Mick Hartley

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Problem Solved

I suppose what makes this “airplane-treadmill” question (via Anthony) so compelling is that each side’s so sure they’re right. Here’s the basic scenario:

Imagine a plane is sitting on a massive conveyor belt, as wide and as long as a runway. The conveyer belt is designed to exactly match the speed of the wheels, moving in the opposite direction. Can the plane take off?

There are now 852 comments at the NYT site. I haven’t read them all, but, really, what an exercise in talking scientific-sounding bollocks. Of course the plane won’t fucking take off. Jesus Christ!

OK, the controversy’s now over everybody. Time to return to your normal lives.

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25 responses to “Problem Solved”

  1. jeffrey Mushens Avatar
    jeffrey Mushens

    Of course it can take off when it gets to the appropriate speed for the airflow over the wings to provide sufficient lift.

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  2. Dom Avatar
    Dom

    Actually, I love these paradoxes, and I collect alot of them. Here’s a new one.
    Say you are in a boat, with a slow leak. If I bail the water out at least as fast as it gets in, the boat never sinks. There is energy in the water as it falls from my pail back to the ocean, but it is equal to the energy I exert when I bail. That’s how it should be — no energy lost or gained.
    Now, let’s say I place a hose over the hole in the boat, and curve it over the side. Same situation — the water is leaving as fast as it enters, so I never sink. There is still energy in the water leaving the hose, like a tiny water-fall. Only now I’m not working. Have I gotten free energy? Do I have a perpetual motion machine?

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  3. Mick H Avatar
    Mick H

    Jeffrey – well it never gets to the appropriate speed, does it? Cos it’s on top of a conveyor belt which, by definition in the setting up of the problem, makes sure it stays stationary wrt the ground and the air. And no, the movement of the air caused by the engine – jet or propellor – wouldn’t be enough on its own. If the plane was attached to the ground so it couldn’t go forward but could go up and down, then however hard you revved up the engine, you’d never see the plane start to rise up.
    Dom – how could the water go through the hose, from lower (the leak) to higher (above the surface of the surrounding water)?

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  4. P. Froward Avatar
    P. Froward

    Picture your car on a conveyor belt. Take it out of gear and take your foot off the brake, so the car can roll freely. Start the belt. The car will move in the direction the belt is moving. If the belt starts with a jerk, the car may roll forward a bit relative to the belt; if the belt starts smoothly, the car’s liable to roll very little. In either case, the car’s wheels are not frictionless, and if you keep it up, the car will move in the direction the belt is trying to move it.
    Since it’s a question about physics, you might as well assume that the laws of physics all apply, and that includes friction.
    Here’s the rub[1]: Picture a 747[2] blasting away like the dickens with all four engines. How fast must the conveyor belt move to counteract that much force? Quite possibly faster than is physically possible, or at least faster than the current state of conveyor-belt design and construction can support.
    This is either a) a physics question in which the laws of physics are optional — which is idiotic; or b) a question about the design and construction of very large high-performance conveyor belts — which can be addressed meaningfully only by a specialist, and whose answer is not final because the state of the art will change.
    Pointless, either way.
    But yeah, if the plane is limited by the laws of physics and the belt is not, the plane won’t take off. If the wheels have no more problem with friction than the belt has, the plane can take off just as it pleases. The question either way is what, if anything, is counteracting the thrust of the engines?
    [1] Gedit? Gedit? Friction, rub?
    [2] Airbus products, designed as they are by government employees (more or less) in a socially just social democratic socialist society, are presumably less affected by the laws of nature.
    On the hose issue, anybody ever heard of a siphon?

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  5. P. Froward Avatar
    P. Froward

    I think people are taking the speed part to mean that you can take it as a given that one of the ground rules is that surface of the belt, and the outer surface of the wheels, are moving at the same speed. “Same speed” is “same speed” whether it’s zero or greater than zero. In other words, they think the “designed to” clause is a handwave which, in plain English, translates to “for reasons unknown, the plane remains motionless”.
    So the question they’re answering is this one:
    “An airplane is motionless relative to the ground. Is it going to take off?”
    Well, duh! Neither is a bowling ball, or Spain.
    Er… Unless there’s one hell of a headwind. Anybody consider that? And a Harrier could just float straight up, smirking. Somebody at the link mentioned that, naturally.

