Plane on a coneyor belt
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@chris fullmer said:
I fail to see how this is a different question? We've established that the conveyor belt can move however fast it wants. The rotational speed of the wheels has nothing to do with the plane moving forward, as long as the brakes aren't on and there's nothing physically holding the plane to the ground.
So the plane still takes off.
Chris
i agree
pav
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I also agree .... however! see if brakes stop an F16 from taking off.
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Ok, well just focus on the system of the wheel for the moment.
For the plane to take off it must have forward velocity relative to the ground (assuming its a still day.) If the plane has forwad velocity so do the wheels...
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but the conveyor belt moving backwards doesn't push backwards at all on the plane. The wheels are free spinning, they will just spin faster to accommodate the conveyor belt while the plane moves forwards.
Here's what I think it would take to stall the plane on a conveyor belt:
The conveyor belt would have to move backwards at the speed at which the propellers/turbine are capable of moving air through them. So if the propeller speeds up air to 1000mph (or km/h), then the conveyor would have to move the plane backwards at that rate, so that their would be air rushing backwards into the prop/turbine at the same speed at which it could be sucked in. That seems more like it. So the conveyor has to move at the speed of the air rushing through the propeller.
Chris
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But the wheels would have to be able to spin infinitely fast to accommodate the plane taking off and the conveyor belt, and infinity=impossible.
To work it trough with numbers: the plane starts moving at 1 mph, thus the wheels are also turning at 1 mph, the conveyor belt spins to accommodate this meaning that the wheel is then doing 2 mph (aeroplane speed+conveyor belt.) the conveyor belt then has to speed up again to match the wheel speed which gives a wheel speed of 4 mph. You can keep going in this fashion for as long as you like, there is no end to the sequence.
The root of the problem lies in that for the plane to take off the wheel must have forward velocity, but while the conveyor belt is there the wheels cant have forward velocity.
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the wheel doesnt have its own velocity, it has spin. It is always at the same velocity as the plane. So as soon as the conveyor goes backwards, the whold plane does, until the plane kicks on its engines and pulls itself forward through the air. At that time, the wheels spin faster only because their speed is equal to the speed of the conveyor, plus the speed of the plane. The velocity is the same as the plane's though. the conveyor belt can't hold up their velocity, it only affects their spin.
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My above reasoning works if you use spin instead of velocity.
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Remus,
You are still presupposing that the backward motion of the belt can exert a significant effect on a plane powering forward...enough to cancel out any forward motion...it can't. You might as well try to lasso the plane with a smoke ring.
Everyone would agree that the plane could not take off if its groundspeed remained at zero, but that's the essence of the problem...it won't.
You could see that happening in the Mythbusters clip. It wasn't the case that the plane was travelling as fast as the car and then some...enough extra to get some lift. They were both travelling at the same speed; but the belt can't hold the plane motionless any more than it could if it were being towed by a rocket. The wheels are irrelevant; spinning or otherwise. They do little more than keep the aircraft level. It would work exactly the same if the plane was on skids and the belt had a low coefficient of friction.Think of it this way. A car wheel in high revs on a muddy surface throws a ton of mud backwards. It is exerting a very substantial force in the opposite direction to its motion. A plane wheel in high revs on the same surface does absolutely nothing other than roll over it. The only force it is exerting is downwards, until it reaches takeoff speed. The reverse is also true...if the aircraft wheel exerts no lateral force on the ground, then the ground exerts no opposing lateral force on the wheel; certainly not enough to hold it stationary, however fast it travels. It's a completely false proposition.
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I'm afraid my example is the only way in which this would work. Logic it through and see if I missed anything. The conveyor belt has to move backwards at the speed at which air could be sucked in to the propellers, thereby canceling out the propellers ability to work, so the plane would sit still with its engines burning full speed. The wheels would therefore not be spinning at all and the conveyor would in fact be moving at its own speed, plus the speed (zero) of the wheels).
Chris
though once the plane is moving that fast backwards, you have to ignore all the wind coming backwards at it. I don't know if its possible to ignore that though.
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Chris, I don't understand what you mean. what has the conveyor to do with wind speed?
but to the idea that the plane can't be stopped by the conveyor belt:
you allways asume, that the wheels have no frictional resistance whatsoever. but this is wrong. if that were true, you only needed to speed up a car once and it would roll on forever (almost a perpeto mobile).
but no matter how good the bearings are, wheels will allways have some tiny amount of frictional resistance.
I have no idea about physics or maths. but asume that 1/1.000 of the rotation energy of the wheel is transformed into warmth by this resistance.
that only means, that the conveyor has to rotate 1.000 x faster than the plane is pushing forward.so you simply need an incredibly fast conveyor to stop the plane from moving forward - therefore stopping it from taking off.
