Frequency in Units of Distance

I have annoying commenters. They nitpick what I say and point out errors in my thinking – or if there are no errors, they take it beyond where I thought it could be taken and find new ways of looking at it. After I wrote about frequency relative to trip length last week, Colin Parker pointed out on the Fediverse that this can be simplified into thinking about frequency not in units of time (trains or buses per hour), but in units of distance (trains or buses per km of route). This post is dedicated to developing this idea on various kinds of transit service, including buses and trains.

The key unit throughout, as Colin points out, is the number of buses available per route, the assumption being that the average trip length is proportional to the average route length. However, this is not a perfect assumption, because then the introduction of network effects changes things – generally in the direction of shorter average trip length, as passengers are likelier to transfer, in turn forcing agencies to run more vehicles on a given route to remain useful. Conversely, timed transfers permit running fewer vehicles, or by the same token more routes with the same resources – but the network had better have a strong node to connect to after a series of vehicle changes, more like the Swiss rail network than like a small American city’s bus network.

Frequency and resources

On a bus network with even frequency across all routes, the following formula governs frequency, as I discussed six years ago:

Daily service hours * average speed per hour = daily trips * network length

When Eric and I proposed our Brooklyn bus redesign, we were working with a service-hour budget of about 10,800 per weekday; status quo as of 2017-8 was 11 km/h, 550 km, and thus 216 daily trips (108 per direction), averaging around a bus per 11 minutes during the daytime, while we were proposing speed up treatments and a redesign to change these figures to 15 km/h, 355 km, and thus 456 daily trips (228 per direction). The six-minute service ideal over 16 hours requires 188 trips per direction; the difference between 188 and 228 is due to higher frequencies on the busiest routes, which need the capacity.

To express this in units of length, we essentially eliminate time from the above dimensional analysis. Daily service hours is a dimensionless quantity: 10,800 hours per weekday means 450 buses circulating at a given time on average, in practice about 570 during the daytime but not many more than 100 buses circulating overnight. If there are 570 buses circulating at a given time, then a 550 km network will average a bus every 1.9 km and a 355 km one will average a bus every 1.25 km. With pre-corona New York bus trips averaging 3.4 km unlinked, a bus every 1.9 km means the maximum headway is a little higher than half the trip time, and a bus every 1.25 km means the maximum headway is a little higher than one third the trip time, independently of speed.

This calculation already illustrates one consequence of looking at frequency in units of distance and not time: your city probably needs to aggressively prune its bus network to limit the wait times relative to overall trip times.

Route length and trip length

On an isolated bus or train route, serving an idealized geography with a destination at its center and isotropic origins along the line, the average trip length is exactly one quarter of the route length. The frequency of service in units of distance should therefore be one eighth of the route length, requiring 16 vehicles to run service plus spares and turnarounds. This is around 18-20 vehicles in isolation, though bear in mind, the 10,800 service hours/day figure for Brooklyn buses above is only for revenue service, and thus already incorporates the margin for turnaround times and deadheads.

Colin points out that where he lives, in Atlanta, bus routes usually have around four vehicles circulating per route at a given time, rather than 16. With the above assumptions, this means that the average wait is twice the average trip time, which goes a long way to explaining why Atlanta’s bus service quality is so poor.

But then, different assumptions of how people travel can reduce the number 16:

  1. If destinations are isotropic, then the average trip length rises from one quarter of the route length to 3/8 of the route length, and then the frequency should be 1.5/8 of the route length, which requires 11 vehicles in revenue service.
  2. If origins are not isotropic, then the average trip length can rise or fall, depending on whether they are likelier to be farther out or closer in. A natural density gradient means origins are disproportionately closer-in, but then in a city with a natural density gradient and only four buses to spare per route, the route is likely to be cut well short of the end of the built-up area. If the end of the route is chosen to be a high-density anchor, then the origins relative to the route itself may be disproportionately farther out. In the limiting case, in which the average trip is half the route length, only eight buses are needed to circulate.

To be clear, this is for a two-tailed route; a one-tailed route, connecting city center at one end to outlying areas at the other, needs half the bus service, but then a city needs twice as many such routes for its network.

The impact of transfers

Transfers can either reduce the required amount of service for it to be worth running or increase it, depending on type. The general rule is that untimed transfers occurring at many points along the line reduce the average unlinked trip and therefore force the city to run more service, while timed transfers occurring at a central node lengthen the effective trip relative to the wait time and therefore permit the city to run less service. In practice, this describes both how existing bus practices work in North America, and even why the Swiss rail network is so enamored with timed connections.

To the point of untimed transfers, their benefit is that there can be very many of them. On an idealized grid – let’s call it Toronto, or maybe Vancouver, or maybe Chicago – every grid corner is a transfer point between an east-west and a north-south route, and passengers can get from anywhere to anywhere. But then they have to wait multiple times; in transit usage statistics, this is seen in low average unlinked trip lengths. New York, as mentioned above, averages 3.4 km bus trips, with a network heavily based on bus-subway transfers; Chicago averages a not much higher 3.9 km. This can sort of work for New York with its okay if not great relative frequency, and I think also for Chicago; Vancouver proper (not so much its suburbs) and Toronto have especially strong all-day frequencies. But weaker transit networks can’t do this – the transfers can still exist but are too onerous. For example, Los Angeles has about the same total bus resources as Chicago but has to spread them across a much larger network, with longer average trip times to boot, and is not meaningfully competitive. The untimed grid, then, is a good feature for transit cities, which have the resources and demand to support the required frequencies.

Not for nothing, rapid transit networks love untimed transfers, and often actively prefer to spread them across multiple stations, to avoid overwhelming the transfer corridors. Subways are only built on routes that are strong enough to have many vehicles circulating, to the point that all but the shortest trips have low ratios of wait to in-vehicle times. They are also usually radial, aiming to get passengers to connect between any pair of stations with just one transfer; Berlin, Paris, and New York are among the main exceptions. These features make untimed transfers tolerable, in ways they aren’t on weaker systems; not for nothing, a city with enough resources for a 100 km bus network and nothing else does not mimic a 100 km subway network.

Timed transfers have the opposite effect as untimed transfers. By definition, a timed transfer means the wait is designed to be very short, ideally zero. At this point, the unlinked trip length ceases to be meaningful – the quantity that should be compared with frequency is the entire trip with all timed transfers included. In particular, lower frequencies may be justifiable, because passengers travel to much more than just the single bus or rail route.

This can be seen in small-city American bus networks, or some night bus networks, albeit not with good quality. It can be seen much more so on transfer-based rail networks like Switzerland’s. The idealized timed transfer network comprises many routes all converging on one node where they are timed to arrive and depart simultaneously, with very short transfers; this is called a knot in German transit planning and a pulse in American transit planning. American networks like this typically run a single bus circulating on each one-tailed route; the average wait works out to be four times longer than the average unlinked trip, and still twice as long as a transfer trip, which helps explain why ridership on such networks is a rounding error, and this system is only used for last-resort transportation in small cities where transit is little more than a soup kitchen or on night bus networks that are hardly more ridden. It would be better to redo such networks, pruning weaker routes to run more service on stronger ones, at least two per one-tailed route and ideally more.

But then the Swiss rail network is very effective, even though it’s based on a similar principle: there’s no way to fill more frequent trains than one every hour to many outlying towns, and even what are midsize cities by Swiss standards can’t support more than a train every half hour, so that many routes have a service offer of two to four vehicles circulating at a given time. However, on this network, the timed transfers are more complex than the idealized pulse – there are many knots with pulses, and they work to connect people to much bigger destinations than could be done with sporadic one-seat rides. A succession of timed connections can get one from a small town in eastern Switzerland to St. Gallen, then Zurich, then Basel, stretching the effective trip to hours, and making the hourly base frequency relatively tolerable. The key feature is that the timed transfers work because while individual links are weak enough to need them, there are some major nodes that they can connect to, often far away from the towns that make the most use of the knot system.

Frequency is Relative

Five years ago, I wrote a blog post about frequency-ridership spirals, mentioning as a side comment that the impact of mass transit frequency on ridership can be lumped together with the trip time. I’d like to develop this point here, and talk about how it affects various kinds of public transportation, including intercity trains.

