Eastern European High-Speed Rail

Last night, I poked around my ridership model for intercity rail in the context of what could be done in Eastern Europe. This is the same model I’ve used for the United States for three years, but here I am more confident in its predictions, at least at overall level if not at the level of specific city pairs.

The model is, to be clear, primitive. I project that the ridership between two metropolitan area pairs A and B, with populations in millions and distance d in kilometers, is

75,000\cdot\mbox{Pop}_{A}^{0.8}\cdot\mbox{Pop}_{B}^{0.8}/\max\{d, 500\}^{2}

The gravity model is trained on some Shinkansen, TGV, and AVE city pairs; it is not perfect even in Japan, overrating inter-island and through-Tokyo ridership, and underrates Taiwanese ridership. But in the range of distances typical of the workhorse TGV and Shinkansen connections it does fit; the 0.8 exponent represents diseconomies of scale, as larger metropolitan areas have a longer distance between the average home or destination and the train station, and empirically the exponent holds up when I break big metro areas into pieces with different distances to other areas.

With that in mind, here’s the network to be tested:

A full-resolution image, with most cities labeled via the OpenStreetMap layer, can be found here.

In short, the point of the network is to connect the main and secondary cities of the four Visegrád Group countries, which are the densest in Eastern Europe and the closest to preexisting Western European networks. Berlin-Dresden becomes a full high-speed line, with an onward connection to Prague, Brno, Olomouc, and Ostrava, which conveniently lie on a single line. From Brno, trains go south to Vienna or Bratislava and thence Budapest. From Ostrava, trains either go into Katowice or via an upgrade of an existing bypass line to Kraków; Kraków gets a connection to Lviv via the collinear cities of Tarnów, Dębica, and Rzeszów. Poland gets a series of Y-shaped lines connecting Berlin, Warsaw, and Katowice via Łódź, while the Berlin-Łódź section itself is two legs of a Y with Gdańsk and the Tricity area. A faster alternate route from Poznań to Katowice via Wrocław and Opole rounds up the network.

The spreadsheet with metro populations, approximate distances, and ridership projections can be found here. Metro area populations are taken from a variety of sources, such as Eurostat; I don’t have a good feel for Polish numbers, so I sanity-checked them with Wikipedia’s multi-source list. The network as proposed is 2,770 km in the spreadsheet not counting Berlin-Dresden, but could be a few tens of km off. This is similar in size to the French LGV network, in a region of similar overall population, and the model says there would be 103 million trips generating 48 billion passenger-km, neither figure counting internal German travel; the domestic TGVs had 51.6 billion passenger-km in 2019 (source, p. 46).

Domestic networks

The network provides a fairly complete coverage of Czechia, and a reasonable one of Poland. Slovakia is too small for such a network, and Hungary’s secondary cities are small and never collinear with Budapest, and therefore these two countries only get international service.

Czechia here benefits from a linear population distribution, and the biggest miss, Plzeň, is collinear with the rest of Czechia as well and could potentially get a heavily-tunneled onward route to Bavaria with a connection to Munich, Nuremberg, or both. Czechia also benefits from atypically strong connecting urban rail – Prague may have Europe’s highest rail ridership per capita depending on metro area definitions, and Brno, with a metro area that on the widest reasonable definition has about a million people, had 195 million tram trips in 2019 (source, PDF-p. 36).

The main challenge for Czech high-speed rail construction is that costs would be high. Prague Metro construction costs have exploded in the last decade, for which I have only an inkling of an explanation; more to the point, the hilly topography north of Prague and the difficulty of finding fast approaches would force extensive tunneling. In fact, current plans assume even more tunneling: the Dresden-Prague planning is for a long base tunnel for the dual use of passenger and freight rail, instead of a steep-grade passenger-only route with little tunneling so that the classical line can be given over to freight trains and tourist passenger trains up Saxon Switzerland.

In Poland, the urban geography is more spread out. There is little collinearity, and the positions of the main cities are such that any network of lines would involve significant detours. Łódź is so far south that it forces Warsaw-Gdańsk to detour (as on this map) or go directly with little useful service from Gdańsk to Germany and western Poland (as on a map I made in 2020). Wrocław is at an awkward spot unless there’s a line directly to Dresden. Eastern Polish cities are never at sufficient scale to justify lines by themselves, orphaning Białystok and, unless there’s a Warsaw-Lviv line, Lublin. Warsaw itself is remarkably undersize: in a country almost as large as Spain, it is less than half the metro area population of Madrid. Thankfully, construction is straightforward, and there are enough cities at sufficient density, generally with decent tram connections (and a metro in Warsaw), that it can work.

International trips and Metcalfe’s law

While the internal networks in Czechia and Poland can expect reasonable traffic density, there is no hope of building them by themselves. Too much traffic relies on international connections. The busiest station on the network as depicted above would be Berlin, as it is by far the largest city. Progress in this direction requires international cooperation to build physical high-speed lines, and not just Alpine base tunnels, which are not appropriate for the Germany-Czechia case.

Metcalfe’s law rears its head again, in that every end of the network contributes a greater share of passenger-km to the system than its share of the length. For example, the most peripheral node, Gdańsk and Bydgoszcz, requires 230 km from the pivot of the Y with Poznań and Łódź, or 8.3% – but Gdańsk and Bydgoszcz contribute 11.8 million passengers (11.5% of total) and 6.4 billion passenger-km (13.3% of total). The only place where this is not true is Wrocław and Opole, since there is an alternate route from Berlin to Katowice that’s only somewhat longer; even there, this route adds 350 km (12.6%) and contributes around 5,000 p-km (10.4%) taking into account reduced ridership from longer Berlin-Katowice trips, hardly a laggard.

