A simple physics-based model to describe incline walking applied to least-cost path analysis

In recent years, the principle of least-cost path (LCP) analysis has increasingly been applied to reconstruct the trajectory of ancient roads. In this paper, we focus on the most frequently used input for LCP modelling, the calculation of walking speeds on an inclined surface. Currently, a limited number of empirically derived incline walking cost functions are being applied to calculate LCPs based on digital elevation models. Here, we introduce a simple, physics-based analysis of walking speed on an inclined surface as a function of a limited number of physical parameters that we argue are better suited for modelling walking on an inclined surface. This function shows that the additional travel time for incline walking is solely determined by the height to be conquered and is independent of the exact incline slope, resulting in different LCP models when compared to empirically derived functions. We also extend the approach to model movement speed for carts pulled by horses or oxen. This model is easily implemented in GRASS GIS and applied in a small study area in the Netherlands.