The Airplane and the Treadmill

Cecil's Columns/Staff Reports
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http://www.straightdope.com/columns/060203.html

I would like to question again this topic upon the nature of a plane achieving flight.

Firstoff, a plane creates lift through drag force, which is achieved through the turbines creating thrust.

What I want to question is whether the plane truly is two systems (the wheels/treadmill and the air/turbines) unless the plane has drag force. While it is true the wheels of a plane are to add or reduce friction for the plane overall, it is also true that without reaching takeoff velocity relative to the ambient air - which would have to be in the frame of the Earth, the plane is ultimately without any drag force, thus without any life, and thus with its weight on the wheels. It would be stuck to being one system - theoretically, it could be visualized as replacing the wheels with a frictionless surface and having the turbines provide acceleration.

Now, if this treadmill were to be completely perfect as to negate all acceleration that is created by the turbines, the plane would be at zero velocity relative to the Earth - even if the wheels don’t provide any acceleration and spin madly, for every mps² the turbines provided, it would have to ultimately go back to the wheels as there is no lift. Thus, wouldn’t it be that the plane would not be able to reach the takeoff velocity and thus be confined to the ground.

I guess what I’m trying to say is that I have a problem with:
“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.”

I can see that with the turbine thrust, the plane will move forward at the usual speed relative to the ground on the treadmill, however I am not sure how the air would be moving along with the treadmill - sure the turbines would be sucking in the air, but ultimately all the acceleration would be completely horizontal. The wings would be without any relative velocity to the Earth - with the air it needs to take off.

Perhaps the problem lies with my understanding of the problem - I am assuming that for any acceleration that the plane itself manages to muster, the treadmill will accelerate in the opposite direction. Or perhaps the treadmill itself being reduced to a large slab of completely frictionless material.

Hope to hear back.

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Previous threads:

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Also, Cecil wrote a whole 'nother column on the subject.

I’d say it’s more likely you interpretation of the problem, not your understanding. In my experience, confusion about this problem usually arises because different people make different basic assumptions about what’s moving with respect to what, and how fast. Nothing wrong with interpreting the problem differently (and coming up with a different answer), but it does make it hard to understand what other people mean if you don’t realize they’re assuming something different. In addition, there are different versions of the problem that have different word choices, which imply different scenarios.

Anyway, here’s a rundown of all the various scenarios I can think of.

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No, the plane doesn’t just move forward relative to the treadmill. It moves forward relative to the air, since that’s what the engines are pushing against, and there’s nothing the treadmill can do to stop it.

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Make it stop.

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I agree. If you make the treadmill stop, then it will just be like any other stationary runway surface so the problem goes away.

Or is that not what you meant? :smiley:

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So, the only thing ‘linking’ the ‘plane-air’ system to the ‘wheel-ground’ system is the friction in the bearings in the wheels.

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No. There’s also the rotational inertia of the wheels.

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Make it STOP!!!

Nothing to see here, folks, move along…

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One of my father’s friends had a cousin in the Air Force during the conflict in Vietnam, and this cousin actually heard of a “famous” experiment relating to this very issue.

At one base he met an aeronautics engineer who was serving his time over there. This engineer, as a hobby, used to draw small models of jet engines and discuss the merits with the pilots of the fighter planes. Strictly for fun.

Except that one day one of the mechanics there, a pretty bright guy, told him that he could probably build one of those models and make it work. I guess they were bored because it became a project for them. They started with three engine models. The first one they built didn’t work at all, and the engineer then figured out that the same flaw applied to the second model, so by the laws of probability they knew that there was a 2/3 chance that the third one would do the trick.

They finished it along with a model airplane body built of small parts “rescued” from the repair shed and had it fly a short distance. One of the pilots who was always making fun of the “Dien Boeing Phu” factory as he called it, made them a bet that their thing couldn’t even get off a moving walkway. The engineer supposedly proved to him that it was mathematically impossible for the plane to stay stuck and the distance it would cover would be 0.999999999… of the length of the runway (which of course is the same as one times the length, meaning all the whole length). Long story short, they rigged up a 27-foot kind of treadmill hooked up to a bicycle and set their plane on it. Even though the guy on the bicycle was pedalling as fast as he could, faster than the wheels on the model plane were turning, the plane shot over the complete length of its “runway” and zoomed off into the brush. The story became legendary around the local airmen and I’m told that the whole nine yards test flight was a running joke that people used to plague the pilot who lost the bet.

I remember seeing an old photo of that model jet. They did a good job of making it look nice. They drew flames on the side and painted a name on the fuselage, but darn if I can’t remember what it was. It was some unusual english word ending with the letters “gry”.

