A Problem Unique to Long-Barreled Rifles

[Jim Boatright]

Yes, JB.IC, I see that the muzzle speed dy/dt function calculation got garbaged up since I had it correct a few days ago. I have been mostly working with the muzzle position y(t) function. I fixed it again.
At bullet release, 1328 microseconds, the muzzle position is slowing almost to an upward moving stop at 1413 mu-sec. The upward speed is 2.3 mm/sec which is not really going to disturb the pitch of the bullet nose down very much during its exit from the barrel. Here is a pdf of the corrected spreadsheet.
Anyone who wishes to use this tool for their own rifle and loads will need the current "live" Excel workbook. QuickLOAD and Excel software are both also required.

 

[Jim Boatright]

This example load is accurate in the rifle for which it was developed because bullets exit when the muzzle is almost to an upward-moving halt, and because this exit timing provides positive "compensation" for the usual variation in muzzle velocities within a group of shots. Compensation involves lower muzzle pointing angles for faster, earlier exiting bullets and vise-versa.

As far as I know, this compensation tuning was discovered by British rifle tuners about 100 years ago while tuning No.1 Mark III* SMLE's for long-range target accuracy.

If one wished to tune for bullet exit times even closer to the time of upward muzzle halt, one could reduce the powder charge a few tenths of a grain or use a slightly heavier bullet to delay bullet exit slightly without affecting anything else appreciably. Changing barrel length also affects bullet exit times directly, so it is not an independent variable.
Jim Boatright

 

[Dai Bando]

Tubb will come up with a powder to rub on the bbl that fixes this issue 80% and a matching reticle that gets the other 20%.

 

[JB.IC]

my QL seems to be off.

All the cartridge dimensions are 100% correct. The only uncertainty is the max case capacity but I’m using the 33XC and Tubb has said it’s 139 gn H2O. The filling/L.R. % seems to be correct however.

The MV it spits out is always about 140 FPS slower. Maybe this has something to do with difference in bore diameter? That’s something I don’t have the tools to check.

id imagine this is an acceptable tolerance all things considered but how does this variation apply to the muzzle position calculation?

Also Jim based off the examples you posted on your excel workbook, the new version that’s posted is missing some of the inputs compared to the examples you posted.

 

[Jim Boatright]

The two things I adjust in QL to get closer agreement with chronographed MV are first Shot-Start pressure in the powder panel (for bullet hardness and throat roughness and angle) and then Weighting Factor in the cartridge panel (mainly for the amount of "necking down" of cross-sectional area in the interior of bottlenecked cartridges. If QL suggests WF of 0.50 for your 33XC, I would try 0.52 instead, for example.
I have continued developing the barrel motion calculations in my spreadsheet, including improvements in the Data Input screen, as I have been using it more myself. My current barrel motion calculations are based on a Gaussian function model approximating the base-pressure curve, which is working quite well. I have also added an exponential vibration damping function to allow for continued "ringing" of the barrel vibrations after the initial peak of base-pressure driving function has passed.
I will update the Excel workbook and accompanying write-up when I am satisfied with them.
Jim Boatright

 

[JB.IC]

I adjusted Short Start Pressure. It went from 3626 psi to 12200 psi. I’m loading -0.03 off the lands btw. This gives me the correct MV.

WF was set for 0.55 by default of the program. It says it suggest 0.33 for over bore bottleneck cases.

if I adjust WF to 0.33 then I have to adjust SSP to 8600 psi which seems to be a less drastic adjustment compared to the one previously mentioned. With these adjustments, it gives me the correct MV and then I went to the other powder I tested as well and the numbers it gave for MV were almost exactly what I got. QL gave a 15fps faster result.

appreciate the help Jim!

 

[Jim Boatright]

Yes, straight-walled cases should have a WF of essentially 1.0 in QL, while the proverbial "50 BMG case necked down to fire phonograph needles" would be close to 0.10.
I have had to use SS pressures of 12 ksi for some of my monolithic copper solids in QL, but usually around 8 ksi, even for them. Hard military or tough thick-jacketed hunting bullets require 5-6 ksi, while really soft alloy lead-cored match bullets having thin (annealed) jackets run about 2.4 ksi with the usual bullet jumps. Bullet seating depth is a big factor, with BR-style jam-seated bullets requiring much larger SS pressures.
Your chronograph distance is also a factor in MV measurements, as is use of an MB or suppressor. I have successfully compared inductive-sensing MagnetoSpeed and optical-sensing Oehler 35P readings, and now use microwave LabRadar readings (for convenience) which tend to be measured farther downrange. An inertia-triggering accessory for the LabRadar unit seems to provide the most reliable triggering for nearest-to-muzzle readings. A red dot alignment sight accessory is also best for LabRadar measurements all the way out to 100-yard targets with larger than 30-caliber bullets. I also use a substantial baffle C-clamped to the shooting bench to protect the LabRadar unit from direct muzzle blast for more consistent measurements. I recommend a piece of 3/8-inch plywood through-bolted along the bottom edge between two pieces of 1.5-inch angle iron for constructing the baffle. The baffle deflects a lot of pressure with each shot.
Jim Boatright

