Which tube stations are closest together on the London Underground?
As part of my attempt at the Tube Challenge I'll run between some stations - though I don't know which ones yet. To incorporate this possibility into the modelling I need to calculate the time that these runs would take, and whilst calculating the data for this I realised I'd also generate a list of which stations are geographically closest to one another on the London Underground network as a byproduct.
I started off with the longitude and latitude co-ordinates for each station that I had gathered in an earlier phase of the project. Thus the distances mentioned in this blog post are between the points used to indicate the station on a map, rather than actual track distances between platforms at different stations (on that measure Leicester Square and Covent Garden are regarded as the two closest stations).
Using the trusty Haversine formula again I generated a 270 x 270 table showing the straight line distances between all 270 stations that comprise the Tube Challenge. As I'm interested in the actual distance I need to run, rather than distance as the crow flies, I added 15% onto each distance. In the late 90s transport companies would typically add on either 40% or 25% to the straight line path when estimating distances depending on whether the route modelled used the fastest roads or went for the shortest distance. I figure that being on foot gives even greater flexibility and indeed checking some random combinations with google maps the 15% turns out to be a pretty decent approximation.
I came up with 170 station pairs that were within 1km of one another. Removing stations on the same line, those on opposite sides of the Thames (15% doesn't seem enough to have added on in those cases), plus cases involving stations that count twice within the rules of the Tube Challenge (e.g., Hammersmith, Paddington) I was left with 47 stations.
The 10 geographically closest stations on the London Underground network, which are not on the same line, are:
My model gives the furthest separated stations as being Chesham and Upminster (fairly evident from this earlier work) with a 'running' distance of 71km. Checking some examples against Google Maps shows good agreement:
Looks good. I'll convert the distances obtained into estimated running times. On a treadmill I can do 5km in a little under 18 minutes, and 1km in a little over 3mins. In order to not die I'll probably be running somewhat slower than that on the streets of London so will adjust accordingly, plus I'll add on two minutes for getting out and back into the underground system.
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