An explanation on barrel harmonics.

[gitrdun]

I was prompted to post this due to the fellow's post on having poor performance on GMX bullets. The POI wasn't was expected with supposedly higher muzzle velocity bullets, the POI was in fact lower with his current ammunition than it was with the lower velocity ammo that he was using in the past. Barrel harmonics are often mentioned, but misunderstood. I hope to shed some light on this as harmonics is often a misused terminology.

I'll start by posting this diagram:



All objects, barrels included vibrate when excited by an external force at their own natural frequency, also known as their resonant frequency. What determines resonance is mass for the most part. Thus a heavy barrel will have a higher natural frequency than a light barrel. Referring to my diagram, the wave length will be shorter. A lighter barrel has a longer wave length. This wave length, aside from mass can be affected by pressure points such as those created be your stock for-end. Free floating is good as it allows the barrel to vibrate at it's own natural frequency without obstructions. Pressure points can also be good with light barrels as it drives the natural frequency upward and shortens the wave lenght. But the caveat here is that the barrel must remain in full contact with the pressure point at all times. This is why when purposely imparting a pressure point, we generally look for about 8 lbs. (rule of thumb).

Should the bullet exit the barrel at a "node" it will shoot high in relation to the world. Not bad if it does it consistently. Your sights, be they irons or optics can compensate for that.

Should the bullet exit the barrel at an "anti node", it will shoot low in relation to the world. Again, not bad either as long as it does it consitstently.

Now that we know that the exiting force which excites your barrel into it's harmonics or natural frequency, consistently no matter what powder charge you choose, because it acts much like a hammer striking the barrel and setting it into vibration. The only other thing that will determine where the bullet hits your target is the velocity of the bullet. A faster bullet may exit the barrel at it's node, thus putting it higher on target. While a slightly slower bullet may just hit the anti-node on it's way out of the barrel, thus putting it lower. This can work the other way around as well, and by that I mean that a fast bullet could hit an anti-node and a slow bullet hit a node on it's way out of the barrel.

Thus, faster muzzle velocity does not necessarily mean a higher point of impact than formerly used lower muzzle velocity bullet. It all depends on where the end of the muzzle in it's free form of vibration is when the bullet exits the muzzle.

People often claim that changing powder charge and altering muzzle velocity affects barrel harmonics. That is incorrect. Barrel harmonics or more accurately "resonance" can only be changed by mass and pressure points. All that velocity affects is when the bullet exits the muzzle, at a node, any anti-node or somewhere in between. Thus, giving a variety of results on target.

[Rman]

Nodes are always predictable, within tolerances, regardless of barrel length, diameter, projectile weight, powder charge, powder type (burn rate), cartridge overall length, or any other variable you wish to introduce, pertaining to internal ballistics.
I realize you will call me a troll, and whole bunch of other names, because I am disagreeing with you, but how does one measure 8.0001 pounds of upward force on a barrel, exactly?
More powder equals more pressure, to a certain point. More powder leads to greater velocity, again in most cases. Generally, you would have to overcome a pile physics in order to increase a powder charge, and get a lower point of impact.
If you change your wording from lighter barrel to shorter barrel, when referring to wave length, you would be correct. Again, when speaking about nodes, barrel weight, in general, has much less to do with it, than barrel length.

"Thus, faster muzzle velocity does not necessarily mean a higher point of impact than formerly used lower muzzle velocity bullet. It all depends on where the end of the muzzle in it's free form of vibration is when the bullet exits the muzzle."

This just kind of makes sense, doesn't it? A faster muzzle velocity, given the same projectile, will always have a higher point of impact than a lower velocity? Unless you are talking barrel deflection?
When chasing nodes, it is best to look at velocity spread and standard deviation. These are the best indicators of node identification. Regardless of barrel position, either high, or low node exit, the velocity spread and SD will give the most repeatable results, given that a reliable and repeatable chronograph is used.

