Train or Plane

21 April 2024

The other day, I embarked on a journey from my hometown of Aarhus in Denmark to Delft in the Netherlands, covering approximately 830 kilometers. Normally, I would have opted for air travel for such a trip, but this time I chose the railway due to recommendations and climate concerns.

As I prepared for my journey, a thought occurred to me: what about scalability and boundedness? If air travel was banned, could a railway theoretically accommodate the mobility needs of society? How long would it take to upgrade the railway infrastructure to match airway capacity in Europe? Would it even be feasible?

To put it another way, can the European railway infrastructure be adapted to meet the necessary mobility demands without relying on air travel? (see Note on Mobility below)

Travel can be viewed as nodes and edges in a graph or space. The capacity of such a graph would then depend on the number of edges between the nodes and the capacity of each edge to carry passengers. As passengers move in discrete quanta (a plane or a train) and not in a continual flow, we can break down the edge capacity into the number of passengers per quantum and the quanta per time unit. For the sake of simplicity, let's define the following:

Node or \(N\)

This represents a train station or an airport.

Edge or \(E\)

The transport line connecting two Travel Nodes, i.e. a railway track or a flight route between two airports.

Quantum or \(Q\)

This represents the unit of travel, i.e., a plane or a train. The size of the Quantum is the number of passengers in one unit.

Edge Capacity or \(C\)

This represent the number of Quantum per year for a given Edge. We'll assume that all Railway Edges has the same Capacity and ditto for the all the Airway Edges.

Now, let's examine the differences between a train graph and a plane graph. Train-space, in essence, is below two-dimensional as the number of edges is fixed, and each edge carries \(Q_T\) sequentially. In contrast, plane-space is almost three-dimensional, as each edge can accommodate multiple parallel \(Q_P\). Although planes operate within fixed airways, expanding those routes might be easier than upgrading tracks on the ground.

Another distinction lies in the nodes themselves: train-space features both minor and major nodes. To travel from major node \(N_1\) to major node \(N_2\) (\(N_1 \rightarrow N_2\)), you must pass through a sequence of minor nodes \(m_1, m_2, ..., m_N\). In contrast, plane-space consists only of major nodes. However, in both spaces, you may need to traverse multiple major nodes to reach your destination \(N_1 \xrightarrow{N_i,N_{i+1},...,N_{m}} N_2\).

The two differences influence the overall capacity of existing plane-space and train-space. The plane-space model is fundamentally more effective than the train-space due to these disparities.

What about the nodes themselves and their number of edges? Again, the plane-space wins the capacity tug-of-war. A node in train-space has a fixed number of edges, requiring significant infrastructure changes to expand. In contrast, airports are situated outside cities and have no fixed number of incoming/outgoing edges or, at least, their bound is much higher than that for train-space.

Lastly, when examining the quanta of both spaces, we favor the train-space. A \(Q_T\) can be easily expanded by adding more train cars to the train, as seen in long freight trains in the USA. Expanding \(Q_P\), however, will not scale as planes can't just be made bigger and bigger.

So, how will all this play out in the real world? It looks like the plane-space have a much higher capacity. This could be analysed by realising models based on the above, maybe using Agent Based Modelling --- or at least much more reasoning.

Going through Europe

As I mentioned earlier, I embarked on a journey from Aarhus to Delft, experiencing the current state of European railways firsthand. Initially, booking my ticket was straightforward - a few emails exchanged with a travel agency specializing in rail travel, and I had it secured. The specific ticket I purchased was significantly cheaper than a comparable plane ticket, which was great. Although the journey involved four transfers across Europe, and I had to pass by many small \(m_i\), I was optimistic about enjoying the comfort of long train rides as three of the five segments were between two and three hours, leaving ample time for work and leisure.

However, things started going awry from the first transfer in Germany. An error in the signal system between Berlin and Hamburg resulted in a two-hour delay in Hamburg, which meant I would miss my connecting train in Osnabrück. Luckily, Deutsche Bahn gave me a new itenerary and I continued toward Osnabrück. Unfortunately, when I arrived in Osnabrück, I missed my connection once again and now the DB ticket office had closed. This meant I could only get yet a new itenerary but not book any seatings. To make matters worse, the revised itinerary required an additional \(N_T\), but then I got to see The Hague.

As a result, instead of arriving mid-evening as planned, I arrived at midnight, having spent three hours longer than expected at various train stations. I had also visited six stations instead of the initially intended five.

