# Amtrak’s Continued Ignorance

There was a congressional hearing about high-speed rail. Henry Miller in comments here took notes – thanks for this, much appreciated! The overall content was lacking; the politicians seemed like they were spinning their wheels, not because they themselves were bad (Reps. Tom Malinowski, Peter DeFazio, and Seth Moulton all raised interesting issues) but because they were getting ignorant advice from the witnesses, none of whom has any experience in successful high-speed rail networks. Among those, Amtrak deserves the most demerits, and its head, William Flynn, should lose his job purely over that testimony, if the reporting of what he said is accurate.

Flynn, based on both what Henry said in comments and on reporting in Politico Pro, said that Amtrak needs a trust fund on the model of that for American highways – and said that this is “the most important lesson we can learn” from countries with high-speed rail.

The rub is that countries with high-speed rail do not in fact have such trust funds. Financing models vary by country, but do not look like the American highway trust fund. For example, French LGVs are funded line-by-line, with the decision on each specific line taken at the highest level of government, with financing coming either purely from the public sector (as with the LGV Est) or from a higher-cost PPP (as with the LGV Sud-Europe-Atlantique).

To understand why, it’s important to understand the relationship between politics and the civil service in functioning, high-capacity states. Politicians make big decisions on spending priorities, and then the civil service implements those decisions. There is little political input on routing decisions, and the exceptions where there is tend to have the worst, highest-cost programs. So the planning is done by the civil service, which then presents a preliminary design for politicians. But the elected politicians have the final word on the yes-no decision whether to fund, and can also ask for high-level modifications (“reduce the budget,” “give the unions the wage increases they demand,” etc.).

The American highway trust fund inverts this principle. Going back to Thomas MacDonald, federal highway builders had internal sources of money without having to ask elected politicians for regular appropriations. In contrast, politicians exerted considerably petty power over routing. For example, in Twentieth-Century Sprawl, Owen Gutfreund points out that in the early planning for what became the Interstate highways, the FDR administration reduced the scope of roads to be built in Vermont from four planned routes to two in retaliation for its voting Republican in 1936. In The Big Roads, Earl Swift also notes that MacDonald himself did not think the Interstates could pay for themselves through tolls, but, due to pressure by politicians to write a positive report, the resulting report’s coauthor proposed toll-free motorways instead, hence the prohibition on tolling Interstates. MacDonald himself was fired by the Eisenhower administration for expressing concern that the roads were hollowing out the American rail network and proposing cars-and-trains investment instead of cars-only.

And here we have Amtrak’s CEO not only supporting that model, but also lying that this model is how high-speed rail has been built. In reality, no such trust funds exist anywhere with high-speed rail. I don’t know why Flynn says such a thing, which not only is verifiably wrong, but also has no reason to be believed in the first place – there is no grain of truth to it, no trust fund-like model for high-speed rail megaprojects.

As with most such fraud, he is probably lying to himself and not just to the people who pay his salary. Americans, as a collective, are wantonly ignorant of the rest of the world. The only time they interact with the rest of the world, especially countries that don’t speak English, is through intermediaries in international consulting, who get the skewed sample of world projects that invite in international consultants, omitting the bulk of public works built in states with in-house design capacity. Individual Americans can be knowledgeable, but their knowledge is not respected, even by people who profess their interest in state capacity. Thus, no matter how smart individual Americans can get, collectively America remains incurious.

This is the most acute in mainline rail. I suspect that this relates to the rail industry’s highway envy. For a railroader like Flynn, steeped in a culture that is technologically and institutionally reactionary and looks back to its heyday in the first half of the 20th century, the enemy, that is the Interstate system, is the obvious model for how to build. That this model produced severe cost overruns on the highways themselves does not matter; that treating rails institutionally like roads is inappropriate does not matter; that systems that get as much ridership in two days (cf. JR East) as Amtrak gets in an entire year and deliver a profit to their shareholders doing so work differently does not matter. The future, which is not in the United States in this field and hasn’t been in 60 years, is one in which people like Flynn do not even qualify for an internship.

And if Flynn wouldn’t qualify for an internship, why is he allowed to be the CEO? He should lose his job. The people who briefed him should lose their jobs. It is likely that full replacement of Amtrak’s planning staff and possibly the line workers too would be a big win for riders. Even total liquidation could well be a net positive relative to status quo: most Amtrak routes have no social value, and the one route that does, the Northeast Corridor, could well produce a more competent institution from among the ashes.

Without liquidation, it is still advisable to sideline Amtrak until it can be put out of its delayed customers’ misery. The best way forward institutionally is to set up an agency responsible for all Northeastern passenger rail operations, to subsume and replace Amtrak and the commuter rail operators. It will be run by people who can speak to the difference between French, German, and Japanese high-speed rail operating models, and who know how to implement integrated timed transfer networks and intermodal fare integration. It will buy imported equipment if there is no domestic equivalent for a similar price, and use standard European or East Asian methods for track geometry machines, signaling (ACSES is thankfully an Americanized variant of the European standard, ETCS), safety systems, timetabling, and so on. The United States has no shortage of dedicated people who speak Spanish, and secondarily Japanese, Korean, Chinese, Italian, German, or French.

Moreover, since in many cases the knowledge does exist among Americans but isn’t valued, it is important to let American civil servants interview for such an agency. I expect that most would come from an urban transit background, where in my experience the people are more curious than in mainline rail. But American railroaders too could join if they demonstrate sufficient knowledge of advanced-world operations.

That said, under no circumstances should the organizational culture be allowed to turn into anything like present-day American railroading. Current workers who do not qualify for this agency are to be laid off, perhaps with a pro-rated pension for partial service, and told to seek private-sector work. Flynn himself has no role to play in any successful rail agency. He must go, and it’s almost certain that the rest of Amtrak’s management should as well. Every day he stays in his job is a day American railroading plans based on assumptions that can be easily verified to be fraudulent.

# The United States Needs to Learn How to Learn

I just saw an announcement from November of 2020 in which the Federal Transit Administration proposes to study international best practices… in on-demand public transit.

It goes without saying that the international best practice in on-demand micromobility is “don’t.” The strongest urban public transport networks that I know of range from not making any use of it to only doing so peripherally, like Berlin. In fact, both France and Germany have rules on taxis that forbid Uber from pricing itself below the regulated rates; Japan, too, banned Uber from operating after it tried to engage in the usual adversarial games with the state that it is so familiar with from the US.

And yet, here we see an FTA program attempting to learn from other countries not how to write a rail timetable, or how to modernize regional rail, or how to design a coordinated infrastructure plan, or how to integrate fares, or how to do intermodal service planning, or how to build subways affordably. It’s perhaps not even aware of those and other concepts that make the difference between the 40% modal split of so many big and medium-size European cities and the 10-15% modal splits that non-New York American cities top at.

Instead, the FTA is asking about a peripheral technology that markets itself very aggressively to shareholders and VCs so that it can ask for more money to fund its losses.

Earlier today I saw a new announcement of congressional hearings about high-speed rail. There are 12 witnesses on the list, of whom none has any experience with actual high-speed rail. They’re American politicians plus people who either run low-speed trains (Amtrak, Brightline) or promise new vaporware technology (Hyperloop*2, Northeast Maglev). American politicians and their staffers are not that stupid, and know that there are strong HSR programs in various European and Asian countries, and yet, in the age of Zoom, they did not think to bring in executives from JR East, DB, SNCF, SBB, etc., or historians of these systems, to discuss their challenges and recommendations.