"People often claim that changing powder charge and altering muzzle velocity affects barrel harmonics. That is incorrect. Barrel harmonics or more accurately "resonance" can only be changed by mass and pressure points. All that velocity affects is when the bullet exits the muzzle, at a node, any anti-node or somewhere in between. Thus, giving a variety of results on target."

Using your own theory's as stated in your post, this would be incorrect. You said that:
"All objects, barrels included vibrate when excited by an external force at their own natural frequency, also known as their resonant frequency"
And this is correct, given that the amount of external force remains constant. Increase the amount of external force, and you will change the frequency/resonance.
Hit a cymbal softly, it will resonate at a certain frequency, hit it harder, and that frequency changes. Lower powder charge, different frequency than a higher powder charge. Changing powder charge certainly does affect barrel harmonics, as you are imparting a larger of smaller external force.


This is very high end physics, mathematics, and statistics. Without identifying all of the constants and variables, the outcomes will vary.



R.

[marxman]

i think he is correct about harmonics but i dont see a pressure point changing it just damping it out unless it is like pressing on a fret which i doubt.. is a node not where the muzzle is in least motion? an antinode could be low or high. a different powder charge wont change it just get it there at the right time i dont think it changes harmonics. my cleaning brush rings my tikka and cz barrels somewhere around 5000 hz thats just a guess. i dont see how a small powder charge change could significantly change anything at a wavelength that long however it may be making related harmonics at much higher frequencies that i cant hear. musical instruments have many related harmonics that give them their sound. i never heard a cymbal change frequency by hitting it harder.

[Rman]

The way I see it, a node is like a kid on a swing set, in that the kid slows, and even stops at the top and bottom of the swing. Same as in a barrel. Push the kid harder, the place at where he slows and stops changes position, same as in a barrel. Now, if the kid drags a foot (pressure point) that height and swing path changes.

Like a clean sine wave and a dirty one?

Soooo....If the frequency doesn't change when you hit a cymbal harder, what does? Amplitude? I can't remember the terminology...Either way, something changes...Is this the speed of the frequency?

This is right in line with what Git does for work, so I'm sure he'll explain it...


R.

[brendan's dad]

Hit a cymbal softly, it will resonate at a certain frequency, hit it harder, and that frequency changes. Lower powder charge, different frequency than a higher powder charge. Changing powder charge certainly does affect barrel harmonics, as you are imparting a larger of smaller external force.

WRONG

All you have changed is volume and how much time it will resonate. Frequency won't change. A tuning fork does not change frequency no matter how hard you hit it; that is why they always produce a constant frequency. Kinda hard to have a standard tune on a piano if this wasn't so!


If you change your wording from lighter barrel to shorter barrel, when referring to wave length, you would be correct. Again, when speaking about nodes, barrel weight, in general, has much less to do with it, than barrel length.

HALF RIGHT

Actually length, diameter, and material composition(mass) will all effect frequency; this is no different then when we speak about an arrows "spine".

As the OP stated, when you increase or decrease powder, you are causing the projectile to exit at a different point in the cycle due to increase or decrease velocity; you have done nothing to change the frequency. If barrels did not have a constant frequency regardless of force applied then we would have no consistency in accuracy.

As far as pressure points go, the barrel will have 1 frequency from the bore to the point and then change frequencies from the point to the muzzle. I have not changed the barrel diameter or material, just the length, so in the this case the frequency would increase on both sides of the pressure point. Again same as a tuning fork, to change frequency I change length, I don't hit it harder. That is why a certain amount of upward pressure (8 lbs) is recommended so that this pressure remains constant resulting in repeatable frequency changes.

Why do we free float a barrel? External pressure to a barrel will change frequency. Even you hand on top of a barrel when bench shooting has noticeable results. Your hand will change the frequency the same as an applied "pressure point."

The one issue we have not spoken of is temperature. In effect increase temperature changes 1 of the 3 factor which is "material composition." Luckily it only changes it temporarily and returns to normal after cool down.

In my experience gitrdun is bang on in his post and thanks for posting.

