Monday, 8 September 2008

Something intelligent

As much as I hate to do this and add to the many lame people in the interworld discussing this particular "puzzle" I'm going to anyway, I have no shame!

Prompted by the latestxkcd comic, or more precisely the roll over joke, which if you don't know about, go back and read all the comics again but hover your mouse over the image after reading it for further goodness, I decided to look up the airplane(aeroplane)/treadmill problem thingy, which boils down to this:

A plane is standing on a runway that can move (some sort of band conveyor). The plane moves in one direction, while the conveyor moves in the opposite direction. This conveyor has a control system that tracks the plane speed and tunes the speed of the conveyor to be exactly the same (but in the opposite direction). Can the plane take off?

There are a number of blog/forum posts referencing this problem and giving there various answers, which seem to be predominantly yes.

this site has some interesting stuff about it and so does a google search for airplane treadmill problem.

Anyway I want to see what you guys thing, seeing you're all intelligent. I have my own theory, which is probably wrong, but for the time being I think it's right, but not being a physicist/whatever I could be missing something fundamental.

The majority of answers go thusly, plane fires jets, treadmill moves, wheels go round, but plane takes off because of the air flow caused by the jets.

I disagree, I think that the jets are the propulsion which moves the plane through the air or across the ground, depending on where it is. What I understand produces lift is the air flow above and below the wings, which creates negative pressure above the wing lifting it up (this could be faulty physics though). This is caused by the plane moving through the air at a high speed, either because it's already there and jetting through the air or because it's gathered sufficient speed from moving along the ground. So if the ground is moving at the same rate as the jets are trying to push the plane forwards it will not gain any airspeed so not take off, as the air above and below the wings will not be moving (well it probably will be, but not enough). The jets are simply sucking in air and pushing it back out creating propulsion but not an airflow over the wings. I guess it's kinda like if the air started to move at the same speed as a plane in the air but in the opposite direction, it wouldn't have any lift so would fall out of the sky.

Anyway that's my thinkings, what be yours??

14 comments:

TheTelf said...

It's always seemed to me in this scenario (and I've heard of it before), that the plane would not stay on the 'treadmill'. If it was wheel power alone causing the plane to reach take-off speed, then maybe, but it seems to me like the jets move the plane relative to the air, rather than the ground.

Hence, as the engines speed up, the wheels will just end up going round as fast as needs be to allow the plane to move forward.

If you're standing on a skateboard which is resting on a treadmill, you can still move up and down the treadmill by levering yourself on an external entity (in your case, a wall or a rail, in the case of the plane, the air).

That's my reading of it, anyway, but physics was possibly my weakest point at school (at least in terms of sciences), so take my opinion with all necessary pinches of salt.

Andy J. Wotherspoon said...

hahahaha, lovin' the parkour reference. I wonder if the scenario is floored in some ways, it seems that the most common reasoning is that the plane will simply move too fast for the threadmill/wheels and thus take off, where as I think, but could be wrong, that the deviser was more trying to say, if the plane was to use it's full powers of propulsion but not actually move through the horizontal plane, would it actually take off. Joe suggested altering it to have the plane attached to poles (infinitely strong ones), allowing the plane to move in the Y axis but no other. Thus when the jets (or whatever means it uses to propel itself) are going would it rise off the floor? Again I think not.

Andy J. Wotherspoon said...

also, the title has no relation to the problem, as to be honest I don't really think it's something clever at all, more a vaguely interesting problem that has no real meaning and can be talked about by people wishing to sound intelligent, but in actual fact are not. I merely wanted a title that was intelligent so decided to go with a description of what I wanted the title to be as this saved me the trouble of becoming intelligent.

TheTelf said...

Yeah, if the plane can't move horizontally, then it won't take off, I agree on that, but unless the plane is moving forward by wheel power alone (which it won't be if it's trying to take off), a treadmill won't be enough to stop it. In the case of the plane held in place with rods or whatever, it won't take off, like you say, but that's a different problem from the basic treadmill one.

On your other point, I don't know if the puzzle can be 'intelligent', but anything that provokes debate is certainly interesting.

James said...

I brought this up at work and a colleague said surely not, or else it would effectively take off vertically (having no speed with respect to the air), which is silly.

(which is silly is probably my favourite ending to a scientific proof)

TheTelf said...

Which problem did you bring up? The original treadmill one, or the modified one in the comments?

James said...

the original one

though my understanding of the problem would be that no matter how fast the engines are pushing the plane it still won't travel any distance along the ground because of the treadmill and hence won't be able to generate any lift. Kind of like you don't feel the wind in your face when you're using an exercise bike no matter how fast you peddle.

TheTelf said...

I disagree, I think the treadmill wouldn't be able to stop the plane from moving forwards.

- The engines will move the plane relative to the air.
- The engines are not affected by the treadmill.
- The treadmill doesn't affect the air.
- If the treadmill speeds up, it will cause the wheels of the plane to rotate faster, but this will not slow the plane down relative to the air.

Technically, if the treadmill moves fast enough, it could cause the wheels to reach their maximum rotational speed, possibly causing the plane's speed relative to the air to have some upper limit, but since we're talking about giant treadmills, I think we can probably dispense with such puny physical restrictions.

IMO, the plane in the original problem would take off.

Hanspan said...

Clearly the only way to resolve this is to build a giant treadmill capable of equalling the speed at which the wheels of the plane can turn....

I also think it's worth being careful not to mix up our terminology - some of us are talking about jets and some of us are talking about engines, and while I'm aware that a jet engine is what sits under the wing of a plane, what I'm not clear on is whether there are separate engines that power the wheels on their own. Do planes use jet engines on incredibly low settings just to drive round airports, for example? Or is there a separate propulsion for that.

I think the plane couldn't take off, because even if it was moving relative to the air, by virtue of air being sucked through the jet engines, it wouldn't create enough lift because it's not designed to do so. It needs the run-up as well as the engines to get flying. After all, if you could build a regular plane with the regular wing design that just took off vertically, you would do so, for the savings on space alone.

TheTelf said...

But it would have a run up. If you were watching from the side, it would look exactly like a normal take off, except the wheels would be turning twice as fast because the ground happened to be moving backwards.

And my understanding of taxiing planes was that they used independently powered wheels for slow movement, rather than using the main engines.

joebloggs said...

I believe that planes do indeed have no power through their wheels, and I also think Patrick isn't talking about a vertical take off. He's saying that the plane would still move forward. I guess this may involve some friction between the wheels and the treadmill, but I'm guessing insufficient to keep the plane from sliding forwards.

TheTelf said...

xkcd ftw, as usual.

Hanspan said...

I feel slightly vindicated by some of that... because when I was going on about definitions, I did actually have the thought "how are they defining the speed of the wheels?" and xkcd seems to be saying you can't answer the question easily because it's badly asked in the first place...

Hanspan said...

Also, ( love how "wrong on the internet" has become part of everyone's (and by everyone and I mean me and Randall's, and who knows, maybe yours too?) daily lexicon.

And perhaps someone can explain to me, what is it with scientists and loving Richard Feynman? One of my exes practically wanted to have his babies...