Mythbusters to take on "the plane and the treadmill" conundrum?

[archiloco]

Originally posted by: MasonLuke

Originally posted by: smack Down

Originally posted by: jimbob200521

Originally posted by: smack Down

Originally posted by: jimbob200521

Originally posted by: MasonLuke

Originally posted by: mugs
Wow MasonLuke, way to look like an idiot and an asshole at the same time. :laugh:

You and everyone else who thinks the plane will take take is sooooo stupid.
Stubborn little $hits

Kids, please dont forget the original premise that the treadmill moves in the equal and opposite direction of the wheels.

Once again kids, plane needs forward movement to get lift. Without it, a plane cannot take off. you kids ever watch a plane take off from a carrier? it its catapulted FORWARD and without that forward movement there is no lift.

When the wheels spin on the treadmill, the treadmill is moving in the exact opposite speed and direction, so the plane is stationary. no forward movement, no lift, no flight.
/end

please dont be stupid all your life, and listen to reason. stop with the friction or tighing a rope and pulling it forward or whatever it may be.

This is going to be my last response to one of your posts as you clearly do not understand this.

You say that the plane needs forward motion to take off. Correct, no one is arguing that it does not. What people (you) are arguing over is whether or not the plane would have forward movement in the given scenario. The answer is that it would have forward movement b/c the jets/propeller propel the plane forward. The wheels on the plane are not going to do enough to stop the plane.

You say that in the original problem, "the treadmill moves in equal and opposite direction of the wheels". Although what you said is true, it is also true that it was stated in the original problem is that it (treadmill) would match the planes speed in the opposite direction. Since ground speed is different than air speed (air speed is not effected (enough) by ground speed to matter), the plane would continue to move. Also remember that force is different than wheel speed. The wheels on the plane will be turning at the opposite speed, not force, that the plane is moving. The wheels will turn really really fast, that is all.

Finally, I would like to refer to a previous statement I made:

For those that say that the plane would not take off, do you realize that you are saying that a plane is driven via it's wheels?

Do you realize that that is what you are saying, MasonLuke?

No one is saying a plane is driving by it wheels.

The question is if the treadmill matches the speed of the plane relative to the treadmill surface (ie speed the wheels see) -- Plane doesn't take off OR the treadmill matches the ground speed of the plane -- Plane takes off.

You are correct and incorrect at the same time, let me explain...

You said that

"The question is if the treadmill matches the speed of the plane relative to the treadmill surface (ie speed the wheels see) -- Plane doesn't take off"

The statement you made is correct, the treadmill would match the planes speed relative to the treadmill. The conclusion you came to is incorrect, however; the plane would take off. The treadmill would be matching the planes forward speed by spinning in the opposite direction of the plane at an equal speed. So if the plane is going forward at 100mph, the treadmill would be going the opposite direction at 100mph, meaning the wheels on the plane would move at 200mph.

So, could you explain to me how the wheels would stop the plane (if you are of the belief that the plane would not take off, that is)?

Wow, please reread what you just wrote. Simply by definition of the problem that why forward movement is impossible. In your example you broke the condition requiring the treadmill to match the wheel speed by having the wheel go at 200 mph yet the treadmill is only running at 100 mph .

LOL

Sorry kids for calling you stupid, but hopefully you have learned something from all this.
You dont know not because you are stupid, but because you are ignorant. Remember, learning is half the battle.

but you are assuming the wheels are a frictionless vehicle for the forward thrust of the jet engines (imagine no wheels there would be so much friction). that is their purpose to provide a frictionless surface for the jet engines to do their thing. but what if they can't go forward (the treadmill negating the wheels spin) no forward movement. that's just my two cents.

 

[jimbob200521]

Originally posted by: smack Down

Originally posted by: jimbob200521

Originally posted by: smack Down

Originally posted by: jimbob200521

Originally posted by: MasonLuke

Originally posted by: mugs
Wow MasonLuke, way to look like an idiot and an asshole at the same time. :laugh:

You and everyone else who thinks the plane will take take is sooooo stupid.
Stubborn little $hits

Kids, please dont forget the original premise that the treadmill moves in the equal and opposite direction of the wheels.

Once again kids, plane needs forward movement to get lift. Without it, a plane cannot take off. you kids ever watch a plane take off from a carrier? it its catapulted FORWARD and without that forward movement there is no lift.

When the wheels spin on the treadmill, the treadmill is moving in the exact opposite speed and direction, so the plane is stationary. no forward movement, no lift, no flight.
/end

please dont be stupid all your life, and listen to reason. stop with the friction or tighing a rope and pulling it forward or whatever it may be.

This is going to be my last response to one of your posts as you clearly do not understand this.

You say that the plane needs forward motion to take off. Correct, no one is arguing that it does not. What people (you) are arguing over is whether or not the plane would have forward movement in the given scenario. The answer is that it would have forward movement b/c the jets/propeller propel the plane forward. The wheels on the plane are not going to do enough to stop the plane.

You say that in the original problem, "the treadmill moves in equal and opposite direction of the wheels". Although what you said is true, it is also true that it was stated in the original problem is that it (treadmill) would match the planes speed in the opposite direction. Since ground speed is different than air speed (air speed is not effected (enough) by ground speed to matter), the plane would continue to move. Also remember that force is different than wheel speed. The wheels on the plane will be turning at the opposite speed, not force, that the plane is moving. The wheels will turn really really fast, that is all.

