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Conservation of Momentum

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Walter
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Conservation of Momentum

#81

Post by Walter » Mon Jun 10, 2013 7:04 pm

gordonjudd wrote:I hope that Walter can explain what is providing the source of the negative x force at the bottom of the loop that would be required to maintain a momentum change in the fly leg even though there is no tension on the end of the rod leg while it remains airborne.

There is certainly a momentum change going on in the top leg of the bead chain in the last two videos. If Newton was correct that a momentum change requires a force (and you would have to be pretty ballsy to argue with Newton's second law) what is providing the necessary force in those last two videos?
Gordy - I've already told you to read my very first post in this thread. These types of comments indicate that you still have not done that. When you have read the post feel free to ask questions.

Now for some observations from the first cast in your earlier video:



Have you noticed that near the end of the loop unrolling that the loop seems to slow its descent and actually appears to be climbing? Does that mean that bead chain loops also have the ability to defy gravity? Does the skin effect that pulls a fly line loop upwards through the air work for bead chains too? It would be hard to understand how from this video because in this case the fly leg is actually on the bottom and not on the top. That would mean that the skin effect should be pulling this loop down rather than up...
"There can be only one." - The Highlander. :pirate:

PS. I have a flying tank. Your argument is irrelevant.

PSS. How to generate a climbing loop through control of the casting stroke is left as a (considerable) exercise to the reader.

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Lasse Karlsson
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Conservation of Momentum

#82

Post by Lasse Karlsson » Mon Jun 10, 2013 7:51 pm

gordonjudd wrote:
What happens if you do not speed up the lower leg and release it later?
Lasse,
It depends.

When the rod leg is angled down and back after a late release of the rod leg the bead chain loop does roll out. You can see in the last video the rate of roll out increases when the rod leg touches the ground.
Gordy
Cool, now if you could find somewhere high enough we could see if you could get that loop to unfurl on it's own time and not from the increased tension, that is expected anyway...

Cheers
Lasse
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***Bring Mark back!!!!!! ***

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gordonjudd
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Conservation of Momentum

#83

Post by gordonjudd » Mon Jun 10, 2013 9:15 pm

Gordy - I've already told you to read my very first post in this thread. These types of comments indicate that you still have not done that. When you have read the post feel free to ask questions.
Walter,
Did I miss something in that post? Here is what I read:
When it comes to a fly leg increasing in speed as it gets shorter you have to ask where the application of force is happening in order for the change of velocity to be happening. It comes from me applying a retarding (not retarded :D ) force on the line with the rod tip. This pulls on the rod leg which pulls on the fly leg via the loop.
That quote is all well and good and explains why when I hold onto the rod leg of the bead chain there will be force to produce a momentum change in the fly leg (I.e. there is no COM going on as long as there is a force applied to the bottom end of the loop). Aside from the effects of drag forces and gravity there is very little momentum change when the rod leg is released and thus the line flies through the air without any shortening of the fly leg as can be seen in the flying spaghetti examples.

Consequently, just as with all of the other examples the line will roll out when there is a force applied to the end of the rod leg whether or not the linear mass density is very low as was the case with the yarn or if it is very high as with the bead chain.

But that does not explain why the loop continues to roll out when there is no force on the rod end of the line in those last two videos. I hope you can see the rod leg is just sailing along so there is no x-directed force on it until it touches the ground in the last video.

Thus once again:
"I hope that Walter can explain what is providing the source of the negative x force at the bottom of the loop that would be required to maintain a momentum change in the fly leg even though there is no tension on the end of the rod leg while it remains airborne."
That would mean that the skin effect should be pulling this loop down rather than up...
That is always the case for skin friction on an inclined section of line that has a positive slope. The upward force (and significant +y acceleration it produces in light lines) comes from form drag. Form drag also produces an upward force on the bead chain but it results in negligible +y acceleration since the mass of the bead chain loop is so large.
Have you noticed that near the end of the loop unrolling that the loop seems to slow its descent and actually appears to be climbing?
If you look at the direction the rod leg is pulling on the bottom of the loop I think you will see where the upward force is coming from near the end of the roll out.

Gordy

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Walter
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Conservation of Momentum

#84

Post by Walter » Mon Jun 10, 2013 10:17 pm

gordonjudd wrote:Thus once again:
"I hope that Walter can explain what is providing the source of the negative x force at the bottom of the loop that would be required to maintain a momentum change in the fly leg even though there is no tension on the end of the rod leg while it remains airborne."
Gordy - in response to your first bead chain video in this thread I made the following comment:
Gordy - It appears (so it may or may not be the case) in the second part of your video that you are throwing the line with a loop shape in it rather than forming a loop and then letting it go.
Lasse had a similar comment. In the case where you throw the line (again, I'm not saying you did, it just appears that way on the video) with a loop shape in it nothing would happen. The line would simply fly like spaghetti which it basically did.

