The whole issue of barrel whip and optimum loads has gotten quite a bit of discussion going. It piqued my curiosity, and I've done some measurements and calculations that may help clarify the situation.

Nobody has demonstrated the shape of the barrel whip arc to my complete satisfaction, but there are reasons to believe that a slender ellipse or figure 8, or perhaps just a line, are probably the most common. Since the math is much easier for the simple linear case, and since it will give a result quite close to a slender ellipse or figure 8, I'm using that as the model.

It is counterintuitive for a lot of people, but a bullet is quite easily moved left/right or up/down, even though it may be going 3,000 fps forward. With that in mind, there are two components to inaccuracy that could contributed by barrel whip 1) The vibration of the barrel causes the bullet to leave the muzzle with a small component of velocity up/down or left/right, caused by the barrel vibration, and 2) The barrel is slightly bent off axis, directing the bullet to a point other than the one you planned.

For the linear case, the amount the barrel is bent is A*cos(w*t+d), where w is 2*pi/T (usually a Greek letter omega, but not in this font). "A" is the amplitude of the barrel vibration (zero to peak), t is elapsed time, and T is the time required for one complete barrel oscillation. In this case, we can just set d to zero and ignore it. And we'll only be interested in things happening either in the middle or the end of the arc, so that makes t very easy to handle.

The speed of the moving muzzle is the first derivative of the position, or -w*A*sin(w*t). This is the maximum amount of up/down or left/right speed the barrel can impart to the bullet.

To put some numbers to this, you have to know the amplitude of the vibration, and you have to know how long once cycle takes.

A decent estimate of the amplitude of barrel whip is about plus or minus .005". In this case, it is not important that this number be extremely precise, since it appears in both the numbers we will be comparing at the end of this.

I hooked a microphone up to an oscilloscope, and thunked the 24" barrel of my Turkington. The resonant frequency is about 450 Hz, so T is about .0022 seconds.

Plugging in the numbers in the velocity equation, we find that a bullet that exits the muzzle in the center of the arc will be given an up/down or left/right velocity of about 14 inches per second. Allowing .1 second for the bullet to transit 100 yards, the resulting error is about 1.4".

At the end of the arc, the barrel slows down considerably. In fact, there is a moment where it stops for an instant. A bullet exiting at, or near this point will receive no up/down or left/right velocity.

Bullets exiting near the center of the arc experience another form of inaccuracy, "mis-direction". Different cartridges will have different transit times for their bullets. Two bullets with the with slightly different transit times will have a greater distance between POI's if they exit in the middle of the arc, than they will if the exit near the end of the arc.

We can put an upper limit on this mis-direction with the simple ratio .005"/.66 yards = x/100 yards. Solving for x will give you the distance between POI's of two bullets, one which exits in the center of the ar, and one that exits near the end. The result is .75". (.66 yards is the length of a 24" barrel, and 100 yards is the length of my shooting range.) Since bullets transit the barrel in about .0013 seconds, and the differences between cartridges are small compared to this, it is fair to conclude that the mis-direction error of real cartridges is much smaller than the maximum value, .75".

Conclusion: The dominant factor in inaccuracy caused by barrel whip is the up/down or left/right velocity that the barrel imparts to the bullet. The mis-direction error is much smaller. This is the exact opposite of what I had always assumed.

Audette, OCW, and the BOSS all work by getting the bullet to exit near the end of the arc, where the effects of barrel whip are minimum. Audette and OCW accomplish this by adjusting bullet transit time, and the BOSS does this by adjusting the resonant frequency of the barrel. If the shape of the arc were not slender or linear, none of these methods would work. Since they do work, it is fair to conclude that the pattern of the arc is usually slender.

I love this stuff..

But a question comes to mind.

If the T=time for one full cycle, and that is .002 second,
and t=0.0013 second for the bullet to traverse the barrel,

Then it would appear unlikely that moving the bullet seating depth up or back a distance of .005 inch or even .05 inch would make much of a difference for the exact position in the .002 second cycle for the barrel location at the time of bullet exit.

If it takes .002 second for one cycle, and .0013 for bullet in the barrel, then the whole time the bullet is in the barrel is only one half cycle. ROUGHLY speaking.

Did I miss something?

Thanks for getting this thread going.

