Posted by: Ian | June 5, 2012

How hills and fatigue affect cycling performance

It can be hard when you look at the stats from a bunch of your cycling activities to know which rides were the good ones. Hills, weather, wind speed, fitness and fatigue all have an impact on average speed, not to mention the bike, wheels and so forth. Of all of these factors, the one that you know from Physics is bound to have a major impact is the degree of hilliness (assuming you’re not only riding on the flat). Isolating this as an explanatory variable for both how hard a ride is, as measured by heart rate, and how fast you ride is quite easy to do…

Over the past three days I’ve ridden, along with my friend Joerg, the Tour of Wessex. I’ll post more on this later but for now it provides a good dataset for looking at the impact of hills. The three days were respectively 106, 118 and 112 miles long and had (according to my Garmin) 5,800, 6,500 and 8,100 feet of ascent. I set my Garmin 800 up to give me a split every mile. Looking at the data later on Garmin Connect, I can see my average speed and heart rate over each mile. I can also work out the average gradient by simply subtracting the feet of descent from the feet of ascent and dividing by the number of feet in a mile. This, in effect, implements gradient smoothing since it makes a mile that goes up and then down a steep hill look the same, gradient-wise, as a flat mile – but that’s okay for my purposes.

Over the three days of the Wessex I can then graph my speed as a function of gradient:

On the first two days (red and green lines) speed drops essentially linearly as gradient increases, and increases linearly as the gradient gets more negative (downhill). On day three (the blue line) the relationship is still linear at gentle gradients but becomes non-linear on both steep uphills and downhills. On the downhills this is because there were a number of severe descents on day three on which I resorted to the brakes. The uphill end is also explained by looking at the difference between more or less severe hills. For example, take the three blue dots in the bottom right box of the Day 3 chart. The two that are grouped together reflect me cycling up the very steady gradient of Porlock Hill at 10 mph. In contrast, the solitary dot at the far bottom right is me struggling up the start of the traversal across Exmoor – at 7 mph – shortly afterwards. This starts with a 25% ramp, then the gradient chops and changes in short bursts until the descent into Exford. Here it’s much harder to keep up a good speed, despite the average gradient being similar.

Apart from this bimodal behaviour at the extremes of gradient, the function is linear. The intercept of the best line fit gives a speed on the flat for the ride. Over the three days this was 18.6, 18.2 and 17.0 mph respectively. I believe this to be a better measure to use than simple average speed for comparing different events, so long as they are of reasonable distance.

As well as looking at the effect of gradient on speed, it’s equally possible to look at its impact on heart rate. Using the same methodology over the same three days of the Wessex but here overlaying them on one chart gives this:

The effect of fatigue is clear. Again, a straight line gives a good fit in each case. In each of the three days the impact of a one degree increase/decrease in gradient is to raise/lower heart rate by around 3 bpm, which is consistent with previous long rides. However, the implied average heart rate on the flat fell from 149 bpm on day 1 to 139 bpm on day 2 and then 133 on day 3.

If I run the same analysis for park loops – 10 miles flat out round Regent’s Park – I get very different numbers. Here, my implied heart rate on the flat last time was 166 bpm, with a 6 bpm penalty/saving for each 1% change in gradient. This reflects the fact that in this (shorter) activity I’m on the limit all the time.

Joerg points out that it might be faster overall to target a flatter Heart Rate/Gradient curve for long rides. From experience, this is what I tend to do if I ride with a power meter. On the uphills I can see that I’m often putting down an exceptional number of Watts, for me: perhaps I’d be wise to get into a low gear and spin it more. In contrast, on the flats I can see that the power readings can get anaemic as I ease off. Quite probably it would be smarter to even out the power, and hence the heart rate, on long rides generally.

This is analysis anyone with a Garmin or equivalent device can quite easily run using only free software. I find it interesting and possibly even useful.



  1. Interesting stuff. My average speeds were 18.1, 17.9 & 16.8 mph over the 3 days so ties in with your stats. Looking forward to reading your write ups. I’ve blogged on day 1 but have mostly impersonated a vegetable today! 😉

    • Thanks. This methodology doesn’t necessarily give a “flat” speed equal to your average speed, even on a circular ride, and you were actually faster than us. (Our averages were 17.4 mph for each of the first two days and 15.7 mph on day three.) Nice riding! I read and enjoyed your bikevcar day 1 blog earlier and it should prompt me to do mine – but like you, I’m doing very little today other than enjoying being at home when it’s raining outside.

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