Optimum number of platforms

[Waddon]

I'm just trying to work something out in my head... if a terminus station was receiving a pretty frequent service of electric multiple unit trains, say one arriving every 2-3 minutes, what would be the ideal number of platforms to accommodate such a service, without trains having to wait for a platform to be available?

Assuming for the moment that such a service was headway based, rather than timetable based, and including allowances for reasonable crew turnaround time, boarding/alighting of passengers, the occasional train fault etc. and assuming no grade seperation of arrival and departure lines, so some services would have to cross the paths of others?

 

[The Planner]

How can it not be timetable based? I take it there is enough S&C to do all moves? How many trains are you talking?

 

[Waddon]

Ok make it timetable based, yes there would be sufficient S&C, trains arriving every 2-3 minutes, as stated in the first post (I'm assuming a high frequency commuter type service).

The concept I'm trying to get at is how many platforms in a terminus would be ideal to accommodate the service as described. Obviously one platform would be insufficient, and twenty would be overdoing it.

 

[bradders1983]

Depends if you are allowing more than one train occupying a platform or not

 

[jasonkerner]

Wouldn't there be quite a lot of variables with this, apart from frequency of arriving trains?

You'd need to know average unload / load time, length of train (longer trains take longer to load), averages passengers per carriage (or assume 1 type of train always), peak volumes (ie, rush hour would be busier compared to a Sunday morning). You'd also need to know the number of destinations that could possibly be visited by the departing trains, and where they crossover.

If you assumed just one terminus station at the end of the track, connected to another terminus station at the other end, then two platforms would be enough in case you had a train arriving and then unloading Vs another departing. You could get away with one, assuming a constant journey time that doesn't vary and the trains crossover in the middle (think trains that go on coastline piers for tourists).

The length of platform would also be a factor too because if you think somewhere like Manchester Piccadilly, you could have a 11-car pendo or 2 shorter TPE services in the same platform. If a platform could have 2 services in, then that would require less platforms.

Just my 2c....

 

[Islineclear3_1]

I'd imagine as well as whether there will be a requirement to berth empty stock in between busy periods if sidings or other berthing facilities are not available locally - clearly this will use up valuable platform space

 

[deltic]

I'm just trying to work something out in my head... if a terminus station was receiving a pretty frequent service of electric multiple unit trains, say one arriving every 2-3 minutes, what would be the ideal number of platforms to accommodate such a service, without trains having to wait for a platform to be available?

Assuming for the moment that such a service was headway based, rather than timetable based, and including allowances for reasonable crew turnaround time, boarding/alighting of passengers, the occasional train fault etc. and assuming no grade seperation of arrival and departure lines, so some services would have to cross the paths of others?

Brixton and Elephant & Castle tube stations can turn around 20-30 trains an hour using 2 terminal platforms

 

[swt_passenger]

Brixton and Elephant & Castle tube stations can turn around 20-30 trains an hour using 2 terminal platforms

The Vic aims to get 34 tph over the full line from the next timetable change, and then 36 tph in the future? It is one of the claims for the recent Walthamstow alterations anyway.

 

[TheNewNo2]

Most LU lines seem to have terminals with three platforms. They could probably get away with two, but three means you don't usually need to do any stepping back. Plus it allows some flexibility.

Of course what tends to restrict capacity more is the station throat - if you only have at-grade crossings, it's pretty limiting. If however you allow a flyover then it ensures you can have one train arriving as another departs.

 

[miami]

The Vic aims to get 34 tph over the full line from the next timetable change, and then 36 tph in the future? It is one of the claims for the recent Walthamstow alterations anyway.

But don't victoria lines get suplemented by trains to/from Seven Sisters? Do all trains turn at Brixton?

At Thomasland there's a passing place, a turntable at each end, and a track for the loco to run past the carriages at both ends

https://www.youtube.com/watch?v=2767B3BWzRE

 

[swt_passenger]

But don't victoria lines get suplemented by trains to/from Seven Sisters? Do all trains turn at Brixton?

The Walthamstow crossover works were specifically intended to remove the short workings to/from Seven Sisters. In the May 2016 timetable they state all trains will run the whole route. I think all trains run to Brixton already, except during perturbations. (Maybe also except at start and end of service.)

