I know that, you know that but thats the point of the question to make people think, "does the runway wheel arrangement have any influence over the outcome?"( when it clearly doesn't) "will the aircraft take off" (which it does)
I'm a bit in the middle here, I know the answer yet having to pose the question without giving too much away
A jet is accellerated by the thrust of the engine. If the wheels are moving or not makes no difference there
Not necessarily....
Back to physics 101 guys...
OK, lets move on to Physics 102 (or 101 and a half)
I'd like to bring up the minor detail of those wheels. Do they have a significant mass?
The opnening post problem states that "..the wheels of the jet plane has encoders that relay wheel speed to the conveyor runway which instantaneously matches the speed but in the reverse direction to the way the jet plane is facing"
Note: The signal from the encoders is not the jets linear speed but the angular velocity of the wheels.
So:
a) The jet thrust moves the plane forwards.
b) Therefore the wheels rotate forwards.
c) The belt responds by moving backwards.
d) Causing the wheels to rotate forwards more (and so basically back to b) again)
We have positive feed back here, and the belt will be driven faster and faster until something brakes. Lets assume nothing brakes.
One argument is that the wheels have no effect on the plane motion as they are on friction less axles.
BUT. If they have mass then they have inertia, and specifically a moment of inertia. The belt trying to rotate them forwards will actually drag them backwards down the run way. The thrust of the plane would have to overcome this drag in order to accelerate to take of speed. BUT as the belt is in a wild runaway mode with all that positive feed back any mass on the wheels will soon result in a huge reverse pull on the plane and it may not take off.
Try this simple experiment:
Ignore the plane for a bit and let's use a rolling pin to represent the wheels with some mass.
Let's use a sheet of paper to represent the conveyor belt.
Place the sheet of paper on a flat smooth surface.
Place the rolling pin on the paper near the top edge say.
Mark on the flat surface where the pin is.
Now pull the paper out from under the pin causing it to roll. Accelerating smoothly.
Mark on the flat surface where the pin is when it leaves the paper.
Observe how you have dragged the pin in the direction of the paper whilst accelerating the paper out from under it!
Now, if that rolling pin was the wheels of our plane the planes thrust would have to overcome that reverse drag, the heavier the wheels the worse it is. But given the runaway positive feed back control system it can't win. It can't accelerate to take off speed.
Given that the problem suspends reality by talking about frictionless bearings and instantaneous control loop we could be forgiven for assuming wheels of zero mass in which case there is no reverse drag due to wheel inertia and the plane flies again:)
We could also assume frictionless contact between wheels and conveyor, in which case the wheels never even start to rotate and the conveyor stays stationary as a result. And the plane flies?
By the way, the Myth busters experiment seems flawed they seem to be dragging the conveyor backwards at a speed to match the forward speed of the plane. But our problem does not use linear plane speed but wheel angular velocity.
I meant it has no influence on the aircrafts movement through space or air, only the thrusters have that influence to move the aircrafts wings through the air.
the wheels will have travelled many more times the distance that the aircraft would have due to the two totally different action /reactions as pointed out so elegantly by Ron in post #42
Assumptions are the name of the game with this scenario I believe as it can throw up many combinations of thought processes but there is only one correct solution.................AFAIK
I meant it has no influence on the aircrafts movement through space or air, only the thrusters have that influence to move the aircrafts wings through the air.
Do the experiment with the rolling pin I suggested. It will convince you that because the wheels have mass and hence moment of inertia, and because the wheels have frictional contact with the conveyor the conveyor can indeed have influence on the linear motion of the plane along the runway, not just the thrusters.
As the control system seems to be set up to provide a huge pull backwards on the conveyor for the smallest forward movement of the plane this effect could overwhelm the thrusters and stop the plane taking off. (Unless it can take off in reverse of course)
Assumptions are the name of the game with this scenario....but there is only one correct solution.
