.50 Caliber Conical Bullet Stability

[WP79Vet]

The next steps in my quest for a good-shooting, full-bore, all-lead elk bullet for my 1-48 twist Renegade involve punching some holes in paper. Since before Christmas, though, it's been too cold and snowy for paper punching in this neck of the woods, and it's likely to stay that way until the middle of March. So... to keep cabin fever at bay and do something relevant to finding my perfect bullet, I've started looking into bullet stability.

To get started, I Googled bullet stability in various ways, and read everything I could find. The most helpful information was a simple overview of bullet stability on the Bison Ballistics website (Bullet Stability). That led me to four fairly technical papers describing the Miller Rule, first proposed in 2005, which has replaced the much older Greenhill Rule for estimating the rifling twist which is needed to stabilize a bullet - or conversely and more commonly, for estimating the stability of a given bullet when fired at a given rate of twist. Used in the latter way, the Miller Rule calculates a number called the "Gyroscopic Stability Factor", Sg, as a function of bullet weight, bullet length, bullet diameter, bullet velocity, and air density (derived from air temperature and either absolute air pressure or altitude). At a given muzzle velocity and bullet weight, Sg increases with:

- Faster twist
- Shorter, fatter bullet
- Lower air density (higher altitude and/or higher temperature)

All writers pretty much agree that when Sg is less than 1.0, a bullet will be completely unstable, and when Sg is between 1.0 and 1.3, a bullet will be marginally stable. Some writers consider an Sg between 1.3 and 1.5 to produce the best accuracy, at a cost of some increase in the drag force on the bullet, and thus more arc in the trajectory. Other writers - maybe the majority - feel that an Sg above 1.5 is the best for all shooting, and especially for long-range (600 or 1,000 yard) shooting. Some writers feel that a bullet is "over stabilized" if Sg is greater than 2.0, while others argue that the notion of over stabilization is a myth. I think that for muzzle loaders firing full-bore soft lead bullets, over-stabilization is a serious issue, for reasons I'll discuss in a follow-on post. To make matters more confusing, some writers also refer to "dynamic stability", and to a "Dynamic Stability Factor" (Sd) as a measure of a bullet's ability to resist aerodynamic forces that are very difficult to estimate, and are therefore left unspecified. Because calculation of Sg includes air density, it must account for at least some aerodynamic forces, but nothing I've read so far - including the technical paper in which Miller first stated his rule and how it was derived - gives any inkling about which aerodynamic forces are accounted for by Sg, which are accounted for by Sd, or how Sd might be calculated. Hmmmm......

At this point, the extent to which the Miller Rule applies to muzzle loader bullets is also unclear to me because everything I've found on quantifying bullet stability has come from either the military or the long-range target shooting community, and both are mostly interested in relatively long, sharp-pointed, boattail bullets. Nevertheless, simple rules for bullet stability seem to work surprisingly well, even far outside the conditions under which they were derived. The Greenhill Rule, for example, was derived in the 1870s from observation of football shaped, subsonic artillery projectiles. According to Miller, the Greenhill Rule still works surprisingly well for spitzer boattail bullets traveling at 2,800 fps, but "is not as good for Black Powder velocities." Miller derived his rule by finding the simple function of the variables I listed above which best fit a library of measured Sg factors for 29 military projectiles. However, the Miller Rule still works surprisingly well for every projectile which it's been used to evaluate - including 5 inch rockets that are made from aluminum (!), and the Miller Rule seems to be widely accepted in shooting communities that are especially interested in bullet stability.

With these uncertainties in mind, I turned to using Bison's online Sg calculator, Bullet Gyroscopic Stability Calculator to run stability calculations for fifteen .50 caliber bullets and two .45 caliber bullets. Because Sg varies with bullet velocity, rate of twist, and air density (and thus air temperature and altitude), I ran the calculations for each bullet at 2 rates of twist (1-28 and 1-48), 2 velocities (corresponding to Hogdon's estimates of velocities for a bullet of similar weight with 80 and 100 grains of T7 3F), 2 temperatures (0 and 70 degrees F), and 3 altitudes (sea level, 3000 feet, and 6,000 feet). The complete results are in the attached spreadsheet. Because I'm up against the character limit for posts on this forum, I will comment on the calculations in a follow-up post.

 

[michiganmuzzy]

Ive just run a quick bullet calculation in the calculator you linked to and the JBM stability calculator here JBM - Calculations - Stability
Putting in all the info i have for a known good shooting lead bullet in two of my MLs. Bison came up with over stabilized at 5.76. JBM came up with 5.86 but didnt call it overstabilized.
Neither inquire about distance. Could it be that after some yardage we will see the effect, but not at normal hunting ranges, like out to only 150-200yds? Or put another way, is the velocity a bigger factor?

 

[ETipp]

The next steps in my quest for a good-shooting, full-bore, all-lead elk bullet for my 1-48 twist Renegade involve punching some holes in paper. Since before Christmas, though, it's been too cold and snowy for paper punching in this neck of the woods, and it's likely to stay that way until the middle of March. So... to keep cabin fever at bay and do something relevant to finding my perfect bullet, I've started looking into bullet stability.

