I stated many many posts ago that the problem is poorly stated.

I violated the statement of the problem (that the treadmill could match the wheel speed)

You violated Newton's second law (by postulating a magical force).

You can't satisfy both Newton's 2nd law and the problem statement in a natural system that doesn't mechanically fail.

It seems that the fundamental question/situation has changed. Are folks now suggesting that the treadmill is applying a force great enough to the wheels at an angle to counteract the force of the jet engines?

Where am I going wrong? if the treadmill moves at the backwards at the same speed the plane moves forward, I'm seeing the plane able to take off, although the wheels will be spinning twice as fast as non treadmill take off. I dunno, maybe I'm not understanding the question properly..

I believe Orange is.

phrom is not.

The plane isn't actually moving forward. When you say "the wheels will be spinning twice as fast," no. The speed of the treadmill equals the speed of the wheels.

Since the plane isn't moving forward, there's no lift.

No. As I said just moments ago, the thrust doesn't have to be counteracted. The thrust is driving the treadmill. More thrust = faster treadmill. The treadmill is able to spin just as fast as necessary to keep up with the plane's wheels (which is also specified in the original problem).

If he's going to do that, why not just tether the plane to an immovable object directly behind it and define it as part of the treadmill.

I'm not postulating a magical force or changing the fundamental question. The original question says that the treadmill will ALWAYS match the speed of the plane's wheels. This means that the plane and the treadmill are in an escalating battle to out-accelerate each other. You guys are not taking into account the rotational acceleration of the wheels. That will consume ALL of the energy in the system so that there is nothing left to propel the plane forward. It's too simplistic to ignore that rotational acceleration.

The problem statement (at least some versions of it) say the treadmill moves at the same rate as the wheels of the plane.

This statement causes a violation of Newton's second law.

Why?

Ah..

Experimental verification please, for a vehicle in which the drive force is not imparted directly to the wheels. Rocket car works fine, but show me.

I've suggested a variant that actually avoids the "motor on the treadmill will blow up" problem.

My posts and the responses to them are a bit off the beaten track (although I believe it may have become the beaten track, at least tonight).

Send me the money. All I need is the video recorder and the rocket engine - I can (generously) supply the rest.

Alternatively, you can try emailing my experiment to the Mythbusters guys, but will they ever read it? I think I have a better chance of getting a video recorder from you. ;)

I WILL keep an eye out for something already online, though. Perhaps I can come up with a smarter search string than I've been using.

The plane wheels can never go faster than the treadmill because the original question said that the treadmill is designed to ALWAYS go as fast as the plane's wheels. Because of that statement we have to assume that as the plane accelerates and starts to gain on the treadmill, some control makes the treadmill accelerate and convert the plane's incremental thrust into ROTATIONAL acceleration and momentum in the wheels. By the way the problem is defined, the plane can never convert thrust into a higher incremental wheel speed versus the treadmill. THis has no basis in reality, and therefore cannot be proved by a simple experiment.
(At least it would require very complicated machinery to balance a model plane's thrust and treadmill acceleration)