I think we need to agree on a definition of tailwind component.
My definition: Component of wind parallell to the intended direction of travel.
BTW, you will be crabbing 27 degrees into the wind in the given example. The headwind component (you will never get a TWC at all if you want to remain on track) will then be
50*cos(90-26) = 23 K.
With a TAS of 112 K and a GS of 100 K...
So with GS-TAS or vice versa it is either 100 - 112 = -22 or 112 - 100 = -22. I think not.
Cheers,
Fred
Edited to get the signs of the erroneous TWC components right. 22 knots of HWC is -22 knots of TWC...