Cannot be, if I assume frictionless axles, as given, I might feel free to assume frictionless contact between wheel and conveyor (Why not)
In that case the wheels never turn, the conveyor never moves and the plane flies unhindered.
If I assume a lot of friction from wheel to conveyor, and good heavy wheels, that conveyor can have a large influence on the plane by virtue of having to rotate the wheels ever faster. In doing so the wheels will push the plane backwards as in the rolling pin experiment.
If I assume a lot of friction from wheel to conveyor, and good heavy wheels, that conveyor can have a large influence on the plane by virtue of having to rotate the wheels ever faster. In doing so the wheels will push the plane backwards as in the rolling pin experiment.
No, that reasoning is flawed, I'm afraid. Remember that for every part of the wheel that's moving backward, there's an equal part on the top that's going forward, so there's no net force vector pulling on the frictionless axle. The only force acting on the axle and the plane as a whole is the jet thrust. And the only influence the ever-faster-spinning wheels would have is to provide gyroscopic stability to the plane as it takes off and to make turning ... um ... interesting.
The issue isn't so much whether a plane can take off independent of what the wheels are doing, but it's whether the conditions allow for the plane to move. The original conditions were poorly stated, but implied that the runway moved like a treadmill and used a control system that would keep the center of the wheels stationary. Of course, the only solution for this is that the plane could not move, which means that the engines could not produce any thrust.
The new and improved description only states that a dot on the wheels must match dots on the runway. This implies that there is no slippage between the wheels and the runway. However, the description isn't complete enough to actually determine how the runway moves, but it does allow the plane to move freely. Under the new description, the plane can take off.
This "puzzle" is similar to stuff I encounter at work all the time. A customer discovers a problem in one of our systems, and provides either a very vague description of how the problem happens, or they provide a very elaborate description with unnecessary details to reproduce the issue. With the vague description we have to go back and forth with them to find out exactly how they encountered the problem. With the elaborate description we have to weed out the unnecessary stuff so that we don't have to completely reproduce the customer's environment to reproduce the problem.
At some point, Skylight might give us enough details to accurately understand his version of the problem. Of course, once he does that it's no longer a puzzle, and the answer is obvious.
This "puzzle" is similar to stuff I encounter at work all the time. A customer discovers a problem in one of our systems, and provides either a very vague description of how the problem happens, or they provide a very elaborate description with unnecessary details to reproduce the issue. With the vague description we have to go back and forth with them to find out exactly how they encountered the problem. With the elaborate description we have to weed out the unnecessary stuff so that we don't have to completely reproduce the customer's environment to reproduce the problem.
If someone in the plane ran forward and hit the bulkhead the plane would move forward a small amount causing the wheel to rotate a small amount and the runway would compensate. This would cause the wheel to move more and the runway to compensate more. this would continue to build until the tires were rotating at a speed where they would explode and the plane would be stuck on the runway and as such would not fly.
As long as he doesn't start kicking the back of my seat!!!!! ;-)
>what information is conveyed
The left to right "movement" (knight rider style)
The same as the information of a beam movement from the laser pointer being pointed and moved between points in the sky that are farther apart than the speed of light.
But again, what information is being conveyed? That is... what information originating at point A is received at point B with the arrival of the photon beam? The aliens on planets A and B are only going to see a flash of photons racing by into deep space.
(A tangent from the airplane/conveyor topic, but fun!!)
I guess I never really understood the question. I thought that the jet was hypothetically fixed in place (by whatever means) and that only the ground under it was moving. I didn't think a conveyor would hold a jet in place, I was just thinking of the control experiments on Mythbusters where they tether it to the treadmill.
I guess some other people might not understand the question either.
So basically the question is, can you exert force upon something in one direction and expect it to not move that direction because a lesser force is acting upon it in another direction? The answer becomes pretty obvious at that point.
If the jet were to stay still you'd need two equal opposing forces, or no thrust would work too hehe.
Also, look at the energy the treadmill can produce and compare that to the jet. When they're both equal there's a chance but it would require a mechanical connection to the jet like the engine.
