Now that I’ve closed the comments on the question of the airplane and the conveyor belt, I’m still getting emails calling me an idiot for thinking that the plane will take off. Having believed that after first hearing the question and formulating several reasons reinforcing my belief, I can sympathize with that POV, but that doesn’t change the fact that I was initially wrong and that if you believe the plane won’t take off, you’re wrong too[1].
The only thing is, I’m not sure how to prove it to you if you don’t understand the problem and the physics involved. I guess I could urge you to read the question and answer again carefully. I could tell you that not only does the conveyor belt not keep the plane stationary with respect to the ground but it *can’t* keep that plane stationary with respect to the ground[2] and once you know that, of course it’ll take off. My pal Mouser has a Ph.d in Physics from MIT and he says the plane will take off:
The airplane would take off normally, with the wheels spinning twice as fast as normal and a *slight* reduction in acceleration due to added friction.
Is that enough to convince you?
[1] This situation reminds me of Richard Dawkins’ and Jerry Coyne’s assertion that “one side can be wrong”.
[2] The motion of the conveyor belt does nothing[3] to affect the movement of the plane when the plane is in motion…it doesn’t matter if it’s moving forward, backward, at 2 MPH, or at 400 MPH. If the plane were on castors that could spin freely from side to side as well as front to back, that treadmill could be spinning 100 MPH to the left and the plane would take off.
[3] Well, almost nothing. The friction of the turning wheels will slow things down a bit, but not enough to not make the plane take off. After all, the main function of the wheels of a plane is to provide a near-frictionless interface with the ground (or whatever the plane happens to be taking off from).
This question posed to Cecil at The Straight Dope has occupied most of my day today:
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?”
I’ll give you a few moments to think about that before discussing the answer…
…
…
…
Cecil says that the obvious answer — that the plane does not take off because it remains stationary relative to the ground and the air — is wrong. The plane, he says, can take off:
But of course cars and planes don’t work the same way. A car’s wheels are its means of propulsion—they push the road backwards (relatively speaking), and the car moves forward. In contrast, a plane’s wheels aren’t motorized; their purpose is to reduce friction during takeoff (and add it, by braking, when landing). What gets a plane moving are its propellers or jet turbines, which shove the air backward and thereby impel the plane forward. What the wheels, conveyor belt, etc, are up to is largely irrelevant. Let me repeat: Once the pilot fires up the engines, the plane moves forward at pretty much the usual speed relative to the ground—and more importantly the air—regardless of how fast the conveyor belt is moving backward. This generates lift on the wings, and the plane takes off. All the conveyor belt does is, as you correctly conclude, make the plane’s wheels spin madly.
After reading the question this morning and discussing it with Meg for, oh, about 3 hours on and off, I was convinced that Cecil was wrong. There’s no way that plane could take off. The conveyor belt keeps pace with the speed of the plane, which means the plane remains stationary from the POV of an observer on the ground, and therefore cannot lift off.
Then I read Cecil’s answer again this evening and I’ve changed my mind; I’m fairly certain he’s right. For a sufficiently long conveyor belt, that plane is taking off. It doesn’t matter what the conveyor belt is doing because the airplane’s energy is acting on the air, not the belt. I had better luck simplifying the problem like so: imagine instead of a plane, you’ve got a rocket with wheels sitting on that belt. When that rocket fires, it’s eventually going to rocket off the end of that belt…which means that it doesn’t remain stationary to the ground and if it had wings, it would fly.
What do you think? Can that plane take off?
See also Feynman’s submerged sprinkler problem and an old argument of Newton and Huygens: can you swim faster through water or syrup?
Update: Well, that got out of control in a hurry…almost 300 comments in about 16 hours. I had to delete a bunch of trolling comments and it’s not productive to keep going, so I closed it. Thanks for the, er, discussion and remember, the plane takes off. :)
The Onion provides a list of new guidelines from the Transportation Security Administration. “Vermont and New York cheddars can be brought on board, but not Wisconsin cheddar — by far the sharpest cheese in the cheddar family”.
Photos of some difficult runways on which to land a plane. (via tmn)
Update: Oops, looks like that link has some NSFW ads on it. Sorry about that and thanks to everyone who wrote in. I totally didn’t see the ads when I looked at the photos before…my ad blindness is now complete if I’m missing pr0n.
A Boeing 777 lifted off from Hong Kong last night enroute to London with an eye toward breaking the world record for greatest distance flown by a commercial airliner (13,423 miles in 22 hours, 22 minutes).
Papalotzin is a project to follow the migration of the monarch butterfly from Canada to Mexico in an ultralight airplane (they call it their big butterfly). They’ve made it as far as NYC so far and are blogging and taking pictures as they go. (via gurgly)
Stay Connected