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Kacie Jane

30 tph (or "How many trains can you fit on a track?")

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Sometimes I pretend to know everything, and I certainly do not. So I'm going to ask an honest question that seems to keep coming up.

 

The (4)(5), (6), (7), and (E)(F) -- am I missing any? -- all run at or close to 30 tph during rush hours, so I do understand people's assumption that okay, 30 tph is the maximum.

 

But just because certain lines are capable of handling such insane headways, that doesn't mean all of them are, right? For instance, whenever someone suggests extending the E back to Brooklyn (usually to take over the Lefferts branch of the A), people always say that the Cranberry St Tunnels are at capacity. Well, the A and C combined only run 16 tph at their peak, so if you add the E in, that's only 31 -- cut a train here or there and *poof* everything should be fine, right?

 

Theoretically, one could fit a combo like the (C)(F)(M)(R) onto one track if absolutely necessary with a total of 30 tph. What matters is the tph (6, 8, 8, 8 in the example above), not the number of services.

 

Sorry to single you out, NX Express, but this is another bit of logic I take issue with. I think the number of services does matter a great deal. For each service you add to a track, somewhere along the line you add a switch, and where you have a switch, you have a wonderful potential for a delay. I would imagine that it's far easier to squeeze 15 (4)s and 15 (5)s (or better yet, 30 (7)s) onto a single track than it would be to squeeze 6 ©s, 8 (F)s, 8(M)s and 8®s.

 

So anyway, those are my thoughts, and that's why whenever I'm participating on one of the "game" threads, or discussing a real-life G.O., I would never have more than 3 services on a track, and preferably not more than 2.

 

I know I said I'd ask an honest question, and I never quite got around to it. What I'm looking for is someone to debate me on this, but with something more substantial than "30 tph".

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Sometimes I pretend to know everything, and I certainly do not. So I'm going to ask an honest question that seems to keep coming up.

 

The (4)(5), (6), (7), and (E)(F) -- am I missing any? -- all run at or close to 30 tph during rush hours, so I do understand people's assumption that okay, 30 tph is the maximum.

 

But just because certain lines are capable of handling such insane headways, that doesn't mean all of them are, right? For instance, whenever someone suggests extending the E back to Brooklyn (usually to take over the Lefferts branch of the A), people always say that the Cranberry St Tunnels are at capacity. Well, the A and C combined only run 16 tph at their peak, so if you add the E in, that's only 31 -- cut a train here or there and *poof* everything should be fine, right?

 

 

 

Sorry to single you out, NX Express, but this is another bit of logic I take issue with. I think the number of services does matter a great deal. For each service you add to a track, somewhere along the line you add a switch, and where you have a switch, you have a wonderful potential for a delay. I would imagine that it's far easier to squeeze 15 (4)s and 15 (5)s (or better yet, 30 (7)s) onto a single track than it would be to squeeze 6 ©s, 8 (F)s, 8(M)s and 8®s.

 

So anyway, those are my thoughts, and that's why whenever I'm participating on one of the "game" threads, or discussing a real-life G.O., I would never have more than 3 services on a track, and preferably not more than 2.

 

I know I said I'd ask an honest question, and I never quite got around to it. What I'm looking for is someone to debate me on this, but with something more substantial than "30 tph".

 

If 30 tph is the "maximum" then lines do not matter. However, when switching gets involved, then I would say the max is 20-23 tph.

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If 30 tph is the "maximum" then lines do not matter. However, when switching gets involved, then I would say the max is 20-23 tph.

 

:confused: Ummm.... what? So the lines do not matter, but if switching is involved, then it does? If there's more than one line, then there's switching somewhere.

 

Look, obviously 30 tph is the maximum if there's little to no switching.... and if everything else on the line (signals, etc.) is capable of handling it. (Otherwise, why does the (L) only run 15 tph?)

 

What I want to know is... is it actually possible to squeeze four or five lines on a single track? One person on the fastrack thread said essentially, "Well, sure, they'd just have to put out a supplemental schedule to ensure that everything got timed perfectly," and I accept that this may be so. But it seems to me that once a single train gets delayed slightly and gets to a junction out of turn, it could very quickly become a recipe for disaster.

