1. I'm trying to work out financial ROIs on American high-speed lines, and boy do the lines radiating out of Chicago all suck.
2. My methodology uses advanced algorithms and techniques by people like this one (art credit: the late William O'Connor). 
3. You take the populations of the 2 metro areas connected, in millions. You multiply. You raise to the 0.8th power. You divide by 4.
4. That's your annual ridership, in millions. It's trained on Tokyo-Sendai: ((35*2.2)^0.8)/4 = 8.1. jreast.co.jp/e/investor/ar/…
5. It's valid for lines taking 1-4 hours: longer distances = more use of scheduled transport and less use of slower cars.
6. Spanish ridership follows the same model. French ridership, with lower fares, overperforms it by a factor of maybe 1.5 on average.
7. Anyway, with that in mind, let's do the Northeast Corridor, and ignore interregional connections like NY-New Haven and NY-Philly.
8. Combined statistical area pops are Boston = 8, NY = 22, Philly = 7, DC = 10. W/o NY-Philly, it's ~32 million riders per segment.
9. That is, each segment of the NEC can expect around 32 million p-km per route-km (and NY-Philly a lot more when we include it).
10. Now, everything that's a branch or extension of the NEC gets to benefit from piggybacking on the NEC.
11. Take New Haven-Springfield. Hartford + Springfield = 2 million. Add up links to NY, Philly, DC, and it's 10 million pax, right?
12. Well, actually... New Haven-Springfield is about 100 km's worth of route, but NY-Springfield generates 210 p-km of revenue per pax.
13. And DC-Springfield is 460 p-km per pax for just 100 km of construction costs. So the return on construction costs invested is great.
14. It's a variant on Metcalfe's law. But it applies only to branches and extensions (NH-Springfield, Boston-Portland, etc.).
15. Lines not using the NEC, like NY-Buffalo, don't benefit from such piggyback, and have much lower expected traffic densities.
16. That said, if we don't think there's an international connection penalty, then NY-Toronto is strong, ~15 million pax by itself.
17. Then once NY-Buffalo-Toronto exists, Boston-Albany and (assuming no penalty) Albany-Montreal can piggyback.
18. The same piggyback effect supports Philly-Pittsburgh across its higher construction costs because of Appalachian tunneling.
19. If we think NY-Cleveland, ~3.5 hours by HSR, follows the same distance-independent model, then even that piggybacks.
20. Pittsburgh-Cleveland is maybe 200 km of construction. NY-Cleveland via Philly and Pittsburgh is 790 km on the rail route.
21. Per the model, we get (22*3)^0.8/4 = 7 million annual pax, or 5.6 billion p-km for 200 km of construction, which is very strong.
22. And let's not forget Philly: (7*3)^0.8/4 = 2.9m pax, 1.8b p-km. DC adds 3.8m pax, 3.3b p-km (but lower revenue bc roundabout route).
23. So completing the link from the Northeast to the Midwest looks strong just from an East Coast-Cleveland piggyback perspective.
24. And then there's the internal Midwestern network, and everything falls apart - Chicago is too small and the cities aren't collinear.
25. The strongest line is Chicago (10)-Toledo (0.6), 370 km, splitting toward Detroit (5), 100 km, and Cleveland (3), 180 km.
26. So we add up 4 city pairs on this Y-system, omitting Toledo-Cleveland and Toledo-Detroit.
27. Pax by city pair:
CHI-TOL.: 1m, 370m p-km
CHI-DTW.: 6m, 2.8b p-km
CHI-CLE: 4m, 2.2b p-km
DTW-CKE: 2m, 560m p-km
6b p-km/650 km = 9.2m
CHI-TOL.: 1m, 370m p-km
CHI-DTW.: 6m, 2.8b p-km
CHI-CLE: 4m, 2.2b p-km
DTW-CKE: 2m, 560m p-km
6b p-km/650 km = 9.2m
28. The above calculation, showing Chicago-Cleveland/Detroit has 1/4 the density of the NEC, ignores land use.
29. If we do consider land use, the NEC holds up by a model trained on Japanese, French, and Spanish data. The Midwest probably doesn't.
30. Now, Chicago does have a pretty strong central business district, so maybe the malus for lines to it isn't big. But Detroit-Cleveland?
31. This is where city distribution matters. One line gets you trains from Paris to Lyon, Marseille, Toulon, Nice.
32. Add in the facts that France overperforms (maybe it's sub-Japan fares, maybe it's something else) and Paris-Lyon was unusually cheap...
33. I'm deliberately not mentioning costs or fares. But the Midwest's flat expanses still cost ~$20m/km to build in.
34. And don't forget, the NEC is cheap to build on too, since so much of it already exists and only needs minor facelifts.
35. It's true that including Detroit-Toronto makes the whole shebang look noticeably better. But.
36. Chicago-Toronto is 840 km of revenue on 310 km of new construction between Detroit and the hookup to NY-Toronto in Aldershot.
37. Toronto = 8m; Chicago-Toronto adds 7b p-km, Detroit-Toronto 1.8b. So the combined system is 15m p-km/km. Okay, not amazing.
38. And God help you if the international malus and the Detroit and Cleveland land use maluses are serious.
39. It does because of Boston-Cleveland and Chicago-Buffalo piggybacking, if you believe the model works at 4 hours.
40. The South may actually be okay thanks to serial piggybacking on the NEC along the Piedmont cities of I-85.
41. DC-Richmond (1) is 180 km of construction; NY-Richmond is 540*3 = 1.6b p-km, and with Philly and Boston you get up to 3.2b.
42. You have to worry about land use malus, though, especially farther south where the cities get out of New York's potential orbit.
43. I believe the reason for the 0.8 exponent in the model is exactly this - high access time in large regions.
44. Theoretically the exponent should be 1, but the data fits a 0.8 exponent better, because the ass end of Chiba is far from Tokyo Station.
45. Finally: a bunch of people in @-replies are asking about Texas and Florida. They do not benefit from any piggybacking, sadly.
46. Yeah, though as @declanthewise points out, the numbers get better if you project populations to 2030.
47. And Texas gets a severe land use malus, counteracting the "Texas builds housing so the urban population actually grows" bonus.
48. So anyway, Dallas-Houston is marginal in this methodology, as is Chicago-Detroit/Cleveland. Florida is a lot worse.
49. It's weak, about 5m p-km/km (more north of Indy, less south). You can scrounge 1.5m more if Milwaukee preexists.
50. If you're okay with 2% fiscal ROIs you maaaaay be able to get away with building the Chicago hub network to CLE/DTW, STL, MSP, IND/CVG?
51. In contrast, the core NEC and the piggybacks at least down to Charlotte are 10%+, and even Atlanta is respectable (it's huge, for one).
52. Of course, the exact numbers assume that my model is accurate - see tweet #2 for illustration. But the principle is robust. /end
