Some Research on Bullet Flight Path Dynamics

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“Can the group MOA dispersion decrease going down range?”

7/11/05

I finally had to re-read the section in McCoy's book "Modern External Ballistics"[1] to get to confirm this assertion that it is possible for a group size in terms of MOA to get smaller at longer ranges for some projectiles.

This is unquestionably true. I have observed this myself at the range, and Chapter 11, Section 4 discusses this clearly. They even do an analysis for a 168 grain SMK, 0.308 bullet. Here is a quick summary:

If the bullet yaws coming out of the muzzle, you can observe three distinct errors or deviations from the "perfect" trajectory. The first is "Aerodynamic Jump", which is a complicated way of saying that the bullet will go in the direction of the tip as it yaws at the exact moment of exit. This causes the majority of the deviation from the "perfect" path that we see. Just what causes the bullet to yaw at that exact moment is what I am most interested in studying, and is the essence of the research into the Acoustic Shock Wave theories.

The second error is a "Epicyclic Swerve", which is a fancy way of saying that the bullet chases its tip as it wobbles (precesses, like a top) as it flies along. This causes aerodynamic forces to make the bullet travel in a helical path around the now disturbed path (remember the Jump error!). For most small arms bullets, the damping forces on this wobble are very small, and in the case of the 168 grain SMK, are actually positive, meaning that the helix INCREASES in size as it goes down range. In other words, it doesn't go to sleep, it gets more awake! So, if the Swerve component is on the order of 0.25", it stays at this level, or gets slightly bigger as the bullet goes down range. If you keep the Jump error small then this is what you will observe, a 0.5" group at 100, and 0.5" at 200, etc. Here is where you can see that the MOA can actually decrease at longer ranges. The group size never decreases, but the dispersion in terms of MOA does. A subtle but important difference.

The third error aptly called "Drift", is a steady (and increasing with range) drift of the flight path to the left or the right as a result of gyroscopic precession from the aerodynamic force applied as the bullet drops. Even though the bullet is moving forward at over 2000 feet per second, it drops (accelerates downward) in exactly the same manner as if it were dropped  off the loading bench. As the bullet's downward velocity component increases, a small aerodynamic force is applied under the tip of the bullet, which tries to push the tip up. Since the bullet is spinning like a gyroscope (right hand spin for this example), this upward twist force or torque will result in the nose of the bullet yawing to the right. This yaw is called the "yaw of repose". This yaw in turn causes the bullet to steer a bit to the right (following the nose). The longer the bullet is in the air,  the more the downward velocity increases, which causes a continually increasing the yaw of repose, which makes the bullet drift to the right even faster. For our class of projectiles this drift to the right is quite small, on the order of 15 inches for a 0.308 caliber bullet at 1000 yards. It is also fairly predictable, and can be seen as a predictable bias to our long range POI.

So, we are left with an initial Jump that does most of the damage, and a helical Swerve component that comes along with an off-angle departure. The helix stays about the same as the bullet travels downrange, so the Jump is what we see as the major factor for group size dispersion. If we get the Jump down (excellent bullet balance, neck/case/bullet/throat alignment, excellent barrel, excellent crown), then we start to see the helical component. Some say that the "bullet goes to sleep" at longer ranges. It is actually that the Jump error accumulates as range increases, and swamps out the helical Swerve. The Swerve error is still there, you just can't see it as it is dominated by the initial Jump error.

Yep, it's true!

So, I can now say that the OBT theory clearly supports the prediction of the best time to leave the barrel so that the Jump (incidental yaw from barrel muzzle change in shape and rotational angle due to the shock wave strains) is minimized. The POI is still determined by the main vibration modes of the barrel, but the dispersion is all Jump. Minimize Jump, and the Swerve component is also minimized (assuming that the bullets are of high quality).