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metropatakt, part 2

Metropatakt – how does it work?

How can we apply the concepts and techniques of integrated clock-face timetabling to Metropa’s proposal/vision of the European Railway Network? What steps are needed?

Step 1: Define the base frequency

The main characteristic of a clock-face timetable is that is cyclically repeats itself. On all lines, at least one train will run per cycle time. On certain lines, trains can run more often, as long as the number of trains per cycle time is an integer. For Metropatakt, the proposed base frequency is 120 minutes, one train every 2nd hour. This is already the standard frequency used for most Eurocity lines in Europe. On sections where 2 lines run in parallel, the frequency can be doubled to a train every hour. It is also possible to reach this on sections with only 1 line but with high demand, by adding extra trains that run on only a part of the whole line.

Step 2: Define the moment of symmetry

In a timetable where there is a train once per 120 minutes on every line, trains in opposite direction will meet each other exactly every 60 minutes. To ensure that optimised transfer times work out as planned in all directions, it is crucial that the timetable is such that opposite trains on all lines meet each other at the same moment. This characteristic of each repetitive regular timetable is called the ‘moment/minute of symmetry’. The standard practice in most European railways today is to have a symmetry minute of 00, meaning that trains in opposite directions meet each other once per hour exactly on the full hour. Metropatakt will following this.

Wikipedia provides good background information on this topic:

Step 3: Define the line scheme

A important property of a clock-face timetable is that all trains run along a defined set of routes or lines. For Metropatakt, this step seems to be very easy to solve. Metropa saw the light as a schema of lines, before anything else. But the line scheme of Metropa, although visually very attractive and a great source of inspiration and imagination, has some practical drawbacks when using it as the basis for a pan-European integrated timetable. There are several locations where the routes of the Metropa lines take a suboptimal route considering the geographical reality. Also the presence of ring lines and several branches or sub-lines makes the timetabling more complex than needed.

A later post will be specifically dedicated to this topic and present an alternative line scheme that is better suited to realise an integrated clock-face timetable.

Step 4: Define the travel time between nodes

As described at step 2, with a base frequency of 120 minutes, trains on opposite directions will meet each other every hour on the full hour. It is therefore attractive to plan the timetable such that on those stations were 2 or more lines meet, trains from all directions will arrive a few minutes before the full hour and leave that note a few minutes later. In this way, passengers can change from their arriving Metropatakt train to any other Metropatakt line with a short transfer time. To achieve this at several transfer hubs, the gross travel time (including a few minutes for transfers) between those hubs must be a multiple of full hours. On those parts of the network where combined lines run every hour, the gross travel time between hubs may also be a multiple of half hours, as opposite trains will meet every 30 minutes.

Step 5: What is a realistic speed?

To choose a desired number of full or half hour as travel time between hubs, a balance must be found between ambition and realism. When taking the straight line distance between cities, average travel speeds above 200 km/h are very hard to realise. The Thalys high speed trains from Paris to Brussels, which run at 300 km/h most of the distance, need 82 minutes to cover a straight line distance of 264 km, which is an average speed of 193 km/h. The significant difference between top speed and average speed is caused by two factors. First, the distance along the railway track is always longer than the straight line distance and secondly, time is lost when the train drives slower inside cities when leaving and approaching the station. Average straight line speeds close to 200 km/h are only realistic between big cities where the demand justifies construction of dedicated lines for at least 300 km/h and where there is relatively flat terrain that allows building railways in a straight line.

On many parts of the network, average speeds up to 150 km/h are more feasible. On some sections which more complex terrain and less demand, an average straight line speed of around 100 km/h will still be acceptable. With such a speed, the train is still very competitive against private cars, which on highways will almost never have an average straight line speed above 80 km/h. It will still be significantly faster than today on most relations. The ICE high speed train between Frankfurt and München today needs 3h23 (203 minutes). For a straight line distance of 305 km, this brings the average speed to only 90 km/h. The travel time by car on empty roads for the same relation is 3h49 minutes, 80 km/h on average.

Step 6: Metropatakt

Following these steps, sometimes performed iteratively, a timetable can be devised for Metropatakt. This timetable offers smooth long distance train travel on the European continent. Not all relations can be offered with direct lines, but an integrated clock-face timetable ensures that if you need to transfer from one line to another, the waiting time will be short. In most cases, your connecting train will arrive to the transfer station at the same time as your original train and they will depart at the same time a few minutes later. With this, travelling by train across Europe will feel like travelling by metro in a big city, exactly like the vision evoked by the Metropa map.

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