I'm struggling with the announcement, published in the latest issue of RAIL Magazine (No. 675 July 27th 2011), that Thameslink is intending to introduce Automatic Train Operation (ATO) on their core section, using the European Train Control System (ETCS), and to get up to 30 trains per hour per direction with it. I'm wondering how they will do it. RAIL reports that they will have station "dwell" times of 45 seconds and they are allowing 30s to arrive and depart, to give what we call a "platform re-occupation time" of 75s. This is, to be kind, very ambitious. In reality, it's a bit of a spin and, if they are think they will ever get 30 trains per hour, they are not being realistic. Let's look at why.
First, we must make some assumptions. We know the trains will be 12-cars long - that's 240m; and I doubt they will approach any of the inner area stations on the route at more than 35 mph, although some approaches might be less.
In considering the train's braking, we have to allow for rail conditions. On metros that use ATO in tunnels, where the rails are dry, they can get a brake rate of 1m/s² but we have to allow for wet rails, so lets say 0.65m/s², to be safe.
Now, when calculating train throughput, you have to assume that all trains will run under clear signals. If they don't, the service will slow down. This means that the train approaching the station must not be shown a red or yellow signal, or the equivalent speed reduction command on the ATO system. To ensure this, the rear of the train in front must be completely clear of the platform and of the starting signal, plus a safety distance, which in ATO circles is usually 50m.
In looking at how we do the calculations, a diagram might help. It looks like this:
Now, the maths. Our basic parameters are as follows:
Maximum train speed = 35 mph or 15.6m/s;
Train and platform length = 240m;
Signal safety margin 50m;
ATO brake deceleration rate = 0.65m/s²;
ATO brake distance (35mph to 0mph) = 188m;
Train acceleration rate = 0.9m/s² (generous but we can assume Thameslink will buy a powerful train);
ATO response time = 3s.
The calculation for the distance the train travels for platform re-occupation is:
188m (the home signal approach distance) + 50m safety margin at 35 mph; then the platform: 52m at 35 mph plus 188m braking to the stop. Then, looking at the rear of the train, it starts and accelerates up to 35 mph. This takes 136m. The rear has to clear the rest of the platform (104m) and the Starting signal margin (50m) to clear the way for the following train which must be 188m on the approach to the home signal.
The time it takes to cover all this is (188m + 50m margin + 52m platform entrance @ 35mph = 18.6s) + (188m braking into station = 12s) + (136m acceleration to 35mph = 17.4s) + (the 104m remaining of the platform + 50m margin = 9.8s) to give a total of 57.8s. Then we have to add in the standing time in the platform (the dwell) of 45s as suggested by Thameslink. This gives a total of 102.8 seconds between trains. I've added 3s as an allowance for the ATO kit to respond to the signals and this gives 105.8 seconds. I cannot decipher where Thameslink got 75s from.
Wonderful, you say. This is equivalent to 34 trains per hour! Plenty of room for more trains then. Well, no. It's not as simple as that. It never is, is it? We have assumed that every train will arrive at the first home signal braking point at exactly at the moment the previous train has cleared the starting signal margin, but it never happens like that, as any commuter will tell you. With trains coming into the central section of Thameslink from all over South East England, the chances of geting that sort of punctuality are zero. A sensible, experienced operator will tell you that you should allow a large margin - at least 30% has been suggested by the UIC (the European-based Union of Railways). This allows for time to change routes, variations in station stop time, higher speeds on outer sections of line, small variations in performance and minor delays.
The 30% operating margin will reduce our throughput to roundly 23 trains per hour. Much more sensible and much more like what we will get. Operators could do that, if they are on their toes and there aren't too many PIOTs (Passengers Ill On Train) incidents during the morning rush hour.
To go back to the Thameslink spin and their 75 seconds (I'm not sure where this figure came from but it must have been a rather grubby envelope), the problem is that it attempts to describe what's called the "signalled headway", not the "operating headway". The signalled headway is the technical stuff we have calculated here but the operating headway includes the 30% margin and shows how frequently trains could actually operate. They are quite different, as we can see.