In rec.aviation.student tman inv@lid wrote:
Here's why I wonder about that. Let's suppose 65 KAS before and after a
180 turn from a 10 KT headwind. OK, before the turn, your groundspeed
is 55KTS and after the turn your groundspeed is 75KTS. Your intertial
frame of reference is tied to the g/speed, not the a/speed. So -- the
kinetic energy of the aircraft and contents is about 33% higher
(75/55)^2. That energy is only going to come from one place with no
power -- trading in altitude (potential energy) for kinetic energy.

This simply does not make any sense.

Kinetic energy, like velocity, is a relative quantity. You cannot look at
an object and say, "it has X joules of KE". You can only talk about KE
relative to some frame of reference. Just like velocity.

So forget about KE. It's in the same boat as velocity, so look at
velocity. You make a turn and suddenly you gain a bunch of groundspeed.
Where does the extra speed come from? It comes because you're maneuvering
relative to a medium, the air, which is itself moving. Your KE relative to
that medium is exactly the same as it was, so no energy has to come from
anywhere.

--
Michael Ash
Rogue Amoeba Software