Metcalfe’s Law for High-Speed Rail

I wrote a Twitter thread about high-speed rail in the United States that I’d like to expand to a full post, because it illustrates a key network design principle. It comes from Metcalfe’s law: the value of a network is proportional to the square of the number of nodes. The upshot is that once you start a high-speed rail network, the benefits to extending it in every direction are large even if the subsequent cities connected are not nearly so large as on the initial segment. Conversely, isolated networks from the initial segments are of lower value.

The implication for the United States is that, first of all, it should invest in high-speed rail on the entire Northeast Corridor from Boston to Washington, aiming for 3-3.5 hour end-to-end trip times. And as the Corridor is completed, the priority should be extensions in all directions: south to Atlanta, north to Springfield and (by legacy rail) Portland, west to Pittsburgh and Cleveland, northwest to Upstate New York and Toronto.

The model

To quantify the benefits, I’m going to look purely at railroad finances: construction costs go out, annual profits go in. Intercity high-speed rail pretty much universally turns an operating profit, the question is just how it compares with interest on capital construction. For this, in turn, we need to estimate ridership. Here is an illustrative photo of the sophistication of the model I am using:

In the picture: someone who gets on the train without letting you get off first. Credit: William O’Connor.

The theoretical model for ridership is called a gravity model: ridership between two cities of populations Pop_A and Pop_B at distance d is proportional to


However, two complications arise. First of all, there are some diseconomies of scale: the trip time from the train station to one’s ultimate destination is likely to be much higher if the city is as huge as Tokyo or New York than if it is smaller. Empirically, this can be resolved by raising the populations of both cities to an exponent slightly less than 1; on the data I have, which is Japanese (east and west of Tokyo), Spanish (Madrid-Barcelona, Madrid-Seville), and French (see post here – all its sources link-rotted), the best exponent looks like 0.8.

And second, at short distance, the gravity model fails for two reasons: first, access time dominates so in-vehicle time is less important, and second, passengers drive more and take fast trains less. In fact, on the data I’m most certain of the quality of – that from Japan – ridership seems insensitive to distance up to and beyond the distance of Tokyo-Osaka, which is 515 km by Shinkansen. Tokyo-Hiroshima, 821 km and 3:55 by Shinkansen, underperforms Tokyo-Osaka by a factor of about 1.6 if the model is \mbox{Pop}_{A}^{0.8}\cdot\mbox{Pop}_{B}^{0.8} if we lump in air with rail traffic; of course, air travel time is incredibly insensitive to distance over this range, so it may not be fair to do so. French data taken about 3 hours out of Paris overperforms the mid-distance Shinkansen, although that’s partly an artifact of lower fares on the TGV.

To square this circle, I’m going to make the following assumption: the model is,

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

If the populations of the two metro areas so connected are in millions then the best constant for the model is 75,000: that is, take out the number the formula spits, multiply by 500^{2} = 250,000 to get rid of the denominator at low d, multiply by 0.3, and make that your annual number of passengers in millions.

Finally, operating costs are set at $0.05/seat-km or $0.07/passenger-km, which is somewhat lower than on the TGV but realistic given how overstaffed and peaky the TGV is. This is inclusive of the capital costs of rolling stock, but not of fixed infrastructure. Fares are set at $0.135/passenger-km, a figure chosen to make New York-Boston and New York-Washington exactly $49 each, but on trips longer than 770 km, the fares rise more slowly so that profit is capped at $50/trip. Of note, Shinkansen fares are about $0.23/p-km on average, so training data on Shinkansen fares for a network that’s supposed to charge lower fares yields conservative ridership estimates; I try to be conservative since my model is, as the picture may indicate, not the most reliable.

The model on the Northeast Corridor

The Northeast Corridor connects four metropolitan areas: Boston (8 million people), New York (22), Philadelphia (7), Washington (10). All populations cover combined statistical areas, just as the metropolitan area definitions in Japan are expansive and include faraway exurbs. In the Northeast, the CSAs lump together some independent metro areas, such as Baltimore-Washington, but the largest of the subsidiary metro areas, including Baltimore, Providence, New Haven, and Trenton, are along the Northeast Corridor and would get their own stations.

The distances are 360 km Boston-New York, 140 km New York-Philadelphia, 220 km Philadelphia-Washington. I am not going to take into account subsidiary stations in passenger-km calculations, for simplicity’s sake. Splitting Baltimore apart from Washington would actually raise ridership by a little, first because the 0.8 exponent means that combining metro areas reduces ridership, and second because Boston-bound ridership is higher if we assume the destination is a little bit closer.

The highest-ridership city pair is New York-Washington. Per the formula above, we get

0.3\cdot 22^{0.8}\cdot 10^{0.8} = 22.44 \mbox{mio. pax/year.}

By the same formula, New York-Boston is 18.77 million, New York-Philadelphia is 16.87 million, Washington-Philadelphia is 8.98 million, and Boston-Philadelphia is 7.51 million. All of these are within the 500 km limit in which we assume distance doesn’t matter. Finally, Boston-Washington is

75,000\cdot 10^{0.8}\cdot 8^{0.8}/720^{2} = 4.82 \mbox{mio. pax/year.}

Overall, this is 79.4 million annual passengers, excluding shorter-distance commuter travel like New York-New Haven. Taking distance traveled into account, this is 26.4 billion annual p-km, generating $1.7 billion of operating profit. What I think it should cost to generate this service is investments that, with good value engineering that has been missing from all plans in the last 12 or so years, should cost in the low teens, say $13 billion. If costs can be held to $13 billion, or just less than $20 million per kilometer for a line of which about two-thirds of the physical infrastructure is good enough, then the financial return on investment is 13%. Not bad.

Of note, traffic density is fairly symmetric at the two ends. At the southern end, between Philadelphia and Washington, total traffic density is 36.24 million passengers per year; at the northern end, between New York and Boston, it is 31.1 million. So there should be some extra trains just for New York-Philadelphia, where the expected traffic density is 51.64 million – perhaps ones diverting west to inland Pennsylvania, perhaps interregional trains making an extra stop or two running 5-10 minutes slower than the trains to Washington – but otherwise trains should run on the entire corridor from Boston to Washington.

Also of note, I don’t expect much peakiness on the line – probably none outside the New York-Philadelphia segment. Short-distance lines, including New York-New Haven and New York-Philadelphia, have a rush hour peak in travel. But longer-range intercity lines generate weekend leisure travel and same-day business travel, both of which tend to peak outside the regular rush hour; TGV traffic, heavily weighted toward longer-range city pairs, peaks on Friday and Sunday, with weaker weekday ridership to balance it out. The Northeast Corridor thus benefits from mixing cities at various ranges, with the various peaks mostly canceling each other out. It’s plausible to get away with running service at a regular interval of every 15 minutes all day, with extra trains on New York-Philadelphia.

The Northeast Corridor and Metcalfe’s law

Two examples of Metcalfe’s law in action can be found on the corridor, one for an expansion and one for a contraction.

The contraction would be to ignore Boston and just focus on New York-Washington. The traffic density is higher there, for one. Moreover, no extensive civil infrastructure is required, only some small fixes in Maryland and New Jersey, a rebuild of the catenary, and rebuilds of the station throat interlockings. However, this is less prudent than it seems, because Boston doesn’t just generate traffic on New York-Boston, but also on New York-Washington, on trains bound from points south of New York to Boston.

If we exclude Boston, we have just three city pairs on what is left: New York-Washington, New York-Philadelphia, Washington-Philadelphia. They total 48.3 million passengers per year and 12.4 billion p-km – in other words, slightly less than half the p-km of the entire line including Boston. What’s more, there’s an extra fudge factor, not modeled in my ridership screen, coming from peakiness: a shorter line is one with a more prominent rush hour peak, as the longer trips on Boston-Washington are not included, and this ends up requiring more rush hour-only equipment and increases operating expenses per p-km.

The expansion is, in this section, one that is almost part of the Northeast Corridor today: New Haven-Springfield. The line is unelectrified today despite substantial investment by Connecticut, which like other American states is allergic to rail electrification for reasons that are beyond me. Speeds today are low, even though the right-of-way is straight. However, investment in bypasses and in speedups on the highest-quality legacy segment is possible, and would connect Hartford and Springfield to New York and points south.

The Hartford-Springfield region has 2 million people, and Springfield is 100 km from New Haven and 210 from New York. We apply our usual model and get New York-Springfield ridership of 6.19 million, Philadelphia-Springfield ridership of 2.48 million, and Washington-Springfield ridership of 3.3 million. In passenger-kilometers, these three city pairs amount to 1.3 billion, 620 million, and 1.55 billion respectively, for a total of 3.47 billion, which I will round to 3.5 billion to avoid giving the impression that the model is reliable to 3 significant figures (or even 2, to be honest).

So we have 3.5 billion additional p-km for just 100 km of new construction, or 35 million p-km per km of construction. Note that the expected density on New Haven-Springfield based on the model is just 12 million passengers – the remaining p-km are on the core Northeast Corridor, as passengers from New York and points south travel on a portion of the corridor to get up to the branch to Springfield. So even though the expected traffic is very light, the impact on revenue per kilometer of construction is comparable to that of the base corridor. If costs can be held to $2 billion, which is low-end for an entirely greenfield line but reasonable for service that would partly run on the existing legacy line, then the return on investment is $0.065*3.5/$2 = 11%, almost as high as on the base Northeast Corridor.

Further extensions

Portland (0.7)

To the north, it is valuable to run upgraded legacy trains between Boston and Portland, with a short connection to high-speed trains at South Station. Estimating ridership and revenue there is dicier, because the trains are slower and the data is trained on high-speed trains. We assume 190 km of revenue, as is the current length of the line. But costs and the ridership-suppressing effect of distance are charged at 350 km, roughly scaled for time.

With this in mind, ridership on Boston-Portland is 1.19 million, ridership on New York-Portland is 1.33 million, ridership on Philadelphia-Portland is 0.37 million, and ridership on Washington-Portland is 0.31 million. In total, this is about 1.5 billion p-km, of which 45 million, all from Washington, are beyond the 770 km at which fares are $0.135/km and are charged at the lower rate of $0.07/km. Altogether it’s around $200 million a year in revenue. Costs are around $140 million, including extra costs for service south of Boston. Operating profits are fairly low, but Boston-Portland legacy trains don’t cost per km nearly as much as high-speed rail; electrification and some track work can be done for maybe $600 million, for an ROI of 10%.

Of course, this ROI does not exist without high-speed rail the Northeast Corridor and without the separately-charged North-South Rail Link for local and regional trains. Like other tails, Boston-Portland is valuable once the mainline preexists – it isn’t so great on its own.

The South

The route from Washington to Atlanta has a sequence of cities roughly following the I-85 corridor. They are small and sprawly, but are still valuable to connect thanks to Metcalfe’s law. These include Richmond (1, and 180 km from Washington), Raleigh (2, and 240 km from Richmond), the Piedmont Triad (1.6, 120 km), Charlotte (2.6, 150 km), Greenville (1.4, 160 km), and finally Atlanta (7, 230 km).

The line is long, 50% longer than the Northeast Corridor. With quite sprawly cities in North Carolina and few good rights-of-way, takings and viaducts are needed and would raise construction costs, to perhaps $30 billion. Moreover, there is probably an intercity rail ridership penalty because these cities do not have public transportation; the model does not incorporate such a penalty, which should be regarded as a risk with investments made appropriately. And yet, each city in sequence generates ridership on the line to its north, creating decent ROI if we assume the model applies literally.

Take Richmond. It’s a small city, generating 1.89 million annual riders to Washington, 1.42 million to Philadelphia, 3.05 million to New York, 0.49 million to Boston. But this is 2.9 billion p-km for just 180 km of new construction, and nearly all of these p-km are chargeable at the full rate, giving us a total of $190 million in annual operating profit. If construction can be kept to $5 billion, this is just short of 4% ROI, which is not amazing but is decent for how small Richmond is compared with the cities to its north.

This calculation cascades farther south. We have the following table of ridership levels, in millions of annual passengers as always:

City N\City S Richmond Triangle Triad Charlotte Greenville Atlanta
Boston 0.49 0.66 0.36 0.43 0.21 0.58
New York 3.05 3.14 1.6 1.73 0.79 2.03
Philadelphia 1.42 1.87 0.9 0.92 0.41 1.13
Washington 1.89 3.3 2.36 2.13 0.86 1.92
Richmond 0.64 0.44 0.62 0.22 0.44
Triangle 0.76 1.12 0.68 1.42
Triad 0.94 0.57 1.78
Charlotte 0.84 3.06
Greenville 1.9

This leads to the following operating profits, in millions of dollars per year:

City N\City S Richmond Triangle Triad Charlotte Greenville Atlanta
Boston 24.5 33 18 21.5 10.5 29
New York 107.06 157 80 86.5 39.5 101.5
Philadelphia 36.92 77.79 44.46 46 16.5 56.5
Washington 22.11 90.09 82.84 95.53 43 96
Richmond 9.98 10.3 20.55 9.58 88
Triangle 5.93 19.66 19.01 60.92
Triad 9.17 11.49 62.48
Charlotte 8.74 77.57
Greenville 19.76

This totals to $1.8 billion a year, or an ROI of 6%. This is not a safe number – a hefty share of the figure comes from city pairs that trains would connect in 3.5+ hours, like New York-Charlotte, Washington-Atlanta, and even the 5.5-hour New York-Atlanta, in which range the model has essentially two data points (Tokyo-Hiroshima, Paris-Nice). Another noticeable share comes from intra-South connections, in which neither city in the pair has a strong center or a public transport network to connect the station with destinations.

But thankfully, because this line can build itself up by accretion of extensions, starting with Washington-Raleigh and seeing how ridership holds up would not create a white elephant, just missed benefits if the model is in fact correct.

Harrisburg (0.7), Pittsburgh (2.5), and Cleveland (3)

The Keystone corridor is an interesting example of a branch that gets stronger if it is longer. The reason for this is that Harrisburg is pretty small, and Harrisburg-Pittsburgh requires painful tunneling across the Appalachians. Philadelphia-Harrisburg is 170 km and can probably be done for $4 billion; Harrisburg-Pittsburgh is 280 km and, as a pure guess, requires around 40 kilometers of tunnel, let’s say $14 billion. Pittsburgh-Cleveland is 200 km and may require some tunneling near the Pittsburgh end to bypass suburban sprawl without good rights-of-way, but not too much – figure it for $6 billion.

For the benefits, we make a table similar to that for the South, but smaller. Of note, Washington-Harrisburg is 390 km and about 1:45, and costs accordingly to operate, but can only charge for 220 km, or $30, barely more than breakeven rate, because the straight line distance is short and high fares may not be competitive with driving on I-83. The straight line distance is even shorter than 220, about 190 via Baltimore, but Washington-Philadelphia is 220. Trains from Washington are assumed to earn the usual marginal profit west of Harrisburg, $0.065/km up to a maximum of $50, which is not reached even in Cleveland.

Finally, note that Cleveland has a big difference between the population of the core metro area (2 million) and the combined one (3.5), like Boston and Washington. Here we don’t take the bigger population but split the difference, since the biggest subsidiary regions in the combined area, Akron and Canton, could plausibly be on the line – and if they’re not then the line can serve Youngstown (0.7), and then 2^{0.8} + 0.7^{0.8} \approx 3^{0.8}. Note, finally, that Boston-Cleveland is faster via Albany and Buffalo, so the line through Pittsburgh is not considered even if it is built first.

