If you're interested in air rifle barrel vibrations and how they can be tuned to improve accuracy, please check out my recent post in the UK forum, Shooting the Breeze at:
If you're interested in air rifle barrel vibrations and how they can be tuned to improve accuracy, please check out my recent post in the UK forum, Shooting the Breeze at:
Though I doubt you will get much reaction from them. Hope they prove me wrong. 😉
It's very nice to see in full the scientific approach to Muzzle Harmonics tuning.
A few more interesting ideas:
- Barrels are not uniform radially. In tests performed using Steyrs as test benches, it was found that rotating the barrel did produce somewhat dramatic effects, meaning that barrels are not radially uniform. Some actions are capable of being "indexed" meaning that you can rotate the barrel till you find the orientation that is best for your conditions, but spring-piston airguns do not, generally, allow that.
- The way the HPM (High Performance Muzzleweight) works in the new DIANA Mod 54 Air King Pro is precisely based on the notion that the harmonics are dependent on the TORQUE at the end of the barrel (being that the barrel acts like a single end supported beam), therefore the modes of oscillation of the barrel can be altered by MOVING a weight as well as by CHANGING the weight.
- IN the same way that very tall (slender) buildings can be protected by the "earthquake dampers" that are installed at the upper floors, the barrel's harmonics can be "tamed" using a "floating" weight. Perhaps, if you send me back the Tamer I sent you, I can revise it to the MkII and you can re-test it?
Thanks again for throwing some light into the "dark arts" of airgun tunning.
Good job!!! Could you please post all the graphics directly here? If not, to view them I'd need to create yet another account on yet another website that will likely track me.
It was my understanding that the "barrel vibrations" were otherwise known as standing waves. In a first approximation, the muzzle (crown) moves in a two dimensional constellation defined by the many end points of deviation from the perfectly horizontal. And you are completely correct - you do not want a "zero of function" (zero amplitude node) at the crown. As you say, you simply need near perfect consistency such that the crown is always in the same place in the constellation when the projectile exits. Then you can sight it in linearly.
That's why I'll never own a springer - because they are far too dependent on consistency of hold and position and require experienced intuition (that some might call skill) to shoot well. It's man servicing the machine, not the other way around.
Thanks for your reply. I agree that it's better to re-post everything here. The figures are the most important part of the article and tell the whole story, so it's vital to be able to see them readily. Please find below the full article.
As far as hold-sensitivity with springers goes, the LGU is pretty forgiving. Please find below some 10-shot groups off the bench at 52 yards. I think this would give many sporter PCPs a run for their money! Please check out our 9-part springer series on Hectors blog ( https://www.ctcustomairguns.com/hectors-airgun-blog).
Best wishes,
John
***
Please be forewarned that this post is fairly long and technical! There are a lot of descriptions, details and graphs, but it basically all boils down to Figure 5, where I look at how my LGU air rifle muzzle swings up and down when the pellet exits the muzzle. If you understand Figure 5, you have grasped the main points of this post.
You may be able to aim a rifle barrel accurately at a target, but the problem is that the barrel points in a different direction by the time the pellet leaves the muzzle! I’ve wondered for a long time how the muzzle moves as a shot is fired, so I finally built a system that can measure muzzle orientation on a millisecond timescale. Although I live in the USA, I’m posting this in a British forum since this work was inspired by two Britons, Mr. James Tyler and Dr. Geoffrey Kolbe. I expect that most of you are aware of Jim’s great work and I’ve learned a great deal from his Technical Airgun articles in Airgun World Magazine. Dr. Kolbe has a PhD in experimental physics and has represented the UK in international target shooting competitions. He also founded Border Barrels and Border Ballistics Technologies (BBT).
The work described here initially had nothing to do with airguns. It started when I tried to understand how tuners work for my .22 LR target rifle. I found an excellent article (Using barrel vibrations to tune a barrel) by Dr. Kolbe. This is one of the best articles I've ever read on tuners! The article is super clear and very well documented. It’s nice to see conclusions based on real measurements rather than speculation!
I only wish that Dr. Kolbe would have gone into more detail on how he selected the muzzle weight to tune the rifle (it seems a bit of a coincidence that the only weight he tried in the article worked perfectly on the first try!) and whether different holds (prone, offhand, loose vs tight, etc) would affect the results. I suspect that the relatively short dwell time (time from sear tripping to bullet exiting the barrel) of rimfire rifles would make Dr. Kolbe’s results applicable for different holds, but this tuning could be more hold-dependent for the much slower dwell-time in air rifles. Through the work that I describe here, I found the dwell time in my rimfire rifle was around 3 ms, which is significantly shorter than the ~10 ms dwell time in my LGU.
I also found an article (Precision Shooting Magazine - March- 2005 (Vol. 52 - No. 11)) that Bill Calfee published in Precision Shooting Magazine in March 2005, which unfortunately has some basic flaws. Mr. Calfee has produced some of the most accurate rifles in the world using tuners, but I don’t think his explanation of how the tuners work is correct. On the other hand, the article discussed tests showing that only the orientation of the muzzle at the time of bullet exit matters, and this is a very important, and correct, point!
For an excellent visual analysis of barrel vibrations, please check out:
A lot of people argue that the position of the muzzle should be at a node in displacement (motionless at its equilibrium position) to get the best accuracy, but now that I've thought about this some more, I think that this is wrong. I would argue that the actual position of the muzzle is not that important as long as it's only a few thousandths of an inch above or below the equilibrium position. As long as the barrel ORIENTATION at the crown is the same for each shot, who cares if it's 0.005" above or below the equilibrium position! That will just mean that the POI will be shifted up or down by 0.005". If your rifle can produce groups that show 0.005" shifts at a target, good for you! Of course there will be some vertical velocity added to the bullet as the barrel swings up or down, even if it is perfectly horizontal, so ideally the muzzle is horizontal and stopped at either the top or bottom of its swing when the bullet leaves the barrel.
At a displacement NODE, despite the POSITION of the muzzle not changing, the ORIENTATION of the muzzle changes the most! The only way to go through zero displacement at a node is to have a positive displacement on one side (moving along the barrel) of the node and a negative displacement on the other side. So the barrel at a displacement node has to be angled up or down, not horizontally. At an ANTINODE, the parts of the barrel just in front and behind the antinode have both moved in the same direction (for example up), so the barrel will be pointing horizontally. This is much more easily explained with pictures, so I've included a photo (Fig. 1) of a lecture demo that I do in one of my classes. Notice that at the antinode, the string is horizontal and all parts of the string in that area have moved up together. At the node, the string to the left of the node has moved up and the string to the right of the node has moved down. You can clearly see that at the node, the slope of the string changes the most, sometimes pointing down and half a cycle later pointing up. The photo exposure was too slow and captured the entire range of motion of the string, but if I had a fast camera you would see a simple sine wave. Of course, since the muzzle end of a barrel is free to swing, it’s impossible to get a node at the muzzle, but my point here is that even if one could get a node at the muzzle, it wouldn’t be a good thing!