The rule of thumb I’ve advocated for in ETA reports (for example, on commuter rail) is that the maximum headway should be no more than half the trip time. Untimed transfers reset the clock, since passengers have to wait another time every time they make such a transfer; timed transfers do not, but are rare enough that local public transportation doesn’t usually need to consider them in service planning. Intercity transportation can follow the same rule of thumb, but can also get away with worse frequency since passengers time themselves to arrive shortly before the train does; in particular, hourly trains between cities that are three hours apart are frequent enough that increasing service is valuable only insofar as it provides more capacity, and is unlikely to lead to higher ridership through shorter waits.

Wait and transfer penalties

In the literature on modeling public transportation ridership, it is universal that passengers prefer spending time on board a moving vehicle to waiting for a vehicle, walking to the station, or walking between platforms. This preference is expressed as a factor, called the waiting or transfer penalty. different models have different levels for these penalties; passengers also likely have different penalties depending on circumstances, such as familiarity with the route or how much luggage they’re carrying.

The papers I’ve seen have penalties ranging from 1.75 (in the MTA’s model) to 3 (the higher end cited in Lago-Mayworm-McEnroe). I usually model with 2, in Teulings-Ossokina-de Groot. The factor of 2 has the advantage of consistency with an assumption that passengers don’t have a wait penalty but do assume a worst-case scenario for waits, so that the generalized travel time is equal to the maximum headway plus the in-vehicle travel time.

Update 4-19: I was just alerted to a new study by Yap-Wong-Cats using London ridership, finding an out-of-vehicle penalty factor of 1.94 pre-pandemic and 1.92 post-pandemic.

The impact of frequency relative to trip time

If the elasticity of ridership with respect to the generalized travel time, summing the headway and in-vehicle travel time but not walking time to and from the station, is e, then we can compute the elasticity of ridership with respect to frequency as a fraction of e. If the current headway is a proportion r of the in-vehicle trip time, that is to say a fraction r/(r+1) of the generalized travel time, then the elasticity is er/(r+1).

In Lago-Mayworm-McEnroe, the value of e appears to be 0.8. This means that if r = 0.5, the elasticity of ridership with respect to frequency is 0.267. The paper doesn’t quantify elasticities relative to different levels of r but only relative to absolute frequencies, but 0.267 is within the range it finds for different frequencies, dipping to 0.22 for high-frequency lines. Other papers have different figures of e, often higher in the long run as passengers adjust, but those go up to around 1 or, reasoning backward from a VTPI report, a little higher.

Of notes:

  1. The value of r is not constant across different uses of the same line. A commuter traveling from near the outer end of a subway line to city center faces much lower r than a traveler going a short distance, within city center or within a large outlying neighborhood. In particular, r is generally lower for commutes than for non-commute trips, which is why the latter are more sensitive to frequency.
  2. Systems that rely on extensive transfers can have very high values of r with short in-vehicle trips. New York averages 13.5 minutes per unlinked subway trip, with many trips facing an effective off-peak headway of 10 or even 12 minutes, at which point e is high enough that increasing off-peak frequency could pay for itself through higher paying ridership (see analysis in a blog post and an ETA report). This, again, depends on the type of trip – commuters may pick an apartment or a job based on ease of travel, reducing the need to transfer, but their non-commute trips are usually a collection of irregular trips to various destinations and are likelier to involve a transfer.
  3. The cost of higher frequency depends on mode (it’s higher on buses than trains) and time of day (it’s very low on off-peak trains until it matches peak frequency). Together with points 1 and 2, this argues in favor of raising the off-peak frequency on urban and inner suburban trains, potentially to the point of matching peak frequency. On longer-range commuter trains, the impact of frequency on ridership is lower, and thus the marginal cost may be such that a ratio of peak to off-peak service larger than 1 is desirable.

Intercity trains

The papers I’m citing aim to fit elasticity factors to observed ridership on local and regional public transportation. Intercity rail has its own set of models, with different assumptions. Frequency again matters, but because passengers time themselves to arrive at the departing station shortly before the train leaves, its impact is reduced.

I don’t know the elasticity of intercity rail ridership with respect to frequency; Cascetta-Coppola have the elasticity of ridership with respect to in-vehicle trip time as about -2, while Börjesson has it at -1.5 for business travel and -1 for non-business travel with a rough rule of thumb trying to approximate the impact of frequency. At the level of the sanity check, the low frequency of TGV services is not visible in TGV ridership between the provinces and Paris, compared with Japan (which charges higher fares) and as far as I can tell from a few data points Germany. TGV ridership between the provinces is bad, but that involves trains with service gaps that are much larger than the trip times, reaching six hours between Marseille and Lyon. In contrast, those three-hour gaps in service between Paris and cities three hours away by TGV don’t seem to impact ridership visibly.

What this means is that intercity trains do need a certain baseline frequency. The German system of a train every two hours on every city pair is wise, in light of the typical intercity rail travel distances in a large country with slow trains. Higher frequency is warranted if the cities are bigger and therefore require more service, or if they are closer together in time through either a short geographical distance or higher speeds. New York and Philadelphia are about 1:10 apart by rail, and high-speed rail could cut this to about 45 minutes; half-hourly frequencies in the current situation are sufficient that more service would have a second-order effect, and even with high-speed rail, a train every 15 minutes is more than enough for all purposes except capacity (the current offer is 3-4 trains an hour with irregular spacing). Frequency is freedom, but this depends on trip times; what works for four-station subway trips is not what works for trips between cities 140 km apart, let alone 360 km, and vice versa.

What is Incrementalism, Anyway?

The American conversation about high-speed rail has an internal debate that greatly bothers me, about whether investments should be incremental or not. An interview with the author of a new book about the Northeast Corridor reminded me of this; this is not the focus of the interview, but there was an invocation of incremental vs. full-fat high-speed rail, which doesn’t really mean much. The problem is that the debate over incrementalism can be broken down into separate categories – infrastructure, top speed, planning paradigm, operations, marketing; for example, investment can be mostly on existing tracks or mostly on a new right-of-way, or something in between, but this is a separate questions from whether operations planning should remain similar to how it works today or be thrown away in favor of something entirely new. And what’s more, in some cases the answers to these questions have negative rather than positive correlations – for example, the most aggressively revolutionary answer for infrastructure is putting high-speed trains on dedicated tracks the entire way, including new urban approaches and tunnels at all major cities, but this also implies a deeply conservative operating paradigm with respect to commuter rail.

Instead of talking about incrementalism, it’s better to think in terms of these questions separately. As always, one must start with goals, and then move on to service planning, constraints, and budgets.

Planners who instead start with absolute political demands, like “use preexisting rights-of-way and never carve new ones through private property,” end up failing; California High-Speed Rail began with that demand, as a result of which it planned to use existing freight rail corridors that pass through unserved small towns with grade crossings; this was untenable, so eventually the High-Speed Rail Authority switched to swerving around these unserved towns through farmland, but by then it had made implicit promises to the farmers not to use eminent domain on their land, and when it had to violate the promise, it led to political controversy.

Switzerland

Instead of California’s negative example, we can look to more successful ones, none of which is in an English-speaking country. I bring up Switzerland over and over, because as far as infrastructure goes, it has an incremental intercity rail network – there are only a handful of recently-built high-speed lines and they’re both slow (usually 200 km/h, occasionally 250 km/h) and discontinuous – but its service planning is innovative. This has several features:

Infrastructure-rolling stock-timetable integration

To reduce the costs of infrastructure, Swiss planning integrates the decision of what kind of train to run into the investment plan. To avoid having to spend money on lengthening platforms, Switzerland bought double-deck trains as part of its Rail 2000 plan; double-deckers have their drawbacks, mainly in passenger egress time, but in the case of Switzerland, which has small cities with a surplus of platform tracks, double-deckers are the right choice.

California made many other errors, but its decision to get single-deck trains is correct in its use case: the high-speed trainset market is almost entirely single-deck, and the issue of platform length is not relevant to captive high-speed rail since the number of stations that need high-speed rail service is small and controllable.

