Tuesday, September 19, 2006

On the Chirality of London Underground train maps

The reopening of the Waterloo and City line means that now is a good time to discuss the chirality of maps on tube trains.

Let me set the scene.

You're sitting on a moving train in the "usual" style. That is: you're facing other commuters and the walls of the tunnel are in front of you and behind you (the front of the train is thus to your left or right).

You look up and see the route map for that line. It is probably linear, perhaps with a loop or a few branches at one or other end.

An interesting question then arises: does the direction of the train correspond with the direction implied by the map? That is: if you're travelling rightwards, does the map correctly identify that the next station is to the right?

Perhaps it does. Perhaps it doesn't.

Now you stand up, look menacingly at somebody on the opposite bank of seats and take their seat as they correctly sense you are performing an important experiment and choose to sit elsewhere. You now perform the same procedure as before. You look up and ask yourself whether the train is travelling the direction suggested by the map.

And this is where it gets interesting.

On some trains on some lines, the maps are accurate. This means that London Underground have gone to the trouble of producing two versions of the maps - a different one for each side of the train). On other trains, they use the same version of the map on both sides of the train - which means that one will be accurate and one will be "the wrong way round".

The question is: why is this the case and on which trains do they get it "right"?

In some cases, it's just not possible to get it right: The Piccadilly and Central lines, for example, have a loop which mean that, without getting out of your seat, the train would sometimes be travelling in the direction suggested by the map and sometimes not. In such cases, printing two versions is unnecessary - indeed, it runs the risk of having both maps being wrong.

However, on the Jubilee Line (with no loops and no branches), it would be possible to get it right (I can't remember if they actually do).

If a tube train has two maps - one for the left hand side and one for the right hand side of each carriage then we say it is chiral. Otherwise, we do not.

The question I am inviting you to help me answer is: can we compile a list of which lines have chiral maps on their trains and which do not?

Enquiring minds need answers.



[UPDATE 2006-09-19 19:21]


It appears I may have, entirely unintentionally, given the impression that I was sad clever enough to observe these phenomena. The blame should be spread more widely. As Henry politely poins out,

"As you will recall, on 30 October 2005 - following from her examination of a cellphone advertisement - Polly raised this important issue with the results for the Jubilee and Piccadilly lines. Other notable events in this subject's history: line investigations (you, me, Polly); coining of the term "chirality" for this phenomenon (me), mathematical discourse (Mark, Polly), investigation and discussion of depot positioning and sequence-changing stock movements (Ben, me), proposed solution for the London case (me)."
Never let it be said that I don't spread the blame for such triviality as widely as possible.

25 comments:

andyp said...

Oh. My. God.

HP said...

The British tube map hasn't advanced one iota since it's inception...it is still just a map...on the other hand, check out Hong Kong's MTR!

Now, I'm not sure whether the maps reflect the direction of travel. But who cares when there are lights to indicate which stations you are travelling between, and in what direction. Then, when you arrive at the station, the station glows.
Simple but incredibly brilliant!

http://images.nycsubway.org//i31000/img_31637.jpg

DarkKnight said...

Actually, a loop wouldn't make it wrong if you considered going right as clockwise.

The problem is that trains don't always run in the same direction on the tracks. They can turn round and hence would then have the map wrong (particularly on the picadilly line where there is a small loop to change direction of travel)

Richard Brown said...

Darkknight: sorry - I didn't explain myself properly. When I talked of a loop, I was thinking of the Central Line's Hainault Loop or the Piccadilly's Heathrow loop. Whilst on the loop you're fine, but when you rejoin the linear part of the track, the effect is as if somebody had picked up the entire train and turned it around. e.g. imagine you had been travelling to Heathrow and seated such that you were travelling to the right and that the map showed heathrow to the right. By the time you had gone round the loop and were travelling back towards central london, you would still be travelling "right" but the map would still be showing Heathrow to the right, when really it's now to the left. That's the problem I was trying to get at (I think!)

hp Yes... I guess lights could be a technological solution to this problem... but there's still something aesthetically unpleasing about lights that travel counter to the direction of the train :-p

Henry said...

I'm very impressed with your ability to pass this off as your own research topic.

