Arithmetic Lessons for Fleet Planners

Today’s Commission meeting included one of the more embarrassing presentations I have seen at the TTC in some time.  It wasn’t meant that way, but that’s how it came off.  The topic was the Subway Service Improvement Plan.

The first problem was that this is really two reports in one.  The first major topic is delays, their causes and what the TTC is doing or can do to reduce them.  This material was presented in a less than thrilling manner, and most Commissioners were visibly not paying attention.

The second topic was the subway car fleet plan.  This has always been something of a black art influenced as much by whatever size order Bombardier needs to have for Thunder Bay this week rather than solid planning.  However, when the TTC’s own numbers don’t add up and there are blatant mistakes in the analysis, that’s when it gets embarrassing.

The report is not available online, and you will have to take my word for the material as I don’t feel like scanning the whole thing in.  A warning for the faint of heart.  This post contains a lot of numbers and a discussion of service levels and fleet requirements.  If this isn’t your cup of tea, skip the rest of this item.

Current plans for the subway fleet will eventually see all of the T1 cars isolated on the Bloor-Danforth and Sheppard lines, while the new Toronto Rockets will provide service on Yonge-University-Spadina.  Each fleet can be analyzed separately.


The TTC expects to receive three sets of Toronto Rocket cars:

  • 234 (39 trainsets) to replace the H4 and H5 equipment
  • 126 (21 trainsets) to replace the H6 cars
  • 48 (8 trainsets) for the Spadina extension

Among the claims made for the TR cars are:

  • 10 times improvement in reliability that will allow a reduction in the spare ratio from 19% (the current fleet average) to 10%
  • 13% greater capacity due to the unit train design with gangways between all cars.

Current operations on the YUS require 48 trains of which 4 are used to fill gaps.  The basic service characteristics are:

  • The headway is 141 seconds south of St. Clair West in the am peak.  This corresponds to 25.53 trains/hour.
  • The capacity of a train for service design purposes is 1000 (although crush loads of 1200 are possible).  Therefore, the design capacity of current service is 25,530/hour.  (Crush capacity would be about 30,000, but this could not be sustained for an extended period due to longer station dwell times with very crowded trains.)
  • To field 48 trains, the TTC must have a total of 57 trains (9 spares are 19% of the scheduled service).  This could be reduced slightly if the gap trains are taken from the spare pool, but it is unclear whether this is the TTC’s practice.

If the entire service is replaced with TRs, this would have the following effects:

  • The capacity of the service would go up by 13% to 28,850/hour.
  • The spare requirement would drop to 5 trainsets.

So far, so good, except that the TTC counts the capacity improvement as a credit against the number of cars they require.  If you reduce the fleet to compensate for added capacity of trainsets, then you are not changing the capacity of the route.  If you are going to provide more capacity, then it follows as the night the day that you have to run the same number of trains.  The only saving comes in the spare allowance.

Therefore, at this point, the requirement for trains on YUS is 53 (48 plus 5 spares).

Next comes Automatic Train Control.  Here the TTC’s calculation really comes off of the rails.  ATC is claimed to save 10% on travel times.  In effect, the trains will get from Finch to Downsview 10% faster than they do today thanks, it is claimed, to their ability to run closer together.  For my money, this is hogwash, especially outside of the peak period when trains are never close enough together for ATC to make a difference in running times.  What is actually happening, I believe, is that trains will probably have better performance characteristics and will be able to cover the line faster.

This is an issue going back decades to debates over “high rate” operation on the subway.  From my own experience riding the YUS on high-rate trains, as well as experience on BD when it was scheduled to operate that way, a 10% saving in trip time would be easily achieved, although most of the saving will come north of Bloor Street due to wider station spacings and hills.  “High rate” was abandoned due to problems with motor instability on the H1 cars at top speed, concerns with the need for better track maintenance and power consumption.  There was also a desire to justify a large car order, and a scheme that would actually save on the fleet size was anathema to both the TTC and Queen’s Park.

In any event, the running time from Finch to Downsview will drop by 10%, and this will add 10% to the capacity of the line provided that the same number of trains operates at a reduced headway, something that ATC makes possible.  However, once again, the TTC takes the reduced travel time as a credit against the fleet size.  This is nonsense.

If the same trains operate 10% faster:

  • The number of trains/hour goes up from 25.53 to 28.09, and the headway falls from 141 seconds to 128 seconds.
  • The design capacity goes up from 28,850 to 31,735 per hour, an increase of about 24% over today’s operation.

