# The Greta Effect

Bloomberg is reporting that Germany and Sweden are seeing a trend of reduced domestic air travel and greater rail usage. In Germany, intercontinental air traffic is up 2% year-over-year and international European traffic is down 2%, but domestic traffic has crashed in the last few months and is down 12% now. In Sweden, domestic air traffic is down 11%.

The Greta effect

Greta Thunberg famously crossed the Atlantic by sailboat to avoid personally contributing to greenhouse gas emissions. But she’s fairly practical about alternatives and said right out that she travels in such conditions to highlight how difficult complete decarbonization is. She is also very insistent on the fact that while changes in behavior are nice, collective political action is still needed.

Moreover, the young (as in, younger than me) Greens I meet in Germany are themselves practical as well. The more committed might take a train to France or Italy, but there’s not much interest in back-to-the-land 1960s communes, degrowth, or political revolution in the sense of the socialists and anarchists. Nor have I seen anti-nuclear sentiments recently – the one anti-nuclear sign I saw at the September 20th climate march, which had 100,000 people in attendance, was held by a pensioner and someone who looked 40, whereas the median age at the rally looked like 20.

It’s relatively easy to change travel behavior to avoid domestic flying in Germany as well as Sweden. Domestic rail travel pain in Germany means hourly Hamburg-Munich and Berlin-Stuttgart trains take 5:40 each. International rail travel pain means Berlin-Paris trains take 8:11 with a short transfer that I don’t trust DB or SNCF to meet. Domestic trains only get this long if many transfers are needed, in which case the main competition to the train is the car rather than the airplane, or if one needs to travel between Umeå (population 123,000) and central or southern Sweden. It’s thus likely that the shift in travel pattern reflects a change in consumer desires to avoid polluting – other explanations, such as the grounding of the 737 MAX, would equally affect domestic and European air travel.

Upcoming carbon taxation

Germany has been planning climate legislation for years, but the September 20th protest created a lot of pressure on the government to enact an aggressive package. A carbon tax will begin at €25/t-CO2 in 2021 and rise to €55/t by 2025, where the original plan was to only go up to €35/t. Sweden has had a carbon tax going back to 1991; starting in 2014, the Löfven cabinet has hiked the tax on industry to match the tax on transportation, both currently at €114/t. The effects on the German economy are to be seen, but in Sweden, economic growth has been healthy throughout this period, ahead of any not-newly-industrialized developed country save Australia (although the differences near the top are small).

In addition to the German carbon tax package, the EU is planning to levy a carbon tax on jet fuel for internal flights; so far, international emissions, including international aviation and shipping, are not subject to carbon tax. A leaked report suggests the EU is considering a tax of €330 per 1,000 liters of jet fuel, which corresponds to a hefty €130/t-CO2, the high figure coming from the fact that a ton of CO2 emitted at high altitude causes more global warming than one emitted at ground level. A very fuel-efficient plane like the A320neo consumes 2.25 liters per 100 seat-km on a 1,200 km flight, raising fares on a full flight by €9.06, which is not a game changer but is noticeable at low-cost carrier rates.

Planning for busier trains

The upshot is that demand for flights in Europe is likely to go down, shifting toward rail. The article linked above about the Greta effect says that DB expects its intercity rail traffic to double to 260 million passengers a year by 2040. The article makes no mention of which further investments in intercity rail DB is assuming, but a virtuous cycle is likely: higher ridership justifies more investment, and faster and more convenient trains attract higher ridership.

Of note, the weakness of international rail in Europe points to international connections as an investment priority. In Sweden, trains from Stockholm are fast toward Gothenburg and Malmö, averaging almost 140 km/h, and there are unfunded plans for high-speed rail connecting the three largest cities. However, Stockholm-Oslo trains are quite slow (about 6 hours for what looks like 500 km), even though Oslo is bigger than Gothenburg and Malmö and there are extensive economic and cultural connections between the Nordic countries. The Greens have called for Stockholm-Oslo high-speed rail, and the government should work with Norway on establishing such a line.

In Germany, the situation is different. London and Paris are vast cities, and Paris is within reasonable high-speed rail distance of most of Germany, with good connections on the French side and poor ones on the German one. Trains between Paris and Frankfurt take about 3:48, of which 1:47 is between Paris and Saarbrücken on the German side of the border, a distance of 380 km, and then 2:00 is between Saarbrücken and Frankfurt, a distance of about 200 km by rail and 160 by air. In Belgium, the existing high-speed line east of Brussels is compromised to the point of being slower between Brussels and Liège or Aachen than legacy lines like Stockholm-Gothenburg or London-Manchester.

The reason the map of the high-speed rail I think Germany should build is heavy on international connections is mostly that Europe is gradually building thicker international economic and social connections. However, a future with more expensive air travel and a consumer taste for greener ways of travel does not change the basic picture, and makes it more urgent.

(Map legend: blue is existing or under-construction lines, red is lines that are either in planning or not even in planning but should be built.)

Speed and capacity

DB’s forecast for 260 million annual rail travelers argues in favor of building more capacity. However, in no way does this conflict with building a dedicated high-speed rail network for Germany. On the contrary, the bypasses providing relief to congested lines are already planned to be high-speed: this was the case for the Tokaido Shinkansen and LGV Sud-Est decades ago, and this is now the case for HS2 and the planned Frankfurt-Mannheim express connection.