 

[JB.IC]

Yes, straight-walled cases should have a WF of essentially 1.0, while the proverbial "50 BMG case necked down to fire phonograph needles" would be close to zero.
I have had to use SS pressures of 12 ksi for some of my monolithic copper solids, but usually around 8 ksi, even for them. Hard military or tough thick-jacketed hunting bullets require 5-6 ksi, while really soft lead-cored match bullets having thin (annealed) jackets run about 2.4 ksi. Bullet seating depth is also a big factor, with jam-seated bullets requiring larger SS pressures.
Your chronograph distance is also a factor in MV measurements, as is use of an MB or suppressor. I have successfully compared inductive-sensing MagnetoSpeed and optical-sensing Oehler 35P readings, and now use microwave LabRadar readings (for convenience) which tend to be measured further downrange. An inertia-triggering accessory for the LabRadar unit seems to provide the most reliable triggering. A red dot alignment sight accessory is also best for LabRadar measurements out to 100-yard targets with larger than 30-caliber bullets. I also use a substantial baffle C-clamped to the shooting bench to protect the LabRadar unit from direct muzzle blast for more consistent measurements. I recommend 3/8-inch plywood through-bolted along the bottom edge between two pieces of 1.5-inch angle iron for constructing the baffle.
Jim Boatright

I also use a Labradar and a inertia-trigger. I typically shoot suppressed but I’m waiting on a thread adapter for my 33XC barrel for my suppressor as my barrel is 3/4” and my suppressor is 7/8”.

I typically have the Labradar a few inches in front of the muzzle off to the side about 8”. Between that and my magnetospeed, they’re normally within 12 FPS of each other. It’s easy to true the difference in MV.


I noticed there’s an “#NAME?” error on the Muzzle Motion worksheet. The error is traced to the L column under the SUM(mm). I have only put inputs on the Data Input worksheet.

 

[Jim Boatright]

Hello again, all;
I have not been entirely idle during this pandemic and ammo component shortage. I have installed a new Oehler System 89 BC Chronograph in my indoor test range. I have developed a new working theory about why my long copper bullets have been inaccurate and produced highly variable BC's even (especially) over the first 100 yards of flight. Lateral acceleration of the barrel causes "tip-off" tumbling of the bullet as it clears the muzzle. This is ballistically termed "initial yaw-rate" and is part of the projectile's total angular momentum (vector) carried over into subsequent ballistic flight. It is possible to tune a barrel and load together so as simultaneously to minimize both this lateral force and lateral velocity applied to the bullet during exit from the muzzle.
The attached PDF's explain how this works and how the muzzle motions are now calculated in a new Excel spreadsheet. Please email me at <[email protected]> so that I can attach the spreadsheet workbook in reply.

 

[brianf]

I know this goes against some theory…and not wanting to start a shot storm lol

but I’ve seen more than a few high speed camera videos (not a shaky cellphone, but true high speed with reference points behind it) that make it look like the barrel doesn’t move until the bullet is out of the barrel.

that goes against “common” sense but a picture is worth a thousand words.

also they were measuring the vert not horizontal.

I couldn’t believe it myself

just food for thought

 

[Jim Boatright]

I know this goes against some theory…and not wanting to start a shot storm lol

but I’ve seen more than a few high speed camera videos (not a shaky cellphone, but true high speed with reference points behind it) that make it look like the barrel doesn’t move until the bullet is out of the barrel.

that goes against “common” sense but a picture is worth a thousand words.

also they were measuring the vert not horizontal.

I couldn’t believe it myself

just food for thought

I doubt that one could visually detect muzzle vertical displacements from its neutral position of well under 0.100 millimeters with all the commotion of firing the rifle. These vibration amplitudes are small, but their effects are mighty. However, the cross-track acceleration of the muzzle might be accelerating the tail of the bullet laterally (up or down) at 125 "G's" as it is exiting the muzzle, compared to perhaps 125,000 "G's" of peak linear acceleration.
The y(t) plots shown are in microns (millionths of a meter); the y-dot(t) plots are in millimeters per second; and the y-double-dot(t) plots are shown in meters per second squared. My long copper ULD bullets need a lateral acceleration less than 10 m/s^2 during bullet exit to avoid the serious yaw-rate (tumbling) problems discussed here.

 

[Macht]

I know this goes against some theory…and not wanting to start a shot storm lol

but I’ve seen more than a few high speed camera videos (not a shaky cellphone, but true high speed with reference points behind it) that make it look like the barrel doesn’t move until the bullet is out of the barrel.

that goes against “common” sense but a picture is worth a thousand words.

also they were measuring the vert not horizontal.