[Rman]

As you see in my last post, I now understand that the frequency itself does not change, but what does? What is this called? Is it the speed of the frequency?

It now appears that we are talking about two different things? Nodes and frequency?

"All you have changed is volume and how much time it will resonate. Frequency won't change. A tuning fork does not change frequency no matter how hard you hit it; that is why they always produce a constant frequency."

It is the resonation time that I am referring to. This appears to be the variable?
Is this not the node(s) that we look for?

"As the OP stated, when you increase or decrease powder, you are causing the projectile to exit at a different point in the cycle due to increase or decrease velocity; you have done nothing to change the frequency. If barrels did not have a constant frequency regardless of force applied then we would have no consistency in accuracy"

Ok...so, if I can't change the frequency in my given barrel, as it is a constant, then why is it important at all?
Would I not be much better off decreasing my variables?

I see now that we are speaking to two different things...

R.

[densa44]

These are the kind of posts we (I) need.

There is no reason to believe that the barrel will vibrate in a vertical direction, is there, it could vibrate say from NW to SE. Is that correct?

Second question that I have been thinking about for some time, if the bullet leaves the muzzle when the barrel is not at a node, won't the bullet have an up or down vector added to its flight?

I have one more I guess, what is you best guess about how far apart the nodes are? We could measure that in fps of the bullets?

When we see targets with bullets where they shouldn't be, from a good shooter, I have always suspected it was a slight variation in MV combined with un damped barrel harmonics.

More science is always welcome.

[Bushrat]

Link to Varmint Al's page where he shows various configurations of barrel vibration. They are exaggerated but gives you the gist of what happens when a rifle is fired.

http://varmintal.com/amode.htm

Another that shows what stress your bolt takes when fired

http://varmintal.com/abolt.htm

[Rman]

Originally Posted by densa44

These are the kind of posts we (I) need.

There is no reason to believe that the barrel will vibrate in a vertical direction, is there, it could vibrate say from NW to SE. Is that correct?

Second question that I have been thinking about for some time, if the bullet leaves the muzzle when the barrel is not at a node, won't the bullet have an up or down vector added to its flight?

I have one more I guess, what is you best guess about how far apart the nodes are? We could measure that in fps of the bullets?

When we see targets with bullets where they shouldn't be, from a good shooter, I have always suspected it was a slight variation in MV combined with un damped barrel harmonics.

More science is always welcome.

There is lots going on in this thread! Again...with regards to frequency, I will defer to Git...
With regards to nodes, I'll try my best.

The answer to your first question is yes. There are two things to watch for, vertical and horizontal dispersion.

The answer to the second question is also yes, and this is where your velocity spread and SD numbers come into play. To me, it doesn't really matter at what point, upper or lower, the bullet exits the barrel, as long as it is consistent.

The answer to your third question is also yes, although within a certain tolerance.

There are many variables involved with bullets going where they are not supposed to go, and this what most shooters try and minimize. Wind , barrel temperature, measurement accuracy, the list goes on. There is a pile of factors in misplaced bullet impact.

R.

[brendan's dad]

Ok...so, if I can't change the frequency in my given barrel, as it is a constant, then why is it important at all?
Would I not be much better off decreasing my variables?


Never said you can not change the frequency....., but what will not change frequency is force applied. You need to change the barrel length, material composition, or diameter to effect change in frequency.

Actually we normal do everything we can to avoid frequency change by having a free floated barrel or allowing cool down times a the range.

For factory ammo shooters they are limited to trying different brands to find the sweet spot. Re-loaders can play with powder and projectiles to achieve the same or often better results.

As the bullet exits the muzzle, the optimal position in the cycle is dead center and this will provide the most repeatable and consistent results. The further your exit point is from dead center, the more you are relying on the rifling and bullet quality to stabilize the flight. So since you have introduced more factors into the equation there is a greater chance for inconsistencies.

Finding the optimal sweet spot or center of the cycle is the same in theory as paper tuning a bow setup. You are attempting to find the most consistent and perfect flight right from the muzzle of the barrel.

