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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.
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.