I couldn’t believe it myself

just food for thought

Adding on to what Jim already shared: the spatial resolution of video is heavily dependent on lens magnification and is therefore also related to field of view. The point of that statement is that any video that is zoomed out enough to see bullet exit and show the majority of the rifle barrel won't have the ability to resolve barrel motion on the micron scale. Barrel motion during the in-bore period will be on the order of 30 microns, the camera will likely only be resolving on the order of 100s of microns at best.

 

[brianf]

So in a round about way…do you guys believe in positive compensation?

and do you think minute movements that are not easily seen possibly causing it?

@Macht
@Jim Boatright

I’ve been fine tooth combing range data from a few different sources that shows positive compensation might not be a “thing” but if the barrel is steering bullets…it might be???

thanks

 

[Jim Boatright]

For most rifle barrels not having massive muzzle attachments, the front portion of the barrel bends up or down about a pivot point located about 20-percent of the barrel length L behind the muzzle. If the muzzle is moving vertically upward (positive Delta-V) at the group mean bullet exit time (tm), an individual shot exiting at time t will be launched with a super-elevation angle Theta given by

Theta = ArcTan[(Delta-V)*(t - tm)/(0.20*L)]

Thus, slower shots will be launched with positive (upward) super-elevation angles to compensate (more or less) for their expected greater gravitational drop at the target distance. This compensation can be expected to be exact at some particular target distance; over-compensating at shorter ranges and undercompensating at longer ranges. If the muzzle were moving downward at tm, no compensation would be possible.

I should point out that non-zero vertical-plane pitching rates imparted to the fired bullets produce horizontal angular trajectory deflections due to the deflection leading the yaw-rate direction by 90-degrees in the sense of the rifling twist. Thus, a nose-upward initial yaw-rate produces a rightward bullet impact on the target face with right-hand twist rifling. This aerodynamic jump deflection occurs during the first half of the first coning cycle of the bullet in ballistic flight. Projecting this horizontal trajectory deflection backwards would point toward a deflection vertex located about 20 yards in front of the muzzle (or 25-percent of the flight distance covered during the first coning cycle).

 

[JB.IC]

Jim,
Is it possible that the reason tuners have shown to improve group size is simply because extra mass is at the end of the barrel which prevent extreme muzzle movement that would otherwise cause large group sizes?

I have noticed in previous rifles that simply adding a suppressor has improved group sizes. I think my suppressor adds a little over 1.25lbs to my muzzle.

 

[brianf]

Jim,
Is it possible that the reason tuners have shown to improve group size is simply because extra mass is at the end of the barrel which prevent extreme muzzle movement that would otherwise cause large group sizes?

I have noticed in previous rifles that simply adding a suppressor has improved group sizes. I think my suppressor adds a little over 1.25lbs to my muzzle.

That’s where I was going next but the more I research all the ones who believe in tuners and positive compensation do not have hard data shot by shot, over a chrono etc.

So it’s “mystery” because the ones who have actual data show its all lost in the noise and the ones who shoot it in paper do not have the data…

 

[JB.IC]

That’s where I was going next but the more I research all the ones who believe in tuners and positive compensation do not have hard data shot by shot, over a chrono etc.

So it’s “mystery” because the ones who have actual data show its all lost in the noise and the ones who shoot it in paper do not have the data…

I have tuners installed on some of my barrels. I have never once used them to tune a load because I find bullet seating depth test have produced precise enough groups. Maybe they work. Maybe they don’t. But what’s common for me is I end up having a relatively heavy muzzle attachment. Maybe this has something to do with keeping the muzzle from pivoting too much. I haven’t tested that enough to know.

I have watch several tuning videos and from what I can recall all the videos do not explore statistical evidence in their tuning method results. They shoot two to three groups and then make a change. Some how a three shot group is valid. I do not know any shooting competition that deals with precision exclusively, only considers three shots in a group. I use 10 shots at the same POA as a minimum for my group validation. I also do more than one group and I follow up before every match with groups to double check.

I have did test where I have shot three shots at say 5 different targets and they have in a lot of cases been close to one hole. Yet you can see their POI is slightly different. Adding them together takes say a 0.2moa group to 0.5moa group. This is why I have a hard time considering the evidence for their tuning process. I want to be specific and emphasize their tuning process and not the tuner itself. Something is happening for sure when extra weight is place on the end of a barrel.

But I have yet to see a large enough sample to say that a tuner turned a gun shooting 1moa to 1/2moa for every single group. I primarily shoot with suppressors. So that means I have my suppressor muzzle thread adapter, suppressor adapter that matches the muzzle adapter, the suppressor itself, the suppressor cover, and in some cases a tuner. In all my testing when I load develop, I do not normally have issues shooting at or under 1/2moa when I do seating depth test.

All of this makes me wonder if just attaching the extra weight to the muzzle causes something to happen that increases precision.

