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Now that I see how the conversation is going, I feel I can jump in without persuading the topic. Yes, my neighbor does not ride, and yes he feels that a cross wind is helpful to the cyclist. His argument is that if it is not a head wind, then it is helping the cyclist. Like the wind will wrap around the back of the cyclist and push the cyclist forward somehow.

I think one could argue that if the force of wind 'pushes' the cycles to the left or right, during travel, that this is a form of resistance. The cyclist will 'waste' energy compensating for the wind pushing the off the vector of travel, forcing the cyclist to turn into the wind slightly.

I am not sure the magic angle, but I would even go as far as to say that a tail wind at a steep angle, nearly perpendicular to the cyclist, is still a from of resistance. The cyclist will have resistance greater than the help the wind is doing pushing the bicyclist.