Timetable integration is even more important. If the point is to build a rail network for more than just point-to-point trips connecting Zurich, Basel, Bern, and Geneva, then trains have to connect at certain nodes; already in the 1970s, SBB timetables were such that trains arrived at Zurich shortly before the hour every hour and departed on or shortly after the hour. The Rail 2000 plan expanded these timed connections, called Knoten or knots, to more cities, and prioritized speed increases that would enable trains to connect two knots in just less than an hour, to avoid wasting time for passengers and equipment. The slogan is run trains as fast as necessary, not as fast as possible: expensive investment is justifiable to get the trip times between two knots to be a little less than an hour instead of a little more than an hour, but beyond that, it isn’t worth it, because connecting passengers would not benefit.

Tunnels where necessary

The incremental approach of Rail 2000, borne out of a political need to limit construction costs, is sometimes cited by German rail advocates and NIMBYs who assume that Switzerland does not build physical infrastructure. Since the 1980s, when investment in the Zurich S-Bahn and Rail 2000 began, Switzerland has built rail tunnels with gusto, and not just across the Alpine mountain passes for freight but also in and between cities to speed up passenger trains and create more capacity. Relative to population, Switzerland has built more rail tunnel per capita than Germany since the 1980s, let alone France, excluding the trans-Alpine base tunnels.

So overall, this is a program that’s very incremental and conservative when it comes to top speed (200 km/h, rarely 250), and moderately incremental when it comes to infrastructure but does build strategic bypasses, tunnels to allow trains to run as fast as necessary, and capacity improvements. But its planning paradigm and operations are both innovative – Rail 2000 was the first national plan to integrate infrastructure improvements into a knot system, and its successes have been exported into the Netherlands, Austria, and more slowly Germany.

Incrementalism in operations versus in infrastructure

The current trip times between New York and New Haven are 1:37 on intercity trains and 2:02 to 2:08 on commuter trains depending on how many stops they skip between Stamford and New Haven. The technical capability of modern trainsets with modern timetabling is 52 minutes on intercity trains and about 1:17 on commuter trains making the stopping patterns of today’s 2:08 trains.

This requires a single deviation from the right-of-way, at Shell Interlocking just south of New Rochelle, which deviation is calibrated not to damage a historic building close to the track and may not require any building demolitions at all; the main purpose of the Shell Interlocking project is to grade-separate the junction for more capacity, not to plow a right-of-way for fast trains. The impact of this single project on the schedule is hard to quantify but large, because it simplifies timetabling to the point that late trains on one line would not delay others on connecting lines; Switzerland pads the timetable 7%, whereas the TGV network (largely on dedicated tracks, thus relatively insulated from delays) pads 11-14%, and the much more exposed German intercity rail network pads 20-30%. The extent of timetable padding in and around New York is comparable to the German level or even worse; those two-hour trip times include what appears to be about 25 minutes of padding. The related LIRR has what appears to be 32% padding on its Main Line, as of nine years ago.

So in that sense, it’s possible to be fairly conservative with infrastructure, while upending operations completely through tighter scheduling and better trainsets. This should then be reinforced through upending planning completely through providing fewer train stopping patterns, in order to, again, reduce the dependence of different train types on one another.

Is this incremental? It doesn’t involve a lot of physical construction, so in a way, the answer is yes. The equivalent of Shell on the opposite side of New York, Hunter Interlocking, is on the slate of thoroughly incremental improvement projects that New Jersey Transit wishes to invest in, and while it has not been funded yet unfortunately, it is fairly likely to be funded soon.

But it also means throwing out 70 years of how American rail agencies have thought about operations. American agencies separate commuter and intercity rail into different classes of train with price differentiation, rather than letting passengers ride intercity trains within a large metropolitan area for the same price as commuter rail so long as they don’t book a seat. They don’t run repeating timetables all day, but instead aim to provide each suburban station direct service to city center with as few stops as possible at rush hour, with little concern for the off-peak. They certainly don’t integrate infrastructure with rolling stock or timetable decisions.

Incrementalism in different parts of the corridor

The answer to questions of incrementalism does not have to be the same across the country, or even across different parts of the same line. It matters whether the line is easy to bypass, how many passengers are affected, what the cost is, and so on.

Between New York and New Haven, it’s possible to reduce trip times by 7 minutes through various bypasses requiring new rights-of-way, including some tunneling and takings of a number of houses in the low hundreds, generally in wealthy areas. My estimate for how much these bypasses should cost is around $5 billion in total. Is it worth it? Maybe. But it’s not really necessary, and there are lower-hanging fruit elsewhere. (One bypass, west of Stamford, may be desirable – it would save maybe 100 seconds for maybe $500 million, and also provide more capacity on a more constrained section, whereas the other potential bypasses are east of Stamford, where there is much less commuter traffic.)

Between New Haven and Kingston, in contrast, the same $5 billion in bypass would permit a 320 km/h line to run continuously from just east of New Haven to not far south of Providence, with no tunnels, and limited takings. The difference in trip times is 25 minutes. Is that worth it? It should be – it’s a factor of around 1.2 in the New York-Boston trip times, so close to a factor of 1.5 in the projected ridership, which means its value is comparable to spending $15 billion on the difference between this service (including the $5 billion for the bypass) and not having any trains between New York and Boston at all.

South of New York, the more Devin and I look at the infrastructure, the more convinced I am that significant deviations from the right-of-way are unnecessary. The curves on the line are just not that significant, and there are long stretches in New Jersey where the current infrastructure is good and just needs cheap fixes to signals and electrification, not tunnels. Even very tight curves that should be fixed, like Frankford Junction in Philadelphia, are justifiable on the basis of a high benefit-cost ratio but are not make-or-break decisions; getting the timetabling integration right is much more important. This could, again, be construed to mean incrementalism, but we’re also looking at New York-Philadelphia trip times of around 46 minutes where the Acela takes about 1:09 today.

Overall, this program can be described as incremental in the sense of, over than 500 km between Boston and Philadelphia, only proposing 120 km of new right-of-way, plus a handful of junction fixes, switch rebuilds, and curve modifications; curve regradings within the right-of-way can be done by a track-laying machine cheaply and quickly. But it also assumes running trains without any of the many overly conservative assumptions of service in the United States, which used to be enshrined in FRA regulations but no longer are, concerning speed on curves, signaling, rolling stock quality, etc. If the trip time between Boston and Philadelphia is reduced by a factor of 1.8, how incremental is this program, exactly?

Incrementalism in marketing and fares

Finally, there are questions about business planning, marketing, segmentation, and fares. Here, the incremental option depends on what is the prior norm. In France, after market research in advance of the TGV showed that passengers expected the new trains to charge premium fares, SNCF heavily marketed the trains as TGV pour tous, promising to charge the same fares for 260 km/h trains as for 160 km/h ones. Since then, TGV fares have been revamped to resemble airline pricing with fare buckets, but the average fares remain low, around 0.11€/km. But international trains run by companies where SNCF has majority stake, namely Thalys and Eurostar, charge premium fares, going exclusively after the business travel market.

This, too, can be done as a break from the past or as a more incremental system. The American system on the Northeast Corridor is, frankly, bad: there are Acela and Regional trains, branded separately with separate tickets, the Regionals charging around twice as much as European intercity trains per km and the Acelas more than three times as much. Incrementalism means keeping this distinction – but then again, this distinction was not traditional and was instead created for the new Acela trains as they entered into service in 2000. (California High-Speed Rail promised even lower fares than the European average in the 2000s.)

Conclusion

There’s no single meaning to incrementalism in rail investment. Systems that are recognized for avoiding flashy infrastructure can be highly innovative in other ways, as is the case for Rail 2000. At the same time, such systems often do build extensive new infrastructure, just not in ways that makes for sleek maps of high-speed rail infrastructure in the mold of Japan, France, or now China.

What’s more, the question of how much to break from the past in infrastructure, operations, or even marketing depends on both what the past is and what the local geography is. The same planner could come to different conclusions for different lines, or different sections on the same line; it leads to bad planning if the assumption is that the entire line must be turned into 300+ km/h high-speed rail at once or none of it may be, instead of different sections having different solutions. Benefit-cost analyses need to rule the day, with prioritization based on centrally planned criteria of ridership and costs, rather than demands to be incremental or to be bold.

Trucking and Grocery Prices

In dedication to people who argue in favor of urban motorways on the grounds that they’re necessary for truck access and cheap consumer goods, here are, at the same scale, the motorway networks of New York, London, Paris, and Berlin. While perusing these maps, note that grocery prices in New York are significantly higher than in its European counterparts. Boston is included as well, for an example of an American city with fewer inherent access issues coming from wide rivers with few bridges; grocery prices in Boston are lower than in New York but higher than in Paris and Berlin (I don’t remember how London compares).