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  6. Mick H Avatar
    Mick H

    Well yes, exactly. That’s the way I read it, and that’s why I was amazed that anyone could think the plane would take off. But what you say in your first comment is interesting – the key question is, what’s counteracting the thrust of the engines? People are saying, well, the friction in the wheels can’t be enough, so the plane has to move forward, ie fly. But I’m reading the way the problem is set up as ruling that out. So, whatever, it’s got that ambiguity built in…
    As for Dom’s boat – siphons work from higher to lower, but as I understood it, this is lower (below the waterline) to higher (above the surface, “like a tiny waterfall”).

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  7. Dom Avatar
    Dom

    “how could the water go through the hose, from lower (the leak) to higher (above the surface of the surrounding water)?”
    The water does that anyway. If there is a hole in the boat, the water spouts up — and then lands in the boat to sink it. But what if the spouting went off to the side (via the hose) so that it lands not in the boat but back into the ocean, leaving the boat dry. There is nothing to sink the boat, and nothing to stop the leak.

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  8. Dom Avatar
    Dom

    Say I have an infinite supply of balls labeled 1, 2, 3… Now at 1 minute before noon, I place balls labeled 1 through 10 in an urn, and throw out ball #1. At half-minute before noon, I place balls labelled 11 through 20 in the urn, and throw out ball #11. Then 21 through 30, throw out #21. And so on. How many balls are in the urn at noon. Infinite. Name any ball and I can tell you if it is in the urn or not.
    Now say at 1 minute before noon, I place balls labelled 1 through 10 in the urn and throw out ball #1. At half-minute before noon, I place balls labelled 11 through 20 in the urn, and throw out ball #2. Then 21 through 30, throw out #3. And so on. This is the same operation — get 10 balls, throw out 1. All that has changed is the label of the ball thrown out each time. But how many balls are in the urn at noon this time? None. Name any ball and I can tell you the exact time it was thrown out.

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  9. Mick H Avatar
    Mick H

    “If there is a hole in the boat, the water spouts up — and then lands in the boat to sink it.” It wouldn’t spout up higher than the water level of the sea – which is what you’re supposing.
    As for the infinite balls – well, it’s one of those Achilles-and-the-tortoise type deals, isn’t it? Playing around with the meaning of infinity.

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  10. DaninVan Avatar
    DaninVan

    Uh, folks; planes don’t need wheels to take off, skis or pontoons work just fine, thanks very much. The point is LACK of friction with the ground, until the thrust generated by the engines generates enough forward speed to allow liftoff.
    We’re looking at apples and oranges when you compare planes with ground vehicles which DEPEND on friction with the ground, but ONLY IF THE ENERGY IS DELIVERED THROUGH THE WHEELS. A perfect example of both cases is a hovercraft which of course can’t ‘fly’ but also doesn’t contact the ground (or conveyor belt).
    The only issue with the problem presented is whether the wheels could sustain the higher rpms likely caused by the conveyor driving them; they have no mechanical connection to the momemtum of the plane, they’re free wheeling during takeoff.

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  11. DaninVan Avatar
    DaninVan

    Oops sorry, make that ‘momentum.’

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  12. Anthony Avatar
    Anthony

    I have a friend who works at the Jet Propulsion Laboratory, at the California Institute of Technology. his take on this is as follows.
    The answer is that the plane can take off. Wheels are irrelevant: skids are also seen on airplanes, as are floats. The thrust comes from the air (via the engines), and the conveyor belt will not therefore affect the forward motion that generates the lift.

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  13. Mick H Avatar
    Mick H

    Hmm. Yes, wheels are irrelevant, but this is saying that an observer standing nearby would see the plane lift off vertically. In other words, the power of the engine on its own will cause sufficient air-flow to lift the plane, without any forward motion. Jet Propulsion Lab or not, I don’t think I believe that.
    If it’s true though it could have huge implications for airports in crowded cities. Just keep the plane stationary (a cable at the back?) until it’s risen high enough, then just let go. No more long runways. Though I haven’t quite worked out what you’d do about landing.

