A Problem Unique to Long-Barreled Rifles

[Jim Boatright]

I was asked several years ago by David Tubb to explain ballistically why crosswinds favored riflemen shooting barrels made with twist direction matching the crosswind direction--L to R winds favoring LH twist barrels, and vice-versa. I could find nothing in aeroballistics showing any asymmetry at all. Well, now I can explain the problem. It happens when the barrel length used is so long that the load being fired cannot be adjusted so that bullets exit the muzzle after its first halting of the muzzle's recoil-driven downward motion. Bullets fired from extra long barrels are always given a pitch-up (nose high) attitude and positive pitch-rate upon exiting the muzzle due to its downward motion.

The attached paper explains this problem in detail. An active Excel spreadsheet allows the reader to calculate the natural vibration mode frequencies for any set of barrel dimension and (isotropic) material specs. I did not address carbon fiber barrels nor muzzle attachments. I worked an example for a 44-inch, 8-pound, 4140 Cro-Mo steel, 50-caliber barrel firing an 850-gr bullet at 2722 fps from a 50 BMG cartridge. The maximum tunable barrel length turned out to be 32 inches in that example.

I mentioned David's solution which is to have matched pairs of LH and RH twist barrels available for each match.

Unfortunately, the figures are in the Excel workbook which I cannot attach here. I will attach them to an email for anyone who would like it. My new email address is <[email protected]> .

 

[Jim Boatright]

I made PDF's of the Figures and what the spreadsheet would look like. The active Excel workbook will have to be emailed unless it perhaps can be posted here as a Resource.

 

[1moaoff]

Intriguing

 

[vinniedelpino]

Who the hell has matched barrels in LH/RH twist for each match?

 

[THEIS]

Hi,

@Jim Boatright
I will be compiling an email to you over next couple days while I digest the paper.

I have some ideas to go over with you again.

Edited To Add:
Email Sent.
I finally had time to briefly review the first attached PDF and at this very moment I am attempting to reflect where I went wrong in my life's decisions in regards to how come I have to work so hard in attempting to grasp what was written, lol.

Sincerely,
Theis

 

[THEIS]

Hi,

The excel spreadsheet has been posted in the Resources section for Jim.

Lets see if it attaches here too.

Sincerely,
Theis

 

[Smittiac]

Hi,

The excel spreadsheet has been posted in the Resources section for Jim.

Lets see if it attaches here too.

Sincerely,
Theis

That be the XML sir not the spreadsheet itself but the coding for the page.

 

[THEIS]

That be the XML sir not the spreadsheet itself but the coding for the page.

Hi,

O shit, it opens properly on my end; both the Resources section and this thread.
Let me try something else.

Sincerely,
Theis

 

[timintx]

Awesome explanation Mr Boatright. It makes perfect sense. Thank you for the explanation.

Tim in Tx

 

[Boatninja]

Everything opened for me. I am going to print this out and look at it a little more and also mail it to some friends of mine that don't do internet, my wife as well so she will understand why I need another rifle. That certainly does explain it, all this time I thought left hand twist was for left handed people and right, well you get it.

 

[gnochi]

That certainly does explain it, all this time I thought left hand twist was for left handed people and right, well you get it.

If anything, the exact opposite is true.

 

[Boatninja]

If anything, the exact opposite is true.

Don't spoil it for me, I'n getting a new barrel.

 

[Jim Boatright]

Speaking of exact opposites, I heard back from David Tubb who has researched this topic thoroughly that his observational findings are the reverse of what I just published. What that tells me is that I have oversimplified the problem of muzzle motions for clarity in explanation. All of the coning motion effects I discussed are quite valid. David's 28-inch rifle barrels in his T2000 target rifles (tested in 284 Win with Sierra 180 MK's and in 6XC with 115 DTAC bullets) are just firing their bullets with slightly Nose-Down attitudes in initial ballistic flight.

My error was in stating that Mode 2 shaped rifle barrel distortions were the most critically important. I went back and studied Al Harrall's (VarmintAL.com) wonderful rifle barrel dynamics animations produced using his LS-DYNA Finite Element Analysis (FEA) computer program. Sure enough, his studies showed that Mode 3 shaped recoil distortions dominated for all of his (short) barrels which he modeled. This also agrees with a careful re-reading of Harold Vaughn's chapter on barrel vibrations. Mode 3 muzzle motions are initially upward for about one millisecond, which would tip the fired bullet's noses downward if they exit the muzzle during that interval.

I will incorporate this fresh understanding into an upcoming Version 02 of this paper, which will necessarily be slightly longer and more complicated. This subject of rifle barrel vibration mode versus recoil-driven distortions has been hotly debated for generations among engineers. I kind of accidentally stepped into it coming from the ballistics side.

Nothing is ever as simple as it should be until after it is fully understood.

