Oh, ok. I was still working on the principle of zero wind speed

QUOTE=iaink;5559739]
The motion of the conveyer simply makes the wheels go faster, but does not have any serious effect on the velocity of the aircraft itself.

What the wheels do relative to the runway is totally unimportant, they have no influence on the speed of the plane one way or the other, they cant, because they are not powered.[/QUOTE]

Not quite true.

Let us suppose the treadmill starts up first and moves, nose to tail, at 1k/hr. Does the plane (a) stay geostatic (using koogar’s definition) with its wheels rolling ‘forward’ or (b) does it remain stationary on the moving treadmill with the wheels stationary. If (a) then I go along with your point of view BUT if (b) then I am correct. The plane is moving ‘backwards’ with the treadmill at 1k/h. If we now start the engines and apply a thrust equal to a forward speed of 1k/h what is the net result?. As the plane is moving forward at 1k/h and the treadmill is moving it backwards at 1k/h the net result must be a stationary plane. You can ramp this to any speed you like but the result will be the same.

Not quite true.

Let us suppose the treadmill starts up first and moves, nose to tail, at 1k/hr. Does the plane (a) stay geostatic (using koogar’s definition) with its wheels rolling ‘forward’ or (b) does it remain stationary on the moving treadmill with the wheels stationary. If (a) then I go along with your point of view BUT if (b) then I am correct. The plane is moving ‘backwards’ with the treadmill at 1k/h. If we now start the engines and apply a thrust equal to a forward speed of 1k/h what is the net result?. As the plane is moving forward at 1k/h and the treadmill is moving it backwards at 1k/h the net result must be a stationary plane. You can ramp this to any speed you like but the result will be the same.[/QUOTE]

The engines thrust is against the air, it's 1k/h is relative to the air, not the belt.
The rolling resistance of the wheels is small, if you assume it at zero for a moment, you will see that the plane will stay in the same position when the belt moves, even with the engines off.

Imagine you are on a treadmill on rollerskates. If the treadmill starts up but you do nothing, you'll go backwards, but if I come along and start pushing you in the back, you'll stay in the same place relative to the ground around the treadmill, or if I give you an almighty shove in the back, you'll go forward.
Think of the aircraft's engines as the big shove in the back: Apply a big enough shove and you'll go fast enough to move forward regardless of the speed of the treadmill.

Jeesus H. There's people from all over the Empire joining in this thread!

I'm not going to repeat my explanation here. You can find it in the Barbie or in the Trailer Park.

Excuse me sorry? What sort of reply was that to - Jeesus H. There's people from all over the Empire joining in this thread!

The original question was ... match the speed of the plane exactly but moves in the opposite direction. The engines are running at take-off thrust, the brakes are off, etc. Everything is normal save for the fact the plane is on a treadmill. Can the plane take off?
If the treadmill is moving backwards at 50k/hr and the plane is at its max speed of 50k/hr it is, as you say, stationary relative to the ground around the treadmill and as it's at its max speed it can't be 'shoved' any harder so I don't see how it can move forward and take off.

An aircraft in the air goes forward, without anything in contact with it or moving underneath it. The wheels are not the driving force on an a/c, as with a car. The thrust of the engines (up to 57,900lbs on the 744) powers the aircraft, the force of the hot compressed air leaving the engine pushes against the near static cooler air behind. Once inertia is overcome, the aircraft will move forward relative to the air mass, the wheels rotate freely, relative to the forward motion of the aircraft (they have no driving mechanism). Assuming this fictitious belt was moving underneath the a/c, the speed of rotation of the wheels would be greater than on a static surface, however the aircraft would still move through air mass exactly the same as on a paved runway.

If the belt was increased to 2x the speed, the aircraft would not go backwards, the wheels would go round a lot faster. Neither does it matter which way the belt goes, the a/c will still move in opposite the direction of thrust.

The treadmill and rotating wheels have nothing to do with the movement of the aircraft with the engines at take off power. It would however put a whole new dimension on an aborted take off!

That would be fine if the question was worded "the treadmill moves in the reverse direction fast enough to prevent the plane from moving" but it does not, you have changed the premise of the question. Also the treadmill would have to go at impossible speeds to do this as the amount friction in a wheel setup is fairly static (the resistance is primarily from tyre deformation, wheel bearing deformation and lubricant displacement - not friction from components rubbing). The speed you would have to spin the wheels to match the power output of the engine would be phenomenal and certainly waaay beyond the point of self destruction.

Another problem with the way you propose, lets go back to your 1k/h example for this where you made the treadmill go backwards at 1k/h and then used the engines to counteract this so the plane is geostatic again. The problem is right there, the plane is geostatic, i.e. it's speed is 0. Why is the treadmill now moving at 1k/h? That breaks the main premise of the question that the treadmill matches the speed of the plane but in the opposite direction!

I think what is more interesting is how this simple question can cause so much debate. The obvious (to most people) answer is wrong, the right answer is clear, yet this discussion has been going on all over the interweb for years now. Great stuff

Not many ladies on this thread so I thought I would proffer a female opinion. The airplane can take off , as per Bill S. I also thought aeroplanes don't have brakes, merely reverse thrust, in other words as other people have said the wheels do not transmit motion to the plane, they merely allow the plane not to slide on its belly during take off and landing.

Gryphea

Oh no, they have brakes, great big expensive ones, with like 6 disks in each and god alone knows how many pads and sets of callipers

Lets play at this

If this was a hover craft could it take off if it was on the belt.......Yes !!!(A No Brainer)

So consider the friction at the wheels as insignificant compared to the engine thrust

Extrapolate the idea

Thanks, but let's not overlook Steve P, Oakvillian, tom17, and the others who weighed in correctly. Even iaink came around

OH I GET IT!!
Did take till the 8th page