If you multiply the populations of the metro areas served as a proxy for HSR ridership, then by comparison to Shinkansen lines as well as the AVE, New York-Washington traffic should be about 15-20 million passengers per year. It’s even higher if we include Madrid-Seville, an overperformer with more ridership than Madrid-Barcelona. This is just between the two metro areas, excluding additional passengers to Philadelphia. This raises two questions: what does the data suggest about modifying product-of-populations as a proxy, perhaps to account for distance? And, more importantly, is such ridership realistic for the Northeast Corridor?

First, at least on the Shinkansen and the AVE, in the range of distances up to nearly 4 hours, there’s no effect of distance on ridership, especially if we combine air and rail ridership. (We’re trying to apply this analysis to a city pair on which trains will take not much more than an hour and a half; end-to-end air traffic can be assumed to be zero.) Beyond that, Tokyo-Fukuoka air and rail ridership combined still underperforms shorter-distance links. One explanation is that as distance increases, total travel volume decreases, but rail and then air market share grows at the expense of cars and buses, and in the 1.5-4-hour range, these effects more or less cancel out. At longer distances, there is no longer much highway travel for trains and planes to poach.

With distance ignored, large cities consistently underperform small cities. This is not a surprise based on SNCF’s refined gravity model of ridership, in which travel volume is proportional not to the product of the city populations, but to the product raised to an exponent lower than 1. SNCF uses an empirically derived exponent, between 0.8 and 0.9, and AVE and Shinkansen data is indeed more consistent with that range. Some city pairs still underperform in a way that can’t be explained by population and distance, such as Tokyo-Okayama, but the exponent perfectly explains why Tokyo-Osaka underperforms a model with exponent 1.

So what about the Northeast Corridor? Current Amtrak ridership between New York and Washington is 1.74 million, but that’s just between Penn Station and Union Station. Amtrak provides its top 10 city pairs in the Northeast in its Master Plan, which include New York-Baltimore and New York-BWI, at 650,000 between them. I don’t know the ridership on more minor city pairs, such as those involving Newark or Stamford. I would guess the total including those is about 3-3.5 million; this is based just on extrapolating that of the top-10 markets on the southern half of the line just under half the ridership is between the New York and Washington metro areas, and applying a fudge factor to account for the fact that secondary markets not involving New York-Washington are less likely to make the top 10.

In contrast, based on comparison to the Shinkansen and AVE, we should expect HSR ridership of 15-20 million, about 5 times what I believe the present ridership is. (In fact, based on comparison to the lower-fare KTX, it should be if anything higher.) This is despite the fact that the current trip time is either 2:47 or 3:25 whereas with HSR it would be about 1:35. The importance of this is that we can’t expect induced demand to quintuple ridership out of halving trip time, but instead we need to explain this based on competition with cars and buses.

Part of this competition has to be about fares. Amtrak charges very high fares (see the route performance report) – on average, 28 cents per km on the Regional, and 48 on the Acela. Shinkansen fares average 23 cents per km on Tokaido, 20 on Sanyo, and 24 on the JR East network. That said, the shorter distance of New York-Washington means that absolute fares are not higher, particularly on the cheaper option. However, high fare per km does mean the trip is less competitive with cheap express buses and with driving.

This comes in addition to travel time. The Regional is an hour faster than Megabus; HSR that is three hours faster Megabus, especially if it’s also cheaper than today’s Regional, could make a serious dent in the Megabus network. Express buses already have trouble with secondary markets, because those can’t piggyback on primary markets as intermediate stops the way they can with trains. Better trains could poach the express bus market and reduce it to where it was ten years ago.

At the range of the top-performing city pairs, most people take trains rather than use roads. I do not have data for individual city pairs in Japan (but see here for Korea, where HSR overperforms, perhaps due to lower fares, which are about 15 cents per km before discounts), but at the distance of New York-Washington, 360 km, trains get a little more than half the total mode share and cars get the other half. Amtrak’s 2010 Vision says that the current rail mode share on the entire Northeast Corridor is 6%; it does not say what the share on New York-Washington is, but I’ve seen 14% elsewhere (no reference, sorry), and the Vision says that incremental Master Plan improvements will raise it to 26%. Of course going from 14% to 50% also involves induced demand, and this means the expected rise in ridership is a higher factor, potentially a factor of 5.