As you will recall, on 30 October 2005 - following from her examination of a cellphone advertisement - Polly raised this important issue with the results for the Jubilee and Piccadilly lines. Other notable events in this subject's history: line investigations (you, me, Polly); coining of the term "chirality" for this phenomenon (me), mathematical discourse (Mark, Polly), investigation and discussion of depot positioning and sequence-changing stock movements (Ben, me), proposed solution for the London case (me).

Richard Brown said...

If you check your email, I believe you will see that I stated my intent to publish at 09:21 BST today.

However, I accept that, to avoid any misguided perception of impropriety, it would be advisable to make a minor edit to the post to make it clear that it wasn't all my own work.... :-p

polly said...

It is convenient to use the Piccadilly line as an example for justified non-chirality of maps, and it is a useful addition to the example of the circle line because of the need for the distinction between o- and p-loops. Here I am morally, if not quite legally, obliged to credit Ben for this underused terminology. But I think that it is important that someone mention that throughout the suspension of Piccadilly line services to Heathrow terminal 4, the map has betrayed no loop, and the maps on the Piccadilly line have been reprinted in their entirety, rather than amended with a sticker job. Therefore I assume that either there remains a secret, non-passenger carrying loop at Heathrow, or that the carriers have dispensed with pleasing, but non-value-adding attention to their maps. An investigation of the W&C line - assuming the six-month upgrade went as far as the reprinting of the maps - would reveal which is the case. This investigation is absent from your post, but I cannot judge too harshly, as I - transport charlatan that I am - failed to visit the exhibition of the new Victoria line trains in Euston.

As of April 2006, they actually get it right on the Victoria, Jubilee, W&C and Bakerloo lines, and we've failed to find any topological reason why they couldn't do so on any lines except the Circle. On some maps the Central line appears to have a loop, but allegedly (here I credit cheshireEyelashes) the trains on the eastern branch never go through Woodford: they merely turn.

polly said...

Darknight says:

Actually, a loop wouldn't make it wrong if you considered going right as clockwise.

Perhaps, with training, one could think this way. But there is a physical reason that Circle line trains don't go round the same way all the time: the differential wearing on each side of the wheels. I credit Ben for this knowledge.

Henry: thank you for protecting my share of earthly glory.

Richard Brown said...

Thank you, Polly.

You were correct to notice that I failed to comment on the refurbished W&C rolling stock. The reason is that I forgot it had reopened when I went to work yesterday and I forgot to check when I used it this morning.

I didn't use it this evening because I'm coming to the perverse conclusion that taking the District to Blackfriars and walking is a more pleasant way to get to work....

I'll take the W&C tomorrow and report back...

Henry said...

Polly: actually it was I that imparted the knowledge around the Circle line reversal for even axle wear; it is one of my most treasured factoids. I gather the trains go out of service then go round the Aldgate triangle.


Richard:

I didn't use it this evening because I'm coming to the perverse conclusion that taking the District to Blackfriars and walking is a more pleasant way to get to work....

Oooh, after everything you said about my analysis of TfL's journey recommendations!

--

Anyway... I think these analyses are sufficient justification to propose my hypothesis. The natural state is chirality; decision to implement non-chiral maps is down to any justification that it might be confusing. This includes any of the following cases:

1. There is a possibility of the train being put into reverse formation (subservice shared stock).

2. There is a loop (Circle, Piccadilly; as Polly says, *not* Central if you look carefully enough).

3. There is a bifurcation (Northern, Piccadilly, Central, etc)

4. There is predominant East-West travel (H&C and many others counted in (3)).

This leads us to an interesting conclusion:

Desire not to put "wrong" maps up is certainly a driver, but the principal requirement is that passengers are not confused, with a liberal interpretation of "confusion": chiral maps are successful if people don't notice they're there. Essentially, it would look wrong if Heathrow were on the right or the Hainault loop were on the left, but people just don't notice if Stanmore moves from the left to the right. This is demonstrated by the H&C example, which is the boundary condition for (4) as it exceptionally falls into no other category.

Richard Brown said...

Condition #4 may well be the key.

You will be shocked to learn that the refurbished W&C stock has non-chiral maps. Bank always appears to the right of the diagram.

Any remaining reason I may have had for using that line has been removed.

I will therefore formally (but partially) retract my hilarity at the suggestion that using the District line to get to work could be valid and continue to go to work via Blackfriars.

polly said...

Since my last post I've remembered that our investigation into the chirality of the pre-refurbishment W&C was inconclusive.