Do the experiment with the rolling pin I suggested. It will convince you that because the wheels have mass and hence moment of inertia, and because the wheels have frictional contact with the conveyor the conveyor can indeed have influence on the linear motion of the plane along the runway, not just the thrusters.
As the control system seems to be set up to provide a huge pull backwards on the conveyor for the smallest forward movement of the plane this effect could overwhelm the thrusters and stop the plane taking off. (Unless it can take off in reverse of course)
Cannot be, if I assume frictionless axles, as given, I might feel free to assume frictionless contact between wheel and conveyor (Why not)
In that case the wheels never turn, the conveyor never moves and the plane flies unhindered.
If I assume a lot of friction from wheel to conveyor, and good heavy wheels, that conveyor can have a large influence on the plane by virtue of having to rotate the wheels ever faster. In doing so the wheels will push the plane backwards as in the rolling pin experiment.
The rolling pin experiment is not the answer as it has friction between the roller part(wheel) and the handle part(axle)
the frictionless bearings in the wheels cannot "push" the aircraft as they just slip and spin there is no transfer of a force to the planes fixed axle from the wheels.
Is there infinite friction between the tires (or tyres) and the belt?
Are all mechanical interfaces of infinite strength to handle any thrust applied or overcome any mechanical stresses involved?
How much thrust do I have? Infinite?
If you strap large ENOUGH thrust unit to something, it will fly...it may not be aerodynamic flight and may have nothing to do with air movement over airfoils but IT WILL FLY.
This is getting a bit ridiculous with assumptions. We're almost to the point of "assuming every condition that makes it impossible for the airplane to take off is in effect, can the airplane take off?"
Ok the engineers are asking for more detailed descriptions, let me state that the plane initially stands still , there is friction between the tyres and runway but the bearings are frictionless
the runway control system is not initially sensing any movement of the wheels and the runway drive is therefore static. The drive rollers have friction obviously with the runway belt.
the drive system is 99.9999999999999999999999999999999999999999999999......add as many digits here as you like.......% efficient and acts almost immediately
The pilot starts the thrusters and pulls the throttle back as normally he would, as far as he is concerned he is flying a normal jet plane on a normal runway (no one told him otherwise).
To counter the arguments that the runway would never start a groundsman observing the jet thrusters working quick as a flash presses a button to kickstart the runway moving in the opposite direction the plane is facing, due to the tyre /runway friction the wheels move and the feedback system takes over.(remember that the bearings are frictionless so no transfer of energy is made with the axle the wheels just freewheel.
Have I missed anything? Hopefully this will satisfy the engineers amongst you
I am surprised that the argument that I am mixing real world physics with fantasy(frictionless bearings) hasn't reared it's head yet, I believe it's this that makes the solution so hard to answer as like physics at this time is hitting the barrier of experimentation versus theoretical it's hard to come to a definitive solution when you don't know all the answers. I have always felt that this scenario fits in well with the above.
Is there infinite friction between the tires (or tyres) and the belt?
Are all mechanical interfaces of infinite strength to handle any thrust applied or overcome any mechanical stresses involved?
How much thrust do I have? Infinite?
Yes all components are indestructible, The plane has enough thrust as in normal conditions for take off
Won't the tires eventually break contact with the runway due to air being forced between the tire and runway, just like a hydroplaning car, "airplaning" so to speak.
Barring any effect like I mentioned in #139 I'm moving into the it stays put camp based on the conditions that have been set.
I'm basing this on agreement with Heaters post #123 that a force is applied to the axles in the same direction as the runway is moving whenever the wheels (unless they have no mass) are accelerating.
Phil's argument against this force in #129 only applies if the wheels are at constant speed.
So you are saying that the wheels will have an influence on the aircraft?
How would this be if no friction is in the bearing to transfer the necessary energy to push against the axle and try to stop the aircraft from moving?
