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The moving runway thought puzzle


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1 hour ago, Brian Cooper said:

I must confess to being very amused with this thread.

 

Okay, chaps, imagine this conveyor belt is on an aircraft carrier. 

It doesn't matter if the belt is running forwards or backwards, the aeroplane will still get airborne in exactly the same time/distance. . . . . Because the aeroplane isn't  attached to the runway. 

I agree completely that an aircraft on a conveyor belt will take off with a wheel speed equal to the conveyor belt plus airspeed and on a conventionally driven belt the aircraft essentially doesn’t care about the motion of the belt (less frictional/tyre drag effects). 
 

Sadly, the conditions stated in the question don’t allow this real world approximation to occur. 
 

In order to start accelerating airspeed, the wheels must turn faster than the conveyor belt.  It will do this when modelled on a demonstration system BUT the wheels will have turned faster than  the conveyor belt.  In the theoretical case posed by the original question, the system can only remain at rest. If you allow an almost imperceptible lag in matching wheel and belt speed then yes, the aircraft will eventually take off with the wheels at approximately twice normal rotation. 

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On 30/03/2023 at 21:48, J D 8 said:

Plane on a conveyour belt  by Mythbusters avaiable on Youtube 

 Your first assumption is wrong LHF. Plane does not care if on static or moving surface, it moves forward and lifts off in the normal way.

Yep, you're quite correct. I had a lightbulb moment and realised that the wheels are not acting on the belt, the whole issue revolves around the propeller acting on the air.

 

QED! 😀

 

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4 minutes ago, Lima Hotel Foxtrot said:

Yep, you're quite correct. I had a lightbulb moment and realised that the wheels are not acting on the belt, the whole issue revolves around the propeller acting on the air.

 

QED! 😀

 

Yes the propeller acts on the air but it has to get the whole plane to move so that the air across the wings will give lift for take-off.

Air moved just by the propeller will not give lift. 

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5 hours ago, David Ovenden said:

Which for me means its not worth spending any time on. In real life the plane would take off. End of story

Thereby lies the problem.  It’s a theoretical discussion - are we considering the simple physics of an aircraft on a moving runway or the situation as described in the question?

 

If all factors are taken into account, you must consider frictional effects which will require the aircraft wheels to turn faster than the belt speed to accelerate in the air mass due to the negative velocity component imparted by the belt via the frictional effect. Yes, this will be overcome by the aircraft’s thrust but it doesn’t comply with the strict parameters of the question. 

 

 

 

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11 hours ago, John Stainforth said:

To this tired and lame "thought puzzle" I say R.I.P.

I agree. When I originally posted I really didn't realise it has been done to death several times over. When someone mentioned RCG I googled and saw it has been resurrected there a few times since 2005! As @David Ovenden and @Martin Harris - Moderator and others have suggested, it is a logic puzzle that doesn't translate to real life. In real life the plane would take off. It's like the hare and the tortoise- logically, each time the hare caught up with the tortoise it will have moved on a little bit, and so on add infinitum, so it could never catch it, but in reality it could. At least this has put my mind at rest that there is no solution within the parameters of the question.

Edited by paul devereux
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