A World Exclusive in Mapping London Transport

As the Gall-Peters projection astonished viewers who had hitherto been used to Mercator, this map will revolutionise the way we all see our Londons. Well I would say that, my dad provided it. Read on for his methodology:

"This was inspired by the new London Tube map, which tries to be more faithful to the geography than the Beck diagrams.

I have distorted the geographic map as follows. First, I observed that the area of main interest is roughly in a rectangle of A4 landscape shape, centred approximately on Waterloo.

Then I multiplied the Y co-ordinates of all the points by √2 to make the diagram square.

Next I scaled the distances from the centre by using the hyperbolic tangent function; as r tends to infinity, tanh r tends to 1. This means that any distance will necessarily fit into a finite circle. There is a scaling distance involved; if this is low (say 12 km) then the centre area will be uncluttered, but the distant stations will be very squashed together. If it is high (say 30 km) then the diagram is closer to the geographical one. A value of 20 km is about right for most purposes.

Now it remains to divide the new Y distances by √2 to bring the diagram back onto a rectangle.

At this point the diagram is elliptical. This means there is quite a lot of white space in the corners of the page. Therefore as an optional extra I turned the circles on the square sheet into “supercircles”.

A normal circle of radius a has the equation x2 + y2 = a2. A “supercircle” has the equation xn + yn = an where n is any number greater than 2. As n grows, the “supercircle” approaches a square. I took n = 4, which yields a square with rounded corners. It also happens to be mathematically tractable.

It is not too hard to see that, whatever the scaling employed, the angular bearings from Waterloo remain true; only the distances are distorted. The diagrams have distance contours in light blue at 5 km intervals, and radial lines at 10° intervals. These start at 2 km from the centre, giving an extra distance marker inside the 5 km contour.

The data file for the map has two sources. The locations of the stations, intermediate points and points on the Thames are lifted from Google Maps. The lines and colours are based on TFL’s Oyster map, with minor differences.

The stations are “pie charts” with the colours showing which lines are served. Mostly no distinction is made between a colour and the same colour dotted, except when both are present together. All the points on the diagram are joined by straight lines, if necessary of multiple colours.

There are a few “issues” as the software people say, meaning problems. In no particular order, the known ones are:

The Piccadilly line has been obscured by Thameslink between Highbury & Islington and Drayton Park.

The roles of Canonbury and Gospel Oak as partial termini are not made clear.

The fact that DLR trains go the either Bank or Tower Gateway, but not both, is not clear.

The fact that on the “Saucepan Line” (ex Circle Line) trains terminate in one direction at Edgware Rd is not clear.

The fact that Bethnal Green is not a stop for trains towards Stratford is not clear; the station is shown as grey and white as a hint.

The Bank loop of the Northern line is shown dotted; this is because these trains do not use Mornington Crescent.

The high speed line from St Pancras is just shown in the vicinity of St Pancras, Stratford International and the River Thames.

Spelling of stations might not be consistent, and may even be wrong. The “pie charts” of the stations have not been carefully checked."