Actually, thinking about it, the "Monentum" and "Kinetic Energy" crowd are correct. The vectors should resolve themselves even to an observer on the ground.
And they DO!
The mistake many people are making (Mike O of the impressive credentials chief amongst them) is to substitute Speed for Velocity. They are two very different things.
Speed is a scalar quantity and as such only has magnitude whilsy velocity is a vector quantity and thus has magnitude AND direction.
Turn an aircraft through 180deg at a constant speed in nil wind and you haven't changed it's speed, but you HAVE changed it's velocity.By how much? Well, do the vector diagram.
To change a vector of, say, 100kts due west to one of 100kts due east you must add a vector of 200kts to the East. You do this by tilting the lift vector, or reversing your harriers nozzels or however. The result is a delta vee of 200 kts.
Now lets introduce a head wind of fiftey knots. Your ground speed is fiftey knots. We introduce the same angular acceleration by tilting our lift vector or whatever in exactley the same way as nil wind.
Now we are heading due east with an airspeed of 100kts and a ground speed of 150kts.
Our velocity with reference to the ground has changed from 50kts to the west to 150kts to the east. A change of? 200kts to the east, exactley the same as in nil wind.
The "down wind turn" is a crock.