A largely dedicated network for high-speed passenger rail, with freight using the legacy lines, improves intercity rail reliability, allowing average speeds to rise to be closer to their theoretical technical maximums. Average speeds of 250 km/h on a few lines are plausible, as on Paris-Strasbourg or Madrid-Barcelona. Moreover, through-tunnels enabling intercity trains to run through Frankfurt and possibly Munich without reversing direction facilitate planning high-speed rail as a separate system. Timed connections with regional trains remain important, but critical trunks like Frankfurt-Cologne and Berlin-Hanover can run very frequently.

The schedule I tried writing for the above map in which domestic city pairs mostly run every half hour all day, interlining on a few trunks, assumes ridership of about 250 million. This is not the same as DB’s forecast of 260 million: this counts only high-speed rail riders, and assumes the average trip is 350 km long. To get from DB’s forecast to 87.5 billion p-km per year requires the virtuous cycle of higher ridership and more investment to work over time, but this is plausible given high levels of investment.

Green convenience

When Greta talks about systemic solutions, she understands that it’s important to make it easier to live a comfortable life without greenhouse gas emissions and harder to live one with high emissions. There are many aspects to green convenience: carbon-free electricity (largely achieved in Sweden but not in Germany), pedestrian- and bike-friendly streets, urban and periurban public transport, intercity and freight rail, passive solar design, urban density, carbon-free industrial power generation.

In every case, it’s important to seize upon any social, economic, or political trend that facilitates the green option. If people want to live in big central cities, then governments should make it easy to build housing there so that more people can enjoy the low-carbon wealth of Munich or Stockholm rather than live in cheap declining rural areas and drive. If people support solar power, then governments should leverage its political popularity and subsidize it to decarbonize electricity.

In the case of intercity transportation, a shift in taste toward intercity rail is a cause for celebration. Europe is full of intercity trunk lines ranging from ones that scream “build me now” no matter what (HS2, completing Berlin-Munich, etc.) to speculative ones. Any positive shift toward rail justifies adding ever more marginal intercity rail lines to the network. Perhaps if the network I mapped was justified before the Greta effect, after the Greta effect the most marginal parts of the network (like Stuttgart-Würzburg) are on more solid footing, while unmapped marginal lines like Munich-Prague or even Bremen-Oldenburg-Groningen become plausible.

But celebration does not mean idleness. Climate change is a systemic issue. The state must plan ahead, using the shift toward rail to plan further investments now so that they open in the 2020s and early 30s. This way, the rail network will meet near- and medium-term growth in demand, while stimulating long-term growth, to be satisfied through future investment, paid by taxes on the richer Germany of the 2030s. Good transit activists should take a page from Greta’s refusal to treat good news as grounds for letting up, and demand intensive investment in Europe’s rail network to ensure that green travel will be more convenient, featuring higher speeds rather than more sitting on luggage in the corridors of full trains.

# The Brooklyn Bus Redesign is Out!

Marron just published my and Eric Goldwyn’s Brooklyn bus redesign proposal (with many thanks to Juliet Eldred for doing the graphics and design). The substance isn’t really changed from what we discussed last year. The delay in publication has had a few causes, of which I believe the biggest is that I completely missed that the links to many of the references in the lit review were dead and thus could not be typeset.

Instead of retyping an old blog post, I want to emphasize a few things that have come up in the last year. Some are specific to New York, others more general within the US. The idea of a bus redesign, introduced to the American discourse by Jarrett at the beginning of this decade, has gotten steadily more popular, and New York is beginning its own process, starting with the Bronx; in that context, it’s worthwhile pointing out specifics that Eric and I have learned from the Brooklyn process.

The redesign is a process, not a one-and-done program

Cities change. The point of a bus redesign is to let the bus network reflect the city of today and not that of when bus routes were set, typically when the streetcars were removed in the postwar era. The upshot is that the city can expect to change in the future, which means further bus redesigns may be necessary.

Instead of letting bus networks drift away from serving the city as is and doing a big redesign once in a generation, cities should change buses on an ongoing basis. American transit agencies are learning the principles of bus redesign this decade. They can and should use these principles for forward planning, tweaking bus routes as needed. Any of the following changes can trigger small changes in bus service:

• New development
• Shifts in commuting patterns even without new development
• Changes in traffic patterns
• Changes in the urban rail network
• Long-term changes in driver labor, maintenance, etc.
• Changes in bus technology, such as ride quality, dispatching, or pollution levels

In New York, the biggest ongoing change is probably the urban rail network. There are no subway extensions planned for Brooklyn, but there is expansion of subway accessibility, which changes the optimal bus network since some buses, like the B25 and B63, have no reason to exist if the subway lines they parallel are made accessible. There has been extensive activism about priorities here. To its credit, the MTA is accelerating accessibility retrofits, even though construction costs are extremely high.

New York’s current redesign process is flawed

Eric and I have heard negative feedback from various people involved in the process. Some are planners. One is a community activist, enough of a railfan and busfan not to NIMBY changes for the sake of NIMBYism, but nonetheless disaffected with how the Bronx redesign went.

As far as I can tell, the problem with the current process is that it’s too timid. In the Bronx, this timidity is understandable. The borough’s bus network is mostly good enough. The most important change in the Bronx is to speed up the buses through off-board fare collection, stop consolidation, bus lanes on main streets, and conditional signal priority, and plug the extra speed into higher frequency.

