Martin Bier, a physics professor at East Carolina University in North Carolina, became intrigued by this debate and decided to explore the physics, and a little project ensued. In the American Journal of Physics, he shares his finding that ultimately, the wind turns out to be of negligible consequence.
First, a little background: From a physics perspective, cycling is easier to comprehend than running.
"In running, the motion of the legs is repeatedly accelerated and decelerated, and the runner's center of mass moves up and down," said Bier. "Cycling uses 'rolling,' which is much smoother and faster, and more efficient—all of the work is purely against gravity and friction."
But there's something odd about air resistance. The force of air friction you fight goes up with the square of your speed. If air resistance is the main thing limiting your speed—which is true for a cyclist on flat ground or going downhill—then to double your speed, you need four times the force. Tripling your speed requires nine times as much force. But, on the other hand, when cycling uphill, your speed is much slower, so air resistance isn't a big factor.