The maps

The scale isn’t exactly the same – it’s all sampled from the same zoom level on OpenStreetMaps; New York is at 40° 45′ N and Berlin is at 52° 30′ N, so technically the Berlin map is at a 1.25 times closer zoom level than the New York map, and the others are in between. But it’s close. Motorways are in red; the Périphérique, delineating the boundary between Paris and its suburbs, is a full freeway, but is inconsistently depicted in red, since it gives right-of-way to entering over through-traffic, typical for regular roads but not of freeways, even though otherwise it is built to freeway standards.

Discussion

The Périphérique is at city limits; within it, 2.1 million people live, and 1.9 million work, representing 32% of Ile-de-France’s total as of 2020. There are no motorways within this zone; there were a few but they have been boulevardized under the mayoralty of Anne Hidalgo, and simultaneously, at-grade arterial roads have had lanes reduced to make room for bike lanes, sidewalk expansion, and pedestrian plazas. Berlin Greens love to negatively contrast the city with Paris, since Berlin is slowly expanding the A100 Autobahn counterclockwise along the Ring (in the above map, the Ring is in black; the under-construction 16th segment of A100 is from the place labeled A113 north to just short of the river), and is not narrowing boulevards to make room for bike lanes. But the A100 ring isn’t even complete, nor is there any plan to complete it; the controversial 17th segment is just a few kilometers across the river. On net, the Autobahn network here is smaller than in Ile-de-France, and looks similar in size per capita. London is even more under-freewayed – the M25 ring encloses nearly the entire city, population 8.8 million, and within it are only a handful of radial motorways, none penetrating into Central London.

The contrast with American cities is stark. New York is, by American standards, under-freewayed, legacy of early freeway revolts going back to the 1950s and the opposition to the Lower Manhattan Expressway, which would have connected the Holland Tunnel with the Manhattan and Williamsburg Bridges; see map here. There’s practically no penetration into Manhattan, just stub connections to the bridges and tunnels. But Manhattan is not 2.1 million people but 1.6 million – and we should probably subtract Washington Heights (200,000 people in CB 12) since it is crossed by a freeway or even all of Upper Manhattan (650,000 in CBs 9-12). Immediately outside Manhattan, there are ample freeways, crossing close-in neighborhoods in Brooklyn, Queens, the South Bronx, and Jersey City. The city is not automobile-friendly, but it has considerably more car and truck capacity than its European counterparts. Boston, with a less anti-freeway history than New York, has penetration all the way to Downtown Boston, with the Central Artery, now the Big Dig, having all-controlled-access through-connections to points north, west, and south.

Grocery prices

Americans who defend the status quo of urban freeways keep asking about truck access; this played a role in the debate over what to do about the Brooklyn-Queens Expressway’s Downtown Brooklyn section. Against shutting it down, some New Yorkers said, there is the issue of the heavy truck traffic, and where it would go. This then led to American triumphalism about how truck access is important for cheap groceries and other goods, to avoid urban traffic.

And that argument does not survive a trip to a New York (or other urban American) supermarket and another trip to a German or French one. German supermarkets are famously cheap, and have been entering the UK and US, where their greater efficiency in delivering goods has put pressure on local competitors. Walmart, as famously inexpensive as Aldi and Lidl (and generally unavailable in large cities), has had to lower prices to compete. Carrefour and Casino do not operate in the US or UK, and my impression of American urbanists is that they stereotype Carrefour as expensive because they associate it with their expensive French vacations, but outside cities they are French-speaking Walmarts, and even in Paris their prices, while higher, are not much higher than those of German chains in Germany and are much lower than anything available in New York.

While the UK has not given the world any discount retailer like Walmart, Carrefour, or Lidl, its own prices are distinctly lower than in the US, at least as far as the cities are concerned. UK wages are infamously lower than US wages these days, but the UK has such high interregional inequality that wages in London, where the comparison was made, are not too different from wages in New York, especially for people who are not working in tech or other high-wage fields (see national inequality numbers here). In Germany, where inequality is similar to that of the UK or a tad lower, and average wages are higher, I’ve seen Aldi advertise 20€/hour positions; the cookies and cottage cheese that I buy are 1€ per pack where a New York supermarket would charge maybe $3 for a comparable product.

Retail and freight

Retail is a labor-intensive industry. Its costs are dominated by the wages and benefits of the employees. Both the overall profit margins and the operating income per employee are low; increases in wages are visible in prices. If the delivery trucks get stuck in traffic, are charged a congestion tax, have restricted delivery hours, or otherwise have to deal with any of the consequences of urban anti-car policy, the impact on retail efficiency is low.

The connection between automobility and cheap retail is not that auto-oriented cities have an easier time providing cheap goods; Boston is rather auto-oriented by European standards and has expensive retail and the same is true of the other secondary transit cities of the United States. Rather, it’s that postwar innovations in retail efficiency have included, among other things, adapting to new mass motorization, through the invention of the hypermarket by Walmart and Carrefour. But the main innovation is not the car, but rather the idea of buying in bulk to reduce prices; Aldi achieves the same bulk buying with smaller stores, through using off-brand private labels. In the American context, Walmart and other discount retailers have with few exceptions not bothered providing urban-scale stores, because in a country with, as of 2019, a 90% car modal split and a 9% transit-and-active-transportation modal split for people not working from home, it’s more convenient to just ignore the small urban patches that have other transportation needs. In France and Germany, equally cheap discounters do go after the urban market – New York groceries are dominated by high-cost local and regional chains, Paris and Berlin ones are dominated by the same national chains that sell in periurban areas – and offer low-cost goods.

The upshot is that a city can engage in the same anti-car urban policies as Paris and not at all see this in retail prices. This is especially remarkable since Paris’s policies do not include congestion pricing – Hidalgo is of the opinion that rationing road space through prices is too neoliberal; normally, congestion pricing regimes remove cars used by commuters and marginal non-commute personal trips, whereas commercial traffic happily pays a few pounds to get there faster. Even with the sort of anti-car policies that disproportionately hurt commercial traffic more than congestion pricing, Paris has significantly cheaper retail than New York (or Boston, San Francisco, etc.).

And Berlin, for all of its urbanist cultural cringe toward Paris, needs to be classified alongside Paris and not alongside American cities. The city does not have a large motorway network, and its inner-urban neighborhoods are not fast drive-throughs. And yet in the center of the city, next to pedestrian plazas, retailers like Edeka and Kaufland charge 1€ for items that New York chains outside Manhattan sell for $2.5-4. Urban-scale retail deliveries are that unimportant to the retail industry.

Venture Capital Firms Shift to Green Infrastructure

Several Bay Area major venture capital firms announce that they will shift their portfolios toward funding physical green infrastructure, including solar and wind power generation, utility lines, hydroelectric dams, environmental remediation projects for dams, and passenger and freight rail.

One founder of a firm in the public transit industry, speaking on condition of anonymity because the deal is still in process, points out that other VC investments have not been successful in the last 10-15 years. Cryptocurrencies, NFTs, and other blockchain technologies have not succeeded in transforming the finance sector; the Metaverse flopped; AI investments in driverless cars are still a long way from deployment, while LLMs are disappointing compared with expectations of artificial general intelligence. In contrast, the founder explains, there are great opportunities for new passenger rail lines and renewable and at places nuclear power.

Another founder points out the example of Brightline West and says that with upcoming reforms in permitting, pushed by many of the same VCs, it will be profitable to complete new domestic and international intercity rail lines between cities; a $15 billion investment in connecting Chicago, Detroit, and Cleveland is underway.

On Sand Hill Roads, VC attitudes to the new investment are jubilant. One VC admits to never having heard much about public transit, but, after a three-day factfinding mission can tell you everything you could possibly want to know about the Singapore MRT. Other VCs say that Peter Thiel and Mark Zuckerberg are both especially interested in funding public transit initiatives after Elon Musk retweeted the X account TruthSeeker1488 saying that public transit is a conspiracy by international finance communists.