While flight delays are common, the railways' ground bound complexity means that journeys require many more segments. I've never experienced more than two segments when flying within Europe, and this trip would have had only one if I'd taken a plane - except for a bus segment and train segment at the beginning and end. The issue is that railway travel in Europe has numerous components, or "cogs in the machine," and it seems those cogs are very much worn out. In Denmark, the railways' reliability has been very poor in recent years, with Germany's rail network facing similar issues – as I overhead some Germans talk about on a platform somewhere along the way. With many outdated components, it's no surprise that things go wrong, as they did on this journey. If my purpose were leisure, though, I might view this as an adventure, but for professional travel, it's unacceptable.

To make matters worse, none of the train stations I visited had amenities such as waiting areas, restaurants, or bars, on par with the standard in airports. Additionally, train stations offer little protection from the weather, making a cold spring day even more unpleasant.

So, to accommodate a greater number of travelers, we need a significant upgrade to our infrastructure: more tracks, more trains, better trains, larger stations, better stations, and longer hauls across Europe designed for the professional traveler.

A Look at the Statistics

In Denmark we have 300 million train passengers per year (BANE21), and 8 million of those (2.3%) cross Storebælt. The latter could be considered as a proxy for the number of journeys, that could have been done on a plane, i.e. non-local journeys.

According to Eurostat (rail_pa_typepas), 7,240 millions passengers are transported by train each year in EU. So, if we use the factor above, we get a number of 193 million non-local train passengers per year. This is probably completely wrong, but 🤷‍♂️

According to Eurostat, the number of air passengers in EU (ttr00012) amounts to 821 millions per year and we can now estimate that four times as many non-local passengers travel by air as by train.

The question now is whether the train-space in principle can accommodate 4 times its current capacity, and what would be needed to make this possible in practice? And would it scale into the future? Could Aarhus train station or Copenhagen train station quadruple the number of passengers?

To reach that number, new technology will probably not be necessary; there's still potential for expansion in Europe with existing technology, such as monorails and maglev trains—or just more and better regular trains. Hm, well, shouldn't they all be electrical trains for the climate agrument to be valid?

So, for this trip I took the train. If more and more people did that, the railway industry would probably grow accordingly. So, if we believe that our railway infrastructure can support the needed mobility, that would be good, that's what we should do.

On the other hand, if we realize that a train infrastructure cannot support the needed mobility, we would need to rely on air transportation. However, for a better climate and a better future for our society, we need to put pressure on the plane industry to shift towards more sustainable technology. Passengers can't do this by buying tickets; we need political pressure.

In my view, we must continue to use air transportation, which off course should be a more climate-friendly technology. This is forthcoming, but will it arrive in time? Should we stop flying until this technology becomes available, and literally wait at home while only using trains for essential journeys (which would result in no upgrade of the railway infrastructure)? It would be ideal if there were ground-based travel options that could accommodate non-leisure trips, but achieving this would require an enormous effort, which itself might be climate problematic and only relevant, if we could model a scenario in which the railways could support the needed mobility.

In Conclusion

The european railways are not acceptable for long distance profesional travels. They might work for leisure travels, where you don't expect to work and you're in no hurry or if you can use very specific intercity routes with few Nodes. So, from now on I either stay at home (bad for society and the future) or go by plane (bad for society and the future).

Before we invest huge amounts on modernizing the European railways, I would argue that we need to see models of the feasibility of those modernized railways and stations' ability to carry enough passengers before we should vote for such a solution. Maybe they already exists, and if I ever stumple upon some, I'll update this conclusion 😉

A Note on Mobility

To move forward with society and civilization, we must not require a less mobile society. We live by interactions and communications and to move forward as a society, we need more mobility and not less and we need face to face interactions.

In my view, this is not the same as the exponential growth of capitalism and is not in oppsition to e.g., the donut-economy. I'm focusing on scientific and social growth and development that does not have to be accelerating — it must just not come to a halt.

So, while this cannot be disjointed from the economy, I hope we can have growth without sacrificing the near future and we need growth to have a far future.

References

BANE21: Rail transport of passengers by unit and type of transport BANE21, DST

Passenger transport by type of transport (detailed reporting only) doi.org/10.2908/RAIL_PA_TYPEPAS

Air transport of passengers by country (yearly data)doi.org/10.2908/TTR00012

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