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The moving runway thought puzzle


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I remember reading about this years ago, and for the life of me I can't remember how it was eventually resolved, though I know it was. Can anyone sum up the solution in a sentence or two?:

A model stands on a conveyor belt. As you open the throttle to take off, the conveyor belt moves backwards under the model at the same speed that the wheels start to turn, and continues to match the speed of the wheels. Can the plane take off?

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No, because the aircraft will rise due to the airflow over the wing not the rotation of the wheels, Unless the conveyor is fitted with some sort of blade to move the air the wing is effectively in still air. If this worked aircraft carriers would not need catapults.

 

 

 

 

Edited by Robert Cracknell
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What have the wheels and conveyor belt got to do with it?

If the throttle is opened the plane will move forward through the air driven by the propeller or the jet output and should eventually take off.

Unless of course the plane is moved by the engine driving the wheels, in which case any such plane wouldn't fly for long even if it did take off 😀.

 

Dick

Edited by Dickw
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1 hour ago, paul devereux said:

A model stands on a conveyor belt. As you open the throttle to take off, the conveyor belt moves backwards under the model at the same speed that the wheels start to turn, and continues to match the speed of the wheels.

The wheels would just be going twice as fast as normal at take off.

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The wheels would just be going twice as fast as normal at take off.

 

The instantaneous speed at the point which they "start to turn" is zero.

Therefore, the conveyor belt never moves.

Plane takes off.

We never have to consider this ridiculous proposition again.

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10 minutes ago, Nigel R said:

 

 

The instantaneous speed at the point which they "start to turn" is zero.

Therefore, the conveyor belt never moves.

Plane takes off.

We never have to consider this ridiculous proposition again.

What if it's a 'driven' belt and increases in speed to keep the plane at a stand-still ?

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friction between conveyor belt and aircraft dictates how much and how quickly energy can be transferred to the belt to the aircraft... perhaps the question then becomes, can the energy put out by aircraft's propulsion mechanism overpower that energy transferred to the aircraft by the belt?

 

what's the speed limit of the belt? infinite? the power of the aircraft? also infinite? the heat at which the grease in the wheels boils and prevents the wheels turning? does the aircraft even use wheels? maybe it stands on skis? or floats?  the wheels that are turning - are they the wheels inside the conveyor belt? is there a tailwind, a headwind or a crosswind to affect the aircraft?

 

it's a deliberately badly designed problem, intended to incite violence on internet forums tease out mechanical knowledge, rather than to have 'an answer'.

 

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10 minutes ago, Zflyer said:

A bit like travelling at the speed of light in a car. If you turned the headlights on would they create a beam???

Or would the photon energy of the light, slow the car down to the point where it disappeared up its own exhaust pipe?

 

 

Edited by Gary Manuel
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6 minutes ago, Andy J said:

Think what is happening is that the airflow generated by the prop is generating lift as it flows over the wing hence the aircraft becomes airborne.

So a plane held on its brakes till the prop was turning at max speed would take off? I'm trying to understand the physics behind it.

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2 hours ago, Chris Bott - Moderator said:

18 pages here, if you're really that interested. 

 

 

If the wheel rotational speed always matches the conveyor speed but in the opposite direction- then - whatever the thrust from the engines, the aircraft will remain totally stationary. If it is stationary the wings cannot generate any lift at all - so no it cant take off and wouldnt even move forwards or backwards.

My analogy would be - imagine being on a running machine and as you constantly increase your pace you balance that by constantly speeding up the conveyor that you are running on - you will stay in the same place on the machine.

I reckon.......!!

 

I’d have also thought no, simply by the fact that if the engines were not running but the belt was going backwards the plane would move backwards. If the engines then were then started and the thrust resulting in the wheels turning forward to exactly match the belt under all conditions the plane would simply stand still. Thus to me it’s quite difficult to see how it could take off. How far does a person on a running machine actually move forward? All the forward movement is transformed into rearward movement, resulting in the runner staying in one place.

 

I've had a quick look, it is still not clear, I seem to remember a conclusive answer to the problem. Perhaps there wasn't one.

Edited by paul devereux
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As for the brakes being applied along with full power think the pitch torque on either the tail or nose wheel would introducing a countering force to the lift which can only be marginal given little of the wing would be in the moving airflow.

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A plane needs to roll forward on it's wheels against a static surface  to create lift. 

 

Increae in throttle = Wheel rotation.

Wheel rotation = opposing speed of belt rotation. 

Therefore the wheel rotation and belt speed cancel each other out. 

Therefore the plane is stationary. 

Therefore no airflow over the wings. 

Therefore no lift. 

 

QED. 

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