Stability Formula for Aluminum Tipped Bullets (Spreadsheet linked)

[Michael Courtney]

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 linked below. 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.

http://forum.accurateshooter.com/index.php?topic=3854528.0

 

[trickytune]

Michael Courtney this is a very interesting spreadsheet thank you. But I am going to question it. I am looking at buying a bolt action 223 to run Berger 75g, Amax 75g, Nosler CC 77g. All of which in other calculators require a 1:8 twist. But with this it looks like I can get away with a 1:9" which opens up my choices a whole lot. I want to try and stay close to the 1.5 Sg to get full bc as well as pointed out by Brian Litz. Are you confident that this is accurate enough to buy a rifle on? Im buying the rifle to suit the ammo so it has to work 100% or its down the road and buy another. Im thinking Savage 1:9" rather than Tikka 1:8" now.

TIA

 

[FEENIX]

I knew that somehow this will transition to Bryan Litz's/Berger's stability formula. lightbulb

 

[Michael Courtney]

Michael Courtney this is a very interesting spreadsheet thank you. But I am going to question it. I am looking at buying a bolt action 223 to run Berger 75g, Amax 75g, Nosler CC 77g. All of which in other calculators require a 1:8 twist. But with this it looks like I can get away with a 1:9" which opens up my choices a whole lot. I want to try and stay close to the 1.5 Sg to get full bc as well as pointed out by Brian Litz. Are you confident that this is accurate enough to buy a rifle on? Im buying the rifle to suit the ammo so it has to work 100% or its down the road and buy another. Im thinking Savage 1:9" rather than Tikka 1:8" now.

TIA

I do not think we have measured the depth of the open tips on the Berger 75 or Nosler CC 77. You really need accurate numbers for all the fields in the spreadsheet to get a reliable prediction within the accuracy of the formula. For the numbers I have for the 75 AMAX, the plastic tipped formula gives Sg close to 1.3 at sea level under standard conditions in a 1 in 9" twist barrel. You'll be in trouble if the barrel is really 1 in 9.25" or on a cold winter day.

If I had personally measured the bullets and I was confident in the twist rate of the barrel manufacturer and I knew the environmental conditions I intended to shoot in, I would not hesitate to buy a barrel where the formula predicted an SG of 1.5. Unless you're at a pretty good elevation, I don't think I can recommend a 1 in 9" twist for the 75 AMAX.

At high elevations, we've shot the 69 grain NCC from a 1 in 12" twist with a SG close to 1.5 and BC of 0.290. The "lost" BC is more likely due to Nosler's propensity for inflating BC claims rather than insufficiency in stability.

 

[idaho elk hunter]

I knew that somehow this will transition to Bryan Litz's/Berger's stability formula. lightbulb

Everyone thinks that Berger and their employees are the only ones with knowledge and intellect. This is a sorry state of affairs. Many others are as good if not better.

I do think Berger has a good product, but I don't think Bryan is the only capable engineer in the world.
Why doesn't some one check out Mike Courtenys education?
Maybe there is two people in this world that went to grad school? Maybe?

The internet has made us all professionals overnight. Therefore we have the knowledge to judge others by our professional wisdom.

 

[Edd]

Michael Courtney

Maybe you can answer a question for me. In a previous thread you indicated you had done some testing on the Berger 30 cal 230 gr match hybrid bullet. Can you tell me the Sg of that bullet at 0 ft altitude, 0°F, 2850 fps, and a 9.5 inch twist?

 

[Michael Courtney]

Michael Courtney

Maybe you can answer a question for me. In a previous thread you indicated you had done some testing on the Berger 30 cal 230 gr match hybrid bullet. Can you tell me the Sg of that bullet at 0 ft altitude, 0°F, 2850 fps, and a 9.5 inch twist?

This has not be approved for public release yet. But if you can measure the total length and the depth of the open tip, you can compute it yourself with the spreadsheet at the link. Our work with these bullets is under non-disclosure agreement. The spreadsheet has been approved for public release.

Why give a man a fish when you can teach him to fish?

 

[fmajor]

This has not be approved for public release yet. But if you can measure the total length and the depth of the open tip, you can compute it yourself with the spreadsheet at the link. Our work with these bullets is under non-disclosure agreement. The spreadsheet has been approved for public release.

Why give a man a fish when you can teach him to fish?

Heh heh! This is a tool like an electron microscope - we novices (or maybe better said, "novices like me") may understand there is some tiny stuff to look at, but we're not sophisticated enough to use the device!

All the same, thanks so much for sharing some of your expertise and the efforts put into such amazing analytical tools.

 

[Michael Courtney]

Heh heh! This is a tool like an electron microscope - we novices (or maybe better said, "novices like me") may understand there is some tiny stuff to look at, but we're not sophisticated enough to use the device!

All the same, thanks so much for sharing some of your expertise and the efforts put into such amazing analytical tools.

The only bits of additional info other than that required by standard ballistics calculators are the total length of the bullet (measured with a caliper) and the length of the plastic tip, aluminum tip, or cavity in the front of an open tipped match. To measure the depth of an OTM cavity, we use a mechanical pencil for the ones where the graphite will fit. Just adjust the pencil lead (graphite) until it hits bottom and measure the length of the graphite. The "Full Density" length is then the total length minus the length of the pencil lead required to reach bottom (the cavity depth).

