Metcalfe’s Law for High-Speed Rail, Redux

Americans are in big infrastructure spending mood, and my post from February using Metcalfe’s law to argue in favor of expansive high-speed rail in the eastern half of the United States has been attracting renewed attention. That post looked at how Metcalfe’s law that the value of a network rises in proportion to the square of the number of nodes implied that once a strong HSR corridor existed, for example the Northeast Corridor, extensions would be strong as well even if they connected much smaller cities. People have been asking me to extend that analysis to more lines that do not touch the Northeast Corridor, so here goes.

As a reminder, I’m using a simple gravity model, of the following level of sophistication:

He doesn’t put his axe down when standing on a crowded train, either. Credit: Anaterate.

The model is that the annual ridership in millions between two metropolitan areas A and B, with populations in the millions, is,

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

The theoretical reason for the 0.8 exponents is diseconomies of scale: the average person in Tokyo is farther from Tokyo Station than the average person in a small city is from their respective intercity rail station. Empirically, the best fit exponent for observed data in Japan and Europe is 0.8 – see sources in my previous post and in this post (sourced to since-rotted links) for France. The 500 km minimum is an artifact of the impact of station access time and the option of driving instead of taking the train.

Fares are set at typical Continental European levels rather than Japanese ones. As in the previous post, this means $0.135 per passenger-km, which breaks down as $0.07/p-km in operating expenses including rolling stock but excluding infrastructure and $0.065/p-km in profit, up to a total profit of $50/passenger. Beyond $50 in profit, which normally occurs at 770 km, fares only rise with operating expenses, to be more competitive with airlines. The goal is to find lines that have annual profits of more than 2-3% of construction costs.

A note of caution on the model

There are arguments to be made to refine the gravity model above in either direction. Ridership estimates in Britain are well above what the model predicts. High Speed 2 projects 3 trains per hour between London and Birmingham, running nonstop between the two cities so that no other city pairs can be added. The model gives an annual ridership equal to,

75,000\cdot 14^{0.8}\cdot 3^{0.8}/500^{2} = 5.97,

which fills around 1 train per hour in each direction to 50% of seated capacity. It’s possible the model does give higher ridership figures for very close-by cities – London and Birmingham are only 180 km apart – or it’s possible some unknown factor exists. Or HS2’s traffic estimates could be completely off.

In the case of the US, it’s likely any HSR will run faster than legacy 1960s Shinkansen. However, there’s a serious malus coming from higher car ownership, lower car traffic levels, and much weaker city centers. This is unlikely to be a problem for traffic to New York, but the last post dealt with that, whereas today we’re looking mostly at lines that aren’t about New York. Even Chicago is extremely auto-oriented by the standards of London or Paris, let alone Tokyo.

Metcalfe’s law for HSR in the Midwest: the initial line

The Midwest benefits from two things: it is flat, which reduces construction costs to $20-25 million per km if European norms are followed, and it has near-megacity Chicago in the middle. Unfortunately, Chicago is big but not big enough, and while the secondary cities are pretty big, there aren’t additional medium-size cities nearby the way Lyon has Saint-Etienne, Marseille has Toulon, etc. HSR can succeed, but the return on investment is for the most part marginal. The one exception is lines that can leverage the Northeastern network, including eventually not just the Northeast Corridor but also tie-ins to Pittsburgh and Cleveland, both of which are at reasonable HSR distance from New York.

By itself, the core Midwestern network would connect Chicago (10 million people) with Toledo (0.8, a distance of 370 km) and thence split toward Detroit (5 million, 100 km from Toledo) and Cleveland (3 million, 180 km). This leads to the following O&D ridership matrix, in millions:

City W\City EToledoDetroitCleveland
Chicago1.586.863.77
Toledo0.910.6
Detroit2.62

And in annual operating profits, in millions of dollars:

City W\City EToledoDetroitCleveland
Chicago38.08209.56134.68
Toledo5.917.07
Detroit47.65

This is not a lot of ROI. It’s $443 million a year, for a 650 km system, which should cost maybe $15 billion. It’s 3% by itself, which isn’t horrible, but compares poorly with Northeastern lines even though it connects the Midwest’s numbers 1, 2, and 4 metro regions.

In contrast, suppose a Northeastern system preexists, or perhaps is built at the same time, including a Pittsburgh-Cleveland connection. What then? Well, the question is really what the ROI is on connections from west of Cleveland to east of Cleveland. There are four metro areas east of Cleveland on the way to New York: Pittsburgh (2.5 million, 200 km from Cleveland), Harrisburg (0.7, 280 km from Pittsburgh), Philadelphia (7 million, 170 km from Harrisburg), New York (22 million, 140 km from Philadelphia). Washington has 10 million people and is 220 km from Philadelphia, but because a Washington-Philadelphia-Harrisburg route is circuitous, trains can only charge for 220 km, which is $29.70, and then earn the usual rate of $0.135/km farther west up to a maximum of $50 in profit, which is reached 730 km west of Harrisburg, or somewhat west of Toledo. With this in mind, we use the same pair of tables as above for the new city pairs, first ridership and then operating income:

City W\City EPittsburghHarrisburgPhiladelphiaNew YorkWashington
Chicago1.750.341.563.121.48
Toledo0.520.110.430.790.36
Detroit2.260.351.492.811.3
City W\City EPittsburghHarrisburgPhiladelphiaNew YorkWashington
Chicago85.3616.7777.94156.2374.03
Toledo12.94.6421.639.5317.95
Detroit70.617.4774.53140.7364.84

The total operating income is $875 million a year, which combines with our internal $443 million to produce an 8.8% ROI. This relies on estimating HSR ridership at hefty distances – New York-Chicago is 1,340 km and around 5 hours, New York-Detroit is 1,070 km and around 4 hours. But we do have ridership estimates for city pairs of that magnitude in both Europe and Japan and they’re fine, except for airline-dominated Tokyo-Fukuoka. If anything, this is more robust than making assumptions on how many people are willing to travel by train between two cities without public transportation like Cleveland and Detroit.

Metcalfe’s law for the Midwest: further lines

Past plans for a Chicago-centered Midwestern HSR network called for four spokes: east toward Cleveland and Detroit, northwest toward Milwaukee and Minneapolis, southeast toward Indianapolis and Cincinnati, and southwest toward St. Louis and perhaps Kansas City. These spokes do pan out financially, but the ROI is not great. Even a line that doesn’t touch Chicago can work, namely HSR between Cleveland, Columbus, and Cincinnati – those three cities are too small and weak-centered to produce internal ridership, but New York-Columbus is in similar shape to New York-Detroit.

Milwaukee (2 million, 140 km from Chicago)

Milwaukee’s metro area touches Chicago’s. HSR between the two cities alone is not worth it, since at this distance, top speed isn’t as relevant as station access time. However, the addition of other cities makes this worthwhile. Since Milwaukee is just on city, we put ridership and operating income in the same table:

CityRidershipOperating income
Chicago3.329.99
Toledo0.4213.92
Detroit1.2750.42
Cleveland0.6629.62
Pittsburgh0.3417.16
Harrisburg0.073.59
Philadelphia0.3417.25
New York0.7135.34
Washington0.3316.3

The ROI within the Midwest alone on what should be about $3 billion in construction is around 4% – higher than the bare Chicago-Cleveland/Detroit system. With Northeastern tie-ins, this rises to 7%, if one is confident in second-order but noticeable extra revenue from trains from New York, which would necessarily be a two-seat ride and take almost 6 hours with transfer time.

St. Louis (3 million, 460 km from Chicago) and Kansas City (2.5 million, 400 km from St. Louis)

The Chicago-St. Louis line has received some investments in the last 10 years that the state of Illinois pretends are high-speed rail. Those are expensive – there’s extensive surplus extraction by actors including politicians and the freight railroads – and perform exactly as one should expect trains that are slower than the legacy trains that the TGV replaced 40 years ago. However, this says nothing about whether trains that Europeans and East Asians would recognize as fast could succeed on that corridor. Could they?

A reasonable estimate for the Chicago-St. Louis construction cost is $10 billion; St. Louis-Kansas City would be another $10 billion, perhaps slightly costlier per km because Missouri’s terrain isn’t quite so flat as Illinois’s. Ignoring transfer penalties, we get the following ridership and operating income out of it:

City N\City SWSt. LouisKansas City
Cleveland0.430.19
Toledo0.220.09
Detroit0.760.32
Chicago4.561.33
Milwaukee0.870.27
St. Louis1.5
City N\City SWSt. LouisKansas City
Cleveland21.329.45
Toledo10.974.32
Detroit37.8415.99
Chicago136.366.59
Milwaukee34.0713.59
St. Louis39.1

St. Louis generates 6.84 million riders and $240 million in operating profit, which is above our 2% minimum but not by much. Moreover, 6.84 million riders means a train every hour, at which point there are real frequency artifacts for a service that shouldn’t take much longer than an hour and a half to Chicago. So it’s marginal, though still plausible. But if this is plausible, Kansas City isn’t: it generates $150 million. There are small intermediate stop locations like Springfield and Columbia, but they’re too small to make a difference.

The Ohio Hub

The four largest metro areas of Ohio are roughly collinear. Going southwest of Cleveland, one has Columbus (2.5 million, 220 km), then Dayton (1 million, 110 km), and finally Cincinnati (2.3 million, 90 km). Construction costs are likely to be low because of the terrain – only around Cincinnati are there significant hills. 420 km for $10 billion is plausible. What is the ridership, and what is the revenue?

