Can a plane which is placed on a sufficiently long treadmill which can run at a speed matching the acceleration of the plane trying to take off (in the opposite direction, of course), finally take off ?

There won't be enough air passing around the wings to produce lift.
Just like walking/running on a treadmill doesn't get you anywhere.

I guess it wouldnt... the plane has to double its speed so tat it cancels out the deceleration and then it can take-off

or maybe its btr to experiment wit it to conclude wat will happen

no.... planes fly due to the lift generated by the wings which are caused
by the relative air moving over(and under) the wing.

in this case as the plane is effectively standing still , the relative airspeed over the wings is zero .... so no lift

also if this were to be the case then it would be possible to launch planes simply by putting
them on purpose designed conveyors ... so no airports would be required.

Wrong... it seems !

http://kottke.org/06/02/plane-conveyor-belt

http://kottke.org/06/02/planes-conveyor-belt-2

http://kottke.org/13/09/will-an-airplane-on-a-treadmill-take-off

yes the explanation is correct .... the plane will take off as the thrust of the propeller
will push the plane forward irrespective of the speed the wheels are turning.

I should have left it open ended for a little while more, to see if other opinions would come in.  But I was also worried about people doing the first thing they do these days, which is to google for the right answer.

http://blog.xkcd.com/2008/09/09/the-goddamn-airplane-on-the-goddamn-treadmill/

Apparently there are lengthy discussions, and a lot of people were in the "it does NOT take off camp".

http://boingboing.net/2006/12/11/airplanetreadmill-pr.html

If seen closely the plane did not take of from a stand still it was running for 50-60 mtrs.... good enough for a plane of that size to take off.

The experiment which mythbusters performed was nowhere near precise.
The 'treadmill' was much slower than the plane!
It was like running on a treadmill faster than its set speed!
This really is a heck of a topic to discuss about.

The pilot in this video never considers that the tyres are not completely friction-less as compared to the plane so even if the   tyres are going 200+ the plane wouldn't take off.
 

its pretty simple if we look into the basic on how the airplane flies.

unlike the car. planes have nothing to do with the contact with the ground( they are not meant to taxi around) and again unlike cars the engines do not produce power at the wheels in contact with the ground.

the prop pulls( or push in some cases) the aircraft forward and not turn the wheels so irrespective of what speed the wheels are turning the plane will move forward creating an airspeed enough for takeoff...

a lot more explanation can be added i suppose

damn the video came in while i was typing 

Approximately US $ 25,000 was wasted on this hoax - production / post production, sponsorship and transmission rights.. As is the case with hyped programmes like Mythbusters and Bear Grylls. If the plane had even lifted off the ground for a nano second without the propeller in motion - THAT would have proved something - Pure lift generated by wind flowing over an aerofoil - generated by the reverse motion of the conveyor belt.

Take a Hot Wheels car, grease the axles and put it on a 2" inch wide cloth ribbon - 2 feet in length. Place the whole set up on the floor. Now hold each end of the ribbon and move it in a quick reverse flick motion to where the car is facing. Does the car move? Hardly. The wheels spin to move the car forward but the road (the ribbon) moves backwards. Friction = net result = ZERO forward motion. The car practically stays stationary. Now ask a friend to flick the car forward as you drag the ribbon backward. Does it move? You bet it does.

Similarly, the undercarriage of the plane would have spun wildly to accommodate the 'reverse treadmill effect' and the aircraft would have hardly moved. Now add the full power of the engine and a spinning prop. Different story altogether.

Big deal!

the case of the jet engine is wrong... the engines are pushing the aircraft forward. the wheels are just to reduce friction. the jet engines exert force on the air to move forward.
direction of force is backward.
even if you have a treadmill under the aircraft moving at a 100 m/s, the aircraft still won't go UP into the air, until their is sufficient wind flowing over the wings. that's what wings are for!
it is like you standing on a treadmill wearing rollerskates. there is a wall behind the treadmill. let us assume friction is 0. we will stay in one place, while the treadmill moves under us. now push against the wall. you will start moving opposite to the direction of applied force ie:away from the wall. the speed of your wheels will increase a lot.

