- Formula
- Pace
- Sample values
- References
- See also
Formula
Walking velocity:
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°.[6]
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.
Pace
Pace is the reciprocal of speed.[8][9] For Tobler's hiking function it can be calculated from the following conversion:[9]
where
p = pace [s/m]
m = gradient uphill or downhill (dh/dx = S in Tobler's formula),
Sample values
| Slope (deg) | Gradient (dh/dx) | 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 |
References
1. ^1 2 {{cite journal |last1=Magyari-Sáska |first1=Zsolt |last2=Dombay |first2=Ştefan |year=2012 |title=Determining minimum hiking time using DEM |journal=Geographia Napocensis |volume=Anul VI |issue=2 |pages=124–129 |publisher=Academia Romana - Filiala Cluj Colectivul de Geografie |url=http://geographianapocensis.acad-cluj.ro/Revista/volume/nr_2_2012/pdf/Magyari_Dombay.pdf |accessdate=21 March 2013}}
2. ^1 {{cite book |last1=Kondo |first1=Yasuhisa |last2=Seino |first2=Yoichi |editor-first=Bernard |editor-last=Frischer |series=BAR International Series |title=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 |publisher=Archaeopress |location=Oxford u.a. |year=2010 |pages=158–165 |chapter=GPS-aided Walking Experiments and Data-driven Travel Cost Modeling on the Historical Road of Nakasendō-Kisoji (Central Highland Japan)| chapterurl=https://www.academia.edu/670947 |accessdate=21 March 2013 }}
3. ^1 {{cite book |last1=Imhof |first1=Eduard |year=1950 |title=Gelaende und Karte |publisher=Rentsch, Zurich}}
4. ^1 [https://gis.e-education.psu.edu/sites/default/files/capstone/Irtenkauf_596B_20140430.docx Analyzing Tobler’s Hiking Function and Naismith’s Rule Using Crowd-Sourced GPS Data]. Erik Irtenkauf. The Pennsylvania State University. May 2014
5. ^1 {{cite journal |last=Kay |first=A. |title=Route Choice in Hilly Terrain |journal=Geogr Anal |volume=44 |issue=2 |pages=87–108 |date=2012 |url=http://www.lboro.ac.uk/microsites/maths/research/preprints/papers10/10-10.pdf |archive-url=https://wayback.archive-it.org/all/20121114225956/http://www.lboro.ac.uk/microsites/maths/research/preprints/papers10/10-10.pdf |dead-url=yes |archive-date=2012-11-14 |doi=10.1111/j.1538-4632.2012.00838.x |accessdate=19 January 2017 |citeseerx=10.1.1.391.1203 }}
6. ^1 2 {{cite journal |last=Kay |first=A. |title=Pace and critical gradient for hill runners: an analysis of race records |journal=Journal of Quantitative Analysis in Sports |volume=8 |issue=4 |pages= |date=November 2012 |url=https://dspace.lboro.ac.uk/dspace-jspui/bitstream/2134/16478/1/PaceCG_published.pdf |doi=10.1515/1559-0410.1456 |issn=1559-0410 |accessdate=19 January 2017}}
Available also in HTML format.[1][2][3][4][5][6]2. ^1 {{cite book |last1=Kondo |first1=Yasuhisa |last2=Seino |first2=Yoichi |editor-first=Bernard |editor-last=Frischer |series=BAR International Series |title=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 |publisher=Archaeopress |location=Oxford u.a. |year=2010 |pages=158–165 |chapter=GPS-aided Walking Experiments and Data-driven Travel Cost Modeling on the Historical Road of Nakasendō-Kisoji (Central Highland Japan)| chapterurl=https://www.academia.edu/670947 |accessdate=21 March 2013 }}
3. ^1 {{cite book |last1=Imhof |first1=Eduard |year=1950 |title=Gelaende und Karte |publisher=Rentsch, Zurich}}
4. ^1 [https://gis.e-education.psu.edu/sites/default/files/capstone/Irtenkauf_596B_20140430.docx Analyzing Tobler’s Hiking Function and Naismith’s Rule Using Crowd-Sourced GPS Data]. Erik Irtenkauf. The Pennsylvania State University. May 2014
5. ^1 {{cite journal |last=Kay |first=A. |title=Route Choice in Hilly Terrain |journal=Geogr Anal |volume=44 |issue=2 |pages=87–108 |date=2012 |url=http://www.lboro.ac.uk/microsites/maths/research/preprints/papers10/10-10.pdf |archive-url=https://wayback.archive-it.org/all/20121114225956/http://www.lboro.ac.uk/microsites/maths/research/preprints/papers10/10-10.pdf |dead-url=yes |archive-date=2012-11-14 |doi=10.1111/j.1538-4632.2012.00838.x |accessdate=19 January 2017 |citeseerx=10.1.1.391.1203 }}
6. ^1 2 {{cite journal |last=Kay |first=A. |title=Pace and critical gradient for hill runners: an analysis of race records |journal=Journal of Quantitative Analysis in Sports |volume=8 |issue=4 |pages= |date=November 2012 |url=https://dspace.lboro.ac.uk/dspace-jspui/bitstream/2134/16478/1/PaceCG_published.pdf |doi=10.1515/1559-0410.1456 |issn=1559-0410 |accessdate=19 January 2017}}
}}
See also
- Naismith's rule
- Preferred walking speed
1 : Hiking
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- Acanthochitina
- Acanthochitina barbata
- Acanthochitona bednalli
- Acanthochitona garnoti
- Acanthochiton fascicularis
- Acanthochiton turtoni
- Acanthocinus fastidiosus
- Acanthocinus hollandicus
- Acanthocinus piliger
- Acanthocinus pruinosus
- Acanthoclininae
- Acanthoclita acrocroca
- Acanthoclita balanoptycha
- Acanthoclita balia
- Acanthoclita iridorphna
- Acanthoclymenia
- Acanthocnemus nigricans
- Acanthocobitis botia
- Acanthocobitis rubidipinnis
- Acanthocolpiata
- Acanthocotyle
- Acanthocotyle elegans
- Acanthocotylidae
- Acanthodactylus aegyptius