City E\City WColumbusDaytonCincinnati
New York1.810.711.18
Philadelphia0.980.370.6
Washington0.830.10.55
Harrisburg0.240.090.14
Pittsburgh1.30.560.79
Cleveland1.50.721.41
Columbus0.621.22
Dayton0.58
City E\City WColumbusDaytonCincinnati
New York90.7135.4459.13
Philadelphia48.9118.5230.25
Washington39.794.9327.68
Harrisburg10.94.36.78
Pittsburgh35.4819.1431.87
Cleveland21.515.538.4
Columbus4.4615.81
Dayton3.42

The total operating income is $563 million a year, which is 5.6% ROI. The biggest cells – New York-Columbus, New York-Cincinnati, Philadelphia-Columbus, Washington-Columbus – are reasonably certain. The internal Midwestern numbers are more suspect, as are the numbers involving Pittsburgh – these are cities where car ownership approaches 100% and the remainder are carless out of poverty, and the destinations are fairly decentralized.

Indianapolis and points south

Indianapolis (2.5 million, 280 km from Chicago) is an attractive-looking target. By itself it’s not much, just like slightly-bigger St. Louis, but unlike St. Louis, it has cities behind it in Cincinnati (170 km) and Louisville (1.5 million, 180 km) that are not as far from everything as Kansas City is. Moreover, Indianapolis-Cincinnati also unlocks travel to Columbus, probably with a transfer because the bluffs around Cincinnati force trains from both Indianapolis and Columbus to enter from the north, without through-service.

South of Louisville, it’s attractive to go south to Nashville (2 million, 270 km from Louisville), Chattanooga (1 million, 200 km), and finally Atlanta (7 million, 180 km). But unlike the New York-Atlanta and the New York-Chicago legs of the triangle, the Chicago-Atlanta leg is decent but not amazing, since it omits the largest city.

City S\City NMilwaukeeChicagoIndianapolisLouisvilleNashvilleChattanooga
Indianapolis1.093.94
Cincinnati0.733.691.22
Dayton0.281.620.62
Columbus0.442.331.3
Louisville0.52.620.86
Nashville0.31.551.090.72
Chattanooga0.110.550.370.410.52
Atlanta0.41.821.071.162.481.42
City S\City NMilwaukeeChicagoIndianapolisLouisvilleNashvilleChattanooga
Indianapolis29.6871.7
Cincinnati28.01107.813.43
Dayton12.4856.9610.55
Columbus21.7798.4932.1
Louisville19.5778.2810.1
Nashville1573.3631.812.68
Chattanooga5.727.3615.6112.686.79
Atlanta19.8291.153.7449.2161.216.65

Reasonable construction costs are $6 billion to Indianapolis, $4 billion to each of Cincinnati and Louisville, $7 billion to Nashville, $6 billion to Chattanooga, and $5 billion to Atlanta. Indianapolis itself doesn’t generate sufficient ROI, but with the addition of Cincinnati it is pretty strong, the combined system generating $483 million, or 4.8% ROI. Then Louisville generates $108 million, or 2.7%; Nashville generates $133 million, or 1.9%; and Chattanooga and Atlanta together generate $360 million, or 3.3%. Note that the last segment generates the highest ROI, and moreover it is not really possible to start from Atlanta and move north, since Chattanooga alone doesn’t generate significant ridership to cities northeast of Atlanta, as those cities are either small (Greenville, Charlotte) or far (Washington).

Update 12-21: Madison (0.9 million, 120 km from Milwaukee) and Minneapolis (4 million, 400 km from Madison)

The above calculations are for expansions from the first Midwestern core line connecting metro regions #1, 2, and 4 to on another. But what about the #3 region, Minneapolis? Minneapolis has a metro area of 4 million, and is by far the largest Midwestern region with population growth, having grown 9% between 2010 and 2019, whereas Chicago, Detroit, and St. Louis were flat and Cleveland declined.

It should not surprise that Chicago-Minneapolis traffic alone is insufficient to justify HSR, given that Chicago-Detroit alone is not and that line requires service to Cleveland as well as points east. Fortunately, Minneapolis’s location is such that through-service from much of the rest of the Midwest is plausible. Distances are long – this isn’t the Northeast or Western Europe – but trips between Minneapolis and secondary cities like Cleveland, Detroit, Cincinnati, and Indianapolis become much faster by rail than by car. Even St. Louis-Minneapolis is feasible, even though nowadays there’s a mostly direct all-freeway route that’s 900 km long vs. 1,120 by HSR. Midwestern travel today is dominated by the car and not the plane, since car ownership is universal and flying between two secondary cities is not necessarily convenient or cheap.

We get the following matrix of ridership:

City S\City NMadisonMinneapolis
Cleveland0.250.37
Toledo0.150.18
Detroit0.470.65
Columbus0.170.28
Dayton0.110.16
Cincinnati0.270.36
Louisville0.180.25
Indianapolis0.490.54
St. Louis0.320.44
Chicago1.743.29
Milwaukee0.481.46
Madison0.84

And here is the matrix of operating income:

City S\City NMadisonMinneapolis
Cleveland12.6518.7
Toledo5.958.96
Detroit22.2432.26
Columbus8.6613.79
Dayton5.397.89
Cincinnati12.2917.96
Louisville8.6112.53
Indianapolis17.2726.78
St. Louis14.9921.82
Chicago29.4141.28
Milwaukee3.7449.48
Madison21.73

A reasonable construction cost for Milwaukee-Minneapolis is around $13 billion. Overall operating income is $514 million a year, so 4% ROI; one can even scratch a few fractions of 1% by including extra ridership from connections from points east of Cleveland, but I’m comfortable rounding New York-Minneapolis ridership over 2,000 km and a probably-untimed transfer in Chicago from 0.67 million to zero. At most, including East Coast-Minneapolis rail ridership provides cushion against unresolved questions such as whether people would take a 4.5-hour train between Detroit and Minneapolis or continue driving for 10 hours plus rest stops.

Metcalfe’s law in California

In California, the definition of a metro area is dicey. The combined statistical area for the Bay Area has 9.7 million people, but that includes Merced, Modesto, and Stockton, all of which are geographically in the Central Valley and would get dedicated HSR stations, some on a different branch from that going toward the Bay proper. In fact, we have 9.7^0.8 = 6.16, but if we sum each individual MSA component and raise its population to the 0.8th power, even omitting ones without planned HSR stations like Santa Cruz and Napa, we get a total of about 7. So we should use the higher figure. Likewise, in Los Angeles, taking the CSA population yields 18.7^0.8 = 10.41 whereas summing the constituent metro areas separately yields 11.3, and summing the counties, all of which are supposed to have stations, yields 12.8. We use the higher figure, 12.

Together we get 25 million intercity riders, before applying the distance penalty. The distance depends on which pair of stations we look at, since we’re summing over many different stations; it also depends on alignment choices, which don’t all have the same average speed, which means that trip time, whence the distance malus, is not perfectly congruent to distance. To simplify, we assume that LA-SF is 2:45, which at Shinkansen speed is 650 km; this is shorter than the actual LA-SF distance under most alignments, though not by much, and it’s longer than actual distances to subsidiary Northern California destinations.

With this in mind, our formula spits out 14.79 million intercity rail trips. This is a lot lower than California HSR estimates. Those estimates also include San Diego (3 million, 190 km from LA), Bakersfield (0.9 million, 180 km), Fresno (1.3 million, 170 km from Bakersfield), and Sacramento (2.6 million, 270 km from Fresno, 230 km from SF). None of these adds a lot, though. The reasons for the discrepancy include,

  • California HSR assumed heavy HSR commuter traffic – Palmdale-Los Angeles was one of the top city pairs.
  • California HSR assumed somewhat lower fares than the European norm, standing at $79 for LA-SF.
  • California was projecting population into the future, and may have assumed less NIMBYism than the state presently has.
  • The California HSR model may have had flaws; one such flaw was overestimating the impact of frequency at the LA-SF range, to the point that pruning branches such as to San Jose was said to increase ridership by improving frequency to the remaining destinations.

Not that the numbers coming out of my model are bad. The LA-SF numbers alone are worth $625 million in operating profits a year, and with Bakersfield and Fresno this grows to $875 million. The cost of the project without San Diego and Sacramento tie-ins should be on the order of $25-30 billion, in today’s money. Sacramento is maybe 90 extra km and $2 billion depending on alignment, and generates another $260 million or so; Metcalfe’s law is practically a free gift when you have a 90 km spur in flat geography. San Diego is probably something like $6 billion, the higher cost coming from the constrained urban environment and the need for some viaducts and one short tunnel, and adds around $240 million in operating profits.

I am of course aware that at no point was the cost of California HSR $25 billion in 2020 terms. In 2008 the state promised $33 billion in 2008 dollars. The discrepancy comes from some catastrophically bad decisions regarding scope at every stage of the planning phase and bad procurement. But if one looks at what the project needed rather than what has been built in the Central Valley and plugs in standardized costs, the answer is around $25 billion.

145 comments

    • Alon Levy

      Toronto-Detroit is fine but only thanks to Metcalfe’s law – Toronto-Chicago is strong, and lets the railroad earn 770 km of profit per passenger on just 360 km of Toronto-Detroit route, of which a decent amount (Toronto-Aldershot, for one) preexists; much depends on whether the existing Detroit-Windsor rail tunnel is usable.