City E\City W Harrisburg Pittsburgh Cleveland
Boston 0.66 0.91
New York 2.67 5.32 3.43
Philadelphia 1.07 2.96 2.03
Washington 1.42 2.19 1.51
Harrisburg 0.47 0.54
Pittsburgh 1.5

And as before, using the special malus for the roundabout Washington-Harrisburg route, we have the following operating revenues in millions of annual dollars:

City E\City W Harrisburg Pittsburgh Cleveland
Boston 28.74 45.5
New York 53.8 204.02 171.5
Philadelphia 11.82 86.58 85.77
Washington 3.41 45.11 50.74
Harrisburg 8.55 16.85
Pittsburgh 19.5

Note that the relatively easy to build segment to Harrisburg only generates $98 million in operating profit on $4 billion in construction costs, just less 2.5% ROI – Harrisburg is almost as big as Richmond, but it’s a branch and not a direct extension. Then Pittsburgh generates $390 million on $14 billion, or 2.8%. But Cleveland, easier to build to and bigger than Pittsburgh, manages to generate $344 million on $6 billion, finally a respectable ROI of 6%.

The northern cross

What may be caled the northern cross or the Albany cross – that is, a cruciform system consisting of lines from Albany to New York, Boston, Montreal, and Toronto – is an interesting case of a system where Metcalfe’s law again applies and encourages going big rather than small.

To apply the model, we make a crucial assumption: the same formula calibrated to domestic travel works internationally. Eurostar severely underperforms it – it has 10 million annual riders, of whom around 7-8 million go between London and Paris, where the formula predicts 18 million. Eurostar fares are very high, and has mandatory security theater and a slow boarding process that breaks down at peak travel time, and this may be enough to explain the low ridership. But then again, domestic TGVs overperform the model.

We also make a secondary assumption: fares charged are for actual distance traveled, even though the New York-Toronto routing isn’t the most direct.

We start with the New York-Toronto leg by itself. It connects New York to Albany (1.2, 220 km), Utica (0.3, 140 km from Albany), Syracuse (0.8, 80 km), Rochester (1.1, 120), Buffalo (1.2, 110), and Toronto (8, 160 km). Toronto’s metro population ranges between 6 million and 9 million depending on definition, and the high-end figure of 8 million is justifiable by the fact that Niagara Falls and Hamilton are on the line.

City S\City N Albany Utica Syracuse Rochester Buffalo Toronto
Washington 1.63 0.35 0.62 0.6 0.52 1.76
Philadelphia 1.65 0.54 0.88 0.78 0.63 2
New York 4.12 1.36 2.67 3.06 2.29 6.81
Albany 0.13 0.26 0.37 0.4 1.23
Utica 0.09 0.12 0.13 0.6
Syracuse 0.24 0.26 1.19
Rochester 0.37 1.71
Buffalo 1.83

And in operating profit:

City S\City N Albany Utica Syracuse Rochester Buffalo Toronto
Washington 61.45 16.38 31 30 26 88
Philadelphia 38.61 17.55 33.18 35.49 31.5 100
New York 58.92 31.84 76.36 109.4 99.73 340.5
Albany 1.18 3.72 8.18 11.7 48.77
Utica 0.47 2.03 3.13 18.33
Syracuse 1.87 3.89 30.17
Rochester 2.65 30.01
Buffalo 19.03

New York-Albany should cost maybe $5 billion to build and generates $160 million a year in operating profit, just 3.2%. But Albany-Buffalo, for around $11 billion extra, generates $580 million, about 5.2%. And then Buffalo-Toronto, assuming no international penalty, should cost on the order of $3 billion (much of the line in the Toronto suburbs automatically follows from the ongoing electrification project) and generate $670 milion. So the last segment, Buffalo-Toronto, returns around 20% if New York-Buffalo preexists; even if there’s a serious international malus, the ROI is very high. Everything combined is around 7%.

None of this is robust. The model handwaves the forced transfer at Penn Station – through-service from points south to Albany and points north would be excellent given expected traffic levels, but the approaches to both Albany and Philadelphia point west. The model also assumes New York-Toronto fares are in line with rail distance, even though the route is 50% longer by rail than by air. Finally, it assumes no international penalty. A 7% ROI is robust to any one of these assumptions failing, but if all fail, the route drops in profitability.

Or, rather, the base route does. Just as completing Buffalo-Toronto makes New York-Buffalo seem far stronger, so do the two additional legs of the northern cross strengthen the initial Empire Corridor. Here’s the Boston-Albany leg, at 260 km, with Springfield at kp 135, recalling that Hartford and Springfield count as one region of 2 million:

City W\City E Boston Springfield
Springfield 2.76
Albany 1.83 0.6
Utica 0.6 0.2
Syracuse 1.32 0.44
Rochester 1.19 0.56
Buffalo 0.91 0.46
Toronto 2.76 1.28

And in revenue:

City W\City E Boston Springfield
Springfield 24.22
Albany 30.93 4.88
Utica 15.6 3.45
Syracuse 41.18 9.87
Rochester 46.41 16.93
Buffalo 45.5 17.19
Toronto 138 61.15

$450 million a year, of which nearly half comes out of connecting Toronto to Massachusetts and Hartford, is not a lot, but then constructing 260 km of high-speed rail is not that expensive either; my best guess is around $7 billion, with some tunnels between Springfield and the summit to the west but also some approaches at both ends that would already exist. This is 6.4% ROI, which is better than New York-Toronto gets without the assistance of Philadelphia and Washington even though that route connects to a bigger city and requires less tunneling.

The final leg of the northern cross is to Montreal (4, 370 km from Albany), and is the most speculative. If the model has an international malus, it may well apply here, crossing not just a national border but also a linguistic one. It may apply with no or limited penalty, if the underperformance of Eurostar can be ascribed entirely to fares; but if it applies and is serious, then there is less cushion for mistakes than there is for trains to Toronto. The only intermediate city is Burlington (0.2, kp 220 from Albany), which exists largely for state-level completeness. Note also that Buffalo-Montreal is faster via Toronto and is thus omitted, while Buffalo-Burlington would have third-order impact.

City ESW\City N Burlington Montreal
Washington 0.2 1.59
Philadelphia 0.29 2.02
New York 0.98 7.74
Albany 0.1 1.05
Boston 0.44 3.02
Springfield 0.14 1.58
Utica 0.03 0.33
Syracuse 0.06 0.49
Rochester 0.07 0.5
Burlington 0.25

And in operating revenue:

City ESW\City N Burlington Montreal
Washington 10 31.8
Philadelphia 10.93 95.85
New York 28.03 296.83
Albany 1.43 25.25
Boston 13.73 123.67
Springfield 3.14 50.84
Utica 0.7 10.94
Syracuse 1.72 18.79
Rochester 2.55 23.08
Burlington 2.44

This is $750 million a yeer, of which Burlington furnishes about 10%, and New York-Montreal about 40%. This isn’t bad ROI – about $10 billion is a reasonable construction cost – but since 90% of it is about Montreal, any serious international or interlinguistic penalty leads to a big drop in profitability. Worse, if traffic drops, there may be a frequency-ridership spiral – I am writing timetables assuming half-hourly frequency, which is just enough for the model’s projected 18 million passengers per year, but if ridership is off by a factor of more than 2, then hourly frequencies start taking a bite out of the nearer markets and trains start running less full.

Lines that do not touch the Northeast Corridor

In the previous sections, I’ve argued in favor of building out a high-speed rail network out of the Northeast Corridor, on the grounds that extensions would be profitable toward Pittsburgh-Cleveland, Montreal, Buffalo-Toronto, and Atlanta. What about other lines?

The answer is that lines that do not feed into the Northeast somehow are a lot weaker. California can get decent ridership out of Los Angeles-San Francisco and thence extensions to Sacramento and San Diego are pretty strong, but the traffic density per the model is both well below California HSR Authority projections and well below the Northeast Corridor.

And it gets worse in parts of the country without a Los Angeles-size city anchoring everything. Texas is currently building a Dallas (8)-Houston (7) high-speed line, using private money by Texas Central, a railroad owned by JR Central using Shinkansen technology. The model predicts 7.5 million annual riders between the two regions, and the system’s public ridership projections for the near term are pretty close. Moreover, construction costs are pretty high, $15 billion for 380 km, despite the flat terrain. If the operating costs and fares are what I’m projecting, the financial ROI is 1.2%.

What’s more, Texas can expect ridership to underperform any model trained on European or Japanese cities. Tokyo has the world’s largest central business district, and maintains high density of destinations at a distance of several kilometers from Tokyo Station as well, and 20-something rapid transit lines depending on how one counts feed this center. Paris is smaller but has a strong center and urban rail connections. The provincial cities in both countries are lower-density and have higher car ownership, but that’s still okay, because people from those cities are not driving into the capital. By the same token, trains to New York should not underperform a model trained on Japan, Spain, or France. But Texas is completely different, with very weak centers, no public transportation to speak of, and no walkable cores near the train stations. The penalty for poor public transport connections is likely to be serious.

The situation in the Midwest is more hopeful than in Texas, but still dicey. Chicago just isn’t that big. Yes, it’s about the same size as Paris, but the cities ringing it don’t form neat lines the way Lyon and Marseille are on the same line out of Paris, just with a short spur rather than through-service.

The funniest thing about the Midwest is that high-speed rail construction there may be justifiable as an accretion of western extensions from the Northeast and Keystone Corridors. Cleveland-Detroit (5) is 280 km long, and would put Detroit 1,070 km and slightly more than 4 hours away from New York. The distance penalty is hefty, but 2.81 million annual users is still a lot over such distance, and the $140 million in operating profits get to around 2.5% ROI on construction costs in flat Midwestern land, without taking any other connections into consideration: Chicago-Cleveland, Chicago-Detroit, Philadelphia-Detroit, Pittsburgh-Detroit, New York-Toledo, Washington-Detroit.

Even New York-Chicago is a fairly solid line per the model: it’s 1,340 km and slightly longer than 5 hours, but there is still a lot of travel volume between the two cities, mostly by air. The model says 3.12 annual high-speed rail riders, somewhat fewer than the current O&D flight volume (4.68 million annualized from 2018 Q2), which is believable by comparison with Paris-Nice’s mode share (70% air, 30% rail, ignoring all other modes). The required mode share is still more favorable to rail, but the airports in New York and Chicago have more congestion and more delays than in Nice, turning what is a little more than an hour in the air into a three-hour flight schedule.

In contrast, just starting from Chicago-Cleveland (550 km)/Detroit (470 km), without any other connections (and without Pittsburgh-Cleveland), would not be financially great. Ignoring Toledo, the three cities generate 13 million annual riders, 6 billion annual p-km, and $400 million in annual operating income, for a system that would take perhaps $13 billion to construct, perhaps slightly more.

What this means for high-speed rail construction

Metcalfe’s law implies that high-speed rail networks get stronger as they add more nodes, even if those nodes are somewhat weaker than the initial ones. But it gives guideines for how to build such networks more broadly:

  • Don’t cheap out by only building a short segment.
  • Once the initial segment is in place, invest in extending it and building branches off it as soon as possible, in preference to building unconnected segments elsewhere.
  • A relatively empty tail may still be financially successful if it fills a trunk line.
  • Unless all your cities are on one line, try to build a mesh of lines to allow many origin-destination pairs.
  • You’ll always run into a frontier of marginal lines, so value-engineer infrastructure as much as possible to push that frontier forward.
  • Be wary of lines for which the analysis involves extrapolation, for example if neither city has a strong center or usable public transport.

High-speed rail is cheap to run when there’s enough scale to fill trains – high speeds ensure that labor and equipment cost per seat-km are fairly low. This means that self-sustaining profits are viable, and once they’re in place, they can generate further borrowing capacity for rapid expansion.

The limit is not the sky. Beyond a certain point, no realistic value engineering can make lines financially viable. Sometimes the cities are just too small or too far apart. But a realistic limit for the United States is still most likely much farther than anyone proposing immediate investment plans thinks: the Northeast Corridor can generate good returns if investment there is ever done competently, and branches and extensions to smaller and less dense cities are still more viable than they look at first glance.


  1. ckrueger99

    Pure genius. Beautiful post, as per your usual standard.
    Question: Your ROIs are sensitive to having reasonable infrastructure costs. How likely is this?

    • Alon Levy

      Actually likelier outside the NEC, regrettably. A line with 13% financial ROI will have special interests ringing it like sharks ring a shipwrecked sailor waiting for a piece of meat; the only line with that ROI that Europe managed to build, Paris-Lyon, got built because it was the first so nobody realized it would be such a winner. Of note, the value engineering I am pushing for aims to reduce American construction costs to those of France today and not those of France in the 1980s, which were single-digit millions per kilometer in geography that isn’t any easier than on the LGV Sud-Europe Atlantique or Est phase 1.

      • Herbert

        I fear the problem is systemic and unless the U.S. builds up a competent civil service (fat chance of that) there’s nothing that can be done.

        After all, consultants are even more expensive

        • Eric

          Texas Central Rail seems to be basically run by Japanese and Spanish experts and to be done quite competently. Yes this very post criticizes their financial outlook, but it seems fares can be set to double the assumption of this post and still attract riders, in which case the ROI should be about 3x what you say here.

          Maybe the solution is to sell off the Northeast Corridor to some foreign company which can run it more competently than Amtrak can?

  2. Eric

    1) According to your numbers, Pittsburgh is 3.57 times bigger than Harrisburg (2.5/0.7), but Pittsburgh-NYC ridership is 3.79 times bigger than Harrisburg-NYC (204.02/53.8). How is this possible, when the longer distance to Pittsburg and the 0.8 power for population should tend to depress ridership relative to size? I think the same question can be asked about other number pairs.

    2) How does expected population growth (rapid in Texas, almost nonexistent in the Northeast) affect this picture?

    3) What about variations in construction costs? Shouldn’t we expect construction costs on the NYC corridor to be at least twice what they are anywhere else (except California)?

    • Diego Beghin

      Re 1) The 3.79 ratio you computed is operational profits, which are a function of passenger-km, not raw passenger numbers. The ridership ratio is 5.32/2.67 = 2.

      • Eric

        You’re right, I forgot the fact that you can charge a higher fare for a longer trip.

    • Alon Levy

      Ad 2: yes, this does boost Texas, but only up to a point. Its urban growth is extremely suburban, and the CBDs aren’t getting stronger – Dallas has high office vacancy in the CBD and office growth in Plano.

      Ad 3: no, construction costs on the NEC should be lower, because the only place where large-scale civil infrastructure construction is required is Connecticut. South of New York there are maybe five locations where noticeable divergence from the current right-of-way is useful (Elizabeth, Metuchen, Frankford Junction, the DE/MD border, the West Baltimore tunnels) plus a handful of small curve modifications.

      • SB

        Aren’t you ignoring the fact current capacity problems at North River Tunnels?
        Any additional capacity will require new tunnels.

        • Alon Levy

          Yeah, I am. You can do bare-NEC service without new tunnels (lengthen the trains, get better about running them on time, and remember these trains have more capacity than the shorter express trains NJT runs out to Trenton), but yeah, once the branches start getting built you need more. But also the new tunnels should be on the order of $2 billion, it’s not that expensive to build 5 km of tunnel without new station caverns – remember that at Citybanan costs it’d be $1.5 billion with a cavern, and the underwater premium might only get it up to $2 billion.

