Chatelet-Les Halles has a problem with passenger circulation. It has exceedingly wide platforms – the main platforms, used by the RER A and B, are 17 meters wide – but getting between the platform level and the rest of the station runs into a bottleneck. There are not enough stairs and escalators between the platform and the mezzanine, and as a result, queues develop after every train arrival at rush hour. Similar queues are observed at the Gare du Nord RER platforms. The situation at Les Halles is especially frustrating, since it’s not a constrained station. The platforms are so wide they could very easily have four or even six escalators per access point flanking a wide staircase; instead, there are only two escalators, an acceptable situation at most stations but not at a station as important as Les Halles.
This is generally an underrated concern in the largest cities. In smaller cities, the minimum number of access points required for coverage (e.g. one per short subway platform, two per long platform) is enough even at rush hour. But once daily ridership at a station goes into the high five figures or the six figures, a crunch is unavoidable.
There are two degrees of crunch. The first, and worse, is when the capacity of the escalators and stairs is not enough to clear all passengers until the next train arrives. In practice, this forces trains to come less often, or to spread across more platforms than otherwise necessary; Penn Station’s New Jersey Transit platforms are that bad. The situation at Les Halles and Gare du Nord is a second, less bad degree of crunch: passengers clear the platform well before the next train arrives, but there’s nonetheless a significant queue at the bottom of the escalator pits. This adds 30-60 seconds to passenger trip times, a nontrivial proportion of total trip time (it’s a few percent for passengers within the city and inner suburbs). Avoiding even the less bad crunch thus has noticeable benefits to passengers.
The capacity of a horizontal walkway is 81 passengers per minute per meter of width (link, p. 7-10). This is for bidirectional travel. Unidirectional capacity is a little higher, multidirectional capacity a little lower. Subway platforms and passages are typically around 5 meters wide, so they can move 400 passengers per minute – maybe a little more since the big crunch is passengers heading out, so it’s unidirectional with a few salmons (passengers arrive at the station uniformly but leave in clumps when the train arrives). Busier stations often have exits at opposite ends of the platform, so it’s really 400*2 = 800. Queues are unlikely to form, since trains at best arrive 2 minutes apart, and it’s uncommon for a train to both be full and unload all passengers at one station.
An escalator step can be 60 cm, 80 cm, or 1 meter wide, with another 60 cm of handrail and gear space on both sides. On public transit, only the widest option is used, giving 1.6 meters of width. The theoretical capacity is 9,000 passengers per hour, but the practical capacity is 6,000-7,000 (link, p. 13), or 100-120 per minute. This is more than pedestrian walking capacity per unit of step width, but less per unit of escalator pit width. So a pedestrian walkway ending in a battery of escalators will have a queue, unless the width of the escalator bank is more than that of the walkway leading to it.
Moreover, escalators aren’t just at the end of the station. The busiest train stations have multiple access points per platform, to spread the alighting passengers across different sections of the platform. But mid-platform access points have inherently lower capacity, since they compete for scarce platform width with horizontal circulation. It appears that leaving around 2 meters on each side, and dedicating the rest to vertical circulation, is enough to guarantee convenient passenger access to the entire platform; in a crunch, most passengers take the first access point up, especially if there’s a mezzanine (which there is at Les Halles).
Should New York invest in better commuter rail operations, it will face a bigger risk of queues than Paris has. This is for two reasons. First, New York has much higher job density in Midtown than Paris has anywhere, about 200,000/km^2 vs. perhaps 100,000 around La Defense and the Opera (my figures for both areas in Paris have huge fudge factors; my figure for New York comes from OnTheMap and is exact). And second, Manhattan’s north-south orientation makes it difficult to spread demand across multiple CBD stations on many commuter rail lines. One of the underrated features of a Penn Station-Grand Central connection is that through-trains would have passengers spread across two CBD stops, but other through-running regional rail lines would not have even that – at best they’d serve multiple CBDs, with one Midtown stop (e.g. my line 4 here).
