Check out this Graph

OldSpook - that is superb data. I like theory - but data is King!

Good stuff! The overall group size and mean radius were smallest at 130mm so why not use that position? Or am I reading the data wrong?

Really shows harmonics at werq good job.

Okay thanks for explaining the strategy. It makes sense.

I’m curious is either of these favorable locations happen to correspond to the 4/7 or 3/7 factors. I was looking at a picture of the Stormrider and comparing to my Plinkster (CR600W) and soon decided it was futile to estimate with so many potential little differences.

Will you measure the distance from the center of the original barrel band to the muzzle (include the muzzle brake)?

Then how far from the original barrel band would each of these favorable locations be for the second band? 

What will be the result of two barrel bands at the two best nodes? Is there room to try that? 

Each successive barrel band will increase the resonant frequency which means that anti-nodes (areas of high amplitude) are occurring more frequently. By itself, that would be a bad thing because it means there is a greater random probability that the muzzle will be in a slightly different place as the pellet emerges into the world, owing to slightly different dwell times (in this context, I’m referring to how long the pellet spends in the barrel…not the valve dwell time that is more commonly discussed). However it will also be at a reduced amplitude so there is typically a net benefit, just as you might expect by starting with an extraordinarily stiff barrel in the first place.

With that said, the law of diminishing returns begins working its way in pretty soon. For most barrels, even ones that we may be tempted to call soda straws (e.g. the long 7/16” OD barrels Crosman uses on the Maximus or Discovery), you quickly reach the point where adding another band has no discernable benefit in the presence of the other factors that cause random dispersion/scattering of pellets on target (wind, pellet defects, basic accuracy of the barrel, etc.). 

Thanks for the pic and detailed measurements of the barrel bands and other features. I think the single biggest factor that makes it hard to predict the optimal location is the presence of the muzzle brake. It detracts from the otherwise homogenous nature of the bare barrel. For example, theory predicts the bare barrel would benefit most from the second barrel band being at approximately 291mm as opposed to the 318mm where you have it. I’m inclined to think the effective length of the unsupported portion (from the perspective the vibration mode translated to the muzzle) lies somewhere between the end of the barrel and the end of the muzzle brake, and that is congruent with your actual location. 

Or it may be a classic case of reasoning the data to fit the conclusion FWIW, I’m not totally pulling this reasoning out of thin air. For example, if we treated the overall length (meaning including the muzzle brake) as the relevant measurement, that would predict the optimal location of the second band at 384mm. That’s much further forward than your actual location, and not as close as the previous prediction that assumed only the bare barrel. Differences of 66mm and 27mm, respectively. However my guess is the presence of the muzzle brake only increases the effective length of the barrel by a small amount because its vibration characteristics are most influenced by the long and relatively thin section of barrel between the original barrel band and the muzzle brake.

At the very least, it’s reassuring that the location is not closer to something that could be considered a halfway point. That would be a head scratcher for sure.

On a more general note, an interesting aspect of harmonic tuning is that it’s not just about minimizing the amplitude of the vibration at the muzzle, but also recognizing that it’s beneficial to arrive at a state of tune that places the pellet at the muzzle just as the muzzle is at a peak (or a trough) of its vibration. That’s because the muzzle spends a greater amount of time at these locations, meaning it’s more likely to be at a consistent place as pellets arrive to the muzzle at slightly different times. If instead pellets are arriving at the muzzle nearer a zero crossing, the muzzle is in the process of swinging with great velocity toward a peak or trough. Of course, lacking a way to observe this behavior directly, there’s a bit of trial and error associated with it. That’s why it can be intensely frustrating when accuracy inexplicably goes to pot, but it is simultaneously encouraging to realize that you’re perhaps never more than one tweak away from changing a “pretty good” to an “outstanding”.

I would like to see the original data set ran 5 to 10 times, noting the max/min/avg of the tests prior to concluding that there were no other offending variables effecting the results of said tests, meaning if they're as conclusive as presumed, you should get identical results every single test you run with different barrel band positions. Other than that, I certainly look forward to further tests and hope you continue down the path! GL.



-Matt

Great idea, and good work. I am going to try this to get the correct placement of my barrel bands. Impressed with what the actual data shows.