WingFlaps schrieb:

A direction change in a
plane is always due to acceleration (and that means more drag). That's
Newtonian physics.

Right.

You go from up wind direction (takeoff is usually
up wind) to turn in the wind direction to land down wind. There's an
acceleration, it is a change in _velocity_

Wrong.

it creates drag, it costs
height and that's the important bit. Now do you understand -TURNS are
not free,

Right.

Your're mixing up two completely different things. Of course, turns are
never "free". They cost energy due to higher drag, resulting from higher
speed, higher wingload and control deflection.

*But*: It absolutely doesn't matter whether you turn from headwind into
tailwind or vice versa. Your airspeed does *not* change. (Of course the
vector does, but not its magnitude.) Your groundspeed changes, but
that's not relevant. Your sentence "Now we add in the energy losses from
having to accelerate with the wind" can only be interpreted that you
think groundspeed would matter because you somehow had to "acceleerate"
to catch up with the wind speed when turning from head to tail wind.
Which is utter nonsense, Newtonianly spoken.