I'd been waiting for someone to mention rotational speed, RPM or RPS (revolutions per second) which is the key to stability once the bullet is in the air. RPS is determined by rate of twist and muzzle velocity.
I'm not familiar with the intricacies of bullet aerodynamics, just aware that they exist. The RB is probably the simplest of all bullet shapes, but it has one characteristic that really puzzles me. For any given diameter ball, there seems to be a rather narrow range of RPS that provides the best stability and accuracy, whether the ball is traveling 800 fps or 2000 fps.
That's why short barreled, low velocity pistols need a fast twist and high speed longrifles need a slow twist. For example:
A .50 caliber pistol with an MV of 800 fps needs a twist of at least 1:28, as deermanok pointed out in post number 15.
(800 ft/sec) X (12 in/ft) = 9600 in/sec
(9600 in/sec) / (28 in/rev) = 342 rev/sec or 342 RPS
A .50 caliber 42" long rifle with an MV of 2000 fps needs a twist of about 1:66.
(2000 ft/sec) X (12 in/ft) = 24,000 in/sec
(24,000 in/sec) / (66 in/rev) = 363 rev/sec or 363 RPS
The .50 caliber RB's speed has been increased by a factor of 2.5 (and gone from subsonic to supersonic air flow) but the RPS for good accuracy is virtually unchanged. For a .50 caliber RB roughly 350 RPS seems to be the optimum rotational speed for the best stability and accuracy regardless of MV (that can be produced with black powder).
First, rps is dependent on velocity. The faster an object goes, the more rotation is required to stalize it. This may go against 'common sense' but it is a fact.
RPM or RPS is dependent on velocity. The faster an object moves the more rotation is required to stabilize it. Which is exactly what happens when a bullet travels faster. The rotational velocity increases. The amount of turns per inch are the same; However, the number of rotations per second have increased. So, since the RPS have increased or decreased as needed with velocity, all is fine.
There is a differnce in twist rates for Handguns and rifles. Rifles, which are more inherently accurate, use the twist for accuracy. Hanguns use it for stability within a smaller distance, because they are not as accurate. So don't get caught up in apples and oranges argument on that.
Now, as far as the formula:
Dr Greenhill was a mathematician who came up with this formula, which is still used. It has to be accurate or firearms manufacturers would have abandoned it long ago. Also, this is a rule of thumb. It gets you into the ballpark. Actually, it gets you into the infield. Now, a munitions manufacturer, like Hornady or Remington would use the Miller Test, but we don't need to get that far down into the weeds. The numbers I gave are correct. One can argue over a few inches per twist (1:70 vs 1:72), but this is essentially correct.
https://en.wikipedia.org/wiki/Alfred_George_Greenhill
There is also the Miller Test Rule; However, since we are dealing with lead only, Greenhill's formula works great and it is pretty accurate. Miller deals with alloys and copper jackets, so bullet weight is used as well as mass. (Mass is density within a given volume, where weight is independent of volume.) Since lead's weight and mass are consistant, there is no need to deal with any of this.
If you worked out the formula both ways, with our larger bores, you come up within a fraction of an inch. The difference really shows up with small calibers with high velicity. Also, note Greenhill uses a standard velocity index of 150 for lower velocities (under 2,800' per second) whereas Miller is precise .
https://en.wikipedia.org/wiki/Miller_twist_rule
Barrel Rifling 101: Types, Twist Rates, and More
https://gununiversity.com/barrel-rifling-101/