Re: The science to twist rates
To the OP, there are many bullet twist calculators that are public access online... input the bullet details and it tells you the required twist or if you designate a twist it will tell you the stability factor. Just google it, there are more than a few.
Now for the others, MikeCr, its gets a bit more complicated than that...
You know the don miller type stability calculators are SIMPLIFIED stability calculators because its too hard to know or measure certain physical properties required for the proper unadulterated stability equations. The REAL UNSIMPLIFIED stability equations use the following;
axial and transverse moments of inertia (which is one of the difficult things to measure or calculate)
Overturning moment related to normal force, center of gravity and angle of attack or yaw (again difficult to measure/calc without a wind tunnel)
Transverse radii of gyration (another difficult one)
Crosssectional area or frontal area
diameter or caliber (perhaps these combine for your "displacement" mikeCr?)
air density
spin rate
velocity
mass
The miller stability type formulas make approximations and assumptions which are fairly accurate for our typical bullets we use today so that we dont have to know the difficult things outlined above. However, its not perfect and some things can vary quite considerably.
For example, if your comparing a bullet with a plastic tip or a large void behind the meplat jacket where there is no lead core present, this can change the transverse inertia moment and transverse radii of gyration quite considerably and therefore the approximation given by the miller formula, underestimates the stability by an appreciable margin.
Something else to consider with regard to the spin/velocity ratio increasing as a bullet flys downrange. This is true, and commonly a bullet gets more stable the further it flys... However, again it doesnt always hold true. One thing thats overlooked is whilst this is happening, the pitching or overturning moment INCREASES with decreasing velocity due to the center of pressure moving further forward with decreasing mach number. This offsets some, or in extreme cases all, of the stability increase from the spin/velocity ratio increasing downrange. The overturning moment is highest in the transonic region, where its overturning moment is usually about DOUBLE that of when the same bullet is flying at mach 2.5 or a typical rifle muzzle velocity. This is why many bullets destabilize in the transonic region, despite having a much higher static stability factor than when it left the muzzle! However it can happen before the transonic region, if the stability factor is marginal and/or the aerodynamic design of the bullet is condusive to a rapid rise in pitching moment with decreasing velocity.
