5.1.3 Switchbacks and critical slope

The straightforward implementation of effective slope results in small-scale zigzags, which are not realistic. Instead the cost of curves should be taken into account for least-cost calculations (Herzog 2013b).

When considering switchbacks, the concept of critical slope is important, i.e. the slope where progress in hairpin curves is more effective than directly ascending or descending the steep gradient (Llobera and Sluckin 2007). For walkers, the critical slope is at about 25% for both descending and ascending paths; this value is a compromise between speed and energy optimisation. This is a broad minimum, most of the gradients within the range of 15–40% are still fairly efficient (Minetti 1995). This limitation can be overcome by construction work, i.e. stairs or ladders.

Riding horses or pack animals require paths without stairs or ladders, and probably the critical slope relating to these animals is different. However, the differences in critical slope are only relevant if the animals are not able to follow the footpaths created by the people. But the critical slope of cart and wagon routes is below that of pedestrians. It is for this reason that in Sweden some of the old routes were substituted in the 17th century by new roads for wheeled traffic that were designed to avoid 'mean hills' (Mörner 2001, 267).