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What is a "Node"?

So, if I'm understanding this correctly (which might be assuming too much!), the goal is to have the barrel vibrating point when the bullet exits the barrel where it intersects with the straight line in Tiratore's helpful figure above in Post #12. This can be accomplished by variations in the powder charge and seating depth. The indication that you have accomplished this is that the group is small and unchanging in POI over small variations in both of these variables. Correct?

Yep, pretty much.

Now it can get way in depth and nasty if we were to dive down into the math and theory but ultimately it all comes down to what you just said.
 
I see 'node' as a decreased rate of influence from common(or target) variables.
We should probably qualify the nodes, associating which variable is brought into contribution/discussion.
seating
primer
Powder
Pressure
vibration
recoil/rest/system vibration

They all affect each other to some degree, but some combination conditions lead to better or worse results, no matter what you do otherwise.
For instance, an adjustable forearm stop isn't just to keep a gun from falling off the rest.. It's setting could potentially make a difference to accuracy, regardless of other load attributes. Would this be called a rest-node? If you can adjust it worse-better-worse maybe it should be.
 
I was following this intently, and now find myself not sure if I have been taken in by a mad run amuk children or something else I am just that nieve! Yep I guess you had me there for a minute, seeking knowledge and I found you! How lucky for me, I'll watch to stay my distance at the range if we ever should meet! What is safe distance 3-5 words- yards- miles you pick!
 
So, if I'm understanding this correctly (which might be assuming too much!), the goal is to have the barrel vibrating point when the bullet exits the barrel where it intersects with the straight line in Tiratore's helpful figure above in Post #12. This can be accomplished by variations in the powder charge and seating depth. The indication that you have accomplished this is that the group is small and unchanging in POI over small variations in both of these variables. Correct?

Don't think about it too much. Just shoot and let the target tell the tale.
 
I think I know the strict meaning of a node (as an intersection of lines), but I'm curious about how the term is being used in the context of accurate shooting.

In some usages, the term seems to be synonymous with "optimal powder/charge/bullet combination.

What do you guys who use the term understand it to mean?


As Tiratore explained there is optimal time for a bullet to exit the barrel. Chris Long ( http://www.the-long-family.com/optimal barrel time.htm ), an electronics engineer, developed a mathematical model that helps one identify the optimal muzzle velocity for a given length of a barrel. As Chris explains in his papers, his model does not account for all the variables, ie, primers, barrel contours, etc.., but it is still a valuable tool.

You need to read his papers, to get a good grip on the subject and you need to have a copy of QuickLoad to make use of it. But here's his table.

Regards.

Joe

Capture 2.JPG
 
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Someone might have put together a theoretical model of what barrel vibration might look like.

But this is a very complicated problem with way too many variables to reduce to a calculus equation.

Shooting that barrel and letting your target tell you what it likes will solve the problem

That has been done and, with respect to complexity, yes and no. Yes, if one chases all possible variables like variation in the material's (barrel, in this case) homogeneity from a metallurgical standpoint. It becomes a question of significance (will it matter) and practicality (can it be reasonably measured).

Given a medium (again, a barrel in this case), one need not worry about the variation of energy introduced to the system with respect to the timing of a 'node', since the frequency of the vibrations does not change. A guitar string produces the same note (frequency) regardless of how firmly it is plucked. Variation in energy results in variation in amplitude, the distance between the high and low extremes of the sinusoid. As ladder tests confirm, vertical spread is not a linear function of velocity. The amplitude of barrel vibration is also in play.

'Nodes', as we use the term, are located in places where the velocity of the vibrating system is slowing down, momentarily reaches 0, and reverses direction. Visualize the guitar string again - the velocity of the string's movement, regardless of how firmly it is plucked, is momentarily 0 at the very top and very bottom of its travel and it slows materially relative to its maximum velocity during the transition on either side. In this sense, it is indeed differential calculus. The first derivative of the frequency/amplitude function yields the slope of a tangent line at a given point. Nothing more than the rate of change. That rate of change is 0 at the extremes of amplitude, the highest and lowest points relative to the x axis of the sinusoid, and the rate of change is progressively smaller as these points are approached from either direction. The rate of change is at its maximum where the frequency/amplitude function crosses the x axis. In practical terms, 'nodes' are located at the top and bottom of a barrel's frequency of vibration and the barrel's velocity of vibration is highest when the barrel is 'straight', or right in the middle of its amplitude of vibration.