In practice, the only way to build such a network incrementally is to start from the strongest link, such as Paris-Lyon in France. But no such link exists in Eastern Europe, where the four largest metro regions combined – Warsaw, Kyiv, Budapest, Prague – are about the same size as Ile-de-France. Instead, the network should accrete from already existing lines in Germany and Austria. The spreadsheet omits ridership coming from onward connections to West German cities like Hamburg or Hanover, both fairly close to Berlin by rail, a list that grows every time Germany opens another high-speed line. Thus, a Czech network integrated with Germany and Austria could succeed on its own, leading up to Poland.

But this can’t work in a haphazard way. Czechia generally knows what it needs, but more international cooperation with a stronger EU role is required to make sure everything falls into place – to make sure cross-border rail infrastructure is seamless enough people actually take the train. This just isn’t the kind of network that can accrete bottom-up.


  1. Sean Cunneen

    It’s kind of awkward that Vienna ends up on a branch, forcing trains to be split between it and Bratislava despite their close proximity, but looking at a map I see that putting it on the line to Bratislava would probably require creating a new (expensive) crossing of the Danube, so I suppose its not worth it.

    • Sean Cunneen

      The river crossing you chose does seem to be used by a S-bahn line running every 30 minutes (an oddly low frequency for something so close to the city core), which makes 3 stops in between the merge point at the bridge and Hbf, two of which lack bypass tracks, and 3 hourly regional trains, two of which go to Bratislava, which skip these intermediate stops. The Although there is clearly plenty of spare capacity there, mixing three different speed classes of trains could lead to reliability problems without strong timetable discipline, so a dedicated crossing for HSR that allowed trains to run through Vienna to Bratislava could have other benefits.

    • Sean Cunneen

      I suppose the reliability problems might be solved by just making the regional trains make all of the S-bahn stops since it seems both the regionals and the s-bahn trains over the bridge follow the line to Bratislava, with the S-bahn trains and one of the three regionals short turning. HSR could take over Vienna to Bratislava travel so speed would now be less important for the regionals. Then there would only be the HSR sharing tracks with one stopping pattern.

      • Sean Cunneen

        Correction: all 3 s-bahn stops between the bridge and Hbf lack bypass tracks and the regional trains stop at one of them.

    • Matthew Hutton

      Vienna is definitely worth the diversion to run a full through service to, especially as it has very strong connections to a bunch of other places in Western Europe.

    • Basil Marte

      I would expect that the “branch” in Vienna continues to the Westbahn. On the other hand, this suggests a wye, to enable (München/Salzbug/Linz)-Vienna-Bratislava-(Győr-Budapest) service.

      • Alon Levy

        Yeah, I’m assuming the highest-intensity service goes Munich-Vienna-Bratislava-Budapest and Berlin-Prague-Vienna. It’s pretty awkward that the splits are where they are – it would be easier if the branch point were beyond Brno rather than just before it, and in recognition of that awkwardness, current Czech plans call for a south Brno transfer stop, to enable Bohemians to go to Bratislava directly while still maintaining a recognizable Takt with good transfers.

        • Sean Cunneen

          I see. You didn’t include the Munich-Vienna line on your map so I thought you saw it as a possible later expansion rather than a part of the core system.

        • djasa

          If you indeed do assume a wye next to Vienna with non-stop Bratislava/Czechia trains, odds are IMO high that an upgrade of a current Kúty-Bratislava line to 200 km/h plus two point upgrades (bypass of Břeclav station and easing of curve at Kúty: https://en.mapy.cz/s/buvufobete ) can attain the same Czechia-Bratislava travel times with lower speeds and thus operating costs than a detour around Vienna.

          • Alon Levy

            Wait – when I draw an alignment for the line via near-Vienna I get 150-155 km, whereas the existing line is 145.

          • djasa

            Do you go through Břeclav? Alignment around Mikulov seems implausible to me, combo of persistent environmentalists NIMBYs and incompetent roads authority made planned higway delayed by some 20 years (and counting). The wye approach could probably work if current lines south of Břeclav get to capacity, then I could imagine new HSL on Austrian bank of Morava (March) river with a wye somewhere between Gänserndorf and Marchegg.

          • Alon Levy

            I was assuming either diverging somewhat north of Břeclav, or even going via the other side of the lake and wying somewhere near Wolkersdorf. But some of the options near Vienna are out because NIMBYs like vacationing in those hills and made some of them into protected national parks (Teddy Roosevelt-style conservationism needs to die in a fire).

          • Sascha Claus

            upgrade of a current Kúty-Bratislava line to 200 km/h plus two point upgrades (bypass of Břeclav station and easing of curve at Kúty: https://en.mapy.cz/s/buvufobete )

            Your map is missing the easing of the curve at Kúty: http://en.mapy.cz/s/ponesohoga 😉

            same Czechia-Bratislava travel times with lower speeds and thus operating costs than a detour around Vienna.

            But the closer the wye gets to Vienna, the smaller the detour to make a stop in Vienna for CZ-SK trains. And by going via Vienna, you get more frequency by combining travel markets.

    • Michal Formanek

      Actually, direct CZ-HU route trough Bratislava makes sense. Czecho-Slovak ties are stronger than to Austria.

    • Mikel

      If you want to have Prague-Brno-Vienna-Bratislava on a single line and on the cheap, you could maybe build a new line on the flat terrain between Brno and Hollabrunn, use the existing tracks to cross the Danube at Tulln, and then plug into the existing Wienerwald tunnel to serve Wien Hbf from the west.

      After which you have two options. One is to upgrade the current line to Bratislava on the north side of the Danube, which then allows for through service to Budapest or deeper into Slovakia. The other is to serve Vienna Airport -a destination that generates some traffic by itself- and build a new line from there to Bratislava on the south side of the river. The drawback of the latter is that, unless you want to spend a ton of money on bridges and tunnels near Bratislava, you can only serve it on the much less central Petržalka station, or loop around to Hlavna which would impose a time penalty on travelers going further east.