One of my biggest questions is whether rimfire tuners work by making the barrel orientation the same from shot to shot, or if they actually compensate for varying bullet velocity by releasing shots on the muzzle upswing, in which case faster bullets leave earlier when the barrel is not pointed up as much, and slower bullets leave a bit later, when the barrel is pointed up more, reducing vertical dispersion at the target due to muzzle velocity variation. Slower bullets drop more on the way to the target, but are launched at a higher angle to compensate for this. This is called positive compensation. When handloading for centerfire rifles, I always thought that optimal accuracy was obtained with the bullet leaving the barrel when the muzzle POSITION was at the highest or lowest part of its swing, when it was stopped at the those ends. Now I realize that the key isn't so much that the position of the muzzle has stopped moving, but that its ORIENTATION is fixed for a brief moment, before it starts swing back to the middle of its swing. If the muzzle is truly at a displacement antinode, then the muzzle is always horizontal, so then the timing of the bullet exit wouldn't be very critical, but I don't think that's usually the case. Again, a moving barrel will give the bullet some transverse velocity, so it helps to have the barrel motion stopped at an end point of its swing. I assumed that rimfire tuners did the same thing, but it looks like you can take advantage of the swinging muzzle to compensate for muzzle velocity variations.
Maybe muzzle velocity variation isn't as critical for centerfire rifles (typically 20 fps extreme spread out of 3000 fps average velocity) as it is for slower moving rimfire rounds, which drop a lot more on the way to target? The vertical drop goes as the bullet’s time of flight squared, so a rimfire bullet moving at one third the velocity of a centerfire bullet takes three times as long to reach the same target but drops NINE times more! So with rimfires, velocity compensation is more important and with centerfires we just want to make sure the orientation of the muzzle is relatively constant when the bullet exits. Of course, at longer ranges muzzle velocity variation is critical for centerfire rifles as well, but this is usually handled by finding loads that decrease the muzzle velocity extreme spread rather than tuning for positive compensation, as far as I know.
I was so inspired by Dr. Kolbe's work that built my own "angle-o-meter." In the following section I briefly describe the setup and present results on my Walther LGU air rifle.
Figure 2 shows photos of the angle-o-meter instrumentation. I borrowed a balanced photodiode detector from my lab and used LEDs from two cheap flashlights. A polarizer sheet is taped to the muzzle and placed between the LEDs and the photodiodes. Two polarizers at +45 and -45 degrees (with respect to the polarizer sheet mounted on the barrel) are taped in front of the photodiode detectors. As the muzzle orientation changes, the large polarizer that is attached to the muzzle rotates with the muzzle, which increases the amount of light going to one photodiode detector and decreases the intensity at the other detector. Remember that as the angle between two polarizers changes, the amount of light going through the polarizers also changes. This difference is amplified and sent to an oscilloscope. Since the signal is directly related to the orientation of the muzzle, we can keep track of the muzzle orientation with a sub-millisecond time resolution. Please see Dr. Kolbe’s article for a more detailed description of this technique.
Since the muzzle orientation signal is small and not very consistent as parameters are changed, I made my own contact microphone (Make a Contact Microphone) to trigger the shot on the oscilloscope. I also got this idea from Dr. Kolbe’s article. Figure 3 shows the contact microphone that picks up the sound of the sear clicking when the trigger is pulled and sends a signal to the trigger the oscilloscope. This is the first time I used an actual rifle trigger to trigger an oscilloscope! The microphone is glued to a rare earth magnet and is placed on the receiver near the LGU's trigger. Since the microphone is picking up the sound/vibrations of the sear fall, we now have an accurate way to measure the dwell time of rifles!
Figure 4 shows the muzzle configuration with the muzzle baffle and latch attached. Note that I had to reverse the direction of the latch so that it wouldn’t interfere with my magnetic latching system. I’ll refer to these two pieces as the “muzzle brake” from now on, although I’m not sure that’s the correct term. The mass of this two-piece muzzle brake is around 100 g. The underlever is held by a DIY magnetic latch. For more details on this modification and my LGU please check:
Since I don’t use the underlever latch, my LGU can be fired with the muzzle brake removed.
In Fig. 5 I fire my LGU with and without the muzzle brake attached. This figure contains everything that I’m trying to convey in this post, so I’m going to try to explain it as clearly and thoroughly as possible. If you understand this figure, you’ve grasped the essence of this entire post!
