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.

Formula

Walking velocity:

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

{\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]

^ ^a ^b 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. 93 (1). National center for geographic information and analysis. Retrieved 21 March 2013. HTML {{cite journal}}: External link in |quote= (help)
^ Magyari-Sáska, Zsolt; Dombay, Ştefan (2012). "Determining minimum hiking time using DEM" (PDF). Geographia Napocensis. Anul VI (2). Academia Romana - Filiala Cluj Colectivul de Geografie: 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 (ed.). 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. {{cite book}}: |access-date= requires |url= (help); External link in |chapterurl= (help); Unknown parameter |chapterurl= ignored (|chapter-url= suggested) (help)