You are welcome.
For general information it must also be considered that all stability calculators are not intended for all bullets. Any calculator based on the Miller formula for instance, cannot be used to calculate anything other than lead or jacketed lead core bullets. For a different specific gravity (SG) such as copper or brass, one would need a calculator based on the method developed by McCoy.
A typical Miller formula calculator would ask for caliber, weight, length, twist, speed, temperature and altitude. The McCoy method, in addition to the parameters of the Miller formula, also asks for ogive length, meplat diameter, material density, boat tail length, boat tail angle and the shape of the ogive.
Take a solid copper bullet and enter the following data in a Miller based formula for gyroscopic stability (Sg).
Caliber: .300 (Humor me)
Weight: 150gr
Length: 1.25"
Twist: 10"
Speed: 3000fps
Temperature: 59
Altitude: 0
The Sg calculated would be about 2.1
Enter the above data into a McCoy calculator as well as:
Ogive Length: 0.669"
Meplat Diameter: 0.087"
Material Density (SG): 8.95
Boat Tail Length: 0.244"
Base Diameter: 0.256"
Head Shape: 1 (for a typical slender bullet forebody)
The calculated Sg would be around 1.66 which is correct for solid copper.
Finding a McCoy calculator: Search for "McCoy Twist Rate Formula"
I'm not a mathematician or physicist and I'm not as credible as Gerard so please don't take this as an argument. Just my experiences and subsequent opinions based on those.
I prefer to use the Miller method even for 100% copper bullets. My reasoning is because even though miller doesn't account for material density (accepted nominal values are 8.89 for copper and 10.7 for jacketed lead) it does account for weight, caliber and length not just length and caliber like early equations used. This allows for proportionate values to be used. For example, using the Miller method, if you compare equal caliber, air density, velocity and length but change the weight, the stability factor increases as weight goes up. Using a density factor here would also work similarly but to simplify things, it's using proportion. Obviously a 190 grain 30 caliber bullet 1.38" long is denser than another 190 of equal nose and boat tail profile that is greater in length. The Miller method does reflect this. Whether you have two 190s of equal density but having different lengths (due to form factors) or having two 190s of equal form factors but different lengths (due to different densities) the Miller method reflects these both. IMHO it is a very simple yet also very accurate method for both the leaded and unleaded bullets.
A 30 caliber 177 grain all copper GS bullet with a length of 1.540" is considerably longer than the 30 caliber 178 BTHP Hornady jacketed lead bullet at 1.340". Granted, the 177 is sleeker, there is only so much streamlining you can do be it jacketed lead or all copper. My point is that with the limitations it should be obvious by looking at the GS 177 (knowing it weighs 177 grains) that it is not jacketed lead. A bullet with the dimensions of a 208 Amax either weighs 208 grains if made of jacketed lead or 177 grains if made of copper. The Miller shows that even though the 177 and 208 are of very similar dimensions that the 208 is much more stable for a given twist at a given velocity reflecting how density plays into bullet stability, it just doesn't use an official density factor. It uses caliber, length and weight as a reference.
To validate my theory is a couple of experiments I did a few years back. I was trying to validate the accuracy of Miller method. One test was the 208 Amax in a 12x barrel. The other was the 177 GS bullet in an 11x barrel. Since we're talking about the Miller versus all copper, I'll go with the 177.
Right before I was planning a trip to Arizona, I decided to use that opportunity to test the Miller method. I had some 177s on hand as well as an 11x barrel. The Miller formula showed for my location and velocity I should be just under 1.0. Between .98 and .99. 11 degrees F. and 29.98" mercury. At 100 yards none of the bullets were sideways but severely key holed. Some looked like they were dang near at 45 degrees when the entered. Velocity was 2752 avg. It was obvious that these were less than stable. I never fired them at 200 yards but I'm sure they would have gotten worse. Going to Arizona and shooting in 24.95" Hg., 60 degrees F. showed textbook round holes at 100-300 yards. The Miller method showed a 1.3 stability factor which is in line with the results.
My results were similar with the 208 in a 12x. They stabilized in warm air but not cold air as predicted by Miller. When Miller said .99-1.0, they were key holing and by 700 yards they were getting worse. Any less than that such as .97-.99 and lower, they key holed worse early on. I got identical results using the Miller method using both all copper bullets and jacketed lead.
I'm not saying Miller is better or that McCoy is not right, I just think the miller is pretty good and more usable than many think. Including for all copper bullets.
Will the Miller method work every time? Maybe not. But I think if you're just looking to see if you have a chance of being stable or not with a given combo, the Miller method can show you whether or not its worth your time to try or a waste of your time to try.