To get started, I Googled bullet stability in various ways, and read everything I could find. The most helpful information was a simple overview of bullet stability on the Bison Ballistics website (Bullet Stability). That led me to four fairly technical papers describing the Miller Rule, first proposed in 2005, which has replaced the much older Greenhill Rule for estimating the rifling twist which is needed to stabilize a bullet - or conversely and more commonly, for estimating the stability of a given bullet when fired at a given rate of twist. Used in the latter way, the Miller Rule calculates a number called the "Gyroscopic Stability Factor", Sg, as a function of bullet weight, bullet length, bullet diameter, bullet velocity, and air density (derived from air temperature and either absolute air pressure or altitude). At a given muzzle velocity and bullet weight, Sg increases with:

- Faster twist
- Shorter, fatter bullet
- Lower air density (higher altitude and/or higher temperature)

All writers pretty much agree that when Sg is less than 1.0, a bullet will be completely unstable, and when Sg is between 1.0 and 1.3, a bullet will be marginally stable. Some writers consider an Sg between 1.3 and 1.5 to produce the best accuracy, at a cost of some increase in the drag force on the bullet, and thus more arc in the trajectory. Other writers - maybe the majority - feel that an Sg above 1.5 is the best for all shooting, and especially for long-range (600 or 1,000 yard) shooting. Some writers feel that a bullet is "over stabilized" if Sg is greater than 2.0, while others argue that the notion of over stabilization is a myth. I think that for muzzle loaders firing full-bore soft lead bullets, over-stabilization is a serious issue, for reasons I'll discuss in a follow-on post. To make matters more confusing, some writers also refer to "dynamic stability", and to a "Dynamic Stability Factor" (Sd) as a measure of a bullet's ability to resist aerodynamic forces that are very difficult to estimate, and are therefore left unspecified. Because calculation of Sg includes air density, it must account for at least some aerodynamic forces, but nothing I've read so far - including the technical paper in which Miller first stated his rule and how it was derived - gives any inkling about which aerodynamic forces are accounted for by Sg, which are accounted for by Sd, or how Sd might be calculated. Hmmmm......

At this point, the extent to which the Miller Rule applies to muzzle loader bullets is also unclear to me because everything I've found on quantifying bullet stability has come from either the military or the long-range target shooting community, and both are mostly interested in relatively long, sharp-pointed, boattail bullets. Nevertheless, simple rules for bullet stability seem to work surprisingly well, even far outside the conditions under which they were derived. The Greenhill Rule, for example, was derived in the 1870s from observation of football shaped, subsonic artillery projectiles. According to Miller, the Greenhill Rule still works surprisingly well for spitzer boattail bullets traveling at 2,800 fps, but "is not as good for Black Powder velocities." Miller derived his rule by finding the simple function of the variables I listed above which best fit a library of measured Sg factors for 29 military projectiles. However, the Miller Rule still works surprisingly well for every projectile which it's been used to evaluate - including 5 inch rockets that are made from aluminum (!), and the Miller Rule seems to be widely accepted in shooting communities that are especially interested in bullet stability.

With these uncertainties in mind, I turned to using Bison's online Sg calculator, Bullet Gyroscopic Stability Calculator to run stability calculations for fifteen .50 caliber bullets and two .45 caliber bullets. Because Sg varies with bullet velocity, rate of twist, and air density (and thus air temperature and altitude), I ran the calculations for each bullet at 2 rates of twist (1-28 and 1-48), 2 velocities (corresponding to Hogdon's estimates of velocities for a bullet of similar weight with 80 and 100 grains of T7 3F), 2 temperatures (0 and 70 degrees F), and 3 altitudes (sea level, 3000 feet, and 6,000 feet). The complete results are in the attached spreadsheet. Because I'm up against the character limit for posts on this forum, I will comment on the calculations in a follow-up post.

Lots of good information there. Researching ballistics can be almost like a retirement plan.
Been there, done that.

 

[ETipp]

If one is searching for a proven heavy conical for their ML, I would recommend searching threads from Idaho Lewis and Idaho Ron. Those two has it figured out. I know that if I ever move back out west and ML hunt for elk again, I would use the same approach as they do.

 

[snapbang]

Tipp, I just picked up a Knight 45 with a 1/20 and another with a 1/30 twist. Members here said use 350 grain bullets for the 1/30. I have some given to me years ago by other members. I loaded and shot them and they all reach the same point of impact and grouped excellent with 70, 75, and 80 weighed grains of T7.

When I get the 1/20 prepped Ill reach out again and ask some members here which to shoot.

I applaud your research and understanding of the subject on stability. If you want to make it easy for your self just state the gun and twist you have and ask, who is shooting conicals and what conical is it. Im thinking for elk you will want to shoot the heaviest with the most powder that is accurate.

In addition I thought the Great Plains bullet in 50 cal was made just for the 1/48 twist. So maybe go a little heavier?????

My personal thought here.
Throw the foot pounds of power out the window. I read that a lot of conicals have low energy at 200 yards. Yet a 300-400 grain or heavier bullet is still traveling at 1000 fps. No varmint is going to stand up to a 400 grain bullet at 1000 fet per second. I remember Lewis shooting the 1200 yard target and the bullets getting all mashed up. My personal opinion is if your shooting a conical and you can hit the target it will die. Regardless of how far away it is.

With this dedication Tipp I have no doubt you have an elk in your future. Show us the pics.

 

[ETipp]

Tipp, I just picked up a Knight 45 with a 1/20 and another with a 1/30 twist. Members here said use 350 grain bullets for the 1/30. I have some given to me years ago by other members. I loaded and shot them and they all reach the same point of impact and grouped excellent with 70, 75, and 80 weighed grains of T7.