      Buffalo-Cleveland… maybe? Chicago-Buffalo is not thaaaaaaaat strong by itself, and Boston-Cleveland adds some but it’s probably marginal even with all else included.

      • anonymouse

        The Detroit-Windsor tunnel is double track but doesn’t have enough clearance for double stack freight so there was a proposal to build a new tunnel that would be big enough. If that happens, it would make a lot of sense to turn over the existing tunnel to passenger use.

  1. Bobson Dugnutt

    If the US does engage in a national high speed rail program, politics will likely induce some log-rolling and get some larger metros that would bring the averages down.

    What would the Texas T-bone look like if Dallas, Houston, Austin and San Antonio were connected? Or would they instead be a triangle?

    Would Dallas-Oklahoma-Kansas-Kansas City pan out? How about Dallas-Arkansas-Memphis? Or a Gulf Coast line via Houston-Louisiana-Mississippi-Alabama and Florida? Would SoCal-Vegas and SoCal-Phoenix-Tucson work? How about Seattle-Portland-Boise-Salt Lake City?

    • Alon Levy

      Connecting to Kansas City from the other direction just isn’t worth it at current populations. Dallas-Houston is decent, but what’s less decent is that above-ground construction costs $40 million per km because the project is so politically precarious Texas Central builds too many viaducts in preference to at-grade rail with French-style land swap deals. The T-bone idea is in retrospect pretty weird, prioritizing smaller regions over Houston – but a reverse T, with a San Antonio-Austin-College Station leg hitting the Dallas-Houston line, could be interesting.

      SoCal-Vegas is weird because Vegas has weird travel patterns as a dedicated tourism region and this tourism often comes from LA – Orlando is similar in the first regard but not in the second, in that the tourism there is almost never from other Floridians. This leads to elevated traffic levels, but also unusually peaky ones, which messes up with operating expenses. It’s probably worth it but it depends a lot on questions of construction costs between LA and San Bernardino and whether it’s possible to cross Cajon Pass at grade. In contrast, SoCal-Phoenix is most likely good. But then Phoenix-Tucson is pretty weak – unlike along the Atlantic Coast, population density is low, so cities are spaced farther apart and there’s less opportunity for accretion of ridership.

      • df1982

        Apart from on Friday evenings, the weekend Vegas peak is different to the regular weekday peak, so if a SoCal-Vegas line is integrated into CAHSR then it could use rolling stock from elsewhere in the system during its peak periods, which would help defray costs. I would also think that with a HSR line there would be healthy Vegas-LA traffic which would conform more to a regular weekday cycle.

        • Alon Levy

          Yes, that’s plausible. Something important that I’m handwaving in these posts that I probably shouldn’t is the issue of peakiness. It behaves differently in different systems, and because my main interest is the Northeast Corridor, I ignore it because the NEC’s urban geography is unusually low-peakiness.

          • adirondacker12800

            And, on the NEC three different classes of service and varying service patterns. Which gets people confused. That’s too bad.

        • Bobson Dugnutt

          @df1982, If Nevada were to pay for a line linking its two major population centers, it could build a SoCal bypass by serving California population centers rather than the emptyness between the Las Vegas Valley and Carson City-Reno. It would use the current CAHSR right of way but there would be a junction in Bakersfield toward the Antelope Valley, Victor Valley and Barstow (bus connections could be provided to Fort Irwin and 29 Palms military bases).

    • Michael Noda

      Oklahoma City – Kansas City is 8 hours at conventional-diesel speeds (on the nose in the last Lone Star timetable before the Carter cuts), so if OKC is big enough to be connected to Texas, that’s a decent place for a night train bridge between the separate networks, with a 22:00-06:00 schedule in both directions allowing for Midwest-Dallas by a morning meeting, and Texas-Chicago by mid-morning. The timings get a lot less convenient if you’re restricted to conventional speeds all the way down to Fort Worth, though.

      • AJ

        Chicago to Dallas would be like Madrid to Brussels – is there much end to end rail ridership between those cities, or at that point do people just fly?

        If I was trying to provide overnight services, I would just run a point-to-point sleeper bus before I’d built rail in the great plains.

        • Herbert

          Having an electrified freight route transcontinental has its own benefits, as Russia can attest to…

          • AJ

            Those freight routes already exists. Electrifying them is unrelated to passenger service.

          • Herbert

            The big base tunnels of Switzerland were built for freight first and foremost. Where’s the base tunnel across the Rocky Mountains?

          • Eric2

            The Rocky Mountains can be bypassed to the north to the south without tunnels, and there already exist busy freight routes there. The Alps don’t have a comparable bypass.

          • Alon Levy

            There is a single-track tunnel across the Rockies. It was built by the state as a prestige project for Denver and has no real reason to exist; once UP bought the Denver and Rio Grande Western, it shifted all the mainline traffic to the Overland Route. Now that coal is dead, the tunnel has 7 trains per day (link), and I think that’s 7 in both directions and not in each direction, so 2 of these 7 are Amtrak.

        • john

          At long distances like that, I would think the point wouldn’t really be end-to-end trips, but connecting the populations/communities in between to both ends (and each other): not many Chicago Dallas trips, but STL CHI, KC Dallas, STL Dallas, KC OKC, etc, and all kinds of smaller towns and cities linked to cities with HSR stations by car/bus/regional train. And at that point you’re looking at broader political/social/economic benefits* (business growth targeted towards cities along the line, regional commuters along the line, funding votes, travel-mode-share, lowered emissions, etc.) as much as, or more than, the finances of the railroad itself. Although, I would also think that would work better if the two end-cities were closer together, Chicago to Dallas seems kind of far; Chicago/KC or Chicago/Minneapolis would work if KC/Minn were each twice as big as it is. Then again, Chicago/Dallas is comparable in distance to NYC/Chicago or NYC/Atlanta, and in these posts y’all have been talking about those as plausible, so [shrugs].

          *I believe the term is positive externalities?

          • adirondacker12800

            There are people in Ohio and Indiana. Not so much in Oklahoma and Kansas. Pete Buttigieg comes from itty bitty little South Bend Indiana. It’s combined statistical area …. is a combined statistical area … and is bigger than metro Witchita. There’s a whole lot of nothing out there, west of the Mississippi.

  2. Gok (@Gok)

    I know you are typically skeptical of international links, but the Great Lakes Megapolis is a thing. Extensions to Canada would make sense, particularly given the less car-centric nature of many Canadian cities.

    Chicago Toledo HSR would also want to stop in South Bend (~0.8K), especially given…recent political developments.

    Another possible Midwest corridor: Chicago/Quad Cities/Des Moines/Omaha. It would not get much ridership by the formula but would be very cheap to build.

    • Alon Levy

      Yeah, South Bend provides extra ridership. But not that much – it’s not a big city, and when I did the preliminary work before writing this post (e.g. when I wrote the previous post) I didn’t even look at ridership to Toledo. South Bend adds 0.9% to the ROI of the Chicago-Detroit/Cleveland line in the presence of the east-of-Cleveland network.

      Chicago-Omaha is just too weak. Construction costs are low, yes, but ridership is even lower. The Quad Cities, Des Moines, and Omaha CSAs have 2.1 million people between them, so somewhat less than St. Louis over 50% longer distance.

      • Bobson Dugnutt

        Do Notre Dame and the other universities in and around South Bend provide a ridership bump?

        • Eric2

          That’s a good topic in general – there are many such small cities with a university which could provide outsized ridership. Madison WI, Champaign IL, Columbia MO, College Station TX, etc. Does the university provide a significant boost?

          • Henry Miller

            That depends on getting the universities on board. MIT and Havard have an agreement where students at on can register for classes at the other, no need to apply. If you can get similar agreements it can get a lot of riders on a semester (which needs to be a thing). Politically this gets tricky as there are several state universities involved, and so you need to figure out tuition.

            The problems are solvable, and it would help out all states to be in. However I’m not sure if anyone can pull it off.

          • fjod

            My intuition from the UK and the Netherlands is that stations in university towns slightly overperform, and that part of this is likely down to the sort of businesses and people that cluster around universities. But it is really hard to prove this as university towns in both countries also disproportionately attract tourists.

          • Herbert

            University students tend to do a lot of traveling bu tend to be very cost conscious when doing the traveling…

    • AJ

      The alternative to South Bend would be the follow the I94 corridor, or even I96 (Grand Rapids is the economic center of western Michigan & would loop in the state capital and two large university centers), if the primary goal was the connect Chicago and Detroit, the two largest & most important cities in the Midwest. Chicago-Cleveland ridership would suffer, but at that distance people who value time would still fly even with HSR? Given the literal nothingness between South Bend and Toledo, I94 might be more interesting with the ability to add more local stops underneath the Chicago-Detroit express service than anything I80 could do between South Bend and Cleveland. With a HSR station in Michigan City, South Bend would be adequately served using the existing South Shore Line alignment for a short shuttle between Mich City and SB.

      • Michael Whelan

        This would unacceptably slow traffic between the NEC and Chicago by diverting it through Michigan. Grand Rapids and Lansing can get electrified branch lines. Heck, just upgrade the existing Wolverine, Blue Water, and Pere Marquette routes with electrification and speed fixes.

