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Are Expensive Bicycle Wheels Worth the Money? Let’s Check the Physics

In this video, you see a cyclist testing new aerodynamic wheels from Zipp. Swapping your wheels may seem like a small change, but can make a big difference. From his tests, the rider discovers:

  • With conventional wheels, he can ride 20 minutes at an average speed of 41.12 kph with an average power of 379 watts.
  • With the Zipp 808 NSW aero wheels he rides 51 minutes at an average speed of 41.13 kph and average power of 344 watts.

Before looking at power and energy, I should go over two small details.

First, how do you measure power? Cyclists can measure power by installing a small computer, called a power meter, that measures the input torque at the pedals or crankshaft and records the rotation angle at timed intervals. If you know the torque and angle, you can calculate the input energy. Dividing this energy by time gives you power.

La te xi t 1

Second, this isn’t a perfect test of aerodynamics. If you really want to examine the effect of the new wheels, you probably would have to put a bike with a dummy in a wind tunnel. When the reviewer takes his second ride, many things could have changed—wind, body position, amount of sweat on the body—and impacted performance. Let’s assume the only thing that changed was the wheels.

Air Drag and Power

What happens when you ride a bike? If you are moving at a constant speed, then the net force on the bike-human system must be zero. In a slightly simplified view, I can draw the following force diagram:

Spring 2016 Sketches key

The vertical forces (gravity pulling down and the ground pushing up) don’t really matter here. Just forget about them and pay attention to the horizontal forces. First, let’s look at the air drag. Air acts in complicated ways when an object passes through it. But who cares when we can make a simple model of air drag force? Here’s an expression for the magnitude of this force:

La te xi t 1

In this model, the air force is proportional to the square of the bike’s speed (v). For the other terms, we have:

  • ρ is the density of air (around 1.0 kg/m3).
  • A is the cross sectional area of the bike plus the rider (how much of the object interacts with the air).
  • Finally, C is the drag coefficient. This parameter depends upon the shape of the object. If you change the wheels, it is the value of C that should change.

The second horizontal force is the frictional force. An interaction between the road and the tires propels the bike. I know what you’re thinking: Doesn’t the human propel the bike? In a sense, yes. But the reality is sort of complicated. The rider’s power goes through the pedals and chain to the wheel, which turns. But the force comes from the tire pushing against the road. So for our energy perspective on this problem let’s just say the human provides the friction force.

Clearly the faster the biker