[Structural Integrity]

Originally Posted by meglamaniac

Ok here's how I understand what Mark is saying (I'm prepared to be corrected!):

Imagine the plane is stationary at the end of the runway, but the treadmill is already moving. So the wheels on the plane are turning, but the plane itself isn't moving.

Now imagine the plane goes through normal takeoff proceedure and the treadmill speed stays constant. I think we can all agree that under these circumstances the plane would take off.

Now add in the treadmill matching the speed of the plane. The only way it would NOT take off is if the friction from the wheels (strictly the friction from the wheel bearings) as the speed of the wheels increases is sufficient to counteract the thrust of the engines. Which clearly isn't remotely close to being the case, or planes wouldn't take off anyway and wheels would be pointless.

So the plane takes off.

Am I right Mark?

Let's make this more difficult, and add in relativity.
So, when mister pilot turns up the throttle the engines start to displace air, and the big plane starts to move relative to the air.
But then there's the evil threadmill, running in the opposite direction of the wheels.
But mister pilot is amused because the takeoff is not affected by the relative speed to the threadmill, but only to the relative speed to the air. And since the threadmill has no effect on the speed of the air, even if running in the opposite direction, the plane will take off just fine.

So we have a mile-long threadmill, and a plane happilly taking off over it because no matter how fast the threadmill makes the wheels turn, the engines cleave through the air anyway.

Now, I begin to wonder what happens if due to a poor calibration of the threadmill the speed of the threadmill begins to reach the speed of light. Then the wheels of the plane would spin around at the speed of light. Now, as we know when things approach the speed of light, their relative mass reaches infinity. I don't think a plane could take off with wheels attached to it that weigh an infinite amount of pounds.

So, the answer to this whole problem lies in the calibration of the threadmill. And who is responsible for calibration threadmills? Exactly! The tech crew.
Now sadly I do not have any numbers about the performance of the tech crew that calibrates the threadmill, but if anyone could toss them in I am sure we can accurately solve this issue. Perhaps we even get a nobel prize for only spending three pages of a thread for solving it!