        • D Rock

          You seem to not realize that upgrading Michigan rail has already happened and more is underway. Amtrak owns the track between Porter, IN and Kalamazoo and MDOT owns the track from Kalamazoo to Dearborn (for Amtrak usage). The Porter-Kalamazoo track now supports 110 MPH service; and, the Kalamazoo-Dearborn track supports 89 MPH (up from 30 MPH) and is being worked on to also support 110 MPH. So… diverting traffic through Amtrak-prioritized rail in Michigan makes far more sense than going straight through Indiana and South Bend. If anything, commuter rail to South Bend can hook up with HSR in Michigan City.

          • Alon Levy

            The legacy track in Michigan is of no use to a high-speed rail network. It’s too curvy. Nor is the top speed particularly impressive – what matters is overall trip times, and Amtrak is really bad at optimizing these (look at the Chicago-St. Louis average speed, for example).

          • adirondacker12800

            Michigan is too curvy but the New Haven line isn’t. Okay.
            It’s Michigan, they can buy some really flat farmland from the really straight ROW into Detroit to the really straight ROW on the other side of the curves and those downtown stations, such as they are can have service, every two hours, on a slower train, a short one.
            That CSX and NS didn’t want to divvy up Detroit and it’s Conrail tells me there is a lot going on there.

            Click to access MI_Rail_Map_553909_7.pdf

          • Alon Levy

            Yes, you can realign the Michigan line and built HSR parallel to it. Or, for the same cost, you can build on I-90 and serve Cleveland and Detroit on the same line.

            (Don’t forget, I think New York-New Haven needs higher-than-world-average cost for HSR per km, because of the Bridgeport tunnel and the viaducts elsewhere. It’s just that I interpret that to mean around $4 billion, not $100+ billion.)

          • adirondacker12800

            Try to keep three things in mind at once.
            The one that most people miss is that Detroit is NORTH of Windsor Ontario.
            Buffalo is halfway to Chicago via Albany and Pittsburgh is halfway to Chicago via Philadelphia.
            The high demand market is Chicago-Detroit-Toronto. Not Toledo-Cleveland-Buffalo. And the shortest route from Buffalo to Detroit is through Hamilton Ontario, not Toledo Ohio. Or to Chicago.

            The lower demand trains from Cleveland and Toledo, that are going to Chicago can go through Detroit. On the tracks that are there for Detroit-Cleveland, Detroit-Pittsburgh, Detroit-Philadelphia and Detroit-New York. You don’t have to worry about Columbus, Dayton and Cincinnati because their trains to Chicago will be going through Indianapolis, not Toledo. That all depends on convincing people in Indiana and Ohio that trains are not a plot to sap the precious bodily fluids of Real Americans(tm). Michganders seem to be warming up to the idea because the state owns a really nice straight ROW that almost makes it into downtown Detroit.

            There might be if you really stretch your imagination be a million people in metro Stamford. There are 7 million on Long Island. If you want to add a million people to New York City they aren’t all going to be living on the Upper West Side.
            You aren’t going to be building viaducts in Fairfield County. You might get away with plopping a TBM down in Rye New York and pointing it at New Haven. They’ll sue that the ventilation building between the Metro North tracks and Turnpike will ruin the bucolic charms of both.

          • Alon Levy

            New York-Chicago is shorter via Philadelphia, Pittsburgh, and Cleveland than via Albany, Buffalo, London, and Detroit.

            And building viaducts in Fairfield County is absolutely possible, PAMPA lost its lawsuit even in CEQA-land.

          • adirondacker12800

            There are enough people in the Midwest and Northeast for there to be TWO routes between them. It’s a bit shorter from Chicago to New York through Pittsburgh. That doesn’t make Buffalo is less halfway-ish for someone in Detroit that wants to go to Boston. On tracks that would be there for the Chicago-Toronto trade and the Northeast-Toronto trade. That can be used by people in Syracuse who want to go to Boston or Philadelphia or people in Utica who want to get anywhere or people in Cleveland who want to get to Hartford or Toronto or….. It’s Chicago-Detroit-Toronto overlaid with Detroit-Montreal and some Chicago-Montreal or Toronto-Albany-for-the-rest-of-the-Northeast. Because except for people who are afraid of flying no one is going to be taking the train from the East Coast to Chicago.

            I’m gonna hazard a guess that Connecticut doesn’t follow California regulations for most things. A tiny fraction of people in a state with 38 million people affect things less than the people who make up around one third of the state’s population. Connecticuters are competent lawyers compared to the clowns the Californians BANANAs were able to buy new luxury automobiles for. The Californians were trying to upgrade an existing railroad, not build new viaducts over roads only vaguely associated with the railroad. Roads that people have been suggesting widening for century and Route 15/Meritt Parkway and the Connecticut Turnpike were built for instead. Wikipedia says getting the Turnpike upgraded to Interstate standards took 30 years, they came up with all sorts of lawsuits. And are already screeching that putting trains next to the Turnpike, east of New Haven, will ruin it’s charms. You aren’t going to build viaducts over Ye Olde Historick Boston Post Road to save 15 minutes. Or anywhere in Fairfield County. You are looking at plopping a TBM down in the wasteland around the interchange of I-95/New England Thruway, I-287/Cross Westchester, I-684 and the railroad, Rye and coming up for air just west of Union Station New Haven. With vicious fights over cutting down weed trees between the Metro North tracks and the Connecticut Turnpike for the ventilation buildings.

            Assuming they are able to pull off the 30-30-30 plan sometime before 2258, it means Stamford-Boston would be 1:30. Instead of 1:15. Stamford-DC would be 2:30 instead of 2:15. The only thing that could beat 2:30 to Washington DC is Marine One landing on the White House Lawn. Or 3:00 versus 3:10 from Boston to DC. Settling for 4:15 means people still fly. And use capacity at DCA. Which is never going to be significantly expanded.

            More than one thing at time:

            None of that changes that there will be 8 million people on Long Island and still somewhere around a million in Metro Stamford. They all need MOAR trains, passenger and freight because double decking the Long Island Expressway, Cross Bronx Expressway and the Connecticut Turnpike won’t be cheap or pretty. Probably the BQE/Gowanus, Staten Island and NJ Turnpike too.

            You get Senators and House members from the hinterlands on board for the deal because they want to fly home from DCA not IAD out in the wilds of Virginia. The flights from Boston and New York along with the puddle jumpers from Hartford, Albany etc. go away there can be flights to somewhere else. And if less Northeasterners are changing planes in New York area airports there can be more flights to the hinterlands to New York. They’ll protest weakly but know that they’ll be able to schmooze with donors in Philadelphia and New York easier. ….. though there was the scandal with the Trump Admin. official, there are so many scandal plagued Trump Admin officials I forget which one, who chartered a jet to fly to Philadelphia. They really are that stupid. More flights from DCA means the ones who like to have bit of fun while changing planes will have more opportunities.

          • Alon Levy

            California regulations are strictly NIMBY-friendlier than in other states, thanks to CEQA. Connecticut in contrast managed to expropriate land for private use and get it validated under Kelo.

            Buffalo-Cleveland is a cool route, yes. At least if you believe my modeling, which is a big if, the biggest use case is for Toronto-Ohio trains (it’s faster to do Toronto-Cleveland via Buffalo than via Detroit).

          • adirondacker12800

            Kelo was poor people in New London. Not rich people in Cos Cob. It was reverse Robin Hood, taking from the poor to give to the rich. Ya know, New London where they aren’t like those poindexters, that pay lots of taxes to support them, in southwestern Connecticut. Not the best example in the world because the major tenant said “We’ve changed our mind. good luck with YOUR redevelopment”. It’s still un-re-developed. Seems that Ms. Kelo wasn’t as in love with house or New London either and has moved.

            https://en.wikipedia.org/wiki/Kelo_v._City_of_New_London

            Buffalo isn’t the best example in the world either because they erased a lot of railroad when the Thruway came through and even more when Conrail abandoned things. You can’t get from Cleveland to Buffalo anymore. You can get to Depew but you can’t get to Buffalo easily. It wouldn’t be the worst thing in the world if the Toonerville Trolley from Downtown Buffalo met every train at Buffalo Central just outside of downtown. Don’t try to wedge everything into one solution for the clusters around the western end of the lake.

            Airfares and destinations change from moment to moment. When I checked a few years ago there were two flights a day between Hartford and Cleveland. At monopoly fares. I just checked, airlines are screwy right now but the fastest connecting flight is 3:45 and the other ones are longer. Albany to Cleveland doesn’t have non-stop either and the fastest is 3:39. Or Rochester or Syracuse. Utica doesn’t have commercial service. Neither does Worcester. Providence has connecting flights at 3:45-ish or more too. Cleveland to Depew is Cleveland to all of New England that isn’t easy to get to/from Logan. Until the airlines change their minds again.

    • Henry Miller

      The Chicago-Omaha line ends in Lincoln not Omaha. The last leg is profitable just as commuter rail. (assuming we are not stupid about construction costs)

      Even though I would use this line (I live in the quad cities and make regular trips to Des Moines), I’m afraid Alon is right, there just isn’t enough people along it. The only people seriously trying to get this going would be happy with 1920’s practices including steam engines. Millions of been invested in upgrades alone the line to enable that type of line.

