I just read someone's response and I want to make a comment:
I thought the entire purpose of the airplane/treadmill scenario was to allow a plane to take off with almost no runway. The treadmill moves backwards at the aircrafts takeoff speed (say 60kts), so the airplane adds thrust that should accelerate it to 60 kts. Treadmill moves back at 60kts, airplane moves forward at 60kts (-60 + 60 = 0), so the airplane is not moving with regards to a fixed reference point on the ground. No air is flowing over the wings.
In that case, the airplane WILL NOT FLY! It cannot happen.
However, it sounds to me like you guys are saying the treadmill can move back at 60kts, and the airplane would need to add thrust equivalent to accelerating to 120kts. Therefore, relative to a fixed point on the ground, the airplane would be moving at 60kts. Therefore 60kts of air would be flowing over the wing, and of course the airplane WILL FLY!
But that begs the question... What the heck is the point of this???????????????????????????????