Physics of Fitness Fridays - Biking and Running, What a...Drag? (pt 2)

Last week we discussed the drag force acting on you when you move through the air. What happens when you have a tailwind or headwind?

Remember that the drag force is proportional to your cross-sectional area A and the square of your velocity v.

As it turns out, the velocity v should be your velocity relative to the wind. Thus, we replace the v in the previous equation with v-vwind.

If we’re running into a headwind, vwind is in the opposite direction of our motion and we consider the velocity negative; thus, v-vwind makes us add the speeds together; so if you are running at 6mph and face a 4mph headwind, your relative speed with respect to the wind is 10mph. If you were running at 6mph and had a 4mph tailwind, your relative speed becomes 2mph.

For a headwind, since the speeds add, you will always face a greater drag force relative to if there is no wind. For example, if the wind speed is half of your speed, your drag force increases by more than a factor of 2. Oof!

On the other hand, if you have a tailwind that is half of your speed, the drag force is reduced by a factor of four relative to no wind (ie, it’s 25% of the drag with no wind). SWEEEET!

If you compare headwinds and tailwinds as a function of your speed (for example, 25% your speed, 50% your speed, up to 5x your speed), you can see that the drag force for a headwind rises pretty rapidly. A tailwind, on the other hand, decreases the drag force until vwind matches your speed, where the drag force is canceled out! If the tailwind continues to increase, you start to get a boost. Note that a tailwind never helps you out as much as a headwind will slow you down.

So if you’re running or biking in the wind, you can always re-adjust your course so that the wind is forever at your back. Of course, that might make for a pretty random trip…you might not even get home! Good luck!