Most know that Don Miller published an accurate formula for computing gyroscopic stability of constant (or near constant) density bullets in 2005. This formula has been incorporated in several ballistics calculators including JBM, ColdBore, etc. Don knew that his formula would be overly conservative (predict low stabilities) for bullets whose density varied significantly along their length, so when I contacted him in 2010, he was eager to collaborate and develop an accurate formula for plastic tipped bullets which we experimentally validated in 2011 and published in Precision Shooting in early 2012. This formula has also been incorporated in several ballistics calculators.
Before Don passed away in 2012, he expressed a desire that his formula be adapted for open tipped match bullets and we shared some ideas for the development and testing of a stability formula for open tipped match bullets. This formula was validated experimentally and published earlier this year.
As aluminum tipped bullets have become more popular, the requests for info on stability of aluminum tipped bullets have increased, so yesterday, we finally added a formula for aluminum tipped bullets to the spreadsheet. Due to the paucity of aluminum tipped bullets, this formula has not yet been experimentally validated, so for now, we are estimating its uncertainty as 10% rather than 5% for the constant density, plastic tipped, and open tipped match formulas that have been experimentally tested. This formula is essentially a linearly interpolation (or weighted average) between two formulas that are known good (the constant density case and the plastic tipped case).
Like all ballistic calculators, the accuracy of the outputs depends on the accuracy of the inputs. You really need an accurate bullet weight, total length, length of the full density portion, twist rate, and environmental conditions. A reloading scale, calipers, and Kestrel are sufficient, but the claimed barrel twist rate of the manufacturer usually is not. There are some good sources on measuring it yourself.
The spreadsheet is attached. We welcome valuable experiential feedback on the accuracy of our formulas, but feedback is difficult to assess if the inputs have not been measured with confidence and if it does not include specific observations about why you think the bullet is or is not stable. Theoretical discussions are less valuable unless you are comparing our predictions with those of PRODAS. Accuracy observations are harder to relate to stability than observations of key holing, significant yaw, or accurately measured ballistic coefficients.
The adapted stability formula generally predicts a higher gyroscopic stability for aluminum tipped bullets than the original formula that assumes constant density. This is because the moment of inertia about the tumbling axis is lower for aluminum tipped bullets than for bullets of more constant density. The practical result is that a given rifle barrel might actually stabilize an aluminum tipped bullet in cases where stability of a constant density bullet of the same weight, caliber, and length, might me marginal or less than 1.0.
Before Don passed away in 2012, he expressed a desire that his formula be adapted for open tipped match bullets and we shared some ideas for the development and testing of a stability formula for open tipped match bullets. This formula was validated experimentally and published earlier this year.
As aluminum tipped bullets have become more popular, the requests for info on stability of aluminum tipped bullets have increased, so yesterday, we finally added a formula for aluminum tipped bullets to the spreadsheet. Due to the paucity of aluminum tipped bullets, this formula has not yet been experimentally validated, so for now, we are estimating its uncertainty as 10% rather than 5% for the constant density, plastic tipped, and open tipped match formulas that have been experimentally tested. This formula is essentially a linearly interpolation (or weighted average) between two formulas that are known good (the constant density case and the plastic tipped case).
Like all ballistic calculators, the accuracy of the outputs depends on the accuracy of the inputs. You really need an accurate bullet weight, total length, length of the full density portion, twist rate, and environmental conditions. A reloading scale, calipers, and Kestrel are sufficient, but the claimed barrel twist rate of the manufacturer usually is not. There are some good sources on measuring it yourself.
The spreadsheet is attached. We welcome valuable experiential feedback on the accuracy of our formulas, but feedback is difficult to assess if the inputs have not been measured with confidence and if it does not include specific observations about why you think the bullet is or is not stable. Theoretical discussions are less valuable unless you are comparing our predictions with those of PRODAS. Accuracy observations are harder to relate to stability than observations of key holing, significant yaw, or accurately measured ballistic coefficients.
The adapted stability formula generally predicts a higher gyroscopic stability for aluminum tipped bullets than the original formula that assumes constant density. This is because the moment of inertia about the tumbling axis is lower for aluminum tipped bullets than for bullets of more constant density. The practical result is that a given rifle barrel might actually stabilize an aluminum tipped bullet in cases where stability of a constant density bullet of the same weight, caliber, and length, might me marginal or less than 1.0.