I bring up these two different examples from the FTA and Congress because the US has trouble with learning from other places. It’s not just that it barely recognizes it needs to do so; it’s that, having not done so in the past, it does not know how to. It does not know how to form an exchange program, or what questions to ask, or what implementation details to focus on. Hearing of a problem with a public agency, its first instinct is to privatize the state to a consultancy staffed by the agency’s retirees, who have the same groupthink of the current publicly-employed managers but collect a higher paycheck for worse advice.

Worse, this is a nationwide problem. Amtrak can and should fully replace its senior management with people who know how to run a modern intercity railroads, who are not Americans. But then middle management will still think it knows better and refuse to learn what a tropical algebra is or how it is significant for rail schedule planning. They do not know how to learn, and they do not recognize that it’s a problem. This percolates down to planners and line workers, and I don’t think Americans are ready for a conversation about full workforce replacement at underperforming agencies.

This will not improve as long as the United States does not reduce its level of pride to that typical of Southern Europe or Turkey. When you’re this far behind, you cannot be proud. It’s hard with American wages being this high – the useless managers even in the public sector earn more than their Northern European counterparts and therefore will not naturally find Northern Europe to have any soft power over them. Wearing sackcloth and ashes comes more naturally with Italian or Spanish wages. But it’s necessary given how far behind the US is, and bringing in people who are an American’s ideal of what a manager ought to be rather than people who know how to run a high-speed passenger railroad is a step backward.

# Sanity-Checking My HSR Ridership Model

In previous posts about modeling high-speed rail ridership, I used a gravity model for the estimation. While poking around with spreadsheets, I figured out that a good way to sanity-check the model is to run it on existing high-speed rail systems with known ridership. It turns out that the model fits the data decently but not amazingly, and tends to overestimate ridership at long distances (800 km+) and underestimate it at short ones.

The model

The model I use is a gravity model, with the constant trained on Shinkansen data from JR East and JR Central (PDF-p. 4):

$\mbox{Ridership } = 75000\cdot\mbox{Pop}_{A}^{0.8}\cdot\mbox{Pop}_{B}^{0.8}/\max\{\mbox{distance}, 500\}^{2}$

The populations of metro areas A and B are in millions, distance is in km, and ridership is in millions per year in both directions combined.

The data

I’ve tested the model on two datasets: Shinkansen, and Taiwan HSR. These are island systems with a finite, controllable number of stations; Taiwan, a single-line system, is especially easy to model. The km-points are taken from line lengths; but mini-Shinkansen lines have artificially inflated lengths to account for the greater travel time, by a factor of about 2.7, to be compatible with an average express train speed of about 220 km/h. This means the model will overrate their passenger-km, but it’s not a significant source of error as they are fairly small cities – were they bigger they’d get full Shinkansen.

Metro areas are combined, and when a metro area has several stations, they are merged and only the most prominent is depicted, such as Tokyo, Shin-Osaka, and Taipei.. In Japan I use the broader category of major metropolitan area wherever possible, with the exception of Shizuoka-Hamamatsu, which are not merged as they were distinct until recently and remain two separate city cores that only share suburbs on the margins. Otherwise I use the smaller metropolitan employment area, as the MMA is only defined for the largest cities, and not for (say) Aomori or Kanazawa.

In Taiwan there’s no real definition of metro area. The secondary cities are single-tier municipalities encompassing the metro area plus some rural areas; I take what Wikipedia calls the urban part, which is nearly the same as the municipality. Taipei and New Taipei are merged – there’s a stop in New Taipei but New Taipei is really a suburb of Taipei spreading in all directions; but Taoyuan is kept separate, as it tries to develop its own core and lies only in one direction from Taipei, to its west. Outside the cities I use county populations where the stop seems to serve the center of the county, but Chiayi is expansive and I focus on the independent Chiayi City plus the suburb the station is in, and Changhua’s station is very peripheral to the county, most of which is closer to Taichung.

Both countries charge similar fares – Wikipedia has Taiwan charging, in PPP terms, $0.25/p-km, which is close to the Shinkansen average, and compares with about$0.15/p-km in Continental Europe. In addition, both have linear population distribution, Japan along the Taiheiyo Belt and Taiwan along the west coast.

Results

The model massively underrates the ridership of THSR. It believes ridership is 26 million a year, with a total of 4.465 billion p-km; the actual numbers are 67 million and 12 billion respectively as of 2019, per Wikipedia. I have not seen ridership by city pairs, only boardings per station. The numbers do not make it obvious if there is more very short-distance ridership than I expect. The average trip length I predict is 172 km; the actual average is 178. Taichung has slightly more ridership than Zuoying, where in reality Taichung and Kaohsiung have the same populations, but Zuoying is not quite at city center whereas Taichung also draws from Changhua County, whereas the Changhua station has very low ridership. Overall, to the extent the shape of the model is correct, the minimum of 500 km in the denominator cannot be too wrong – or, if it is, the minimum must be more than the Taipei-Kaohsiung distance of 339 km or not much less than it.

In Japan, the situation is less clear. Total Shinkansen ridership is 438 million as of financial year 2018-9, per Wikipedia; this is the last year before corona, as the years end on 3-31 and in March of 2020 Japanese ridership was already suppressed due to social distancing. Passenger-km on JR East, JR Central, and JR West totaled around 100 billion, with Hokkaido and Kyushu adding scant numbers, but these are railroad-km, and the Shinkansen charges based on the distance along the legacy line and not the Shinkansen, inflating p-km by somewhat less than 10%.

In contrast, my model thinks total Shinkansen ridership is 389 million and p-km sum to 170.815 billion. The 389 vs. 438 discrepancy is easy to explain – my model ignores intra-metropolitan trips, and we know that they exist because there are some Shinkansen commuters in towns like Mishima. However, 100 vs. 171 billion p-km is harder. For this, there are several explanations, all plausible, and yet none completely satisfactory:

• About 40 billion of the p-km involve riding through Tokyo, of which 21 billion are from the Tohoku Shinkansen and 19 from the Joetsu and Hokuriku Shinkansen. There are no through-trains, and the through-trips via Joetsu and especially Hokuriku are circuitous.
• Yamagata and Akita between them generate around 6 billion p-km per the model; this is an overestimate, as the spreadsheet does not distinguish km that are really stand-ins for trip time from km that are actually traveled.
• A total of 6.5 billion p-km per the model are diagonal between the Tohoku, Joetsu, and Hokuriku Shinkansen; in reality, connecting at Omiya or Takasaki is so circuitous that I expect nearly everyone drives.
• Inter-island trips are especially likely to be done by air. Tokyo-Fukuoka has a rail-air modal split of 7.4-92.6, over a distance of 5 hours, and Nagoya-Fukuoka is only 51-49, over a distance of 3:20. This is bad for rail by European standards, where 5 hours is typically 20-30% for rail and 3:20 is a clear majority, and even by intra-Honshu Japanese standards, where Tokyo-Hiroshima at 3:55 is 68-32 and Tokyo-Okayama at 3:15 is 70-30.

All trip categories above are disproportionately long, helping explain why the model underpredicts ridership while overpredicting p-km. Subtracting all of the above one gets to not much more than 100 billion.

The model does nail certain aspects of Shinkansen ridership. Tokyo-Sendai, Tokyo-Hiroshima, and Tokyo-Okayama are easy – the model was trained in part on those specific city pairs. But in adition, overall ridership out of Tokyo and Osaka is very close to total JR Central ridership in these two regions. The model slightly overpredicts Osaka but that is expected since it lumps the Keihanshin region together whereas JR Central would not count Kobe.