In the top of Fig. 5, I show the impact of two shots fired from the benchrested rifle at a target 20 yards away. The aiming square on the left was used for my LGU with the muzzle brake attached. The shot went about 1.5 inches high and to the right. The aiming square on the right was used for my LGU without the muzzle brake attached. The shot went about 0.5 inches low and to the right. I was surprised that the 100 gram muzzle brake could make such a big difference in the point of impact (POI). The bottom part of Fig. 5 shows five traces that were acquired using my angle-o-meter during the shot cycles for these two shots. The top blue trace shows the sound signal from the contact microphone for the shot that was fired with the muzzle brake attached. The sound signal without the muzzle brake looks almost exactly the same, so I didn’t show it here. The first blip in this trace is from the sear falling and it lets us know when the shot cycle began. The middle two traces are the most important, showing the orientation of the muzzle with (light blue) and without (gray) the muzzle brake attached. About 0.008 s after the sear falls, the muzzle points up, then down, and then continues to oscillate. There is an overall downward orientation trend after 0.015 s. The blue and gray curves look similar, but it is clear that the dips and peaks of the blue trace (shot fired with the muzzle brake attached) are shifted to the right, to later times. This is not surprising, as the extra mass of the muzzle brake at the end of the barrel should slow down the barrel oscillations. This is exactly what Dr. Kolbe found when he attached a 200 g weight to the end of his test rifle barrel. The bottom two traces show the signals from the light gates in front of the muzzle, with the orange trace from the shot fired with the muzzle brake attached and the yellow trace from the shot without the muzzle brake. The first pulse in the light gate traces marks when the pellet passes through the first light gate. The red vertical line marks when the pellet left the muzzle, which is 6” in front of the first light gate and therefore 0.5 ms earlier than the first light gate pulse. I lined up all the traces so that the pellet exit times were the same. The slower muzzle oscillations with the muzzle brake attached mean that the pellet exit occurs while the muzzle orientation is sweeping downwards (where the vertical red pellet exit line intersects the light blue trace). This is not a good time for the pellet to exit for two reasons. First, small differences in muzzle velocity mean that pellets will exit with the muzzle pointing in different directions, and therefore go to different places. Second, slower pellets will exit later than faster pellets, which results in the slower pellets leaving the muzzle when it is pointed more downward than faster pellets. This exacerbates the vertical dispersion of pellets, with faster pellets dropping less over the same distance and also being launched at a higher angle than slower pellets. This is the opposite of the positive compensation that Dr. Kolbe was seeking. Without the muzzle brake, the pellet leaves the muzzle during the first dip in its muzzle orientation oscillations (where the vertical red pellet exit line intersects the gray trace). During the dip, the muzzle orientation is stationary, as it stops its downward motion and is about to begin swinging back up. Therefore pellets with different velocities that exit the muzzle at slightly different times will be launched at the same, lower angle, than pellets that leave the rifle with the muzzle brake attached. This explains why the pellet POI was higher with the muzzle brake attached than with the muzzle brake removed! This behavior also explains why there may be more vertical dispersion when the muzzle brake is attached, in which case pellets are leaving the muzzle when it is swinging most rapidly, while pellets that leave the muzzle without the muzzle brake attached tend to leave the muzzle when it’s stopped at the bottom of its swing. We have not achieved positive compensation by removing the muzzle brake, but at least the orientation of the muzzle is fairly constant for pellets exiting at different times!
Figure 6 shows the reproducibility of these results. Shots 2, 4, and 6 (labeled A) were made with the muzzle brake attached while shots 3, 5, and 7 (labeled B) were made with the muzzle brake removed. We see the same POI differences that were discussed for Fig. 5.
Figure 7 shows the angle-o-meter traces for shots 2-7. The scope traces show shots with the muzzle brake attached (see Fig. 4 photo) in the left column and the bare muzzle in the right column. In each graph I plot the voltage for one of the photodiode detectors (gray curve at top), the signal from the contact microphone (blue curve that is second from top), the muzzle orientation (orange curve that is third from the top), and the pellet going through the light gates (bottom, yellow curve). As with Fig. 5, I took into account the travel time of the pellet from the muzzle to the first light gate, and determined the actual pellet exit time, which is given by the vertical red line. It's nice to have the second light gate, which allows me to determine the muzzle velocity each time to get the pellet exit time more accurately. Please note that the muzzle is pointing up more for the weighted muzzle than for the bare muzzle when the pellet exits the muzzle, which is consistent with the POI differences. This is shown by the horizontal black dashed lines. The POI difference allows me to roughly calibrate the orange curve to determine muzzle angle for a given voltage signal. I get around 0.26 degrees per volt.
I’ve done some preliminary test on how different holds affect POI and how this shows up with the angle-o-meter. When I hold my LGU (or for that matter any springer I’ve tried so far) tightly against my shoulder off the bench, the POI goes up about 0.5” at 20 yards compared to when I use a loose artillery hold, where my shoulder doesn’t touch the butt pad. When I shoot the rifle in the field target sitting position, I also get shots landing about ½” high at 20 yards compared to the artillery hold off the bench. Maybe this is also due to increased shoulder pressure on the buttpad in the FT sitting position? I discuss this in Ch. 2 (Figs.2.6 and 2.7) in Hector’s blog (Hector's Airgun Blog). In Fig. 8, I shot my LGU off the bench with a tight hold against the shoulder (Run 9) and a loose artillery hold without any shoulder pressure on the buttpad (Run 10). The two shots in Run 10 were consistently lower than the three shots in Run 9. When I look at two “typical” shots using the angle-o-meter, the muzzle orientation with the tight hold (gray trace) tends be at a slightly higher angle and the oscillations tend to be a bit slower than with the loose hold (blue trace). As a result, the pellet exits when the muzzle is pointing higher up with the tight hold. Why the oscillations slow down with the tight hold is not clear, but if it is real, it is an interesting result. I suspect that is has something to do with my upper body mass recoiling with the rifle for the tight hold. Since springers are hold sensitive, the usefulness of tuning the rifle with the angle-o-meter may be limited, but if you use a fairly consistent artillery hold in different positions or if you shoot a lot from the bench, then the optimal configuration should work for most of your shots.
I hope that this presentation made sense and that you found the results interesting. Please find below some takeaways:
1. Removing the muzzle brake on my LGU causes faster muzzle oscillations resulting in the pellet exiting near a dip in the oscillations. This causes a lower POI and may be the reason why my LGU is more accurate without the muzzle brake.
2. The muzzle of my LGU initially dips down about 0.05 degrees and then oscillates with an amplitude of about 0.1 degrees at a frequency of around 600 Hz. I always wondered how the muzzle moved on firing, so this is nice to know!
3. This may be a new way to tune air rifles! By fiddling with the muzzle orientation oscillations, one may be able to do velocity compensation? Of course, MV compensation would work best at only one distance, which may explain why some rifles have smaller vertical dispersion (in MOA) at longer ranges than at shorter ranges? Has anyone seen something like this?
4. For the first time, I could measure dwell time of an air rifle, from sear release (making a sound that's picked up by the contact microphone) to pellet exit. The dwell time in my LGU is 10.0±0.3 milliseconds, which about four times longer than in my target 0.22” rimfire rifle.
5. In a few shots I was able to determine why the muzzle brake caused shots to go high and increased vertical dispersion in my LGU. It took hundreds (maybe more?) of rounds to convince myself that there was slightly more vertical dispersion when the muzzle brake was attached. Therefore, I'm not sure that shooting a few groups will always explain what is going on, especially if the effect is subtle/small. With the muzzle angle measurement I could see that the extra muzzle weight caused the pellet to exit the barrel when the orientation of the barrel was changing rapidly, which made it very clear that small muzzle velocity fluctuations would cause more vertical dispersion. Also the muzzle was swinging down, which is exactly the opposite of what you want. In this case, faster pellets get launched at a higher angle, which causes even more vertical spreading due to MV variations. Please check out Ch. 8 when it comes out in the next few weeks in Hector’s blog (Hector's Airgun Blog). In that chapter I discuss the accuracy difference in my LGU with and without the muzzle baffle. I refer to the muzzle baffle as the “muzzle cap” and didn’t attached the underlever latch in that chapter, so the added weight at the muzzle is smaller and the oscillations aren’t slowed down as much as they are with both the muzzle baffle and underlever latch attached. I expect that if I attached the underlever latch in addition to the muzzle baffle, I would have seen even more vertical dispersion at the target.
