An empirical basis for route choice in cycling

Abstract

We used data from international cycle stage races to examine a rule for cyclists that is similar to Naismith's rule. Naismith's rule is used by walkers to estimate travel times for routes involving climb (i.e. the vertical distance component of a route). The rule is also used in route choice decision-making to compare differing, competing routes. We developed such a rule for use in cycling events, and also considered an extension of the climb-distance rule to take account of the effect of type of terrain or rideability. A simple analysis of the data suggests that 1 m of vertical travel on a bicycle can be considered to be equivalent to approximately 8 m of horizontal travel. Thus the equivalent distance of a route may be calculated by taking its horizontal distance component and adding eight times its vertical distance component. The result obtained was shown to be in accord with mathematical models that relate cycling power to speed and gradient. An index that considers the effect of terrain is also reported, and incorporated into an equivalent distance model. Tentative values for the terrain or rideability index are suggested, and we argue that a distance of 1 km over good off-road terrain is equivalent to a distance of 2 km on-road, and that a distance of 1 km over poor off-road terrain is equivalent to a distance of 4 km on-road.

Keywords:

• Cycling
• Naismith's rule
• navigation
• regression

Acknowledgements

Special thanks to Edward Rhodes and David Dealtree who spent a cold day in the Peak District to help collect data, and to the anonymous referees for their helpful suggestions for improvement of the paper.