Hyper Stabilized Bullets - Jim Boatright

Jim Boatright

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Feb 21, 2018
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Twist rates can be generalized as "n calibers per turn" by dividing the twist in inches or millimeters per turn by the bore ID (1.0 calibers) in the same distance units. The helix angle (a) of the rifling is also an apt description of how the bullet "sees" the rifling as it is being engraved and spun-up during firing. This helix angle a is actually the Arc-Tangent of 3.1416/n, where n is still "calibers per turn." When n = 20 calibers per turn, the helix angle a is actually 8.93 degrees. The "small angle approximation" we often use would say a = 180/20 = 9 degrees. Close, but not quite precise.

Mechanically, we often use a ramp angle of 25 degrees as a practical limit for this type linear-to-rotary motion transfer. This would correspond to n = 6.7 calibers per turn as a "maximum bullet spin-up" ratio. That angle might also work OK mechanically with monolithic copper rifle bullets in the larger rifle calibers. This 25-degree angle actually derives from the coefficient of static friction (0.5) sometimes used for non-lubricated steel on steel. 26.5 degrees is the ramp angle at which a typical dry steel block might start to slide down a steel inclined plane. Careful lab measurements would increase that maximum inclination angle significantly.

In reloading for 20 calibers per turn barrels, the twist-rate effect is buried in the usual load development variables. I believe that leads us to favor about one notch slower-burning powders than with slow-twist barrels when we are reloading the typically "over-bore" cartridge cases used in ELR shooting. The effect is small, though. Probably similar to the variations caused by volatile solvent evaporation and absorption of water from the air with the canister-grade rifle propellants which we use.
 

THEIS

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Hi,

Can any of you please tell me if you get out pencil and paper when reading some of Jim's replies?

Please tell me I am not the only one that has to put pencil to paper to ensure I am correctly following what he says lol.

Sometimes my paper even looks like Wilie Coyote reading the Acme rocket instructions lol.

Sincerely,
Theis
 

Skookum

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May 6, 2017
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Hi,

Can any of you please tell me if you get out pencil and paper when reading some of Jim's replies?

Please tell me I am not the only one that has to put pencil to paper to ensure I am correctly following what he says lol.

Sometimes my paper even looks like Wilie Coyote reading the Acme rocket instructions lol.

Sincerely,
Theis
Yep, I have a close associate who is a mechanical engineer. I have actually had to use him as a translator on some posts.:D
 
Feb 7, 2013
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Hi,

Can any of you please tell me if you get out pencil and paper when reading some of Jim's replies?

Please tell me I am not the only one that has to put pencil to paper to ensure I am correctly following what he says lol.

Sometimes my paper even looks like Wilie Coyote reading the Acme rocket instructions lol.

Sincerely,
Theis
LOL Theis -- no I just wait for you smart guys to tell me that I can use a 6.75 twist in my 338 or whatever n of 20 thingies equals and that my H1000 might need to be Retumbo
 
Dec 30, 2017
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Jim,

Good info!

You mentioned that one might have to move to a slightly slower powder for the faster twists. A lot of the ELR shooters are shooting the slowest powders available and going to a slower powder is not an option. I would think that using a bore rider type bullet or other designs that reduces the bearing surface size might help here. Using a HBN coating might also show some benefits too!
 
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TresMon

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Dec 3, 2007
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I have a Gain Twist Barrel, 338 Norma, that is a 13-5.4 Twist

I can manage this with that barrel

Ive been out of the loop for a little while but Ive never heard of a gain barrel gaining more than 2-3" of twist. May I ask who makes such a barrel? That's exciting.
 
Dec 30, 2017
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Jim,

So I got thinking...If you should drill out the base of the bullet then the bullets moment of inertia will change and the bullet will resist being spun up compared to a solid copper. Inversely, it would resist being spun down.... Correct?

So, if this is true we would need a little less twist but trade off some of the BC due to having a lighter bullet. Of course, since it is lighter it will exit the barrel faster.

.....Trying to wrap my head around your new bullet designs and the external ballistics....Compromises, tradeoffs, etc...

Maybe you could use a hypothetical example using a 750 grain solid copper .50 BMG with a BC of 1.00 and an exit speed of 2800 fps. Of course we will use your recommended 10 twist.

1) To keep it simple we will use standard sea level and 2000 yards.

(a) Other than improved accuracy, what gains in velocity, at 2000 yards would be seen over a standard 15 twist?


2) If we drilled from the base and made the bullet 10% lighter or 675 grains and using a faster exit speed of 3000 fps...

(a) What would the BC of the bullet be now that it has less mass?

(b) How much less twist (slower) could we get away with compared to the 750 grain solid @10 twist?

(c) Would there be enough ballistic gains with the lighter, faster bullet. Such as a flatter, more efficient trajectory up to the transonic region?