Jim Boatright

 

[Jim Boatright]

I have redone the analysis of the 50 BMG example considering all possible barrel vibration modes, and the results are the same for that long 44-inch barrel. The best estimate of the downward muzzle speed at bullet exit is 4.75 ips. The muzzle is moving upward from the start of motion at 1.008 msec until it first stops at 1.731 msec. After that halt, it moves rapidly downward at about this 4.75 ips speed steadily until it stops again at 2.727 msec. However, the 850-gr bullet exited at 2.194 msec (+/- very little). I doubt that any 50 BMG load can be tuned to that length barrel. Best reserve it for shooting in right-to-left crosswinds. If the wind is blowing the wrong way, just turn around 180 degrees.

 

[taliv]

fascinating! would the max tunable length of 6mm and 6.5mm barrels be longer or shorter than the 50cal?

 

[DWavid]

Intriguing! Now I need both barrels.....

 

[Jim Boatright]

fascinating! would the max tunable length of 6mm and 6.5mm barrels be longer or shorter than the 50cal?

For any caliber smaller than about 0.400-inch, the size of the hole makes very little difference with target barrels.

 

[Larke]

Intriguing! Makes perfect sense

 

[THEIS]

Hi,

Ok so I have now had a little more time to soak in the information which just leads to more questions on my brain...

1. Do you think the barrel length tunability in regards to projectile exiting timeframe/position/etc can be manipulated with external barrel tuners?
A. If ammunition/projectile B was set to require a 28.5" barrel for optimal timing; could we manipulate that length by 1/2, 3/4, 1", etc with the utilization of external barrel tuners?

2. Is there a way to add a tuner length of travel and tuner mass section to the excel formula to see what the calculations run?

Sincerely,
Theis

 

[Jim Boatright]

First, let me say that I have significantly expanded my spreadsheet calculations, specifically to include the first seven modes of transverse vertical plane shear-wave vibrations. This study is based upon a new approach I came up with to consider the the recoil torque applied to the barrel to be impulsive, applied at the instant of peak base pressure behind the bullet, as far as timing the barrel response. I then model an "excitation spectrum" based upon a Fourier Transform of the shape of that base pressure curve as calculated by QuickLOAD. The peak excitation frequency is that of a sine wave which fits its first quarter cycle to the rise time of the base pressure. Graphs of the sums of all mode displacements are quite interesting.

As to modeling the addition of barrel attachments, I recommend use of a fully dynamic Finite Element Analysis program like Al Harral's LS-DYNA. He has several such investigations on his great website, VarmintAl.com. His conclusion is that any attachment lowers all of the mode frequencies and shifts the nodes forward, but by insignificantly small amounts--much less than the fraction of mass of attachment to mass of barrel.. The main benefit is reduction in the amplitudes of the modes excited. I think somewhere in his many studies he also mentioned that moderate barrel taper is not much different than the straight cylinder OD barrel I used.

I will be happy to share this spreadsheet with anyone interested. I put in my 338 LM test barrel specs, and it showed our QL bullet exit was right in the middle of a long sharp downward muzzle motion at over 4 ips, which explains why we could not tune an accurate load. I will shorten the barrel from 27 inches to 25.5 inches to hit a wide muzzle halted condition at bullet exit. I am awaiting a new custom 338 LM reamer from Dave Kiff. It is now promised on the 27th of this month and this year.

I am attaching a graph (PDF) of the muzzle positions for each microsecond starting with t=0 at 10-percent chamber pressure (as used by QL).

Jim Boatright

 

[timintx]

Varmint Al has helped me and so many people much on this vibration subjects with the FEA program for 20 years or so beginning with bolt and action loading which I found very fascinating then he progressed in to barrel vibrations , I am so grateful for his wisdom and discussion over the years as with you too Mr Boatright. I dont know if this will help with your 338 endeavor but , bringing a node to the muzzle reduces the linear dispersion but produces higher angular dispersion , meaning the only node that is beneficial should be at the target and not the muzzle. In the modes I use for long and extreme range accuracy that are primarily vertically oriented and effecting on target the straight bull barrels have very little effect on target with differing muzzle weighting compared to smaller diameters, The natural frequencies are the highest and in with Varmint Al's estimation will usually hit the muzzle 7-8 times and are randomly oriented not vertically,That was a problem for me. The window of exit time in FPS that the vibration will travel from end to end is around 150 FPS and 160 FPS with a 28 inch barrel. In detailed testing the main cause of this randomly oriented vibration mode is bolt lug lock up and the case slamming into the chamber wall, tighter or fire formed neck sized only cases produced significantly smaller dispersion but only when the high frequency was at the muzzle upon bullets exit , in addition heavy silicon grease on the bolt lugs reduced it 10%-20% more and down to near zero over machine oil. A powder change equal to 30FPS change will bring the exit timing to a point in which the vibration is not at the muzzle and random dispersion goes away and goes back to vertically oriented grouping in which is corrected by weighting the muzzle. Now if you trim the barrel shorter your higher frequency mode will be faster and so will the exit time which will produce the same effect at any length change.They will cancel each other out if you have a velocity exit time that is due to this mode, the only way I have found to correct this condition is to change the exit time or extend the muzzle length without extending bore length. Good luck to you sir in your tests and thanks again for your articles over the years.

