The "Aeroplane on treadmill" conundrum...
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3. Coveyor belt moves backwards therefore opposing this forward motion
Hold a toy car in the air then press it onto a moving treadmill such that the wheels spin up, but the car does not move relative to the air or the fixed ground outwith the treadmill. You are holding the toy car in a fixed place, with the only effect being that the treadmill causes the wheels to spin.
Now use your hands to move the toy car "up" the treadmill, in the opposite direction to that at which the belt is moving.
What are your hands doing? They are applying an external force to the car, NOT RELATED to the moving belt system, in order to move it relative to the air. In this case, the reaction is between your hands and the surfaces of the toy car. This is the EXACT SAME FORCE the engines on an aircraft would provide, with the reaction in that case being between the air (every bit as "external" to the system as your hands), the engines and their exhaust.
Does anyone HONESTLY believe that they will not be able to push a simple toy car up a moving supermarket checkout belt, or exercise machine? The principle is almost exactly the same as that of the aircraft on the conveyor belt runway as far as I can see, and it works fine! The aircraft would fly.
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Alcohol does not help!
After a non-alcohol induced think I have to say that what I posted earlier was Bo**ocks!
With the exception of the nominal friction of the gear - of course it would move forward - unless the conveyor was capable of infinitive speed which would of course set the gear on fire!
The prop is biting the air and the air is not conneted to the ground - so apart from spinning the wheels, nothing would change!
Coat is on - left the building!
With the exception of the nominal friction of the gear - of course it would move forward - unless the conveyor was capable of infinitive speed which would of course set the gear on fire!
The prop is biting the air and the air is not conneted to the ground - so apart from spinning the wheels, nothing would change!
Coat is on - left the building!
J.A.F.O
How does the conveyor belt move the aircraft backwards?
Because the aeroplane is sat on the conveyor belt.
If your aeroplane is only ever stationary or moving relative to air and not ground you must have a terrible time finding it once you've parked and then the earth has rotated underneath it while you're away.
Or, is that what tie downs are for?
How does the conveyor belt move the aircraft backwards?
Because the aeroplane is sat on the conveyor belt.
If your aeroplane is only ever stationary or moving relative to air and not ground you must have a terrible time finding it once you've parked and then the earth has rotated underneath it while you're away.
Or, is that what tie downs are for?
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you must have a terrible time finding it once you've parked and then the earth has rotated underneath it while you're away.
That's a perfectly fair point - but becomes irrelevant once the engines have started pushing against the air!
If you sit the toy car/plane/whatever on the treadmill/conveyor belt/whatever,
and turn it on, the vehicle will move back with the treadmill, like you say.
Why? Because friction within the wheel bearings inhibits them from spinning up and allows the force on the wheel by the conveyor belt to be "transferred" to the entire aircraft.
This frictional force is very, very small, but clearly evident - on normal ground it may take more power to get an aircraft moving initially than just to taxi along once already moving. The engines, in providing slightly more power, have overcame the small force of friction within the wheel system, and allowed them to spin!
This is exactly what happens when the conveyor belt is moving and the engines are applying force in the opposite direction. The conveyor belt "tries" to move the aircraft backwards, but the only way it can do this is through the small amount of friction in the wheel bearings. The engines have already overcame this friction, as they would when taxying on normal ground, so the net effect is that the engines push the aircraft forwards relative to the air, whilst the conveyor belt simply spins the wheels faster than they normally would (as a component of both the forwards motion of the aircraft and the rotational point of the wheels, and the backwards motion of the conveyor belt).
Funky
You've been very patient but if you don't stop explaining it I might be forced to admit that I was wrong and that - given a long enough conveyor belt for the aircraft to gain sufficient airspeed - the aeroplane may just fly, perhaps.
I won't be on Pprune for a little while so I'll leave you all debating the length of conveyor belt needed for the average light aircraft and working out effective groundspeed on take-off.
I might then admit that the emperor has on a pair of socks at least.
You've been very patient but if you don't stop explaining it I might be forced to admit that I was wrong and that - given a long enough conveyor belt for the aircraft to gain sufficient airspeed - the aeroplane may just fly, perhaps.
I won't be on Pprune for a little while so I'll leave you all debating the length of conveyor belt needed for the average light aircraft and working out effective groundspeed on take-off.
I might then admit that the emperor has on a pair of socks at least.
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J.A.F.O
The belt length would be virtually the same as the normal takeoff run on a runway.
I am considering emailing the production company that does the telly programs on weird science experiments suggesting it.
