Originally Posted by
David Bierbaum
Actually, this part isn't really true per-se. (Sciencey nitpicking of no real consequence ahead!)
Your self-generated headwind component is your self-generated headwind component, regardless of the crosswind component. The crosswind won't add to your headwind, and your self-generated headwind will be the same even with no wind at all, since it's the "headwind" generated by you pushing yourself through the air. The added burden crosswind provides to your forward motion, will come entirely from the friction of the tires on the road as you counter-steer against the crosswind...
The crosswind and self-generated headwind vectors add together to make it feel more like a headwind, however, so that the faster you go, the more messed-up the wind situation feels to you, as a rider.
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Actually it's a bit more complicated than that because wind resistance isn't linear. When you combine the crosswind with the bicycle's forward speed you get an apparent wind speed higher than either. Since wind drag is proportional to the square of wind speed, when you calculate the drag at the higher speed, then divide it back into the two vectors, the forward drag component is higher than it would have been in still air.
So it's not at all an illusion that riding across the wind is harder than riding in still air.