Nagoya is more overpredicted, and it is possible that it is uniquely auto-oriented and this slightly reduces rail ridership, by maybe 25% below modeled prediction. If that is what is happening, then the constant 500 in the denominator of the model as well as 75,000 in the numerator should be adjusted – the reason for the choice of 500 is that Tokyo-Nagoya and Tokyo-Osaka ridership levels both follow the same model if the exponent is 0.8 and distance is ignored; if in fact Nagoya has a 25% malus then to countermand it the constant in the maximum should be lowered slightly, to 430 or a little less.

It’s tempting to rewrite the model in terms of travel time and then set the constant at 2 hours (and not 2.5 hours as I did when trying to model Germany). But note that it’s far from enough to explain the model’s gross underprediction of Taiwanese HSR ridership, an underprediction that exists across all distances in Taiwan. Nor is it possible to lower the 75,000 constant in the numerator and address any of the underprediction of Taiwan.

# Tilting Trains and Technological Dead-Ends

The history of tilting trains is on my mind, because it’s easy to take a technological advance and declare it a solution to a problem without first producing it at scale. I know that 10 years ago I was a big fan of tilting trains in comments and early posts, based on both academic literature on the subject and existing practices. Unfortunately, this turned into a technological dead-end because the maintenance costs were too high, disproportionate to the real speed benefits, and further work has gone in different directions. I bring this up because it’s a good example of how even a solution that has been proven to work at scale can turn out to be a dead-end.

What is tilting?

It is a way of getting trains to run at higher cant deficiency.

What is cant deficiency?

Okay. Let’s derive this from physical first principles.

The lateral acceleration on a train going on a curve is given by the formula a = v^2/r. For example, if the speed is 180 km/h, which is 50 m/s, and the curve radius is 2,000 meters, then the acceleration is 50^2/2000 = 1.25 m/s^2.

Now, on pretty much any curve, a road or railway will be banked, with the outer side elevated above the inner side. On a railway this is not called banking, but rather superelevation or cant. That way, gravity countermands some of the centrifugal force felt by the train. The formula on standard-gauge track is that 150 mm of cant equal 1 m/s^2 of lateral acceleration. The cant is free speed – if the train is perfectly canted then there is no centrifugal force felt by the passengers or the train systems, and the balance between the force on the inner and outer rail is perfect, as if there is no curve at all.

The maximum superelevation on a railway is 200 mm, but it only exists on some Shinkansen lines. More typical of high-speed rail is 160-180 mm, and on conventional rail the range is more like 130-160; moreover, if trains are expected to run at low speed, for example if the line is dominated by slow freight traffic or sometimes even if the railroad just hasn’t bothered increasing the speed limit, cant will be even lower, down to 50-80 mm on many American examples. Therefore, on passenger trains, it is always desirable to run faster, that is to combine the cant with some lateral acceleration felt by the passengers. Wikipedia has a force diagram:

The resultant force, the downward-pointing green arrow, doesn’t point directly toward the train floor, because the train goes faster than the balance speed. This is fine – some lateral acceleration is acceptable. This can be expressed in units of acceleration, that is v^2/r with the contribution of cant netted out, but in regulations it’s instead expressed in theoretical additional superelevation required to balance, that is in mm (or inches, in the US). This is called cant deficiency, unbalanced superelevation, or underbalance, and follows the same 150 mm = 1 m/s^2 formula on standard-gauge track.

Note also that it is possible to have cant excess, that is negative cant deficiency. This occurs when the cant chosen for a curve is a compromise between faster and slower trains, and the slower trains are so much slower the direction of the net force is toward the inner rail and not the outer rail. This is a common occurrence when passenger and freight trains share a line owned by a passenger rail-centric authority (a freight rail-centric one will just set the cant for freight balance). It can also occur when local and express passenger trains share a line – there are some canted curves at stations in southeastern Connecticut on the Northeast Corridor.

The maximum cant deficiency is ordinarily in the 130-160 mm range, depending on the national regulations. So ordinarily, you add up the maximum cant and cant deficiency and get a lateral acceleration of about 2 m/s^2, which is what I base all of my regional rail timetables on.

You may also note that the net force vector is not just of different direction from the vertical relative to the carbody but also of slightly greater magnitude. This is an issue I cited as a problem for Hyperloop, which intends to use far higher cant than a regular train, but at the scale of a regular train, it is not relevant. The magnitude of a vector consisting of a 9.8 m/s^2 weight force and a 2 m/s^2 centrifugal force is 10 m/s^2.

Okay, so how does tilt interact with this?

To understand tilt, first we need to understand the issue of suspension.

A good example of suspension in action is American regulations on cant deficiency. As of the early 2010s, the FRA regulations depend on train testing, but are in practice, 6″, or about 150 mm. But previously the blanket rule was 3″, with 4-5″ allowed only by exception, mocked by 2000s-era advocates as “the magic high-speed rail waiver.” This is a matter of carbody suspension, which can be readily seen in the force diagram in the above secetion, in which the train rests on springs.

The issue with suspension is that, because the carbody is sprung, it is subject to centrifugal force, and will naturally suspend to the outside of the curve. In the following diagram, the train is moving away from the viewer and turning left, so the inside rail is on the left and the the outside rail is on the right:

The cant is 150 mm, and the cant deficiency is held to be 150 mm as well, but the carbody sways a few degrees (about 3) to the outside of the curve, which adds to the perceived lateral acceleration, increasing it from 1 m/s^2 to about 1.5. This is typical of a modern passenger train; the old FRA regulations on the matter were based on an experiment from the 1950s using New Haven Railroad trains with unusually soft suspension, tilting so far to the outside of the curve that even 3″ cant deficiency was enough to produce about 1.5 m/s^2 of lateral force felt by the passengers.

By the same token, a train with theoretically perfectly rigid suspension could have 225 mm of cant deficiency and satisfy regulators, but such a train doesn’t quite exist.

Here comes tilt. Tilt is a mechanism that shifts the springs so that the carbody leans not to the outside of the curve but to its inside. The Pendolino technology is theoretically capable of 300 mm of cant deficiency, and practically of 270. This does not mean passengers feel 1.8-2 m/s^2 of lateral acceleration; the train’s bogies feel that, but are designed to be capable of running safely, while the passengers feel far less. In fact the Pendolino had to limit the tilt just to make sure passengers would feel some lateral acceleration, because it was capable of reducing the carbody centrifugal force to zero and this led to motion sickness as passengers saw the horizon rise and fall without any centrifugal force giving motion cues.

Two lower cant deficiency-technology than Pendolino-style tilt are notable, as those are not technological dead-ends, and in fact remain in production. Those are the Talgo and the Shinkansen active suspension. The Talgo has no axles, and incorporates a gravity-based pendular system in which the train is sprung not from the bottom up but from the top down; this still isn’t enough to permit 225 mm of cant deficiency, but high-speed versions like the AVRIL permit 180, which is respectable. The Shinkansen active suspension is computer-controlled, like the Pendolino, but only tilts 2 degrees, allowing up to 180 mm of cant deficiency.

What is the use case of tilting, then?

