## NAME

r.walk

## DESCRIPTION

r.walk outputs a raster map layer showing the lowest cumulative cost of moving between each cell and the user-specified starting points. It uses an input elevation raster map layer whose cell category values represent elevation, combined with a second input raster map layer whose cell values represent friction costs. This function is similar to r.cost, but in addiction to a friction map, it considers an anisotropic travel time due to the different walking speed associated with downhill and uphill movements.

The formula from Aitken 1977/Langmuir 1984 (based on Naismith's rule for walking times) has been used to estimate the cost parameters of specific slope intervals:

T= [(a)*(Delta S)] + [(b)*(Delta H uphill)] + [(c)*(Delta H moderate downhill)] + [(d)*(Delta H steep downhill)]

where:
T is time of movement in seconds,
Delta S is the distance covered in meters,
Delta H is the altitude difference in meter.

The a, b, c, d parameters take in account movement speed in the different conditions and are linked to:

- a: underfoot condition (a=1/walking_speed)
- b: underfoot condition and cost associated to movement uphill
- c: underfoot condition and cost associated to movement moderate downhill
- d: underfoot condition and cost associated to movement steep downhill
It has been proved that moving downhill is favourable up to a specific slope value threshold, after that it becomes unfavourable. The default slope value threshold (slope factor) is -0.2125, corresponding to tan(-12), calibrated on human behaviour (>5 and <12 degrees: moderate downhill; >12 degrees: steep downhill). The default values for a, b, c, d are those proposed by Langmuir (0.72, 6.0, 1.9998, -1.9998), based on man walking effort in standard conditions.

The lambda parameter of the linear equation combining movement and friction costs:
total cost = movement time cost + (lambda) * friction costs
must be set in the option section of r.walk.

For a more accurate result, the "knight's move" option can be used (although it is more time consuming). In the diagram below, the center location (O) represents a grid cell from which cumulative distances are calculated. Those neighbours marked with an x are always considered for cumulative cost updates. With the "knight's move" option, the neighbours marked with a K are also considered.

      K   K
    K x x x K
      x O x
    K x x x K
      K   K

The minimum cumulative costs are computed using Dijkstra's algorithm, that find an optimum solution (for more details see r.cost, that uses the same algorithm).

Once r.walk computes the cumulative cost map as a linear combination of friction cost (from friction map) and the altitude and distance covered (from the digital elevation model), r.drain can be used to find the minimum cost path.

## SEE ALSO

r.cost, r.drain, r.in.ascii, r.mapcalc, r.out.ascii

## REFERENCES

- Aitken, R. 1977. Wilderness areas in Scotland. Unpublished Ph.D. thesis. University of Aberdeen.
- Steno Fontanari, University of Trento, Italy, Ingegneria per l'Ambiente e il Territorio, 2000-2001. Svilluppo di metodologie GIS per la determinazione dell'accessibilità territoriale come supporto alle decisioni nella gestione ambientale.
- Langmuir, E. 1984. Mountaincraft and leadership. The Scottish Sports Council/MLTB. Cordee, Leicester.

## AUTHORS

Based on r.cost written by :

Antony Awaida,
Intelligent Engineering
Systems Laboratory,
M.I.T.
James Westervelt,
U.S.Army Construction Engineering Research Laboratory

Updated for Grass 5
Pierre de Mouveaux (pmx@audiovu.com)

Initial version of r.walk:

Steno Fontanari, 2002

Current version of r.walk:

Franceschetti Simone, Sorrentino Diego, Mussi Fabiano and Pasolli Mattia
Correction by: Fontanari Steno, Napolitano Maurizio and Flor Roberto
In collaboration with: Franchi Matteo, Vaglia Beatrice, Bartucca Luisa, Fava Valentina and Tolotti Mathias, 2004

Updated for Grass 6.1

Roberto Flor and Markus Neteler

Last changed: $Date: 2011-11-08 12:29:50 +0100 (Tue, 08 Nov 2011) $

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