Road network distances and detours in Europe: Radial profiles and city size effects

The form and the size of cities influence their social, economic and environmental outcomes. The form of a city is itself influenced by the shape of its road network, but this relationship and how it is affected by city size are unclear. We analyse how road distances to the main centre vary across 300 European cities and how radial physical detours (i.e. the distance on the road network compared to the Euclidean distance) are affected by city size and extent. We use landuse and population data to sample potential residences and compute the fastest routes to the main centre. We find a linear relationship between road and Euclidean distances, and for the first time document an average radial physical detour of 1.343 across Europe. We then rescale distance bands so to make cities of different population size comparable and show the effect of different urban delineations. We find that physical detour ratios increase when core cities only are considered without suburbs. At the urban region scale, radial physical detours increase with city size, especially when other significant geographical factors (latitude, longitude, elevation change and proximity to coast) are controlled for. When the central part of cities only is considered, larger cities have smaller radial physical detours.