Math, science, and barrel fluting

[chkunz]

Would modify that to the following:

of the same weight and length the fluted barrel is stiffer and that concept seems to be easily overlooked by some in this type of discussion.

I agree.

 

[chkunz]

Are I beams tested in a single plane of deflection? If so,is that a reasonable comparison to a barrel that vibrates(bends) in a more circular fashion?

I say no,but could be wrong.

I only mentioned I beams to make the point about the moment of inertia term in the beam equations.

 

[dcali]

Are I beams tested in a single plane of deflection? If so,is that a reasonable comparison to a barrel that vibrates(bends) in a more circular fashion?

I say no,but could be wrong.

In short, barrels don't vibrate circularly. In depth, buckle up... this is going to get stupid.

This is complicated, but I think it is actually important to understanding how barrel vibrations work. If anyone is having a hard time getting what resonant frequency really means, think of a weight on a string. if you swing it back and forth at just the right frequency, you can get the weight to swing higher and higher. That's the resonant frequency. If you swing it too slow or too fast, it will still move, but the motion won't build on itself. Every structure has a resonant frequency at which a load (in this case, your hand) will cause the structure to resonate (for the deformations to tend to build up).

I'm going to switch over to barrels now, rather than general structures, because they're simpler and what we care about, but the above all applies.

In my post above I mentioned that there are multiple resonant frequencies. Engineers call these "modes". Every mode has a shape. The barrel will tend to vibrate in that shape when driven at the frequency of that mode. The first, and slowest mode will have a simple whipping back and forth shape. The next higher mode will have a bend to it in between the muzzle and chamber, mode shapes tend to get more complex as the frequencies get higher. They also get harder to excite.

For a visualization of mode shapes, Varmint Al's page shows a good example: https://www.varmintal.com/amode.htm In real life, only the first few modes are important, but there are technically a near infinite number - imagine each atom individually vibrating in various patterns at higher and higher frequencies.

That's just for the one barrel he modeled and how he constrained it. The exact shape, order, and frequency of the modes depends on the geometry (contour, flutes, caliber, length), the material that the barrel is made of (basically steel), temperature (slightly), and how it is held (a soft hold will change vs bolting to a bench). (Note mode 4 - it looks particularly onerous. Thankfully it's at a very high frequency).

So why is this important? This is hard to visualize, but when you fire a rifle, the resulting forces also have their own frequency content. Much like a complex sound contains a variety of frequencies (as opposed to a tuning fork, which ideally only has one), dynamic forces (like the ignition of the charge and travel of a bullet) also work in multiple frequencies at the same time. So the barrel's resonant frequencies will be exited by the portion of the load that matches their own frequency. For example, if a barrel has modes at 80 and 400 Hz, those mode shapes will come alive in proportion to the amount of the load's spectrum is at 80 or 400 Hz.

So how do two mode shapes happen at the same time? It's complicated, but they basically add together, but the lower modes will dominate. So if you look at real life, where there are many frequencies contained within the shot, and maybe a half dozen resonant modes, you can get some very complex vibrations.

But notice that I haven't said anything about the direction or placement of the load. This matters tremendously, as you might imagine. If you look at a rifle, it's not a round, symmetrical tube held in place by a ball joint in the center of the stock's butt plate. A weird rifle like that would likely have very little vibration that we would need to tune. A real rifle is asymmetrical - the stock is on the bottom, the scope on the top, there's an ejection port, a bolt handle, a trigger, etc. All of those weights hanging off the side of the bore cause inertial loads when the rifle recoils. Those loads all tend to bend the rifle in one direction or another. But since the majority of the weight and is in the vertical plane (the stock and scope), the primary load direction is also in the vertical plane, so you get the up and down whipping of the barrel that we all know and love - the source of our ability to use positive compensation.

And since I'm on a roll, I'll keep going. Remember when I said that all structures have resonant frequencies and mode shapes? Well that applies to actions and stocks too. In fact, if you look at the rifle as a whole, it has it's own set of modes. At the end of the day, that's what we're dealing with - we don't have barrels clamped to grounded concrete blocks. As you might imagine, these mode shapes can get very complex and real world complications like bolted joints, damping, thermal deformations, etc make it all very, very complex.

