Final answer to the airplane on a long treadmill problem ...

[Ruiner]

exactly, i understand/comprehend that perfectly. i guess what i am really curious about, and something that originally put doubt into my head (as well as countless others who have thought about this), is that when the thrust from the engines starts to push the plane forward, what exactly are the wheels doing? as in, what is the speed of the wheels? (even though i realize this is arbitrary!)

The wheels are spinning and nothing else! That is the fun of it. The wheels ONLY spin, freely! Actually, the wheels will spin at twice the rate of forward motion of the plane as the treadmill is doing the same speed in reverse.

So, the plane is moving at 100knots forward and the treadmill is doing 100knots in reverse...the wheels are spinning (and ONLY SPINNING) at 200knots. They still have no affect on the plane's forward motion. All the treadmill does is spin the wheels.

[ShooterMcGavin]

The wheels are spinning and nothing else! That is the fun of it. The wheels ONLY spin, freely! Actually, the wheels will spin at twice the rate of forward motion of the plane as the treadmill is doing the same speed in reverse.

So, the plane is moving at 100knots forward and the treadmill is doing 100knots in reverse...the wheels are spinning (and ONLY SPINNING) at 200knots. They still have no affect on the plane's forward motion. All the treadmill does is spin the wheels.

perfect! that was my thinking originally, that in order for the plane to MOVE FORWARD, the RATE at which the wheels were spinning could not equal the rate of the treadmill moving against it (and speed of the treadmill and the wheels really have no bearing on whether or not the plane will take off). see? i'm with ya, just had to make sure i was understanding all parts of this "situation"

[Ruiner]

perfect! that was my thinking originally, that in order for the plane to MOVE FORWARD, the RATE at which the wheels were spinning could not equal the rate of the treadmill moving against it (and speed of the treadmill and the wheels really have no bearing on whether or not the plane will take off). see? i'm with ya, just had to make sure i was understanding all parts of this "situation"

Your logic is still off. It has NOTHING to do with how fast the wheels are spinning, NOTHING. As I said earlier, a plane could take off with NO wheels on the snow or no wheels in the water or locked wheels on a sheet of ice.

The plane has to overcome the friction produced by the wheels. Since the wheels are free spinning, then the only friction that they are producing comes from the bearings... that's it. Once it overcomes that little bit of friction, the plane moves forward.

[ShooterMcGavin]

Your logic is still off. It has NOTHING to do with how fast the wheels are spinning, NOTHING. As I said earlier, a plane could take off with NO wheels on the snow or no wheels in the water or locked wheels on a sheet of ice.

The plane has to overcome the friction produced by the wheels. Since the wheels are free spinning, then the only friction that they are producing comes from the bearings... that's it. Once it overcomes that little bit of friction, the plane moves forward.

i think maybe you're misunderstanding me or i didn't explain myself well enough? i understand the speed of the wheels have nothing to do with this equation, it's all about the force that's being applied by the engines. however, and please tell me if this is where i'm wrong, i believe the wheels must spin at a higher rate than the treadmill moving against it AS A BYPRODUCT of the force being applied to move the plane forward. because if this is not the case, then why is it that the wheels would freely spin at twice the rate of the treadmill? hope this clears it up for good

[Ruiner]

i think maybe you're misunderstanding me or i didn't explain myself well enough? i understand the speed of the wheels have nothing to do with this equation, it's all about the force that's being applied by the engines. however, and please tell me if this is where i'm wrong, i believe the wheels must spin at a higher rate than the treadmill moving against it AS A BYPRODUCT of the force being applied to move the plane forward. because if this is not the case, then why is it that the wheels would freely spin at twice the rate of the treadmill? hope this clears it up for good

Look at it this way: if the plane was in the air and YOU were making the wheels on the plane spin, would the plane fall out of the air? That's all that the treadmill is doing...spinning the wheels. NOTHING MORE.

Look at the diagram again and you will understand why the wheels spin at the plane's forward speed + the treadmill's speed:

[ShooterMcGavin]

Look at it this way: if the plane was in the air and YOU were making the wheels on the plane spin, would the plane fall out of the air? That's all that the treadmill is doing...spinning the wheels. NOTHING MORE.

Look at the diagram again and you will understand why the wheels spin at the plane's forward speed + the treadmill's speed:

can't see the pic cuz it's being blocked by websense but i understand what you're saying and even though i don't think i'm expressing it correctly, what i'm saying is what you're saying

and to hopefully prove that i do fully comprehend, here's a simple followup question that you can easily answer: would it be possible to have/build a treadmill that will move/accelerate in a manner in which it will actually keep the plane in the same spot and grounded?

[Ruiner]

can't see the pic cuz it's being blocked by websense but i understand what you're saying and even though i don't think i'm expressing it correctly, what i'm saying is what you're saying

and to hopefully prove that i do fully comprehend, here's a simple followup question that you can easily answer: would it be possible to have/build a treadmill that will move/accelerate in a manner in which it will actually keep the plane in the same spot and grounded?

As long as the wheels are free rolling (neutral), no, not really. There is a small amount of friction in the wheel bearings. If the plane's thrust matches that friction, exactly, then the plane will stay stationary. Once the plane's thrust passes that friction amount, the plane will move forward.