# Path Distance Allocation - confirmation needed

Discussion created by nicueber on Nov 27, 2013
After thinking twice in a slightly wrong direction I kindly ask you for some feedback if this time I'm on the right track.

I'm doing a path distance allocation analysis in ArcGIS 10.1 inside the model builder.
My cost layer represents travel time in minutes per km, the features are health centers as a point layer. The surface is given with a DEM. All in a 90x90m resolution. Because I base my analysis on travel time by foot in a hilly terrain I added a vertical factor table based on Tobler's function. (I calculated in excel the speeds for each 0.25 degree slope and then the factor by dividing the speed at 0 degree slope by the speed for each row. The 0.25 degree steps with the according factor are now in the vertical factor table.) As a vertical raster I've set the DEM again,

Does this sound plausible to you?

In this context: Did anyone tried Tobler's function in Excel yet? I found different sources, one saying you should take the slope in hundredth of percents, Tobler himself said the slope is the tangens of the angle. I calculated this in Excel with =6*EXP(1)^(-3,5*(ABS(S+0,05))) Where S is the slope =TAN(ALPHA*PI()/180) (ALPHA being the angle). Maybe someone can clarify this for me.

And another question in the path distance context: How can the distance layer be read? I get results up to 314524 (with the vertical factor), only up to 191149 without the vertical factor. Using a road network the maximum distance to a health center is about 15km, 10km in straight line distance. So what does this distance in the distance layer tell me?