If you get a proper loop started and then release the rod leg then the fast moving fly leg has a slow moving rod leg attached to it. The fly leg exerts a force in the positive X direction on the rod leg because they each have inertia and want to resist a change. The rod leg pulls back with an equal and opposite force in the negative X direction. The rod leg responds by moving in the positive X direction (momentum goes from zero to positive momentum). The fly leg responds by getting shorter and, depending on its length or (more correctly) its mass, changing its speed.

If you release the rod leg when it is very short it has very little mass so its pull on the fly leg is small and the fly leg does not need to give up much momentum for the rod leg to be brought up to the same speed so this will happen quickly and then things will begin to tumble. When the rod leg is much longer than the fly leg, the fly leg will have to give up all of its momentum in order for the two legs to have the same speed. Then the tumbling will begin.

We can use CoM to determine how much M the fly leg has to give up before both legs are travelling at the same velocity and the tumbling begins. Let's say the line is divided equally between the two when you release the rod leg and the the mass of each leg is M for a total mass of 2M. If velocity of the fly leg is V when you release the rod leg we know that the initial momentum is MV. So if the total mass when both rod legs are moving at the same speed is 2M then the final velocity of the total mass must be 1/2 V. Whether the fly leg speeds up or slows down during this equalization is probably something you can figure out much more easily than I can based on your demonstrated math skills.

Hope this makes sense.

Walter
"There can be only one." - The Highlander. :pirate:

PS. I have a flying tank. Your argument is irrelevant.

PSS. How to generate a climbing loop through control of the casting stroke is left as a (considerable) exercise to the reader.

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gordonjudd
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Conservation of Momentum

#85

Post by gordonjudd » Tue Jun 11, 2013 12:28 am

We can use CoM to determine how much M the fly leg has to give up before both legs are travelling at the same velocity and the tumbling begins.Hope this makes sense.
Walter,
I don't understand that reasoning as it appears to me the angled down rod leg is propagating at the same speed as the loop and yet the fly leg is still getting shorter. I don't think it is nearly that complicated or there is any COM going on when the fly leg's momentum is changing.
Image
Look at the long diagonal length of chain that is angled back on the rod leg as it is propagating. The length of that angled section is changing with time, but I think you can see there needs to be a tension in the rod leg of the chain where it joins the bottom of the loop to offset the weight of the chain that is hanging down below that point. If I have done the trig correctly the offsetting tension in the bead chain would be around T*cos(theta)=m*g where m is equal to rho_l*y_length of the angled section and theta is angle off of the vertical which is around 60 degrees in the frame grab above. It will no doubt be somewhat less than that since that point is changing its y height as the loop is propagating.

The force in the -x direction from the hanging chain will be equal to T*sin(theta). That negative x-directed force will produce a momentum change in the fly leg of the loop. In the last case where the rod leg touched down the added friction force will cause the loop to unroll a bit faster.

We don't see the same effect with yarn since its hanging weight is so much smaller than the bead chain especially in this case where its hanging y_m mass is near zero since the running section of the rod leg near the horizontal.
Image
When the rod leg is not angled down and back the x-directed force is negligible for the spaghetti bead chain cases as well.

Gordy

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gordonjudd
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Conservation of Momentum

#86

Post by gordonjudd » Tue Jun 11, 2013 1:15 am

Even without air resistance momentum is not conserved when the loop propagates.
Energy will however be conserved if there is no air resistance.

These conservation principles always apply/work (if applied correctly), but when making models we are always making assumptions which are more or less wrong (assuming air drag is zero is obviously wrong in fly casting). Still we can use these simplified models and results/solutions to get a better understanding of what is going on in the "real world"
and
CoM is not the tool to understand how the fly leg speed changes. The convenient way is to write that the variation in kinetic energy of the moving part of the line (neglecting the influence of the gravity)
As Grunde and Merlin have noted the important consideration in how the velocity of the loop changes as the moving mass in the fly leg changes it related to the energies involved, not some sort of bastardized COM model.

Hendry has shown that absent drag losses the acceleration you get to keep a constant K.E. in the moving mass of the fly leg is about half of what it would be if there was no momentum change. That is a sizable difference and in order to maintain constant momentum; energy would have to be added to the system, and aside from pulling back on the rod leg that is not going to happen.

Nevertheless the propagation increase can be sizeable when the mass density of the line is high as shown in this example for a bead chain loop.

Here are the tracking dots on the front of the loop taken at 33 ms intervals in that video.
Image

You can see the separation between the dots gets longer and longer as the mass in the fly leg shortens which indicates the loop speed is increasing since the energy lost to drag is very small compared to the K.E. associated with the moving mass of the bead chain.

From the excel plot below you can see the propagation of the loop increased by a factor of around four for this short length of bead chain.
Image

I have yet to see a measured fly velocity profile for an actual cast, but I hope someday Lasse or Aitor can provide that missing link to all this theory.

Gordy

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Walter
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Conservation of Momentum

#87

Post by Walter » Tue Jun 11, 2013 4:08 am

gordonjudd wrote:
Even without air resistance momentum is not conserved when the loop propagates.
Energy will however be conserved if there is no air resistance.