6. The muzzle orientation traces explain why slower pellets might actually have a higher POI than faster pellets. It all depends on which way the muzzle is pointing when the pellet exits!
I should note that the muzzle swing may not be strictly up and down. There is clear side to side movement that depends on muzzle weight as the POI shows in Figs. 5 and 6. In this post the angle-o-meter was set up to measure vertical motion, but one could easily mount the polarizer sheet horizontally at the muzzle to measure the side-to side motion.
People have done high speed photography to look at the muzzles of air rifles during a shot, but as far as I know, this is the first time that muzzle angle of an air rifle was measured directly on a sub-ms timescale using Dr. Kolbe’s system! These measurements give us new insights into the behavior of air rifles and could be useful for making them more accurate. Thanks for slogging your way through this post! I'm looking forward to hearing from you.
Thanks for your reply. The response and interest on Shooting the Breeze was actually quite good, with 400 views in 48 hours and 15 replies. ?
I'd be happy to re-test the modified tamer, but I suspect that my LGU is shooting about as well as it's going to and any changes will only make things worse.
@johnc well, if you are convinced, then that will probably be true for you. Shooting is 75-90% mental. 😉
Two notes here:
- I call the barrel vibrations "harmonics" NOT because they are multiples of each, or because the modes of oscillation can be clearly defined, but because, the Standard Profesional way of analyzing ANY machine's vibrations is by Fourier Analysis. And the software with which I started looking at vibrations of the muzzle almost 4 years ago with my friend Gerardo Quiroga used 3D accelerometers. So there was a LOT more data available.
- Any simile made between a barrel and a vibrating string is bound to have problems because barrels act more like cantilever beams than like instrument strings. The BIG problem of the DIANA 56 and most of the Pro-/Pro-Compact models is the HUGE weight at the muzzle, that DOES act like a "fixation anchor" in space through inertia, and creates a LOT more vibrations than those that it solves.
I wonder if two different (and in opposing senses) gradated line screens could measure the POSITION of the muzzle, or at least the DISPLACEMENT OF THE MUZZLE during the shot cycle. The wave determining the total displacement of the muzzle needs to be of lower frequency than the high frequency vibrations of the "attitude" or "angle of attack" of the muzzle, and therefore, the deviations imparted to the pellet must be much bigger. Just a theory.
I find the concept of a cantilevered beam very interesting, having spent most of my career in architecture/structural engineering/construction.
Two of the most accurate open-sight springers I have owned SEEM to have taken this into account. One was the Belgian Hyscore 801, which had a very elegantly tapered barrel from breach to muzzle. The other is a pre-war Haenel III, which has a roughly 2.5" long thickened shoulder in front of the breach block.
Bending is maximized at mid-span in a simple beam, and at the unsupported end in a cantilever, but shear is maximized at the connection point in either case. But this is only applicable to static loads. Dynamic loads are MUCH harder to understand. But, intuitively, it would seem that a thicker connection point at the end of a cantilevered beam would reduce potential bending due to induced dynamic loads.
Very interesting article, John! Thanks for sharing it.
I have a question.
You mention numbers for muzzle vibration of 0.005" (I assume this is peak-to-peak) at 600Hz. Some arithmetic translates this amplitude and frequency into a maximum lateral velocity (as the muzzle passes through zero deflection) of...
(0.005"/ 2) x 600Hz x 2pi = 9.4 inches per second = 0.79fps
If the gun in question has an MV of ~825fps, 0.79fps of transverse velocity would translate to...
arcsin(0.79 / 825) = 0.05 degrees
...of pellet trajectory deflection.
My question: Is the fact that this simple calculation of transverse oscillation so closely matches your figure for angular oscillation only a coincidence?
Thanks for the reply and the thought-provoking analysis. I haven't been able to figure out how to determine the displacement of the muzzle; I can only measure the orientation. The displacement of 0.005" was just a rough estimate based on what other people measure (and I'm not even sure from where I got it).
You do bring up an excellent point about transverse velocity. I completely neglected transverse velocity in my analysis, but transverse velocity could be quite important and may enable us to estimate the amplitude of the displacement, as you have done. If the max transverse velocity is 0.79 fps (assuming the muzzle displacement really is 0.005" and the muzzle frequency is 600 Hz), then the deflection of pellets due to transverse velocity is up to ~0.7" at 20 yards. This means that a pellet leaving the muzzle at the middle of the downward swing should hit about 0.7" low at 20 yards, certainly not negligible! I see pellets that leave near the middle of the swing hitting a about 1.5" higher than those that leave at the bottom of the swing (where transverse velocity is zero), which means that the POI of the pellets leaving at the bottom of the swing is actually 0.7"+1.5"=2.2" below the POI zero (muzzle horizontal and not moving). This means that either the barrel orientation is pointing down more at the bottom of the swing than I originally estimated or that the transverse velocity is smaller (displacement of the muzzle is much less than 0.005").
I don't think Kolbe worried about small differences in transverse velocity in his analysis. Not only is the orientation of the muzzle different at different bullet exit times, the transverse velocity is also slightly different. Kolbe's bullet exit times are pretty close to the end of the barrel swing, where transverse velocity is small, so maybe the differences in transverse velocity in his measurements are much smaller than differences due to muzzle orientation? By the same token, at the end of the muzzle swing the orientation doesn't change much either, so there may be no way to get rid of the effects of transverse velocity and one cannot ignore it?
I hope that I haven't confused things even more, but I agree that transverse velocity is important if the muzzle displacement is on the order of 0.005" or bigger.
Thanks for your reply. We need more people like you to help with this. I'm afraid that my understanding of the vibration of barrels is based on a simplified picture of strings that are either clamped or completely free to move at the ends. You get the same sinusoidal solutions; it's just that the boundary conditions are different. I'm not sure how well this applies to a cantilevered steel beam.
Thanks for the reply and the thought-provoking analysis. I haven't been able to figure out how to determine the displacement of the muzzle; I can only measure the orientation. The displacement of 0.005" was just a rough estimate based on what other people measure (and I'm not even sure from where I got it).
