747 on a treadmill conundrum..

[pocaracas]

The way I remember hearing about this "problem", a few years ago, it was with a treadmill that moves backwards so as to counteract the forward motion of the plane. It doesn't matter if it rolls as fast as the wheels, or faster than the wheels, it just moves at the speed of the plane itself, in an attempt to push it backwards, thus keeping the air around the wings always the same and, thus, the plane wouldn't take off.

However, if we assume that the plane is already moving, there is already some air going through the wings. The plane is moving due to its own engine, so, no matter how fast the treadmill pushes back, considering the wheels are free to roll as fast as they may (no drag in the axles), the plane will keep moving through the air and the treadmill's influence will be negligible.

Even if the plane starts from a resting state, the treadmill should not influence the motion of the plane through the air, because it will just cause the wheels to spin twice as fast. Yes there will be a grater drag force, keeping the plane attached to the treadmill, but remember, the treadmill will only move as fast as the plane, never faster. The plane will never go backwards, due to the treadmill. So, sooner or later, the engine's power overcomes the ground drag force and the plane moves forward through the air.