Plane on a coneyor belt
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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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my embarrasingly German english and little vocabulary stops me from being co-presenter. on the other hand, that could be a laugh.
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i think that would be a wicked combo.
i speak exceptionally quickly, and slip in and out of "market slang" and "impress the client" lingo.
it's like talking to someon with dual personality who is heavily dosed up on MDMA
so i'm told.
pav
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sounds marvellous! and we film all this in front of a green screen and replace the background with a new SketchUp interior design for every episode!
and we use the "proper animation" tool to move chairs and such! and the face/edge-styles change during the show... can't wait to start with it.
you don't happen to have a hd-camera and a big green screen at home,do you?
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i do have a HD camera as it goes.
as far a a big screen goes, i only have the one for my home cinema, not sure it's gonna be big enough (only 2.5m x 2m)
good for the screening of the pilot episode though!
pav
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Im sure a big green tarp would be fine
When does the pilot episode air btw? wouldnt want to miss your debut... -
we will definitely announce the pilot, of course.
the problem is not so much the screen itself - you only need a (preferably non reflective) unicoloured face. a bright green is very unlikely to turn up in the scene (unless pav insists to wear a bright green shirt - then we have to get a blue screen. but I tend to wear blue jeans...
).the big problem is the lighting. every bit of the screen has to recieve exactly the same amount of lighting. otherwise you get a gradient, where the colour difference is too big. so you have to give the tool that deletes the chosen colour (in premiere or avid for example), a too big range.
and for this lighting we need big lighting screens (point a light source not directly at the green screen, but at a white rectangle, that reflects the light to the green screen to create a diffuse light (without shadows and highlights).
so we need several of those and then we need a luxmeter to precisely measure the amount of light at every point of the green screen. and such a luxmeter is quite expensive as far as I know...but it would be sooooo great to have "in SketchUp environment" scenes...
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