Jameister

Deep stuff, but I follow you. I don't get all of the math, but I do get the concept. Thanks for taking time to post.

Your case for the elongated vibration pattern makes perfect sense--so much so that it would be hard to make a case for any other pattern and still match it to realities such as the calming effect of the Browning BOSS system or the extreme POI shifts from seating depth changes.

Now...

What are your thoughts on this: We often note that chrongraph data shows that the tightest extreme spreads do not group the best on the target. One possibility, I believe, is that these tight extreme spreads are tight by mere virtue of the "straight" or "un-bent" barrel. The bullets are not negotiating a curve, or bend, so they fly relatively unimpeded from the muzzle. But since no two cartridges are likely to fire exactly the same, the small (10 to 15 fps) velocity spread turns into a fairly egregious spread on the target. (Maybe your equation would help to prove or disprove this notion).

Conversely, near the end of the whip, on the node, the barrel is at full bend. Bullets are negotiating the full curve, and the barrel's state is changing fast and furious here. The muzzle is, as you mention, coming to a very abrupt halt, and preparing to change directions. To my way of thinking, this would provide a very tumultuous condition for maintaining tight extreme velocity spreads, though an ideal situation for tightness of group. And this may explain why we generally don't see the tightest ES's printing the best groups.

One more thing... When you mention what I'll call the lateral velocity of the bullet being released during the straight and fast moving portion of the vibration whip, would you think there might be an additional error factor induced by the exiting gasses as they "sweep" behind the bullet? What I mean is that the muzzle is moving quickly aside of the just released bullet, and the blast of gasses might induce a tip or "yaw" to the bullet as it first begins flight. I'm even thinking that a boat tail design might be more susceptible to this effect.

Just musings...

Thanks, Denton, for sharing your thoughts and engineer's expertise.

Dan

JMeister,

I don't think you're missing anything... I actually think you're getting it, and in the process helping me to "get" something as well, which is that for the entire range of possible barrel times, we might not be able to "run the course" of the entire vibration whip. We may have to settle for whatever node is attainable...

Of course, these OAL changes do alter pressure when they are moved in one direction or the other in a large enough jump. So the vibration dynamic might totally change for, say, a cartridge which is moved to a .035" deeper seat.

I think the notion that we can't work from one end of an individual cycle to the other with mere seating depth changes is worth further discussion.

Dan

Dan. if I may.

the .005 inch vertical distance of the muzzel, at .002 seconds per full cycle time, when reduced to a velocity vector, is .005 inches/.002 second. or 5/2 or 2.5 inches per second in the vertical direction, compared to a horizontal velocity vector of 24 inches/0.0013 second, which by these given figures, would be 24/.0013 inches/second. which is a large number indeed (1538 feet per second, although I think that the acceleration from zero speed to probable 2500 or 3000 fps has been taken into account already).

Anyway, the vertical (or sideways) component is nada compared to the longitudinal component. Not to say that yaw is not important, but the relative whipping of the barrel gases on teh bullet would be way behind the tail of the bullet.\

just my thoughts on the matter.

I still wait for more basis of the .002 seconds per cycle on the barrel vibrations.. WOuld the harmonics of a thumped barrel equal the CONTROLLING vibratory or cyclic harmonic of the powder charge or the bullet into the rifling vibrations?

curious.

Some interesting questions! One of them, I can put to rest: When "whacked" with a fast shock, the barrel rings at its natural frequency, whether the whack is a firing pin, primer, etc. or the flat of my fingernail.

I did come to the same conclusion you did: the bullet exits at about the peak of the first half cycle. For good accuracy, the "sweet spot" may not be very big.

So here's a quickie on short, stiff barrels: They will ring at a higher frequency, and with lower amplitude. Both factors reduce the error due to whip. So that's consistent with experience.

I agree that seating depth probably gets results more by altering pressure and time than transit distance. At least that makes more sense to me.

Gasses? Heckifino.

Check out this web page for some good thoughts and well stated conceptual theories. adn some fine diagrammatix of barrel harmonics.

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

THis guy varmint al has some great pictures of barrels in the first, second, third, and fourth moments of vibration. I took the chance to compare his frequencies to the ones above, and his second moments are like the 450 Hz you "rang".

