The only time you are really going to see a difference in accuracy because of bullet yaw is when the bullet passes through the transonic state and in most cases, that is well beyond a 1,000 yards in most cases.
Not exactly. If a bullet’s stability is insufficient to damp the limit cycle yaw, drag increases and the bullet’s sensitivity to wind and air currents increases, which can degrade accuracy even before the bullet reaches the transonic range. Of course, non-zero limit cycle yaw does also decrease dynamic stability as the bullet passes through the transonic zone, as well. And transonic can occur even at 800 yards or closer with common .308 and .223 loads.
Good discussion here. One aspect of bullet stability affecting dispersion (increase in group size) that I haven’t seen mentioned yet is bullet concentricity and imbalance. Depending on other sources of dispersion, this may get “lost in the noise”, but dispersion at the muzzle due to bullet imbalance is proportional to rotational speed, the degree of imbalance of the bullet, and at distance this dispersion becomes proportional to flight time. While dispersion due to parallax and other aiming error is linear with distance, dispersion due to bullet imbalance is exponential with distance. And increased stability increases this dispersion.
Dispersion at long distance is really the net effect of multiple sources of dispersion, some of which offset each other. Increased stability can increase group size due to bullet imbalance, but decrease group size due to reduced drag, wind drift, velocity variation, and dynamic destabilization as the bullet goes through the transonic range. Whether increased stability will lead to larger or smaller groups at long distance partly depends on how concentric the bullets are, how much the the BC changes with increased stability, how much wind variation there is, how much muzzle velocity variation there is between shots, and how the bullet behaves in the transonic regime.
Now in response to the OP, the first part of the question deals with how long it takes for a bullet to stabilize. There are two components of gyroscopic stability, nutation and precession. Nutation is fast and small circular motion, precession is slower and larger. Together they make up what is known as the epicyclic motion that the bullet’s tip traces out (Google it for some decent visualizations), and result in less stability than a bullet with no epicyclic motion. Bryan Litz has done some modelling and testing, and has found that nutation typically damps out by 100 yards, but precession can persist much further, resulting in the limit cycle yaw.
