Is a work of art, for its time. The main limitation to Greenhill is his work was all done with black powder weapons - cannons in fact. This limits the velocity range to around 1800 to 2100 fps. The second limitation is he only had pretty much cylindrical with rounded or pointy end projectiles.
The limitation doesn't make it wrong, just limited. The Greenhill formula is still a pretty good rough guide to twist rate need. However, I've never been able to discover if the formula gives the minimum twist needed for projectile stability or the optimum twist for projectile stability. My guess, based on using the formula and my own experience, is it is the minimum rate. (Participants are free to disagree.)
Concerning the velocity factor limitation. Greenhill only used two constants in regard to velocity; one for less than 1800 fps and one for over 1800 fps. I rather think that constant - actually a modifier - changes with greater velocity. As velocity increases, the actual spin of the projectile increases in terms of RPM, generating greater stability. Simultaneously, atmospheric resistance increases and therefore a tendency to yaw in flight, generating lesser stability. The lessened stability outweighs the greater stability, so the twist rate must be altered. However, not being independently wealthy or having a government grant, I cannot currently explore the mathematics involved.
Also missing from the equation is the concept of ballistic coefficient. In Greenhill's day, all projectiles were either round balls, or a cylindrical body with a more or less pointy front. Spitzer, long radius ogive and boat-tail bullets change the equation. Again, I cannot currently explore this phenomenon.
Still, Greenhill is a good place to start. It is in fact, the best starting place we have.
I do know this much:
The M14 has a 20 inch barrel and delivers a pretty good velocity for general use. I would consider 20 inches to be the minimum for a
general or sporting use rifle.
Most of the .30 caliber rifles run about a 1 in 10 twist. For most purposes, that's a bit over spun.
The longer (heavier, usually) the bullet, the more spin is required.
A lot of overspin is better than just a little underspin. If one errors in choosing a twist rate, err on the faster twist side.
There! The benefits of my vast knowledge and experience.
You're on your own, bunky.