Hypothetical question…
A plane is standing on a runway that can move like a giant conveyor belt. The plane applys full forward power and attempts to take off. This conveyer has a control system that tracks the plane’s speed and tunes the speed of the conveyer to be exactly the same but in the opposite direction, similar to a treadmill.
The question is:
Will the plane take off or not?
what kind of plane is it, hypothetically?
Hypothetically it could be a Cesna or a 747 or the Girls Gone Wild Party Plane.
If you need a size and wieght to do calculations, let’s say it’s a 747.
If no air is moving, and as far as I can tell its not, then the plane will not fly.
Its just the same as a car on a dyno you can run the car as fast as you want on rollers but all that happens is the wheels move.
No, it will not…planes fly by creating the unequal air pressure (less air pressure above the wing), which they do by moving the air across the wind…unless you have about a 300 mile an hour wind blowing towards the front of the plane, it isn’t going anywhere
thats like saying if i run real fast on a tread mill will i take off…never happen theres no pressure forcing the air up so no take off…now if we were talking harrier jets then yes it could take off.
no its not, because you can’t take off if you’re running along the ground normally. but a plane can.
anyhoo, no, it won’t take off, for reasons already said.
at first i though it would fly but then i thought about it and i think yes it will stay in the same place.
Great puzzle, Racenut, you sure stumped the peanut gallery!
C’mon guys, think about it! Does the plane use it’s wheels to fly? No!
The treadmill doesn’t affect the air very much… even a treadmill the size of a runway. At best it would create a slight headwind, comparable to a light breeze. This would actually help the plane take off!
The plane achieves forward momentum by creating thrust. Its engines push against the surrounding air (not the runway) and by Newton’s third law (opposite and equal reaction) the plane is pushed forward. When the plane is “pushed” long enough it will achieve the necessary speed for takeoff.
The only real consequence of the treadmill is that the plane’s wheels will spin 2x as fast as if the plane were taking off from stationary ground.
Edit: Also, if the plane “just stayed in place” then, by Racenut’s hypothetical design, the runway / conveyer belt would just stay in place… it’d be like a normal runway. Why, then would the plane stay in place?
I think the way people answer is more interesting than the question itself. Really illustrates how people think differently. For me, it took me longer to read the question than it did for me to figure out that the plane would still take off. But the place I got this from has over 100 posts and some of them are still trying to figure it out.
a plane is able to take off because of the shape of the wing and the air going over and under the wing. the top of the wing is curved, so air going over the wing has to go further than air going under the wing. this decreases the air pressure over the wing, so the air under the wing is able to push it up. since there is no air going over the wing when its just on a big treadmill, it wouldn’t be able to take off.
I think Maestro was right. The plane is still going to move, regardless of conveyor speed. Unlike a runner, it’s not pushing against the ground. Unless the conveyor has some other way to keep the plane from moving, it’s going to accelerate. Barring a breakdown in the efficiency of the wheel bearings on the plane (assuming a speed equivalent of several times maximum landing speed), the plane should be able to attain a relatively normal takeoff speed in about the same distance it would on solid ground.
Unless you would like to re-write the question.
Mr. Potter, could you please come up to the front of the class and explain this nonsense? What does a treadmill have to do with air?
Let me lay it down so you can pick it up…
The wheels are in contact with the ground, but they spin freely so the plane can move freely over the ground (be it stationary or moving). The wings are in contact with the air. Engines are connected to the wings. The engines push against the air, but the air pushes back (Newton’s third law). This causes the wings to move with respect to the air. Eventually the wings move fast enough (with respect to the air) that they generate lift (Bernoulli’s principle). The generation of lift has NOTHING to do with the motion of the wings relative to the ground.
Granted, air is a fluid. And we all know that when we put a spoon in a bowl of water and stir, eventually the water moves with the spoon. This is because fluids have viscosity… the spoon pulls the water near the spoon along with it. But the further away you get from the spoon (imagine stirring a swimming pool with a spoon) the less the fluid is influenced by the spoon. You can stir a small portion of the shallow end of the pool with a spoon, but the deep end will remain undisturbed.
In the case of the treadmill runway, the treadmill will pull a bit of the air along with it… but not much. Air is much less viscous than water. Try it yourself… find a treadmill, put it on high, and see if you notice any air flow above the surface of the treadmill. I’ll guarantee you it’ll be hard to detect (unless your treadmill can go at 100 mph+ 
). Hence the treadmill runway won’t disturb the air around the plane’s wings enough to have a noticable effect.
Sure, the plane’s wheels are in contact with the ground. But the wheels are mounted on bearings. Take a skateboard and put it on a treadmill. Notice that if you hold the skateboard still while the treadmill runs, the wheels will spin. Also notice that if you push the skateboard forward on the treadmill, it will move forward and the wheels will spin slightly faster. The same thing is happening with the plane… the force of the engine’s thrust against the air is the same as the force of your arm against the skateboard… no matter how fast the treadmill goes (as long as bearings don’t fail, as Mr. Foss has pointed out), the skateboard or plane can still move with respect to the stationary ground.
Class dismissed!
well yeah, its perfectly possible, if the plane is moving as fast in relation to the ground as it is when its not on a treadmill. but I assumed that the airplane would actually be stationary, just the wheels would be spinning and the treadmill would be moving under it.
See?
yeah, so the plane really will be stationary, it’ll just have its wheels moving…so it won’t take off!
It seems to me that the conveyor belt system would require more power from a plane’s propulsion than on a conventional runway in order to take off. This is because, when a plane normally takes off, the entire wings are dragged through the air, whereas, on the conveyor belt system, the parts of the wings that are the closest to the prop/engine would have the most air movement over them. So, perhaps, the tips of the wings wouldn’t provide as much lift as they do in the conventional case.
It will take off, the belt will only effect the speed of the wheels, not the spped of the plane. Some of you people are dumber than i thought,
I heartily agree with Maestro8, Kc, et al…
As long as the landing gear wheels spin freely, it doesn’t matter how fast the treadmill moves - the plane will have no trouble taking off. The “treadmill” could move at twice the plane’s speed and it still wouldn’t matter.
You folks who think the plane will have trouble or won’t take off at all aren’t reasoning through this correctly.
It is stated in the original problem, that the treadmill can keep up with the speed of the plane. The plane will never move relative to the ground, hence, it will never take off.