Airplane / Treadmill Voting Booth

[Don Rickles]

At least before the idiocy was confined to one thread. Jesus, people, just shut the fuck up and put your boyfriends' cocks back in your mouths. Nobody gives a shit what internet retards think about unlikely hypothetical questions.

[P_McPoser]

Most. Unfunny. Alias. Ever. (EVER).

[DerJaeger]

Damnit. How do I reverse my vote? My first thought was that the plane would not take off, but I'm now convinced the aircraft would take off. Think about it this way: Despite the way the question is worded, the speed of the conveyer belt has nothing to do with the airspeed of the aircraft.

[huck4bucks]

huck4bucks, if you're running on a threadmill and i push you in the back would you move forward? even if the threadmill suddenly switched to double the speed?

No. The treadmill would calculate how hard you pushed me (speed) and immediately counter that with reverse motion.

Then I'd pick myself up and push you back. Get your own treadmill, asshole.

Despite the way the question is worded, the speed of the conveyer belt has nothing to do with the airspeed of the aircraft.

Exactly. Treadmill speed = 100,000 mph. Airspeed of the aircraft = 0 mph

[smitchell333]

This isn't the only place this question has created lengthy debate

http://www.kottke.org/06/02/plane-conveyor-belt

Here's a way to test this at home if you have a toy car:

"You can test this with a piece of paper and a matchbox car (which has free rolling wheels like an airplane… or like a car in neutral.) Place the paper on a table, and place the matchbox car on the paper. Take your hand, and hold the car still with a lightly placed finger on top of the car. At this point you are providing no forward thrust, and the “conveyor belt” is not moving. The car remains stationary. Now, continuing to hold the airplane with a lightly placed finger, and start to pull the paper out from under the car, in the backwards direction. According to Neal’s logic, the car should push back on your finger with the same force that you are exerting on the paper… but this is not what will happen. You will find that your lightly placed finger is not stressed to any noticeable extent. The paper will slide out, and the wheels will spin, but the car will not be propelled backwards. The reason for this is is that the rotation of the wheels is not related to the movement of the matchbox car except by the very small friction component of the axle, which your lightly placed finger can easily control."

[ill-advised strategy]

what if the toy car had bottle rockets on it

[f2f]

what if you pulled back the paper at infinite speed? i bet the friction will not be "miniscule" then

[steve]

Perhaps I could have saved a lot of time.. but the straight dope has already sounded off on this issue, in two separate articles, with some remarkable insight. It should be the bottom line in this discussion..

And if you don't want to read it (you should), the plane does take off.

First article:

Excuse me--did I hear somebody say Monty Hall?

On first encounter this question, which has been showing up all over the Net, seems inane because the answer seems so obvious. However, as with the infamous Monty-Hall-three-doors-and-one-prize-problem (see The Straight Dope: "On Let's Make a Deal" you pick Door #1, 02-Nov-1990), the obvious answer is wrong, and you, Berj, are right--the plane takes off normally, with no need to specify frictionless wheels or any other such foolishness. You're also right that the question is often worded badly, leading to confusion, arguments, etc. In short, we've got a topic screaming for the Straight Dope.

First the obvious-but-wrong answer. The unwary tend to reason by analogy to a car on a conveyor belt--if the conveyor moves backward at the same rate that the car's wheels rotate forward, the net result is that the car remains stationary. An aircraft in the same situation, they figure, would stay planted on the ground, since there'd be no air rushing over the wings to give it lift. 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.

A thought experiment commonly cited in discussions of this question is to imagine you're standing on a health-club treadmill in rollerblades while holding a rope attached to the wall in front of you. The treadmill starts; simultaneously you begin to haul in the rope. Although you'll have to overcome some initial friction tugging you backward, in short order you'll be able to pull yourself forward easily.

As you point out, one problem here is the wording of the question. Your version straightforwardly states that the conveyor moves backward at the same rate that the plane moves forward. If the plane's forward speed is 100 miles per hour, the conveyor rolls 100 MPH backward, and the wheels rotate at 200 MPH. Assuming you've got Indy-car-quality tires and wheel bearings, no problem. However, some versions put matters this way: "The conveyer belt is designed to exactly match the speed of the wheels at any given time, moving in the opposite direction of rotation." This language leads to a paradox: If the plane moves forward at 5 MPH, then its wheels will do likewise, and the treadmill will go 5 MPH backward. But if the treadmill is going 5 MPH backward, then the wheels are really turning 10 MPH forward. But if the wheels are going 10 MPH forward . . . Soon the foolish have persuaded themselves that the treadmill must operate at infinite speed. Nonsense. The question thus stated asks the impossible -- simply put, that A = A + 5 -- and so cannot be framed in this way. Everything clear now? Maybe not. But believe this: The plane takes off.

