Yes, you misunderstand.

The conveyer matches the speed of the wheels. But the wheels rotate at any speed - they don't matter. All they do is stop the plane from rubbing on the ground. The engines are still thrusting against the air (as it were), and so the plane still moves forwards.

You are thinking of a car type system, where power is delivered via the wheels. If it was a car, the car wouldn't move. But a plane's wheels don't actually do anything other than lower friction.

Okay, some other scenarioes to think about... Ice - lock the wheels and consider ice? Could it still take off? Yes. Consider water and floats, with a strong current. Will the plane take off if the current happened to match the speed of the plane (ignoring the viscous effects of water )? Yes. The medium on which the plane is sitting doesn't matter in the slightest.

Not seen the mythbusters thing. Linkage?

Quote from tristancliffe :

What details Kegetys?

- The plane is said to be "moving" but it is not specified what moves it
- What kind of plane is it? (Does it have wheels? Frictionless wheels?)
- "Plane's speed" is what speed? Relative to ground, air, or the belt? Or the wheel rotation speed?

Quote from tristancliffe :

Not seen the mythbusters thing. Linkage?

http://es.youtube.com/watch?v=YORCk1BN7QY

And yup, I think I've understand it now
I was thinking of conveyor matching the speed of the wheels instead the speed of the plane

The whole question is so self-evident it hurts how anyone could get it wrong. As long as the speed difference between the air and the airplane is =0 the plane won't take off. Simply because the wings don't generate enough lift to beat the gravity.

Quote from Hyperactive :

The whole question is so self-evident it hurts how anyone could get it wrong. As long as the speed difference between the air and the airplane is =0 the plane won't take off. Simply because the wings don't generate enough lift to beat the gravity.

Well that's what I thought.
the entire reason a place leaves the ground is due to air passing the wings. The thrust from the engines merely generates the forward movement to create the wind speed required to create the lift.

I was just thrown off by these people above me claiming otherwise

Quote from tristancliffe :

The plane would move, but the wheels would move twice as fast because of the conveyer belt. You could reverse the conveyer belt, so the wheels don't move at all, and it would still take off.

Hint: Ignore wheel speed, as it is not important on a plane.

im not sure the wheels on most planes are speced for twice the take off speed
the wheels failing under the unsually high rotational speed causing a sudden spike in rolling resistance and a subsequent nosedive isnt that far off from a resonable scenario

It think it basically all comes down to whether you think of this as a theoretical math problem, or if you think of it like a practical problem (I'm going with mrodgers' posted variation of the riddle in the following, since otherwise it's clear cut that the plane takes off).

As a math problem you have an equation where (all speeds relative to the ground) the rotational speed of the wheels equals the speed of the conveyor belt + the speed of the plane itself. Additionally the speed of the conveyor belt must must match the rotational speed of the wheels. To satisfy these two conditions the speed of the plane must be 0, and the plane won't take off (no airspeed).

In practice though, if you put a plane on a conveyor belt it will take off (as shown by the Mythbusters). It's impossible to build a conveyor belt that always matches the rotational speed of the wheel as long as the plane itself is moving, which it will once the engine is running. Defining the speed of the conveyor belt as the opposite of the wheels' rotational speed makes no sense practically, because it's impossible to do.

Quote from wien :

Defining the speed of the conveyor belt as the opposite of the wheels' rotational speed makes no sense practically, because it's impossible to do.

it is possible but the planes prop/jet would have to run more or less at idle which shows how daft the question really is

I want to know how Mythbusters think they can generate sufficient lift with a wind speed of zero to lift a plane off the ground. The air around the plane is not passing it, therefor there is nothing pushing it upward.

If you can explain that, then I'll accept it

Quote from Dajmin :

I want to know how Mythbusters think they can generate sufficient lift with a wind speed of zero to lift a plane off the ground.

Where does it say they think that? No one with half a brain would think the plane would take off at an air speed of 0.

Obviously it can take off, since it's powered by the thrust produced by the engine, as long as the gear withstands the high rotating speed of the wheels.
The tapis roulant thing just can't stop the plane, since it isn't powered by the wheels.

Quote from wien :

Where does it say they think that? No one with half a brain would think the plane would take off at an air speed of 0.

Quote from The Straight Dope link :

The question thus stated asks the impossible -- simply put, that A = A + 5 -- and so cannot be framed in this way. Everything clear now? Maybe not. But believe this: The plane takes off.

