Range Report New Formula for Gyroscopic Stability of Open Tipped Match Style Rifle Bullets

[Michael Courtney]

New Formula for Gyroscopic Stability of Open Tipped Match Style Rifle Bullets

A paper describing our new formula for the gyroscopic stability of open tipped match bullets has just been published by Cornell University Library. Don Miller knew that the assumption of constant density used to develop his original twist formula would tend to underestimate the stability of open tipped match bullets, and shared some very good ideas which proved useful in formulating a more accurate equation. I have a spreadsheet implementation of the new formula, along with the previous formulas for constant density bullets and plastic tipped bullets. See: New Formula for Gyroscopic Stability of Open Tipped Match Style Rifle Bullets for download.

http://arxiv.org/ftp/arxiv/papers/1401/1401.4187.pdf

Abstract: Earlier work has produced formulas for predicting stability of rifle bullets of near uniform density and also for plastic-tipped rifle bullets. These formulas have been shown to be accurate to within 5%. However, the original Miller twist formula for metal bullets of near uniform density underestimates the stability of match style open tipped rifle bullets having a significant empty volume in the tip. This paper presents a new formula for accurately estimating the stability of these open tipped match style rifle bullets from parameters easily obtained such as the bullet mass, length, and depth of the empty space in the tip. The formula is tested by measuring the aerodynamic drag vs. predicted stability of several bullets over a range of stabilities.

 

[damoncali]

Cool. The BC vs Sg relationship is worthy of more study. I've never seen it done quite in that way.

 

[Michael Courtney]

Cool. The BC vs Sg relationship is worthy of more study. I've never seen it done quite in that way.

We gave a lot of thought in developing an experimental design with a continuous dependent variable. Varying Sg and only looking at "it tumbles" or "it doesn't tumble" is using a binary dependent variable and not nearly as sensitive to what is happening. The Litz experiment showing different BCs for different Sg gave us the idea to use BC as the dependent variable, and we were pretty sure it would work after consulting the Sierra manuals discussing the same subject.

Other possibilities for experimental observables that might be sensitive to stability (group size, yaw cards, high speed video, etc.) are subject to confounding factors and/or require a lot more shots to yield the same essential information. BC is a reliable indicator of the onset of instability as Sg is lowered from 1.4 to 1.0.

 

[trigger29]

Unfortunately I don't have excel on this pc yet, and can't seem to open the spreadsheet. I'd like to see what it says on my custom lathe turned hollowpoint hunting bullets, as they're very long, and probably shouldn't stabilize, but they have a huge cavity in the nose, .800" deep, and always have flown well.

 

[Michael Courtney]

Unfortunately I don't have excel on this pc yet, and can't seem to open the spreadsheet. I'd like to see what it says on my custom lathe turned hollowpoint hunting bullets, as they're very long, and probably shouldn't stabilize, but they have a huge cavity in the nose, .800" deep, and always have flown well.

The paper suggests that the formula might not work well for an open tip deeper than 30% of the overall length. If you post the bullet weight, caliber, length, nose depth, and twist rate, I can run the numbers for standard conditions. For depths greater than 30% of the total length, I'd suggest entering the full density length as 70% of the total length.

You can also download Libre Office or Open Office and try out various scenarios. I use both and try and avoid MicroSoft whenever possible.

 

[trigger29]

Bullet is 1.700" long solid copper with the first .200 being an aluminum tip, and then a cavity .600" deep behind that.

 

[Michael Courtney]

Bullet is 1.700" long solid copper with the first .200 being an aluminum tip, and then a cavity .600" deep behind that.

We have a formula for plastic tips and a formula for open tipped match bullets, but aluminum tipped bullets is something we haven't given much consideration to. An aluminum tip with a big hollow cavity behind it is another complication. Aluminum is 3 times as dense as plastic and about 1/3 the density of copper. The open tipped formula might give a good estimate of the copper base without the aluminum tip, and that would be a reasonable upper limit. The constant density formula might give a reasonable lower bound. The real stability should be between these two values.

To compute the upper and lower bounds, I'd need to total length with the Al tip and the length without the Al tip, along with the caliber, weight, and twist rate.

 

[Michael Courtney]

There are important differences between Sg (gyroscopic stability) and dynamic stability. If a bullet has gyroscopic stability when it leaves the muzzle, it will maintain gyroscopic stability at all ranges, as Litz describes in his book on applied ballistics.

Dynamic stability is different, as shown in the figure attached for the M855 bullet.

Inferences regarding dynamic stability should not be made from Sg values. Some references on dynamic stability:

http://www.dtic.mil/ndia/2011ballistics/11894.pdf

http://www.arl.army.mil/arlreports/2010/ARL-TR-5182.pdf

http://www.fulton-armory.com/faqs/Genl-FAQs/Fly/longr.htm

 

[Bob 964]

Where would/could one find a list of full densities for different bullets? Specifically, the Berger 155 and 215 Hybrid Match bullets. Is there a spreadsheet available?

