You still don’t understand. The plane will move forward unless the treadmill is moving much, much, much faster than the takeoff speed if there is realistic friction, and will move forward no matter how fast the treadmill is going if you neglect the friction in the wheel axles.
I’m pretty much going to echo Musicat here. The problem is that, intuitively, it seems that moving at higher velocity requires higher force. It’s intuitive because some losses (air resistance, for example) increase with speed, and because activities like running or skating just take more effort at higher speed.
However, force isn’t really related to velocity, it’s related to acceleration.
This particular problem (the plane on a treadmill, or the fan-guy on rollerskates) strips away some of the losses and the answer isn’t intuitive any more. (And it doesn’t help that there’s probably some velocity dependence in the wheel friction, so there’s a little truth to the intuition, only not so much as you might think…)
Sure, that’s right. Or, rather, it could be right. The issue is that different folks make different assumptions about the original problem, and different assumptions lead to different conclusions. As long as you’re clear about the wording of the problem (which varies!) and your assumptions, and proceed to a logical conclusion, you’re right. See, for example, this post in this very thread for a rundown of different scenarios.
Sure. Or rather, “sure”, if you’re making the right assumptions up front. Everyone agrees that if the plane stays stationary with respect to the air, it will not take off. Most of the argument revolves around whether or not the plane really will be stationary. And the answer to that depends on the wording of the problem and the assumptions you make. See, for example, this post in this very thread for a rundown of different scenarios.
And inertia of the wheels, don’t forget. If you neglect friction and inertia (which is not unreasonable, if you’re gonna talk about ultra-fast treadmills), the plane will move forward no matter how fast the treadmill is going. With inertia, force coupling between the treadmill and plane is still possible.
We may be nearing the point where your rundown needs to become a “sticky,” and is required reading for anyone who wishes to post.
This deserves a lot of emphasis. Many in the “does not take off” camp seem to feel that those in the other camp somehow believe a plane can fly without airspeed. Yet there’s thus far no evidence that anyone actually holds that belief.
Quoth hanguker:
Yes, exactly. The plane will move forward (relative to the air, the ground, and everything else other than the treadmill), and will lift off at just the same distance as it would on a runway. The difficulty is that many folks don’t seem to grasp that, for some reason. Many people seem to think that the treadmill will stop the airplane from moving, even though there’s no practical way for it to do so.
Physicists forgive me, I am but a simple designer. A few points:
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This is 85% thought experiment, 15% physics question. The assumption here, as realistically implausible as it seems, is that the treadmill perfectly counteracts the thrust of the engines, and the plane has zero lateral movement relative to the Earth, and more importantly, the surrounding air.
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I’ve read through this entire thread, plus the comments on Boing Boing, and only one person mentioned Bernoulli. If the plane’s wings, relative to the surrounding air, has no movement in the appropriate direction, there is no airspeed, there is no lift generated, and there is no takeoff. End of story. Everyone wants to take about friction and groundspeed and thrust. When do we discuss wings and lift, which are, you know, the only reasons most planes are capable of taking off and maintaining flight (except for, of course VTOL aircraft)?
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A better question would be this: put a stationary aircraft in a wind tunnel capable of generating infinite airspeed…does the plane take off?
In light of everything, I think a lot of people (including myself) would be satisfied if the question simple stated “…would the plane would MOVE FORWARD, generate lift, and take off?” Then it would be a resounding yes because of the thrust generated by the engine. However…
I think many, MANY people are attracted to this question because it seemingly purports that the treadmill will generate lift and the plane will rise from a stationary position once the treadmill/wheels reach take-off velocity…which is BS.
I’m kind of disappointed with the amount of time I put into reading and considering this flawed question now…who’s with me? :smack:
Fer crying out loud. As others have said, I really think this thread (indeed every thread on this subject) needs to utilize the little known feature of vBulletin by which you can set it so you can only post if you’ve visited a special page which requires you to tick a box saying “I have read Zut’s post #66 and still wish to post.”
thebristolkid nobody is suggesting that the plane will take off without air movement over the wings. The argument is about whether the plane will move so as to create that air movement.
Better in the sense of “more obvious, less fun” perhaps.
Thought experiment, Chronos. There’s nothing wrong with saying, “assuming the treadmill can achieve any velocity required, then what happens when…” No more than saying, “assuming we could build a spaceship that could approach the speed of light, then what happens when…”
In fact, if your measuring stick is practicality, you could test this airplane-on-a-treadmill thing relatively easily (relative compared to constructing a forever-accelerating spaceship) by tinkering with the airplane. Depending on what you wanted to show, you could construct a small-scale plane with enormous tires, and/or high friction wheel hubs, and/or underpowered engines, and/or substantial lift and/or whatever.
No one’s discussing wings and lift because everyone knows airspeed is required for lift. People are talking about friction and groundspeed and thrust because the question boils down to: will the plane move forward? And the answer to that depends on the wording of the problem and the assumptions you make. See, for example, this post in this very thread for a rundown of different scenarios.