Well, the speed is higher. How much higher the speed is depends on the underlying cant. The active tilt systems developed for the Pendolino, the Advanced Passenger Train, and ICE T are fundamentally designed for mixed-traffic lines. On those lines, there is no chance of superelevating the curves 200 mm – one freight locomotive at cant excess would demolish the inner track, and the freight loads would shift unacceptably toward the inner rail. A more realistic cant if there is much slow freight traffic is 80 mm, in which case the difference between 150 and 300 mm of cant deficiency corresponds to a speed ratio of $\sqrt{(80+300)/(80+150)} = 1.285$.

Note that the square root in the formula, coming from the fact that acceleration formula contains a square of the speed, means that the higher the cant, the less we care about cant deficiency. Moreover, at very high speed, 300 mm of cant deficiency, already problematic at medium speed (the Pendolino had to be derated to 270), is unstable when there is significant wind. Martin Lindahl’s thesis, the first link in the introduction, runs computer simulations at 350 km/h and finds that, with safety margins incorporated, the maximum feasible cant deficiency is 250 mm. On dedicated high-speed track, the speed ratio is then $\sqrt{(200+250)/(200+130)} = 1.168$, a more modest ratio than on mixed track.

The result is that for very high-speed rail applications, Pendolino-level tilting was never developed. The maximum cant deficiency on a production train capable of running at 300 km/h or faster is 9″ (230 mm) on the Avelia Liberty, a bespoke train that cost about double per car what 300 km/h trains cost in Europe. To speed up legacy Shinkansen lines, JR Central and JR East have developed active suspension, stretching the 2.5 km curves of the Tokaido Shinkansen from the 1950s and 60s to allow 285 km/h with the latest N700 trains, and allowing 360 km/h on the 4 km curves of the Tohoku Shinkansen.

What happened to the Pendolino?

The Pendolino and similar trains, such as the ICE T, have faced high maintenance costs. Active tilting taxes the train’s mechanics, and it’s inherently a compromise between maintenance costs and cant deficiency – this is why the Pendolino runs at 270 mm where it was originally capable of 300 mm. The Shinkansen’s active suspension is explicitly a compromise between costs and speed, tilted toward lower cant deficiency because the trains are used on high-superelevation lines. The Talgo’s passive tilt system is much easier to maintain, but also permits a smaller tilt angle.

The Pendolino itself is a fine product, with the tilt removed. Alstom uses it as its standard 250 km/h train, at lower cost than 350 km/h trains. It runs in China as CRH5, and Poland bought a non-tilting Pendolino fleet for its high-speed rail service.

Other medium-speed tilt trains still run, but the maintenance costs are high to the point that future orders are unlikely to include tilt. Germany has a handful of tilt trains included in the Deutschlandtakt, but the market for them is small. Sweden is happy with the X2000, but its next speedup of intercity rail will not involve tilting trains on mostly legacy track as Lindahl’s thesis investigated, but conventional non-tilting high-speed trains on new 320 km/h track to be built at a cost that is low by any global standard but still high for how small and sparsely-populated Sweden is.

In contrast, trainsets with 180 mm cant deficiency are still going strong. JR Central recently increased the maximum speed on the Tokaido Shinkansen from 270 to 285 km/h, and Talgo keeps churning out equipment and exports some of it outside Spain.

# High-Speed Rail and Connecting Transit

Noah Smith is skeptical about high-speed rail in the United States. He makes a bunch of different arguments against it, but I want to zoom in on the first, the issue of connecting transit, which Noah is far from the first person to bring up. It’s a genuine drawback of rail planning in the United States, but it’s very easy to overrate its importance. Connecting transit is useful, as is the related issue of city centralization, but its effect, serious as it is, is only on already marginal high-speed routes, like Atlanta-Memphis or Dallas-Kansas City. Los Angeles suffers from lacking connecting transit, but it’s also so big that nothing it connects to is marginal. Finally, high-speed rail and urban centralization are not in competition, but rather are complements, as in the history of the TGV.

Connections and centralization

Modal choice is about door-to-door trip times. This is why a large majority of people take a train that takes three hours over a plane that takes one: hardly anyone lives near the airport or has an airport as their ultimate destination. In practice, people are much likelier to be living near and traveling to a destination near a city center station.

The importance of connections then is that connecting urban transit extends the range of the train station. I didn’t live at Gare de Lyon or Gare de l’Est, but I could take the Métro there and it was a short trip, much shorter and more reliable than taking the RER to the airport, which made it easier for me to ride the TGV. With reliable connections, I showed up at Gare de l’Est four minutes before a train to Saarbrücken was due to depart, printed my ticket on-site, and walked leisurely to the platform, boarding still with two minutes to spare.

Regional rail has the same effect, at longer range. It’s not as convenient as urban rail, but it feeds the main intercity rail station and is timetabled, so if the system is punctual, passengers can time themselves to the main train station. In Switzerland the connections are even timed, enabling people who travel from smaller cities like St. Gallen to points west to transfer at Zurich Hauptbahnhof within a short window. However, this is completely absent from France: the regional trains are unreliable, and Paris has through-running on the RER but no single central station that can collect connections from secondary centers like Meaux or Versailles.

Finally, centralization is important because the reach of an urban transportation system is measured in units of time and not distance. Even racists who are afraid of taking the trains in Paris and rely exclusively on cars can take a cab from a train station to their ultimate destination and be there shortly. The average speed of the Métro is low, around 25 km/h, but Paris’s density and centralization mean that it’s enough to connect from the main TGV stations to where one lives or works.

But the US doesn’t have that, right?

What Noah gets wrong is that the US has connecting transit as in Paris in a number of big cities, and nearly every even semi-plausible high-speed line connects to at least one such city. Here’s Noah on New York:

The best thing about using the Shinkansen in Japan is that you can get to and from the high-speed rail station using a dense, convenient network of local trains. In America there is no such network. Thus, when I imagine taking the train from SF to L.A., I imagine taking a scooter or an Uber to and from the train station. In L.A., which is so spread out that I probably won’t stay in a small area, I imagine I’d rent a car. That’s a very different experience from using the Shinkansen in Japan. And in NYC, it would mean dealing with the nightmare that is Penn Station — a thoroughly stressful and inconvenient experience.

Let’s discuss New York now; Los Angeles deserves a separate section in this post. Noah lived on Long Island for years; he could connect to any intercity train by taking the LIRR to Penn Station and changing there. It’s this connection that he describes as a nightmare. But the question is, a nightmare compared to what? It’s clearly far less convenient than the timed Swiss connections, or even untimed connections between the Berlin S-Bahn and intercity trains. But the LIRR is a timetabled train, and while delays happen, they’re measured in minutes, not tens of minutes. Passengers can time themselves to arrive 10 minutes before the intercity train departs, even today.

All of this gets easier if a minimally competent agency is in charge and track numbers are scheduled in advance and printed on the ticket as they are here or in Japan. Penn Station is crowded, but it’s not a stampede crush and people who know their commuter train arrives on track 19 and the intercity train leaves on track 14, as written in the ticket, can make the connection in 3 minutes.

The secondary transit cities of the US are dicier. Their modal splits are all in the teens; San Francisco (excluding Silicon Valley) is the highest, with 17.5%. In that way, they’re comparable to Lyon, Marseille, Nice, Bordeaux, Toulouse, Strasbourg, and Lille. However, the way non-New York transit systems work in the US is, the system is usually semi-decent at ferrying people to and from city center, it’s just not strong for other destinations. In Boston, for example, people could transfer to the subway at South Station or Back Bay and cover a decent chunk of urban destinations. It’s nowhere nearly as good as the options for Paris or Berlin, but it’s not the same as not having any connecting transit.