Local and Intercity Rail are Complements

An argument in my comments section is reminding me of a discussion by American transit advocates 15 years ago, I think by The Overhead Wire, about the tension between funding local transit and high-speed rail. I forget who it was – probably Jeff Wood himself – pointing out that the argument in 2008-9 about whether the priority was local transit or intercity rail didn’t make much sense. There are separate questions of how to allocate funding for intercity transportation and how to do the same for local transportation, and in both cases the same group of activists can push for a more favorable rail : car funding ratio. Jeff was talking about this in the sense of political activism; the purpose of this post is to explain the same concept from the point of view of public transportation connectivity and network effects. This is not an obvious observation, judging by how many people argue to the contrary – years ago I had a debate with Noah Smith about this, in which he said the US shouldn’t build high-speed rail like the Shinkansen before building urban rail systems like those of Japanese cities (see my side here and here).

I’ve written about related issues before, namely, in 2022 when I recommended that countries invest against type. For example, France with its TGV-centric investment strategy should invest in connecting regional lines, whereas Germany with its hourly regional train connections should invest in completing its high-speed rail network. It’s also worthwhile to reread what I wrote about Metcalfe’s law for high-speed rail in 2020, here and here. Metcalfe’s law is an abstract rule about how the value of a network with n nodes is proportional to n^2, and Odlyzko-Tilly argue strongly that it is wrong and in fact the value is n\log n; my post just looks at specific high-speed rail connections rather than trying to abstract it out, but the point is that in the presence of an initial network, even weaker-looking extensions can be worth it because of the connections to more nodes. Finally, this builds on what I said five days ago about subway-intercity rail connections.

The combined point is that whenever two forms of local, regional, or intercity public transportation connect, investments in one strengthen the case for investments in the other.

In some edge cases, those investments can even be the same thing. I’ve been arguing for maybe 12 years that MBTA electrification complements Northeast Corridor high-speed rail investment, because running fast electric multiple units (EMUs) on the Providence Line and its branches instead of slow diesel locomotive-hauled trains means intercity trains wouldn’t get stuck behind commuter trains. Similarly, I blogged five years ago, and have been doing much more serious analysis recently with Devin Wilkins, that coordinating commuter rail and intercity rail schedules on the New Haven Line would produce very large speed gains, on the order of 40-45 minutes, for both intercity and commuter trains.

But those are edge cases, borne of exceptionally poor management and operations by Amtrak and the commuter railroads in the Northeast. Usually, investments clearly are mostly about one thing and not another – building a subway line is not an intercity rail project, and building greenfield high-speed rail is not a local or regional rail project.

And yet, they remain complements. The time savings that better operations and maintenance can produce on the New Haven Line are also present on other commuter lines in New York, for example on the LIRR (see also here, here, and here); they don’t speed up intercity trains, but do mean that people originating in the suburbs have much faster effective trips to where they’d take intercity rail. The same is true for physical investments in concrete: the North-South Rail Link in Boston and a Penn Station-Grand Central connection in New York both make it easier for passengers to connect to intercity trains, in addition to benefits for local and regional travel, and conversely, fast intercity trains strengthen the case for these two projects since they’d connect passengers to better intercity service.

Concretely, let’s take two New York-area commuter lines, of which one will definitely never have to interface with intercity rail and one probably will not either. The definitely line is the Morristown Line: right now it enters New York via the same North River Tunnels as all other trains from points west, intercity or regional, but the plan for the Gateway Tunnel is to segregate service so that the Morris and Essex Lines use the new tunnel and the Northeast Corridor intercity and commuter trains use the old tunnel, and so in the future they are not planned to interact. The probably line is the LIRR Main Line, which currently doesn’t interface with intercity trains as I explain in my post about the LIRR and Northeast Corridor, and which should keep not interfacing, but there are Amtrak plans to send a few daily intercities onto it.

Currently, the trip time from Morristown to New York is around 1:09 off-peak, with some peak-only express trains doing it in 1:01. With better operations and maintenance, it should take 0:47. The upshot is that passengers traveling from Morristown to Boston today have to do the trip in 1:09 plus 3:42-3:49 (Acela) or 4:15-4:35 (Regional). The commuter rail improvements, which other than Gateway and about one unfunded tie-in do not involve significant investment in concrete, turn the 4:51 plus transfer time trip to 4:29 plus transfer time – say 5 hours with the transfer, since the intercities run hourly and the transfers are untimed and, given the number of different branches coming in from New Jersey, cannot be timed. High-speed rail, say doing New York-Boston in 2 hours flat (which involves an I-95 bypass from New Haven to Kingston but no other significant deviations from the right-of-way), would make it 2:47 with a transfer time capped at 10 minutes, so maximum 2:57. In effect, these two investments combine to give people from Morristown an effective 41% reduction in trip time to Boston, which increases trip generation by a factor of 2.87. Of course, far more people from Morristown are interested in traveling to New York than to Boston, but the point is that in the presence of cheap interventions to rationalize and speed up commuter rail, intercity rail looks better.

The same is true from the other direction, from the LIRR Main Line. The two busiest suburban stations in the United States are on 2000s and 10s numbers Ronkonkoma and Hicksville, each with about 10,000 weekday boardings. Ronkonkoma-Penn Station is 1:18 and Hicksville-Penn Station is 0:42 off-peak; a few peak express trains per day do the trip a few minutes faster from Ronkonkoma by skipping Hicksville, but the fastest looks like 1:15. If the schedule is rationalized, Ronkonkoma is about 0:57 from New York and Hicksville 0:31, on trains making more stops than today. I don’t have to-the-minute New York-Washington schedules with high-speed rail yet, but I suspect 1:50 plus or minus 10 minutes is about right, down from 2:53-3:01 on the Acela and 3:17-3:38 on the Regional. So the current timetable for Ronkonkoma-Washington is, with a half-hour transfer time, around 4:45 today and 2:57 in the future, which is a 38% reduction in time and a factor of 2.59 increase in the propensity to travel. From Hicksville, the corresponding reduction is from 4:09 to 2:31, a 39% reduction and a factor of 2.72 increase in trip generation. Again, Long Islanders are far more interested in traveling to Manhattan than to Washington, but a factor of 2.59-2.72 increase in trip generation is nothing to scoff at.

The issue here is that once the cheap upgrades are done, the expensive ones start making more sense – and this is true for both intercity and regional trains. The New York-Boston timetable assumes an I-95 bypass between New Haven and Kingston, saving trains around 24 minutes, at a cost of maybe $5 billion; those 24 minutes matter more when they cut the trip time from 2:24 to 2:00 than when the current trip time is about 3:45 and the capacity on the line is so limited any increase in underlying demand has to go to higher fares, not more throughput. For suburban travelers, the gains are smaller, but still, going from 5:00 to 4:36 matters less than going from 3:21 to 2:57.

Conversely, the expensive upgrades for regional trains – by which I mean multi-billion dollars tunnels, not $300 million junction grade separations like Hunter or the few tens of millions of dollars on upgrading the junction and railyard at Summit – work better in a better-operated system. Electronics before concrete, not instead of concrete – in fact, good operations (i.e. good electronics) create more demand for megaprojects.

At no point are these really in competition, not just because flashy commuter rail projects complement intercity rail through mutual feeding, but also because the benefits for non-connecting passengers are so different that different funding mechanisms make sense. The North-South Rail Link has some benefits to intercity travel, as part of the same program with high-speed rail on the Northeast Corridor, and as such, it could be studied as part of the same program, if there is enough money in the budget for it, which there is not. Conversely, it has very strong local benefits, ideal for a funding partnership between the federal government and Massachusetts; similarly, New York commuter rail improvements are ideal for a funding partnership between the federal government, New York State, New Jersey, and very occasionally Connecticut.

In contrast, intercity rail benefits people who are far away from where construction is done: extensive bypasses built in Connecticut would create a small number of jobs in Connecticut temporarily, but the bigger benefits would accrue not just to residents of the state (through better New Haven-Boston and perhaps New Haven-New York trip times) but mostly to residents of neighboring states traveling through Connecticut. This is why there’s generally more national coordination of intercity rail planning than of regional rail planning: the German federal government, too, partly funds S-Bahn projects in major German cities, but isn’t involved in planning S21 S15 or the second S-Bahn trunk in Munich, whereas it is very involved in decisions on building high-speed rail lines. The situation in France is similar – the state is involved in decisions on LGVs and on Parisian transit but not on provincial transit, though it helps fund the latter; despite the similarity in the broad outlines of the funding structure, the outcomes are different, which should mean that the differences between France and Germany do not boil down to funding mechanisms or to inherent competition between intercity rail funds and regional rail funds.