Tim in Tx

 

[Jim Boatright]

Yes, I worked with Al Harral ten or twelve years ago on chamber wall and bolt-lug triaxial von Mises stress calculations. I was successfully able to hand calculate stresses for a few key points which agreed well with his LS-DYNA computer program results. Back then, we "agreed to disagree" about the relative importance of barrel distortion under load and barrel natural vibration modes at the instant of bullet exit. Now, I can see that we were both mostly right. My new "Impulsive Recoil Torque" approach to timing and quantifying muzzle motions shows that Al's "forced distortion" is in fact a short barrel's dominant Mode 3 transverse wave shape.

There are actually three recoil caused conditions of the last inch, or so, of the barrels bore behind the muzzle crown which significantly affect the subsequent flight of the fired bullet: (1) Muzzle pointing direction, (2) Muzzle position, and (3) Muzzle cross-bore motion speed. Of these, (2) muzzle position is negligible. Al Harral seemed to think that (1) muzzle pointing direction was all important in long range accuracy. In testing my new bullet design, we have found that (3) muzzle speed is the most important tuning factor because it affects the bullet's initial yaw attitude and yaw-rate going into ballistic flight. Muzzle speeds between 1 and 6 inches per second (ips) at bullet exit, result in large and variable aerodynamic jumps and greatly decrease accuracy. Fortunately, both Muzzle pointing direction and cross-bore speed are most stable simultaneously at the instants of muzzle motion reversals, which is why we must tune for bullet exit very near one of those times. For long barrels, there are none, or at most one, of those halt times available within your load-tuning range. For short barrels, there are usually two tuning nodes available: "too slow" or "too fast" in bullet exit velocity. By selecting a lower reversal time of exit (downward to upward motion reversal point), we can enjoy the added benefit of long-range "compensation" for bullets of varying muzzle exit velocities. Perfect pressure sealing by the bullet in the bore (barrel obturation) can produce shot groups having negligible extreme velocity spreads. Use "soft" match-type jacketed bullets or base-drilled monolithic copper bullets in rifling patterns designed for best obturation (like Gary Schneider's P5 rifling).

When a shear wave reflects from the impedance change at either end of the rifle barrel, several things occur. If the end is also a vibration node (at the receiver end of the barrel) the primary reflected wave starts forward again with its vibration phase reversed. The muzzle end is an antinode, producing no phase reversal in reflected shear waves. The other things which happen include loss of wave energy into other vibration modes and wave polarizations. I believe that many rifles suffer horizontal plane barrel vibrations due to the eccentric mass of the bolt handle. I would recommend use of titanium bolt handle shafts and lightweight polymer bolt knobs for target rifle bolt-actions.

The bolt body itself can cause serious barrel vibrations during firing if it is a loose fit within the receiver bore. That problem is addressed by sleeving the bolt body, front and rear, and installing "Borden Bumps" on the front sleeve for zero clearance there when the bolt is rotated into battery. When the bolt is in battery, it should have no detectable (or measurable) play at its front or rear ends and should also be coaxial with its receiver. Only then will its machined-true lugs and lug seats bear the bolt thrust evenly. "Flopping around" of the rear end of the bolt body during firing generates large amplitude, high-frequency shear-wave vibrations which couple through to the rifle barrel. When only one bolt lug is bearing while bolt-thrust is building up, the rear of the bolt body slams from the top of its rear clearance to bottoming out with all Remington 700 style overriding sear fire control actions (which elevate the rear of the bolt when in battery). Vice versa for Mauser-style direct pull (downward) sear releases.

Jim Boatright

 

[Macht]

This is an interesting thread, I have a few comments/questions. To start, when you say:

In testing my new bullet design, we have found that (3) muzzle speed is the most important tuning factor because it affects the bullet's initial yaw attitude and yaw-rate going into ballistic flight. Muzzle speeds between 1 and 6 inches per second (ips) at bullet exit, result in large and variable aerodynamic jumps and greatly decrease accuracy.

how are you determining the relative significance of the factors? Are you determining a range of realistic variation in each parameter and then running a 6DOF (or your own coning motion code) for each, holding the others constant?

Fortunately, both Muzzle pointing direction and cross-bore speed are most stable simultaneously at the instants of muzzle motion reversals, which is why we must tune for bullet exit very near one of those times.

Is this statement made based on your most recent spreadsheet? My own finite element modeling (24" barrels) indicates that this is not necessarily true.

I believe that many rifles suffer horizontal plane barrel vibrations due to the eccentric mass of the bolt handle. I would recommend use of titanium bolt handle shafts and lightweight polymer bolt knobs for target rifle bolt-actions.

