Formula for estimating hiking speed
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] Waldo Tobler . This function was estimated from empirical data of Eduard Imhof .[ 4]
Walking velocity:
W
=
6
e
− − -->
3.5
|
d
h
d
x
+
0.05
|
{\displaystyle W=6e^{\displaystyle -3.5\left\vert {\frac {dh}{dx}}+0.05\right\vert }}
d
h
d
x
=
S
=
tan
-->
θ θ -->
{\displaystyle {\frac {dh}{dx}}=S=\tan \theta }
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] [ 7]
p
=
0.6
e
3.5
|
m
+
0.05
|
{\displaystyle p=0.6e^{\displaystyle 3.5\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
Pace in minutes per kilometer or mile vs. slope angle for Tobler's hiking function.
Slope
Gradient
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
^ 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 format.^ a b 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. Retrieved 21 March 2013 . ^ Imhof, Eduard (1950). Gelaende und Karte . Rentsch, Zurich. ^ Analyzing Tobler's Hiking Function and Naismith's Rule Using Crowd-Sourced GPS Data . Erik Irtenkauf. The Pennsylvania State University. May 2014^ Kay, A. (2012). "Route Choice in Hilly Terrain" (PDF) . Geogr Anal . 44 (2): 87– 108. CiteSeerX 10.1.1.391.1203 doi :10.1111/j.1538-4632.2012.00838.x . Archived from the original (PDF) on 2012-11-14. Retrieved 19 January 2017 . ^ a b Kay, A. (November 2012). "Pace and critical gradient for hill runners: an analysis of race records" (PDF) . Journal of Quantitative Analysis in Sports . 8 (4). doi :10.1515/1559-0410.1456 . ISSN 1559-0410 . Retrieved 19 January 2017 .
