Barrel Harmonics Associated With The Target

[gunsandgunsmithing]

So easy but many find a way to make it hard.

Yessir!

 

[Dave M.]

Charlie,
I read through your entire paper (twice actually) and it seems you certainly have done a great deal of work and are definitely on the right track. Check your formula in the middle of page #7 (see below):

 

[MagnumW]

Ballistic slope always negative so could be confusing minusing a negative . I could see equations using implied absolute value of ballistic slope, but yea consistency within one paper would be important. Glad to see this work. Ive been plotting speeds of shots at 100 to see if best 1000 yard loads show up with higher speed shots a hair lower at 100. I know not to waste time getting bugholes at 100!

 

[Dave M.]

Ballistic slope always negative so could be confusing minusing a negative . I could see equations using implied absolute value of ballistic slope, but yea consistency within one paper would be important. Glad to see this work. Ive been plotting speeds of shots at 100 to see if best 1000 yard loads show up with higher speed shots a hair lower at 100. I know not to waste time getting bugholes at 100!

Agree. I do all of my testing for long range at 100 and 200 yards, and it has served me quite well up to this point. Now if I had the ability to shoot at 1000 yards whenever I wanted to within a couple hours drive, I would certainly do more tuning at 1000 yards. Unfortunately, I don’t have this ability.
Dave

 

[dcali]

This is interesting. I haven't had the time to go through it in detail - I haven't checked hte math or anything like that, but I had a few comments:

You left out the work done by Malloc in 1901 (!!). I think it deserves inclusion for posterity. It's attached to this post for those interested in the history of this sort of thing.

As for frequencies, you'll find that they are a bit of a moving target - less so if you use a rail gun or something like that, but the way a rifle is held will move the frequencies, and possibly even the order of the vibration modes. Consistency in this is critical when trying to measure them. Calculations should be taken with a grain of salt - neither the simple beam calculations nor the complex finite element models will get them right. What it typically done with models like that is to build and run the model, and then build and instrument the corresponding hardware. You then do your best (it's a black art) to make the model match the hardware. If you've done a good job with that and haven't had to resort to too many fudge factors, you can use the model to predict the impact of changes to the hardware. This is a difficult and time consuming process, but you can't just build a model and say "well, the frequency is xxx hz". That's not how it works. If this were done, it would be a very useful tool in designing actions. But you have to do it over and over and it can't be reused for different designs. It's a major engineering task.

OBT is just wrong. I don't know how else to say it. The bullet can't move sideways if the barrel is pointed forward and not moving. I don't even agree with the premise that kicks it all off. Rifles DON'T tend to all shoot the same loads accurately. And then there's the interpretation - the strain calculated at the muzzle is *less than the variation in surface finish* - that's nothing. Zero. I didn't check his math either, but I have no reason to doubt it. Assuming it's right, it's irrelevant. The sooner we move away from the OBT stuff the better if you ask me. It's a red herring.

The key here, and Vaughn made some successful attempts at this, is to determine the driving forces and how they resonate. If memory serves, Vaughn found that the the two biggest drivers were the bolt thrust and the firing pin fall. I can't think of anything else that might come into play, but one might wonder if something subtle could happen between primer impact and bullet exit. In any case, simply repeating Vaughn's experiment, but with modern instrumentation and rifles would be very useful in understanding what's going on. Instrumentation is MUCH better and cheaper today. I would very much like to see someone do this. I'd even kick in a little money towards the effort. (I have wanted to do this for years now, but I have to at some point admit that I don't have the time and cash to do it properly).

With both dry and live fire, a rifle instrumented with accelerometers should be able to give you a time series that can be run through an FFT (Fast Fourier Transform). What that tells you is which frequencies are being excited. Those will be the modes of vibration that are driven by forces at the same frequency - presumably due to firing pin and bolt thrust, but who knows - maybe more peaks would emerge.

What to do with that information is the next question. Vaughn's approach was to isolate them away, or to remove asymmetry in the action. Tuning them with a tuner is another option - PROVIDED that the tuner is intelligently matched to the rifle and that the frequencies and amplitudes are of the magnitude that a tuner can be made to work. That's not a given. But you really can't figure out what to do about them unless you know which frequencies are being driven, and ideally, what those modes look like.

Everyone likes to talk about tuners, but I think there is work that could be done in bedding systems and perhaps ignition systems that would be interesting to pursue. One could imagine that you could tune the *action* rather than the barrel.

In any case, good food for thought. When I get a minute I'll see if I can dig into the math you've done and see if I have anything to add.