The MTA treats it as part of a separate process – select bus service (“SBS”) – and even though planning these two aspects separately is workable, the MTA does not understand that they are related and that speedups provide crucial resources for higher frequency. The problem here is with operating cost estimation. Like the other American agencies where I’ve asked, the MTA assumes bus costs scale with service-km, and thus higher speeds don’t change frequency. In reality, bus costs, dominated by driver wages, scale with service-hours. Higher speeds can be plugged one-to-one into higher frequency. In Brooklyn, only 30% of the benefits we estimate come from changing the network, and the other 70% come from speeding up the buses.

But Brooklyn is not the Bronx. The Bronx is largely good enough, in ways Brooklyn isn’t. Brooklyn is not terrible, but the bus network has too many circuitous or duplicative routes. Eric and I have consolidated about 530 km of bus route down to 350, without any of the coverage vs. ridership tradeoffs common to areas with less isotropic population density than Brooklyn. The MTA needs to be bolder in Brooklyn, and even bolder than that in Queens, if the redesign is to succeed.

The 14th Street bus lane

Eric and I encountered some political resistance to the idea of mass installation of bus lanes. Local interests listen to people with local connections, who are usually drivers. Transit riders are disproportionately riding to city center jobs, and have citywide rather than local political identities. When I went to an Open New York meeting, people began with a round of introductions in which people say their names and where they live, and the about 20 attendees represented maybe 15 different city neighborhoods. The upshot is that like Open New York’s mission of building more housing, the mission of diverting scarce street space from drivers to bus riders is best done on a citywide rather than street-by-street basis.

There is some hope of such a transformation happening. The bus lane on 14th Street survived a nuisance lawsuit, and ridership rose 17% almost immediately after it opened. The success is stark enough that a citywide increase in installation is plausible. City council speaker Corey Johnson promised to install 48 km of bus lane per year were he to be elected mayor, which is too passive but could do some good on the busiest routes.

# Quick Note: What is Culture, Anyway?

Six weeks ago, I talked about the Anglosphere in context of its high construction costs, especially recently. In comes Bella Wang, and in a much greater generality, asserts,

In the context of transportation, there are some empirical observations from construction cost and mode share data:

• American transit usage underperforms any other first-world standard
• Anglosphere construction costs are very high
• Ex-colonies in the third world have very high construction costs

We can take all three observations to be matters of culture, but really culture is a measure of ignorance. It’s easy to list so many US-rest-of-world cultural differences, and still possible to list Anglosphere-rest-of-world differences that cover Singapore. But the question, which of them are relevant and which aren’t?, is still critical.

Separately, there’s the question, how deep is a specific cultural attribute? The example I want to zoom in on is the issue of hyperlocalism and too many stakeholders. In Brooks-Liscow, it’s identified as a key contributing factor to rising highway construction costs in the US since the 1960s (“citizen voice”) alongside rising incomes. In addition, one expert Eric and I talked to mentioned the multiplicity of stakeholders, as well as many other issues, not all of which I think are relevant.

From one angle, hyperlocalism goes very deep in American culture. Some of it is relatively recent, coming from the white middle class’s desire to maintain local control as the only way to legally prevent integration. Some of it is older – New England had a lot of local empowerment in the 18th and 19th centuries, and unlike in Europe, local elites were viewed as leaders who brought freedom rather than as the main obstacles to freedom.

But from another angle, the specific mechanism through which hyperlocalism acts is not that deep. The local gadfly who launches nuisance lawsuits against everything is a figure of derision; the politician who cuts through the red tape and knocks some heads together and gets things done is a figure of worship and a prime candidate for higher office. If anything, the reason things do not get done in the United States is that politicians prefer to play it safe and knock heads together on low-risk, low-reward projects, hence for example Andrew Cuomo’s proposal for a LaGuardia air train that goes the wrong way but avoids a NIMBY fight from 20 years ago.

The example of Cuomo’s air train, in turn, introduces another attribute: do-nothing politicians. That’s a fairly American problem – other high-cost countries, like Britain and Canada, have politicians that build extravagant projects at high cost, but those projects (HS2, Ontario Line, etc.) are actually useful. Is it a result of an American legal regime that favors the state against the individual and therefore cannot guarantee security of property unless the government credibly pledges to be slow and stupid? Or is it a contingent effect of a handful of governors being slow and stupid in 2019, which may change if someone more competent is elected in the future?

The ultimate question is “can anything get better?”. There’s a lot of evidence in both directions when it comes to American construction costs; when it comes to transit usage in the vast majority of the United States where there is no public transit, the same is true but right now I believe the evidence is stronger on the “no” side.

# What I Mean When I Say Cities Have no Transit

On social media and various forums, I have an expression for a variety of cities: “it has no public transportation.” This concerns just about the entire United States excluding a handful of cities like New York, San Francisco, and Chicago; Los Angeles notably is not among these handful, but has no public transportation, and neither do any cities in the South or the Midwest except Chicago. I want to talk a bit more about what I mean by this. I obviously don’t mean that literally there is no scheduled public transportation in these cities; I’ve taken these non-existent transit systems, in Los Angeles on a visit and in Providence when I lived there. But I mean that there’s something about such places distinguishing them from the bad-but-existing transit category of Boston, Chicago, Nice, etc.

Whatever you’re doing isn’t working

Let’s use an 8% cutoff for trips to work. This number is fully motivated reasoning: the metro area (MSA, not CSA) of Philadelphia is just above this cutoff, and I would not say it has no public transportation, at least not in the current state of the system. Bad, yes, but it exists. I may be missing some areas, but I don’t think I am: the list of American metro areas that meet that cutoff is New York, San Francisco, Boston, Washington, Chicago, Fairfield County, Seattle, Kitsap County, Philadelphia, Honolulu. 70% of American transit commuters live in one of these MSAs. Go down to 6% and you also get Portland and Baltimore, adding about 2.5% of US transit commuters.

