I Hate the Flats
May 7, 2010 9:54 am
While most cyclists might dread the hills, I seem to be the opposite. When I am with a fast group of guys I can barely hang on, especially if there is a headwind. Once we reach the hill, my heart rate will actually go down and I may even go ahead of much of the pack.
In trying to understand why this is the case, I have calculated the power requirements. If I had a power meter, I guess I could measure it directly, but calculating it will work fine. I am short and relatively lightweight. I would like to compare myself to a bigger guy, say someone who is 6 ft. 2 in. tall and weighs 200 lbs, compared with my 5 ft. 6 in. and 140 lbs. I have run the power required on different situations and put them in a table below. I will assume a 20 lb. bike in both cases.
To make the comparison easier to follow, let’s assume both riders can climb a 10% grade at the same rate, and that rate is their maximum power output. If we calculate the power required for each rider to accomplish this, we can then see how much reserve power is left for different scenarios. If we are riding together on a flat road, with no wind, at 23 mph, I need to put out 91% of my maximum power output, while Mr. Big only needs to use 73%. If we now have a 15 mph headwind and travel at 15 mph, I have to increase my power to 96% of my maximum, and am dying trying to keep up. Mr. Big only needs to go to 79%. We know that human physiology is not linear and the closer one gets to their maximum ability the harder it becomes to achieve even a small increase in output.
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Franz
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Mr. Big Guy
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5’6″, 140 lbs
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6’2″, 200 lbs
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Average Power
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Percent
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Average Power
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Percent
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| Flat, 23 mph, no wind |
252 watts
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91%
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277 watts
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73%
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| Flat, 15 mph, 15 mph headwind |
262 watts
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96%
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300 watts
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79%
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| Climb, 8 mph, 10% grade |
276 watts
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100%
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377 watts
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100%
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Of course we could look at things a bit different. Using the above table, let’s say both riders, traveling at 15 mph with a 15 mph headwind (on Malech) are putting out 95% of their maximum capacity when they hit the hill with a 10% grade. In that case I would be able to climb at 8 mph by putting out 100%, while the big guy will have to drop his speed because his 100% would be 315 watts which means he can only climb the hill at 6.7 mph. If the hill is Metcalf, which averages a 10% grade, that means I can reach the top in 13:20 (about my PR) but Mr. Big will need 16 minutes.
Now you know why I hate flats and love the hills.
2 Responses to “I Hate the Flats”
What did you assume for CdA? A simple scaling analysis, assuming fixed BMI, suggests that A of the rider (around 2/3 total CdA) is proportional to the 3/4 power of mass (mass proportional to height squared, so height proportional to square root of mass, so depth and width each proportional to fourth root of mass, so width times height proportional to 3/4 power of mass). At constant power/mass, therefore, the advantage of the bigger rider is then only the fourth root of mass, not counting the bike wind resistance (which will also scale somewhat with rider height).
If height is fixed, and BMI is varied, then the dependence of wind resistance on mass would then be weaker: the square root of mass rather than the 3/4 power, yielding a square-root rather than fourth-root advantage to the bigger rider with the same power/mass.. So if BMI and height were both changing, you could analyze the effect in two steps.
I am using a rule of thumb that the frontal area in square meters is 0.35 times the person’s height in meters. For the coefficient Ca I used 0.5, which is typically used. See my other post on power calculations at: http://www.blog.ultracycle.net/2010/05/cycling-power-calculations . It contains all the parameters and formulas I used. It also contains some references.
The two type of riders I picked have a different BMI, intentionally to illustrate my point since some large cyclists do have a higher BMI than I do, especially if they are muscular. BMI is not a very good concept in the first place, especially with dealing with athletes.
On the hill climbs on the Ultra Distance website, if people put in their weight, height and bike weight, the site will then calculate their average power output for the climb. See http://www.ultracycle.net
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