The TTC plans to extend the short turn operation from St. Clair West to Glencairn in 2010/2011 with a requirement for 3 more trains.  This takes us to a fleet of:

  • 47 trains for service, 4 gap trains, and 5 spares for a total of 56 trains. 

The TTC also allows for 5 additional trains for extra capacity.  I have not factored them in here as I get the added capacity through reduced headways and larger trains.  If that really is the intent, then my numbers to this point are low by 5 to 6 trainsets.

Some claims about future operations speak of a 50% increase in capacity.  To achieve the additional 26% increase relative to current service (over and above the 24% we get from greater train capacity and shorter running times) will require 26% more trains.

  • The number of trains/hour would rise from 28.09 to 33.89, and the headway would fall from 128 to 106 seconds.  This is getting into territory where minor disruptions will cause serious backlogs of service.
  • 47 trains are required for scheduled service with the Glencairn extension
  • 26% raises this number to 59
  • 1 additional spare train is required
  • This gives us 59 for service, 4 gap trains (unchanged) and 6 spares for a total of 69 trainsets.

Only 60 trainsets are on order. 

The TTC has included the Spadina trainsets in their analysis as part of the available fleet even though they have not increased the service requirement to compensate for the extension of the line.  This is simply a mistake, but an expensive one if the same trains are counted for two purposes.

An alternative way to provide more capacity is the proposed 7th car in the TR trains.  This would be a 50-foot long car (existing cars are 75) that would bring a trainset exactly to the length of existing station platforms.  The added capacity is only about 10% (50 feet added to a 450 foot long train), and so there would still be a need for more trains to bring the total capacity of the line up to 50% relative to today’s operation.

However, I believe that the 7-car trains have some merit because their added capacity would allow for slightly wider headways at a given capacity.  In the example above, this would reduce the fleet requirement to about 62 trainsets and require a minimum headway of about 117 seconds.  This is tight, but doable.


The BD line now operates with 42 trains on a 2’24” am peak headway.  A big question here is how many spares we really need.

The TTC has used a factor of 19%, but this is for a mixed fleet of H and T1 cars.  I find it hard to believe that the T1 cars, which were supposed to be such an improvement over the H-series, require this high a spare factor.  Moreover, the TTC has projects underway to improve their reliability.  By the time the BD line is running exclusively with T1’s, there should be a reduction in maintenance requirements for this line.  It may not be as dramatic as the drop from 19 to 10% on YUS, but there certainly should be some improvement.

If we assume a spare factor of 15% on BD, this means that we need about 6 spare trains for a total fleet of 48 trains.  The actual fleet of T1 cars is 372 or 62 trains.  From this, deduct 24 cars to provide for the Sheppard line leaving a balance of 348 cars or 58 trains.  This would allow for considerable improvement in BD service except for the basic problem that the signal system cannot handle many more trains on that line.

Some T1’s could be retrofitted with ATC for use on YUS, although they would have lower capacity than the TRs especially if these were configured as 7-car units, and we would need to be sure that they could actually achieve the claimed 10% reduction in travel times.  This could also bring the net fleet requirement for YUS down possibly even removing the need for the Spadina extension trains.


The TTC’s subway fleet planning often does not make sense and does not present a complete picture of the evolving requirements for subway cars.  The fact that the YUS and BD lines will now have separate fleets further complicates planning.

A related issue is the question of the transfer capacity at Bloor-Yonge where an almost unchanged BD service (and station) must somehow absorb passengers arriving on YUS at a much greater rate than today during the PM peak.  Putting much more capacity on YUS may be attractive in theory, but unwise in practice.

All of this probably sounds rather arcane until we remember that a subway trainset costs close to $20-million and presumptions that we can increase the capacity of existing lines substantially may be misguided.  Alternatives for the YUS corridor including both short-haul and long-haul relief services (the downtown relief lines discussed here as well as significant improvements to GO rail) must be included in our plans. 

13 thoughts on “Arithmetic Lessons for Fleet Planners

  1. The 7th subway car scheme has always interested me as a way to increase line capacity without having to mess around with headways. If they were to add a 50-foot section to the end of the TR, the capacity improvements (10% as you note) could justify the added expense, especially considering that the trains are not yet built. I do wonder if the geometry of the turnbacks would be able to handle a longer train though. Having ATC of course makes stopping at stations a non-issue.

    I’ve sometimes thought that if they could somehow add a 50-foot car to present H- and T- series trains, it might still be possible to operate without ATC. The drivers are generally quite good at stopping in the right place, and if they could instead stop the trains right at the very end of the platform, the distance from the cab to the first/last set of doors would probably ensure that nobody ended up stepping out into a tunnel. I’m sure there are reasons that make this impractical, not the least being cost of special cars, but an interesting though experiment about how B-D capacity could be increased anyway. Any thoughts?

