Writing my Eastern Europe high-speed rail post meant I needed to go back to my ridership projection model for high-speed trains. This model aims to analyze large networks like the entire Shinkansen or TGV and project traffic for extensions of these systems, for upgrade of partially-built networks like that of Germany, and for entirely new systems like any proposal for the United States. To compensate for the relative paucity of training data, the model has as few variables as possible – just four:

The populations of metro areas A and B are in millions, distance is in kilometers, and ridership is in millions for year. The four constants – 75,000, 0.8, 500, and 2 – are roughly motivated by Shinkansen data, with some European sanity-checks; the 0.8 exponent is also motivated by some practical attempts to subdivide metropolitan areas into pieces, some on the line and some off it. But is this right?

And as it turns out, the model nails trips from Tokyo to most metropolitan areas in Honshu. Defining Tokyo as the prefecture plus Kanagawa, Chiba, and Saitama Prefectures (#15-18 in the spreadsheet), the spreadsheet says there are 2,742,200 annual JR trips between there and Aomori Prefecture (#6); the spreadsheet predicts 2.59 million trips between Tokyo and the prefecture’s two cities, Aomori and Hachinohe.

Two years ago already, I made a spreadsheet with the model’s predictions for ridership between each pair of metro areas on the Shinkansen network. This can be compared with actual numbers of prefecture-to-prefecture trips by mode (except cars). For most long-distance trips, the numbers in the second sheet matter, comprising all Japan Railways trips; for interregional ones for which slow lines maybe an alternative, it is perhaps better to use the fourth sheet, which excludes season passes used by regular commuters. The numbers in the spreadsheet are directional, so cells should be added to the ones diagonally across.

The problem is that the model severely overpredicts inter-island trips. Tokyo-Fukuoka is 4.61 million per the model; the actual count per the spreadsheet (Fukuoka is #44) is 1,203,600. Tokyo-Hakodate (#4) is likewise 954,000 in the model and 378,200 in reality. Osaka-Fukuoka fares better but still notably underperforms: the model says 10.2 million, whereas the spreadsheet, defining Osaka as Osaka, Kyoto, and Hyogo Prefectures (#30-32), gives 7,162,900, even though the distance is similar to that of Tokyo-Osaka.

Another category that the model overpredicts is trips through Tokyo. Those are less convenient by Shinkansen as they require a transfer, and the transfers are not timed, though the frequency on the Tokaido Shinkansen is such that untimed transfers are not the end of the world. The model predicts Osaka-Sendai at 2.21 million and Nagoya-Sendai at 1.97 million; the spreadsheet says metro Osaka-Miyagi Prefecture (#8) is 194,500 trips, and from metro Nagoya (Aichi Prefecture, #27) it’s 234,300. It’s not even quite a matter of distance: Osaka-Sendai is 840 km, about the same as Tokyo-Hiroshima, which the model gets correctly. It’s just a through-Tokyo effect, like the inter-island effect.

Fortunately both categories can be corrected by taking plane trips into account, listed on the last sheet. Tokyo-Fukuoka by both air and rail is not 1,203,600 trips but 12,313,300; this is a five-hour trip, at which point in Europe the modal split is fairly even, for example on Paris-Nice (p. 3) or more generally in France (source, p. 33). If we include air trips, Osaka-Fukuoka is 8,199,900, Tokyo-Hakodate is 1,482,200, Osaka-Sendai is 1,624,000, Nagoya-Sendai is 445,100. If we take the combined air-rail market and apply more common European modal splits, there is no inter-island penalty, just a bit of a penalty for Osaka-Sendai and a big penalty for Nagoya-Sendai.

Finally, the model chokes on short-distance ridership, generally underpredicting it. It’s hard to exactly count between two relatively close provincial cities, since very short regional trips are included and not just intercity ones. But even excluding season passes, Miyagi-Aomori is 1,140,400 trips a year, where my model says 446,000.

The dicier situation is that of Tokyo-Shizuoka (#26). My model predicts 14.1 million annual trips between Tokyo and the combination of Shizuoka and Hamamatsu, the two largest cities between Tokyo and Nagoya. The spreadsheet gives the number at 37,264,700, or 26,458,300 excluding passes. Even that likely includes some legacy rail trips: there are 9,382,000 non-pass trips between Shizuoka and Kanagawa Prefectures and 15,646,300 between Shizuoka and Tokyo itself, where from Nagoya and Osaka the ratio is more like 1:4; Shin-Yokohama is located in a less central place than Yokohama Station, and I suspect most of the 9.4 million figure rides the Tokaido Main Line.