In such as case "frictionless" typically applies to rotational motion of the wheel, not translational. Think of a case of typical engineering problems where a frictionless pulley is used, if the axle of the pulley didn't take load the pulley would just fall to the ground, and that isn't the correct answer.
Ah are we getting down to molecular levels and mass passing through mass if no friction?
But what about the bonds between atoms?
the axle can just sit on the frictionless bearing such as a ski sits on ice or water , but there would be no transfer of energy when the plane or runway moves at that point of contact due to no friction.
Ah are we getting down to molecular levels and mass passing through mass if no friction?
But what about the bonds between atoms?
lol, no, not really. Think about it, if "frictionless" means that the wheel/axle cannot transfer force to the plane, how do they hold it up.
C.W.
Edit - "Frictionless" is typically used to say that you don't need to account for energy lost as heat due to friction, otherwise relatively simple problems become pretty complex.
There is a force applied to the axles from the structure connecting them to the plane. Some of this force is applied to the mass of the axles to accelerate them in the direction of travel. The rest of the force is applied against the wheels to accelerate them also. Even though the bearings are frictionless, some of the force must also be applied to turn the wheels because they have a certain moment of inertia. All of the forces balance out so that F = ma is satistfied throughout the entire structure of the plane. All of the forces will move the plane down the runway until it takes off.
There is a force applied to the axles from the structure connecting them to the plane. Some of this force is applied to the mass of the axles to accelerate them in the direction of travel. The rest of the force is applied against the wheels to accelerate them also. Even though the bearings are frictionless, some of the force must also be applied to turn the wheels because they have a certain moment of inertia. All of the forces balance out so that F = ma is satistfied throughout the entire structure of the plane. All of the forces will move the plane down the runway until it takes off.
Anytime the jet makes forward progress the speed of the runway will increase causing the wheels to accelerate which will apply a force to the axle in the opposite direction of travel. Due to the problem conditions there is no upper bound to this force so it will always increase to enforce the condition of matching runway speed to wheel speed.
Anytime the jet makes forward progress the speed of the runway will increase causing the wheels to accelerate which will apply a force to the axle in the opposite direction of travel. Due to the problem conditions there is no upper bound to this force so it will always increase to enforce the condition of matching runway speed to wheel speed.
C.W.
I disagree with the bolded part, you have to have friction to do this
From the original post "You have a jet plane sitting on a runway which happens to be a conveyor belt, the wheels of the jet plane has encoders that relay wheel speed to the conveyor runway which instantaneously matches the speed but in the reverse direction to the way the jet plane is facing, "
To me this implies the condition that for a given rotation of the wheel resulting in a forward motion of dX, the runway will match that by moving -dX.
If we assume that the wheel cannot skid then no matter what justification is used to say that the plane takes of requires the condition to be broken.
Comments
I'm a bit in the middle here, I know the answer yet having to pose the question without giving too much away
In saying that is there actually a solution?
I'd like to bring up the minor detail of those wheels. Do they have a significant mass?
The opnening post problem states that "..the wheels of the jet plane has encoders that relay wheel speed to the conveyor runway which instantaneously matches the speed but in the reverse direction to the way the jet plane is facing"
Note: The signal from the encoders is not the jets linear speed but the angular velocity of the wheels.
So:
a) The jet thrust moves the plane forwards.
b) Therefore the wheels rotate forwards.
c) The belt responds by moving backwards.
d) Causing the wheels to rotate forwards more (and so basically back to b) again)
We have positive feed back here, and the belt will be driven faster and faster until something brakes. Lets assume nothing brakes.
One argument is that the wheels have no effect on the plane motion as they are on friction less axles.
BUT. If they have mass then they have inertia, and specifically a moment of inertia. The belt trying to rotate them forwards will actually drag them backwards down the run way. The thrust of the plane would have to overcome this drag in order to accelerate to take of speed. BUT as the belt is in a wild runaway mode with all that positive feed back any mass on the wheels will soon result in a huge reverse pull on the plane and it may not take off.
