Sorry for flogging a dead horse, but this is my brainteaser for the day, so I want to get to the bottom of it :lol:
Thus the idea was simply to take a target wind vector (apparent wind over the flight deck = 30 knots AWS@351°AWA), subtract the true wind vector from it and get the velocity vector to complete the wind triangle.
This was essentially my idea as well, but given that TWA is provided in the global frame and AWA in the carrier-fixed frame, can you just subtract the vectors?
In my solution, we know two sides of the wind triangle (a = 6, b = 30) and the angle opposite a (alpha=9). So we get the angle opposite b with the law of sines: beta = asin(b/a * sin(alpha)) [2 solutions!] and the third angle from gamma = 180-alpha-beta.
Now we can map that triangle into the global frame from the given direction rho=140 of a to get the carrier heading
tau = rho + gamma - pi + alpha
and the carrier speed as the length of the third side of the wind triangle, again from the law of sines:
c = a*sin(gamma)/sin(alpha)
with the two solutions I posted above, unless I made a mistake.
To mix it up a bit, I'd like to pose a modified problem:
Given the same wind of 6 ktn towards 140 deg and the same flight deck rotation of -9 deg, and given a constant carrier speed of 30 ktn, and a constant aircraft approach TAS of 100 ktn, which direction should the carrier go so that the pilot can simply line up with the runway centreline as if she was landing on a fixed runway with no wind?
[Hint: if the carrier was going at 6 ktn, the trivial answer would be 140 deg, but since it is faster it must be rotated to produce a larger cross-wind component]