Hyper Stabilized Bullets - Jim Boatright

[Jim Boatright]

Now for the real stupid question of the day. I realize this is probably like bringing a knife to a gun fight, but golf uses dimples to stabilize the flight of the ball. Any value in doing that in the area between 113 and 115 for stabilization?

Hello, FSG;

There are no stupid questions in aerodynamics. The dimpling of golf balls has to do with preventing "attached flow" in ultra-low-speed aerodynamics. I believe it minimizes hooking and slicing effects while increasing flight durations. It is sudden flow attachment which causes a curve ball to break suddenly and a knuckle ball to jump randomly at a certain airspeed. Low-speed aerodynamics of spherical projectiles is just weird. For that matter, look at the transonic behavior of a 9/16-inch diameter sphere.

As to your question about airflow over the boat-tail surfaces, it is already in turbulent boundary layer flow for my bullet design in any rifle caliber. I want that flow field to remain attached to the conical BT surface in order to direct that flow smoothly toward a compression point 3.2-calibers behind the base of the bullet. I believe that design might promote base pressure recovery by partially entrapping the shed wake vortices and pulling them along with the bullet. That is how an "effective boat-tail" design is supposed to work anyway. The rear corner of the BT is machined sharp for this flow-directing purpose. Any radius there greatly promotes alternate vortex shedding which increases drag and causes flight instability, especially at transonic airspeeds.

Jim Boatright

 

[CPierce]

Jim, it might be helpful to post your "Third Generation Long-Range Rifle Bullets" paper with the Admin's approval. Might answer a lot of these questions

 

[bohem]

Hello, Bohem;
I tried to keep my bullet design clean and simple to minimize secondary shocking--always keeping nose-drag, base-drag, and boundary layer (BL) skin friction in mind a lot. I defined "1.0 calibers" to be the bore ID plus 0.0002-inch to help reduce nose-drag versus using the groove ID +0.0002 (machine tolerance). I wanted the laminar BL flow over the ogive to trip reliably into turbulent flow at the 4.5-degree break angle at the base of the 3.2-caliber secant ogive (with RT/R = 0.5). Bullet OAL is 5.60-calibers. I wanted the turbulent BL to slide cleanly off the sharp-cornered BT toward a compression point 3.2 calibers behind the base of the BT. I selected the 7.5-degree cone angle for the ramp up to groove ID with both BL flow and bullet alignment guidance in the chamber throat in mind. It all seems to work. The rifle bullet design ends up looking somewhat similar to the M549 155 mm artillery projectile.

The Mach 2.5 airspeed comes from David's test of the 225-gr version of the 338-caliber bullets. His range is 995.7 yards and time of flight in a 21 mph tailwind was 1.068 seconds at 65 degrees F. Correcting for air distance travelled in 1.068 seconds yields a time-average airspeed of Mach 2.46. His Oehler System 88 with square-array acoustic mics at target distance (i believe) calculated an average BC(G1) of 0.794 for 5 shots and 2325 fps (Mach 2.070) arrival speed. His average MV was 3378 fps (Mach 3.008). So, Mach 2.46 sounds about right for this 1000-yard BC measurement. Oehler still uses the old ASM atmosphere. I used ICAO with McDRAG. Air density is 0.5 percent greater with the sea-level ICAO atmosphere. McDRAG had estimated a BC(G1) of 0.703 at Mach 2.5. If we attribute the remaining 12.4 percent difference in BC's to David's bullets being hyper-stabilized at an initial Sg of 2.75 from his 7.5-inch twist Schneider barrel, we could reasonably scale up other McDrag estimates similarly for other hyper-stabilized rifle bullets until they can be test-fired. That's why I said Mach 2.5 BC(G1) approaching 1.00.

By the way, to estimate initial Sg for those base-drilled bullets, I scaled the effective length of the base-drilled bullets from their actual length by the square root of the Iy/Ix ratios after/before drilling, and then used that effective length in McGYRO and Don Miller's Sg estimators. That is, I used the radius of gyration ratios ky/kx to scale the effective length reduction. I calculate the mass properties by numerical integration in my spreadsheet bullet design tool. Dan's copper bullet-making material seems to have a density of 8.84 grams per cc.

Jim Boatright

Jim Boatright

OK, that answers my question then.

 

[LastShot300]

May I ask if there is some body of evidence of what this hyper flight actually does or if at least it really happens? Besides Davifd Tubb limited experience and some PRODAS runs anything else coming from real world experience or radar measurements? So far, it's a nice paper but lacking in supporting data. Don't get me wrong, all this stuff is valuable but science requires actual validation of any theory. Another thing I don't get is the difference, if any, between this "hyper stable state" and "over stable".Hopefully Jim will chime in.

 

[Lowlight]

An interesting addition to this conversation, as yesterday I was playing with ColdBore using my data from the 7 Twist 260 I have. It's a shorter barrel, 20" and I am shooting the 136gr Scenar. I was using the data from my Copper Creek Load which, I had saved with the Impact Databook page,

MV: 2775
DA 6000
Raw inputs
24.91
65 degrees
30%
39 Lat
290 Az
Wind 6MPH - 270 degrees

Sight Height 2.5
Twist 1-7
100 yard zero

Bullet Length 1.347
Bullet Weight 136
BC .545 *

Drops to confirm

500 - 2.4 (sub moa plate) / .2 Wind
600 - 3.5 / .2 Wind
800 - 5.2 / .4 Wind
900 - 6.2 (sub moa plate) / .4 Wind
1125 - 9.2 / .6 Wind

I ran the BC calculator to determine my new BC and ColdBore actually gave me .680 ? Changing that alone lined up my data pretty well. In a program like JBM, I had to change my MV to 2850fps to line it up. It's as close as any other program got, although just changing the BC in CB 1.0 it was perfect.

After speaking with Gus, he said if the DK/DC factor is moved more than 10% go to the BC. So the DC only moved it to 5.4 Mils at 800, so I reset that and used the utility to flush out the BC. Giving me .680 I was like, Ok, and sure enough, it was perfect for every range.

Next to went to the Spin & Stability section and at 2775 up to 2900fps the Stability just touches on being overstable but the two methods are very different. If you go to 2950fps it's overstable,

So being on that edge, it appears to have increased the BC by a wide margin. I have noticed more consistent drops with the rifle, but also that software is having a hard time with it. Especially in the wind.

Almost everything (Except ColdBore with the BC change) is almost double the wind calls. They cannot manage the wind drops at all. They also increase the drop (800 vs 900 yards) when using the factory BC, you need that inflated BC to actually line, 800, 900, 1125 up.

The Greenhill data seems to be correct vs the Miller data.

 

[FlaShooterG]

Jim, it might be helpful to post your "Third Generation Long-Range Rifle Bullets" paper with the Admin's approval. Might answer a lot of these questions

I would love to see it.

 

[Quickshot]

May I ask if there is some body of evidence of what this hyper flight actually does or if at least it really happens? Besides Davifd Tubb limited experience and some PRODAS runs anything else coming from real world experience or radar measurements?