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Jakob,
But that wasn't the question. Certanly if you had a conveyor capable of infinite speed it could exert enough drag on the wheels to stop the plane advancing. You could achieve the same thing by chaining the undercarriage to a fixed object.
The question was can you stop the plane by having the conveyor go backwards at the same speed as the plane's forward motion. I quote: "This conveyer has a control system that tracks the plane speed and tunes the speed of the conveyer to be exactly the same (but in the opposite direction)." The answer is no. The moments of force just don't add up.I think the main problem is that it's not a very scientific question. It talks about the plane's speed. What speed?...groundspeed or airspeed?...an aircraft only has those two. Yet the question involves some weird speed relative to to a fixed point on a moving surface. That sends the whole thing into a circular argument, because that speed is, itself, influenced by the speed of the conveyor. That's probably why the debate has gone on for 5 pages. It falls into the realm of "How long is a piece of string?"
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but you are refering to the first question now, don't you? where the conveyor adopts the speed of the aircraft, therefore is not able to stop it.
but if the conveyor has a sensor that detects the movement of the plane. if the plane moves forward, the conveyor will accelerate until the plane doen't move forward anymore.
that would eventually (at a very high speed of the conveyor) keep the plane from moving relatively to it's surroundings.to completely solve the mystery we have to set up a formula with all important variables, like:
weight of the plane
frictional resistance of the wheels
conveyor speed
subjective plane speed
objective plane speed
we need someone to calculate how much energy is lost due to frictional resistance. then we need to know how fast the plane has to be to take off. then we can calculate how fast the conveyor has to be to stop the plane from moving forward...
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@plot-paris said:
but you are refering to the first question now, don't you? where the conveyor adopts the speed of the aircraft, therefore is not able to stop it.
but if the conveyor has a sensor that detects the movement of the plane. if the plane moves forward, the conveyor will accelerate until the plane doen't move forward anymore.
that would eventually (at a very high speed of the conveyor) keep the plane from moving relatively to it's surroundings.to completely solve the mystery we have to set up a formula with all important variables, like:
weight of the plane
frictional resistance of the wheels
conveyor speed
subjective plane speed
objective plane speed
we need someone to calculate how much energy is lost due to frictional resistance. then we need to know how fast the plane has to be to take off. then we can calculate how fast the conveyor has to be to stop the plane from moving forward...
no no no no no
the converyor belt would never fully compensate for the planes thrust, remember the wheels are free-wheeling, like stated before all it would do is make the wheels spin even faster.
look at it this way, could a converyor belt travelling in the opposite direction to a landing plane stop it's movement? no.
pav
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I thought we'd moved on to the second question now?
Alan, referring to the first question i agree with you, the plane can take off. The second question is a different matter entirely.
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Sorry Remus, I didn't see the second part.
To be honest, I don't think it would make much difference. Think of a ski-plane on a teflon-coated conveyor. By that I mean that the rotational speed of the wheels is largely irrelevant...as is the speed of the surface they are rolling over. Obviously, in the real world, they'd eventually overheat, seize up and then we're into a whole new calculation; but this isn't the real world.
Certainly the plane is slightly handicapped by whatever resistance is offered by its undercarriage, but the conveyor is equally handicapped by the inertia (if not forward momentum) of the plane. This would get more acute the faster it moved. It's the old tablecloth trick. -
It does make quite a bit of difference, actually.
Re-read the my post with the numbers in.
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Alan, you mentioned it: Overheating of the tyres.
and this overheating is literally lost forwart movement, transferred into another form of energy - heat.again I take the example of pav on his treadmill. this time pav took his old skateboard. now he is standing on is board on the treadmill. when he turns on the training device, he is suddenly transported backwards. to prevent this, he grasps the handrail in front of him.
now we have a similar situation to the plane on the conveyor. the conveyor is moving backwards but the plane is keeping it's position by applying a forward thrust that is not dependent on the conveyor's surface.
back to pav. he really enjoys this experience, turning up the treadmill to its maximum speed. there he is racing faster than he ever did before on his skate board - without even moving. cool!
but after a minute or so his arms start to ache! at the same time the wheels of his board get quite warm..
why do his arms ache? because the frictional resistance of the wheels transferred some of the backwards-movement of the treadmill to the board and therefore to pav. he had to compensate this backwards-movement with the power of his arms. it was not much - but after a while it was exhausting nevertheless.
and now pav thinks: "what would have happened, if my treadmill could run with 10 times the speed? or even a 100 times?"
I hope this little anecdote out of pavs life helps to understand this little experiment
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he he he, feel like i'm famous!
pav
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you ARE, pav!
whe should start producing a tv-series, where some blokes discuss a problem (like this plane-conveyor-thing), use loads of examples out of PAV's every day life, and finally don't come to a conclusion!
that could be a true success!
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that would be awesome!
but what could we call it?
plot would you like to be co-presenter, or executive producer? ha ha
pav
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