I agree that any eccentric mass matters. That said, most actions are inherently asymmetric and suffer from this anyway. You mention the Vaughn book, his work on making the action as symmetric as possible was certainly enlightening.

The bolt body itself can cause serious barrel vibrations during firing if it is a loose fit within the receiver bore... ..."Flopping around" of the rear end of the bolt body during firing generates large amplitude, high-frequency shear-wave vibrations which couple through to the rifle barrel.

Is this something you've measured or modeled? It does seem likely, but I've never seen literature actually showing this.

Thanks for your time!

 

[Jim Boatright]

This is an interesting thread, I have a few comments/questions. To start, when you say:

how are you determining the relative significance of the factors? Are you determining a range of realistic variation in each parameter and then running a 6DOF (or your own coning motion code) for each, holding the others constant?

I wish I had my own 6-DoF simulator. I have a good number of PRODAS runs and one run from Bryan Litz, and I have worn out my first copy of Bob McCoy's book. I have a reasonably good understanding of how and why aerodynamic coning motion works. David Tubb fired 3 different bullet designs over hia Oehler System 88 to 1,000 yards. Our bullets showed very low air drag, but lots of variance--calculated target impact velocities had much more spread than the launch velocities had. I put this down to varying initial yaw and yaw-rate. Accuracy was also "so so." Our monolithic copper bullets have an unusually large distance from their CG location back to the point of last contact with the muzzle, which makes them unusually subject to yaw and yaw-rate tipping during the perhaps 10 to 50 microseconds of bullet exit time. Downward muzzle speed at exit time tips the bullets "pitch-up," and vice versa. JAB

Is this statement made based on your most recent spreadsheet? My own finite element modeling (24" barrels) indicates that this is not necessarily true.

Yes, I have been making many runs of a much more complete spreadsheet taking into account all of the first 7 transverse vibration modes. I will be happy to supply it to any and all who request it (except perhaps to China). I don't do FEA work, but Al Harral has (VarmintAl.com) using his own LS-DYNA program. He thinks that muzzle motions are all recoil driven barrel distortions. I think that no transverse vibrations happen at the muzzle until t = t(peak base pressure) + shear wave propagation delay at 3250 m/s. Then, the natural modes are excited based upon where each mode frequency lines up with the excitation spectrum. The base-pressure curve is quite Gaussian looking, so its Fourier transform is also a Gaussian. The peak excitation frequency is determined by fitting a quarter wave to the rapid, but finite, rise time, and always seems to fall between the Mode 2 and Mode 3 natural frequencies. I set the overall vibration amplitude multiplier to 0.00040-inch based on Harold Vaughn's and Al Harral's work, and considering primarily Mode 2 and Mode 3. The even numbered modes start off negative. The total "all Modes" amplitude sums are plotted for the next 2000 microseconds. Al also thinks group sizes on target are determined only by muzzle pointing direction at bullet exit. That has changed with our understanding of the flying bullet's coning motion. JAB

I agree that any eccentric mass matters. That said, most actions are inherently asymmetric and suffer from this anyway. You mention the Vaughn book, his work on making the action as symmetric as possible was certainly enlightening.

Yes, I wore out my first copy of his book too. JAB


Is this something you've measured or modeled? It does seem likely, but I've never seen literature actually showing this.

I had 8 years of rifle making experience (as Boatright Custom Guns, Inc.), primarily blueprinting (about 200) Remington 700 style actions. We guaranteed 0.25-MOA accuracy and shipped that group along with the rifle. We always sleeved the bolts and installed Jim Borden's "Borden Bumps" (with his reluctant permission) on the front bolt sleeve. With everything done but bolt sleeving, the rifles would shoot 0.5-MOA in my indoor 105-yard range. After bolt sleeving the same rifle would consistently shoot 0.25-MOA 5-shot groups. JAB

Thanks for your time!

 

[308pirate]

Who the hell has matched barrels in LH/RH twist for each match?

David Tubb


duh...…..LOL

Seriously, the man leaves nothing on the table.

 

[JB.IC]

I don’t fully understand everything being discussed because I just started reading this thread but my initial question would be how does one determine optimal barrel length to ensure the barrel will produce precision groups? Or how does one determine a barrel length that will allow a wide tunable load window?

without having in direct evidence or scientific method to prove this but I have noticed in the past that shooting short barrels <20” made it really easy to tune loads. Meaning I didn’t have to try very hard to find a good load. 26” took a little more effort but nothing crazy. My 30” barrel was giving me some fuss but I found a load eventually.

 

[vinniedelpino]

I don’t fully understand everything being discussed because I just started reading this thread but my initial question would be how does one determine optimal barrel length to ensure the barrel will produce precision groups? Or how does one determine a barrel length that will allow a wide tunable load window?

without having in direct evidence or scientific method to prove this but I have noticed in the past that shooting short barrels <20” made it really easy to tune loads. Meaning I didn’t have to try very hard to find a good load. 26” took a little more effort but nothing crazy. My 30” barrel was giving me some fuss but I found a load eventually.