I thought we decided that the H&C couldn't be used as an example in support of the east-west theory, as it shares stock with the Circle line and thus chirality is precluded by 2.

Ben said...

On some maps the Central line appears to have a loop, but allegedly (here I credit cheshireEyelashes) the trains on the eastern branch never go through Woodford: they merely turn.

Yes, but trains can still stop at Woodford (at the same platforms) from either direction; so chiral maps on a train there that came via Hainault would have the opposite sense to those on a train that came from South Woodford. This might be momentarily disorientating.

Richard Brown said...

Please let me know when we have reached agreement and I will prepare a summary posting, maybe even with colour coding...

Henry said...

Polly: yes you're right about H&C using shared stock -- mea culpa.

I still stand by my confusion hypothesis and suspect that - despite its branch - the ELL would be chiral were its stock not shared with the Metropolitan Line.

I think we have the underlying social cause of the muddier water: that owing to the growth of wealthy London on its western side, with little tube penetration to the south, tubes on the E-W axis are likely to proliferate branches. My claim is that it is the E-W axis, not the branches that preclude chirality.

To summarise, my suggestion is that any of the following, exhibited by any of the lines served by each stock, implies non-chiral maps for that stock:

1. Predominant E-W linearity

2. Operational O loops in service

3. Operational stock reversals

The only possible counterexample I can think of is the Northern Line. I don't know how or where the NL depot is, or how it is configured. If it is impossible for trains to reverse formation by using the depot, then (2) should be weakened as follows:

2. Operational O or P loops in service.

Ben said...

The Northern Line has a loop at Kennington between its south and north platforms on the Charing Cross branch. (The loop is not accessible to the Bank branch. This explains how there's normally a train "magically" waiting there if you have to change going northbound.)

andyp said...

I'm mildly impressed. Against the odds, you've managed to choose a topic that interests more than 2 other people. Maybe your blog traffic will improve, after all.

Richard Brown said...

I'm mildly impressed. Against the odds, you've managed to choose a topic that interests more than 2 other people. Maybe your blog traffic will improve, after all.

*Sigh*... Jealousy is never admirable....

Richard Brown said...

The Northern Line has a loop at Kennington between its south and north platforms on the Charing Cross branch. (The loop is not accessible to the Bank branch. This explains how there's normally a train "magically" waiting there if you have to change going northbound.)

Wow... something I didn't know about the tube.... A loop does seem excessive, though.... why could it not be a "tweezer" junction (a la Bank station for the DLR... i.e. two tracks merge such that the train simply drives into the merged portion, the points change and then it reverses onto the other track)?

Richard Brown said...

Henry: 3. Operational stock reversals

Do you mean trains changing direction or trains acting as if they had been picked up and rotated through 180 degrees?

Henry said...

As Ben says it is a loop; from http://www.davros.org/rail/culg/northern.html

At Kennington, the Charing Cross branch surrounds the older City branch, with cross-platform interchange in each direction. Trains from Charing Cross can then run towards Morden, or else turn round using a large loop and return back northwards (this loop cannot be reached from the City branch). Alternatively, trains from either branch can use a central turnback siding south of the station.

See also

http://www.geocities.com/Athens/Acropolis/7069/ltkenn.gif

Googling implies that a loop was built rather than a terminating platform purely so the driver would not have to change ends, but I'm happy to be corrected.

Richard: I mean that a train traveling from A to B with end e1 closer to A and end e2 closer to B is said to have undergone stock reversal if following the reversal e2 is closer to A and e1 closer to B. An example would be - as referenced by Polly - the Circle line where a stock reversal takes place every few circuits so that axles wear evenly. Another example - we now know thanks to Ben - is the Charing Cross - Kennington - Charing Cross Northern Line maneuver.

Quentin said...

Hmmm, I'll just say this. You never fail to surprise me Mr Brown.

Richard Brown said...

Quentin, I'll take that as the compliment I so know it was....

Henry - thanks for the explanation (and the interesting spelling of manoeuvre)

Henry said...

Gah; haven't you anything better to do than critique your friends' spelling?

I woz bearly edjacated ya now.

Richard Brown said...

Gah; haven't you anything better to do than critique your friends' spelling?

Henry - this is a thread about the chirality of tube maps. Is the answer to your question not obvious from the context? :-p