Finally, I would like to refer to a previous statement I made:

For those that say that the plane would not take off, do you realize that you are saying that a plane is driven via it's wheels?

Do you realize that that is what you are saying, MasonLuke?

No one is saying a plane is driving by it wheels.

The question is if the treadmill matches the speed of the plane relative to the treadmill surface (ie speed the wheels see) -- Plane doesn't take off OR the treadmill matches the ground speed of the plane -- Plane takes off.

You are correct and incorrect at the same time, let me explain...

You said that

"The question is if the treadmill matches the speed of the plane relative to the treadmill surface (ie speed the wheels see) -- Plane doesn't take off"

The statement you made is correct, the treadmill would match the planes speed relative to the treadmill. The conclusion you came to is incorrect, however; the plane would take off. The treadmill would be matching the planes forward speed by spinning in the opposite direction of the plane at an equal speed. So if the plane is going forward at 100mph, the treadmill would be going the opposite direction at 100mph, meaning the wheels on the plane would move at 200mph.

So, could you explain to me how the wheels would stop the plane (if you are of the belief that the plane would not take off, that is)?

Wow, please reread what you just wrote. Simply by definition of the problem that why forward movement is impossible. In your example you broke the condition requiring the treadmill to match the wheel speed by having the wheel go at 200 mph yet the treadmill is only running at 100 mph .

If you go by that logic, then the problem itself is impossible. The wheels would spin at the speed of infinite.

But I do see what you are saying. My wording may have been poor, so let me try again.

The treadmill, as I understand it, is supposed to match the speed of the plane, not the speed of the wheels. That is quite a difference, and my mistake.

So if the plane is moving at 100mph the the treadmill would move at 100mph in the opposite direction. So as a result, the wheels would just spin super fast.

 

[smack Down]

Originally posted by: jimbob200521

Originally posted by: smack Down

Originally posted by: jimbob200521

Originally posted by: smack Down

Originally posted by: jimbob200521

Originally posted by: MasonLuke

Originally posted by: mugs
Wow MasonLuke, way to look like an idiot and an asshole at the same time. :laugh:

You and everyone else who thinks the plane will take take is sooooo stupid.
Stubborn little $hits

Kids, please dont forget the original premise that the treadmill moves in the equal and opposite direction of the wheels.

Once again kids, plane needs forward movement to get lift. Without it, a plane cannot take off. you kids ever watch a plane take off from a carrier? it its catapulted FORWARD and without that forward movement there is no lift.

When the wheels spin on the treadmill, the treadmill is moving in the exact opposite speed and direction, so the plane is stationary. no forward movement, no lift, no flight.
/end

please dont be stupid all your life, and listen to reason. stop with the friction or tighing a rope and pulling it forward or whatever it may be.

This is going to be my last response to one of your posts as you clearly do not understand this.

You say that the plane needs forward motion to take off. Correct, no one is arguing that it does not. What people (you) are arguing over is whether or not the plane would have forward movement in the given scenario. The answer is that it would have forward movement b/c the jets/propeller propel the plane forward. The wheels on the plane are not going to do enough to stop the plane.

You say that in the original problem, "the treadmill moves in equal and opposite direction of the wheels". Although what you said is true, it is also true that it was stated in the original problem is that it (treadmill) would match the planes speed in the opposite direction. Since ground speed is different than air speed (air speed is not effected (enough) by ground speed to matter), the plane would continue to move. Also remember that force is different than wheel speed. The wheels on the plane will be turning at the opposite speed, not force, that the plane is moving. The wheels will turn really really fast, that is all.

Finally, I would like to refer to a previous statement I made:

For those that say that the plane would not take off, do you realize that you are saying that a plane is driven via it's wheels?

Do you realize that that is what you are saying, MasonLuke?

No one is saying a plane is driving by it wheels.

The question is if the treadmill matches the speed of the plane relative to the treadmill surface (ie speed the wheels see) -- Plane doesn't take off OR the treadmill matches the ground speed of the plane -- Plane takes off.

You are correct and incorrect at the same time, let me explain...

You said that

"The question is if the treadmill matches the speed of the plane relative to the treadmill surface (ie speed the wheels see) -- Plane doesn't take off"

The statement you made is correct, the treadmill would match the planes speed relative to the treadmill. The conclusion you came to is incorrect, however; the plane would take off. The treadmill would be matching the planes forward speed by spinning in the opposite direction of the plane at an equal speed. So if the plane is going forward at 100mph, the treadmill would be going the opposite direction at 100mph, meaning the wheels on the plane would move at 200mph.

So, could you explain to me how the wheels would stop the plane (if you are of the belief that the plane would not take off, that is)?

Wow, please reread what you just wrote. Simply by definition of the problem that why forward movement is impossible. In your example you broke the condition requiring the treadmill to match the wheel speed by having the wheel go at 200 mph yet the treadmill is only running at 100 mph .

If you go by that logic, then the problem itself is impossible. The wheels would spin at the speed of infinite.

But I do see what you are saying. My wording may have been poor, so let me try again.

The treadmill, as I understand it, is supposed to match the speed of the plane, not the speed of the wheels. That is quite a difference, and my mistake.

So if the plane is moving at 100mph the the treadmill would move at 100mph in the opposite direction. So as a result, the wheels would just spin super fast.

Like I said there are two ways to read the question.

 

[JasonVaritekMVP]

I beg you please read this.

