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Tobler's hiking function

Formula for estimating hiking speed From Wikipedia, the free encyclopedia

Tobler's hiking function
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Tobler's hiking function is an exponential function determining the hiking speed, taking into account the slope angle.[1][2][3] It was formulated by Waldo Tobler. This function was estimated from empirical data of the Swiss cartography professor Eduard Imhof.[4]

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Tobler's hiking function – walking speed vs. slope angle chart.

Formula

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Walking velocity:

where

W = walking velocity [km/h][2]
dh = elevation difference,
dx = distance,
S = slope,
θ = angle of slope (inclination).

The velocity on the flat terrain is 5 km / h, the maximum speed of 6 km / h is achieved roughly at -2.86°.[5]

On flat terrain this formula works out to 5 km/h. For off-path travel, this value should be multiplied by 3/5, for horseback by 5/4.[1]

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Pace

Pace is the reciprocal of speed.[6][7] For Tobler's hiking function it can be calculated from the following conversion:[7]

where

p = pace [s/m]
m = gradient uphill or downhill (dh/dx = S in Tobler's formula),
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Sample values

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Pace in minutes per kilometer or mile vs. slope angle for Tobler's hiking function.
More information Slope (deg), Gradient (dh/dx) ...

See also

References

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