trains here in the UK

          • adirondacker12800

            If I am to believe everything I read in Wikipedia you need some trains with a speed that high first. Where are they? The trains or the crossings? Again, apparently, the only with line with speeds higher than 200 kph is the one between St. Pancreas and the tunnel to France.
            Searching the extensive article on railroad crossings in the U.K. for “max” I come up with 100mph/160kph.

          • Herbert

            To my knowledge the brits are the only ones who tried to get so much speed out of legacy signaling. In continental Europe everything above 160 km/h has its own rules, including its own signaling system (supposedly ETCS from here on out) and no level crossings.

            In the US the legacy signalling system has of course been limited to 79mph

          • fjod

            Herbert – That may be the case for Germany, but running at 200kph on ‘legacy’ signalling is perfectly common in Sweden and France among others. FWIW Sweden has plenty of level crossings on these lines too.

          • Benjamin Turon

            It is FRA regulations that limit crossings to a speed to 110-mph, for 125 they require a barrier that can stop a fully loaded dump truck (as opposed to a passenger car, where such gates do exist) so no go above 110-mph. About 20 years ago the FRA did a 125-mph grade crossing study on the Hudson Line which determined that the risk did not increase much from 90 to 110 to 125, this was done for the failed Turboliner rebuild program of the Pataki Era. There are several crossings in 110-mph territory on the Empire Corridor, none of them a major highway, the question is would the travel savings of 125 vs 110 be worth the cost of grade separation? The CSX right-of-way does have significant curvature in the Mohawk Valley and between Syracuse and Rochester as the railroad follows waterways. Primarily though CSX will not accept speeds higher than 90-mph, so to go faster you need a dedicated passenger right-of-way, utilizing CSX only to enter cities.

          • adirondacker12800

            High speed trains can go around curves. They need to be very broad. They can be between Little Falls and Denver. Not that there is ever going to be high speed trains to Denver.
            Do the annoying first year algebra question. The eastbound express freight train leaves Buffalo for Selkirk every half hour and averages 50 mph. The high speed passenger train leaves Buffalo Central every 15 minutes and averages 150. How many freight trains does it pass? Unless you want to sneak in a occasional passenger train moving at the same speed as the busy freights they need separate tracks.
            Building grade separations for a 126mph railroad west of Little Falls in 2021 is really really stupid. This stuff is all interrelated. Build four grade separated tracks across Upstate New York and a few billion dollars of freight tunnel from Jersey City to Brooklyn or double deck the New Jersey Turnpike, the Long Island Expressway and the Connecticut Turnpike. Triple decking the George Washington Bridge and the Cross Bronx Expressway won’t be cheap either. Neither will the half trillion dollar artificial island off the Lower Bay, for the fourth NYC airport.

          • Herbert

            Citation needed on 200 km/h operation with conventional signals.

            It may not be ETCS (in Germany in many cases it’s still LZB) but it is something different from the old visual signal system

      • Russell.FL

        It’s hard to conceive of anything they can do for NY-Albany to get it faster than 1:45, at best. Faster than that, you’d have to build a completely dedicated right of way. You would essentially be building through some of the most expensive real estate in one of the highest property-rights countries in the world. Seems like a better approach would be to have frequent, every hour on the hour service, perhaps one each for a “non-stop” service that continues upstate and an “all-stops” service with a timed transfer at Albany to allow those from the local stops to continue upstate every hour. Electrification of the entire line would help, but I don’t think that gets you to 1:30 even with a non-stop service.

        • Alon Levy

          The US doesn’t actually have strong property rights protections in eminent domain cases. Americans just assume other countries don’t have individual rights protections.

        • Benjamin Turon

          The SNCF (yes that SNCF) did a study in 1986 for NYSDOT that after conducting some test runs with the Turboliners, concluded that with a top speed of 110-mph the 141 mile Penn Station-Rensselaer run could be made in 111 minutes non-stop (80-mph average speed) and 118 minutes with 4 stops (75-mph average speed) – both which are 15 and 5 minutes faster than the 2hr 05min of the Empire Corridor DEIS. With electrification and utilizing a tilt-train like Alstom’s Avelia Liberty slightly faster travel times might be possible.

          In the US property rights protections in eminent domain cases are indeed poor since private property can even be taken by the government in the “public” interest for use by another private party who the local/state government deems will make better use of the land, for example seizing waterfront homes to be replaced with condos that will generate greater property taxes.

          Or Gov. Andrew Cuomo taking several blocks of Midtown Manhattan around Penn Station to hand over to Vornado Realty to build super tall towers, replacing “blighted” midrise office buildings, hotels, department stores, apartments, condos, and a church. What stops such projects is legal cases that go on forever, very bad publicity, key supporting politicians losing elections, resigning, or going to prison, and general incompetence by public authorities… like the California High Speed Rail Authority.

          This is how “urban renewal” became possible in the Postwar Era, before WW2 eminent domain was more narrowly defined by the US Congress and the federal courts to uses for government, transportation, water, and power. That’s why Rockefeller Center as a few rowhouses imbedded in the complex’s buildings, these were the holdouts who refuse to sell, most of the land the complex was built on was owned by Columbia University and was sold to Rockefeller for the project.

  2. barbarian2000

    “The 0.8 exponent in the formula for ridership means that if we get to divide a single metropolitan area into subregions, then its ridership will increase. This is only justifiable if trains serve all such subregions; if the trains only serve some subregions, then we have to subtract them out. When we analyze New York or Tokyo, we can’t just add up each part of the metropolitan area separately – if we do so we must remove unserved sections like Long Island or Chiba, and the effect turns out to be similar to just lumping the metro area together.”

    Surely if the trains only serve some subregions, you subtract the served subregions out of the total but still keep the rest? For instance, if you serve Long Island with HSR, then passengers in Yonkers will still continue going to Penn Station to take the train from there

    • Alon Levy

      Yep. It’s just that usually this calculation ends up having a similar effect to just lumping the entire combined area together.

    • adirondacker12800

      Passengers in Yonkers can go to Buffalo or Montreal without passing through Manhattan. Not many of them but they can. They can even get to Boston that way. But it’s so execrably slow it’s faster to go to Manhattan and backtrack through New Rochelle. Local buses to New Rochelle would likely be fastest.

  3. Rover030

    You mention that between Cologne and Frankfurt, the system functions more like a rapid transit system than a takt based system.

    Have you written about the transition between rapid transit and takt based scheduling within one system? I’m thinking of the Dutch Intercity rail system in the Randstad, where this causes challenges. I’m thinking of the Amsterdam/Schiphol – Utrecht – ‘s Hertogenbosch/Arnhem system, where each leg next year has 6 IC trains per hour which combines to 12 on the 4 track Utrecht – Amsterdam Bijlmer line. However, because the lines branch into lines with 2 trains per hour and there is extensive (reverse) interlining, there are timed cross-platform interchanges at every major station. This causes a lot of 3-5 minute dwell times, that in practice are longer because the padding time is not included in those dwell times. This extends cross-country trips by up to 20 minutes.