Thanks, John, for the thoughtful response.
The relationship between muzzle angle and displacement would seem to "hinge" (pun will soon become obvious) on the shape of the vibrating barrel. If we could assume (we can't -- quite) that all the bending of the barrel occured at the breech where the greater mass of the gun holds it stationary, like so...
...then for 0.05 degrees of angle, we'd get 0.00042ft of deflection for every foot of barrel length, and therefore at 600Hz, 1.6fps of transverse velocity, making displacement more important than angle for typical airgun MVs and barrel lengths.
But of course vibrating barrels (or as Jim says, cantilevered beams) don't vibrate as if there were a hinge at the breech. So how good (or bad) is approximating their motion as if they did?
Solving the necessary math is beyond me, but Dr. Google found this...
This graphical approx. suggests that the "effective" length of an actual beam (barrel) is about 71% of its total length, producing a quick and dirty approx. of transverse velocity for a barrel vibrating at 600Hz through 0.05 degrees of 1.1fps/foot.
Suggesting that transverse velocity is the dominant effect over angle by a substantial margin.
PS: To generalize the math a bit (i.e., separate it from the assumptions that a = 0.05, MV = 825, and frequency = 600Hz). let...
a = maximum deflection angle (degrees and < 1)
L = barrel length (assume uniform barrel diameter)
MV = fps
f = barrel vibration frequency...
Then...
D = peak muzzle displacement = 0.71 * a * L / 57.3 (note: 57.3 = degrees / radian)
V = peak transverse velocity = 2 * pi * f * D = 2 * pi * f * 0.71 * a * L / 57.3
p = peak pellet trajectory deflection angle (due to transverse velocity) = 57.3 * V / MV = 57.3 * 2 * pi * f * 0.71 * D = 2 * pi * f * 0.71 * a * L / MV
p = 4.5 * f * a * L / MV
So, when would we have p > a and therefore transverse velocity more important than angle?
I (finally) made it all the way through Kolbe's article, and agree with you that he never considers muzzle displacement nor transverse velocity. But (as I understood it) neither did he consider muzzle angle per-se.
Kolbe's goal was to use the rate of change of muzzle angle as compensation for variation in muzzle velocity as reflected in the bullet's transit time from breech to muzzle, and to use barrel tuning to adjust the timing relationship between them so that the former canceled the latter. For his test rig, 6MOA/ms was the magic number to get muzzle flip to change just the right amount (up or down) to correct for muzzle velocity changes (down or up) at his particular chosen range from muzzle to target of 50m.
Said MV compensation (6MOA/ms) only worked at that range (50m). Shorter range would require less, longer range more.
Note that this intention to use muzzle vibration to correct for an entirely different factor of interior ballistics (MV) would seem to be very different from wanting to reduce or cancel the effects of muzzle vibration altogether, which (unless I misunderstood) is your object.
Thanks for the reply and the thought-provoking analysis. I haven't been able to figure out how to determine the displacement of the muzzle; I can only measure the orientation.
Hi John,
I think I may have come up with a way to make that displacement measurement.
In general, I would agree with Steve that the transverse displacement of the muzzle is more important than the angle of the muzzle at the moment of pellet release.
What, to me, is an unrealistic approach is to leave/make the rifle to operate in "thin air".
While a free-standing object will rotate around its center of mass, once a gun is shouldered, held, and supported, the whole mass distributions change, and what would have been a radius for the torque to be developed from a force applied at a certain point, changes radically.
In actual firing, most shoulder-fired guns in precision/accuracy oriented pursuits are supported at some point between trigger guard and end of fore-stock (most because long range BPCR shooters support their barrels directly on crossed sticks). So, the "torque" changes from whatever the "free-floating" gun does to something less (radius decreases, torque decreases).
My personal tests and experience show that the biggest excursion I have observed in guns with very light barrels (14 mm's OD), and no Muzzle pieces of any sort are of the order of +/- 1 mrad. at around 12 ft-lbs. (20 mm's @ 20 meters in each single direction)
Go up to a 15 mm's OD barrel and that is cut by about ½ (20 mm's overall at 20 meters)
Go up to 16 mm's OD barrel and it is further cut by ¼ (15 mm's overall at 20 meters)
If you shim and sleeve a 16 mm's barrel up to 18 mm's OD, then you cut that by 1/8 (about 12.5 mm's overall at 20 meters).
Now, these experiments coincide with other's results.
What has been pointed out about the JUNCTION of the barrel to the breechblock has also been proven to be correct.
This is an interesting video:
That shows the importance of the rest used.
What can be seen here in the Y-X plane is ALSO happening in the other planes, but somewhat less pronounced because the point of support in these real life firings is always UNDER the gun.
BUT if, when hunting, you place your gun directly in contact with a tree or other lateral support, you will see the POI "bounce" away from the support point.
I LIKE the idea of measuring stuff, what I still cannot get myself to like is the idea of a gun fired "in a vacuum" LOL!
In general, I would agree with Steve that the transverse displacement of the muzzle is more important than the angle of the muzzle at the moment of pellet release.
What, to me, is an unrealistic approach is to leave/make the rifle to operate in "thin air".
While a free-standing object will rotate around its center of mass, once a gun is shouldered, held, and supported, the whole mass distributions change, and what would have been a radius for the torque to be developed from a force applied at a certain point, changes radically.
In actual firing, most shoulder-fired guns in precision/accuracy oriented pursuits are supported at some point between trigger guard and end of fore-stock (most because long range BPCR shooters support their barrels directly on crossed sticks). So, the "torque" changes from whatever the "free-floating" gun does to something less (radius decreases, torque decreases).
I agree, Hector. If a springer's POI wasn't sensitive to how it's held, whence cometh their famous hold-sensitivity?
However, isn't the favored point of support point you so aptly describe usually at or near the balance point, hence directly below the center of mass, and therefore as close as the shooter can get to allowing the gun, when it recoils, to freely rotate around the CM?
So while taking recoil measurements from the unrestrained gun (unrestrained at least in the vertical plane) may fall short of perfect duplication of any individual shooter's style, of all the possible choices, isn't it the best generally-applicable approximation the experimenter can choose?
In general, I would agree with Steve that the transverse displacement of the muzzle is more important than the angle of the muzzle at the moment of pellet release.
What, to me, is an unrealistic approach is to leave/make the rifle to operate in "thin air".
While a free-standing object will rotate around its center of mass, once a gun is shouldered, held, and supported, the whole mass distributions change, and what would have been a radius for the torque to be developed from a force applied at a certain point, changes radically.
