Barrel Behaviour Theory

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wsftr
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Re: Barrel Behaviour Theory

#46 Postby wsftr » Wed Jun 06, 2018 3:43 pm

GSells wrote:It’s funny how you say the last 6” of the muzzle as this is where I’ve shoved the pink cricket handle grip rubber on my bart .284 ( smithed by Fairbarn) . And also where I say secondary orings should be placed . I would love to spill the beans on how to tune the barrel with orings . But again I’m sure people who have the passion will work it out ! It’s been very interesting read and my head hurts too!
Some of it goes way over it lol! I’ll try and stay out of Peter’s thread and let The people who know contribute!

Again very interesting thread !


How about before and after pictures of the groups for the non believers that o rings can make a difference. There is possibly enough theory up here now to explain outcomes.

GSells
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Re: Barrel Behaviour Theory

#47 Postby GSells » Wed Jun 06, 2018 5:22 pm

wsftr wrote:
GSells wrote:It’s funny how you say the last 6” of the muzzle as this is where I’ve shoved the pink cricket handle grip rubber on my bart .284 ( smithed by Fairbarn) . And also where I say secondary orings should be placed . I would love to spill the beans on how to tune the barrel with orings . But again I’m sure people who have the passion will work it out ! It’s been very interesting read and my head hurts too!
Some of it goes way over it lol! I’ll try and stay out of Peter’s thread and let The people who know contribute!

Again very interesting thread !


How about before and after pictures of the groups for the non believers that o rings can make a difference. There is possibly enough theory up here now to explain outcomes.


I had the same debate with Jasmay about 12 months ago ! I totally agree it need to be tested ! But I’m not about to touch my barrels that are doing quite fine especially the bart .284 !!
I’ll leave it to the more enterprising and passionate souls to test , where I stopped .
47014C11-B1D0-4203-9696-34444E35F93C.jpeg

This is what I said at the time about 12 months ago on Se Qld fb page
“The first 6 shots out of the 280 Ai at 100 m's . 175 smk 51.3 2213sc at 2450 fps fire form run in load !
Lilja barrel 1:9 twist . I am very happy ! Very rarely do u see them group straight out of the barrel ,And that slow too!”

So I can only show u results , whether it’s from harmonic modifiers or not ? Well I’ll leave that up to the fraternity to decide ?
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wsftr
Posts: 52
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Re: Barrel Behaviour Theory

#48 Postby wsftr » Wed Jun 06, 2018 5:55 pm

ok - I miss-understood your post, but thanks for the pic. i was thinking there might be something that showed how wide the tune was or something like that, which could in turn be related back to the theories presented.
Anyways I won't get this off topic.

GSells
Posts: 267
Joined: Sun Aug 13, 2017 11:04 pm

Re: Barrel Behaviour Theory

#49 Postby GSells » Wed Jun 06, 2018 7:16 pm

wsftr wrote:ok - I miss-understood your post, but thanks for the pic. i was thinking there might be something that showed how wide the tune was or something like that, which could in turn be related back to the theories presented.
Anyways I won't get this off topic.


No worries , time to let the real people have a crack at it ! I will say and I've used mass weights with o rings for the above pic , but the tune for me in the past has seemed qite broad . Regards Graham .

!Peter!
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Re: Barrel Behaviour Theory

#50 Postby !Peter! » Wed Jun 06, 2018 11:07 pm

To continue on with some more theory...

The material presented in the physics classroom is idealised and reasonably represents many waves found. However, as is always the case, the simple idealised equations don't reasonably represent all situations.

In the case of a rifle system, the idealised wave equation don't reasonably represent the barrel's behaviour, particularly transverse waves. This is not to say the material of the physics classroom is not relevant.

The classical theory applied to things like a rifle barrel is Euler–Bernoulli beam theory. I'll leave it to you to search the internet to find out more if you want but BE WARNED, the maths does require formal post secondary maths. Never the less you can still look at the pictures. :)

It should be noted that if you apply Euler–Bernoulli beam theory to something like a guitar string you will get the same answer as using the idealised wave equations but the maths used will be much more advanced.

