Give Up Blog

Wednesday, December 13, 2006

A physicist weighs in

The physicists (Rob Knop) have weighed in on the treadmill problem.

The irritating thing? He just destroyed the whole problem.

Answer : they're both wrong. Not about the "yes" or "no", but about the explanations. In fact, the whole question, with the implicit assumptions behind it, doesn’t make any sense whatsoever. It's a nonsensible question posed as if there were a proper "yes" or "no" answer... and, thus, anybody who writes trying to justify one or the other position is forced into using some misconception.

...

Here's the real answer: You wouldn't be able to keep an airplane on the treadmill. Hence, the attempts to answer the question fall flat on their face. Mark, and others, correctly state that the wheels are ultimately irrelevant to the taking off of an airplane, that it's the movement of the plane through the air that matters. The thought experiment that is created, however, is an airplane that's still due to the action of the treadmill. This wouldn't work. As the aircraft's engines are pulling it through the air, eventually it would start to skid forward along the treadmill. Depending on how the treadmill was set, it would either be more or less efficient in its initial acceleration, but it would move forward across the treadmill.

That's fine, it's a thought problem that creates a somewhat impossible condition. I get what he's saying, I was just ignoring the issue of the wheels and treadmill and looking at this as a question asking if the plane was held fixed relative to the ground's reference frame, and engines were on at full thrust, would it take off? Of course not. You could make a take off argument that's based on the impossibility of holding a plane still under these conditions, but I still feel that's missing the point, which was the importance of thrust vs. lift for flight (which was the source of a lot of the really bad physics explanations on the comment threads). The treadmill really is a bad example of how you could hold a plane still while allowing it to ostensibly gun its engines to full speed (because the pilot would have to exert pressure on the breaks to allow the treadmill to keep the plane still). Maybe a better way to put it would be to just chain the plane to a post, so it's engines do not give it forward acceleration, does the plane move upwards? Nope. If you cut the chain? Nope, not until it moves a few hundred feet will the plane acquire the conditions necessary for lift.

Labels: physics

4 Comments:

Toby said...

Well, the problem here is that when you assume that the treadmill *must be* holding the airplane still (either because you think a plane accelerates like a car, or you think that the question imposes this fact by fiat), you're making a faulty assumption. The original question, properly posed, makes no such assertion; instead, readers who fall victim to the misdirection merely infer that it is the case.

When Mr. Knop says "The thought experiment that is created, however, is an airplane that’s sitll due to the action of the treadmill," he's wrong, because that is not suggested by the original question, it's a fiction created in the head of the puzzler:

"The problem says the airplane isn't moving, so obviously it can't take off"

"The problem says the airplane isn't moving, but that's stupid, of course it is, so it takes off"

Either way, the problem does NOT say that the airplane isn't moving, does it?

2:26 PM, December 13, 2006

Rev. Dr. said...

Mark updated the boing boing post that I think completes the discussion (including my comment as quitter).

This paragraph I think does the best to explain it was Mark was arguing with Salon's airplane expert.

Me: You know, the problem is that the question is poorly constructed. No matter how fast the treadmill goes, the thrust of the plane will cause it to move forward. If the treadmill was going 1000 miles an hour, the plane's wheels would be going 1000 mph + whatever speed the plane was moving forward. So then some kind of sensor in the treadmill would increase the speed of the treadmill to match the higher speed of the plane's wheels. Of course, when the treadmill's speed increases, the plane's wheels speed up to match the new speed of the treadmill, plus the speed caused by engine thrust. The speed of the treadmill and the wheels both approach infinity, but the wheels are always going to be moving faster. The best the treadmill can do is lag behind.

Patrick: I thought the version of the question that Pogue presented specifically stated that the treadmill would always increase its speed to match that of the plane's tires. How *possible* that might be is one thing, but I believe the point was to emphasize that the plane would not, could not, move forward. I assumed that was part of the scenario. Otherwise, why even bother with the treadmill in the first place? It's not a brain teaser about wheel friction, it's about relative motion, and understanding what gets a plane off the ground.

Me: If it's just about a plane rolling on a treadmill with no air running past it, then it seems like a dull question. Most people assume that if a treadmill were rolling backwards at the normal speed for a jet takeoff, the thrust of the jet would not be enough to counteract the backwards movement of the treadmill. But of course, in the real world, it would. To me, this is more interesting. But I agree with you -- if the rule is that the plane is not allowed to move forward because of some kind of magical treadmill that can move as fast as the wheels of the plane (even though they have to move faster than the treadmill because of the speed increase they get from the thrust), then the plane will not fly.

2:57 PM, December 13, 2006

toby said...

"why even bother with the treadmill in the first place? It's not a brain teaser about wheel friction, it's about relative motion, and understanding what gets a plane off the ground."

Of course it is. It's not a brain teaser, it's a trivia question with an initial misdirection. The tendency to inflate the query into something more worthy is just, well, inflating the query.

I've written about it on my blog at www.jasminecola.com, for what it's worth.

8:11 PM, December 13, 2006

Kris Overstreet said...

If the plane is not permitted to move in reference to the ground, then the whole question is pointless. Of course an immobilized object won't fly!

That is most certainly NOT the nature of the question. The question is whether or not forward motion on the ground is necessary for heavier-than-air flight. In such a question thrust is VERY much relevant; if thrust is greater than the total inert mass, then yes, the plane will eventually lift off.

Harrier jump jets, Osprey transports, helicopters and rockets all prove this point- that's the whole point of VTOL. Even a rocket, which generates no wing lift at all, is still by definition flying.

3:11 PM, December 14, 2006