This is generally how OBT tables are produced. I'm sure not many are sitting on the edges of their seats waiting for further mention of differential calculus ...
 
Nodes are obviously complex and aggravating. My last target showed a group of ten spread somewhat vertically like a figure "8" with the fouling shot right in the middle at the intersection, and two subgroups top and bottom. The subgroup on top was slightly tighter and slower. The fouling shot hit dead center allright, but the velocity was right in between the top and bottom groups also. Perhaps this indicates that my best 'node' is up top? I mean, I don't know - I need to think in practical terms, with all due respect to the harmonicists. Should I try loading a lower charge to optimize this upper group next week? Anybody else have groups like this?

Thx in advance to our moderator for patience and to the website for generosity. - TH
 
Not only all the variables you mentioned but every barrel is unique.

And...JLT "agrees" in his guitar string analogy. (I think) Size of and tension on the string create the condition for the frequency. Barrel contours, material used and the process in making the barrel(I.e. Induced Stresses) all contribute to each barrels "uniqueness".
 
sweet vs sour.jpg
Harold Vaughn, in his book "Rifle Accuracy Facts" theorized that tuning was done to have the bullet exit the barrel where unavoidable small changes in bore time (related to velocity) had the least effect on where the bullet strikes the target. In his testing, he showed that as velocity was increased, the position on the target did not simply reflect the drop due to gravity acting on the bullet, but did also reflect some vertical motion of the barrel. He showed the position on the target varied as a sinusoidal function of bore time or the related velocity. The sinusoid in the figure is based on his test results. If a number of shots were fired, with some reasonable variation in muzzle velocity, at an average muzzle velocity of 3300 fps the vertical positions due to barrel vibration would be as shown in the purple circles in the figure. This is where the first derivative of position with respect to velocity is zero. Note that the range of vertical position is small. At the inflection point, around 3200 fps, where the slope is maximum, the same number of shots with the same variation produces a large variation in vertical position. To avoid confusion, I've tended to call the point where the position range is small the "sweet spot" and where it is large the "sour spot" since the term "node" already has a meaning.

The existence and reason for "sweet" and "sour" spots caused by vertical vibration (standing vibration) of the barrel as defined by Vaughn is still the subject of much discussion.
 
And...JLT "agrees" in his guitar string analogy. (I think) Size of and tension on the string create the condition for the frequency. Barrel contours, material used and the process in making the barrel(I.e. Induced Stresses) all contribute to each barrels "uniqueness".
I agree in an absolute sense. Two barrels of seemingly identical dimensions and made of the same material may very well (almost certainly) have different harmonic characteristics. The question of materiality remains, but the frequency of a system can be measured easily and in three planes. The rest is just math. What cannot be accounted for prospectively are the variations in energy that result in different amplitudes (velocity differences). These variations don't change the center of the 'node', or sweet spot as Tiratore described, just the width.

At the end of the day, it does come down to 'shoot it and see' but it is possible to narrow the window of experimentation by a lot. Hence the popularity of QuickLoad and similar applications.

Heisenberg's Uncertainty Principle affects just about everything.
 
Shouldn't bullets leaving at the lower half of their velocity spread plus upper half of barrel time spread depart at higher angles above the LOS than faster ones so their drop difference at target range be compensated for?

If so, that better not happen on the muzzle axis down swing.

Doesn't a barrel whip and wiggle at the same set of several frequencies for every shot?

Mechanical engineers doing vibration analysis will disagree with Long's speed of sound in barrel steel he used for his OBT numbers.
Two barrels of seemingly identical dimensions and made of the same material may very well (almost certainly) have different harmonic characteristics.
I disagree; that contradicts the laws of physics.

Those same ME's also know barrels of identical profiles and dimensions and made of the same material will have identical fundamental frequencies and higher harmonic ones thereof; their shape and mass are identical. Middle C metal tube (bar) on musical chimes (xylophones) vibrates at the same frequencies across hundreds of them made when smacked at any angle. They've all got the same physical properties.
 
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I disagree; that contradicts the laws of physics.

