Climbing Power Formula
I came across an interesting formula yesterday that may be used to predict how much power is necessary to climb a given hill on a bike. It's from Allen Lim, PhD. Allen has a long list of accomplishments related to power-based cycling the most notable of which is consulting with Floyd Landis. Floyd credits Allen with determining what he would have to do powerwise to win the now infamous stage 17 of the 2006 Tour de France. I haven't talked with Allen in some time and no longer have his email address after a computer crash this past fall so I haven't been able to confirm what I'm about to show you. But it seems to work so I suspect it's right.
Dr. Lim's formula to estimate the power necessary to climb a hill:
bike + rider weight (kg) x 9.8 x elevation gain (meters) / time (seconds) = power (watts). Add 10% for rolling and air resistance.
So yesterday I tested it. I climbed a known one-mile hill and captured the data on my power meter. Here are my metrics from that climb:
Weight of my Cervelo Soloist with 1 water bottle - 8.18kg
Body weight with winter clothes, shoes, etc - 74.55kg
Elevation gain (est based on average 5% grade) - 78.87m
Time to climb hill - 312 seconds
Plugging all of these into the formula and adding 10% predicts that it would take me 225 watts to climb this hill. The actual was 218. Remarkably close, especially when you consider that I am estimating the elevation gain and there is some variation between power meter readings.
Of course this formula could be used to figure out how long it would take you to climb a given hill in a race at a certain power output by simply rearranging the formula components. You could also use it to figure out how much faster you would climb a hill if you reduced your total system weight by a given amount but kept power the same.
Interesting stuff. If Allen sees this I hope he comments.