Details here: http://content.tfl.gov.uk/rup-20151016-part-1-item06-walthamstow-blockade.pdf

 

[61653 HTAFC]

Assuming no constraints on space or budget, the optimum number of platforms is in fact just the one, as long is it is located on a balloon loop... No need for drivers to change ends, just call there as if it was another intermediate station.

 

[AndyNLondon]

But don't victoria lines get suplemented by trains to/from Seven Sisters? Do all trains turn at Brixton?

Those are the opposite ends of the line - at the southern end everything (ordinarily) terminates/starts at Brixton, at the northern end it's split between Seven Sisters & Walthamstow Central

 

[QueensCurve]

Brixton and Elephant & Castle tube stations can turn around 20-30 trains an hour using 2 terminal platforms

What sort of track layout do they use for this? Crossovers at the entrance to the platforms or a heashunt beyond? If the latter, does it require the driver to walk down the train or can a train crew "step up"?

 

[jopsuk]

What sort of track layout do they use for this? Crossovers at the entrance to the platforms or a heashunt beyond? If the latter, does it require the driver to walk down the train or can a train crew "step up"?

You can see LU track layouts here. The only station with a dedicated "headshunt" arrangement on LU is the Picadilly Line at Heathrow Terminal 5- despite that not being a particularly busy or high frequency location. The W&C shunts into the depot at Waterloo, similarly at Barking H&C trains can terminate at platform 2 and reverse via the sidings to start again at Platform 6 OR use the bay platform 3. The DLR at Bank also has a headshunt arrangement, and Crossrail will have for Paddington terminators. Kennington has a balloon loop though the use of this will be much reduced by the Battersea extension. As far as I know at Morden and Upminster trains generally terminate in any of the platforms and then return, if they're not going out of service into the depot

I think LU does make extensive use of "stepping up"- on busy platforms drivers simply could not walk the length of the train in the time required.

 

[MarkyT]

LU do really well with ATO and fairly small tube trains at a number of two platform termini as described above. If the train operator is always going to be in the front cab then step-back working is really necessary at these desired high frequencies of up to 36 TPH, especially at peak times when it may be difficult for crew to fight through crowds to change ends. DLR can reverse an amazing 20 TPH in it's single turnback siding at Bank but there's no need for the driver to change ends or to open and close doors because the train reverses empty beyond the two platforms, arranged as dedicated arrival and departure lines so there's no jostle between the two groups on either platform. The trains are also short on the DLR, so that helps with total numbers boarding and alighting. On National Rail with bigger trains four platform terminals typically handle up to 16 TPH so that's four per hour per platform. Some railways throughout the world handle higher than that for suburban type operations in smaller stations, but other methods might also be used, such as crew stepping back as on LU, platforms on either side of each track (quicker arrival discharge and possible separation of arrival and departure crowds).

 

[30907]

Holborn Viaduct used to manage 5 consecutive arrivals 3 minutes apart with 3 platforms and from memory Waterloo 1-4 was 21tph in the 70s. Both were in SUB/EPB days though, and I don't think that could be kept to now.
Charing Cross has 6 with a theoretical capacity of 30tph through Met Junction but I don't think quite that many are timetabled.

 

[rf_ioliver]

I'm just trying to work something out in my head... if a terminus station was receiving a pretty frequent service of electric multiple unit trains, say one arriving every 2-3 minutes, what would be the ideal number of platforms to accommodate such a service, without trains having to wait for a platform to be available?

Assuming for the moment that such a service was headway based, rather than timetable based, and including allowances for reasonable crew turnaround time, boarding/alighting of passengers, the occasional train fault etc. and assuming no grade seperation of arrival and departure lines, so some services would have to cross the paths of others?

Theoretically one platform, but this of course depends upon many factors such as the length and speed of the train in and out of the station (primarily acceleration/deceleration), then the speed of moving pax on and off, then the speed of getting a crew from one end to the other.

The latter can be optimised by having a crew at the ready and the speed of pax can be optimised by using two platforms but one track, eg: the Gatwick terminal shuttles, and also by strictly controlling where the pax stand and the size of the groups getting on and off, plus a few other mobility factors.

The speed at which a train enters the station and more importantly its deceleration is critical, along with the length of the train. I can't do the calculus in my head but let's say it takes 20s to enter the station and 20s to leave with 30s for pax and crew - this would give a theoretical upper limit of around 51 trains per hour.

