Northeast Corridor, 95% Cheaper: Frankford Junction

Amtrak’s plan for high-speed rail on the Northeast Corridor, at a cost of about $290 billion depending on the exact alternative chosen, is unacceptably costly. I went into some details of where excess cost comes from in an older post. In this post, I hope to start a series in which I focus on a specific part of the Northeast Corridor and propose a cheaper alternative than what the NEC Future plan assumes is necessary. The title is taken from a post of mine from four years ago; since then, the projected costs have doubled, hence the title is changed from 90% cheaper to 95% cheaper. In this post, I am going to focus on untangling Frankford Junction.

Frankford Junction is one of the slowest parts of the Northeast Corridor today south of New York. It has a sharp S-curve, imposing a speed limit of 50 mph, or 80 km/h. While worse slowdowns exist, they are all very close to station throats. For example, Zoo Junction just north of Philadelphia 30th Street Station has a curve with radius about 400 meters and an interlocking, so that superelevation is low. The speed limit is low (30 mph, or 50 km/h), but it’s only about 2 km out of the station; it costs about 2 minutes, and with proper superelevation and tilting the speed limit could be doubled, reducing the time cost to 25 seconds. In contrast, Frankford Junction is about 13 km out of 30th Street Station; an 80 km/h restriction there, in the middle of what could be a 200 km/h zone, makes it uneconomic for trains to accelerate to high speed before they clear the junction. This impacts about 4 km, making it a 108-second slowdown, which can be mitigated by either more tilting or a wider curve. In reality, a mixture is required.

The NEC Future plan for high-speed rail, the $290 billion Alternative 3, avoids the Frankford Junction S-curve entirely by tunneling under Center City and building a new HSR station near Market East, a more central location than 30th Street; see PDF-pp. 19, 20, and 78 of Appendix A of the environmental impact statement. This option should be instantly disposed of: 30th Street is close enough to the Philadelphia CBD, and well-connected enough to the region by public transit, that it is no worse a station choice than Shin-Osaka. The Tokaido Shinkansen could not serve Osaka Station as a through-station without tunneling; since Japan National Railways wanted to be able to extend HSR onward, as it eventually did with the Sanyo Shinkansen, it chose to serve Osaka via a new station, Shin-Osaka, 3 km away from the main station. Given the expense of long tunnels under Philadelphia, the slightly less optimal station today should be retained as good enough.

A lower-powered plan providing some HSR functionality, Alternative 2, does not include a new tunnel under Philadelphia, but instead bypasses Frankford Junction. On Appendix A, this is on PDF-pp. 19, 20, and 70. Unfortunately, the bypass is in a tunnel, which appears to be about 4 kilometers. The tunnel has to cross under a minor stream, Frankford Creek, adding to the cost. Instead, I am going to propose an alignment that bypasses the tunnel, with moderate takings, entirely above ground.

In brief, to minimize trip times without excessive construction, it is best to use the highest superelevation and cant deficiency that HSR technology supports today. The maximum superelevation is 200 mm, on the Tokaido Shinkansen (link, PDF-p. 41); there were plans to raise superelevation to 200 mm on the Tohoku Shinkansen, to permit a maximum speed of 360 km/h, but they were shelved as that speed created problems unrelated to superelevation, including noise, pantograph wear, and long braking distances. The maximum cant deficiency on existing trainsets capable of more than 300 km/h is about 180 mm, including the E5/E6 Shinkansen and the Talgo 350 and Talgo AVRIL. Tilting trains capable of nearly 300 mm cant deficiency exist, but are limited to 250 km/h so far. With 200 mm superelevation and 175 mm cant deficiency, speed in meters per second equals square root of (2.5 * curve radius in meters); the minimum curve radius for 200 km/h is then 1,235 meters.

An S-curve requires some distance to reverse the curve, to avoid shocking the train and the passengers with a large jerk, in which they suddenly change from being flung to the right to being flung to the left. If you have ridden a subway, sitting while the train was decelerating, you must have noticed that as the train decelerated, you felt some force pushing you forward, but once the train came to a complete stop, you’d be pulled backward. This is the jerk: your muscles adjusted to being pushed forward and resisting by pulling backward, and once the train stopped, they’d pull you back while adjusting back to the lack of motion. This is why S-curves built a long time ago, before this was well-understood, impose low speed limits.

With today’s computer-assisted design and engineering, it’s possible to design perfect S-curves with constant, low jerk. The limits are described in the above link on PDF-pp. 30 and 38. With the above-described specs, both sets of standards described in the link require 160 meters of ramp. For a single transition from tangent track to a fully superelevated curve, this can be modeled very accurately as 80 meters of straight track plus the circular curve (half the transition spiral is within the curve); the displacement from an actual spiral curve is small. For an S-curve, this requires double the usual transition, so 160 meters of tangent track between the two circles; bear in mind that this distance grows linearly with speed, so on full-speed 360 km/h track, nearly 300 meters are required.

