Airplane on a converter belt question.

[sushijerk]

I recently heard this and gave it a lot of thought:

Suppose a normal commercial airplane is ready to begin takeoff. The thrusters are turned on and the wheels of the airplane begin to move forward. However, the plane is on a converter belt which is rigged to move/spin in the opposite direction of the plane at the exact speed of the wheels. Image that there is a electronic device gauging the speed of the wheels and then immediately relays the information to the belt to accelerate/deccelerate accordingly. Will the plane ever be able to achieve takeoff?

[MidGe]

use the search facilty... been discussed to death already

[sushijerk]

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use the search facilty... been discussed to death already

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Really? Doh. A mechanical engineering friend of mine said the answer is yes, but I'm still not sure why.

[MidGe]

plane + conveyor belt

BTW, whether an aeroplane takes off or not has nothing to do with runway speed (A/c carrier), aeroplane ground speed, or torque on the wheels. If it's airspeed is greater than take-off speed it will take off. I have seen planes flying backwards relative to the ground and they were not falling. lol.

[madnak]

The plane will take off. The wheels aren't moving the plane forward, they're just spinning idly.

[Benman]

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The plane will take off. The wheels aren't moving the plane forward, they're just spinning idly.

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Yes and no. This is entirely true if the conveyor belt's velocity adjustment happens quickly/simultaneously with the increasing thrust of the engines. The best analogy is this: imagine you're standing on an area rug wearing well-oiled rollerblades. If a very strong person "pulled the rug out from under you", you wouldn't accellerate backwards at the same speed of the rug. You'd essentially stay in place relative to the room as the rug rolled out from under you, a sort of skidding effect. As the coveyor belt accelerates simultaneously with the increase in thrust, the same thing would likely occur with the plane, and most of the increased backwards velocity of the conveyor belt would be converted to increased wheel speed rather than increased speed of the plane itself. So far so good.

But, imagine if the conveyor belt began to move backwards very slowly, before you turned the engines on. If the initial acceleration of the conveyor belt was slow enough, there wouldn't be any skidding/spinning effect, and the weight of the plane would keep the whole plane "glued" to the conveyor belt, which is accellerating backwards at a very small rate. Even if there was a small amount of skid/spinning at first, if the backwards movement of the belt was gentle enough that skidding/spinning would eventually end and the plane would eventually be moving backwards at the same rate as the conveyor belt (just as you would be moving backwards relative to the room if the guy didn't yank the carpet out from under you but rather ever so slowly started to drag it backwards with you on it). Once the plane reaches -10 mph relative to its surroundings, then that is a true negative velocity that would require a certain amount of thrust just to get the plane back to relative motionless (vis a vis the surrounding ground/air). At that point, a given level of thrust from the engines that would normally move the plane forward at 10mph would only suffice to keep you stationary relative to the surrounding air, thus creating no lift.

As the speed of the conveyor belt increases backwards (again slowly enough that the weight of the plane cancels out the skidding/spinning effect) to a sufficient degree, other forces will come into play that may aid the plane. One, the backwards moving plane will encounter negative wind drag, and this will begin to create skidding/spinning that will slow the planes backwards motion.

The real answer to this overall paradox depends on how suddenly the conveyor belt adjusts to increases in thrust. If the conveyor belt doesn't start until the pilot guns the engines, he could probably take off by applying maximum thrust as quickly as possible. Because jets have so much thrust, the conveyor belt would have to begin its backwards motion so rapidly that most of the backwards motion would be converted to wheel spin, which does not move the plane backwards (even in the absence of forward thrust). If the pilot applied thrust too slowly, he might never make it however, as the conveyor belt could be accelerated slowly enough to avoid/minimize spin.

[purnell]

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plane + conveyor belt

BTW, whether an aeroplane takes off or not has nothing to do with runway speed (A/c carrier), aeroplane ground speed, or torque on the wheels. If it's airspeed is greater than take-off speed it will take off. I have seen planes flying backwards relative to the ground and they were not falling. lol.

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While this is correct, aircraft carriers use a steam-powered catapult to accelerate the aircraft to the required speed in the very short distance available. If the catapult fails, the aircraft nearly always falls into the sea.

[MidGe]

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While this is correct, aircraft carriers use a steam-powered catapult to accelerate the aircraft to the required speed in the very short distance available. If the catapult fails, the aircraft nearly always falls into the sea.

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This true of most high performance aircrafts, it is not so, of some other aircrafts (and I am talking about conventional a/c not STOL or VTOL). The reason is that whatever the plane, if it can reach its minimum take-off speed minus headwind by the end of the deck, there are no issues except the margin of safety. There are many examples of such unassisted take-offs from a/c carriers for demonstration, exhibition or routine actions. I don't even think that all a/c carriers have catapults... (see russia).

[mindflayer]

The answer is generally no.
Wind speed over the wings creates lift.

(modern) Air plane engines do Not pull air over the wings, they suck air in (at whatever speed the plane is moving at) and throw it out at high velocity, creating thrust, pushing the plane. It is the air speed over the wings that create lift.
Wheel speed is not relavent to takeoff speed.

A plane with a normal (no wind) takeoff speed of say 100mph in a 60mph headwind would lift off with a wheelspeed of 40mph.
The same plane in a 60mph tailwind would need a wheelspeed of 160 to lift off.

The conveyor has the effect of creating a tailwind of equal speed to the wheel speed.
So at a wheel speed of 100mph the conveyor essentially creates a tailwind of 100mph. (zero wind speed over the wing) At 200mph wheel speed .. tail wind of 200mph (zero wind speed over the wing etc) The plane cannot take off.

Ok that said .. if you take a say Fokker Triplane (the Red Baron's plane) with short wings and a propeller engine, you can make a case that the enging actually increases the wind speed over the wings (to some degree and has a chance of taking off.)

[Sharkey]

There are two forces acting on the plane: thrust and friction.

The engines provide the (forward) thrust.

The (backward) frictional force (from the tires on the conveyor belt, the wheel assembly, etc) is the same as would be encountered by the plane coasting to a stop after landing, excluding air friction.

Any forward motion by the plane indicates a wheel speed faster than the belt speed, so the conveyor belt compensates by accelerating and continues doing so as long as the plane advances, until backward friction equals forward thrust, and the plane stops.