Perhaps there is a first moment with lower frequencies overlooked? that would fit the idea of a findable sweet spot a little more readily.

instead of one long wave, Varmint als example shows 13 wavelengths along his barrel, each would then be about 2 inches long, and the sweet spot would then be moving only one inch from top to bottom of the wave.

I think.

its late and I will sleep on this.

Thanks for the thread.

As complex as this discussion is sounding there are numerous components that are not being directly addressed. The whip is begun when the bullet leaves the cartridge and pressure peaks. The resonance pulse travels through the metal forward and back many times before the bullet exits the muzzle. Another pulse (diminishing in amplitude travels with the bullet in the form of a pressure bulge. These two pulses and differences in barrel dimensions around its diameter all contribute to how much and in what direction the barrel whips. Short, bull barrels with sleeves pressed over them are most resistant to whip because the combination of dis-similar metals, thick barrel cross section, and short distance aiding to rigidity. The Boss (and similar) systems tune the resonant pulse to match / discourage the pressure pulse reducing or timing the whip to a point where accuracy is achieved. To the best of my knowledge there has been precious little research done to study these phenomenon.

PaulS

denton,
Vaughn, theoretically calculated the bullet deflection attributable to barrel vibration much as you did. One significant difference from my memory (I'm coming to you via the 'magic" of Hotel Room Web TV) is between your expeerimental methods of measuring the resonant freq of your respective barrels and the results obtained. While you "thunked" and measured on o-scope, vaughn used an accelerometer mounted on the barrel. IIRC, Vaughn documented multiple modes of vibrations, the most significant of which was the third mode with a freq of 1.2kHZ. Again IIRC (book not handy) the second mode was at ~400 cycles similar to what you measured.

My guess is that the differing results are attributable to different modes becoming significant depending on how het barrel is rung (thunked vs shot). Of course, you were both measuring off of different barrels (his a Rem 721) which by my guess would cause a lesser difference. In his case, his empirical testing confirmed his calculations.

Thoughts? I can try to put vaughn's real numbers in there when I get home and have a chance to look it up.

[ 03-07-2003, 12:13: Message edited by: Chris F ]

"My guess is that the differing results are attributable to different modes becoming significant depending on how the barrel is rung (thunked vs shot)." Chris F

I think this is a pertinent observation. While we know that a "bell" rings at the same basic frequency, the point that the clapper (force) stikes the bell, and the momentum of that force will cause it to sound differently--due, I suppose to the altered primary frequency. (Strike a drummer's cymbal near the bell, and then on the rim, and hear the difference).

So, can it be that the 450 hz measurement won't be, as Chris surmises, the primary in the case of the actual rifle shot? This could mean that both nodes (if you accept the "two node notion") might be within the reach of the bullet's barrel time window...

This is important... Whatever the model consensus--assuming we might come to some agreeable conclusions--the model must support the fact that some load recipes will shoot extremely well in the overwhelming majority of rifles chambered for them. The 175 grain Sierra Matchking in the .308, driven by 45.0 grains of Varget is one of many such loads. It shoots well under MOA in practically any .308 it is tried in--very few exceptions. Any vibration whip thesis would have to allow for this phenomenon.

Dan

I think a big reason some loads shoot well in all rifles is pragmatic, not dynamic. I mentioned this in another thread on case trimming, of all things. One huge factor in accuracy is alignment of the cartridge/bullet with the barrel. This is well documented. Almost all of these "magic" loads mentioned that shoot well in all guns are heavy for caliber bullets with a long bearing surface. In all commercial rifle chambers, the chamber(particularly) the neck is way too large to align the cartridge. Therefore the load is offcenter. However, chamber throats are very precise and only .001 to .002 over bullet diameter. There is no real variation gun to gun here. With a long bullet, there is enough support in the throat of the chamber to assure good alignment. This alignment issue is the whole reason benchresters use tight neck chamber reamers("bench rest reamers") and carefully turned and reamed case necks. I suspect alignment may also play a big role in the seating depth issue. Short bullets, when seated out, provide much better and consistent alignment. Seating out may be much more important than the relationship between the bullet and the lands. Most of these seating depth stories follow the path of "I began at so and so and increased slowly until the accuracy dramatically improved". This could be because the ogive of the bullet was passed and suddenly the full diameter of the bullet entered the throat.