--CECIL ADAMS

second article:

Cecil, always enjoy your column, however you've got this [airplane and conveyor belt business] absolutely wrong. . . --strafe, via the Straight Dope Message Board

It's all about the interpretation of the question. Unfortunately, Cecil commingled two different interpretations in his column. --zut, via the SDMB

My confidence in Cecil has taken a gigantic hit. . . Cecil has fallen into the common trap of believing that the velocity of the treadmill in this case is what is important. It's not. What is important is the acceleration of the treadmill. I swear, on pain of retaking physics before I graduate as an ME, that if I accelerate the treadmill at a rate of 2 x (force from engines)/(mass of tires) that the plane goes absolutely nowhere. treis, via the SDMB

Cecil replies:

I knew this was going to happen. Everyone else, forgive me. This week's column is for the geeks.

Here's the original question: "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?" (The Straight Dope: 060203.)

The implicit assumption is that if the conveyor belt's speed backward exactly counteracts the airplane's "speed" (whatever that means) forward, the plane remains stationary relative to the earth and, more importantly, to the air. (We assume the winds are calm.) With no wind moving past its wings, the plane generates no lift and can't take off.

But the assumption is false. While the conveyor does exert some modest backward force on the plane, that force is easily overcome by the thrust of the engines pulling the plane ahead. The plane moves forward at roughly its usual speed relative to the ground and air, generates lift, and takes off. Many people have a hard time grasping this (although it can be easily demonstrated in the lab), but eventually they do, smack their foreheads, and move on. We'll call this Basic Realization #1.

Message-board discussions of this question tend to feature a lot of posters who haven't yet arrived at BR #1 talking right past those who have, insisting more and more loudly that the plane won't take off. Then there's a whole other breed of disputants who, whether or not they've cracked the riddle as originally posed, prefer to reframe it by proposing progressively more esoteric assumptions, refinements, analogies, etc. Often they arrive at a separate question entirely: Is there a way to set up the conveyor so that it overcomes the thrust of the engines and the plane remains stationary and doesn't take off?

The answer is yes. Understanding why is Basic Realization #2.

The conveyor doesn't exert much backward force on the plane, but it does exert some. Everyone intuitively understands this. To return to the analogy in my original column, if you're standing on a treadmill wearing rollerblades while holding a rope attached to the wall in front of you, and the treadmill is switched on, your feet will initially be tugged backwards. Partly this is due to friction in the rollerblade wheel bearings, but partly--this is key--it's because the treadmill is accelerating the rollerblade wheels and in the process imparting some angular (rotary) but some linear (backward) momentum to them. You experience the latter as backward force. Eventually the treadmill reaches a constant speed and the rollerblade wheels cease to accelerate. At this point you can easily haul in the rope and pull yourself forward.

But what if the treadmill continues to accelerate? Different story. In principle it's possible to accelerate the treadmill at a rate that will exactly counteract any forward force you care to apply. (This is a departure from the original question, which said the conveyor belt compensated for the plane's speed,, not its force.) The only mathematics needed to demonstrate this is the well-known physics axiom F = ma--that is, force equals mass times acceleration. Given that the conveyor exerts some backward force F on the plane, we simply crank up the acceleration as much as necessary to equal any forward force F generated by its engines. Result: The plane stands still and doesn't take off. Welcome to BR #2.

You may say it's impossible to build a constantly accelerating treadmill, that eventually we run into the limitation imposed by the speed of light, etc. True but irrelevant--BR #2 has an intrinsic elegance that transcends such practical concerns. Why didn't I bring it up in the first place then? You've got to be kidding. It took an entire column to get BR #1 across, and a second one to convey (I hope) BR #2. One fricking thing at a time.

--CECIL ADAMS

http://www.straightdope.com/columns/060203.html
http://www.straightdope.com/columns/060303.html

[ill-advised strategy]

infinate bottle rockets

[focus]

"You can test this with a piece of paper and a matchbox car (which has free rolling wheels like an airplane… or like a car in neutral.) Place the paper on a table, and place the matchbox car on the paper. Take your hand, and hold the car still with a lightly placed finger on top of the car. At this point you are providing no forward thrust, and the “conveyor belt” is not moving. The car remains stationary. Now, continuing to hold the airplane with a lightly placed finger, and start to pull the paper out from under the car, in the backwards direction. According to Neal’s logic, the car should push back on your finger with the same force that you are exerting on the paper… but this is not what will happen. You will find that your lightly placed finger is not stressed to any noticeable extent. The paper will slide out, and the wheels will spin, but the car will not be propelled backwards. The reason for this is is that the rotation of the wheels is not related to the movement of the matchbox car except by the very small friction component of the axle, which your lightly placed finger can easily control."