When I computed the needs for vertical circulation at a Fulton Street regional rail station in this post, I was just trying to avoid the worse kind of crunch, coming up with a way to include 16 platform-end escalators (12 up, 4 down in the morning peak) and 16 mid-platform escalators (8 up, 8 down) on a 300-meter long two-level station. It’s likely that the escalator requirement should be higher, to avoid delaying passengers by 1-1.5 minutes at a time. With four tracks (two on a Grand Central-Staten Island line, two on a Pavonia-Brooklyn line) and 12-car trains arriving every 2 minutes, in theory the station could see 240,000 incoming passengers per hour, or 4,000 per minute. In reality, splitting passengers between Grand Central and the Financial District on what I call line 4 means that a sizable majority of riders wouldn’t be getting off in Lower Manhattan. When I tried to compute capacity needs I used a limit passenger volume of 120,000 per hour, and given Midtown’s prominence over Lower Manhattan, even 90,000 is defensible.
90,000 per hour is still 1,500 per minute, or 3,000-4,000 if we are to avoid minute-long queues. A single up escalator is limited to about 100-120 people per minute, which means that twenty up escalators is too little; thirty or even forty are needed. This requires a wider platform, not for horizontal passenger circulation or for safety, but purely for escalator space, the limiting factor. I proposed an 8-meter platform, with space for four escalators per end (two ends per platform, two platforms on two different levels), but this suggests the tube diameter should be bigger, to allow 10-meter platforms and six escalators per end, giving four up escalators per end. This is 16 up escalators. Another 16-20 up escalators can be provided mid-platform: the plan for eight up escalators involved eight access points interspersed along the platform, and 10-meter platforms are wide enough width to include three escalators (two up, one down) per bank and on the border of allowing four (three up, one down).
The situation at the Midtown stations in New York is less constrained. Expected volumes are higher, but Grand Central and Penn Station both spread passengers among multiple platforms. In the near term, Penn Station needs to add more vertical circulation at the New Jersey Transit platforms. The LIRR remodeled its section of the station to add more access points in the 1990s (e.g. West End Concourse), but New Jersey Transit is only doing so now, as part of phase 1 of Moynihan Station, and it’s still not adding as many, since its platforms are shorter and don’t extend as far to the west.
Nonetheless, given the number of proposals out there for improving Penn Station, including ReThinkNYC and Penn Design’s plan, it’s important to think of longer-term plans for better vertical circulation. When I proposed eliminating Penn Station’s above-ground infrastructure, I came up with a design for six approach tracks (including a new Hudson tunnel connecting to Grand Central), each splitting into two platform tracks facing the same platform; the six platforms would each be 15 meters wide, but unlike Les Halles, each of six access points would have six escalators, four up and two down in the morning peak, or alternatively four escalators and a wide staircase (the climb is 13 meters, equivalent to a five-floor walkup). There would be ample capacity for anything; emptying a full 12-car train would take forty seconds, and it’s unlikely an entire 12-car train would empty.
Traditionally, proposals for new mainline rail tunnels across the Hudson enter Penn Station’s southern tracks, which are used by New Jersey Transit. This includes the ARC incarnations that connected to Penn Station’s preexisting tracks, Amtrak’s Gateway, and the Institute for Rational Urban Mobility’s through-running counter plan to ARC. To my knowledge, ARC-North proposals, entering the northern tracks used by the LIRR, have not been investigated. I am not ready to sign off on ARC-North yet and in fact called it a troll proposal, but I believe it deserves more study and is probably superior to southern proposals except at high levels of investment.
While this in principle only concerns the configuration of the tunnels across the Hudson, it has implications about the configuration of Penn itself and the service plan supported by the infrastructure. The one element of the various Penn Station redesign ideas that isn’t relevant is the look of the station itself; this is also the least important element for passenger throughput. Penn Station’s failure to look like a cathedral is a lesser problem in a city that is full of multi-billion dollar starchitect-designed ugliness.
First, some principles for tunnel design. A good infrastructure proposal should have the following elements:
1. A through-running service plan. It matters which line at the New Jersey (or Hudson Line) end connects to which line at the Long Island or Connecticut end, since this influences the interlockings. It also matters where people are expected to transfer, since this influences platform crowding; ideally, transfers should be handled at Secaucus and Sunnyside.