Anyways those are some of my thoughts.

 

[brianf]

I’m on the same boat as of now.

Hoping to hear the exact opposite from a “tuner guy” so I mind-fuck-it to death before I fall asleep lol

 

[Jim Boatright]

If a load and barrel combination is not going to work, shooting 2 or 3 shots is enough to determine that fact. If the combination looks promising, then shoot 5- or 10-shot groups for confirmation. Most modern benchrest competitions measure 5-shot groups for extreme center-to-center spread; like 0.1635 inches at 100 yards. Do not just measure outside-to-outside and subtract one caliber. Spitzer rifle bullets leave a smaller hole in the paper than their full caliber. You can purchase a caliper blade attachment having a clear window with small circles etched along a direction-reference line for accurately measuring one-hole groups. Used with a resettable Mitutoyo electronic caliper, group measuring is straightforward. AFAIK, all BR competitors use jam-seating of the bullets in their case necks thinned to about 0.0090-inch thickness (or less). Light-duty arbor presses are used with L. E. Wilson seating dies so you can feel the very light bullet seating forces involved. If the bullet seating feels even slightly "off," that round is set aside for fouling or wind reading.

Rigidly attaching any mass to the muzzle of any rifle barrel always increases the "vibrational length (L)" of that rifle barrel. This, in turn, reduces all of that barrel's natural vibrational mode frequencies which are each inversely proportional to the square of L. However, the recoil torque driven barrel vibration excitation spectrum for a given cartridge load remains unaffected by adding a muzzle attachment. As all of the resonant mode frequencies shift lower with added muzzle-attached mass, the dominant mode being excited typically shifts from Mode 2 to Mode 3. Mode 2 amplitude is thus typically decreased, but Modes 3 and higher vibrate with greater amplitudes. I estimate Mode 1 amplitude statically based on the actual length of the rifle barrel (as measured externally from receiver face to muzzle crown), so it is not affected by adding barrel attachments.

 

[Earnhardt]

Absolutely amazing thread!
Great info Jim!
(and the others)

Thank you

 

[Jim Boatright]

Thanks, Earnhardt. So far, only one guy has requested the new Excel spreadsheet, though. And he is from Slovenia.

 

[JB.IC]

I’m curious if there can be any independent variables isolated that can provide a generalization for what barrel characteristics should be used for certain types of cartridges. I’m sure some quantitative analysis and a lot of money could conclude this idea.

For instance, if someone wanted to shoot a Z type cartridge then a barrel would need to be a minimum Y type of contour at a maximum X barrel length. This generalization would be a guide towards selecting a barrel and cartridge without needing to crunch the numbers.

It might look something like this:
Z = 300WM, 300PRC, or 300NM
Y = minimum Heavy Varmint
X = maximum barrel length 30”

I’m sure muzzle device weight would need to be included as well.

Or does the amplitude of the independent variables impact the dependent variable too much to make any generalizations that are useful?

 

[Jim Boatright]

Yes, one is always tempted to generalize before all the data is known. This problem of recoil-caused barrel vibrations affecting muzzle motions at bullet exit time is complicated because the muzzle motions at any instant are always the algebraic sum of at least three disparate resonant frequencies of vibrations having significant amplitudes. This, at least in my analysis, is why results are so sensitive to even minor changes in barrel dimensions, materials, and attachments. Even the accuracies of making those measurements, weighings, and CG locations becomes important.

That being said, I have experimented with the spreadsheet calculations enough to begin to see some patterns.
1. Short barrels are much easier to "tune" by adding reasonable muzzle mass.
2. Adding a muzzle-attached mass always reduces resonant frequencies of all vibrational modes. This has the effect of increasing the vibrational length of the barrel and "pulling" the frontmost vibrational nodes toward the crown of the actual muzzle. Longer rifle barrels require more mass to be attached near the muzzle to achieve similar results compared to shorter barrels.
3. Tapering the barrel blank always reduces the vibrational length of the installed barrel (below its physical length) which decreases Mode 1 frequency and increases all higher mode frequencies. This complicates the analysis of muzzle motions, especially when combined with adding muzzle-attached masses. [I believe the spreadsheet calculations use a reasonable approach to handling this complexity.]
4. Barrel-block rifle designs allow shortening the vibrational length of the exposed barrel ahead of the barrel-block, thereby gaining the tuning advantages of a 6 to 10-inch shorter barrel length, while retaining the greater ballistic efficiency of the longer barrel length. By independently attaching the barrelled action, stock, and scope to the bedded barrel-block, each component vibrates independently during recoil, with minimum cross-coupling between them. [The action and barrel are free-floating with no stock contact.] I am building a barrel-block 338 Lapua Magnum test rifle to explore this further.

