Originally Posted by
j41captn
How about this? You're flying straight and level heading due north 360', 100 kts. indicated airspeed with a ground speed of 50 kts. (50 kts headwind). You do a 45' bank turn to the south 180'. What will your ground speed be at the moment you level your wings? Will it be 150 kts instantly or will it take a moment to get your momentum up?
If your airspeed is 100 knots at all times, your ground speed will be 150 knots when you are headed south. This is arithmetic, not physics. But unless you are concerned with something like navigation, what does it matter what your ground speed is?
Here's a simple proof, suggested by a discussion in another one of these threads:
1. Suppose you are flying a 2000-pound plane due east on a calm day at 100 mph. Calculate your momentum.
2. Now turn the plane 180 degrees until you are flying due west at 100 mph. Calculate your momentum.
3. Calculate the difference between these two momentums.
4. Now do the same calculations, with the same 100 mph airspeed, but with a wind blowing straight from the east at 50 mph.
5. Unless you made a mistake in your arithmetic, the change in momentum in still air and with the 50 mph wind will be the same. So the change in momentum turning from east to west is not affected by the presence of wind.
I've forgotten who first pointed this out, or I'd give him credit.