You are missing a factor here. Even if there is no friction in the wheel bearings, if the treadmill starts moving the plane will move with it, not just sit there stationary. The wheels have inertia. Getting them to spin requires adding rotational momentum from the treadmill, and this will couple with the axle to generate force on the plane in the direction of the treadmill motion.
Yeah, but I think the general consensus is that the force required to overcome the inertia of the wheels is very small compared to what the planes engines can generate.
Unless you accelerate the rotation speed of the wheels up to fantastic speeds in a very short amount of time, percentage wise there just isn’t enough extra inertia to matter.
I was refuting Musicat’s claim that if the plane’s engines were off and the treadmill started slowly ramping up to 1 MPH, the plane would sit stationary with respect to the ground with the wheels turning.
Dude, that would be awesome.
To anyone’s knowledge, has a Doper ever posted a concise summary of all the different assumptions inherent in the treadmill question as stated, as well as a review of said assumptions’ necessary ramifications? Maybe someone who seems to have a grasp of things, oh, I don’t know, say **Zut **for example, could do so in this very thread, and save us all from the relentless rehashings.
Such a thing may not be possible. It would truly require a dizzying intellect.
True dat. Nobody ever went broke underestimating the intelligence of the American public. Or something.
Besides, if Zut’s so smart, why ain’t he rich?
The wind flow comes from the thrust of the engine acting upon the plane. The treadmill is totally irrelevant, except under one highly improbable condition that leads to the paradox of infinite treadmill speed.
When will people understand that the wheels are irrelevant to the concept of a plane moving? (not directed at the VERY limited number of people here who truly comprehend what happens if the wheels are forced to go super super fast…)
I’m beginning to come to the conclusion that the premise of the plane, its wheels and the treadmill is a flawed interaction.
Let us add the fairly non-controversial rider that the treadmill with the plane on it is sitting on the ground. We shall have as our reference for motion the ground. That is we shall discuss the motion of all other things with reference to the ground which at the beginning of the experiment is not moving relative to any other object in the scenario and does not itself accelerate or decelerate during the experiment.
The wheels of the plane are not driven, that is, they passively rotate as the plane taxis forward or backward.
The treadmill only moves to match the movement of wheels.
The wheels shall not turn if the plane does not advance with reference to the ground given that everything is at rest to begin with.
If the plane is to advance it must also do so relative to the treadmill, but we are told that the belt treadmill will move in an equal and opposite fashion to the wheels.
Those arguing that the plane will remain motionless relative to the ground must also argue that the plane never moves in the first place.
However, if the plane has not moved, then the wheels will not have moved, so the treadmill will not move.
Herein lies the problem of the interaction. The argument immediately becomes circular (as we have seen within the thread), not withstanding some excellent knowledge of Newtonian physics by several posters, because of the disconnect between the cause of the motion of the wheels and the wheel’s motion.
We have struck a failure of logic.
You can re-run the whole thing with the wheels and the treadmill turning at some constant rate and the logic will still fail.
I think that’s reading a bit too much into the problem. There’s no requirement that the treadmill match the wheel speed with zero error.
In a real engineering setting, you’d build a feedback circuit that would control the treadmill with some small dither. “Small enough” dither will give a good enough result. If you wanted less dither, you’d build a better feedback circuit and/or improve the smoothness of the input signal (wheel velocity in this case). And if we’re postulating mile-long, high-powered, heat-resistant, infinitely-accelerating treadmills anyway, I don’t see a problem with assuming a control circuit that matches speed to within whatever error band you desire.
These kinds of problems don’t depend on zero-error physical parameters. For instance, suppose someone asked, “what happens when two cars of the same mass, going the same speed, crash head-on?” The answer of “the question exhibits failed logic, because two cars can never go exactly the same speed” is less than enlightening.
In addition, if you’re actually worried about the treadmill perfectly matching the wheels, remember that the tires are made out of rubber. Rubber flexes. The tire distorts where it contacts the ground, and it shears under torque loading, and it slips and skids a bit at the edges of the contact patch, and the whole thing’s rather messy if you’re trying to exactly match the speed of the tire.
I will amend my statement to “…There is little friction in the wheel bearings…” (removing the “none”), as unless we have a frictionless bearing, there will always be some friction.
But not a lot. Absent the bearing friction, if the treadmill starts moving, the plane will not move with it. With friction, the plane will be slightly affected. We seem to agree that the bearing friction is very little compared to other forces at work in the overall problem.
To reiterate,
No, it won’t. Why would it? What exactly is “couple with the axle”?
Yes it will. Even absent bearing friction, the wheels still have mass. If the treadmill changes speed (i.e., accelerates), and the tires don’t slip, the wheels must also accelerate. The acceleration requires force (F=ma, right?), and the force is tranferred to the fuselage of the plane, which must also move. This is what Cecil calls “BR#2” in his second column on the subject.
He also give a thumbnail explanation, which has the advantage of being short and the disadvantage of glossing over some of the whys. I give a more substantial explanation in this post in an older thread. There’s also a long, meandering argument about about how this works that takes up the last four pages or so of the same thread, if you have the stomach for it.