There are Doppler plots that show faster twists have lower supersonic drag. I think Hornady published one. I've heard rumors that Warner is going back to the RADAR range. Maybe they will measure their bullets out of barrels with various twists?
Cheers,

 

[FlaShooterG]

There are Doppler plots that show faster twists have lower supersonic drag. I think Hornady published one. I've heard rumors that Warner is going back to the RADAR range. Maybe they will measure their bullets out of barrels with various twists?
Cheers,

Thanks to all for indulging me. So in my mind, this begs the question whether a faster twist (say 1:7) is always better than a slower (1:9) twist for long range with a solid round?Obviously there are variants for caliber, but as a general concept. I know Jim said it’s the bullet, but does increase in spin rate always result in a more stable long range round?

 

[LastShot300]

An interesting addition to this conversation, as yesterday I was playing with ColdBore using my data from the 7 Twist 260 I have. It's a shorter barrel, 20" and I am shooting the 136gr Scenar. I was using the data from my Copper Creek Load which, I had saved with the Impact Databook page,

MV: 2775
DA 6000
Raw inputs
24.91
65 degrees
30%
39 Lat
290 Az
Wind 6MPH - 270 degrees

Sight Height 2.5
Twist 1-7
100 yard zero

Bullet Length 1.347
Bullet Weight 136
BC .545 *

Drops to confirm

500 - 2.4 (sub moa plate) / .2 Wind
600 - 3.5 / .2 Wind
800 - 5.2 / .4 Wind
900 - 6.2 (sub moa plate) / .4 Wind
1125 - 9.2 / .6 Wind

I ran the BC calculator to determine my new BC and ColdBore actually gave me .680 ? Changing that alone lined up my data pretty well. In a program like JBM, I had to change my MV to 2850fps to line it up. It's as close as any other program got, although just changing the BC in CB 1.0 it was perfect.

After speaking with Gus, he said if the DK/DC factor is moved more than 10% go to the BC. So the DC only moved it to 5.4 Mils at 800, so I reset that and used the utility to flush out the BC. Giving me .680 I was like, Ok, and sure enough, it was perfect for every range.

Next to went to the Spin & Stability section and at 2775 up to 2900fps the Stability just touches on being overstable but the two methods are very different. If you go to 2950fps it's overstable,

So being on that edge, it appears to have increased the BC by a wide margin. I have noticed more consistent drops with the rifle, but also that software is having a hard time with it. Especially in the wind.

Almost everything (Except ColdBore with the BC change) is almost double the wind calls. They cannot manage the wind drops at all. They also increase the drop (800 vs 900 yards) when using the factory BC, you need that inflated BC to actually line, 800, 900, 1125 up.

The Greenhill data seems to be correct vs the Miller data.

LL thanks a lot for sharing your insight on the internals of how to get the most out of CB. I've Learned a lot new. Really impressive stuff.

 

[Jim Boatright]

May I ask if there is some body of evidence of what this hyper flight actually does or if at least it really happens? Besides Davifd Tubb limited experience and some PRODAS runs anything else coming from real world experience or radar measurements? So far, it's a nice paper but lacking in supporting data. Don't get me wrong, all this stuff is valuable but science requires actual validation of any theory. Another thing I don't get is the difference, if any, between this "hyper stable state" and "over stable".Hopefully Jim will chime in.

Hello, LS300;
I suppose that would be a fair question. I am putting out theories and claims without rigorous peer-review and consensus. That often happens when discoveries are first made. I am too old and no longer have the eyesight to test this stuff myself. I was kind of hoping to encourage younger, better riflemen to do that test work for their own edification and amusement. I simply hope to steer your thinking in profitable directions.

An understanding of Coning Theory is required to explain or understand hyper-stability. I developed that novel Coning Theory as a retired engineer and an ardent amatuer ballistician. The "pro's" don't like that an amatuer might have the effrontery to do such a thing, and refuse even to consider that it might be correct--in short, they ignore it and continue plodding along, set in their ways. They also do not like someone saying they might be wrong. I summarized that theory for you in the first part of this subject paper on hyper-stability. To my knowledge, not one member of the establishment "ballistics" community has even commented on this hyper-stability paper, much less found any fault with it. There are apparently few "peers" remaining with the capability or inclination to consider anything new since about 1980--ballistics is a "mature field," no longer open to new developments.

Most fired rifle bullets have always eventually entered hyper-stability flight mode far downrange with Sg greater than 3 and minimum coning angle flight. I don't think anyone had previously thought how valuable it could be to spin their rifle bullets fast enough to achieve hyper-stability before that bullet first encounters the undisturbed ambient air mass outside the muzzle blast zone. Potential drag is always greatest early in flight because dynamic pressure is always greatest there in un-powered flight. Ballisticians have always warned against "over-stabilizing" your rifle bullets, or something bad will surely happen. Perhaps, it will "turn your knees black," as Momma used to warn her children. So, I made up the term "hyper-stability" to use for this instead. With lead-core bullets, there might have been slight justification for avoiding high initial spin-rates, but technology is moving beyond that with CNC copper-alloy bullet making. I simply propose using those new bullets to their full potential by throwing off the shackles of outmoded thinking. Please let me know if anything bad happens to you or your copper bullets when you try this.

I eagerly await any theoretical disputation or practical experimental disproof of Coning Theory or any of its ramifications, including hyper-stability of rifle bullets.

Jim Boatright

 

[FlaShooterG]

Hello, LS300;
I suppose that would be a fair question. I am putting out theories and claims without rigorous peer-review and consensus. That often happens when discoveries are first made. I am too old and no longer have the eyesight to test this stuff myself. I was kind of hoping to encourage younger, better riflemen to do that test work for their own edification and amusement. I simply hope to steer your thinking in profitable directions.

An understanding of Coning Theory is required to explain or understand hyper-stability. I developed that novel Coning Theory as a retired engineer and an ardent amatuer ballistician. The "pro's" don't like that an amatuer might have the effrontery to do such a thing, and refuse even to consider that it might be correct--in short, they ignore it and continue plodding along, set in their ways. They also do not like someone saying they might be wrong. I summarized that theory for you in the first part of this subject paper on hyper-stability. To my knowledge, not one member of the establishment "ballistics" community has even commented on this hyper-stability paper, much less found any fault with it. There are apparently few "peers" remaining with the capability or inclination to consider anything new since about 1980--ballistics is a "mature field," no longer open to new developments.

Most fired rifle bullets have always eventually entered hyper-stability flight mode far downrange with Sg greater than 3 and minimum coning angle flight. I don't think anyone had previously thought how valuable it could be to spin their rifle bullets fast enough to achieve hyper-stability before that bullet first encounters the undisturbed ambient air mass outside the muzzle blast zone. Potential drag is always greatest early in flight because dynamic pressure is always greatest there in un-powered flight. Ballisticians have always warned against "over-stabilizing" your rifle bullets, or something bad will surely happen. Perhaps, it will "turn your knees black," as Momma used to warn her children. So, I made up the term "hyper-stability" to use for this instead. With lead-core bullets, there might have been slight justification for avoiding high initial spin-rates, but technology is moving beyond that with CNC copper-alloy bullet making. I simply propose using those new bullets to their full potential by throwing off the shackles of outmoded thinking. Please let me know if anything bad happens to you or your copper bullets when you try this.

