# What goes up must come down: working out the impact of hills on the difficulty of a race

## Tim Beeson-Jones is fresh out of his fluid mechanics PhD at the University of Cambridge and has been to developing our analytical tools at LetsDoThis.com

Try racing up Ben Nevis at a speed that would impress a mountain goat and you’ll find it’s a lot harder than running the same distance on the flat. But by how much? Tim has been doing a bit of research to try and find out.

William W. Naismith was a Scottish mountaineer who walked upon mountains green and pastures pleasant towards the end of the Victorian era. A hiking legend, he completed the first winter ascent of the North-East Buttress of Ben Nevis in 1896, and at the age of 60 he walked the casual distance of 100km from Glasgow to the summit of Ben Lomand and back in just 20 hours. Naismith founded the Scottish Mountaineering Club and, fortunately for us, documented his trips.

The last sentence of one of his post-jaunt reports was the very helpful note that “men should allow 1 hour per 3 miles on the map and an additional 1 hour per 2000 feet of ascent”. It has been noted that, for most runners, this is roughly equivalent to saying “to account for any changes in elevation, add on 8 times the distance of ascent to the distance you thought you were going”. This is really handy for people who find themselves orienteering in hilly areas as they can then work out the Flat Equivalent Distance (FED) of, say, going over a hill rather than round it and then choose the shorter route. But how accurate is this rule?

We reckon with its unrelenting up’s and down’s, that 42k marathon is really more like a monster 58k ultra…

Naismith arrived at this equivalence through a lifetime of experience (and also a good old fashioned finger in the air). It is, however, a slightly simplistic model insofar as the additional time doesn’t explicitly depend on the slope of the hill, just the total ascent. It also doesn’t account for what happens when you’re going downhill. Indeed, one might expect a shallow downhill gradient to be beneficial until a critical steepness is reached, at which point one might expect further steepness to slow you down as you try and keep your balance. We’ve used the research from a leading UK sports university to gain insight into the relationship between the additional effort required and slope (including both positive and negative incline). Building on this, we’ve calculated the FEDs for a number of different popular races and found some interesting results. For example, if you were disappointed with your time on the CTS Dorset Marathon then fear not! We reckon with its unrelenting up’s and down’s, that 42k marathon is really more like a monster 58k ultra, so don’t sweat it. Or in fact do…loads.

This information will do a few things:

1. It feeds into the difficulty rating we’re developing so you know what you’re signing up for when you book an event through letsdothis.com.
2. Once you’ve decided to take the plunge, if you tell us roughly what time you might run it on the flat (or your target overall pace) then you can use the split guide we’re developing to balance out the different sections, with hilliness factored in.
3. Finally, this info feeds into the predictor we’re developing, which will give people times to aim for given past performances and their training data. Watch this space!
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