Nor are things improving. Some parts of the US are seeing rising mode shares. The most notable is Seattle, which is serious about permitting urban housing, and has tunneling construction costs that would only get Europeans fired rather than simply not existing in democratic Continental Europe. But other cities that occasionally win accolades from American urbanists for investing in public transportation just aren’t cutting it. In the 2006-17 period, chosen because that’s what the ACS makes available, Denver went from 4.6% to 4.4%, Los Angeles from 6.1% to 4.8%, and Portland from 6.4% to 6.3%; in the praised-by-urbanists set, only Minneapolis went up, from 4% to 4.8%.

Let’s unpack what this means: whatever Los Angeles has been doing in the last 10+ years has gotten its mode share down – and that’s without counting the fact that the Inland Empire, officially a separate metro area, is growing much faster and has an even lower mode share, as people drive further and further from jobs to qualify for a mortgage. Portland and Denver have done a lot of supposedly good things with their light rail networks, but are standing still. Portland’s stagnation goes back at least to 1980, while Vancouver has built SkyTrain, a high-rise downtown, and Metrotown, and at 20% has a higher (and rising) mode share than any American metro area save New York.

Tabula rasa

When a metro area has 2-3% mode share, it’s best to treat it as tabula rasa. Yes, there are people who ride the buses and trains today, but so few that the advantages of from-scratch design are usually greater than the disadvantage coming from the risk to current ridership. The 2-3% figure really depends on the situation – I don’t want to give it as an ironclad figure.

Suburbs of very large cities (read: New York) approaching 10% may still be best treated the same way: commuter rail systems like the LIRR are really shuttles that extend auto-oriented suburbia into the city rather than the reverse. Sadly, where I say such suburbs have no transit as a positive statement, an MBTA general manager said “commuter rail is not public transit” as a normative statement.

The situations of extremely low-mode share metro areas and low-mode share suburbs are not exactly the same. For one, existing ridership is higher on Long Island than in Cleveland or St. Louis so there’s more risk if (for example) supernumerary workers go on strike to fight efficiency improvements, but the reward is much greater. We know how to squeeze high ridership out of regional rail in the suburbs, even low-density ones, since the city has so many jobs in the center. Moreover, we know which ready sources of ridership are suppressed by current operating patterns: working-class reverse-commuters, people who work non-traditional hours regardless of class, and peak-direction commuters getting off short of city center.

The tabula rasa concept notably does not mean the infrastructure doesn’t exist. Los Angeles has the physical infrastructure of a rail network. Long Island and Westchester have many rail lines pointing toward Manhattan. However, the operating patterns and development are deficient and little to no accommodation should be made for them. In the suburbs of New York and a handful of other American cities this concerns premium fares, low off-peak frequency, and lack of integration with local buses. In American metro areas with low overall ridership this concerns weak city centers, lack of TOD even when it could succeed (for example in Los Angeles and San Diego), local political systems that view transit as an excuse to get federal funds for other things such as road repaving, and, as in suburbia, low off-peak frequency. The problems vary, but the fact that there are severe problems remains.

The other element of tabula rasa is social. There is almost never any knowledge base in those areas about how good transit works, because people who’ve only lived there have by definition not regularly used even bad-but-existing public transport. Whatever local activists of all stripes have been doing in Los Angeles is not working. Understanding why from them can be valuable, for the same reason I talk to planners at poorly-run agencies like the MTA and the MBTA to understand what’s wrong, but all local practices should be considered suspect unless corroborated in an area with at least decent public transportation.

On giving offense

The people who complain about my use of “no transit” to refer to the vast majority of the United States are not making a semantic nitpick or asking for clarification. They specifically complain I give offense by erasing 2-3% of the population of Cleveland and St. Louis, or 1% of the population of Kansas City. (I name these cities and not 6% Portland because that’s what people have complained about to me.)

So let’s unpack what this means. I point out that in the vast majority of the United States, excepting a handful of regions all of which are politically stereotyped as Not Real America partly because they have public transit, has buses and trains that are so useless they might as well not exist. I point out that this remains the case despite extensive construction in many cities – Dallas has 150 km of light rail, which is respectable for a city of its size, Denver keeps expanding its network and has something resembling frequent regional rail, and so on. The problem is that I do not conveniently blame this on a political faction of others, be it Republicans, unions, moderates, drivers, or whoever. I genuinely think it’s the fault of everyone who’s had any amount of power, and this includes community organizations that keep identifying as always losing even when they repeatedly succeed in blocking changes they dislike.

This is American culture. Even the denigration of New York and other cities where there is public transportation is part of that culture; there are certain aspects of San Francisco, Boston, and Philadelphia that are useful for other parts of the US to emulate. But accepting that requires understanding that there is to a good approximation no contribution coming from no-transit cities (and this again includes Portland and Los Angeles, it’s not just Cleveland or Dallas).

Part of the problem is that the US defines itself so much around cars and car culture that the presence of public transportation is enough to make something feel not really American. The result is that any exhortation to learn from places with trains with decent ridership is bound to offend; I might as well tell Americans to move to Tokyo and learn Japanese and never come back to the West. But sadly for Americans, reality can be offensive. The culture of Real America has to change, at least when it comes to how to treat transportation and cities.

