Bernoulli would be proud of you.

yes it will take off

I got this from the straight dope....read on


An airplane taxies in one direction on a moving conveyor belt going the opposite direction. Can the plane take off?
03-Feb-2006


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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 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

Cecil replies:

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

Is it too late for a flux capacitor joke?

quote:

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Keegan is the one who is really right here, though. The whole f-in thing would quickly explode.

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No, Keegan is an idiot for failing to let his imagination handle a purely theoretical problem and focusing on the non-important mechanical aspects.

It's NEVER too late for a flux capacitor joke.

but that can only take you back in time @ flux capacitor

doesn't matter once the plane its 88 mph.
your gonna see some serious sh*t

Toucan: Have at it.

polpunk: Thanks for the confirmation.

Goose: Bernoulli knew when to quit when he was ahead.

( ... rimshot! ... )

MY GOD I CAN'T BELIEVE I MISSED THIS. AND SINCE I AM THE ROCKET SCIENTIST.

The answer is it WOULD NOT fly because you people don't understand how LIFT actually works.


If you want me to explain it I will

true @ videoag98


i thought they would stop after the apple orange thing....but it goes on

well let's hear it...

The speed of the conveyor belt has no effect on the applied force of lift across the wings.

I'm not smart enough to make a flux capacitor joke

Rats

MY GOD I CAN'T BELIEVE I MISSED THIS. AND SINCE I AM THE ROCKET SCIENTIST.

The answer is it WOULD fly because you people don't understand how LIFT actually works.


If you want me to explain it I will

Whoa! He's serious now!

think

Brennus -

please do explain

That old Faithful is partly right

Beyond the thrust aspects of modern aircraft, lift is simply a function of the shape of the wing. The curvature of one side of the wing creates a longer path for the air molecules to travel than on the flat side of the wing (from front to back). This results in a pressure drop creating an upward force.

Again,

For this example, the speed of the conveyor belt has no effect on the lift capacity of the wing nor the propulsion.





[This message has been edited by IIIHorn (edited 11/30/2006 2:08p).]

so only one of you two is a rocket scientist?

i said that one page one....though not so clearly @ IIIHorn

The answer to the question is in this situation CAN the "sucking" of air either by props or a jet produce enough "Lift: when flowing over the wing.

the answer is in theory is "yes" if you actually got the tread mill to work AND you had a small enough "closed" block of air around the plane.

In practical terms even if you got the tread mill to work lift is produced by " a change in momentum of the air and plane" ( bernoulli's principal is an EFFECT) and you couldn't get enough air momentum change because the plane was not ACTUALLY moving relation to the full air mass around the plane


and idiots BRENNUS = OLD FAITHFUL

I'm not sure this was set-up correctly. The treadmill is supposed to move such that the plane doesn't move relative to stationary, correct?

will the speed of the air around the wing actually be enough to create lift?

it's hard to visualize.

relative to a fixed point away from the treadmill the plane will not be moving. is it really moving through the close proximity air fast enough?

theoretically it isn't moving through the air at all. theoretically it is still.

I don't think it will fly.

IIIHORN trust me on this one my AErodynamics professor SPECIFFICALLY STATED that

quote:

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This results in a pressure drop creating an upward force.

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which is Bernoulli's ie lower pressure on top, greater on bottom is NOT what causes lift,

Change in momentum of the total air mass IS

quote:

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The treadmill is supposed to move such that the plane doesn't move relative to stationary, correct?

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The forward movement of the plane is not dependent upon the conveyor belt. The wheels are not providing propulsion so the conveyor belt is not creating a force in the opposite direction of the desired forward movement. The wheels will simply turn faster than if the conveyor belt were not moving.

Have you glued the wheels to the conveyor belt?

Can a wing create lift when the air around it is only moving by the intake of a jet engine?

Once in flight you have the air moving across it due to forward motion, but if the wing is being restrained to stay in a fixed postion, is there enough air speed to create lift?

quote:

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The forward movement of the plane is not dependent upon the conveyor belt

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It's not a question of where he grips it! It's a simple question of weight ratios!

When I initially read the problem, I thought he just said it wrong and that the point was for the plane to be stationary.

I still don't think it will fly. The fact that the belt is matching the speed, means that the plane is not moving, or MAYBE barely moving foward, and BARELY does not generate much air flow. There's no air flow over the wings if the plane is not moving (Unless we're talking about a serious headwind), and no airflow over the wings means it's not leaving the ground. If you were standing on the wing of a plane during a normal take off, you wouldn't be on for very long as you would get blown off because of the AIR FLOWing past you. If the experiment in question were to actually be done, and someone was standing on the wing, the plane would not have AIR FLOWing over the wings, and that person would be able to stay on.

Atleast that's what I see in MY head.

Old Faithful,

I am an engineer and attempted to word this without getting into the aspects of air mass momentum.

But,

This portion of the discussion is basically moot since the plane will function relatively normally on a moving conveyor belt as it would on a landing strip. Hence, the effect of the conveyor belt will have no effect on the aerodynamic aspects which creates flight. One might contend that the discussion has gone off into irrelevant tangents.

Beyond this hypothetical and discussing this at a greater level would place you at a great advantage for my arena is just the oilfield.



[This message has been edited by IIIHorn (edited 11/30/2006 2:25p).]

those who say it will take off have assumed frictionless wheel bearings.

If the conveyor was infinitely powerful and fast, it could travel fast enough to impart enough negative force to the plane thru the friction in the wheel bearings, to exactly counter the forward force imparted to the plane by the thrust of the engines.

Look at it this way. If you're in a boat and run the prop up to 100% but forgot to untie one of the lines, all the water flow in the world won't get you going. If you take model the friction in the wheels, it IS possible to stop the plane from moving relative to the ground.

Keegan's right... it's all about stating your assumptions.

Mechanical engineer.

IIIHorn,
Well, not if the wheels are frictionless. I understand the concept that the wheels do not create the forward locomotion on a plane.

I thought the set-up was to "assume the plane stays stationary due to this magic treadmill".

It sounds like you guys are arguing that it wouldn't stay stationary because there is not enough friction and the wheels on a plane are free-rolling (Which I agree with).

quote:

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Can a wing create lift when the air around it is only moving by the intake of a jet engine?

Once in flight you have the air moving across it due to forward motion, but if the wing is being restrained to stay in a fixed postion, is there enough air speed to create lift?

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This is exactly the right question and what I am trying to state above in my two examples.


If you had a large box around the plane, open on the front and back and you ignored the rest of the air outside. WOULd the engines suck enough AIR through to actually cause a change in momentum to cause LIFT to occur. I don't know but I don't think so, that is why i gave the two ansewrs