Thanks for putting all that in one place.
Welcome to the forum.
No, it's not so simple as you suggested. As the bullet goes slower the drag forces trying to turn if off course are also lessened so that less gyroscopic spin is required and the twist, as you hypothesized it, is still likely to be faster than required.
The Greenhill forumla was developed by George Greenhill for 19th century artillery shells. It happens to work OK for a range of modern supersonic rifle bullets as well. However, you can do better with calculations based on the late Robert McCoy's book, Modern Exterior Ballistics. These are available in free online calculators into which you just plug the numbers. They are at the JBM calculator web site
. One of McCoys colleagues, Don Miller, has an updated version of the Greenhill formula that adds velocity, weight, temperature and air pressure into the equation. This calculates the gyroscopic stability factor, s
is a number that equals 1 when the bullet is on the ragged edge of instability. Under 1, and the bullet tumbles, spins off in arcs, hits the target sideways (keyholes) and otherwise makes general mayhem. Above 1, the bullet is stable, but if it is too close to 1 it won't settle well in its flight bath and its accuracy won't usually be best. Harold Vaughn thinks s
=1.4 is about ideal. Don Miller thinks s
=1.5 is about ideal. Pretty close to one another.
If you spin the bullet still faster than is required for s
gets larger. This exaggerates errors in the distribution of mass which cause wobble. But modern bullets are made pretty well, and you usually have to spin them awfully fast to get into trouble with so-called "overstabilization". The military usually sets twist so s
=2 or a bit more at standard meteorological conditions. This ensures that in extremely dense atmosphere, such as antarctic temperatures, the s
still won't drop below 1. Different conditions will change its gyroscopic stability factor, however.
I have an Excel file I put together that uses Don Miller's formula that you can download free for use at my file repository