          • Eric

            But in reality, they are already talking about spending $20 billion not $2 billion on these tunnels. And when they are actually built, the cost will probably be more like $50 or $100 billion.

          • adirondacker12800

            I didn’t read it. I’ll worry about reading it when it’s actually got funding. I vaguely remember that the study to get the money for a more detailed Major Investment Study recommended spending the money on getting freight out of Baltimore. It’s better for the freight companies.

          • john

            Yup. Which is actually fine by me, since we as a country need to move more freight by rail, and we in Baltimore are better off with a freight-path alternative to the existing B&P tunnel and the downtown CSX Howard Street tunnel. (Of course I’m not going to advocate shifting freight *away* from our port, and our city that really needs more jobs, not fewer. Except hazmats; hazmat loads that are just passing through should go somewhere less populated.)

            If you look on PDF pg 33 (ROD section IV pg 26), there’s a cost breakdown. ~$2 billion for actually building the whole thing sounds more or less reasonable, at least by current American cost-standards. The nearly $500 million for “Engineering Cost[s]” is iffier–some of those subcategories are a little vague to my outsider eyes–but not crazy excessive, just needs a little clarification, probably followed by some pruning. But then…ah yes, nearly TWO BILLION DOLLARS of sweet, sweet padding, waste and corruption, packed into the “Design Development/Risk” category, and “Escalation & Risk”, each rich in vague subcategories. The latter even contains a subcategory called “Design Development & Risk Costs” for $385 mil, even though the “Design Development/Risk” category already contains subcat’s “New Tunnel Design Development” for $573 mil, and “New Tunnel-Risk Costs” for $190 mil. And what is “Construction & F/A” ($580 mil)?

            I get that all the costs are in 2015 dollars (why tho?) and there will be inflation between now and any completion date, whether the hoped-for 2025 or later, but why not just adjust the “real” construction and engineering costs for inflation? My take, which naturally is not going to happen: Fund only the Construction section, maybe the Engineering section after clarification of what exactly the engineers are billing for, but say no to the other two categories until every tiny detail is spelled out honestly–and still say no to most if not all of it. Getting design and engineering work right before anything is actually built is critical to the built work, well, working without falling apart, but it can’t possibly cost $2.5 billion to design and engineer a $2 billion structure. And I have a hard time believing “New Tunnel Design Development” alone requires more money than all the engineering costs *combined*


          • Alon Levy

            “By current American standards” is doing a lot of work. No, $2 billion isn’t reasonable. It’s a few km of tunnel without major stations. And American rail freight volumes are in decline nowadays because of the death of coal; if the industry didn’t want to participate in the B&P replacement study in the 2000s back when volumes were increasing, it has no reason to participate now. Just make it two tracks and use the old tunnels if need be. And FFS set up an electric district, diesel locomotives don’t belong in a modern big city.

          • adirondacker12800

            Well….freight out of downtown Baltimore. I very very vaguely remember tunnel from one side of the harbor to the other. Plenty of space when the coal docks on one side go bankrupt and the tank farms on the other do too. I’ll worry about it when they find funding. Like I’ll worry about Cross Harbor across New York Harbor when they decide to fund that.

          • adirondacker12800

            I vaguely remember that they did consult the freight companies and they said something along the lines of “spend less money on something better for us”. I stumbled a across a link to the ROD because I stumbled across an article about how the NIMBYs and BANANAs have stirred up the neighborhoods who are worried about air pollution. Electric trains don’t create much. Not at the tracks anyway. Neighborhoods that have the pollution now because the current tunnels spew exhaust into them. …it’s not Amtrak’s fault that your state government is too cheap to have electric locomotives and diesel locomotives. Go talk the neighbors around Penn Station who traded electric trains for diesel trains….

          • john

            With you all the way on electrification; that’s Hogan’s unforced error, atop many years of transit being the red-headed stepchild of state government (why hello, centuries of racism and anti-urban prejudice even apart from racism! Did you know, there was once a state law requiring 16 and 17 yr olds from the city to automatically be charged as adults in all felony cases–I think it was just felonies, off the top of my head–while teens in the rest of the state were default charged as juveniles? And this was even *before* the city became majority black. It was repealed in the 1960s, but the sentiment lives on),

            Poor “current American standards” carries a heavy burden, and I’m going to have pick up some of adirondacker’s signature cynicism (it burns, it burrrnnsss…) and say that it will take at least several years, if not a decade or three, of sustained reform before that load can be lightened enough to get costs to something *actually* reasonable, like the ~$1 billion figure for the entire B&P replacement project (engineering, construction, and all) I dimly remember from the very optimistic, and generic, MARC plan a decade or so ago.

  3. Henry Miller

    How do we get competence? This is a political problem and neither party cares. Get me a speech at the ground breaking, and/or the grand opening and then I’m gone. At least in Texas it is a private company, which means the taxpayer isn’t on the hook for another wasted line to nowhere (as the Republicans will call it).

    • Matthew Hutton

      Pay better (especially at the top), make sure you follow modern workplace culture, don’t promote incompetent people to senior management.

      • Henry Miller

        Pay better… That isn’t going to be popular with the democrats that object to high salaries for the 1%. It won’t be popular with the republicans who want to be seen as cutting waste- here is the one place they can live up to the promise.

        Can you come up with something realistic? (This is a rhetorical question)

      • michaelrjames

        Pay better (especially at the top), make sure you follow modern workplace culture, don’t promote incompetent people to senior management.

        It is pretty clear from the history of the past 4 decades that this theory has been comprehensively disproved. That is, that you need to pay top rates to get top talent. In fact, all it seems to do is to ensure that you select out the greediest people from the pool. People, who almost by definition, are more interested in reward (and again by definition, easiest reward with least work or responsibility) than anything else. Such people often concentrate on fudging the figures to achieve the illusion of “success” and of course to maximise their performance-related bonuses. In the Anglosphere the only reason why some people work in government related to transit etc is to gain a few years experience so as to jump to those big-paying jobs that will reward their insider-knowledge and sometimes connections. By itself (though there are other factors) this explains why building infrastructure in the Anglosphere is so much more expensive (HS2 must be approaching ten times what Japan, China or Europe would pay) and fraught with roadblocks and political trauma.

        Interesting that it was reported yesterday that Boris is in discussions with Chinese rail builders (CRRC, state-owned of course) who claim they could build HS2 in 5 years, not the 25+y in the current plans, and at a fraction of the cost. When you consider that all of HS2 is barely more than Paris-Lyon that was built almost 40 years ago, and China has built 10,000km HSR in the past decade, none of this is fantasy … Of course the vested interests will viciously oppose any such takeover, and to be fair it is hard to see how the Chinese could do it without importing all their practices including armies of workers etc, cheap state finance etc. Perhaps he should get a firm quotation from CRRC and take it to a referendum (he’s good at that!).

        Do you seriously believe if you recruited some hotshot CEO and paid him/her a fortune, that CaHSR or HS2 would be transformed magically? No, the only way, probably now beyond political reach, is to bring these projects back entirely within government instead of the realm of overpaid consultants and financial companies who have overplayed their hand in gaming the most out of taxpayer funded projects so much that the projects are falling over before they really start.

        • Alon Levy

          Do you want me to point out the subway lines in my database that are being built by the PRC outside its borders? They’re a lot of things, but fast or cheap they’re not.

          And I don’t know about British wages, but American ones in the public sector are pretty consistently below-market at all levels.

          • michaelrjames

            That’s why I said it was unlikely–either to be considered seriously by the UK, or to be possible within an Anglosphere context. But it would be consonant with the “freedom to trade with the world” rhetoric of extremist Brexiteers.
            Yeah, ain’t gonna happen.

            Of course China does win some work on many of these big projects, just not at the serious-money end which will always be controlled by the usual suspects and their army of overpaid consultants. Take the replacement of the SF-Oakland East Bay bridge segment. Turns out no American company has the ability or experience to construct the span required so it was contracted to the Chinese who built it and then literally floated the giant thing across the Pacific on giant pontoons. But this had nothing to do with the explosion of costs of the project from $250m to $6.5bn (probably more, I haven’t kept up to date). Though there are reports the Chinese job was below spec and necessitated a lot of retro and expensive remediation; maybe but who knows. The American contractors probably negotiated a rock-bottom price to maximise their own margins, and of course all this retrospective remediation work afflicts all these Anglosphere projects to explode their costs (and contractors profits?). In her history of the project UC Berkeley’s Karen Frick “suggests that officials pay more attention to “transaction cost economics”—an approach that “analyzes project development over time,” she writes, in an effort to identify the precise “political and economic origins” of new costs.”.

            To which one can only say doh.

          • michaelrjames

            And I don’t know about British wages, but American ones in the public sector are pretty consistently below-market at all levels.

            Again, either you misread me or I poorly stated what I meant. Obviously public sector* jobs are well below market rates for equivalent jobs in the private sector. That is part of the problem; or at least the revolving doors between these sectors. It is that which needs to be squashed. Plenty of talented people are willing to work for public sector wages, and the security offered and accompanying non-compete clauses in contracts actually reinforce this, while rotating doors fuel the exact opposite.

            *An exception is at the highest levels where public servants are now paid at roughly private sector market rates, on that ludicrous principle that you won’t attract good enough talent for the job! I don’t think such a theory passed the sniff test when it first appeared in the 80s but it assuredly doesn’t in any analysis of its outcome over the past 4 decades. Of course outside the Anglosphere, there is not quite the outrageous compensation to either top public servants or private-sector management. Example is Japan, and the attempt by Carlos Ghosn to award himself globalised gangster-CEO compensation (or hide it) was assuredly part of the reason all other Japanese CEOs finally had enough and threw him in jail (which is not to defend Japanese “justice” which as a 99% conviction rate based more on “face” and “setting an example” than actual guilt).

          • Alon Levy

            At the managerial level the US still pays below-market. At the political appointee and agency head level, sure, it pays a lot, but even project managers get paid well below market wages, and are chained to the job until they can collect a pension after 25-30 year of service (and then they parachute to the private sector to work as consultants).

          • michaelrjames

            but even project managers get paid well below market wages, and are chained to the job until they can collect a pension after 25-30 year of service

            Obviously it needs to be those who have decision-making power that must be “chained to the job”.
            Honestly, I don’t know what the solution to this (Anglosphere) problem is. Once this culture becomes entrenched it is devishly difficult to reverse, and just feeds on itself like a black hole. This is my “glass half-full” for Brexit: this state of mind emanating from the UK was at risk of infecting all the EU. Maybe it already has.

    • Herbert

      We should privatize highways… Like totally deregulated, you can just buy small chunks and charge arbitrary tolls…

  4. SB

    Cross border penalty could be broken down into border control penalty and linguistic penalty.
    For example Eurostar has both, Paris-Frankfurt has linguistic and NYC-Toronto has border control.

    • Herbert

      Paris Frankfurt has lower frequency than virtually any link out of Frankfurt to a major (500k+) German city

      • michaelrjames

        Ha, maybe Brexit will change that! As (or if?) more of those international banksters relocate to Frankfurt and La Defense, surely luxury HSR will appeal to them more than even private jets which still must be tedious–necessitating, car to airport, security-theatre, and reverse at destination. (Though maybe it is possible by helicopter? Recently I read that the head of the family-owned Ferrero-Roche lived in Monaco and commuted each day to the company HQ, just north of Genoa, by private helicopter.)

        BTW, for pax using HSR between Frankfurt and Paris (and/or London) language really isn’t an issue. Even French top management speak English these days, and German elites … well, they speak better English than most English or Americans (true, not exactly difficult).

        • adirondacker12800

          If you are using your own private jet there is no security theater. If it’s rented private jet your terminal isn’t one that hoi polloi use.

          • michaelrjames

            If you are using your own private jet there is no security theater.

            Because terrorists don’t use, or hijack, private jets?
            Or is this just the prerogative of billionaires?
            Don’t answer. Obvious. No mystery how Ghosn escaped Japan and changed planes in Istanbul …

  5. oevans82

    You’ll have to forgive me for getting a little bit lost in the details here, but am I correct that this model assumes point-to-point lines between all nodes, and that all nodes are cities? Is there any way that this assumption could be changed to cause some routes that would otherwise be marginal, to make sense?

    Imagine 3 cities, arranged such that each city lies on the vertex of an equilateral triangle. Say the length of each edge of this triangle is 300km. Building HSR routes along each of the edges would involve 900km of construction, and assuming average speeds of 200km/h, trip times of 1.5 hours.

    What if we were to add another node at the centroid of said triangle, and build just a single line from each vertex, to the centroid. Assuming a high speed wye at this centroid, that would mean the distance between each of the nodes via the centroid is 346.4km, or a trip time of 103 minutes, an increase of 15%; whereas the total amount of construction drops to 519.4km, a decrease of 42%.

    Could this be used to make otherwise marginal lines worthwhile? For an extreme example, a direct, point-to-point line from Pittsburgh to Washington might be a poor performer, and connecting from DC to Pittsburgh in Philadelphia is likewise very roundabout; but if you can build a line from Washington connecting to an extant Philadelphia-Pittsburgh line at somewhere like Chambersburg, leveraging the most difficult, mountainous part of the route that has already been built, and building a line through relatively less challenging terrain from Chambersburg and then entering DC via the (mostly straight) MARC Brunswick Line.

    I have a feeling that this trick might help some of the marginal/poor corridors in the midwest and Ohio, too.

    • Car(e)-Free LA

      To be fair, just routing the line from the NEC out of the DMV area could be the best option. Philadelphia-Baltimore-Fredrick-Hagerstown-Pittsburgh is only 45km longer than Philadelphia-Lancaster-Harrisburg-Altoona-Pittsburgh. Going via DC and Dulles Airport adds another 60km. Anyway, doing this allows much easier service between the Midwest, Maryland, Virginia, and the Carolinas at the cost of serving Harrisburg. Besides, Philly-Harrisburg already has pretty good service, and expanding electric clockface service to all the cities of South-Central Pennsylvania, tying into the HSR mainlines at Baltimore, Hagerstown, and Philadelphia could open up more markets than just serving Harrisburg directly.

        • adirondacker12800

          He’s got a Hagerstown fetish.
          Using Google’s road distances as an analog for rail distances:
          Pittsburgh-DC. I-76, I-70, I-270 it’s 247 miles or 397 kilometers.
          Pittsburgh-Baltimore, 1-76, I-70 is 248/300
          Pittsburgh-Harrisburg-Baltimore, I-76, I-83 is 283/456 … an extra 60 km is 20 minutes? I-70, I-270 and I-83 go through hilly suburbs which probably means tunnels. and it doesn’t really matter much for Baltimore because relentlessly heading to DC adds DC-Baltimore to the trip to Baltimore. You want to aim for the NEC north of Baltimore to avoid tunnel in Baltimore is
          Pittsburg-Harrisburg-ClaytonMD-Baltimore-DC is 295/475. Meh. Harrisburg to Clayton is 72/113. That’s a lot cheaper than burrowing to Hagerstown.