When I get the 1/20 prepped Ill reach out again and ask some members here which to shoot.

I applaud your research and understanding of the subject on stability. If you want to make it easy for your self just state the gun and twist you have and ask, who is shooting conicals and what conical is it. Im thinking for elk you will want to shoot the heaviest with the most powder that is accurate.

In addition I thought the Great Plains bullet in 50 cal was made just for the 1/48 twist. So maybe go a little heavier?????

My personal thought here.
Throw the foot pounds of power out the window. I read that a lot of conicals have low energy at 200 yards. Yet a 300-400 grain or heavier bullet is still traveling at 1000 fps. No varmint is going to stand up to a 400 grain bullet at 1000 fet per second. I remember Lewis shooting the 1200 yard target and the bullets getting all mashed up. My personal opinion is if your shooting a conical and you can hit the target it will die. Regardless of how far away it is.

With this dedication Tipp I have no doubt you have an elk in your future. Show us the pics.

Honestly I really have very little experience with inline's. I just sold the only one I had because they are just not my cup of tea. From my limited testing with that Knight Rifle I found it likes shorter projectiles. Actually, I shot it very little to even know what was optimum. However, from what testing I did do with my sons inline, I found it likes Hornady 240 grain XTP's with the green sabots. I shot a few different projectiles out of that rifle for a couple of weeks. Some of which were 290 grain bore diameter. For that ML, the 240 XTP's with two 50 grain 777 pellets are the most accurate I found at 100 yards. I believe that rifle has a 1-28 twist. It was shooting a fuzz over a 1 inch group or so.

I would say to pick a couple different bullets you want to try and go test them. ML, like many other firearms, tend to be a little different on what they prefer to digest. What I have typically done over the years when searching for a new bullet, especially in a center fire, is to first look at the BC when taking the distance I plan on shooting in mind. I next consider the penetration I would expect of such projectile I may be interested in. So accuracy first then projectile performance once it hits its target.

Thank you but actually I am not looking for a an elk load for any of my ML,s. I have killed elk with my .50 with a Maxi Ball out to what I had figured 150 yards or so. If I were to move back out west where I'm from I would most likely go back to using my .50 with a heavier weight conical. I believe Lewis and Ron both use a 500 grain conical wrapped in a paper patch. I know that Lewis has posted that he measured the bore of his ML and had a mold made to fit the custom barrel accordingly.

With that said, I have killed plenty of deer with that same 360 grain Maxi Ball round using the same powder and charge. 80 grains of 3F black powder. All were with .50's. IMO, there is something about those heavy ML projectiles that makes a difference on big game. Penetration and longer shots for sure. I have only recovered two out of many. They just keep on going. What I have noticed over the years is I've shot deer that was darn near directly under me. I actually saw the .50 cal hole open up on one deer. The buck just took a few steps, stopped, and fell over. It didn't even act as if it were hit. This has been the case with every single one I have shot, with the exception of one. And that was a bad shot in the neck. Still got the deer but it could have been better. Everyone one of those kills was with hard cast Maxi Balls, which I no longer use. None of which has went any farther than maybe 20 yards or so. Most fall within a very few steps.

Also, my GPR is a .54 caliber. I want to go back to shooting round ball now that I live east of the big muddy river.

Not a stability thing here, but if you want to see some penetration testing on different ML projectiles, if you haven't already done so, I suggest you look up some Youtube videos of: I love muzzleloaders.

 

[45-70]

If one is searching for a proven heavy conical for their ML, I would recommend searching threads from Idaho Lewis and Idaho Ron. Those two has it figured out. I know that if I ever move back out west and ML hunt for elk again, I would use the same approach as they do.

 

[45-70]

Fury bullets out of Knight .50 at 100 yds

 

[ETipp]

That's some nice groups. About like I got out of my sons CVA inline with 240 grain XTP's. Anytime you can obtain that kind of accuracy, you are doing alright.

 

[WP79Vet]

Ive just run a quick bullet calculation in the calculator you linked to and the JBM stability calculator here JBM - Calculations - Stability
Putting in all the info i have for a known good shooting lead bullet in two of my MLs. Bison came up with over stabilized at 5.76. JBM came up with 5.86 but didnt call it overstabilized.
Neither inquire about distance. Could it be that after some yardage we will see the effect, but not at normal hunting ranges, like out to only 150-200yds? Or put another way, is the velocity a bigger factor?

The gyroscopic stability of a bullet actually INCREASES as it flies downrange. That's because spin, which gives a bullet stability, decreases much slower than velocity as the bullet flies downrange. Because most aerodynamic forces on the bullet will decrease with decreasing velocity, the bullet becomes MORE stable as it flies downrange. So... if a bullet starts tumbling due to gyroscopic instability, it will do so very close to the muzzle. And that does happen: In one celebrated and much-analyzed example that happened at a long-range target competition held in 1988, one of the leading competitors unexpectedly experienced terrible accuracy and tumbling bullets. It turns out that his rifle, load, and bullets were producing Sg factors in the range of 1.1 at 59 F, so they were accurate and adequately stable at 59 F. The competition took place on a day when the air temperature was -10 F, however, and that was enough to reduce the calculated Sg factor of his bullets to somewhere in the range of .95 to .99. And yes, his bullets tumbled, which gives confidence in use of Sg - and simple rules for calculating Sg - as a practical measure of bullet stability.

