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By the way, what is the proof that the airplane can "turn that airplane downwind faster than it moves with the air mass" ?
Timebuilder said:The proof is the loss of airspeed.
You don't need to have ground as a part of the picture, or frame if you like, in order to have a wind. All you need is the airplane, and you have relative wind. Wind has very little mass or inertia, and the airplane has a great deal of both, by comparison.
Now add to the relative wind a movement of the airmass compared to a fixed point in space. It doesn't have to be the ground, just a fixed point. Now, heading into that wind gives you an increase of relative wind, and indicated airspeed, since we measure airspeed from a probe that points forward. If you change directions slowly, the wind can continue to effect the aircraft through the turn as the airplane decellerates toward the fixed point, and accelerates away from the fixed point, describing a hyperbolic function. The mass of moving air has sufficient time to act upon the heavy mass of the aircraft, overcoming its inertia to return to a state of equilibrium. If the direction of the aircraft is changed too quickly, then there will be a lag time before that stablized state is regained as the air acts upon the aircraft, overcoming the inertia from one vector and begining to add energy to the new vector.