I came across this ridiculous Internet argument today, via xkcd. I find it both amusing, and worrying, the number of people who insist that the plane will not take off. This is a classic example of what philosophers call a thought experiment, and demonstrates only what most thought experiments demonstrate: that our intuitions about even quite simple phenomena are often very wide of the mark. In this case, the intuition is that a vehicle on a treadmill will not move if the treadmill matches the speed of its wheels. While this is true for vehicles (and people) that get their forward thrust from pushing against the ground, an aeroplane certainly doesn’t. The thrust here comes from the propellers or jet turbines that push against the air. These generate an enormous force backwards, which, as per Newton, generates an equal and opposite force pushing the plane forward. If you draw a diagram and label the force arrows (as in school physics lessons), you will see an enormous forward arrow with the only opposing forces being air resistance and a tiny amount of friction from the wheels. It is a basic law of mechanics that when there is a net force acting on an object in a certain direction, then that object will accelerate in that direction. No amount of fast spinning treadmills can reverse the laws of physics. As others mentioned, the wheels will simply spin faster, as they are acted on by forces both from the aeroplane and the treadmill. The wheels decouple the rest of the plane from this treadmill force, and thus the transferred force is negligible. This is, after all, the entire point of having wheels on a plane, and not for instance just having skis.
Neil Madden 