To complicate things further, while my model underpredicts trips of around 150-200 km, it doesn’t do so to Tokyo-Sendai (10.5 million predicted, 10,924,000 actual), Tokyo-Nagoya (32.4 million predicted, 28,391,100 actual), or Tokyo-Niigata (11.1 million counting Nagaoka and Sanjo, 10,436,600 actual), and it actually overpredicts Nagoya-Osaka (19.2 million; the actual is 13,026,800). Thus, I am still reluctant to change the 500 km minimum in the denominator below which distance is deemed to no longer matter, even if I include a fudge factor for Nagoya’s repeated underperformance.

The one snag that may be worth addressing is the scale issue inherent in the 0.8 exponent. The exponent seems broadly correct from Japanese data. Moreover, when I break metro areas like New York into smaller constituents and compute their individual trip times to other places to apply the formula to each, the exponent seems correct: large metropolitan areas are so big that many of those smaller pieces are far from the train (for example, Long Island) and have additional trip time to consider, reducing overall ridership.

However, the 0.8 exponent also means that as the area of study grows, the model expects per capita trips to rise. Doubling the population of every metro area increases overall ridership by a factor of about three, which may be correct at small scale (it probably means those regions get stronger connecting lines and better train frequency), but should fail at large scale. Evidently, Taiwan overperforms the model by a factor of about three. Just shrinking the exponent to 0.5 wouldn’t work – it would lead to massive underprediction of Tokyo-Osaka ridership and overprediction of Tokyo-Sendai, Tokyo-Hiroshima, and Nagoya-anywhere. There may need to be a fudge factor for systemwide population.

Best I can say is that you should trust the model in the range of system sizes between Spain and Japan, so around 45 to 120 million. It may be possible to go above 120 million in geographically larger regions, like the Eastern United States (around 190 million) or even the entirety of the EU from Warsaw westward (around 370 million), if the large geographic extent means that in practice the network has its own diseconomies of scale from the long end-to-end distance. In other words, the pure 0.8 exponent is obviously false if we double the population of each metro area – but if we instead double the size of the area of study by including more cities in it, then the average distance grows and then the exponent of 2 in the denominator countermands the effect.

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

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.

There was reporting in the Sun, since officially denied, that Britain is planning to cut Euston from its high-speed rail project and run trains only as far a Old Oak Common, a future development site west of Central London. I assume given the source and lack of any other confirmation that the plans are to run to Euston as planned. But what if the story is not completely fake news, and there are plans to cut on construction at Euston? I can see a cut being positive value engineering, using space at the station more efficiently.

What’s the issue with High Speed 2?

High Speed 2 is an extremely expensive line. Among proper intercity high-speed rail lines (as opposed to suburban lines running at medium speed), it is the most expensive in our database per kilometer. The projected cost as of 2019-20 is about the same as that of all lines built to date in Germany and France combined; Germany has about 1,000 km of newly-built high-speed lines and France 2,500, whereas HS2 is planned to be 530 km.

The high costs are related to some massive scope creep, including tunnels in relatively flat terrain through the Chilterns, dug essentially because the area has rich NIMBYs and the British state decided not to fight them. Those are already in advanced enough construction that I don’t think descoping them and building the line at-grade with compulsory purchase of land is viable. However, some of the scope is new stations, which British defenders of the system insist are necessary. Birmingham is to get an entirely new station at Curzon Street, and London Euston is to get a substantial increase in size, with additional tracks and approaches. This is said to be necessary for capacity reasons.

Are new stations necessary for capacity?

No. Euston today has 16 platform tracks; it had 18 before HS2 construction started. The S-Bahn-quality Watford DC line can use two; the remaining slow services at the station amount to around 10-12 trains per hour, which S-Bahn-quality terminals like Saint-Lazare on the RER E and Catalunya on the Barcelona Rodalies network can comfortably turn on four tracks; those two comparisons turn 16 and 24 trains per hour on four tracks, respectively. The services out of Euston branch more than the RER and Rodalies, but this is mostly a mix of stopping patterns, largely on the same legacy line.

Then there’s HS2 itself. The line is expected to get very high ridership, justifiably: all cities along the line are larger than their comparison cases on the LGV Sud-Est, often substantially, and the projection is that very high capacity is required, on the order of 16 trains per hour. This stretches high-speed rail to its limit: the Shinkansen, which mixes local and express trains on double track, peaks around 14-15 trains per hour, and the complexly branched TGV around 12. HS2 expects to do better perhaps through better signals but also through having a simpler stopping pattern on its most congested section, between London and the bifurcation at Birmingham Interchange, on which trains are to run nonstop.