      Though I do wonder if it would work if there was also a Minneapolis->Kansas City line (with possible continuation to Dallas). Chicago to Kansas City via Des Moines in only about half an hour more than via St Louis, and you avoid the terrain of Missouri (though Iowa is only slightly better). That is would system effects make this more useful if there were other lines to connect to in the midwest? (there is also a Winnipeg-Fargo-Souix Falls-Omaha-Kansas city route – again too small on its own, but with a system in place maybe more useful)

  3. hgm

    > trains that are slower than the legacy trains that the TGV replaced 40 years ago

    Also slower than passenger trains that ran this route in the 1930s

  4. Eric2

    Some typos:

    “The model is that the annual ridership in millions between two metropolitan areas A and B, with populations in the millions, is,”

    The equation that follows this is broken

    ” San Diego is probably something like $6 million,”

    You mean billion I assume

  5. seb

    Could there be a mistake in your London-Birmingham calculation, or am I just misunderstanding the formula? If the distance is 180km, one needs divide by 180 squared and not 500 squared as we have to take the minimum between those two numbers.

    • df1982

      I took it as being the distance factor has a floor of 500km, because under that the station access times become a bigger factor in total travel times, meaning the benefits of HSR are proportionally less. In other words, 500km is the sweet spot.

      That said, if your model predicts half a train an hour between Birmingham and London on HS2 then there is something obviously wrong with it. Right now there are at least 4 trains per hour between the two cities (2 Avanti West Coast, 2 Chiltern) on a significantly slower alignment, and by all accounts these trains are not overly empty (quite the opposite if complaints about crowding are anything to go by).

      • Alon Levy

        Yeah, it’s supposed to be a maximum, not a minimum. I’m fixing the formula accordingly; the numbers in the tables go by the correct formula, not the one with the typo.

        London-Birmingham under the formula is 1 400-meter tph, and 50% capacity means that rush hour seats are pretty full. The ICE averages 50% seated capacity and is full in busy times, this isn’t the TGV and its what’s-a-takt timetabling.

      • Matthew Hutton

        Don’t forget the Birmingham to London trains also pick people up in Coventry, Milton Keynes, Leamington Spa, Banbury and Bicester. Plus as driving into London is a pain there will be some Park and Ride travel as well.

        • df1982

          Coventry and Milton Keynes have a couple of hundred thousand people each, and those other towns are tiny. London has a metro pop of 14m, Birmingham 2.9m, and they’re at a distance where HSR starts to rack up a distinct time advantage over driving/conventional rail. If that city pair can’t give you enough patronage to fill up a decent frequency of trains, then where can? I think the proposed service of 3 400m trains per hour seems pretty reasonable.

          • Matthew Hutton

            Obviously smaller places don’t demand much investment – but Bicester has 2 million a year, Banbury and leamington spa have 3 million passengers a year, Coventry and Milton Keynes have 7-8 million a year and some of the smaller places have getting on for a million passengers a year. Based on $50k per daily rider it’d be worth spending $200 million to support a city/town the size of Bicester for example – certainly some of these smaller cities that are moderately close to New York or Chicago could be worth an hourly or half hourly train to stop at a park and ride with a bus service.

  6. adirondacker12800

    The 500 km minimum is an artifact of the impact of station access time and the option of driving instead of taking the train.

    That we are a two car household and it’s free to park at the station in Saratoga Springs doesn’t make it easier to drive or park in New York, Philadelphia or D.C. We drive to Boston or Montreal because the once a day train is slower than a bus. 0.8 is too low. Albany-Rennselaer has 800,000 annual passengers now with trains that are as fast as driving. And effectively only one direction of travel.

    Click to access NEWYORK19.pdf

    Something is definitely screwy with Hudson.

    • Alon Levy

      500 km minimum does not mean people don’t ride the train if it’s shorter! All it means for the purposes of my model is that people take the train at exactly the same rate at all distances up to 500, so for example NY-Philly ridership should be similar to NY-DC even though NY-Philly is much closer and at longer distances than 500 km people do take the train less.

      This may not be a correct assumption, and London-Birmingham in particular stresses it somewhat. But Tokyo-Sendai and Tokyo-Nagoya affirm it, and Tokyo-Niigata is actually below the predicted value despite Niigata’s ski tourism sector.

  7. Henry Miller

    Considering all of those places are car centric, is the above realistic? You said ” there’s a serious malus coming from higher car ownership, lower car traffic levels, and much weaker city centers”, but then didn’t indicate how you account for that.

    If I’m going between any of the cities on your list I’m probably going to drive just because I already have a car and once I get there I need to get around. A few cities there is enough to do that you can attract me to the train, but for the most part you can’t beat the flexibility of a personal car once you get there. When you have a good system on the other end to get where you want to go, then HSR is useful. Thus it seems like your population numbers shouldn’t be the entire city, but the much smaller number of destinations near frequent local transit.

    If we don’t assume ample parking near the HSR stations, then you also need to drop down to the local population that has access to transit.

    Note that we don’t need to assume good local transit on the source end, but I do at the destination. HSR isn’t show up and go frequent in general so we only need whatever coverage transit exists locally syncs to the HSR. Once you get there though you probably want to run a few errands so the more ability you have to get the done you are willing to take the train vs drive. This might not be correct (it certainly is as a whole, but seems like it should be close enough), but it seems reasonable to me.

    The cities that connect to NYC with good ROI are worth doing. They should get close to the numbers you provide and the useful HSR network will aid their local transit. However I think for farther you cities you are dreaming, the numbers won’t work out. People who are very time sensitive will still fly and rent a car, while those who are less time sensitive will find for a little extra time they don’t need to rent a car on the other end, plus if their errands run long they don’t miss their train home.

    People keep quoting $.50/mile (number varies) for a car, but that ignores the fact that most of the costs for a car don’t change if the car is sitting in the garage or being driving, so HSR is less competitive. HSR also loses if you have that one person going since the cost for the car is the same.

    • Eric2

      HSR lets you work/relax while riding, and you can take an Uber at the destination. So I don’t the difference is quite so dramatic.

      • adirondacker12800

        If you are taking the kids along it’s likely to go visit the grandparents or the aunts and uncles. They can pick you up at the station.

        • df1982

          Also having a car at your destination can be a millstone as much as a bonus, particularly if you are going to be staying in the downtowns of places like Chicago, San Francisco, Seattle, Philly, etc. (this is not to mention NY). You have to worry about finding parking as well as paying for it for the duration of your stay, dealing with traffic, etc., etc. In many cases it is easier to just rely on walking, transit, and taxis/Uber as a last resort, much as the millions of Americans who presently fly between cities do (or did before Covid).

          • Henry Miller

            Yes, but large portions of the city are not downtown. I thought I was clear that if your destination is where there is good transportation then driving doesn’t make sense. However that is only 20-30% of the places that you might
            want to go. The compare cities to get this formula have much better local transportation on both ends.

            Nobody with kids will take Uber, they don’t have car seats. Likewise they won’t have their parents pick them up because the kids can’t get in the car. You fly (car seats fly free) and rent a car that you leave the car seats in, you take public transportation everywhere so you don’t need car seats, or you drive.

            Which is why I think Alon is overly generous in his estimates. He is including people who will drive.

          • adirondacker12800

            Most people aren’t traveling with children that need car seats. Maybe in episodes of Ozzie and Harriet they travel with children but most people travel with without children.
            Why wouldn’t you be able to take the car seat on the train?

          • Herbert

            From the time I worked at an airport, I can tell you that people definitely travel with kids who need car seats. Granted, mostly leisure/vfr, but still…

          • df1982

            @Henry Miller: what types of intercity travel are there? I would suggest the following, broadly speaking:

            – business trips
            – tourist trips/events (concerts, sport, etc.)
            – long-distance commuting
            – visiting family/friends/loved ones

            Of these, I would say the first three overwhelmingly involve destinations in the central core of the city which can be done largely car-free (the exception being major ex-centric tourist destinations like Disneyland, but these will often be served by transit or even directly by HSR anyway), and only the last involves dispersed destinations across the metro area. And even then, if you’re visiting family for Thanksgiving or whatever you will often either be staying with them the whole time, or have access to their car if you do need to get around.

            So for the majority of people there is not a huge amount of need for your own car at the destination, which is partly why flying has become popular even at relatively short distances, despite how unpleasant the whole experience is.

      • michaelrjames

        @Eric2: “HSR lets you work/relax while riding, and you can take an Uber at the destination.”

        This can’t be over-stated. I think very few Americans either consider it or understand it, though perhaps exempting those who regularly use the NEC Amtrak (but many of those also don’t really appreciate the difference between genuine HSR and Amtrak’s crippled version). And Joe Biden* who commuted for decades by (slow) train between Wilmington and DC (and he could walk to his office, not sure about his home). I am sure he found that time to be valuable in processing his daily busy-ness, and get thru more reports and analyses than he otherwise would have. In the tech age it is even more relevant though of course with a two-edged sword for the easily distracted.
        The calm and quiet and flexibility of a HSR train ride is a revelation for most when they first take one.
        It’s why the priority for the US, both strategically and tactically should be to get one HSR line built, then give every American a subsidised ride on it. It needs to be true HSR (no half-arsed or crippled version, it must be at least 300km/h), span a reasonable distance (spanning 100 or even 200km is not convincing enough) and be centre-to-centre no matter the cost etc (it would be interesting what happens with the Texas HSR terminating in both cities’ outer zones but a risky one, and certainly not one to break the car dependence). As I’ve said on this blog many times, LA to LV is the best bet even if geographically challenging (and expensive?) because of these factors and the important fact that most users will be a cross-section of America.
        …………..
        *I am making assumptions/projecting about Joe Biden and his experience which by now I should no is dangerous with Americans of any stripe. Does he retain a good feeling about trains from his long-distance commuting?