Edit: One other thing that struck me about Vaughn's book. There's a brief section where he mentions his efforts to attach a lead sleeve to a barrel (that failed mechanically). He didn't really explain why. But you have to assume he was trying to significantly slow the frequency down, which is the opposite of convention wisdom that we all hear so often about stiffer barrels and actions. Frequency is basically proportional to the square root of (stiffness/mass) - Vaughn was trying to add mass without adding stiffness. I can't help but wonder what drove him to do that. This is also worthy of investigation.

Edit two: It's also interesting to note that the resonant frequency of a cantilever beam is highly dependent on length - proportional to 1/length^4. That has always struck me as notable, particularly when it comes to tuners.

 

[gunsandgunsmithing]

This is interesting. I haven't had the time to go through it in detail - I haven't checked hte math or anything like that, but I had a few comments:

You left out the work done by Malloc in 1901 (!!). I think it deserves inclusion for posterity. It's attached to this post for those interested in the history of this sort of thing.

As for frequencies, you'll find that they are a bit of a moving target - less so if you use a rail gun or something like that, but the way a rifle is held will move the frequencies, and possibly even the order of the vibration modes. Consistency in this is critical when trying to measure them. Calculations should be taken with a grain of salt - neither the simple beam calculations nor the complex finite element models will get them right. What it typically done with models like that is to build and run the model, and then build and instrument the corresponding hardware. You then do your best (it's a black art) to make the model match the hardware. If you've done a good job with that and haven't had to resort to too many fudge factors, you can use the model to predict the impact of changes to the hardware. This is a difficult and time consuming process, but you can't just build a model and say "well, the frequency is xxx hz". That's not how it works. If this were done, it would be a very useful tool in designing actions. But you have to do it over and over and it can't be reused for different designs. It's a major engineering task.

OBT is just wrong. I don't know how else to say it. The bullet can't move sideways if the barrel is pointed forward and not moving. I don't even agree with the premise that kicks it all off. Rifles DON'T tend to all shoot the same loads accurately. And then there's the interpretation - the strain calculated at the muzzle is *less than the variation in surface finish* - that's nothing. Zero. I didn't check his math either, but I have no reason to doubt it. Assuming it's right, it's irrelevant. The sooner we move away from the OBT stuff the better if you ask me. It's a red herring.

The key here, and Vaughn made some successful attempts at this, is to determine the driving forces and how they resonate. If memory serves, Vaughn found that the the two biggest drivers were the bolt thrust and the firing pin fall. I can't think of anything else that might come into play, but one might wonder if something subtle could happen between primer impact and bullet exit. In any case, simply repeating Vaughn's experiment, but with modern instrumentation and rifles would be very useful in understanding what's going on. Instrumentation is MUCH better and cheaper today. I would very much like to see someone do this. I'd even kick in a little money towards the effort. (I have wanted to do this for years now, but I have to at some point admit that I don't have the time and cash to do it properly).

With both dry and live fire, a rifle instrumented with accelerometers should be able to give you a time series that can be run through an FFT (Fast Fourier Transform). What that tells you is which frequencies are being excited. Those will be the modes of vibration that are driven by forces at the same frequency - presumably due to firing pin and bolt thrust, but who knows - maybe more peaks would emerge.

What to do with that information is the next question. Vaughn's approach was to isolate them away, or to remove asymmetry in the action. Tuning them with a tuner is another option - PROVIDED that the tuner is intelligently matched to the rifle and that the frequencies and amplitudes are of the magnitude that a tuner can be made to work. That's not a given. But you really can't figure out what to do about them unless you know which frequencies are being driven, and ideally, what those modes look like.

Everyone likes to talk about tuners, but I think there is work that could be done in bedding systems and perhaps ignition systems that would be interesting to pursue. One could imagine that you could tune the *action* rather than the barrel.

In any case, good food for thought. When I get a minute I'll see if I can dig into the math you've done and see if I have anything to add.


Edit: One other thing that struck me about Vaughn's book. There's a brief section where he mentions his efforts to attach a lead sleeve to a barrel (that failed mechanically). He didn't really explain why. But you have to assume he was trying to significantly slow the frequency down, which is the opposite of convention wisdom that we all hear so often about stiffer barrels and actions. Frequency is basically proportional to the square root of (stiffness/mass) - Vaughn was trying to add mass without adding stiffness. I can't help but wonder what drove him to do that. This is also worthy of investigation.

Edit two: It's also interesting to note that the resonant frequency of a cantilever beam is highly dependent on length - proportional to 1/length^4. That has always struck me as notable, particularly when it comes to tuners.

Very good post on this Damon.

 

[tom]

One could imagine that you could tune the *action* rather than the barrel.

You don't have to imagine it, you're correct, I've seen it....and seen it repeat. But not with any instruments in my case (caveman), but by shooting the same powder "ladders", and switching out fire controls.

Old picture, but here I was in my "caveman lab".




