Using ArcMap 10.2, I'm trying to calculate the path distance around some archaeological sites and later the least cost path to the nearest water source. I'm interested to see how far the site's inhabitants could have walked in a given time. In the path-distance tool, there is an option to add a horizontal and/or vertical factor for a more accurate cost of travel time on different terrains and slopes.Most of the area is comfortable to walk so I don't want a complicated surface factor, only to add one area of increased time-cost because of sand dunes. I managed to add the cost of the slope as the vertical factor using Tobler's (1993) method, but can't find how to determine the relative increase in time-cost of walking on sand, as the horizontal factor. I only found a paper discussing the increase in energetic cost: http://jeb.biologists.org/content/jexbio/201/13/2071.full.pdf According to the authors, the cost of walking on sand is 2.1-2.7 times more energy consuming than walking on a hard surface (at the same speed). So far I haven't tried to add a cost for the sandy areas because I don't know what the factor should be. or put another way, I don't know how much more time it would realistically take to cross a sandy cell, compared to a non-sandy cell.
Does anyone have an idea how to calculate the difference in time, if say, the energy was the same?
Does anyone know of previous publications where this is mentioned?