For narrower OTM openings, we use a narrow drill bit and a sharpie to mark the depth. One might also use a needle or similar rigid narrow object.

Don Miller worked hard to create formulas that could be used by the average reloader, and we've tried to maintain that perspective.

 

[FEENIX]

Everyone thinks that Berger and their employees are the only ones with knowledge and intellect. This is a sorry state of affairs. Many others are as good if not better.

I do think Berger has a good product, but I don't think Bryan is the only capable engineer in the world.
Why doesn't some one check out Mike Courtenys education?
Maybe there is two people in this world that went to grad school? Maybe?

The internet has made us all professionals overnight. Therefore we have the knowledge to judge others by our professional wisdom.

I honestly don't think anyone here is questioning his education or think Bryan is the only capable ballistician as each bullet manufacturers have their own or Berger is the only game in town. Let the end users be the ultimate judge and move on ... that's all!

Peace out!

 

[trickytune]

I have measured Berger 52g .224 target at 4.5mm cavity (.177") and the 6.5mm Berger hybrid at 5mm cavity (.197") so without getting my hands on the actual thing I would estimate the 75-77g Berger cavity around .177". Most likely I will just use 77g Custom Competitions or Berger 77g OTM. Here is the output data I get on Berger OTM.
Caliber 0.224
Bullet Weight 77
Bullet Length 1.029
Barrel Twist 9
muzzle velocity 2500
Temperature 59
Pressure 29.92
Bullet Length 0.852

Sg(CD) = 1.207
Sg(PT) = 1.725
Sg(OTM) =1.570
Sg(AT)= 1.622


So this changes things from not really stable enough to completely stable. It does not get that cold here.

 

[Michael Courtney]

I have measured Berger 52g .224 target at 4.5mm cavity (.177") and the 6.5mm Berger hybrid at 5mm cavity (.197") so without getting my hands on the actual thing I would estimate the 75-77g Berger cavity around .177". Most likely I will just use 77g Custom Competitions or Berger 77g OTM. Here is the output data I get on Berger OTM.
Caliber 0.224
Bullet Weight 77
Bullet Length 1.029
Barrel Twist 9
muzzle velocity 2500
Temperature 59
Pressure 29.92
Bullet Length 0.852

Sg(CD) = 1.207
Sg(PT) = 1.725
Sg(OTM) =1.570
Sg(AT)= 1.622


So this changes things from not really stable enough to completely stable. It does not get that cold here.

You need to decide if being "more likely than not" to have an SG of at least 1.5 is good enough, or if you really need to be sure you have an SG of at least 1.5. If we were to buy a 1 in 9" Savage rifle to shoot any of the three bullets you have mentioned with a SG of 1.5 or higher, we'd have it in mind that there is a good chance we'd have to replace the factory barrel with a 1 in 8.5" or faster custom barrel to reach our goal.

When we really need to be sure, we tend to perform a "worst case" analysis rather than an analysis using the best available estimates. (In reality, there is some complex stats involved, but the approach below gives the gist in a way more readers can understand). Here is how one might run the numbers for one of our shooting ranges in South Louisiana.

Rather than use a likely atmospheric pressure, one might use a worst case pressure of 30.6 in Hg.

Temperature: 30 deg F

Bullet OAL: 1.039"

OTM depth: 0.07"

Twist rate: 1 in 9.25"

Bullet weight: 76.9 grains

Worst case SG: 1.126

Of course, once you've measured lengths and OTM depths from a couple boxes of bullets and confirmed that the barrel twist really is 1 in 9.00", one can adjust the analysis to those numbers.

OTM depths have a lot more variation than plastic tip lengths. Due to the short length and thick jacket, I think estimating the OTM depth at .177" is likely too much. The longer 75 grain Match VLD with an OAL of 1.063 might have an OTM depth close to that or longer, but I doubt that the shorter 77 grain bullet does.

When choosing a barrel twist slower than a manufacturer's recommendation to shoot at sea level, you need to take good care in getting good inputs for the stability calculations or be prepared to buy a faster twist barrel if you get bit by Murphy.

 

[Michael Courtney]

A few comments are in order, given the varied techniques used to produce aluminum tipped bullets.

The accuracy of the stability formula depends on a quality made bullet. Corbin sells the aluminum bullet tips, and we are aware that a number of amateur bullet makers are making these bullets, either with the Corbin dies or by modifying an existing off-the-shelf bullet to accept the new tip.

If the manufacturing process disturbs the bullet symmetry so that the center of gravity is no longer along the bullet axis, the bullet will be much less stable than expected. Further, a noticeable seam or shoulder where the base of the tip meets the main body of the bullet will create much greater drag at the front of the bullet, thus increasing the overturning moment and reducing SG.

If your bullets are made with the same quality as the 50 cal AMAX and the better custom makers that are using Corbin's aluminum tips, you can expect the stability calculator to provide accurate results.

 

[fmajor]

Please excuse my ignorance here (my education lies in a different subject matter), but what do;
Sg(CD) = 1.207
Sg(PT) = 1.725
Sg(OTM) =1.570
Sg(AT)= 1.622

mean? I'm guessing the values in parenthesis are specific bullet references? but "Sg" is beyond me....