# I’m Giving a Talk About Construction Costs Tomorrow

By popular demand, I’m giving the talk I gave 2 weeks ago at NYU, again. The database will be revised slightly to include more examples (like Ukraine, which I added between when I gave the talk and when I blogged about it), and I may switch around a few things, but it should be similar to what I already said.

Where? Halyards in Brooklyn at 3rd Avenue and 6th Street, near the 4th Avenue/9th Street subway stop where the F/G and R intersect.

When? Monday December 2nd at 9 pm, for an hour.

Do I need to RSVP? No.

Will there be food? To some extent – the bar has minimal selection, although what it does have on the menu seems better for the price than most American bar food (which, to be fair, is like saying “better public transportation than Los Angeles”).

# Little Things That Matter: Jerk

When you ride a subway train, and the train decelerates to its station, you feel your body pulled forward, and your muscles tense to adjust, but then when the train reaches a sudden stop, you are suddenly flung backward, since you are no longer decelerating, but your muscles take time to relax and stop fighting a braking that no longer exist. This effect is called jerk, and is defined to be change in acceleration, just as acceleration is change in speed and speed is change in position. Controlling jerk is crucial for a smooth railway ride. Unfortunately, American mainline rail is not good at this, leading to noticeable jolts by passengers even though speed limits on curves and acceleration rates are very conservative.

This is particularly important for speeding up mainline trains around New York and other legacy cities in the US, like Boston. Speeding up the slowest segments is more important than speeding up the fastest ones; my schedules for New York-New Haven trains, cutting trip times from 2:09 to 1:24, save 4 minutes between Grand Central and 59th Street just through avoiding slowdowns in the interlocking. The interlocking is slow because the switches have very conservative speed limits relative to curve radius (that is, lateral acceleration), which in turn is because they are not designed with good lateral jerk control. The good news is that replacing the necessary infrastructure is not so onerous, provided the railroads know what they need to do and avoid running heavy diesel locomotives on delicate infrastructure.

Spirals and jerk

In practice, the worst jerk is usually not forward or backward, except in the last fraction of a second at the end of acceleration. This is because it takes about a second for train motors to rev up, which controls jerk during acceleration. Rather, the worst is sideways, because it is possible to design curves that transition abruptly from straight track, on which there is no lateral acceleration, to curved track, on which there is, in the form of centrifugal force centripetal force.

To reduce jerk, the transition from straight track to a circular arc is done gradually. There are a number of usable transition curve (see Romain Bosquet’s thesis, PDF-p. 36), but the most common by far is called the clothoid, which has the property of having constant change in curvature per unit of arc length – that is, constant jerk. Different countries have different standards for how long the clothoid should be, that is what the maximum lateral jerk is. Per Martin Lindahl’s thesis, the limit in Sweden is 55 mm/s (PDF-p. 30) and that in Germany is 69.44 mm/s (PDF-p. 38), both measured in units of cant deficiency; in SI units, this is 0.367 m/s^3 and 0.463 m/s^3 respectively. In France, the regular limit is 50 mm/s (Bosquet’s thesis, PDF-p. 35), that is 0.333 m/s^2, but it is specifically waived in turnouts.

Track switches are somehow accepted as sites of very high jerk. A presentation about various technical limits in France notes on p. 106 that in switches (“appareils de voie” or “aiguilles” or “aiguillages,” depending on source, just like “switch” vs. “turnout” in English), the jerk can be increased to 100 and even 125 mm/s. On p. 107 it even asserts that in exceptional circumstances, abrupt change in cant deficiency of up to 50 mm on main track and 100 on the diverging direction on a switch is allowed; see also PDF-pp. 13-15 of a pan-European presentation. Abrupt changes are not good for passengers, but will not derail a train.

Second derivative control, that is acceleration and cant deficiency, can be done using calculus and trigonometry tools. Third derivative control, that is clothoids and jerk, requires numerical calculations, but fortunately they are approximated well by pretending the clothoid is half straight line, half circular arc, with the length determined by the maximum jerk. Working from first principles, it’s possible to figure out that at typical turnout needs – e.g. move a train from one track to a parallel track 4 meters away – the clothoid is far longer than the curve itself, and at 50 mm/s jerk and 150 mm cant deficiency it’s not even possible to hit a curve radius of 250 meters.

Turnouts are inherently compromises. The question is just where to compromise. Here, for example, is a French turnout design, in two forms: 0.11 and 0.085. The numbers denoting the tangent of the angle at the frog, and the radius is proportional to the inverse square of the number, thus the speed is proportional to the inverse of the number. The sharper turnout, the 0.11, has a radius of 281 meters, a maximum speed of 50 km/h, and a total length of 26 meters from point to frog (“lead” in US usage), of which the clothoid curve (“point”) takes up 11, to limit jerk to 125 mm/s at a cant deficiency of 100 mm. The 0.085 turnout has a radius of 485 meters, a maximum speed of 65 km/h, a lead of about 38 meters, and a point of about 14.5 meters.

In Germany, turnouts have somewhat independent numbers and radii – some have shorter leads than others. The numbers are the inverse of those of France, so what France calls 0.11, Germany calls 1:9, but at the end of the day, the curve radius is the important part, with a cant deficiency of 100 mm. A higher cant deficiency may be desirable, but lengthening the point requires almost as much space as just increasing the curve radius, so might as well stick with the more comfortable limits.