          • Car(e)-Free LA

            Nope. The best route is almost certainly from Baltimore (with a wye just west of Baltimore) to Pittsburgh. It works out so wekk because Baltimore is just 70 km south of Philadelphia but 130 km west. Therefore, the line from Baltimore to Pittsburgh is 320 km, versus 430 km from Philadelphia or 550 km with a Harrisburg-Baltimore spur. Moreover, the Baltimore-Pittsburgh route, roughly following the I-70 corridor, requires 80 km of tunnels, just 5 km more than the route from Philadelphia. Therefore, Philadelphia-Pittsburgh via Baltimore takes 2:00. Via Harrisburg, it takes 1:40. Meanwhile, Washington-Pittsburgh via Hagerstown takes 1:30. Via Harrisburg, it takes 1:55. Somehow, I think cutting 230 km of HSR track to add 20 minutes on trip times from Philly and points north and cutting 20 minutes on trip times from Washington and points south is a good deal. Even with the addition, New York-Chicago in 5:30 or so should be possible. Using the savings to implement a takt-based electrified intercity rail system in Eastern Pennsylvania should be more than worth the money.

          • adirondacker12800

            The not the best. There’s 20 million people in metro New York and 6 million in metro Philadelphia and 10 million in Washington and Baltimore. They have 26 million reasons to want to get to New York as fast as possible and 10 million to get to Baltimore or DC. Once they get to Washington DC they can go to Virginia. Where there are just under 6 million not already in the metro DC area. Many of whom won’t be near a train station. Or they can go to Boston where there are 10 million people in Massachusetts, Connecticut and Rhode Island. Who will be near a train station. Trade ya metro Richmond with 1.2 million for metro Albany with 1.1. Decisions, decisions. 16 million people or 36 million. What they going to decide…..

          • Car(e)-Free LA

            @Alon Levy
            Just by crayoning across a topographic map of the region, looking to ensure a proper curve radius and minimize distance and tunnel length. I came up with 75 km of tunnel on Philadelphia-Pittsburgh and 80 km of tunnel on Baltimore-Pittsburgh. There could certainly be variation either way, but the bands of Appalachian mountains are fairly consistent over the area so the tunnel length isn’t going to vary too much whether the northerly or southerly route is selected. You can take a look at my maps here:

            You’re right, but is it worth the extra cost? Is it worth spending ~ $8 billion to cut 15-20 minutes off trips from Pittsburgh to the 36 million people north of Philly and adding 20-25 minutes on trips to the 16 million people between Baltimore and Charlotte? Personally, I don’t think those time savings are worth it. You could do a lot of other projects with that money.

          • adirondacker12800

            There’s 25 million people in Maryland, Virginia, DC and North Carolina. That’s eleven million less reasons to go there from Detroit, Ohio and Pittsburgh. The 36 million includes metro Philadelphia because you won’t be able to get there without going through Maryland. It’s a bit more because I didn’t include metro Harrisburg or Lancaster.

          • Car(e)-Free LA

            I get that. Regardless, going through Maryland doesn’t add that much trip time and saves a lot of money. Therefore, I think it’s the better alternative.

          • adirondacker12800

            It costs money to make 11 million more trips longer

          • Car(e)-Free LA

            But how much? How many people are willing to travel from New York-Pittsburgh in 2:15 via Harrisburg but not in 2:30 via Baltimore? I’m inclined to think the percentage decrease at that time difference is fairly small. How many more trips do you gain if you can use the $8 billion saved, for example, to add an Akron-Columbus spur onto the network and connect New York-Columbus in 3:45? I think it’s more than the New York-Pittsburgh trips lost because the trip takes 15 minutes longer. Obviously, these extra 15 minutes would affect longer trips where flying is more competitive, but even in the case of New York-Chicago, for example, I doubt there would be that big an impact on ridership if the trip takes 5:15 via Harrisburg or 5:30 via Baltimore. It just isn’t that big of a time difference.

          • adirondacker12800

            You do understand that it’s one big long unbroken suburb from Springfield Massachusetts to beyond Wilmington Delaware and to get the kinds of speed you think you can get it has to be in a tunnel?

          • Car(e)-Free LA

            I don’t think that’s true. If you want to get up to 330 km/h on the NEC, it should be possible to do above grade, but it does require significant deviation from the current NEC ROW. For example, from Newark-Philadelphia, it should be possible to complete the trip in 0:35 along a greenfield alignment without much tunneling averaging 250 km/h by minimizing curves and routing through less developed areas east of 95 or else immediately alongside already loud highways through industrial areas. The closest analogy to this is Taiwan HSR. On the other hand, by roughly following the current NEC route, it seems unlikely to complete this same trip in less than 0:45, averaging 170 km/h. At most, this greenfield alignment would cost $6 billion more than a NEC alignment (and it would free up the NEC to be used exclusively for regional rail). I’m inclined to think spending $6 billion to cut NY-Philadelphia 10 minutes is a much better deal than spending $8 billion to cut Philadelphia-Pittsburgh 15.

            A map of what this might look like can be found here:
            Green=speed limits of up to 330 km/h. (Light green is tunneled)
            Blue=speed limits of up to 240 km/h. (Light blue is tunneled.)

          • Car(e)-Free LA

            ^^ Certainly, it might not be worth spending the $6 billion to speed up NY-PHL to 330 km/h, but it seems wrong to me to spend billions extra burrowing through the Appalachians to save 15 minutes on trips from PHL and NY to the Midwest, but not similar amounts of money to cut similar amounts of time off most trips along the Eastern Seaboard.

          • Car(e)-Free LA

            ^^ It might not be worth spending $6 billion to cut NY-PHL by 10 minutes and add a lot of capacity, but it seems silly to me to spend billions to cut PHL-PIT by 15 minutes over what it would otherwise be and not make similar expenditures to shorten travel times along the much more important Northeast Corridor.

          • Alon Levy

            But Newark-Philadelphia is pretty straight… the Elizabeth S-curve is a problem, albeit a smaller one than Amtrak thinks (at modern jerk levels it’s good for about 140 km/h, and with a high 8-figure straightening it’s good for 200 or even 240+); Metuchen requires some easement to get from 160 to 250+ but what inside the controlling curve is one suburban office (=low value, low NIMBYism). The curve in the middle of the fast New Brunswick-Trenton zone has a light S-curve that can be fixed pretty easily. Then you’re at Frankford Junction, which is a bit more complicated to fix, but still, high 8 figures, maybe low 9. An N700 could do New York-Philadelphia in 36 technical minutes this way.

          • ckrueger99

            I don’t know how you account for this, but HSR to Pittsburgh that doesn’t include Harrisburg could be politically difficult in this state.

          • Car(e)-Free LA

            @Alon Levy. The issue is New York-Newark. Assuming all trains stop at Newark, it’s going to take at least 10 minutes just from NYP to I-78. That means you’re expecting to get from Newark-Philadelphia in 26 minutes. That requires average speeds above 300 km/h, which just isn’t happening. Even at an average of 250 km/h, that’s going to take 35 minutes, which means passing through central Trenton, New Brunswick, and Elizabeth at over 300 km/h. That just isn’t going to happen, and it would be pretty awful for the people who live there. You can get around this problem with a bypass along the turnpike from Newark Airport to Monmouth Junction, but that’s going to cost $2 billion, and you still haven’t fixed Trenton and North Philly.

            @ckrueger99 You might be right, but it would depend on whether this is a federal or state program. Perhaps giving the Keystone treatment to Philly-Reading, Baltimore-York-Harrisburg, and New York-Allentown-Reading-Harrisburg would be acceptable compensation. It would still cost less than HSR via Harrisburg and would connect everything of note except Scranton in the eastern half of PA.

          • ckrueger99

            There have been discussions here about AMTK ceding the HAR-PHL mainline to PA and the Keystone to SEPTA (or at least the HAR-PHL portion of it), allowing SEPTA better control over Main Line scheduling and operations. Maybe SEPTA runs those Keystones go through the PHL tunnel and head out the SEPTA mainline to Reading and Allentown in a 50/50 ratio? Hmm.

          • Car(e)-Free LA

            Makes a lot of sense. Personally, I’ve always thought all of Philly and New York made sense as a single regional rail authority (LIRR+Metro North+NJT+SEPTA). May as well unify everything from Harrisburg-Wilmington-New London-Springfield-Poughkeepsie-Allentown into a single authority with run-through trains, clockface schedules, unified fares, and consistent service patterns (metro, regional, and express trains, for example). It could make a lot of sense just to contrain Amtrak to the Northeast high speed mainline and a few other routes (NY-Albany, Baltimore-Pittsburgh, NY-Scranton-Rochester, Albany-Boston, and so on.)

          • adirondacker12800

            I want your dealer’s numbers. They have good stuff.
            East of I-95, in Philadelphia, not New Jersey, is the Delaware River and both of them squiggle much more than the existing ROW. The Turnpike isn’t I-anything south of exit 6. North of exit 6 anything would have to be elevated over the road. And over the complicated ramps that get all the traffic to a single toll plaza. Allentown is north of Philadelphia, the Main Line runs to the west. There is never going to be a tunnel to PHL because rational people are not going to take a train to PHL and pass up using EWR or BWI because the same high speed train will be passing them.

            Alon, you aren’t going to tear down wide swaths of Elizabeth. The ROW is six tracks wide on either side of Elizabeth. The trains that aren’t going to be stopping in Elizabeth anyway don’t have to pass the platforms. They can be in a realllly short tunnel that connects the centermost tracks. Until sometime far far far in the future when it needs 8, which will probably never happen. Then you build a tunnel from Secaucus to New Brunswick. Another set of short tunnels connecting the center northbound and the center southbound to each other means you can abandon four tracks through Elizabeth’s platforms and ease the curve a lot. For the trains that are going slow because they are stopping at Elmora and North Elizabeth too. Three would be nice so some of the NJTransit North Jersey Coast line peak direction expresses aren’t clogging the Trenton express tracks. Toy with that when there are 40 NJTransit trains an hour to Midtown and 20 an hour to Wall Street. M12-y things because the pantographs can’t be up in the Atlantic Avenue tunnel. Unless you are digging up Atlantic Avenue because the hipsters have been priced out Bedford-Stuy and making their way to Carnarsie and Woodhaven. And you want four tracks or even six on Atlantic.
            Turn on the terrain option in Google maps. It’s obvious why the Metuchen squiggles are there. Suburban office building? The one nestled between the tracks and six lanes of I-287 and it’s exit ramps? That might be expensive to relocate. Bite the bullet. There would be much rending of clothes and lamentation but using the very straight roads for a short cut and cover tunnel from Colonia to Edison means Metropark can have island platforms for the Trenton expresses and the once an hour Regional that stops there, using the existing tracks. And there are six tracks of ROW allll the way to Trenton except at New Brunswick. Take the fairly frequent NJTransit local to an intercity station or schedule yourself for the once an hour Regional that stops in Princeton Junction and Metropark too.
            Wilmington will be hard. Give up. They get a few times an hour on Regionals which isn’t awful because it’s almost exactly halfway between NY and DC. A bit longer matters less. The tracks etc. are going to be there for SEPTA so the expense is TVM. And some squiggles in Maryland that are out in the middle of nowhere that should be cheap to fix.

          • Car(e)-Free LA

            Look at the map for my HSR proposal through Jersey: I was referring to running the HSR line through the sparsely developed section of Jersey east of the turnpike from South Amboy to Exit 6, then paralleling 95 over the Delaware and utilizing the ROW from Linconia to Feltonville, then using the NEC, cutting off the Zoo Junction, and ending at 30th Street Station. Regarding Allentown, a sensible system without any new construction would probably look like this: That said, you’re right about there being no need for a HSR stop at PHL–it isn’t worth it, and getting out of 30th Street to the south at 200 km/h without any tunneling should be possible.

            You’re right that tearing down Elizabeth is unreasonable. That said, forcing six tracks through the city (two of them dedicated to HSR) is possible, but hitting 300 km/h+ speeds (which should be the goal) just shouldn’t happen in the middle of a dense suburb. That’s why a new alignment alongside the Turnpike through Union County makes so much sense. You don’t have to touch the NEC and hitting max HSR speeds isn’t a big deal. It certainly makes more sense than a tunnel from Secaucus to New Brunswick.

            Not sure what you’d do with more than two tracks on Atlantic. Where do you feed the trains east of Jamaica and into Westchester/New Jersey?

            The issue with running HSR along the NEC from Metropark to Trenton is the same as going through Elizabeth–putting in 6 tracks is easy but you’ll never hit the speeds you want to. A greenfield alignment through Middlesex, Mercer, and Burlington counties alleviates this.

            Finally, Wilmington should be easy enough to fix. There is no need to put up with slow speeds anywhere along the NEC except from Newark-Bronx and along the final approaches into Washington and Boston. A route through the city could look like this, with overtake tracks around the station itself, which wouldn’t require through-HSR service to drop below 200 km/h:

          • adirondacker12800

            You have no idea of the scale.

            I did look at the crayon scrawl. I lived in New Jersey most of my life you have no idea of the density either.

            There is no “east of the NJ Turnpike” for most of it. There are some wide open spaces between it and the very busy freight line it follows in Union County but then run in to leafy suburban neighborhoods that look just like the ones along the NEC. That are there because the very busy freight line was the Central of New Jersey to Jersey City. Before there was a Turnpike taking the train to get to the ferry looked real good. That isn’t going anywhere because its busy. There is no median either. The Jersey Barrier is interrupted to hold up the complicated ramps to the toll plaza. That are in the way on the east side of main roadway except perhaps at 13A. There is no “east side” of the Turnpike. Not for very straight tracks that very fast trains can travel on. Unless you want to elevate things over four levels of highway and ramps connecting them.

            There already is 6 tracks or more of ROW from Newark to Trenton with a few narrow places like the viaduct in Elizabeth which is over the abandoned Central Railroad viaduct or the bridge over the Raritan River just north of New Brunswick. That it’s only four in New Brunswick is okay, for now, because all of the traffic on the North Jersey Coast line diverges off at Rahway. Raritan Valley line and North Jersey Coast trains on the outermost tracks. North Brunswick locals and Trenton expresses on the center tracks of the three tracks that leaves all of the two tracks in the middle of those six tracks for trains to Philadelphia and beyond. That are two tracks away from anyone that will notice the noise they are making. That were grade separated and electrified before limited access highways went over them or under them. Some day far far in the future when Harrisburg has three trains an hour to New York the one that stops a lot can squeeze itself in between the commuter expresses. Unless cars and airplanes get banned that is probably enough capacity forever. If it isn’t, in 2253, they can contemplate using the New Jersey Turnpike. Skipping everything between Washington D.C. and Kearny New Jersey.

            There’s already ten tracks of railroad in East New York. The LIRR with few stops, the express tracks on the Fulton Street Subway with a few more and the local tracks on the Fulton, Jamaica and Carnarsie lines. The Fulton stops short of Jamaica, the Carnarsie doesn’t even head that way and the Jamaica doesn’t need to go past Jamaica. East of Jamaica they’ll have a choice of LIRR to Grand Central, Penn Station or Wall Street. The few dozen of them an hour that want to go to Woodhaven can change trains. That leaves space on the trains that do stop in Woodhaven for the people in Woodhaven to use. Second Avenue expresses not LIRR. That go out Utopia Parkway so the people schlepping on a bus to Kew Gardens have a train and the ones that schlep to the World Trade Center and schlep some more can schlep from a Second Avenue station. Or the ones that take the bus to Flushing to get to Midtown to get to Wall Street can get to Wall Street. You have no idea of the scale.

