The legendary omniscient Cecil Adams answered this in his column the Straight Dope (the same way as you did) eleven months ago:

http://www.straightdope.com/columns/060203.html

He got attacked for this, and did a column "for the geeks" where he took it a step further to figure out how you could keep the plane stationary.

http://www.straightdope.com/columns/060303.html

Enjoy!

Cecil answered the question after it was posed and intensely debated for nine long pages on the Straight Dope Message Boards:

http://boards.straightdope.com/sdmb/showthread.php?t=348452&highlight=plane+treadmill

More physics wanking than you can shake a stick at...

The treadmill has no effect on the plane; once the plane starts moving the treadmill, "designed to exactly match the speed of the wheels, moving in the opposite direction," won't push the plane back. Conduct a thought experiment the next time you fly in a plane, and you'll see that your experience as a passenger would be precisely the same.

You could indeed create a treadmill that would keep a car in the same place. The car's thrust is applied through its tires. That's probably what people can't get past.

Because if the treadmill can, in fact, match the speed of wheels traveling fast enough for the plane to take off, then why not turn the plane around, and take off on treadmill power? That would be something!

The column states:

"A car won't accelerate on a treadmill; the belt will always match the rotation of the tires. You will not accelerate on a treadmill; the belt always runs in sync with your footfalls."

No, that's, incorrect. If I set a treadmill to run at 3MPH, I will accelerate if I run faster than 3MPH. Similarly, if I run slower than 3MPH, I'll move backwards (and off the treadmill).

Same deal with a car. If the car's engine is spinning fast enough to propel the car forward at 50 MPH on a road, and it's placed on a treadmill running at 10 MPH, the car will move forward at 40 MPH.

"But an airplane is different. An airplane's wheels are not powered by gears or a drive train."

How a device (or person) is powered is tangential to the basic question. The treadmill is driven by a motor, rotating at a certain speed and moving the belt of the treadmill at a certain rate. This motor is decoupled from what's making the car or person move (engine and drivetrain, or muscles and feet), and so the car/person goes at a rate of their intrinsic speed, minus the speed of the treadmill belt.

For starters, the question is badly posed. As Patrick notes, the conveyer can't match the speed of the wheels. That's like asking if the plane will fly if 1=0. The way the question is usually posed is "will the plane fly if the conveyer matches the speed of the PLANE".

And friction has very little to do with the solution. Stand on a treadmill in a pair of skates, and pull yourself forward with a rope. It doesn't matter what speed you set the treadmill to, you can still pull yourself forward. All the treadmill does is spin the wheels faster, at two times your pulling speed. The wheels certainly won't "slide"! The plane's engines pull the plane forward in just the same way, using air instead of a rope. The treadmill is largely irrelevant, and most any plane could take off under these circumstances.

It all depends on the way the engines of the plane are arranged, and how they generate airspeed. After all, the plain needs airspeed, not ground speed.

Do the engines push air under the wings? Then the plane will actually be pulled downward. Do they generate an artificial wind? Then there is a chance the plane can take off. Is the treadmill also influencing airflow? If so, then that also may suck downward or aid takeoff, depending on the airflow regions. I also suspect terrain plays a role, influencing how well the engines can generate the needed artificial winds.

So, yeah. A definite "maybe". The whole point of the mental exercise, I think, was to get budding engineers to stop thinking about the wheels and groundspeed, and remember to think about airspeed for lift.

It would still sit on the ground for hours delayed for god knows what reason while the flight attendants listlessly threatened you with arrest if you had to go to the bathroom.

Same deal with a car. If the car's engine is spinning fast enough to propel the car forward at 50 MPH on a road, and it's placed on a treadmill running at 10 MPH, the car will move forward at 40 MPH.

You weren't paying attention. The whole premise is based on this hypothetical treadmill keeping pace with the rotation of the tires. Thus, the treadmill isn't running at 10 mph, it's running at whatever mph the car is - thus, the car is stationary, period.

The point of this question is to ask if the wheels need to turn for the plane to take off.

By "exactly match the speed of the wheels" it means cancel out the rotation of the wheels.

The whole point of this question is to teach students not to read more into a question than is there.

Of course it will take off. The wheels don't drive an airplane.

Sheesh.

The four forces acting on the center of gravity of the aircraft are Thrust, Drag, Lift, and Weight. Assuming that the bearings in the wheels are not perfectly frictionless, the wheels will provide a very, very small contribution to the drag.

The treadmill is irrelevant. As the engines spool up, the thrust will increase and the aircraft will accelerate until enough lift is generated for the aircraft to fly.

Why don't you just dump the Airbus from the flawed premise and get youself a Harrier?

http://en.wikipedia.org/wiki/AV-8_Harrier_II

if the treadmill is matching the speed of the wheels, then the wheels must be stationary and remain, unmoved, on a fixed point on the treadmill. assuming that inertia can be easily overcome, there is nothing preventing the treadmill from moving the whole mess forward - while the wheels remain fixed to that point on the treadmill - to the airspeed necessary for takeoff, no? everything moves forward, yet the relative speed of the wheels and treadmill match exactly.