Calculating Headwind/Tailwind component

Ramy wrote:
Thankfully, some flight computers such as 302 provide TAS, so my solution was always to subtract TAS from ground speed to determine HW/TW component, but I am surprised that not all flight computers use this simple calculation to provide instantaneous HW/TW component. After discussing it with some, it was suggested that my assumption is wrong, and that HW != TAS-GS when cross wind is presented. I am not sure why though.

This formula is correct:

Wind = TAS - GS

... but only if you use vectors. If you use only the magnitude, you're
wrong, because you're ignoring the direction of these vectors.

Taking an extreme example: your airspeed is 40kt, wind is 30kt from
the right (i.e. no head wind). You would think that your ground speed
is 40kt because you have no head wind. But since the cross wind
displaces you, your ground speed is really 50 kt (according to
Pythagoras: square root of 30^2 + 40^2).

Btw. XCSoar shows head wind component in an InfoBox. The true one.
And if you have airspeed input (e.g. with a CAI302), you get wind in
straight glide nearly instantly.

Max