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skye, if you really think that fail pic was warranted, you should post one for yourself...
...and then take algebra again.
The only way to keep the plane from moving forward is for the rolling resistance to equal the thrust of the engine, which would make the air speed of the plane zero. In order to accomplish this, you must assume that the plane and the conveyor are both indestructible...which is impossible. This is necessary because while your sensors and feedback attempt to make x=x+c for c!=0 the conveyor will accelerate infinitely until it spins so fast that the rolling ********* of the plane equals the thrust of the plane.
Theoretically it is possible...but in reality, where things break and have limits, it is not.
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How is this thread still going?
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Every person at work that I have talked to all assumed the plane being stationary was a given in the myth. Because, of #@$#@ing course the plane would take off if it was moving at take off speed in relation to the ground.
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I thought that somehow the treadmill (conveyor) had a system that could judge the speed of the airplane going forward and would counteract that speed to keep the plane in the exact same spot. I thought that the question was (and looking at some previous posts they thought the same thing) whether or not the fact that the airplane's engine was a full thrust but it was not moving forward and generating lift, had any impact on whether it would take off.
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My point was that it doesn't make one damn bit of difference what speed the conveyor is moving at.
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We're very talented here at TexAgs.
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on paper where anything is possible, it does.
When the conveyor is traveling at somewhere around 6 lyps [exaggeration] the rolling resistance becomes so great that it counteracts the 248,400 lbs of thrust (assuming the plane is a 747-400 with GE turbines running at full power)
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I thought that somehow the treadmill (conveyor) had a system that could judge the speed of the airplane going forward and would counteract that speed to keep the plane in the exact same spot.
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Rebel, I think the problem here is the simple minds of those trying to describe the myth. They leave out too many unknowns.
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They leave out too many unknowns.
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Texaggie7nine...think of it this way....the wheels of the plane rotate freely around the axle, and are not connected to a drive shaft like a car.
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Look Red Sky and others - I am not an engineer and I am not a physicist. I always thought that this was a theoretical question. I thought that that if the conveyor belt moved at the same speed the airplane was moving, the wheels would simply spin and the plane would stay in the same place. I think this is what a lot of people believe also.
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If this was not the case, then why did the question even put the part in about the belt moving at the SAME speed in reverse as the plane was going forward. The question seemed to make a big point about this factor. Instead it could have stated that the conveyor belt was moving in the opposite direction at twice or 1 and a 1/2 the speed of the plane.
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Like what the "speed" is in relation to.
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Which does not make one damned bit of difference
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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.
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So with the myth "the plane is moving at take off speed" if that is in relation to the ground, then it takes off, regardless of what else you throw into the equation unless you are going to bring up wind movement, or a different force of gravity.