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.

[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

[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.

[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.