    At what point should you say: the frequency is high enough, not everyone gets a direct train on every city combination, and we won’t time the transfers anymore because a maximum 5/7.5/10 minute transfer is acceptable if we can speed up trips?

    I imagine Switzerland has similar trade-offs in the core of the Zurich S-Bahn, and in the coming years when they implement their 2025 and 2035 expansion programs.

  4. Herbert

    Nuremberg and Dresden both have roughly half a million inhabitants. Prague of course has more than that. Why in the triangle of those cities are Dresden and Prague the only ones that get a direct link? Is it because such a link is already proposed? – the proposal, at any rate, includes what would become both country’s largest tunnel underneath the ore mountains. And if I read what news there is about the project correctly, German NIMBYs may succeed in getting even more tunneling done on the German side to alleviate noise concerns

    • Onux

      I would assume that since getting to Dresden also gets you to Berlin, the Prague-Berlin ridership far outweighs any of the other city pairs in question. Plus Dres-Nur and Nur-Prague are only slightly shorter than Berlin-Prague, let alone just the Prague-Dresden link. Too much track for too little ridership to complete the triangle.

    • Alon Levy

      The original reason was to do Berlin-Prague. But there’s also a good reason to do Nuremberg-Prague, which shortens Frankfurt-Prague and Cologne-Prague by half an hour (but Dortmund-Prague is still faster via Berlin), and enables Munich-Prague.

      • Herbert

        It may well be due to both cities being airline hubs, but Frankfurt-Prague has non-negligible air traffic. Plus the existing link from Nuremberg to Prague is so bad, even DB ran buses for the longest time…

        Also: the proposed link underneath the Ore Mountains will almost certainly have high freight demand as it will be the Czech Republic’s best access to the North Sea ports. Just like the existing line through the Elbe valley currently is, but I can see demands to remove a lot of the freight traffic from that line as it crosses a national park

        • Herbert

          Also also: Nuremberg city limits immediately abut both Erlangen (100k) and Fürth (100k) and there are both existing and proposed rapid transit links between those cities. Now… How you count them is entirely a question of the model, but there are quite a few ICEs that stop both in Nuremberg and in Erlangen as well as a number that run through Erlangen without stopping…

          • Alon Levy

            I look at metro areas, so obviously Erlangen and Fürth count within the Nuremberg region. The question is how big to go – the Verkehrsverbund is enormous. In the table I’m constructing I went with the entirety of Mittelfranken as the region, but it might still be too big.

          • Herbert

            I think it’s reasonable to go with the area served by a continuous urban rail system. So hopefully by the end of this decade that’ll include Erlangen and Herzogenaurach as served by the

  5. Onux

    I think that evaluating travel time rather than distance is a major improvement on your model, however, is 2:30 really the floor for ridership? Empirically, city pairs at or just over 2:30 travel time still seem to have a 10-30% mode share via air (Tokyo-Osaka, Madrid to Barcelona or Seville). Yet there are also city pairs at a 2:00 travel time or less have no flights between them or less than 5% mode share (Paris-Brussels, Taipei-Kaohsiung). Shouldn’t the floor be lowered to 2:00 (or 1:45/1:30? – technically you can still find direct Paris-Brussels flights despite Thalys taking 1:20, but that might have more to do with follow on connections)?

    At the other end, shouldn’t there be a max time? Your model is still going to predict some non-negligible ridership for LA-NYC via HSR, even though empirical evidence says effectively no one would ride it that far except as a tourist journey in itself, rather than as a transportation option.

    • Henry Miller

      The model predicts .7 million passengers per year for a NYC-LA rail in 13 hours. That sounds about right for the number of people who hate flying and thus take the train, and tourists where the train the reason for the trip. It also is approximately nobody, I’m not sure how you call it non-negligible. Of course in the real world the time would be longer both because geography will force a longer route, and you won’t do a non-stop train between those cities even if the HSR rails existed.

      • Onux

        In 2019, total air traffic between LA and NYC (all airports in each metro area) was approx. 5.2M. So 0.7M would be 11-13% of the rail/air split (depending on it the 0.7M came from air, or would be non-flyers who currently drive/bus) – at 13 hours. Today Tokyo-Fukuoka gets a 8%/92% rail/air split with a 5 hr time on the Shinkansen. I doubt more than doubling the journey length would lead better mode split on the LA-NYC route.

        0.7M pass/yr is not approximately nobody; in 2019 total air passengers from Atlanta to Las Vegas was 0.77M.

        The model needs a ceiling if it is going to have a floor.

        • Bobson Dugnutt

          @Onux, start by modeling a service that could plausibly be provided.

          I can’t stress this enough. The U.S. can have a national rail network without having a national rail network.

          One more time for those in the back: The U.S. can have a national rail network without having a national rail network.

          The U.S. government should be able to study, plan, identify corridors, finance construction, and set engineering and design standards. It should then create districts that would span across state boundaries to deal with corridor-specific issues. The alternative is direct management by Congress, and 50 years of the lived experience of Amtrak shows this approach has been an abject disaster.

          The U.S. does not, can not, and should not have the capacity to literally run a single train line from coast to coast. If/when the U.S. manages to stitch together high-speed rail corridors that can link the Atlantic and Pacific, let the passengers MacGyver themselves an itinerary and chronicle their adventures.

          Let’s start with what we know are the physical constraints of trains at any given speed. They can’t climb steep grades very well. They need straight tracks or very wide turning radii if curves are needed. And be mindful of innumeracy — 220 mph is a top speed, not the cruising speed. The average drops considerably when you factor acceleration from and deceleration to 0. It’s impossible to achieve a cruising speed to match the top speed.

          There’s a practical limit in time and distance for high-speed trains. One common measurement is 400 miles end-to-end. Another way to think about this is what timepoint are you trying to make? A 4-hour time window for a one-way end-to-end trip has something informative for passengers and the railroad.

          If you’re using the distance limit, 400 miles in 4-hours is a 100 mph cruising speed. (That’s a hypothetical target I offered for a Minneapolis to Chicago route with 8 stations.) Manage 125 mph and the wall expands to 500 mph or about 3’15” on that same MSP-CHI route. Manage 150 mph and the wall expands to 600 mph or about 2’45” on that same MSP-CHI route, with Milwaukee and Madison now within daily commuting distance.

          Achieving 150 mph or higher cruising speeds would get you closer to the holy grail of a transcontinental HSR, with most medium or large metro areas east of the Mississippi getting a stop. Chicago to New York City is still not feasible, but with a timed connection in Cleveland … You can, however, tie together a corridor making a Chicago to Atlanta day trip feasible if you only made one stop per state along the way (Indianapolis, Louisville, Nashville). Chicago to Dallas could be done in 6-8 hours with a connection in Kansas City.

