This is actually pretty funny, because here in Phx... The early morning has wind out of the NE coming from the mountains. As the day warms, the air is pushed back into the mountains... so you get a headwind heading out on the Beeline highway in the early morning. If you ride out till afternoon, your return on the same rode is indeed a headwind :|

Hold on. The first thing we learn in the first semester physics class is the concept of Frame of Reference. The bicycle can't tell the difference between moving 30mph ground speed in still air or 5mph ground speed + 25mph headwind. The drag is the same. 30mph of wind is moving over the object.

It doesn't take any power to stand still in a 25mph wind, but it does take FORCE, which you obtain from the ground friction, and you compensate for this force to keep from falling over by leaning into the wind.

Just like it doesn't take any power to stand on a 20% grade until you move.

I think the internet calculator you're using is just wrong.

This would all be well and good if moving air behaved exactly like still air, but it doesn't. Air that's moving in different ways has different consequences for a cyclist, which is why drafting works at all. And friction is not (not!) force. The fact remains that you don't need to exert yourself at the same level you would to ride 25 mph just to stand still in a 25 mph wind. Still, I take your point about standing on a hill.

Why this is true, I can't tell you. I won't pretend to know much of anything about the aerodynamics or physics behind it. But my own experience and the actual data, calculators, charts, whatever I've been able to look up do suggest that the effect of wind speed on power is very different from the effect of riding through still air at the same nominal speed.