Since I have no data, I proclaim this another theory. If someone wants to really test the bullet seating depth/vibration theory and disprove the alignment theory, then the bullet seating tests need to be run with a cylindrical bullet in in a long throated rifle. Advance the bullet in stages, and see if a minimum in group size actually occurs, or if it improves and then remains steady.

I think a lot of important items are not considered in all these vibration theories. Modern target rifles are capable of shooting almost 1 hole groups. How much of this is due to vibration control and how much is due to paying attention to all the other critical items? In .22 benchrest, it takes .2 inch groups to be competitive. These guns are all chambered so that the bullet is actually pushed into the rifling. The same was true of the centerfire breechloading black powder guns of the past. The bullet was seated into the rifling and then the cartridge inserted behind it. The .22 shooters use barrel tuners to control vibration and they work. No one worries about why. However, the improvement is in the range of a few hundreths of an inch in group size. You can bet that it is the last issue they address. It is not the key to accuracy in a properly constructed rifle.

Wow! Lots of things to think about.

I think that it is correct that there are many different kinds of vibration going on. The issue is finding which ones are important in accuracy.

When I thunked my barrel, I got the classic damped sinewave. If second or third harmonics were mixed with a fundamental, and were signficant, they should have been seen in the scope trace, and they were not. That leaves the possibility that the barrel was ringing purely on an overtone, or that it was ringing on its fundamental. I'll have to think about that for a minute, but my intuition is that it would ring at the fundamental unless we gave it a good reason to do otherwise........ or that the overtones are quite a bit less than the fundamental.

Of course, you have the possiblity of longitudinal and torsional vibrations too, as the link mentioned. So far, I can't conjure up a physical model that makes them important in accuracy.

At any rate, this is a great discussion. Thanks to everyone for the (deep) thoughts and comments.

Denton,

Help me some with the math...

How might we calculate the time elapsed from primer strike until the muzzle reaches "full bend," or the first node of the major frequency?

I ask this because I'm trying to put some sense with the universal load notion. Somehow, these recipes are having the bullet arrive on a good node in 80 to 90 percent of the rifles they are tested in...

Here's a couple more such recipes: .223 Remington, 40 grain bullet, 28.0 grains 748... or 55 grain bullet with 26.6 grains of W748.

Got a .243 win? I'll bet you that 39.8 grains of IMR 3031 will push 58 to 60 grain bullets (seated to an OAL of 2.600") into tiny groups.

How does this work???

I've heretofore believed that these loads were simply not vibration whip dependent--in other words they simply ignite, burn, and accelerate so consistently that they don't need a good node to group.
I'm wondering now, though, if there might be something inherent in the recipe that causes just about any barrel to be at full bend when the bullet reaches the muzzle... Sounds almost ridiculous, really... But these loads--and there are quite a number of them--simply work!
So again, I offer this notion not as a tangent--but rather as a real world observation that may help lead us to a useful model of what's really going on...

Thanks for everyone's time and thoughts on this,

Dan

Since my math was simply intended to find out which type of deflection was most important, I allowed myself some simplifications.

The exact answer to the question of time from pin strike to muzzle exit would involve instrumenting the rifle. A good model would involve integration. My model was extremely simple: The bullet leaves the muzzle at around 3000 fps, so its average speed is probably somewhere around 1500 fps, and it has to travel about 2 feet.... quick and dirty, and in the ballpark.

I've puzzled a bit over the evidence that OCW seems to produce good results in various rifles. I do not know why this should be so. I suspect that rifle manufacturers may test with some type of common commercial ammo, and adjust barrel contour, leade, etc., until they get a design that shoots well with common ammo. If so, perhaps what we are doing is finding a reload that has the same transit time as whatever ammo they used to develop the rifle. As I said, I don't know.

It may also turn out that my theory is all wet, and there is something intrinsic in the optimum load, independent of barrel dynamics.

That's the fun of it: See if you can figure it out, see if your theory will stand scrutiny, scrap it, fix it, or publish it as the outcome dictates.

Thanks for the continued attention, Denton.

The average factory barrel idea is worth considering... I mean, basically, the rifle manufacturers have to produce something that is likely to shoot the most common factory ammo or it won't sell. You're right. So that's a possibility.

