First of all, sorry (again) about the length of time between posts lately. There's a good, and fortunately temporary, reason for this which I will address shortly because I really want to post this first.
Many of you are familiar with Cecil Adams' The Straight Dope, and with the message boards (forum) associated therewith.
This week's Straight Dope newsletter addressed a sort of brain teaser or puzzle which has apparently been making the rounds on the internet lately, although I haven't seen it anywhere else yet. It goes like this:
An airplane taxies in one direction on a moving conveyor belt going the opposite direction. Can the plane take off?
Dear Cecil:
Please, please, please settle this question. The discussion has been going on for ages, and any time someone mentions the words "airplane" or "conveyor belt" everyone starts right back up. Here's the original problem essentially as it was posed to us: "A plane is standing on a runway that can move (some sort of band conveyer). The plane moves in one direction, while the conveyer moves in the opposite direction. This conveyer has a control system that tracks the plane speed and tunes the speed of the conveyer to be exactly the same (but in the opposite direction). Can the plane take off?"
There are some difficulties with the wording of the problem, specifically regarding how we define speed, but the spirit of the situation is clear. The solution is also clear to me (and many others), but a staunch group of unbelievers won't accept it. My conclusion is that the plane does take off. Planes, whether jet or propeller, work by pulling [or pushing] themselves through the air. The rotation of their tires results from this forward movement, and has no bearing on the behavior of a plane during takeoff. I claim the only difference between a regular plane and one on a conveyor belt is that the conveyor belt plane's wheels will spin twice as fast during takeoff. Please, Cecil, show us that it's not only theoretically possible (with frictionless wheels) but it's actually possible too. --Berj A. Doudian, via e-mail
Now, rather than quote "Unca Cecil's" answer, I'll cut to the chase and state that, of course the plane takes off. It seems odd to me that there should even be a debate about that.
But what's even more incredible is that this column spawned a forum thread that, as of this writing, already has 409 posts, with more being added even as we speak. This, to me, is incredible.
One characteristic of the SDMB is the (mostly) consistent level of thoughtfulness and intelligence amongst the posters. With a few exceptions, these boards are not populated by many of those who do not think carefully about what they are saying or who simply don't know what they're talking about, which makes this thread all the more unusual.
There are not only those who have taken both sides of this issue, this is, the plane either can or cannot take off, but there are a few who have started out in the "can't take off" camp but were converted along the way. Incredibly, though, there's at least one poster who went from "can take off" to "I'm no longer so sure." And, to make matters worse, some posters in both camps use obviously faulty arguments to make their cases.
Most of the trouble comes from the strong temptation to make the problem seem way more complicated than it is. In addition, many folks can't get past the idea that, since a car rolling along the same conveyor belt would indeed have a net speed of zero, an airplane will have no difficulty attaining sufficient forward velocity to take off, since, unlike an automobile, an airplane's forward momentum is not imparted by its wheels. The plane does not move forward because its wheels are rotating. Its wheels rotate because it's moving. The plane's engines do not "push against" the ground in order to move, so it really doesn't care what the conveyor belt is doing (except for a relatively small amount of reverse force imparted to the plane via the friction of the wheel bearings).
Read Cecil's column and let me know if you think there is any ambiguity in it. Several posters have stated that his answer, while correct, is poorly worded, which, while perhaps true, seems to me to be mostly a cop-out. The puzzle, as stated, can be answered without a lot of physics and technobabble.
At any rate, tell me if you think I'm wrong here, but I think the whole issue is pretty obvious.