Destination centralization

The connecting transit critique of high-speed rail in the American discourse goes back at least to the Obama era; Richard Mlynarik used it to argue against what he views as inflated California HSR ridership expectations, and everyone who commented on transit blogs in 2008-9 had to address the critique in one way or another. In 2012, I posted about the issue of destination centralization, that is, that destinations are more centralized than origins, especially at long distance. For example, at the time Manhattan had 22% of New York metro jobs, but 36% of jobs involving out-of-county commuting – and the longer the trip, the likelier one’s destination is to be in Manhattan.

The data I looked at was the distribution of five-star hotels, which are incredibly centralized. Depending on data sources, 50 out of 56 such hotels in metro New York were in Manhattan, or perhaps 36 in 37. In Boston, either all are in Downtown or Back Bay, or all but one are and the one is in Cambridge, a few Red Line stops from South Station. In Philadelphia, they’re in Center City.

In New York, there are clusters of lower-priced hotels outside Manhattan. The biggest such clusters are in strategic locations in Queens, Brooklyn, or North Jersey with maximally convenient access to Manhattan, where tourists and business travelers cluster. Some hotels serve suburban office parks, such as the various Central Jersey hotels I would go to gaming conventions at, but they’re smaller and lower-end.

In the Bay Area, Richard argued in favor of the primacy of San Francisco over San Jose by citing broader data on interregional travel. San Francisco, per his dataset, absolutely dominated. More recent data can be seen here, measuring tourism revenue rather than visitor numbers, but San Francisco with 900,000 people is about comparable to Santa Clara, Alameda, and San Mateo Counties combined with their 4.4 million people. There is also a comparison of international arrivals to San Jose and San Francisco – there are several times as many of the latter; I cannot find domestic arrival numbers for San Jose that might compare with San Francisco’s 26 million visitors in 2019.

The upshot is that high-speed rail does not need to connect two strongly-centered cities to be comparable in ridership to existing lines in Europe and East Asia. It only needs to connect one. People may need to drive to a park-and-ride or take a taxi to the train station, but if their destination is New York or any of the secondary transit cities of the US, it is likely to be fairly close to the train station, even if most employment isn’t.

The Los Angeles exception

Noah is on stronger grounds when he criticizes Los Angeles. Even Los Angeles has 1.5 subway lines connecting to Union Station, soon to be augmented with the Regional Connector, but the city is weakly-centered, and a car or taxi connection to one’s ultimate destination is likely. Moreover, the destinations within Los Angeles are not centered on Downtown; for example, high-end hotels are the most likely to be found on the Westside.

However, there are two saving graces for trains to Los Angeles. The first is that Los Angeles’s transit ridership is so low because the city’s job geography is so decentralized that the network is bad at connecting local origins with local destinations. If it is guaranteed that one of the two points connected is Union Station, the city’s network is still bad for its size, but becomes usable. The under-construction Westside subway will open later this decade, providing decent (if not good) connectivity from the train station to high-end destinations in that part of the region.

The second and more important saving grace is that Los Angeles is huge. The absence of connecting transit is a serious malus for intercity rail, but people can still take a taxi, and that may add half an hour to the trip and a cab fare, but we know what adding half an hour to a three-hour train trip does and it’s a 1.5th-order effect. A 1.5th-order effect can turn a line that is projected to get a marginal 2.5% return on investment into one with a below-cost-of-capital 1.5% return. It cannot do this to lines serving Los Angeles, none of which are economically marginal, thanks to Los Angeles’s size. On my map, the only line connecting to Los Angeles that a straight gravity model doesn’t love at first sight is Los Angeles-Las Vegas, and this is a connection we know overperforms the model because of the unique tourism draw of Las Vegas.

On the same map, the other connection that everyone (including myself until I ran the number) is skeptical of, Atlanta-Florida, has the same issue as Los Angeles-Las Vegas: it connects to a very strong tourism region, and the train station would serve the biggest tourist attractions. (This is also true in the case of Los Angeles, where Anaheim is still supposed to get a station within a short shuttle distance to Disneyland.) So my model thinks it’s only 2.5% ROI, but the strong tourism volume is such that I am confident the model remains correct even with the malus for weak job centralization in both Atlanta and the cities of Florida.

High-Speed Rail and Connecting Transit

Noah makes a broader point portraying intercity and regional public transport in opposition:

Building high-speed rail without having a usable network of local trains instinctively feels like putting the cart before the horse. If I had a choice between being able to train around San Francisco conveniently, or quickly get between SF and San Jose, I’d choose either of those over being able to take a Shinkansen-style train to L.A. or Seattle. The lack of local trains and fast commuter rail simply limits my travel options much more than the lack of high-speed rail. A local train network without HSR is great; HSR lines without local trains seem like something that’s at best slightly better than what we have now.

And yes, I realize that money earmarked for “high-speed rail” sometimes goes to create faster commuter rail, and that’s good. But that doesn’t answer the question of what these maps are for.

Noah is pooh-poohing the connection between intercity and regional transit as “the money sometimes goes to create faster commuter rail,” but he’s underestimating what this means, in two ways.

First, on the Northeast Corridor specifically, any improvement to intercity transit automatically improves commuter rail. The reason is that the most cost-effective speed treatments there are shared. By far the cheapest minutes saved on the corridor come from speeding up the station throats by installing more modern turnouts and removing speed limits that exist due to agency inertia rather than the state of the physical infrastructure. Trains can save two minutes between South Station and Back Bay alone on a high seven to low eight figures budget for rebuilding the interlocking. These improvements speed up commuter rail and intercity rail equally.

Moreover, in higher speed zones, it’s necessary to invest in organization before concrete and schedule trains with timed overtakes. But this too improves the quality of regional rail. Boston-Providence trains need to be electrified and run faster to get out of intercity trains’ way more easily; even with trains holding twice for an overtake, this speeds up Providence-Boston travel by 15 minutes even while adding station stops. New York-New Haven trains had better run faster on both short- and long-distance connections – and the difference between improving intercity rail this way and in a way that is indifferent to integration with regional rail is the difference between doing it for $15 billion and doing it for$150 billion.

And second, in cities that are not traditional transit cities, high-speed rail is a really good catalyst for expanding a central business district around the station. The best example for this is Lyon. Lyon built a dedicated central business district at Part-Dieu, the Metro, and the LGV Sud-Est simultaneously. This was not sequenced as local transit first, then high-speed rail. Rather, the selection of the site for a high-speed rail station, within the city but just outside its traditional center, was simultaneous with the construction of the new business district and of an urban rail system serving it.

This is particularly useful for cities that, by virtue of size (Dallas) or location (Cleveland) could be high-speed rail hubs but do not have strong city centers. In Cleveland, demand for housing in the city is extremely weak, to the point that houses sell for well below construction costs, and demand for city center office space is likewise weak; but a train that gets to Chicago in 2 hours and to New York in about 3:15 can make the area immediately around the station more desirable. In Dallas this is more complicated because it would be the system’s primary city, but a location with convenient rail access to Houston is likely to become more desirable for office space as well. This is not in competition with local transit – it complements it, by giving existing light rail lines and potential commuter rail lines a meatier city center to connect suburban areas with.

Public Transport and Scale

Noah asks what the proposal maps are for. The answer is, they are proposals for improvement in passenger rail. There is a real issue of scale and details, which is why those maps don’t depict literally every connection. For that, there are smaller-scale maps, in the same way there is the TransitMatters proposal for Regional Rail in the Boston area, or maps I’ve made for timed connections in New England and Upstate New York between intercity and regional trains. At lower-altitude zoom there’s also the issue of local connections to buses.