American turnouts look similar to French or German ones, at first glance. I’ve seen a number of different designs; here’s one by CSX, on PDF-pp. 22 (#8) and 24 (#10), the numbers being very roughly comparable to German ones and inverses of French ones. CSX’s #10 has a curve radius of 779.39′, or 238 meters, and a lead of 24 meters, both numbers slightly tighter than the French 0.11. The radius is proportional to the square of the number, and so speed is proportional to the number.

However, the cant deficiency is just 50 mm. The point is not always curved; Amtrak’s low-number switches are not, so the change in cant deficiency is abrupt. Judging by what I experience every time I take a train between New York and New Haven, Metro-North’s switches have abrupt change in cant deficiency even on the mainline. The recommended standards by AREMA involve a curved point, but the point is still much shorter than in France (19.5′, or just under 6 meters, on a #12), so a 125 mm/s jerk only gets one up to about 62 mm cant deficiency.

The reason for this is that European turnouts are curved through the frog, whereas American ones are always straight at the frog. Extremely heavy American freight trains do not interact well with curved frogs and long points.

One might ask, why bother with such turnout design on rail segments that never see a heavy freight locomotive or 130-ton freight car? And on segments that do see the odd freight locomotive, like the approaches to Grand Central and Penn Station with the rare dual-mode locomotive, why not kick out anything that doesn’t interact well with advanced track design? Making a handful of passengers transfer would save around 4 minutes of trip time on the last mile into Grand Central alone for everyone else, not to mention time savings farther up the line.

# Fare Regulations

Public transportation companies may have the ability to raise fares arbitrarily based on market demands, for examples British buses outside London and American freight railroads. Or they may be subject to regulations capping the fare, for example Japanese railroads. Mixed systems exist as well, such as British rail fares. In Britain, the privatized, mostly deregulated approach is so commonly accepted that a Conservative recently called Labour dangerous socialists for proposing municipalizing bus systems, as in such socialist states as the US, Japan, Germany, etc. In reality, in the case of rail specifically (and perhaps buses as well), there’s a theoretical case with some empirical backing for why reasonable fare caps as in Japan can lead to more investment and more capacity, whereas wholly unregulated fares lead to hoarding and capacity cuts to create shortages.

The model

I’m stealing the economic model for this post from Paul Krugman, who used it to explain the California blackouts of 2000-1. The demand curve is inelastic: the demand is 1,000 units at $20/unit, decreasing to 900 units at$1,000/unit, at which point the curve goes flat. The supply curve is a constant $20/unit, but the market is oligopolistic (say, there are very high barriers to entry because building your own power plant is hard), and there are 5 producers, each with 200 units. If the price is regulated at$20/unit, each producer will supply 200 units. If the price is unregulated, then each producer alone gets an incentive to hold back production, since 100*1000 > 200*20, and then production will be curtailed to 900 units.

The model is simplified in a number of ways: real supply curves slope up; the part about demand going flat at 900 units is unrealistic and exists purely to avoid dealing with optimizing where at 800-something units each producer has an incentive to go back to producing more; capacity constraints involve escalating production costs rather than a God-given restriction on the number of suppliers and their capacity. But with all these caveats, it fits markets that have the following characteristics:

• There are steep barriers to entry, for example if large amounts of capital are required to enter (to build a power plant, set up a rail operating company, etc.).
• Demand is highly inelastic.
• Adding new capacity is expensive.

The issue of capacity

In rail, we can start plugging real numbers for both demand elasticity and the cost of new capacity.

In the above model the price elasticity is -0.0244 in the 900-1,000 units range, which is ridiculously inelastic, on purpose so as to highlight how the model works. TCRP Report 95 says the elasticity in a number of large cities studied is about -0.18, and a VTPI review in a mixture of cities and circumstances (peak vs. off-peak, bus vs. rail, etc.) asserts a short-term average of about -0.3. Unregulated fares will lead to supply reductions if the elasticity times the number of producers is more than -1 (or less than 1 if you flip signs); if no producer has <18% of the market, there will be supply restrictions under unregulated fares, just as a monopolist will hold back supply and raise fares if demand is inelastic.

The cost of new capacity of course depends on the line and the characteristics of competition between different railroads. It’s higher in Japan, where separate railroads run their own lines and trains, than in Britain, where different companies franchise to run trains on the same tracks. But even in Britain, getting a franchise requires a commitment to running service for many years. The significance of this is that the long-run public transport ridership elasticity with respect to fare is more elastic (VTPI recommends a range of -0.6 to -0.9), with a few estimates even going below -1.

For the purposes of this section, we do not distinguish capital from operating costs. Thus, the cost of new capacity is not given in units of capital costs, but in units of operating costs: if increasing service by 1% raises operating expenses by 2% counting the extra investment required, then we say the supply elasticity is 2. Note that supply curves slope up so the elasticity is always positive, but the elasticity can be below 1, for example if economies of scale are more important than the need to invest in new capacity.

Set the following variables: u is quantity of service, r is total revenue (thus, fare is r/u), c is total costs. The railroad is assumed profitable, so r > c. We are interested in the change in profit based on quantity of service, i.e.

