 CYCLING PERFORMANCE TIPS
Last updated: 4/23/2010

Effects of a hill on energy needs for cycling

I often receive questions re the energy expenditure on hills versus the flats. For example:

Q. I was wondering if you knew the relationship between speed and effort for a given gradient. Obviously, when climbing you are using most of your effort to overcome the force of gravity. Is the relationship between speed and effort linear (i.e. to double your speed on a climb you need to use double the power / watts) or squared (i.e. to double your speed takes four times the power) or something else? JC The basic energy requirements for the flats versus a slope are based on these formula. But if you want a quick and easy way to do the "what-ifs", there is a great little calculator for Speed For Given Power found at Analytic Cycling - a very nice collection of calculators for the cyclist interested in the technical aspects of energy use on a bike.

I did a few quick what-ifs and following are the results. (I tested the calculator to assure myself it took into account the exponential increase in resistance related to wind resistance which becomes a significant factor at speeds over 15 mph - it does).

First, what happens if one wants to keep energy output steady i.e. you want a speed on a slope that keeps your heart rate the same. How much should you slow down. Assumptions:

• Power 250 watts
• Frontal Area 0.5 m2
• Coefficient Wind Drag 0.5
• Air Density 1.226 kg/m3
• Weight Rider & Bike 75 kg
• Coefficient of Rolling 0.004 At speeds of 20 to 25 mph, one needs to slow approximately 2.5 to 3 miles per hour for each degree increase in the slope of the hill - or increase heart rate and energy expenditure. At slower speeds, only 1 to 2 mph as almost all the energy differential is being applied to overcoming gravity and very little to overcoming wind resistance.

I decided it would be interesting to look at it from the other direction i.e. how much extra enery (in watts) would one need to use to keep speed constant. This assumes that wind resistance is uncahged and all the extra energy goes into ovecoming gravity. Here is the result making these assumptions:

• Speed = 25.12 mph
• Air Density 1.226 kg/m3
• Weight Rider & Bike = 75 kg Since wind resistance stays equal (speed is steady), there is a linear relationship of an additional 80 Watts required for every 1% increase in slope.

A. Now back to the original question. As you can see from this discussion, this requires a knowledge of the slope of the hill as well as wind resistance. I decided it would be easiest to go back to the calculator and, assuming you were riding at a relatively easy 5 mph on a slope of 4%, calculate how much more work it would be to climb the same slope at 10 mph and then at 15 (assuming you were really chasing your buddy). The answer for a 75 kg bike and rider were:

• 5 mph = 74 Watts of energy
• 10 mph = 158 Watts
• 15 = 263 Watts

So double the speed and it will take twice the energy.