Adding a second platform would optimise this a little in that you have additional time, around 70s in the above example to get the train, crew and pax ready, but this is more resiliance than anything. An educated guess could probably give you an addition 10 trains per hour - again, need to do the maths (queueing theory this time).

The main bottleneck would be any interference between the incomming and outgoing trains. This can be optimised by having, say, a cross-over or balloon loop. If trains at this point could be spaced as close together as possible in that as one train clears the platform and another enters, I guess you could get to over 70 trains per hour easily (for some definitions of "easily"!)

However as soon as anything goes wrong you've got delays with a single track/platform. Increasing the number of platforms at least keeps things moving albeit with a reduced capacity (from over 60 down to 50, using above theoretical maximums).

You can optimise further by treating the terminal station as a through station by having sidings for preparing and turning trains after the terminal.

Another good rule of thumb is that 70% capacity is a good limit to guarantee some kind of smooth running. So, my guess with 2 platforms and the above figures, 40 trains per hour is the practical limit. 3 platforms gives additional resilience just in case things go really badly wrong.

A more knowledgeable person will confirm that some London Underground stations are equipped with sidings to take trains out of the system to reduce the load when things are getting badly delayed.

The maths is fairly straightforward, but gets complexquickly. I'm not an expert in this area but https://en.wikipedia.org/wiki/Queueing_theory should give you a flavour.

t.

Ian

NB: maths done in head and with some BIG assumptions (YMMV) and the above probably contains mistakes

 

[MarkyT]

The only station with a dedicated "headshunt" arrangement on LU is the Picadilly Line at Heathrow Terminal 5- despite that not being a particularly busy or high frequency location.

At Heathrow, such an arrangement keeps arriving and departing passengers segregated and avoids them conflicting at the doors. That might be important in the 'higher luggage' airport application and might save a few seconds for both the loading and unloading operations.

DLR achieves up to 20 TPH with only one such headshunt. Under automation, the trains can reverse again immediately as soon as the points have changed, and there's no need to open and close doors as the train is running empty in and out of the reversing siding.

Back at Heathrow I expect only the north headshunt is used routinely. This allows the other empty siding to be used as an overrun tunnel with a full length overlap set along it, allowing a higher speed arrival run-in than if the junction or siding ahead was blocked by a previous train changing ends or shunting. When the trains and signalling finally get upgraded on the Piccadilly, it may become possible to use both sidings more easily and gain a higher capacity.

Paddington Crossrail turn-back will have two reversing sidings I understand, sited for minimal conflict between the two through running lines, and to the west of the station beyond the portal, so well outside the overlap zone. Whether either siding is occupied or not can thus have no impact on arrival run-in speed from the east.

 

[miami]

Heathrow is strange -- the Heathrow Express terminated, then you can't board while they undergo a "security theatre check". Sigh.

If you had a 30 second gap between trains and a 5 minute dwell time you could run with 10 platforms (call it 12 for a bit of safety), terminating 120 trains per minute -- have the approach track split off for all the platforms, and have the departures merge together, and have them looping out.

>---\-\-\-\-\-\-\-\-\-\
    | | | | | | | | | |
    0 1 2 3 4 5 6 7 8 9
    | | | | | | | | | |
<---/-/-/-/-/-/-/-/-/-/

00 - platform 9 arrive
00.5 - 8 arrive
01 - 7 arrive
01.5 - 6 arrive
02 - 5 arrive
02.5 - 4 arrive
03 - 3 arrive
03.5 - 2 arrive
04 - 1 arrive, 9 depart after 4 minutes
04.5 - 0 arrive, 8 depart after 4 minutes
05 - 9 arrive, 7 depart after 4 minutes
05.5 - 8 arrive, 6 depart
06 - 7 arrive, 5 depart

etc. etc

You'd have to build you approach and depart tracks so they're a similar length from where it starts to fan out

Works in TTD. with a 100m train, decelleration and acceleration on each of the individual platform lines, and a line speed of 80mph 30 seconds is 10 train lengths, 27 seconds from the back of one train and the start of another -- plenty of space.

Of course if you put intermediate 2 platform stops in it all goes pear-shaped.