  2. wiesmann

    Maybe worth mentioning is the work on the Budapest–Belgrade–Skopje–Athens line, which would give some weight to the connection to Budapest.

    • Alon Levy

      The Balkans are a world of pain:

      1. The population density isn’t really there. Between Budapest and Athens, a straight-line distance of 1,120 km, the only million-plus metro areas are Belgrade and Thessaloniki.
      2. The topography past Belgrade is straight from hell.
      3. The cities aren’t really collinear – Sofia isn’t really between Belgrade and Greece.
      4. These areas are depopulating due to their weak economies – this isn’t Czechia, which is about even with Italian or Spanish GDP per capita and had 5% population growth last year because its 2% unemployment economy attracted that many Ukrainian refugees.
      5. The political situation is dicey around Serbia: Serbia is so Russophilic that it can’t join the EU, which means any line through it has to deal with border bullshit and probably inevitable Thalys-style extraction of surplus from business travelers.

      Any passenger rail investment there is basically the equivalent of building Interstates or running Amtrak through the Dakotas and Montana: it exists for continental empire building, not for commercial reasons. This might even be politically viable as far as Romania, but in Serbia, the only place with even semi-reasonable geography, the politics goes the other way.

      • wiesmann

        For all its posturing, Serbia is heavily dependant on the west: the diaspora living and working there brings a significant part of the economy (remittances are 7% of the GDP) and many companies handle jobs that are outsourced from the west (the IT sector in Belgrade notably). Europeans can enter the country with an ID card, Russian need a passport and can only stay 30 days…

        Currently this flow of Gastarbeiters and people visiting their family go by bus, car, or cheap airlines. The main drawback of the plane is the limited amount of luggage (people carry lots of things), so there could be some opportunity for reasonably fast train lines.

        The geography from Belgrade to Niš is not _that_ bad, you probably won’t be able to build 300 Km/h lines, but the stated goal of 200 Km/h line seems feasible.

        More generally, I had the feeling the development of corridor X was largely driven by freight considerations: unloading the cargo from China in the Piraeus harbour, maybe do some product assembly in Serbia where work safety regulations can be overlooked and ship into Europe. Same goes for Turkey, I remember that at some point many European fridges were assembled there from Chinese components…

        • Basil Marte

          Yes, the Hungarian part of the Budapest-Belgrade line is very much designed for freight — hence 160 km/h track design speed. And given the single design traffic, it mostly avoids settlements or otherwise being potentially useful for passenger traffic (of whatever speed).

          Hungarian enthusiasts, partly because they call BS on the traffic projection, would have liked to suggest the existing Budapest-Cegléd-Kecskemét-Szeged-(Belgrade) line, with double-tracking the Cegléd-Szeged segment (which would also benefit passenger traffic) in case someone wants to improve infrastructure on a mainline. Should the traffic projections be anything close to accurate, justifying a double-track line for freight, then the radial lines around Budapest (notably, Budapest-Győr) become the bottleneck.

          In my opinion, the telos of any “iron Danube” would be to reach Istanbul, whether they go via Sofia/Bucharest and Belgrade/Timisoara (if avoiding Serbia), whatever they are to transport.

  3. Richard Gadsden

    I think your design is orphaning Białystok because it’s on the edge of the region of consideration rather than because it isn’t on the way to anywhere.

    Warsaw-Białystok-Kaunas-Riga-Parnu-Tallinn is collinear, so the international connection should be the way to connect Białystok to this network. Indeed, isn’t that the route for Rail Baltica?

    Some of the other gaps you’ve identified might be resolved by considering places that aren’t on the map. For instance, Vienna is not a dead-end branch – that would obviously connect through Vienna to the west, so you’d get Munich-Salzburg-Linz-Vienna-Brno by connecting through Vienna.

    I wonder what a Kraków-Košice-Debrecen-Cluj-Brașov-Bucharest line would sketch out like? That’s the only way I can see any useful connection being built through non-Bratislava Slovakia and non-Budapest Hungary.

    I’ve always assumed that the likely routes through South-Eastern Europe are Vienna-Zagreb-Belgrade, Venice-(Trieste)-Ljubjlana-Zagreb, (Vienna-Bratislava-)Budapest-Belgrade, Belgrade-Skopje-Athens (either via or with a branch into Thessaloniki), Belgrade-Sofia-Plovdiv-Edirne-Istanbul, either Bucharest-Istanbul and Bucharest-Sofia or Bucharest-Plovdiv to connect to both Sofia and Istanbul, Bucharest-Belgrade (maybe; there isn’t much in between; alternatively, Bucharest-Timisoara and then connect to the Budapest-Belgrade line) and something northbound out of Bucharest – either Ploesti-Brasov-Cluj-Debrecen-Kosice-Krakow (probably with a Budapest-Debrecen connection) or the flatter route going Galati-Iasi-Chernivtsi-Ivano-Frankivsk-Lviv, or conceivably both.

    Some sort of Greece-Turkey route (Thessaloniki-Edirne would be the most natural) might make economic sense but seems politically unlikely. Thessaloniki-Sofia might be more likely, or possibly Skopje-Sofia could get more ridership. There look to be a bunch of places along the Adriatic that are missed, and they’re all cities that you’d try to route a line through, but I don’t think any of them are big enough in their own right to generate an entire line. It is remarkable that there are four capital cities (Sarajevo, Podgorica, Tirana, Pristina) and their entire countries missed.

    • Sascha Claus

      Warsaw-Białystok-Kaunas-Riga-Parnu-Tallinn is collinear, so the international connection should be the way to connect Białystok to this network. Indeed, isn’t that the route for Rail Baltica?