If I shoot factory ammo and I can shoot sub 2" moa (always, no exceptions) this may be acceptable since I am hunter and limit my shots to under 200. Most likely in this situation the time and effort is not put in to find the proper ammo for the rifle and the bullet is exiting on an valley or peak of the frequency.

This thread is valuable because it informs people that if they shoot a faster bullet of equal weight that there is nothing wrong if they have a lower POI.

[Robmcleod82]

I believe the change in the frequency Rman is referring to is the amplitude.

[greylynx]

I was told years ago that placing a piece of tape stuck to the inside of the fore -end of the stock with contact to the barrel at a critical point determined by previous experimentation would "clean" your sin wave.

Therefore improving resonance.

Is there any truth to this tape theory ?

Would I be correct in thinking of the sin wave out of a rifle acting in a similar manner to EM waves that can be controlled by capacitance?

I am sure that formal barrel resonance would be measured with an oscilloscope, I just do not have the background information in totally understanding the concept.

Are we talking Frequency modulation, or Amplitude modulation, or both?

[Dick284]

Originally Posted by greylynx

I was told years ago that placing a piece of tape stuck to the inside of the fore -end of the stock with contact to the barrel at a critical point determined by previous experimentation would "clean" your sin wave.

Therefore improving resonance.

Is there any truth to this tape theory ?

Would I be correct in thinking of the sin wave out of a rifle acting in a similar manner to EM waves that can be controlled by capacitance?

I am sure that formal barrel resonance would be measured with an oscilloscope, I just do not have the background information in totally understanding the concept.

Are we talking Frequency modulation, or Amplitude modulation, or both?

Or is it a case of attenuation?

[greylynx]

Originally Posted by Dick284

Or is it a case of attenuation?

I do not know Dick 284

Anyone know of a book I can stick by big nose into to start figuring this stuff out?

I have been reading Dr. A.J. Jones book on how sin waves down a barrel can affect the shot pattern given the individual mass of the pellets.

I am just asking questions, and sources of reference.

I will leave the expert opinions to you and the other posters.

[Dick284]

Originally Posted by greylynx

I do not know Dick 284

Anyone know of a book I can stick by big nose into to start figuring this stuff out?

I have been reading Dr. A.J. Jones book on how sin waves down a barrel can affect the shot pattern given the individual mass of the pellets.

I am just asking questions, and sources of reference.

I will leave the expert opinions to you and the other posters.

From the dribs and drabs out there, it's likely a case of all of the above.

The science if it can be called that is very much in its infancy.
Change the velocity, change the pressure, change the rate of change of pressure, change the bearing surface, change the gilding metal, and expect things to change.
That's my take on it, how it changes is the wild card!

[greylynx]

Originally Posted by Dick284

From the dribs and drabs out there, it's likely a case of all of the above.

The science if it can be called that is very much in its infancy.
Change the velocity, change the pressure, change the rate of change of pressure, change the bearing surface, change the gilding metal, and expect things to change.
That's my take on it, how it changes is the wild card!

Thank Dick 284

I have a feeling if I start a literature search on internal ballistics involving sin waves I will be over my head in calculus equations very quickly. Triple integrals were never my favourite.

I will look though.


Thanks.

[James 1]

Putting all the math aside. You definately want to be at one of the nodes or anti-nodes when the bullet exits the barrel. Being a newbie at reloading, I went out and tested different powder charges and I found that as the powder levels went up that some of the bullets impacted lower. Therefore the barrel has to be whipping. Now, I also have a remington 700 that shoots different with a bi-pod on it. Should I be removing the pressure points on the stock and then develope a load on my rifle or will this cause the rifle to "open up" the groups and then I will need to fix the stock? Right now I can see the theory and it makes sense, but I am a little nervous to remove the pressure points.