Unfortunatly i don't think it would take up much air time though for the setup costs.
You could have a a conveyer at an open air mine and a remote controlled aircraft. With the belt turned off do a take off measure it. Then turn the belt on. These things run at way more than Vr for a remote controlled aircraft. And then do it again and compare the TO distance.
And if it helps imagine that the aircraft doesn't have any gear at all. Its held on 3 skids with no wheels. The skids would be equivalent to wheel speed of zero so the belt speed would be zero. Would you expect a skid under carrage plane to take off?
This would be equivalent to a snow kitted plane like the antartic survey twin otters.
And i also have read a story about a high performance fighter who's throttles stuck on a high powed ground run. With the hand brake on and the full pressure of a 16 stone bloke who doesn't want to go flying on the toe brakes. It still managed to build up enough speed that take off was going to happen so he took the brakes off so the tyres wouldn't blow and became airbourne. Because the aircraft was in maint the bang seat was US with rockets removed. I believe he managed to get the aircraft back safely and got an award for getting it back in one peice
The belt length would be virtually the same as the normal takeoff run on a runway.
I am considering emailing the production company that does the telly programs on weird science experiments suggesting it.
Unfortunatly i don't think it would take up much air time though for the setup costs.
You could have a a conveyer at an open air mine and a remote controlled aircraft. With the belt turned off do a take off measure it. Then turn the belt on. These things run at way more than Vr for a remote controlled aircraft. And then do it again and compare the TO distance.
And if it helps imagine that the aircraft doesn't have any gear at all. Its held on 3 skids with no wheels. The skids would be equivalent to wheel speed of zero so the belt speed would be zero. Would you expect a skid under carrage plane to take off?
This would be equivalent to a snow kitted plane like the antartic survey twin otters.
And i also have read a story about a high performance fighter who's throttles stuck on a high powed ground run. With the hand brake on and the full pressure of a 16 stone bloke who doesn't want to go flying on the toe brakes. It still managed to build up enough speed that take off was going to happen so he took the brakes off so the tyres wouldn't blow and became airbourne. Because the aircraft was in maint the bang seat was US with rockets removed. I believe he managed to get the aircraft back safely and got an award for getting it back in one peice
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Originally Posted by J.A.F.O.
J.A.F.O
you must have a terrible time finding it once you've parked and then the earth has rotated underneath it while you're away.
you must have a terrible time finding it once you've parked and then the earth has rotated underneath it while you're away.
TPK
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Excellent thread. I too found the question misleading and originally jumped to the wrong conclusion. I agree that, as described, the aircraft would take off normally. However, it's interesting to wonder where the question came from, and whether it was deliberately worded to be a trick question, or is it more likely the person who wrote didn't know what they were on about.
I guess it's similar to how setting a crossword is harder than solving one.
"A plane is standing on a runway that can move (some sort of band conveyer). The plane moves in one direction, while the conveyer moves in the opposite direction. 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). Can the plane take off?"
The bit about the conveyer going at exactly the same speed in the other direction is clearly meant to mislead the reader into thinking that the two speeds cancel out in some way - if not, why "exactly" the same speed?
The question setter seems to be deliberately trying to make you visualise a situation analagous to a runner running on a treadmill, though this could never happen in practice.
Another point which may not have come across clearly enough in all the previous posts is this - imagine the aircraft sitting on the conveyor, engines off, brakes off, conveyor off. Now, the conveyor starts moving at, say, 20mph backwards. The aircraft will *not* suddenly accelerate backwards to keep pace with the conveyor - assuming frictionless wheels, it wouldn't move at all; in practice, it will sit still, the wheels will spin up to the normal 20mph rpms, and there will be a small frictional force from the tyres which will slowly accelerate the aircraft backwards.
Now then - downwind turn, anybody?
I guess it's similar to how setting a crossword is harder than solving one.
"A plane is standing on a runway that can move (some sort of band conveyer). The plane moves in one direction, while the conveyer moves in the opposite direction. 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). Can the plane take off?"
The bit about the conveyer going at exactly the same speed in the other direction is clearly meant to mislead the reader into thinking that the two speeds cancel out in some way - if not, why "exactly" the same speed?
The question setter seems to be deliberately trying to make you visualise a situation analagous to a runner running on a treadmill, though this could never happen in practice.
