Originally Posted by
Gadget freak
So the answer is that the air speeds (velocities relative to the bulk air mass) are constant while the ground speeds ( velocities relative to the earth) are not. Kinetic energy is relative to an inertial frame of reference and the V in 0.5*m*V^2 is velocity relative to the earth so the aircraft is being accelerated by the air mass that is moving relative to the ground.
I didn't ask what the change in airspeed was I asked what the change in
velocity is. That wasn't an accident. Velocity is a vector quantity, and that's what kinetic energy is based on. This is the fundamental piece of knowledge you're missing which is preventing you from correctly understanding the physics here. Fitter2 has already given the correct answer, but I'll repeat is in a little more detail; The change in velocity in the turn is 200 knots. Going from 50 knots eastbound to 150 knots westbound is a net acceleration of 200 knots. going from 100 knots eastbound to 100 knots westbound is a net acceleration of 200 knots. The change in velocity is 200 knots relative to the frame of reference of the ground; the change in velocity is 200 knots relative to the air mass moving over the ground at 50 knots, and in the no wind condition the the ground based frame of reference and the frame of reference of the air are the same, so the change in velocity of the calm air airplane is 200 knots in either case. Bottom line is that in all frames of refrence, in both the wind and no wind case the change in velocity is identical. So, if the change in velocity is identical, then the change in kinetic energy must be identical.
Originally Posted by
Gadget freak
Kinetic energy is relative to an inertial frame of reference ...
This warrants a specific comment. This is true, as far as it goes, but from your statement it appears that you don't understand what an "inertial frame of reference" is. An inertial frame of reference is quite simply, an unaccelerated frame of reference, a frame of reference which isn't changing velocity. In this scenario, both the ground and the uniform air mass moving at a constant velocity over the ground are inertial frames of reference.
Some points to ponder:
What is acceleration? (the physics definition, not the non-technical "going faster" meaning.)
Is turning flight accelerated flight or is it unaccelerated flight?