Guys, if I figured out the way you are reasoning, you are saying that if TAS is greater than GS, we have headwind, if it's smaller, we have tailwind. Is that what you mean? I'm not sure that it is the correct definition.
I'm looking at this problem in the same way as a crosswind landing: if we are landing on RWY 18 and the wind is 150°/20 kt, then we say that we have a headwind component of 17 kt and a crosswind component of 10 kt, and those components are referred to the ground track, not a/c heading. En-route it's exactly the same thing, is it not?
Fly from A to B, then back from B to A, where the wind is 90° across track ... and you will have a headwind in both directions
No, I will have a TAS higher than the GS, to compensate for the crosswind, which makes me travel farther in the air mass than I would on the ground, but that doesn't make the wind vector a headwind, it just stays a crosswind. "To head into wind" does not coincide with having a headwind, as I see it.
Is there any book that defines head/tailwind as "the component of the wind vector relative to the aircraft heading"? I would be interested in seeing one.
Deeday