Originally Posted by
J.P.
I respectfully disagree with your analysis. Drag exists only in opposition to motion. Since all of the motion is in the forward direction, in the case of a cross wind, only the self generated head wind contributes to drag. As others have explained you still have to expend extra energy fighting a cross wind even though it doesn’t increase drag.
You're trying to balance on the head of a pin. We both agree that the crosswind does increase the total resistance. If we don't, then I await an explanation for the greater effort needed. So if you don't want to call it drag, you need to give it another name, and explanation of the mechanism.
Part of the problem is that you're only looking at the bicycle with respect to the ground. But while the bike is riding
ON the ground, it's moving
through the air, and it's the effects of moving through that air which is the issue.
If in doubt, I suggest you draw a free body diagram and account for all the forces needed to maintain equilibrium when a bicycle moves at constant speed in a cross wind.