# Calculating cost, in time, of walking on sand with ArcMap?

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?

• In the network dataset, add field e.g (time_sand) and define it as time with multiple by the factor you have. – Moh Mar 29 '18 at 12:03
• What have you tried? Please edit the question to specify the exact software in use, tell us what value you chose, how you attempted to mask it into the cost surfaces, and what problem you encountered. Please take the Tour to better understand how the GIS SE "Focused question / Best answer" model operates. – Vince Mar 29 '18 at 12:04
• "I don't know how much more time it would realistically take to cross a sandy cell" It sounds like all you need to do is find a beach or a playground and time yourself walking over sand. – Dan C Apr 3 '18 at 20:10

If the assumed rate of walk were, say, 7 kilometers per hour (kph), then a traveller would be able to walk up to 7 kilometers in one hour. Dependent on the units of your gis layer, you would then need to determine the length of time it takes to cross one unit of your layer. I am going to infer that unit is meters because it seems like you were going to use this equation for local analysis. Using the logic above,
1 hour = 3600 seconds
7 kilometers = 7000 meters
3600 seconds / 7000 meters = .51428 seconds to travel one meter
this becomes the cost to travel one unit.

All following input layers like slope or walking on sand become modifiers to the original cost. If, for instance, you decided to use 2.1 as the modifier for walking on sand, then the resulting pixel that you modify will be 1.08; or 2.7 would be 1.38857.

An arbitrary slope value of 20 degrees, might cost the traveller 1.8, which would then by used to modify the previous analysis by multiplying it by 1.8

Travel on sand factor of x: cost * slope factor = new cost
2.1: 1.08 * 1.8 = 1.944
2.7: 1.38857 * 1.8 = 2.49942

As described, these are the basic principles of creating a cost layer. It is also important to note that ArcGIS automatically factors in the ~1.44 for travelling diagonally. The resulting cost distance layer will calculate how far (in time) a traveller could travel in a specified amount of time. The tool cost path could be used to derive the least cost path between two defined points (one of which would be the point of origin used to when building the cost distance analysis). Corridor Analysis could be used to derive a general corridor from two points by running cost distance on both points and then adding the results together.

• Does ArcGIS account for the raster cell size when calculating travel cost? In the example we assign 0.51425 seconds per meter for basic, unimpeded travel. Let's Consider the underlying raster is 20m x 20m pixel size. Would ArcGIS apply the 0.51425 for travel time straight across the entire cell? Or would they factor in the cell size? – toferkey Apr 15 '19 at 18:48
• I found in the "Path Distance" tool help section, that they do in fact account for cell size resolution and it's based on map units. Thank you. – toferkey Apr 15 '19 at 19:14