The following is curious:

I have two .308's that will shoot 125 grain Nosler BT's into 1/2 MOA with 51.5 grains of W748 behind them. One is a 22" Remington 788, and the other is a Savage 10FP with a heavy 24" barrel. The Savage has the accuracy edge, but the old 788 isn't far behind. These two barrels could hardly be more different... But both do have 1:10 twists, and both are likely to have similar chamber dimensions.

This, too, is of considerable interest:
http://www.serveroptions.com/ubb/ultimatebb.php?ubb=get_topic;f=6;t=007488#000009

The rifle used to shoot these targets was a 26" free floated Browning A-bolt, chambered in 7mm Rem Mag. The load was kept the same, and seating depth was adjusted in very small increments, and LOOK at the POI shift. But the groups remain relatively small. (There does seem to be an inclination toward stringing in some of the groups, but the strings are so short the bullet holes touch).

So what does that likely mean?

I would have ventured a guess about two weeks ago, but all of you guys have me rethinking much.

Perhaps we'll come to some conclusions together...

Dan

That issue MAY be very simple: He failed to randomize. Barrel temperature is a surprisingly strong factor in pressure and muzzle velocity, independent of ambient temperature. As the barrel heated up, pressures and MV's increased, transit time decreased, and he fell out of the sweet spot.

Randomization is known as "the cheapest insurance you can get for the money." That is, it is usually free, and it can do a lot to protect you from an unanticipated variable.

Dan and Denton and Art and the others:

Perhaps we overlook the obvious: the OCW loads are near enough to the maximums that there islittle chance for a more "modal, or nodal, or harmonious" load to be found that coincides with a sweet spot in the vibration cycle(s).

So maybe it is just OCW finds the last (fastest)sweet spot load that beats the wilder or more complex part of the lowest frequency vibration to the muzzle, either on the first traverse, or on the second traverse, or maybe even the third, leaving the seating depth changes to optimize for the next longer wave length mode,node,or cycle.

This would likely be for only one twist rate. Since the watermelon theory would require that different twist rates would affect different torsion and radial cycles. These would make up the minor circles within the larger ellipse, to give the figuer 8 or even the shamrock effect.

The funniest thing about all these, is that we have basically resigned ouselves to theories that describe the donut, with the hole in the center what we are trying to hit!!

Well, here is some more to consider...

The 175 grain Sierra Matchking/45.0 grain Varget load (.308 win) shoots equally well in 1:10 twist and 1:12 twist bores. My Savage 10FP shoots great with this load, and about 20 other rifles belonging to various members of snipershide.com are shooting this load so well that further load development by the individual shooters was abandoned in favor of this recipe. The rifles are Remingtons, Winchesters, Rugers, and some custom rifles--as well as other Savages.

What about this:

The initial shock wave will have a particular velocity running through the barrel's steel. This wave originates at the chamber, and moves forward, along the barrel's length.

I have no idea what the velocity of this main shock wave will be... But,

What if, with the OCW load, we're looking at the relationship between this shock wave and the bullet's arrival at the muzzle?

It would seem plausible that the initial shock wave would bend the barrel to its limit in one direction on the first pass. The reflex will of course have the muzzle very swiftly swinging to the opposing node.

Hang with me here...

The elapsed time from the first node to the opposing node might just--for whatever reason--be about the right amount of time for the bullet to make it to the muzzle--so the bullet arrives at the muzzle when the muzzle reaches the "second node" for the first time.

Might the OCW load have the right balance of initial shock wave vs. bullet transit time, such that the bullet simply arrives at the muzzle on the first pass through the second node?

(Or if the times don't crunch, perhaps the second pass through the first node, or second pass through the second node, etc...)



Dan

Hmmmm.... I think that the actual important physics may be a lot simpler than all that.

Yes, there is a longitudinal shock wave that starts at the chamber, and propagates to the muzzle at about 11,000 fps, reflects off the muzzle, returns to the chamber, and back to the muzzle. Basically, the barrel is getting shorter and longer by a small amount, and I don't see how that changes POI.

Yes, there is a torsional vibration from spinning up and releasing the bullet. The barrel twists and untwists. Again, I haven't been able to imagine any reason that this would change POI.

The barrel has the transverse (cantilever beam) bending vibration, which may be on the fundamental resonance, or from vibration on a harmonically related frequency. It does not matter whether the barrel is vibrating on a fundamental, or a harmonic frequency, the same math applies in describing the linear model of the arc of the muzzle. This model provides a good reason to believe that this mode is important.

