747 on a treadmill conundrum..

[Anomalocaris]

They will result in some drag because their bearings are not totally frictionless. But wheel drag will be negligible next to the thrust of the engines, or the aerodynamic drag on the aircraft resulting from forward motion. So the wheels will have little effect whether it is rolling on the treadmill or a concrete runway.

The rated speed of the tires are a concern. Airplane tires, like car tires, have a rated speed. Putting the plane on a treadmill will cause them to roll twice as fast as normal and likely exceed rated tire speed. I don't know how long they will last and whether they will survive one complete take off run. But I don't think this kind of detail is what the original puzzle was getting at. The original puzzle was about pulling the leg of people who don't much about how aerodynamic flight work in principle.

Or what causes the plane's forward propulsion for that matter. I thought about this this morning in terms of the Kitty Hawk planes that were pedal powered, but since the peddles turned the prop not the wheels, the problem remains the same with regard to the treadmill.

It's speed relative to the air not the ground that matters for flight. If you don't believe it all you have to do is think about how an airfoil kite flies. It's not going anywhere relative to the ground, but wind-speed lifts it and keeps it aloft and drag from the string hold the angle of attack. http://en.wikipedia.org/wiki/Foil_kite

A plane that is propelled by turning its wheel while rolling on the ground can't really fly. As its wheel spins faster and the plane moves faster, it's wings will start to develop lift, which would lessen the weight on the wheel, which would in turn reduce the friction between tire and ground, leading to loss of traction and propulsive efficiency. Just before the plane reaches the speed where lift can exceed weight, the lift would almost equal weight, and the drive wheel will be almost completely unloaded, and adding power to the wheel will cause it to spin without friction or traction with ground.

So a plane propelled by its wheels could not quite cross the threshold of speed where lift would surpass weight.

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Not if you read fast as describing the velocity of the axle or center of the wheel, as oppose to tangential velocity at the rim or tread of the tire. As the axle of the wheel move forward at X mph, the treadmill moves backwards at -X mph.

In the absence of any stated reference point for velocity to be measured against, This is how I interpret treadmill moving backwards at the same velocity as the wheel.

The velocity of the axle is radial and not measured in miles per hour. It doesn't make sense to compare a radial velocity to a linear velocity.

The question is simply badly worded. So badly worded that it yields two contradictory conclusions, both of which are consistent with the wording of the question. One which relies on a literal interpretation of the phrase about the conveyor belt, the other of which relies upon trying to interpret what the author meant, ignoring the literal implication of what was actually said.

No, the velocity of the axle is linear and horizontal in the none rotating frame of reference. The axle is bolted to the landing gear and the plane.