Plane and a conveyor belt

Actually, if the wheel axles are frictionless, the aircraft will take off. You can spin the wheels as fast as you like (i.e. run the treadmill as fast as you like), and provided the aircraft has sufficient thrust to move itself forward - it'll move. Although in the real world, they're not frictionless as a stationary unpowered aircraft on a treadmill which accelerated would move to some degree.

If they're not frictionless, then provided you can exert enough speed on the treadmill to keep the aircraft in place due to friction, it won't take off. But again, do to that, you'd likely melt the tyres or the bearings due to the heat produced long before, at which point the fuselage would hit the belt and it would go horribly wrong.

So which is it - frictionless or not?

Frictionless, it flies. With friction, you will be able to keep it in one place (assuming you can run the treadmill in such a way as to produce enough friction), before the gear is destroyed (in which case, it'll get trashed most likely).

The assumption is that because the conveyor is moving backwards to the plane that it does not move. This is incorrect. The plane moves forward as normal while the wheels spin faster. The wheels on the plane have very little to do with planes forward movement other than allowing as little friction as possible.

Cars are driven by the wheels but planes are pulled by the engines. This force has no connection to the surface what so ever.

(Did a post just vanish?)

If the wheels are frictionless, the aircraft will take off.

But it doesn't say that in the original question.

Yes, but the question doesn't say how fast you can run the treadmill up to or what the wheels are capable of before failure.

There are two answers, depending on which assumptions you want to make, none of which are given in the question.

So we're ALL right!!!

GROUP HUG!!!!!!!!!!!!!!!!!!!!!!!!!!

Jon - Yes, the wheels are irrelevant, UNLESS the friction produced by the bearings is greater than the thrust of the engines, as you say.

However, at very high treadmill speeds, assuming the gear wasn't destroyed, could you not in theory, create a large enough force of friction to counteract the thrust - i.e. assuming a low powered SEP and an infinite speed treadmill?

Imagine it this way…

 

Imagine holding a model aircraft on a strip of paper [representing a conveyor]. Hold the model aircraft perfectly stationary with your left hand in regard to the ground [not the conveyor] Aircraft pointing to the left.

 

Now whip the strip of paper from underneath, to the right, with your left hand while keeping the model aircraft perfectly still.

 

What happens? The wheels spin as fast as the strip of paper [conveyor] induces. And the plane remains stationary in regard to the ground and surrounding air.

 

Now do the same again, but move your hand holding the model aircraft in the opposite direction.

 

What happens? Does the model aircraft move forward in relation the ground? Of course it does.

 

Your muscular force, the movement of your left hand is equivalent to the thrust from the propeller.

Its very simple - unless there is enough airflow over the wings it will not fly and if the forward speed of the aircraft supplied by the engines is matched by the rearwards moving belt it will stand still and not fly - Wheels have nothing to do with it.

 There is enough airflow over the wing. The aircraft will move forward. The wheels spin faster to accommodate that.

SimUK wrote: If the belt was to run in reverse, would the plane take off backwards?

Yes.

In that example you are getting no drag on the paper from the aircraft. If you put an A320 on a bit of paper and whipped it backwards, the aircraft would move backwards with it. If you put the engines on and pulled back the paper back with enough speed and force, the drag on the paper would stop the aircraft moving forwards. If you could keep winding up the force of the paper being pulled so that it kept counteracting the force of the thrust then then aircraft would remain in the same space.