The Last Word on Wind

I won’t mention the wind again. After this post. Really. I think. For this last wind post, I thought I’d provide some math you could use. If you ride.

You have to pedal to overcome the forces that would like to keep you planted in one place. The forces at work are friction, gravity and wind resistance. There is, of course, also the attraction of the easy chair and a cold drink, but we’ll save an analysis of that force for a future posting. And, to further limit our scope, we’ll only talk about wind resistance here, leaving friction and gravity (i.e. hills) for another day when I don’t ride. Didn’t ride today, by the way.

The force that a wind moving at a speed V exerts on a rider is approximated by this really useful equation:

F = 0.5 x C x A x d x V x V

A is the frontal area of the object that the wind pushes on and d is the density of the air. C is a factor that accounts for the aerodynamics of the bike and rider. Engineers determine this factor by a careful process of experimentation which produces ambiguous enough results that, in the end, they just have to guess. An agreed upon “reasonable” value for C is 0.5. A highly streamlined bike and rider would be represented by lower values. A rider carrying a sheet of plywood crossways to the wind would be given much higher values of C. It is also generally accepted (I checked on one web site) that the area A is about 0.5 square meters for bike and rider. So the rider with the plywood gets hit twice: higher C and a much larger A. I guess that’s why you don’t see too much plywood toting amongst cyclists. Except in Uganda.

Then we have the density. For air at sea level, d = 1.22 kilograms per square meter. As an apparent reward to bikers who climb big hills, God let the density go down with altitude. At 1500 meters, it is a whooping 20% lower than at sea level. Density is also lower on hot days. So, why is it so hard to climb a hill on a 90 degree day?

As noted in an earlier post, the force exerted by the wind increases as the square of the speed, V x V. See, it is in the equation. But that’s not the whole story. I know you are asking yourselves, “How much effort is required to move against this force?” Glad you asked. The work (that’s a technical term) is the force times distance moved. The power (another technical term) required is the force times the distance per unit of time. I know most of you have already figured this out, but distance per unit time is speed, or V. So the power or rate we use energy to move through the wind is F x V. Notice how bad this gets. The power, which is measured in calories – see where we are going with this? – increases with the CUBE of the speed or V x V x V. So, we need to stoke the furnace with 8 times more calories to move in a 10 mph wind than it takes if the wind is 5 mph.

We are almost done. The last detail is this speed V. It is, of course, the RELATIVE speed between the air and the biker. If you are riding at a speed of Vyou and you have a headwind of Vwind, then V=Vyou+Vwind. Bummer. But if, in the rare case when the sun, moon and all the planets (including that new one they found recently) align over Cadott, Wisconsin and you have a tailwind, V=Vyou-Vwind. You can see in this unlikey event that if you are moving at 15 mph with a 15 mph tailwind, V=0 and you owe NOTHING to the wind. Oh well, no sense pondering the impossible. Well, highly improbable.

So, there you have it. Useful math. Enjoy. Oh, yes, there WILL be a test!

Total ~ 1261.7 miles