In looking at the table of Sg values that I calculated for various ML bullets, several things stand out:

1. Sg for a given bullet is most heavily influenced by twist rate, as expected. Even at sea level and 0 F, every bullet I considered is well-stabilized or over-stabilized by a 1-28 twist, but for a 1-48 twist under these conditions, only the bullets which weigh less than 350 grains are well-stabilized, and neither of the .45 caliber sabot bullets is well-stabilized. So... if a shooter is primarily interested in sabots and exceptionally long, heavy bullets, a 1-28 twist is definitely the way to go. As mentioned in my original post, though, I feel that over-stabilization CAN be a concern for muzzle loader bullets. I will elaborate on that in a following post.

2. Altitude has a fairly dramatic influence on bullet stability: At 3000 feet and 0 F, a 1-48 twist will even stabilize the TC Cheapshot sabot bullet, which has a deep hollow point. One suspects that if a short, fat pistol bullet with a shallower hollow point, like the .452 Hornady 300 grain XTP Mag, were used in a .50 caliber sabot, it would be even more stable in a 1-48 twist. In addition, at 3000 ft and 0 F, a 1-48 twist will stabilize most of the full-bore conicals that weigh up to 415 grains - the exceptions being the 300 grain Hornady FPB and the Hornady Great Plains bullets (both FP and HP) - all of which are exceptionally long for their weight. At 6000 feet, a 1-48 twist will stabilize every bullet except for the Hornady SST sabot and the FPB. All of my hunting here in Central Montana will be done at altitudes between 3000 and 7,500 feet, and temperatures between -10 F and 70 F (with most of my hunting above 5,000 feet) so the 1-48 twist barrel on my TC Renegade will stabilize a big range of potential conical hunting bullets: A few sabots and many full-bore conicals up to 415 grains - provided that I pick particularly short, fat bullets - like Idaholewis' 50-415I bullet - for weights greater than 400 grains.

3. Air temperature has some influence on bullet stability, as expected from the fact that colder air is denser than warmer air, and denser air will produce greater aerodynamic forces. However, the density of air varies with ABSOLUTE air temperature (ie degrees from absolute zero on the "Kelvin" scale: On the Kelvin scale, the freezing temperature of water at sea level is 273.1 degrees, it is 0 degrees C and it is 32 degrees F), so the air density difference between 0 degrees F and 70 degrees F isn't great as one might think. It is, however, enough to cause changes in Sg up to as much as 0.3 in some of the shorter, fatter bullets I considered, which can be very significant if that bullet is being used close to the edge of gyroscopic stability.

4. For a given bullet weight, a shorter, fatter bullet will be more stable than a longer bullet, as expected: Compare Lewis' 50-415I to the much longer No Excuses 420 in a 1-48 twist barrel. This true because if both bullets are shot from the same barrel, and are thus spinning at the same rate, a short, fat bullet will have more angular momentum than a longer, thinner bullet. Because the shorter, fatter bullet has more angular momentum, it takes greater aerodynamic forces to de-stabilize it.

5. All other things being equal, muzzle velocity has little influence on bullet stability, which surprised me until I thought about it a little more carefully: From a given barrel, a faster muzzle velocity produces a higher rate of bullet spin, and thus greater angular momentum, but that is largely cancelled out by the fact that aerodynamic forces also increase with increasing bullet velocity.

Several writings that I've studied so far mention "dynamic" phenomena which cause bullets that start out with acceptable stability to tumble at longer ranges. But none of the writers elaborate on what these phenomena are, or give any specific bullet characteristics or flight parameters which might lead to these dynamic phenomena. The only thing I've read so far is that when bullets lose enough velocity to cross from supersonic velocities to subsonic velocities as they travel downrange, they are prone to unspecified flight problems in the "trans-sonic" velocity range, and long-range target shooters are therefore careful to avoid loads for which their bullets are likely to cross into the trans-sonic range prior to reaching the target.

 

[WP79Vet]

If one is searching for a proven heavy conical for their ML, I would recommend searching threads from Idaho Lewis and Idaho Ron. Those two has it figured out. I know that if I ever move back out west and ML hunt for elk again, I would use the same approach as they do.

For altitudes above 3000 feet, Idaholewis' 50-415I bullet stabilizes well in a 1-48 if used at typical Montana hunting temps. Idahoron's 500 S&W bullet doesn't stabilize well in a 1-48 twist barrel at typical temperatures unless used at altitudes of about 6000 feet. Ron tells me that all of his rifles have 1-28 twists, and I'm sure that the 500 S&W bullets he casts for his rifles work very well for him.

 

[WP79Vet]

Lots of good information there. Researching ballistics can be almost like a retirement plan.
Been there, done that.

Although my PhD and research experience are in optical physics, I've had a fair bit of formal training in ballistics (parts of various West Point physics, weapons systems engineering, and fluid dynamics courses, parts of my Army basic and advanced cannon battery officer courses, and parts of a Stanford grad school physics course), but none of it touched on bullet stability, even though these courses did go into considerable detail on most other aspects of ballistics. And, as far as I know, bullet stability has never been an issue in any of my practical experience (life-long gun nut and hunter who started reloading centerfire ammo at age 10, cannon battery fire direction officer, executive officer, and commander). To me, then, the technical aspects of bullet stability are new and interesting, and they must also be important to us smokepole folk, because if they weren't, our rifles couldn't be had with widely varying rates of twist. That's borne out by what I found in calculating Sg under the wide range of conditions reflected in the table attached to my original post.

