Route choice in mountain navigation, Naismith's rule, and the equivalence of distance and climb

Abstract

In this paper, I consider decision making about routes in mountain navigation. In particular, I discuss Naismith's rule, a method of calculating journey times in mountainous terrain, and its use for route choice. The rule is essentially concerned with the equivalence, in terms of time duration, between climb or ascent and distance travelled. Naismith himself described a rule that is purported to be based on trigonometry and simple assumptions about rate of ascent; his rule with regard to hill-walking implies that 1 m of ascent is equivalent to 7.92 m of horizontal travel (1:7.92). The analysis of data on fell running records presented here supports Naismith's rule and it is recommended that male runners and walkers use a 1:8 equivalence ratio and females a 1:10 ratio. The present findings are contrasted with those based on the analysis of data relating to treadmill running experiments (1:3.3), and with those based on the analysis of times for a mountain road-relay (1:4.4). Analysis of cycling data suggests a similar rule (1:8.2) for cycling on mountainous roads and tracks.

Keywords:

• Naismith's rule
• regression analysis
• extreme values

Acknowledgements

I am grateful to the referees for their comments and suggestions, which greatly improved the paper. Thanks also go to Susan Harvey of HARVEY Maps for the digital reproduction of the section of the Lake District map used in Figure 1.