If the treadmill was to match the speed of the wheels this would be impossible. But the spirit of the myth could be tested by setting a treadmill, say.. twice the normal liftoff air speed of a plane.

"Yes, but the problem says that the treadmill must MATCH the speed. If you assume that that means "speed of the wheels" then this condition cannot be met. Therefore this interpretation of the problem statement cannot be correct as it requires an impossible situation."
keeping this in mind, we must conclude that the treadmill matches airspeed... therefore the aircraft could takeoff

Just go and run on a treadmill for a few minutes and then tell me if you felt the wind in your face. P.S. fans and A/C don't count.

[quote]Just go and run on a treadmill for a few minutes and then tell me if you felt the wind in your face. P.S. fans and A/C don't count.[/quote]

Airplanes don't run down the runway using legs. Wrong analogy. Think again.

I've got a quick question for those who believe that the plane will take off. What would happen to the plane if you started the treadmill without starting the engine of the plane? Would the plane remain stationary or would it move bakwards due to the motion of the treadmill?

[quote]What would happen to the plane if you started the treadmill without starting the engine of the plane? Would the plane remain stationary or would it move bakwards due to the motion of the treadmill?[/quote]

The wheels would spin and it would eventually move backward if you did not start the engines. You could probably idle the engines slowly and hold the airplane still on the belt if that was your goal. But as soon as you supplied significant thrust for takeoff, it would move down the belt almost as if the belt were not even there.

No one who states that the airplane can move forward on the belt and fly is saying that the belt imparts zero force through the free spinning wheels. It is just a very small insignificant force. AND, you would have to have the engines off or throttled down extremely low in order for the belt to move the airplane backwards.

If you were to hold a skateboard down on a moving treadmill, would you have to put great force to move the skateboard opposite the movement of the belt even if the belt is moving very fast? The answer is NO. Yet, if you let go of the skateboard the belt would be able to move it. Right?

[quote]The wheels would spin and it would eventually move backward if you did not start the engines. You could probably idle the engines slowly and hold the airplane still on the belt if that was your goal.[/quote]

I think that you are underestimating the forces of friction, gravity, and air pressure. The plane would move back before the wheels really got going at all, especially on a propelor powered plane. It takes quite a bit of thrust to get the mass of the plane started. Even if the plane is idleing normally it would move backwards with the force of the treadmill. As the thrust of the engine catches up with and starts to push the plane forward the speed of the treadmill is adjusted to counteract the forward motion of the plain, thus keeping it stationary while the wheels are spinning. The cycle continues and the plane remains stationary, never gaining enough air speed to relieve the effects of wheel friction, gravitity, and an atmosphere of air pressure holding it down. Does the plane still take flight?

[quote]As the thrust of the engine catches up with and starts to push the plane forward the speed of the treadmill is adjusted to counteract the forward motion of the plain, thus keeping it stationary while the wheels are spinning. The cycle continues and the plane remains stationary, never gaining enough air speed to relieve the effects of wheel friction, gravitity, and an atmosphere of air pressure holding it down.[/quote]

And that is the flaw in your thinking. The treadmill is a red herring. The treadmill cannot impart significant force to hold the airplane back any more than a treadmill can prevent you from moving the skateboard opposite its movement by speeding up.

Besides, since the treadmill is set to move in the opposite direction at the exact speed of the airplane and, as you say, the airplane is not moving. Then why is the belt moving at all? Since the airplane speed is zero, as you say, then the belt speed should also be zero. Right?

Go to the following site:

http://hingedelephant.wordpress.com/2007/02/27/4/

There are a lot of good explanations there about why the airplane moves forward on the belt and flies. If after reading through that and you still don't think that the airplane can fly, then come back here and tell us what in there you disagree with, please.

Thanks for the help. It all makes a lot more sense now. The posts on the website were very well thought out and posed ideas that I hadn't thought of yet. Very thought provoking.

[quote]As the thrust of the engine catches up with and starts to push the plane forward the speed of the treadmill is adjusted to counteract the forward motion of the plain[/quote]

Where does the problem say the belt counteracts the forward motion of the plane? It doesn't - it says it -matches- the forward motion in the opposite direction. Belt and plane have their own separate power sources. Plane moves east, belt moves west.

Thanks for being open minded enough to really read through the explanations and think logically about it.

Many times people get so fixated on the red herring conveyor belt, that they blind themselves to considering the logical explanations about why the conveyor cannot impart significant force to hold the airplane back.

I think that he is a convert now, nsttrack.

Try this, put a matchbox car on the treadmill and watch what happens. The matchbox car has just wheels at either end of an axle and rolls free like a plane. Let me know when you get tired of picking the car up off the floor.

But you're not applying any force to the car. The airplane's engines would apply force to the airplane. No one is saying the conveyor could not move the airplane if there were no opposing forces.

Did you read the explanations at http://hingedelephant.wordpress.com/2007/02/27/4/ ?

Hey Rick...!! Pass the Cheese Please...!!

"Try this, put a matchbox car on the treadmill and watch what happens. The matchbox car has just wheels at either end of an axle and rolls free like a plane. Let me know when you get tired of picking the car up off the floor"

if you were to hold the matchbox car in place, you would not have to pick it up off the floor... and the description or the myth would have the conveyor belt reverse and make the airplane move forward as soon as it started moving backwards anyway.
but if the car is just sitting there, then the belt would not be moving anyway.
since the belt counteracts the forward speed, the wheels on the airplane would only have to spin twice as fast as they would normally at takeoff. which, the friction of the wheels spinning is somewhat insignificant in comparison to the wind drag on an airplane.

[quote]The airplane's engines would apply force to the airplane.[/quote]
The planes engine does not apply force to the plane, it applies force to the air to create thrust not lift.

Air Craft carriers use catapults to launch all kinds of planes. The wheels have no roll, other than to give the planes something to move easily on while taking off and landing. If you remove the catapault, and place a treadmill in it's place, the results will be the same... The plane will launch.

[quote]The planes engine does not apply force to the plane, it applies force to the air to create thrust not lift[/quote]
the engines do apply force to the airplane... a force which is greater than the wheel friction....

I think that the one thing you are not understanding is that airplane speed is not measured by how fast the wheels are moving, it is measured by how fast the airplane is moving with respect to the air around it...
therefore, if the airplane has a takeoff speed of 50knotts then the airplane would have a forward speed of 50 knotts and the treadmill would have a reverse speed of 50 knotts... therefore the wheels on the airplane would be rolling at 100 knotts... which wheels on airplanes are free rolling anyway

[quote]If you remove the catapault, and place a treadmill in it's place, the results will be the same... The plane will launch.[/quote]

After the plane puts out more thrust to overcome the speed of the treadmill.