Try this simple experiment:
Ignore the plane for a bit and let's use a rolling pin to represent the wheels with some mass.
Let's use a sheet of paper to represent the conveyor belt.
Place the sheet of paper on a flat smooth surface.
Place the rolling pin on the paper near the top edge say.
Mark on the flat surface where the pin is.
Now pull the paper out from under the pin causing it to roll. Accelerating smoothly.
Mark on the flat surface where the pin is when it leaves the paper.
Observe how you have dragged the pin in the direction of the paper whilst accelerating the paper out from under it!
Now, if that rolling pin was the wheels of our plane the planes thrust would have to overcome that reverse drag, the heavier the wheels the worse it is. But given the runaway positive feed back control system it can't win. It can't accelerate to take off speed.
Given that the problem suspends reality by talking about frictionless bearings and instantaneous control loop we could be forgiven for assuming wheels of zero mass in which case there is no reverse drag due to wheel inertia and the plane flies again:)
We could also assume frictionless contact between wheels and conveyor, in which case the wheels never even start to rotate and the conveyor stays stationary as a result. And the plane flies?
By the way, the Myth busters experiment seems flawed they seem to be dragging the conveyor backwards at a speed to match the forward speed of the plane. But our problem does not use linear plane speed but wheel angular velocity.
Just notice your post:
I think my suggested experiment above shows is does have an influence. Not so clear any more, what assumptions are we allowed to make?
the wheels will have travelled many more times the distance that the aircraft would have due to the two totally different action /reactions as pointed out so elegantly by Ron in post #42
Assumptions are the name of the game with this scenario I believe as it can throw up many combinations of thought processes but there is only one correct solution.................AFAIK
Do the experiment with the rolling pin I suggested. It will convince you that because the wheels have mass and hence moment of inertia, and because the wheels have frictional contact with the conveyor the conveyor can indeed have influence on the linear motion of the plane along the runway, not just the thrusters.
As the control system seems to be set up to provide a huge pull backwards on the conveyor for the smallest forward movement of the plane this effect could overwhelm the thrusters and stop the plane taking off. (Unless it can take off in reverse of course)
Cannot be, if I assume frictionless axles, as given, I might feel free to assume frictionless contact between wheel and conveyor (Why not)
In that case the wheels never turn, the conveyor never moves and the plane flies unhindered.
If I assume a lot of friction from wheel to conveyor, and good heavy wheels, that conveyor can have a large influence on the plane by virtue of having to rotate the wheels ever faster. In doing so the wheels will push the plane backwards as in the rolling pin experiment.
-Phil
The new and improved description only states that a dot on the wheels must match dots on the runway. This implies that there is no slippage between the wheels and the runway. However, the description isn't complete enough to actually determine how the runway moves, but it does allow the plane to move freely. Under the new description, the plane can take off.
This "puzzle" is similar to stuff I encounter at work all the time. A customer discovers a problem in one of our systems, and provides either a very vague description of how the problem happens, or they provide a very elaborate description with unnecessary details to reproduce the issue. With the vague description we have to go back and forth with them to find out exactly how they encountered the problem. With the elaborate description we have to weed out the unnecessary stuff so that we don't have to completely reproduce the customer's environment to reproduce the problem.
At some point, Skylight might give us enough details to accurately understand his version of the problem. Of course, once he does that it's no longer a puzzle, and the answer is obvious.
'Kinda like the forum in general!
-Phil
As long as he doesn't start kicking the back of my seat!!!!! ;-)
@
But again, what information is being conveyed? That is... what information originating at point A is received at point B with the arrival of the photon beam? The aliens on planets A and B are only going to see a flash of photons racing by into deep space.
(A tangent from the airplane/conveyor topic, but fun!!)
@
I guess some other people might not understand the question either.
So basically the question is, can you exert force upon something in one direction and expect it to not move that direction because a lesser force is acting upon it in another direction? The answer becomes pretty obvious at that point.
If the jet were to stay still you'd need two equal opposing forces, or no thrust would work too hehe.