In actual firing, most shoulder-fired guns in precision/accuracy oriented pursuits are supported at some point between trigger guard and end of fore-stock (most because long range BPCR shooters support their barrels directly on crossed sticks). So, the "torque" changes from whatever the "free-floating" gun does to something less (radius decreases, torque decreases).
I agree, Hector. If a springer's POI wasn't sensitive to how it's held, whence cometh their famous hold-sensitivity?
However, isn't the favored point of support point you so aptly describe usually at or near the balance point, hence directly below the center of mass, and therefore as close as the shooter can get to allowing the gun, when it recoils, to freely rotate around the CM?
So while taking recoil measurements from the unrestrained gun (unrestrained at least in the vertical plane) may fall short of perfect duplication of any individual shooter's style, of all the possible choices, isn't it the best generally-applicable approximation the experimenter can choose?
Thanks, as always, for your expert opinions.
That depends on the shooter, AND the gun, Steve.
As I noted, BPCR shooters support directly the barrel of their long guns, USUALLY somewhere near the front third. SOME FT shooters, usually those that use the "bent arm" type of support use some point near to the trigger guard because it approximates the CoG/CoM of the gun. BUT the problem with that position is that it cramps the body's breathing space.
Personally, I prefer to hold my FT gun the same way I would hold a High Power rifle (7.62X51), and that is with a "firm grip/cheekweld and shoulder contact". A more "open position" allows for better breathing and in long matches it does make a difference. In this sense, the 54 is definitely the best gun. Though the 430L, even without the sled system, does also very well indeed.
Recently, I have also foregone all "accoutrements" (jacket, harness, sling, hamster, etc.) in favour of what I have called "Simple FT", and that requires a different hold (not "Artillery"), and demands better consistency from the shooter. But the results are more enjoyable.
If you look at this picture:
You can see better what I mean.
At 65 YO I do not have the flexibility of the great younger shooters (like Leo Gonzales, Nathan Thomas, Steve English), but I do find that this position allows me to at least "be in the same block" LOL!
The other factor that drastically alters the recoil movement in ANY form of shooting is the weight of the scope. Most FT scopes are in the 2-2½ lbs weight range, and the big mass at the "top" of the gun also changes where the CoM/CoG would be, therefore altering the vibrations of the muzzle.
My personal opinion is that a well tuned springer is "hold sensitive" in the sense that you need to learn how to hold THAT gun, but once you have found a good hold, the orientation/elevation of the shot to be taken, does not change too much the accuracy/precision of the POI (except for the allowance needed for trajectory along the angle itself).
Most modern "fixed barrel" airguns are, in reality "free floated barrel" guns, so the age old method of changing the bedding is not as useful, as there are no "barrel bedding" points; though most guns react well to some tuning of the stock screws for the specific pellet and power level being used.
Even for BR shooting, our conversations with other shooters that have problems precisely "resting the rifle at the balance point" have shown that most guns do NOT "like" being rested there and prefer a more forward position. Where exactly, again, depends on the gun, the pellet and the power level.
IF I had to give a general advise about where to start, I would say that a good starting point are the forend screws. So, substantially forward of the CoG/CoM. From there a little fiddling fore and aft will tell you quickly what the gun likes.
The other factor that drastically alters the recoil movement in ANY form of shooting is the weight of the scope. Most FT scopes are in the 2-2½ lbs weight range, and the big mass at the "top" of the gun also changes where the CoM/CoG would be, therefore altering the vibrations of the muzzle.
...
That is certainly true, Hector. In fact so much mass added above the piston's (and therefore recoil's) axis of action, might come very close to making it pass right through the CoM. This would of course eliminate the tendency of reaction to piston acceleration (both recoil and surge) to rotate the gun around the CoM, altogether.
That would leave only off-axis force applied at points of contact between the gun and points of support (e.g., the shooter) to provide gun-rotating and POI-shifting torque.
That is definitely true when shooters use "Sporter" stocks as I am using now in my 430 L²S²P
But, as you can read in John's Chap 6, the weight of an FT stock can be much more than the weight of the scope.
To put some ROUGH numbers (because wood is an organic material that can vary in density quite drastically) into this statement:
- An LGU/LGV "Sporter" stock weighs 2# 8 Oz.
- The LGV Ultra action weighs 7# 2 Oz.
- The scope and mount in John's rifle must weigh about 3# 1 Oz.
- John's gun weighed originally 12#11 Oz.
Changing the OEM stock for the "DIY FT stock" took the gun to 16# 5 Oz
SO, the FT stock weighs 6# 2 Oz. or about twice what the scope and mount weigh.
For a refresher:
As you can see, MOST of this weight is WELL UNDER the recoil axis (just look at the butt section of the stock). And so, a large, heavy scope does not "do" as much as it would when the stock is a simpler affair.
Being that most of the stock is UNDER the recoil axis, it would seem logical to assume that the FT guns mostly tend to spin in such a way that the muzzle gets elevated for every shot, and that would be a reason to use the "over the shoulder" hook that so many FT shooters use.
It would also explain why, IMHE, the LGV's benefit greatly from short, heavy scopes located at the rear of the action. And why the LGV Ultra with the synthetic stock exhibited this behaviour to a greater level than the wood stocked counterparts.
And yet, in the overall results there is little difference (half a pellet diameter) in the overall grouping performance.
Thanks for the comment, it started some wheels in my head, LOL!
That is definitely true when shooters use "Sporter" stocks as I am using now in my 430 L²S²P
But, as you can read in John's Chap 6, the weight of an FT stock can be much more than the weight of the scope.
To put some ROUGH numbers (because wood is an organic material that can vary in density quite drastically) into this statement:
- An LGU/LGV "Sporter" stock weighs 2# 8 Oz.
- The LGV Ultra action weighs 7# 2 Oz.
- The scope and mount in John's rifle must weigh about 3# 1 Oz.
- John's gun weighed originally 12#11 Oz.
Changing the OEM stock for the "DIY FT stock" took the gun to 16# 5 Oz
SO, the FT stock weighs 6# 2 Oz. or about twice what the scope and mount weigh.
For a refresher:
As you can see, MOST of this weight is WELL UNDER the recoil axis (just look at the butt section of the stock). And so, a large, heavy scope does not "do" as much as it would when the stock is a simpler affair.
