Looking in the literature for ways to compare mountain trails with varying climbing distances I came across two different ways to adjust for the climbs and to calculate the equivalent flat distance of mountainous trails with varying elevation profiles. The first method (Method A in figures below) I found is described in Saugy’s paper entitled “Alterations of Neuromuscular Function after the World’s Most Challenging Mountain Ultra-Marathon” comparing Tor des Géants (TDG) with UTMB published in PLoS ONE 2103; 8: e65596. They used the formula flat-equivalent distance = distance (km)+ positive elevation change (meters)/100 and this yields a value of 570 km for the full TDG course and 264 km for UTMB. I have not found the reference for this formula and whether it has been validated or used before.
The second method (Method
B in figures below) I found was the so called Naismith's rule, invented by the Scottish
mountaineer William W. Naismith already in 1892. According to this rule 3 miles
(=15,840 feet) of distance is equivalent in time terms to 2000 feet of climb. In
other words, 1 meter of ascent is equivalent to 7.92 (=15840/2000) meters of horizontal
distance so time would be a linear function of ascent and distance. Obviously, Naismith’s rule has been widely
used for long time and has been proven useful for walking in particular in
hilly terrain with moderate slopes and not too technical terrain. A recent
publication tested whether if it would be applicable in shorter fell running
competitions and found a good correlation between time and flat equivalent
distance using the correction (see figure below) (Scarf “Route choice in
mountain navigation, Naismith’s rule, and the equivalence of distance and climb”
Journal of Sports Sciences 2007; 25: 719 – 726).
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From Scarf 2007 |
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From Kay 2012. Pace versus gradient |
I have looked at some
of the more popular and well-known mountain ultramarathon trail races over 100
miles in order to see whether the method found in Saugy’s paper (Method A) or
Naismith’s rule (Method B) can be applied also in longer distances. Not
surprisingly, the course record times of 100 mile races varied quite
extensively from just under 15 hours to over 25 hours (see table below).
The variation in
course records appeared to be at least partly a function of the amount of
elevation gain (D+) and both methods to adjust for this appeared actually quite
good (see figure below where blue denotes original distance, red distance
adjusted to method A and green distance adjusted to method B [Naismith’s rule]).
Just looking at the
original record speed as a function of the elevation gain (D+) shows
surprisingly good correlation among the races around 100 miles (again, blue
original speed, red speed adjusted by method A and green speed adjusted to
method B [Naismith's rule]).
There are not many
races even longer than 100 miles, but adding Tor des Géants (TDG) to the
calculations appear to make the methods less predictable, but still quite good (in the figures below the same color coding
applies to WSER, UTMB, Hardrock100 and TDG). I have not added Barkley Marathons
to any of the figures as that race with its extreme course profile and
conditions really is an outlier.
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Comparison of WSER, UTMB, Hardrock100 & TDG |
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Comparison of WSER, UTMB, Hardrock100 & TDG |
In summary, when
comparing mountain ultramarathons positive elevation gain (D+) appears to be a
very important factor in order to determine course record times and speeds. I
have done some preliminary calculations of two methods to determine the
equivalent flat distance of some of the well-known races and found that both
methods are quite good albeit there is certainly room for improvement taking
into account for instance average slope of climbs, technical passages and
ground conditions, the average altitude over sea level etc. Furthermore, the
course record time might not reflect how non-elite runners will perform and how
the adjustment method would work for them. Nevertheless, regardless I think
that this exercise shows the obvious that if you are planning to run a mountain
ultramarathon it is very important to collect climbing distance.
For what it's worth, Barkley distance is most likely 125 to 130 miles, not the claimed 100 miles, so its D+/km would actually be a bit lower.
ReplyDeleteInteresting analysis. Thanks.
Thanks Jon! Interesting, assuming a distance of around 205 kilometers makes the D+/km for Barkley a more reasonable 87.9. The adjusted distances will be 385 km and 348 km with the methods above - and the race suddenly fits much better in the models. It is still somewhat of an outlier though and judging by the finish rate not everything is about D+
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