I eagerly await any theoretical disputation or practical experimental disproof of Coning Theory or any of its ramifications, including hyper-stability of rifle bullets.

Jim Boatright

There appears to be a link to your coning theory on the hide at: https://www.snipershide.com/coning-theory-of-bullet-motion/
It doesn't seem to work. At least not for me. Is there any way we can get the link re-established???

 

[THEIS]

There appears to be a link to your coning theory on the hide at: https://www.snipershide.com/coning-theory-of-bullet-motion/
It doesn't seem to work. At least not for me. Is there any way we can get the link re-established???

Hi,

FSG...I am not sure if this link is the exact same document as the previous link but here you go.

https://arxiv.org/ftp/arxiv/papers/1205/1205.2071.pdf

Sincerely,
Theis

 

[LastShot300]

Hello, LS300;
I suppose that would be a fair question. I am putting out theories and claims without rigorous peer-review and consensus. That often happens when discoveries are first made. I am too old and no longer have the eyesight to test this stuff myself. I was kind of hoping to encourage younger, better riflemen to do that test work for their own edification and amusement. I simply hope to steer your thinking in profitable directions.

Jim Boatright

Thanks for coming back with your response Jim. If your peers have reviewed your paper then it's more than enough for me. We just have to wait for the field results that confirm the ULD hyper stable state.

 

[Jim Boatright]

If somebody could PM a good email address to me, I would be happy to send back a PDF attachment of my latest version of the "bullet design" paper for posting in your "Resources" section perhaps. It is an overly-long, all inclusive 42-page log of my bullet design thinking and the development process. I have recently updated it. It is still in my primitive Word format, and not the nice re-formatting which Gustavo did for the Hyper-Stability paper and the earlier CWAJ and Spin-Drift papers which he co-authored.

The Coning Theory paper on ArchiveX dates from 2012 and really needs to be updated. ResearchGate picked up that old version a couple of years ago and replaced the updated version I had supplied to them with the original paper. I have developed Coning Theory ramifications quite a bit since then. The basics are still the same, though. People all over the world are reading this old paper, and I really should update it everywhere. It will take a concerted effort for a couple of days for me to update it, but it really needs doing.

I also wrote a short paper this winter entitled The Mean Trajectory for ballisticians explaining the remaining problems in classic aeroballistics which need updating in light of Coning Theory. I explained why the spin-axis pitch and yaw data plotted in their traditional Wind Axes plots are inconsistent with each other. I discovered from PRODAS data that the horizontal Spin-Drift trajectory is just a scaled-down version of the vertical-plane flight path at ranges beyond about 150 yards, simply rotated 90 degrees about the extended bore axis at firing time. As expected, I received no response from ballisticians. Anyway, I could supply a PDF of that paper also.

Jim Boatright

 

[Jim Boatright]

Thanks for coming back with your response Jim. If your peers have reviewed your paper then it's more than enough for me. We just have to wait for the field results that confirm the ULD hyper stable state.

Hi again, LS300;

Quite the contrary. Ballisticians are Mechanical Engineers who will not willingly converse in the applicable language of physics called "Classical Mechanics." For example, they happily interchange (and confuse) bullet weight (a force dependent upon the local gravitational field and upon the "centrifugal force" due to the spin-rate of the earth) and bullet mass, which is usually constant. I only wish they would make the effort to peer-review my work in ballistics. Ballisticians, for example, are not even willing to admit that the free-flying, spin-stabilized rifle bullet is a "gyroscope." They persist in using "slow mode" and "fast mode" terminology instead of simply saying "precession and nutation", the accepted terms in physics. They use "dimensionless" canonical units in their elegant calculus, which was worked out earlier by brilliant people, but then have great difficulty converting back into real physical values for actual numerical calculations. They completely ignore dimensional analysis which is a valuable tool used by physicists in studying relationships. The principles of Conservation of Energy and Conservation of Momentum are foreign concepts in ballistics. Etc.

I am currently working on finding new relationships between the gyroscopic stability (Sg) of the spinning rifle bullet and its coning angle (alpha) in flight. I have made some progress, but am not ready to present anything just yet. Dynamic stability is a complicated subject, but I think it can be made clearer.

Jim Boatright

 

[FlaShooterG]

Hi,

FSG...I am not sure if this link is the exact same document as the previous link but here you go.

https://arxiv.org/ftp/arxiv/papers/1205/1205.2071.pdf

Sincerely,
Theis

Awesome.
Just started reading it. Great paper so far.

 

[THEIS]

Hi,

2 additional resource documents from Jim Boatright posted in "Resources" section

Sincerely,
Theis

 

[TripleBull]

2 additional resource documents from Jim Boatright posted in "Resources" section

Thank you for putting those up, Theis. I'm knee deep in the "3rd Generation LR Bullets" article.

 

[THEIS]

Hi,

Here are a few things that "hyper stabilization" sheds another light on for me....Let me preface this by saying I speak "BE" (Ballistic Ebonics) so please understand that the below is not written in proper ballistic language

Way back years and years ago when the 408CT was first released; the notion (Yuma Radar proven btw) that the 419gr projectiles BC actually increased at approximately the 900 yards over the BC at muzzle velocity with 13.25 twist rate was considered crazy. How in the world does the BC increase while the velocity is decreasing was a huge debate all over the internet.

Way back years and years ago when the 375CT was first released; the notion that the 350gr projectiles BC actually increased at approximately the 750 yards over the BC at muzzle velocity with 11.25 twist rate was once again considered crazy. BUT when people starting going to 10 twist (when Lawton closed) the BC then increased at approximately the 575 yards over the BC at muzzle velocity it started becoming a little more clear to people that those solids performed better the faster twist used.
The problem with this "Proof" was that about the same time period the projectiles got heavier for caliber since barrel makers were willing to make faster twist barrels.

Fast forward to today and Jims "Hyper Stabilization" theory it all makes scientific sense. Those BCs went up at the slower velocities because that was when the stabilization finally become optimized with that twist rate. So for me it makes sense that the closer to the muzzle we can get full stabilization the better downrange results we will get.

Kinda like back in the 11.25 twist 375 days everyone was talking about they didn't group worth a shit under 600-700 yards but when switched to the 10 twist 375 days everyone was saying the were starting to group better at 300-400 yards.

Sincerely,
Theis

 

[TripleBull]

Frank,

In your Bartlein Barrels Rifling Machine video:

https://www.snipershide.com/shootin...l-break-in-question-please-just-read.6873492/

You mention that for gain twist barrels, subtle is better. Can you be more specific in the context of this thread? So if you want the muzzle end twist to be 20 calibers, is there a rule of thumb for starting twist?

 

[THEIS]

Hi,

Not speaking for LL but I am pretty sure his "subtle" is geared more towards jacketed projectiles as to where the majority of this thread is geared towards solids.
Bartlein barrels recommends a 3/4 gain twist if I remember correctly.
The solids are not prone to damage from spinning too fast too soon type of thing so I think the rifling profile (To Balance Pressure) is more important in regards to solids than the rifling twist rate.