        • Herbert

          Biden is a very outspoken supporter of passenger rail. Whether that’ll translate to policy during his time in office will be a different question…

          • Henry Miller

            Will it translate to useful support or will he hire people who think the 1920s was the peak of train operating practice? I wouldn’t be surprised if his support ends up putting money into finding a source other than coal to fire a steam engine.

          • adirondacker12800

            He is used to fast electric trains with level boarding. They’ve been electric since the 30s.

      • michaelrjames

        Oops, forgot my little joke/snark …
        “and you can take an Uber at the destination”

        Surely Eric2, you mean take a bus?
        And as Uber has just pulled out of its autonomous vehicle project, it won’t be a Uber AV bus either!

        • Eric2

          Buses are not a time-competitive option in Midwestern cities (except maybe parts of Chicago)

  8. Matthew A da Silva

    From your analysis, would this order of priority make sense for an Eastern US HSR program? I imagine past the top 3 politics/geographical parity might take precedence over cost-benefit, but this is my pure cost-benefit take from reading both your posts.

    1. NEC Modernization
    2. DC-Richmond-Raleigh-Charlotte-Atlanta
    3. Philly-Harrisburg-Pittsburgh-Cleveland
    4. Chicago-Toledo-Cleveland/Detroit
    5. Atlanta-Orlando-Tampa/Miami
    6. Chicago-Milwaukee-Madison-Minneapolis
    7. Boston/NYC-Albany-Buffalo-Cleveland
    8.Chicago-Indianapolis-Cincinnati
    9. Cincinnati-Louisville-Nashville-Atlanta
    10. Cleveland-Columbus-Cincinnati

    • AJ

      I’m surprised Chicago-Milwaukee-Madison is rated so poorly. The Hiawatha, the Amtrak line that connects Milwaukee and Chicago (with a good on-the-way stop at Milwaukee’s airport), is Amtrak’s the best non-NYC, non-CA route. Is the route simply too short to stand out in HSR analysis?

      • Eric2

        Madison is too small, and Milwaukee close enough to Chicago that it’s easier to drive destination to destination than to use downtown rail stations.

        • AJ

          The immense density of Chicago’s loop and the high cost of parking in most of Chicago should mean that rail into Chicago is competitive with driving no matter the distance?

          Madison is small, but has good density around a prospective HSR station, a nuance that wouldn’t be captured in Alon’s input of CSA population totals

          • Alon Levy

            The HSR station in Madison would be around the airport, since it’s not really possible for a through-train to serve the isthmus.

          • Anon

            @Alon, what about a route on the rails paralleling John Nolen Drive and Campus Drive?

          • Eric2

            Yes travel to the Loop and nearby is easier by train, but not travel to the suburbs, where most people and probably a majority of jobs are located.

          • Harald

            The current plan for a future rail station puts it in a brownfield development site (former Oscar Mayer meat plant) north of downtown. https://imgur.com/Z0J1FHh The development plan (adopted only this year) calls for creating 2500 housing units of mixed density, but I think nobody really is counting on rail happening any time soon. https://www.cityofmadison.com/dpced/planning/documents/OscarMayerSpecialAreaPlan.pdf Connections to downtown would be via the city’s second BRT line (first line hopefully coming in 2023)

  9. Matthew Hutton

    What’s the maximum distance one can go in a car with kids in a day without it being extremely painful?

    Leave at 8am, stop at 10am for a coffee for 30 minutes, then stop at 12:30 for lunch for an hour, then at 3:30 for 30 minutes for tea, then stop at 6pm for dinner for an hour, then drive until 9pm. Then @ 55mph average (which gives a traffic allowance) is 450 miles, and that is an epic day.

    Comparatively if you allow 90 minutes to get to the station, 3 hours for a high speed train and 30 minutes to pick up a rental car is a lot quicker.

    Cost wise it is roughly a wash as the train would be about $300 return for two adults and a child with 50% discount, so you’d need to rent a car for $150 which seems about right to break even with driving which would cost $450 at $0.50 a mile.

    • Alon Levy

      It depends on much on who is driving! There are people who like to stop over for coffee for half an hour as you say, and there are people who are perfectly comfortable driving 10 hours with only a half-hour stop in the middle for food. It also depends on the car – my suspicion is that this is more comfortable in a bigger car, e.g. American-size SUVs.

    • jcranmer

      Depends on the age of the kids. If you get an early morning start, say 5:00 AM, the kids will immediately go back to sleep in the car and you’ll get 2-3 hours before they wake up, and you’ll get to exit your metropolitan area without contending with traffic. You’ll need to schedule an hour for each meal, and about a half-hour for each break, which has to happen about every 1-2 hours when kids are awake. (For older kids, break times are probably going to be shorter and less frequent, but if you’ve got grade-school-aged, a lot of time isn’t moving). My experience driving is that you can generally only sustain about a 14-15 hour driving day max, but you might be able to push another hour or two with multiple drivers.

      Out of a 15-hour driving day, you’re therefore spending maybe 9 hours actually driving. If you’re talking the Midwest, you’re looking at roughly 70mph driving speeds for most of that drive, maybe 60mph if you’re driving through/around a city and it’s not rush hour. It’s a very different case from the NEC, there simply aren’t dense enough populations to have heavy day-round traffic. So you’re looking at about a 600 mile range for a single day if you’ve got young kids, another 150 miles if you have older kids.

      We’ve done Chicago-DC, about 750 miles, as a single day drive, but it was routinely a two-day drive when we were younger. 450 miles (about Boston-DC) isn’t all that epic of a driving day IMHO–I don’t even bother waking up early and I still arrive at my destination well before supper.

      • Matthew Hutton

        I’ve done my maths wrong and it’s a 10 hour day with 550 miles of driving possible @55mph. Still if you can do 70mph (and I forget how empty parts of the US are) that’d give you 700 miles.

        Even with 700 miles your train day would be 90 minutes to catch the train, 4h40 @ 150mph average plus 30 minutes to get a rental car and then an hour to the final destination so that’s ~8 hours vs 13 hours elapsed by car directly.

        • df1982

          If you have kids, I feel that the train wins hand down as long as it’s even remotely time-competitive. They can move around if they get restless, there are usually tray tables that they can play games on, a bistro car for meal breaks, and Deutsche Bahn now even has family compartments where children can play on the floor. And depending on the child there is the fast train excitement factor keeping them occupied. I can comfortably do up to about 4 hours on a train with my three-year-old. He also likes going for drives, but the same amount of time strapped into a car seat would send him crazy.

          • Henry Miller

            That depends on how you get around at your destination. If you have transit when you get there the train wins even if it is more expensive (remember most of the cost of a car is fixed you have to make payments even if it is in your driveway, so the incrimental costs are gas). However if there is no transit to your final destination you drive because the car is more flexible.

          • adirondacker12800

            so the incrimental costs are gas
            Only if you cook the books real hard. Most people don’t bother to keep books.

          • Bobson Dugnutt

            @df1982, The experience of the relatively frequent Amtrak lines in California shows that children and the parents who love them love trains. The most touristy is the Pacific Surfliner. Parents seem to be able to afford train fares at current prices, and there would likely be child fares or weekend/off-peak family pack fares.

            Some advantages for families is that kids can walk around on the train, they don’t have to stop travel to go to the bathroom, and food is sold on board.

            We can’t assume that parents would be a formidable anti-train bloc because they theoretically would still favor cars because of ticket shock. Look at existing train patterns and see whether there are families riding.

          • Matthew Hutton

            Henry, isn’t that a fairly niche occurrence, if you buy the car outright or get a loan/PCP and aim to keep the car beyond the loan term it doesn’t apply. Even if you buy the car on PCP and will return at the end of the loan period and are anywhere close to the mileage limit it doesn’t apply.

            And renting cars in the US is cheap, so I’m not sure why you are against that as an option.

          • Henry Miller

            @adirondacker12800 I’ve kept my books, the incremental cost of my minivan: gas and maintenance is ~$.20/mile, I used to have a small car that was about $.11/mile (calculated when diesel was $3/gallon so cheaper now). The rest of the $.50 the IRS allows is for payments and insurance, but these costs are the same if you leave the car home. For a 1000 mile round trip that works out to $200. For two people the train is already more expensive, plus you don’t get the car when you get there.

            @Matthew Hutton I don’t think that is niche in the midwest. Almost everybody already has a car. There are a large amount of people who trade in the cars when the trade in value is enough that their payments don’t go up (Detroit makes a ton of money every year for a reason). Even the most frugal buy a used car every 3-5 years (most families have more than one car, and replace them when they wear out). Even if the car is paid for, it is still sitting in the driveway unused.

            Renting cars is not very cheap – $75/day (small cars are cheaper). For one day that isn’t too bad, but for 3 days you can pay for all your gas for the trip just on savings for the rental car. For trips where flying is better the extra hotels and time off become a factor, but the subject here is trains, so at most you add 2 extra days to account for the hotel (and time off work).

            Note that I’m working in terms of those who already own a car. If you don’t have a car the economics change. The larger the group the more things work out in favor of taking the car.

          • Matthew Hutton

            When I rent a car (in advance obviously) I typically pay £150 for a week – and less when I’ve rented one in the US.