 

[brianf]

Yes, one is always tempted to generalize before all the data is known. This problem of recoil-caused barrel vibrations affecting muzzle motions at bullet exit time is complicated because the muzzle motions at any instant are always the algebraic sum of at least three disparate resonant frequencies of vibrations having significant amplitudes. This, at least in my analysis, is why results are so sensitive to even minor changes in barrel dimensions, materials, and attachments. Even the accuracies of making those measurements, weighings, and CG locations becomes important.

That being said, I have experimented with the spreadsheet calculations enough to begin to see some patterns.
1. Short barrels are much easier to "tune" by adding reasonable muzzle mass.
2. Adding a muzzle-attached mass always reduces resonant frequencies of all vibrational modes. This has the effect of increasing the vibrational length of the barrel and "pulling" the frontmost vibrational nodes toward the crown of the actual muzzle. Longer rifle barrels require more mass to be attached near the muzzle to achieve similar results compared to shorter barrels.
3. Tapering the barrel blank always reduces the vibrational length of the installed barrel (below its physical length) which decreases Mode 1 frequency and increases all higher mode frequencies. This complicates the analysis of muzzle motions, especially when combined with adding muzzle-attached masses. [I believe the spreadsheet calculations use a reasonable approach to handling this complexity.]
4. Barrel-block rifle designs allow shortening the vibrational length of the exposed barrel ahead of the barrel-block, thereby gaining the tuning advantages of a 6 to 10-inch shorter barrel length, while retaining the greater ballistic efficiency of the longer barrel length. By independently attaching the barrelled action, stock, and scope to the bedded barrel-block, each component vibrates independently during recoil, with minimum cross-coupling between them. [The action and barrel are free-floating with no stock contact.] I am building a barrel-block 338 Lapua Magnum test rifle to explore this further.

4. Barrel-block rifle designs allow shortening the vibrational length of the exposed barrel ahead of the barrel-block, thereby gaining the tuning advantages of a 6 to 10-inch shorter barrel length, while retaining the greater ballistic efficiency of the longer barrel length. By independently attaching the barrelled action, stock, and scope to the bedded barrel-block, each component vibrates independently during recoil, with minimum cross-coupling between them. [The action and barrel are free-floating with no stock contact.] I am building a barrel-block 338 Lapua Magnum test rifle to explore this further.


if im following correctly, then ultimate accuracy/shortening of the vibration length would be to "barrel block" the entire barrel from action to muzzle

in theory if i were building a rail gun for benchrest i should have one continuous block of material from action tang to the muzzle virtually eliminating vibration length obtaining almost no bullet timing issues

which in turn will let me load any cartridge length/jump (minus the extreme) and creating a weapon system that is almost bullet jump insensitive

 

[Jim Boatright]

4. Barrel-block rifle designs allow shortening the vibrational length of the exposed barrel ahead of the barrel-block, thereby gaining the tuning advantages of a 6 to 10-inch shorter barrel length, while retaining the greater ballistic efficiency of the longer barrel length. By independently attaching the barrelled action, stock, and scope to the bedded barrel-block, each component vibrates independently during recoil, with minimum cross-coupling between them. [The action and barrel are free-floating with no stock contact.] I am building a barrel-block 338 Lapua Magnum test rifle to explore this further.


if im following correctly, then ultimate accuracy/shortening of the vibration length would be to "barrel block" the entire barrel from action to muzzle

in theory if i were building a rail gun for benchrest i should have one continuous block of material from action tang to the muzzle virtually eliminating vibration length obtaining almost no bullet timing issues

which in turn will let me load any cartridge length/jump (minus the extreme) and creating a weapon system that is almost bullet jump insensitive

Yes, one could do all that, but it would be extrapolating to the absurd. I am trying to allow real rifles to fire CNC turned copper bullets to achieve their full designed-in aeroballistic and accuracy performance levels. Any way they can be launched into ballistic flight with consistent muzzle velocities and with near-zero initial yaw and yaw-rate will produce astounding shooting results: thirty percent less air drag than with conventional bullets, almost impervious to crosswinds, and truly benchrest competition levels of target accuracy. Unfortunately, barrel-to-load tuning for minimum lateral force at the muzzle during bullet exit seems to be required to achieve the near-zero initial yaw-rate goal.

 

[brianf]

I understand the premise of solids…I’m actually buying a hoplite arms rifle just for that reason.

another absurd example…

what about creating a rifle stock that has the stock/barreled action interface at the muzzle.

If you hold the muzzle in a barrel clamp the action can act like the tail of a dog yet the dogs head never moves..

just thinking outside the box…possibly a bull pup configuration of sorts

 

[357Max]

Yes, one could do all that, but it would be extrapolating to the absurd. I am trying to allow real rifles to fire CNC turned copper bullets to achieve their full designed-in aeroballistic and accuracy performance levels. Any way they can be launched into ballistic flight with consistent muzzle velocities and with near-zero initial yaw and yaw-rate will produce astounding shooting results: thirty percent less air drag than with conventional bullets, almost impervious to crosswinds, and truly benchrest competition levels of target accuracy. Unfortunately, barrel-to-load tuning for minimum lateral force at the muzzle during bullet exit seems to be required to achieve the near-zero initial yaw-rate goal.

