# Average power math?

Discussion in 'Power Training' started by jcm01, Jan 2, 2014.

1. ### jcm01 New Member

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I did a 25 mile loop the other day. It took me exactly 80 minutes and I averaged 230 watts according to my PM. I did the exact same ride a few days later and was able to shave 2 minutes off the ride, doing it in 78 minutes. My PM said I averaged 231 watts this second time. That seems off to me?? It seems to me that 2 minutes should translate into more than 1 additional watt. What do others think about this? Is there any way I can sanity check this with some simple math?

For example, assuming all other variables are the same (wind conditions, bike weight, etc.), is there any way to determine my average power for this second ride knowing the numbers from my first ride and that I did the second ride 2 minutes faster. Thanks!

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2. ### dhk2 Active Member

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I'll take a shot at your question by looking at your average speeds. For the first ride, 80 minutes gives you an average of 18.75 mph. For the second, 78 minutes is 19.23 mph. The online calculator at analyticcycling.com will do the math using estimated parameters for frontal area, drag coefficient, road surface, rider weight (default values are already entered). Keeping all those constant, only changing speed will allow you to compare the estimated power outputs required for both cases.

Just plugged in some numbers there and got 157 watts for 18.75 mph, and 167 watts for 19.23. Doing a "sanity check", 167/157 yields 1.064, meaning it's 6.4% more power than 157. This looks to be right in the ballpark, because if the power was all aero drag, your power would have to increase by the cube of the speed factor, 19.23/18.75, which is 1.079, and if the power was all rolling resistance, the power would just increase by the linear factor of 19.23/18.75, or 1.0256. Since most of the resistance is aero at these speeds, the result is what I'd expect.

So yes, agree your hunch was correct: saving 2 minutes takes about 10 watts more power. But this assumes perfectly identical conditions. Say on the second run you wore a tighter jersey and kept it zipped up, or had a little better aero position on the bike, that could explain the speed difference with only 1 added watt of power.

3. ### jcm01 New Member

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Thank you for your response! Good stuff. I hear you that conditions are never identical, however I think they were pretty close. I wore the same thing and was on the same bike only a few days later. The one variable that was probably different however was the wind conditions. In any event, even 5 watts difference makes more sense to me than 1 watt. Now I have to figure out why my meter might have been low that day...or high the first day! Hmmm...

4. ### dkrenik Member

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I think that your time would be better utilized in testing under more controllable conditions (inside on a trainer). Otherwise you're just taking too many SWAG's to make any analysis useful.

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I think you're wasting your time, but if you want to take your analysis a bit further, here are some things to do:
1. Break your course down to a set of segments, in which each segment has a relatively constant grade and magnetic heading. I have no idea how many segments you need because it depends on the course. It could be 4 or 40.
2. For each segment, compute your AP, NP and elapsed time
3. Assuming that your bike, wheels and tires were identical and your body position in each segment was consistent, the differences in elapsed time for the segment should be explained by AP and wind direction/velocity
4. It's worthless to compare your elapsed time for the whole course unless you managed your power identically in each segment. I can easily produce two completely different elapsed times for a course if I use my power differently in the various segments.

6. ### jcm01 New Member

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Ok, this might explain some (or most) of it. Hadn't really thought of it like this. Good to know. Thanks

7. ### RChung New Member

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I think you're wasting your time, but if you want to take your analysis a bit further, here are some things to do:
1. Break your course down to a set of segments, in which each segment has a relatively constant grade and magnetic heading. I have no idea how many segments you need because it depends on the course. It could be 4 or 40.
2. For each segment, compute your AP, NP and elapsed time
3. Assuming that your bike, wheels and tires were identical and your body position in each segment was consistent, the differences in elapsed time for the segment should be explained by AP and wind direction/velocity
4. It's worthless to compare your elapsed time for the whole course unless you managed your power identically in each segment. I can easily produce two completely different elapsed times for a course if I use my power differently in the various segments.

I've learned a lot by comparing multiple runs over the same course, and I don't manage my power identically at all. You just have to know what you're doing in order to make it an informative comparison.

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