So now that we know how a barrel, or more importantly, a rifle vibrates, we're done right? Nope. All of the above is the *simple* case where force driving the vibration is constant and steady. In a rifle shot, it's a transient, dynamic force. It starts, it builds, it decreases, and it ends all over a relatively short time frame (a couple milliseconds of barrel time). What this means is that we're not simply seeing the steady state "sine wave" that you're probably imaging. We see the cumulative, combined deflections of the dynamic vibrations as the force changes from instant to instant. Complex as hell. At the end of the day, what we have is more akin to cracking a whip than a tuning fork. But it's not just a simple crack - it's got elements of all those modes throwing a wrench into things - subtle side to side or circular or diagonal effects, higher frequency sine wave motion as the rifle whips - all of that sort of thing.

So the primary method of tuning a rifle is to time the bullet to exit the barrel at the most advantageous point. How, exactly, that is done, is still a mystery (if anyone has an explanation for why seating depth matters so much, I'm all ears). Tuners are also a little more complex than they first might appear. There is the gross effect of their weight, but the *tiny* movements (Mike Ezell's tuner only moves .001" per tick, if I recall) that we see making real impacts are most likely operating on higher modes. I can't confirm that with any precision, but the fact that they change the shape of the group and not just its elevation shows you that it has to be true.

So long story short, this is how rifles vibrate. It's complex, impossible to predict with the precision we require, and it *changes* from shooter to shooter and from bullet to bullet, powder to powder, shot to shot.

That's why the old timers are always saying "go test it". Understanding the theory is helpful in terms of figuring out what to test and change, but that's all it's good for. Test, test, test. It's the only way.

And to get back on topic, flutes play a small role in all this, and the fact that it's all so complicated shows you why there is no set answer as to whether or not they're good or bad.


Net Takeaway
If your eyes glossed over, the punchline is that barrel vibrations are extremely complex, change a lot, and you can't figure it out. You have to test.

 

[gunsandgunsmithing]

In short, barrels don't vibrate circularly. In depth, buckle up... this is going to get stupid.

This is complicated, but I think it is actually important to understanding how barrel vibrations work. If anyone is having a hard time getting what resonant frequency really means, think of a weight on a string. if you swing it back and forth at just the right frequency, you can get the weight to swing higher and higher. That's the resonant frequency. If you swing it too slow or too fast, it will still move, but the motion won't build on itself. Every structure has a resonant frequency at which a load (in this case, your hand) will cause the structure to resonate (for the deformations to tend to build up).

I'm going to switch over to barrels now, rather than general structures, because they're simpler and what we care about, but the above all applies.

In my post above I mentioned that there are multiple resonant frequencies. Engineers call these "modes". Every mode has a shape. The barrel will tend to vibrate in that shape when driven at the frequency of that mode. The first, and slowest mode will have a simple whipping back and forth shape. The next higher mode will have a bend to it in between the muzzle and chamber, mode shapes tend to get more complex as the frequencies get higher. They also get harder to excite.

For a visualization of mode shapes, Varmint Al's page shows a good example: https://www.varmintal.com/amode.htm In real life, only the first few modes are important, but there are technically a near infinite number - imagine each atom individually vibrating in various patterns at higher and higher frequencies.

That's just for the one barrel he modeled and how he constrained it. The exact shape, order, and frequency of the modes depends on the geometry (contour, flutes, caliber, length), the material that the barrel is made of (basically steel), temperature (slightly), and how it is held (a soft hold will change vs bolting to a bench). (Note mode 4 - it looks particularly onerous. Thankfully it's at a very high frequency).

So why is this important? This is hard to visualize, but when you fire a rifle, the resulting forces also have their own frequency content. Much like a complex sound contains a variety of frequencies (as opposed to a tuning fork, which ideally only has one), dynamic forces (like the ignition of the charge and travel of a bullet) also work in multiple frequencies at the same time. So the barrel's resonant frequencies will be exited by the portion of the load that matches their own frequency. For example, if a barrel has modes at 80 and 400 Hz, those mode shapes will come alive in proportion to the amount of the load's spectrum is at 80 or 400 Hz.