Being that most of the stock is UNDER the recoil axis, it would seem logical to assume that the FT guns mostly tend to spin in such a way that the muzzle gets elevated for every shot, and that would be a reason to use the "over the shoulder" hook that so many FT shooters use.
It would also explain why, IMHE, the LGV's benefit greatly from short, heavy scopes located at the rear of the action. And why the LGV Ultra with the synthetic stock exhibited this behaviour to a greater level than the wood stocked counterparts.
And yet, in the overall results there is little difference (half a pellet diameter) in the overall grouping performance.
Yes, I certainly can see that the DIY stock masses twice as much as scope and mount. Thanks for that info.
However, here's a parting thought before bedtime.
The effect of any given mass on the location of the CoM relative to the axis of recoil, depends not only on the amount of mass, but just as much on the perpendicular distance (i.e., lever arm) separating mass and axis. Therefore while, for example, the mass of the DIY forearm is undoubtedly significant, it's so near the axis of recoil that it probably contributes relatively little to moving the CoM away from the axis. Meanwhile, the tall mount and scope probably contribute more than simply considering their weight would suggest.
Maybe this is (at least part) of the explanation for only a half-pellet-diameter effect from 3# 10oz of extra stock?
Yes, I certainly can see that the DIY stock masses twice as much as scope and mount. Thanks for that info.
However, here's a parting thought before bedtime.
The effect of any given mass on the location of the CoM relative to the axis of recoil, depends not only on the amount of mass, but just as much on the perpendicular distance (i.e., lever arm) separating mass and axis. Therefore while, for example, the mass of the DIY forearm is undoubtedly significant, it's so near the axis of recoil that it probably contributes relatively little to moving the CoM away from the axis. Meanwhile, the tall mount and scope probably contribute more than simply considering their weight would suggest.
Maybe this is (at least part) of the explanation for only a half-pellet-diameter effect from 3# 10oz of extra stock?
Cheers,
Steve
I agree. When I was talking of mass being well under, I was referring to the butt section, that usually takes between 1/3 and 3/8 ths of the weight of a stock.
And it also explains why benchrest guns are not really "shootable" under real field conditions (regardless of their overall weight).
Microfit is now doing an interesting thing with their BR/Target stocks: almost completely hollowing out the off side of the butt section, thereby concentrating most of the weight of the stock in the heavy forearm.
This idea would also explain why slender/linear stocks are perceived to be more "shootable" than convoluted stocks, and why the modern design of stocks that make the guns less "hold sensitive" are gaining ground.
I made some new barrel vibration measurements where weight was systematically added to the muzzle. I mapped out the muzzle motion using POI changes as well as the Kolbe crossed-polarizer system (angle-o-meter) that was used in this post. This may be a more systematic way to tune an air rifle.
You guys are all brilliant but You have given me a headache. At 77 all I care about is maintaining a 1/2 " group at 50 yards without wind. It really is a very interesting topic but end results to me would likely not make a significant difference on the match results ladder. That means to me right now we are all playing with close to the same vibration problems which equal pretty much a level playing field. I feel by the time that changes I will be history. We do have great minds in this game. May the search for excellence live forever. Thank you for making my old head vibrate 🙄
Interesting extension to the work performed before, thanks!
I wasn't able to see the pictures in detail, but I think I understood.
I am still not convinced that the ANGLE of the muzzle is independent of the POSITION of the muzzle.
To accept this would mean to accept that there ARE nodes and antinodes ALONG the barrel, and that is a very hard thing to prove. Especially in a spring gun that is bucking like a bronco for every shot. Even in a RF, the pressures involved in the firing cycle are enough to exploit the minute differences in material and geometry of a barrel to induce a lot more motion to the different sections of a barrel, even more so in a CF, but in an airgun, there is not enough pressure inside the barrel.
AND, I still maintain that airgun barrels work as cantilevered beams, not as strings that are attached at both end points. At least, not within the time frame of the shot cycle and pellet leaving the muzzle moment.
As you may recall, the HPM (High Performance Muzzleweight) works by VARYING the APPARENT length of the beam, and this is where people REALLY DO NOT REALIZE how high the frequency of vibration is, you read highly respected tuners/smiths telling people that they have made tests placing weight in positions along the barrel which undoubtedly are inches apart. And yet, we know, from the experience of dozens of users that use the HPM, that SMALL increments (1.5 mm's) are needed to resolve differences. Some users make special spacers in 0.5 mm's
Moving weights along the barrel by inches at a time opens the test to any number of possibilities. None of them good.
At 12 ft-lbs, and with barrels in the 0.625" OD region, there is a PERIODICITY of about 4-5 spacers (5 to 6.5 mm's), that is consistent. Meaning that if a barrel shoots well with 3-4 spacers, it will shoot well again with 7-8 spacers. AND this is with weights in the 60 grams region. We have also demonstrated that the POSITION of the POI changes as the apparent length of the beam changes, to me, that is a proof that the position of the muzzle is correlated to the angle.
What I really missed from both your entries was some reference to the Monte Carlo simulations that you made to show that the best use of 100 test shots was 10 X 10 shot groups. AND I think it is high time that we stopped just measuring group size and start using Mean Deviation from POA, as this is a more useful / simultaneous measure of precision and accuracy.
For academic purposes, what probably needs to be done is to calculate the angle of the muzzle, by assuming a beam that is 3/4 the length of the barrel and using the muzzle displacement as the endpoint for that angle. If this approaches the results you measured, then the angle exists, but is dependent on the position of the muzzle.
From the practical side, many shooters are using their HPM's to tune to a specific pellet and MV, if that means that my theories are wrong, it's OK, I will still maintain that the HPM is a device that works, even if we do not FULLY understand "why"
Thanks for your detailed post. I agree that muzzle orientation and muzzle position most certainly are not independent of each other and didn't mean to give that impression! My point was that muzzle orientation may be a more important parameter, since the POI due to muzzle orientation scales with distance (unlike a uniform translation of the whole rifle) and we typically point the rifle, tipping it around a fulcrum in order to aim, rather than moving the entire rifle up/down/sideways. When we say the muzzle is at a higher position, we usually mean that it's higher than the rest of the barrel (or the barrel center line), but that really means that it's pointing up. It's a subtle distinction, but I think the muzzle orientation tells us more about where the pellet will go than the muzzle's absolute position (in which case we also need to think about the barrel position right before the muzzle,which of course is how we determine the orientation!).
I wouldn't be surprised if muzzle orientation and muzzle position were extremely closely correlated, especially at early times before the rest of the rifle/barrel have had much time to move.