 

[Dallas4rceMarine]

I tried reading the article from your first post but there is just way too much stuff in there to get lost in.

can you post just the formula here without all the explanations so that we can just plug and play the numbers?

also has this new formula ben given to the guys over that run the Ballistic AE iPhone app? Since I paid $30 for the app I would like them to have the best most up to date formulas!

thanks!

 

[Bob 964]

can you post just the formula here without all the explanations so that we can just plug and play the numbers?

You can find the Excel spreadsheet and formulas here:

New Formula for Gyroscopic Stability of Open Tipped Match Style Rifle Bullets

 

[Dallas4rceMarine]

Gracias Amigo! what's the word on this formula making its way over to Ballistic AE??

 

[Michael Courtney]

Gracias Amigo! what's the word on this formula making its way over to Ballistic AE??

I don't know. You should email and ask them. I don't have time to run around pushing the formulas on all the ballistic software.

A few companies have sent me their software and asked me to double check that a formula is properly coded, which I have done.

 

[Dallas4rceMarine]

roger that, they have a thread going on here http://www.snipershide.com/shooting...11-ballistic-ae-what-missing-you-want-12.html asking for input and I added in about this new formula. Hopefully they pick it up soon.

 

[Bob 964]

I don't know. You should email and ask them. I don't have time to run around pushing the formulas on all the ballistic software.

A few companies have sent me their software and asked me to double check that a formula is properly coded, which I have done.

I would love to see Ballistics AE incorporate this new formula into its program, and I am encouraged by the fact that companies are sending their software to Mr. Courtney to see if the formula has been properly coded; BUT... without the data (e.g., the full density, length of nose depth, etc.) for different bullets, the formula will not be of much help. To repeat my earlier question, does anyone have a list/spreadsheet of these data? If not for all bullets, does anyone have the nose depth length data on the Berger Match Hybrids in .308?

 

[Michael Courtney]

I apologize if there has been a misunderstanding. The only bullet data you need to use the formula are the total length and the "full density length." Both can be determined with a caliper and likely some common household item.

For a plastic tipped bullet, the "full density length" is the length of the metal part of the bullet, or the total length minus the length of the plastic tip.

For an open tipped match bullet, the "full density length" is the total length minus the depth of the open tip. If the hole is wide enough, I determine this with a mechanical pencil by inserting the lead as far as it will go and then measuring the length of the lead inserted with a caliper. A small drill bit or similar item also works, but you should mark it with a marker and average 5-10 readings to ensure accurate results.

 

[Bob 964]

I apologize if there has been a misunderstanding. The only bullet data you need to use the formula are the total length and the "full density length." Both can be determined with a caliper and likely some common household item.

For a plastic tipped bullet, the "full density length" is the length of the metal part of the bullet, or the total length minus the length of the plastic tip.

For an open tipped match bullet, the "full density length" is the total length minus the depth of the open tip. If the hole is wide enough, I determine this with a mechanical pencil by inserting the lead as far as it will go and then measuring the length of the lead inserted with a caliper. A small drill bit or similar item also works, but you should mark it with a marker and average 5-10 readings to ensure accurate results.

No misunderstanding on my part. Your formula and its application are pretty straight-forward. I was hoping someone (i.e., Berger Bullets) had the data on the depth of the open tip for their Hybrid bullets and would be willing to share it. Absent that, I had pretty much resigned myself to measuring that depth using your method (or one substantially similar).

 

[rmfield]

Michael, thank-you for all of your work and thanks for posting the info here. Good stuff!

 

[Deleted member 10043]

tag

 

[marduk185]

does this data also translate into terminal stability/instability within the target medium or are we only talking about external dynamic properties here? i have been curious about match bullets practical effectiveness out of sbr platforms is why i ask.

 

[Deleted member 10043]

It is an improved Miller formula for OTM match and plastic tip bullets.


Sent from my iPod touch using Tapatalk

 

[Michael Courtney]

does this data also translate into terminal stability/instability within the target medium or are we only talking about external dynamic properties here? i have been curious about match bullets practical effectiveness out of sbr platforms is why i ask.

In principle, the stability formula might be adapted to work if you could compute the retarding force in the target medium to obtain the overturning moment. In practice, computing the retarding force a priori (before shooting into the medium) is very difficult, especially if the bullet deforms at all, as most do. Since one has to shoot into gelatin to estimate the retarding forces, the same experiment can be used directly to see if and at what depth a bullet tumbles.

Adaptation of the formula would probably work for a medium like water, where the retarding force simply increases with medium density. But gelatin and inhomogeneous media like tissue are much different.

Complicating the tumbling question further is the fact that depth at tumbling depends sensitively on the small angle between the bullet axis and travel direction at impact. Bullets that impact at 5 degrees tumble much shallower than bullets that impact at 1 degree. Since this angle changes as the bullet is in flight, predicting tumbling depth is a complex problem.