Jim - Has anyone tested your bullet designs from a structured barrel? From what I've read they eliminate tune sensitivity better than any other method I've seen.

Hopefully the below will be somewhat coherent. I'm tired, been a long week. This may apply to what your chasing. The layout would likley need to change to accommodate a muzzle break, but the concept could apply.

I'm very curious to get your thoughts on a different approach to a tuner I've been working on. It's more of a hybrid dampener tuner.
The adjustable muzzle mass sleeve's the barrel with an o-ring array between the sleeve and the barrel. So far it has produced positive results on target on my otherwise stock B14R rim-fire test platform. Best 5 shot groups @ 100y were .183 with Eley 10x & .182 with with SK LR match. That was with a bi-pod + rear squeeze bag. Those best to date results were with 3 of 5 possible o-rings installed in the front, center, and back positions. I did shoot the same lots of ammo with bare muzzle and although I cant quantify exactly, the improvement was very apparent. Since I don't have a labradar I'll be extending one of the front stock mounted weight rods to mount my Magneto speed to.

I'm about to start testing with all 5 o-rings installed & thus far have only tested 70 durometer o-rings. The current design (version #2) is using large coarse threads on the sleeve - muzzle adapter & it is the o-ring compression that prevents it from spinning. The idea is to allow the sleeve/mass to float on the o-rings via the coarse threads.

The # of possible tuning variables is well a lot! O-ring durometer, Qty, spacing, compression, location from muzzle, & mass weight.

I'm really think this approach has merit, however I've never found any documentation for previous work on this. Everything I can find on the subject is either for traditional mass tuners or a big rubber doughnut type dampener. Never both combined.

I'm working on a version 3 that would allow the sleeve to truly float.

Someone such as yourself with your engineering and math knowledge could probably make much better progress in figuring out at least the baseline starting point for the many variables. Hell even If I manage to get this dialed in pretty well on the rim-fire, it'll be back to square 1 when switching to CF.

Pic's below are current Version #2

muzzle thread adapter with smooth i.d.

Sleeve/mass with o-rings. o-ring groove depth in sleeve adjusted for barrel taper to give same compression on all 5 o-rings. Compression could be varied ring- ring giving another tuning option.

installed.

 

[brianf]

I have toyed with a similar idea but I started thinking about how the rubber will react to different outside temps and aging.

loved to see how it works out

 

[Jim Boatright]

I understand the premise of solids…I’m actually buying a hoplite arms rifle just for that reason.

another absurd example…

what about creating a rifle stock that has the stock/barreled action interface at the muzzle.

If you hold the muzzle in a barrel clamp the action can act like the tail of a dog yet the dogs head never moves..

just thinking outside the box…possibly a bull pup configuration of sorts

Dr. Franklin Mann, author of The Bullet's Flight (1909), experimented with many different rifle and barrel support setups, including clamping the muzzle of a barrelled action into a heavy rigid vise. I do not recall that he found any approach consistently better than using proper benchrest firing technique.

 

[Jim Boatright]

Jim - Has anyone tested your bullet designs from a structured barrel? From what I've read they eliminate tune sensitivity better than any other method I've seen.

Hopefully the below will be somewhat coherent. I'm tired, been a long week. This may apply to what your chasing. The layout would likley need to change to accommodate a muzzle break, but the concept could apply.

I'm very curious to get your thoughts on a different approach to a tuner I've been working on. It's more of a hybrid dampener tuner.
The adjustable muzzle mass sleeve's the barrel with an o-ring array between the sleeve and the barrel. So far it has produced positive results on target on my otherwise stock B14R rim-fire test platform. Best 5 shot groups @ 100y were .183 with Eley 10x & .182 with with SK LR match. That was with a bi-pod + rear squeeze bag. Those best to date results were with 3 of 5 possible o-rings installed in the front, center, and back positions. I did shoot the same lots of ammo with bare muzzle and although I cant quantify exactly, the improvement was very apparent. Since I don't have a labradar I'll be extending one of the front stock mounted weight rods to mount my Magneto speed to.

I'm about to start testing with all 5 o-rings installed & thus far have only tested 70 durometer o-rings. The current design (version #2) is using large coarse threads on the sleeve - muzzle adapter & it is the o-ring compression that prevents it from spinning. The idea is to allow the sleeve/mass to float on the o-rings via the coarse threads.

The # of possible tuning variables is well a lot! O-ring durometer, Qty, spacing, compression, location from muzzle, & mass weight.

I'm really think this approach has merit, however I've never found any documentation for previous work on this. Everything I can find on the subject is either for traditional mass tuners or a big rubber doughnut type dampener. Never both combined.