          West of the Mississippi, you have the dual problems of mountains and vast distances between large cities’ pairs. On the West Coast, the largest cities are oriented north to south. California’s cities are ideal because they are large enough and spaced widely enough to be the just-right balance of speed and ridership. Yet once you get to Sacramento, there are just two metros with 1M+: Portland and Seattle. And we are dealing with very challenging terrain here. You can get within 500 miles if you aggressively straighten the route while serving the two Oregon university towns, Medford and Redding (two ~250K metros), Chico and SMF airport. On paper, it looks attractive … in reality, this route would be committing crimes against humanity, ecology and economy.

          The only conceivable transcontinental link is L.A., Phoenix, Tucson and El Paso. That Tucson-El Paso stretch had better generate unprecedented ridership. It’s still another 500 miles between El Paso, whose economy encompasses two states and two nations, and one of the prosperous Texas cities in the triangle/T-bone.

          • adirondacker12800

            The modeling service would say “there are two metro areas of a million a piece in the 1,000 miles between Phoenix and San Antonio. one in the 1,200 miles between Denver and Sacramento and none in the 1,600 miles between Minneapolis and Seattle. NO”

          • Herbert

            Real world high speed trains often have journey times on the train that exceed four hours.

            If for example you can get a Munich-Frankfurt, a Frankfurt-Hamburg, a Hamburg-Copenhagen trip out of the same train, why not run it Munich-Copenhagen? Granted, this applies more to the US east coast than the center and west of the country, but it’s not entirely outside the realm of possibility.

            Another thing is sleeper trains: evidence shows that there is a certain class of traveler who even at price points that disadvantage rail (and let’s face it: air travel in the U.S. is more expensive than in Europe) prefer waking up rested at their destination ready for the day’s task over taking the red eye or flying in on the evening before and adding a hotel to the cost.

            Now, 200+ km/h capable sleeper trains are a rare breed (iirc the youngest order by the Austrian railways calls for 230 km/h capability and there is of course China) and it is questionable whether they would pencil out econocratically, but there is certainly a political case to be made for serving as many House districts and Senate seats as possible…

          • Alon Levy

            I’m really squeamish about the maintenance implications of night trains – high-speed tracks need regular nighttime maintenance windows. Japan notably doesn’t run night trains on the Shinkansen network and France doesn’t on the LGVs. I know it’s being done here and I also know maintenance costs here are lower than in France, but I want to be certain there are adequate maintenance windows.

          • Benjamin Turon

            I would think that conventional lines (even in Japan) work well enough for overnight trains, as the trains are basically a combination of night bus (coach) and rolling hotel (sleeper) so journey times of 6 to 10 hours are acceptable, especially if it saves you a hotel stay.

          • adirondacker12800

            Your fare has to reflect 24 hours of room rental – it’s not going to be in service during the day – on a low capacity car. And 12 hours of staff instead of 4 for your 3 hour trip. People who want to take a land cruise across the Rockies can take the special connecting HSR train from New York that whisks them to Saint Louis or Kansas City during the day to have the car attendant welcoming them to the whole settling into your Pullman sleeper experience. Something loitering at one of the platforms for a few hours won’t matter as much in the evening.

          • Phake Nick

            One thing with high speed night train is that, you can only run that train 1 trip each day, unless you plan to serve daytime passengers with beds to sit on which is not a great idea (China is doing this), and as such it would result in lower utilization
            Another thing with maintenance is that high speed trains themselves also need checkup every certain distance they have operated. That is why despite China having already constructed high speed rail to Xinjiang, they still haven’t managed to run a train directly from Beijing to Xinjiang despite it would be immensely symbolical to them politically.
            As for high speed track maintenance window, I believe it is required because you cannot have the trains travel on 1 track at 200+ km/h and then have maintenance personnel working safely on the track next to it. It would be safe if the train didn’t travel at 200+ km/h, and is how conventional speed trains operate at night alongside maintenance personnel.
            For Shinkansen, decades ago Japan actually floated the idea of running Sleeper Shinkansen by parking the train at a station mid-way in 0am-6am (both for noise reason and maintenance window), in order to let passengers depart later than last flight and arrive destination before than first flight. But due to the economical reason of utilization cited above, it didn’t materialize.
            As for conventional overnight train, in Japan they are okish popular but the yield isn’t high enough to justify making new overnight trains and they would rather motivate passenger buying high speed train tickets which cost more, and instead they would invest in cruise train as a form of overnight service instead which are sold as tour package and cost a lot more to ride on. For regular overnight services, railway companies are selling overnight bus tickets through their bus division instead.

            But one thing positive about high speed night train across the rocky mountains is that, if you really are going to build such a rail line despite the anticipated low cost and expensive construction cost, you can actually schedule the maintenance window in the daytime and let the trains run across the section at night, since the number of cities nearby would be so little that there wouldn’t be too much demand in the day and there also wouldn’t be too much noise complain in the night

          • Onux

            @Bobson Dugnutt

            I am not advocating for LA-NYC HSR. Quite the opposite, I am pointing out that Alon’s formula still includes semi-decent ridership (~10% of air travel) for LA-NY when most people (including you and I) believe it would be a low single digit percentage at best.

            I was evaluating LA-NYC to argue that Alon’s formula needs a ceiling as well as a floor – it needs a time beyond which city pairs no longer contribute ridership, as it is too small to matter. Alon’s use of Metcalf’s law and his formula runs the risk of making certain long range routes or links (i.e. ATL-Jacksonville) look better than they should due higher ridership from distant city pairs than would actually exist. You believe the limit is 4 hours, based on data I have seen 5 hours might be more reasonable.

            According to this link (page 15: the rail/air split is best modeled as the difference in time between the two (I assume actual time in train/plane not including station/airport access time, but it is not stated). It is not a steady exponential decline like Alon’s formula, it drops steeply between the train being 1 to 3 hours longer, and ridership is very low when the train is 4 hours longer or more.

        • Henry Miller

          How many people drive that trip today? The number is not 0, but you are taking riders from that as well.

          In the end we will never know. The model says the line isn’t worth building. Thus we can argue as long as we care, there William never be a real test anywhere close to the limits.

          • Bobson Dugnutt

            @Henry Miller, you can model a potential PDX-Sacramento high-speed rail line. They’re within 500 miles and are dotted with a lot of small metros. The ridership would be not bad.

            But you shouldn’t model a potential PDX-Sacramento line. Mother Nature is the ultimate NIMBY here. This line would need straightening from the existing Coast Starlight track, and serve Medford instead of Klamath Falls. That means a lot of tunneling and/or mountain removal.

            Construction and operations would be running through a very catastrophe-prone area. Between Sacramento and Oroville is a giant flood plain. This area is also prone to earthquakes, drought and fires — which often converge.

