Euclidean versus network distance

An important distinction runs through every accessibility study:

• impedance in Euclidean space, as the crow flies
• impedance over a network, along roads, paths, tracks or waterways

The GeoDMS can compute both, but networks are used wherever realism matters.

Why the difference is not a constant

The route from a dwelling to a facility is rarely a straight line. The ratio between network distance and straight line distance, the detour factor, is often quoted as roughly 1.2 to 1.4 for dense urban road networks, but treating it as a constant is exactly where Euclidean approximations go wrong.

The discrepancy is largest precisely where it matters most.

• Barriers. Water that can only be crossed by a bridge, a railway line with few crossings, a motorway acting as a wall. Two dwellings 200 m apart across a canal may be 2 km apart on foot.
• Network sparsity. In rural areas with few roads, detour factors are both larger and far more variable.
• Mode differences. A pedestrian may cross a park a car must drive around, and a car may use a motorway a cyclist cannot enter. Euclidean distance is mode blind by construction.
• Directionality. One way streets, turn restrictions and tidal flow make $d_{ij} \neq d_{ji}$, something Euclidean distance can never represent.

Because the error is systematic rather than random, it does not cancel out when averaged over a region. It biases results against exactly the neighbourhoods that are cut off by barriers.

When Euclidean distance is still defensible

• As a pre filter: select candidate destinations within a generous straight line radius before running network routing, which can cut computation by orders of magnitude. Choose the radius from the maximum plausible detour factor, not the average one.
• For very coarse regional comparisons where the network is dense and homogeneous.
• Where no network data exists for the area or the mode.

In the last case, report it as a limitation rather than a method.

Related

• Travel impedance
• Network data sources
• Zoning and spatial units, a second source of distance error, independent of this one