I think the question is better phrased as "Can" the plane take-off instead of "will" the plane take-off. If the question is "can"...then, Yes, the plane Can take-off. But in original problem, it makes it sound, to me, like the plane isn't moving forward. Not because it can't, but because it isn't.
Plane on a Treadmill
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Will and Can, in my mind, makes all the difference. Maybe it is because I drank way too much tequila last night.
Will the plane take-off is hard to determine from the problem statement as posted here. Will requires certain conditions; namely, the wings need to be moving through the air. I can't tell from the original problem statement if those conditions are present. To me, it sounds like the plane is stationary relative to the air and won't take-off.
Can the plane take-off is a much easier question. The plane can take-off.
Will the plane take-off is hard to determine from the problem statement as posted here. Will requires certain conditions; namely, the wings need to be moving through the air. I can't tell from the original problem statement if those conditions are present. To me, it sounds like the plane is stationary relative to the air and won't take-off.
Can the plane take-off is a much easier question. The plane can take-off.
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The thing that people can't seem to overcome is that the treadmill means nothing in this problem. The treadmill could be going equal to wheel speed, air speed, or the bus in the movie Speed, it doesn't matter. A planes wheels make no difference in it's attempt to take off, the only thing they need to be able to do is spin freely and produce as little friction as possible so that the thrust of the planes engines are able to over come it and propel the plane. Since a planes wheels are carefully designed and engineered, we can assume that that is the case.
Just an FYI - the episode will air Jan 30th 9pm for the Myth Busters to settle this once and for all!!
I think it's important to separate a REAL plane from the theoretical plane posed in this question. Put wheels on the wright flyer, and I don't think the thing has enough thrust to overcome the friction that a treadmill could produce, within the mechanical limits of the wheels, even though it would be able to take off under it's own power otherwise. Heck, leave the wheels out of it, and just let the thing sit on it's skids. That demonstrates the problem even better.
Put an F-22 on the same treadmill and it isn't a question that the F-22 takes off. It's IN THEORY possible to develop a system in which an airplane won't be able to overcome the forces that the treadmill can impart on the wheels of the aircraft. In reality, almost any airplane will be able to take off on any treadmill that's physically possible to build.
Put an F-22 on the same treadmill and it isn't a question that the F-22 takes off. It's IN THEORY possible to develop a system in which an airplane won't be able to overcome the forces that the treadmill can impart on the wheels of the aircraft. In reality, almost any airplane will be able to take off on any treadmill that's physically possible to build.
Thing is, skids would provide much more friction than is normally present in the wheel bearings of the landing gear.
If you were to somehow build a treadmill with a surface of ice and use skids on the plane, that would be much more comparable. In fact, if you think of it that way, its even more obvious that the plane would take off.
If you were to somehow build a treadmill with a surface of ice and use skids on the plane, that would be much more comparable. In fact, if you think of it that way, its even more obvious that the plane would take off.
But the fact that there IS friction present in the wheel system is the point. You have to separate the theory from the reality. Yes, in reality, we have low friction bearings, and lots of thrust, and any reasonable plane will take off. In theory, if you're dealing with an infinitely fast and infinitely long treadmill, you can generate infinite friction in the wheel bearings. This ignores all the material science that will cause everything to fail well before the system overcomes the amount of forward thrust provided by the propulsion system.
You also have to think about an aircraft with different levels of thrust. If you put an engine that was just powerful enough to move an airplane at 1 MPH on it, and then put the airplane on a treadmill and moved the treadmill enough to create enough friction to negate the forward moment created by the engine, the plane wouldn't move. Obviously, most planes have far more powerful engines, but you're dealing with infinity here, so it's just a question of finding the insane point where you overcome the obvious by applying the obscene.
The issues of infinite friction and an infinitely long runway are another couple of red herrings in this argument.
F=(m)(a), where F is the net thrust of the engines, and (m) is the mass of the plane. F is changing so minutely during takeoff that (a), for practical purposes is constant.
The take off speed of a 747 is about 180 MPH, and a big full 747 requies about 10,000 ft of runway. So start the treadmill and set it at an accelration rate higher than that of the 747. As soon as the pilot pushes the engines to full throttle, the 747 is going to start moving forward relative to the Earth at whatever (a) calculates to be. The planes wheels are going to start spinning and generating some friction, but the rotational speed of the wheels is not even going to get remotely close to infinite speed, because the plane is going to hit its lift off velocity after a couple of minutes, and it will lift off the ground.
Thus, the plane wheels are never going to spin up to these incredible speeds where you would be approaching infinite friction in the wheel bearing assembly.
Speed always has to be measured relative to something.
If the plane does not move relative to the air and the landscape in general it will not take off. Everyone should be able to agree on that. Those that are saying it won't take off are working under this assumption.
If the plane does move relative to the air, which it likely would because the wheel bearing friction would not overcome the thrust generated by the engines in most planes, then the plane can take off. Those saying that it can take off are working under this assumption.
I can come up with situations where "the speed of the plane is equal to the speed of the treadmill" that fit both scenarios depending on what those speeds are relative too.
You're assuming a constant velocity treadmill. If you can increase the speed of the treadmill to match the force being applied by the engines, you could hold a plane still. The control input for the speed of the treadmill would be the force of the thrust from the engines, not the speed of the wheels.
If you add up all the forces, then, they cancel out, and a=0.
It's all just theoretical, though, since it's virtually impossible to demonstrate in reality.
No one said anything about theory... The question is will a plane on a treadmill take off. The answer is it will...
You cannot make a treadmill that will go infinitely fast, and you can't make wheels or bearings that negate friction... So it is all academic.
We live in the real world.
You cannot make a treadmill that will go infinitely fast, and you can't make wheels or bearings that negate friction... So it is all academic.
We live in the real world.
Well you can't build an infinitely long treadmill either, so the whole question is really theoretical. In THEORY you could. In fact, knowing what the rolling coefficient of friction for the wheels is, the thrust of the engines, and the mass of the aircraft, I would think you could quite easily figure out how fast the treadmill would have to go to keep the plane stationary.
Also, I hope my 1000th post isn't in this tread :no:
I'm gonna make you have your 1,000th post in this thread.... With modern wheels and bearings wouldn't the treadmill have to be going at least a few hundred miles and hour... maybe more, and if it could go that fast wouldn't it only take a very small amount of thrust to overcome the speed?
And if it is so easy to get to this speed the treadmill wouldn't have to be infinitely long would it?
And if it is so easy to get to this speed the treadmill wouldn't have to be infinitely long would it?
So basically the question is "will a plane on a treadmill take off?" The answer is no. No forward motion = no change in pressure = no lift.
Some are deviating from the actual question and concentrating more on the non-realism of creating such a treadmill. The two issues don't answer the same question.
Can such a treadmill be created and contain the aircraft? Probably not. But that's not the point of the question.
Some are deviating from the actual question and concentrating more on the non-realism of creating such a treadmill. The two issues don't answer the same question.
Can such a treadmill be created and contain the aircraft? Probably not. But that's not the point of the question.
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