Well, not really. If the bullet were entrained in the air mass, then spindrift couldn't happen in still air, but it does.
If you drive through a snow shower at a constant highway speed at night (headlights on) you will see the snow rushing at your windshield like a starfield on a Star Trek bridge viewscreen. If the wind starts blowing at a constant speed across the road, instead of the snow hitting your car on the side, you see it come toward your windshield from an angle. That angle is the direction of the intercept path snowflakes are coming along to your car. It is equal to the arctangent of the car speed divided into the crosswind speed. If your car is going 60 mph and the crosswind is 10 mph, the arctangent of 10/60 is 9.46°, so the snow will appear to be coming from 9.46° off of straight ahead. Moreover, the speed with which the snow comes at your car is the square root of the sum of the squares of the two velocities, or 60.83 mph, some of the speed coming from your car and some from the crosswind. The combined winds as a net angle and speed is called a wind vector.
Well, the same thing happens with air molecules and your bullet as did with the snowflakes and car. If your bullet is traveling 2000 mph (2933 fps) and the crosswind is 10 mph, the combined speed and angle are 2000.025 mph and 0.2865°. So the bullet sees a headwind of that slightly greater speed coming at it from that small angle off straight ahead. The force of that off-angle wind causes the bullet to precess around its center of gravity until it settles flying into the angled wind. So the bullet is now going downrange cocked at that small angle (gnoring the the yaw of repose), and with the angled air stream blowing over it from nose to tail. This means drag on the bullet is no longer straight back toward the rifle that fired it, but rather it is pulling back on the bullet at that small angle. This means drag not only slows the bullet down, but pulls it slightly to the side.
In the case of a crosswind that is faster than the bullet, the vector angle simply exceeds 45°.
In 1852 a French artillery officer named Isadore Didion published a coursebook on basic ballistics with a simple formula for calculating wind deflection. You calculate the time of flight the projectile would have in a vacuum, which is the range divided by the muzzle velocity. This is because a vacuum creates no drag and doesn't slow the projectile down. Then you subtract that number from the actual time of flight (found by multiple ballistic pendulum firings at multiple ranges back then). The difference in time represents the overall effect of drag as a function of time. If you multiply that time by the crosswind speed, you get the inches of deflection because the crosswind component of the wind vector has an effect proportional to overall drag since the vector combines the two winds.
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