Sincerely,
Theis

 

[LastShot300]

Hi,

Here are a few things that "hyper stabilization" sheds another light on for me....Let me preface this by saying I speak "BE" (Ballistic Ebonics) so please understand that the below is not written in proper ballistic language

Way back years and years ago when the 408CT was first released; the notion (Yuma Radar proven btw) that the 419gr projectiles BC actually increased at approximately the 900 yards over the BC at muzzle velocity with 13.25 twist rate was considered crazy. How in the world does the BC increase while the velocity is decreasing was a huge debate all over the internet.

Way back years and years ago when the 375CT was first released; the notion that the 350gr projectiles BC actually increased at approximately the 750 yards over the BC at muzzle velocity with 11.25 twist rate was once again considered crazy. BUT when people starting going to 10 twist (when Lawton closed) the BC then increased at approximately the 575 yards over the BC at muzzle velocity it started becoming a little more clear to people that those solids performed better the faster twist used.
The problem with this "Proof" was that about the same time period the projectiles got heavier for caliber since barrel makers were willing to make faster twist barrels.

Fast forward to today and Jims "Hyper Stabilization" theory it all makes scientific sense. Those BCs went up at the slower velocities because that was when the stabilization finally become optimized with that twist rate. So for me it makes sense that the closer to the muzzle we can get full stabilization the better downrange results we will get.

Kinda like back in the 11.25 twist 375 days everyone was talking about they didn't group worth a shit under 600-700 yards but when switched to the 10 twist 375 days everyone was saying the were starting to group better at 300-400 yards.

Sincerely,
Theis

Very informative historical background.

 

[bohem]

Hello, LS300;
I suppose that would be a fair question. I am putting out theories and claims without rigorous peer-review and consensus. That often happens when discoveries are first made. I am too old and no longer have the eyesight to test this stuff myself. I was kind of hoping to encourage younger, better riflemen to do that test work for their own edification and amusement. I simply hope to steer your thinking in profitable directions.

An understanding of Coning Theory is required to explain or understand hyper-stability. I developed that novel Coning Theory as a retired engineer and an ardent amatuer ballistician. The "pro's" don't like that an amatuer might have the effrontery to do such a thing, and refuse even to consider that it might be correct--in short, they ignore it and continue plodding along, set in their ways. They also do not like someone saying they might be wrong. I summarized that theory for you in the first part of this subject paper on hyper-stability. To my knowledge, not one member of the establishment "ballistics" community has even commented on this hyper-stability paper, much less found any fault with it. There are apparently few "peers" remaining with the capability or inclination to consider anything new since about 1980--ballistics is a "mature field," no longer open to new developments.

Most fired rifle bullets have always eventually entered hyper-stability flight mode far downrange with Sg greater than 3 and minimum coning angle flight. I don't think anyone had previously thought how valuable it could be to spin their rifle bullets fast enough to achieve hyper-stability before that bullet first encounters the undisturbed ambient air mass outside the muzzle blast zone. Potential drag is always greatest early in flight because dynamic pressure is always greatest there in un-powered flight. Ballisticians have always warned against "over-stabilizing" your rifle bullets, or something bad will surely happen. Perhaps, it will "turn your knees black," as Momma used to warn her children. So, I made up the term "hyper-stability" to use for this instead. With lead-core bullets, there might have been slight justification for avoiding high initial spin-rates, but technology is moving beyond that with CNC copper-alloy bullet making. I simply propose using those new bullets to their full potential by throwing off the shackles of outmoded thinking. Please let me know if anything bad happens to you or your copper bullets when you try this.

I eagerly await any theoretical disputation or practical experimental disproof of Coning Theory or any of its ramifications, including hyper-stability of rifle bullets.

Jim Boatright

The quick proposal of data that I can suggest comes from the 180 Flatline 30c bullet that has been shot by a number of folks in a number of twists from 10 down to 8 and through acoustic as well as doppler.

The initial BC measurement published by Warners came from my testing method and an aparatus owned by @Jeffvn with bullets shot from his 10 twist 308 Win rifle.

We shot them at such a setup that we got the high speed flight over a total measured distance of appx 1500 yards from this 10 twist.
We also shot them from a 9 twist 3006 going appx 200fps faster and ran the come-ups against the BC measured from the 308 in the 10 twist. Unfortunately the data from the 9 twist shots was corrupted on the acoustic approach for that day and we ran out of time to retest it later upon discovering it.

The 180's shot from a 9tw lined up and hit the waterlines as expected using the BC measured from the 10 twist rifle barrel. This was done past 1600yards.

Applied Ballistics initially tested these 180's and shot them from a 10 twist and an 8 twist on their acoustic method. The published G7 BC from Warners and the published G7 from AB on the initial test in November 2015 was 0.001 different (0.347 vs. 0.348) for the data from AB's 8 twist and our 10 twist.

Hornady kindly tested the bullet in a 10 and 8 twist. The data was minorly different, appx 1.5%
There has been a demonstration to show that a faster twist rate improves BC but the actual effect is minute for a bullet that is properly stabilised at the muzzle.

At the time of publication of the AB data in Nov 2015 the Berger Sg calculator predicted a 13% improvement in the 180's BC by simply shooting it in an 8 twist instead of the 10 twist. Since we published data from the 10 twist and AB published data from an 8 twist that was effectively identical there is a disconnect somewhere.

Either the test data was flawed by one of the parties or the Berger Sg calculator was spitting out junk.
About 16 months later Hornady was kind enough to test the projectiles over Doppler radar and confirmed the BC's to match well within the published error bound of the test that I/We published with the 180 Flatline. That leads me to believe the Berger Sg calculator was erroneous for the 180 Flatline. it has since shown to be erroneous for the 198 and 361 as well with the Doppler testing that was performed.


With what @THEIS said on the 375's and 408 I suspect that the mismatch actually lies in the coning motion behavior that Mr. Boatright is discussing however rather than calling it "hyper stabilized" I am thinking maybe more like "properly stabilized". I certainly agree with his statement above about refusing to call something "over stabilized".

The epicyclic motion stability equilibrium forms show that you can have a conditionally stable projectile with a fast arm that is well within the equilibrium boundary and a slow arm that is tracing on the edge of it. This projectile can be decay into an unstable motion where it falls out of the sky (downrange effects of the tail on the 168 SMK 30c bullet from overturning behaviors due to huge Magnuss moment effects) or it can have a decaying behavior that damps out and turns stable and flies downrange just fine. With something that's truly "on the edge" it could just be wind that pushes the projectile from one side of the bound to the other.

We are seeing some understanding on it and the coning motion approach is on the right track and I applaud Mr. Boatright's efforts on this.

I don't have a 10.3 or 10.5 or 10.7 twist 30 caliber barrel to try it out but I suspect what we could do is take an 11 twist rifle barrel and shoot 180's in calm atmospheric conditions where the atltitude can give us the margin to make them stable, then shoot them on a very windy day and watch everything go to hell in a handbasket. I've seen those results before with the 195gr 7+ caliber long 7mm that I mentioned above with holes drilled up the back. Super windy days the testing went to shit and at the time we didn't quite understand enough of what we were seeing so the subsequent tests where performed with holes drilled deeper when what should have been done is to get a day with less wind and see how we did again.