            Wilmington is not easy to fix because there are very sharp curves on either side of the station. When it’s six an hour they don’t all have to stop there.

            The trains don’t go to Allentown or Reading anymore because the tracks squiggle all over the place to get through the mountains. Buses are faster. To make things faster than buses you have to carve new ROW. Through mountains.

          • Nathanael

            The Philadelphia-Quakertown-Allentown route is Straighter Than You Think and would not require many improvements. SEPTA shut it for historic political reasons, nothing more.

            The Lebanon-Easton-Bethlehem-Allentown route is indeed full of curves.
            The Reading-Pottstown-Philadelphia route follows every curve of the river and really isn’t OK.

        • Eric

          If someday we need six tracks out of NYC, then yes it probably makes sense to put tracks 5+6 on the Turnpike. And possibly even follow the Turnpike past Newark, all the way to Secaucus. And possibly even follow the Turnpike south all the way to Delaware, to speed up NYC-DC (and points south) trains. And possibly build these tracks as maglev rather than conventional HSR.

          That said, we’re a very long way from needing this. In the meantime there is plenty of room for improving the existing 4 tracks…

          • Alon Levy

            The existing viaducts have continuous space for 5 tracks up to the junction in Rahway and the right-of-way has space for 6, IIRC with one incursion in Elizabeth by a parking garage that should be redeveloped anyway.

          • adirondacker12800

            The New Jersey Turnpike, by design, bypasses everything. So that things that are passing through aren’t in downtown. So does I-295 in Delaware. Put things out on the Turnpike you bypass Delaware, Pennsylvania and New Jersey. Do it with maglev the market is Washington, Baltimore and New York. You add to the mayhem in Penn Station New York because people going to Boston are changing trains there. Unless you want to build maglev to Montreal and Boston it’s not a good a idea. Then people from Delaware, Pennsylvania and New Jersey are adding to the mayhem in Penn Station because they don’t have maglev stations and want to use more conventional trains to change in New York to get to Boston and Montreal. And it’s not really amenable to at grade construction because you are running into an overpass quite often. Or the interchange to get between the Turnpike, the toll plaza, I-295 and local traffic. Bridge across the Delaware is cheaper than a tunnel across Philadelphia but it’s not cheap. But then the only reason you need a tunnel across Philadelphia is because clueless people think there isn’t any way to get from 30th Street to Suburban and that people in Connecticut and Virginia have the urge to use an airport in Pennsylvania to go to the West Coast or Europe.

          • adirondacker12800

            It does look like the flood plain regulations have kept anything except parking out of the Elizabeth River flood plain, it does flood, quite often. You are spending a lot of money and years of grief during construction so that people who aren’t stopping in Elizabeth can mosey a bit faster past the platforms they aren’t stopping at. Or you spend a bit more, avoid a lot of the grief and for a long time you don’t need a second set of short tunnels. If ever. Four short tracks of tunnel speeds up everything not stopping in Elizabeth and three tracks up on the viaduct are good enough for Matawan locals and Trenton locals. Even when there are 20 trains an hour to Wall Street.
            … Wall Street trains must go to Penn Station Newark or they won’t use them. PATH would be faster. Maybe not all of them but most of them have to go to Newark. Some of them are okay because 12 car M8-ish has a lot more capacity than 10 car PATH. You are only going to be sending 12 car trains to Wall Street aren’t you?

    • Brendan Dawe

      While I to some extent accept the assertion that the future is not retro, I wonder if it would be useful in such a situation to re-electrify the old Port Road Branch between the NEC at the Susquehanna River Bridge and Harrisburg. If you have the traffic density, and you can get enough speed out of legacy-line improvements, plausibly it would make sense as it did for the Mid-Century PRR to route Washington-Midwest trains by that route. I’d guesstimate you’d need to make the Port Road average 120 km/h to be time competitive with a all-LGV route by way of Philadelphia

      • john

        That might work, theoretically. Would have to have two slow-go sections (or short viaducts) through: Port Deposit, Md (tracks mere yards from an entire tiny town of National Historic Register buildings, plus a grade crossing leading to the town dock and riverfront condos), and Columbia, PA (another historic river town, considerably bigger than Port Deposit but not big, with the tracks too close to buildings for ~75 mph through-trains to be welcomed with open arms).

      • adirondacker12800

        Just because it looked like a good idea in 1877 doesn’t mean it will look like a good idea in 2077 when someone gets around to thinking perhaps trying to find money for studying it.

  6. Brendan Dawe

    I’m really surprised by the extent that Montreal-Ottawa-Toronto is such a dog under this model, only a 1.67% return assuming you can do it for $12B without applying any malus for the language barrier.

    Does beat Vancouver-Portland (1.5%) though

  7. Jacob Manaker

    The model handwaves the forced transfer at Penn Station – through-service from points south to Albany and points north would be excellent given expected traffic levels, but the approaches to both Albany and Philadelphia point west.

    Well, that begs the question: how much would it cost to build HSR running into Penn Station from the East? IIRC, your proposals for modernizing NYC commuter rail had a connection in the right direction Grand Central-Penn. Even without modernizing the NYC commuter lines, it looks like there’s an industrial branch running along the east side of the Harlem that connects the MTA’s Highbridge yard to Port Morris. But in either case, the route south of Spuyten Duyvil seems relatively curvy. Is there enough slack in your projections from a week ago to use it? Is there a better route?

    • adirondacker12800

      Everything will be stopping in Manhattan. The slight curves and the really sharp one south of 39th street don’t matter as much because the train will be going slow. HSR to Grand Central is fabulous if you are staying at the Grand Hyatt. Once you get out of walking distance to Grand Central you are getting on the subway anyway and getting to Penn Station instead isn’t all that much different. Meh. Not for the billions of dollars it would cost to build. And people who are staying at the Grand Hyatt have enough money for a short cab ride. Meh.

      • Car(e)-Free LA

        That said, Grand Central does have the massive new 8-track terminal for ESA service, and repurposing that for Intercity Rail and building a tunnel out to New Jersey could be an effective solution. The terminal doesn’t really have a roll in through-running NY regional rail service and Gateway alone won’t have enough cross-Hudson capacity for improved regional rail and ultra-frequent HSR. It would bring HSR service to GCT and probably cost less than upgrading Penn to 14 long enough through-running platforms with 8 tracks of feed on either end.

        • adirondacker12800

          the 160,000 Long Islanders who have been waiting more than 50 years for it to open might be a bit peeved.

          • Car(e)-Free LA

            They can make do with ultra-frequent service to Penn, NJ, and Westchester as compensation. Regardless, terminating regional rail service in the center of a city is almost always a bad idea.

          • adirondacker12800

            They have ultra frequent service to Long Island now. It doesn’t have enough capacity. Which is why they are spending 10 billion to divert people out of Penn Station. You have no concept of the scale.

          • Car(e)-Free LA

            If LIRR takes over all four East River tunnels and everything is through-running, then 40 trains per hour on the LIRR should not be difficult. That’s a train every 12 minutes per branch, or every 8 minutes if another route through Lower Manhattan is opened. Both are considerably better than what exists today.

          • Car(e)-Free LA

            That’s true. I just assumed the line from Long Island City-Jamaica was capped out at 40 tph to keep service reliable, although I suppose it might be higher. (I excluded the Port Washington branch unintentionally.) Regardless, any comprehensive NY Regional Rail plan should have all services passing through Manhattan, which frees up ESA platforms at GCT.

          • Alon Levy

            The ESA tunnel doesn’t have enough clearance for a high-speed trainset with a pantograph and catenary.

          • adirondacker12800

            37 without or without Amtrak and perhaps a NJTransit train or two sneaking to or from Sunnyside?. They finagle stuff by terminating diesel service in Long Island City, change trains in Jamaica and terminating electric trains in Brooklyn, change trains in Jamaica.
            ….. there is that pesky problem of pantographs getting torn off in the tunnel. The peskier problem is that 40 trains an hour is not enough capacity. Not if you want to relieve capacity problems in Mott Haven by sending New Haven line trains to Penn Station.
            He has no concept of the scale.

      • Matthew Hutton

        Changing trains in London (or Paris) between stations costs you at least 30 minutes, so if running the high speed railway to both Penn and Grand Central saves you that sort of time it could be worth it.

        • adirondacker12800

          If I want to get from Philadelphia to Boston I don’t have to change trains. There’s not a whole lot of changing trains between Grand Central and Penn Station involved in most trips. And it’s not that getting to Penn Station from someplace not Grand Central is awful, it can be annoying. Too bad.

  8. Med

    Sweet dreams, pal. The right of way issue will make any transportation project in a Democratic society prohibitive, both schedule wise and dollar wise.

    • Alon Levy

      Democratic societies manage to carve rights-of-way for high-speed rail just fine – in fact better than China and its high-cost viaducts.

      • michaelrjames

        Med was confusing the USA with a democratic society!
        Unfortunately it doesn’t have the autocratic power like the PRC to push public-interest projects to completion.
        No accident that it was Eisenhower, who also invented the term MIC, who knew he had to declare the IHS as a matter of national security to get it built.

          • adirondacker12800

            The Swedes don’t sit around claiming they are the richest country in the world and out of the other side of mouth say there is no money for nothing.

          • Alon Levy

            You’ll be surprised, the government keeps running budget surpluses and saying it won’t engage in fiscal stimulus unless it’s definitively sure it’s in a recession.

          • Lee Ratner

            We are getting into the very tricky realm of culture and politics. Sweden’s political system like nearly all other democratic political systems is a lot less kludgy than the American political system. The United States has a system filled with lots of veto points that makes it hard to stop and complete projects. It also has a long anti-urban bias, partially fueled by racism and partially just a hatred of cities, that other countries do not. Since transit is associated with cities, American officials tend to be less enthused about funding it and tax payers paying for it.

          • adirondacker12800

            I thought the way Keynesianism was supposed to work when the economy is good the government runs surpluses so they pay down debt and then when the economy is bad they borrow money to encourage the economy to become good again. If the economy is good they should have surpluses. Which doesn’t tell you anything about how much they spend on infrastructure or health care or education or … Or how much they spend on building fighter jets domestically so they can maintain their neutrality. And highways with long straight sections that make good runways. And viewed one way building fighter jets is just something a bit more useful than Keynes’ example of having people dig holes that other people then fill. Works that way in the U.S. too U.S. Air Force is one of the largest employers in North Dakota……

          • Alon Levy

            The way it works in Germany is, the government runs large surpluses when the economy is good and also when economic growth dips down to 1.1%. Then when the economy is bad there are brief deficits, followed by years of deficit-scolding countries with 10%+ unemployment. Meanwhile, DB is expecting to be hitting capacity problems on the trains pretty soon…

            As a reminder, the neo-Nazi party here was originally formed in opposition to bailing out Greece, on the grounds that the Greeks were lazy and didn’t deserve it. Only in 2015 did it transform from a party that was only as racist as the ordinary conservatives to an extreme-right party focusing on racism above all else (and more recently soft Holocaust denial and anti-Semitism).

          • michaelrjames

            Adirondacker actually understood my intent. The problem with the US is that it is neither a democracy–that can muddle thru and get things done–nor an autocracy that sometimes can achieve great things. Like building >10,000km of HSR in a decade. Instead it has morphed into a timocracy and now showing its long trend towards oligarcy which actually it was originally designed as. Next step, ochlocracy?

          • michaelrjames

            Timocracy is what they seem to be intent on getting in November: two billionaires duking it out for rights to play with the entire train set (I know, a poor metaphor for the US …). Maybe the next cycle will be Bezos versus Zuckerberg …

          • Oreg

            For the record, while the AfD (Alternative for Germany) is certainly racist, they are not commonly considered neo-Nazi but right-wing populist. With their far-right wing (“Flügel”), however, the distinction is indeed not clear.

          • Alon Levy

            Has Höcke been expelled? Have the people who called the Holocaust memorial shameful been expelled? No? Then they’re a neo-Nazi party.

          • Oreg

            Höcke, who is also the source of that memorial quote, is the leading figure of the “Flügel” I mentioned. A court ruled that he can be called a fascist. No disagreement there.

            As for the AfD as a whole, I think there are important differences between right-wing populists and a Nazi party like the NPD. As a result, the populists get a lot more votes in many parts of Europe these days (AfD, RN, SVP, FPÖ, Lega, VB, PVV, Fidesz, PiS, Finns, SD, Vox, UKIP etc.) and that seems to make them much more dangerous.

          • Alon Levy

            In Thuringia the party is run by the Flügel and somehow FDP and CDU thought it was fine to form a (very loose) coalition with it.

            On the list of parties you’re mentioning, I kind of want to take PiS and maybe Vox out? PiS is authoritarian and right-wing, but it is not europhobic, essentially because it views NATO as the alternative to Russian imperialism; it has a different vision for the EU, one in which refugees are sent back to die in warzones, but this isn’t the same as the europhobia of AfD, R-Haine, VB, Fidesz, etc.

          • Oreg

            Indeed, what happened in Thuringia is shocking.

            The PiS administration certainly seems in permanent conflict with the EU. Euroscepticism is common among right-wing populists but not necessarily a defining quality. That would be anti-elite rhetoric for which the EU is but one easy target.

            “R-Haine” — nice.

  9. Ryan R Kennedy

    I think you are perhaps a little dismissive of the network effects of California. In addition to LA, SF, SD and SAC you also have Las Vegas and Phoenix which are large and growing cities with strong cultural connections and perfect high-speed rail distances away from Los Angeles. The CAHSR line is being routed through the Antelope valley which would offer direct service to Las Vegas, for instance without any additional tunneling and service between SF and Las Vegas without needing to stop in LA, like the Paris bypass on the TGV for UK/BENELUX passengers to Lyon or Marseille.

    • Nilo

      Yeah and the Palmdale line is pure trash that shouldn’t be built. The line should go through the Tejon Pass to save (12!!!!) minutes of run time between LA and SF. Considering how both SD and LA are substantially bigger than Las Vegas saving almost a quarter hour and several billion dollars is not inconsiderable.

    • Alon Levy

      The Antelope Valley route costs billions more in tunnels to get to and from Palmdale. And no, California HSR is not being routed there, because the governor canceled it, mostly because costs exploded.

      And the Paris bypass is a bad piece of infrastructure and has made it harder for the TGV to expand its ridership (I wrote about this here, 2 weeks ago).

      • Nilo

        I think saying the Governor cancelled it is a little too severe. They’ll at least have all the engineering analysis done, and the Central Valley Segment built. Seems obvious that the thing to do is 2021 if there’s a democrat is seek more federal dollars. Hopefully somebody introduces CAHSR to the words “Tejon Pass” by then.

      • Nathanael

        The governor didn’t cancel it. Costs didn’t explode (it’s mostly an artifact of phony accounting procedures based on guesstimated future inflation). And the Palmdale to Bakersfield segment is almost certainly getting built. Though I have my suspicions that it’ll be “switch to low speed from there to LA” for a long time, since the Palmdale-LA process is generating no-good routes right now.

        Nobody can come up with viable Tejon Pass routes. There’s one possible but really sketchy route via Tejon which actually does go into the Antelope Valley (west of the Oso Pumping Plant) but it’s got no room for error if there are any geological problems. And if you think they had trouble with NIMBYs in Bakersfield (they did), it’ll be worse trying to run south through Bakersfield than it was trying to run east (which got approved).

