Here is the result -- it's not a spoiler, because anyone who truly understands the basic physics involved, will not be surprised to hear that the goddamn plane takes off.
However, I've since come to the conclusion that Plane on a Treadmill looks like a physics question, but it's actually a psychology question.
If you're one of those people who thought the plane in the Mythbusters setup wouldn't take off, the answer is simple:
- Your understanding of physics isn't quite as strong as you thought
- You can't wrap your head around the fact that people and cars behave differently from planes
- You should probably pay more attention to the nice demo and animation they did
- You're being stubborn (or deliberately obtuse), because you're sticking to an interpretation of the problem that doesn't make sense and that requires magic
- You're probably never going to change your mind, because the Mythbusters folks basically demonstrated it as good as you can get, and by sticking to your opinion in the face of proof, you're taking it out of the realm of fact and science and officially joining the realm of the 9/11 Truthers and Moon landing hoax conspiracy theorists and Creationists.
The main, physics part of the problem is that people hear "treadmill," and they think back to their experience running on a treadmill or driving on a dynamometer, and try to apply that to an airplane on a treadmill, which is superficially similar but actually completely different.
The other, psychological part of the problem is that the wording of the original question that most people saw isn't very good. In fact, the original wording stinks on ice.
This is because it allows an interpretation of the question that is self-negating -- the "speed" bit can be read as stating right off the bat that the plane can't move forward (relative to a fixed point to the ground), no matter what. Which means it won't take off. Period.
(I held this interpretation for about 5 minutes -- I originally thought the plane wouldn't take off. I came around shortly after.)
The problem with the "doesn't move forward, no matter what" interpretation of the question is twofold:
- It's not a question anymore. It's pointless -- you've taken a moderately interesting thought experiment and turned it into a reading comprehension exercise.
- It requires a magical treadmill.
However, if skip the rope and rely solely on the treadmill -- you can keep a person or a car from moving forward, but you can't do it with a plane (or a rocket car, or a rollerblader with a Wile E. Coyote jetpack), unless the treadmill itself is magical.
The only forces holding the plane back are the friction of the wheels against the treadmill; inertia; and friction in the bearings and with the air: All of which are real, but vastly overwhelmed by the forward thrust of the engine.
If you insist on sticking with this "things don't move forward, for anything (even planes)" treadmill, it has to move fast enough so that the relatively tiny, tiny friction forces are magnified enough to overcome the thrust of the engines. Almost infinitely fast, in fact. Which is fine: You've now got an impossible, magical treadmill.
What you don't have is a real world physics problem anymore, the kind they test on Mythbusters. At best, it becomes a metaphysics question, like "Can God microwave a burrito so hot He can't eat it?"
So here's the psychology question -- pick the statement which best describes you:
- I would do anything to be right, even if it means picking an arcane interpretation of a self-defeating question that requires magic and keeps things completely in the realm of theory, precluding any possibility of doing something cool
- I would rather have something you can actually build, like a big-ass treadmill, scaled-up to handle a plane and match the speed of the wheels (which is just an engineering problem -- merely impractical, not impossible)
- Shut up, I don't like physics, engineering, psychology, or you.
- The plane will move forward (relative to a fixed point on the ground).
- The plane will take off.
- People will keep complaining and keep arguing.