The basic ideas are pretty simple: Aerodynamic forces cause projectiles that aren't perfectly spherical to tumble in flight, and there are two common approaches to overcoming that:

1) Use aerodynamic forces to maintain the orientations of projectiles like arrows, rockets, and the projectiles shot from today's smoothbore tank cannons by putting stabilizing fins on their tail ends, and by concentrating most of their mass at the forward end of the projectile; and

2) Use rifling in the barrels of small arms and most kinds of cannons to turn their streamlined bullets into gyroscopes that spin about an axis which is aligned with the desired flight path. Although most streamlined bullets are aerodynamically unstable because their centers of mass are towards the tail of the projectile - and thus to the rear of their aerodynamic centers of pressure - if such a bullet is spinning at the right speed, it will resist changes in the orientation of its spin axis, just like a child's toy gyroscope which is spinning at the right speed can be made to sit in a highly unstable position on the rim of a water glass because tipping off the rim would change the orientation of its spin axis.

So.... what rate of spin will produce optimal flight for a given bullet? It turns out that this is a very complicated question which involves the velocity at which the bullet is fired, the density of the air through which the bullet travels (which is a function of air temperature, altitude, and weather conditions), and the weight, diameter, length, and shape of the bullet as well as the materials from which the bullet is made, how they are distributed, and how well the bullet is aligned with the bore of the rifle as it is fired. Here are the basic considerations:

On one hand, you don't want the bullet to spin too fast for the following reasons:
1) You want the spin axis of the bullet to follow the flight direction of the bullet as closely as possible, because that minimizes loss of velocity due to air resistance, and it minimizes lateral drift in the bullet's flight path caused by aerodynamic forces arising from spin which is not aligned with the flight path - the same mechanism that causes any kind of ball to follow a curved path if it's spinning on an axis which is not aligned with the flight path. This is one reason that over stabilization affects accuracy. If you put enough torque on the axis of a spinning bullet (or any other kind of gyroscope) over a long enough period of time you can cause it to change direction, and if the bullet is not spinning too fast, its spin axis will follow the flight path fairly well due to the combination of gravity and some of the aerodynamic forces.;
2) As a bullet leaves the barrel of a rifle, it flies away in the direction that its center of mass was traveling at the moment of exit. Because no bullet is perfectly made, and no bullet is ever perfectly aligned with the bore of a rifle, a bullet's center of mass is never exactly on the axis of spin. As the bullet travels down a rifled barrel, then, its center of mass spirals around the centerline of the barrel, and when it leaves the barrel, it flies away in the direction of the spiral at the moment of departure. That direction is never the same for any two bullets because the imperfections in loading alignment and mass distribution are different for every bullet, and are unknown to the shooter. The slower the bullet is spinning, however, the smaller the angle between the departing direction of the bullet and the centerline of the barrel will be, and the tighter the bullets will group on the target. This is another reason that over stabilization affects accuracy, and it is a particularly important reason to keep spin speeds relatively low for ML rifles shooting cast bullets made of soft lead because casting imperfections, the need for at least some force to start such bullets into the barrel, the difficulty of getting the bullets started straight, and the likelihood of deforming a soft lead bullet in a loading process which requires force are likely to result in a bullet center of mass that is significantly off the axis of spin.;
3) Spin speeds that are too high can cause a bullet to fly apart once it leaves the barrel, although this is rarely a problem for bullets with muzzle velocities of less than maybe 3.500 fps - not a concern for ML rifles; and
4) Upon target impact, high spin speeds can cause bullets to tumble, fragment, or follow unexpected paths through the target - probably not a concern for ML rifles because spin speeds are relatively low.

On the other hand, the bullet must be spinning fast enough for:
1) The spin axis of the bullet to resist the aerodynamic forces that cause bullets to tumble; and
2) The axis of the bullet to be stable in direction instead of precessing and nutating around the direction of flight.

To really understand bullet stability, you have to know the bullet's moments of inertia, and the aerodynamic forces acting on the bullet:

1) The principles of calculating a bullet's moments of inertia are understood very well. However, calculating an actual angular momentum for a real spinning object, even for simple geometric shapes, is generally a sophomore-level undergraduate physics problem because it requires multi-variate calculus and detailed knowledge of the bullet's shape and mass distribution, and the latter two facts are difficult to obtain with much accuracy unless you have a good optical comparator, or the bullet has a simple geometric shape. That's one of the reasons that Miller spent so much effort to develop a simple rule which uses only bullet weight, length, and diameter - and why his simple rule is widely used.

2) Aerodynamic forces are very poorly understood: Consider that humanity has spent literally trillions of dollars over many millenia on arrow, bullet, ship, aircraft, and rocket design.... but NASA and the US military still use elaborate towing tanks and wind tunnels to test nearly all aspects of their designs, even in this day of super-computers that are capable of doing literally billions of calculations per second, and solving differential equations that humans can barely formulate, let alone begin to solve. From what I've read, the Army's Ballistic Research Laboratory (Now part of the Army Research Lab) is the only organization in the United States which has sufficient resources to actually measure the aerodynamic forces which destabilize bullets - and that's why Miller used their library of measurements to develop his simple rule for bullet stability.

