Tobler's hiking function

From Wikipedia, the free encyclopedia
Jump to: navigation, search
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]


Walking velocity:


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]


  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. 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[edit]