      Rail Baltic, that strange beast where one wonders how much of “not a clue” about railways one can have …

      A broad gauge line with Spanish-style a gauge changing station at the border would suffice for 200 to 250 km/h. A standard gauge line only makes sense if you bild it for at least 300 km/h, i. e. a proper high-speed line.

      And then they take the single track broad-gauge line with its double-track ROW and build a standard-gauge track (no double gauge!) on next to the broad gauge to Kaunas, resulting in two single-tracked lines. And the tiny stations on both sides of the border both have at-grade level crossings for platform access, ruling out any hope of not-low speed trains …

      This only makes sense if you think in terms of quickly moving military equipment, which doesn’t seem to far-fetched since last year.

      • Matthew Hutton

        I’m pretty sure Paris-Barcelona, Paris-Milan and Paris-Munich are all little quicker than the 145km/h that the 200km/h max London-Edinburgh trains manage on an hourly basis. And that’s even given that substantial chunks of those routes are on 300 or 320km/h high speed lines.

  4. Nicolas Ball-Jones

    I like your point that the only way to start the network is to start from the strongest link. I realize California (and maybe Las Vegas) high speed rail is an absolute mess, but where should they have started building it if they were going to do it at all? My guess has always been LA to San Diego, but I’m happy to be disabused if this notion.

    • Richard Mlynarik

      San Jose—Fremont—Tracy and LA—Tejon—Bakersfield.
      Politically driven, but, unlike the real world shitshow, not utterly totally completely worse than useless.

    • Alon Levy

      The idea for California High-Speed Rail was to build the system at once. The problem is that while they committed enough money for Los Angeles-San Francisco at Spanish or 1990s French costs, they were short by a factor of maybe three relative to 2008 projections and more like six relative to later ones.

      But in the absence of a lot of money to build Los Angeles-San Francisco in one go, yeah, it’s best to improve Los Angeles-San Diego to Northeast Corridor standards (without the premium Northeast Corridor fares).

  5. joeshupac

    Assuming, hypothetically, that there were no political problems, how might Moscow, St Petersburg, and Istanbul impact this network?

  6. Eric2

    I’m surprised you put a bypass for Katowice, and didn’t put a bypass for Poznan. I guess you think Berlin-Krakow (and further east) trips will go through Prague?

    • Alon Levy

      Katowice already has a decent bypass used by trains from Czechia to Kraków, while the tracks through the built-up area are slow; the bypass also goes through Auschwitz and passes close to Bielsko-Biała. Poznań has good legacy urban approach rights-of-way, no preexisting bypass, and nothing of significance for a bypass to serve.

  7. Michal Formanek

    One thing not mentioned here are capacity bottlenecks on current routes.

    In Czechia, this is quite substantil argument for new high speed lines as some current lines are in full capacity, which constrains also freight, namely:
    DE-CZ crossing Dečín-Dresden
    Choceň-Česká Trebová

    also Plzeň – Norimberg coridor improvement is mich needed for freight.

    • Alon Levy

      The freight bottleneck can be relieved by moving the fast passenger trains away from the line. That leaves passenger trains that have no need to be fast. Going up the Elbe from Dresden, the population density drops like a rock past Pirna; the only place that gets cut off by building a passenger-dedicated high-speed train and making the old line freight-primary is Děčín, which is frankly not important enough to justify a 50 km base tunnel.

      • Sascha Claus

        Track capacity also drops after Pirna, from 4 to 2 tracks. The remainder sees heavy daytrip traffic from Dresden (and beyond) at the appropriate times, but outside of the times, that shouldn’t be too much of a nuisance for freight traffic.

  8. Michal Formanek

    In general, central Europe has high density, but dispersed population, which I think favours rather medium speed, but denser network. Current trend is to modernise eyisting lines to 160-200 km/h.

    But whether it is really substantialy chepaer to build tracks for 200km/h then for 300km/h, I am not sure about that. I would like to know your opininion about speed/ coverage dilema.

    • Alon Levy

      I think Czechia specifically is very good geography for 300. The cities are collinear and the connection from Prague to Dresden needs an entirely new right-of-way anyway. Poland could do 200 for its domestic needs, but anything going to Germany or Ukraine or any part of Czechia past Ostrava should be faster.

      I need to blog about this, but, intercity rail doesn’t really have a speed vs. coverage dilemma. The issue is that a 300 km/h high-speed rail network makes the regional lines stronger rather than weaker, first because the segregation of trains by speed makes both the fast and the slow trains more reliable, and second because the regional lines have more places to connect to using the transfer to the faster trains (or, if you’re France, through-service). Much more of the critique of high-speed rail in Europe boils down to boomers who romanticize the trains they took in their youth than anyone would like to admit.

  9. Sean Cunneen

    The Bialystock-Warsaw line looks very straight on google maps. Unfortunately it seems to be only 2 track with grade crossings and lots of intermediate stops in tiny villages, with the fastest current trains (making 8 stops) averaging only 76 kph. I wonder if it could be upgraded in the fashion of the British legacy lines and connect Bialystock to the high speed network through a transfer at Warsaw

  10. Bryan Anderson

    Could an extension from Lviv to Kyiv make sense? Estimating it at 500 km, with 3.6M metro area population for Kyiv (there are higher and lower estimates, this seemed like a credible midpoint) and getting Zhytomyr (about 0.3M) for free along the way, I get 5.5M passengers and 6.7B passenger-km per year for Kyiv and Zhytomyr combined. That’s about 12% of the total passenger-km and about 15% of the total track km, so not quite as good as the Gdansk extension.

    Is that a plausible extension? Even if it’s only marginally worth it, it seems politically appealing for Ukraine’s European integration. Additionally, one could lengthen the line a bit to the north (to get Rivne) or the south (for Ternopil and Khmelnytskyi), but I didn’t run the numbers for those.

    • Alon Levy

      In theory, yes, probably via Vinnytsia rather than Zhytomyr.