I'm working on a version 3 that would allow the sleeve to truly float.

Someone such as yourself with your engineering and math knowledge could probably make much better progress in figuring out at least the baseline starting point for the many variables. Hell even If I manage to get this dialed in pretty well on the rim-fire, it'll be back to square 1 when switching to CF.

Pic's below are current Version #2

muzzle thread adapter with smooth i.d.
View attachment 7704743
View attachment 7704745

Sleeve/mass with o-rings. o-ring groove depth in sleeve adjusted for barrel taper to give same compression on all 5 o-rings. Compression could be varied ring- ring giving another tuning option.
View attachment 7704746

installed.
View attachment 7704747

1. The mathematical description of vibration modes gets much more difficult for rifle barrels made of non-isotropic materials such as carbon fiber wrapped steel core barrels. While firing results might be better, putting numbers on the muzzle motions would not be practical (at least to me).

2. I was competing in IR 50/50 benchrest rimfire matches up until about 25 years ago and tried many barrel tuning and vibration damping setups. I eventually grew disenchanted with the quality of rimfire ammo and switched to centerfire BR competition.
The barrel dwell time for rimfire bullets is so long that initial distortion effects have completely disappeared, leaving only gradually damping resonant vibrations affecting the barrel at bullet exit time. These damping rates are likely to be frequency dependent. The relative phasings of the initial vibration modes is probably blurred out after several milliseconds of standing wave vibrations bouncing back and forth. My spreadsheet calculations are based on these phasings remaining fixed and very little damping having taken place at bullet exit.
I found that a straight cylindrical barrel about 22 inches long and of 0.8 to 0.9-inch OD was easily tuned for minimum lateral muzzle velocity using an available rigidly attached, lightweight aluminum muzzle tuner attachment. Setting headspace to match your ammo is also required. Back then, I settled on a Winchester 52D chamber.
I tried a few damping setups using RTV silicone (from GE) for the damping media with limited success. I got the idea to reverse any muzzle attachments so that the mass would not be increased during a match by the build-up of bullet lube slung off as each bullet clears the muzzle. I located the front vibration node at about 20-percent behind the bare muzzle, and endeavored to shift that front node nearer to the muzzle with added barrel masses. I ended up just using a 2-pound mass clamped just behind the muzzle with set screws, and won some matches in the 13-pound class with that rifle.

3. Adding non-rigidly attached muzzle attachments using vibration damping materials has effects which are difficult to predict quantitatively. Very much "cut and try." That is why I do not include attaching suppressors having non-zero second moments of inertia as calculable muzzle attachments. All muzzle attachments are treated as rigidly attached "point masses" in my formulations.

4. Centerfire barrel tuning is quite different. The initial recoil-induced distortions are still affecting the muzzle at bullet exit unless the barrel is really long. That is what my spreadsheet calculations attempt to quantify. Long copper bullets also need tuning for minimum lateral muzzle acceleration to minimize "tip off" tumbling imparted during bullet exit.

Email me at <[email protected]> for a reply having the Excel workbook as an attachment. I have tried to make the data input easier and have added more graphing of the results. The worked example in the spreadsheet shows how lateral acceleration and lateral velocity can both be minimized at the muzzle for some bullet exit times.

 

[JB.IC]

Yes, one is always tempted to generalize before all the data is known. This problem of recoil-caused barrel vibrations affecting muzzle motions at bullet exit time is complicated because the muzzle motions at any instant are always the algebraic sum of at least three disparate resonant frequencies of vibrations having significant amplitudes. This, at least in my analysis, is why results are so sensitive to even minor changes in barrel dimensions, materials, and attachments. Even the accuracies of making those measurements, weighings, and CG locations becomes important.

That being said, I have experimented with the spreadsheet calculations enough to begin to see some patterns.
1. Short barrels are much easier to "tune" by adding reasonable muzzle mass.
2. Adding a muzzle-attached mass always reduces resonant frequencies of all vibrational modes. This has the effect of increasing the vibrational length of the barrel and "pulling" the frontmost vibrational nodes toward the crown of the actual muzzle. Longer rifle barrels require more mass to be attached near the muzzle to achieve similar results compared to shorter barrels.
3. Tapering the barrel blank always reduces the vibrational length of the installed barrel (below its physical length) which decreases Mode 1 frequency and increases all higher mode frequencies. This complicates the analysis of muzzle motions, especially when combined with adding muzzle-attached masses. [I believe the spreadsheet calculations use a reasonable approach to handling this complexity.]
4. Barrel-block rifle designs allow shortening the vibrational length of the exposed barrel ahead of the barrel-block, thereby gaining the tuning advantages of a 6 to 10-inch shorter barrel length, while retaining the greater ballistic efficiency of the longer barrel length. By independently attaching the barrelled action, stock, and scope to the bedded barrel-block, each component vibrates independently during recoil, with minimum cross-coupling between them. [The action and barrel are free-floating with no stock contact.] I am building a barrel-block 338 Lapua Magnum test rifle to explore this further.

