How much longer do you have to drive than the crow has to fly?

Abstract

When traveling by car from one location to another, our route is constrained by the road network. The network distance between the two locations is generally longer than the geodetic distance as the crow flies. We report a systematic relation between the statistical properties of these two distances. Empirically, we find a robust scaling between network and geodetic distance distributions for a variety of large motorway networks. A simple consequence is that we typically have to drive $1.3\pm0.1$ times longer than the crow flies. This scaling is not present in standard random networks; rather, it requires non-random adjacency. We develop a set of rules to build a realistic motorway network, also consistent with the above scaling. We hypothesize that the scaling reflects a compromise between two societal needs: high efficiency and accessibility on the one hand, and limitation of costs and other burdens on the other.