It is the Greenhill Formula. I originally got it from an article in the Washington Arms collector magazine by Lewis Braun. Here is the wiki link for the Greenhill Formula.
http://en.m.wikipedia.org/wiki/Alfred_George_Greenhill
I realize this is quite an old thread, however I use the Greenhill formula regularly. While it provides a very good indicator of possible stability and twist rate, there are some outside factors that get into play. Aside from the internal factor which is the rate of twist, temperature, altitude and speed, all play a role. I don't know if someone brought this up because I haven't read the entire thread, but a bullet that isn't optimally stabilized doesn't achieve its designated ballistic coefficient.
Speed helps somewhat but not all that much, perhaps one or two percent. In order for a bullet flying at 3000 fps in a 30 caliber barrel with a rate of twist of 1/11 to have the flying stability factor of a bullet shot at that speed in a 1/10 twist, that one inch difference requires the bullet fired in the 1/11 twist to be 1500fps to 2000 fps faster ... meaning it is nearly out of the question to compensate with speed.
Altitude makes short work of compensating. At 8000 feet of altitude a bullet that is not properly stabilized at sea level may be (generally is) perfectly well stabilized. Even a 3-4000 feet difference is substantial. A bullet shot at one range can be better stabilized than at another range situated at lower elevation.
Temperature is also a factor that affects stability more than speed, the hotter, the better. Not by as much of a margin as altitude but it does improve stability substantially.
A factor of 1.5 is a "stable" bullet. It if is less than 1.5, then, it may be stabilized but the ballistic coefficient may be 2-3 or more percentage points short...
Another element that is very important and that cannot be calculated accurately using formulas that incorporate bullet length (they all do) is bearing surface. My firsthand experience was shooting a silhouette rifle in the mid 1980s. A Sako in .308 with a MacMillan silhouette stock and a Canjar set trigger, topped with one of the latest fixed 15. Leupold scopes with adjustable turret for windage and elevation. The set up was superbly accurate. To 100, 200 and 385 metres. I shot a 168 grains Hornady BTHP bullet. For longer range work on the steel rams at 500 metres (547 yards) I was shooting a 190 grains Sierra BTHP. The rate of twist in my barrel was 1/12. The 190 grains Sierra bullet shot groups of 1/2 to 3/4 inches at 400 yards. Not 1/2 a moa at 100, but actual sub moa groups at 400 on a regular basis in practice.... I was quite happy with its accuracy as it toppled every ram it hit meaning it was still flying true at 500 metres. Muzzle velocity was approximately 2450 fps. The stability factor of that bullet calls for a rate of twist of 1/10.35 (any standard 30 caliber bullet would stabilize it very well). 1/12 was well short.
After I started to use the various formulas for bullets stability I decided to give Sierra a call. I was told that the reason that particular bullet was very stable in a 1/12 twist was because of its
purposely short bearing surface of .379 for a total bullet length of 1.375. A bearing surface of 28 % !! This was done to allow it to be shot in different barrel twists. While I shot it regularly at 1500 feet in altitude, I competed at 4000 feet which enhanced the bullet's stability. While still not achieving its potential ballistic coefficient. Sierra gives a B.C. of .51 for this bullet, (I had to call to obtain it). What it may have achieved in my rifle at 4000 feet of altitude was probably closer to .43 to .45.
Applying the Greenhill formula, squaring the diameter in thousands of an inch, multiplying by 150 and dividing by 1.375 the result would have definitely made anyone believe the rate of twist of my barrel wasn't adequate.
Bearing surface alone isn't sufficient a criteria to judge. Some target bullets that are extremely long with very moderate bearing surfaces will simply not stabilize unless one is using the appropriate rate of twist or close to it in their barrels. The weight of non bearing surfaces do affect stability in flight. The Sierra bullet I shot is still made and is exceptionally well balanced for an older product. It was then a heavy for caliber bullet, nowadays the heavy for caliber bullets weigh 30, 40 and even 50 grains more and are finicky to stabilize but when it is done, they have phenomenal ballistic coefficients.
There are advantages and disadvantages to rates of twist. A fast rate of twist will stabilize better but at very high speed will help disintegrate light bullets with lighter jackets as soon as they are in flight. They will not take the centrifugal force exerted on them which is why varmint barrels often have a slower twist. A fast twist with conventional bullets does enhance accuracy but also raises pressure somewhat and may lose 1 to 1.5% in speed. A slower twist relieves pressure somewhat and enhances speed by 1 to 1.5%, at times, less. Caliber plays a factor as well. The smaller bores being more sensitive. The heavy bores are also less finicky when it comes to stability. Their bullets not being exceptionally long.
There are no hard and fast rules. Bullets that are supposed to need a 1/9.5 twist may stabilize in slower twists. This includes long target bullets. i.e, 220 grains in 30 caliber which would require at least a 1/10 twist rate but it would stabilize a bullet that shows a requirement of a slightly faster twist. There is some give. Rate of twist is very important but not as critical and unforgiving as one may think. It does however vary from one bullet manufacturer to another. The quality of a bore plays a big part in how well a bullet is stabilized because of the uniformity of high end barrels but at equal twits quality only serves to achieve accuracy not faster gyroscopic speed.
I know this is lengthy but I felt inspired by the topic. Forgive me if it is too long.