I’m not going to try using this method to estimate shorter-distance ridership, because then car ownership, sprawl levels, etc. become a much bigger issue, and quick-and-dirty sanity checks don’t work and are no replacement for serious ridership studies. But we can apply the method to other longer-distance portions of the Northeast Corridor. If we use the lower end of the scale, we get New York-Washington at 15 million annual passengers or a little more, New York-Boston at 15 million or a little less, Boston-Washington at 6 million, Boston-Philadelphia at 5 million.

As a secondary sanity check, the Boston-Washington air market is about 2.5 million, and for HSR to get 2.5 times as much ridership on a formerly air-dominated city pair as the pre-HSR air travel volume is the same performance Eurostar got.

All four metro areas should be interpreted as broadly as possible, to maintain comparability with Japanese metro areas, whose definition is loose and roughly comparable to the American combined statistical area. So there are just four cities on the Northeast Corridor, really. This is still not all the ridership there is – there is still New York-Philadelphia and Philadelphia-Washington, I’m just less comfortable making even an ex-recto estimate. But even without those two potentially high-ridership city pairs, we get high passenger density on all segments of the line.

Update: although I have not found city-to-city ridership data from France, I have found region-to-region numbers from Paris to the southwest. I also have some air traffic volumes from which we can deduce air/rail markets: on Paris-Nice the TGV has a 31% share of the air/rail market; on Paris-Marseille I’ve seen numbers ranging from 60% to 83%, and for this post’s purposes I’m going to assume 70%. We get air/rail traffic numbers from Paris to Marseille (5.2 million, but this grows to 9.2 million if we assume 83% TGV share and declines to 3.9 million if we assume 60%), Nice (4.2 million), Midi-Pyrenees (3.2 million), Aquitaine (5.5 million), and Poitou-Charentes (3.3 million). With the exception of the Midi-Pyrenees number, which represents a fairly long distance, all overperform the Shinkansen. Ignoring distance as always and using an exponent of 0.8, Paris-Marseille overperforms Tokyo-Sendai by a factor of 1.85, Paris-Nice by 2.21, Paris-Midi-Pyrenees by 0.77 (i.e. it underperforms), Paris-Aquitaine by 1.26, and Paris-Poitou-Charentes by 1.22. Per-kilometer fares are much lower than on Shinkansen – indeed SNCF’s total revenue, both high- and low-speed, divided just by TGV passenger-km, is €0.14 – and this can contribute to the higher traffic.

Paris-Nice can be explained as a major leisure corridor, similar to the unusually high passenger traffic to Florida or Las Vegas. But bear in mind that Nice and Marseille are metro areas and not entire regions, and under any assumption that Bordeaux and Toulouse get a greater share of the travel to Paris than the rural areas in their respective regions, they will overperform by a substantial margin. Although French metro areas are defined less loosely than Japanese ones, which can skew the Marseille and Nice numbers, the Aquitaine and Midi-Pyrenees numbers are if anything defined too loosely due to the inclusion of outright rural departments.

Carolyn Maloney, the Congresswoman representing Manhattan’s East Side, gave an interview to the Globe and Mail in which she called for high-speed rail between New York and Canadian cities. She did not specify which cities, but presumably those are Montreal and Toronto. The article quoted Andrew Cuomo as saying that connecting New York to Montreal and Toronto would be “transformative,” though it did not mention that Cuomo killed plans for HSR from New York to Buffalo. It is unclear to me whether Maloney is serious, or merely as serious as Cuomo; for the purposes of this post, let us assume that she is serious. Is it justifiable to build HSR from New York to Montreal and Toronto?

Long-time readers will know that I am skeptical of international HSR lines. But let me explain why I think New York-Toronto could be successful, while New York-Montreal could not.

First, perhaps because of the common language, the travel markets from the US to Montreal underperform those to Toronto. According to Statscan data, Toronto has about three times as many travelers to New York, Chicago, Los Angeles, and the other top metro areas in the US as Montreal does. The two cities’ metro area population ratio is only about 1.5:1; this is indeed the ratio of their travel markets to leisure destinations such as Las Vegas and Miami. US data generally points to higher numbers, sometimes by a substantial margin; it also points to a ratio of about 2.5-3:1 between Toronto and Montreal travel, this time even to Las Vegas and Miami. (US data excludes planes with up to 60 seats, but these are only about 20% of New York-Toronto departures, and of course a smaller proportion of seats.)