            And payments and insurance don’t apply if you leave the car at home. If you have a PCP you pay that per mile you drive, and anyway the more miles you do the sooner the car needs to be scrapped.

    • Herbert

      When my sister had to travel cross country with her kids, she much preferred the train…

  10. AJ

    How do you treat Akron and Canton in these models? Are those rolled in with Cleveland in your analysis? Having lived in all 3 metros, Akron would merit a station just as much as a Toledo or Dayton, particularly on the way to Columbus and/or Pittsburgh.

    • Alon Levy

      I split the difference by treating Cleveland, whose CSA population is actually 3.5 million, as a single metro area of 3 million. The model is pretty agnostic on where the trains go through – the options are Canton/Akron, or Youngstown, so the sizes are pretty similar, and it decomposes as roughly the same as a single region of 3 million.

      • AJ

        Oh ok – so the model is agnostic if HSR Is is literally just one station serving Cleveland the city, or a series of stations that serve Cleveland, Akron, etc. within the CSA?

        • Alon Levy

          It’s agnostic about Cleveland + Youngstown vs. Cleveland + Akron, etc. There absolutely are second-order effects from such decisions, the model is just too crude to capture them.

          • adirondacker12800

            In the flat parts of Ohio building tracks will be cheap. Akron can be on the tracks to Columbus and beyond and Youngstown can be on the tracks to Pittsburgh and beyond.

          • Alon Levy

            Akron is awkwardly too far east to be on the 3C route. Cleveland-Columbus more likely goes through the airport and maybe Mansfield.

  11. Anon

    Are denver and salt lake city too far from anything? Does a transcontinental HSR line pan out, on any route?

    • Alon Levy

      To put things in perspective, if Denver and Salt Lake City each grew by a factor of 3, to 11 million and 8 million people respectively, and if tunnels across the Rockies only cost as much as normal above-ground construction, HSR between them would come close but still not quite make financial sense. That’s how isolated that area is.

        • Matthew Hutton

          Firstly that’s a vanity project that doesn’t make money, secondly that line is supposed to eventually extend to Europe, which means you’ve got 600 million potential customers at one end and ~1.5 billion (including SE Asia) at the other – albeit at a distance of 8000km.

          • Herbert

            At those distances, trains are mostly relevant for cargo.

            If you’re doing the Transsib end to end as a pax, you don’t much care if the fastest train does it in seven days or in three…

          • Matthew Hutton

            I took at a look at https://pedestrianobservations.com/2020/03/20/eurail/ and the London-Warsaw time is 7h50. Then if you do Warsaw-Minsk-Moscow-Nur Saltan-Urumqi (which is basically a great circle as well as including the most plausible stops) would take 16h20 at 300km/h, then take the 2020 estimate (from https://en.wikipedia.org/wiki/High-speed_rail_in_China#Track_network) for the time from Urumqi to Beijing of 12h meaning you’re looking at around a 37 hours travel time from London to Beijing with stops.

            Clearly it is not competitive with flying on time – a direct flight takes 10 hours. But if we can’t/don’t want to fly anymore due to climate change it doesn’t cause international travel to cease to exist. The 10 or so days that it currently takes via the Trans-Siberian isn’t serious.

          • adirondacker12800

            We can make net-zero jet fuel. There will be airplanes.

          • Herbert

            Even if we do make net zero jet fuel, it will make flying more expensive in real terms than it currently is. And even if energy prices come down in relative terms, that benefits trains which run on electricity, too. It’d be interesting with infrastructure essentially paid for where the breakeven is at which a rail journey becomes more expensive due to “hotel costs” (i.e. maintaining a sleeper) vs. the higher fuel consumption of airplanes and the more operators/pax seat and so on….

          • Matthew Hutton

            Plus changing trains and the train having more stops is a lot less painful than for aeroplanes. Every time I look at flights involving changing planes it takes hours and hours longer than a direct flight – whereas you can change trains in 15-30 minutes assuming they are reliable and on time.

      • Anon

        Yeah, beckoning to the original transcontinental railroad.. seems like the southern route is the best choice (albeit still falling short? is that right?)

        On paper, you hit 4 of the 10 largest metro areas (LA, Pheonix, Dallas, Houston) on what is presumably a flatter route

        • Eric2

          The Gadsden Purchase was done to secure a flat rail ROW for the US. The ROW would be Phoenix->Tucson->El Paso->Dallas or San Antonio. All these segments are good enough for crayoning, but won’t be financially viable for at least another generation.

          • Herbert

            “Financially viable” is neoliberal gaslighting. Not a single highway delivers a profit once you account for noise and pollution and traffic fatalities. Yet they’re still built.

          • Eric2

            I see you’re rejecting the entire premise of this blog post and discussion

          • adirondacker12800

            It’s never going to be viable. there’s a whole lot of nothing between San Antonio and Phoenix.

          • Anon

            There is, though if costs are low..

            Personally I favor a route going to Dallas. Faster through trips to places further east, bigger metro area, and with a few more stops possible. Something like Pheonix, Tucson, Las Cruces, El Paso, Odessa/Midland, and then either San Angelo – San Antonio, or Abilene – Dallas

            I think, politically, the stop in New Mexico is basically required.
            So that’s, what, 3 or 4 million of intermediate population in 1600 km? (Ciudad Juarez inflates the El Paso numbers)
            8 to 10 hours between LA and Dallas, so basically a sleeper HSR kind of distance, with more reasonable travel times for any other pairs including Pheonix – Dallas. Better connections to other texas cities, and the San Bernardino route down to san diego make the route more and more worth building

          • adirondacker12800

            Because it’s cheaper and faster to fly, even with synthetic jet fuel ?

          • Herbert

            This blog post tries to convince those who believe in the “infrastructure must be profitable to exist” mantra the neoliberals have drilled into us. It is good that it shows that even under such a weird assumption HSR still makes sense in the U.S.

            But the world does not actually work like that. The real world is more favorable to infrastructure spending than neoliberal ideology. A state does not have to run profitable state run ventures. The state run ventures need to provide more benefit (how ever one chooses to calculate that) then cost (how ever one chooses to calculate that) and rail infrastructure is virtually always beneficial in the net.

          • Eric2

            “rail infrastructure is virtually always beneficial in the net”

            This is nonsense. A rail line from Nuuk to Nanortalik, Greenland, would not be beneficial in the net. So too for innumerable other conceivable rail lines. “Rail infrastructure is virtually always beneficial” is only true if you restrict yourself artificially to some particular subset of possible rail lines. But by doing so, you are making a tautological no-true-Scotsman argument.

            What you really should be saying is that a rail line which covers over 50% of its costs from fares is likely to be beneficial on the net. 50% of course is just a random number I chose, but you need to provide an argument for what the actual number is. I agree with you that it’s less than 100%, but it’s definitely not 0% either.

          • michaelrjames

            @Eric2

            Herbert wasn’t making that argument. I suppose some complete dud rail lines have been built but very few (most duds were popular once but fell into disuse/disfavour). But the beancounter arguments are narrow and simplistic to the point of idiocy. Flyvbjerg* actually claims that the Chunnel should never have been built because, you know, it cost a lot and … poor financial performance .. whatever. To know how wrong that is, one only needs to see the tens of thousands of trucks building up in Calais and Dover, not to mention that 10m pax who choose to train it instead of flying.

            *I wonder if Flyvbjerg, sitting in his Oxford chair licking the boots of neoliberals and austerians, is expecting to get on Boris’ New Years honour list?

          • michaelrjames

            Any hesitation in my poor opinion of Flyvjberg has been definitively lost by his latest idiocies:

            https://www.bbc.com/news/business-55624103
            Prof Flyvbjerg says another problem with large-scale, high-speed rail projects is that they take so long to complete that better alternatives might be available before completion. For example, the first stage of the HS2 isn’t due to open until 2028 at the earliest.
            He’s hopeful that Elon Musk’s Hyperloop – whereby pods containing passengers travel at great speed through vacuum tubes – might turn out to be a better, more cost-effective alternative to high-speed rail. Another alternative might be autonomous electric cars that can travel bumper-to-bumper at high speed.

            This is a poor article (from the BBC!). The ‘analysis’ of economic performance is superficial.

      • Bobson Dugnutt

        @Alon Levy, I think Salt Lake City might have all the rail it needs and its substantial cities are within commuting distance of SLC. Local transit in this area is operated by a statewide agency.

        There was a piece by Jarrett Walker on Human Transit and he suggested Colorado pursue a statewide intercity bus network to connect its cities to Denver.

          • Bobson Dugnutt

            @Herbert: But the terrain though.

            Denver is in an awkward spot as a major metro area up so high. Salt Lake City is the nearest big city of similar size and there’s little except for resort towns in the way of ridership. Kansas City is the nearest city east, but a vast distance through sparsely populated Kansas. Albuquerque and El Paso are large cities to the south, and there are Colorado Springs and Pueblo on the way, but the topography may prove too much.

          • jcranmer

            The entire region between I-25 and I-35/I-29, which roughly bracket the High Plains, is extremely sparsely populated. The largest towns are in Texas, and even the largest comes in at a paltry ~322k MSA [1]. North of Texas, there are just two MSAs, the mammoth Rapid City, SD (140k) and Bismarck, ND (130k).