However, 16 trains per hour can still turn on about six platform tracks. This is not easy: the Tohoku Shinkansen turns 14 on four tracks, but this is a limit case, famous not just in rail media but also in business media as successful optimization of infrastructure. Nonetheless, given how constrained the site is, it’s useful to learn from the best and not the average. If it’s possible to descope the plans to add new tracks to Euston, this should be done; present plans for Euston cost billions.

Is this happening?

Maybe. Britain is aware of the situation at Tokyo Station, although it seems more interested in looking for reasons not to learn than in learning. Perhaps very high costs are leading to a reevaluation, in which Euston can be made smaller than in current plans and trains can turn more efficiently.

But again, the ultimate source on this said nothing of this sort, and is unreliable. So who knows?

I’ve been uploading videos about high-speed rail lately, of which the most recent, from a week ago, is a return to my attempt at producing a high-speed rail map proposal for the eastern half of the United States. I streamed and then blogged a map here with followup here, but having looked at the model more, I’d like to do a refinement – both to introduce a slightly bigger map and explain why it is so, and talk about the issue of connecting low-speed lines. Along the way, I feel like I must talk about an issue mentioned in comments occasionally about the politics of only connecting major metropolitan areas, especially since this map still has fewer lines than various state wishlists stapled by Amtrak; this is especially important because one of the motivations for this post is a criticism of current plans by Matt Yglesias.

The map

A full-size (6 MB) version of the map can be found here. This is not intended as a comprehensive map of all desirable low-speed connections – I made no effort to include the Northeastern ones, which I wrote about in the context of New England and Upstate New York, and which Ben She has done good work on in the context of eastern Pennsylvania and the mid-Atlantic. Rather, I want to focus on the Midwest.

But first, to explain a little more about why this map includes more red (high-speed) lines than previously, the reason has to do with my spreadsheet for computing ridership density based on Metcalfe’s law. The original posts computed everything by hand, which meant that some low-ridership city pairs I just rounded to zero; the spreadsheet does include them, making every line look much stronger. This, in particular, makes St. Louis-Kansas City and Atlanta-Birmingham, omitted last year, and Nashville-Memphis, suggested last year as a maybe, solid propositions.

A note of caution is still advised. Those weak city pairs that aggregate to sufficient ridership for significant return on investment are often at long distance, such as Kansas City-New York. The ridership model is trained on Shinkansen data out of Tokyo and sanity-checked with some French, German, and Spanish data, but the same model overpredicts Shinkansen ridership on inter-island trips for which planes are a convenient alternative, like Tokyo-Fukuoka or Tokyo-Hakodate. This makes me reluctant to add a Kansas City-Dallas connection, which the spreadsheet thinks generates a bit more than $1 million in annual operating profit per km of new construction: the extra ridership out of Kansas City-Dallas includes some very long-distance trips like Dallas-Detroit, for which the model is likely an overprediction.

The truth is likely between the spreadsheet and the handmade version of the model; while the Shinkansen is not competitive with planes when trains take five hours, European high-speed trains are, for example Paris-Nice. This leads to the inclusion of the new sections, but the exclusion of Kansas City-Dallas. Note also that I did look at Birmingham-New Orleans and Memphis-Little Rock, and both were weak even in the spreadsheet (though I did not attempt Birmingham-New Orleans-Houston) – the Deep South is too low-density and rural to support as expansive a system.

But the topic of this post is not the South, but the Midwest.

Midwestern urban geography

The United States is usually a country of fewer, bigger metropolitan areas, like rich Asia and unlike Europe; unlike both Europe and Asia, American cities are very decentralized, and the exceptions are in the Northeast and West, not the Midwest. In particular, naive comparisons of Midwestern to French high-speed rail corridors are unwarranted: while Chicago is of the same approximate size as Paris, and secondary Midwestern metropolitan areas like Detroit and St. Louis are substantially larger than French ones like Lyon and Marseille, Lyon and Marseille are ringed by many small metropolitan areas with their own TGV service, whereas at the same radius, St. Louis has only its suburbs.