In addition, New York-Toronto may be in a similar situation to New York-London, in which the two cities’ common industry (finance) leads to more business travel. For some evidence of this effect, the Canadian data shows that Calgary and Houston, the two countries’ respective oil capitals, are each other’s top air market on the other side of the border. The same is of course true of financial capitals New York and Toronto, though as the largest cities in their respective countries, this is less surprising. But we should not overinterpret this effect: the New York-Toronto air market is still just 900,000 people a year (according to Canada) or 1.5 million (according to the US), though it far beats New York-Montreal’s 300,000 or 600,000.

Even 1.5 million times an induced demand factor is not enough to build HSR by itself. We could add existing travel volumes from New York to Niagara Falls and from Toronto to Buffalo, but most likely they are not enough by themselves.

The main reason New York-Toronto could be defensible is that a large majority of the New York-Toronto construction would not be done just for New York-Toronto travel. HSR on the Empire Corridor, up to Buffalo, is justifiable entirely based on domestic traffic. At the other end, the Lakeshore West corridor, which already can sustain medium speeds (GO’s top speed is 150 km/h), should be electrified and retrofitted with passing sidings based entirely on local commuter traffic. There are about 100 km between Buffalo and Hamilton, and 160 between Buffalo and Toronto, compared with 850 between New York and Toronto. Since HSR fares and operating profits roughly scale with distance traveled, the operating revenue of the lower-trafficked 100 km between Buffalo and Hamilton should really be multiplied by 8.5. If New York-Toronto traffic is about 3.5 million a year, a similar multiple of preexisting air traffic as Eurostar, then we can expect the construction of the 100 km to add about 3 billion passenger-km a year; 30 million passenger-km of revenue per km of route to be constructed is very good, comparable to the Sanyo Shinkansen. If we need to use New York-Toronto traffic to justify even Toronto-Hamilton upgrades, then we’ll have 18.5 million passenger-km of revenue per km of construction, comparable to the JR East Shinkansen network.

Of course these passenger densities, and hence returns on investment, are not available to the full line; they’re only available to this last link completing New York-Toronto. To enjoy such favorable ratio the preexisting routes must already be in place. We cannot use the 30 million passenger-km/km figure to justify building New York-Buffalo as a first step toward New York-Toronto. If Maloney intends to do that, then she is setting the line up for failure; 3.5 million passenger-km/km is too little. Amtrak has about the same on the Northeast Corridor, from which it squeezes operating profits, but the capital construction was paid by private railroads between 1831 and 1917; building a greenfield line for this performance is unwarranted. At most, we can use it to add to domestic traffic in case the merits of a domestic line are close to good enough but not quite.

New York-Montreal does not have the same advantage as New York-Toronto. Not only is the travel volume much smaller to being with, but also it would require building about 360 km of route, in the rolling hills of Vermont, to create a link of 590 km. Very little of that 360 km is a reasonable commuter rail route by itself – on the line I sketched to measure distance, only 30. So at best this is 330 out of 590. If we attempt the same calculation as for New York-Toronto, we obtain just 2.7 million passenger-km/km. Moreover, the intermediate markets are much weaker than US-Niagara Falls or Buffalo-Toronto. For now, HSR between New York and Montreal should remain an unfulfilled dream of Montreal boosters.

Of course, it’s possible that Maloney just emphasized the possible connections to Canada, and her actual drive is going to be Empire Corridor HSR, which is a welcome change from Cuomo’s opposition. Canadians do not vote in US elections. In that case, a link to Toronto would become stronger, because of the piggybacking on preexisting New York-Buffalo HSR. The line would hinge entirely on constructibility over the river and border control issues then. International links underperform, but sometimes they are short enough relative to the possibility to be worth it.

One common argument for building HSR is that it will help decongest airports, by displacing high-volume short-distance flights. This can result in a permanent reduction in air travel, reducing environmental impact, or a diversion of capacity to longer-distance flights, or perhaps a combination of both. The question is then how much air travel can be diverted.