Image
The pictures above show the first four natural frequencies and normal modes of a uniform beam in various types of arrangements. This was extracted from table 7.3 in Harris’ Shock and Vibration Handbook (5th edition).

As you can see the shape changes depending on how the ends are supported. When that talk about a hinged end, the end is free to rotate but not move vertically or horizontally. A clamped end is fixed and cannot move. And finally, a free end is free to move however it wants.

A barrelled action bolted into a rigid machine rest would be best represented by a Clamped-Free beam. A barrelled action in a stock like F Class and TR is not well represented by any of them as the action end can move in all directions but not freely. The best approximation would be a Free-Free beam.

Another impact of the departure from the idealised wave is that not all wave travel at the same speed. The speed of a longitudinal wave is the speed of sound in the material. This speed can be found readily on the internet, just search for "speed of sound in steel". However, the speed of a transverse wave is different and varies depending on the frequency of the wave. The simplest discussion on this is from the work of Geoffrey Kolbe found here http://www.geoffrey-kolbe.com/articles/rimfire_accuracy/transverse_vibrations_on_a_beam.pdf

I'll leave it here for the moment as this is a lot for people to digest if you haven't been exposed to this area.
Last edited by !Peter! on Sat Jun 09, 2018 2:48 am, edited 2 times in total.

williada
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Re: Barrel Behaviour Theory

#51 Postby williada » Wed Jun 06, 2018 11:15 pm

Its a pain getting timed out on this site when typing and it looks like more edits than there were. I added a bit more to previous post to rather than write a separate one to cover John's question. Lead on Peter.

John T
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Location: Brisbane

Re: Barrel Behaviour Theory

#52 Postby John T » Thu Jun 07, 2018 12:10 am

Calling all trombone players.

Are trombone wave forms comparable to what happens in a rifle? Think of the slide as the bullet.

In "position", the slide produces an harmonic, a note, out of "position" it produces a clanger.

Regards,
John Tracey.
6.6.18

!Peter!
Posts: 88
Joined: Sun Oct 30, 2016 6:35 am

Re: Barrel Behaviour Theory

#53 Postby !Peter! » Thu Jun 07, 2018 12:51 am

John T wrote:Calling all trombone players.

Are trombone wave forms comparable to what happens in a rifle? Think of the slide as the bullet.

In "position", the slide produces an harmonic, a note, out of "position" it produces a clanger.

Regards,
John Tracey.
6.6.18

In a rimfire rifle I think it has some merit but in a centerfire rifle i don't because the bullet is quickly accelerated to above the speed of sound and any wave in the air in front of the bullet would be traveling at the speed of sound so any wave in front of the bullet would be compressed by the bullet before it could propagate forward. Another way to express it is the wave in front cannot out run the bullet.

sungazer
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Re: Barrel Behaviour Theory

#54 Postby sungazer » Thu Jun 07, 2018 11:43 am

I would argue the point re the action being free to move. I would have said that the clamped free would fit the rifle better. The action is pretty well bedded and then pulled pretty tight into that bedding. Surly that is a clamped end?

!Peter!
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Re: Barrel Behaviour Theory

#55 Postby !Peter! » Thu Jun 07, 2018 12:45 pm

sungazer wrote:I would argue the point re the action being free to move. I would have said that the clamped free would fit the rifle better. The action is pretty well bedded and then pulled pretty tight into that bedding. Surly that is a clamped end?

But can the action cause the stock to flex? Can the action move the stock with respect to a fixed point on the ground?

williada
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Re: Barrel Behaviour Theory

#56 Postby williada » Thu Jun 07, 2018 2:29 pm

John the way to think about this IMO is there are a few different systems operating. To get my head around this, I broke the systems into macro (big) and micro systems (small). The macro to me indicates the direction which something is flung and the micro represents the precision of which something is flung in a direction.
I think Peter is moving through the macro part first looking at key forces. To me the whole rifle system, stock bags and all could be viewed as beam theory and where things are clamped etc. in a macro system.