3) If we filled the drilled base with aluminum ( 2/3 lighter than copper ) making it now essentially a solid again weighing 700 grains....

(a) Would there be any ballistic advantages to doing this design other than the added viability of that having a malleable aluminum core might make for a great hunting bullet?


Yes, I understand most of the physics in your hyper stabilized bullet ideas and see the benefits of you ''thinking out of the box''

BUT... I think for all of us that are math challenged, we would like to see some numbers that show it will be worth the cost and time to make the switch over. In other words " Old school vs New school "

Many Thanks
 
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Jim Boatright

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Feb 21, 2018
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Jim,

So I got thinking...If you should drill out the base of the bullet then the bullets moment of inertia will change and the bullet will resist being spun up compared to a solid copper. Inversely, it would resist being spun down.... Correct?

So, if this is true we would need a little less twist but trade off some of the BC due to having a lighter bullet. Of course, since it is lighter it will exit the barrel faster.

.....Trying to wrap my head around your new bullet designs and the external ballistics....Compromises, tradeoffs, etc...

Maybe you could use a hypothetical example using a 750 grain solid copper .50 BMG with a BC of 1.00 and an exit speed of 2800 fps. Of course we will use your recommended 10 twist.

1) To keep it simple we will use standard sea level and 2000 yards.

(a) Other than improved accuracy, what gains in velocity, at 2000 yards would be seen over a standard 15 twist?


2) If we drilled from the base and made the bullet 10% lighter or 675 grains and using a faster exit speed of 3000 fps...

(a) What would the BC of the bullet be now that it has less mass?

(b) How much less twist (slower) could we get away with compared to the 750 grain solid @10 twist?

(c) Would there be enough ballistic gains with the lighter, faster bullet. Such as a flatter, more efficient trajectory up to the transonic region?


3) If we filled the drilled base with aluminum ( 2/3 lighter than copper ) making it now essentially a solid again weighing 700 grains....

(a) Would there be any ballistic advantages to doing this design other than the added viability of that having a malleable aluminum core might make for a great hunting bullet?


Yes, I understand most of the physics in your hyper stabilized bullet ideas and see the benefits of you ''thinking out of the box''

BUT... I think for all of us that are math challenged, we would like to see some numbers that show it will be worth the cost and time to make the switch over. In other words " Old school vs New school "

Many Thanks
These are thoughtful and intelligent questions, MP, and I will attempt to answer them all, but it will require some thought and effort to do so properly.

First, I will explain the rationale for base-drilling certain of my copper ULD bullets. The cost in bullet performance of removing 6.9-percent of the solid monolithic bullet's mass is solely the 6.9-percent reduction in the Ballistic Coefficient (BC) of that base-drilled bullet. There are several advantages attributable to this base-drilling: 1) The 6.9-percent lighter bullet can be fired about 3.5-percent faster, for a wash in kinetic energy right from the muzzle. 2) Removal of this particularly troublesome mass near the spin-axis, but far from the CG of the bullet, makes the base-drilled bullet much easier to spin-stabilize in aerodynamic flight without directly affecting that bullet's ULD aerodynamic shape. 3) Ducting the base pressure inside the rear driving band allows that rifling-engraved rear driving band to expand elastically into the rifling grooves of the steel barrel--resulting in perfect sealing (obturation) of the hot powder gases at, or near, peak chamber pressure--just when it is most needed. [Smaller-caliber copper ULD bullets expand enough elastically for perfect obturation due to their higher inertial forces of acceleration. Larger-caliber copper bullets can use this additional help to expand enough for perfect obturation during firing. "Elastic" expansion of either type means that the bullets resume their "as manufactured" shape upon exiting the muzzle of the rifle barrel.], and 4) The effective combustion chamber volume of the parent cartridge case is increased slightly by this base-drilling, allowing a slightly larger powder charge to be loaded without increasing peak chamber pressure.

In the British Engineering System of units, which we use, BC is given in units of pounds of bullet weight divided by the square of the bullet diameter in inches-- that is, in pounds per square inch, or PSI. This is the "ballistic sectional density" portion of BC. If bullet weight is given in grains, it must be divided by 7000 to convert it into pounds. The BC of a rifle bullet is this "ballistic sectional density" divided by its "form factor" ratio of that bullet's aerodynamic drag coefficients (at each Mach-speed through the air) divided by the drag coefficients carefully measured for the reference projectile at each airspeed. The BC of any "Reference Projectile" is 1.0 PSI by definition. Each Gavre-standard reference projectile (G1, G7, etc.) weighs 1.0 pounds and is 1.0 inches in diameter. Its dimensionless "form-factor" ratio (i) is also 1.0 by definition, just because it is a "reference" projectile. If the drag curve for a rifle bullet (Cd versus Mach-speed) does not have the same shape as that of the selected reference projectile, its "form factor" ratio will vary with airspeed instead of being a nice constant ratio. That is why the BC(G1) of modern rifle bullets has to be given for various "velocity bands," and why ballisticians tend not to use BC very much if actual drag coefficient (Cd) data is available. Because the G7 reference projectile defines the basic shape of our "VLD" rifle bullets, their BC(G7) values are significantly less "velocity-dependent."