However, this phenomenon of fewer, bigger metro areas has exceptions. Michigan, in particular, has a slightly more European geography. Using the smaller numbers produced by the metropolitan statistical area (MSA) calculation rather than the broader combined statistical area (CSA), Metro Detroit has 43% of Michigan’s population as of the 2020 census. The median Michigander lives in the Grand Rapids MSA, with 1.1 million people, fewer than the US-wide median of 1.6-1.7 million. Michigan is a fairly urban state, and below Grand Rapids is a succession of six-figure metropolitan areas: Ann Arbor, Lansing, Flint, Kalamazoo, Battle Creek, Saginaw.

Ohio is similar to Michigan. Its three main metro areas, excluding Cincinnati’s out-of-state suburbs, have just a hair less than half the state’s population; the median Buckeye therefore lives in Dayton, MSA population 800,000. Moreover, the southern half of Michigan has fairly high population density, as does Ohio – nothing as dense as the Northeast or Germany, but they’re comparable to France.

This geography lends itself to an expansive intercity rail network: the cities are relatively close to one another, and there are many of them meriting a connection. In Ohio, this happens to take the form of an entirely high-speed network, since Cleveland, Columbus, Dayton, and Cincinnati all lie on one line, and then the most natural east-west route between the Northeast and the Midwest passes through Cleveland and Toledo. Ohio, in this case, is a state with fairly good geography for low-speed intercity rail that just happens to also have good geography for high-speed rail due to its location. Michigan, in contrast, is not on the way between much, and thus should get a low-speed rail network, including both connections to Chicago (such as to Grand Rapids) and an intra-state network.

Wisconsin has many, smaller cities as well: the median resident is in an MSA of around 200,000 people, currently Racine. Fortunately, many of those cities lie on just one line between Chicago and Minneapolis, plus a low-speed branch up to Green Bay. Unfortunately, coverage is lacking by the standards of Ohio, Michigan, or much more big city-dominated Illinois and Minnesota.

Getting low-speed rail right

I am happy to report that in Michigan and Ohio at least, good projects for low-speed rail are pursued. When I streamed my video, I was told in Twitch chat that Michigan is looking into funding a Detroit-Lansing-Grand Rapids intercity train. Ohio likewise has long had ideas for a statewide network, beginning with the Cleveland-Cincinnati spine.

It is unfortunate that these projects are not planned well. In a future post, I should write more about the concept of the wrong project versus the right project done poorly; I obliquely pointed this out when writing about leakage in the context of urban transit, where some American cities have poor project prioritization (such as Los Angeles) whereas others choose more or less the right projects but execute them poorly (such as New York and San Francisco). In this schema, the current plans for low-speed rail are often the right project, done wrong.

What I mean by this is that there’s a set of best industry practices for getting low-speed (that is, legacy) rail right, emanating out of Germany and surrounding countries, especially Switzerland. These include,

• Integration of timetable planning and infrastructure, to minimize construction costs – if higher costs are acceptable, just build high-speed rail.
• A clockface all-day schedule with a minimum of one train every two hours, and ideally a train every hour if the distances are shorter or the cities are bigger.
• Timed connections at major nodes to both other intercity trains within the same network and regional mass transit (such as regional trains or connecting buses).
• Reliability-centric planning, in which sources of delays are to be proactively eliminated – on a system this tightly coordinated, delays on one line propagate across the entire system.
• An average speed of around 100-130 km/h – the higher numbers are more appropriate in flat terrain.

Marco Chitti has an excellent post that I must revisit in the future giving more detailed guidelines, mostly at regional level but also with an eye toward national intercity rail planning.

The upshot is that trying to incrementally build up ridership for a few trains per day does not work. The US has a few trains per day on a few corridors now, such as Chicago-Detroit, and daily trains on most others, and this hasn’t built up ridership. The low-speed, low-frequency intercity trains Europe had before the introduction of the TGV in France and the high-frequency, tightly-linked InterCity network in Germany were rapidly losing market share to cars and planes. To build such a network now would be like to build infrastructures wired telephones in a developing country rather than just skipping straight to cellphones as developing countries have.

Politics and Matt Yglesias’s post

Matt likes pointing out that current transportation plans in the United States are deficient, and to link to my posts as a better alternative. There was a lot of dunking on Matt’s post about this (as there is on anything that Matt writes) by left-identified people who, in effect, think daily or twice-daily trains between small cities are a great investment. This dunking usually takes the form of “how dare Matt, a lifelong East Coaster, tell people in [insert Midwestern town] that they don’t deserve trains?”. In a less abrasive form, some people in comments here, like Pharisee, have made the point that these expansive maps proposing daily trains to many places have good geographic coverage whereas what I propose does not. Let me explain why this line of thinking is wrong.