            There’s a bigger problem than this corridor’s ridership underperforming. What if the corridor overperforms? Say the line makes a ground-level day trip possible between Portland and Sacramento. The spots in between are strikingly beautiful. The Redding area and the Rogue Valley would be exurbs. Tourism would spike. So, you might have a scenario where Portlanders or Californians might take a train to a Sierras sojourn for, say, a weekend gender reveal party. And they set the forest on fire.

            That actually happened. (Granted, it was in Southern California. Northern California had the Martian sky fire around the same time. )

          • adirondacker12800

            I vote for Chicago-Saint Louis-Kansas city which slightly shorter, serves more people, can have more connections and is on the Great Plains which are flat.

          • Herbert

            The Japanese build rail lines through earthquake prone territory without issue.

            The Swiss tunnel under formidable mountain massifs without issue.

            The Germans have high speed trains climb 4% slopes without issue.

            The existing rail line between Dresden and Prague goes through a national park.

            All those sound like excuses of the country that cancelled Apollo, not the can do attitude of the country that put a man on the moon…

          • Bobson Dugnutt

            @Herbert, the problem is not a deficit of pride or ingenuity in the U.S. Although, I fear for national self-esteem reasons, America would prefer to think through things itself and make costly mistakes along the way.

            If we’re talking about the hazards present in the Portland-Sacramento corridor, the problem is that natural disasters can (no pun intended) cascade. A major earthquake can spark massive wildfires through fallen power lines or ruptured gas lines. There is also the danger of a dam failure, from a quake or deterioration over time. See the 2017 Oroville dam crisis. The wildfires, like the recent Paradise tragedy, scar long beyond the inferno, as it looses soil and makes mud/landslides and avalanches more probable. Railroad tracks could be permanently damaged; trains could become entombed or run hard into a column of dirt or snow at a high speed.

            We can build this line, but we shouldn’t.

          • Phake Nick

            “Beautiful scenery” and “Many small towns” are good reason to support a scenic conventional train service that can maybe charge a premium by offering cruise train service. Not reasons to build a high speed line which depends on ridership to and from large cities.
            And if you have the ridership, then even if you face disaster after completing the line, you’ll have enough financial stream to repair it after each disaster.

          • adirondacker12800

            I’ve changed my mind. Kansas City-St Louis-Indianapolis. Chicago-St Louis makes sense independently. The trains from Kansas City can use the same tracks. Cleveland-Columbus-Dayton-Cincinnati makes sense too. That will prove the Indianans, that trains don’t sap the precious bodily fluids of Real Americans and want some high speed trains to Chicago themselves. It’s 358 road miles from Columbus to Chicago but only 117 miles/188 km between Dayton and Indianapolis. Some of that may be parts of the Columbus-Dayton tracks. It’s only 561/903 to Cleveland from St Louis. From a Sacramento-Portland line you can get to metro Bend. With less than a quarter of million people.

          • Bobson Dugnutt

            @adirondacker12800, I second you on the “orbital” routes you suggest. I was thinking of these alignments for my maps as well.

            The Midwest hub city would first focus on lines radiating out of Chicago, ideally 500 miles or 4 hours one-way out (if we can find corridors to hit 150 mph or 175 mph, we could push the boundary to 600 or 700 miles).

            St. Louis from Chicago is 250 to 300 miles, depending on which alignment you choose. This is assuming you must serve two stops along the way: Springfield, the capital, and Midway Airport. Which of the three gets the rose?
            1. Peoria. It’s the 4th-largest metro in Illinois (400,000) and with little in the way between Joliet and Springfield, would have the fewest stops and give you the highest speeds.
            2. Bloomington-Normal. It’s the straightest route to Springfield and St. Louis, and you have Illinois State in the middle. This route has the smallest of the MSAs and a few tiny cities/counties on the way, though.
            3. Champaign-Urbana and Decatur. This one gives the longest of the routes, but it does have Illinois’ flagship university and will provide massive college athletic traffic. C-U and Decatur combined have about 330,000 population.

            St. Louis would be a satellite of Chicago, because with 3 million in the metro and it offering a great deal of similar 1M+ metros within its orbit, it would complement the Midwest and Southern networks and help us get a national rail network.

            I agree with your KC routes. The Missouri trunk (connecting to KC), will allow for Chicago-STL-KC, with a transfer at KC to Dallas via Wichita and Oklahoma City. I’d start the eastern route out of STL and serve Indianapolis, Dayton and Columbus. I was thinking Pittsburgh, but it’s too hilly.

            Other routes:
            1. The Kentuckian. St. Louis, Evansville (315K), Louisville (2.7M and connections to Chicago and Atlanta), Frankfort (capital) and Lexington (750K and the flagship university). The route is only 325 miles. If you want to upsize by another 100 miles of track, you could get to Cincinnati, but the right angle would require and out-of-the-way station. On the other hand, this would be one of the few geometric triangles worth filling (Cincinnati at the northeast, Lexington at the southeast and Louisville at the southwest).
            2. Mississippi River. This is controversial. Using Human Transit parlance, this would be a “coverage” route. Passenger traffic wouldn’t be particularly strong; there are only 4 metros with 1M+ population: Twin Cities, St. Louis, Memphis and New Orleans. This might make sense once the Chicago hub is built out, though. You’d have 3 corridors, with STL in the middle. Minneapolis-St. Louis has La Crosse (again!, so we could “borrow” the MSP-Chicago line), Dubuque (tiny at 97K, but if the MPS-CHI route gets too crowded this could allow a bypass to CHI via Rockford), the Quad Cities (nearly 750K), Quincy/Hannibal (150K), Lambert Airport and St. Louis.

            South, the route looks better. You can go to Carbondale and serve the Southern Illinois campus there, Cape Girardeau (250K), Jonesboro (130K and Arkansas State U) and Memphis. You can get a reasonably fast CHI-STL-MEM line and the route would pencil out. South of Memphis, you can serve Tunica (redneck Vegas) and be Mississippi’s north-south train, serving Ole Miss, Jackson (capital and connections to Dallas and Atlanta), Hattiesburg and New Orleans.

            3. Broken Arrow. St. Louis to Springfield (470K), Fort Leonard Wood (the three counties near it combine for 150K or so), Springfield (470K), Joplin (nearly 300K), Tulsa (1.2M) and Oklahoma City (1.5M). Oklahoma City offers connections to Dallas, Wichita and Kansas City. You can bolster ridership by diverting to Northwest Arkansas from Joplin, though you’re going to go over the 500 mile boundary. You do pick up a 525K metro, a university, and Fort Smith about 50 miles south adds another 300K to the potential ridership pool.

