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Naismith's rule

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Rule of thumb for hiking time

Naismith's rule[1][2]<br>Naismith's rule helps with the planning of a walking or hiking expedition by calculating how long it will take to travel the intended route, including any extra time taken when walking uphill. This rule of thumb was devised by William W. Naismith, a Scottish mountaineer, in 1892.[1][3][4] A modern version can be formulated as follows:

Allow one hour for every 3 miles (5 km) forward, plus an additional hour for every 2,000 feet (600 m) of ascent.[2][5]

Assumptions and calculations<br>[edit]

Pace[6] in minutes per kilometre or mile vs. slope angle resulting from Naismith's rule[7] for basal speeds of<br>5 km/h and 4 km/h.[n 1]<br>The original Naismith's rule from 1892 says that one should allow one hour per three miles on the map and an additional hour per 2000 feet of ascent.[1][4] It is included in the last sentence of his report from a trip.[1][8]

Today it is formulated in many ways. Naismith's 1 h / 3 mi + 1 h / 2000 ft can be replaced by:

1 h / 3 mi (5 km) + 1 h / 2000 ft (600 m)[2][5][9]

1 h / 5 km (3 mi) + 1/2 h / 300 m (1000 ft)[10][11][12]

3 mph + ½ h / 1000 ft<br>5 km/h + ½ h / 300 m[13][n 2]

12 min / 1 km + 10 min / 100 m[8]

The basic rule assumes hikers of reasonable fitness, on typical terrain, and 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.[citation needed]

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.[citation needed]

In practice, the results of Naismith's rule are usually considered the minimum time necessary to complete a route, though modern adaptations and hiking time calculators account for terrain difficulty, elevation gain, and individual fitness levels.[14]

When walking in groups, Naismith’s rule is generally applied based on the pace of the slowest member to ensure the group remains together. This adjustment accounts for variations in fitness, terrain difficulty, and rest needs among participants.[13]

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. Part of the definition of trekking is that it is over terrain on 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 minute for every 10 metres of ascent.[15]

A plot of walking speed versus slope resulting from Naismith's rule[7] and Langmuir corrections[7][16] for base speeds of 5 km/h and 4 km/h compared to Tobler's hiking function.[17][n 1]<br>Scarf's equivalence between distance and climb<br>[edit]

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.[18]

Professor Philip Scarf, Associate Dean of Research and Innovation and Professor of Applied Statistics at the University of Salford,[19] in research published in 2008, gives the following formula:[4]

equivalent distance = x + α·y<br>where:

x = horizontal distance<br>y = vertical distance<br>α = 7.92 (3 mi / 2000 ft[18][4][20]), called Naismith’s number by Scarf[18][4][20]<br>That is, 7.92 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, 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.[18] Scarf proposed this equivalence in 1998.[4][6]

As you can see the forward, the Scarf's assumption allows also to calculate the time for each speed, not just one as in case of the original Naismith rule.

Pace<br>[edit]

Pace is the reciprocal of speed. It can be calculated here from the following...