It's not Mythbusters I meant, it's the website linked in the OP. I was distracted by people mentioning Mythbusters

Quote from Dajmin :

It's not Mythbusters I meant, it's the website linked in the OP. I was distracted by people mentioning Mythbusters

So you don't believe the last statement in the quote you posted? Is that it?

As I said above; Mathematically you can come to the conclusion that the forward speed of the plane (5 in the equation you posted) must always be 0 to satisfy all conditions of the riddle/myth. If that's how you look at it, then yes the plane will stay on the ground because you aren't allowed to power it up or you'll break the precondition of the riddle.

Practically though, once you power up the plane and gun it it will take off. Preconditions be damned.

Consider this. The plane is 1ft in the air flying along. All is well.

Beneath it is a conveyer belt moving in the other direction at the same speed as the plane (we'll assume no wind on the day, so ground and air speed are the same).

That works doesn't it.

So what difference does some wheels touching the ground make?

no because once the engine forces the plane to move along the runway, the wheel speed increases, but the conveyer belt doesn't, this is cheating :P

The movement speed is not in question here, just lift.

Remove the wheels from the equation because they're irrelevant. As has already been posted, the only thing plane wheels do is stop the fuselage scraping the ground. Also, the engines are irrelevant because they only generate forward movement, not lift. So the airspeed of the plane is 0mph.

Lift is generated (as you know) by air pushing under the wings.
If the plane is not moving through the air (or more importantly, if the air is not moving under the wings), what is pushing the plane upward?

But if the coonveyer belt increases in speed expenetionally matching the wheels, the plane thrust would be cancelled out, no air would pass over the wings and it couldn't acheive lift off

Ergo, both are irrelevant

Quote from Thorvertonian :

But if the coonveyer belt increases in speed expenetionally matching the wheels, the plane thrust would be cancelled out, no air would pass over the wings and it couldn't acheive lift off

It´s impossible for the conveier to match the speed of the wheels (unless the speed of the wheels is 0). As explained here:

Quote :

However, some versions put matters this way: "The conveyer belt is designed to exactly match the speed of the wheels at any given time, moving in the opposite direction of rotation." This language leads to a paradox: If the plane moves forward at 5 MPH, then its wheels will do likewise, and the treadmill will go 5 MPH backward. But if the treadmill is going 5 MPH backward, then the wheels are really turning 10 MPH forward. But if the wheels are going 10 MPH forward . . . Soon the foolish have persuaded themselves that the treadmill must operate at infinite speed. Nonsense. The question thus stated asks the impossible -- simply put, that A = A + 5 -- and so cannot be framed in this way. Everything clear now? Maybe not. But believe this: The plane takes off.

How can the plane's thrust be cancelled out by it's wheels or the conveyor belt? That makes no sense.

thats wrong, if the PLANE is moving fowards at 5mph, and treadmill backwards at 5mph, then the wheels turn at 10mph....

if the wheels turn at 10mph and the treadmill at 10mph, the plane can't move

(wheels) 5mph --> = <-- 5mph (conveyor belt)

5 + (-5) = 0mph

If all the coveyor belt did was speed the plane up, the entire puzzle is irrelevant.

Quote from Thorvertonian :

thats wrong, if the PLANE is moving fowards at 5mph, and treadmill backwards at 5mph, then the wheels turn at 10mph....

if the wheels turn at 10mph and the treadmill at 10mph, the plane can't move

... and if the treadmill is moving at 10 mph then the wheels are moving at 15 mph.

If the treadmill moves at 15 mph then the wheels are moving at 20 mph...

See a pattern?

No they aren't, the wheels only move faster if the plane is moving, as soon as it produces thrust and speeds the wheels up, if the treadmill is kept at the same speed as the wheels, then the plane will NOT move

if the wheels have more rotational speed than the conveyer belt, than the riddle is false, as the speeds aren't the same!

Jeez, lets look at the facts here. The plane's propeller pushes against the air. No matter what the damn wheels are doing the propeller is capable of moving the plane. Right? So since the speed of the plane can be more than 0, the wheels can have more rotational speed than the conveyor belt. Right? This means that practically (though not mathematically) the assertion that the conveyor always matches the rotational speed of the wheels is flawed. It can't be done. Such a conveyor belt is impossible to build.