Not a bad analogy. NOW, what's actually happening here IS NOT the above. What's happening here is the car is pushed forwards by one finger, and your other hand is pulling the paper back at exactly the same speed that the car is being pushed forwards. The wheels spin at double the speed of the forward motion of the car. But the car is still moving fowards, the paper is still moving backwards, and we all continue to exist.

[focus]

huck4bucks, if you're running on a threadmill and i push you in the back would you move forward? even if the threadmill suddenly switched to double the speed?

On THIS treadmill, if the treadmill's going the same speed backwards as huck4bucks is moving forwards.... he's already moving forwards. He's already moving forwards. Let me say that again: In reference to the world around him, he's already moving forwards. Huck4Bucks will be moving forwards. He has to, if the treadmill is going backwards, he must be going forwards. Don't worry your wee little head about what his feet are doing, it doesn't matter.

If you push him in the back, he'll move forwards at a faster rate, the treadmill will move backwards at a faster rate, and his legs (which really aren't a pertinent part of the problem, in the world of this treadmill) will be running at twice the faster rate.

[smitchell333]

More discussion over here. http://tetongravity.com/forums/attac...1&d=1172027002
This is a Physics and science forum and plenty there argued against take off.


What if you ride a switch 720 to mute grab onto the conveyor belt - then what?

[TomK]

"In theory, there is no difference between theory and practice. But, in practice, there is." ~ Jan L. A. van de Snepscheut/Yogi Berra

In theory, the plane never moves forward with respect to the earth.
In practice, it does (and therefore takes off.)

[Telenater]

what if you pulled back the paper at infinite speed? i bet the friction will not be "miniscule" then

Actually, until you reach the point at which you start to get mechanical failure of the bearing system(the coefficient of rolling resistance changes) or the plane experiences lift (changing the effective weight on the wheels) the friction of the wheels resisting the plane's movement will remain essentially constant.

[focus]

In theory, the plane never moves forward with respect to the earth.

That isn't the theory.

The overwhelming idiocy of the WORLD is just blowing my mind.....

my god.

Even this straight dope guy can't fucking get his "implicit assumptions" right.

[smmokan]

OK, I've been reading this thread but didn't bother thinking about the question or any of the answers... and for what its worth, I know that the plane WILL take off. For those naysayers, think about this- on a plane, the wheels are completely independent; they don't generate any force required for the plane to take off. They just spin. The treadmill will slow the plane down a little bit (by some coefficient of the friction between the wheels and the treadmill), but it won't matter much. The wheels will simply spin faster, and the plane will take off due to the force generated by the jet engines.

You're all making the mistake thinking of it like a car- where the wheels generate the force required to move. This isn't the case with the plane. Smitchell made a good analogy above.

[focus]

You're all making the mistake thinking of it like a car- where the wheels generate the force required to move. This isn't the case with the plane. Smitchell made a good analogy above.

I'm only gonna say this like 12 more times, so pay attention.

Thinking about it like a car is NOT your mistake. You don't understand the question/situation itself.

[smmokan]

I didn't make a mistake... I got the question right.

[The AD]

You don't understand the question/situation itself.

Jesus, focus, would you get off your fucking high horse.

[smitchell333]

I've posed the question to 2 engineers I know. One a licensed pilot.

They both got it wrong - answering the plane wouldn't take off.

[f2f]

Actually, until you reach the point at which you start to get mechanical failure of the bearing system(the coefficient of rolling resistance changes) or the plane experiences lift (changing the effective weight on the wheels) the friction of the wheels resisting the plane's movement will remain essentially constant.

but we're speaking infinite speed, man, Infinite!

∞

[Core Shot]

I'm so embarrassed that there are only 51 smart people to offset the 30 morons that have no concept of the laws of physics.

Wonder how well they comprehend things like snowpack, windloading, crystal metamorphosis, sintering, bonding and shear strength?

[EPSkis]

Most. Unfunny. Alias. Ever. (EVER).

Untrue.

There's Ogre & OBF.

[DJSapp]

I'm so embarrassed that there are only 51 smart people to offset the 30 morons that have no concept of the laws of physics.

Wonder how well they comprehend things like snowpack, windloading, crystal metamorphosis, sintering, bonding and shear strength?

But dude, you don't need to worry about that shit, all you need is some bacon and a studfinder.

[P_McPoser]

OP. This thread is pointless if you hid the fucking people's choices.