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Old 03-05-2006, 09:06 PM
zut zut is offline
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Join Date: Apr 2000
Location: Detroit, MI
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Originally Posted by David Simmons
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.
But remember that the conveyor responds to engine thrust with a change in acceleration, not just a change in velocity. For example, you calculated a nominal required acceleration in your linked post, based on some mass and thrust assumptions.

If we ignore physical limitations for a second, then what would happen in a perfect system would be that the plane's engines would light off, the treadmill would respond with the constant acceleration that you calculated, all the forces would balance, and the plane wouldn't move. Right?

In a less-than-perfect control system, there would be some lag in the response. So the plane's engines would light off and the plane would surge forward slightly before the treadmill had a chance to respond. The control system would register the increased wheel speed, and respond with a larger treadmill acceleration than the steady-state acceleration you calculated. The increased acceleration would transmit more force to the plane, slowing it down, until plane speed = 0. Then wheel speed = conveyor speed (even though both are still accelerating!) and everyone's happy.
Originally Posted by David Simmons
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.
Can't argue there. Interpreting the problem this way (with an ever-accelerating belt keeping the plane stationary) is pretty clearly a thought experiment, and not practical at all. Unless...I recall someone in the previous thread suggesting an RC model outfitted with very heavy wheels. It's possible something like that would be test-able.