Naismith's Rule

by John Hardwick

Generations of hill walkers will be familiar with Naismith’s rule (1892) for estimating walking times, viz 1 hour for about 5km along the flat plus 1 hour for every 600m of ascent.

One can calculate an equivalent ‘total’ distance, dubbed the Naismith distance by Scarf (2008), by dividing the level change by 600m to give the ascent time and multiplying this by 5km to give the extra distance. GPS trackers such as the Strava App or MemoryMap give both distance on the flat d in km, level change h in metres and moving time (i.e. the elapsed time less the time when no movement occurs during breaks) so it is straightforward to check walk times against Naismith’s rule. Scarf’s Naismith equivalent distance in km is given by d + 0.00833h.

My walks during the lockdowns until end of February 2021 and extending back two years are plotted in the graph as blue crosses. The red dots are a couple of Alpine routes from the AAC(UK) 70th anniversary meet from the Rudolfshütte in 2018. The black line represents Naismith’s rule; the gradient of the line is the pace in time per km of 0.2 hours (12 minutes).

The walks are well represented by Naismith’s rule. Three groupings are evident. Local Ramblers Association group walks, greater than 16km and involving several hundred metres of ascent tend to lie below the Naismith line at a pace a few percent faster than the rule. Solo longer walks tend to lie above the line due to slower pace on the rougher terrain of the Dark Peak and Lake District. Shorter lockdown walks from home were on good paths and lie on the Naismith line.

Two outlying points with the slowest and fastest paces are marked with the 3.12 hour and 1.37 hour time labels respectively. The slow pace corresponds to an ascent of Cadillac Mountain at Bar Harbor, Maine in 2019 on a hot summer’s day with time taken trying to find a plaque in the rocks marking the true summit point. The fastest was an ascent of the Grouse Grind above Vancouver, autumn 2019, comprising an 853m ascent via a well-maintained stairway over a distance of 2.9km. Fell runners and those out for a gentle stroll would have trend gradients lower and greater respectively.

While the Alpine routes lie near the rule line, don’t think these were respectable times! We were two parties of relative strangers so inevitably quite a lot of time was spent roping up on the glacier in addition to breaks. For route planning a calculator is available at www.wildwalks.com/bushcraft/technical-stuff/naismiths-rule.html

Granatspitze from the Sonnblick Kees
Photos by John Hardwick

The steep Grouse Grind stairway

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