[catnthehat]

Harold Vaughn's book on rifle accuracy facts covers this stuff as well as a lot of other topics .
Cat

[Cement Bench]

try the book

understanding firearms ballistics by robert A rinker 4th edition at least

Cement Bench

[gitrdun]

Originally Posted by James 1

Putting all the math aside. You definately want to be at one of the nodes or anti-nodes when the bullet exits the barrel. Being a newbie at reloading, I went out and tested different powder charges and I found that as the powder levels went up that some of the bullets impacted lower. Therefore the barrel has to be whipping. Now, I also have a remington 700 that shoots different with a bi-pod on it. Should I be removing the pressure points on the stock and then develope a load on my rifle or will this cause the rifle to "open up" the groups and then I will need to fix the stock? Right now I can see the theory and it makes sense, but I am a little nervous to remove the pressure points.

Trying to answer your questions chronologically:

1. Your barrel is whipping as you've noted, they all do to some extent. A heavier barrel in comparison should have a shorter wave lenght in between nodes (thus a higher natural or resonant frequency). The amplitude should also be smaller (the distance between the peak of a node and the anti-node).

2. The bullet will exit the muzzle at a node, the anti-node or somewhere in between. Hard if not impossible to predict. It doens't matter so much as long as it is consistent.

3. Pressure points that are intentionaly created at the factory appear at the tip of the forend. Generally either proud wood or some bedding compound. In my experience I've seen it on pencil thin barrels. I have a Rem 700 Mountain Rifle with a very thin barrel. One would expect it to have an intentional pressure point, but it doesn't and shoots very well. On the other hand, a friend was doing some load development for a Browning (can't recall if it was an X or A bolt). Frustration set in when decent groups could not be achieved. I placed a pressure point on the forend using Acraglas and the results immediately showed desirable grouping.

4. If the gun you mention has a factory pressure point, and you now add a bi-pod, said bi-pod now becomes part of the system which determines the barrel's resonance. This doesn't necessarily spell disaster unless.....the pressure point isn't thick enough so that when the barrel whips upward, it now becomes slightly detached from the pressure point. In this case the barrel leaves the pressure point on it's way up and then strikes it on the way down. I think someone mentioned a "dirty wave" form. I can concure with that as the wave form rather than being nicely sinusoidal will have a chopped and flat peak. In my world of machinery diagnostics, we jokingly refer to this as "Bart Simpson's head" lol. But, this chopped waveform when it appears on my analyzer screen is a good indication that I should be looking for loose anchor bolts, oversize bearing housing bore or under size journals etc.

5. Removing the pressure point to test results isn't the end of the world either. A pressure point can be re-established if your results are less than desirable.

The fact that your increase in powder charge resulted in lower POI truly clarifies the existence of barrel whip and it's effect. Even though you label yourself as a "newbie reloader", you seem diligent enough to observe your firearm's reaction to increased powder charges.

Sims Laboratories makes a barrel vibration dampener, I think of it more as a tuning object as you slide it the length of the barrel for varied results. They're inexpensive, I paid $15.00 for mine. It's mounted on my .223 standard profile barrel as an experiment. If your gun is shooting 1.5" groups and you wish to achieve sub-moa, you need to go back to the loading bench etc. as by my findings they don't produce such dramatic improvements. However, they seem to work if you're looking to shave another 3/8" from your grouping as might be necessary to compete in a varmint class match.

[nekred]

Frequency is how fast it vibrates,

Amplitude is by how much.....

Heavier barrells have less amplitude,
More enegry (powder etc.) increases amplitude....

I can't draw it here but think of this the whole system is vibrating and as the bullet moves down the barrel this vibration frequency changes.... take a pea and put it through a pipe and the noise pitch changes indicating a frequency change..... this is not a doppler shift vbut a true frequency change (doppler shift is the apparent change in frequency as a sound emitter in motion is moving towards or away from the receiver....