      In practice, Ukraine is so poor that it introduces new error terms into the analysis; the issue is that construction costs are the same regardless of income (and Ukraine’s metro construction costs are kind of high) and to a large extent so are operating costs, while passengers’ ability to afford fares is not. The income factor isn’t too relevant to the V4 – Czechia is about as rich as Japan or Spain or Italy and the other three are only marginally poorer – but it is to Ukraine.

      Thankfully, at least Ukraine doesn’t have my other error term. My formula has a problem with overestimating long-distance ridership, but that comes from air-rail competition – and in Ukraine I expect five-hour rail trips to be done by train, not by air.

      • Eric2

        Morocco has HSR and it’s poorer than Ukraine (and doesn’t connect to any richer countries). How does Morocco fit your models?

        • Alon Levy

          Ooh, good question. IRJ says ridership was 2.4 million in 2021. The formula predicts 2 million from Tangier to the other three cities using the populations on this list, which appears to be metro population, not city proper. I’m not sure how to include the shorter-distance markets on the upgraded legacy portions of the route – if we split the difference and just include the longest of them Casablanca-Kenitra, then the formula says 2.47 million, but if also include Casablanca-Rabat and Rabat-Kenitra then the formula gives 4.3 million.

  11. Tom the first and best

    A Trelleborg-Stralsund tunnel* might change the economics of Poznań-Szczecin-Stralsund high-speed line by allowing the trains to continue on to Malmö and Copenhagen.

    * Also solves Oresund bridge rail capacity issues for freight without Denmark dragging its heels likely over eroding its income tax base into Sweden.

      • Tom the first and best

        I am aware of the Fehmarn Belt Tunnel project. While it is a good project, it does not fix Oresund rail capacity issues (it actually brings them to the fore because it moves them closer to the top of the bottleneck list for Nordic-mainland Europe rail traffic) and therefore, at some point, an additional track pair connecting Sweden to either Denmark or Germany will be needed.

        The options connecting to Denmark may be too close to Copenhagen for Denmark`s liking (potential tax base migration issues, is a theory I have come across), requires more infrastructure in Denmark and, without an additional tunnel (Gedser-Rostock), doesn`t connect to Central and Eastern Europe as well as a Trelleborg-Stralsund tunnel that the Danes can`t stop (and has fewer issues for the Danes anyway).

        A Trelleborg-Stralsund link also avoids Denmark`s 25kV AC 50Hz electrification (it would connect the Nordic and Germanic 15kV AC 16.7Hz systems).

        • Sascha Claus

          If the Øresundsbroen gets full, one could build a new Helsingør – Helsingborg link, double track Helsingborg – Hässleholm, double track and electrify Helsingør – Hillerød and build a new line Hillerød – Roskilde. Oh, wait … Denmark and Sweden mull Helsingør – Helsingborg fixed link (2018).

          A Trelleborg-Stralsund link also avoids Denmark`s 25kV AC 50Hz electrification (it would connect the Nordic and Germanic 15kV AC 16.7Hz systems).

          And in 2030+, that would be a problem because …?

          • Alon Levy

            It’s not even a problem today – the problem is lower frequency, not higher frequency; any 16.7 Hz motor is also a 50 Hz motor, it’s the other direction that’s hard.

          • adirondacker12800

            It’s very unlikely anything today will be running on what comes out of the wire, whatever it is. It gets converted to DC and the inverrters do their magic to fit the load. Low frequency transformers are bigger. Something other than grid frequency needs it’s own generation and distribution system or converters or both.

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  14. Sascha Claus

    You put the branching point east of Poznan at Gniezno. Did you try to put the split further east to fit Toruń (pop. ca. 200,000) or at least Inowrocław (73,000) onto the high-speed network?

    Toruń and Bydgoszcz looks like a real pain, so the former might have to make do with an upgraded medium-speed line (200–250 km/h) to Olsztyn.

  15. djasa

    Alon, several notes:

    I think that your model deserves an adjustion for one phenomenon: https://pedestrianobservations.com/2011/06/19/international-links-underperform/
    Two anecdotal observations from Brno supporting this:
    – there is always huge turnover of passengers of IC/EC/RJ/rj trains over here
    – trains to Slovakia carry usually more passengers overall towards the border than trains to Austria, in spite of Bratislava being fraction of population of Vienna

    Re inappropriate base tunnels – Germany’s Bundesministerium only started taking Erzgebirgstunnel seriously after being forced to release more detailed rail traffic stuff which had revealed Dresden-Děčín segment as IIRC 4th busiest for rail freight. Passenger trains should piggyback on it…

    Re Brno pop: 1.0M looks like a stretch. The whole South Moravian Region has around 1.25M. Brno + metropolitan area have 0.5M “permanent residents”, add 50-100k university students, some 10s of thousands of expats, some 10s of thousands of people who avoid the hassle of moving their “permanent residence” and we’re at plausible 600-700k. 800k at best.

    Re Brno South stop. My personal speculation is that motivation for this thing and a bypass towards Ostrava is twofold:
    – decouple the HSR project from the clusterfuck of “Brno Station Expulsion” (officially in English called “relocation”). And if the “Železniční uzel Brno” eventually gets build, to ensure that the through HSR trains won’t be impacted by low capacity of the reformed juction (which has already some history of planned in a way that wouldn’t handle then-current levels of traffic and with further expansion virtually impossible)
    – to be able to attain reasonable travel times to Ostrava and especially Olomouc (which would be otherwise faster via 1845 line)

    BTW I got to an counterintuitive conclusion regarding train speeds regarding Czech HSR. A conclusion that the officially assumed 300km/h Berlin-Czechia-Vienna service is a nonsense. Provided that Germany will neglect Berlin-Dresden as it historically does, we could assume that just 200 of 650 km would be at 300 km/h territory. The rest would be 200-230. And with this much slowness penalty, Czechs price sensitiveness penalty and state-border-despite-same-lang Berlin-Vienna penalty and much of traffic on Brno-Prague line by 200km/h trains as well, it’s almost impossible to make any sensible use of 300.
    OTOH I can very well imagine that domestic service could actually achieve enough passengers to pay for 300 km/h operation.

