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metropatakt #03 – optimise the line scheme

Aktualisiert: vor 3 Tagen


metropatakt Teil 3 – Optimierung  des Linienschemas (text in DE)


As explained in the previous blog post, one of the steps required when designing an integrated clock-face timetable is to define the line scheme. Wouldn’t it be most logical to simply take the line scheme that is the defining visual image of Metropa?


Properties of the Metropa line scheme

The main goal of the original Metropa line scheme figure is to express an emotional vision. A vision in which the entirety of Europe is covered by a metro-like transport system, interconnecting all citizens and regions without borders. The line scheme that is on the Metropa figure is ‘imaginary’ in the literal sense, it is in the first place an image. An image that evokes and amplifies the vision of Metropa.


This text elaborates the concept of a cross-continental line scheme on a technical-theoretical level. Although visually attractive, the original Metropa line scheme has some properties that pose practical difficulties when using it as the basis to plan a pan-European integrated timetable. The goal here is to define a refined version of the line scheme that works as the basis of an integrated clock-face timetable. The outcome is just another representation of a cross-continental line scheme. One which is less of an ‘image’ and a little bit more of a technical plan, while still quite some steps away from realistic implementation.


Ring lines

Ring lines are not really attractive on the geographical scale of the European continent. They work fine in the public transport network inside a city, which station spacing of 500 m to 1000 m. But the ratio between time gained on saved transfers vs. time lost on additional detour kilometres doesn't work out so nicely on the bigger scale. On a city scale, the travel time between 2 stations is between 1 and 2 minutes and the time lost when changing to another line is somewhere between 3 and 6 minutes. On average, it is worth to travel an extra distance of about 3 stations to save one transfer to another line. On the continent scale, the travel time between two stations will be between 1 and 2 hours, while the integrated timetable aims to achieve that the time lost when changing to another line will be between 15 and 30 minutes. With these parameters, taking a ring line via a longer route to save a transfer will make your travel significantly longer.


Missing links

Some links that are already today served by high-speed long distance trains are not present on the original Metropa map. Some examples include: Berlin - Nürnberg, Paris - Stuttgart, Amsterdam – Köln and Bordeaux - Basque Country (Bilbao / Hendaye).


Alignment to geography

There are some locations where the network has a structure that includes links over difficult geography instead of the geographically more obvious alternatives.

Some example of sub-optimal links include: Paris - Milano via Genève, whereas the more logical route goes via Lyon and the Mont Cenis base tunnel; Warszawa - Budapest via Krakow, whereas the more logical route goes via the Moravian Gate and Bratislava and Frankfurt - Zürich via Stuttgart, whereas the more logical route goes via the Upper Rhine valley and Basel.

Another example is the link between Pescara and Split, carrying the Med and Pan lines. This link crosses the Adriatic See as its widest place, more than 200km. The more logical route between Roma and Athina would go via Puglia and have a much shorter crossing (90km) to southern Albania.


How to refine the line scheme?

A refined line scheme is proposed as the basis of the integrated clock-face timetable of Metropatakt. The core principles remain the same: A network of lines that cross the entirety of the European continent, provide transfer to each other at key locations and connect all of Europe’s important cities.


Following Europe’s main geographical features

To allow long journeys with few changes, it helps to have lines that cross Europe from one end to the other. To accommodate this, the lines will be oriented in the same direction as the defining geographical features of Europe. In this way, almost straight lines can be drawn from Scandinavia to the Iberian peninsula, from the north of the British Isles to the south of the Italian peninsula, and from the Atlantic coast to the Black Sea. The lines will follow the main features of Europe’s geography, crossing the main bodies of water and mountain ranges at the most convenient locations.


Combining to a triangle-based grid network

To ensure an optimal coverage of the whole continent, the long lines are combined into a grid. The grid will have 3 axes of orientation in accordance with the continent’s geography:



Axis 1: Northeast - Southwest (roughly 30° - 210°)

Axis 2: Northwest - Southeast (roughly 330° - 120°).

Axis 3: West - East (roughly 270° - 90°).


When drawing several parallel lines along these 3 axes, a grid will emerge which encloses a set of triangles. The grid will be shaped such that the lines in the different directions cross each other at Europe’s important cities.

A triangle-based grid with 3 axes has the advantage that the detour between two nodes that are not on the same line is considerably shorter than on a square-based grid with only 2 axes with the same number of lines.




Figure: Detour between to points in a square-based grid vs. a triangle-based grid


Connect big and middle-sized cities

To ensure that as much Europeans as possible can profit from access to the Metropa(takt) network, it should serve as many cities as possible. But at the same time, long-distance trains should not stop at every small town, as this would slow them down too much. As a rough guidance, cities that have an urban area population of at least half a million are considered to be big enough to be served by the Metropa(takt) network. In parts of Europe where such cities are scarce, train will also stop at somewhat smaller cities, to ensure sufficient access to the network.



The refined line scheme for Metropatakt

Following the steps described above, a refined version of the line scheme is drawn on the map of the European continent. It consist of 27 lines following the 3 axes of orientation with the lower numbers representing the main corridors and higher numbers forming supporting corridors that refine the grid. Together, these lines form a network that connects 250 cities across the European continent. It reflects the same visionary dream that is evoked by the original Metropa map while being one step closer to what is possible when it comes to real implementation.






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Nico Huurman
Nico Huurman
04 jul 2023

Please note: The figure of the refined line scheme has now been replaced with a high-resolution version.

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