$\frac{dr}{du} - \frac{dc}{du}.$

The important thing to note is that price controls keep dr/du higher in an oligopoly (but not in a competitive environment, like housing – a single landlord can’t meaningfully create a housing shortage). With price controls, we get

$\frac{dr}{du} = \frac{r}{u} = \mbox{constant fare}$

whereas without price controls, with elasticity $e_{d} < 0$, we get

$\frac{dr}{du} = \frac{r}{u} + \frac{r}{ue_{d}} = \frac{r}{u}(1 + 1/e_{d}).$

And likewise, with supply elasticity $e_{s} > 0$, we get

$\frac{dc}{du} = \frac{c}{ue_{s}}.$

Note, moreover, that price controls as construed in Japan let operating companies recover profits, letting them raise prices if they invest in more capacity, so that dr/du is actually higher than r/u.

The real world

I do not know to what extent the lack of fare regulation on many British trains contributes to capacity shortages. However, there is some evidence that the same situation is holding back investment in the United States, on Amtrak. Amtrak is a monopolist facing some fare regulations, for example congressional rules limiting the spread between the lowest and highest fares on a given train, but within its ability to set its own capacity in the medium run, it has relatively free hand, and in fact a strong incentive to maximize fares, in order to subsidize money-losing trains outside the Northeast Corridor.

Amtrak generally runs the trains it has on the Northeast Corridor, without explicitly holding back on capacity. However, this is in an environment with very low utilization rates. There are 20 Acela trainsets, but only 16 run in service at a given time, giving them the moniker “hangar queens.” There is no real interest within Amtrak at raising speed just enough to be able to run consistent service intervals, for example hourly with two trainsets coupled to form a 16-car train south of New York. Nor is there any interest in making small investments to permit such long trainsets to run – most Acela stops from New York to the south have platforms long or almost long enough for such trains, but the rest need to be lengthened, within right-of-way so that the cost is positive but low.

In the future, capacity cliffs may prove serious enough to stymie American passenger rail development. Right now the main obstacle are Amtrak itself and obstructive commuter railroads such as Metro-North, but assuming competent, profit-maximizing investment plans, it is not so expensive to invest in capacity and speed so as to permit around 4 long high-speed trains per hour north of New York (or even New Haven) and 6 south of it. But then the next few trains per hour require further bypasses, for example four-tracking most of the Providence Line. High supply elasticity – let’s say around 2 – is plausible. Then eventually a dedicated pathway to intercity trains through New York becomes necessary, raising supply elasticity even higher. In an environment with uncapped, profit-maximizing fares, a rational Amtrak management may well just keep what it has and jack up prices rather than build more capacity.

# I Gave a Talk About Transportation in Connecticut

I gave a second talk this week about transportation, this time at Hartford Station, concerning the plans for Connecticut transportation. The starting point is Governor Lamont’s $21 billion plan for investment, including both expansion and repairs (read: the State of Good Repair black hole), of which$14 billion is highways, $6.2 billion is rail, and$450 million is buses. But most of the talk concerns what Connecticut should be doing, rather than the specifics of Lamont’s plan.

Here are my slides. The talk itself took around 40-45 minutes out of a nearly 2-hour meeting, so it was designed around taking many questions, and around further explanations. Something I didn’t put in the slides but explained verbally is how easy the modern track renewal process is. Nowadays, there are machines that use no infrastructure except the tracks themselves, running on the tracks at very low speed (slower than walking) and systematically replacing the rails, ties, and ballast. They can also regrade the tracks’ superelevation angle independently of the drainage angle, changing the tracks’ cant as they go. The upshot is that increasing the cant on tracks is almost cost-free, and would enable large increases in train speed on both regional and intercity trains.

Other technology that has negative cost in the future is getting higher-performance EMUs than the current equipment. The current trains are obsolete technology, built around superseded federal regulations. There’s no point in getting more of the same. They’re okay to run until end of life, but new purchases should involve electrification and modern European EMUs. Whereas infrastructure costs are rising (see here and here), technology costs are falling in real terms. The fall in train costs is not so quick as that of computer costs, but still the rolling stock factories are designed around making products for the 2020s, not the 1990s, and retooling them for older technology costs extra.

Hence my slogan from the talk: better things are possible, on a budget.

One question I was asked at the talk that I didn’t have an answer to was, why is construction in Connecticut so expensive? Plans for infill stations are budgeted extravagantly, ranging between $50 million and$100 million without any special construction difficulties. Boston builds infill stations (counting high-platform upgrades as infill since the preexisting stations have no facilities) for \$20-30 million counting various hidden costs (e.g. regular MBTA employees, like project managers, count as operating and not capital costs even if they only work on capital costs); Berlin does for €10-20 million.

After the talk, Roger Senserrich explained to me (and a planner at the MBTA confirmed to me) that in Connecticut there’s no in-house design at all. Massachusetts has a mix of in-house design review, with the team stymied by uncompetitive wages making hiring and retention difficult, and outsourcing work to consultants. CDOT exclusively outsources to consultants, and has no in-house expertise to evaluate whether the contracts are fair or whether it’s being overcharged.

# I Gave a Talk About Construction Costs

Two years ago, I gave a talk at NYU about regional rail, and as promised, uploaded slides the next day for discussion. Yesterday I gave another such talk, about construction costs.

But here there are two things to upload: the slides, and the data table. I’ve been intermittently adding cities to a spreadsheet of various urban rapid transit lines and their construction costs, and by now there is a total of 207 distinct items, ranging from 1 km extensions to 3-figure packages like 200-km GPX and 160-km Delhi Metro phases. The total length of the lines in this database right now is 3610 km, of which 2090 are underground. These are almost exclusively new lines – most of them aren’t even open, and most of the rest opened this decade, so be cautious since much of the cost estimation is ex ante and a number of the soon-to-open line on the list have had serious cost overruns.