I happen to think the micro forces are more important for final tune when we cross from a beam and natural frequencies to the dynamics of a tube and interactive frequencies of a moving bullet with additional forces such as torque and accelerating velocity physically changing the physical size of the bore. To some extent you are not too far off the beam, (pardon the pun) with the trombone effect but it is more so on the beam rather than the air but the hydraulic action does count and air mass does matter in the precision stakes. The problem is if we pick one element of an interactive system it is not necessarily representative of the system as a whole. Hopefully we can see step by step how things work.

I see the interactive forces of the moving bullet in some sense like you but acting as a changing boundary of reflection of forces activating a tube in a mechanical sense on one hand with the interference of the macro forces in the medium acting on the forward and aft movements of vibration in a closed system behind the bullet before the bullet has exited. It is very, very complex. Of course forward of the bullet is a micro system which forms an anti-node at high frequency at the muzzle in a mechanical sense in the medium because it is an open end. Behind that is a bigger system with the closed end of the bolt face and the open end of the muzzle and behind that is a bigger system again of the whole rifle and behind that the how the whole system is suspended. It’s like a Russian doll, you open it, and there is another doll inside. Open that and there is another doll inside that and so on until you get to the last doll. The treasure is the last doll. Where these forces coincide at an appropriate reflection point at the muzzle on an anti-node as seen in manual map of different shots indicating different vibration patterns in the charge test it has proven to be a precision point for accuracy. It’s easier to see the outcome on paper. Well for me anyway through lots of experiments firing thousands of rounds under controlled test conditions.

So yes, it could be viewed as a trombone element in the medium of the steel (Speed of Sound 19,000 fps approximately) in a micro tune of high frequency vibration and to a lesser degree the air (1130 fps approximately). But the external air mass IMO does act as a force determining the node distance from the muzzle as a blocking force outside the muzzle which effects precision on a micro tune. We may only see the anti-node in the groups on an open system at the muzzle on the paper if the atmospheric node is in the right place or we may see close to a node group at the muzzle if the next upper node is further out from the muzzle in the atmosphere in a simple sense in a micro tune. I think it was Cub Cooper who differentiated the beam system from the tube system. But we have to look at the elements to see how they work as a whole then decide how to optimize them. Systems swing, oscillate and vibrate on different scales.

sungazer
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Re: Barrel Behaviour Theory

#57 Postby sungazer » Thu Jun 07, 2018 4:42 pm

Ok if we take just the speed of sound as the first component of causing waves at 19000 fps it takes 1.57*10-4 to travel the 3ft. The bullet takes 1ms. So in this 1ms time period the speed of sound can reflect a total of 3 times to the muzzle end and back (6.3 in total) Therefore we dont need to look behond the 3rd harmonic for this component. Does that sound about right?

!Peter!
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Re: Barrel Behaviour Theory

#58 Postby !Peter! » Fri Jun 08, 2018 10:12 am

sungazer wrote:Ok if we take just the speed of sound as the first component of causing waves at 19000 fps it takes 1.57*10-4 to travel the 3ft. The bullet takes 1ms. So in this 1ms time period the speed of sound can reflect a total of 3 times to the muzzle end and back (6.3 in total) Therefore we dont need to look behond the 3rd harmonic for this component. Does that sound about right?

Except the bit about the 3rd harmonic.

A harmonic is another name of a standing wave and a travelling wave does not always turn into a standing wave.

!Peter!
Posts: 88
Joined: Sun Oct 30, 2016 6:35 am

Re: Barrel Behaviour Theory

#59 Postby !Peter! » Fri Jun 08, 2018 10:28 am

Continuing on…

The beam modes shown in my previous post are only in the one direction. In a real barrel there are many more types of modes. VarmintAl has produced an animation (see link below) of the first 8 modes with the action held rigid. Using the terms in my previous he has modeled it as Fixed-Free beam
http://www.varmintal.com/amode.htm

Read this page carefully as he makes some key points that can be missed if you just look at the pictures.