I certainly agree that barrels act as vibrating cantilevers and most definitely not as strings attached at both ends, but some famous people like Bill Calfee and a writer in UK's Airgunner magazine have used this picture, so I'm trying to address that misconception. I'm not assuming anything about harmonics, nodes or vibration patterns. In this experiment I actually measure the muzzle orientation (using POI at 20 yd and the angle-o-meter) and try to get the pellet to exit the barrel when the orientation is changing the least with time (is at an extremum).
I must admit that tuners are a mystery to me and many of the explanations of how they work don't make sense to me since I have little/no experience with mechanical engineering/modeling. My main challenge with tuners is that I've found it very time-consuming and frustrating (and expensive if you need to buy/load ammo for a powderburner) trying to get them optimized. I'm also very puzzled by people who can find the tuner's optimum setting with a few 3-shot groups. As you mentioned, since group sizes can vary a lot, using group size to determine how well a tuner is working will take a lot of shots to get some statistical significance. This is why I'm not a big believer in ladder testing centerfire handloads and looking for flatter spots in the POI and/or muzzle velocity vs powder weight graph. Of course, just because I don't understand how tuners work, doesn't mean that they don't work! There's a lot evidence that they work quite well!
With the technique that I present here, one can see (by looking at POI and/or the angle-o-meter traces, NOT the group sizes!) pretty quickly how much mass needs to be added to get the pellet to leave at an orientation extremum. I'm not claiming that this is the best way to improve accuracy, but at least it's a way that makes sense to me.
PS I said that group sizes can vary a lot, so it's hard to decide on whether your tune is working by measuring group sizes. I should have mentioned that there will also be some variation in POI (like group size), but in this case the POI shifts (due to adding muzzle mass and changing the muzzle orientation when the pellet leaves the barrel) are big compared to the uncertainty in POI. Also, I have a feeling that the variation in where group is centered will be more reliable than the size of a group, but I never tested this expectation.
It is always a pleasure and a privilege to converse with you, John.
A couple of points that, perhaps I did not stress enough:
1.- Since the only things visible for non-members of the UK forum you posted are thumbnails, it is hard to assess exactly what is being shown there. From your redaction, we would agree that the position of the muzzle in time, depends on the location of the masses along the cantilevered beam that is the barrel.
2.- Since we agree that the POA is determined by rotating the barrel around some "center of rotation" that is usually the center of the buttpad, then we must agree that it is the RESISTING TORQUE at the end of the muzzle what is changing. And that it can change in two ways: a) adding variable mass to the end of the barrel (which is what you have been doing) b) Moving a constant mass along the barrel's muzzle (which is what I have been doing).
BOTH change the resisting torque.
Since you say that you think that adding a variable mass at the end is working, I do not see why moving a constant mass would not. In the end, you are changing the resisting torque.
And ALL Harmonics tuners work the same. Problem with tuners that have been commercialized so far is that the vibrations of the spring gun, get them out of adjustment. The "virtue" of the HPM is that it WORKS WITH THE GUN'S RECOIL, to set itself in place and then it cannot move unless some PHYSICAL element is added or removed.
Yes, it takes a LOT of patience to tune a barrel to a pellet, that is why I recommend choosing two "apparently best" settings and then testing extensively at distance. One of the beauties of airguns is that a 500 shot test costs only $12.00, which is not the case in CF or RF.
Within the realm of the HPM, Steve Herr is the champion because he made spacers that would allow him to adjust the HPM in "fractions of the integer" (which is about 1.4 mm's because the nominally 1.5 mm cord diameter of the O'Ring spacers gets compressed inside the HPM). Steve was able to distinguish this shooting from a BR.
Since I shoot from the knee (as you do), I am happy with using integer adjustment settings.
Yes, it is a complication over the UK's approach of "find a batch of magical pellets and just shoot them", but it is also somewhat more "democratic" because not everyone can stash away a dozen thousands of pellets to shoot for a few years.
Furthermore, I have found that the specific setting for the HPM is dependent on the support point of the rifle. Because even though we move the barrel around a central point that is the center of the buttpad, the point where the gun is supported when the shot cycle starts also dictates the point around where all the rotational vectors act.
When DIANA was testing the HPM idea, they discarded it at first because "according to DIANA's tests, the HPM offered no difference in POI and/or grouping capabilities of the rifles".
When I inquired HOW they were testing it, it came out that they had developed a massive carriage where the action was screwed and shot from there. once they were told how people shoot the rifles, they ended up understanding and it became an OEM accessory for the AirKing Pro.
The last thing I need to comment is that most UK shooters limit themselves to PCP's, the amount of vibrations in a spring gun far surpasses the ones in a PCP.
There is a way to make harmonics tuner for the LGU 😉 ... Just saying, LOL!
Again, thanks for the article, keep well and shoot straight!
I didn't realize that only the thumbnails showed up for non-members at Shooting the Breeze! Thanks for letting me know! The story is told by the figures, which are more important than the text, so please find the full-size figures below:
Thanks for all the interesting and insightful info that you've provided. I have a lot more to think about.
Part of the issue about barrel harmonics is that there are ignorant people making videos and saying things that confuse the whole thing. IF the whole point of TRANSVERSE VELOCITY OF THE MUZZLE (to separate it from the muzzle velocity) is misunderstood, then people are trying to prove something that is wrong from the start, and it may even be that it is wrong because a lot of these self-styled "experts" do not know the difference between precision and accuracy.
I could give you several examples, but they are really irrelevant. The sad thing is the confusion they create and how a LOT of readers/viewers prefer to believe what is in a video, rather than think for themselves.
One thing that is notable is that the "architecture" of the LGU seems to limit somehow the horizontal spread tendency. When we tune the Dianas, we see the spread of the groups going from vertical to horizontal and then back, but when you look at your LGU, it is MUCH less, I wonder if it has to do with the location of the added mass, that is offset vertically and that induces a "skew" to the system.
Even when tuning MY LGU (and adding an LDC in the process), the oscillations were also radial, in all directions, and the displacement of the weight (45 grams) showed also the rotating tendency of groups to spread horizontally to vertically and then horizontally again. And this is also striking to me, you are making changes that are, IMHO, too drastic. 100 grams is like adding TWO HPM's and 333 grams, well that is 5 HPM's. I think we need to look at much smaller changes.
Now, after the addition of the Ultra-Light Piston, the re-tune of the harmonics became a lot less variable.
To ME, this tells us that the MAIN generator of the harmonics in our barrels, is the piston's weight.
