# UKC

## / Optimum hill profile

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A hypothetical question: Given a circular run loop that repeatedly involves gentle climbs followed by steeper descents, would it be quicker running in the other direction?

I appreciate this will most likely vary a lot depending on the steepness - and therefore the runnability of the gradients, but let's assume the uphills are only a few percent inclined and the descents are runnable at speed without feeling like you're braking.

I prefer "running" uphill on slight gradients as opposed to running downhill on similiar gradients - especially if the surface is loose / rocky

Hmm, would depend on the surface for me

Hmm, interesting one. I think we need some empirical evidence - say 5x sets in each direction sound alright?

We have an annual race up and down our local hill - Birnam Hill, near Dunkeld. It is very steep on one side and gentle on the other, and all on good paths. The race is usually run up the steep side and down the gentle, but a couple of years ago it was run the opposite way - and the times were generally slower.

It is going to depend on a few factors, length, exact profiles. A few examples I can think of lend themselves to different answers

I regularly do a 1 mile road loop on a business park, which rises about 15m over 400m, then drops 15m over 250m, when run clockwise. It is a good bit faster clockwise than anti-clockwise.

My club is organising a 6 mile road race on Friday, is has more than 150m of ascent, the ascent probably totals 1.5 miles total distance, descent is probably 3 miles. That is definitely slower in reverse, although the average descent gradient isn't much it has some steep sections that really get the legs, so maybe not a fair comparison.

Thanks all. I suppose I'd hoped for a particular reason why one might be faster than the other, in a similar way that there's a good reason why you never gain as much time on a downhill as you've lost on the equivalent uphill. Curious to hear completely contradictory examples though. Might need further study ;-)

I've wondered the same with the wind and or cycling. The advantages of the push, never feels as though it offsets the work against it.

Running. Angle must be critical.. so steep that you are only power walking up and shallow enough down you feel like you are striding out for free.. up the steep bit on Ingleborough from the pub then down to Horton for example.

I think the answer is "it depends". On the hill profiles, the runner's strengths and motivations, where in the course you hit it, etc. One more thought: local 5k race up the road that rises slowly over 2k and then loses height more quickly (only about 20m) in the last k. Generally considered a PB type course.

If you use Tobler's hiking function https://en.wikipedia.org/wiki/Tobler%27s_hiking_function as the model for pace as a function of slope angle, then the model has an optimal angle which maximises pace (going downhill). For walking the optimal angle is about 3 degrees, but for running it is more like 6 degrees (see https://dspace.lboro.ac.uk/dspace-jspui/bitstream/2134/16478/1/PaceCG_published.pdf ).

Lets assume that the run has an uphill section at constant angle followed by a downhill section at a constant angle and that the net height gain is zero. Then, (assuming I got the maths correct) provided that either angle is greater than the optimal angle, it turns out to be quicker to go up the steeper slope and down the gentler one. The dominant effect is because you spend more of the horizontal distance going downhill. If both angles are less than the optimal angle the opposite is true: going up the gentler slope is faster, but the effect is quite small.

Post edited at 20:57

I was just about to post the same conclusion but for a different reason.

I start from an observation of my own hill running where I note that rate of ascent is remarkably constant from one hill and one day to the next. So velocity in the vertical direction is roughly constant. That means that you should try and maximise speed in the horizontal direction which means that you should spend the least amount of distance going slowly i.e. uphill and the most amount of distance going quickly i.e. downhill. Therefore better to go up the short side and down the long side.

I hope that makes sense?

Birkenhead parkrun is a good shout for this as an experiment. Each of three laps starts with a long, steady downhill and there is a shorter uphill to finish. It’s my PB course and I feel this profile suits my running at pace.

Thanks Mark. That sounds quite like the kind of theoretical reasoning I was hoping for!

> Birkenhead parkrun is a good shout for this as an experiment. Each of three laps starts with a long, steady downhill and there is a shorter uphill to finish. It’s my PB course and I feel this profile suits my running at pace.

In which case you should try it in reverse one day. Or, even better, petition the course organisers to reverse the direction for one week, and then we'll instantly have a volume of empirical test data!