 

[Lynn Jr]

Mr Boatright
If I am reading your 9 page article correctly the solid bullets should be more accurate than the lead core jacketed bullets?
I remember you posting on a Benchrest forum years ago but I have never seen a solid bullet beat a jacketed bullet at a 600-1000 yard Benchrest match?
Has a solid bullet set any Benchrest Records?
I notice your data doesn't include any subsonic flight or transitioning?
ELR for the matches I run starts at 2000 yards and moves out in 500 yard increments.
Any idea on how well your new design transitions? Or when such information will be available?

 

[Jim Boatright]

Hello, Gentlemen;
Thanks for the kind words, Theis. I was not aware of those historical arguments.

I should emphasize that launching your copper-alloy bullets with initial Sg >2.5 alone will not always guarantee initial hyper-stable flight. The bullet also has to be launched with as little initial yaw as possible. Usually initial yaw is due to in-bore yaw, but it can also be caused by turbulence within a muzzle brake. Ballisticians learned long ago how to induce bullet yaw for study purposes by using a muzzle attachment called suitably enough a "yaw inducer." Look it up in McCoy's book or elsewhere. As the high-pressure propellent gasses begin to pass up the bullet beyond the crown of the barrel, your bullet is essentially flying backwards through those gasses. As the bullet passes through successive baffles in your MB, the relative velocity of the gasses bypassing it can be controlled by carefulling increasing the clearances inside each baffle toward the muzzle as the remaining gas pressure drops. We need those muzzle brakes in ELR shooting, so try to make them so as to minimize bullet yaw disturbances.

I mentioned working on discovering relationships between the frictional damping of the bullet's coning motion and that bullet's yaw-drag coefficient. I theorized that the kinetic energy of forward motion lost by the bullet due to yaw-drag (considered separately) would match the decay in orbital kinetic energy of the coning bullet as its coning angle is damping down. From those energy considerations, I have been able to derive the classic aeroballistic exponential damping formulation along with an expression for the size of the slow-mode damping coefficient needed for hyper-stable flight. That is some progress, so far. I hope eventually to show that yaw-drag directly causes that damping of the coning angle and to formulate the gyroscopic stability necessary to achieve hyper-stable flight in terms of the bullet's classic lift, drag, and over-turning moment coefficients.

Jim Boatright

 

[Jim Boatright]

Mr Boatright
If I am reading your 9 page article correctly the solid bullets should be more accurate than the lead core jacketed bullets?
I remember you posting on a Benchrest forum years ago but I have never seen a solid bullet beat a jacketed bullet at a 600-1000 yard Benchrest match?
Has a solid bullet set any Benchrest Records?
I notice your data doesn't include any subsonic flight or transitioning?
ELR for the matches I run starts at 2000 yards and moves out in 500 yard increments.
Any idea on how well your new design transitions? Or when such information will be available?

Hello, Lynn, Jr;
Those are all good questions which can only be answered by future firing-test results. So far, very few monolithic bullets have been fired correctly to allow them to perform to their potentials. As I discuss in my bullet design paper which Theis posted here (in Resources) this morning, I plan some day to produce a 65-grain polymer-cored copper 6 mm bullet just for the BR crowd and their 6-PPC cartridges. I expect that bullet should eventually come to dominate those matches.

As to transonic and subsonic flight, monolithic bullets fired as if they were lead-core bullets will continue to fail as they have done. I hope and believe that firing them properly will greatly improve on that. There is just not enough data available for study to allow me to say what will happen to them. I can assert with some backing (McCoy) that the transonic airspeed region is a lot narrower velocity spread with ULD bullets than with less "aerodynamic" bullets. For ULD bullets, the transonic region starts at Mach 1.1 (at about 2000 yards downrange) instead of at Mach 1.25, and ends at Mach 0.9 instead of Mach 0.8. The ULD bullet is truly optimized for supersonic flight. I know how to design bullets for optimum transonic and subsonic flight, and this ULD bullet design is not one.

Jim Boatright

 

[TripleBull]

Not speaking for LL but I am pretty sure his "subtle" is geared more towards jacketed projectiles as to where the majority of this thread is geared towards solids.

Go look at the video. It's around post 40 or so in the thread I linked. Frank mentioned a barrel of his for monolithics, then a sentence or two after said to the Bartlein machinist: "You're finding subtle is better for gain twist" or something like that.

 

[Lowlight]

Subtle works better with jacketed bullets. We are trying to speed up the twist rate without damaging the bullet or lead underneath.

I think 1 to 1 is good, but Bartlein is recommending 3/4 twist when it comes to jacketed bullets.

The service rifle guys are going much more extreme with 14 to 6 twists, that is for a 556. For 6mm and up they are generally 3/4. I was always warned against going heavy like the Norma Barrel I have that Jeff Spoke about, the 13-5.4 twist we have. The designed figured a jacketed 338 bullet would not survive the twist rate. So I never tried one.

Solids and Jackets are two different animals in this context you have to adjust accordingly

 

[Jeffvn]

to follow up on what Frank said - these super fast gain twist tubes were made exclusively for shooting solid projectiles.

Being a nosy guy, I wanted to see what happened if I shot a jacketed .338 (specifically Sierra 300 Gr. @ 2,950+ fps) from my gain twist barrel (5.4" exit). I was confident the jacket would come apart. I was correct (I took the muzzle break off to reduce possibility the pill came apart in my face). Very few bullets made the berm at 100 yards (the ones that did were all over the place - spread was something like 5-6 feet), most came apart roughly 20-25 yards from the muzzle (shards of jacket and splatters of lead visible on the ground roughly 25-30 yards down range. The ones that did make the berm were not penetrating very far, with jacket pieces just below the dirt surface.

I suspect, but have not tested, that you could run a solid, with a sintered core of a heavy mass - like tungsten - and it might be ok, it would all depend how thick you left the jacketed portion of the bullet.

Jeffvn

 

[Bender]

Just a fly on the wall..... excellent reading

 

[TripleBull]

to follow up on what Frank said - these super fast gain twist tubes were made exclusively for shooting solid projectiles.

For sure I'm thinking of shooting solids with a gain twist barrel. Jim's papers mention BC improvements on the order of 10-20% and that's mind-boggling.

Very few bullets made the berm at 100 yards (the ones that did were all over the place - spread was something like 5-6 feet), most came apart roughly 20-25 yards from the muzzle (shards of jacket and splatters of lead visible on the ground roughly 25-30 yards down range. The ones that did make the berm were not penetrating very far, with jacket pieces just below the dirt surface.

Sort of a high tech shotgun rifle hybrid...

I suspect, but have not tested, that you could run a solid, with a sintered core of a heavy mass - like tungsten - and it might be ok, it would all depend how thick you left the jacketed portion of the bullet.

Sounds interesting. And expensive!

 

[FlaShooterG]

Very cool paper. Based on it, would we not want to make sure that the center of the bullet/rifling contact is as close to the CG as possible to reduce any variances in the barrel when it is picking up the high rate of spin?

