Last weekend was Open House, a fantastic chance to check out some amazing buildings and sites around London. Visiting Farringdon’s future Crossrail station, however, reminded me of a worrying thought I’d had some years prior:

Crossrail, vaunted as the solution to all London’s problems, isn’t being built with enough escalators in each station. And we’re really going to regret that in years to come.

Surely my non-technical opinion is irrelevant, you would hope, because this has all been worked out by proper transport planners and engineers, people will degrees, and more than my B in Maths at GCSE. Sadly experience teaches us that this isn’t always the case. The Victoria Line is a good example: escalators were taken out of the plans as part of cost-saving efforts ahead of construction.

More recently there are the shortcomings at points on the Jubilee Line. At Canada Water, the two escalators from Jubilee to East London Line proved to be vastly fewer than needed. At North Greenwich, the station closed a mere six years after opening for the addition of another escalator “to meet demand from development on the peninsula” – development that was entirely predictable and was indeed one of the main reasons the station was being built in the first place

My point is, TfL does get these things wrong, either through cock-up, or through a need to deliver something to a budget. So, how many escalators should you have in a Crossrail station? Time to do some maths!

In 2002, academics at the Indian Institute of Management and the LSE conducted a study on escalator capacity. Behaviours can change capacity (see Holborn’s foolish experiments with banning walking on the left), but basically, on the London Underground, you can move 110 people per minute (ppm) on one standard escalator: that’s 6600 per hour.

The shiny nine car class 345 trains ordered for Crossrail have a capacity of 1500 people. Crucially, the platforms have been built long enough to extend this to 11 cars, for a potential capacity per train of around 1,800. Crossrail is planning for 24 trains per hour (tph), but the line was designed for 30 tph to be possible. Once those changes are brought into use, and with trains in two directions, that gives us a maximum number of people passing through a central Crossrail station at peak time of 108,000.

It’s not likely that everyone is not going to get off every train at one station except in an emergency. But at peak times, the idea that half the passengers on a train might get off at key stations – Liverpool Street, say – does not seem unreasonable. After all, from the east this service replaces the Shenfield metro, so many people will have commutes planned around alighting at that station; and from the west, Crossrail will be far the fastest and most pleasant route into the City.

With half the potential capacity alighting at Liverpool Street - some 54,000 passengers per hour - you would require eight up escalators to remove the arriving passengers from the platform at the rate they arrive. That’s before you’ve provided any down capacity, which will also be in high demand from passengers arriving from mainline services wanting to get to the West End and Canary Wharf.

So how many escalators does Crossrail have planned for its Liverpool Street station? It appears to be six. Six is the number of escalators the Victoria Line’s planners put in to serve Victoria Station, which became inadequate in the 1990s, and where TfL ending up spending £700m on a painful project to add three more.

It’s also three fewer than the nine that serve the Central Line at Liverpool Street – a line with a total capacity of slightly more than half that of Crossrail. If nine is what’s needed for the Central Line at Liverpool Street, and the Victoria Line at Victoria, scaling up to Crossrail’s foreseeable passenger capacity would suggest a potential requirement of 16.

And then there’s maintenance. As everyone who has regularly used a tube station knows, three escalators being present does not mean three escalators will be available. Every ten years or so, they close them off one at a time for maintenance that seems to take between six months and a year.

Perhaps this is all nonsense; perhaps they have got it right this time. But I fear that, a decade or two from now, when those same engineers start costing up the remarkably expensive “Liverpool Street Crossrail Platform Access Enhancement Project”, I’ll have a moment of schadenfreude, which I can enjoy for a few minutes as I queue to get off the platform.

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