Some Research on Bullet
Flight Path Dynamics
“Can the group MOA dispersion
decrease going down range?”
I finally had to re-read the
section in McCoy's book "Modern External Ballistics"
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
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
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).