        • Alon Levy

          I do not think they had trouble with NIMBYs. The signature theme of California HSR is that it constantly beats NIMBYs in court, even politically powerful ones like those of PAMPA. NIMBYs are used as an excuse to do what the HSR Authority wanted to do anyway, like Pacheco and the “muh Tri-Ciies NIMBYs” line.

    • Reedman Bassoon

      Today’s news from California transportation (
      1) The estimated cost for HSR went up (again) by $1.3 billion, to $80.3 billion. The estimated date for completing the link from the Central Valley to San Jose has moved-out to late 2031. It is estimated that 20% of the track for the Central Valley piece will be laid by 2022.
      2) Over the last four years, BART usage on nights and weekends has dropped by 10 million passengers. BART surveyed riders and the reasons given are 1) going out less on nights and weekend, 2) too few trains, 3) dirty trains, 4) fear of crime, and 5) fear of homeless on trains.
      3) In keeping with #4 above — a BART passenger was beaten with a chain in an unprovoked attack aboard a train in Oakland.

    • myb6

      Can’t answer this like our host could, but I was curious and took a stab. My spreadsheet is probably wrong somewhere but it spat out “Not Great”: assuming a round 25B in cost (prob an underestimate) and using Chi/Ind/Lou/Nash/Chat/Atl, I got just 2.7% ROI. I think for a line of that length you really need a third heavy-hitter city.

  10. jonsalmans

    Thanks Alon, great post. Your $14 billion estimate for a link between Harrisburg and Pittsburgh may be too low. PennDOT paid some engineering consultants to look into it a few years ago and they came up with a $38.3 billion price estimate.

    See the full report here:

    Click to access Keystone_West-Feasibility_Report_And_SDP_August2014.pdf

    I am not sure how to judge how reasonable their estimate is.

    I would love to see high speed rail connecting Pittsburgh, where I live, to other cities. I wonder if the higher price would be justified if the line continued from Cleveland to connect to Chicago.

    • Alon Levy

      It looks like they didn’t try to optimize alt 4 very much, e.g. it has that connection to Altoona and follows the Turnpike instead of diverging to minimize tunneling based on the performance specs of a 350 km/h train rather than a 130 km/h car.

      Then again, they didn’t try to value-engineer anything else, hence the $13 billion budget for the legacy-route alt 3, WTF?

      • jonsalmans

        The discussion on page 34 states that the $38 billion price does not include the connection between Bedford and Altoona shown on the map on page 31.

        The turnpike and legacy routes, when built, were both selected as pathways that would minimize tunneling. The turnpike route is much straighter than the legacy Pennsylvania turnpike line.

        I could see a route that didn’t follow the turnpike to potentially be straighter and therefore faster, but it seems unlikely to me that such a route would reduce tunneling or cost.

        Gannett Fleming, the consultant company that put together this report, also recently prepared an implausibly high estimate for the cost of extending the East Busway in Pittsburgh so I have some skepticism that the rail project will actually cost $38 billion. However I don’t have any firm basis for this skepticism.

        I would favor additional study of high speed rail over the $2 million hyperloop study that is Penndot’s current focus.

      • jcranmer

        Well, the Turnpike (in the Ridge-and-Valley/Allegheny Front at least) is basically the Southern Pennsylvania repurposed as a highway… which means it isn’t even based on something as fast as a 130 km/h car.

        • Alon Levy

          Between when it opened and when the US entered WW2 there was no speed limit, but I don’t know how fast cars went in practice. IIRC (from Wikipedia maybe?) cars would go 100 mph, but maybe only on some stretches but not others?

          • jonsalmans

            The Pennsylvania turnpike is pretty straight for large segments. The report I linked estimates this alignment would reduce the travel time by rail from Pittsburgh to Harrisburg from the current 5.5 hours to 1 hour 40 minutes, including the time to make two stops in between (see page 32). This corresponds to an average speed of 122 mph or 196 kph on the 204 mile alignment.

            So more higher speed rail than true high speed rail.

          • jcranmer

            Wikipedia has some pictures of 70 mph speed limits before the national 55 limit was set. However, that’s only a sign that it’s happened on some portion of the route, and the turnpike west of Pittsburgh and in the Great Appalachian Valley is pretty amenable to high speeds.

            The Allegheny tunnel and the climb up to it is still 55mph, and that’s after reengineering the approach (it used to be 45mph IIRC); the other tunnels are also still 55mph, although I suspect that’s more a tunnel thing. That said, there’s still a lot of curves in the Ridge and Valley region that are still advisory 55mph, even if the straighter sections are 70mph. It’s been quite some time since I last drove on it, but I’m definitely more comfortable traveling at 70 on I-68 than the turnpike.

          • adirondacker12800

            Pittsburgh to Harrisburg is good enough and Harrisburg to Philadelphia is good enough it means it’s too slow for Cleveland to New York and Philadelphia or Detroit to Philadelphia and nothing gets built west of Pittsburgh. Or fast enough for Pittsburgh to New York. Fly through Newark, you can watch the high speed trains not stop at the airport.

    • Nathanael

      If you’re trying to actually reach intermediate cities, which is generally desirable, the correct route west of Harrisburg is via State College, which may seem to be quite a bit of a detour, but if you’re digging huge new tunnels anyway, might as well actually stop at the only major traffic generator between Pittsburgh and Harrisburg.

      • adirondacker12800

        There are a quarter of a million people in metropolitan State College. They can get the urge to have Japanese levels of high speed rail usage it works out to a 50 passenger bus once an hour 16 hours a day to the high speed rail station with good access to the Turnpike halfway-ish between Harrisburg and Pittsburgh. Like it will be someday from Binghamton to Syracuse. Or Ithaca to Syracuse. Probably less because people who own cars will just drive to the cheap parking at the station.

        • Matthew Hutton

          Honestly I think express buses to an outlying station on HSR is an underrated way of doing things.

          • Eric2

            If they are timed to match the trains, which I’m sure half of operators will screw up.

          • adirondacker12800

            The bus is going run once an hour. There will be multiple trains in each direction.

  11. anonymouse

    Using this ridership model, it looks like the strongest corridor in Mexico is Mexico City-Queretaro-Celaya-Irapuato-Leon-Guadalajara, with a branch to Aguascalientes, and each segment of the line adds substantially to ridership. Puebla does quite well too for such a short line (though one that would likely have significant geological challenges threading its way between volcanoes, likely with a lot of tunneling), and becomes more worth it as part of a wider network. The geography heading north toward Monterrey is much more challenging, given the huge gap between San Luis Potosi and Saltillo, and the not exactly huge sizes of those two cities, and it seems most of the value in that corridor comes from connecting to Mexico City.

  12. R. W. Rynerson

    Thank you all for this analysis. In miniature I’ve seen Metcalfe’s Law working on suburban transit networks.

    Regarding American attitudes concerning electrification, you overlooked Colorado’s commuter rail “S-Bahn” lines. If their wired mileage was laid out from Arvada on the Moffat Line it would reach to Denver’s Winter Park. (Both GE and Westinghouse pitched electrification of this line in the steam-to-Diesel transition.)

    In development of the Colorado system, however, I witnessed rather direct lobbying for Diesel operation. And the B-Line’s proposed extension into Boulder County is tangled with many issues, including upscale neighbors who oppose electrification that might affect their view of the mountains.

    • Alon Levy

      Denver’s system is just weird. It looks like a modern S-Bahn system but with lines in the middle of nowhere, with very little development, I think?

      • adirondacker12800

        You don’t want me to find pictures of the what is now the Flushing line being built through farms do you? It’s a lot cheaper to build it through the middle of nowhere and then zone it for higher densities when it’s nowhere than when it’s somewhere.

        • Alon Levy

          Queens’ population had doubled in the previous decade and would double in the next one. Nowhere in Denver are such growth rates happening.

          • adirondacker12800

            Twice not-much isn’t a lot. Ten percent of a lot is much more. Traffic congestion isn’t lineal, it goes from “this is bad” to “I could get out and walk faster” very quickly. And when it does that there’s no place to park. WIkipedia says the A line in Denver, the one that uses 60Hz only Silverliners without traps, gets 20,000 riders a day. How that compare to busy SEPTA lines?

          • Michael Noda

            I presume Adirondacker’s question is rhetorical, but for anyone who’s curious, the busiest SEPTA RRD line is Paoli/Thorndale, with just under 21K riders per day. Second place is Lansdale/Doylestown, with 16K riders/day.

      • R. W. Rynerson

        a-12800 is right, the Denver “S-Bahn” is built to lead development as well as serving existing traffic. There’s always a question as to whether that’s a good idea, but “fixed guideway” plans under state law have to be approved by the Denver Regional Council of Governments, as well as the normal NEPA process favoring NIMBY’s and consultant-driven planning. Ironically, the DRCOG requirement was part of a 1990 effort to stop the Regional Transportation District from building rail lines. It backfired.

        The Denver commuter rail lines are all integrated with the bus and LRT system, so the lack of walk-distance ridership is not a complete disadvantage. And developers are rapidly filling in the walk real estate gaps. I should add, however, that one should be wary of 2019 and 2020 ridership numbers because of labor shortages on connecting bus and LRT lines that are leading to horrible cancellations. (I shudder to think of how short of operators this system would be if it was all BRT, as proposed in the 80’s.)

        Here’s some other information that can be correlated with maps:

        Click to access rail-station-activity-May19.pdf

        This is summer APC data, so it’s low, but latest posted and picks up new stations. Friday, Saturday and Sunday data by stations is not posted because it goes up and down like a yo-yo due to sports events and festivals.

  13. myb6

    Really interesting article.

    Using your formulas, an isolated tripod from Toledo covering (Milwaukee, Chicago, South Bend/Elkhart, Toledo, Detroit, London, Toronto, Cleveland [pop 3.5 to be consistent], Pittsburgh), and excluding all P-km from Toronto->Cle/Pitts because it’s the wrong way round Lake Erie, and my quick/dirty (and probably wrong somewhere) excel spat out 21B P-km for $1.4B operating profit. Based on your construction guesstimates, infra should be on the order of $30B, so 4.5% ROI. Would appreciate if someone were inclined to double-check this.

    Obviously Toronto an important component, but even if we hack off 1/3 of the international P-km as a penalty, I got 4% ROI.

    In the spirit of Metcalfe, it’d be nice to then compare ROIs once we account that the tripod would connect to keystone and northern-x and thereby the NEC. That’s too many city-pairs for me, given that I’m supposed be working.

    • Alon Levy

      Yeah, Chicago-Toronto and Detroit-Toronto make Chicago-Detroit-Toronto look better. And then there’s nontrivial p-km out of New York-Detroit, New York-Chicago, Philadelphia-Detroit, Philadelphia-Chicago.

      • Nathanael

        I’ve often said, with nothing more than the general principle of network effects to back me, that after establishing decent, reliable, reasonable-speed service on the NEC and its branches, next priority is to connect the “NEC network” to Chicago and its branches. Just hooking the two networks together properly has huge network effects.

        Alon, however, has given the first quantitative model I’ve seen of the network effects.

  14. adirondacker12800

    a hefty share of the figure comes from city pairs that trains would connect in 3.5+ hours, like New York-Charlotte

    The meme of 3 hours or 500 miles/800kilometers comes from before going through an airport took so long. It’s more like 4. And places with lousy airport access, more. 4-4.5 has even wended it’s way into Wikipedia’s article on high speed rail with a respectable citation.

    3.5 for Manhattan isn’t bad. It’s Manhattan. …….You’ve been to the airport…

    A really quick check of Google’s flight information the non-stops from Newark to Charlotte are two hours. Curb at Penn Station Newark to when the doors close on the train is 10, 15 minutes, and that is generous. Curb at Newark Airport to the time the door closes on the airplane is an hour and that would be risky. From the time the door opens on the plane to the time I get to the curb is lonnnnnnnng. Not as long as getting on the plane but we all go through one door and there is a trek to the curb. At any airport. Even if you are really lucky and get a gate close to the curb. 3:15 to Charlotte looks real good. So does 3:30 from Manhattan. Especially if I’m doing EWR-CLT because I’m still eating the time from Penn Station New York to Newark Airport. On train that loitered at Secaucus and has a longer than usual dwell at Penn Station Newark. Pesky PATH passengers.

    Four hours is quite good for the major stations on the NEC. And longer for Manhattan considering the pain of getting to and from the airports.

    • Luke

      I still tend to feel that comparisons purely with air travel slightly misses some of the U.S. (maybe North American) case against high speed rail. For one, over *most* (not all) distances that high speed rail is or could plausibly be the dominant mode of travel, it competes with buses and (again, especially in the North American context) cars, not planes. This dovetails unfortunately well with the autocentrism of most (North) American cities, and therefore cars are already a sunk cost for anyone who can afford one. The marginal utility cost is therefore higher in basically paying for a new transit use mode (a train) because you’re already paying for another (a car). The data in this link is somewhat older, but cars maintain a dominant mode share up to distances of slightly >1000km, because people already have a car, because they need one to get around their hometowns. ( Especially as a lot of American hub cities are, themselves, fairly suburbanized and autocentric, unlike countries with very dense primary metros well-served by public transit but less dense and less well-served secondary cities (I’m thinking particularly of France, Spain, Italy, and South Korea), there is no terminus of most trips which are not as-well (or better) served by a car as they are public transit

      This does get into the messy discussion of how to deautocentrize (neologism for the day) American cities, for the sake of equality, environment, and marginal utility (which still ultimately favors free time on a train in transit-oriented metros over lost time driving in auto-oriented ones), but the truth is that it seems like it ought to be easier to get people to use public transit if A.) they’re already used to it on a regular basis, and B.) they don’t have resources already locked away, awaiting to be utilized, in their driveways. As satisfying as these back-of-the-book calculations are, and as simple as the solutions they suggest ought to be to implement, the primary obstacle–until it goes away–is going to be our idiotic dedication to using the least space-efficient travel mode available, in every situation, regardless of how much sense it makes, even if it means local air pollution and global warming, sitting in endless traffic jams, wasting valueless money and invaluable time.

      There’s not a revelatory word in anything I’ve said, but sometimes it feels like the beatings must continue until morale improves.

      • Herbert

        People who take a bus need a non car connection. As do people who fly. And you can set up car rental at the train station same as at the airport…

      • electricangel

        For one, over *most* (not all) distances that high speed rail is or could plausibly be the dominant mode of travel, it competes with buses and (again, especially in the North American context) cars, not planes.
        I’d have to disagree here, having used bus, rail, and plane to commute between NY and Boston.

        Planes require travel to an airport, which is not in the central region of the city. In Boston, there is a bus to a heavy rail subway to get to downtown; the same situation obtains in NYC, where the Q70 does a very good job of swiftly transporting passengers from LGA terminals to a subway in Jackson heights and the LIRR at Woodside. Both bus shuttles to subways suffer from the threat of airport traffic delays, with Boston’s having a maddening 10-minute stop at the car rental counter on the way TO the airport. Even so, I only had two issues with both buses overall causing delays due to variable traffic loads.

        Buses and trains both originate within the central core of the city. Buses have a slight disadvantage here in that it’s economical only to run them downtown to downtown, skipping intermediate cities excepting maybe New Haven. City to city, it’s possible to pay as little as $12 on a bus. Trains stop at intermediate cities. In the NY area, these are New Rochelle, Stamford (a particularly important node,as it’s an Acela stop) and places in NJ I didn’t care about; in Boston, route 128. So it’s possible to dwell in an outlying area and still take a train, but not a bus.

