Chad Perrin: SOB

30 September 2008

Plane/Treadmill Conundrum — are you for real?

Filed under: Geek,inanity — apotheon @ 01:39

As described in a straitdope.com discussion of the Plain/Treadmill Conundrum, there’s this thought experiment circulating on the Internet right now. I had no idea such a stupid damned thing was making the rounds until I saw the alt text for an xkcd comic that mentioned it.

The supposed conundrum is roughly as follows:

You have a commercial jet. You set it on a huge conveyor belt, of a length arbitrarily great enough to perform your stupid little experiment without problems. The conveyor belt somehow measures the tangential speed of the surface of the wheel’s tire, and accelerates to match that speed relative to the ground. It also magically doesn’t generate air movement to interfere with the experiment. Thus, if you were driving on this conveyor belt in a car, no matter how hard you pressed on the gas pedal, you’d remain in place relative to the ground around the conveyor belt. Would the plane take off?

That’s no damned conundrum at all. It’s a stupid question. The only reason the aircraft might not take off is the fact that the landing gear of the aircraft might fail before it achieved sufficient airspeed to lift off. The wheels and conveyor belt would just accelerate infinitely fast as the aircraft started moving forward, causing obviously unavoidable catastrophic damage to the wheels and/or conveyor belt. As such, if you don’t assume no damage will occur to the various parts involved, I guess the aircraft might not take off since the landing gear and conveyor belt would fail effectively instantly and the nose of the aircraft would plow into the ground. If you do assume no damage will occur and ignore the friction problems of things like the bearings in the wheels so you can have your silly experiment without problems, you’d have tires and belt moving fast enough to suffer absurd relativistic effects while the aircraft just smoothly moved forward and lifted off the ground like nothing was wrong.

Of course, we really don’t know what happens when the tangential speed of a tire’s surface exceeds the speed of light, so . . . who knows what would really happen?

I guess we’re ignoring relativity, too, for this. I guess the plane takes off. Well, glad that’s settled.

Didn’t anyone teach these children that it’s the engine exhaust thrust and airflow over lifting surfaces that makes an aircraft fly, and not the spinning of the wheels?

Can we have a thought experiment that makes sense now, please?

7 Comments

  1. Well, the treadmill will have to be fairly wide to support the plane, and it’s surface will have to be fairly rough to keep the plane’s wheels turning and so if it runs for long enough it will drag air past the plane at an increasing rate untilthe plane lifts off ;-)

    Comment by Ole Phat Stu — 1 October 2008 @ 10:07

  2. Basically, there are about a dozen (or more) different ways one could come up with the answer that the plane would take off, and the only way it would fail to take off (without assuming something like “there’s no atmosphere”) is if the plane’s landing gear stops holding it up so that it crashes into the ground, or you forgot to put fuel in it, or something like that.

    In other words, only if you violate the spirit of the thought experiment does it fail to take off. All this speculation about how fast the conveyor belt moves is immaterial to any arguments that the plane won’t take off, and it boggles my mind that there’s any argument on the matter at all. Didn’t any of these people go to high school?

    Comment by apotheon — 1 October 2008 @ 11:15

  3. Chad, if you’re worried about ignorance, just count those who vote for palin on november 4th.

    Comment by Ole Phat Stu — 1 October 2008 @ 09:24

  4. Chad, if you’re worried about ignorance, just count those who vote for palin on november 4th.

    More accurately, I could count those who vote for McCain/Palin and those who vote for Obama/Biden.

    Anyway . . . yeah, but that’s a different kind of ignorance than the type I lament here. In fact, this may be something worse than mere ignorance: it’s a bit more like innate incompetence. At least one could chalk up political stupidities to a desire to believe something untrue, or to a tendency to prefer binary decisions. Purely social factors apply. What’s the excuse for failing to understand the irrelevance of a conveyor belt in the ability of an airplane to fly?

    Comment by apotheon — 2 October 2008 @ 10:08

  5. Ah, this is refreshing indeed! Not only that, but this post has kindled my sense of world community at a very deep and personal level. Now whenever I add my little “because I’m bitter” line I can also proudly say “like Chad over there.”

    =D

    Fred

    Comment by the_blunderbuss — 2 October 2008 @ 10:47

  6. I’m honored to be included in that community. Thank you.

    Comment by apotheon — 2 October 2008 @ 10:52

  7. I’ll admit I’m a sucker for thought experiments, and mythbusters tackled this (though I’ve not actually seen the episode) semi-recently (I’ve been hearing it for a couple years on flying sites).

    I think the problem people have with the experiment is not that they don’t understand the physics of flight to be: propeller/jet pulls plane forward and accelerates until the wings are moving fast enough that the air pressure under them is greater than the air pressure over them and it takes off. Which is, a fair enough explanation of airplane flight (Well, in prop planes, and depending on engine placement, the airflow generated by the prop itself will move enough air over the wings to generate the lift needed).

    I think the problem people have is that they then “understand” that by spinning the wheels backwards they are preventing the plane from moving forward via the thrust from the prop/jet. I think the presumption is then that the wheels are, while not “powered” they are somehow constraining how fast the plane is moving forward while on the ground, and if you can keep them “pulling” the plane back via the wheels as fast as the engine would be pulling it through the air, that sufficient velocity would never be reached to generate the air pressure under the wings to allow for lift-off.

    The problem people have is in understanding that while the wheels are rolling, the prop/jet isn’t pushing against the ground, but against the air… and doesn’t care how fast or slow the wheels are spinning (take a seaplane for instance). The wheels will just spin faster than they would on non-moving ground until the conveyor can’t keep up and the plane is moving fast enough to take off (or they break and it crashes, or relativity sets in and they disappear into the past… or is it future). As with many thought experiments, the problem comes in the structure of the set-up, and which real-world factors you need to ignore.

    I’d be interested to see the difference the drive would make as to the performance of the experiment for that matter (Jet engine makes it tougher to build a conveyor that would match it for thrust, but the jet engines would also not push air over the wing to create the lift at stand-still, so the wheel friction is a bigger factor. Cessna would not be as hard to compensate for in your conveyor building, but the propeller would actually generate over-wing airflow that should make it easier to take off at a slower conveyor speed). I know of RC planes that generate enough lift when you crank the engine up that you can just hold them in your hand and let them go with the engine revving and the airspeed generated by the prop is enough to give them sufficient take-off lift.

    I’m actually not sure this sort of ignorance is much different than political ignorance because it’s largely just a matter of which factors you’re going to ignore, or never learn about, for whatever reason you may have.

    Comment by CharlesP — 6 October 2008 @ 01:43

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