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That sideforce is what rotates the bullet about its CG to align with the Relative Wind the moment it leaves the barrel.
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Sierra has a great explanation of what is going on to include measured results. Just like any aerial vehicle a bullet oscillates as it seeks equilibrium. Those oscillations are minor to the outcome.
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When a bullet exits the muzzle of a gun, it immediately begins some angular pitching and yawing motions which have several possible causes including the crosswind. These angular motions are small, cyclical, and transient. They typically start out with amplitudes of a degree or so, and damp out, or at least damp to some very small residual values, after the bullet travels a relatively short distance. From our experience measuring ballistic coefficients, these motions damp within 100 yards or less of bullet travel downrange. Throughout the trajectory, including the initial transient period, the bullet has an “average” angular orientation which aligns the longitudinal axis almost exactly with Vbullet relative to the air. In this orientation the principal aerodynamic force on the bullet is drag, which acts in a direction opposite to Vbullet relative to the air. The side forces on the bullet are essentially nulled in this “average” angular orientation.
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The bullet does not feel the wind. It rotates about the CG upon muzzle exist during its transition to exterior ballistics and becomes a creature of the air moving with but not feeling the movement of that volume of air.