 

As an aside, take note that the (:P and (M) are both ending early for the 6th Avenue Fastrack. Obviously the B is a special case -- it can't get to Brighton from 8th Avenue, so there's no reason for both it and the D to run -- but in theory, there's no reason for the M to end early, or for that matter, for the C to run express. At 10:00, the (D)(E)(F) run 5 + 6 + 6 = 17 tph. If 30 tph were truly the maximum, there's no reason the C and M couldn't be shoehorned in there as well to make 27 tph.

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:confused: Ummm.... what? So the lines do not matter, but if switching is involved, then it does? If there's more than one line, then there's switching somewhere.

 

Look, obviously 30 tph is the maximum if there's little to no switching.... and if everything else on the line (signals, etc.) is capable of handling it. (Otherwise, why does the (L) only run 15 tph?)

 

What I want to know is... is it actually possible to squeeze four or five lines on a single track? One person on the fastrack thread said essentially, "Well, sure, they'd just have to put out a supplemental schedule to ensure that everything got timed perfectly," and I accept that this may be so. But it seems to me that once a single train gets delayed slightly and gets to a junction out of turn, it could very quickly become a recipe for disaster.

 

As an aside, take note that the (:P and (M) are both ending early for the 6th Avenue Fastrack. Obviously the B is a special case -- it can't get to Brighton from 8th Avenue, so there's no reason for both it and the D to run -- but in theory, there's no reason for the M to end early, or for that matter, for the C to run express. At 10:00, the (D)(E)(F) run 5 + 6 + 6 = 17 tph. If 30 tph were truly the maximum, there's no reason the C and M couldn't be shoehorned in there as well to make 27 tph.

 

Here is the math. If 2 lines share 2 tracks it would be 15 TPH each, but to have 4 lines share 2 tracks it would have to be reduced to 7.5 TPH for each line. That would mean 7 or 8 trains per line. That is barely any service for people and would be radically useless. For example let's create a fictional line with 4 train services using 2 tracks. Their letters are (P) (U) (X) (Y). Now all four of them shares 2 tracks. So basically their would be 7 (P) trains an hour, 7 (U) trains an hour, 7 (X) trains an hour, and 7 (Y) trains per hour, but then this service won't be efficient because there would more lines but fewer service. A sacrifice no one would like. So no it's not possible.

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:confused: Ummm.... what? So the lines do not matter, but if switching is involved, then it does? If there's more than one line, then there's switching somewhere.

 

Look, obviously 30 tph is the maximum if there's little to no switching.... and if everything else on the line (signals, etc.) is capable of handling it. (Otherwise, why does the (L) only run 15 tph?)

 

What I want to know is... is it actually possible to squeeze four or five lines on a single track? One person on the fastrack thread said essentially, "Well, sure, they'd just have to put out a supplemental schedule to ensure that everything got timed perfectly," and I accept that this may be so. But it seems to me that once a single train gets delayed slightly and gets to a junction out of turn, it could very quickly become a recipe for disaster.

 

As an aside, take note that the (:P and (M) are both ending early for the 6th Avenue Fastrack. Obviously the B is a special case -- it can't get to Brighton from 8th Avenue, so there's no reason for both it and the D to run -- but in theory, there's no reason for the M to end early, or for that matter, for the C to run express. At 10:00, the (D)(E)(F) run 5 + 6 + 6 = 17 tph. If 30 tph were truly the maximum, there's no reason the C and M couldn't be shoehorned in there as well to make 27 tph.

 

If there is more than one line, the switching involved dosen't have to be significant. Between Queens Plz & 36 St, the switching involved dosen't cause many delays.

 

It is probably not possible to do 4-5 lines though. For example, if all Queens Bl lines were forced to use the local tracks, the headways would be 7-8 tph. (E) & (F) riders may rather walk!

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Here is the math. If 2 lines share 2 tracks it would be 15 TPH each, but to have 4 lines share 2 tracks it would have to be reduced to 7.5 TPH for each line. That would mean 7 or 8 trains per line. That is barely any service for people and would be radically useless. For example let's create a fictional line with 4 train services using 2 tracks. Their letters are (P) (U) (X) (Y). Now all four of them shares 2 tracks. So basically their would be 7 (P) trains an hour, 7 (U) trains an hour, 7 (X) trains an hour, and 7 (Y) trains per hour, but then this service won't be efficient because there would more lines but fewer service. A sacrifice no one would like. So no it's not possible.