The United States Has Too Few Road Tunnels

The Francis Scott Key Bridge in Baltimore collapsed after a drifting freighter hit one of its supports; so far, six people are presumed dead. Immediately after the disaster, people were asking if it could be prevented, and it became clear that it is not possible to build a bridge anchor that can withstand the impact of a modern ship, even at low speed. However, it was then pointed out to me on Mastodon that it’s not normal in Europe to have such a bridge over a shipping channel; instead, roads go in tunnel. I started looking, and got to a place that connects my interest in construction costs with that of cross-cultural learning. Europe has far more road tunneling than the US does, thanks to the lower construction costs here; it also has better harmonization of regulations of what can go in tunnels and what cannot. The bridge collapse is a corner case of where the American system fails – it’s a once in several decades event – but it does showcase deep problems with building infrastructure.

Road tunnels

The United States has very little road tunneling for its size. This list has a lot of dead links and out of date numbers, but in the US, the FHWA has a current database in which the tunnels sum to 220 km. Germany had 150 km in 1999, and has tendered about 170 km of new tunnel since 2000 of which only 48 are still under construction. France has 238 km of road tunnel; the two longest and the 10th longest, totaling 28 km, cross the Alpine border with Italy, but even excluding those, 210 is almost as much as the US on one fifth the population. Italy of course has more tunneling, as can be expected from its topography, but France (ex-borders) and Germany are not more mountainous than the US, do not have fjords and skerries like Norway, and don’t even have rias like Chesapeake Bay and the Lower Hudson. Japan, with its mountainous island geography, has around 5,000 km of road tunnel.

The United States builds so few tunnels that it’s hard to create any large database of American road tunnels and their costs. Moreover, it has even fewer urban road tunnels, and the few it does have, like the Big Dig and more recently the Alaskan Way Viaduct replacement tunnel, have become bywords for extreme costs, creating distaste even among pro-highway urban politicians for more and leading to project cancellations. With that in mind, the State Route 99 tunnel replacing the Alaskan Way Viaduct is 3 km long and cost $2.15 billion in 2009-19, which is $2.77 billion in 2023 dollars and $920 million/km, with just four lanes, two in each direction.

In Europe, this is not at all an exhaustive database; it represents where I’ve lived and what I’ve studied, but these are all complex urban tunnels in dense environments:

  • Stockholm: the six-lane Förbifart Stockholm project to build long bypass roads in Stockholm using congestion pricing money, after acrimonious political debates over how to allocate the money between roads and public transport, comprises 17 km of tunnel (plus 4 km above-ground) including underwater segments, for an updated cost of 51.5 billion kronor in 2021 prices, or $6.97 billion in 2023 PPPs, or $410 million/km. The project is well underway and its current cost represents a large overrun over the original estimate.
  • Paris: the four-lane A86 ring road was completed in 2011 with 15.5 km of new tunnel, including 10 in a duplex tunnel, at a cost of 2.2 billion €. I’ve seen sources saying that the cost applies only to the duplex section, but the EIB claims 1.7 billion € for the duplex. Physical construction was done 2005-7; deflating from 2006 prices, this is $4.18 billion in 2023 PPPs, or $270 million/km. This is a tunnel with atypically restricted clearances – commercial vehicles are entirely banned, as are vehicles running on compressed natural gas, due to fire concerns after the Mont-Blanc Tunnel fire.
  • Berlin: the four-lane 2.4 km long Tunnel Tiergarten Spreebogen (TTS) project was dug 2002-4, for 390 million €, or $790 million in 2023 PPPs and $330 million/km. This tunnel goes under the river and under the contemporarily built Berlin Hauptbahnhof urban renewal but also under a park. The controversial A100 17th segment plan comprises 4.1 km of which 2.7 are to be in tunnel, officially for 800 million € but that estimate is out of date and a rougher but more current estimate is 1 billion €. The exchange rate value of the euro today belies how much stronger it is in PPP terms: this is $1.45 billion, or $537 million/km if we assume the above-ground section is free, somewhat less if we cost it too. The 17th segment tunnel is, I believe, to have six lanes; the under-construction 16th segment has six lanes.

Crossing shipping channels

The busiest container ports in Europe are, by far, Rotterdam, Antwerp, and Hamburg, in this order. Rotterdam and Antwerp do not, as far as I’ve been able to tell from Google Earth tourism, have any road bridge over the shipping channels. Hamburg has one, the Köhlbrandbrücke (anchored on land, not water), on the way to one of the container berths, and some movable bridges like the Kattwykbrücke on the way to other berths – and there are plans to replace this with a new crossing, by bridge, with higher clearance below, with a tunnel elsewhere on the route. The next tranche of European ports are generally coastal – Le Havre, Bremerhaven, Valencia, Algeciras, Piraeus, Constanța – so it is not surprising the shipping channels are bridge-free; but Rotterdam, Antwerp, and Hamburg, are all on rivers, crossed by tunnel.

American ports usually have bridges over shipping channels, even when they are next to the ocean, as at the Ports of Los Angeles and Long Beach. This is not universal – crossings in Hampton Roads have tunnels – but it’s the trend. Of note, the US does occasionally tunnel under deep channels (again, Hampton Roads); that the Netherlands tunnels in Rotterdam is especially remarkable given how Holland is a floodplain with very difficult tunnel construction in alluvial soil.

Hazardous material regulations

Tunnels do not permit all traffic, due to fire risk. For example, the Mont-Blanc Tunnel requires vehicles heavier than 3.5 tons to undergo a safety inspection before entering to ensure they don’t carry prohibited dangerous goods. In Europe, this is governed by the ADR; all European countries are party to it, even ones not in the EU, and so are some non-European ones. Tunnels can be classified locally between A (no restrictions) and E (most restrictive).

The United States is not party to the ADR. It has its own set of regulations for transportation of hazardous materials (hazmat), with different classifications – and those differ by state. Here are the rules in Maryland. They’re restrictive enough that significant road freight had to use the Key Bridge, because the alternative routes have tunnels that it is banned from entering. Port Authority has different rules, permitting certain hazmat through the Lincoln Tunnel with an official escort. Somehow, the rules are not uniform in the United States even though it is a country and Europe is not; Russia and Ukraine may be at war with each other, but they have the same transportation of dangerous goods regulations.

Subway-Intercity Rail Connections

Something Onux said in comments on yesterday’s post, about connecting Brooklyn to intercity rail, got me thinking more about how metro lines and intercity rail can connect better. This matters for mature cities that build little infrastructure like New York or Berlin, but also for developing-world cities with large construction programs ahead of them. For the most part, a better subway system is automatically one that can also serve the train station better – the train station is usually an important destination for urban travel and therefore, usually the same things that make for a stronger subway system also make for better subway-intercity rail connections.

Subways and commuter trains

Like gender, transit mode is a spectrum. There are extensive systems that are clearly metro and ones that are clearly commuter rail, but also things in between, like the RER A, and by this schema, the Tokyo and Seoul subways are fairly modequeer.

The scope of this post is generally pure subway systems – even the most metro-like commuter lines, like the RER A and the Berlin S-Bahn, use mainline rail rights-of-way and usually naturally come to connect with intercity train stations. Of note, RER A planning, as soon as SNCF got involved, was modified to ensure the line would connect with Gare de Lyon and Gare Saint-Lazare; previous RATP-only plans had the line serving Bastille and not Gare de Lyon, and Concorde and not Auber. So here, the first rule is that metro (and metro-like commuter rail) plans should, when possible, be modified to have the lines serve mainline train stations.

Which train stations?

A city designing a subway system should ensure to serve the train station. This involves nontrivial questions about which train stations exactly.

On the one hand, opening more train stations allows for more opportunities for metro connections. In Boston, all intercity trains serve South Station and Back Bay, with connections to the Red and Orange Lines respectively. In Berlin, north-south intercity trains call not just at Hauptbahnhof, which connects to the Stadtbahn and (since 2020) U5, but also Gesundbrunnen and Südkreuz, which connect to the northern and southern legs of the Ringbahn and to the North-South Tunnel; Gesunbrunnen also has a U8 connection. In contrast, trains into Paris only call at the main terminal, and intercity trains in New York only stop at Penn Station.