    • Alon Levy

      1. I’m making a specific assumption about international trips, which is that the underperformance is caused by high prices in all comparison cases (Eurostar, Thalys, and US-Canada flights), the first two caused by predatory monopolistic SNCF behavior outside its borders and the last by insufficient competition. In Europe, not a single cross-border intercity railroad is as well-run as local domestic counterparts, since Thalys and Eurostar are expensive and Eurostar also has security theater and all other borders have low-speed gaps at or adjacent to the border like Brussels-Antwerp or the German side of Paris-Frankfurt.

      2. Does Dresden-Děčín still need a base tunnel if the fast passenger trains are kicked out? And even then – a freight-only base tunnel can be designed with tighter curves, while a passenger-only line needs little to no tunneling, to the point that it might still be more cost-effective to build two separate lines.

      3. Yeah, I’m not at all sold on Eurostat’s metro area sizes in Eastern Europe; the sanity checks from the same source for Germany, France, and Spain are all okay but imperfect, and the high population quoted for Lille suggests to me the methodology might just choke in high-background-density areas. Then again, South Moravia is nowhere near as dense as Nord-Pas-de-Calais. Wikipedia quotes the domestic estimate for the metro area population as 700,000. The main reason 1 million looks even semi-plausible is that 195 million annual tram trips is a lot for a region of 700,000.

      4. Brno South might even be viable… if you believe my spreadsheet, the total traffic density from Prague south is around 24 million passengers, or around four 16-car trains per hour (one train is 900 seats, probably 500 filled; there are around 16 useful hours a day and two directions, so 1 tph = 16,000 passengers/day = 5.84 million passengers/year). Those split fairly cleanly as one to Vienna, one to Bratislava and Budapest, two to Ostrava and beyond. I presume in practice the ridership to Vienna would be disproportionately German, yeah. So a split between Brno South and Brno hl. n. isn’t awful.

      5. I was assuming any Prague-Brno alignment would go directly, via Jihlava. Or is the plan to go via Pardubice instead and then branch to Olomouc and Ostrava?

      • Sascha Claus

        2. Does Dresden-Děčín still need a base tunnel if the fast passenger trains are kicked out? And even then – a freight-only base tunnel can be designed with tighter curves, while a passenger-only line needs little to no tunneling, to the point that it might still be more cost-effective to build two separate lines.

        Two separate lines, one near the Elbe/Labe valley and one near the Weiße Elster/Bílý Halštrov valley? 😀 One has to wonder how many freight trains would pick other routes, if there were any other double-tracked, electrified ones available.

        • djasa

          Elster route doesn’t make much sense, you’d climb 10-20 ‰ ramps to cross over 600+ m high watershed which would only get you to upper Eger river basin without getting much closer to where the traffic is destined. It’s still very removed from the rest of Czechia and for Bavaria, route through Hof already exists while historical Cheb-Wiesau section of Bavaria-Cheb-Saxonia route is missing.

          Compare with route using Labe valley and watershed crossings near Česká Třebová (Böhmisch Trübau :D). Slopes are within 6-8 ‰ and the watershed is only at 430 and 455 m ASL, allowing full-length/weight trains to be pulled by single 4-axle loco throughout.

          There is indeed a missing double track electrified route with mild climbs – to Bavaria from Plzeň via Furth im Wald.

      • djasa

        1. I don’t believe that that’s full story. It seems to me based on other stuff (passenger car traffic intensities for example) that language and state borders are indeed some barriers that harm to business and non-business alike with visible result of ridership drops

        2. it still does. No trains are actually fast over here and number of passenger trains is quite negligible over there – see tweet with a string diagram

        3. that’s urban geography. Most of the city is reasonably dense and for some neighbourhoods, trams are actually fastest way to get to city center and some jobs centers, in addition both central part of the city and peripheries got really clogged with cars. The trends however still aren’t good with central sections of tram network at capacity but with no intentions neither to remove cars from its way nor to even study some feasible subway (or half-subway) solution. :/

        4. Prague-Brno(-Bratislava/Wien) market currently supports 2 long-distance trains of 7-9 cars per hour. Quadrupling that with travel times slashed to ~1 h from current 2.5 doesn’t seem far fetched to me (although some people laugh such a notion)

        5. It’s still planned to go close to Jihlava, it will just leave Prague to the east and then turn right and approach Jihlava from north. Previous iterations studied also routing around Benešov (piggybacking on reserve for 200 km/h new line from Prague to Bystřice u Benešova where suburban traffic drops and actual 160km/h line to České Budějovice starts) however it’d have to navigate more rugged terrain and it wouldn’t ease capacity crunch around Prague until completion of full line up to Přerov
        On web linked by Richard Mlynarik (thanks! It’s quite new, I didn’t visit it myself so far), this page links to maps.

        • Sascha Claus

          0. Elster route doesn’t make much sense, you’d climb 10-20 ‰ ramps to cross over 600+ m high watershed which would only get you to upper Eger river basin without getting much closer to where the traffic is destined.

          And how would a goverment-subsidized banking (helper loco) service stack up against a base tunnel, cost-wise?

