How does Sg affect terminal performance?

[Western Living]

I've read some claims that Sg affects terminal performance. For example, Hammer Bullets claims:

"Each of our bullets has a required minimum twist rate that is calculated at sea level using the Miller Twist Formula. We use sea level as the standard to ensure that there is enough rpm’s for proper terminal performance. While the Miller Formula calculates stability for ballistic flight, we are most concerned with hunting performance and ensuring that there is enough stability for proper terminal performance. The required minimum twist rate is based on a gyroscopic stability factor (SG) of 1.5. An SG of 1.5 or higher is needed to achieve full bc value and expected terminal ballistics. In our impact testing for terminal performance, we have found that marginal SG (less than 1.5sg calculated at sea level) hinders a bullets ability to stay on track and open reliably for proper terminal performance."

In short, they're claiming their bullets may be stable in flight with a Miller-formula Sg of 1.5 at lower atmospheric pressures (high altitude, warmer temps), but unless the Sg would be 1.5 at sea-level, then the bullet may not have enough stability for terminal performance even at lower pressures.

I shoot at high altitude. The last mule deer was taken at 9200 feet. Achieving a Miller-formula Sg of 1.5 and in-flight stability is easier in these conditions, and I can use longer bullets than I could if I were at sea-level.

If the Miller formula defines what's required for in-flight stability, how can we quantify what's required for terminal performance? At sea-level, a bullet that requires 1:8 twist for a 1.5 Sg might only require a 1:10 twist at 9000 feet for the same Sg. But what will happen to terminal performance in game?

link to Miller calculator: https://www.jbmballistics.com/cgi-bin/jbmstab-5.1.cgi
link to pressure calc: https://www.omnicalculator.com/physics/air-pressure-at-altitude

 

[DocUSMCRetired]

For hunting game you should be looking at the optimal game weight formula.
(V^3*W^2)*1.5*(10^-12) = Optimal Game Weight in lbs
V is velocity in FPS
W is weight of the bullet in grains.

Example. .308 175gr at 2550 fps

(2550^3*175^2)*1.5*(10^-12) = 762lbs

But you need to account for the velocity at the animal not at the muzzle. So to correct for this lets say we are now firing a .308 185gr Juggernaut @ 2550fps but the conditions are 20deg F, Pressure 29.41, Humidity 30% etc. and the Target is at 600 yards.

In this case the velocity would be 1652fps and KE is 1122ft-lbs. So: (1652^3*185^2)*1.5*(10^-12) = 231lbs.

So you need to account for the actual velocity at the target, not the muzzle.

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As for why stability and an SG is important is because below 1.5 SG you lose performance. We can describe this loss as a known factor in BC which results in more drag. This in turn means the bullet is slowing faster than the shooter expects which will effect the impact kinetic energy, as well as the predicted firing solution (possible miss or wounding shot). So you want to keep the SG above 1.5 to ensure the best flight dynamics.

Lastly I will add that rotational degradation is far slower than velocity degradation. Meaning if you start at say SG 1.7 you should maintain Optimal performance as the spin rate won't be slowing as fast as the forward velocity.