I actually took my controls with me to deep creek a couple weeks ago. I only shot the control I competed on last year vs. the one I would much rather "run". I gave it a different primer, hoping for different results, but it was a no go. The losing one did have one small group though, but no way I'd enter an agg season with it.


Tom

 

[CharlieNC]

You don't have to imagine it, you're correct, I've seen it....and seen it repeat. But not with any instruments in my case (caveman), but by shooting the same powder "ladders", and switching out fire controls.

Old picture, but here I was in my "caveman lab".

View attachment 1400465


I actually took my controls with me to deep creek a couple weeks ago. I only shot the control I competed on last year vs. the one I would much rather "run". I gave it a different primer, hoping for different results, but it was a no go. The losing one did have one small group though, but no way I'd enter an agg season with it.
View attachment 1400477

Tom

Tom you are at least partially responsible responsible for my expose' into this investigation! The 1000yd target ladders you posted a number of years ago were very intruiging and interesting, demonstrating the major-then minor- movement in the POI, and to me demonstrated it "must" be due to positive compensation. But why, what barrel frequency, was the reason? Subsequent study led me to the works of Vaughn where he showed that the POI on the target could be used to determine the barrel frequency associated with the target, which is the gist of what I was trying to portray and a method to calculate it. Whereas the engineering calculations, vibration measurement, etc are only associated tools to help further understand, and don't matter much unless reflected on the target. It is the movement of the POI ladder on the target which tells what is important!

 

[tom]

Tom you are at least partially responsible responsible for my expose' into this investigation! The 1000yd target ladders you posted a number of years ago were very intruiging and interesting, demonstrating the major-then minor- movement in the POI, and to me demonstrated it "must" be due to positive compensation. But why, what barrel frequency, was the reason? Subsequent study led me to the works of Vaughn where he showed that the POI on the target could be used to determine the barrel frequency associated with the target, which is the gist of what I was trying to portray and a method to calculate it. Whereas the engineering calculations, vibration measurement, etc are only associated tools to help further understand, and don't matter much unless reflected on the target. It is the movement of the POI ladder on the target which tells what is important!

Cool! I'm out breaking in a new "lab" today!



Tom

 

[dcali]

You don't have to imagine it, you're correct, I've seen it....and seen it repeat. But not with any instruments in my case (caveman), but by shooting the same powder "ladders", and switching out fire controls.

Old picture, but here I was in my "caveman lab".

View attachment 1400465


I actually took my controls with me to deep creek a couple weeks ago. I only shot the control I competed on last year vs. the one I would much rather "run". I gave it a different primer, hoping for different results, but it was a no go. The losing one did have one small group though, but no way I'd enter an agg season with it.
View attachment 1400477

Tom

Interesting. How does it work?

 

[tom]

Interesting. How does it work?

Lol, I have no clue really. But I could make the rifle shoot wide and flat, or diagnol, or narrow and taller by switching controls. In that rifle, with that primer, bullet, powder combo it was repeatable.

Tom

 

[dcali]

Lol, I have no clue really. But I could make the rifle shoot wide and flat, or diagnol, or narrow and taller by switching controls. In that rifle, with that primer, bullet, powder combo it was repeatable.

Tom

That is very interesting. We should be able to develop an action that does that on purpose.

 

[Titan]

...
Edit: One other thing that struck me about Vaughn's book. There's a brief section where he mentions his efforts to attach a lead sleeve to a barrel (that failed mechanically). He didn't really explain why. But you have to assume he was trying to significantly slow the frequency down, which is the opposite of convention wisdom that we all hear so often about stiffer barrels and actions. Frequency is basically proportional to the square root of (stiffness/mass) - Vaughn was trying to add mass without adding stiffness. I can't help but wonder what drove him to do that. This is also worthy of investigation.

Edit two: It's also interesting to note that the resonant frequency of a cantilever beam is highly dependent on length - proportional to 1/length^4. That has always struck me as notable, particularly when it comes to tuners.

I believe page 81 of rifle accuracy facts goes into why you would attempt to increase the weight of the barrel and he only provides a graph of projected muzzle movement on what he terms a standard unmodified rifle, I imagine the benefit of increase the mass on a standard truck axel 1.25 would be less.

 

[gunsandgunsmithing]

I believe page 81 of rifle accuracy facts goes into why you would attempt to increase the weight of the barrel and he only provides a graph of projected muzzle movement on what he terms a standard unmodified rifle, I imagine the benefit of increase the mass on a standard truck axel 1.25 would be less.

I'm not sure how to interpret your post but there's a very good resource online that determines muzzle deflection on different contours and lengths. It's a function of Dan Lilja's(the bbl maker) barrel weight calculator program. It's a good tool for both bbl weight and bbl stiffness. Many people assume a 1.250 bbl is stiffer than say a HV contour. It is per inch, but not necessarily so at the common lengths where we often see 1.250 bbls used. Try it out. I have trouble with the excel file but the .exe file works great for me. Here ya go.

