Naismith's rule

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A plot of walking speed versus slope resulting from Naismith's rule [1] and Langmuir corrections [1][2] for base speeds of 5 km/h and 4 km/h compared to Tobler's hiking function.[3]

Naismith's rule is a rule of thumb that helps in the planning of a walking or hiking expedition by calculating how long it will take to walk the route, including the extra time taken when walking uphill. The rule assumes that travel will be on trails, footpaths, or reasonably easy ground; it is possible to apply adjustments or "corrections" for more challenging terrain, although it cannot be used for scrambling routes. In the grading system used in North America, Naismith's rule applies only to hikes rated Class 1 on the Yosemite Decimal System, and not to Class 2 or higher. The rule was devised by William W. Naismith, a Scottish mountaineer, in 1892.[4] The basic rule is as follows:

  • Allow 1 hour for every 5 kilometres (3.1 mi) forward, plus 1 hour for every 600 metres (2,000 ft) of ascent.
  • When walking in groups, calculate for the speed of the slowest person.

Assumptions and calculations[edit]

The basic rule assumes hikers of reasonable fitness, on typical terrain, under normal conditions. It does not account for delays, such as extended breaks for rest or sightseeing, or for navigational obstacles. For planning expeditions a team leader may use Naismith's rule in putting together a route card.

Alternatively, the rule can be used to determine the equivalent flat distance of a route. This is achieved by recognising that Naismith's rule implies an equivalence between distance and climb in time terms: 3 miles (=15,840 feet) of distance is equivalent in time terms to 2000 feet of climb. That is, 7.92 (=15840/2000) units of distance are equivalent to 1 unit of climb. For convenience an 8 to 1 rule can be used. So, for example, if a route is 20 kilometres (12 mi) with 1600 metres of climb (as is the case on leg 1 of the Bob Graham Round, Keswick to Threlkeld), the equivalent flat distance of this route is 20+(1.6×8)=32.8 kilometres (20.4 mi). Assuming an individual can maintain a speed on the flat of 5 km/h (walking pace), the route will take 6 hours and 34 minutes. The simplicity of this approach is that the time taken can be easily adjusted for an individual's own (chosen) speed on the flat; at 8 km/h (flat speed) the route will take 4 hours and 6 minutes. The rule has been tested on fell running times and found to be reliable.[5]

In practice, the results of Naismith's rule are usually considered the minimum time necessary to complete a route.

Naismith's rule appears in UK statute law (although not by name). The Adventure Activities Licensing Regulations apply to providers of various activities including "trekking", and part of the definition of trekking is that it is over terrain from which it would take more than 30 minutes to reach a road or refuge (by the quickest safe route) based on a walking speed of 5 kilometres per hour plus an additional one minute for every 10 metres of ascent.[6]

Modifications[edit]

Over the years several adjustments have been formulated in an attempt to make the rule more accurate. The simplest correction is to add 25 or 50% to the time predicted using Naismith's rule. While this may be more accurate for some people or under certain conditions, it does not explicitly account for any additional variables. The accuracy of some corrections is disputed by some,[7] in particular the speed at which walkers descend a gentle grade. Other common corrections are:

  • When walking on uneven or unstable terrain, allow 1 hour for every 4 kilometres (2.5 mi) forward, instead of 1 hour per 5 kilometres (3.1 mi).
  • On a gentle decline (about 5-12°), subtract 10 minutes per 1000 feet of descent. On a steep decline (over 12°), add 10 minutes per 1000 feet of descent.

Tranter's corrections[edit]

Tranter's corrections make adjustments for fitness and fatigue. Fitness is determined by the time it takes to climb 1000 feet over a distance of ½ mile (800 m). Additional adjustments for uneven or unstable terrain or conditions can be estimated by dropping one or more fitness levels.

Individual fitness in minutes Time taken in hours estimated using Naismith's rule
2 3 4 5 6 7 8 9 10 12 14 16 18 20 22 24
15 (very fit) 1 1.5 2 2.75 3.5 4.5 5.5 6.75 7.75 10 12.5 14.5 17 19.5 22 24
20 1.25 2.25 3.25 4.5 5.5 6.5 7.75 8.75 10 12.5 15 17.5 20 23
25 1.5 3 4.25 5.5 7 8.5 10 11.5 13.25 15 17.5
30 2 3.5 5 6.75 8.5 10.5 12.5 14.5
40 2.75 4.25 5.75 7.5 9.5 11.5 Too much to be attempted
50 (unfit) 3.25 4.75 6.5 8.5

For example, if Naismith's rule estimates a journey time of 9 hours and your fitness level is 25, you should allow 11.5 hours.

Aitken - Langmuir corrections[edit]

Aitken (1977) assumes that a base speed of 5 km/h can be maintained on paths, tracks and roads, while this is reduced to 4 km/h on all other surfaces.[8][9]

Langmuir (1984) assumes a base speed of 4 km/h and makes the following further refinements:

  • subtract 10 minutes for every 300 meters of descent for slopes between 5 degrees and 12 degrees
  • add 10 minutes for every 300 meters of descent for slopes greater than 12 degrees.[2][9]

See also[edit]

References[edit]

  1. ^ a b c 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): 124–9. Retrieved 21 March 2013. 
  2. ^ a b c Langmuir, Eric (1984). Mountaincraft and Leadership. Official Handbook of the Mountain Leader Training Boards of Great Britain and Northern Ireland. Edinburgh Scotland: Britain & Scottish Sports Council. 
  3. ^ a b Tobler, W (February 1993). "Three presentations on geographical analysis and modeling: Non-isotropic geographic modeling speculations on the geometry of geography global spatial analysis" (PDF). National Center for Geographic Information and Analysis Technical Report. 93 (1): 1–24. Retrieved 21 March 2013. HTML 
  4. ^ a b Thompson, S (2010). "1865-1914: gentlemen and gymnasts". Unjustifiable risk? The story of British climbing (1st ed.). Singapore: KHL Printing. pp. 51–122. ISBN 978-1-85284-627-5. 
  5. ^ a b http://www.informaworld.com/smpp/content~db=all~content=a773450587
  6. ^ See definition of "travelling time" in The Adventure Activities Licensing Regulations 1996, section 2 and The Adventure Activities Licensing Regulations 2004, section 2.
  7. ^ a b of downhill correction for Naismith's rule
  8. ^ a b Aitken, Robert (1977). Wilderness Areas in Scotland, unpublished Ph.D. Thesis. University of Aberdeen. Aberdeen. 
  9. ^ a b c Caffin, Roger. "FAQ - Navigation: Walking Speed - Naismith's Rule". Retrieved 23 March 2013. 

External links[edit]