All these vibrations surely do take place, and are almost certainly independent of each other. The important issue is which contribute significantly to shifting the POI. So far, the cantilever mode is the only one that I have reason to believe is important.

Back at home again...
Lessee...first off, Green788, "Mode" does not equal "Node". You are confusing the two. Might I suggest a course or book on general physics? I myself struggle mightily with the some of the words too...me being just a Sanitation Engineer. But when I get stuck, I'm fortunate to be able to call over the neighbor's 7 year old for help with the really tough concepts.

Art S,
Vaughn touched on your seating question tangentially. He calculated dispersion then empirically tested to verify dispersion due to misalignment of the bullet entering the throat. He also calculated, then measured the effect of a "non-square" bullet base. His take on the benchrest situation was the near perfect alignment of the tight neck/chamber, plus the "correcting" effect of seating into the lands negated any potential error in a bench gun.

Denton, I have a friend in AZ named Jim Ristow that believes like you that as long as velocities are matched, loads should shoot identically in a given rifle. I initially scoffed at his theory until I thought about how intelligent this guy is. I will allow that adding your condition of same barrel transit time would make his theory more plausible to me. I was going to pick his brain a bit more on this during my trip, but he decided he didn't want to drive 2-1/2 hours in the cold and rain to have me buy him dinner - what a pansy

Denton,
It's been said more than a few times on this board; you should pick up Vaughn's book. He goes into the details of his efforts to eliminate the source of the vibration moment at the source - the receiver ring. This differs from the efforts of the folks on a recently posted link who are trying to use barrel shape to minimize vibration.

He measures the various modes of vibration and flags the third mode as being most significant in his sporter barrel. He then works to minimize the vibrations in this mode - and does so successfully all the while documenting the results with holes on paper.

He did not address any longitudinal or torsional moments other than to remove their influence from his measurement of the "third mode" (they're just "noise" in his model).

In order for all this "math" and theory to apply you have to assume that the barrel dimensions are perfectly concentric and homogenous. I'm sorry but in the real world that just doesn't happen. The harmonics of a barrel are mixed with the minute differences in dimensions and consistancy of the metal that makes up the barrel. You have harmonic nodes, presssure nodes and the variables in the makeup in the barrel to consider when trying to account for the oscillations in any given barrel. To make matters worse no two barrels are the same so trying to compare two weapons and make some kind of sense from that comparison is futile.

Look at it this way: two barrels, air gauged at the same internally and measured externally the same to within .0001 inch will have different harmonics due to the differences in alloy composition along the length of the barrels. there is no way to make two barrels identical. So any "formulae" used to approximate a universal rule for definition of barrel whip will eventually fail. It is far easier to work up a load that shoots well in YOUR gun than it is to apply that as a formula to "all" similar weapons.

PaulS

Axially elongating and compressing the barrel will contract and expand the bore diameter. Perhaps those "universal" loads are "tuned" loads..... As was surmised earlier the variety of signals generated would be timed differently and interract. Not only in the frequency/wavelength, but the point of origin, nature of the wave, source strength, source duration, source orientation, phase and more. All of these variables are within the realm of siesmology. If you were a germ living on your barrel it be an earthquake. A big earthquake. When you vary the components in your load you are changing the variables that have the most influence. I am not sure if anything in nature does not have a resonant frequency. I know a .308 diameter tube does. The "universal" 308 load may be more "compatible" with 308's due to the source strength of the powder ignition, the duration of the ignition and other things I have missed. Other sources are (in no particular order) the hammer strike, the firing pin strike, primer ignition, case expasion(does it slam?), the bullet hitting the lands, a compresing/expanding bore will modulate the signal generated by the bullet grinding its way through that twisted pipe. The vibrations/harmonics/waves/shocks/modes are propagated through the steel, contured and reflected by anything in the barrel like screw holes, sights, rifling, accelerometer?. All sound waves at around MACH17. These reflections and interactions can be regenerative or degenerative. Just like your tub has a certain speed it likes the water to be sloshed back and fourth, a single ended tube, such as a gun bore has it's own particular speed (frequency) it likes. The frequency of the bore, a major variable,could be what the "universal load" is matching. Microphones do not have the dynamic range, or the bandwith to capture all these signals. That is why some frequency bands will be missing. Some waves are unipolar and an accelerometer won't see a car wreck at axis Y if it is looking at axis X. Accelerometers do not have the bandwidth either. The figure eight? With that all that signal crashing you will not get the shape of a clean tone (for figure eight you need to tones, out of phase). What that steel noodle of a barrel will do is flip, flop, zig,zag, hummmmmmmmm, stop, scream, flip...... in little amounts that will be riding on larger patterns of motion. A tuned load would probably give a more uniform "whatever" pattern because there would be less signal mixing with complementary frequencies. Maybe the dominant signals will be the slow ass ones that the bullet speeds past.The particular frequencies involved are the most infulential. Some may have noticed I used "mode" here. Since the word is multi-modal I can be wreckless with it's application. I have a physics book. It's way behind my Common Courtesy book. For those of you who do not have your physics book you should go here Physics
Much and helpful is the information there. All that tuition and now they give the knowledge away?!
Question about the "universal loads". Was there any common characteristic to the rifles that did not do well? Does the the barrel shockwave kill the germs that live on it? It is refreshing to have a cooperative, helping "collective" (Seven of Nine fan)that answers questions and raises questions yet to be asked.