At this point in my career I have no interest in taking up bullet stability in a serious way, and the Sg calculations in my table are enough to guide stability aspects of choosing ML bullets for personal use. However, I'd like to have a little better understanding of the relevant aerodynamic forces, and I'd like to have much better understanding of which aerodyamic forces are accounted for in calculating the gyroscopic stability factor (Sg), how the dynamic stability factor (Sd) is calculated, and which aerodynamic forces are addressed by Sd. I'd also like to get a better feel for how well the Miller Rule works for typical ML bullet shapes. To that end, I've ordered a copy of the Bible for technical ballistics - Dr. Bob McCoy's Modern Exterior Ballistics: The Launch and Flight Dynamics of Symmetric Projectiles - and plan to spend some time reading the relevant chapters in a serious way.

 

[Hatchet Jack]

With my 1-48 twist Renegade and Invest Arm barrels shooting 460 grain conicals. I get my best accuracy with 65 to 80 grains of Swiss 2F and a wool wad. Most others I have talked to and read of get about the same with their 1-48 twist barrels. With the Hornady 385 grain Great Plains conicals, best loads seem to be 80 to 100 grains of powder. (no wads needed)
Best thing to do is stop reading, analyzing and over thinking things. Just start shooting.

 

[ETipp]

Although my PhD and research experience are in optical physics, I've had a fair bit of formal training in ballistics (parts of various West Point physics, weapons systems engineering, and fluid dynamics courses, parts of my Army basic and advanced cannon battery officer courses, and parts of a Stanford grad school physics course), but none of it touched on bullet stability, even though these courses did go into considerable detail on most other aspects of ballistics. And, as far as I know, bullet stability has never been an issue in any of my practical experience (life-long gun nut and hunter who started reloading centerfire ammo at age 10, cannon battery fire direction officer, executive officer, and commander). To me, then, the technical aspects of bullet stability are new and interesting, and they must also be important to us smokepole folk, because if they weren't, our rifles couldn't be had with widely varying rates of twist. That's borne out by what I found in calculating Sg under the wide range of conditions reflected in the table attached to my original post.

The basic ideas are pretty simple: Aerodynamic forces cause projectiles that aren't perfectly spherical to tumble in flight, and there are two common approaches to overcoming that:

1) Use aerodynamic forces to maintain the orientations of projectiles like arrows, rockets, and the projectiles shot from today's smoothbore tank cannons by putting stabilizing fins on their tail ends, and by concentrating most of their mass at the forward end of the projectile; and

2) Use rifling in the barrels of small arms and most kinds of cannons to turn their streamlined bullets into gyroscopes that spin about an axis which is aligned with the desired flight path. Although most streamlined bullets are aerodynamically unstable because their centers of mass are towards the tail of the projectile - and thus to the rear of their aerodynamic centers of pressure - if such a bullet is spinning at the right speed, it will resist changes in the orientation of its spin axis, just like a child's toy gyroscope which is spinning at the right speed can be made to sit in a highly unstable position on the rim of a water glass because tipping off the rim would change the orientation of its spin axis.

So.... what rate of spin will produce optimal flight for a given bullet? It turns out that this is a very complicated question which involves the velocity at which the bullet is fired, the density of the air through which the bullet travels (which is a function of air temperature, altitude, and weather conditions), and the weight, diameter, length, and shape of the bullet as well as the materials from which the bullet is made, how they are distributed, and how well the bullet is aligned with the bore of the rifle as it is fired. Here are the basic considerations:

On one hand, you don't want the bullet to spin too fast for the following reasons:
1) You want the spin axis of the bullet to follow the flight direction of the bullet as closely as possible, because that minimizes loss of velocity due to air resistance, and it minimizes lateral drift in the bullet's flight path caused by aerodynamic forces arising from spin which is not aligned with the flight path - the same mechanism that causes any kind of ball to follow a curved path if it's spinning on an axis which is not aligned with the flight path. This is one reason that over stabilization affects accuracy. If you put enough torque on the axis of a spinning bullet (or any other kind of gyroscope) over a long enough period of time you can cause it to change direction, and if the bullet is not spinning too fast, its spin axis will follow the flight path fairly well due to the combination of gravity and some of the aerodynamic forces.;
2) As a bullet leaves the barrel of a rifle, it flies away in the direction that its center of mass was traveling at the moment of exit. Because no bullet is perfectly made, and no bullet is ever perfectly aligned with the bore of a rifle, a bullet's center of mass is never exactly on the axis of spin. As the bullet travels down a rifled barrel, then, its center of mass spirals around the centerline of the barrel, and when it leaves the barrel, it flies away in the direction of the spiral at the moment of departure. That direction is never the same for any two bullets because the imperfections in loading alignment and mass distribution are different for every bullet, and are unknown to the shooter. The slower the bullet is spinning, however, the smaller the angle between the departing direction of the bullet and the centerline of the barrel will be, and the tighter the bullets will group on the target. This is another reason that over stabilization affects accuracy, and it is a particularly important reason to keep spin speeds relatively low for ML rifles shooting cast bullets made of soft lead because casting imperfections, the need for at least some force to start such bullets into the barrel, the difficulty of getting the bullets started straight, and the likelihood of deforming a soft lead bullet in a loading process which requires force are likely to result in a bullet center of mass that is significantly off the axis of spin.;
3) Spin speeds that are too high can cause a bullet to fly apart once it leaves the barrel, although this is rarely a problem for bullets with muzzle velocities of less than maybe 3.500 fps - not a concern for ML rifles; and
4) Upon target impact, high spin speeds can cause bullets to tumble, fragment, or follow unexpected paths through the target - probably not a concern for ML rifles because spin speeds are relatively low.