Nodes are important.... any vibrating object has point where there has to be a mode where +amplitude and -amplitude meet and cancel.... Having the bullet exit in time with one of these nodes means that usually the rifles accuracy is maximised.... Howver the vibration amplitude of the rifle barrell is measured very small incements... shooter error masks most of the error one could get from this. The theory of "inherently accurate" cartridges is usually attributed to the fact that a factory catridge happens to make proper barrell harmonics in factory barrells by fluke just happens to work out....


This works with arrows too and is important for node tuning.... the best place to have the rest is located on an arrow node.... however having the rest located on the place that is more consistent for the archer is even more important.... because the amount of amplitude in arrow vibration is nowhere near the amplitude of an archer in most cases.

[nekred]

Originally Posted by Dick284

From the dribs and drabs out there, it's likely a case of all of the above.

The science if it can be called that is very much in its infancy.
Change the velocity, change the pressure, change the rate of change of pressure, change the bearing surface, change the gilding metal, and expect things to change.
That's my take on it, how it changes is the wild card!

This is not in its infancy has been used for many years with tank guns and artillery pieces, ship guns etc. all the way back to the days of cannons...

think about this how does one artillery round hit a specific patch of dirt from 4 miles away and annihilate anything in a 30m radius.....

[260 Rem]

One of the issues that can occur with "factory wood pressure points" is that they are not always centered on the bottom of the barrel, and may not even be "level" from side-to-side. When I used to tinker with these, I would:
1. Free float the barrel and see if would shoot. If so, leave it be!
2. Install a "neutral" bedding block (an inch wide strip of bedding compound with the gaurd screws torqued to 40in/lbs on an unpillared wooden stock. The idea is for the bedding compound to contact the barrel contour, but exert no significant pressure. If it shoots, leave it be.
3. To add a quantifiable amount of pressure, install a strip of alum pop can between the bedding block and barrel ... torque ...shoot. If it shoots leave it be!
4. Add another strip of alum and repeat.
This method makes it pretty easy for novice tinkers to control the pressure and test results. If you don't have a torque wrench, just put a mark on the gaurd screw/trigger gaurd to insurte you get the same torque each time.

[nekred]

This is what r and d teams for militaries have been doing... of course it is through private contractors looking to supply the next best weapon to large militaries... contractors like FN, CZ, Remington, Colt, etc....

There are many classified articles on this stuff, and it slowly gets released for recreational use...

1993 a rifle was developed that was declassified in past 10 years that was developed as a counter sniper weapon. The rifles was not the part that is classified but the ballistics book and development still is not out for public use yet. but no matter how much rifle technology has improved.... it is still the shooter and not the weapon....

[nekred]

Pressure point.... think of a guitar string vibrating and where you put pressure between the string and the fret affects the sound therefore wavelength of frequecy has changed.... what you hear is only vibrateion from lower part of string where it is amplified by acoustics or electronics... smae with rifle what happens between bolt and pressure point is not relevant...what happens between pressure point and barrel end is....

[nekred]

Also the bullet moving down the barrell acts as a moving pressure point....

[nekred]

Lots opf complexity and instead of doing calculus and hypothetical brain aching stuff we can use a process like iteration.....


This is where we shoot a load and use it as a baseline... change one variable slightly and see what results are like and determine next change... if it gets better good.... if not go back a step and try something else....

When it comes to what is faster.... well with scientific methodology applied to load development quite often the iteration method works faster....

Like someone said I dont need to put my head up a bulls arse to figure bull chit out....

[Sashi]

When the bullet is fired, The barrel will vibrate, not necessarily at it's resonant frequency. The trick is to find the right combination of components to get the barrel vibrating at it's resonant frequency or one of it's harmonics. This way the bullet exits the barrel in the same orientation each time. Any other frequency of vibration will cause the groups to open up.

[Fredo]

You people make my head spin with all of those parameters you juggle with

For me, once recipe and COAL are found:
Dong on gong: good, happy
no dong : I did not do my part, me suck, I know gun and bullet are good

And that's all I care about!

Interesting post tho, but I like to KISS and shoot more than doing those expert foreplay techniques before trigger intercourse

[gopher]

Mathematics is a game played according to simple rules…