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<chuckling> We bow in awe to superior wit! :smiley:

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Well, what the hell. I’ll try to explain it in a simple way.

Plane on a normal runway: The plane’s engines push on the air, which pushes back on the engines, which moves the plane forward. The wheels turn because the ground is moving backwards relative to the wheels (because the plane is moving forward). The friction between the wheels and the wheel bearings exerts a miniscule force on the plane, slowing it ever so slightly, but not enough to make a difference. Plane takes off.

Plane on a treadmill: The plane’s engines push on the air, which pushes back on the engines, which moves the plane forward. The wheels turn because the ground is moving backwards relative to the wheels (because the plane is moving forward AND the treadmill is moving backward). The friction between the wheels and the wheel bearings exerts a miniscule force on the plane, slowing it ever so slightly, but not enough to make a difference. Plane takes off.

As we can see, the only difference is that when the plane is on a treadmill, the wheels will spin faster. You could probably prevent the plane from taking off if you moved the treadmill fast enough to explode the wheel bearings from the friction of spinning so fast, but that would be pretty hard to do.

Now, we should all STFU and never speak of this again.

–FCOD

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These days I’m wondering which approaches infinity faster: the number of threads about planes on treadmills, or the number of threads about whether 0.999… equals 1.

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Just wondering: wouldn’t it be easier to ignore the thread than taking the time to open it, then posting a complaint that it’s already been covered? You realize that every time you do that, it bumps the thread up to the top, right?

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Cough, Hack, Lift is due to the Bernoulli Effect, hack cough.

I third the motion to make this go away.

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Actually, it’s the Magnus effect. The wings of a plane push air down (in much the same way the blades of a fan propel air), and thus the air pushes up on the wings (as required by Newton’s third law of motion.)

Unfortunately, there are many wrong explanations of flight out there, which attribute lift solely to a difference in the velocity of the air passing above the wing and below, due to the shape of the wing itself. Such a velocity difference creates a difference in pressure between the two sides of the wing (the Bernoulli effect). However, that can’t be the whole story, since (1) for there to be a net upward force on the plane there must be a net downward force on the air, and (2) some stunt planes can fly upside down so clearly it’s not all about the shape of the wing.

With regard to the plane on a treadmill:
Anyone who reads the previous threads and still doesn’t get it probably won’t be swayed by any further comments. However, for those too lazy to read the previous threads, let me summarize:

(1) The plane must move relative to the air in order to generate lift.

(2) If you stop the plane from moving forward relative to the air (say, by chaining it to the ground), then it won’t generate lift, and won’t take off.

(3) If on the other hand you simply reduce the force exerted by the ground to zero (say, by putting the plane on frictionless ice) then the plane will still move forward and will still take off. Ice planes in fact do this (although in that case the friction isn’t quite zero).

(4) Some people seem to take the treadmill as exerting a force that would stop the plane from moving forward. However, I’d say a more sensible interpretation is that it simply negates all force between the ground and the plane. In that case, the plane still takes off.

Note the key difference between an airplane and an automobile: An automobile’s engine spins the tires, and the friction between the tires and ground propels the car forward. In contrast, a plane’s engine drives the propeller or jets, which push directly on the air. Thus, the car can’t propel itself forward over a frictionless surface, but the plane can.

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Why is it that everyone who wants this topic to go away, says it AFTER giving their explanation of why they believe whether the plane will fly or not?

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That depends on what your initial assumptions are.

That depends on what your initial assumptions are.

That depends on what your initial assumptions are.

If y’all are gonna 'splain the answer to this problem, it would help if you didn’t fall into the same error of not stating your basic interpretation of the problem, which is what makes this such a contentious and oft-argued question in the first place.

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I am ignoring for the sake of simplicity the case where the treadmill accelerates at a constant and ludicrous rate to stop the plane via the rotational inertia of the wheels. Even if one considers that case, though, the plane still takes off, though for different reasons. I am also ignoring the case where the treadmill somehow destroys the plane, as uninteresting, since it’s patently obvious that a destroyed plane won’t take off. I am further ignoring the case where the treadmill magically stops the plane from moving, since magic is not subject to physical discussions.

Is there something I missed?

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(bolding added)

(bolding added)

My interpretation is that the treadmill negates all force between ground and plane. How can I put that more clearly?

(Obviously, I’m talking about negating the frictional force, not the normal force keeping the plane from falling into the earth.)

The most common alternative interpretation, a treadmill that somehow exerts a force on the plane’s wheels strong enough to counterbalance the thrust provided by the plane’s engines, seems absurd, both because you’d need some kind of magic super-treadmill and some kind of magic super-wheels.