Paul,

I agree with you that each barrel will have its own set of harmonics, and likely its own unique primary frequency. They will all be different.

With that said, as Denton is alluding to, the major factor affecting POI is primarily--if not exclusively--the main orbital whip of the muzzle. One barrel's whip might look like the elongated figure 8, another's might look more like a kidney shape, for instance. A third may appear nearly perfectly elliptical... The exact shape struck by all of the muzzles could only be known by scientifically measuring all of them, so that's out...
But the model of the opposing nodes (by node I'm referring to the dictionary definition of same: a point, line, or surface of a vibrating body or system that is free or relatively free from vibratory motion) seems to hold true for any barrel that can be persuaded to group its shots.

I'm inclined toward Dentons notion that secondary harmonics are not significant enough to make noteable shifts in POI on the target.

Dan

Peppe LeBoom,

Your post appeared as I typed my last one. Mention of the Merriam-Webster definition of "node" wasn't a response to your words... (And thanks for the "courtesy" )...

Anyway,

The rifles that shoot these seeming universal loads well are of various configurations, thin and heavy barreled, short and long barreled. The ones which don't shoot the loads well--if they have a common trait it would be that they are custom rifle barrels with custom cut chambers. Some custom barrels are shooting the .308 load mentioned earlier quite well, but the barrels which don't have luck with this load are custom barrels--if that tells you anything.

You may be on to something with the musing that these loads may create similar responses in barrels which share the same bore diameter... Can you expound on this? How might the effect in a thin barrel versus heavy barrel, for instance, be seemingly negated by such a load?

Thanks,

Dan

Chris F... Thanks for recommending that book. It sounds like he's done a lot of useful work in this area. It may well be that the third harmonic is the important one, and could easily be that this is the vibration mode I was observing in my Turkington. Whether a harmonic or the fundamental, the simple harmonic motion model works.

Some of the research I've seen uses accelerometers on the muzzle. I find that a bit worrisome, since accelerometers have enough mass to significantly change the characteristics of the barrel. Also, the accelerometer responds to acceleration, which is a problem if you are trying to characterize velocity or position. Strain gauges and proximity probes are probably a better choice for two-dimensional work. If all you're worried about is resonant frequency, a microphone is just fine.

Of course, there are a lot of things happening, all at once. Under the circumstances, it is important to sort out which have a strong influence, and which have weaker influences. Just as Dan drew for us earlier on another thread, there will usually be one or two strong effects, and the weaker effects will show up as noise, riding on the main signal.

There is the old story of the mathemetician and the physicist who were told they could have a pretty girl, and each time they advanced toward her, they could move half the remaining distance. The mathemetician immediately left in disgust, because he knew that he could never reduce the distance to zero. The physicist was overjoyed, because he knew that he could get close enough for practical purposes. The same is true for most of the models we use. Practically all of them are approximations. The question is not whether they contain error, because they do. The question is whether the error is small enough that we can get useful results from the model.

