Plane on a treadmill .. to be on Mythbusters

[omgwtfbbq]

Non Sequor said:

I had to think about omg's point for a few minutes. I remember from physics that as a wheel turns against a surface, friction pushes the wheel which causes the motion. The magnitude and direction of the friction is proportional to the difference between the speed of the rim of the wheel and the wheel's forward speed (or in this case the apparent speed of the wheel). If the speed of the rim matches the forward speed then no net acceleration is experienced. All of this should apply regardless of whether the wheel is driving the motion or something else is pushing the wheel and the friction is making it turn. So it should stop the plane from moving if they can keep the treadmill matching the speed of the wheels which may be difficult since they have to make sure that the treadmill can supply sufficient power when the belt is moving at takeoff speed.

Regardless, this is a pretty stupid one to test. If they do succeed in keeping it still there's no conceivable way for it to get any lift. No motion means no apparent wind. No apparent wind means no lift.

 

EDIT: I think I misstated something. If the treadmill matches the wheel's speed, the friction should be equal and opposite to the thrust. I may have messed something up above, but I'm fairly certain that's how it works out.

The problem with your thinking is of course "if the treadmill matches the wheel's speed". Of course, if they match then that means the plane is not moving. In my scenario, however, the speed of the wheel exceeds the speed of the treadmill, no matter how fast the treadmill moves. The deal is that the motion of the wheel is not what drives the plane, it's the jets (or propellers) that drive it. If you move the ground backwards as you push the plane forwards all that happens is the wheels spin faster. The increase in friction is minimal (the friction between the wheels and the ground remains the same, it's only the internal friction between the wheel and the bearings which is changing)

If they can match the speed of the treadmill to the speed of the wheels of course it will stop moving, that's how relative motion works. My point is that they will NOT do that, because moving the treadmill faster will simply make the wheels spin faster rather than slowing down the plane, and this is completely dependant on what is providing the force. If the wheels provide the force, then that force is applied against the treadmill, and the plane will move relative to the treadmill. However, since the engines provide the force that drives the plane forwards, and this force is applied against the air, the wheels will do nothing. Imagine you're on a flying plane, and you try to slow it down by frantically spinning its wheels. That is essentially the scenario you're depicting here. The only thing the ground is doing is providing a small amount of friction against the wheels.