Tobler's hiking function

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

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]

Formula

Walking velocity:

${\displaystyle W=6e^{\displaystyle -3.5\left\vert {\frac {dh}{dx}}+0.05\right\vert }}$

${\displaystyle {\frac {dh}{dx}}=S=\tan \Theta }$

where

dh = elevation difference,

dx = distance,

S = slope,

Θ = angle of slope (inclination).

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

References

1. Tobler, Waldo (February 1993). "Three presentations on geographical analysis and modeling: Non-isotropic geographic modeling speculations on the geometry of geography global spatial analysis" (PDF). Technical report. National center for geographic information and analysis. 93 (1). Retrieved 21 March 2013. HTML
2. Magyari-Sáska, Zsolt; Dombay, Ştefan (2012). "Determining minimum hiking time using DEM" (PDF). Geographia Napocensis. Academia Romana - Filiala Cluj Colectivul de Geografie. Anul VI (2): 124–129. Retrieved 21 March 2013.
3. Kondo, Yasuhisa; Seino, Yoichi (2010). "GPS-aided Walking Experiments and Data-driven Travel Cost Modeling on the Historical Road of Nakasendō-Kisoji (Central Highland Japan)". In Frischer, Bernard. Making history interactive: computer applications and quantitative methods in archaeology (CAA); proceedings of the 37th international conference, Williamsburg, Virginia, United States of America, March 22 - 26, 2009. BAR International Series. Oxford u.a.: Archaeopress. pp. 158–165. Retrieved 21 March 2013.
4. Imhof, Eduard (1950). Gelaende und Karte. Rentsch, Zurich.

See also

• Naismith's rule
• Preferred walking speed