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Old 03-05-2006, 07:46 PM
David Simmons David Simmons is offline
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Join Date: Nov 2001
Posts: 12,684
Originally Posted by zut
Stable, though, in the sense that the conveyor could theoretically hold the plane in position to within an arbitrarily small distance, and small perturbations in thrust only require small changes in belt acceleration to hold it in place. Until the system bumps into the real physical limitations, of course.
You'll have to go through this process for me step by step. If the wheel speed (in the conveyer matches wheel speed case) is the plane speed plus the conveyor speed, how can the conveyor ever be going fast enough? It seems to me that if the plane moves at all, the converyer will just go to its maximum speed and stay there.

Plane and conveyor speed are relative to the ground. Wheel speed is the peripheral speed of the wheel.

wheel speed = plane speed + conveyor speed

conveyor speed = wheel speed - plane speed

Until the conveyor is going fast enough for the force required to accelerate the wheel equals the engine thrust the plane speed won't be zero. The conveyor speed then can't match the wheel speed because it is slower by the plane speed. Based on computations in this post I don't see how the required wheel acceleration force can be achieved before any reasonable, or even unreasonable, system limits out.

There is the problem of bearing friction. Such friction is usually taken to be a constant times the velocity. This will make the force opposing engine thrust grow faster than just the force required to accelerate the wheel alone. That reduces the required wheel speed for balanced forces. However the forces tending to throws the tire off the rim and the tire speed limit will probably be reached before force balance is reached even with friction helping the retarding force.