would a plane take off if..

[Wedge1126]

The conveyer belt is designed to exactly match the speed of the wheels at any given time, moving in the opposite direction of rotation.

If the conveyor belt exactly matches the speed of the wheels, then the plane is stationary.

I think the common description of this problem states that the conveyor belt matches the speed of the airplane. In which case, the plane does take off.

[AKHog]

If the conveyor belt exactly matches the speed of the wheels, then the plane is stationary.

I think the common description of this problem states that the conveyor belt matches the speed of the airplane. In which case, the plane does take off.

Exactly! 

[Getback]

One, must only...ask why do planes fly! Grasshopper.

[AKHog]

One, must only...ask why do planes fly! Grasshopper.

Because of relative wind moving over an airfoil with a positive angle of attack, pure and simple.

If the plane can't move, then it can't generate relative wind, and it can't fly.

[Raptor]

Besides the original question being a paradox, the plane would take off. Notice in the mythbusters example that the plane took off exactly like it would without the tarp? By your theory it should have at least taken longer to achieve flight.

If you put a car on a conveyor belt under the same principles, it would not move. Now... the applicable question for the airplane would be:
If you put a fan behind an aircraft that instantly created a downwind equal to the speed of the airplane, would it take off?

[CAP1]

this is very simple.

if for whatever reason, there is no airflow over the wings, the plane will/can not fly.

[AKHog]

Besides the original question being a paradox, the plane would take off. Notice in the mythbusters example that the plane took off exactly like it would without the tarp? By your theory it should have at least taken longer to achieve flight.

Wheels moving at 60mph or 120mph generate very little difference in drag. I would guess the plane in mythbusters did take more time to take off but by a very small amount.

If they had a way to accelerate the tarp to several hundred miles per hour then you would start to see significant increase in distance. If they could accelerate the tarp to infinity as the original question presumes, then the plane would simply never move.

[sluggish]

It's called rotational inertia (look it up) and unless the plane has enough thrust to get to takeoff speed while the wheels are locked, it won't fly.

[AWwrgwy]

Wow.

This is a yearly topic three years in a row now:

O' Club January 2008
O' Club January 2007


wrongway

[Oleg]

There is no hope for humanity

[Casca]

One, must only...ask why do planes fly! Grasshopper.

Money

[DREDger]

It flies.  It doesn't accelerate because of the wheels, they just roll.  The prop/jet thrust accelerates the aircraft through the air and that isn't affected by any treadmill contraption.  All the treadmill would do is make the wheels spin faster as it took off.

Lot of posts on this,  but go to bottom of page 1, Karnak has it spot on.

The plane will fly,  however on a conveyor belt the wheels will be rolling twice as fast...simple.

At time T=0, the plane is stationary however the conveyor belt is making the wheels role at a given speed.

Thrust is then applied by propeller.  The plane and air are independent of the conveyor belt.  So as the plane begins to move forward, the wheels now are moving even faster.  

[lengro]

Another way of visualizing why it takes off:

1) Connect the plane (with engine off) to a powerfull glider winch launcher, the plane doesn't care where the forward pointing force comes from.

2) The winch launcher is placed on solid ground, so it will pull the plane closer - the opposite moving conveyor can't do anything about the shortening of the rope.

3) As the winch rotates faster the plane accelerates forward - and takes off.

(The winch however must work a *tiny* bit harder compared to take off without moving conveyor, due to the change in the wheels rotational inertia and friction in wheel bearings)  

[Saxman]

DRED,

What they're asking is what happens should the treadmill continue accelerating to keep pace with the speed of the wheels, ignoring ALL mechanical impossibilities and looking at it completely from a theoretical standpoint. I misread the OP on that, and it IS a completely different question than what the Mythbusters tested. The Mythbusters were testing the argument that the plane wouldn't take off on a treadmill matching its takeoff speed.

However even viewed as theoretically, the airplane WILL take off because its wheels are ALWAYS moving faster than the conveyor belt. Look at it this way:

An aircraft has a takeoff speed of 60mph with the conveyor belt at 0mph. The plane's wheels spin at 60mph on takeoff. You accelerate your conveyor belt to 60mph, which would match the speed of the wheels at the time the conveyor belt was at a stopped state. However because the aircraft's propulsion system is independent of its wheels, which are free-spinning, it still continues accelerating to its 60mph takeoff speed, with its wheels now spinning at 120mph.

So you accelerate your conveyor belt to 120mph. The plane continues to accelerate until its wheels are spinning at 180mph.

When the conveyor belt is at 180mph the wheels are at 240mph, etc, etc, etc.

No matter how fast the conveyor belt is spinning the wheels are ALWAYS going to be 60mph faster and the plane will take off.

[Yossarian]

Everyone who has said that it will not take off is wrong.  Here's why:

Imagine you have two conveyor belts next to each other.  One has a car on it, the other has an aeroplane on it.

You then start up both the aeroplane and the car, move their engines to full power, and turn on the conveyor belts to match the speeds of the vehicles.



Now, you're probably wondering: why bother with the car?

Here's the answer: the car accelerates by rotating its wheels against the surface of the road.  KEY POINT: the car moves forward by rotating its wheels against the surface of the road - if you lift it off the road, it will stop accelerating.  If the road beneath it is moving backwards at the same speed as the wheels are moving the car forward, then there will be NO net motion of the car.


HOWEVER, the aeroplane accelerates by using it's propeller to push air backwards.  KEY POINT: the aeroplane moves by pulling on the air with its propeller - if you lift it off the ground, it will continue accelerating.  Even if the runway beneath the aeroplane starts to move backwards at the same speed as the aeroplane is moving forward, the propeller will STILL be pulling the aeroplane forwards, REGARDLESS of what is happening with the wheels.

Hence, the plane will accelerate, and take off.

EDIT: Saxman beat me to it