            Connecting a line along the I-25 corridor shouldn’t be too challenging in terms of terrain. In Colorado (and Wyoming/Montana for that matter, although the population of the I-25 cities there is again small), you’re largely following the eastern edge of the mountain chain. In New Mexico and Texas, it’s the banks of the Rio Grande. The main challenge is crossing the mountains in southern Colorado, as the Rio Grande is effectively west of the first mountain bank. Offhand, the Denver & Rio Grande route over La Veta doesn’t look too challenging (although that’s not the same as cheap!). Alternatively, Atchison, Topeka & Santa Fe’s route over Raton also looks easy enough, if a bit more circuitous.

            [1] Strictly speaking, Lincoln, NE is actually larger, but I’d prefer to continue the imaginary boundary line somewhat west of north from Wichita to hit Grand Island rather than following I-35 northeast to Kansas City. Not that Grand Island’s a large city–it’s one of the smallest MSAs–but it’s a better approximation of the High Plains boundary. The highways don’t mark the boundary very effectively in the central latitudes of the US.

  12. Herbert

    The Wikipedia article on hsr has a formula to estimate the hsr share of air+ rail markets. Do they produce similar numbers to those in this write-up?

    • Matthew Hutton

      Honestly I treat a flight as taking all day as generally that’s how it mostly works out. So if HSR is less than a day it’s worth considering on environmental grounds (and you know flying sucks).

      That would give you a range of 10 hours or so at 300km/h with 90 minutes at each end.

    • Alon Levy

      I’m not really looking at modal splits – the problem is that data on rail vs. car modal split is much harder to find than vs. air. In Japan, my formula is pretty good at predicting the Shinkansen ridership of various Tokyo-to-province city pairs, except notably Tokyo-Fukuoka. My formula says Tokyo-Fukuoka should have 4.6 million annual rail passengers; in fact it has 11 million air+rail passengers (link, PDF-p. 3), but they split as 10% rail, 90% air, which is unusual when trains take 5 hours. Paris-Nice, on which the TGV takes 5:30, has a 30-70 split.

      • Andrew in Ezo

        Alon, around 70% of Tokaido/Sanyo Shinkansen passengers are business travelers, and a 5 hour trip each way would be too much for a one day business r/t (higaeri shuchou) from say corporate HQ to a branch office or vice versa. There is also the factor of Fukuoka being more in the business orbit of Osaka/Kansai/Western Japan, with customers concentrated in that area. Similarly, Sapporo being in Eastern Japan is predominantly in the Tokyo sphere of influence.

        • Andrew in Ezo

          To add, Fukuoka benefits from having an airport conveniently located near the CBD.

          • Frederick

            Also to add, the US military has bases in Japan and these bases have no-fly zones. Passenger airlines need to take detours to go around these bases, so it takes longer than air trips of the same distance in other countries.

            Most Japanese cities don’t have an airport near CBD either because they started air transport later (and have to find land farther from CBD), or because the closest airport is used by the US military.

          • Herbert

            The tendency in non Anglophone countries has been to shut down airports close to the CBD because of noise and space issues. Berlin did so (twice over). Munich did so. Hamburg seriously considered it (Kaltenkirchen) and Warsaw is in the process of doing so…

          • yuuka

            Apart from Fukuoka, Haneda and Osaka-Itami exist, then again the public-transit route from Itami to downtown Osaka is trash and in plenty of cases it’s easier to get to Osaka-Kansai.

            AFAIK the only similar case to what you describe is in Sapporo, where Okadama airport was reduced to intra-Hokkaido prop plane flights and everything was packed off to New Chitose, an hour away.

          • Andrew in Ezo

            Osaka Itami may not have the most ideal public transport links to the CBD, but it is far, far more popular than KIX for domestic travelers, ANA and JAL have widebody flights to HND on half hour intervals, while KIX has something like a handful of narrowbody services plus the LCCs, at least pre-covid. Limousine bus service Itami to Umeda takes 30 min, while KIX to Umeda is an hour. Of course the taxi ride is much cheaper from Itami due to the shorter distance.
            Okadama was never a big airport for inter-prefecture air travel (too short a runway), when domestic commercial passenger air travel restarted in 1951, the first flights from Hokkaido to Tokyo Haneda were from Chitose Airport.

      • Matthew Hutton

        Tourists from other countries also would likely do London-Tokyo then go by train stopping off to Fukuoka and then fly back.

      • Herbert

        Experience shows that the introduction of hsr service alone has no huge effect on car modeshare. Air modeshare us much more sensitive to the introduction of faster competition

        • Alon Levy

          It did here… https://www.merkur.de/wirtschaft/schnellfahrstrecke-fuer-ice-bahn-haengt-zwischen-muenchen-und-berlin-flugzeug-ab-zr-10774052.html

          “Rund 1,2 Millionen Reisende seien im zurückliegenden Jahr vom Flugzeug auf die Bahn gewechselt und etwa eine Million vom Privatwagen.”

          In contrast with the actual 4.4 million figure, my formula predicts that Berlin (5)-Erfurt (0.3)-Nuremberg (1.8)-Munich/Ingolstadt (4.7) should have 6.75 million passengers, but this is not a particularly fast service, so Berlin-Nuremberg’s ridership probably looks more like the distance is 650 km for 3:00 service and Berlin-Munich’s like 900 km for 4:05, and when you apply these penalties you get a predicted ridership of 4.6 million.

          Likewise, the Bundestag says 4.9 million people used the Nuremberg-Erfurt segment in 2018 (source, PDF-p. 2), and if you strip away Nuremberg-Munich and Berlin-Erfurt but add in passengers from Leipzig and Dresden to Bavaria, with penalty for travel time, you get very close to the predicted number.

          • Herbert

            Berlin-Nuremberg flights were entirely wiped out by the introduction of HSR (and parenthetically the elimination of Air Berlin which had had a hub in Berlin, but that happened before the opening of VDE8) And even in 1970 there were 155 000 people flying Berlin to Nuremberg on PanAm…

  13. yuuka

    This is quite interesting in light of some reports that the Malaysian government allegedly wants to shorten the proposed KL-Singapore HSR to Johor Bahru across the border, and expect passengers from Singapore to make their own way across the border.

    Could such a model be used to weigh the impact of taking away Singapore (population: approx 6 million) from the line? A lot of the towns the HSR would pass (and thus, have intra-Malaysia local service) are typically only hovering around 200k population.

    https://en.wikipedia.org/wiki/List_of_cities_and_towns_in_Malaysia_by_population

    • Herbert

      The existing options of getting from Johor Bahru to Singapore are pretty lousy. There was talk of a “cross border metro” but if they’re too cowardly for hsr, they won’t even think of a cross border metro. So people whose destination is Singapore will continue flying rather than deal with the headaches of congestion and border control…

      • michaelrjames

        Surely, all north-south long-distance trains terminate in Singapore not Johor Bahru? Like the Singapore-Bangkok train (I took the slow version half a lifetime ago). I hardly think the Malaysians would want to lose the biggest and richest market for any such trains, HSR especially. It’s probably an attempt to winkle some S$ towards its capital cost which may not be so silly an idea because Singapore will be one of the biggest beneficiaries of such a line.

          • michaelrjames

            @Matthew Hutton:

            You made me read the whole thing! Here is the relevant bit:

            seat61:
            When starting in Singapore, you first need to transfer to Johor Bahru Sentral…
            Until 2011 trains left from the wonderfully faded grandeur of Singapore’s art deco railway station, built in 1932. Sadly, the Singapore government took it over from the Malaysians and promptly closed it, so trains to Kuala Lumpur and the north now leave from Johor Bahru Sentral Station just north of the causeway inside Malaysia. Shuttle trains operate from Woodlands Train Checkpoint just south of the causeway to JB Sentral, or you can take a frequent local bus all the way from central Singapore to JB Sentral. The options for transferring to or from downtown Singapore are explained here,

            So, weirdly, the train I took about 40 years ago was more convenient than today. This was the action of the Singaporean government not Malaysia; it happened when Malaysia’s sovereignty over the rail tracks into the station expired in 2011.
            But there is land reserved for the future HSR terminal in Jurong East (which is central north-west on the island) but now not before 2030. On the old Art-Deco terminus in central Singapore: (wiki)
            “The main building of the railway station was gazetted as a national monument on 9 April 2011,[4] completing one of the objectives of the new Points of Agreement between Malaysia and Singapore. It will be a future site for Cantonment MRT station, one of the stations for Circle MRT line Stage 6.”

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  15. inaoifeble

    The eastern part of Lake Erie is quite shallow (the average depth is 21 feet, none of it is deeper than 15 meters); it seems like you could build some combination of a tunnel and a causeway quite inexpensively over that portion of the lake, allowing you to have Detroit as the triple point between Chicago-Toronto and Chicago-Cleveland, which seems like it would be a massive improvement over having Toledo as your triple point

    A single line with Chicago, Cleveland, and Detroit seems like it would have operational benefits in terms of scheduling, while also allowing the inclusion of Ann Arbor (home of the University of Michigan, 46,000 students) and South Bend (home of the University of Notre Dame, 12,000 students) on the same line, which would probably outperform their relative size, considering the massive popularity of both of their football programs, and the number of high earning graduates from each school living in major cities in the Midwest

    You might be able to further justify the link if you included a pair of freight lines as well (which would perhaps be easier with a tunnel), though I’m sure nothing about adding on 2 international crossings to a intranational high speed rail link would be easy, though I do think building a line into Canada as part of the initial HSR rollout improves the likelihood of eventually building a Chicago-Toronto line, which is already one of the most popular air routes in North America

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