On the other hand, extra stations like Back Bay and delay trains. The questions that need to be answered when deciding whether to add stations on an intercity line are,

  • How constructible is the new station? In New York, this question rules out additional stops; some of the through-running plans involve a Penn Station-Grand Central connection to be used by intercity trains, but there are other reasons to keep it commuter rail-only (for example, it would make track-sharing on the Harlem Line even harder).
  • How fast is the line around the new station? More stations are acceptable in already slow zones (reducing the stop penalty), on lines where most trips take a long time (reducing the impact of a given stop penalty). Back Bay and Südkreuz are in slow areas; Gesundbrunnen is north of Hauptbahnhof where nearly passengers are going south of Berlin, so it’s free from the perspective of passengers’ time.
  • How valuable are the connections? This depends on factors like the ease of internal subway transfers, but mostly on which subway lines the line can connect to. Parisian train terminals should in theory get subsidiary stations because internal Métro transfers are so annoying, but there’s not much to connect to – just the M2/M6 ring, generally with no stations over the tracks.

Subway operations

In general, most things that improve subway operations in general also improve connectivity to the train station. For example, in New York, speeding up the trains would be noticeable enough to induce more ridership for all trips, including access to Penn Station; this could be done through reducing flagging restrictions (which we briefly mention at ETA), among other things. The same is true of reliability, frequency, and other common demands of transit advocates.

Also in New York, deinterlining would generally be an unalloyed good for Penn Station-bound passengers. The reason is that the north-south trunk lines in Manhattan, other than the 4/5/6, either serve Penn Station or get to Herald Square one long block away. The most critical place to deinterline is at DeKalb Avenue in Brooklyn, where the B/D/N/Q switch from a pattern in which the B and D share one track pair and the N and Q share another to one in which the B and Q share a pair and the D and N share a pair; the current situation is so delicate that trains are delayed two minutes just at this junction. The B/D and N/Q trunk lines in Manhattan are generally very close to each other, so that the drawback of deinterlining is reduced, but when it comes to serving Penn Station, the drawback is entirely eliminated, since both lines serve Herald Square.

If anything, it’s faster to list areas where subway service quality and subway service quality to the train station specifically are not the same than to list areas where they are:

  • The train station is in city center, and so circumferential transit, generally important, doesn’t generally connect to the station; exceptions like the Ringbahn exist but are uncommon.
  • If too many lines connect to the one station, then the station may become overloaded. Three lines are probably fine – Stockholm has all three T-bana lines serving T-Centralen, adjacent to the mainline Stockholm Central Station, and there is considerable but not dangerous crowding. But beyond that, metro networks need to start spreading out.
  • Some American Sunbelt cities if anything have a subway connection to the train station, for example Los Angeles, without having good service in general. In Los Angeles, the one heavy rail trunk connects to Union Station and so does one branch of the Regional Connector; the city’s problems with subway-intercity rail connections are that it doesn’t really have a subway and that it doesn’t really have intercity rail either.

Intercity Trains and Long Island

Amtrak wants to extend three daily Northeast Corridor trains to Long Island. It’s a bad idea – for one, if the timetable can accommodate three daily trains, it can accommodate an hourly train – but beyond the frequency point, this is for fairly deep reasons, and it took me years of studying timetabling on the corridor to understand why. In short, the timetabling introduces too many points of failure, and meanwhile, the alternative of sending all trains that arrive in New York from Philadelphia and Washington onward to New Haven is appealing. To be clear, there are benefits to the Long Island routing, they’re just smaller than the operational costs; there’s a reason this post is notably not tagged “incompetence.”

How to connect the Northeast Corridor with Long Island

Map of the Northeast Corridor and LIRR Main Line; the Northeast Corridor is depicted with extensive bypasses in Connecticut and small curve modifications in New Jersey and Pennsylvania

The Northeast Corridor has asymmetric demand on its two halves. North of New York, it connects the city with Boston. But south of New York, it connects to both Philadelphia and Washington. As a result, the line can always expect to have more traffic south of New York than north of it; today, this difference is magnified by the lower average speed of the northern half, due to the slowness of the line in Connecticut. Today, many trains terminate in New York and don’t run farther north; in the last 20 years, Amtrak has also gone back and forth on whether some trains should divert north at New Haven and run to Springfield or whether such service should only be provided with shuttle trains with a timed connection. Extending service to Long Island is one way to resolve the asymmetry of demand.

Such an extension would stop at the major stattions on the LIRR Main Line. The most important is Jamaica, with a connection to JFK; then, in the suburbs, it would be interesting to stop at least at Mineola and Hicksville and probably also go as far as Ronkonkoma, the end of the line depicted on the map. Amtrak’s proposed service makes exactly these stops plus one, Deer Park between Hicksville and Ronkonkoma.

The entire Main Line is electrified, but with third rail, not catenary. The trains for it therefore would need to be dual-voltage. This requires a dedicated fleet, but it’s not too hard to procure – it’s easier to go from AC to DC than in the opposite direction, and Amtrak and the LIRR already have dual-mode diesel locomotives with third rail shoes, so they could ask for shoes on catenary electric locomotives (or on EMUs).

The main benefit of doing this, as opposed to short-turning surplus Northeast Corridor trains in New York, is that it provides direct service to Long Island. In theory, this provides access to the 2.9 million people living on Long Island. In practice, the shed is somewhat smaller, because people living near LIRR branches that are not the Main Line would be connecting by train anyway and then the difference between connecting at Jamaica and connecting at Penn Station is not material; that said, Ronkonkoma has a large parking lot accessible from all of Suffolk County, and between it and significant parts of Nassau County near the Main Line, this is still 2 million people. There aren’t many destinations on Long Island, which has atypically little job sprawl for an American suburb, but 2 million originating passengers plus people boarding at Jamaica plus people going to Jamaica for JFK is a significant benefit. (How significant I can’t tell you – the tools I have for ridership estimation aren’t granular enough to detect the LIRR-Amtrak transfer penalty at Penn Station.)

My early Northeast Corridor ideas did include such service, for the above reasons. However, there are two serious drawbacks, detailed below.

Timetabling considerations

Under current plans, there is little interaction between the LIRR and the Northeast Corridor. There are two separate routes into Penn Station from the east, one via 32nd Street (“southern tunnels”) and one via 33rd (“northern tunnels”), each a two-track line with one track in each direction. The North River Tunnels, connecting Penn Station with New Jersey and the rest of the United States, face the southern tunnels; the Gateway tunnels under construction to double trans-Hudson capacity are not planned to pair with the northern tunnels, but rather to connect to stub-end tracks facing 31st Street. For this reason, Amtrak always or almost always enters Penn Station from the east using the southern tunnels; the northern tunnels do have some station tracks that connect to them and still allow through-service to the west, but the moves through the station interlocking are more complex and more constrained.

As seen on the map, east of Penn Station, the Northeast Corridor is to the north of the LIRR. Thus, Amtrak has to transition from being south of the LIRR to being north of it. This used to be done at-grade, with conflict with same-direction trains (but not opposite-direction ones); it has since been grade-separated, at excessive cost. With much LIRR service diverted to Grand Central via the East Side Access tunnel, current traffic can be divided so that LIRR Main Line service exclusively uses the northern tunnels and Northeast Corridor (Amtrak or commuter rail under the soon to open Penn Station Access project) service exclusively uses the southern tunnels; the one LIRR branch not going through Jamaica, the Port Washington Branch, can use the southern tunnels as if it is a Penn Station Access branch. This is not too far from how current service is organized anyway, with the LIRR preferring the northern (high-numbered) tracks at Penn Station, Amtrak the middle ones, and New Jersey Transit the southern ones with the stub end:

The status quo, including any modification thereto that keeps the LIRR (except the Port Washington Branch) separate from the Northeast Corridor, means that all timetabling complexity on the LIRR is localized to the LIRR. LIRR timetabling has to deal with all of the following issues today:

  • There are many different branches, all of which want to go to Manhattan rather than to Brooklyn, and to a large extent they also want to go on the express tracks between Jamaica and Manhattan rather than the local tracks.
  • There are two Manhattan terminals and no place to transfer between trains to different ones except Jamaica; an infill station at Sunnyside Yards, permitting trains from the LIRR going to Grand Central to exchange passengers with Penn Station Access trains, would be helpful, but does not currently exist.
  • The outer Port Jefferson Branch is unelectrified and single-track and yet has fairly high ridership, so that isolating it with shuttle trains is infeasible except in the extreme short run pending electrification.
  • All junctions east of Jamaica are flat.
  • The Main Line has three tracks east of Floral Park, the third recently opened at very high cost, purely for peak-direction express trains, but cannot easily schedule express trains in both directions.