          • adirondacker12800

            Airports are highly overrated as train stations. It just looks like a lot of people. It’s the same people loitering around multiple times.
            Fascinated foamers get all frothy trying to convince me that I should be excited about an hour and half train ride to Newark Airport, an Airtrain ride to the terminal, waiting in lines longer than the ones in Albany, to get through security, so I can take a non-stop that is slightly faster than the non-stops I can get in Albany. Or use one of the non-stops from Albany to a hub, walk across the concourse to a connecting flight and get there as fast as an hour and a half train ride to Newark for the non-stop from Newark.
            The trains to Detroit or Cleveland can share tracks until someplace in Indiana. Likely the ones to Indianapolis too. Or perhaps the ones to Indianapolis can share with the ones to Saint Louis. The Midwesterners can fight it out in 2060.

    • df1982

      I agree that introducing a 500km floor seems too high, as there surely is an appreciable difference in ridership between a city-pair that is 1 hour away as opposed to the same city-pair with a 2-2.5 hour journey. But this raises the question: what do you count as ridership? Only riders on bonafide high-speed trains or all riders between the cities, including those who choose to rider on slower, cheaper trains along the same alignment? I.e. in Frankfurt-Mannheim, would it just be ICE or also RB/RE passengers? In NY-New Haven just NEC passengers or also Metro-North? And then how do you factor in intermediate riders, e.g. Frankfurt-Darmstadt or NY-Bridgeport?

      Also, what figures do you use to calculate metro population areas? I haven’t seen anywhere that states that “Frankfurt” has 4 million people. The usual definitions are:

      City: 750k (obviously too restrictive, as it relies on artificial political boundaries, although it is the definition of a city that Germans most readily use)
      Urban Area: 2.7 million
      Metropolitan Region 5.8 million (obviously way too expansive, since it includes places like Fulda and Gießen, which might be commutable from Frankfurt but aren’t very useful for calculating intercity ridership).

      So it seems like urban area is probably the best definition to use.

      • Alon Levy

        Pricing high- and low-speed trains should be the same. Ein Ticket für alles.

        Frankfurt-Darmstadt is purely a regional connection – the planned NBS (for capacity) doesn’t stop there.

        German metropolitan area definitions are incredibly weird. German urbanism, unlike American, French, or Asian urbanism, consists of distinct city cores with open space between them rather than contiguous urban sprawl, so doing an international sanity check is often impossible. There are official metropolitan regions but they’re not defined consistently, and neither are the Verkehrsverbund boundaries. I tried going by S-Bahn reach and by mutually exclusive regions, so metro Frankfurt consists of all of Hesse-Darmstadt minus the one Kreis that is in the Rhine-Neckar region, and Mainz is a separate region despite being on the Frankfurt S-Bahn.

        • adirondacker12800

          It made sense in 1970 when they were using para-mutuel machines to print the tickets at the agent’s window. And collating all the information for the monthly reports on a computer with less horsepower than the one in your toaster. Even then the all parlor-car trains had premium fares and faster speeds than the all coach trains. ( Metroliners were all-parlor car trains with a parlor car fee. ) Most places in North America aren’t going to have slow trains and fast trains, they are going to be lucky to have trains at all. Differential fares in the few places where there will be more than a train hour means the Philadelphians pick the slightly slower train to New York or DC freeing up seats on the slightly faster train from Boston to DC. Like they do now. Where there are rich people who spend the money to brag that they took Acela.

          • Herbert

            Mixing speeds is bad for capacity and if you solve that problem through timed overtakes, you add vulnerability to the timetable.

            That’s why on the Nuremberg-Ingolstadt hsl you got the (until at least late last decade) only “regional” trains in Germany that routinely run faster than 160 km/h.

            Heck, they even equipped the Alstom Coradia continental with ETCS for the “S5” (a curious “S-Bahn” with two stops and less frequency than some REs…)

          • adirondacker12800

            Between New York and Philadelphia the timed overtakes can happen on the four center tracks of the six. While in motion. In New Jersey anyway. The twice an hour train that goes through Suburban can be scheduled to weave itself between the four SEPTA trains on the line on the four tracks that are between Philadelphia and Trenton.
            ….. youse people have no concept of the scale, there are four or more tracks, right now, between Stamford and Wilmington.

      • adirondacker12800

        They let people from the hinterlands use the station in the city. People from the hinterlands can make their way to the train station. Just like they do to the airport. There isn’t a lot of them but taken together, for all the little places in the catchment, its significant. Even the people from farther out than the hinterlands. Who have no other choice.
        That there is no traffic and it’s easy to park out here in the woods doesn’t make the Lincoln Tunnel any less congested. Or make it easier to park in Manhattan. Or Boston. Or Philadelphia. Or Washington D.C. Or Brooklyn or Queens that have more people each than metro Baltimore. Where it’s not very easy to park either. That has bad traffic too.

    • Alon Levy

      In the 300 km range there’s a lot of car ridership – I don’t have a reference anymore but I remember reading that more people drive than take the Shinkansen between Tokyo and Nagoya, and only at the Tokyo-Osaka range does the Shinkansen have a majority of the ridership.

        • Herbert

          Car riders are the most mode fixated.

          Usually the only thing that significantly changes car ridership is a major biographical event – birth of a child, marriage, divorce, move to a new neighborhood, etc.

          That’s why it is important to build the public transit infrastructure before people move to a neighborhood…

          • Frederick

            It cannot be helped in Nagoya.

            Toyota’s HQ is located just over 30 km away from Nagoya. This is also why private car has a much larger modal split in Nagoya than in Osaka or Tokyo.

      • df1982

        Surely a 1-1.5 hour train would be pretty competitive against a 3-hour car ride over 300km. And the total volume against a 500km city-pair would be much higher. For one, you start getting to the point where daily commuting is viable. Do you have any other real world examples for comparing patronage, e.g. Berlin-Hamburg vs Berlin-Munich, Paris-Brussels vs Paris-Amsterdam, London-Liverpool vs London-Newcastle.

        • Henry Miller

          When HSR times are less than about 2 hours you need to consider total door to door time not train time. People don’t live next to the station and travel to the next station. The stations are really places people travel to because they have to. For some who count as possible riders in the model it is half an hour by car, or 1 hour by what passes for transit out on the edges of the MSA. There are some people on your 300km line that will find it faster to drive, and another significant share will find the convenience of having their personal car once they get there worth a little extra time.

          For longer HSR trips we can ignore the time to get to the station on either end, but not on short trips.

      • Phake Nick

        Source: 全国幹線旅客純流動調査
        Modal share for Tokyo ←→ Aichi:
        2010: Train 87% Car 10%
        2015: Train 82% Bus 5% Car 12%
        Model share for Kanagawa ←→ Aichi:
        2010: Train 70% Car 30%
        2015: Train 60% Bus 2% Car 38%

        Kanagawa includes Yokohama and Aichi include Nagoya
        between the two time points, in 2012 a new expressway opened between Kanagawa and Nagoya
        Almost all rail share here should be Shinkansen

        • Phake Nick

          Note, in the same report, it mentioned that generally for people doing 200-300km trip, the model share is “Train 16% Bus 3% Car 81%”, while for 300-500km trip, it is “Plane 2% Train 43% Bus 4% Car 50%”, yet given the provided Tokyo to Nagoya data, I guess this data is screwed by trips that have no convenient rail services

          • Andrew in Ezo

            Yes, it seems people living in southern Kanto (Kanagawa Pref,) would find the easy access to the Tomei Expressway a better option than schlepping it to ShinYokohama for the Shinkansen. Also, the fact that the Tokai region has very high automobile license possession rates and car mode share double of of both the Kansai and Kanto regions probably figures into the numbers.