Here is a drawing of two circles and a tangent track between them. The curve of course consists only of a short arc of each circle. The straight segment is a little less than 700 meters, which permits a gentle spiral. The curves have radius 1,250 meters. Takings include a charter school, a wholesale retailer, an auto shop, and what appears to be industrial parking lots, but as far as I can tell no residences (and if I’m wrong, then very few residences, all very close to industrial sites). The charter school, First Philadelphia Preparatory, is expanding, from 900 students in 2012-3 to an expected 1,800 in 2018-9. School construction costs in Pennsylvania are high, and $100 million is expected for a school of that size; see also table 5 on PDF-p. 7 here for national figures. The remaining takings are likely to cost a fraction of this one. Even with the high cost of takings, it is better to realign about 2 kilometers of track above-ground, at perhaps $150 million, than to build 4 km of tunnel, at $1.5 billion; both figures are based on cost items within the NEC Future . This represents a saving of about 83% over Alternative 2, which is projected to cost $116-121 billion excluding rolling stock (PDF-p. 42 of chapter 9 of the EIS).

Given the long spiral length, it may be feasible to avoid the charter school entirely. This would probably require shrinking curve radius slightly, permitting 180 or 190 km/h rather than 200 km/h. However, the travel time cost is measured in seconds: with about 11 km from the end of Zoo Junction to the northern end of Frankford Junction, of which 1 is required just to accelerate to speed, the difference between 200 and 180 km/h is 20 seconds. Further savings, reducing this time difference, are possible if the speed limit without taking the school is 190, or if trains accelerate to 200, decelerate to curve speed, and accelerate again to the north. This option would improve the cost saving over Alternative 2 to about 90%.

The correct way forward for affordable improvement of the Northeast Corridor is to look for ways in which expensive infrastructure can be avoided. If a tunnel can be replaced by a viaduct at the cost of a few extra takings, it should be. If an expensive undertaking can be avoided at the cost of perhaps 10 seconds of extra travel time, then it probably should be avoided. There should be some idea of how much it’s acceptable to spend per minute of marginal travel time saving, by segment: the New York-Philadelphia segment has the heaviest traffic and thus should have the highest maximum cost per unit of time saved. But even then, $100 million for 20 seconds is probably too high, and $100 million for 10 seconds is certainly too high.



  1. Anton Willy Dubrau

    This is neat.

    It would be cool if there was some sort of tool that would allow you to draw a line on google maps, specify the rolling stock and some constraints (like super-elevation and dwell times), and then it would give you the curve radii, a speed graph etc.

    • Alon Levy

      I thought about it! Apparently building in a rolling stock performance calculator is trivial; integrating everything with Google Earth or another mapping tool is the hard part.

      • liamblank

        While working at ReThink Studio, I have developed a pretty reliable method for calculating trip time estimations for existing and proposed rail lines. Let me know if you’d like to discuss this in more detail sometime.

        • Alon Levy

          Can you talk a bit more about your method? What I normally do for travel time estimation is plug in train performance parameters to get the acceleration and deceleration penalties for a slowdown from speed x to speed y.

          In this post I didn’t really do that, because a slowdown near a station doesn’t quite work this way – instead, it delays the train’s acceleration. Heading north from Philly, a train goes at the maximum speed of the Zoo Junction curve, and then at the maximum speed of Frankford Junction (unless Frankford is so low that it’s useful to accelerate, decelerate for the junction, and accelerate again), and then at maximum line speed east of Frankford. The difference between 180 km/h and 200 km/h is then equal to the difference between running between a point north of Zoo where an accelerating train reaches 180 km/h and the north end of Frankford at 180 and running between these points at 200. No acceleration penalty needs to be computed, because the train is accelerating from 0 at Philly to line speed north of Frankford anyway, so it’s just a matter of whether this stretch of about 10 km is done at 180 or at 200.

  2. Robert Jackel

    The idea that a station in Market East would be more centrally located is also outdated. At this point, the CBD is steadily moving west towards 30th St., and much of the major construction in Philadelphia is either in West Philadelphia, near the current station, or right across the river from it.

    So, not only would your idea likely save money, it probably also creates a more optimal outcome regardless of spending.

  3. Stephen Stofka

    Neat idea.

