Do cities sit where moving around costs the least energy?

Anyone who has cycled up a hill knows that distance is only half of the story. A kilometre uphill costs a lot more than a flat one. Cities are built on real terrain, with real hills, valleys, rivers and coastlines. So we wondered whether the shape of a city reflects the energy it takes to move through it.

That is the question behind our new preprint, Mobility energetic balance frames spatial configuration of cities, written with Enrique Cano-Suñén, Ana Ruiz-Varona and José Javier Ramasco.

The idea: move the city, keep everything else

You can’t rebuild a city somewhere else to see what happens, but you can do it on a computer. For each city we take three ingredients:

• the road network, from OpenStreetMap;
• the terrain, from a digital elevation model;
• the travel demand, meaning who goes where, estimated as origin–destination flows from geolocated social-media records.

We then pick the road network up and put it back down on the same landscape in a slightly different position. We shift it by up to a few kilometres, rotate it by up to 40°, or stretch it along one axis. The travel demand stays the same; only the layout’s relationship with the terrain changes. If the real city is “well placed”, most of these alternatives should cost more energy to move around in.

A deliberately simple energy measure

We don’t try to model every engine and every traffic light. For each trip along the network, the energy has two parts:

\[E_{\text{trip}} \;\approx\; \underbrace{\alpha \, L}_{\text{horizontal}} \;+\; \underbrace{m\,g\,\Delta h^{+}}_{\text{climbing}}\]

where $L$ is the route length and $\Delta h^{+}$ is the total uphill elevation gained along the way. Going downhill afterwards doesn’t give the energy back. The constants correspond to a typical private car. The point isn’t the absolute number. It’s a fair, comparable yardstick between the real city and its displaced copies.

Routes are chosen by shortest path, not by lowest energy, so the result isn’t baked into the routing.

What we found

We looked at 56 cities in Europe, the Americas, Asia and Oceania, using functional urban areas, which include the commuting zone and not just the historic core.

• In 26 cities the real layout is the lowest-energy option among all the alternatives we tested.
• In 4 cities a slightly displaced layout would be cheaper, and only by about 0.5–2.5%.
• The remaining cities are constrained: coastlines, lakes or the edges of the data rule out most displacements, so the comparison isn’t meaningful.

The exceptions are the interesting part. In Bogotá the “cheaper” shift pushes the city west onto the floodplain of the Bogotá River. In Bandung it moves toward volcanic highlands. In Buenos Aires and Brussels it runs into a delta and into large railway and logistics infrastructure. In other words, the terrain-energy argument still holds, but other constraints win.

The climbing effort is also very unequal. Roughly 10% of street segments carry more than 60% of all the uphill work. A handful of steep, busy corridors take most of the cost of a city’s topography.

Why it matters for planning

This doesn’t prove that cities are “optimal”, and it says nothing directly about how each city grew historically. What it does show is a measurable, consistent link between topography and urban organisation. That fits a picture where streets, mobility and terrain have adapted to each other over time.

There’s also a practical angle. In a test on Barcelona we placed 25,000 new residents at five candidate sites with similar horizontal distances. The extra daily movement energy differed by about 20% between the best and the worst site, and almost all of the difference came from climbing. When cities plan growth or densification, terrain-related movement costs are worth putting on the table next to distance.

Limitations

Social-media data over-represent some groups. The energy model is car-based. African cities are missing for lack of data. The results depend on how the urban area is defined, and administrative boundaries give a noticeably different picture than functional urban areas. All of this is discussed in the paper.

📄 Read the preprint: arXiv:2610.21558