Lessons Learned from Ballistic Coefficient Testing
Much has been written in previous editions
of Sierras Reloading Manuals about our BC measurements. We
now have more than 30 years of experience in measuring BC values
for Sierras line of sporting bullets, as well as some bullets
from other manufacturers, and we have learned a great deal. Our
observations and lessons learned through this experience are enumerated
and summarized below.
1. Ballistic coefficients must be measured
by firing tests. We have tried to
determine BC values by the method of Coxe and Beugless. We also
have tried to determine BC values using bullets of similar shapes
to scale the values based on bullet weights and diameters. But we
have never been successful in accurately predicting BC values, or
determining these values by any method other than firing tests.
2. The ballistic coefficient of each bullet
changes with velocity of the bullet as it flies. The
ballistic coefficient of a bullet is not constant with bullet velocity.
The reason that the BC changes with velocity is that the standard
drag function (the G1 drag function) does not characterize the aerodynamic
drag on any sporting bullet throughout the full range of its velocity
from the gun muzzle to impact. When a bullet is fired with a supersonic
muzzle velocity, as its velocity falls there can be a gradual change
in ballistic coefficient until the bullet reaches a velocity near
1600 fps (which is in the upper transonic velocity region). When
the bullet velocity falls below 1600 fps, radical changes in ballistic
coefficient begin to occur. In the next subsection, we will show
some examples of this phenomenon for both rifle and handgun bullets.
When the bullet velocity is greater than
1600 fps, the G1 drag function is a reasonable model from which to
compute the aerodynamic drag on a bullet. The gradual changes in BC
value with velocity can be handled in trajectory calculations by adjusting
the BC values used in those calculations by changing
the BC stepwise as the bullet traverses four or five velocity regions.
The trajectory will start with the bullet velocity in one of those
velocity regions. As the bullet velocity decreases and crosses the
boundary between that initial velocity region and the next lower region,
the BC is changed to the value corresponding to the next lower region.
This process is repeated as the bullet velocity falls through successively
lower velocity regions.
When the bullet velocity is less than
1600 fps, the G1 drag function just does not characterize the aerodynamic
drag on the bullet. This causes the BC values to vary widely as
the bullet velocity falls through the speed of sound (about 1120
fps) and to lower subsonic velocities. The step change method of
adjusting BC values is, at best, a crude approximation. This situation
is mitigated somewhat by the fact that aerodynamic drag on a bullet
diminishes dramatically in the lower transonic and subsonic velocity
regions. Consequently, the effect of large ballistic coefficient
errors on bullet trajectories is much less than when the bullet
velocities are above 1600 fps. For handgun bullet trajectories,
the effect is also lessened by the fact that ranges to the targets
or the game animals are considerably shorter than for rifles. But
at the present time, accurate long-range trajectories simply cannot
be calculated for bullets that travel at lower transonic and subsonic
velocities. This affects the ballistics of rifle cartridges such
as the 30-30 Winchester, 35 Remington, 444 Marlin, 45-70, and the
Whisper class of cartridges, as well as all handgun
cartridges chambered in rifles.
This is an area of continuing research
for these authors. Ballistic coefficient data have been gathered
for a variety of rifle and handgun bullets at transonic and subsonic
velocities. Investigations are under way to find modifications to
the G1 drag function at velocities below 1600 fps that will enable
ballistic coefficients to remain reasonably constant in this velocity
region. We hope to be able to report successfully on this research
effort at a later date.
3. The G1 drag function is the best standard
drag model to use. We have tested
several drag functions (G1 for sporting bullets; GL for lead bullets;
G5 for boat tail bullets; and G6 for flat base, sharp pointed, fully
jacketed bullets). For each drag function we have measured BC values
referenced to that function and observed how those BC values change
with bullet velocity. We have chosen G1 because the changes in BC
values with bullet velocity are least, and because there is a vast
database in the literature on BC values referenced to the G1 standard.
Also, to our knowledge all projectile manufacturers refer their
published BC values to the G1 drag function, which facilitates comparisons
among bullets of different calibers, weights, shapes and manufacturers.
4. Any of the firing test methods measures
a ballistic coefficient of the bullet as it flies through the air,
including effects imparted by the gun, the cartridge, and firing
point environmental conditions, as well as imperfections in the
bullet. Theoretically, the BC of a bullet depends only on its weight,
caliber and shape. But in a practical sense, the measured BC of
a bullet also depends on many other effects.
