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Long ranges

Up to this point, we have only considered bullets at close distances from
the muzzle. We have met well-designed military projectiles and over-stabilized
pistol and revolver bullets, but all of them showed dynamic stability.
In other words, the maximum yaw angle, which occurs close to the muzzle,
is damped out as the bullet moves on. After a traveling distance of a few
thousand calibers, depending on the damping rate, the transient yaw angle
practically approaches zero.
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The yaw of repose

Now let us consider a stable bullet, which has traveled a considerably
longer distance. If the transient yaw has been damped out for a dynamically
stable spin-stabilized projectile, does that mean that the bullet's longitudinal
axis *exactly* coincides with the direction of movement of the CG?
It can be found from a mathematical treatment that the bullet's longitudinal
axis and the direction of the velocity of the CG deviate by a small angle,
which is said to be the* ***equilibrium yaw** or the** yaw
of repose **.
For right-handed spin bullets, the bullet's axis of symmetry generally
points to the right and a little bit upward with respect to the direction
of the velocity vector- indicating the direction into which the CG moves
- , just as shown in the figure .

As an effect of this small inclination, there is a continuous air stream,
which tends to deflect the bullet to the right. Thus the occurrence of
the yaw of repose is the reason for bullet drift to the right (for right-handed
spin) or to the left (for left-handed spin).

Usually, the yaw of repose is a very small angle and measures only fractions
of a degree. The figure
shows the variation of the yaw of repose angle along the trajectory for
a 7.62 x 51 NATO M80 bullet fired at 32°. Although, in this example, the
yaw of repose never exceeds half a degree, the resulting side drift at
impact almost amounts to 100 yards.