Another point which may not have come across clearly enough in all the previous posts is this - imagine the aircraft sitting on the conveyor, engines off, brakes off, conveyor off. Now, the conveyor starts moving at, say, 20mph backwards. The aircraft will *not* suddenly accelerate backwards to keep pace with the conveyor - assuming frictionless wheels, it wouldn't move at all; in practice, it will sit still, the wheels will spin up to the normal 20mph rpms, and there will be a small frictional force from the tyres which will slowly accelerate the aircraft backwards.
Now then - downwind turn, anybody?
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Just to remind some of the original question...
So we are assuming the treadmill CAN keep up with the speed of the a/c.
It won't fly!
tKF
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)
It won't fly!
tKF
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tKF,
Agreed, if there were anything acting in the system to prevent the aircraft moving forward, it could never fly. The problem with the question is that there's nothing in the described system that will prevent the aircraft moving forward. The 'trick' in the question is that the reader is tempted to assume that the conveyor moving backwards will stop the aircraft moving forward - but the question doesn't actually say that explicitly, and it couldn't happen in practice.
This is all assuming low / zero friction at the wheels / tyres, of course - if the pilot is lazily resting his feet on the toe brakes then, of course, the aircraft will be dragged backwards with the conveyor.
Agreed, if there were anything acting in the system to prevent the aircraft moving forward, it could never fly. The problem with the question is that there's nothing in the described system that will prevent the aircraft moving forward. The 'trick' in the question is that the reader is tempted to assume that the conveyor moving backwards will stop the aircraft moving forward - but the question doesn't actually say that explicitly, and it couldn't happen in practice.
This is all assuming low / zero friction at the wheels / tyres, of course - if the pilot is lazily resting his feet on the toe brakes then, of course, the aircraft will be dragged backwards with the conveyor.
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Again, looking at my quote from the original question.
If the speed acting against the motion of the aeroplane (ie the treadmill) is the same as the speed of the a/c (as the question states), then the forces are equal - therefore it has no forward speed - therefore it can't fly!
tKF
If the speed acting against the motion of the aeroplane (ie the treadmill) is the same as the speed of the a/c (as the question states), then the forces are equal - therefore it has no forward speed - therefore it can't fly!
tKF
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You are sitting in Tipsy Nipper, situated on the aforementioned conveyor. The conveyor starts to move. The aircraft will move with it because its wheel bearings are not frictionless. An observer at the end of the conveyor tosses you a slightly elastic rope which is secured to the ground. If you hold on, as you reach the end of the slack in the rope you will slow down relative to the conveyor. You start to pull yourself towards the end of the belt. The conveyor speeds up to oppose you. This is irrelevant, you will reach the end of the conveyor very shortly, because the thrust system is entirely unconnected to the conveyor and the only opposing force other than the normal weight/inertia of the aircraft is the friction of the wheel bearings. The force of pulling on the rope is equivalent to the thrust of the engine/prop.
If a man can overcome the conveyor slowly, the engine will have no problem in doing so quickly.
IMHO the aircraft will fly.
Unless, of course, the question really requires us to consider a real world physical property i.e. friction in bearings, together with a physical impossibility i.e. a conveyor belt capable of almost instant acceleration and practically infinite speed. In which case the conveyor will simply accelerate to the point where the drag from the bearings will equal the thrust from the power unit.
If a man can overcome the conveyor slowly, the engine will have no problem in doing so quickly.
IMHO the aircraft will fly.
Unless, of course, the question really requires us to consider a real world physical property i.e. friction in bearings, together with a physical impossibility i.e. a conveyor belt capable of almost instant acceleration and practically infinite speed. In which case the conveyor will simply accelerate to the point where the drag from the bearings will equal the thrust from the power unit.
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From my point of view, you're mixing up the terms 'speed' and 'force' a bit too loosely. The speed of the treadmill doesn't 'act on' the aircraft - speeds don't act on anything. It isn't valid to say that, as the speeds are equal, the forces are equal.
I guess it all comes down to how each reader visualises the friction component. From my A-level maths and physics, I automatically discount friction when considering this sort of problem. In theory, you're 100% correct - if the aircraft's wheel bearings produced loads of friction, or if the brakes were dragging, then you could have a situation where all the thrust of the engines was required to overcome the drag of the brakes, just to hold the aricraft at zero airspeed. That's definitely an assumption too far, based on the question, though.
I guess it all comes down to how each reader visualises the friction component. From my A-level maths and physics, I automatically discount friction when considering this sort of problem. In theory, you're 100% correct - if the aircraft's wheel bearings produced loads of friction, or if the brakes were dragging, then you could have a situation where all the thrust of the engines was required to overcome the drag of the brakes, just to hold the aricraft at zero airspeed. That's definitely an assumption too far, based on the question, though.