So how do two mode shapes happen at the same time? It's complicated, but they basically add together, but the lower modes will dominate. So if you look at real life, where there are many frequencies contained within the shot, and maybe a half dozen resonant modes, you can get some very complex vibrations.

But notice that I haven't said anything about the direction or placement of the load. This matters tremendously, as you might imagine. If you look at a rifle, it's not a round, symmetrical tube held in place by a ball joint in the center of the stock's butt plate. A weird rifle like that would likely have very little vibration that we would need to tune. A real rifle is asymmetrical - the stock is on the bottom, the scope on the top, there's an ejection port, a bolt handle, a trigger, etc. All of those weights hanging off the side of the bore cause inertial loads when the rifle recoils. Those loads all tend to bend the rifle in one direction or another. But since the majority of the weight and is in the vertical plane (the stock and scope), the primary load direction is also in the vertical plane, so you get the up and down whipping of the barrel that we all know and love - the source of our ability to use positive compensation.

And since I'm on a roll, I'll keep going. Remember when I said that all structures have resonant frequencies and mode shapes? Well that applies to actions and stocks too. In fact, if you look at the rifle as a whole, it has it's own set of modes. At the end of the day, that's what we're dealing with - we don't have barrels clamped to grounded concrete blocks. As you might imagine, these mode shapes can get very complex and real world complications like bolted joints, damping, thermal deformations, etc make it all very, very complex.

So now that we know how a barrel, or more importantly, a rifle vibrates, we're done right? Nope. All of the above is the *simple* case where force driving the vibration is constant and steady. In a rifle shot, it's a transient, dynamic force. It starts, it builds, it decreases, and it ends all over a relatively short time frame (a couple milliseconds of barrel time). What this means is that we're not simply seeing the steady state "sine wave" that you're probably imaging. We see the cumulative, combined deflections of the dynamic vibrations as the force changes from instant to instant. Complex as hell. At the end of the day, what we have is more akin to cracking a whip than a tuning fork. But it's not just a simple crack - it's got elements of all those modes throwing a wrench into things - subtle side to side or circular or diagonal effects, higher frequency sine wave motion as the rifle whips - all of that sort of thing.

So the primary method of tuning a rifle is to time the bullet to exit the barrel at the most advantageous point. How, exactly, that is done, is still a mystery (if anyone has an explanation for why seating depth matters so much, I'm all ears). Tuners are also a little more complex than they first might appear. There is the gross effect of their weight, but the *tiny* movements (Mike Ezell's tuner only moves .001" per tick, if I recall) that we see making real impacts are most likely operating on higher modes. I can't confirm that with any precision, but the fact that they change the shape of the group and not just its elevation shows you that it has to be true.

So long story short, this is how rifles vibrate. It's complex, impossible to predict with the precision we require, and it *changes* from shooter to shooter and from bullet to bullet, powder to powder, shot to shot.

That's why the old timers are always saying "go test it". Understanding the theory is helpful in terms of figuring out what to test and change, but that's all it's good for. Test, test, test. It's the only way.

And to get back on topic, flutes play a small role in all this, and the fact that it's all so complicated shows you why there is no set answer as to whether or not they're good or bad.


Net Takeaway
If your eyes glossed over, the punchline is that barrel vibrations are extremely complex, change a lot, and you can't figure it out. You have to test.

Another good and informative post, Damon.
I look at it like this...As the tuner is at the end of the barrel, it "sees" and adjusts the "average" of the cumulative frequencies going on behind it.

 

[Nature Boy]

Hey, I’ve got an idea: Gain fluting!

 

[gunsandgunsmithing]

Hey, I’ve got an idea: Gain fluting!

Are those bbls available with 12 twist fluting?