The issue is that the United States is, again, a country that for the most part has fewer, larger metropolitan areas than Europe. The map I made above hits MSAs with a large majority of the country’s population. Of the top 50 as of the 2020 census, the only misses are Denver, Oklahoma City, Salt Lake City, and New Orleans. Denver and Salt Lake City are far from everything else, and the other two are in theory on routes from Texas to the rest of the country but there’s too little population on the way for a connection in the geography of 2022.

Moreover, within the Midwest, coverage is ample. The Midwest is a highly (sub-)urbanized region, much of which has fairly high population density, and the biggest exception to the high density, Minnesota, has a large enough city to justify a line to Chicago by itself (and Milwaukee is on the way, too). The areas that are usually most moralized as Real America – Michigan, Ohio, Pennsylvania – are on the way. This shouldn’t be too surprising: the Real America moralization centers areas with a past industrial history, evoking feelings of nostalgia for midcentury American industrial dominance, and those areas remain major cities today, just relatively poorer than they were in the 1960s. This way, in the Midwest, every state has a large majority of its population in an MSA with a high- or low-speed train station on my map, except Iowa, which is unusually rural.

This is not even out of any consciously political desire to serve these areas. I draw maps out of a ridership model. It just so happens that metropolitan areas of 4 million people situated in dense geographies scream “build high-speed trains to me,” and those include Detroit.

The problem – the reason Matt is so negative on current plans – is that current plans are bad. They are low- and not high-speed rail, which by itself is not horrible, but they’re also bad low-speed rail. Daily trains are just not good. But this does not mean the Midwest can’t or shouldn’t get a good intercity rail network: it should, combining high- and low-speed trains as appropriate.

On my Discord channel, I was reminded of the late-2000s work by some institutional American urbanists about the concept of megaregions. Wikipedia has a good summary of the late-2000s discourse on the subject. In short, there are linear ties across the East Coast from Boston to Washington (“BosWash”), with more or less continuous suburban development in between, and some urbanists tried to generalize this concept to other agglomerations of metropolitan areas, not usually successfully. The American work on this carved most of the country’s population into 10 or 11 megaregions, sometimes annexing portions of Canada, as in the Regional Plan Association’s America 2050 program:

There is a lot to critique about this map. Canada has a strong self-conception as a distinct entity from the United States; while there’s a case for lumping Vancouver with Seattle and Portland as the Pacific Northwest, lumping Toronto with the Midwest is irresponsible. The Hampton Roads region is not meaningfully a periphery of the Northeast, but is rather Southern (for example, it is heavily militarized, and the South has consistently higher enlistment rates than the Northeast). The Rio Grande Valley is not especially connected with New Orleans.

But the core of the program is to propose this as the basis of high-speed rail investment, and that’s where it fails the most visibly. When one of my Discord channel participants posted the map in the channel about high-speed rail, I started talking about my gravity model, and pointed out some patterns that emerge.

For this, consult a table of ridership between any pair of American or Canadian cities in the main connected component of my proposed map:

The table omits Texas, California, and the Pacific Northwest. But it includes lines that I initially considered and rejected, going to Kansas City and Birmingham; the reason is that when I calculated it by hand I omitted very weak long-range connections such as between Boston and the Midwest, whereas the table can automatically calculate them and add them in, producing an estimate of 5 million annual riders between Boston and the entire Midwest region. These extra connections make weak lines like those to Birmingham and Kansas City appear stronger, so those lines are included; it’s plausible they could even justify a connection to Texas via both New Orleans and and Tulsa, but those are not included (and would at any case not impact the analysis below).

The following table includes some connections between two adjacent cities in the table, with their total projected passenger counts. Those are very high numbers, higher than you’d expect; this is because they lump in a great many city pairs – for example, New York-Philadelphia includes all connections from New York, Boston, and Albany to Philadelphia and points south and west, and those sum to a much higher number than just the internal trips on the Northeast Corridor, let alone just trips originating in New York and ending in Philadelphia or the reverse. Also, as a note of caution, there may be small inaccuracies if I mistakenly tabulated very weak markets like Chicago-Charlotte as going via the wrong path; they do not change the main conclusion.