Apparently, your findings are consistent with the experimentation done by Virgil King in the houston warehouse experiments. In short, he (and several colleagues) got their hands on an abandoned warehouse and built a 325 yard range inside, shielded from the elements. They'd start shooting at 10pm when the "air settled" and documented their findings.

After exhaustive testing, he found that 21 3/4" was the optimum barrel length for accuracy, at least for a 6br. At the end of this experiment these guys were shooting relatively light weight rifles consistently in the .025" to .06" range. Virgil was adamant about the 21 3/4" length. The article's worth a read:

Secrets of the Houston Warehouse (angelfire.com)

 

[Jim Boatright]

I am in the process of developing an Excel workbook of spreadsheets which will allow serious riflemen and riflesmiths to enter basic data for candidate rifle barrel-cartridge-bullet-load combinations and produce data showing the vertical-plane muzzle motions caused by transverse barrel vibrations (of all natural vibration modes combined) for each microsecond of possible bullet exit times. I am not accurately calculating the amplitudes of the vibration modes, but am accurately calculating the relative muzzle positions for each possible bullet exit time to the nearest microsecond. The muzzle positions for each microsecond will be visually graphed, and the precise times of the momentary halts (reversals) in that muzzle motion are extracted and displayed. An approximate muzzle speed (in inches per second, upward or downward) at the time of bullet exit is also calculated and shown.

The necessary data input requires running QuickLOAD(c), which you should already be using, for your candidate cartridge-bullet-propellant choice-charge weight-barrel length combination to determine (1) the time of peak base-pressure behind the bullet [or equivalently, 98-percent of the rise time from 10-percent P-Max (t=0 in QL) to its peak value, 100-percent P-Max], and (2) the "barrel time" of bullet exit from the muzzle. That rise time to peak base-pressure is used to calculate (1) the peak frequency of excitation of all barrel transverse vibration modes, and (2) to allow the calculation of the initiation time for those transverse vertical-plane vibrations of all modes. The time of peak base-pressure is also the peak time of the impulsive upward torque caused by recoil force and bending the rear of the rifle barrel upward at the front face of the receiver. Transverse muzzle vibrations can only start after a calculated signalling delay based on barrel length from receiver face to muzzle and a known propagation rate for transverse shear-waves along the rifle barrel as a textbook "long, slender rod" of the specified steel material.

By tuning your load for bullet exit at the time of a "lower" muzzle motion reversal (from downward to upward movement), the rifleman enjoys the benefit of "compensation" where slower (later exiting) bullets are launched at angles slightly more upward to offset some of their extra long-range gravity drop.

Inability to tune your load to match one of its muzzle reversals causes your fired bullets to depart with either upward or downward pitch and pitch-rate. Assuming the CG of the rifle bullet is well ahead of the point of last contact with the bore during bullet exit, downward muzzle motion mechanically produces upward nose pitching, and vice versa. These non-zero pitch attitude and rate values are then amplified by "reverse aerodynamics" during passage of the bullet through the muzzle-blast zone (within the first few inches beyond the muzzle). These rifle bullets then commence ballistic flight with significantly non-zero (and highly variable) initial "aeroballistic yaw" and "yaw-rate" causing each bullet to suffer its own amount of aerodynamic jump deflection of its entire subsequent ballistic trajectory.

If your rifle barrel is only slightly too long for tuning with your selected bullet, you might try loading a much heavier bullet (and using a slower burning powder) to delay its barrel exit time to match the time of the next (later) muzzle reversal. Alternatively, QL might indicate that a much lighter bullet using a maximum load of faster powder could exit at an earlier muzzle halt time. All of this work can be done cheaply without cutting metal and without access to a firing range (and without depleting your stock of hard to replace primers).

I would propose, JB.IC, that once I have developed and verified this spreadsheet program as an Excel workbook, it could be posted in your "Resources" section as a freely available download available to all.

Jim Boatright

 

[Jim Boatright]

Apparently, your findings are consistent with the experimentation done by Virgil King in the houston warehouse experiments. In short, he (and several colleagues) got their hands on an abandoned warehouse and built a 325 yard range inside, shielded from the elements. They'd start shooting at 10pm when the "air settled" and documented their findings.