          1. I don’t believe that that’s full story. It seems to me based on other stuff (passenger car traffic intensities for example) that language and state borders are indeed some barriers that harm to business and non-business alike with visible result of ridership drops

          One should compare the international underperformance with other modes like car and air travel. 🙂

          2. it still does. No trains are actually fast over here and number of passenger trains is quite negligible over there – see tweet with a string diagram
          – 0,5 “fast” tphpd is negligible

          And if the EC trains from Dresden are skipping Děčín with a tunnel right to Ústí nad Labem, surely there would be another fast train route (RE/R) via the valley route to connect Bad Schandau and Děčín with something faster than the S-Bahn.

          Even if it is the only fast from Dresden to Pirna and then serving all stops from Pirna to Děčín.

          • djasa

            And how would a goverment-subsidized banking (helper loco) service stack up against a base tunnel, cost-wise?

            That thing does actually exist between Brno and Kolín, when commenced, the parameters are:
            – 4 locos on 24/7 work or standby
            – line length around 190 km
            – infrastructure manager should pay CZK 244M for 3 years of such a service. I don’t know what operators pay for it, materials I can quickly google suggest that at least for the electricity used

            However. How do you get anywhere else from Cheb? There are just two lines connecting it with the rest of Czechia, both hilly and the one not going to Labe valley single track with very dificult double-tracking.

            One should compare the international underperformance with other modes like car and air travel. 🙂

            IIRC Berlin-Wien and Berlin-München markets behaved similarly with travel to Vienna weaker overall (before VDE8 which made them incomparable)

            And if the EC trains from Dresden are skipping Děčín with a tunnel right to Ústí nad Labem, surely there would be another fast train route (RE/R) via the valley route to connect Bad Schandau and Děčín with something faster than the S-Bahn.

            That’s IMO too tangential. The point is that Dresden wants to free up some capacity for for tiered S-Bahn, residents of the valley want to see number of trains going there lowered, and the volume of traffic the line sees is not unlike that of overloaded Alpine crossings. Overall, the context is pretty similar to that of long base tunnels under the Alps.

          • Alon Levy

            S-Bahn demand drops past Pirna, population is overall shifting to parts of Germany where AfD doesn’t get a plurality, and Saxon Switzerland does not get to randomly grab a few billion euros’ worth of surplus and destroy it so that there are fewer trains visible from people’s houses.

            And the problem with comparing Vienna with Munich is that ÖBB does fun things like mandate seat reservations, incidentally also fucking up Munich-Zurich trains.

          • djasa

            Alon, discard everything but trains per day:
            Mont-Cenis: up to 180 tpd total, up to 126 freight
            Löstchberg: 70-110 freights through base tunnel, 40 more continue using the Bergstrecke. (Autoverlad-Züge seem to be counted separately and they use the Bergstrecke)
            GBT: Am 5. März 2019 wurde der 100’000. Zug durch den Tunnel gezählt. (…) Werktäglich wurden zu dieser Zeit zwischen 130 und 160 Züge pro Tag gezählt, davon rund zwei Drittel Güterzüge und rund ein Drittel Personenzüge. Ultimate capacity given for GBT is 320 tpd
            Brenner: on average 80 total

            Labe valley: 280 trains per day, many of them heavy with single loco. Routes of similar performance are Moravian Gate some 300 km to the east (Přerov-Ostrava) or some lines feeding to Nürnberg-Regensburg(-Wien) lines 300+ km to the west (with Bayern-Sachsen Eisenbahn still wireless) and unlike another bottleneck of Ústí nad Orlicí – Choceň, this doesn’t have any reasonable alternate route which could be make comparable just by a provision of helper service.

          • djasa

            addendum to the previous posts:
            1. I couldn’t find quickly numbers for Pontebbana-Semmering axis however I doubt that they’d be anything greater than other Alpine crossings
            2. I meant of course whole Česká Třebová-Choceň section. The point however stands, this one can be bypassed or augmented by Brno-Havlíčkův Brod-Kolín section for a reasonable cost, Ústí nad Labem-Dresden not really

        • Richard Mlynarik

          Re 5.: Jihlava presentation (just FYI, fund via web search as nagivating spravazeleznic.cz for regional info is a bit of a mess) are quite elaborate: new station on the HS line running adjacent to the E50 motorway; new central Jhihlava station with direct connections to the HS line both northbound and southbound; new alignments to central Jhihlava including tunnels; … all for a city with 50k population. I went down a bit of a WWW rabbit hole on this.

          • Sascha Claus

            Well, it’s the capital of Vysocina and somewhat lonely there among all the other Kraj capitals, so there might be some regional equity politics at play.

            And they’re cheating, as the line from the main station southbound already exists and the northward bend follows an existing motorway, so easier to build. And the tunnels might have been in the plans already, as the Czech don’t seem to shy from improving railways in and around small towns. Looks like the existing City Station will be the new Main Station, Jihlava 21.

          • djasa

            The reasons for this goldplating are IIRC:
            – effort to get Vysočina region administrations’ (whose seat is Jihlava) cooperation. They can delay the project significantly if they sense that NIMBY position can get them some advantage, this is tangible benefit. Sort of more expensive Montabaur
            – the idea to create a triangle in Jihlava and use current Jihlava-město (“Jihlava City”) station as a regional hub without a need to switch direction by trains from southeast at Jihlava-hlavní nádraží (“Jihlava Main Station”) is older than the HSR project. Tying these two together is again a means to make regional politicians interested in HSR project success
            – earlier studies concluded that 300+km/h trains alone would be insufficient to generate enough demand to pay at least the operations and maintenance of the HSL with 300+ km/h trains only and that it’d be unlikely for the line to ever get to a capacity with such a traffic. So the whole concept was shifted in last 10 years to “Rychlá spojení” (“fast connections”, hence RS) meaning that fast regional traffic using slower and cheaper trains. Routing current R11 (see its Brno-Jihlava section) and proposed R33 train lines partially through RS1 HSL is part of this concept

      • Matthew Hutton

        @alon, during Covid I set a goal of not flying if you can get somewhere by land transport within a day.