Those same ME's also know barrels of identical profiles and dimensions and made of the same material will have identical fundamental frequencies and higher harmonic ones thereof; their shape and mass are identical. Middle C metal tube (bar) on musical chimes (xylophones) vibrates at the same frequencies across hundreds of them made when smacked at any angle. They've all got the same physical properties.[/QUOTE]

That would be contrary to physics if the barrels were indeed identical in every respect. I was trying to illustrate the point that two 26" #7 contour Douglas barrels with target crowns chambered for the same cartridge will be different, to some degree. Manufacturing tolerances are not zero, nor are steel alloys perfectly homogeneous. Grab a couple and weigh them on a lab scale - you'll get different numbers. Never in the history of applied chemistry has there been a controlled reaction with perfect yield - minor differences and variables not considered always have an influence on the outcome. That goes back to materiality. Are the differences significant? Many times, the differences are too small to be measured with devices on hand or are perfectly acceptable for their intended use - tuning forks and the middle C bar you mention are examples of this. Increase the resolution of measurement and you will see differences but, practically, we cannot hear a difference of .5 Hz.

In practice, a barrel will not behave in identical fashion from shot to shot. The most obvious influence is the difference in energy introduced into the system. Variations in case capacity, powder charge, neck tension, etc. (all the things we chase in search of repeatable teeny tiny groups) will have some effect on the total energy delivered to the system and at what rate that energy is delivered. Now, take that barrel off the action and strike it twice with the exact same force at the exact same spot and it will respond the same way both times. But, the force needs to be exact and applied at precisely the same spot.

Engineers work within tolerances for a given application. Therein lies the comprehensive difference between a $6,000 BR rig and a Mossberg Patriot.
 
In practice, a barrel will not behave in identical fashion from shot to shot. The most obvious influence is the difference in energy introduced into the system. Variations in case capacity, powder charge, neck tension, etc. (all the things we chase in search of repeatable teeny tiny groups) will have some effect on the total energy delivered to the system and at what rate that energy is delivered.
I agree, but the frequencies won't change. And only tiny changes in frequencies for dimensional ones. How much does a .003" diameter difference across a 28" AMU taper (1.200" to .900" 30 caliber (.0736 square inch bore area) barrel change its resonant frequency?

Those variables you mention change the amplitude of barrel vibrations, not its frequencies. Just like the bore/recoil force, axis angle and displacement from center of movable mass changes what angle and direction bullets leave relative to the line of sight when the firing pin first touches the primer.

Note that parts fit variables across those of the rifle and ammo also effect where the muzzle points at bullet exit. Bolt face to case head mismatch is worth 1/2 MOA or more spread; typically right angles to bolt lugs in battery axis for 2 lug actions.
 
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You guys are nuts

Whole lot of hypothesis out there.

Has any of these geniuses ever gotten a rifle dialed in with their theoretical model?

I will stick with my standard load.development and let the target tell me what the rifle likes.

If they can ever program a CAD machine to create the.perfect rifle barrel with the.load to match all my fun will be gone.
 
I agree. How much does a .003" diameter difference across a 28" AMU taper (1.200" to .900" 30 caliber (.0736 square inch bore area) barrel change its resonant frequency?

Those variables you mention change the amplitude of barrel vibrations, not its frequencies. Just like the bore/recoil force, axis angle and displacement from center of movable mass changes what angle and direction bullets leave relative to the line of sight when the firing pin first touches the primer.

Note that parts fit variables across those of the rifle and ammo also effect where the muzzle points at bullet exit. Bolt face to case head mismatch is worth 1/2 MOA or more spread; typically right angles to bolt lug in battery axis for 2 lug actions.

I agree with you on all counts. Parts fit, especially those parts that are perpendicular to the bore axis (lugs, bolt face) create an oscillation relative to the vertical plane.

You guys are nuts

Whole lot of hypothesis out there.

Has any of these geniuses ever gotten a rifle dialed in with their theoretical model?

I will stick with my standard load.development and let the target tell me what the rifle likes.

If they can ever program a CAD machine to create the.perfect rifle barrel with the.load to match all my fun will be gone.

Not hypotheses. Physical science. And it is not a matter of getting a rifle dialed in. It's more a matter of narrowing the window of experimentation. It's a lot easier on one's time and one's wallet. Applications like QuickLoad can help put us is the neighborhood much faster. Finding the right driveway in the neighborhood still requires bench time and I'd much rather cover a 1.6 grain charge weight spread at .2 grain intervals than a 4 grain charge weight spread .2 grains at a time.
 