 

Thank you for missing the point entirely. I know that 30 divided by 4 is 7.5. My question isn't whether customers would be happy with 7.5 tph, it's whether you could actually fit four lines on a track at 30 tph. During the evening hours -- i.e. during the beginning of Fastrack time -- almost every line runs at 7.5 tph or fewer.

 

Let's assume your fictional PUXY line is a typical 4-track line, and during non-rush hours, each of the lines run at about 7.5 tph. And lets say that some G.O. shuts down either the express or local tracks in one or both directions.

 

My question -- and I honestly didn't think it was that hard to understand -- is would you be able to squeeze all four lines onto the same track without causing massive delays upstream of the switch(es).

 

My instinct says that 30tph is the maximum for one or two lines on a track with modernized equipment. But I would imagine that one you either a) try to squeeze a third, fourth, fifth line or :P fail to update the signals and whatever else allows a line to run smoothly, the maximum frequency would drop pretty dramatically.

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Well 30 tph turn out to be a train every 2 minutes. The problem is that not all of the routes can support such high speed operation, especially if it involves switching. Lets say there are two line segments each mile long, one straight and one curved. The straight one has speed limit of 40mph no timers, wheel detectors, etc., while curved one has timers and it's maximum speed is 20mph. Theoretically first one would have capacity beyond 30 tph and other would be less than 30. That is if we disregard the loading time and time to stop/leave the stations, which would decrease tph for both line one and line two. Now imagine that faster portion is followed by slower, this will result in same tph on line 1 as on line 2.

Thus 30 TPH is not some constant number, it varies directly with average speed of the trains on the line. So if the trains have to switch, you can say bye-bye to 30 tph. Additionally if there is G.O. going on, that means there are workers on track and trains have to slow down, that another minus towards tph.

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On the (6), there is no switching in Manhattan if you notice. The loop is the biggest reason the (6) can maintain that headway and remain smooth, its really just one long line from Pelham to Pelham. 125th going north with the amount of people leaving and boarding serves as a natural buffer often to lighten the load on the switches south of 138 (which are high speed switches by the way and can be taken at 20+). The (7) line has almost exclusively 20mph switches+ among those it uses for regular service (Times Sq, bet Queensboro and Rawson, Main St). Even the ones at 74th for diversions are also 20mph switches.

 

The reason the (4) has the 138 bypass in the peak of the rush hour is because the switches below 138th-GC are faster and can spit out a faster thoroughput then the ones between 138 and 149 (trains have to punch for their lineup leaving 138). The reason the Lex s/b drags in the rush hour is because of the gap fillers at Union Sq that reduce thoroughput with increased dwell time. Grand Central and 125th going north are high dwell time stations as well.

 

What determines maximum thoroughput is a combination of signal block lengths, average train speeds on the track, how sharp the switches are entering and leaving a given stretch of track, and what kind of setup is needed to safely space trains entering and leaving different stretches of track. 30 cannot be maintained if there isn't enough signals to allow trains to run close together, or if train speeds are low on tracks with few signals. On express tracks, there are fewer signals, but the speeds on those tracks make up for that. On local tracks and in areas of curves and switches, the low speeds decrease thoroughput but the sheer amount of signals compensates. Station time (a timer that allows a train to close in on its leader) is the great equalizer that makes up for many deficiencies in track and signal layout to increase thoroughput. In many areas, station time allows the next train to enter a station before the previous one has fully left (seen at 71-Continental often)

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In many areas, station time allows the next train to enter a station before the previous one has fully left (seen at 71-Continental often)

 

I love when they do that! Those trains get awful close sometimes, which is cool, and it gets me on the train faster. A double win.

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I love when they do that! Those trains get awful close sometimes, which is cool, and it gets me on the train faster. A double win.

