5.1 Slope

Table 1 shows the overwhelming importance of the slope cost component in archaeological LCP studies, and so it seems vital to identify appropriate cost models depending on slope.

Several concepts of measuring slope can be found in publications, mainly slope in (tangent) per cent and slope in degrees or radians, but also mathematical slope, i.e. rise over run (Smith et al. 2007, 18). Confusion of these concepts can be found in some archaeological publications dealing with cost functions, and obviously, the LCPs generated on the basis of these cost functions often fail to reconstruct the ancient routes. For Tobler's (1993) slope-dependent cost function in particular, which is based on mathematical slope, the wrong slope concept was published several times: van Leusen (2002, chapter 6, 6) claims that s is slope in degrees; Conolly and Lake (2006, 219) copy this mistake from van Leusen. Kondo (2008) also presents the formula for the Tobler hiking function with slope in degrees but converts it to radians. Wheatley and Gillings (2002, 155) as well as Batten (2007) present the Tobler formula and refer to per cent slope.