The main source I’m using for this is the Office of Aviation Analysis’s master table of all lower-48 origin-and-destination city pairs with at least 10 passengers per day (table 6, 3rd quarter of ’11). The data is less than perfect, because passengers connecting from a domestic flight to an international flight count as O&D passengers, but for our purposes it is good enough.

As a first filter, we can see that out of a million passengers per day, 206,000 are flying distance of up to 500 miles, and 390,000 are flying up to 773, the New York-Chicago distance. Those 39% of travelers constitute a much smaller portion of emissions than 39% but a larger portion of planes. Furthermore, not all can be realistically moved to trains: at the upper end of this range, HSR can compete with air but not decimate service the way it can on shorter trips, and on top of that many city pairs are not located on any realistic HSR corridor.

So as a second filter, let us construct a table, by major city (i.e. the top 7 O&D cities minus Las Vegas), of what the total volume of travel is to HSR-viable markets:

Although HSR can get nontrivial mode share against air even if it takes 5 hours, it does not reduce air traffic at this range, but instead induces demand. So although HSR can produce competition for almost a third of the air traffic coming into the largest US cities, it cannot divert as much air traffic. Meaningful diversion occurs at much shorter range, perhaps 3 hours, and even that diversion is incomplete. When the 3-hour Eurostar opened, Paris-London air traffic was permanently halved, from 4.3 million per year before the Chunnel opened to about 2 million after; once the travel time was further reduced to 2:15 with the opening of High Speed 1, it further decreased, to about 1.3 million on the dominant Heathrow/CDG airport pair.

What this means is that for decongesting airports, the meaningful column is the second from the left, for trips up to 3 hours. We immediately see that HSR can only have a small effect on New York, but conversely can do a great deal in Los Angeles. New York is at a further penalty since the hub system ensures it will remain an international gateway, and so traffic between two different cities still needs to pass through.

For New York, the best things that can be done then are to use larger planes on domestic flights, and find relief airports. In Japan, the domestic flights use widebodies, sometimes even 747s, and this has enabled Tokyo-Sapporo to grow to become the world’s highest-capacity air city pair. In the US there are more airlines and the city pairs are less thick, but there is still room for larger planes than 737s and 757s. In the other direction, faster LIRR service could turn Islip into a better relief airport, but it would still have to overcome the stigma of being too far. HSR could also turn Philadelphia into a reasonable option: using the Airport Line and a freight corridor to the west to bypass some of the Wilmington Line’s curves and reduce travel time should be considered as a full build-out option, and would also put PHL about 45 minutes away from New York.

The New York versus Los Angeles difference is not too surprising once we consider where their respective second cities are located. San Francisco is 700 km from Los Angeles, Boston and Washington are 350 km from New York and Philadelphia 150. Elizabeth of CARRD tells me that on LA-SF the current mode split is 50% air, 50% car. The situation in the Northeast is different – making reasonable assumptions on seat occupancy, even on NY-DC and NY-Boston more people take a bus than fly.

Update: Anonymouse in comments brings a good point about the distribution of short-haul travel within airport systems: there is often proportionately more of it at the secondary airports. Providence actually has less short-distance traffic than Boston and Midway is about even with O’Hare, but in California, much more short-distance traffic is at the secondary airports.

The five LA-area airports between them have 27.5% of their domestic traffic within 3-hour radius, but this splits as 21% at LAX, 35% at Long Beach, 37% at Santa Ana, 40% at Ontario, and 63% at Burbank. The three Bay Area airports between them have 19% of their domestic traffic going to LA and a total of 35% within 5-hour train radius, but this splits as 14% and 29% at SFO, 27% and 48% at San Jose, and 35% and 57% at Oakland.

Notes about the table:

1. The transfer penalty is set at 20 minutes, for city pairs that have no reason to ever have a one-seat ride. Both low- and high-speed connecting services are included, including HSR trains running through to the legacy network; I am not proposing new HSR tracks to Green Bay.

2. Instead of making hard alignment decisions, I simply ignored everything that would be controversial. The change in numbers is trivial. For example, neither South Bend nor Fort Wayne is included; both combined have only 2,000 daily air travelers anywhere in the lower 48, and only a handful of dozens to each of the cities in the table.

