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Bullet Stability – Part 2; RPM, Wind Drift Calculation & Gyroscopic Precession Equation

Excessive twist can be detrimental to accuracy and bullet integrity. The 40-grain bullet for the 22 Hornet is a light, thin jacketed bullet intended to be effective on varmints below about 2000 fps but will disintegrate at velocity of 3000+ fps and high spin rates. If the bullet is over stabilized the point will not follow the trajectory but pitch up offering a sidewise profile to the trajectory. Too low of a twist rate will result in excessive yaw also destroying accuracy and range potential.

Bullet RPM

The formula for rpm of the bullet is:
Where:
V = Muzzle Velocity
RPM = Bullet RPM
TR = Twist Rate
RPM = (V ∙ 720)/T_R or RPM = V ∙ (12/ TR) ∙ 60
720 is a factor converting 1:12 and seconds to revolutions per second.
A 1:12 twist would give 180,000 rpm at a muzzle velocity of 3000 fps. Conversely a 1:8 twist at 3000 fps would be 270,000 rpm. For reference a small block 350 cu. in. Chevy built full race for the drags may survive at 10,000 rpm while most engines will go no more than about 6000 rpm stock. Turbine engines hit 15,000 rpm. As can be seen bullets are tough.

Bullet Spin Drift

It is the spinning of the bullet that causes the bullet to drift in the direction of spin. When the bullet leaves the barrel, it experiences a wobble due to gyroscopic precession. When this wobbling dampens out the bullet assumes Yaw of Repose or equilibrium yaw, spin-wards. The Yaw of Repose is usually less than a half of a degree (0.5 degrees). The bullets axis no longer follows the trajectory and is pointed slightly to the right (right hand spin, most US manufacturers us RH Spin) and pointing up slightly, skidding the bullet to the right. This causes the bullet to move to the right over longer ranges. A 1:12 twist on a .308 bullet of 175 grains would drift to the right about 1 ½ inches at 500 yards and 9 inches out to a 1000-yards. For most hunters, spin drift is inconsequential as most shots are taken under 500 yards. But for the sniper or 1000-yard bench rest competitor it is of concern and must be compensated for. Wind causes two things wind drift with the bullet being pushed in the direction of the wind. Military use a drift chart for a 10-mph wind. A 7.62 NATO, 175 grain Match bullet at 2600 fps.

Bullet Wind Drift Calculator

Correction factor for wind direction. must also be considered. So, 22 inches at 500 yards, but only a 5-mph wind, drop to 11 inches drift. Coming from about your 4.5-5 O’clock position you take 75% of 11 inches or about 8.25 inches. At 500 yards 1 MOA is 5 inches so you would move about 6 clicks on a ¼ MOA scope. Wind does not react directly with the bullets side profile, what happens is that the bullets drag makes the projectile turn into the wind, kind of like a weather vane, keeps the center of pressure on or near the nose. The nose in pushed into the wind while the base is down wind the drag is acting on the bullet in a nose to tail direction.

Gyroscopic Precession Equation

The second effect is gyroscopic precession. A force applied pushes the object in a direction 90 degrees from the force in the direction of the rotation. A bullet with RH twist and a cross wind from the right will then tend to push the bullet down, a RH twist with a wind from the left will tend to raise or lift the bullet. As to the extent of these forces influence only becomes apparent over long ranges and are only a concern beyond 500 yards. However, keep in mind that the 1000-yard group size record is 1.068 inches, that is phenomenal at less than a tenth of a minute of angle.