2. Simple interlockings. Complex interlockings limit train speed, and switches especially do. It should be possible for trains to enter and exit Penn Station at speed. Avoiding slow zones in station throats is an underrated way of improving line haul time at relatively low cost, and the fancier the trains and more upgraded the tracks elsewhere are, the heavier the time penalty of slow throats is.
3. Adequate platforms. Penn Station has less bad platforms than people think – when I timed rush-hour LIRR trains, they emptied in about 90 seconds or a little more – but they’re still not good, especially if we’re assuming large increases in ridership coming from better service. The LIRR has better platforms than New Jersey Transit because it has more access points per platform, but the platforms are still narrow. In the worst case, a plan should consider paving over some tracks to widen the platforms, since Penn’s 21 tracks are more than enough for its traffic.
4. Adequate speed for intercity trains. The current tunnels are limited to 60 miles per hour (97 km/h) because of air resistance generated by non-aerodynamic trains in narrow tunnels. The cross-sectional area of the trains going through the tunnels is about half the cross-sectional area of the tunnels; in new high-speed rail tunnels, the corresponding ratio, called the obstruction ratio, is about 15%. It is possible to squeeze more speed out of the existing tunnels with better aerodynamics and sealing, but 200 km/h is probably impossible, and even slightly lower speeds are a problem if the tunnels are very busy and there is a speed mismatch with unsealed, non-aerodynamic commuter trains. So ideally, the larger-diameter new tunnels should be used by intercity trains. We can plan around one minute of travel time difference; this figure can in reality be anywhere between zero and 2.5 minutes.
5. Separation between intercity trains and Grand Central trains. If there is a Penn-Grand Central tunnel, it should be used exclusively by commuter trains because of the high local travel demand, and because to reduce real estate acquisition cost the curve radius should be low, possibly too low for Shinkansen equipment. This means that if a Hudson tunnel points toward the Penn-Grand Central tunnel, intercity trains should use the other one.
6. Two platform tracks per tunnel track. This improves capacity in two ways. First, rapid transit capacity is a combination of tunnel capacity and station dwell, and splitting each tunnel track between two platform tracks allows slightly higher capacity by deemphasizing the dwell since successive trains use different platform tracks. Paris is limited to 30 tph on the RER A with moving-block signaling, whose central segment has one platform track per tunnel track, but the shared RER B+D tunnel between Gare du Nord and Chatelet-Les Halles gets 32 tph with fixed blocks, where the B and D serve separate platforms at each station. And second, because each train can dwell at the platform for longer, this reduces the need for wider platforms, allowing violations of #3. Ideally, the two platform tracks would face the same platform to improve wayfinding and allow unscheduled track changes in case of train delays.
Now, Penn’s tracks are numbered 1-21, from south to north. There are platforms between tracks 20-21, 18-19, 17-18, 15-16, 13-14, 11-12, 9-10, 7-8, 5-6, 3-4, and 1-2; the 18-19 platform is wider than the rest, as if there was supposed to be another track immediately north of 18. The Hudson tunnels connect to tracks 1-19, the southern pair of the East River tunnels connects to 5-15, the northern pair connects to 15-21. The Hudson tunnels and the southern pair face each other, and trains on tracks 11 and 12 go straight through every switch; the northern pair offers no switch-free option, since the eastbound track faces track 21 and the westbound curves into the interlocking.
Since the Hudson tunnels face the southern pair, a simple proposal for new Hudson tunnels should face the northern pair. This would give 4 tracks between New Jersey and Sunnyside. Each of the two track pairs could point toward either Long Island or Connecticut, because of the Harold Interlocking, flawed as it is. This means intercity trains would use the northern pair and go to Connecticut, other regional trains would use either pair and go to either Connecticut or Long Island, and Harold would be superfluous. New Penn-Grand Central tunnels could be constructed branching from the southern East River tunnel pair. It is possible to also construct the tunnels around the southern pair, with trains from the southern pair either merging heading into the Hudson tunnels or terminating and reversing at Penn Station.
