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#7
03-03-2006, 06:21 PM
 zut Charter Member Join Date: Apr 2000 Location: Detroit, MI Posts: 3,725
Quote:
 Originally Posted by Paradoxic The force generated by the conveyor system itself is what everyone has ignored, and you are still ignoring it.
No I'm not, actually. I even said, "according to the original problem, the plane will be held stationary with respect to the ground, and thus the conveyor belt will apply the necessary force to counteract the thrust." As far as I can tell, I'm agreeing with you.

Quote:
 Originally Posted by Paradoxic Clearly, the physics show that the conveyor system itself has to be responsible for a force equal to the thrust of the engines. That's all it takes. If the force of the conveyor system equals the thrust of the engines, the aircraft can go nowhere.
Let me be pedantic far a moment: If the force of the conveyor system on the plane equals the thrust of the engines, the aircraft can go nowhere. Agreed? Now, the size of that force has to do with the construction of the plane wheels and the motion of the treadmill. According to the original problem, the treadmill will do whatever it takes to keep the plane stationary. And just what that is depends on your assumptions about the setup of the problem.

For example, if the frictional drag in the wheel hub is constant with velocity, the treadmill will continuously accelerate the wheels in order to apply the appropriate force.

Quote:
 Originally Posted by Paradoxic You are making unwarranted assumptions. Please, don't make me have to take time out to demonstrate the math on this...!
What assumptions? I didn't think I really made any at all. And sure, go ahead and do the math. Please do state your assumptions up front, though, because the conclusion is heavily dependent on initial assumptions.

Quote:
 Originally Posted by Paradoxic You cannot ignore the force generated by the conveyor. The conveyor system must be generating a lot of force to move the belt, and that force must go somewhere, right?
Sure, but again, it depends on your assumptions. It takes a lot of force to accelerate a huge conveyor belt with no plane on it at all. That force goes somewhere also, and it's clearly not into the plane.

Quote:
 Originally Posted by Paradoxic But I reject your assumption. I cannot see any fluid dymanics equation where air can become "entrained" with the moving belt. Even if you look at a speeding car, even at 160mph, you can't "entrain" enough air six feet away from the car to be of sufficient velocity to lift an airplane. Again, please don't make me do the ball-busting math on this...
Like I said, it depends on the size and speed of the belt. There must be a boundary layer associated with the belt, and I would think that at some ridiculously high belt speed, the air over the wings would move fast enough to produce adequate lift. Granted, we're talking about awfully high speeds, but awfully high belt speeds are required to keep the plane in place.

Quote:
 Originally Posted by Paradoxic To put it simply: In this closed system, if we've got a turbine-driven conveyor system, such as the turbines used to drive the aircraft, and if this conveyor system uses the same force as the aircraft engines, then this force has to go somewhere.
I honestly can't tell if I agree with you or not. Can you expand on this? For example, in this turbine system, is the belt accelerating, or staying at a constant speed? If we look at the forces and torques applied to the wheel, what would they be?