On the other hand, the bullet must be spinning fast enough for:
1) The spin axis of the bullet to resist the aerodynamic forces that cause bullets to tumble; and
2) The axis of the bullet to be stable in direction instead of precessing and nutating around the direction of flight.

To really understand bullet stability, you have to know the bullet's moments of inertia, and the aerodynamic forces acting on the bullet:

1) The principles of calculating a bullet's moments of inertia are understood very well. However, calculating an actual angular momentum for a real spinning object, even for simple geometric shapes, is generally a sophomore-level undergraduate physics problem because it requires multi-variate calculus and detailed knowledge of the bullet's shape and mass distribution, and the latter two facts are difficult to obtain with much accuracy unless you have a good optical comparator, or the bullet has a simple geometric shape. That's one of the reasons that Miller spent so much effort to develop a simple rule which uses only bullet weight, length, and diameter - and why his simple rule is widely used.

2) Aerodynamic forces are very poorly understood: Consider that humanity has spent literally trillions of dollars over many millenia on arrow, bullet, ship, aircraft, and rocket design.... but NASA and the US military still use elaborate towing tanks and wind tunnels to test nearly all aspects of their designs, even in this day of super-computers that are capable of doing literally billions of calculations per second, and solving differential equations that humans can barely formulate, let along begin to solve. From what I've read, the Army's Ballistic Research Laboratory (Now part of the Army Research Lab) is the only organization in the United States which has sufficient resources to actually measure the aerodynamic forces which destabilize bullets - and that's why Miller used their library of measurements to develop his simple rule for bullet stability.

At this point in my career I have no interest in taking up bullet stability in a serious way, and the Sg calculations in my table are enough to guide stability aspects of choosing ML bullets for personal use. However, I'd like to have a little better understanding of the relevant aerodynamic forces, and I'd like to have much better understanding of which aerodyamic forces are accounted for in calculating the gyroscopic stability factor (Sg), how the dynamic stability factor (Sd) is calculated, and which aerodynamic forces are addressed by Sd. I'd also like to get a better feel for how well the Miller Rule works for typical ML bullet shapes. To that end, I've ordered a copy of the Bible for technical ballistics - Dr. Bob McCoy's Modern Exterior Ballistics: The Launch and Flight Dynamics of Symmetric Projectiles - and plan to spend some time reading the relevant chapters in a serious way.

Very impressive background you have there. Congrats on your accomplishments. Not many out there can match that.

Indeed, a very long and complicated subject. I gave up on it as I didn't see any reason to put myself through any more of it. I came up with something that simplified it for me. Find the BC and compare it to what I am looking for in that caliber/rifle, the distance I plan on shooting, load and go to testing. Been working for me since the early 80's.

 

[snapbang]

Best thing to do is stop reading, analyzing and over thinking things. Just start shooting.

Yep, because each barrel is different. So get a few bullets that interest you and start shooting. It is really the only way to know.

 

[WP79Vet]

Very impressive background you have there. Congrats on your accomplishments. Not many out there can match that.

Indeed, a very long and complicated subject. I gave up on it as I didn't see any reason to put myself through any more of it. I came up with something that simplified it for me. Find the BC and compare it to what I am looking for in that caliber/rifle, the distance I plan on shooting, load and go to testing. Been working for me since the early 80's.

Your approach to choosing bullets works really well for centerfire rifles, and it's the approach that's always worked for me, too.

Seems that most commercial (as opposed to custom) centerfire rifle calibers are made in either a single standard twist, or a very limited range of twists, so the commercial bullets sold for that caliber are pretty sure to be stable with nearly all loads and rifles, and there's really no reason to worry about stability for most calibers unless you've got a rifle with a non-standard twist.

In the artillery world, all of our firing tables are based on hundreds of thousands of rounds which are fired in carefully chosen and extensively instrumented experiments. It takes years to get accurate firing tables put together for new artillery pieces and new projectiles: The world's first electronic computer, the Eniac, was built by the Army during WW II in hopes of speeding this process up. The Eniac met all of its design and performance specs... but it probably had less capability than a $10 modern calculator, and was woefully inadequate for computing firing tables. Looking back, that's no surprise, because today's fastest supercomputers still aren't adequate for computing firing tables. However, I suspect that far less firing data is required today because modern computers are probably capable of filling gaps between experimental shots with calculated shots with enough accuracy to make a good firing table. So... we never worried about bullet stability in the artillery world, either.

 

[WP79Vet]

Yep, because each barrel is different. So get a few bullets that interest you and start shooting. It is really the only way to know.

Shooting results are the final, critical word on everything.... and bullet stability is just one aspect of good shooting results. Nevertheless, stability is a potential cause of poor shooting results that can be eliminated with an hour of simple analysis before a single round is fired (Bullet Gyroscopic Stability Calculator), so the analysis is very worthwhile.

 

[WP79Vet]

Best thing to do is stop reading, analyzing and over thinking things. Just start shooting.

Been too cold and snowy around here to do any paper punching since before Christmas, and probably will be until mid-March...... Reading, analyzing, and thinking about bullets and stability ain't near as much fun as shooting, but it still beats playing Yahtzee....

