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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.

Walking velocity:

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

\( \frac{dh}{dx}=S=\tan\Theta \)


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]

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"
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.

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.

See also

Naismith's rule
Preferred walking speed

Mathematics Encyclopedia

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