After exhaustive testing, he found that 21 3/4" was the optimum barrel length for accuracy, at least for a 6br. At the end of this experiment these guys were shooting relatively light weight rifles consistently in the .025" to .06" range. Virgil was adamant about the 21 3/4" length. The article's worth a read:

Secrets of the Houston Warehouse (angelfire.com)

Yes, I used to shoot at the Pearland Sportsman's Club range with some of Virgil King's later hard-core benchrest friends. That was in the late 1960's and 1970's. Virgil became the night manager of one of the Houston Ship Channel's huge oilfield equipment storage warehouses. They had permission to fabricate and store a heavy portable bench and a heavy portable bullet trap/target holder. I did not get serious about benchrest competition until I retired here to northern Arkansas in 1992. I believe I read "Secrets of the Houston Warehouse" in Precision Shooting Magazine back in the 1990's.
Jim Boatright

 

[vinniedelpino]

Yes, I used to shoot at the Pearland Sportsman's Club range with some of Virgil King's later hard-core benchrest friends. That was in the late 1960's and 1970's. Virgil became the night manager of one of the Houston Ship Channel's huge oilfield equipment storage warehouses. They had permission to fabricate and store a heavy portable bench and a heavy portable bullet trap/target holder. I did not get serious about benchrest competition until I retired here to northern Arkansas in 1992. I believe I read "Secrets of the Houston Warehouse" in Precision Shooting Magazine back in the 1990's.
Jim Boatright

It seems like the theory behind the shorter, fatter barrels makes sense. My most accurate rifle was wearing a 20" barrel, so maybe I'm biased. I don't have the coin to test the theory myself, but if I did, I would.

 

[Macht]

The necessary data input requires running QuickLOAD(c), which you should already be using, for your candidate cartridge-bullet-propellant choice-charge weight-barrel length combination to determine (1) the time of peak base-pressure behind the bullet [or equivalently, 98-percent of the rise time from 10-percent P-Max (t=0 in QL) to its peak value, 100-percent P-Max], and (2) the "barrel time" of bullet exit from the muzzle. That rise time to peak base-pressure is used to calculate (1) the peak frequency of excitation of all barrel transverse vibration modes, and (2) to allow the calculation of the initiation time for those transverse vertical-plane vibrations of all modes. The time of peak base-pressure is also the peak time of the impulsive upward torque caused by recoil force and bending the rear of the rifle barrel upward at the front face of the receiver. Transverse muzzle vibrations can only start after a calculated signalling delay based on barrel length from receiver face to muzzle and a known propagation rate for transverse shear-waves along the rifle barrel as a textbook "long, slender rod" of the specified steel material.

This seems to be ignoring two previous excitation effects. Firing pin travel /impact induces measurable muzzle movement prior to ignition and the initial primer impulse that slams the powder bed into the bullet base prior to full ignition is a t driver of higher frequency vibration. Have you considered trying to incorporate these effects into the model? Or perhaps including things like center-of-mass offset and action stiffness, both of which can be shown to affect barrel movement?

There is an argument to be made that some factors can be neglected because they only affect amplitudes, not relative magnitudes, but anything that changes either the natural frequencies or the excitation frequencies could potentially invalidate the results.

 

[GrumpyOleFart]

I once told someone that if they canted their left twist barrel too far over to the left, the bullet would plough into the ground after 600 metres.
That's wrong isn't it.

 

[Jim Boatright]

This seems to be ignoring two previous excitation effects. Firing pin travel /impact induces measurable muzzle movement prior to ignition and the initial primer impulse that slams the powder bed into the bullet base prior to full ignition is a t driver of higher frequency vibration. Have you considered trying to incorporate these effects into the model? Or perhaps including things like center-of-mass offset and action stiffness, both of which can be shown to affect barrel movement?

There is an argument to be made that some factors can be neglected because they only affect amplitudes, not relative magnitudes, but anything that changes either the natural frequencies or the excitation frequencies could potentially invalidate the results.

Good questions, Macht. Yes, I chose to ignore the higher-frequency striker caused vibrations, and those caused directly by primer ignition. I am also ignoring the often significant barrel vibrations caused by bolt slap during initial bolt-face loading. I am not really trying to calculate the actual amplitudes of the barrel transverse vibrations, just their initiation timing and relative amplitudes. I am applying all of this only at the muzzle of the barrel and at the instant of bullet release.

These calculations require minimum data entry for initialization and are intended to prevent building expensive rifles for which their intended loads cannot be tuned for proper bullet exit with zero yaw and yaw rate. They should also save some of the ammo normally wasted during that tuning process. However, there is ultimately no substitute for careful shooting during load development, including retesting in the shooting conditions of match day.

Jim Boatright

 

[Jim Boatright]

I once told someone that if they canted their left twist barrel too far over to the left, the bullet would plough into the ground after 600 metres.
That's wrong isn't it.

Yeah, and I once explained to a NASA manager why a parallax correction had to be applied between the tracking radar data and the 60-feet away optical acquisition-aid pedestal's synchro data as "adjusting the synchro readings to making exactly 360-degree circles." They installed a coaxial CCTV camera up in the dish with a powerful remote-controlled zoom lens which worked better anyway, thus eliminating the parallax problem. The radar operator spent his spare time watching the housewives sunbathing 5 miles away.