 

[bohem]

For sure I'm thinking of shooting solids with a gain twist barrel. Jim's papers mention BC improvements on the order of 10-20% and that's mind-boggling.

Slight improvements I've seen from testing some pretty aggressive solids. 10-20% is an order of magnitude larger than what I've been able to see with acoustic testing out to 2000yd.

 

[Jim Boatright]

Firing your copper-alloy bullets with an initial Sg greater than 2.5 is a "necessary, but not sufficient" requirement for achieving hyper-stability right from the beginning of ballistic flight (where air-drag is highest). One must also guarantee minimum initial yaw angles of the bullet at launch. Kent's Equation predicts a "first maximum yaw angle" of 25-times the bullet's in-bore yaw angle for long skinny bullets, and any muzzle brake employed may well have functioned as "yaw inducer" if not carefully designed.

In minimizing our bullet's zero-yaw drag CD0 at all airspeeds, bullet designers inadvertently increase their longer bullet's yaw-drag coefficients CDa. For the well-studied 30-caliber 168-gr Sierra International, CDa starts at 4.4 at Mach 2.5 (per McCoy), rises to 7.6 at Mach 1.4, and then falls to 2.9 at Mach 0.95 and below.

If your long copper-alloy bullet had a CD0 of say 0.200 at some initial Mach-speed, it could easily have a CDa value of 8 or larger at that same speed. My calculator tells me that a 20-percent increase in total drag coefficient CD would be 0.240, and that the angle of attack needed for yaw-drag to provide this 0.040 increase in total drag, is just 4 degrees, which is a reasonable coning angle which could easily occur. A 4-degree coning angle could be due to 0.162 degrees of in-bore yaw, for example.

The percentage improvement in BC measurements available by measuring the same bullets in hyper-stable flight from the beginning mainly depends upon just how poorly these bullets had been fired in their earlier measurements. Based on a comparison data set of just one trial, I supposed that the 12.4-percent better than had been predicted by McDRAG, which David Tubb measured at Mach 2.5 for my test bullets might in fact be typical for other similar testing. McDRAG is based on a large population of projectile firing-test data, none of which likely featured early achievement of hyper-stable flight.

I stand by my "10 to 20-percent improvement" statement for now.

Jim Boatright

 

[TripleBull]

By the way, Jim, I keep meaning to request... When you are done with bullets please address the fairer sex.

Sorry, back to your regularly scheduled twist rates.

 

[Jim Boatright]

Sorry, TB, no can do.

I have "revised and extended my remarks" in this Hyper-Stabilized Rifle Bullets paper based on the many questions raised here in this forum and the pertinent comments offered. It is now 10 pages and even more chock full of pearls of wisdom. I have been enjoying the interchange of ideas and information.

I would like for someone to post this new version over the original in Resources. I will see what the Attach Files button below does. Seems to work.

Jim Boatright

 

[Jeffvn]

Jim Boatright

You mention earlier in the thread that most muzzle breaks might actually be inducing yaw at the crown/muzzle based upon the way they handle and divert the gas flow when the projectile has just exited the barrel and is still flying in the gas plume that follows (in reality pushes the projectile out of the barrel) and then goes past the projectile upon exit from the barrel crown. You talk of a muzzle break design that does not induce such yaw, I'm curious what design you think would be required for such a device?

Jeffvn

 

[damoncali]

Jim Boatright

You mention earlier in the thread that most muzzle breaks might actually be inducing yaw at the crown/muzzle based upon the way they handle and divert the gas flow when the projectile has just exited the barrel and is still flying in the gas plume that follows (in reality pushes the projectile out of the barrel) and then goes past the projectile upon exit from the barrel crown. You talk of a muzzle break design that does not induce such yaw, I'm curious what design you think would be required for such a device?

Jeffvn

I can't answer your question, but there's a fascinating paper on M4 accuracy out there that determined that the standard M16 flash suppressor actually improves accuracy very slightly. This surprised me since it's asymmetrical and that can induce yaw, but it turns out that cancels out some other effects. It's a really complex and interesting topic.

 

[FlaShooterG]

Firing your copper-alloy bullets with an initial Sg greater than 2.5 is a "necessary, but not sufficient" requirement for achieving hyper-stability right from the beginning of ballistic flight (where air-drag is highest). One must also guarantee minimum initial yaw angles of the bullet at launch. Kent's Equation predicts a "first maximum yaw angle" of 25-times the bullet's in-bore yaw angle for long skinny bullets, and any muzzle brake employed may well have functioned as "yaw inducer" if not carefully designed.

In minimizing our bullet's zero-yaw drag CD0 at all airspeeds, bullet designers inadvertently increase their longer bullet's yaw-drag coefficients CDa. For the well-studied 30-caliber 168-gr Sierra International, CDa starts at 4.4 at Mach 2.5 (per McCoy), rises to 7.6 at Mach 1.4, and then falls to 2.9 at Mach 0.95 and below.

If your long copper-alloy bullet had a CD0 of say 0.200 at some initial Mach-speed, it could easily have a CDa value of 8 or larger at that same speed. My calculator tells me that a 20-percent increase in total drag coefficient CD would be 0.240, and that the angle of attack needed for yaw-drag to provide this 0.040 increase in total drag, is just 4 degrees, which is a reasonable coning angle which could easily occur. A 4-degree coning angle could be due to 0.162 degrees of in-bore yaw, for example.

The percentage improvement in BC measurements available by measuring the same bullets in hyper-stable flight from the beginning mainly depends upon just how poorly these bullets had been fired in their earlier measurements. Based on a comparison data set of just one trial, I supposed that the 12.4-percent better than had been predicted by McDRAG, which David Tubb measured at Mach 2.5 for my test bullets might in fact be typical for other similar testing. McDRAG is based on a large population of projectile firing-test data, none of which likely featured early achievement of hyper-stable flight.

I stand by my "10 to 20-percent improvement" statement for now.

Jim Boatright

Jim,
It seems that CG and bore yaw would have to be related. If the CG is closer to the rotation center of the rifling as the bullet moves through the barrel, wouldn't it result in less yaw. Am I way off base with that assumption?

 

[sharac]

I think the "secret" of optimization is in seal quality which prevents gas overtake. If you minimize amount of gases that escape and exit before bullet you will get benefits in various areas (from better efficiency to lower chance of those gasses influencing bullet)...

It would be interesting to measure how much yaw is induced through "inner ballistics" and how this amount is distributed between neck tension, bullet uniformity, rifling quality/wear, throat erosion, muzzle crown state but i doubt anyone has this data or is able to share it publicly.. But for artillery and tank/ship guns i'm sure this (and a lot more) exists...

 

[Jim Boatright]

I think the "secret" of optimization is in seal quality which prevents gas overtake. If you minimize amount of gases that escape and exit before bullet you will get benefits in various areas (from better efficiency to lower chance of those gasses influencing bullet)...

It would be interesting to measure how much yaw is induced through "inner ballistics" and how this amount is distributed between neck tension, bullet uniformity, rifling quality/wear, throat erosion, muzzle crown state but i doubt anyone has this data or is able to share it publicly.. But for artillery and tank/ship guns i'm sure this (and a lot more) exists...