    Steve: The 7th cars would go into the middle of the train, not at the end as that would require them to have cabs. The intention is to add these to the 6-car fleet of TRs when the extra capacity is needed. I think a good argument can be made for doing this as part of the original order.

    The H series cars will all be retired in about 4 years, and so this is a non-issue for them. The problem with the T1 cars is that the short version of the TR wouldn’t be compatible with the T1s, and we would need a specially design version of the T1 to do this.

    Turnbacks are not built “tight” and they can all hold a 7-car train.


  2. Sounds like a bit of scripted hypocrisy. In any scientific analysis, including engineering, you have a purpose and a method, so the intended result (you know, an objective) should be clear to these people when they give the presentation, but this doesn’t quite seem to be the case since the purpose is apparently absent and the method is fuzzy (if not porous). It sounds like something worthy of Mystery Science Theatre 3000 treatment (we could call it Mystery Commission Meeting 3000).

    It sounds like they are really taking a leap of faith here. As has been raised numerous times here, particularly with relation to Bloor-Yonge, the slightest disruptions really do kill off any capacity gains, and this worries me a lot. The subways do not run like clockwork during rush hour even in Tokyo (contrary to its reputation), so if the TTC thinks it will be clockwork, they may need a reality check. Once a backlog starts, it will be almost impossible to catch up (if it happens in strategic locations, they can catch up, but what are the odds of that? Murphy’s Law states “you wish”), and service will see little, if any, real improvement in quality and crowding.

    The first day this new service pattern is up and running, bust out a comfy chair by an overpass around Davisville by sunrise, and bring some popcorn, as chaos ensues on the subway action below.

    Steve: Another point I didn’t go into is that TTC scheduling does not allow for the fact that trains only use their peak running times for a limited number of trips during the “peak period”. This translates to queues of trains at terminals, and on closer headways, this will become intolerable.


  3. About the T-1 and the 7th car, couldn’t select married pairs be modified to accomodate the 7th car properly in between them? I guess you would call that a polygamous set of cars.

    With turnbacks and peak running times, isn’t the splitting of termini (Finch/Langstaff and Steeles West/VCC) intended to address that? I don’t think it will work as smoothly as they’d like without tail-track far-side turn-arounds (a-la-St.Clair West), but still does something, doesn’t it?

    Steve: Oooo! Naughty subway cars!

    Yes, the turnbacks make life easier for close headways. There is already a tail track at Finch, and at least one is planned for the Spadina extension. Even so, if we can keep the headway wider by running longer trains, this gives a bit more play.

    From a cost point of view, having fewer trainsets (fewer cabs and sets of control equipment) may offset the extra cost, if any, of a specially sized car for the middle of the train.


  4. When the time comes, or can they even see that far ahead, what are they going to do about train sets on the Sheppard line?

    Steve: In my dissertation above, I reserved 24 T1 cars (6 4-car trains) for that line. They use 4 now, and this allows for expansion to 5 with a spare left over.

    Trainsets for Sheppard are out of the question unless the TTC is going to get some specially-built 300-foot long TRs. The regular sized ones won’t fit in the stations. This would simply mean leaving a few segments out of the middle of a TR train, provided that the equipment is arranged in such a way that this is easy to do (i.e.: there are at least two cars that do not contain a unique piece of gear without which the train won’t run).

    It’s actually preferable to leave T1s on Sheppard because as it is, there are far more T1s than we need to run the BD line, and we have to use up the excess somewhere. I can hear choruses of “extend the line to STC” now. You don’t spend a billion on a subway extension just because you can’t plan your fleet allocations.


  5. Regarding Karl Junkin’s polygamous T1’s, I believe that the cars that Bombardier built for Ankara Turkey are more like an H6 than a T1, but they were built in threesomes, err, married triples. Two cars with a cab at one end and a “trailer” in between (quotes because I am not sure if they were motorized or not, just that they are cabless).

    A shorter version of this cabless car would probably be possible without a huge “new car design” cost.


  6. For the new Toronto Rocket cars, would it not have been simpler to order them slightly longer, so a train would be the full length of the platform? Or where they not even thinking about longer trains when the order was placed?

    Steve: They were looking at 1-for-1 replacements. Indeed, some versions of the fleet plan didn’t acknowledge that the new cars only came in six-car sets and included quantities that would have been partial trains.