An Older Fart

 

[JB.IC]

I am in the process of developing an Excel workbook of spreadsheets which will allow serious riflemen and riflesmiths to enter basic data for candidate rifle barrel-cartridge-bullet-load combinations and produce data showing the vertical-plane muzzle motions caused by transverse barrel vibrations (of all natural vibration modes combined) for each microsecond of possible bullet exit times. I am not accurately calculating the amplitudes of the vibration modes, but am accurately calculating the relative muzzle positions for each possible bullet exit time to the nearest microsecond. The muzzle positions for each microsecond will be visually graphed, and the precise times of the momentary halts (reversals) in that muzzle motion are extracted and displayed. An approximate muzzle speed (in inches per second, upward or downward) at the time of bullet exit is also calculated and shown.

The necessary data input requires running QuickLOAD(c), which you should already be using, for your candidate cartridge-bullet-propellant choice-charge weight-barrel length combination to determine (1) the time of peak base-pressure behind the bullet [or equivalently, 98-percent of the rise time from 10-percent P-Max (t=0 in QL) to its peak value, 100-percent P-Max], and (2) the "barrel time" of bullet exit from the muzzle. That rise time to peak base-pressure is used to calculate (1) the peak frequency of excitation of all barrel transverse vibration modes, and (2) to allow the calculation of the initiation time for those transverse vertical-plane vibrations of all modes. The time of peak base-pressure is also the peak time of the impulsive upward torque caused by recoil force and bending the rear of the rifle barrel upward at the front face of the receiver. Transverse muzzle vibrations can only start after a calculated signalling delay based on barrel length from receiver face to muzzle and a known propagation rate for transverse shear-waves along the rifle barrel as a textbook "long, slender rod" of the specified steel material.

By tuning your load for bullet exit at the time of a "lower" muzzle motion reversal (from downward to upward movement), the rifleman enjoys the benefit of "compensation" where slower (later exiting) bullets are launched at angles slightly more upward to offset some of their extra long-range gravity drop.

Inability to tune your load to match one of its muzzle reversals causes your fired bullets to depart with either upward or downward pitch and pitch-rate. Assuming the CG of the rifle bullet is well ahead of the point of last contact with the bore during bullet exit, downward muzzle motion mechanically produces upward nose pitching, and vice versa. These non-zero pitch attitude and rate values are then amplified by "reverse aerodynamics" during passage of the bullet through the muzzle-blast zone (within the first few inches beyond the muzzle). These rifle bullets then commence ballistic flight with significantly non-zero (and highly variable) initial "aeroballistic yaw" and "yaw-rate" causing each bullet to suffer its own amount of aerodynamic jump deflection of its entire subsequent ballistic trajectory.

If your rifle barrel is only slightly too long for tuning with your selected bullet, you might try loading a much heavier bullet (and using a slower burning powder) to delay its barrel exit time to match the time of the next (later) muzzle reversal. Alternatively, QL might indicate that a much lighter bullet using a maximum load of faster powder could exit at an earlier muzzle halt time. All of this work can be done cheaply without cutting metal and without access to a firing range (and without depleting your stock of hard to replace primers).

I would propose, JB.IC, that once I have developed and verified this spreadsheet program as an Excel workbook, it could be posted in your "Resources" section as a freely available download available to all.

Jim Boatright

this stuff is the exciting part of shooting. I think Jim’s work will help progress our sport with this kind of information.

I think we all knew barrel vibrations was an issue. When I first started reloading I knew I had to tune a load for precision based off “barrel timing.” However complexity of this stuff is not common amongst even the best shooters in our sport.

I personally appreciate the work you’re doing Jim.

I’m currently building a 33XC to shoot 275 CE Lazers. I just re-read your Bullet Obturation paper to jog my memory on what kind of contour to run. I’m planning a 30” 5R barrel. 1.35” for 8” and then tapering to a 1.25” at the muzzle. I’m definitely going for a heavy barrel.

 

[PTPATAW]

I wonder if a suppressor cover dampens any of the vibrations

 

[Jim Boatright]

I have developed an Excel workbook of 4 spreadsheets which facilitates the input of the rifle, barrel, and interior ballistics data needed to calculate muzzle position in millimeters as a function of time since 10-percent of P-Max, as is used in QuickLOAD(c). You can enter your data, and the last spreadsheet shows graphically where the muzzle is and calculates how fast it is moving vertically (in millimeters per second) at the QL-calculated time of bullet exit from the muzzle. We are currently beginning to understand the real ballistic benefits of having rifle bullets exit from an inertially stationary muzzle. The worked example is for a known accurate rifle with a cylindrical barrel and no muzzle attachment.

This seems like it will be a useful tool in developing accurate loads for any rifle. It will also help prevent building rifles which are hopelessly incompatible with their intended loads. The formulations for handling of barrel taper and muzzle attachment weight (mass) are somewhat speculative but seems to be working fairly well. The formulations are based on sound physics otherwise.

I would like someone to post this workbook in the Resources section here for all to use who have Excel and QL (or equivalent). I will post an updated paper which goes with this spreadsheet in a few days.