That's what I was getting at, Sharac. If your MB uses multiple baffles, they should be carefully sized--tightest near the muzzle and increasing slowly in ID toward the front. On the other hand, a single-baffle design like a large "clam shell" allows the gasses to bypass the bullet almost as if there were no MB--until they run up against a rather large hole in the front wall, way ahead of the bullet. Both can work, but you need to take care that not too much gas flow bypasses the bullet within an annular restriction. That is very destabilizing.

Jim Boatright

 

[Jim Boatright]

Jim,
It seems that CG and bore yaw would have to be related. If the CG is closer to the rotation center of the rifling as the bullet moves through the barrel, wouldn't it result in less yaw. Am I way off base with that assumption?

I'm sorry, FSG, but you're going to have to 'splain your question more simply for me. I don't know exactly what you mean. The CG of the bullet should be exactly on the axis of the bore as the bullet is engraved by the rifling, and the axis-of-form of the bullet should be co-linear with the axis of the bore. If the CG is displaced, you get "lateral throw-off." If the bullet is not coaxial with the barrel, you get an "aerodynamic jump" deflection as the coning motion is getting under way. With lead-cored VLD bullets, you usually get both problems.

Jim Boatright

 

[FlaShooterG]

I'm sorry, FSG, but you're going to have to 'splain your question more simply for me. I don't know exactly what you mean. The CG of the bullet should be exactly on the axis of the bore as the bullet is engraved by the rifling, and the axis-of-form of the bullet should be co-linear with the axis of the bore. If the CG is displaced, you get "lateral throw-off." If the bullet is not coaxial with the barrel, you get an "aerodynamic jump" deflection as the coning motion is getting under way. With lead-cored VLD bullets, you usually get both problems.

Jim Boatright

My apologies sir for the confusion. My poorly worded question is regarding your comments in the section "how is hyper-stability achieved?" In it you spoke of "lateral throw off errors and a little bit further down about aerodynamic jump angle. My question is regarding the CG and relation to spin rate/yaw stability. I think I remember a comment somewhere that mentions the contact between the bore and the bullet happens behind the CG. If I am reading what you said correctly, (Page 6 & 7) you brought up yaw angles in the barrel. My question in another way is if yaw in a barrel is a significant concern, and if the center of the contact area with the barrel/bullet that is imparting the spin/rifling to the bullet is away from the center of gravity of the bullet, does it adversely effect the yaw imparted to the round as it moves through the barrel? Hope this question makes more sense and thanks so much for trying to answer it which I believe you did in your last post. Thank you for indulging a non-engineer trying to understand your amazing research.
Thanks so much for your response and the education!!!

 

[jbailey]

I have several questions on this paper-

(1) didn't the BRL at Aberdeen test the heck out the impact of changing twist and resulting ballistic performance? They were looking for the magic setup that would maximize the range of our guns vs the Red commies, so we could safely blast away at them well before they hit the Fulda Gap... Yes, BRL was not testing flat fire trajectories but 45 degree quadrant elevation angles etc. but the basics are the same, within the scope of material results.

(2) Once a bullet is properly stabilized, does increasing the twist (and hence driving up Sg) really have any impact on reducing the angle of attack? I pulled out my copy of McCoy. Ch 9, Fig 9.13 (1/18cal twist) vs Fig 9.15 (1/25cal twist) seems to suggest no, not in any material way.

(3) In your interesting paper, you cite an angle of attack of 5.7 degrees. That seems like a lot. Most loads/barrels will produce 2 degrees or less and this is a maximum value that decreases and changes thru flight. As such, aren't you materially over-estimating the impact on drag from the angle of attack CD?

(4) Back to McCoy, Ch 9, he writes on pg 204 "A comparison of the plots for the 1/18 twist [producing a Sg of 3.1] with those for the 1/25 twist [producing a Sg of 1.6] show that the 105mm M1 shell does not fly significantly, if any better from the from the slower twist of rifling, that gives essentially an optimum muzzle gyroscopic stability factor (Sg = 1.6). The only notable effect of the slower twist is to give a smaller yaw of repose near the summit of the trajectory, and a consequent reduction in the right-hand drift." I guess I'm asking if you are attempting to re-write modern 6-DOF diffy q? If not, where does your hyper-stabilized theory differ within 6-DOF?

Thanks very much for the interesting paper. It was fun and I enjoyed pulling out my old copy of McCoy as a result. I don't believe we will see the 10-20% improvements in BCs from increasing muzzle Sg from 1.6-ish to the 2.7-ish that you propose, but I look forward to seeing where this all goes

 

[Jim Boatright]

I have several questions on this paper-

(1) didn't the BRL at Aberdeen test the heck out the impact of changing twist and resulting ballistic performance? They were looking for the magic setup that would maximize the range of our guns vs the Red commies, so we could safely blast away at them well before they hit the Fulda Gap... Yes, BRL was not testing flat fire trajectories but 45 degree quadrant elevation angles etc. but the basics are the same, within the scope of material results.

(2) Once a bullet is properly stabilized, does increasing the twist (and hence driving up Sg) really have any impact on reducing the angle of attack? I pulled out my copy of McCoy. Ch 9, Fig 9.13 (1/18cal twist) vs Fig 9.15 (1/25cal twist) seems to suggest no, not in any material way.

(3) In your interesting paper, you cite an angle of attack of 5.7 degrees. That seems like a lot. Most loads/barrels will produce 2 degrees or less and this is a maximum value that decreases and changes thru flight. As such, aren't you materially over-estimating the impact on drag from the angle of attack CD?

(4) Back to McCoy, Ch 9, he writes on pg 204 "A comparison of the plots for the 1/18 twist [producing a Sg of 3.1] with those for the 1/25 twist [producing a Sg of 1.6] show that the 105mm M1 shell does not fly significantly, if any better from the from the slower twist of rifling, that gives essentially an optimum muzzle gyroscopic stability factor (Sg = 1.6). The only notable effect of the slower twist is to give a smaller yaw of repose near the summit of the trajectory, and a consequent reduction in the right-hand drift." I guess I'm asking if you are attempting to re-write modern 6-DOF diffy q? If not, where does your hyper-stabilized theory differ within 6-DOF?

Thanks very much for the interesting paper. It was fun and I enjoyed pulling out my old copy of McCoy as a result. I don't believe we will see the 10-20% improvements in BCs from increasing muzzle Sg from 1.6-ish to the 2.7-ish that you propose, but I look forward to seeing where this all goes

Hello, jbailey;

All good questions, JB. I am glad to talk to someone else interested in technical ballistics.

1) Yes, but "indirect fire" or even "maximum range firing" are specifically excluded from this study of rifles in "flat firing." As far as I can tell, high-angle fire is the only situation where "overstabilization" comes into play.

2) A "properly stabilized" lead-cored bullet might have an initial Sg of 1.5 to 2.0, but a "properly stabilized" long-nosed turned copper-alloy" rifle bullet requires an initial Sg of at least 2.5 to fly nose-forward with minimum drag. I strongly suspect the increased stability requirement stems from a much larger coefficient of yaw-drag CDa for these longer bullets (especially at low supersonic and transonic airspeeds), which can seriously increase total drag (CD).

