Originally posted by: mchammer
jagec and SO, while you are correct that a very rapidly spinning tredmill could raise the RPM of the wheels to the point where they would have the "mass" to keep the plane still, in the OP it says that the treadmill would be limited to moving backward at the same speed the wheels (the plane) is moving forward. In that case, the wheels would spin at 2x what their normal RPM would be at any point throughtout the takeoff run. That would not be nearly enough to increase thier "mass" enough.
So basically, there is no way to argue under the terms of the OP that the plane would not take off, save wheel bearing with lots of friction.
Also :beer: to Tom for coming around.
I wasn't talking about relativistic effects. In my example, a Cessna burns through an entire TANK of fuel, and the conveyor ends up going ~2000km/h. I agree you'd need to change the control system from that stated in the OP, however.
Originally posted by: KK
But what the OP said is impossible because there is no way to match the conveyor to the wheels because the engine is going to push it physically forward. Therefore by physically moving forward falsifies the stipulation the the conveyor counteracts any foward wheel movement.
If the belt was able to keep the plane in one position then, no it wouldn't fly, but thats just asking too much from the belt.
There are two interpretations to the control system postulated in the OP. The first interpretation leads to an infinite conveyor speed for any nonzero plane speed. The second leads to a conveyor speed equal to the plane's ground speed ("ground" meaning the stationary area not on the conveyor), but in the opposite direction.
The belt CAN keep the plane in one position, but not with the control system in the OP.