        The last issue is timeliness. In all my bus rides, I literally NEVER experienced an on-time arrival. I suppose to be on time you would need to leave NYC about 10AM to arrive Boston about 2pm, meaning no work in either city on either end. The train is reliably on time, with worst delay being maybe 25 minutes (buses were regularly 2 hours late). Planes between LGA and Boston were on time if one took the first flight of the day between the two cities, with only one of those being late (later planes were often delayed because the aircraft was delayed in arriving at either city). It is not possible to take public transit from NY Suburbs to the airport for the first flight of the day (too early for trains), so this necessitates a taxi fare of $50 at minimum, plus plane fare, a cost over $110 each way. Trains go for as little as $39 for Northeast Regionals and $79 for Acela.

        I guess the point here is that rail competes for the business of travelers whose arrival time is time-sensitive. Here travelers simply cannot take the bus because of unpredictable traffic delays, the same delays that may afflict cars. The bus riders may upgrade to rail if it is cheap enough: rail at $19 between both cities would collapse the bus market. But generally, bus passengers have no better use for their time but to waste it sitting on buses that aren’t costing them a lot of money to get where they are going.

        By contrast, no amount of cutting fares makes the bus attractive to the traveler who needs to arrive in a city center at a predictable time. Both bus and plane are subject to traffic and weather externalities that cause uncertainty in arrival time; the uncertainties with air mean that the time-conscious traveler must allocate an additional hour of buffer time to the expected other times (30 minutes to the airport from downtown; 20 minutes security theater [which is a non-issue on Bos-LGA shuttle flights for Trusted Travelers. I made a Noon departure once after getting off the airport bus at 11:40 in Boston], 90 minutes’ flight including taxiing and sitting in the plane, and then 30 minutes to downtown on the other end) for a total of about 230 minutes, essentially 4 hours, or the exact schedule of the first Acela leaving ny at 6:15 to arrive Boston at 10:15.

        Given that Acela can be cheaper than flying if purchased ahead, and that all the seats are the size of first class on a plane, and that basically all the time on the train can be dedicated to work, its already plane-competitive. Get the time down to 2 hours so that one could depart NY at 6:15 and arrive Boston at 8:15 and no one would take a plane; for now, a plane is the only way to wake up in either city, work 9-5 in the other, and be home by 8:30 pm.

        Tl;dr: buses and rail compete only when rail fares drop to attract bus passengers. Otherwise, they appeal to different categories of travelers entirely.

        • Alon Levy

          Remember that the average rail fare here per p-km is about on a par with the lowest Regional fare bucket. I chose the $0.135/p-km figure specifically for compatibility with the $49 figure for NY-DC and NY-Boston, but it’s right in the middle of ICE and TGV fares. I moreover picked a fare system in which fares are mostly linear in distance, specifically to compete with buses at the short end rather than with planes at the long end; TGV fares are fairly insensitive to length, so that Paris-Lyon, Paris-Marseille, and Paris-Nice cost about the same because Paris-Lyon is effectively a monopoly whereas Paris-Nice is competitive with air.

          • electricangel

            Yes, it’s interesting that your fare of $49 buys an ICE in Germany and a much-slower regional here.
            The fares are expensive here compared to the bus. Even so, they’re quite affordable compared to the plane. Getting HSR to 2 hours NY-BOS basically ends flying between both cities. I imagine that Bos-DC will remain mostly air, but 4 hours via rail gets close.

        • adirondacker12800

          It is not possible to take public transit from NY Suburbs to the airport for the first flight of the day

          If you are a masochist and want to fly in and out of LGA it involves a bus. That runs 24/7 and connects with the subway that runs 24/7. And the LIRR that runs 24/7. NJTransit almost does. First train of the day from New Brunswick to the airport leaves at 4:14 AM and arrives at Newark Airport at 4:50. There are two after midnight, the 12:18 and the 1:40. Both Airtrains run around the clock, on lousy headways in the dead of night but they run. But then if I have to catch the first flight of the day it’s likely to make an early business meeting, I’m on an expense account and the limo to the airport is “free”. And there is a low risk of traffic delays. YMMV if it’s the reverse.

          • electricangel

            I should have said northern suburbs. The first LGA-Bos flight of the day is 6am. The earliest any train stops at 125th Street, where one might catch the M60 to the airport, is about 5:30. If you had a train stopping at 125th at 5am, you might make a 6am flight by bus, given the short TSA delay if you have pre-check.

            Net result from north of the Bronx is that you have to take a car service, or catch the first Northbound train at Stamford. For those not on an expense account, it breaks the camel’s back.

          • adirondacker12800

            If you are on the Hudson line or the Harlem it’s not easy to get to Stamford. And that’s only the people between Larchmont and Stamford because the same trains stop in New Rochelle. There’s a 3:27 that has lots of padding in it’s schedule to account for delays from overnight maintenance that gets to Boston at 7:58. The next one is the 7:01 which gets to Boston at 10:03. That’s a bit late for the first flight of the day to have you in Boston. It’s just too bad the dozen people a month this affects are too frugal to hire a limo.

          • electricangel

            In an alternative realty, the new Tappan Zee bridge would have rail lines across it connecting to Tarrytown, White Plains, and along 287 to Stamford. But since it’s a Cuomo production, no. Getting to Stamford is long and expensive for Hudson Liners, who must change at 125th and pay the fare to goto GCT. Harlem liners can change at Fordham, saving the 8 minutes each way to 125th, since most Stamford-bound morning trains stop there. Even better would be to have NH line trains stop at Woodlawn, shaving an additional 5 minutes in each direction off the travel time.

            “It’s just too bad the dozen people a month this affects are too frugal to hire a limo.”
            Well, there’s something of bad transit planning in that statement. Poor transit system design means that many economic opportunities go unseized. One benefit of being poor in NYC is that The Whole city is accessible for about $65 a month (new poor-favoring monthly pass), so that it’s possible to expand economic opportunities. The travel costs being needlessly inflated by system issues means that, yes, the “dozen” people are affected, and dozens Or hundreds more don’t even take the opportunity because the economic benefits barely exceed the costs.

            I know of a few people for whom increased income and perhaps opportunity was ignored because of the cost of the bridges between the Bronx and Queens. I recall the plan to toll the EastRiver bridges leading to Manhattan while cutting the toll between the Bronx and Queens, and the logic: there are reasonable public transit methods to get to Manhattan, but none between Long Island and the Bronx/Westchester. It wouldn’t stop me, and probably not you, but it moves the needle on acceptable pay substantially higher for the poor on both sides of the river, and so decreases overall regional activity.

            Alon’s post on the decreased-depreciation bonus to NYC residents of transit investments makes this clear. Good transit to airports is opposed by limo companies at the expense of all of us.

          • adirondacker12800

            You want to catch a six AM flight in most of the rest of the world the trains haven’t awoken from their slumber yet if you have to be at the airport at 5 to check in and go through security. They wanna cut the toll because they wanna to cut the toll. Right now if the toll is too high for their tastes there are free crossings they can use, they don’t. Ask New Jerseyans about tolls sometime.

            People who live in Rockland County work in Rockland County. If the don’t work in Rockland county the likeliest place they work is New York County(Manhattan). They already have trains to Manhattan. The next most likely place they work is Bergen County which is where the trains they take to Manhattan get to first. Then Westchester. There aren’t enough people living in Orange and Rockland that work in Westchester for trains and there definitely aren’t enough of them in walking distance of at least one end. People aren’t going to take a bus to the train station, take a short train ride and then get on another bus. Not all of them work hours where there would be anything approaching frequent service either. Or congestion. There aren’t enough Rocklanders working in Westchester for trains.

    • Alon Levy

      It’s not a meme, I’ve criticized the “nobody rides past 3 hours” line that so many SNCF execs believe in in previous posts. However, since the model I’m using for ridership is based on existing city pairs up to about 800 km, and the two longer ones are 1,000 km with one underperforming (Tokyo-Fukuoka) and one connecting to a specialized tourist region (Paris-Nice), I’m less certain in the results in that range.

      • Matthew Hutton

        There are loads of Chinese lines that are over 1000km, or do you not have data for them?

        • Alon Levy

          I don’t, and I also would somewhat discount Chinese data because I expect China to underperform the first world relative to speed and price (of note, China charges somewhat lower fares than Europe and is substantially faster than both Europe and Japan).

          • Herbert

            Chinese aviation is also severely hampered by airspace restrictions imposed by the military and some arguably overtough safety regulations such as no flying in inclement weather

      • adirondacker12800

        Three hours from Paris you begin to run out of France to get to. They have an incentive to continue to believe it. Paris to Toulouse is roughly the same distance as New York to Pittsburgh. Or Pittsburgh to Chicago. Or New York to Buffalo. Or Buffalo to Chicago.
        I wouldn’t take the train from Boston to Chicago or New York to Chicago. Assuming Chicago to Cleveland gets built and NY to Toronto gets built, building all of Ohio, on the “Three Cs” high speed line, to Toronto makes sense because it’s really flat and really straight between Cleveland and Buffalo. Chicago-Boston is “free” because building Boston to Albany makes a lot of sense without Cleveland and beyond. Buffalo and Pittsburgh are roughly halfway between Chicago or Saint Louis and the East Coast. You are tripping over things that make sense in their own context and connecting obscure trips is “free”. This zigs and zags all over the place. Pittsburgh-Cleveland-Toronto is 425 road miles or 683 kilometers…. People have mentioned that getting to the airport in Pittsburgh is no fun, I’ll spare you the horror stories. I know what it’s like out at the airport in Pittsburgh. There’s airport. Pearson isn’t anything to write home about either. It’s an hour and five minute flight and customs and immigration sucks up an hour at Pearson. And expensive. From the curb at the airport to the curb at the airport is three hours if things go well. I’ll leave it to you to divide 683 by 3. Boston to Cleveland is iffy but if I’m starting off in Worcester or Hartford it a looks bit different. ……There’s all sorts of odd things hiding in a network across the Midwest and Northeast.
        ….scale? Chicago is the Midwest’s Paris and New York is Paris and and every aires urbaines in France over a million people. You are tripping over things across the Midwest and Northeast….. if Buffalo is Toulouse and Chicago is Paris, Cleveland is Lyon. Pittsbugh-Cleveland-Chicago is Paris-Lyon-Lyon.

        • Matthew Hutton

          New York Chicago by train could be done in 4.5 hours at the fastest speed of Beijing Shanghai. That feels doable.

          • adirondacker12800

            Not if you want to stop in Cleveland and Pittsburgh. Stopping in North Philadelphia wouldn’t take too long but stopping in Philadelphia would involve turning the train around.

          • adirondacker12800

            You want to make from New York to Chicago in 4.5 hours you don’t stop in Scranton, you don’t stop in Cleveland and you don’t go anywhere near Pittsburgh or Philadelphia. It would be I-80-ish. If you want to make it Chicago-Cleveland-Pittsburgh-Philadelphia-New York it’s much longer. Actually going to the main station in Philadelphia involves a few miles diverging off the route to New York, turning the train around and going back out to the line to New York. Or you stop at North Philadelphia. Or you don’t stop at all. The famous trains didn’t. You took other trains if you wanted Philadelphia. And the the less well know trains, ones that were going to New York stopped at North Philadelphia.

      • Luke

        The problem is less distance than the necessary mode shift to even get people to take a non-car between, e.g., the ~700km Albany-Cleveland trip, or the ~500km Harrisburg-Springfield trip, when most people already own a car and are invested in it as a capital expense, and there’s statistically no transit at either end of their journey, anyway.

        Ultimately, it is a major chore to drive drive these kinds of distances, and suboptimal on basically every axis, but when you’re already inoculated to the hassle of driving from doing it every day, anyway, it seems less so, and when there’s no choice (because of the “freedom” of requiring everyone to own a car to get anywhere), you stop thinking about how little sense it makes. I can’t tell you how many people I’ve talked to in my Greater Boston area town (Manchester, NH) for whom the fact that the whole region would be better served by being less suburbanized and served by good transit is just, like, alien to them.

        I wish I could edit posts here; the message was–as has been stated elsewhere–get people into good, efficient bus services first, and build your settlements around them, and good intra- and intercity rail service will (ceteris paribus) flow necessarily from that.

        • Alon Levy

          Yeah, there’s a reason I keep saying I’m skeptical of things that don’t touch New York for this reason. That said, the TGV maintains respectable mode share in parts of France with bad public transit (Bouches-du-Rhône has a mode share of like 13%, about the same as metro Boston’s, and Paris-BdR overperforms Tokyo-Sendai by a factor of almost 2 even ignoring the distance penalty).

          • Car(e)-Free LA

            To be fair, there are more cities than just NY with acceptable transit and which aren’t particularly car friendly. DC, Toronto, Philadelphia, Chicago, and Boston come to mind as places I’d rather not have a car to deal with. Even cities like Atlanta, Baltimore, Charlotte, are fine as car-free destinations for most non-VFR traffic.

          • Luke

            Yes, but that’s the Riviera; Sendai is not a significant tourist destination; international travel, despite the language penalty, would play a role, there as well, while being relatively even more trivial for Tohoku (especially post-Fukushima Daiichi). The population dynamics are different, too. Like the rest of non-Keihanshin Japan, Sendai is at best flat pop. growth, whereas like the rest of Southern France (and France generally) population growth continues, aided in part by immigration. Bringing the comparo back to the U.S., neither of these countries have the “transit is for losers” mindset that has so long predominated most of the U.S. Again, I’m not bringing up some revolutionary idea that the main barrier to the U.S. making sense (in this context, but also generally) is us just not being quite so thick-headed, but these fairly obvious solutions to ultimately surmountable problems are going to take a lot of not-so-obvious solutions to these ultimately cultural (i.e., messy) problems.

          • Alon Levy

            The Riviera does have a transit-is-for-losers mentality, but you’re right that Paris doesn’t (although the richest parts of Paris have a hefty share of car commuting).

          • Herbert

            The political consensus in Paris seems to be decidedly anti car if election manifestos of mayoral candidates are anything to go by…

          • Alon Levy

            Yeah, and Hidalgo seems to be winning reelection handily, because like Macron at the national level, she’s the least popular option except for all the alternatives.

        • adirondacker12800

          Cleveland has halfway decent transit to lots of places. If the choice is flying to Cleveland or taking the train to Cleveland – from Albany – the train looks real good. Especially since at this moment in time there are apparently no non-stops and flying to Cleveland involves Detroit, Philadelphia or Dulles. Google’s drive time is just over 7 hours and that assumes 65 miles an hour all the way. My bladder isn’t up to that. If it’s not transit friendly, the toll on the Thruway is $15.20 for EZ-PASS. I’d have $15 to go towards cabs.

  15. koranteng

    Odlyzko and Tilly, contra Metcalfe, suggest a lower bound, more like n log(n) for the value of networks and network interconnections at least based on the value of a few general communication networks. Presumably plugging in their models would affect your calculations.

    See A refutation of Metcalfe’s Law and a better estimate for the value of networks and network interconnections

    Click to access metcalfe.pdf

    • Alon Levy

      Ooh! It’s a really cool article, and Odlyzko has been a big influence through his monograph on the Railway Mania.