It sounds if so having a certain muzzle mass attachment is helpful for precision but that is dependent on barrel length and barrel thickness.

Yes, one is always tempted to generalize before all the data is known. This problem of recoil-caused barrel vibrations affecting muzzle motions at bullet exit time is complicated because the muzzle motions at any instant are always the algebraic sum of at least three disparate resonant frequencies of vibrations having significant amplitudes. This, at least in my analysis, is why results are so sensitive to even minor changes in barrel dimensions, materials, and attachments. Even the accuracies of making those measurements, weighings, and CG locations becomes important.

That being said, I have experimented with the spreadsheet calculations enough to begin to see some patterns.
1. Short barrels are much easier to "tune" by adding reasonable muzzle mass.
2. Adding a muzzle-attached mass always reduces resonant frequencies of all vibrational modes. This has the effect of increasing the vibrational length of the barrel and "pulling" the frontmost vibrational nodes toward the crown of the actual muzzle. Longer rifle barrels require more mass to be attached near the muzzle to achieve similar results compared to shorter barrels.
3. Tapering the barrel blank always reduces the vibrational length of the installed barrel (below its physical length) which decreases Mode 1 frequency and increases all higher mode frequencies. This complicates the analysis of muzzle motions, especially when combined with adding muzzle-attached masses. [I believe the spreadsheet calculations use a reasonable approach to handling this complexity.]
4. Barrel-block rifle designs allow shortening the vibrational length of the exposed barrel ahead of the barrel-block, thereby gaining the tuning advantages of a 6 to 10-inch shorter barrel length, while retaining the greater ballistic efficiency of the longer barrel length. By independently attaching the barrelled action, stock, and scope to the bedded barrel-block, each component vibrates independently during recoil, with minimum cross-coupling between them. [The action and barrel are free-floating with no stock contact.] I am building a barrel-block 338 Lapua Magnum test rifle to explore this further.

In context to #2, This has the effect of increasing the vibrational length of the barrel and "pulling" the frontmost vibrational nodes toward the crown of the actual muzzle, I’m assuming this is a desirable effect?
Reading the reply about your time in 22 BR it seems as if a vibrational node is behind the muzzle, it will then be hard to tune the rifle for minimal muzzle movement. But as you mentioned, the effect of initial recoil is long gone in rim fire, yet in center fire it is still there.
I’m just confused when you mention vibrational length growing in this case because I was under the impression that shortening the vibrational length would be beneficial yet I think when you say pulling the vibrational nodes to the crown you mean that it is brining the point in the barrel where minimal muzzle movement occurs to the point where the bullet exits the barrel which then has minimum impact on any yawing of the bullet.

 

[Jim Boatright]

It sounds if so having a certain muzzle mass attachment is helpful for precision but that is dependent on barrel length and barrel thickness.

In context to #2, This has the effect of increasing the vibrational length of the barrel and "pulling" the frontmost vibrational nodes toward the crown of the actual muzzle, I’m assuming this is a desirable effect?
Reading the reply about your time in 22 BR it seems as if a vibrational node is behind the muzzle, it will then be hard to tune the rifle for minimal muzzle movement. But as you mentioned, the effect of initial recoil is long gone in rim fire, yet in center fire it is still there.
I’m just confused when you mention vibrational length growing in this case because I was under the impression that shortening the vibrational length would be beneficial yet I think when you say pulling the vibrational nodes to the crown you mean that it is brining the point in the barrel where minimal muzzle movement occurs to the point where the bullet exits the barrel which then has minimum impact on any yawing of the bullet.

Each barrel vibrates independently at any number of different naturally resonant frequencies fn. I calculate the first 7 vibration modes in the spreadsheet. These are all shear-wave vibrations in a vertical plane traveling along the steel barrel at over 10,000 fps and reflecting off each end of the barrel. Mode 1 has one vibration node (zero amplitude at that frequency) located at the junction with the receiver and the plain muzzle is a full-amplitude antinode. Mode 2 has a second node located about 21-percent behind the muzzle, and the muzzle is still an antinode. And so forth.... The nodes are locations where the reflecting shear waves at one resonant frequency combine destructively (cancel).
Shifting the dominant node location toward the muzzle reduces the bullet's (1) variation with exit times of launch super-elevation angle Theta, (2) its cross-track "kick" velocity Delta-V, and (3) its lateral acceleration A in the bore right behind the muzzle. The lateral force F exerted on the side of the bullet by the bore is given by m*A where m is the mass of the bullet. After the CG of the bullet clears the muzzle, that side force F gradually becomes more and more of an impulsive torque Gamma rotating the bullet (in a tumbling sense) until the point of last contact on the bullet clears the muzzle crown.
I hope this explanation helps.