Denton,

Help me with something... Does the initial shock wave travel from breech to muzzle on a 22" tapered (sporter) barrel in the same amount of time that it travels from breech to muzzle in a 22" heavy (bull) barrel? (This assumes that the shock wave is identically produced, and therefore equal in all respects for both the light and heavy barrels).

I'm thinking it does. Am I wrong?

Dan

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Dan...

Yes, the speed of that particular wave is the same, regardless of barrel shape. It depends only on the modulus of elasticity for the steel. When I quoted 11,000 fps, I simply multiplied the speed of sound in air, 1,100 fps by 10, which is about right for steel. You can probably get a bit more accurate number with a little research.

Green788,
My idea of the resonant frequency in a bore being matched by a load is a speculative explanation of why a specific load has positive results in many rifles. Up until your post I had never heard such a claim. Up until the posts of everyone else on this topic (and varmint al) I would not have made the connection of bore, barrel, load frequencies. From tuning a myriad of resonant devices that span electrical, physical, magnetic I long ago found that I could resonate almost any symetrical chamber from low humming to high whistling. Radar domes, balloons, drainage culvert, steel drums..... they all could be made to sound louder at one tone than another. The tone may have been the center frequency, or (and this is important) it could have been a harmonic of that center frequency. Center frequency is determined by the size and shape of the cavity. A rifles bore is no different. Resonance wise, there is something similar to a bore with a bullet moving down it and that is a slide whistle. The Center frequency of the bore is determined by it's size. Not the size of the material surrounding it ie, a thicker barrel. When a bullet enters the bore the size of the cavity and the center frequency are altered. The change in center frequency follows the change in the bullets' position in the bore. A tuned load will not only compliment the frequency of the bore at rest but possibly also compliment the entire frequency scale for the duration of the charge ignition. I used to have 308. Wish I could try your recipe. Something I do have that would make an interesting comparison is a 358. The center frequency for a 35 cal will be lower. A jacketed handgun bullet of the same weight as the 308 Sierra could be substituted. If we duplicate the 308 load in the 358 I would expect that the 358 load would not give as positive results in many rifles. The 308 recipe would probably give similar results in a .154 or a .616 bore due to matching the loads first harmonic to the bore. Can't test that notion without 175 gr bullets in both cal's. I think a procedure can be developed to measure the X, Y and Z motion of the barrel during a shot. Without interference with the barrel. I'll save that for a discussion dedicated to that.
Denton,
barrel steel may have similar elastic properties but the material will not be homogenous. Variations in density will occur and alter wave propagation the same way atmospheric pressure (air density) alters bullet travel and sound waves. Sound waves are a good analogy to use for this discussion. Not only because thay exist in the barrel, but also because we are familliar with them. Sound waves are compression waves and not all the signals generated in the ignition sequence will be compression waves and they will not travel at the same speed. Higher frequencies are attenuated more than lower frequencies. Higher frequencies will pentrate less material and a thicker barrel will have differences. But, as you said the variations may be negligble. Since we cannot identify these variations we should not rule out there significance. Be careful what you call noise. Better instrumentation can turn noise into a clear signal. Modem connections sound like noise.

The resonant frequency... I believe I'm following you here...

Peppe, If you have a .223 rem chambered rifle, try a 40 grain bullet and 28.0 grains of W748, or perhaps even better, try a 55 grain bullet and 26.6 grains of W748. If you own a 30-06, use a good 165 grain bullet and 57.5 grains of either H4350 or IMR 4350 (in this application, these powders do seem to interchange--it's not always true, however, with the "H" being a little slower than the "IMR.") These recipes should yield very good results. With a 6.5 x 55 Swedish Mauser, try 46.3 grains of RL22 with a 139 to a 142 grain bullet--it works, and works well. There are others, so if you don't have any of the above mentioned rifles, let me know...

This gets more intriguing by the moment...

If the main shock wave travels at about the same speed in any barrel (notwithstanding harmonics), and barrel's with the same bore diameters tend to resonate at the same frequency, smarter folks than I might be able to look at those two conditions and postulate why these OCW loads work so well in such a large number of rifles.

One more load: If you have a .270 win, go to Walmart and pick up a box of Winchester's factory "Super-X" Power Point 130 grain ammo. It's 11 bucks a box, and unless there is something very peculiar about your .270, you're going to find unbelievable accuracy from such an inexpensive load.

Later, folks,

Dan