There are solutions to all of these problems, involving timetable simplification, reduction of express patterns with time saved through much reduced schedule padding, and targeted infrastructure interventions such as electrifying and double-tracking the entire Port Jefferson Branch.

However, Amtrak service throws multiple wrenches in this system. First, it requires a vigorous all-day express service between New York and Hicksville if not Ronkonkoma. Between Floral Park and Hicksville, there are three tracks. Right now the local demand is weak, but this is only because there is little local service, and instead the schedule encourages passengers to drive to Hicksville or Mineola and park there. Any stable timetable has to provide much stronger local service, and this means express trains have to awkwardly use the middle track as a single track. This isn’t impossible – it’s about 15 km of fast tracks with only one intermediate station, Mineola – but it’s constraining. Then the constraint propagates east of Hicksville, where there are only two tracks, and so those express trains have to share tracks with the locals and be timetabled not to conflict.

And second, all these additional conflict points would be transmitted to the entire Northeast Corridor. A delay in Deer Park would propagate to Philadelphia and Washington. Even without delays, the timetabling of the trains in New Jersey would be affected by constraints on Long Island; then the New Jersey timetabling constraints would be transmitted east to Connecticut and Massachusetts. All of this is doable, but at the price of worse schedule padding. I suspect that this is why the proposed Amtrak trip time for New York-Ronkonkoma is 1:25, where off-peak LIRR trains do it in 1:18 making all eight local stops between Ronkonkoma and Hicksville, Mineola, Jamaica, and Woodside. With low padding, which can only be done with more separated out timetables, they could do it in 1:08, making four more net stops.

Trains to New Haven

The other reason I’ve come to believe Northeast Corridor trains shouldn’t go to Jamaica and Long Island is that more trains need to go to Stamford and New Haven. This is for a number of different reasons.

The impact of higher average speed

The higher the average speed of the train, the more significant Boston-Philadelphia and Boston-Washington ridership is. This, in turn, reduces the difference in ridership north and south of New York somewhat, to the point that closer to one train in three doesn’t need to go to Boston than one train in two.

Springfield

Hartford and Springfield can expect significant ridership to New York if there is better service. Right now the line is unelectrified and runs haphazard schedules, but it could be electrified and trains could run through; moreover, any improvement to the New York-Boston line automatically also means New York-Springfield trains get faster, producing more ridership.

New Haven-New York trips

If we break my gravity model of ridership not into larger combined statistical areas but into smaller metropolitan statistical areas, separating out New Haven and Stamford from New York, then we see significant trips between Connecticut and New York. The model, which is purely intercity, at this point projects only 15% less traffic density in the Stamford-New York section than in the New York-Trenton section, counting the impact of Springfield and higher average speed as well.

Commutes from north of New York

There is some reason to believe that there will be much more ridership into New York from the nearby points – New Haven, Stamford, Newark, Trenton (if it has a stop), and Philadelphia – than the model predicts. The model doesn’t take commute trips into account; thus, it projects about 7.78 million annual trips between New York and either Stamford or New Haven, where in fact the New Haven Line was getting 125,000 weekday passengers and 39 million annual passengers in the 2010s, mostly from Connecticut and not Westchester County suburbs. Commute trips, in turn, accrete fairly symmetrically around the main city, reducing the difference in ridership between New York-Philadelphia and New York-New Haven, even though Philadelphia is the much larger city.

Combining everything

With largely symmetric ridership around New York in the core, it’s best to schedule the Northeast Corridor with the same number of trains immediately north and immediately south of it. At New Haven, trains should branch. The gravity model projects a 3:1 ratio between the ridership to Boston and to Springfield. Thus, if there are eight trains per hour between New Haven and Washington, then six should go to Boston and two to Springfield; this is not even that aggressive of an assumption, it’s just hard to timetable without additional bypasses. If there are six trains per hour south of New Haven, which is more delicate to timetable but can be done with much less concrete, then two should still go to Springfield, and they’ll be less full but over this short a section it’s probably worth it, given how important frequency is (hourly vs. half-hourly) for trips that are on the order of an hour and a half to New York.

Trains on the Moon

The US government is contracting defense contractor Northrop Grumman to develop a concept for passenger and freight rail on the Moon, the idea being to use this to transport resources and perhaps build rockets for travel to the rest of the Solar System. Upon seeing this, I immediately set to try figuring out design standards, and it looks like such a railway would have a much harder time developing an alignment than on Earth, because of the impact of low gravity.

The issue is that lunar gravity is 1.6 m/s^2, and not 9.8 as on Earth. This turns out to affect how vehicles can round corners. The formula connecting speed, lateral acceleration, and the curve radius is the same everywhere:

v^2 = r\cdot a

The value of a is measured in the horizontal plane; curves are normally banked (canted/superelevated), so that gravity countermands centrifugal force, but normally, trains are run faster than the perfect balancing speed, since some lateral acceleration in the plane of the body of the train is acceptable. For much more detail, see old of posts of mine here and here.

In rail engineering, lateral acceleration is usually measured not in units of acceleration, but in units of distance, corresponding to how far the track is canted vertically (cant), and to how much the track would need to be canted further to achieve perfect balancing speed (cant deficiency). These units follow the formula

a = (e/k)g

Here, e is total equivalent cant (cant plus cant deficiency), k is the track gauge from the middle of the rail to middle of the rail (around 60 mm more than the usual value of track gauge, which is measured from inner rail to inner rail), and g is gravitational acceleration. On Earth, on standard-gauge railways, this reduces to the formula that 1 m/s^2 of lateral acceleration is equal to 150 mm of total equivalent cant.

The issue with all of this is that the safety limits of both cant and cant deficiency are better expressed in units of distance rather than acceleration, as gravitational acceleration changes; equivalently, the limit value of a is proportional to g. The reason is that cant deficiency is limited by the ability of the train to round the curve safely, without toppling; if the combined force vector of weight and centrifugal force points too far off-center, then the swaying of the train can lead to derailment and catastrophic damage, including deaths. Thus, the limit value of acceleration in the plane of the tracks is best expressed as a proportion of gravitational acceleration, rather than in absolute units. The limit value of cant, in turn, is related to the safety limit of the ability of the train to stand still on canted track in an emergency.

This analysis can be seen in two distinct places in existing rail design standards and speed limits:

  • When the train rounds a vertical curve, there is a minimum curve radius too, governed by both safety and passenger comfort. The minimum curve radius is higher on a crest than on a sag, because on a crest the train’s vertical acceleration slightly countermands gravity, and thus the train does not grip the tracks so well, whereas on a sag the vertical acceleration adds to gravity.
  • The maximum values of cant and cant deficiency are usually fairly close for a given train. Two notable exceptions are high-speed rail, and tilting trains. High-speed rail has higher maximum cant than cant deficiency – German standards are 180 and 130 mm respectively – because cant deficiency is a limiting factor when the train is moving at 300 km/h (and thus potentially sways more) whereas cant is a limiting factor when the train sits still. Tilting trains are the exact opposite: the maximum cant deficiency is very high, reaching 270 mm on some high-maintenance Pendolino sets designed to be light enough and have low enough center of mass to be able to round corners safely, because when the train sits still on canted track the tilt system is assumed not to be working.

The upshot is that a standard-gauge railway on the Moon can expect to have a maximum total equivalent cant of 300 mm or somewhat more, same as on Earth – but that is compatible with a value of a of 0.33 m/s^2. In effect, curve radii have to be six times wider, assuming equal technology. The viaducts required to build such a straight right-of-way are easier to build on the Moon, since they don’t need to support as much weight for a given mass, but more and taller viaducts are still needed, and going around obstacles is not easy.