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  14. Fabian from Israel Avatar
    Fabian from Israel

    “Just keep the plane stationary (a cable at the back?) until it’s risen high enough, then just let go. No more long runways.”
    Well, it works for kites, don’t it? 😉

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  15. DaninVan Avatar
    DaninVan

    Mick H; why do you keep coming back to this no forward motion idea? The conveyor has no practical effect on the planes fwd motion during takeoff. The planes wheels are touching the conveyor OR runway, yes; but in both cases they’re freewheeling…in effect the plane is ‘sliding’ on it’s takeoff. The engines thrust is pushing/pulling the plane fwd, the wheels have no bearing (sorry, bad pun)on the issue. At worst, as I said earlier, they may be spinning at a higher than desired rpm causing a potential tire blowout, but that’s it. You’re still thinking in terms of a drivetrain.

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  16. Mick H Avatar
    Mick H

    I knew I should never have posted on this…
    “why do you keep coming back to this no forward motion idea?” Because that’s how the problem’s set up, as I understand it – “The conveyer belt is designed to exactly match the speed of the wheels, moving in the opposite direction.” A plane is a heavy thing. As long as it gets no upthrust from the air passing around its wings, it’s going to go where its wheels go. I’ll admit that if the conveyor belt were made of ice, so the wheels could get no grip, you’d be right, but that’s not the case.

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  17. DaninVan Avatar
    DaninVan

    Your supposition is only true if there’s no fwd. thrust; the wheels are irrelevant. Have you never run ‘up’ a ‘down’ escalator? Think of the wheels as ballbearings with a load on top and the conveyor beneath with a bearing race actually carrying the weight. How much effort is actually required to prevent the bearing and race from actually moving in the direction of the conveyor motion? Now, add thrust in the oppposite direction.
    Another example: take a bicycle wheel and, holding the axle in both hands perpendicular to the moving conveyor, bring it gently into contact. What happens? If your supposition is correct, you’d be jerked off your feet and sent flying in the direction of conveyor motion. As you know, that’s NOT what happens. The wheel simply starts spinning with virtually no effect on you holding the axle…now, still with the wheel in contact with the conveyor, start walking along beside the conveyor against the direction of its motion. Does that convince you?
    Another thought: when landing, the plane is for all intents standing still and the runway is (like the conveyor) moving at 200+/-MPH. If your supposition were true, the plane would come to a screeching halt as the wheels came into contact; again that’s NOT what happens. The plane requires both the application of wheel brakes AND reverse thrust in order to cancel the planes fwd. momentum. It’d simply run off the end of the runway otherwise.

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  18. Mick H Avatar
    Mick H

    I don’t know Danin Van- I’ve read through what you’ve written about four times, and I still can’t make any sense of it. It may be me of course – I’ve had a couple of glasses of wine, so I’m not at my sharpest. We’re at cross purposes somewhere, but I can’t be bothered to work out where.

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  19. DaninVan Avatar
    DaninVan

    Hey, wine’ll do that! 🙂
    Merry Christmas to you and your visitors, M.H.
    http://www.herkolson.com/names_s/sting_songs/the_windmills_of_your_mind_lyrics.html

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  20. Mick H Avatar
    Mick H

    And a Merry Christmas to you too.

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  21. SnoopyTheGoon Avatar
    SnoopyTheGoon

    Oh, Mick – I haven’s seen this story on NYT, but you have succeeded to recreate the microcosm, so to say! Brilliant.
    And some people wonder why there are so many conspiracy theorists…

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  22. P. Froward Avatar
    P. Froward

    Mick, you’re right, it’s the ambiguity. The only potentially interesting question here is, what influence can the treadmill have on the forward motion of the plane? If the answer to that question is given as a sort of axiom, then the rest is obvious and boring. What the smarter people are really yelling about is what the question is actually asking. And then there’s the field of dumbasses bringing up the rear, with no clear sense what they think the question means, thrashing away at it regardless.

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  23. DaninVan Avatar
    DaninVan

    “…dumbasses…”
    The magnanimous Spirit of Christmas didn’t last long. 😉

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  24. Fridgemonkey Avatar
    Fridgemonkey

    I have a look of total horro on my face. OF COURSE THE FRIGGING PLANE DOESN’T TAKE OFF, It’s not fucking moving.
    Good Lord.

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  25. DaninVan Avatar
    DaninVan

    Fridgemonkey in the lab:

    🙂

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