Sent from a potato using a lamp

Jet??? Where did you get a Jet engine from? Who mentioned a jet engine???

The wording of the question is wrong. If the speed of the airplane is exactly equal to the speed of the conveyor belt, then the plane would stand still with respect to the ground/ air and would not take off.

What they basically mean by the question is that the wheels of the airplane don't slip with respect to the conveyor. Sorry for being technical again, the plane stays still when     
          w(rotational velocity) r(radius) = V(of conveyor)        and takes off when       wr = V(take off) + V(conveyor)

Also, unlike an airplane, a car needs the frictional force of the ground to actually get it to move forward (for cars, bicycles, etc friction on the rear wheels actually help in motion). So, it can't move on a conveyor(moving in the opposite direction). No such problem for an airplane using a propeller to generate thrust. 

But once again, if the speed of the airplane matches that of the conveyor belt, it won't take off. In the video too, the airplane moves with respect to the ground for takeoff. Hence, its forward speed is greater than the speed of the conveyor moving backwards.

vc sir it's mentioned in one of the links... along with a picture of a brachiosaur rocketing up into the air on a 747 engine with 2 pterodactyls for stability

Sent from a potato using a lamp

for an aeroplane to fly these couple have to exist, for it to climb some of this couple have to change, conveyor , no conveyor, winds equal to take off speed the aeroplane has to balance all these four couples of forces, irrespective, for a drag component, there has to be thrust component, which means the engines have to run. for weight component there has to be a lift component, which means there has to air flowing over the wings. for further reading read the entire thread

Quote from: rcpilotacro on December 09, 2010, 08:07:41 PM


firstly in level flight weight= lift =CL ½ σ V² S. CL is coefficient of lift, which depends on your wing angle of attack (position of the nose in level flight) shape, camber etc, ½ σ V² is called the dynamic pressure, simply put, number of air molecules for a given time, ALSO CALLED THE INDICATED AIRSPEED, 'S' is your wing area.

Now, aeroplane has lift and weight acting as one couple (noseup or down will in RC language, will depend on the cg, because weight acts along it, and position of wings because centre of pressure through which the lift acts).

It also has thrust and drag couple acting on it. nose up or down will depend on position of your engine and wings, which if you are not designing, is pretty much taken care of,

Couple of Forces. For aeroplane to fly in level unaccelerated flight all these couple have to balance so that the residual is zero. If the aeroplane is say designed to get airborne at 30 kmph, it will get airborne at 30 kmph, if the wind that is blowing is 30 kmph, the ground speed at which will get airborne will be zero. But remember the thrust drag couple will have to be zero, which means, you have to open power normally as you do in nil wind condition. If the winds are 40 kmph the aeroplane after getting airborne into wind will travel rearward at 10 kmph. With respect to ground, however with respect to air it is still travelling at 30 kmph. Bottom line CL and S being same it is the ½ σ V² (the number of air molecules for a given time above and below the wings) which matter.

another post
http://www.rcindia.org/rc-general-topics/basic-aerodynamics-for-rc-flying/msg53691/#msg53691

Hmmm.. should this be a poll now ? 

Quote from: anwar on September 28, 2013, 04:07:42 PM
Hmmm.. should this be a poll now ? 

why not?

Interesting question; but insufficient data for a clear answer.

We know that the relative velocity of the plane from the ground frame of reference is zero.

But our interest is the Relative Velocity from the air frame of reference. For which we lack data.

How is the conveyor adding to the airspeed? its not. Its only adding to the ground speed. Probably a little due to cohesion of air on the surface of the conveyer but thats too less to make any laminar flow on the surface of the wing.  If it were a wind tunnel, and ir blown, things would be different

A related question  "will a plane flying from east to west reach faster than the one moving from west to east, because the earth below is moving west to east"

Quote from: sanjayrai55 on September 28, 2013, 05:25:38 PM
Interesting question; but insufficient data for a clear answer.
...
But our interest is the Relative Velocity from the air frame of reference. For which we lack data.

Whaaaaaaaaaat ? I thought the question is simple and straight forward !

Will the plane take off, from the eyes of someone who is not on the treadmill and not on the plane... both of which are obvious