A roadmap like Google Maps or a national planning map, shown at such zoom that the entirety of a continental superstate like the United States is in the field of view, will only include the highest level of the transportation hierarchy. In the case of roads, that’s the Interstates, and the map may well omit spurs and loops. At lower altitude, more roads are visible, until eventually at city scale all streets are depicted.

The same is true of public transit – and high-speed rail is ideally planned as public transit at intercity scale. A continental-scale proposal will depict high-speed rail because it depicts all cities at once and therefore what matters at this level is how to get between regions. A state map or regional map such as for New England will depict all regional connections, and a local map will depict bus connections around each train station. At no point are these in competition for resources – good integrated planning means they all work together, so that improvements in regional rail also enable better bus connections, and improvements in intercity rail enable better regional connections.

Is all of this absolutely necessary? No. France manages to make certain connections work without it, and when I try to model this as a door-to-door trip, it’s a factor of 1.5-2 question, not an order of magnitude question. But a factor of 1.5 question is still serious, and it’s one that resolves itself with good public transit planning, rather than with not building high-speed rail at all.

# Modeling High-Speed Rail for Germany

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

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

The model

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

The gravity model to use is approximately,

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

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

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

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

The network

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

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

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

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

The power of polycentricity

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

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

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

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

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

# European Urbanism and High-Speed Rail

Europe has a number of strong national high-speed rail networks, providing much inspiration internally as well as abroad, including in the United States. With Americans looking at an infrastructure bill including high-speed rail funding, there’s a lot of discussion about what can port, hence my proposal map. That said, caution is required when doing naive comparisons with Europe. European urbanism doesn’t work the same as American urbanism, in two ways. First, European cities are more compact and transit-oriented than most American cities, which is why I somewhat discount American lines unless at least one city connected has public transit. And second, Europe has more, smaller cities than the rest of the urbanized world. This post concerns the second issue.

French and American urbanism: an example

A few months ago I poked around European and East Asian metro area lists. The upshot is that whereas in the three East Asian democracies 70% of the population lives in metropolitan areas larger than 1 million, in France only 33% does, and the median resident sorted by metro area size lives in a metro region of 350,000.

We can apply the same analysis to the United States. At the CSA level, the median American lives in Sacramento, population 2.6 million, and 68% live in metro areas of at least 1 million; at the MSA level, the median is Milwaukee, population 1.6 million, and 56% live in metro areas of at least 1 million. American metropolitan areas are unusually weakly-centered, especially at the CSA level, but otherwise they’re pretty typical of the urbanized world; it’s Europe that’s unusual in having such small cities.

The upshot is that people who are not used to this peculiarity of Europe who look at a map of European cities focus on million-plus metro areas, which are not the whole story here, especially not in France. This makes Europe look emptier than it is, which can lead people to overrate how much ridership a high-speed rail network would have at a fixed population.

France and the Midwest

Scott Hand posted a map on Twitter superimposing France on the Midwest with Chicago taking the place of Paris, arguing that they are similar in population and area:

This is a good sanity check: your Midwestern network should be of comparable magnitude to the TGV network, rather than much larger. It’s easy to say, Lyon has 2.5 million people, Detroit has 5 million people, so clearly a line to Detroit is twice as good as one to Lyon, right? But no: French urbanism supplies many more small cities, which must be accounted for as well. At the end of the day, the populations are similar, even though, in addition to Chicago, the map has three cities (Detroit, St. Louis, Cleveland) with larger metro areas than Lyon and six more larger than Marseille (Milwaukee, Indianapolis, Nashville, Cincinnati, Columbus, Pittsburgh).

The LGV Sud-Est

It’s tempting to compare Paris-Lyon to Chicago-St. Louis. Yonah Freemark did this in 2009, and Jarrett Walker already pointed out in comments that the LGV Sud-Est was always about much more than this. On hindsight, I’ll add that even that sells the LGV Sud-Est short. High-speed rail between Paris and Lyon unlocked fast service from Paris to not just Lyon but also the following metro areas, all with 2016 populations:

• Dijon (385,000), demoted from the PLM mainline to a branch but still served
• Grenoble (688,000)
• Saint-Etienne (520,000)
• Chambéry (225,000)
• Annecy (236,000)
• Valence (187,000)
• Vienne (115,000)
• Bourg-en-Bresse (128,000), not on any direct train but still close enough by regional connection or car

What’s more, TGVs would branch from Part-Dieu along legacy lines to serve these smaller cities, albeit at low frequency. Now, with the LGV extending as far south as Marseille, Valence has a through-station on an LGV just outside the built-up area. There’s also Lyria service to thee major Swiss cities; Geneva, a metro area of 1 million, lies on a low-speed extension of the LGV Sud-Est, 3:11 from Paris.

Other than Geneva, which is invisible on the map because it is farther away, the other cities listed are all very small. In the United States, people don’t usually think of metropolitan areas of such size as urban, because they are extremely dispersed and socially identify as not-urban, and because metropolitan America operates at much larger size classes. But they have recognizable urban cores and their populations must be put into any ridership model trying to train data on TGV ridership. In fact, a gravity model with exponent 0.8 predicts that the combined TGV ridership from Paris to all the above cities, excluding Lyon, is nearly twice the ridership on Paris-Lyon.

And in this context, Chicago-St. Louis simply doesn’t compare. St. Louis is somewhat larger than Lyon, yes, but within 60 km, within which radius Lyon has independent Saint-Etienne, Vienne, Bourg, and Mâcon, St. Louis only has its own exurbs. To find a proper Midwestern comparison for the LGV Sud-Est and its extensions toward Marseille, one must go east of Chicago, toward Detroit and Cleveland. Within 60 km Detroit too only has its own CSA plus Windsor, but that CSA has 5 million people, and the same line also reaches Cleveland (CSA population 3.5 million), Toledo (900,000), and Pittsburgh (2.6 million) and points east.

What this means

Having fewer, larger cities doesn’t make it harder to build high-speed rail. On the contrary – it’s easier to serve such a geography. Asia lives off of such geography; Japan and Taiwan serve nearly their entire populations on just a single line, and Korea does on one mainline with a branch. An Asianized France would be able to serve nearly its entire population on the LGV network as-is without needing low-frequency branches to Chambéry- and Valence-scale cities, and an Asianized Germany would be able to just build an all-high-speed network and connect nearly everyone and not just half the population.

There are small cities that happen to lie on convenient corridors between larger cities, the way Valence is between Lyon and Marseille, or Augsburg and Ulm are between Stuttgart and Munich. Other small cities are close enough to large cities that they’re decently-served by a large city-focused rail network, like Saint-Etienne. Those cities are compact, so a large share of the population has access to the train – this is the explanation for the 0.8 exponent in the gravity model of ridership. But overall, most cities of that scale are strewn haphazardly around the country: examples include Limoges, Amiens, and Caen in France, and Osnabrück, Chemnitz, and Rostock here.

However, this doesn’t mean that, in analyzing the impact of population on ridership, we should just pretend the small cities don’t exist. They do, and they supply extra ridership that isn’t visible if one thinks city = metro area of 1 million or more. It’s an understandable way of thinking, but Europe has a lot of ridership generated from intermediate cities and from cities that have a regional rail connection to a big city or a less frequent direct intercity train, and the models have to account for it.