      I will say that I did incorporate a gravity model with an exponent of 2 into my model. I will also add something that is mentioned in one of Paul Krugman’s blog posts that Odlyzko doesn’t mention but is probably aware of: not all nodes are of equal value, so a starter system connecting to just the first few nodes can succeed. In the context of British railways, the four largest cities (London, Birmingham, Manchester, Liverpool) were all connected to one another by the same system by the early 1840s, before the Mania, and the financial success of this system is one of the factors that led to later overinvestment in weaker schemes. In the context of Krugman’s example, telegraphs, it is noted that early telegraph lines in the US were built quickly and successfully by connecting the largest Eastern cities.

      Likewise, here I claim that the ROI on the initial Boston-NY-Philly-DC system exceeds that on nearly any subsequent extension, because these are at the end of the day four huge cities on the same line at appropriate distance, a situation that does not occur elsewhere in North America.

  16. Aaron Moser

    “Texas is currently building a Dallas (8)-Houston (7) high-speed line, using private money by Texas Central, a railroad owned by JR Central using Shinkansen technology. The model predicts 7.5 million annual riders between the two regions, and the system’s public ridership projections for the near term are pretty close.”

    No they have not started construction regardless of what the endless number of boosters in the media may claim. Texas central uses estimates that defy belief. Most supporters say its a busy air route but that fails to consider that many of those flights are connecting flights that could not compete with HSR unless it had airport stops and it will not. Southwest has very large hubs in both Houston and Dallas, American has a big hub in Dallas, United in Houston. You are not going to get that connecting traffic. The only way Texas Central can get its estimated 5.9 million riders is if between 60-80 percent of car users on the route switch to the train and that is not going to happen.

    • Alon Levy

      Yeah, Dallas-Houston has about 1 million O&D air travelers. But that’s fine – at that range the car dominates on O&D traffic, and very high HSR mode share even taking cars into account is likely.

      The first problem is that all of this assumes travel behavior is consistent with what is observed in cities with public transportation; the second is that the construction costs are higher than I’d like by a factor of 1.5-2.

  17. Herbert

    Which results does your formula produce for German city pairs?

    And isn’t a problem the widely different definition of “city population”? Or even “metro area”? They might be somewhat consistent within one country, but across countries there’s often no comparability

    • Alon Levy

      It’s really hard, because the definitions of metro area here are weird. For example, how many people should I count in Munich? I’m tempted to look at the entirety of Oberbayern, at 4 million, because Ingolstadt is on the Berlin-Munich line, but then it’s probably better to just add up Munich and Ingolstadt separately?

      That said, Japanese and Spanish definitions are pretty similar, I think, and French ones are close enough for government work.

    • Mikel

      I was going to ask the same question after trying to use the formula on Barcelona-Andalusia HSR ridership. The population of Barcelona is difficult to define, because it has several layers of suburbs… The official metropolitan area population is 3.24 million.

      For what it’s worth:
      ·Sevilla: metropolitan population 1.69 million, 830 km to Barcelona. The formula then gives an estimate of 424K yearly riders. In 2014, the HSR ridership was 215K. There were also 882K air passengers in 2016.
      ·Córdoba: metropolitan population 0.36 million, 710 km to Barcelona, so estimated ridership = 168K per year. There were 234K riders in 2010, with no air connection.

      In these ridership data only direct trains are counted (i.e. those that bypass Madrid; there is an indeterminate number of passengers transferring at Madrid-Puerta de Atocha), and their frequency is terrible: 3 trains per day in the summer, 2 per day the rest of the year. On the other hand, their average speed is good (195-205 km/h) and the historical/cultural connections between Catalonia and Andalusia are particularly strong.

      • Herbert

        I find it exceedingly weird that Spain is so good at building high speed rail lines yet so terrible at running them efficiently.

        If you build a line, why run anything less than hourly? If speed increases don’t cost much, why not opt for España-Takt?

        • Mikel

          Yeah, it’s very frustrating. The only corridors with such frequency are Madrid-Barcelona (2 tph peak, 1 tph off-peak) and Madird-Sevilla and Madrid-Valencia (~1 tph, kind of). Madrid-Córdoba has better frequency thanks to the interlining of trains from Madrid to Sevilla, Málaga and Granada.

          There are a few reasons for this. The main limitation is Renfe’s weird policy for purchases of rolling stock. There are currently TWELVE* different classes of trains running on the high-speed network, from four different manufacturers and each with different limitations. And they recently placed a “huge” order for… 30 trainsets of two classes. Another problem is that it’s actually three disconnected networks: one radiating from Madrid-Puerta de Atocha, another heading north from Madrid-Chamartín, and a third one joining the Galician cities (a fourth one, the Basque Y, will open in 2024). Combined, these two problems lead to scheduling being kinda complicated, and new branches opening with like 4 trains per day (Granada last year, Burgos and Murcia in the near future).

          As for a country-wide takt, I’m not sure if it’s possible unless you mean a pulsed network centered at Puerta de Atocha, bacause the network is too radial for that and many cross-country trips go through Madrid anyway. The only major crossroads are at Antequera (which already has something superficially resembling timed connections) and Zaragoza (which is limited by the single track tunnel through the city — yes, an actual example of underbuilding).

          *Those are classes 100/100F/102/103/112 (fixed gauge intercity, the 100F can also run in France), 104/114 (fixed gauge regional), 120/120.05/130/730 (variable gauge intercity, the 730 can also run in diesel mode), and 121 (variable gauge regional). Crazy.

          • SB

            Galicia HSR also did opposite of following Metcalfe’s Law by building intra Galicia sections first and not Madrid-Ourense.
            At least Basque Y and Basque-Madrid HSR should be completed at same/similar time.

          • anonymouse

            Galicia HSR was done the way it was because there is approximately nothing between Galicia and Madrid. The biggest city on the way is Zamora, with a population of 60k, whereas Galicia has a number of cities in the 100-200k range that it made a lot of sense to connect before tackling the long route through difficult terrain to Madrid that seems to be too heavy a lift to do all at once and would have been not very useful until it gets at least to Santiago. Also, Coruña-Vigo is short enough that I am sure parts of it are used as a commuter service and it should be viewed more in that context than as a proper HSR.

          • Mikel

            @anonymouse, I don’t think that much thought went into the priorities — the time between start and completion is very different between the intra-Galician network and the Madrid-Ourense mainline because the former happened to be in a more advanced stage of construction when the 2009 recession hit, so it was opened in 2011 while the timeline for the latter was stretched all the way to 2020/2021.

            Indeed, the high speed commuter services inside Galicia have proven pretty succesful, if only because it’s one of the few places where Renfe bothers to offer something resembling 21st-century service. There are even timed connections between the regional trains and the ones that continue to Madrid on the legacy mainline!

  18. Onux

    How would Texas look if the first line were built Hou-Temple-Dal instead of direct Hou-Dal (i.e. two legs of the “T-bone”). Obviously Hou-Dal would take longer, but I’m thinking of being able to add Austin-Dal, San Antonio-Dal, SA-Hou, etc., etc. trip pairs just by completing the line down I-35 from Temple to SA (this also picks up Waco, Killeen-Temple, and College Sta., but combined they are not that large.)

    The TCR route (one leg of the “Texas Triangle”) would require building the entirety of I-35 to get Aus/SA-Dal, but wouldn’t do much to either to Hou.

    • Car(e)-Free LA

      It should be possible to complete the triangle without building full-length legs even with the TCR plan. The Dallas-Austin leg can diverge from the mainline in Navarro County and have parkway stations to the east of Waco and Temple, and the Austin-Houston leg can connect in at Temple and College Station. The harder thing to work out is if/how to serve the rest of the Metroplex, given Downtown Dallas is sort of in a corner.

      • Eric

        I think you go west along Trinity Railway Express (which, incidentally, desperately needs upgrading itself…), then turn north to DFW where there is a second stop, then someday the route could be extended north to OKC and Tulsa.

    • Alon Levy

      The model is not precise enough to look at differences in ridership by how direct the routing is, unfortunately. I think the T-bone is not necessarily the best idea, though, since Dallas-Houston is so circuitous. Perhaps a reverse T might be better, with Dallas-Houston direct (with a slight kink to hit College Station) and then San Antonio-Austin-College Station providing slightly circuitous service on the other two legs of the triangle. This cuts off Waco and Temple, but neither Waco nor Temple is such a big city that it’s that big of a deal.

      I emphasize the word “perhaps” in all of this. Houston is 7^0.8, the San Antonio-Austin leg is 2.5^0.8 + 2.2^0.8; Houston per the model generates 20% more ridership, and the uncertainty in the model is way more than 20%.

      • adirondacker12800

        I come up with a mangled A. There’s no Austin on the Eastern leg.
        San Antonio to Houston road distance is 197 miles or 318 kilometers on I-10
        San Antonio-Austin-Houston is 245/394. Toying around with it much more gets into the weeds about how easy it is to get in and out of Austin and Houston. I’m not in the mood to use to compare that to great circle distances between airports. College Station? Just stop. There’s a lot of travel demand 15, 20 days of the year and the rest of the time it’s filled with college students who can’t afford to travel. From Thanksgiving to Easter because they arrive in the fall in an overstuffed SUV and leave in the spring in an overstuffed SUV. Or college staff who have to be in work. In greater College Station.

  19. electricangel

    One wonders if there isn’t a network-breaking speedup for NY-BOS that wouldn’t cost as much per minute of speed up as other investments. Run Trains from GCT over the straighter and shorter path to New Rochelle (avoid interlocking issues there), which should cut 5-10 minutes from trip times, versus going through Queens and Hell Gate. Amtrak shows the NYP-NRO distance as 19 miles, while Metro North shows 17 GCT-NRO, with generally straighter tracks and no steep inclines.

    • adirondacker12800

      Those pesky pesky suburbanites have overrun the joint. They will be really peeved when the 7:59 from the end of the line gets canceled so the Amtrak train can use the “slot” to arrive at 8:00. Or the one nearest 9:00. Or the canceled departures in the afternoon. And trains still have to go over the Hells Gate because there’s no way to get from Grand Central to New Jersey and beyond.

      • Nathanael

        Alternative G, dammit (the Penn Station – GCT tunnel).

        Performed great on all cost-benefit measures in the studies, *even when the study designers were deliberately trying to not do it*, so they said “Well, the real estate is expensive” and that was the reason given for not doing it. Not kidding.

  20. plaws0

    Great article – thank you! Your talk of DC-Harrisburg traffic sent me down a fun rabbit hole that landed me here: The 1947 map there is what I was after because I couldn’t remember the route of the Port Road, that would shorten that DC-Harrisburg trip dramatically. And yes, it was wired at one time. I have no idea if this route still has rails on it (I’ll continue googling – shouldn’t be hard to find). It doesn’t appear to me that the other freight bypass from Wago Jct to Ballmer had wires but happy to be corrected. That would make the route even more direct but with a length trade-off.

    I didn’t and won’t read all the threads, but I see that you hinted at the special interests that appear when you talk about high RsOI. There seems to be a whole lot of entities today that exist solely to bleed corporations dry of all their assets and then let them go bankrupt long after these entities have “left the building”. I suspect that these are actually the same group of pillagers.

    • adirondacker12800

      It still has rails on it, for freight. It’s doesn’t have 11/12.5 kV lines on it anymore. Part of it still has 138 kV lines because that’s how the electricity gets from Safe Harbor Dam, with dedicated 25Hz generators, to the NEC.

      • plaws0

        Thanks. I’d googled up that it was now under NS ownership. Interesting about the Amtrak power distribution – I gather that’s not the only former Pennsy line that is like that.

        I’m sure NS wouldn’t mind running high speed trains off the corridor up to Harrisburg via this route. 😀

        • adirondacker12800

          That’s the only place they generate 25Hz. The rest of it except for the rotary frequency converter in Metchuen has been converted to new fangled stuff that can be a bit balky. It’s cheaper and more efficient. If they converted to 60Hz all that expensive equipment that has inefficiencies in it goes away. It’s been on Amtrak’s wish list for decades.

          • plaws0

            I remember something about that. North of NHV, it’s all 25 kV/60-Hz, IIRC.

  21. adirondacker12800

    In other news Alstom bought Bombardier.
    And Alstom sent the first Avelia to Colorado for testing. Looks like, one never knows, to have Acela replaced in two years. They can have a chat with the 117th Congress that gets seated on January 3, 2021 about patching them up for another few years to relieve car shortages on the Regionals while another batch of Avelia gets delivered to replace the Regionals. Give Harrisburg to New York direct a whirl…. a few half hourly Regionals… there are times when they sell out… Or Clockers at peak or sumptin.. Empire Service to replace the Late for Sure Limited and the Adironlate?

      • adirondacker12800

        I think the choices are to let it go through or have Bombardier go bankrupt and drag down Airbus while it does… Though I suppose Kawasaki might be amused with the idea. Then you have U.S. and Canadian regulators looking it over.

  22. Daniel Hartig

    When considering the anticipated ridership for certain long range lines, I think you don’t want to underestimate the effect of college towns and state capitals. For example, a line between Kansas City and St. Louis doesn’t sound like anything special, but might be more valuable than otherwise because the line could connect both large cities to Missouri’s state capital (Jefferson City) and flagship university (Columbia). These kind of network effects would help many lines overperform, in my opinion. Chicago-St. Louis connects the biggest city in Illinois to the state capital (Springfield). Madison-Milwaukee does the same, as would Chicago-Gary-Lafayette (Purdue)-Indianapolis. The epitome in the Midwest of this thinking is Cincinnati-Columbus-Cleveland which connects three large cities and the capital and flagship university.

    I argue that statewide in US states large universities and capitals are both unusually high draws for rail traffic; one for college kids with no cars spending weekends at home, the other for day trips to do government business (hearings, lobbying, etc).

    • Alon Levy

      The data I’m training my model on involves lines that connect cities to the national capital. So that bonus is already there in the model, and could be one reason why international links underperform.

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  31. Nathanael

    This is great work. I’d been meaning to do something like this but I never got around to calibrating the gravity model, which you just did. Thank you so much.

    This is honestly the best model I’ve seen in a long time — too many details are known to make a model worse — and I am going to use this in advocacy routinely.

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  36. Martin Smith Hoecker-Martinez

    I think you are being too generous with your exponents. A full square root of the gravity model (i.e. the geometric mean of population divided by distance) has the benefit of giving a metric that’s people per mile. If you wanted to be fancy you could further weight by travel time saved (relative to air or car) and then your metric is a very economic person hours per distance. Including the trip time saved can also impose a minimum trip distance. If you choose a minimum headway for rail (say 30min) versus instantaneous departure for private cars that gives a minimum distance (35 miles). You should also include a minimum effective headway for air travel (90 min or 120 min) so that the more frequent but slower train can be the shortest trip for medium distances.

    • Matthew Hutton

      Car average time isn’t zero. Even in a good scenario you have to reverse your car into or out of your drive. And multi stories or where you have to park on street away from your house are slower. I’d say a typical time would be 5 minutes.

      Access time for the train isn’t that high either. Assuming you have a ticket already I’d allow 2 minutes maybe on foot, 5 maybe by bike and 10 by car depending on traffic. If one needs to buy a ticket from a machine or person maybe add 5 minutes onto those times.

      And cars aren’t really that quick. My average speed by car is probably 60km/h. And I don’t hang around.

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