Rolling Resistance in Climbing
Rolling resistance on the flats is just the weight of the combined cyclist and cycle multiplied by some coefficient of rolling resistance. For asphalt, the coefficient is 0.002. On the flats, the total effort required to overcome rolling resistance is therefore simply the force which remains constant times the distance ridden.
In climbs, rolling resistance is computed in a similar fashion with one exception. It makes a slight adjustment, so small that it is routinely ignored. But it is also worth mentioning.
On the flats, the entire combined weight is directed into the road. But what happens on a slope? In most discussions, the assumption is that in computing rolling resistance on a slope, your weight remains the slope independent of the slope.
But consider a case where you are riding up a nearly vertical hill with a slope of 89°. How much of your weight is directed into the slope and how much straight down. In that case, nearly all of your weight is directed downwards with only a small fraction directed into the slope, that is only 0.017%. If you weighed 175 lbs, that would mean the slope would feel that your weight was only 3 lbs.
Do we really need to worry about this, particularly given a 10° slope is consider an upper limit even for Elite Cyclists. Here is a chart which shows it can be ignored with only minimal impact Each line corresponds to a different weight. For realistic cycling slopes, we are talking about an adjustment in the range of 0.02 lbs.
Computing Total Rolling Resistance Work for a Climb
All of this makes it easy to compute the total work a cyclist needs to perform to make a climb against rolling resistance. They simply need to take the distance to the top and multiply it times the combined cyclist-cycle weight and the coefficient of Rolling Resistance.
The Alpe d’Huze climb is 13.2 km. What is the total effort expended against just rolling resistance? Te coefficient of rolling resistance is 0.002, and the combined cyclist-cycle weight is (126 lbs + 16 lbs) or 142 lbs. Converting to CGS units, 142 lbs is 631.6 newtons. Then the total effort is
WRR(Joules)= wgt(Newtons) * coeff * distance(m)
WRR = 631.6 Newtons * 0.002 * 13.2 km = 16674.24 Joules
If you are curious about not including the slope factor, comparing this to the slope corrected value indicates the above overestimated the work by 56 Joules.
Understanding Total Rolling Resistance Work
Work quantifies the total effort to do a task. What does the number above mean? What is a comparable effort? What are some equivalent energy outputs comparable to dealing with rolling resistance on the Alpe d’Huze?
The human body releases heat energy of 60 Joules per second which is the amount we overestimated the total work.
The total effort of 16.67 kJoules is comparable to:
- Energy release by a 4 Watt light bulb over an hour
- Energy in two alkaline AA Batteries
- Energy in four food calories