# Naismith's rule

(Redirected from Naismith's Rule)
A plot of walking speed versus slope resulting from Naismith's rule [1] and Langmuir corrections [1][2] for basal 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 ascents. This 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

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.

## Modifications

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,[6] 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

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.

 15 (very fit) 20 25 30 40 50 (unfit) 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 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 1.25 2.25 3.25 4.5 5.5 6.5 7.75 8.75 10 12.5 15 17.5 20 23 1.5 3 4.25 5.5 7 8.5 10 11.5 13.25 15 17.5 2 3.5 5 6.75 8.5 10.5 12.5 14.5 2.75 4.25 5.75 7.5 9.5 11.5 Too much to be attempted 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

Aitken (1977) assumes that a basal 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.[7][8]

Langmuir (1984) assumes a basal 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][8]