Ok, I have been reading this internet-age-old argument for a while now and I can stay silent no longer. For the record, I would like to mention that I will be graduating in May with a BSME and part of my career will be modeling mechanical systems. While I have not read all 34 pages of this thread I have read the entireties of other threads on this topic and I have yet to see an explanation that properly describes the problem.

As a matter of form I am going to restate the problem so that there is no ambiguity with regard to my post.

As we all know by know we have an airplane on a conveyor belt. The belt will move at a speed equal and opposite to the tangential speed of the surface of the wheels. The question is will the plane take off. The plane WILL take off as seen below. I will put in a warning however that this is going to be an extremely detailed and overly exact analysis for the purpose of introducing, and then answering any objections.

The reason for the confusion regarding this problem (among the objective crowd, no argument will convince someone who is intent on believing to the contrary despite any argument or evidence) is due to a lack of proper modeling of the system.

First the Assumptions:
1) The entirety of the plane other than the wheels themselves will be treated as a rigid body. This means the object will not deform due to any force applied to it. This also means that any displacement, linear or rotational will be consistent throughout the object. This appears to be irrelevant for the problem but I include this for the sake of precision.
2) The conveyer belt will move perfectly equal and opposite to the wheels. In the real world a closed loop control system would be required to achieve this and despite any ideal design the response would never be perfect. Put another way we will ignore the time delay that would be present in a system of this type.

Note the following refer to 2D modeling which is all that is required to analyze this problem: the axis parallel to the planes desired motion and that perpendicular to the ground are all that is required.

3) The wheels on the plane are free spinning ? this is really where any confusion lies within this problem. The problem is uncertainty with what EXACTLY this means. Assuming a frictionless wheel acts as a ?Pin Support? ? Both x and y forces can be transmitted through this connection. A Moment (or torque) cannot be transmitted through this however. This is key, rotational forces cannot be transmitted through this connection.
4) The interface between the wheel and the treadmill is a ?Contact with a rough surface? ? this means force transmission for both Normal and Tangential to the supporting surface.
The contact definitions for 2D supports was found in ?Engineering Mechanics ? Statics and Dynamics, Bedford and Fowler, 4th edition?

Before we analyze the problem statement I would like to describe a similar problem

Suppose we have an identical plane, on an identical conveyor-runway but the plane has no engines. I think at this point we have established the fact that the thrust comes from the engines and not the wheels. If you turn on the conveyor given the connection interfaces described above, the wheels WILL SPIN equal and opposite to the motion of the conveyor, this rotation is caused by a force applied to a location away from the center of mass of the object. In order to prevent translational motion, a rotating body requires a force couple. In this example the inertial mass of the plane is so many orders of magnitude above the effective x force acting on the plane, that secondary order effects such as air resistance will negate any already negligible movement. This completes the couple. The plane will not move because the primary activity in this connection is rotational and there is no rotational force transmission between the wheels and the plane.

As previously stated the connection types are key, the plane will not move in the X because there are (practically) no forces acting in the X direction on the plane.

The friction between the conveyor and the wheel causes the wheel to rotate, but that is where the motion of the system ends given a frictionless contact between the wheel and the plane. The moment any brakes are applied however the nature of the interface between the plane and the wheel changes and the wheels stops rotating, this means the entirety of the force applied on the wheel from the conveyor acts to move the plane linearly rather than simply spinning the wheel.
A plane with its brakes off given ideal (frictionless pin connection) wheels will not move no matter how fast the conveyor moves.
A plane with its brakes ON will move with the conveyor however the wheels will not spin.

Many have previously mentioned that the engines, not the wheels are responsible for the trust. What is equally if not MORE important is that this relationship goes the other way around, not only do the wheels not act in such a way to move the plane, the ground cannot move the wheels in such a way that the plane moves.

TURN THE ENGINES ON!!!

The only change in the system is that there is now a force acting in the x direction, namely that of the engine thrust. This causes the plane to move in the x direction.
The wheels spinning in the opposite direction are irrelevant as they have no means to impede the translation of the plane. All that happens is they spin really fast backwards while the plane moves forward.

I have ignored takeoff for now because as previously stated an airplane takes off due to lift generated from a pressure differential caused by airflow across the wing. To be very specific, Airfoils are designed such that the path of travel for air is greater above the wing than below the wing, this means the air above the wing must move faster to cover the distance in the same time, and to make fluid dynamics very simple, as velocity increases pressure decreases. The velocity above the wing is higher than the velocity below the wing, the pressure above the wing is lower than that below the wing, and thus lift causes the plane to takeoff.

As long as the plane moves laterally airflow will be present to create lift. So really the only problem that has to be answered is will the plane move laterally with respect to the surrounding air.

Now the real world is not perfect, pin connections are not completely frictionless, but the differences between the real world plane and the idealized version are not so much that the plane will not be able to move laterally preventing takeoff.

Thank you for reading the whole damn thing,

Dave

 

[oznerol]

Originally posted by: JasonVaritekMVP
I beg you please read this.

Ok, I have been reading this internet-age-old argument for a while now and I can stay silent no longer. For the record, I would like to mention that I will be graduating in May with a BSME and part of my career will be modeling mechanical systems. While I have not read all 34 pages of this thread I have read the entireties of other threads on this topic and I have yet to see an explanation that properly describes the problem.

As a matter of form I am going to restate the problem so that there is no ambiguity with regard to my post.