 

[46and2]

If only there was a material we could tightly weave around the barrel that doesn't resonate and would dampen the steel harmonics, some sort of fiber. Kevlar or carbon or something.

 

[Intheshop]

I followed pretty much all of Damoncali's post.

Have built and shot trad bows for way too long(50 years and counting).... we live and die(accuracy) by vibration and strored energy.

OK "if",and form this as a question,the overwhelming direction or whip is in an up/down...... why is there a twisting moment in the bags? I've seen stocks with wider forearms on one side to help with this. That's why I thought recoil was almost as bad in a twisting direction as it is up/down. And that was an outward indicator that the barrel follows this. Rifling vs smoothbore.

Further perspective which dosen't apply to most here; I shoot a metric ton of cast out of rifles from 3kfps 22's up through 30's. The combination of oversized diameter bullets and complete obturation see's these rigs twisting up like a race car at launch. You can track it,very unscientificly through feel as we go from start loads up into the really hot stuff. "Free recoil" only works at lower velocity. But these aren't HV rigs, or flat bttm stocks so maybe that's why it's so bad?

 

[Intheshop]

I only mentioned I beams to make the point about the moment of inertia term in the beam equations.

I got you. It's just that everytime this discussion comes up,structural beams get introduced.

 

[gunsandgunsmithing]

I followed pretty much all of Damoncali's post.

Have built and shot trad bows for way too long(50 years and counting).... we live and die(accuracy) by vibration and strored energy.

OK "if",and form this as a question,the overwhelming direction or whip is in an up/down...... why is there a twisting moment in the bags? I've seen stocks with wider forearms on one side to help with this. That's why I thought recoil was almost as bad in a twisting direction as it is up/down. And that was an outward indicator that the barrel follows this. Rifling vs smoothbore.

Further perspective which dosen't apply to most here; I shoot a metric ton of cast out of rifles from 3kfps 22's up through 30's. The combination of oversized diameter bullets and complete obturation see's these rigs twisting up like a race car at launch. You can track it,very unscientificly through feel as we go from start loads up into the really hot stuff. "Free recoil" only works at lower velocity. But these aren't HV rigs, or flat bttm stocks so maybe that's why it's so bad?

There are indeed rotational forces involved and barrels don't move only vertically. I agree with what you have seen and with what I think you are saying. I've heard it said many times that tuners only affect vertical. This is simply not true, either. I too follow what Damon has to say on this issue, particularly. He's a sharp guy.

 

[davidjoe]

If only there was a material we could tightly weave around the barrel that doesn't resonate and would dampen the steel harmonics, some sort of fiber. Kevlar or carbon or something.

We could even go super crazy and shim some vibration deadening material between the forend of the stock, say over the area that sits on the rest, and the barrel so that two harmonically dissimilar structures gain from the convenient location of each other.

 

[Dusty Stevens]

We could even go super crazy and shim some vibration deadening material between the forend of the stock, say over the area that sits on the rest, and the barrel so that two harmonically dissimilar structures gain from the convenient location of each other.

You mean like the pressure points in a 40x stock that make them shoot so bad nobody even tests to see if they work better?

 

[davidjoe]

You mean like the pressure points in a 40x stock that make them shoot so bad nobody even tests to see if they work better?

I just fashion a simple cradle out of softer, more compressible material than metal on metal, similar to the role of bushings in engine mounts, that both dampen engine vibrations as well as isolate them, without any mechanical downside.

Yes, the 40-X and Win 52 both had pressure points, these were the top precision rifles of each maker, still true. They were adjustable screws. They were installed and in favor through the time we sent men to the moon and flew passengers in Concordes, (undoable now) so folks weren’t exactly dim back then. They aren’t installed anymore, but as they were adjustable from no contact at all to significant pressure, they could not have hurt performance by just existing in the fore end, because they could be always be dialed back to no contact. Those models are still able to win matches decades later.

 

[dcali]

I followed pretty much all of Damoncali's post.

Have built and shot trad bows for way too long(50 years and counting).... we live and die(accuracy) by vibration and strored energy.