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Bear with me I'm drunk, and have been for most of my postings on this thread
Kentish,
The speeds may be the same (opposite in direction but equal in magnitude velocity) but the forces are NOT equal and are not balanced!
Why? Because the forces are not being applied in the same way.
The "force" from the conveyor belt is only one of two things.
If the aircraft is stationary on the belt (i.e. the engines are off/idling), then :-
1. A force occurs between the surface of the tyre and the surface of the belt, due to friction. When the belt moves, this force will always attempt to spin the wheel, assuming the wheel is parallel to the belt. If the belt is moving slowly enough, without any abrupt acceleration, and without any force from the engines, then :-
2. The force between the belt and the tyre is "transferred" as a result of the very small amount of friction within the wheel bearings to the whole of the aircraft. This results in the aircraft moving slowly backwards with the belt. This will only happen if the belt accelerates slowly enough as not to overcome the friction present within the wheels and their axles.
As soon as the engines are throttled up:-
1. The friction within the wheel bearings/axles is overcome when the force between the engines and the air is sufficient. This MUST happen, otherwise aircraft all over the world wouldn't be moving around on the ground under their own power and rolling on their own wheels!
2. Because the friction within the wheels has been "overcome" by the force of the engines acting forwards (the friction still exists, but it is small enough compared to the force applied by the engines to be irrelevant now), there is no way for the frictionary force between the belt and the tyre to be "transferred" to the rest of the aircraft. The conveyor belt now exists solely to spin the wheels of the aircraft, as the engine force has "kick started" the spinning motion of the wheels.
I havn't quite completed Physics A-Level (Advanced Higher up here, way up yonder cold Scotland) and I'm quite intoxicated so I'm probably wrong and some all-empowering might of higher wisdom will come to disprove me later But...I think it will fly! 
By the way, Yorks.PPL posted a relatively simple demonstration of why the plane probably will fly earlier!! It can be seen at http://videos.streetfire.net/player....D-D6BA1A43A06B
For those not convinced by the simplicity of a sheet of paper, an electric fan and a skateboard, you could always try the toy car + treadmill idea, or stick a working model aircraft on a travelator...if you care such!
Kentish,
If the speed acting against the motion of the aeroplane (ie the treadmill) is the same as the speed of the a/c (as the question states), then the forces are equal - therefore it has no forward speed - therefore it can't fly!
Why? Because the forces are not being applied in the same way.
The "force" from the conveyor belt is only one of two things.
If the aircraft is stationary on the belt (i.e. the engines are off/idling), then :-
1. A force occurs between the surface of the tyre and the surface of the belt, due to friction. When the belt moves, this force will always attempt to spin the wheel, assuming the wheel is parallel to the belt. If the belt is moving slowly enough, without any abrupt acceleration, and without any force from the engines, then :-
2. The force between the belt and the tyre is "transferred" as a result of the very small amount of friction within the wheel bearings to the whole of the aircraft. This results in the aircraft moving slowly backwards with the belt. This will only happen if the belt accelerates slowly enough as not to overcome the friction present within the wheels and their axles.
As soon as the engines are throttled up:-
1. The friction within the wheel bearings/axles is overcome when the force between the engines and the air is sufficient. This MUST happen, otherwise aircraft all over the world wouldn't be moving around on the ground under their own power and rolling on their own wheels!
2. Because the friction within the wheels has been "overcome" by the force of the engines acting forwards (the friction still exists, but it is small enough compared to the force applied by the engines to be irrelevant now), there is no way for the frictionary force between the belt and the tyre to be "transferred" to the rest of the aircraft. The conveyor belt now exists solely to spin the wheels of the aircraft, as the engine force has "kick started" the spinning motion of the wheels.
I havn't quite completed Physics A-Level (Advanced Higher up here, way up yonder cold Scotland) and I'm quite intoxicated so I'm probably wrong and some all-empowering might of higher wisdom will come to disprove me later
But...I think it will fly! By the way, Yorks.PPL posted a relatively simple demonstration of why the plane probably will fly earlier!! It can be seen at http://videos.streetfire.net/player....D-D6BA1A43A06B
For those not convinced by the simplicity of a sheet of paper, an electric fan and a skateboard, you could always try the toy car + treadmill idea, or stick a working model aircraft on a travelator...if you care such!
