No. It won’t. Didn’t we just spend two pages refuting this claim?
Powers &8^]
If the engine is idling the airplane won’t move forward (or will move forward slowly) on on the ground. If the ‘ground’ is moving backward, then the airplane will move backward. Of course if you increase the power the treadmill very quickly becomes incapable of keeping the airplane stationary and the airplane flies away.
The point is to create enough friction to overcome thrust.
I do agree that if thrust overcomes friction liftoff will happen. But if enough friction is created to halt forward movement, no liftoff. This could be better visualized if we take off the wheels and put skis on the plane. Even with skis the plane will inch forward on a smooth stationary treadmill surface. But if the treadmill begins to move opposite the planes forward motion the plane will be held in place. If the treadmill was run fast enough the plane could even be made to go backwards at full throttle. The friction will counteract forward thrust. No forward movement no air flow over the wings no lift.
Here is an experiment that anyone who has access to a treadmill, roller blades and a hand held luggage scale can perform. The roller blades will represent the airplane wheels you will be the mass of the plane and your strength will be the engine providing the power or thrust. The treadmill will represent the . . . treadmill.
Tie a rope to the front of the treadmill attach the rope to one end of the scale and hold on to the other end now turn the treadmill on. Your wheels will keep parity with the treadmill. Note the pounds of pressure on the scale. You can easily pull yourself forward. Now increase the speed of the tread mill. Still parity between wheels and treadmill but the pounds of pressure (force) needed to keep you stationary or pull yourself forward will increase. From this you can extrapolate that there is a speed the treadmill could reach that will overcome the force that you can exert to be able to pull yourself forward. You will remain stationary for as long as you can hold on. How is this possible with no wind resistance?
The same holds true for the plane on a treadmill. No forward movement no liftoff. Trouble is like I said, that kind of friction cant be achieved without everything burning up. It can only be done in the mind.
Which brings us back to what I said earlier. The question becomes, ‘If you make it impossible for an airplane to take off, will it take off?’ Everything else is window dressing.
and there it is
Which is why that’s a very poor interpretation of the problem.
You have two choices: it’s a thought experiment meant to get you to realize that the wheels don’t drive the plane, making it different from a car, or it’s a thought experiment meant to get you to realize that a plane can’t take off if a plane can’t take off.
I know which I happen to think is the better thought experiment. 
This isn’t quite accurate. The question never quite gets this silly (not quite). As Zut’s illustrious and deservedly famous post shows, there is still some interest in considering the effect of positing some silly elements (frictionless bearings, infinitely fast treadmills). There is interest for example in considering whether you can impose an ongoing retarding force on something by diverting the energy that would otherwise go into moving the whole object (the plane) into just endlessly accelerating one rotating element of the plane (the wheels).
I think it is. The won’t-take-off camp seems to have an agenda: to make it impossible for an airplane to take off. If the airplane doesn’t move forward, it won’t take off. So they design a magical treadmill that will keep the airplane from moving forward. Thus, ‘If I design a machine that makes it impossible for an airplane to take off, will the airplane take off?’ It’s silly. The question is much better interpreted such that the treadmill is something that could actually be built and tested in the real world; in which case, the airplane does take off but the wheels are spinning twice as fast.
Who said anything about idling? At the point in joesixpack’s post that I quoted, the plane is moving forward. He thinks speeding up the treadmill will make the plane stop moving forward. It won’t.
Powers &8^]
I agree. If it was as Princhester says, why a treadmill? Why not an unbreakable brick wall in front of the plane? Or an unsnappable rope tied to its tail? Why introduce the complexities of a treadmill, if not because of a misconception that a plane works like an automobile?
Powers &8^]
It depends on what principle you think the question is designed to demonstrate. You could, for example, rephrase the “wheels spinning twice as fast” scenario as, “If I allow an airplane to take off with the wheels spinning faster, would the plane still take off?” Which is also kind of silly, once you take it to that point.
On the other hand, the point of presenting the question is to get people to look at the difference between air and ground speed, and/or how forces act on an airplane, and/or whatever it is that’s of interest. Although whatever *that *is, for this *particular *question, winds up being drowned out by people talking past each other–which sort of defeats the purpose.
Even if a plane worked like an automobile (which it doesn’t), there’s no reason to think it couldn’t rotate its wheels twice as fast as normal. So although this could indeed be the “original” intent of the question, it doesn’t illustrate the difference between a plane and a car very well.
(Which, I should point out, isn’t saying that that interpretation of the question is wrong. Just that making an assumption based on what is obvious and what is silly isn’t necessarily definitive.)
Isn’t this the whole crux of the matter? joesixpack is correct in stating that if the treadmill can create enough friction to overcome the thrust then the plane doesn’t take off. What joe and others seem to be missing is that the amount of friction created by the treadmill+wheels is trivial compared to the engine thrust. Thus the plane takes off.
joesixpack said:
I interpret that to mean any plane that does not get significant lift on the wings from the action of the engine/prop/jet. Because any airplane will create airflow - that is the point of the propeller/jet - to move air, and thus give the plane something to push against.