As we all know by know we have an airplane on a conveyor belt. The belt will move at a speed equal and opposite to the tangential speed of the surface of the wheels. The question is will the plane take off. The plane WILL take off as seen below. I will put in a warning however that this is going to be an extremely detailed and overly exact analysis for the purpose of introducing, and then answering any objections.

The reason for the confusion regarding this problem (among the objective crowd, no argument will convince someone who is intent on believing to the contrary despite any argument or evidence) is due to a lack of proper modeling of the system.

First the Assumptions:
1) The entirety of the plane other than the wheels themselves will be treated as a rigid body. This means the object will not deform due to any force applied to it. This also means that any displacement, linear or rotational will be consistent throughout the object. This appears to be irrelevant for the problem but I include this for the sake of precision.
2) The conveyer belt will move perfectly equal and opposite to the wheels. In the real world a closed loop control system would be required to achieve this and despite any ideal design the response would never be perfect. Put another way we will ignore the time delay that would be present in a system of this type.

Note the following refer to 2D modeling which is all that is required to analyze this problem: the axis parallel to the planes desired motion and that perpendicular to the ground are all that is required.

3) The wheels on the plane are free spinning ? this is really where any confusion lies within this problem. The problem is uncertainty with what EXACTLY this means. Assuming a frictionless wheel acts as a ?Pin Support? ? Both x and y forces can be transmitted through this connection. A Moment (or torque) cannot be transmitted through this however. This is key, rotational forces cannot be transmitted through this connection.
4) The interface between the wheel and the treadmill is a ?Contact with a rough surface? ? this means force transmission for both Normal and Tangential to the supporting surface.
The contact definitions for 2D supports was found in ?Engineering Mechanics ? Statics and Dynamics, Bedford and Fowler, 4th edition?

Before we analyze the problem statement I would like to describe a similar problem

Suppose we have an identical plane, on an identical conveyor-runway but the plane has no engines. I think at this point we have established the fact that the thrust comes from the engines and not the wheels. If you turn on the conveyor given the connection interfaces described above, the wheels WILL SPIN equal and opposite to the motion of the conveyor, this rotation is caused by a force applied to a location away from the center of mass of the object. In order to prevent translational motion, a rotating body requires a force couple. In this example the inertial mass of the plane is so many orders of magnitude above the effective x force acting on the plane, that secondary order effects such as air resistance will negate any already negligible movement. This completes the couple. The plane will not move because the primary activity in this connection is rotational and there is no rotational force transmission between the wheels and the plane.

As previously stated the connection types are key, the plane will not move in the X because there are (practically) no forces acting in the X direction on the plane.

The friction between the conveyor and the wheel causes the wheel to rotate, but that is where the motion of the system ends given a frictionless contact between the wheel and the plane. The moment any brakes are applied however the nature of the interface between the plane and the wheel changes and the wheels stops rotating, this means the entirety of the force applied on the wheel from the conveyor acts to move the plane linearly rather than simply spinning the wheel.
A plane with its brakes off given ideal (frictionless pin connection) wheels will not move no matter how fast the conveyor moves.
A plane with its brakes ON will move with the conveyor however the wheels will not spin.

Many have previously mentioned that the engines, not the wheels are responsible for the trust. What is equally if not MORE important is that this relationship goes the other way around, not only do the wheels not act in such a way to move the plane, the ground cannot move the wheels in such a way that the plane moves.

TURN THE ENGINES ON!!!

The only change in the system is that there is now a force acting in the x direction, namely that of the engine thrust. This causes the plane to move in the x direction.
The wheels spinning in the opposite direction are irrelevant as they have no means to impede the translation of the plane. All that happens is they spin really fast backwards while the plane moves forward.

I have ignored takeoff for now because as previously stated an airplane takes off due to lift generated from a pressure differential caused by airflow across the wing. To be very specific, Airfoils are designed such that the path of travel for air is greater above the wing than below the wing, this means the air above the wing must move faster to cover the distance in the same time, and to make fluid dynamics very simple, as velocity increases pressure decreases. The velocity above the wing is higher than the velocity below the wing, the pressure above the wing is lower than that below the wing, and thus lift causes the plane to takeoff.

As long as the plane moves laterally airflow will be present to create lift. So really the only problem that has to be answered is will the plane move laterally with respect to the surrounding air.

Now the real world is not perfect, pin connections are not completely frictionless, but the differences between the real world plane and the idealized version are not so much that the plane will not be able to move laterally preventing takeoff.

Thank you for reading the whole damn thing,

Dave

Alright, you sound smart. I am not disagreeing with you. I just have a question, and it's really all that bothers me about this scenario:

If the wheels are spinning, and the treadmill is going, all while the engines are pushing the plane forward - wouldn't this cause the wheels to "slide" on the surface of the treadmill?

For example, if I'm on rollerblades on a treadmill and I'm holding a rope attached to a pole in front of me, and I pull forward, the wheels would undoubtedly slide. How is that any different in this case?

I was under the impression the question declared that there was no sliding of the wheels, so I'm just wondering what the explanation for that would be. Thanks man.

:beer:

 

[shortylickens]

Alright, I didnt watch that episode of Mythbusters, (actually, I dont watch TV at all, unless its softcore porn).

Can somebody tell me how it went and what they determined and why?

I got sore eyeballs reading this thread and trying to find the results from the show.

