ORIGINAL: Shoe
Here’s a question about airplanes turning from upwind to downwind. Suppose you have a very efficient glider that can make a 180-degree turn maintaining 100 knots and lose only 10 ft of altitude (to eliminate ambiguity say that there in NO motion of the air relative to the ground and it starts 100 ft above sea-level). Next, suppose that the glider is going upwind into a 100-knot headwind. Relative to the ground, the glider would be hovering. As it makes a 180-degree turn, it will accelerate to 200 knots relative to the ground, again losing only 10 ft of altitude. My question is: in the no-wind case, the glider lost 10 ft worth of potential energy, but didn’t gain any kinetic energy. In the 100-knot headwind case, the glider again lost 10 ft worth of potential energy, but gained 200 knots worth of kinetic energy. If it’s true that the wind doesn’t make any difference to an airplane once it leaves the ground, then how did the wind give the plane all that extra kinetic energy?
If kinetic energy is the energy of motion, it is therefore relative in exactly the same fashion as motion itself. Saying the glider has 200 knots groundspeed is equivalent to saying it has so much kinetic energy relative to the surface of the earth. Does the glider at 100 knots airspeed and zero knots groundspeed have zero kinetic engergy? Relative to the earth, yes (not counting it's vertical speed). Relative to the airmass, no.