3) I refer you to Kent's Equation (Eq. 12.78, page 264, MEB of McCoy, but also derived by Murphy). The amplification of the in-bore yaw angle, epsilon, at bullet exit to the "first maximum yaw" angle has two separate multiplicative effects. First the mass distribution effect: Iy/Ix is 7 to 10 for lead-core bullets and 12 to 14.5 (or higher) for long-nosed copper-alloy bullets. So, that mass distribution multiplier goes from about 15 to 20 times epsilon for lead bullets to about 23 to 30 for long-nose copper-alloy bullets. But look at the second multiplier, the initial Sg effect: It can be written as SQRT[Sg/(Sg-1)]. At Sg =1.5, this factor is 1.732. At Sg=3.0, this factor is only 1.225, or just 0.707 times as large. In-bore yawing of the bullet as it is being engraved is a much more serious problem in rifles than most realize. It displaces the CG, causing lateral throw-off, and also causes an initial aerodynamic jump angular deflection of the entire trajectory. Both are serious rifle accuracy limitations. And, a non-zero initial yaw-rate due to in-bore yaw is even worse. Those two bullet yaw problems can also happen within your muzzle brake, even for bullets having zero yaw and yaw-rate when entering the MB.

4) No, I see no need to rewrite the equations of motion or their solutions. I rely upon 6-DoF flight simulations using them to develop and test my analytic expressions concerning rifle bullet motions. I think McCoy was very close to discovering Coning Theory after investigating the vertical direction aerodynamic jump caused by a purely horizontal crosswind right in front of the muzzle. [That phenomenon was brought to his attention by precision-shooting riflemen, like you guys here.] Unfortunately, he died unexpectedly while his MEB book was being readied for publication. Don Miller and many others worked to get it posthumously published for him. That CWAJ has now been formulated from Coning Theory by Gustavo Ruiz and myself. I term the numerical integration of the EoM done in a 6-DoF simulator a "non-analytical" solution. I am seeking "analytical" relationships, so that we need not rely upon 6-DoF simulation (and all of those aeroballistic coefficients) for practical rifle aiming purposes, even at great ranges.

By the way, run any 6-DoF simulation for any rifle bullet in flat firing with zero initial yaw and yaw-rate, with no wind anywhere, and even disabling Coriolis Effect. You will then see what I have been calling "minimum coning angle" flight at least all the way to "maximum supersonic range."

If you will Pm your email, I will send you a current working paper on Dynamic Stability. It is full of false starts and errors, but shows good promise. I believe I have derived the exponential damping formulation for the coning angle-of-attack (alpha) from linear aeroballistic theory and physics. I don't recall seeing that anywhere before. I also believe the barrel twist-rate required (n, in calibers/turn) for steady-state "minimum coning angle" hyper-stable flight can be calculated from something like 2*(kx^-2)*[(CLa+CD0)^2]/(CMa*CDa), all at muzzle speed. Kind of neat, if true. I did assume critical damping to get there, though. Lots of work still needed.

Jim Boatright

 

[Jim Boatright]

My apologies sir for the confusion. My poorly worded question is regarding your comments in the section "how is hyper-stability achieved?" In it you spoke of "lateral throw off errors and a little bit further down about aerodynamic jump angle. My question is regarding the CG and relation to spin rate/yaw stability. I think I remember a comment somewhere that mentions the contact between the bore and the bullet happens behind the CG. If I am reading what you said correctly, (Page 6 & 7) you brought up yaw angles in the barrel. My question in another way is if yaw in a barrel is a significant concern, and if the center of the contact area with the barrel/bullet that is imparting the spin/rifling to the bullet is away from the center of gravity of the bullet, does it adversely effect the yaw imparted to the round as it moves through the barrel? Hope this question makes more sense and thanks so much for trying to answer it which I believe you did in your last post. Thank you for indulging a non-engineer trying to understand your amazing research.
Thanks so much for your response and the education!!!

Actually, the CG of almost any rifle bullet is inside the cylindrical shank of the bullet, up near the base of the nose, or ogive (for circular arc head-shapes). Its location really does not matter in interior ballistics. Bullet alignment in the throat of the barrel is critical because once the rifling is engraved, that it the alignment the bullet will have all the way to muzzle exit. Long-nosed, short-shanked, boat-tailed bullets are easily misaligned. I refer you to the detailed discussion of the "VLD Problem" in my Third Generation Rifle Bullet paper. By the way, artillery projectiles have always been designed for good alignment in the barrel, at least in a new barrel. Balloting becomes a problem in worn-out tubes.

Jim Boatright

 

[THEIS]

I would like for someone to post this new version over the original in Resources. I will see what the Attach Files button below does. Seems to work.

Jim Boatright

Hi,

Done.

Sincereley,
Theis

 

[lash]

Having only read the paper and this thread about hyper stabilization of turned solids, but having a keen interest in the subject, I have to ask what your thoughts are with regards to using a gain twist barrel to achieve the 20 calibers spin rate. Would there be a potential of smeared engraving disrupting/increasing the initial yaw rate in your opinion? I ask, since it seems like a great way to achieve such a high twist rate without increasing the early pressure spike. I'm wondering if a barrel for a .338 for example, in say 9-6.6 or even 10-6.6 gain twist would see any benefit over a straight 6.6 twist barrel.

 

[TripleBull]

Having only read the paper and this thread about hyper stabilization of turned solids, but having a keen interest in the subject, I have to ask what your thoughts are with regards to using a gain twist barrel to achieve the 20 calibers spin rate. Would there be a potential of smeared engraving disrupting/increasing the initial yaw rate in your opinion? I ask, since it seems like a great way to achieve such a high twist rate without increasing the early pressure spike. I'm wondering if a barrel for a .338 for example, in say 9-6.6 or even 10-6.6 gain twist would see any benefit over a straight 6.6 twist barrel.

That's a better way of asking my oversimplified wear question above. When you mention "smeared engraving" I was thinking about the possibility of leaving more shavings in the grooves in a gain twist barrel. I'm close to pulling the trigger on a 20 caliber spin rate barrel, so this decision matters to my wallet. Your point about initial yaw rate may get to the real BC improvement realized, dunno.

 

[magtech]

After reading the article I have a few thoughts on the subject:

The feel of the math here lends itself to earlier studies in the dynamics of bullet flight 40+ years ago. Maybe the initial studies didn't expect extended distances like this so they didn't take the time to research this dynamic further.

The tone of the write-up tells me that this is your way of making a "study" to provide the initial advertisement of a new ELR bullet setup.

Why not take this a step further and do testing with viscous liquid/material injected into the core of a bullet as to serve as a instability buffer. (I haven't looked up to see if anyone has done research on this in the past). This would undoubtedly require advanced bullet construction techniques, but could be pivotal in the creation of a new type of elr bullet.

It's too bad our bullet manufacturing techniques are not advanced enough to provide a gyroscopically controlled internal with rotating external jacket. That would lend itself to a much larger stability factor.

Either of the two items I mentioned could be completed/tested for someone with a large time and budget frame, as was done in the initial study. If anything, it would be an interesting step to see how current technologies could be extended into ELR applications.