Originally posted by: dullard
The belt can go infinitely fast and even then, THE PLANE WILL MOVE FORWARD. The wheels will not exert any significant force against the direction of the engine thrust.
Actually, with infinite speed/acceleration and indestructible wheels, it is possible for the treadmill to interact with the plane body via the angular momentum term. So you can keep the plane stationary, or even make it move backwards, until it runs out of fuel. You don't even need the friction term to assist you.
For any situation that's even close to realistic, both the friction and the angular momentum terms are so small as to be negligible, and the plane takes off.
Originally posted by: RapidSnail
In the treadmill = wheels scenario, the only way for there to be a net of zero would be if the plane was held stationary by a cable or something, right? There is no way for there to be net zero motion if the planes engines move and the treadmill = wheels, correct?
In any real scenario, true.
Until you reach the speed at which the second-order effects like friction and angular momentum get large enough to actually affect the speed of the plane. At that point you CAN actually match the so-called "wheel speed" of the plane with the treadmill. Again...very unrealistic, but possible under certain constraints.Originally posted by: Cerpin Taxt
There's nothing stopping the plane from moving forward, and thus accelerating the wheels, but once that happens you initiate an infinitely recursive self-oscillation where the treadmill must accelerate to match the new speed of the wheels, which in turn accelerates the wheels even more, which then demands that the treadmill accelerates to match the new speed of the wheels, which in turn accelerates the wheels even more, which then demands that the treadmill accelerates to match the new speed of the wheels, which in turn accelerates the wheels even more, which then demands that the treadmill accelerates to match the new speed of the wheels, which in turn accelerates the wheels even more, which then demands that the treadmill accelerates to match the new speed of the wheels, which in turn accelerates the wheels even more, which then demands that the treadmill accelerates to match the new speed of the wheels, which in turn accelerates the wheels even more, which then demands that the treadmill accelerates to match the new speed of the wheels, which in turn accelerates the wheels even more, which then demands that the treadmill accelerates to match the new speed of the wheels, which in turn accelerates the wheels even more, which then demands that the treadmill accelerates to match the new speed of the wheels, which in turn accelerates the wheels even more, which then demands that the treadmill accelerates to match the new speed of the wheels...
Maybe if we had a model plane with weak engines, very robust and heavy wheels, and a treadmill powered by a high-horsepower engine with a very fast response time, we could actually see the effect in real life. Otherwise, it's unlikely.