          • Onux


            Thank you for this helpful data.

            So in Japan:
            Tokyo-Osaka 2:24 64% rail
            Osaka-Fukuoka 2:17 64% rail
            Tokyo-Nagoya 1:35 82-87% rail
            Yokohama-Nagoya 1:17 60-70% rail (car use triples)

            At average Shinkansen speeds of 215-250kph, the 300 km rail/car split from 16%/81% to 43%/50% would take about 1:12-1:24. According to this link ( average Shinkansen travel distance is 308km Tokaido and 251 Sanyo, again in the 1:00-1:30 range.

            In Spain:
            Madrid-Barcelona 2:30 36% rail
            Madrid-Valencia 1:40 46% rail
            Madrid-Seville 2:21 58% rail (outlier in performance compared to Barcelona/Valencia)

            Paris-Brussels is only 1:32 on Thalys, yet there was a large mode shift from car to train after the HSR line was built.

            Overall I would say that Alon should be using a travel time floor of 1:30 not 2:30.

          • Phake Nick

            I think there are larger factors at play than just the travel time that cause the differences in travel mode split between Tokyo/Yokohama, including the comprehensiveness of railway network (which translate to car ownership), and the location of high speed rail station (Yokohama’s high speed rail station is some distance away from town, and most part of Kanagawa need a detour to reach that station)
            It might also be worth-noting that, between Aomori and Hakodate in Japan (Not included in the report due to relatively recent opening of the section), after the Shinkansen service launched, reportedly many passengers who formerly take the train between Aomori and Hakodate have switched to use ferry to travel between the two instead (no road connection between the two cities, conventional rail service discontinued after high speed service launch), mainly due to more expensive fare on the high speed train, as well as the inconvenient location of high speed train stations at both cities, despite the high speed train itself only take less than an hour

    • Herbert

      If you search for flights and trains between Madrid and Barcelona with the apps at your disposal, you’ll see one of the reasons why some prefer flying between the two…

      The other reason is of course hub feeder traffic – you got that even between Nuremberg and Munich…

  6. Phake Nick

    In fact, isn’t the following routes really great corridors for high speed rail service? After seeing the lines being drawn out, it doesn’t really match what people claim about lack of cities on a line in Germany, it’s just that many of those lines are awaiting construction.
    Vienna – Munich – Stuttgart/Nuremberg – Frankfurt – RheinRuhr – Amsterdam
    Warsaw – Prague – Nuremberg – Frankfurt – RheinRuhr – Brussels
    Paris – Brussels – RheinRuhr – Hamburg – Copenhagen
    Berlin – Leipzig – Nuremberg – Stuttgart – Zurich
    Berlin – Leipzig – Frankfurt – Saar – Paris
    Hamburg – Hanover – Frankfurt – Nuremberg/Stuttgart – Munich
    Prague – Munich – Zurich – Geneva – Lyon
    Hamburg – Berlin – Dresden – Prague – Vienna – Budapest

    • Herbert

      A problem with all lines involving the Czech Republic is that the Czech western border is one of the best visible land borders on physical maps – meaning the country is surrounded by mountains on three sides. That is of course no absolute hurdle to rail connections, but it does add complications…

      As for Nuremberg-Stuttgart…. It is indeed frustratingly slow..

      • Phake Nick

        Looking at the topographic map, from Pizen of Czech through Furth im Wald to points further west seems like a viable route
        As for Prague to Dresden it would just need to find a way to slowly ascend into the hill like parallel expressways.

        • Herbert

          The existing Dresden Prague railway is the only electrified link from the Czech Republic to Germany and even if other links are electrified it remains the most direct link to the North Sea ports.

          Any relief line would have to be accessible to freight as well.

          The Elbe valley is curvy and narrow and it goes through a national park. It’s the only even remotely flat stretch of land in the area. So, by process of elimination, we are left with a base tunnel. Which is indeed what is planned for the new line.

    • Alon Levy

      Some nitpicks:

      – The main route from Berlin south doesn’t pass through Leipzig but between Leipzig and Halle and then Erfurt; this was controversial here, since it forced the Thuringia-Bavaria connection to pass through thicker mountains at higher cost.
      – Hanover-Nuremberg doesn’t go through Frankfurt but through Würzburg, courtesy of a rather odd NBS built in the 1980s. The Hamburg connection is precious and held up by NIMBYs (“Y-trasse,” the third leg of the Y being Bremen).

      The busiest corridor that I crayoned is Cologne-Frankfurt, followed by Frankfurt-Mannheim. That’s a natural line, with splits to Karlsruhe-Freiburg-Basel and Stuttgart-Munich. That corridor exists (and right now I believe Frankfurt-Mannheim is the second busiest intercity line in Europe, after Paris-Lyon), but the onward connections kind of suck. Half an hour extra here, half an hour there, and soon it’s no longer high-speed rail.

      • Herbert

        There are plans for getting Nuremberg-Würzburg down to 30 minutes… The current line is stretched way thin and there is a pretty obvious S-Bahn corridor there that’d also need extra capacity, so adding at least one track should be a no brainer already. I hope they build the line fast…

      • Phake Nick

        I’m thinking about if it can collect the demand together and support more frequent services, then it might be worth to run some train from Hanover to Nuremberg through Frankfurt despite the bits of detour

      • Oreg

        > the onward connections kind of suck.

        Just for clarity, this is true for Karlsruhe-Freiburg-Basel (upgrade to 250 km/h under construction), but Mannheim-Stuttgart has been an NBS (280 km/h) for 30 years with an upgrade of the onward connection to Ulm for 250 km/h under construction. The rest of the way to Munich is indeed slower.

        Sadly, the Frankfurt-Mannheim section of the corridor itself is only 200 km/h with the planned upgrade to 300 km/h not even started, yet.

    • Onux

      Why would you send a line from Warsaw south west to Prague (2.7M) instead of west Berlin (5.3M)? Especially if your goal is to get to RheinRhur or Brussels, which are north of Prague/Nuremberg?

      I am surprised a Berlin-Prague-Vienna-Bratislava-Budapest line (the “Five Capitals HSR”) hasn’t been pushed much either as a way for Germany to gain influence in C. Europe or for former Soviet satellites to tie themselves to the Germany/Austrian economies.