 

[smack Down]

Suppose we have an identical plane, on an identical conveyor-runway but the plane has no engines. I think at this point we have established the fact that the thrust comes from the engines and not the wheels. If you turn on the conveyor given the connection interfaces described above, the wheels WILL SPIN equal and opposite to the motion of the conveyor, this rotation is caused by a force applied to a location away from the center of mass of the object. In order to prevent translational motion, a rotating body requires a force couple. In this example the inertial mass of the plane is so many orders of magnitude above the effective x force acting on the plane, that secondary order effects such as air resistance will negate any already negligible movement. This completes the couple.

If I read this right you are saying the force for the wheels is so small it can be ignored. I'm not sure you are correct in ignoring such a force unless you can show it is bounded. If the force isn't bounded then it is infinite because the treadmill will make it so.

 

[So]

Originally posted by: archiloco

Originally posted by: MasonLuke

Originally posted by: smack Down

Originally posted by: jimbob200521

Originally posted by: smack Down

Originally posted by: jimbob200521

Originally posted by: MasonLuke

Originally posted by: mugs
Wow MasonLuke, way to look like an idiot and an asshole at the same time. :laugh:

You and everyone else who thinks the plane will take take is sooooo stupid.
Stubborn little $hits

Kids, please dont forget the original premise that the treadmill moves in the equal and opposite direction of the wheels.

Once again kids, plane needs forward movement to get lift. Without it, a plane cannot take off. you kids ever watch a plane take off from a carrier? it its catapulted FORWARD and without that forward movement there is no lift.

When the wheels spin on the treadmill, the treadmill is moving in the exact opposite speed and direction, so the plane is stationary. no forward movement, no lift, no flight.
/end

please dont be stupid all your life, and listen to reason. stop with the friction or tighing a rope and pulling it forward or whatever it may be.

This is going to be my last response to one of your posts as you clearly do not understand this.

You say that the plane needs forward motion to take off. Correct, no one is arguing that it does not. What people (you) are arguing over is whether or not the plane would have forward movement in the given scenario. The answer is that it would have forward movement b/c the jets/propeller propel the plane forward. The wheels on the plane are not going to do enough to stop the plane.

You say that in the original problem, "the treadmill moves in equal and opposite direction of the wheels". Although what you said is true, it is also true that it was stated in the original problem is that it (treadmill) would match the planes speed in the opposite direction. Since ground speed is different than air speed (air speed is not effected (enough) by ground speed to matter), the plane would continue to move. Also remember that force is different than wheel speed. The wheels on the plane will be turning at the opposite speed, not force, that the plane is moving. The wheels will turn really really fast, that is all.

Finally, I would like to refer to a previous statement I made:

For those that say that the plane would not take off, do you realize that you are saying that a plane is driven via it's wheels?

Do you realize that that is what you are saying, MasonLuke?

No one is saying a plane is driving by it wheels.

The question is if the treadmill matches the speed of the plane relative to the treadmill surface (ie speed the wheels see) -- Plane doesn't take off OR the treadmill matches the ground speed of the plane -- Plane takes off.

You are correct and incorrect at the same time, let me explain...

You said that

"The question is if the treadmill matches the speed of the plane relative to the treadmill surface (ie speed the wheels see) -- Plane doesn't take off"

The statement you made is correct, the treadmill would match the planes speed relative to the treadmill. The conclusion you came to is incorrect, however; the plane would take off. The treadmill would be matching the planes forward speed by spinning in the opposite direction of the plane at an equal speed. So if the plane is going forward at 100mph, the treadmill would be going the opposite direction at 100mph, meaning the wheels on the plane would move at 200mph.

So, could you explain to me how the wheels would stop the plane (if you are of the belief that the plane would not take off, that is)?

Wow, please reread what you just wrote. Simply by definition of the problem that why forward movement is impossible. In your example you broke the condition requiring the treadmill to match the wheel speed by having the wheel go at 200 mph yet the treadmill is only running at 100 mph .

LOL

Sorry kids for calling you stupid, but hopefully you have learned something from all this.
You dont know not because you are stupid, but because you are ignorant. Remember, learning is half the battle.

but you are assuming the wheels are a frictionless vehicle for the forward thrust of the jet engines (imagine no wheels there would be so much friction). that is their purpose to provide a frictionless surface for the jet engines to do their thing. but what if they can't go forward (the treadmill negating the wheels spin) no forward movement. that's just my two cents.

If you treat the wheels as frictionless, no speed of the treadmill can negate the engine force. If you treat the wheels as if they have bearing w/ friction, the speed is still high enough that the plane will almost 100% certainly take off.

If you treat the treadmill as matching the speed of the wheels instead of the fuselage, then you have a paradox, and the problem is nonsensical, since the wheels will instantly be traveling at infinite speed.

 

[So]

Originally posted by: ducci

Originally posted by: JasonVaritekMVP
I beg you please read this.

Ok, I have been reading this internet-age-old argument for a while now and I can stay silent no longer. For the record, I would like to mention that I will be graduating in May with a BSME and part of my career will be modeling mechanical systems. While I have not read all 34 pages of this thread I have read the entireties of other threads on this topic and I have yet to see an explanation that properly describes the problem.

As a matter of form I am going to restate the problem so that there is no ambiguity with regard to my post.

As we all know by know we have an airplane on a conveyor belt. The belt will move at a speed equal and opposite to the tangential speed of the surface of the wheels. The question is will the plane take off. The plane WILL take off as seen below. I will put in a warning however that this is going to be an extremely detailed and overly exact analysis for the purpose of introducing, and then answering any objections.