So yes, that the US has so many large-by-European-standards cities means high-speed rail would work well there. However, it equally means that a naive model that just says “this looks like the LGV Sud-Est” would underperform. A better model has to account for specific city pairs. American city pairs still look okay, even with extreme levels of sprawl at the outer ends, but ultimately this means the US can have a network of approximately the same scope of the LGV network, rather than one that is much denser.

# Zoomers Day Trip to Bielefeld on the ICE

2033-04-01

There’s a rite of passage every year in Berlin of taking a day trip to Bielefeld, an hour and a half away by ICE, every 10 minutes. The idea is to be able to retort to aging millennials who joke that Bielefeld does not exist than they’ve actually been there.

The Abitur is coming soon, and 12th-grade students are supposed to study, but Adam Mansour, Katja Brühl, Max Kleinert, and Nora Martinek are going in Bielefeld. It is not the best day to travel. Friday is a school day, even if it’s short enough it ended at 13:30, and it’s also a popular travel day so the tickets were a bit more expensive, and Adam had to convince his parents it’s worth spending 80€ and all the Germans do it. But at least today it means they don’t have to wake up at 7:00 tomorrow.

On the train going west, Katja keeps complaining about how the train bypasses Magdeburg because of 1980s-90s politics. She says she was looking for labor-related museums in Bielefeld but couldn’t find any; instead, she talks about how the mayor of Hanover is leading a red-black coalition and it’s not the SPD that she’s voting for in September or the SPD that subsidized childcare in Berlin that let her parents afford to have children.

The other three don’t find her annoying. Max and Nora come from much wealthier families, and Nora’s is scratching 10,000€/month, but when Katja talks about how thanks to education reforms pushed on the Länder by the Green-led federal government she could go to the same school as them, they don’t feel either attacked or guilty. They feel happy that they know her and Adam. They listen to what she says about Jusos and housing, the EU, feminism, or comprehensive schools, and it clicks with them because it’s their world too. They know that there are people who resent that the cities are growing faster and associate immigration with social problems; but they associate immigration with Adam’s parents, or with Nora, who only moved to Germany when she was five but who nobody ever calls an immigrant. Adam, in turn, does get called a Syrian immigrant, even though he was born in Germany, his parents having arrived just before the 2015 wave.

There are some American tourists on the train, talking about how pretty Germany is and how they wished the United States could have such a system. Max leans forward and says, “every time they’re on a train, they talk just about the train,” figuring circumlocutions because the Americans might recognize the German word Amerikaner and realize he is talking about them. Nora and Katja giggle, and Adam then joins too.

Otherwise, they try to distract themselves by talking about the exams and about university plans. All plan to go, and all have been told by teachers that they should get good enough grades to go where they want, but Max wants to study medicine and needs to get a 1.0 to get past the numerus clausus. “Do you want me to test you?” Adam asks him.

“Lol.”

They are all competitive about grades, even Katja, who told them once that neoliberal models of academic competition promoted inequality, and the Greens should do more to prevent what she calls the Americanization of German education. But Max told them when they planned the trip last week that he was treating it as his vacation day when he wouldn’t need to think about school.

Getting off the train, they start walking toward city hall; Bielefeld doesn’t have a bikeshare system, unlike Berlin, and bringing a bike on the ICE is not allowed. Adam insists on stopping on the way and taking detours to photograph buildings; most aren’t architecturally notable, but they’re different from how Berlin looks.

They run to the Natural History Museum and the Kunsthalle. The museum closes at 17:00 and they have less than an hour, then less an hour at the Kunsthalle until it closes at 18:00. They furiously photograph exhibits when they don’t have enough time to look at them and talk about them.

Adam is especially frantic at the archeology section, just because of the reminder of what he is giving up. He has read a lot of popular history and for the longest time wanted to go study it, but felt like he wouldn’t be able to get work with a humanistic degree and instead went for the real stream at school. When he met Katja two years ago he felt like this choice was confirmed – Katja for all her political interests is going to study environmental engineering and at no point expressed doubt about it.

Max spits on the Richard Kaselowsky memorial when the staff isn’t looking, distracted by other customers. In Berlin he might not even do this, but in Bielefeld he wouldn’t mind getting thrown out of a museum if worst came to worst. Nora and Adam didn’t know the history so as they go in he tells them Kaselowsky was a Nazi and so was the museum’s founder Rudolf Oetker, and the Oetker heirs had to return a few items that may have been stolen from Jewish owners in the Holocaust.

They find a döner place with good reviews and good falafel for Katja and are eating there. Normally they’d go out and get different things in Berlin, but Bielefeld is still a small city and even with Germany’s rapid immigration in the 2020s it doesn’t have Berlin’s majority-migration-background demographics.

Where they’re sitting overlooks the pedestrianized streets of the old city. There are some bikes, some pedestrians, some walking delivery drones. Berlin has a few of these zones within the Ring but they’re not contiguous and Bild accuses the Greens of promoting car-free zones for everyone except the federal government.

They talk about where they want to go, but Max and Katja are hesitant to publicly say what they feel about where they are. It’s Nora who openly says that she’s having fun and that Bielefeld definitely exists no matter what her parents say, but she wouldn’t want to live here. She doesn’t know if she wants to stay in Berlin – she wants to go to TU Munich, partly to see more places, partly because of some parental pressure to leave home – but Bielefeld feels a little too dörferlich.

They all laugh, and Adam says that judging by how his parents describe Daraa, it was a lot smaller than this. He says that they didn’t ever describe Daraa as especially lively, and always compared it negatively with Berlin when he was young and then eventually they just stopped talking about it, it stopped being important to them. Max and Katja nod and start comparing Bielefeld to parts of Germany they know well through extended family – Max’s father is from Münster and his mother’s family is in Göttingen and Hamburg, Katja’s parents are both from Berlin but her mother has family in Fürstenwalde.

And then somehow it drifts back to the election. Katja is worried the Union might win the election this time, stop free work migration, and freeze the carbon taxes at present levels. Adam doesn’t have family left in Syria but they have a few classmates who have family in India, in Vietnam, in Turkey. For the most part things are okay, but there’s always the occasional teacher or group of students who still think Neukölln and Gesundbrunnen are bad neighborhoods; they know who to avoid because people who are racist always find something negative to say to Adam specifically.

But for now, they have one another, and they have exams to score highly on to move on and go to university, and they have two hours to kill in Bielefeld until the ICE train they booked in advance departs to take them back home.

# High-Speed Rail and the Pacific Northwest

The Pacific Northwest seems like the perfect region for high-speed rail: its cities form a neat line from Vancouver to Portland and points south, grow at high rates with transit-oriented development, and have sizable employment cores around the train station. And yet, when I generated my high-speed rail maps, I could only include it as a marginal case, and even that inclusion was charitable:

(Full-size image is available here.)

There’s been a lot of criticism over why I’m including Atlanta-Jacksonville but not Vancouver-Seattle-Portland, and I’d like to explain why the model says this.

Density

The population density in the Western United States is very low. What this means in practice is that cities are far apart – the best example is Denver, a large metropolitan area that is 537 km from the nearest million-plus metro area (Albuquerque). A high-speed line can connect two cities, maybe three, but will not form the multi-city trunk that one sees in Germany or Italy, or even Spain or France. Lines can still make sense if they serve enormous cities like Los Angeles, but otherwise there just isn’t much.

