Now if we drop the velocity down to 1/3 of the 2000 such as in a pistol, we would have to triple the rate of twist to achive the same RPMs.
Shortstring, I'm just using your post as a jumping off point for the discussion below. I'm not directing this at you!
All of this assumes that round balls have a loss of stability threshold at a certain rpm. IOW, going under those rpms will result in a loss of stability (accuracy) If that is indeed so, then extrapolating to the needed twist of a short barrel (pistol) from the rpms perceived to be needed to stabilize a round ball makes sense. However, it all seems to be balanced on the idea of that minimum rpm threshold.
We can look at the twist rates offered by historical and modern barrel makers for the answer, but that does not tell us anything about rpms needed. I'm convinced that twist rates offered by various barrel makers have been more related to manufacturing limitations than any kind of science. The original Hawken rifles were offered in mostly 1:48. We know now that it is not the ideal twist rate for a large bore rb gun, but yet that is what was used.
One of the Hawken brothers worked at the Harpers Ferry arsenal where he built the 1803 Harpers Ferry rifles. These rifles had a 1:56 twist. Wonder if there was any science to that? Probably not! If there had been, would Hawken have set up to make 1:48 twist barrels?
What about modern barrel makers? When the GPR was first introduced it was built with a 1:66 twist (i have one of those). Later it became a 1:60 twist. So, what was the reasoning behind that? We can suppose all day long that Investarms tested and tried other twists and scientifically concluded that 1:60 is superior. Fat chance, IMO. I suspect it had more to do with streamling or combining manufacturing capabilites with a knowledge that the 1:60 would be perfectly acceptable rather than any idea that it would be superior.
It does not make much sense to apply Greenhill to round balls when seeking the *minimum* twist needed for stability. It is true, IMO, that using the Greenhill to arrive at a twist rate for a rb barrel will result in a satisfactory barrel. But, not necessarily because the formula *applys* to balls, but simply because application of the formula does no harm.
Greenhill was developed in order to predict stability for elongated projectiles that must overcome a minimum of two pressure waves (front and rear) as well as other pressure waves generated by interuptions to the smooth sides of the projectile such as cannelures, etc. Wonder if anybody has shadowgraphs or hi speed photos of any round balls in flight that would show the pressure waves generated by a ball? The other factor that makes the comparison imperfect is the fact that the nose shape of an elongated projectile will have a tendency to overturn due to the forces of wind. The longer and more pointy the nose, the more critical that effect becomes and the more spin that is needed to overcome that effect. No such problem with a ball. As far as I can see there would be no force applied to a ball in flight that would tend to make the ball roll it's frontal surface over to the rear.
BTW, modern (suppository) barrels twist rates are
not determined using the Greenhill formula! If you measure bullet lengths on some of the longer projectiles for .270, .25. 7mm calibers and then apply the Greenhill formula, you will find that they all exceed the length predicted by Greenhill.
Balls from smoothbores could be our baseline in trying to determine the minimum twist (or rpm if you like) that is needed to stabilize and accurize a ball. Experiments that would gradually apply increasing twist to a rifled barrel could get us to a point of understanding the minimum required. That of course would be an expensive and time consuming experiment that most of us, me included, are not able to undertake. My tiny contribution is the ongoing build of a pistol with a nine inch .36 caliber barrel with 1:48 twist that was acquired in the shortening of a GM barrel.
Whenever I read these discussions or see recommendations for twist rates for pistol barrels, I wonder how my little project will shoot. We'll see.
I think we should focus on the minimum required twist to stabilize a ball and maximize accuracy if we want to arrive at the most accurate twist rate for the any given barrel length or proposed velocity. Most experienced rb shooters who have used rifles with varying twist rates have found, and pretty much agree, that there is accuracy degradation when the ball is spun to fast. I myself have found this to be true when shooting .50 and .54 caliber rifles with both fast and slow twist. It's apparent that the slow twist barrels will allow accuracy at higher velocities than the slow (1:48) barrels.
And please, don't get the idea that I'm attacking the accuracy of your favorite TC or other 1:48 rifle. I'm not! I have used 1:48 twist .50 and .54 barrels to good effect in matches and in the field. But, I also know that while I can stoke up my .54 with 1:70 twist and still maintain accuracy, I can't go nearly as high with the faster twist barrels and still retain the accuracy. Especially as ranges reach out to the 50 to 100 yard distances.
None of this is me advocating for heavy charges or high velocities and I don't want to trigger a discussion revolving around the known fact that *it only takes 50 or 60 or whatever grains to kill a deer*, etc., etc.
