would a plane take off if..

[lengro]

Kotrenin,

you are essentially saying that the pilot is not allowed to apply throttle. Because if he does, the plane will take off, thus violating your interpretation of the conditions in the original statement.

But the original statement do allow movement:
"The conveyor belt is designed to exactly match the speed of the wheels at any given time, moving in the opposite direction of rotation"
Movement will only happens if he apply throttle, and if he does - he will take off. There now seems to be a problem with the matching speed condition, so there must be slip between the wheels and conveyor. Or - since speed is defined relative to the observers position, we could be observing from a vehicle driving faster than the conveyor but slower than the plane.

This reminds me of Zeno's "Achilles and the Tortoise" paradox - we know what will happen in reality, therefore we must understand the shortcomings of the paradox. It's not reallity that is broken.

[ImADot]

What if your conveyor belt goes the other way?  Let's say 150mph forward (the wheels are spinning 150mph backward).  Throttle up, prop pulls plane forward, wheels now spinning slower but still backward.  Plane takes off.  Eh?

[grizz441]

The question I have is, say a jet lifts off at 150mph and there is a wind that increases at the exact same rate as the jet accelerates.  (For example, when the jet is going 60mph, the wind is 60mph against it).  Would the jet be able to lift off?  If so, would the jet lift off the ground in place without moving laterally?   I say yes, but I don't know for certain.

[lengro]

What if your conveyor belt goes the other way?  Let's say 150mph forward (the wheels are spinning 150mph backward).  Throttle up, prop pulls plane forward, wheels now spinning slower but still backward.  Plane takes off.  Eh?

No, it doesn't change anything in the paradox

[OOZ662]

[kotrenin]

Kotrenin,

you are essentially saying that the pilot is not allowed to apply throttle. Because if he does, the plane will take off, thus violating your interpretation of the conditions in the original statement.

But the original statement do allow movement:
"The conveyor belt is designed to exactly match the speed of the wheels at any given time, moving in the opposite direction of rotation"
Movement will only happens if he apply throttle, and if he does - he will take off. There now seems to be a problem with the matching speed condition, so there must be slip between the wheels and conveyor. Or - since speed is defined relative to the observers position, we could be observing from a vehicle driving faster than the conveyor but slower than the plane.

This reminds me of Zeno's "Achilles and the Tortoise" paradox - we know what will happen in reality, therefore we must understand the shortcomings of the paradox. It's not reallity that is broken.

lengro,

you are reading too deep into the problem.  Yes this is a paradox.  No matter what the pilot does to increase or decrease thrust, the conveyor belt must always be the same speed as the wheels, that is the central rule to this paradox.  You can throw whatever you want under the wheels, oil, grease, butter, sand paper... the rules of the universe for this problem dictate that the rotation of the wheels and the rotation of the conveyor belt must cancel each other out.  Thus airspeed will always equal 0.  An airplane does not take off the instant forward thrust is applied.  It must travel some distance to reach that speed.

[lengro]

Yes this is a paradox.

The above we can agree in, I will leave it at that

[sluggish]

The problem with this puzzle is that many feel the answer is so obvious that they fail to see the implications of the requirements of the experiment.

As Eagl has shown with his very simple equation, the plane does not fly and the owner and creator of this game agrees.

[RTHolmes]

imagine a plane is sat on the beginning of a massive conveyor belt/travelator type arrangement, as wide and as long as a runway, and intends to take off. The conveyer belt is designed to exactly match the speed of the wheels at any given time, moving in the opposite direction of rotation.

as the plane starts to move forwards, the wheels start to rotate. the conveyor belt instantaniously matches their speed in the opposite direction of rotation counteracting the rotation of the wheels. the plane accelerates down the conveyor to takeoff speed and takes off. at all times during the roll, the conveyor belt is moving at the same speed and the same direction as the aircraft, the wheels are stationary relative to the conveyor.

 

[DYNAMITE]

Not this subject again.

comes up every 1.5 years or so 

[RTHolmes]

hmmm gone a bit quiet now hasnt it?

<< pwns this problem 

[Saxman]

I think it's more a matter of people being tired of debating this issue.

[Kermit de frog]

The plane will not takeoff because it will not be allowed to roll forward.  As soon as the plane moves forward, it will be PUSHED backwards by the conveyor belt.


Now, if you place this experiment in a wind tunnel and set the wind speed to be equal or greater to the airspeed needed for takeoff, then the plane will takeoff even if on a conveyor belt that is matching the wheel speed of the airplane.

(Also, if you are going to try this experiment with a R/C airplane, please ensure that the motor is retarded to a power level that is just enough to achieve takeoff airspeed.)

[RTHolmes]

As soon as the plane moves forward, it will be PUSHED backwards by the conveyor belt.

no it wont, the points of contact between the plane and the conveyor are freewheels (its reasonable to assume that the brakes are off). in fact the wheels wont rotate at all. see my answer above.

[sluggish]

no it wont, the points of contact between the plane and the conveyor are freewheels (its reasonable to assume that the brakes are off). in fact the wheels wont rotate at all. see my answer above.

You, like all who think they know the answer, are not reading the problem correctly.  The conveyor belt matches the speed of the wheels, not the plane.  Although you are correct that there would be relatively little friction involved with rolling the wheels, you are not taking into account the force required to overcome the wheel's rotational inertia (the wheel's desire to stay at rest).  Newton would agree with me on this one.