Here is a question - assuming a 747 on a runway without a treadmill, how much thrust to the engines provide to begin takeoff (starting from 0 speed)? How much friction/resistance to forward motion has to be overcome? What role does the airplane’s not insignificant inertia play in getting the plane moving? Hint: airplanes do not have tow lines to get started. Yes, they have tow vehicles to help move them around the tarmac, but they drive under their own power to taxi to/from runways, and to initiate takeoff.
joesixpack, you are correct that if one produces enough resistance force, the plane cannot take off. But that can better be achieved by chaining the plane to the ground.
Princhester said:
Perhaps that is a question interesting some. The answer seems to be “not for anything reasonably resembling an airplane”, though if you want to design some contraption with 20 ft diameter lead wheels and the engine from a go-kart, you might come up with a device that has wings and can’t overcome a treadmill.
zut said:
I don’t follow you. An automobile gets it’s thrust from the friction between the tires and the ground, so the wheel speed and ground speed/belt speed are coupled. If you get a difference between them, you get skidding, and the car loses control. If you speed up the belt and engine in parallel, they stay synched, and the car stays place. Airplanes get their thrust independent of the wheel friction. Planes may have enough friction between the tires and ground to preclude the plane from moving if the wheels can’t rotate, but skidding only helps the airplane take off.
joesixpack said:
Is this an experiment you have tried? Can you document your results?
I was responding to Powers, who was agreeing with this statement:
If you assume that in the original question, “the treadmill speed matches the speed of the plane” means “the treadmill moves backward with respect to the ground at the same speed the airplane moves forward with respect to the ground,” then the airplane will take off: the plane will move forward, the treadmill will move backward, and the plane wheels will spin twice as fast as normal (which is what Johnny L.A. said).
If you put a car on the treadmill and make the same assumptions, the car will move forward, the treadmill will move backward, and the car wheels will spin twice as fast as normal. Thus the question, interpreted that way, doesn’t do a good job of differentiating between a plane and a car.
Ok, I’m being dense this afternoon. (Yes, I know, perhaps not a needed qualifier! :p) How does this follow? The car only goes as fast as the wheels drive it. If the treadmill matches the turning rate of the wheels, the car cannot go anywhere. It CAN’T turn twice as fast as “normal” because turning twice as fast means it goes faster, but then the treadmill simply goes faster, too.
The thought experiment is designed to highlight the difference between something that goes forward by power of its wheels (and what happens when those wheels interact with a treadmill) and something that is powered by something other than wheels (we could just as easily posit a frictionless sailboat). That’s the difference I think that is being highlighted.
If the treadmill is going -100km/h and the wheels are turning at (measured linearly at the circumference) 200km/h, then the car will move forward at 100km/h. Or, to look at it another way, if the treadmill is going -100km/h and the car is moving forward at 100km/h, then we know that the wheels are turning at 200km/h.
It depends on how you measure the speeds in the problem (that measurement choice is where the “interpreted that way” part of my statement comes from). A speed has to be measured relative to something else. It’s like the old thought problem of a man walking down the aisle of a moving train. How fast the man is traveling depends on how you measure his speed: relative to the train or relative to the ground.
It’s the same issue in the plane-on-a-treadmill problem. Are you measuring the speed of the plane (or car) relative to the ground or relative to the treadmill? Johnny L.A. is measuring the speed of the plane relative to the ground; you’re measuring the speed of the plane (well, car, but whatever) relative to the treadmill.
You’re also using a slightly different form of the problem (which is fine) where the treadmill matches the turning rate of the wheels. That has the advantage of being less open to alternative interpretation, but realize that other people aren’t necessarily using the same form of the question.
Plausible, but then you run into the issue that Johnny L.A. and Princhester and joesixpack are discussing: either the plane violates the premise of the problem, or the treadmill violates the limits of materials science. Which, as you might have gathered, I think makes an interesting thought problem, but not everyone is so inclined.
Ah, I see. The car is actually travelling at 200 kph, relative to the treadmill.
And zut, maybe I wasn’t clear, but this is what I think the thought experiment is talking about. I wasn’t attempting to change it to the concept of the treadmill matching the wheels. I was simply getting frames of reference confused.
This is not surprising. I view myself as constantly stationary, and everything else moving relative to me. It’s an interesting world view, and the mathematics get quite interesting. 
Because the question of whether you can stop a plane moving by putting an object in its path or tying it to something is obvious and dull. The question of whether you can do it with a magical infinitely fast treadmill that is only permitted to interact with the plane’s wheels is amusing. Well, OK. It’s amusing to me.
If it’s not amusing to you, you need to, I dunno, get less sensible or something 
Perhaps so, but the original thought experiment indicates nothing about friction. As phrased, it clearly suggests that the treadmill can stop the plane from moving simply by matching the plane’s speedometer reading. It posits a normal treadmill, operating on the plane as it would on an automobile, with no suggestion that it needs to be able to accelerate at an impossible rate.
Powers &8^]