      • Alon Levy

        Germany doesn’t think in terms of infrastructure as empire building. Czechia is planning on building HSR to use Prague as a waystop on Berlin-Vienna, but it’s being done French-style, with a bypass around Brno; Prague is somehow getting a direction change, and even with SNCF advising, the projected trip time on Dresden-Prague is 55 minutes, which is pretty bad.

      • Phake Nick

        Going by distance, Warsaw via Prague to RheinRhur or via Berlin to RheinRhur should be similar? Although I am not totally sure how it will translate to travel time with speed limit of planned/constructed high sped line in mind.
        Route via Prague should somewhat match Poland’s domestic proposed high speed rail corridor if I am remembering correctly, and it also have Frankfurt on the line compares to the Berlin route which only have Hanover, which is actually more important than RheinRhur or point beyond since those could be five or more hours away

        • Onux

          Warsaw to Cologne is 1,110 km via Berlin road distance. Warsaw to Cologne is 1,319 km via Prague-Nuremburg-Frankfurt road distance. And Cologne is at the south end of RheinRhur, getting to Dortmund/Essen/etc. favors Berlin more.

          Warsaw to Berlin crosses the N. European plain and is completely flat, Warsaw to Prague to Nuremburg crosses mountains twice.

          Alon’s map has 4:30 Warsaw to Dortmund, 5:00 Warsaw to Cologne. If we assume 1:00 Nuremburg to Prague (comparable distance to Berlin-Hannover) and 2:30 Prague to Warsaw (comparable distance to Berlin-Warsaw) then with Alon’s times it is 5:30 Warsaw to Cologne through Frankfurt and 6:00 Warsaw to Dortmund. This assumes crossing the Ore and Beskid mountains at the same average speed as along the flat terrain around Berlin.

    • Brendan Dawe

      ya, that seems an interesting question no, since Columbia has terrible roads and super high air travel right?

      • Eric2

        You mean Colombia the country? Its major cities are surrounded by giant mountains, which makes the roads very slow, and would make HSR very difficult to construct. No wonder its air travel level is high. Probably electric short-range airplanes are the best solution there if our priority is minimizing carbon emissions.

        • Mikel

          Cartagena-Barranquilla seems easy enough, at least as medium-speed rail given the short distance. With the flat terrain between Cali and Armenia and big populations at both ends, Cali-Bogotá doesn’t seem completely insane either, as long as you can find an alignment between Girardot and Bogotá that can surmount the 2,000-meter altitude difference with a reasonable amount of tunneling. On the other hand, with 100 km of mountains in every direction, anything involving Medellín (which happens to have, arguably, the best local transit in the country) is going to be very tough.

          Has anyone ever built a base tunnel under a volcanic mountain range?

          • Car(e)-Free LA

            Cartagena-Barranquilla is definitely too small of a market for HSR. The city pairs which, in the abstract, easily justify HSR are obviously Cali, Medellin, and Bogota–connected at a wye at Armenia. The Bogota branch would also serve Ibague and the Medellin branch should pick up Pereira and Manizales. I have no idea how much it would cost but I’m sure it would be nightmarish. The ridership, however, is definitely there–and only there.

          • jcranmer

            Just a stupid Yanqui judging things from staring at Google, Wikipedia, and topo maps:

            There seems to be three nice, easy-ish North-South valley corridors that would be relatively cheap for construction. Too bad that none of the major cities seems to actually grace these corridors with their presence.

            Cali-Armenia appears to be an easy build, and you could extend that south to Popayán easily enough and north to Pereira, it looks (though I doubt that’s worth it). It looks base tunnel territory to cross Armenia to Ibagué, which gives you access to the north-south corridor from Neiva to Barranquilla. However, this lacks access to Bogotá and Bucaramanga.

            Bogotá looks somewhat accessible via the southwest; it’ll need tunnels and squiggles, but it’s not full base tunnel territory to enter the city. Heading north to Bucaramanga via this inner route is also plausibly of around the same difficulty. (See routes 40 and 45A for the kind of routing I’m pondering). But returning back to the previous broad valley starts looking base tunnel territory, whether you try a northwest route from Bogotá or Bucaramanga. Route 45A out of Bucaramanga is an intriguing alternative

            Medellín, however, looks to be a really tough nut to crack. It’s tough mountains on all sides, and I’m having a hard time finding a water route that doesn’t look to be deep gorge territory. The northeast-ish heading (basically 62) from Medellín seems to be the easiest route. But, again, that takes you in precisely the wrong direction from the #1 and #3 cities. So you have a choice between circuitous routes or picking up several base tunnels.

          • Car(e)-Free LA

            I actually think Medellin might be less difficult than you think and Bogota might be a bit harder. The key with Medellin is getting down to the Cauca River–once you’re at that level, it’s just an issue of crossing conventionally difficult hills along the Eje Cafetero to Cali. To that end, you need a roughly 13 km tunnel from south of Caldas to Fredonia. That isn’t nothing, but it’s in line with the road tunnels Colombia has been building to access Medellin from Santa Fe and Rionegro. The connection to Bogota is a lot harder because it means dropping to the Magdalena River Valley and then climbing back up to Bogota. That basically means a base tunnel from Armenia to Ibague and another really long tunnel from Fusagasuga to the edge of Bogota to make the grade of the ROW workable for trains.

            Considering the types of tunnels Colombia has been building, I honestly think it could be worth it. It would wipe out ~50% of domestic air travel, make Cali, Bogota, and Medellin all 2 hours apart, and massively boost business and tourism. We’re talking about connecting about 22 million people in a medium income country, slashing journey times by like 4x. That’s massive for a system with pretty low mileage.

  7. Mark N.

    I’m glad you’ve posted again about rail in Germany since that gives me a good opportunity, as another expat also living here (I’m from the US), to comment for the first time on your great blog, which I only recently discovered.

    My daily commute (at least in non-Covid times) generally involves taking the S-Bahn from Herrenberg (S1) into downtown Stuttgart, which shares much of the intercity track that continues on to Zurich, and so I have been closely following the many discussions about the southern “Gäubahn” as they call it. I don’t know how familiar you are with this line, but despite years of talk and pressure from the Swiss to increase capacity and speeds, it continues to get treated as an afterthought. A court decision last year, however, has pushed the line suddenly to the forefront of discussions while revealing a huge failure of planning. As it turns out, the initial plan of simply adding a curve to connect the southern route over existing tracks to the Stuttgart airport (before proceeding through the new tunnel to the new main station) depended upon an exception to rail standards which a former DB head of planning over Stuttgart 21 had granted. The paired tracks from the suburb of Vaihingen to the airport weren’t built to intercity standards, but only according to their intended use (at the time) of providing an expansion to the S-Bahn system. The spacing between the tracks is therefore smaller than what the standard for intercity (or even regional) lines allows. The court (clearly correctly) decided that an exception to such a standard for a yet-to-be-built project was ludicrous. However, that means that, only four years away from the planned completion of the new through station, there is no plan how to connect the southern route. But at least now the Gäubahn is finally getting the attention it deserves!