I should point out that the modes animated on this page don’t necessarily occur when the bullet is in the barrel.

A point I should expand on is his comment “a frequency of about 500 Hz will not be able to complete one full cycle before the bullet exits the barrel”. Essentially, the lower the frequency the slower the movement is to a point where the bullet exits the barrel before the movement is great enough to cause a material impact on the bullet.

To illustrate this time aspect further, consider the 1 Hz (wave 1) and 2 Hz (wave 2) standing waves both with an amplitude of 1 below.
Image
At 0 seconds both waves are passing though 0 amplitude.
At 0.01 seconds wave 1 is at 0.06 amplitude and wave 2 is at 0.12 amplitude.
At 0.02 seconds wave 1 is at 0.13 amplitude and wave 2 is at 0.24 amplitude.

Now another aspect...

The sources of waves in a barrel are mostly obvious ie:
    - Firing pin hitting the primer
    - The combustion of the powder
    - Bullet engaging the lands
    - Bullet traveling down the barrel getting accelerated, both linearly and radially

However, one source that is not so obvious is the recoil. The physics to gain a deeper understanding of this is moments and forces.

These types of moments are not the ones that occur when the target comes up and you see the marker and think: How the F#(K did that happen? You can search the internet for “moments and forces” for the physics definition.

Essentially, under recoil the rifle will try to rotate about the center of gravity of the rifle which causes the action to start a transverse wave on the barrel. I’ve previously posted more information about this on posts #6 & 9 in the thread below.
https://www.ozfclass.com/phpbb/viewtopic.php?f=5&t=8394&p=69816#p69816

The only additional thing I’ll add to those previous posts is some more results from Geoffrey Kolbe’s barrel vibration simulator:
Image
Medium Palma barrel with high rifle center of gravity

Image
Medium Palma barrel with low rifle center of gravity

The only parameters changed between these two simulations is the vertical location of the center of gravity. When looking at these graphs the Y axis is the angle of the muzzle.
Last edited by !Peter! on Sat Jun 09, 2018 2:50 am, edited 1 time in total.

williada
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Re: Barrel Behaviour Theory

#60 Postby williada » Fri Jun 08, 2018 12:21 pm

Peter is rightly holding some of the other modes constant before they are introduced to see further changes. When we look at further steps, bear in mind that radial shock waves in steel as opposed to air in a tube are much, much greater. Air tends to have longitudinal reactions in a tube. That means there are outward stress waves from lots of forces acting on the bore dimension which may lead us to optimize bullet bearing surface and diameter to bore size by trying different bullet brands and timing those better suited to stress waves encountered for less retardation/distortion of the bullet and at the muzzle where it counts.

Behind the bullet the bore is closing and in front of the bullet the bore is expanding. In the context of discussion, the recoil is inducing more longitudinal forces with which these other forces interact. The analogy is like a bending snake with a meal inside (bullet) where we can detect the bullets presence as the lump in the guts as it moves longitudinally through the system.

I will just add, one of the least noticeable sources of waves that has one of the highest impacts on precision is the third point of inertia at the muzzle which theorists often neglect as the bullet body emerges from the crown. Higher frequency is generated here and can exacerbate gas blow by with muzzle distortion we call chatter and influence bore angle at the exit. To me minimising the bore size at the muzzle is very important.

In a general context, shock waves have a big effect on bore size. Rinker reports an experiment when cutting a barrel back progressively the diameter of collected bullets fired into water got progressively bigger towards the breech. Now what is this saying about radial stress force and barrel length? It was Rinker who got me to think about the critical size of the re-enforce and an optimum barrel length for .308 in Project Penumbra. To digress, some of the throat cracking we complain about to me is an expansion problem. Fix the re-enforce. Is this why thicker brass like Lapua works? Think about marginal benefits or could we be supplied with wider and longer re-enforces?


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