  7. Good post on the TTC’s faulty math.

    How can the TTC possibly know with absolute certainty at this stage that ATC will save them 10%? It hasn’t been tested under actual service conditions. Now, if the new trains can accelerate faster, that’s different.

    I remember B-D when high-rate was in effect (from ’66 to ‘8?) — it worked on B-D only because the line was straight with very few grades. The G train motors were never “rewound” for high-rate with the “Integrated Subway System” because the TTC knew that the grades and curves on Y-U would offset any gains.

    One more thing — the doors on the old trains opened and closed much faster than the T1s — I assume this was done because leaning hands got pulled into the door slot sometimes? Those few seconds at every station make a big difference in the end-to-end running time.

    We may very well end up spending millions on an upgraded system that just won’t work. Managing closer headways with 2 short-turns is just as tricky as the original “Y”. If they can pull this new YUS scheme off without a hitch, I want the Y back, but this time, as a W.


  8. I think the London Underground used to run trains where the driving end of the cab cars was about 1/3 passengerless (machinery cabinets or something) and I think these ends were allowed to sit in the tunnel away from the platforms. Would some arrangement like this allow the TTC to use all full-length cars instead of special 50-footers?

    Steve: Once you go beyond a 500ft long train, all sorts of problems crop up with signal circuits, carhouses and storage tracks that were not built for the longer trains.


  9. Speaking of the London Underground, I had the chance to use part of the Northern line last month and there was one station where the whole train didn’t fit in the station, so the last car remained mostly in the tunnel and only its forward-most set of doors opened.

    While this is perhaps a reasonable way to handle a one-station situation or even for a temporary measure while waiting for shorter cars to be available (signal circuits notwithstanding), it struck me to be a half-assed procedure, especially for such a “world class” system.


  10. Gee whiz, this sounds like GO Transit!

    Some trains are more cars in length that the platforms can accommodate. The doors open on the cars that are on the platform. Anyone wanting to disembark at that station has to be in the right car. King City, Maple and Newmarket had this problem, so I’m sure there are others.

    In the technology business I’ve heard so may times about how this new thing or that will solve all our problems, or in this case a whole combination of things. My experience has taught me that all that happens is that you have a whole new set of problems you never anticipated.

    It sounds like someone is hoping they’ve made a sacrifice to the right gods, because if they haven’t it isn’t going to be pretty.


  11. You mention that the spare ratio will be cut roughly in half for the new trains due to improved reliability. I wonder whether this would be offset by the fact that the new trains are longer. If you have a problem in one car of a trainset in the current fleet, you can disconnect the impacted married pair of cars and still have the remaining 4 cars to mix and match with another pair. If you have a problem in a trainset for the new fleet, the entire train is out of service. Hopefully we won’t run into these problems off the bat (unless there is some sort of reliability issue resulting from a new vehicle type), but I would think it would come up as an issue as the cars begin to age.

    Steve: I’m only quoting what the TTC claims they will achieve. We shall see, and Bombardier, who make the claims for their higher reliability, will have a lot to answer for if the TTC cannot achieve it.


  12. “The T1’s were supposed to be such an improvement over the H series”.

    You know, they aren’t that cool. They do not really have any appealing design features that make them look good. The H1 – H4 cars have the driver’s windows bent in, for example; the H5’s do not have that, but they do have a white border around one o the driver’s windows. The H6’s do not have any o this, but they are still great. They must stay: apparently they have stronger air conditioning than that of the T1’s – I don’t care about it much, but others feel differently; and they will become wheelchair accesible, so why can’t they stay? They are the first cars built to replace older ones (the Gloucesters), and if they are replaced, that’d mean they are the only cars built to replace older ones, but will be replaced by newer ones. The TTC is making a mistake by removing what I like and keeping what I don’t like much. However, the T1’s will not last forever.

    Steve: The H6’s have reliability problems and are due for a major overhaul. The TTC has worked its budget hocus pocus to show that just building more TRs is cost effective compared to that overhaul, although I suspect that there was a strong dose of make-work for Thunder Bay as there is in so many TTC car orders.


  13. What’s with the married pair stuff? All couplings of cars are the same, whether they’re coupled at the cab end or not. A ‘married pair’ of cars is not linked permenantly as a unit, is it?! So if only one car has a problem, you will need to disconnect only that one car and connect another ONE.

    Steve: No, the TR cars will be built as married trains, not pairs. For one thing, the end cars will have cabs, but the middle cars will not. Where you now have six cabs per train you will have two. The geometry of the cab ends is incompatible with them being in the middle of the train.

    Also, not all trucks will be powered, and the units within the trainsets will not all be interchangeable as they are with the H and T-1 series cars.


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