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| William Naismith, of "the Rule" |
It is taught in Scouting, and expected to be learned and applied to hikes over a significant distance. It's roughly that a fit person can walk 5km/hr, with adjustments for the roughness of terrain, and for acent and descent. The rule implies that 1m of ascent is equivalent to about 8m of horizontal travel.
Problem: Naismith was a mountaineer and an optimist.
It was developed in 1892, 120 years ago. My grandfather used to walk his brothers' lunch out 10 miles to where they were making charcoal in the 1920s. Bushwalkers before WW2 used to compress very long journeys into the day-and-a-half weekend before the 40 Hour Week gave them the whole of Saturday. But: in 2000, as a fat creaky hiker leading kids who're driven to school every day, 5km/h is a figure I don't ever observe even on pavement.
Naismith's Rule has been confirmed empirically by reference to records of 'fell runners' ... but what the hell is that? Turns out it's a kind of race run through the UK countryside by athletes. They aren't carrying 15kg packs, they aren't scrambling up rocks, and they're not going anywhere on 35C Sydney summer days. There are adjustments you can make for 'fitness' ... but how on earth do you calibrate that? The empirical study suggests that men use an 8:1 figure for ascent, but that women use 10:1 ... that's a 25% difference!
So how applicable is it really to hiking in Australian bush? Even on track, we're lucky to average 3km/h with scouts. Get into a bit of dense undergrowth, and you can be lucky to travel at 1/10th of that doughty Scot's speed. What about the load being carried? What about the temperature?
Apparently Naismith used 'trigonometry' to arrive at his rule of thumb, and that's ok, but man is not a purely geometrical being. It's fundamentally a flawed assumption, like the ideal weight calculations which model human bodies as disks.
Hiking is about the expenditure of energy. Converting chemical potential into kinetic in a field of gravitational potential to perform the useful work of holding the body (and pack) off the ground while covering terrain. The efficiency of the conversion depends upon fitness, ambient temperature and humidity. The work to be done depends on terrain - rocky, steep, overgrown.
With DEM data down to 30cm vertical and sub-meter (ie: sub-step) horizontal resolution why aren't we able to point a program at a path file and calculate with exquisite precision the energy consumed by an ideal human physiology under specified load, temperature and humidity. In CGS, dammit! This is not rocket surgery.
Having determined the energetic expenditure required to cover a given terrain-load-temperature-humidity and adjusting for roughness of terrain, one might (just might) be able to accurately forecast time to complete.
Edit: In a kind of Rule34 for Geeks, someone's already had a bash at this problem.