The reason for the confusion regarding this problem (among the objective crowd, no argument will convince someone who is intent on believing to the contrary despite any argument or evidence) is due to a lack of proper modeling of the system.

First the Assumptions:
1) The entirety of the plane other than the wheels themselves will be treated as a rigid body. This means the object will not deform due to any force applied to it. This also means that any displacement, linear or rotational will be consistent throughout the object. This appears to be irrelevant for the problem but I include this for the sake of precision.
2) The conveyer belt will move perfectly equal and opposite to the wheels. In the real world a closed loop control system would be required to achieve this and despite any ideal design the response would never be perfect. Put another way we will ignore the time delay that would be present in a system of this type.

Note the following refer to 2D modeling which is all that is required to analyze this problem: the axis parallel to the planes desired motion and that perpendicular to the ground are all that is required.

3) The wheels on the plane are free spinning ? this is really where any confusion lies within this problem. The problem is uncertainty with what EXACTLY this means. Assuming a frictionless wheel acts as a ?Pin Support? ? Both x and y forces can be transmitted through this connection. A Moment (or torque) cannot be transmitted through this however. This is key, rotational forces cannot be transmitted through this connection.
4) The interface between the wheel and the treadmill is a ?Contact with a rough surface? ? this means force transmission for both Normal and Tangential to the supporting surface.
The contact definitions for 2D supports was found in ?Engineering Mechanics ? Statics and Dynamics, Bedford and Fowler, 4th edition?

Before we analyze the problem statement I would like to describe a similar problem

Suppose we have an identical plane, on an identical conveyor-runway but the plane has no engines. I think at this point we have established the fact that the thrust comes from the engines and not the wheels. If you turn on the conveyor given the connection interfaces described above, the wheels WILL SPIN equal and opposite to the motion of the conveyor, this rotation is caused by a force applied to a location away from the center of mass of the object. In order to prevent translational motion, a rotating body requires a force couple. In this example the inertial mass of the plane is so many orders of magnitude above the effective x force acting on the plane, that secondary order effects such as air resistance will negate any already negligible movement. This completes the couple. The plane will not move because the primary activity in this connection is rotational and there is no rotational force transmission between the wheels and the plane.

As previously stated the connection types are key, the plane will not move in the X because there are (practically) no forces acting in the X direction on the plane.

The friction between the conveyor and the wheel causes the wheel to rotate, but that is where the motion of the system ends given a frictionless contact between the wheel and the plane. The moment any brakes are applied however the nature of the interface between the plane and the wheel changes and the wheels stops rotating, this means the entirety of the force applied on the wheel from the conveyor acts to move the plane linearly rather than simply spinning the wheel.
A plane with its brakes off given ideal (frictionless pin connection) wheels will not move no matter how fast the conveyor moves.
A plane with its brakes ON will move with the conveyor however the wheels will not spin.

Many have previously mentioned that the engines, not the wheels are responsible for the trust. What is equally if not MORE important is that this relationship goes the other way around, not only do the wheels not act in such a way to move the plane, the ground cannot move the wheels in such a way that the plane moves.

TURN THE ENGINES ON!!!

The only change in the system is that there is now a force acting in the x direction, namely that of the engine thrust. This causes the plane to move in the x direction.
The wheels spinning in the opposite direction are irrelevant as they have no means to impede the translation of the plane. All that happens is they spin really fast backwards while the plane moves forward.

I have ignored takeoff for now because as previously stated an airplane takes off due to lift generated from a pressure differential caused by airflow across the wing. To be very specific, Airfoils are designed such that the path of travel for air is greater above the wing than below the wing, this means the air above the wing must move faster to cover the distance in the same time, and to make fluid dynamics very simple, as velocity increases pressure decreases. The velocity above the wing is higher than the velocity below the wing, the pressure above the wing is lower than that below the wing, and thus lift causes the plane to takeoff.

As long as the plane moves laterally airflow will be present to create lift. So really the only problem that has to be answered is will the plane move laterally with respect to the surrounding air.

Now the real world is not perfect, pin connections are not completely frictionless, but the differences between the real world plane and the idealized version are not so much that the plane will not be able to move laterally preventing takeoff.

Thank you for reading the whole damn thing,

Dave

Alright, you sound smart. I am not disagreeing with you. I just have a question, and it's really all that bothers me about this scenario:

If the wheels are spinning, and the treadmill is going, all while the engines are pushing the plane forward - wouldn't this cause the wheels to "slide" on the surface of the treadmill?

For example, if I'm on rollerblades on a treadmill and I'm holding a rope attached to a pole in front of me, and I pull forward, the wheels would undoubtedly slide. How is that any different in this case?

I was under the impression the question declared that there was no sliding of the wheels, so I'm just wondering what the explanation for that would be. Thanks man.

:beer:

He is correct -- and the wheels simply will turn faster.

 

[smack Down]

If you treat the treadmill as matching the speed of the wheels instead of the fuselage, then you have a paradox, and the problem is nonsensical, since the wheels will instantly be traveling at infinite speed.

That is only true if you assume the wheels can't apply a force to the plane.

 

[sao123]

Originally posted by: ducci
Alright, you sound smart. I am not disagreeing with you. I just have a question, and it's really all that bothers me about this scenario:

If the wheels are spinning, and the treadmill is going, all while the engines are pushing the plane forward - wouldn't this cause the wheels to "slide" on the surface of the treadmill?