Has any of these geniuses ever gotten a rifle dialed in with their theoretical model?
Yes. Some have measured barrel behavior when fired then tuned barrels or loads to get as close to perfection as possible. Some use computer software to calculate frequencies, amplitude and axis the barrel wiggles at to predict the bullets departure direction for given bullet barrel times.

Military rifle teams learned in the late 1960's that reloaded once fired cases from their super accurate semiautos had enough out of square case heads that accuracy was worse than new cases produced. None of their bolt faces were squared up. New cases shot near 1/2 MOA tested at 600 yards; case heads very square. Once fired reloaded cases shot 2 to 3 times worse stringing from 7 to 1 o'clock. Proof that bolt faces smacked off center whips barrels moreso at right angles to receiver lugs' axis. Chreighton Audette's tests soon thereafter with 2 lug bolt guns showed shot stringing 9 to 3 o'clock with receiver lugs at 12 and 6 o'clock.

The same physical laws applied to help NASA shoot a car-size craft with a camera to Mars and Jupiter. What MOA fraction of 1st round accuracy calculations did that take?
 
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Yes. Some have measured barrel behavior when fired then tuned barrels or loads to get as close to perfection as possible. Some use computer software to calculate frequencies, amplitude and axis the barrel wiggles at to predict the bullets departure direction for given bullet barrel times.

The same physical laws applied to help NASA shoot a camera to Mars and Jupiter. What MOA fraction of 1st round accuracy did that take?

Oh my god. Comparing a space shot to our little.sport. now that is a stretch.

How many mid flight corrections did it take anyway.

I am a firm believer that ballistics works. No doubt after inputting all the environmental and ballistic information into my kestrel i can come suprisingly close on that first shot.

But what you guys are talking about is predicting where a barrel wiggling like a wet noodle in all directions, with several harmonic resonances going on at the same time, will be pointed at some miliseconds after firing. Now i know we can do a pretty good job of it with trial and error load development but to believe anyone can deal with all these variables in a mathematical model is a stretch.

Hell if it gives you a starting point and makes you feel good about it. Go for it.

But with a.little reading i think most experienced shooters would pick pretty close to the same starting point.
 
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Now i know we can do a pretty good job of it with trial and error load development but to believe anyone can deal with all these variables in a mathematical model is a stretch.
Here are two to stretch your knowledge....

This one shows your own 308 Win barrel dimensions You can enter and how different rifle weight and mass distribution effect the muzzle bullet exit angle with the rifle shot free recoil. Real shooting off ones shoulder will show similar results but more variables exist. Just pick the barrel time your load has; 1.2 thousandths second is average:

http://www.geoffrey-kolbe.com/articles/rimfire_accuracy/barrel_vibrations.htm

Measuring rimfire barrel vibrations tuning it:

http://www.geoffrey-kolbe.com/articles/rimfire_accuracy/tuning_a_barrel.htm

Varmint Al's site has others, here's one...

http://www.varmintal.com/aeste.htm

Best way to see how a rifle and its ammo vibrations and movement while bullets go through its barrel are subject to how it's held is to have several people shoot a rifle and its most accurate ammo. I've seen a 2 MOA spread in range zero's on its sight across four people, several clicks in both windage and elevation.
 
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Here are two to stretch your knowledge....

This one shows your own 308 Win barrel dimensions You can enter and how different rifle weight and mass distribution effect the muzzle bullet exit angle with the rifle shot free recoil. Real shooting off ones shoulder will show similar results but more variables exist. Just pick the barrel time your load has; 1.2 thousandths second is average:

http://www.geoffrey-kolbe.com/articles/rimfire_accuracy/barrel_vibrations.htm

Measuring rimfire barrel vibrations tuning it:

http://www.geoffrey-kolbe.com/articles/rimfire_accuracy/tuning_a_barrel.htm

Varmint Al's site has others, here's one...

http://www.varmintal.com/aeste.htm

Best way to see how a rifle and its ammo vibrations and movement while bullets go through its barrel are subject to how it's held is to have several people shoot a rifle and its most accurate ammo. I've seen a 2 MOA spread in range zero's on its sight across four people, several clicks in both windage and elevation.

Have no interest in how it vibrates. All this physics is not going to change where my bullet goes one bit. I have an engineering degree with decades of experience. I know how difficult it is to solve a problem with this many variables. The scholars start to ignore some variables and make asumptions on others. Makes people sound really smart discussing all the scientific terminology but it doesn't make them shoot better.

Just want to do my load development and shoot my little groups.
 

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