Base-drilling of modern monolithic copper bullets improves their mass properties in several important ways. Removal of bullet material near its spin-axis (its X-axis) very slightly decreases the "radius of gyration" about that X-axis, but it significantly decreases its cross-axis (Y-axis) radius of gyration because the material removed was far from the bullet's CG. The combination of these two effects directly increases the gyroscopic stability (Sg) of the spin-stabilized rifle bullet. For my copper ULD bullets, the Iy/Ix ratio for the solid (Mark I) bullet is 13.5, but it is only 12.0 after base-drilling; increasing the Sg at any spin-rate by 12.5-percent. By shifting the CG of the drilled bullet nearer to its aerodynamic Center-of-Pressure (CP), the lever-arm creating its aerodynamic overturning moment (M) is also significantly reduced. Since Sg is defined in aeroballistics as (P^2)/(4M), decreasing M also increases Sg. [The canonical variable P used by ballisticians is proportional to the spin-rate of the bullet; so increasing the spin-rate of the bullet by 41.4-percent (as proposed for "hyper-stability") will double the Sg of the bullet at any airspeed.]

I hope this clarifies my reasons for base-drilling the versions of my copper ULD bullets intended for "transitional" use in rifles having conventional twist-rate barrels. The Mark II ELR versions of my copper ULD bullets will not have base-drilling because they will be properly fired only from (approximately) 20 calibers per turn fast-twist rifle barrels, where retaining maximum bullet weight is the overriding design goal for achieving maximum supersonic range capability from very large "over-bore" cartridges. The Mk II ELR bullets will be 5.7-calibers in length versus 5.5-calibers for the "transitional" Mk I ULD bullets.

I will post more answers to MP's questions as I work them out.
 
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THEIS

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Hi,

@Jim Boatright
Hope your medical procedures are not too serious. Wishing you the best!! Will talk with you soon.

Thanks for the paper....I have something to read and digest over the next couple days.

Sincerely,
Theis
 
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THEIS

Sergeant of the Hide
Nov 27, 2017
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Hi,

Great news on the medical side!!
Now onto the new article side....kind of on topic and kind of off topic.
I think we should discuss and dive deeper into the stabilization affects of muzzle brakes vs suppressors.
For the sake of conversations lets rule out that we are able to get away without using either a muzzle brake or a suppressor due to recoil of the weapon.

1. Do you think we will see muzzle brakes being redesigned to mimic the 2 stage suppression technology that Dr. Courtney co-authored a paper on for the 2017 International Symposium on Ballistics?
2. Do you think we will see advancement in the 2 stage suppression technology?
3. Do you have any information on the muzzle brake that McPherson was/is developing to reduce the projectile instability caused at the muzzle and that works in conjunction with your hyper-stabilization theory?

Sincerely,
Theis
 
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lash

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Hi,

Great news on the medical side!!
Now onto the new article side....kind of on topic and kind of off topic.
I think we should discuss and dive deeper into the stabilization affects of muzzle brakes vs suppressors.
For the sake of conversations lets rule out that we are able to get away without using either a muzzle brake or a suppressor due to recoil of the weapon.

1. Do you think we will see muzzle brakes being redesigned to mimic the 2 stage suppression technology that Dr. Courtney co-authored a paper on for the 2017 International Symposium on Ballistics?
2. Do you think we will see advancement in the 2 stage suppression technology?
3. Do you have any information on the muzzle brake that McPherson was/is developing to reduce the projectile instability caused at the muzzle and that works in conjunction with your hyper-stabilization theory?

Sincerely,
Theis
You don't pull any punches, do you? I like it! This is where the meat is...where the subject leads naturally.

Some, maybe only a few, but some nonetheless, are wondering this. Since we are impatient and, at least in this one case, like following theory as it is turned to innovation and practice.
 

Jim Boatright

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Feb 21, 2018
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Hi,

Great news on the medical side!!
Now onto the new article side....kind of on topic and kind of off topic.
I think we should discuss and dive deeper into the stabilization affects of muzzle brakes vs suppressors.
For the sake of conversations lets rule out that we are able to get away without using either a muzzle brake or a suppressor due to recoil of the weapon.

1. Do you think we will see muzzle brakes being redesigned to mimic the 2 stage suppression technology that Dr. Courtney co-authored a paper on for the 2017 International Symposium on Ballistics?
2. Do you think we will see advancement in the 2 stage suppression technology?
3. Do you have any information on the muzzle brake that McPherson was/is developing to reduce the projectile instability caused at the muzzle and that works in conjunction with your hyper-stabilization theory?

