Quoted: What is the lightest bullet that will stabilize properly through a 14"-16" 1/9 twist barrel (for .224" bullets)? 20-30 gr,30-40 gr, 45 gr?
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What do you mean "properly stabilize"? Longer bullets fail to be stabilized in slow twists.... not the other way around. The other direction, too light of a bullet, is affect by what some call "overstabilization" In my experience, that is pretty much a myth. You didnt mention the caliber, so I am assuming you mean .223.
Velocity is a factor in this, as well, so it isn't just bullet weight/length. My experience has been, 1/9 has no issue shooting ANY commercial .223 load (under 70 grains), the lightest of which I have seen is the 40gr VMAX and Noslers.
If the bullet doesnt fly apart, it will likely shoot well. I have shot 45 grainers in my 1:8 twist and it groups them VERY well. I have read that the super thin jacketed 40gr noslers will fly apart when they are fired in a 1:7, but havent seen it.
I think this is simply a function of how thin the jacket is, and how fast you push a light projectile. In a 1:9, I imagine you could go even lihgter than 40gr if you wanted to.... but I havent heard of anyone using a lighter bullet than that in .223 rem.