Computer Software - Lilja

We have five files available as a free download as indicated below. These are zipped files. Bullet Design Calculation Program – Available in two formats: Free Download as an Excel file or Free Download as an .exe file- more information on this software.Benchrest Barrel Weight Calculation Program...

riflebarrels.com

 

[dcali]

I believe page 81 of rifle accuracy facts goes into why you would attempt to increase the weight of the barrel and he only provides a graph of projected muzzle movement on what he terms a standard unmodified rifle, I imagine the benefit of increase the mass on a standard truck axel 1.25 would be less.

But why a lead sleeve and not a weight on the end? That's what he didn't quite explain, if memory serves.

 

[ASD9055]

@CharlieNC
I read it once on the screen. Though this is not my field of expertise, I am able to follow along. I do need to read it once more on paper. In my mind, the "transverse" and "longitutinal" descriptions are not clear. I do understand the longittutinal as shown by VamintAI but reading your paper gave me another way we fail to describe the barrel movement. We need to think of it in 4D.
I'll have more comments/questions once I read more.
I think it is great work
Cheers

 

[Titan]

But why a lead sleeve and not a weight on the end? That's what he didn't quite explain, if memory serves

But why a lead sleeve and not a weight on the end? That's what he didn't quite explain, if memory serves.

The lead sleeve reference follows the section on ideal barrel characteristics derived from computer simulations that limit the impact of barrel vibrations, he only states something like a flexible heavy barrel proved "best" in the simulation and to achieve a test case to prove the model he tried to coat a lightweight sporter barrel in lead to retain flexibility while adding mass. What these simulations showed and why a lead jacket or coating would be ideal vs a muzzle weight is not provided in the book. So I agree it is not clear.

 

[CharlieNC]

@CharlieNC
I read it once on the screen. Though this is not my field of expertise, I am able to follow along. I do need to read it once more on paper. In my mind, the "transverse" and "longitutinal" descriptions are not clear. I do understand the longittutinal as shown by VamintAI but reading your paper gave me another way we fail to describe the barrel movement. We need to think of it in 4D.
I'll have more comments/questions once I read more.
I think it is great work
Cheers

Transverse refers to the muzzle moving up/down and sideways as you would typically think. Longitudinal means the "vibration" is along the length of the barrel, which is the way sound is transmitted. To me the interesting aspect is the target shows the vertical transverse vibration occurs at the frequency determined by the speed on sound as it propagates back and forth, longitudinally along the barrel. Glad this is providing an interest for you!

 

[ASD9055]

Transverse refers to the muzzle moving up/down and sideways as you would typically think. Longitudinal means the "vibration" is along the length of the barrel, which is the way sound is transmitted. To me the interesting aspect is the target shows the vertical transverse vibration occurs at the frequency determined by the speed on sound as it propagates back and forth, longitudinally along the barrel. Glad this is providing an interest for you!

I have been intrigued ever since the "doughnut" tuner in the 80's for me. Maybe earlier for others, and then my rifles with BOSS. The thing that was trowing me off with the transverse, was the example of the ruler. It only vibrates up and down, where in my mind the barrel was free to vabrate up and down and side to side, really any direction trasnverse to the length of the barrel.
I was familair with VarmintAI, Long's OBT, OCW, the various forms of Ladder, but not the other references you had. Thank you for that.
If we were able to model the barrel in 4D, that is the three axis and time, we might be able to capture all. But its not in my "tool box".
I'll have to read it again on paper, to digest it. But in my mind you are on the right track for something extremely useful
Again thank you and lookinf orward to hearing about the next chapter.

 

[CharlieNC]

I have been intrigued ever since the "doughnut" tuner in the 80's for me. Maybe earlier for others, and then my rifles with BOSS. The thing that was trowing me off with the transverse, was the example of the ruler. It only vibrates up and down, where in my mind the barrel was free to vabrate up and down and side to side, really any direction trasnverse to the length of the barrel.
I was familair with VarmintAI, Long's OBT, OCW, the various forms of Ladder, but not the other references you had. Thank you for that.
If we were able to model the barrel in 4D, that is the three axis and time, we might be able to capture all. But its not in my "tool box".
I'll have to read it again on paper, to digest it. But in my mind you are on the right track for something extremely useful
Again thank you and lookinf orward to hearing about the next chapter.

The frequencies associated with models occur but are too slow to factor into what happens within the 2 milliseconds when the bullet leaves the barrel. During this time the accelerometer shows transients which later emerge into those frequencies, which are pretty to see and can be more distracting than useful. And they don't show up on the target!