Sincerely,
Theis
Thanks, Theis. I feel fine now.
1. Muzzle brakes and suppressors are sort of opposites in what they do with the gases after porting them away. The most I can see for MB design is to stage the port sizes to more or less equalize the momentum harvesting from each successive chamber for effective recoil reduction.
2. Yes, I suspect there is still room for improvement in suppressor design. I, for one, would like to see an elliptical pressure housing which does not interfere with the sight line so much. Liquid cooling might also be added. Easy disassembly for cleaning would be nice. We might also try some types of renewable wet Brillo pad moderation of gas temperature, pressure, and velocity again.
3. My first LAW MB is due to be delivered tomorrow by USPS Priority Mail from Mic in CO. It is fitted to my 28-inch 7-inch twist Schneider P5 338LM barrel. We will reset the headspace to index it horizontally. It includes a mount for a Magneto-Speed unit below the MB. Mic uses staged, rearward-angled "rocket nozzle" shaped gas ports oriented mostly horizontally at my request. I will report on how it works out. Mic uses a narrow 30-degree muzzle fit for accurate axial centering as well as alignment of the muzzle attachment.
 
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THEIS

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3. My first LAW MB is due to be delivered tomorrow by USPS Priority Mail from Mic in CO. It is fitted to my 28-inch 7-inch twist Schneider P5 338LM barrel. We will reset the headspace to index it horizontally. It includes a mount for a Magneto-Speed unit below the MB. Mic uses staged, rearward-angled "rocket nozzle" shaped gas ports oriented mostly horizontally at my request. I will report on how it works out.
Hi,

PERFECT Timing on my question then :)
Those results are what I am looking forward to.

Sincerely,
Theis
 
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Jim Boatright

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Feb 21, 2018
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Gustavo and I have updated and extended our formulations for calculating yaw of repose and spin drift for long-range rifle bullets. I hope this resolves any questions about these mysterious observed aeroballistic effects. Spin Drift estimations match PRODAS 6-DoF results to within a few thousandths of an inch at 1000 yards.

I have not yet been able to test-fire the new barrel and LAW MB on my 338LM. That is now my next priority.
 

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TripleBull

This one goes to 11
Feb 13, 2017
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Jim: Have you thought about trying to optically measure the epicyclic motion you discuss on p3 and show in the figure of p4? If it's true that the effective shutter speed of a STEAM camera is around 100 picoseconds, a projectile at ~2500fps would travel less than a tenth of a micron per frame, so image quality should be acceptable, even though pixel density would present real limits. You can collect 6 million frames per second, which should be plenty.

How much variation in initial (muzzle exit) trajectory variation would you expect, shot-to-shot? By "trajectory variation" I mean variation in yaw of repose when the projectile exits the muzzle.
 
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Lowlight

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Got the email today on SD,

Numbers keep shrinking that is all I have to say, (See Frank vs the World on SH regarding SD) and I want to see a wider test, most of what I notice is a focus on 30 cal bullets and standard twist rates that have since been modified. We are twisting things different in a lot of ways, so defaulting back to the twist rates of the 80s is gonna keep them close to the old school data.

I want more examples of the effects of wind on the value, the effects of different twist rates, etc.

Look at Hornady they are testing brakes, powders, twist rates, etc on the curves to note the changes, and they are seeing changes. The fact you say it's not necessarily proportional and can vary with different conditions should be explored.
 

Skookum

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The couple of points I took away from the paper are:

A) Spin drift is a drag function, therefore adequately stabilized high BC bullets have less drift than lower BC bullets.

B) decreasing the degree of coning precession decreases yaw of repose, which decreases drift. Spinning bullets faster accomplishes this

C) High BC bullets retain more velocity decreasing time to target, which decreases drift.

D) The amount of drift is some invariant fraction (percent) of drop.

So, my personal rule of thumb has become 2% of drop for conventionally stabilized bullets of 30-32 calibers per turn, and 1% for high BC bullets spun at 28 calibers per turn or faster. Is it spot on? I would bet not, but it seems to be working well enough that my wind math is working better than ever, out past a mile.

Edit: So nobody thinks I'm some kind of a smart guy and actually understood all 51 pages of that paper, I'll just stop you right there.

I am a knuckle dragging fuck, that's what I am. Fortunately for me, I have educated friends who boiled it down and translated it to me. So...there it is.
 
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Lowlight

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Spot on observations,

That was my takeaway also when we were discussing the 2% earlier in the year it seemed like a good rule of thumb, this helps adapt it vs using a 1 rule to fit them all approach.

funny thought with some of the overspinning stuff you have guys going shorter and thus slowing the bullet down and combined with overspinning we see it actually increasing some drift, especially in the 308 families.
 
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