Well, given my experience hiking (which includes multiple trips to the Grand Canyon) hiking down and hiking up take the same amount of time, just different muscles get sore. 
But I see your issue now. You need some kind of directional slope. That's beyond me.
Jerry
---- Original message ----
Date: Thu, 1 Feb 2007 10:53:48 +0100
From: "Miguel Correia" <miguellage.rc@gmail.com>
Subject: Re: [GRASS-user] negative slope values and movement costs
To: grassuser@grass.itc.itThis is my problem:
I want to estimate off-path travelling with Tobler's
hiking function. This function says that, for
example, in a slope value of 10º the travelling
velocity is 3Km/hr and in a slope value of -10º the
velocity is 4km/hr. This generates a friction
surface, in which the cost value is the cost of
traversing that cell in Km/hr. Then, through
r.mapcalc I divide the distance (cell resolution) by
this friction surface to generate another friction
surface with the corresponding time values.
The aim of all this is to generate an accumulative
cost surface (using r.cost with –k flag) from a
given point and then get the isochrones (of 1 hour,
2 hours, etc.).
The problem is that the function needs negative
slope values if the hiker goes downhill or positive
values is the hiker goes uphill. Has you might
imagine, If the slope surface only have positive
values is the same that hiker would always go uphill
and never downhill!Miguel.
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Gerald Nelson
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