3. The travel times are full-build, so, for example, the Northeast Corridor is 1:30 Boston-New York and 1:30 New York-Washington, rather than the slightly higher travel times that should be aimed at initially. Average speeds range from 240 to 300 km/h on high-speed lines (higher in the Midwest, South, and flat portions of the West, lower in the Northeast and the Californian mountain crossings), and 100-130 km/h on upgraded legacy lines.

4. For US-Canada travel, we use T-100 data for international flights (data from September 2011). The data quality is poor since small planes are excluded, causing an underestimate in traffic on such markets as New York-Toronto, but conversely many of those flights would be double-counted because international-domestic transfers count twice. We can assume that the two effects (ignoring international flights outside Canada, and counting domestic-international transfers) cancel out, which is equivalent to assuming that exactly half of international travelers connect domestically.

5. The full list of cities included in each entry in the table is:

New York:
-2:30: the Northeast Corridor, Hartford, the Empire Corridor up to Rochester, Pittsburgh, Richmond, Burlington, Montreal.
2:30-3:00: Buffalo, Raleigh, Portland.
3:00-3:30: Toronto, Ottawa, Cleveland, Norfolk, Greensboro.
3:30-4:00: Charlotte, Toledo, Fayetteville, Lynchburg.
4:00-4:30: Greenville (SC), Greenville (NC), Columbus, Detroit, Roanoke, Nantucket, Columbia (SC).
4:30-5:00: Atlanta, Chicago, Dayton, Cincinnati, Wilmington (NC), Savannah.

Los Angeles:
-2:30: Las Vegas, Phoenix, Sacramento.
2:30-3:00: San Francisco, Tucson.
(This is where my exclusion of unrealistic corridors has the most effect. HSR could connect Los Angeles with Portland and Denver in 5 hours, Salt Lake City in 3:30, and El Paso and Albuquerque in 4:30. But the population is too sparse for the overlapping short trips that make comparably long corridors in the eastern half of the US semi-reasonable.)

Bay Area:
-2:30: the entire Central Valley.
2:30-3:00: Los Angeles.
3:00-3:30: Palm Springs.
3:30-4:00: —
4:00-4:30: San Diego, Las Vegas (assuming a Grapevine and Cajon alignment, which is the worst assumption; if the connector is between Victorville and Palmdale, as officially planned, then it’s about 4:00, and if it’s between Mojave and Barstow, it’s 3:45).
4:30-5:00: Phoenix.

Chicago:
-2:30: the corridors to Minneapolis, Detroit/Cleveland, Cincinnati, and St. Louis; Grand Rapids, Louisville, Dayton, Green Bay, Columbus.
2:30-3:00: Nashville, Pittsburgh, Buffalo, Kansas City, Toronto.
3:00-3:30: Chattanooga, Rochester.
3:30-4:00: Atlanta, Harrisburg, Syracuse.
4:00-4:30: Ottawa, Philadelphia.
4:30-5:00: Montreal, Albany, New York.

Washington-Baltimore:
-2:30: the Northeast Corridor up to New York, the Southeast Corridor down to Charlotte, Fayetteville, Norfolk, Lynchburg.
2:30-3:00: Boston, Hartford, Albany, Pittsburgh, Greenville (SC), Greenville (NC), Roanoke, Columbia (SC).
3:00-3:30: Atlanta, Wilmington (NC), Burlington, Cleveland, Savannah.
3:30-4:00: Montreal, Syracuse, Toledo.
4:00-4:30: Charleston, Birmingham, Jacksonville, Detroit, Columbus, Rochester, Chattanooga, Asheville, Portland.
4:30-5:00: Dayton, Cincinnati, Buffalo, Daytona, Ottawa. (Orlando is very close and some alignments put it just under 5 hours, but not all do.)

Boston:
-2:30: the Northeast Corridor down to Philadelphia, the Empire Corridor up to Rochester, Burlington, Montreal, Hartford, Portland.
2:30-3:00: Washington, Buffalo, Harrisburg.
3:00-3:30: Toronto, Ottawa, Erie, Atlantic City.
3:30-4:00: Cleveland, Pittsburgh, Richmond.
4:00-4:30: Raleigh, Toledo.
4:30-5:00: Norfolk, Greensboro, Detroit, Columbus, Dayton.