These conservation principles always apply/work (if applied correctly), but when making models we are always making assumptions which are more or less wrong (assuming air drag is zero is obviously wrong in fly casting). Still we can use these simplified models and results/solutions to get a better understanding of what is going on in the "real world"
and
CoM is not the tool to understand how the fly leg speed changes. The convenient way is to write that the variation in kinetic energy of the moving part of the line (neglecting the influence of the gravity)
As Grunde and Merlin have noted the important consideration in how the velocity of the loop changes as the moving mass in the fly leg changes it related to the energies involved, not some sort of bastardized COM model.

Hendry has shown that absent drag losses the acceleration you get to keep a constant K.E. in the moving mass of the fly leg is about half of what it would be if there was no momentum change. That is a sizable difference and in order to maintain constant momentum; energy would have to be added to the system, and aside from pulling back on the rod leg that is not going to happen.

Nevertheless the propagation increase can be sizeable when the mass density of the line is high as shown in this example for a bead chain loop.

Here are the tracking dots on the front of the loop taken at 33 ms intervals in that video.
Image

You can see the separation between the dots gets longer and longer as the mass in the fly leg shortens which indicates the loop speed is increasing since the energy lost to drag is very small compared to the K.E. associated with the moving mass of the bead chain.

From the excel plot below you can see the propagation of the loop increased by a factor of around four for this short length of bead chain.
Image

I have yet to see a measured fly velocity profile for an actual cast, but I hope someday Lasse or Aitor can provide that missing link to all this theory.

Gordy
Gordy - you can stop editting your last two posts. I only have one comment to make and that is, "No comment."
"There can be only one." - The Highlander. :pirate:

PS. I have a flying tank. Your argument is irrelevant.

PSS. How to generate a climbing loop through control of the casting stroke is left as a (considerable) exercise to the reader.

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grunde
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Conservation of Momentum

#88

Post by grunde » Tue Jun 11, 2013 5:51 am

gordonjudd wrote:
Even without air resistance momentum is not conserved when the loop propagates.
Energy will however be conserved if there is no air resistance.

These conservation principles always apply/work (if applied correctly), but when making models we are always making assumptions which are more or less wrong (assuming air drag is zero is obviously wrong in fly casting). Still we can use these simplified models and results/solutions to get a better understanding of what is going on in the "real world"
Yes this is something I said...

while this:
and
CoM is not the tool to understand how the fly leg speed changes. The convenient way is to write that the variation in kinetic energy of the moving part of the line (neglecting the influence of the gravity)
obviously is something someone else said...
As Grunde and Merlin have noted the important consideration in how the velocity of the loop changes as the moving mass in the fly leg changes it related to the energies involved, not some sort of bastardized COM model.
I have no idea why you are putting these words into my mouth. And I have absolutely no idea what you are talking about when you say "... some sort of bastardized COM model".

Cheers,
Grunde
"Essentially, all models are wrong, but some are useful."
George E. P. Box

Always question the assumptions!

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Conservation of Momentum

#89

Post by Unregistered » Tue Jun 11, 2013 6:31 am

Walter wrote:If you get a proper loop started and then release the rod leg then the fast moving fly leg has a slow moving rod leg attached to it. The fly leg exerts a force in the positive X direction on the rod leg because they each have inertia and want to resist a change. The rod leg pulls back with an equal and opposite force in the negative X direction. The rod leg responds by moving in the positive X direction (momentum goes from zero to positive momentum). The fly leg responds by getting shorter and, depending on its length or (more correctly) its mass, changing its speed.

If you release the rod leg when it is very short it has very little mass so its pull on the fly leg is small and the fly leg does not need to give up much momentum for the rod leg to be brought up to the same speed so this will happen quickly and then things will begin to tumble. When the rod leg is much longer than the fly leg, the fly leg will have to give up all of its momentum in order for the two legs to have the same speed. Then the tumbling will begin.

We can use CoM to determine how much M the fly leg has to give up before both legs are travelling at the same velocity and the tumbling begins. Let's say the line is divided equally between the two when you release the rod leg and the the mass of each leg is M for a total mass of 2M. If velocity of the fly leg is V when you release the rod leg we know that the initial momentum is MV. So if the total mass when both rod legs are moving at the same speed is 2M then the final velocity of the total mass must be 1/2 V. Whether the fly leg speeds up or slows down during this equalization is probably something you can figure out much more easily than I can based on your demonstrated math skills.

Hope this makes sense.

Walter
Yes, it makes sense, at least to me. Thanks for keeping it simple and understandable for us laymen.

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Paul Arden
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Conservation of Momentum

#90

Post by Paul Arden » Tue Jun 11, 2013 10:12 am

Blimey Magnus, I hope you're not thinking of becoming an engineer :p If there's one thing I've learned from the engineers here it's that at some point they're going to disagree on the physics, and the problem is that this can be at a very technical level using Laws that most people have never heard about. The other thing I've learned is that some of them can be pretty sensitive. This makes things difficult, especially when they get pissed off with each other! But fuck it, there is so much I don't understand and so much that I would really like to understand, I just have to be here!

Thanks for the explanation Gordy. What about casting into a solid wall? There is no loop there to pull the line forward.

Cheers, Paul
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