 

[WP79Vet]

Ive just run a quick bullet calculation in the calculator you linked to and the JBM stability calculator here JBM - Calculations - Stability
Putting in all the info i have for a known good shooting lead bullet in two of my MLs. Bison came up with over stabilized at 5.76. JBM came up with 5.86 but didnt call it overstabilized.

As long as you're seeing good accuracy and Sg greater than maybe 1.4 for a given bullet under the conditions where stability is most likely to be a problem (ie at the coldest temperature and lowest altitude at which you'll be shooting that bullet), I don't think that Sg numbers greater than 2.0 (which Bison calls over stabilized) - maybe even as high as 8 or 9 - are anything to worry about, even though they mean that your bullets are spinning faster than they really have to spin for good stability. Why?

Here are the two things that might be a problem if a bullet is spinning too fast, and why they probably aren't an issue for MLs unless you're seeing accuracy problems of a certain kind:

1) Axis of spin at a big angle to the bullet flight path. With a bullet that's spinning too fast, this can be a big problem for trajectories with lots of curve to them - long range or high angle artillery fire - because the aerodyamic and gravitational forces on the bullet don't put enough torque on the bullet to force the axis of spin to follow the curving trajectory, and the bullet flies nose-high. When the bullet is flying substantially nose-high, two things happen: 1) The bullet will experience "spin-drift," for the same reasons that a baseball curves when a pitcher puts spin on it; and 2) Drag on the bullet increases, because it's flying somewhat sideways. Even for 1000 yard competition, even a relatively slow ML bullet's trajectory probably doesn't have enough curve to it for this to be much of a problem, even if it's spinning quite a bit faster than it needs to spin for good stability (ie Sg more than 2.0) under the firing conditions. At hunting ranges, it's just a non-issue because the trajectory barely curves, and misalignments will be on the order of a degree or so - at most.

2) If the bullet's center of mass isn't located on the axis of spin, as the bullet travels down the barrel its center of mass spirals around the axis of the barrel. When it leaves the barrel, the bullet flies away from the muzzle in a straight line that's in the same direction as the spiral at the instant of departure - which will be at some random angle to the axis of the barrel. Poor accuracy (large groups) will result when bullet centers of mass are substantially off the axis of spin due to casting imperfections, deformation of the bullet or misalignment of the bullet with the barrel caused by need for force in starting or loading bullets, or poor bullet design - and the higher the rate of spin, the worse the accuracy problems will be. This source of inaccuracy is independent of external firing conditions (altitude and temperature), so if you're getting good accuracy with a given bullet, barrel twist, and loading procedure under any firing conditions, this isn't something to worry about even if Sg is much higher than it needs to be for good stability. If accuracy is a problem, you can determine whether bullet center of mass problems are a potential cause by shooting those bullets at a range of different velocities (by using different powder charges): If bullet center of mass problems are making a substantial contribution to accuracy problems (and many things can contribute to accuracy problems at the same time), higher velocities will produce bigger groups, and the higher the velocity, the bigger the group. In that case, sizing bullets for a better barrel fit and easier loading, improving bullet quality through better casting or buying different bullets, changing lubing or loading procedures, choosing a bullet with a design that is less likely to misalign with the barrel, and so forth are potential ways to improve accuracy. Buying a barrel with a slower twist might work too - but that's an expensive way to go.

 

[drpatton]

According to Miller, the Greenhill Rule still works surprisingly well for spitzer boattail bullets traveling at 2,800 fps, but "is not as good for Black Powder velocities."

According to Wikipedia, the Greenhill formula is still used today. I assume it's for Muzzleloader bullets, which tend to be more cylindrical. Yes, there are hollow based designs and hollow points, but evidently, that doesn't change the outcome of the formulas very much. The 1861 Springfield used a 1:72 twist to stabilize the Minnie ball. Springfield target rifles use a 1:66 for the same projectile.

Greenhill used two sets of constants for his equations. For velocities below 2,800 fps he used 150. Above 2,000 fps he used 180. When Greenhill came up with these constants, black powder was the propellant used and velocities for most rifles were low. He obviously, knew this. Cordite wasn't invented until 10 years later.

I hadn't read Miller's statement on the Greenhill formula. The book I read said the results are relatively similar; However, Miller is designed for modern bullet designs, which Greenhill ignores. Greenhill used a cylinder for the bullet type. He uses the bullet length, and the caliber, which gives the circumference and the radius. With those 3 numbers, you can calculate the volume, which is a cylinder.

That said, there is a point at which increased stability does not yield more accuracy. Both, Greenhill and Miller came to this conclusion. Accuracy will eventually level off to its limits with increasing stability. This is the reason both formulas state the best round ball twist is a slow one.

Using Greenhill, because it's quick and easy, a .50 rifle, using a .490 patched round ball, the optimum twist rate is 1:72. The numbers I used are .49 squared (.2401) x 150 = 36.015. Divide that by the bullet length, I'll use .5 = 72.03. I chose those number to gice the quickest twist given the bullet design. Bullet obturation will cause it to almost be .50. I used .49. If I had used .50, the twist would have been slower.

Let's say Greenhill's constant of 150 for lead bullets is too high. We can use 130 instead and the result is 1:63. Since the 150 constant is still used today, it must be the most accurate.

My purpose in writing this is to explain Stability and Accuracy are not synonymous and unfortunately, people tend to think they are. Accuracy requires stability, but only to a point. Then they diverge. Accuracy levels off to its limits, as stability increases.