I hope people make use of this dataset and the preliminary analysis contained in the slides, and I ask that people look at both, since the slides do have some interpretive notes about confounding variables. One note that I did not include in the slides and explained verbally is what source means in the table: media means I’m drawing costs from popular media, trade means trade media like Railway Gazette, plan means official plans (either ex ante or ex post), wiki means Wikipedia (as always, a reliable source for line length and station count, never cost), measured means I measured line length on Google Earth lacking any alternative. One item, Crossrail, has its tunnel cost coming from a freedom of information request submitted by an alert reader who I will credit upon request; the headline budget is somewhat higher as it includes surface improvements, a common confounder for regional rail projects (the RER E extension, for example, splits its budget about 50/50 between the tunnel and above-ground works).

More detailed analysis is forthcoming, either here or in print.

# Urban Freeways and Rapid Transit

A ride-hailing trip today reminded me of something about freeway travel in cities – namely, it is untethered from the surface street network. Oddly enough, for a different reason this is equally true of rapid transit. The commonality to these two ways of travel is that they change the geography of the city, rather than just extending the range of walking along the usual paths as surface arterial streets and surface transit do.

Rapid transit compression

Rapid transit networks compress distances along the lines, and by the same token magnify distances in orthogonal directions. Manhattan is a good example of how this works: north of Midtown the subway only runs north-south, not east-west, so there are separate East Side and West Side cultures. Moreover, as middle-class gentrifiers are displaced by rising rents coming from even richer gentrifiers, they tend to move along subway lines, and thus people from the Upper West Side and Columbia end up in Washington Heights and Inwood.

The contrast here is with surface transit. Bus networks are far too dense to have the same effect. A citywide bus grid would offer 15 km/h transit in all directions in New York, and a tramway grid like what parts of Berlin have (and what big Eastern European cities like Prague and Budapest have) offers 15-20 km/h transit in all directions. It extends walking, in the sense that the most important throughfares probably get their own routes, or if they don’t they are closely parallel with roads with surface transit.

This is not how rapid transit works. A handful of very strong orthogonal routes can and should get rapid transit, hence the Ringbahn, M2/M6 in Paris, and the under-construction M15 – and by the same token, 125th Street in New York should get a subway extension off of Second Avenue. But that still leaves the city with a wealth of major routes that have no reason to get rapid transit, ever. Most of these are crosstown routes, for example the east-west streets of Manhattan, but in less gridded cities they can just be major streets that don’t quite fit into a regionwide radial metro network.

Rapid transit spikiness

I get a lot of pushback when I talk about this, but rapid transit encourages spiky density. This does not mean that every transit city is spiky and every spiky city is a transit city. Density in Paris within the city is fairly uniform, aided by zoning rules that prohibit high-rises even though many could succeed commercially on top of Métro transfer points or RER stations. In the other direction, some American auto-oriented cities have spiky density near transit, like San Diego’s Mission Valley or Atlanta’s Buckhead, but it’s not big enough a development to permit people to comfortably walk and take transit to all destinations.

Nonetheless, for the most part, rapid transit tends to be associated with spiky development forms, especially if it’s been built more recently and if the interstation is long (as in Vancouver, Singapore, Hong Kong, or Stockholm). This isn’t really how a pedestrian city works: pedestrians have no need for spikiness because they don’t have particular distinguished stations – at most, the corner nodes are distinguished, but that includes all corners, which are placed at far shorter intervals than subway stops.

Freeways as street bypasses

Surface transit promotes urban forms that look like an extended pedestrian city. This is equally true of surface roads designed around car access. The car was originally not supposed to take over the entire city, but merely provide convenient intra-urban transportation at a faster speed than walking. It was originally just a faster, more private, more segregated streetcar. The effect on urbanism was to reduce overall density (as did the streetcars and rapid transit in New York, which used to have inhuman overcrowding levels on the Lower East Side), but not to change the urban form beyond that.

Freeways, like rapid transit, are completely different. This does not mean that they change the city in the same way as rapid transit, just that both operate independently of the usual street grid. Freeways, like rapid transit, compress travel distances along the freeway, and simultaneously lengthen them in all other directions because of the effect of traffic congestion.

Moreover, freeways are different from rapid transit in typical alignments. They are far more land-intensive, which is why they tend to be placed in formerly marginal parts of the city. This can include the waterfront if it is originally industrial and low-value, as it was in midcentury America, rather than a place of high-end residential consumption because of the views.

Interface with the street

How does a surface street transit network interface with either rapid transit or freeways?

With rapid transit, the answer is that surface transit is slow, so it should feed rapid transit using transfers, which may be timed if the trains are not so frequent (say, 15 minutes or worse, as is common on suburban rail branches). Rapid transit should then be constructed to connect with surface transit this way, that is the stations should be at intersections with arterial corridors for bus connections.

With freeways, the answer is that often interface is impossible. San Diego provides a convenient example: there is an arterial road that’s great for buses running northward from city center toward the beachfront neighborhood of Pacific Beach. But there’s also a parallel freeway inland, so drivers mostly use the freeway, and commerce on the north-south arterial is neglected. In contrast, the main east-west arterials feeding the freeway are bustling, and one of them has of the city’s strongest buses. Buses can make stops on these arterials and then express to city center on the freeway, but on the freeway itself the buses are not very efficient since there’s minimal turnover, and chaining a few neighborhoods together on one frequent route is usually not possible.