The physical attributes of space, such as the topography, influence the route selection process since they impose a variable friction on movements. Consequently, a route between two locations (1 and 3, but also using intermediate location 2) may use a path that is not necessarily the most direct, but less costly to build and operate. The detour index (direct distance divided by transport distance) illustrates the importance of physical constraints on route selection.
|Route||Direct Distance (1-2-3)||Transport Distance||Detour Index|
|a||20 km||20 km||1.0|
|b||20 km||25 km||0.8|
|c||20 km||30 km||0.666|
Route (a) is the shortest in terms of distance, but not necessarily the least expensive in terms of construction and operating costs. Route (b) represents an attempt to reduce costs, and this is at the expense of a direct path. From a rational viewpoint, route (c) will be the one used to link locations 1 and 3. It offers a compromise between the lost distance (a higher detour) and the supplementary construction costs imposed by higher elevations.