Subway Capacity: some remarks

…and the Vancouver Canada line case. The remarks apply also to LRT unless specified (another post has been dedicated to buses

In a nutshell, the person per hour per direction (pphpd) capacity a subway line can offer, is

(capacity of a train) × (number of train per hour).

Like for buses, the capacity of a train is a function of different parameters, mainly person per square meter occupancy standard, and seats arrangement.

At the difference of low floor buses (and LRT), there is little “protuberance” (such wheel room) on high floor train, and technical room present in a train cabin rather under floor or on roof, are often the result of a tradeoff:

train capacity vs easy maintenance

The theorical capacity of a train, is in fact a direct function of its surface:

(length of the train) × (width of train).

…and a train length, is constrained by the station’s paltforms length, which are typically very expensive to expand.

Train capacity

below is an example of compared train capacity, expressed in term of surface able to accomodate passengers

Train consist	Platform length	width	surface
Vancouver Canada Line	40	3	120
Vancouver Canada Line	50	3	150
Vancouver Skytrain (Expo line)	80	2.65	212
Paris typical subway line	75	2.37	178

For matter of comparison, the theorical Canada line capacity (with 50meters platform) is just 15% lower than on most of the parisian subway lines, such as its line 2 or 5: those lines carry ~100million riders a year.

Behind the seating layout, a train needs in practice several features to effectively reach its theorical capacity. Among them

• Minimal unusable space between cars (and in cars)
• Allow passenger to “overflow” from a car to another one

Intercirculation between cars, usually allows that, but again, some interciruclation layout can be more efficient than other:

On top the skytrain MKII (second generation interior)intercirculation is narrow, impeding free flow movement from car to car, and blocking line of sight at the difference of the Parisian MP89-CA (bottom picture), where the train look like a single “big room”- credit photo top, the Translink’s Buzzer, bottom: wikipedia

Dwelling time and frequency

homogeneous occupancy of a train is also function of the door disposition, but the door layout affect primarily the dwelling time. Short dwelling time is important for a host of reasons, frequency being one of them, and frequency affcet the line capacity:

interval between train can’t be shorter than the station dwelling time

It is hence important to have as much as possible doors, but also have them wide enough, to allow good in/out flow movement. It is also important to avoid that some doors, slow down the boarding/alighting time because they have to handle more traffic flow:

• From a boarding viewpoint, where passengers have no apriori on the location of door on platform, the best way to do that, is to have all the doors equidistant (It make also the best use of the platform space)
• From an alighting perspective, all doors on a car should be equidistant

A 68 meters Vancouver skytrain consist, compared to a 75meterParisian MF01 5 cars consist (operating on line 2,5 and 9): the later has lower theorical capacity because it is narrower, but it has greater practical capacity due mainly to a better intercirculation. Furthermore, all doors are equidistant on the MF01 [1], while on the skytrain MK2, people waiting in red zone have to report on a nearby door zone slowing down the boarding. Similarly people standing in red zone aboard the train are too far from a door slowing down the alighting (or conversely limiting the practical capacity of the train by passenger reluctance to stand too far away of a door).

Track issues

A single track, vs a double track, at the end of a line could be used as a cost saving measure, but obviously it affects the frequency of a train line. That said, if the single track portion is short enough, the impact can be relatively minimal.

Frequency can be be obtained by using a tail track to store trains

The possible frequency is then:

((time to travel for and back the single track) + (dwelling time × number of train to be stored) ) / (number of train stored).

As an example, at Richmond Brighouse station, on the Vancouver’s Canada line

• the tail track past the station can accomodate one stored train [2], and the station another one
• the travel time between Lansdowne and Brighouse is ~90s and a typical station dwelling time ~20s

2 trains run in one cycle on the single track , by using a tail track behind the termini station

2 trains can run every 4mn on the Richmond Brighouse branch of the Canada line.

Because one train can run every 4mn on the Airport line, it is possible to get a train every 80s, or 45 trains per hour, on the common trunk (Bridgeport-Waterfront)

Even, with 40meters long train, the Canada line could provides a capacity of ~15,000pphpd, assuming 330 passengers per train: that is 3 times the actual capacity. Greater frequency are theorically possible with the introduction of short turn train (avoiding the single track section):

3 trains running in one cycle, one being shorturned before the single track section, 2 using the single track section

PS The above numbers for the Canada line, assume the availability of rolling stock, power supply, track signalling, and fast operating switch: All those could need to be upgraded, as well as the stations along the line to handle the corresponding increase in ridership, but it could be no need for heavy civil engineering work/track reconfigutation toward a capacity increase of 15,000+ pphd

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[1] Materiel roulant MF2000, seance 12/12/2000, Conseil d’administration du STIF

[2] Addressing Canada Line capacity questions, Translink, June 3, 2010.