5 kph / 4 kph / 3 kph / 2 kph
1000 metres / 12 min / 15 min / 20 min / 30 min
900 metres / 11 min / 13½ min / 18 min / 27 min
800 metres / 9½ min / 12 min / 16 min / 24 min
700 metres / 8½ min / 10½ min / 14 min / 21 min
600 metres / 7 min / 9 min / 12 min / 18 min
500 metres / 6 min / 7½ min / 10 min / 15 min
400 metres / 5 min / 6 min / 8 min / 12 min
300 metres / 3½ min / 4½ min / 6 min / 9 min
200 metres / 2½ min / 3 min / 4 min / 6 min
100 metres / 1 min / 1½ min / 2 min / 3 min
50 metres / ½ min / ¾ min / 1 min / 1½ min
Fig 1
Naismith's Rule
W.W. Naismith was a founder of the Scottish Mountaineering Club and a formidable walker and his rule is still used to obtain a rough estimate of the time required for a given expedition (Aitken, 1977; Langmuir, 1984). It is thought that the rule gives a reasonable minimum time, but due to the fact that Naismith was an optimist it is proposed by Wilderness Tech Tips (1998) to take the Naismith value and add 50 %. Additional time can be added according to rests, extra carried weight, poor weather and rough underfoot conditions. The basic rule of Naismith states that a walker can maintain a speed of 5 km/h on level ground, but 1 hour needs to be added for every 600m of ascent. Several refinements to Naismith's Rule have been made and another rule, the so called Backpacker's Rule, has been defined (Wilderness Tech Tips, 1998). Aitken (1977) makes refinements according to ground conditions. This assumes that 5 km/h can be maintained on paths tracks and roads, while this is reduced to 4 km/h on all other grounds. Langmuir (1984) makes following further refinements:
Naismith's Rule: 5 km/h plus 1 hour per 600m ascent; minus 10 minutes per 300 m descent for slopes between 5 and 12 degrees; plus 10 minutes per 300m descent for slopes greater than 12 degrees.
Kennedy (1998) states that the rule is applicable to reasonably fit hillwalkers negotiating typical terrain under typical weather conditions. Furthermore he mentions the following factors as having a significant effect on route times:
Terrain and conditions Underfoot
It has to be noticed that only on a good footpath can Naismith's speed of 5 km/h be readily maintained and that on a densely vegetated trackless terrain, hag-ridden ground, or boulder fields a 'time penalty' must to be added. Additionally, Naismith's climbing rate (600m per hour) is unlikely to be achieved whilst rock scrambling. Furthermore, winter conditions can change the walking time remarkably. For example, a cover of soft and drifted snow or snow with a breakable crust can make walking conditions extremely difficult.
Weather
Wind is the most important meteorological factor. Kennedy (1998, p.3) remarks "a strong headwind can more than halve walking speed, a strong crosswind on a exposed ridge can also impede process, by forcing frequent stops to avoid getting blown off!" and "coincidental hail, sleet or snow can add to the trauma - particularly if effective eye protection is not available".
Descent
Naismith's formula makes no special allowance for downhill sections, and only the map distance covered is taken into account at the standard walking pace. The reason why during steep descents a delay occurs is mainly due to the need to take shorter steps, or to reduce the slope angle and extend path length by zig-zagging. Due to the fact the descent affects walking time, the refinements made my Langmuir in 1984 are taken into account and his rule used to model time distances in the current analysis (see section 3.3).
Fitness and load carried
Another factor which obviously contributes to the walking time into an area is the fitness of the hillwalker. Kennedy (1998, p.4) mentions Tranter's correction to take an individual's fitness into account: "An allowance can be made for this factor by use of Tranter's correction. This is in the form of a table, where the basic Naismith estimate for a route is modified by a factor which is dependent on individual fitness level; this in turn can be determined by recording the time taken(Time in Minutes) to climb a set height (300m) over a set distance (800m) at normal walking space. Whereas Naismith's Rule assumes a steady rate, Tranter's correction takes into account the effects of fatigue, such that a reduced mean work rate is assumed for the more demanding excursions."
Time in minutes / Time in hours given by Naismiths Rule2 / 3 / 4 / 5 / 6 / 7 / 8 / 9 / 10 / 12 / 14 / 16 / 18 / 20 / 22 / 24
15 - very fit / 1 / 1.5 / 2 / 2.25 / 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 / 7.5 / 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 / * / * / * / * / * / * / * / * / * / *
50 v unfit / 3.25 / 4.75 / 6.5 / 8.5 / * / * / * / * / * / * / * / * / * / * / * / *
* denotes that the walk is 'too much to be attempted'.
In a study by Kennedy (1998) the ascent time for peaks in two areas were chosen to investigate the reliability of Naismith's Rule; the Lake District 'Wainwrights' and the Munros in the Scottish Highlands. In this study the original Naismith's Rule was applied without Tranter's correction and with no additional allowance made for scrambling routes or steeply descending pitches.
Figure 2 shows that Naismith's Rule is a good predictor for walking time in the Lake District hills within a percentage of 25 percent. On another terrain walking distances may differ significantly. This is the case in the Scottish Munros. Differences occur due to the amount of scrambling required on these routes and the more serious nature of winter routes (most of the points below the lower 25% line are scrambling or winter routes). Furthermore, when walking long distances, a 'fatigue factor' is revealed. This is shown in figure 3.