Most people here will have heard of the plane on a conveyor belt puzzle (plane, conveyor belt, same speed, opposite directions, does the plane take off?). After reading the miniblog at badscience today I saw the video of the supposed mythbusting. At risk of opening a massive can of worms I’m going to reopen the debate here.
“A plane is standing on a runway that can move (some sort of band conveyer). The plane moves in one direction, while the conveyer moves in the opposite direction. This conveyer has a control system that tracks the plane speed and tunes the speed of the conveyer to be exactly the same (but in the opposite direction). Can the plane take off?”
The problem with this question is “What is the speed of the plane measured relative to?”. Relative to the ground it will be zero if the speed of the conveyor in the opposite direction is exactly the same. The planes propeller and the conveyor create an equal and opposite force on the plane and its resulting movement will be nil. Consequently no lift can act on the plane unless there is a particularly strong head wind.
Actually this argument kills the others, if the speed of the plane increases above zero relative to the ground then the conveyor must increase to compensate, resulting in an overall speed of the plane equalling zero. Thus air speed is only equal to that of the wind.
I know I’ve opened a can of worms but before anyone starts pointing at the video remember this. If a plane had was to move forward at X velocity and the ground it was standing on moved at -X velocity, whilst it was in contact with said ground it would have a velocity of 2X relative to the ground and zero relative to the air (assuming no wind and the negligible movement of air from the prop). Thus no lift. Watch the video above, the plane moves relative to the ground (watch the cones) therefore it gets lift.
I must admit I have now got to the point where I can explain/debunk both answers whilst writing this which is probably why this remains a rather pointless puzzle. (still don’t totally agree with the vid, the ambiguous nature of the original question doesn’t help). Anyway…
I can see one fallacy in the thought experiment, though. To quote:
“The planes propeller and the conveyor create an equal and opposite force on the plane and its resulting movement will be nil.”
The thing is, the wheels underneath a plane freewheel. They’re just on bearings, and have marginal friction. Because of this, the conveyor doesn’t actually create any force on the plane. It’s similar to having glasses on a table, with a table cloth beneath them. If you jerk the table cloth out from under them, they remain in place.
As the conveyor increases in speed, this effect becomes greater and any force it does apply on the plane in reverse diminishes. Meanwhile, the force being applied by the propellor is increasing. If the friction between the plane and the belt is sufficient to equal the force produced by the engine, then it will remain stationary. But because the wheels rotate freely with minimal friction, the plane will take off with little difficulty.
As I said in the post I’ve got to the point of being able to argue both answers. Also I’d had a few beers when I wrote that.