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Action - reaction. The wheels won't turn - the conveyor will move with the plane; the forward movement of the wheels moves the conveyor.
Nothing is being applied to the wheels; it's only holding the plane up. Along the lines of spaceship thrusters: no friction needed.
I think you can assume the conveyor acts as a friction-less surface.
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Many years ago at a tiny company where we consumed our lunches together at the conference table we had a similar heated discussion this time re/ if you walked up a down escalator w/o changing your elevation did you do any work? I now can not imagine why this was so perplexing at the time. Then there is Richard Feynman wondering if one can piss whilst upside down.
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Thanks everyone for your replies, the links and the videos.
When I posted this question, little did I imagine that it would raise such an intense discussion. Thanks once again.
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The speed of the wheels is irrelevant - they aren't powered or driven in any way.
The speed of the airflow over the wings is the source of lift, along with the wings angle of incidence.
Assuming the conveyor is moving at the same speed (but in the opposite direction) as the aircraft would be on a normal runway then the aircraft would actually be stationery and the airflow over the wings would effectively be zero and thus not generating any lift?
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Leo56 wrote: Assuming the conveyor is moving at the same speed (but in the opposite direction) as the aircraft would be on a normal runway then the aircraft would actually be stationery and the airflow over the wings would effectively be zero and thus not generating any lift?
I sure would like to see that airplane sitting there on the runway with the engines running at full power, but the plane is standing completely still because its wheels are spinning around. Nothing else is holding the plane back, and the wheels are free running, but in some magical way they still manage to cancel out the full power of the engines.
I'd sure like to see that happen. And also to have a reasonable explanation how it can be possible.
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The airplane does or does not lift off owing to the upward airflow forces on the wings.
If the air does not move relative to the airplane (or vice versa) the plane will stay on the ground.
And the speed of the conveyorbelt relative to the air close by will cause some drag, therefore some
lift, but it is likely to be way too little, unless you add a quite signifant ventilator to help.
That should be pretty obvious, but I miss the joke - if there is one?
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Why wouldn't the engines provide exactly the same thrust on the plane body, giving it the same forward acceleration as on a non-belted runway?
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My understanding was that the engines were not used. If I took that one wrong, sorry.
But engines give forward thrust irrespective of the behavior of the wheels (assuming they can turn), so in that case the plane would go forward anyway, the wheels just having to turn faster in response to the belt.
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If the engines are not running, I would definitely not want the plane to take off!
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Only if you have a really big fan blowing at a speed at least that of the aircrafts V2 (take off) speed. 
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Then the aircraft will go and hit that fan 
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It obviously can since propulsion for airplanes is provided by i/e a jet engine. Airplane doesn't accelerate using wheels, like i/e a car. Conveyor belt would only make the wheels spin faster, and that's it.
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Actually ... no. The conveyor will have an effect and can increase lift - slightly - since it will also drag the air along with it and if that interacts with the wings it effectively act like the plane is going faster. (That's why aircraft carriers always launch steaming full ahead into the wind when launching and recovering aircraft - it adds a few MPH to their airspeed and reduces the chances of a stall.)
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Your answer is confusing. First, you say: actually no, then continue with a reasonable explanation on why some extra lift would be achieved. So, airplane WOULD take off, which I assume was the point of the q. Whether it'd have more lift or no due to conveyor belt is a minor detail.
There's also the matter of how long the conveyor belt is. If it's as long as the runway, then yea, but if it's as long as the airplane, airplane could fall off and probably crash in front of it.
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What a plane needs to take off is lift which is created by the pressure difference between the top and bottom sides of the airfoils (wings). To generate that difference, we use high-speed air flow aimed at the leading edge of the wing. The shape of the wing (an airfoil) makes air pile up in a high-pressure zone under the wing and zip over the top to create a low-pressure zone above the wing. This crazy magic lifts the plane with all of its weight into the air.
To generate the air flow, we generally use the easiest thing at hand, the velocity of the plane itself. On a conveyor belt, it won't move against the wind, but if it's facing into a gale strong enough, it could theoretically lift into the air and its jets would then be sufficient to make it go so long as the gale persists long enough for the jets to achieve enough speed through the air to maintain lift.
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The ONLY way the airplane can take off is if the speed of air respect of the airplane's speed is equal to the minimum speed the airplane needs to take off when the wind is absolutely calm. That is, because the conveyor makes the plane to be static respect to the ground, the only way the plane will take off is if there is a really hard hurricane that accelerates de wind to the plane's take off speed.
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The conveyor is not able to make the airplane stay stationary.
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gervacleto wrote: because the conveyor makes the plane to be static respect to the ground,
How does it do that, with free running wheels? The wheels are the conveyor belt's only contact with the plane, and I cannot see how you can enforce a thrust of the same magnitude (but opposite direction) as the plane engines, through free running wheels.
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Has anyone posted the Mythbusters episode about the question?
I’ve given up trying to be calm. However, I am open to feeling slightly less agitated.
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Yes. An airplane is not propelled forward by the wheels, but by the propeller(s) or jet engines. How fast the wheels are spinning is irrelevant. It may be a little trickier to steer but it'll take off.
If you think 'goto' is evil, try writing an Assembly program without JMP.
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wind speed is all that matters. Nothing else for take off. Not ground speed, not wheel speed. Only the speed with which the plane is moving in relation to the air. This is why planes prefer to take off into the wind. It reduces the amount of time on the ground before liftoff. But again ground speed doesn't matter. Air speed matters.
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Yes. Unlike a car that uses it's engine to turn the wheels to propel it forward, on an airplane the wheels are not what propels the plane at all. Its the thrust being generated by moving air via propellers or jet engines that provides thrust for an airplane, and the medium they are moving in, and what that thrust is relative to, is a sea of air.
Put a boat on wheels, place it so it sits on a conveyor in water, and turn on the propeller. As long as the wheels on the boat that are in contact with the conveyor are free wheeling the boat will move forward.
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In general, no. The movement of the wheels has no effect on lift. To take flight, a craft needs either sufficient airflow across the wings or enough thrust to overcome gravity. A plane can take off from a stationary position, without a conveyor, if there is enough wind and the engine has enough thrust to counteract the drag; the plane would simply rise straight off the ground. Additionally, air craft with very powerful engines, like an F-16, can accelerate vertically. In this case, the wings do not generate lift; the engine itself provides all the lift. Theoretically, an F-16 could take off from a stationary but vertical position. Again, the wheels would not be used for this.
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