    Most interested local lay have suggested using the Erie-Torresdale alignment as a bypass. The advantage to this is apparent: about a mile with a taking at either end. The disadvantages are Frankford Creek for a tunnel and the Erie-Torresdale el stop for an aerial, where the gradient required for clearing under the creek is much more trivial than any attempt at either clearing over the el stop (whose highest point is, I’d guess, ~60 ft in the air) or squeezing a clearance box between the street and the el.

    But even a limited cut-and-cover tunnel with no station boxes would be expensive. Fixing the junction with a perfect S-curve and minimal takings is almost certainly the best available option.

  4. Adirondacker12800

    The market in Philadelphia is big enough – when you can get to Washington in one hour, Boston in two, Cleveland in three or Montreal in four- that there can be a train that serves Suburban and Market East once or twice an hour. For instance Boston to D.C. and Harrisburg to N.Y. via West Trenton. They would be used by people coming and going to metro Philadelphia.

  5. Patrice

    Alon, great piece! This is exactly the topic which your analysis is most valuable. Looking forward to reading the coming ones. Just a side note, IIRC you said a couple years ago that $1 Billion would be enough for constant-tension catenary from NY to WAS. Do you think this is still the case? I struggle to see Amtrak making such a project work given their engineering track record and the complexity of the high tension (utility) wires high above much of the NJ section. On my last trip, I noticed that even the short/simple doubletrack from Secaucus Jct to NYP lacked constant-tension catenary. That seems like a terrible place to have a catenary problem due to heat.

  6. Steve Dunham

    Would the Septa local trains require reduced superelevation (that is, would the superelevation for high-speed trains be too much for trains traversing the curve at, say, 80 mph)? If so, is there a problem with mixing different degrees of superelevation on the same right of way?

    • Alon Levy

      No. At a radius of 1,250 meters, 200 mm superelevation perfectly balance at 147 km/h. At 130 km/h, there are 44 mm of cant excess. Railroads and regulatory agencies dislike cant excess, but in truth it’s equivalent to cant deficiency; 44 mm is no big deal for passenger trains in either direction. If the curve is tightened to 1,120 meters, with 190 km/h intercity trains, to reduce takings, then at 130 km/h cant excess is reduced to 25 mm.

      • Joey

        I’ve heard some arguments about passenger comfort requiring some amount of cant deficiency – i.e. if you look out the window and see the train turning but don’t feel any turning it can induce motion sickness. But at such a large curve radius it might not matter anyway – you’d barely be able to see that the train is turning.

        • Alon Levy

          That’s for when there’s zero cant deficiency, not for when there’s cant excess. When there’s cant excess, you see the horizon rise and fall and notice a small difference in gravity pulling you in the downward direction.

      • Adirondacker12800

        The freight going over the Delair bridge is going to be slower. the local that stops at Bridesburg will be going slower. And if they build a station to connect to the El, that local will be stopped. The local tracks are going to be different.

        • Alon Levy

          Of course. But intercity trains have no business using the local tracks, so it’s fine to fully superelevate the express tracks, which are to be used only by intercity trains and express regional trains (assuming SEPTA chooses to run any).

          • Adirondacker12800

            Last time I looked, before the current meltdown, there were express trains on the Trenton Line. Very likely on the local tracks because they made stops other than Trenton. Unless automobiles get banned the frequency is never going to high enough that they need to use the express tracks.

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  8. greg

    In your opinion, is there any advantage to setting a time goal, such as XX minutes for HSR travel time between Phila and NYC and then using that goal in an attempt to determine a budget? That way I could see that 50 minutes would cost 50 Billion$$, but 60 minutes might only cost 30 B$, and likewise 45 minutes might only be 5 B$ more then a 50 minute trip. I have often thought it would be a good idea to ‘deal with’ the Zoo Junction, but I understand your real world point about the cost of fixing that, whatever the actual dollar cost, would have only a very slight benefit in actual travel time. Thanks

    • Alon Levy

      Yes, very much so. Time goals are of especial importance when planning rolling stock requirements and service patterns: for example, if a railroad is expected to run hourly service, then the travel time goal should be an integer or half-integer number of hours minus turnaround time, to use rolling stock maximally efficiently.

  9. Zack Rules

    Neat idea, this would make a lot of sense, particularly combined with Zoo reworking.

    If Amtrak wanted to run trains through downtown Philadelphia, running them through the City Center Tunnel would make much more sense, especially as that tunnel is at about 60% capacity. The southern end of the tunnel is already connected to the NEC and the northern section could be connected at North Philadelphia via short cut/cover tunnel segment. Trains would have to slow way down to access the tunnel and travel relatively slowly through it but the additional ridership might make up for it, particularly if it ran express throughout the rest of its journey. This would also allow Trenton Line trains to access downtown faster and avoid Zoo.

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