Can someone explain this ?

[big5ifty]

Two screenshots of the Berger stability calculator.

First is typical for a 300 Blackout.

Second is typical for a 300 Win Mag.

Twist rate differs, as it would in reality.

Why is the slower velocity, slower RPM much more stable than the much higher velocity, much higher RPM ?

RPM numbers superimposed in each screenshot.

[janfred]

See what the stability is like at 1,200 fps.

[Ds J]

It probably has to do with the forces at work.

I don't know math well, and understand less of engineering. What I have seen is that sometimes, a second force starts to build up which influences overall performance.

When drilling, one experiences a secondary vibration, especially when drilling masonry. This tends to lessen or even go away when drilling slower.

A similar interweaving of forces might influence the bullet?

[big5ifty]

See what the stability is like at 1,200 fps.

Calculated stability for the 8 twist just goes up with velocity for that configuration.

For the 14 twist it just decreases with decreasing velocity.

[janfred]

You cannot look at just the RPM. You have to take bullet velocity into account as well as the velocity is what governs the actual nose drag force. The higher the force the more RPM you need all else being equal.

Also note in your examples going from a 14 twist to an 8 twist is around 95% increase in RPM at a given velocity.

When supersonic, the nose drag increases non-linear as the velocity increases proportional to the bullet's drag curve. The RPM increase is linear, that is why you can increase the stability factor slightly by just upping the speed. The caveat being that you need a large increase in velocity for a small stability gain

[Tripodmvr]

The stability is largely affected by dividing with the square of the twist rate. Between 8 and 12 twist the ratio is 2.25(144/64) and accounts for the poor stability factor.

https://en.wikipedia.org/wiki/Miller_twist_rule

[Treeman]

"...............................The following formula is one recommended by Miller".
It is at this point that I got lost ?

[Tripodmvr]

Solving Miller's formula for s s gives the stability factor for a known bullet and twist rate:

In this formula values are divided by T = twist squared. The lower the twist rate the smaller the figure used. This is a similar phenomena as with bullet energy (where velocity squared is used), but now only in reverse.

[big5ifty]

I've been reading on how the math is derived, and the physical forces involved

Modern Exterior Ballistics - R.McCoy

and the way I understand it there is an overturning moment between the center of pressure and center of gravity, also influenced by the yaw angle. There is always a yaw angle, there is always a small degree of precession at the nose as the bullet flies.

The magnitude of the overturning moment is overcome by the bullet RPM at a given velocity, and the higher the velocity, the more RPM are required to keep the overturning force from causing the bullet to tumble.

This is why a  bullet travelling slow doesn't need as much twist as the same bullet travelling fast.

It also suggests that if a bullet has the center of pressure at the center of gravity, it can fly faster with a slower twist, so the closer the center of gravity is to the center of pressure, the less RPM is required to stabilise the flight.

[Treeman]

I've been reading on how the math is derived, and the physical forces involved

Modern Exterior Ballistics - R.McCoy

and the way I understand it there is an overturning moment between the center of pressure and center of gravity, also influenced by the yaw angle. There is always a yaw angle, there is always a small degree of precession at the nose as the bullet flies.

The magnitude of the overturning moment is overcome by the bullet RPM at a given velocity, and the higher the velocity, the more RPM are required to keep the overturning force from causing the bullet to tumble.

This is why a  bullet travelling slow doesn't need as much twist as the same bullet travelling fast.

It also suggests that if a bullet has the center of pressure at the center of gravity, it can fly faster with a slower twist, so the closer the center of gravity is to the center of pressure, the less RPM is required to stabilise the flight.

**********************
This I can understand.