City pair	Ridership
Boston-New York	39,299,133
Boston-Springfield	25,482,364
New York-Philadelphia/Harrisburg	139,860,707
Philadelphia-Washington	110,010,205
Washington-Richmond	64,145,050
Richmond-Raleigh	50,425,578
Raleigh-Greensboro	42,654,519
New York-Albany	57,773,629
Philadelphia-Harrisburg	65,639,871
Harrisburg-Pittsburgh	61,110,782
Pittsburgh-Cleveland	62,352,156
Cleveland-Toledo	56,482,182
Cleveland-Columbus	46,046,790
Buffalo-Cleveland	41,584,062

Some observations jump from this (partial) table:

• New York-Boston is much weaker than a lot of segments that are by themselves far weaker than the Northeast Corridor. The reason for this is that a full 31.1 million annual riders on New York-Boston are internal to the Northeast Corridor, whereas the other city pairs require large swaths of the network to be built to have such high traffic.
• From Philadelphia to points west, traffic density is fairly consistent. There’s no separation between a Northeastern and Midwestern megaregion evident in the data: Cleveland has about the same traffic density going east and west, as does Pittsburgh. Rather, it’s the connections between the East Coast and the Midwest, chiefly Philadelphia-Pittsburgh-Cleveland but also the Empire corridor between Albany and Cleveland, that create high ridership.
• Washington-Atlanta is a tail gradually weakening with distance from the Northeast Corridor, rather than an independent corridor.

Outside the US, the same observation about the irrelevance of megaregions to high-speed rail is true. The European attempt to describe a megaregion, the so-called Blue Banana, was constructed explicitly to exclude France – but the highest-traffic density intercity rail link in Europe is between Paris and the bifurcation splitting toward Lyon and Dijon. Frankfurt-Mannheim is a close second, but French intercity trains average around 220 km/h and German ones around 130 km/h depending on the line, and the actually existing high-speed rail network gets higher peak traffic density than the medium-speed one.

Ultimately, high-speed rail as a mode of transportation is a means of connecting metropolitan areas. Whether they fall into megaregions or not is immaterial – some strong links connect distinct regions, like Northeast-Midwest, with higher demand for traffic than some of the internal connections.

I was asked a deceptively simple question on Twitter: why would people bother with taking a train when flying is available? In my (admittedly primitive) modeling for high-speed rail ridership in the US, I’m including some nontrivial ridership and revenue coming from cities at a distance that people do fly, like Boston-Washington, New York-Cleveland, and so on. What gives?

The simplest answer is that evidently people do take trains at such distances. Statista has some examples, all with more rail than air travel; an Air2Rail paper by Arie Bleijenberg has some numbers within Europe in Annex B. The main factor is rail travel time, with a malus for markets with poor rail connectivity (such as anything crossing the Channel). When trains take four hours, as on Paris-Toulon, they have a small majority of the travel market (source, p. 14 – look at the 2009 numbers, the 2023 numbers being a speculation); Paris-Nice manages to have respectable modal split even at 5.5 hours.

But that answer is frustrating. Why do people take trains for 4-5 hours when it’s possible to fly in an hour?

The first answer is door-to-door travel time. This includes all of the following features:

• Airports are far from city centers whereas train stations are almost universally within them; even taking into account that most people don’t live in city center, they tend to have easier access to the train station than to the airport, and then destinations are massively centralized in the city.
• Trains have no security theater to delay passengers, and passengers can get from the station entrance to the platform in 10 minutes if the station is exceptionally labyrinthine and they’re unfamiliar with its layout and two minutes if it’s not or they are.
• Passengers with luggage can take it on the train and don’t have to be further delayed for baggage claim.

All of these features work to make trains more pleasant than planes even when the door-to-door trip times are equal. The sequential queuing for security and then boarding on a plane is a hassle in addition to extra time; of note, in the Air2Rail link, the most glaring underperformance in high-speed rail modal split relative to trip times is for routes crossing the Channel, because they have such queuing courtesy of British paranoia about terrorism in the Chunnel and also charge higher fares.

The advantages of planes over trains are elsewhere. First, planes are faster airport-to-airport than trains are station-to-station, and as a result, a longer distances they are much faster door-to-door and therefore dominant. And second, trains travel in lines whereas planes travel point-to-point; it’s not hard to come up with city pairs that have no reason to have an even semi-direct high-speed railway between them even though they are at rail-appropriate range, for example Nice-Geneva (290 km) or Cincinnati-Charlotte (540 km).

But once the lines exist, they should get substantial passenger traffic – and the modal split with air is very well-documented in the literature and the overall traffic is still fairly well-modeled as well.