For example, if I'm on rollerblades on a treadmill and I'm holding a rope attached to a pole in front of me, and I pull forward, the wheels would undoubtedly slide. How is that any different in this case?

I was under the impression the question declared that there was no sliding of the wheels, so I'm just wondering what the explanation for that would be. Thanks man.

:beer:

The wheels will not slide.... the wheels simply turn faster.
They do not have a theoretical maximal velocity cap.

Originally posted by: smack Down

Suppose we have an identical plane, on an identical conveyor-runway but the plane has no engines. I think at this point we have established the fact that the thrust comes from the engines and not the wheels. If you turn on the conveyor given the connection interfaces described above, the wheels WILL SPIN equal and opposite to the motion of the conveyor, this rotation is caused by a force applied to a location away from the center of mass of the object. In order to prevent translational motion, a rotating body requires a force couple. In this example the inertial mass of the plane is so many orders of magnitude above the effective x force acting on the plane, that secondary order effects such as air resistance will negate any already negligible movement. This completes the couple.

If I read this right you are saying the force for the wheels is so small it can be ignored. I'm not sure you are correct in ignoring such a force unless you can show it is bounded. If the force isn't bounded then it is infinite because the treadmill will make it so.

This number is bounded.
the maximal amount of force capable of being transferred through the rotational axel is equal to the frictional force of that same system.
Since the frictional equation is
F = u * N
u is the coefficient of friction = approximately .05 (for lubricated steel bearings)
N is the perpendicular force = mass of the plane * 9.8M/s^2
regardless of these values, this number is constant, and does not change with repesct to any velocity of the plane, treadmill, or other.

 

[So]

Originally posted by: smack Down

If you treat the treadmill as matching the speed of the wheels instead of the fuselage, then you have a paradox, and the problem is nonsensical, since the wheels will instantly be traveling at infinite speed.

That is only true if you assume the wheels can't apply a force to the plane.

What? No. A it's still a paradox.

 

[gsellis]

Originally posted by: So

Originally posted by: smack Down

If you treat the treadmill as matching the speed of the wheels instead of the fuselage, then you have a paradox, and the problem is nonsensical, since the wheels will instantly be traveling at infinite speed.

That is only true if you assume the wheels can't apply a force to the plane.

What? No. A it's still a paradox.

The only paradox is a place where you can park two boats.

I like the "kids" part. Great chance I am actually older than MasonLuke. I sure understand physical systems better.

 

[MasonLuke]

Most of you kids are not familiar with a plane, so lets relate this to a car. During a smog check your drive wheels are on a roller. Mind you that this is a primitive device and nothing like the treadmill. The treadmill can counter the exact speed of the wheel. When you press the gas, wheels turn, but the car is not in motion. Now imagine 2 rollers, one for the front wheel and one for the back, or just one long one like our treadmill.

Now, instead of the piston engine connected to the wheels, you have one of the jet powered cars. Thrust comes from the jet and is not powering the wheels as in the case of our airplane. More power you turn on the faster the rollers rotate. The car is stationary. If the car is stationary, the plane will be to. And without forward movement, no lift on wings, thus no flight.

 

[So]

Originally posted by: MasonLuke


Most of you kids are not familiar with a plane, so lets relate this to a car. During a smog check your drive wheels are on a roller. Mind you that this is a primitive device and nothing like the treadmill. The treadmill can counter the exact speed of the wheel. When you press the gas, wheels turn, but the car is not in motion. Now imagine 2 rollers, one for the front wheel and one for the back, or just one long one like our treadmill.

Now, instead of the piston engine connected to the wheels, you have one of the jet powered cars. Thrust comes from the jet and is not powering the wheels as in the case of our airplane. More power you turn on the faster the rollers rotate. The car is stationary. If the car is stationary, the plane will be to. And without forward movement, no lift on wings, thus no flight.

You just demonstrated that you have no clue about the difference between a plane and a car, and I'm sure a jet car would roll right off the rollers too.

 

[gsellis]

Originally posted by: MasonLuke


Most of you kids are not familiar with a plane, so lets relate this to a car. During a smog check your drive wheels are on a roller. Mind you that this is a primitive device and nothing like the treadmill. The treadmill can counter the exact speed of the wheel. When you press the gas, wheels turn, but the car is not in motion. Now imagine 2 rollers, one for the front wheel and one for the back, or just one long one like our treadmill.

Now, instead of the piston engine connected to the wheels, you have one of the jet powered cars. Thrust comes from the jet and is not powering the wheels as in the case of our airplane. More power you turn on the faster the rollers rotate. The car is stationary. If the car is stationary, the plane will be to. And without forward movement, no lift on wings, thus no flight.

Little whippersnapper, you have no clue. Thrust is independent of the force applied to the rod that holds the tire in place. The force that the treadmill puts on the tire rotates the tire. Try it. HOLD a Hotwheels car in you hand and put a wheel against the chuck of a drill. Can you move the car if you speed up the drill even more than you are moving the car? The answer is YES, even though you think otherwise. The thrust of an airplane is your hand. The wheel, while having some force translation due to friction, is not effecting your hand significantly.

 

[MasonLuke]

It takes a man to admit he is wrong, thats why i call you kids. anyways, i proved my point that the plane will not fly.

i work in the epicenter of the aerospace industry. Hughes, Raytheon, L3, Boeing, Northrop Grumman, ect are right here. We have engineers with Phds, and i'm embarrass to say, but i did consult with several of them right now and basically they told me to stop playing with these kids. BUT ALL OF THEM SAID THE PLANE CANNOT FLY!

it ends here.

