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The case of the plane and conveyor belt
posted February 08, 2006 at 11:42 pm
This question posed to Cecil at The Straight Dope has occupied most of my day today /*好执着啊~~~*/:
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...
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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 (answer) 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. :)
Reader Comments
280 comments
max says:
The plane gets its lift via the bernoulli effect. This has to do with wing shape and its interaction with air moving rapidly past. If the plane has no motion relative to the wind, there will bo no lift to force the plane up. That plane is going nowhere fast. Kind of.
? by max on Feb 08, 2006 at 11:47 PM
erat says:
The force that makes the plane move forward is air pushing on air, not rubber rolling on asphalt (or conveyor belts). Like Cecil says, the stuff going on at ground level is largely irrelevant.
So, the plane takes off.
? by erat on Feb 08, 2006 at 11:55 PM
Ricardo says:
Exactly what I was thinking. I wasnt even thinking about the wheels... just the fact the plane isn't really moving, therefore no lift force provided to make the plane actually go... up!
An example would be like sitting on those gym bikes with no wheels. You can peddle as fast as you want, but you wont feel the fresh breeze of that speed. No breeze, no wind... no lift!
? by Ricardo on Feb 08, 2006 at 11:58 PM
jeffj says:
The only purpose the wheels serve here is to hold the plane up, and to eliminate most of the friction between the plane and the ground. When the engines fire up, the plane will still start moving forward. The only difference will be that the wheels are turning twice as fast as normal.
? by jeffj on Feb 09, 2006 at 12:03 AM
Jeremy Zawodny says:
I don't know how many of your are pilots, but that plane isn't gonna lift off unless it has a very unusual aspect ratio (wing shape) and an unusually large prop.
The prop produces thrust which helps drag the plane through the air. That air, flowing over the wings, produces lift. The prop is not simply a fan that blows air over the wings.
? by Jeremy Zawodny on Feb 09, 2006 at 12:07 AM
Derek DeMarco says:
Please?!,
I Have been following your page for about a year, from when you first made it known that you were going Pro. And up until this I have had a pretty good feeling about your ability to reason. I have agreed and made movie choices after reading your reviews. But this is a very difficult thing for me to read. If the plane while still on the ground can not make forward progress it can not create the lift necessary to leave the ground. It uses the wheels roll in this way on take off. No matter how much force it can generate it can not leave the ground. Now if there is a major wind blowing at say 150 plus and depending on the size and weight of the plane, but this would have to be a air mass and consistency that would allow the plane to get far enough into the air, and then use the lift generated by the wing and engine. But hey if you pointed the plane stright up (Rocket) or say had the lift generating wing move(helecopter) you could solve the roll to forward speed thing that runways provide for. Because no matter how fast the air is moving through the engines the wind fmoving over and under the wing is the lift.
? by Derek DeMarco on Feb 09, 2006 at 12:09 AM
Bucci says:
If prop thrust were enough to lift the plane up, then the wings would be no larger than the area behind the prop. Clearly, however, wings extend out much further than the props of plans. Consider also jets, which do not thrust any air at all on the wing, the thrust of a jet goes behind the wing.
Planes fly because there is more surface area on the top of the wing than on the bottom (the bottom is flat the top is curved). Because the air has to travel a greater distance over the top than on the bottom, the air gets spread out, as it were, and the air-pressure on the top of the wing is less than on the bottom. Because the air pressure is less, it generates upward lift.
It takes a whole lot of air moving at a rapid speed over a wing to generate lift. The props or jets aren't going to move the plane forward because the plane is on a belt. If the plane is not moving forward, then there is no motion of air over the wings (and remember, the prop blast won't cover the entire wing, so it is not enough). No air moving over the wings? No lift.
That dog won't hunt.
? by Bucci on Feb 09, 2006 at 12:16 AM
Kjell says:
I smell some scientific testing needing to be carried out.
? by Kjell on Feb 09, 2006 at 12:19 AM
Toon Van Acker says:
Just remember that the propulsion is relative to the air, and not the ground. Unless that conveyor belt can move the air above it at the same speed as the plane (but in the opposite direction), it's not going to be stopping any takeoffs.
? by Toon Van Acker on Feb 09, 2006 at 12:19 AM
Chris says:
The question is broken, it seems to me. It says the speed of the belt matches that of the plane, whatever that means, but also implies that the plane is kept in its starting position.
When the plane starts rolling forward at 1 MPH, how fast does the conveyor belt move? 1 MPH the opposite direction? That means the wheels of the place are rolling at 2 MPH but the plane's overall speed is not affected, except perhaps marginally by the added friction in the wheel bearings. The plane accelerates, and assuming the wheels can withstand moving at twice their normal maximum rate of rotation, it takes off.
But if you interpret the question as saying that the plane is somehow kept stationary by the conveyor, then of course there is no way the plane can take off, or move at all. However, if this is your assumption, then you had better be able to think of a mechanism by which the plane is kept stationary. I can't imagine it.
The assumption that the plane never moves seems doubly flawed. Reading the question again, it would seem that while the plane is kept stationary, then the belt is also stationary (it moves at the same speed as the plane but in the opposite direction). So what is the purpose of the conveyor belt anyway?
? by Chris on Feb 09, 2006 at 12:20 AM
Derek DeMarco says:
Now,
After reading Cecil's responce I now have a better understanding of the math problem. He states that if the plane is moving at 5 forward the wheels also move forward. ??? if the plane is mooving the belt is not keeping up the wheels hould only move in a backwards direction. If the belt is set to mach forward thrust. the wheels mach the belt' speed. it is not twice the speed as stated in the 100 plus 100 = 200 example. It is 100 thrust matched by 100 belt = 100 wheels. which is still zero forward and zero lift.
? by Derek DeMarco on Feb 09, 2006 at 12:20 AM
James says:
Max, the first poster, is dead on right. No forward motion relative to the air = no lift.
Relative links would be Science of Wings and Bernoulli's Principal.
? by James on Feb 09, 2006 at 12:20 AM
PhilipJ says:
Anyone who liked this problem would probably like these two as well: the three-cylinders problem and the tether-ball problem.
? by PhilipJ on Feb 09, 2006 at 12:21 AM
jkottke says:
The prop produces thrust which helps drag the plane through the air. That air, flowing over the wings, produces lift. The prop is not simply a fan that blows air over the wings.
Cecil certainly isn't arguing that. The lift is created by the plane moving relative to the air around it (like you said). Prop or jet, the plane will fly.
? by jkottke on Feb 09, 2006 at 12:22 AM
PhilipJ says:
Well, that didn't work.
The three-cylinders problem:
http://biocurious.com/the-three-cylinders-problem The tether-ball problem:
http://scienceblogs.com/principles/2006/02/pop_quiz_hotshot.php? by PhilipJ on Feb 09, 2006 at 12:23 AM
Bryan says:
The fallacy of your logic (as I see it at least), is that you're forgetting something. The wheels of the airplane are connected to the plane, and friction exists between the runway (conveyor belt) and the wheels.
For the plane to take off, it has to reach a certain airspeed - the speed at which the air
[ 此贴被轻风清扬在2006-12-18 13:32重新编辑 ]