Under this plan, all of the numbered principles could be satisfied except #3, and to satisfy #3 every plan requires track paving or other platform modification. It’s also simple to construct: it’s just a new tunnel pair, and ideally also some work on the preexisting southern East River tunnel pair to construct a connection to Grand Central. The one drawback is that, unlike in ARC Alt G, Gateway, and the IRUM plan, the Penn-Grand Central tunnel shares approach tracks to Penn Station with the southern tunnels, reducing capacity. This becomes a problem if ridership from Grand Central, the LIRR, and points east grows to the point of overwhelming three tunnel pairs (the two heading into Penn, and East Side Access). The alternative with the Penn-Grand Central tunnels going around the southern tunnel pair and only merging heading into the Hudson tunnels has more capacity, but interferes with principles #3 and #6.
Track-paving for any plan is hard, because many of the straightest, longest-platform tracks have to be removed. To widen the platforms and improve throughput, there are two ways to pave over tracks, each of which gets rid of about half the station tracks. One is to pave over every other track, guaranteeing each track access to two medium-width platforms; trains could open both doors then, improving egress. The other is to pave every other pair of adjacent tracks lying between platforms, giving each track access to just one very wide platform. The former option is difficult at Penn because there are support columns between adjacent tracks, and a look at New Jersey Transit rolling stock suggests that each train would have 1-2 doors facing a column. We are left with the latter option, paving over, for example, tracks 20, 17, 16, 13, 12, 9, and 8. Each tunnel track would get two platform tracks facing the same platform, except for the westbound northern tunnel track, whose two tracks (21 and 19) would be split because of the aforementioned columns. The lowest-numbered tracks would not be used; the LIRR’s West Side Yard would not be used regularly but instead trains would run on the tracks more often off-peak. The now enlarged platform between tracks 7 and 10 would be lengthened to allow 16-car trains at track 7, which is currently 13 cars long.
Since principles #3 and #6 are both satisfied, the capacity per track can be quite high. The RER B+D achieves 32 tph, but this is split as 20 tph B and 12 tph D, which is suboptimal since two successive trains could both be B, making the dwell a problem. With even alternation between each platform’s two tracks and moving-block signaling, even higher capacity may be possible, reducing the capacity disadvantage of having just two tunnels coming into Penn from the east rather than three.
The IRUM plan, building on ARC Alt G, is quire different. It has three tunnels in each direction: the northern East River tunnels are paired with the Hudson Line via a new short tunnel linking the Empire Connection with the northern Penn Station tracks, the new Hudson tunnels come into the southern station tracks and then continue to Grand Central via new tunnels, and no tracks are paved. Intercity trains have to keep using the old tunnels, necessitating Harold, but that’s money already spent. Principle #3 is violated, or alternatively #6 is if tracks are paved, but there is more track capacity. The risk there is insufficient demand from the Empire Connection, which would leave the northern tunnels underused, reducing the system’s capacity advantage over a two-tunnel option to just a few tph. This plan has to route intercity trains through the old tunnels. Conversely, the advantage is that it easily shoehorns Empire Connection service, which ARC-North does not.
The main difference between ARC-North and IRUM is investment levels. ARC-North is cheaper; it’s more comparable to the bare-bones proposals for ARC(-South) and Gateway that are hinted at but never formally published. At the low investment levels of a bare-bones proposal, ARC-North is superior because it provides better capacity because of the relatively straight train paths through the station. If there’s no connection to Grand Central, then it is not at a capacity disadvantage since Long Island and Connecticut don’t have the demand, and barely have the capacity, to overwhelm three track pairs (including East Side Access again).
Conversely, ARC-North is harder to retrofit for somewhat higher investment. The best that can be done is tunneling to connect the Empire Connection to the southern tracks, digging new tunnels to Long Island as in Alt S, and running trains to just one line, probably Lower Montauk, which goes through serviceable neighborhoods but lacks a direct connection to the existing tunnels to Penn. This provides much better service coverage because of the Montauk connection, but at higher cost since there’s an additional underwater tunnel. It avoids the expensive components of Gateway and ARC, but so does IRUM, which becomes an intermediate level of investment between ARC-North proper and ARC-North with a Montauk tunnel.