 

Its more if the T/O decides to utilize the feature. It is not fullproof and there are many signals that are labeled to have the feature and they in fact do not (one is just outside of Pacific going north on the local track just before the timer in the station, another famous one is north of 116 on the express track on the CPW. A train there can get no closer than roughly one trainlength outside of 116 until the one in 125 begins to leave the station.)

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On the (6), there is no switching in Manhattan if you notice. The loop is the biggest reason the (6) can maintain that headway and remain smooth, its really just one long line from Pelham to Pelham. 125th going north with the amount of people leaving and boarding serves as a natural buffer often to lighten the load on the switches south of 138 (which are high speed switches by the way and can be taken at 20+). The (7) line has almost exclusively 20mph switches+ among those it uses for regular service (Times Sq, bet Queensboro and Rawson, Main St). Even the ones at 74th for diversions are also 20mph switches.

 

The reason the (4) has the 138 bypass in the peak of the rush hour is because the switches below 138th-GC are faster and can spit out a faster thoroughput then the ones between 138 and 149 (trains have to punch for their lineup leaving 138). The reason the Lex s/b drags in the rush hour is because of the gap fillers at Union Sq that reduce thoroughput with increased dwell time. Grand Central and 125th going north are high dwell time stations as well.

 

What determines maximum thoroughput is a combination of signal block lengths, average train speeds on the track, how sharp the switches are entering and leaving a given stretch of track, and what kind of setup is needed to safely space trains entering and leaving different stretches of track. 30 cannot be maintained if there isn't enough signals to allow trains to run close together, or if train speeds are low on tracks with few signals. On express tracks, there are fewer signals, but the speeds on those tracks make up for that. On local tracks and in areas of curves and switches, the low speeds decrease thoroughput but the sheer amount of signals compensates. Station time (a timer that allows a train to close in on its leader) is the great equalizer that makes up for many deficiencies in track and signal layout to increase thoroughput. In many areas, station time allows the next train to enter a station before the previous one has fully left (seen at 71-Continental often)

I've said something less detailed in another thread, but basically, start with 30 t.p.h. (or whatever the raw t.p.h. for the particular route is), and subtract t.p.h. for every penalizing element that comes along the way (low terminal capacity, stations with long dwell times, speed limits, long signal block lengths, switches—especially active ones, etc.). For lines other than Flushing or Canarsie, it'll be difficult to reach full potential.

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In addition to every thing that has been said, there is also another issue.

 

The amount of people using the stations, and just how crowded are the particular trains, and the nature of the service. In the NYC subway, it is generally said that the signal system can handle 30 trains per hour.

 

For example on a commuter line with scheduled trains, having four "lines or routes" share the same set of two tracks for a lengthy stretch of track, even at "7.5 trains per line each hour" could be acceptable given the passenger loads. In addition such a mathematical assumption places the same amount of service on each branch point, which in the real world might not always be the case. The Far Rockaway branch gets service about every 20 minutes, while the Lefferts Branch may indeed have more frequent service.

 

Think about Penn Station where between Manhattan and New Jersey - there is a 100-year old two-track tunnel that handles all of the trains coming from New Jersey into Manhattan. Yes, during the rush hours often both tracks are used in-bound, but often there is heavy traffic on the in-bound or out-bound track.

 

Take a look at the E and F trains has a section that is often said to handle 30 trains per hour. The old 1970's pattern had both E and F trains starting out the 179th Street station, but then the E-trains were on the local tracks to 71st Avenue, while F-trains were on the express tracks until that station. This allowed the 179th Street station to devote its local platforms and 4 lower level layup tracks to handle, terminate and relay E-trains. The inner express tracks at 179th Street used the 4 upper level layup tracks to handle, terminate and relay F-trains. At the other end of these lines - E-trains terminate at the World Trade Center, while F-trains terminate at Kings Highway, Avenue X and Coney Island in Brooklyn. What does all of this mean - that the terminals have to have the opportunity to handle the amount of trains - in order to have such a high rate of train travel. Even though now the picture is a little different with E-trains traveling to Archer Avenue - which due to the placement of switch and signals can only handle 12-trains per hour, and why 3 tph start from 179th Street in the rush hours. The 179th Street terminal is and remains a very capable terminal.

 

All in all - this is an interesting discussion.

Mike

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