    The proposal which seems to have the most momentum so far is surprisingly ambitious: build a 12 km long, dedicated tunnel from Böblingen (south of the initially planned curve) to the airport station. The high costs and extremely long construction time, though, are getting lots of pushback. Another, simpler proposal is to leave the airport station out of the equation and just keep using the existing intercity line into downtown Stuttgart, known as the “Panoramastrecke” because of its picturesque, winding path it takes along the surrounding hills above the city. This line would then terminate in a new, below-grade expansion to the new through station under construction, but perpendicular to the other tracks on the north side. The argument is that this could be relatively inexpensively accomplished since so much of that area on that side of the future station is already dug up due to the construction of a new below-grade S-Bahn line there.

    After looking at these proposals, I even sent in my own idea to various politicians and others involved in the decision process. I basically agree with the alternative proposal that the stop at the airport station isn’t worth the effort — the new, through station should be prioritized. In contrast to that proposal, however, I suggest by-passing the slow, above-ground approach (I think maximum speed is limited to 50 km/h on it) by putting it below grade in a tunnel from Vaihingen to either of the new tunnels being constructed for the new through station on the west side. According to my estimates, it wouldn’t need to be more than 8-9 km long so substantially shorter than the main proposal being discussed. It would also allow higher speeds than the alternative proposal and utilize the through station as planned. I have no illusions that my idea will influence anything, but since the whole thing is already such a huge clusterf***, I thought it sure couldn’t hurt.

    As far as other things I’ve heard which might be of interest to you in regards to Stuttgart, I recently read that a so-called “P-Option” is strongly being considered, which would provide a tunnel link for traffic from the west into the new Canstatt tunnel, which would address one of your main criticisms, I think. There is also talk about adding an additional platform north of the eight already planned in order to better accommodate future capacity needs.

    I can’t say too much about the other aspects of your proposals, but certainly far more dedicated connections need to be built in general. When I traveled to Berlin last summer, I couldn’t believe how slow the ICE still runs for much of it, especially the middle section between Frankfurt and Erfurt. I do question the direct connection you show between Munich and Linz since Salzburg serves as a major rail hub for central Austria (also a major tourist destination in itself), and a stop there would only slightly increase the total distance.

  8. Magnus

    In my opinion Hanover-Strasbourg has some of the same reasons to be NBS as Jacksonville-Atlanta in the US. Hamburg-Strasbourg is a bottleneck in the main European north-south corridor from Scandinavia to Mediterranean. A new line bypassing Göttingen, Kassel, Frankfurt and Mannheim should be considered.

    Now Hamburg-Strasbourg takes 6 to 7 hours, and in your suggestion it would still take almost 4? NBS Hannover-Würzburg in 75 minutes instead of 105 minutes would help a lot, as well as a Stuttgart bypassing connection from Karlsruhe to Heilbronn so Strasbourg-Wursburg could take 60 minutes instead of 75. That gives Hamburg-Strasbourg in 3 hours and possibly Hamburg-Lyon in 5 hours, instead of the current awful situation with 10 hours (or 11 hours by train via Brussels), or 12 hours by car.

    It will also open a huge vacation market for sun seekers from the northern part of Europe, with travelers falling asleep in snow and waking up near the beaches of the Côte d’Azur or possibly Catalonia. In day time Hamburg-Munich and Hamburg-Alps trains will have great joy of a faster connection through the tiny-populated heart of Germany.

    • Alon Levy

      Why does Germany need a bypass around the line through Göttingen and Kassel? It’s not at capacity, and better HSR wouldn’t put it at capacity either. The most crowded line is Frankfurt-Mannheim (today as well as with HSR), followed by Frankfurt-Cologne, so it’s prudent to try to get trains off Frankfurt-Mannheim by building a Frankfurt-Mainz-Saarbrücken route feeding Paris-Est.

      Hamburg-Strasbourg stays on Frankfurt-Mannheim this way, taking around 3:45, but that’s fine, Strasbourg is not a big city and the extra ridership isn’t contributing much to Frankfurt-Mannheim congestion. The big connections from Germany to France avoid the bottleneck entirely – Berlin and Frankfurt connect to Paris via the Frankfurt-Saarbrücken line, Hamburg and the Rhine-Ruhr via Belgium, Munich via Stuttgart and Karlsruhe.

      The main route to Southern Europe doesn’t really pass through France – it’s too roundabout and the Riviera is extremely isolated because of the topography. It passes through Switzerland and Italy. Switzerland’s currently investing in more base tunnels to the point of making Zurich-Lugano mostly a 200-250 km/h high-speed route, timetabled at far longer than it needs to be (2 hours, should be 1 or maybe 1:15). So this way you get Hamburg-Zurich in 4 hours, and then a connection to a train that can get to Milan in maybe 2 hours, and from Milan there are fast domestic Italian trains.

      • adirondacker12800

        The swim to Mallorca is long. At this instant $48 dollars on Ryanair from Frankfort or $106 on Lufthansa. Two and half hours on non-stops. Or I could spend a day changing trains getting someplace and a day changing trains to get back home. A bit more to Ibiza and two and half hours on non-stops. I didn’t fool around with picking a date in 2022 or having it give it to me in Euros.

      • Magnus

        Italy had 62 million international tourist arrivals in 2019, while Spain had 83 and France 89. Mainland Spain a bit lower if you withdraw islands like Baleares and Canarias, of course. I assumed that Lyon–Barcelona was so much faster average speed than crossing the Alps that it would neutralize the fact that Italian coasts are the geographically nearest to North Europe, but if the base tunnels could be so efficient as you describe maybe the numbers could turn around so Italy bypasses Spain in number of tourists in the HSR era of the future! From Milan you have short ways to both coasts, Venice and Rimini on the Adreatic and Genova, Cinque Terre and all the way over to Nice on the Mediterranean side. The weather is probably better over in Alicante, but might not so that much better that bypassing Kassel and Frankfurt is a good idea…

        • Alon Levy

          The biggest tourist destinations in Europe are London and Paris. There are a lot of international arrivals to not-Paris, but they’re incredibly diffuse, and for the most part, the list of the top cities for international tourism in Europe consists of large cities with strong non-tourism economies like London, Paris, Barcelona, Rome, and Prague. Depending on the list, the top places for tourism in Europe that are not among the largest cities are Venice, Mallorca, Florence, and Crete.

      • Oreg

        While the Gotthard Base Tunnel supports speeds of up to 250 km/h, passenger trains are currently run at only 200 km/h in order to interleave them with freight trains going 100 km/h.

  9. Pingback: Sanity-Checking My HSR Ridership Model | Pedestrian Observations
  10. Michel

    Hi can someone give me an example on how to use this version of the gravity model? I didn’t quite get it.

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