OK "if",and form this as a question,the overwhelming direction or whip is in an up/down...... why is there a twisting moment in the bags? I've seen stocks with wider forearms on one side to help with this. That's why I thought recoil was almost as bad in a twisting direction as it is up/down. And that was an outward indicator that the barrel follows this. Rifling vs smoothbore.

Further perspective which dosen't apply to most here; I shoot a metric ton of cast out of rifles from 3kfps 22's up through 30's. The combination of oversized diameter bullets and complete obturation see's these rigs twisting up like a race car at launch. You can track it,very unscientificly through feel as we go from start loads up into the really hot stuff. "Free recoil" only works at lower velocity. But these aren't HV rigs, or flat bttm stocks so maybe that's why it's so bad?

Two things. The torque is the reaction to the torque required to spin up the bullet. It’s rotational recoil.

But I think what you’re getting at is that if there is a rotational force, is that a driver to rotational vibration modes? Yes! Potentially at least. It’s just one of the many considerations to how the rifle flops around when it gets fired. It’s important to note that while the most substantial drivers are in the vertical plane, they’re not *all* there, and even if they were, there the rifle’s structure is not symmetrical, so even they would drive other out of plane vibrations. As I said, it’s all very complex. Harold Vaughn discovered that even the firing pin drop drives vibrations. It’s wild stuff.

 

[Edd]

An acquaintance of mine that spent several years working as an Engineer for a Detroit company once told me, "the math on some of these parts is so complicated that it is sometimes easier to just build one and see if it works".

 

[dcali]

An acquaintance of mine that spent several years working as an Engineer for a Detroit company once told me, "the math on some of these parts is so complicated that it is sometimes easier to just build one and see if it works".

That is the truth.

 

[chop house]

It’s important to note that while the most substantial drivers are in the vertical plane, they’re not *all* there, and even if they were, there the rifle’s structure is not symmetrical, so even they would drive other out of plane vibrations.

It’s rotational recoil.

i happen to be fiddling right now with a .204 that groups 40 grainers at least 5 moa to the right, as well as 2 moa higher, than 32 grain bullets. Granted, they are very different bullet designs and bc's, and the 32's string out low left to high right groups.

 

[johnfred1965]

That is the truth.

No wonder I never made it through engineering school! Damn math! how can they call it math when it is more letters and symbols than numbers Also, damoncali, were you ever a teacher? I actually understood most of what you were saying.

 

[johnfred1965]

i happen to be fiddling right now with a .204 that groups 40 grainers at least 5 moa to the right, as well as 2 moa higher, than 32 grain bullets. Granted, they are very different bullet designs and bc's, and the 32's string out low left to high right groups.

My 204 will do the same but not to that degree l to r. The different weights group great, but not even close to the same place. I built a 20 vartarg for the 32's and only load 40's in my 204 now. To address this thread, neither rifle is fluted, and as long as they group, I don't care about the math!

 

[SPQR70AD]

Ive read thru most of this thread and several like it. I do not have an answer as to whether or not a fluted barrel is more or less stiff than a non fluted barrel but I can say the weight argument doesnt hold water....ie if the barrel is fluted it becomes lighter but less stiff or it will droop less. All of that IMO isnt accurate.
If you take a sheet of printer paper and lay it flat on the table and slide it off the edge it wont be stiff enough to hold its own weight and will droop. Take that same sheet of paper and fold it in to an accordian shape or a fan we all have made one time or another and it will not only hold its on weight but a substantial amount more. Contour can increase or decrease stiffness with out changing weight to more or less. This is the idea I believe behind the "fluting increases stiffness". The shape of an obeject can change its rigidity with out a weight incress or decrease. Weight is in no way a messure of stifness or rigidity.
Just an observation.

that is the way I look at it. take car fenders. they have to put corners ribs edges to increase stiffness cause flat metal would warp. look at metal roofing with all the ribs. without the ribs you would not be able to pick up a sheet without it bending in half. fluting does increase surface area cause the sides of the flutes add to surface area. cant argue with the Army results with spiral fluting which almost resembles the machined ribs in the first thompson sub guns