The gun can affect the measured BC value
in two important ways: spin stabilization and tipoff moments. A
bullet is gyroscopically stabilized by its spin, which is imparted
by the rifling in the barrel. If a bullet is perfectly stabilized
by its spin, then its longitudinal axis (which is also its spin
axis) is almost perfectly aligned with its velocity vector. If a
bullet is not perfectly stabilized (which is usually the case),
the bullet may not be tumbling, but its point undergoes a precessional
rotation as it flies. In previous editions of Sierras Reloading
Manuals we have described this precessional rotation and have called
it coning motion to aid in mental visualization of the
motion. As the bullet flies, the point rotates in a circular arc
around the direction of the velocity vector. Coning motion results
in increased drag on the bullet, and any firing test method then
yields an effective BC value for the bullet that is lower than the
theoretical value. The rifling twist rate in the gun barrel and
the muzzle velocity together control the spin rate of the bullet,
and therefore control its degree of stability.
When a bullet exits the barrel, it generally
has a small angular misalignment, which ballisticians call yaw.
Yaw is caused by tipoff moments of torque applied to the bullet
by powder gases exiting the barrel nonsymmetrically around the bullet,
or by barrel whip or vibrations. This angular misalignment will
cause coning as the bullet begins to fly downrange. Coning can also
be caused by an abrupt exit of the bullet from the barrel into a
crosswind, although BC measurements should never be attempted when
winds exist at the firing point.
The cartridge used in the firing tests
affects the measured BC values mainly through the muzzle velocity
it produces. As noted above, muzzle velocity combines with the twist
rate in the rifling to produce the bullet spin rate, which in turn
controls stability. In addition, BC values change with the instantaneous
velocity of the bullet, and so the muzzle velocity directly affects
the measured BC value of the bullet. For example, a 180 grain 30
caliber bullet can be fired at a much higher muzzle velocity in
the 300 Winchester Magnum than in a 308 Winchester cartridge. The
same is true for a 240 grain 44 caliber bullet from a 44 Magnum
compared to a 44 Special. So, the measured BC values can be expected
to be different just because of the different starting velocities.
Altitude and atmospheric conditions at
the firing point affect the mass density of the air through which
the bullet flies, in turn affecting aerodynamic drag on the bullet.
Measured values of BC will depend on the actual conditions at the
firing point, unless special pains are taken to convert those measurements
to sea level altitude and standard atmospheric conditions at sea
level. Unless this is done, the BC of one bullet cannot be compared
to the BC of another, because the test conditions may be different.
Measurements of BC values must then be reduced to sea level altitude
and standard atmospheric conditions at sea level. Using Sierras
exterior ballistics software program Infinity in the procedures
described in Section 2.3 will perform this reduction to sea level
standard conditions automatically. Otherwise, measured BC values
at nonstandard conditions must be reduced by manual calculations.
Reducing measured values to sea level standard conditions by manual
calculations has been described in preceding issues of Sierras
Reloading Manuals, and these procedures are available from Sierra
The coning motion caused by the initial
yaw of a bullet when it exits the muzzle generally damps out as
the bullet flies that is, it decreases in amplitude as the
bullet travels downrange. This is because the causes of initial
yaw are transient in nature. In other words, these causes occur
only at the muzzle and do not persist as the bullet flies. Also,
the aerodynamic forces caused by the coning motion are restoring
forces (tend to improve stability of the bullet) as long as the
amplitude of the coning motions is not large enough to cause loss
of stability (tumbling). This is the fundamental cause of many anecdotes
heard by these authors that my rifle shoots 1.5 MOA groups
at 100 yards, 0.8 MOA groups at 200 yards, and 0.6 MOA groups at
300 yards. However, some causes of coning motion are not transient
in nature, and can cause sustained coning motions throughout the
flight of the bullet. Any imperfection in bullet structure leading
to a small center of gravity offset from the bullet longitudinal
axis can cause sustained coning motions of the bullet as it flies.
Also, any small aberrations in bullet shape, such as a small imperfection
in point shape or tail shape, can cause sustained coning motions
as the bullet flies. This a very strong reason to shoot bullets
of high manufacturing quality.