That's all fine and dandy and I'm sure you are absolutely correct and I mean no offense but I do not care in the least bit what any "calc" says as I have said time and again, It's a reference point, I'm done debating this with you as I know from previous engagements with you that you can spew facts and numbers all day long but I have yet to see you help anyone or answer the Op's original question ( Case in point, here we are again) I will tell you what I have figured out is folks like you are stuck in a box " What the numbers say rules" and while it works it's way to boring for me, anyone can do what your doing ( Hence the Needmoor fascination) It's really simple , I live on the borderline and your just a board, Have a good dayGyroscopic Stability is provided by the centripetal force of a given bullet construction as it turns -overtaking overturning moments caused by the drag a bullet experiences -forward of it's center of gravity. That's the moment(counter stability) arm length.
Drag loosely increases as a square of velocity, and even with aerodynamic attribute adjustments (drag coefficients), the drag is still increasing with velocity. This is increasing overturning forces.
But (as sometimes overly focused on), increased velocity is equaling higher RPMs. That is causing higher gyroscopic forces to counter drag induced overturning. For a dynamically stable bullet, and enough of this force/counter force balance, we get point forward results.
A common quantity of this drag to overcome is expressed in inches of displacement(here), and for example a bullet is described as needing one turn in 8 inches of displacement. That displacement is air at a standard density, which we're rarely at, so it is a relative displacement.
The quantity in focus is displacement (not RPMs) because it is displacement that varies.
Keep in mind this interaction. That all of this is locked together on muzzle release(the highest challenge to stability).
It's the reason why simply cranking up muzzle velocity does not proportionally crank up gyroscopic stability.
Credible stability calcs(which are not rules of thumb) are very complicated, and you just can't get around the truths they resolve.
With my earlier example, which you can of course run countless similar tests of your own to see, Sg barely climbs with increasing MV/RPMs.
It is so small as to be rationally dismissed as a viable stability solution for field situations.
So I want to circle back to varying displacement.
What happens when bullet velocity slows downrange(due to forward drag) while RPMs slow far less (due to less rotational drag)?
The answer is that Sg climbs.
As the bullet slows, it is displacing less air per turn of the bullet, and this increasing Sg is practically disconnected from RPMs, which are actually dropping(a little). So much for more RPMs meaning higher stability.
What matters is reaching that before a bullet would tumble. You need to get past immediate tumbling on muzzle release. Then you got it from there. I was able to test bullets barely stable from a 223 in 14tw once.
Here at sea level I developed a load with bullets calculated at barely stable, at normal summer temps.
The calcs told me that with only 20deg lower temps, that denser air, I would be technically unstable.
So I tested with this condition, shooting a paper plate at the end of my chrono screens, and sure enough, ~20deg changed round holes to bullet silhouettes. Again, nothing to do with RPMs.
I'm trying to point out that you cannot separate [displacement per turn], into merely [turn rate] to resolve this stuff.
If it were that easy, then long ago, stability requirements would have been expressed in [turn rate] alone.