Also, look at the energy the treadmill can produce and compare that to the jet. When they're both equal there's a chance but it would require a mechanical connection to the jet like the engine.
the frictionless bearings in the wheels cannot "push" the aircraft as they just slip and spin there is no transfer of a force to the planes fixed axle from the wheels.
Are all mechanical interfaces of infinite strength to handle any thrust applied or overcome any mechanical stresses involved?
How much thrust do I have? Infinite?
If you strap large ENOUGH thrust unit to something, it will fly...it may not be aerodynamic flight and may have nothing to do with air movement over airfoils but IT WILL FLY.
This is getting a bit ridiculous with assumptions. We're almost to the point of "assuming every condition that makes it impossible for the airplane to take off is in effect, can the airplane take off?"
the runway control system is not initially sensing any movement of the wheels and the runway drive is therefore static. The drive rollers have friction obviously with the runway belt.
the drive system is 99.9999999999999999999999999999999999999999999999......add as many digits here as you like.......% efficient and acts almost immediately
The pilot starts the thrusters and pulls the throttle back as normally he would, as far as he is concerned he is flying a normal jet plane on a normal runway (no one told him otherwise).
To counter the arguments that the runway would never start a groundsman observing the jet thrusters working quick as a flash presses a button to kickstart the runway moving in the opposite direction the plane is facing, due to the tyre /runway friction the wheels move and the feedback system takes over.(remember that the bearings are frictionless so no transfer of energy is made with the axle the wheels just freewheel.
Have I missed anything? Hopefully this will satisfy the engineers amongst you
I am surprised that the argument that I am mixing real world physics with fantasy(frictionless bearings) hasn't reared it's head yet, I believe it's this that makes the solution so hard to answer as like physics at this time is hitting the barrier of experimentation versus theoretical it's hard to come to a definitive solution when you don't know all the answers. I have always felt that this scenario fits in well with the above.
Won't the tires eventually break contact with the runway due to air being forced between the tire and runway, just like a hydroplaning car, "airplaning" so to speak.
C.W.
I'm basing this on agreement with Heaters post #123 that a force is applied to the axles in the same direction as the runway is moving whenever the wheels (unless they have no mass) are accelerating.
Phil's argument against this force in #129 only applies if the wheels are at constant speed.
C.W.
How would this be if no friction is in the bearing to transfer the necessary energy to push against the axle and try to stop the aircraft from moving?
In such as case "frictionless" typically applies to rotational motion of the wheel, not translational. Think of a case of typical engineering problems where a frictionless pulley is used, if the axle of the pulley didn't take load the pulley would just fall to the ground, and that isn't the correct answer.
C.W.
But what about the bonds between atoms?
the axle can just sit on the frictionless bearing such as a ski sits on ice or water , but there would be no transfer of energy when the plane or runway moves at that point of contact due to no friction.
lol, no, not really. Think about it, if "frictionless" means that the wheel/axle cannot transfer force to the plane, how do they hold it up.
C.W.
Edit - "Frictionless" is typically used to say that you don't need to account for energy lost as heat due to friction, otherwise relatively simple problems become pretty complex.
There is no snipe, no spoon, no Yeti, no frictionless wheels and certainly no giant treadmills.
So everyone's right. We're all winners today.
No reply necessary!
I'm sorry to inform you that on some forums the arguments went to 30+ pages, can you cope with that?
So who says yes it will take off and who says no?
I still maintain that the plane will take off.
Anytime the jet makes forward progress the speed of the runway will increase causing the wheels to accelerate which will apply a force to the axle in the opposite direction of travel. Due to the problem conditions there is no upper bound to this force so it will always increase to enforce the condition of matching runway speed to wheel speed.
C.W.
To me this implies the condition that for a given rotation of the wheel resulting in a forward motion of dX, the runway will match that by moving -dX.
If we assume that the wheel cannot skid then no matter what justification is used to say that the plane takes of requires the condition to be broken.
C.W.