This relates to Metcalfe’s law of network effects. In a dense region, the 500-800 km radius around a city will have so many other cities that network effects are obtained as the system grows. Even Florida, which isn’t dense by European standards, has cities placed closely enough that a medium-size system can connect Miami, Orlando, Tampa, and Jacksonville, and then with a 500 km extension reach Atlanta. The I-85 corridor can likewise accrete cities along the way between Washington and Atlanta and get decent ridership.

In the Pacific Northwest, any intercity infrastructure has to live off Vancouver, Seattle, and Portland – that’s it. Spokane is small, orthogonal to the main line, and separated by mountains; Salem and Eugene are small and Salem is technically in the Portland combined statistical area; California’s cities are very far away and separated by mountains that would take a base tunnel to cross at speed. And Seattle is just not that big – the CSA has 5 million people, about the same as Berlin, which has within 530 km every German metropolitan area.

The model

The model thinks that with Vancouver (2.6)-Seattle (5) at 220 km and Seattle-Portland (3.2) at 280, ridership is as follows, in millions of passengers per year in both directions combined:

In operating profits in millions of dollars per year, this is,

This is $135 million a year. It’s actually more optimistic than the official WSDOT study, which thinks the line can’t make an operating profit at all, due to an error in converting between miles and kilometers. The WSDOT study also thinks the cost of the system is$24-42 billion, which is very high. Nonetheless, a normal cost for Vancouver-Portland HSR is on the order of $15 billion, a bit higher than the norm because of the need for some tunnels and some constrained urban construction through I-5 in Seattle. It isn’t even close. The financial ROI is 0.9%, which is below the rate of return for government debt in the very long run. Even with social benefits included, the rate is very low, maybe 2.5% – and once social benefits come into play, the value of capital rises because competing government investment priorities have social benefits too so it’s best to use the private-sector cost of capital, which is 4-5%. This exercise showcases the value of density to intercity rail networks. You don’t need Dutch density, but Western US density is too low – the network effects are too weak except in and around California. It would be mad to build Atlanta-Jacksonville as a high-speed rail segment on its own, but once the Florida network and the I-85 network preexist, justified by their internal ridership and by the Piedmont’s connections to the Northeast, connecting Atlanta and Jacksonville becomes valuable. Growth The one saving grace of the Pacific Northwest is growth. That’s why it’s even included on the map. Lines in the 1.5-1.8% ROI region are not depicted at all, namely Houston-New Orleans and Dallas-Oklahoma City-Kansas City-St. Louis, both discounted because none of the cities connected has local public transportation or a strong city center. The Pacific Northwest is not discounted, and also benefits from strong growth at all ends. The gravity model says that ridership is proportional to the 0.8th power of the population of each city connected. To get from 0.9% to 2% requires a factor of 2.2 growth, which requires each city to grow by a factor of 2.2^0.625 = 1.65. Is such growth plausible? Yes, in the long run. In 2006-16, Metro Vancouver grew 16%; in 2010-9, the core three-county Seattle metro area (not CSA) grew 16% as well, and the core Portland metro area (again, not CSA) grew 12%. At 16% growth per decade, the populations will rise by the required factor in 34 years, so building for the 20-year horizon and then relying on ridership growth in the 2050s and 60s isn’t bad. But then that has a lot of risk embedded in it – the growth of Seattle is focused on two companies in a similar industry, and that of Vancouver is to a large extent the same industry too. Moreover, the region’s relative YIMBYism can turn into NIMBYism fast. Metro Vancouver’s housing growth is healthy, but the region is fast running out of developable non-residential areas closer in than Surrey, which means it will need to replace single-family housing on the West Side with apartment buildings, which it hasn’t done so far. Growing construction costs are also threatening the ability of both Vancouver and Seattle to feed commuters into their central business districts by rail – Seattle may have built U-Link for costs that exist in Germany, but the Ballard/West Seattle line is$650 million/km and mostly above-ground, and the Broadway subway in Vancouver, while only C\$500 million/km, is still on the expensive side by non-Anglo standards. It’s useful to plan around future growth and safeguard the line, but not to build it just on the promise of future growth, not at this stage.

# High-Speed Rail Followup

My high-speed rail map exploded, thanks to retweets on social media from the Neoliberal account and Matt Yglesias, who posted a cleaner map of my proposal made by Twitter follower Queaugie, who even called me a transit guru:

So, first of all, thanks to Queaugie for making this, it’s much cleaner than my drawings on an OpenStreetMap base; I keep advocating for geographically accurate maps, but schematics do sometimes have their uses. But more to the point, I’d like to give some context to why some lines are and are not included.

Some examples of past maps

Mapped proposals for American high-speed rail go back a while. On the Internet, interest exploded in the 2000s, leading to high hopes for California High-Speed Rail and the Obama stimulus. Yonah Freemark made one at the beginning of 2009, which played a role in his rise to become a superstar public transit wonk. The RPA had its own plan rooted in the concept of megaregions: see here for analysis from 2011 and here for a synthetic map. But the map that’s getting the most airplay is by Alfred Twu, which is very expansive to the point of having two transcontinental connections; it was most recently covered in Vox and tweeted by Secretary of Transportation Pete Buttigieg, which generated so much discussion that I chose to crayon US high-speed rail rather than my original intention of picking a city and crayoning urban rail for it.

How my proposal differs

My map differs from past ones in visible ways – for one, it is not connected. At the time I started to make it, I believed there would be four components: Florida, Texas, California, and the general Eastern network. It turned out late in the process that there’s decent demand for Atlanta-Florida travel, enough to justify connecting Florida to the general network. But Texas and California remain disconnected, as does the marginal case of the Pacific Northwest.

Analytically, I project traffic by a gravity model, depending on the product of two metro areas’ populations; Yonah and the RPA have different methodologies. But the emergent difference is, first of all, that I have a less connected network, and second, that there are some glaring omissions. I believe those omissions are justified and would like to explain why – in effect, why other people overrate connections that I do not include.

Amtrak and stagnating regions

New Orleans was the largest city in the South until overtaken by Houston around 1950. This means that the historic rail network of the United States served it amply, as it was large relative to turn-of-the-century America. Amtrak, formed to preserve a skeleton of the preexisting passenger rail network, retained the importance of New Orleans and gave it three distinct long-distance routes: one to Atlanta and New York, one to Chicago, one on the way between Florida and California. This way, there is more Amtrak service to New Orleans today than to Houston, whose metro area is around five times larger.

Proposals tend to build upon what exists. So most people recognize that at transcontinental scale, high-speed rail is uncompetitive, but at the scale of Atlanta-Birmingham-New Orleans it looks like a reasonable line. It should get decent modal split, if built. The problem is that not many people live in New Orleans today. The population one needs to sustain high-speed rail is large, larger than that of your typical early-20th century city. This can be done either via a megacity that drives ridership, as in France or California, or via high population density so that many midsize cities are close together, as in Germany or Florida; the best geography is when both are present, as in Japan, South Korea, China, and the Northeastern US.

The growth of the South in the last 70 years has not been even. Texas has exploded, and so have Atlanta, Nashville, and the cities of the North Carolina Piedmont. In contrast, New Orleans is stagnant. Farther north, on the margins of the South, Missouri has had about the same population growth since 1920 as New York, and has been steadily losing seats in Congress. St. Louis and Kansas City, like New Orleans, were huge hubs for early-20th century America, but their populations are just not good enough for high-speed rail. Chicago-St. Louis can squeak by, but Kansas City is too far. Memphis is in relative decline as well, but manages to piggyback on Nashville, albeit marginally.