Thank you, and when halloween rolls by, come trick or treatn by my house :beer:

 

[gsellis]

Originally posted by: MasonLuke
It takes a man to admit he is wrong, thats why i call you kids. anyways, i proved my point that the plane will not fly.

i work in the epicenter of the aerospace industry. Hughes, Raytheon, L3, Boeing, Northrop Grumman, ect are right here. We have engineers with Phds, and i'm embarrass to say, but i did consult with several of them right now and basically they told me to stop playing with these kids. BUT ALL OF THEM SAID THE PLANE CANNOT FLY!

it ends here.

Thank you, and when halloween rolls by, come trick or treatn by my house :beer:

Epicenter of aerospace? Rigggghhhttttt..... I guess those folks you consulted are working on the lav systems.

 

[MasonLuke]

dont you think its time to stop jacking off and find a girlfriend?

stubborn little $hits.

 

[Jeff7]

Originally posted by: So

Originally posted by: MasonLuke


Most of you kids are not familiar with a plane, so lets relate this to a car. During a smog check your drive wheels are on a roller. Mind you that this is a primitive device and nothing like the treadmill. The treadmill can counter the exact speed of the wheel. When you press the gas, wheels turn, but the car is not in motion. Now imagine 2 rollers, one for the front wheel and one for the back, or just one long one like our treadmill.

Now, instead of the piston engine connected to the wheels, you have one of the jet powered cars. Thrust comes from the jet and is not powering the wheels as in the case of our airplane. More power you turn on the faster the rollers rotate. The car is stationary. If the car is stationary, the plane will be to. And without forward movement, no lift on wings, thus no flight.

You just demonstrated that you have no clue about the difference between a plane and a car, and I'm sure a jet car would roll right off the rollers too.

Indeed. A car with jet engines doesn't rely on the motion of its wheels - the components whose attempted forward motion is negated by the rollers - and thus, the jet engines will move the car forward.



I submit a new one:
A car in a wind tunnel. Will the car move?

 

[So]

Originally posted by: MasonLuke
It takes a man to admit he is wrong, thats why i call you kids. anyways, i proved my point that the plane will not fly.

i work in the epicenter of the aerospace industry. Hughes, Raytheon, L3, Boeing, Northrop Grumman, ect are right here. We have engineers with Phds, and i'm embarrass to say, but i did consult with several of them right now and basically they told me to stop playing with these kids. BUT ALL OF THEM SAID THE PLANE CANNOT FLY!

it ends here.

Thank you, and when halloween rolls by, come trick or treatn by my house :beer:

Okay, now you're just clearly a liar and a troll.

 

[gsellis]

Originally posted by: So

Originally posted by: MasonLuke
It takes a man to admit he is wrong, thats why i call you kids. anyways, i proved my point that the plane will not fly.

i work in the epicenter of the aerospace industry. Hughes, Raytheon, L3, Boeing, Northrop Grumman, ect are right here. We have engineers with Phds, and i'm embarrass to say, but i did consult with several of them right now and basically they told me to stop playing with these kids. BUT ALL OF THEM SAID THE PLANE CANNOT FLY!

it ends here.

Thank you, and when halloween rolls by, come trick or treatn by my house :beer:

Okay, now you're just clearly a liar and a troll.

I am almost willing to bet that I have worked for the same company for longer than he has been breathing (which is an aerospace transport comp).

 

[MasonLuke]

Originally posted by: So

Originally posted by: MasonLuke
It takes a man to admit he is wrong, thats why i call you kids. anyways, i proved my point that the plane will not fly.

i work in the epicenter of the aerospace industry. Hughes, Raytheon, L3, Boeing, Northrop Grumman, ect are right here. We have engineers with Phds, and i'm embarrass to say, but i did consult with several of them right now and basically they told me to stop playing with these kids. BUT ALL OF THEM SAID THE PLANE CANNOT FLY!

it ends here.

Thank you, and when halloween rolls by, come trick or treatn by my house :beer:

Okay, now you're just clearly a liar and a troll.

what i lie about? Is that the only statement you can make? i cant prove him wrong so i'll call him a liar and a troll. LOL, cute little kid.

 

[sao123]

Originally posted by: MasonLuke


Most of you kids are not familiar with a plane, so lets relate this to a car. During a smog check your drive wheels are on a roller. Mind you that this is a primitive device and nothing like the treadmill. The treadmill can counter the exact speed of the wheel. When you press the gas, wheels turn, but the car is not in motion. Now imagine 2 rollers, one for the front wheel and one for the back, or just one long one like our treadmill.

Now, instead of the piston engine connected to the wheels, you have one of the jet powered cars. Thrust comes from the jet and is not powering the wheels as in the case of our airplane. More power you turn on the faster the rollers rotate. The car is stationary. If the car is stationary, the plane will be to. And without forward movement, no lift on wings, thus no flight.

You have just proven hypothesis 1... you are a complete and total moron.

 

[Safeway]

I asked a pilot and a pilot-in-training what they thought. They both said that the plane wouldn't take off.

Honestly, I have no clue what would happen, though I am partial to the plane not taking off as well. This would be a great undertaking for MythBusters.

Edit:

P.S. to MasonLuke -- This is the way you express opinions. There is no need to force your views on other people, nor is there any need to start a great-fscking-debate over the topic and to move from arguing the topic to insulting the debaters.