        Because of this by the end of the year I’m going to have done 4 return Eurostar trips in 2 years. Cost wise it has always been comparable with an easyJet flight including getting to the airport, taxis late at night and a case in the hold.

        The biggest barriers are:
        * Needing to use bahn.de to work out the scheduling. Yeah bahn.de is awesome but it’s super non intuitive that you have to use the German train website for scheduling.
        * Having to fiddle around with the advanced settings to get sensible gaps between long distance trains and getting the changes in the right place. For example from Milan to London back it seems best to go via Switzerland, but you basically have to magically know that the most sensible place to change onto the TGV is Lausanne and not Geneva as the connection sucks.
        * Inconsistent schedules – for example the 9am Eurostar to Brussels connects well with the train onto Frankfurt, the 11:30am Eurostar misses the connection by 10 minutes and then there’s a 2 hour gap before the next train to Frankfurt.
        * The lack of trains on the Paris bypass line means you have to struggle with the RER, a big challenge for anyone older or with a family.

        And I mean if you’re the median Britain, AKA Worcester woman and want to go on holiday to Benidorm, the train takes 40 hours – no one would do that rather than fly.

      • Michal Formánek

        Brno is nice example of tram ( light rail ) city. It is similar to Zurich, both have dense tram network for city trafic and trains ( S-bahn ) for suburban trips. Both have One central station, in Brno this is also strongest knot of tram network.

        It seems that this tram + S-bahn model works well for cities of certain size, lets say up to 1 milion. In the city, frequent tram with crosroad preference and accessible stops is as fast as metro – real door to door trip if one does not need to go to underground and up. To build tram tracks in street median and maybie bury few busiest sections in the city center to underground is cheaper than full scale metro.

        Now for Brno, it is still expanding its tram network. It would help to build underground sections in Brno center, to increase capacity and speed, but there are no plans for this, just wague idea of north-south something.
        Worse there are plans for relocation of central rail station out of the most important tram knot to other southern location. I think this is madeness, because current railway station could be expanded to nearby lot with supermarket. Main argument for relocation is that high speed trains should not loose time to go to city center, but I think this is bad idea. Because what matters is door to door time, that means also time transfering, waiting for connection or going to railway station.

        I think this idea to create high speed rail stops on perifery, out of connection to other transit is diminishing value of high speed rail in Czechia. Note that Czechia has one of densest rail networks in the world so integration with legacy lines should be paramount. Unfortunatelly, they got some French consultants and now they crayon betroot stations like “Nehvizdy” Praha východ or Roudnice nad Labem, unconected to any other public transport.

        • Michal Formánek

          Compare Brno, Linz or Bratislava, where trams are backbone of public transport to lets say Japan cities like
          Kochi or Nagasaki. Somehow, it is working well here in Central Europe.

        • Matthew Hutton

          Most of the Chiltern railways “parkway” stations are also on decent bus routes to be fair.

  16. Mikel

    I would love to see your crayon for postwar Ukraine, assuming EU funds or even Russian reparations. An interesting problem with German/Polish policentricity, less-than-Spanish population density and very low GDP per capita. What would the #1 priority be here: Kyiv to Kharkiv via Poltava? Kyiv to Donetsk/Luhansk/Mariupol via Dnipro and/or Zaporizhia? Kyiv to Lviv and onward to Poland? Or something not involving Kyiv at all? The existing network might have to be rebuilt entirely in the eastern third of the country after all…

    • Alon Levy

      In Western and Southern Ukraine, I think a giant Y connecting Lviv, Kyiv, and Odesa may work. The spreadsheet is okay on Lviv-Kyiv and that’s even without adding a Warsaw-Lviv connection. East of Kyiv, I can see a line to Poltava splitting to Kharkiv and Dnipro/Zaporizhzhia? Past that, it depends on the postwar borders whether the latter branch can continue to Donetsk.

      But yeah, Ukraine has the same problem as Poland with having undersize cities for how many people it has, and even lower population density.

      • Bryan Anderson

        I’m imagining the nexus of the Y being at Vinnytsia (based on your comment above about Lviv-Kyiv running through that city), which makes me wonder if Vinnytsia-Odesa should run via Chisinau and Tiraspol in a world where the Transnistria issue is resolved favorably for Moldova. Maybe that would open the door to a Romania connection as well, as Chisinau-Bucharest can avoid the Carpathians.

  17. Tomek

    For reference, here is a current plan for the development of Polish HSR (and almost-HSR) in the future: https://www.skyscrapercity.com/attachments/parametry-sieci-kolejowej-po-roku-2035-p180-rys35-jpg.4449589/ (sorry for lousy quality, but you can see the rough location of high speed lines)
    (source: page 180 in https://www.cpk.pl/wp-content/uploads/Analiza-oferty-przewozowej-operatorow-realizujacych-przewozy-na-zasadzie-otwartego-dostepu.pdf)

    Now, the entire CPK (Centralny Port Komunikacyjny, Central Transit Hub) project is likely to be rocked by political changes in the future and I would expect some changes and downscaling. However, some elements are remarkably persistent and have been under consideration, in some form, for decades already:
    – CMK-Północ (railway line number 5) – a line branching off CMK (line number 4, connecting Katowice and Warsaw) near Jaktorów and heading north, towards Gdańsk
    – “Y” line – Y-shaped line(s) from Warsaw, through Łódź (tunnel under the city centre), to Poznań and Wrocław (junction being located in Sieradz), with possible extensions from Poznań to Berlin and from Wrocław to Prague (however, extension to Berlin is not really under planning now, and Wrocław-Prague is even farther out in the dreams, as it redundant with the point below)
    – Katowice – Ostrava link, connecting to the potential future Czech HSR network (and Katowice is already connected to aforementioned railway line number 4 (CMK), which is the only HSR-like line existing currently in Poland)

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