Tobler's hiking function
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 Eduard Imhof.[4]
Contents
Formula
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]
Pace
Pace is the reciprocal of speed.[6][7] For Tobler's hiking function it can be calculated from the following conversion:[7]
- Failed to parse (Missing <code>texvc</code> executable. Please see math/README to configure.): p=0.6e^{\displaystyle3.5\left\vert m+0.05\right\vert}
where
- p = pace [s/m]
- m = gradient uphill or downhill (dh/dx = S in Tobler's formula),
Sample values
| Slope (deg) |
Gradient (dh/dx) |
Speed | Pace | |||
|---|---|---|---|---|---|---|
| km / h | mi / h | min / km | min / mi | s / m | ||
| -60 | -1.73 | 0.02 | 0.01 | 3603.9 | 5799.9 | 216.23 |
| -50 | -1.19 | 0.11 | 0.07 | 543.9 | 875.3 | 32.63 |
| -40 | -0.84 | 0.38 | 0.24 | 158.3 | 254.7 | 9.50 |
| -30 | -0.58 | 0.95 | 0.59 | 63.3 | 101.9 | 3.80 |
| -25 | -0.47 | 1.40 | 0.87 | 42.9 | 69.1 | 2.58 |
| -20 | -0.36 | 2.00 | 1.24 | 30.0 | 48.3 | 1.80 |
| -15 | -0.27 | 2.80 | 1.74 | 21.4 | 34.5 | 1.29 |
| -10 | -0.18 | 3.86 | 2.40 | 15.6 | 25.0 | 0.93 |
| -5 | -0.09 | 5.26 | 3.27 | 11.4 | 18.3 | 0.68 |
| -2.8624 | -0.05 | 6.00 | 3.73 | 10.0 | 16.1 | 0.60 |
| 0 | 0 | 5.04 | 3.13 | 11.9 | 19.2 | 0.71 |
| 1 | 0.02 | 4.74 | 2.94 | 12.7 | 20.4 | 0.76 |
| 5 | 0.09 | 3.71 | 2.30 | 16.2 | 26.0 | 0.97 |
| 10 | 0.18 | 2.72 | 1.69 | 22.1 | 35.5 | 1.32 |
| 15 | 0.27 | 1.97 | 1.23 | 30.4 | 49.0 | 1.83 |
| 20 | 0.36 | 1.41 | 0.88 | 42.6 | 68.5 | 2.56 |
| 25 | 0.47 | 0.98 | 0.61 | 60.9 | 98.1 | 3.66 |
| 30 | 0.58 | 0.67 | 0.41 | 89.9 | 144.6 | 5.39 |
| 40 | 0.84 | 0.27 | 0.17 | 224.6 | 361.5 | 13.48 |
| 50 | 1.19 | 0.08 | 0.05 | 771.8 | 1242.1 | 46.31 |
See also
References
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- ↑ 1.0 1.1 Lua error in package.lua at line 80: module 'strict' not found. Available also in HTML format.
- ↑ 2.0 2.1 Lua error in package.lua at line 80: module 'strict' not found.
- ↑ Lua error in package.lua at line 80: module 'strict' not found.
- ↑ Lua error in package.lua at line 80: module 'strict' not found.
- ↑ Analyzing Tobler's Hiking Function and Naismith's Rule Using Crowd-Sourced GPS Data. Erik Irtenkauf. The Pennsylvania State University. May 2014
- ↑ Lua error in package.lua at line 80: module 'strict' not found.
- ↑ 7.0 7.1 Lua error in package.lua at line 80: module 'strict' not found.