Jim Boatright
<[email protected]>

 

[Macht]

Have you tried to calculate the movement in the horizontal plane?

 

[Jim Boatright]

Well, at this level of analysis, the expected motion of the muzzle in the horizontal plane is ZERO. An asymmetrical receiver will cause some skewing of the plane of transverse barrel excitation. For a typical right-handed ejection port receiver, the shot scatter for different muzzle exit times will be slightly upper right to lower left. Benchrest bolt-actions are often machined symmetrically, left to right, for this reason.

 

[Macht]

I guess that's the point I'm trying to make. To correctly predict vertical motion you also need to know things like receiver asymmetry and the distance from bore axis to rifle center of mass. It's not insignificant either, for a RPR the measured horizontal vibrations are roughly 50% of the amplitude of the vertical vibrations, and they aren't perfectly in phase.

I'm looking forward to seeing your spreadsheets, but I think it might be a bit of a stretch to say that you can predict when the muzzle will be stationary without accounting for those kinds of effects.

Hopefully this isn't coming across as too confrontational, I just know that I've constantly had to change my assessment of what factors actually matter in terms of barrel movement over the past few years of research.

 

[Jim Boatright]

Not at all, Macht. It's just that nobody has ever formulated the vertical-plane shear-wave vibrations before to my knowledge. I do request input of the distance of the rifle CG below the bore line in formulating the amplitudes of the vertical-plane vibrations at the muzzle. Email me and I will send you the Excel workbook as an attachment to my reply. <[email protected]>
Not being a moderator, I can only upload PDF files here on SnipersHide. I guess they are all schmoozing at the SHOT Show.

 

[Jim Boatright]

While I have never tuned up a Ruger Precision Rifle, my suspicion about your horizontal spreads is that the three bolt lugs are either not supported symmetrically in the receiver design, or perhaps they are not bearing the load of bolt-thrust evenly due to uneven bolt-lug/seat engagements while unloaded. Check bolt-lug engagement with red Marks-a-Lot or similar thin indicator fluid. Could a little judicious bolt-lug lapping be in order?
After lapping out any high spots, clean everything thoroughly and apply a light coat of high film strength grease to the locking surfaces of all lugs. Keep them lubed from now on.

 

[Jim Boatright]

Here is my finalized paper on the subject of tuning the rifle barrel and load together. I have tried to re-write both the paper and the spreadsheets for easier use and understanding. [I took out most of the equations and physics lectures.] I know the screenshots of the large spreadsheets are difficult to read, but they are the best I could do without being able to post the Excel workbook.
Jim Boatright
<[email protected]>

 

[acudaowner]

I guess the angle of the dangle is relative to the swirl of your pearl , or the sheen of your bean lol , but you say left hand twist works better in the wind than right hand twist maybe that's only true with wind from left to right could not the right to left wind use the other right hand twist or visa versa . which might prefer right hand twist and if that were true would you carry around different twisted barrels just to shoot in different wind moving in different directions and wind that was swirling around all willy nilly which would you pick then ? or if you went to Australia where everything spins counter clock wise would these results not reverse like the water in a toilet ? it would be neat to see how much of the results were just the wind or the effects of the earths magnetic core churning and if it affects any of it . Or what happens when earth's magnetic poles flip every so often .

 

[JB.IC]

Jim I tried to post the one you sent me via email a few weeks ago and it wouldn’t allow me to post it.

 

[Jim Boatright]

I really need to post the current Excel workbook. I believe Theis posted the earlier one in Resources, and this new one should replace that old one. But, I will need to send it to you as an email attachment. Only a couple of guys have asked me for one so far.
Jim Boatright
<[email protected]>

 

[THEIS]

Hi,

Version 3 PDF updated to the Resources section.
For some reason I thought I had already updated it for everyone.

Sincerely,
Theis

 

[6.5SH]

I really need to post the current Excel workbook. I believe Theis posted the earlier one in Resources, and this new one should replace that old one. But, I will need to send it to you as an email attachment. Only a couple of guys have asked me for one so far.
Jim Boatright
<[email protected]>

You should be able to attach .zip files.

Assuming you are on Windows, in Explorer right click your excel file>Send to>Compressed (zipped) folder. Attach the .zip file it creates.

 

[Jim Boatright]

Windows will not let me compress an Excel file, 6.5SH.
Here are pdf files of the paper which goes with a re-done workbook. There are many fewer simplifying assumptions made with this approach. It shows how the driving function and the resonant frequency responses occur at the muzzle.
PDF images of the 4 spreadsheets referenced are also attached. They contain data for the worked example. Due to its table sizes, the fourth sheet is 18 pages, but only the first is of concern.
Jim Boatright

 

[JB.IC]

The kind of take away I’m seeing from your example is that if all else being equal, the barrel would benefit from being a tad longer. But since length and weight changes the calculations, it would be uncertain. But what is certain is that the barrel is releasing the bullet in a downward motion which pitches the bullet up(??)