**2.3.1.2
Important Precautions and Points to Consider**
There are several important precautions
and points to consider when measuring ballistic coefficients by
this method.

1. Errors in the measurements. There
are many sources of errors that can affect BC measurements. They
can be separated into two categories: random errors and systematic
errors. A random error is an error that may occur in any test round,
but that changes in magnitude or direction (i.e., an erroneous increase
or decrease in BC value) from one test round to the next. Typical
sources of random errors are round-to-round variations in bullet
weight, jacket thickness, core homogeneity, etc. A property of random
errors is that they can be effectively removed by averaging the
BC measurements of several test rounds. We typically fire at least
10 test rounds for each bullet type at each velocity level that
we choose for measuring the BC value.

The other category of errors is systematic
errors. A systematic error is a consistent error that occurs in
every test round fired and is nearly the same magnitude and always
of the same direction (i.e., always an erroneous increase or always
an erroneous decrease in BC value) from one round to the next. Systematic
errors are very bad, and every effort must be made to eliminate
their sources.

The most important sources of systematic
errors are errors in the measured distances between chronograph
screens and in the measured range distance from the initial velocity
chronograph to the final velocity chronograph. For example, suppose
the separation distance between screens 1 and 2 in Figure 2.3-1
is supposed to be 10.0 feet. However, when we set up the screens,
we make a measurement error of 1/16 inch, so that the true distance
is 10.0 feet plus 1/16 inch (10.0052 ft). This error is consistent
for every round fired, so that it is a systematic error source for
the BC value.

Consider round 1 in Table 2.3-1. The chronograph
really measures a travel time between screens 1 and 2, and then
divides the erroneous distance 10.0 feet by this travel time to
give an initial velocity of 2742 fps, which would contain a systematic
velocity error. Then, the travel time between screens must have
been 3647 microseconds (that is, 10.0 ft divided by 2742 fps). If
the true distance of 10.0052 feet had been divided by this travel
time, the true initial velocity should have been 2743.4 fps. Now,
most chronographs do not read to tenths of a fps; they round off
to the nearest whole fps. So our initial velocity chronograph should
have indicated a velocity of 2743 fps, instead of 2742 fps. Using
Infinity, it is easy to verify that the BC value for round 1 should
then have been 0.4560 for this example, instead of 0.4583. [Note
that the roundoff imprecision in the chronographed velocity results
in a random error, not a systematic error, in BC value. This error
can be effectively removed by averaging over several test rounds.]
This example illustrates that a measurement error of about 1 part
in 2000 in the separation distance between screens 1 and 2 will
cause a systematic error in BC value of about 1 part in 200. That
is, the small error in separation distance causes an error in BC
value that is ten times larger – a very high sensitivity. A
similar analysis will show that a measurement error of 1 part in
2000 in the separation distance between screens 3 and 4 of the final
velocity chronograph (see Figure 2.3-1) will cause another systematic
error of about 1 part in 200 in the measured BC value. Again, this
is a very high error sensitivity. The multiplication factor of 10
in these error sensitivities applies to this particular example.
In another situation, the error sensitivities would still be high,
but the factor of 10 might change upward or downward.

This high sensitivity of systematic errors
in BC to errors in the separation distances between the screens
of the chronographs is primarily why we use a separation distance
of at least 10 feet between screens in Sierra’s test range.
Chronographs are available with screen separation distances of 1
or 2 feet. These chronographs are convenient because of their light
weight and portability, and they are adequate for the purposes of
load development where velocity measurement errors of 10 or 20 fps
are tolerable. However to measure ballistic coefficients, systematic
errors must be no more than 1 part in 2000, and hopefully less than
that. For a screen separation distance of 1.0 foot, the maximum
separation distance error would then need to be no more than 0.006
inch. Mechanical tolerances in mounting the screens on their supporting
structure and positioning the active sensor within each screen are
likely to be greater than this number. So, these chronographs should
never be used for BC measurements, despite their convenience.

The situation is not as critical for the
separation distance between the two chronographs. If somehow we
made an error of one part in 2000 in measuring the 103 yard separation
distance (i.e., an error of about 2 inches), this error source would
contribute a systematic error of about 1 part in 2000 in the BC
value. This is a one-to-one error sensitivity, but it shows that
we must carefully measure the range separation distance between
the two chronographs. We cannot afford an error of a yard, or even
a foot.

2. The measured BC value must be calculated
for each round individually, and then statistical analysis can be
applied to the results. We need to
obtain an average BC value from our measurements, to reduce or eliminate
random errors, and to obtain a proper value for trajectory computations.
To do this, we must calculate
the BC of each test round individually, and then average the resulting
values to obtain the average BC for the bullet type at each velocity
level chosen for the measurements. We cannot
first average all the initial velocity
values, then average all the final velocity values, and then calculate
a BC value from these average velocity values. This approach would
lead to an erroneous average BC value, because of the laws of mathematical
statistics. Also, there is useful information in the standard deviation
and extreme spread of the individual BC values. These statistical
parameters yield some knowledge of the stability of the bullets
as they fly, as well as the quality provided by the manufacturing
process.

3. The BC value for a bullet is likely
to vary with bullet velocity as the bullet flies. We
have made this point in all of the previous editions of Sierra’s
Reloading Manuals. The reason is that the standard drag model (called
the G1 drag model) is not a perfect representation of the aerodynamic
drag on sporting bullets over the full range of bullet velocities.
Therefore, Sierra follows a policy of measuring the BC of each bullet
at several different velocity levels and then publishing BC values
for each bullet within up to five velocity ranges that together
span the total velocity range for the bullet. A glance at the table
of BC values for Sierra bullets elsewhere in this manual will illustrate
how these values are published. Sierra’s Infinity
exterior ballistics program uses
all five BC values for each bullet to compute trajectories for any
Sierra bullet.

4. The measured BC value is valid for
a certain range of bullet velocity. When
the range distance between the two chronographs (see Figure 2.3-1)
is relatively short — like 100 yds for rifle bullets or 50
yds for handgun bullets — the difference between the initial
velocity and final velocity of each round should be no more than
10 percent of the initial velocity. For example, for round 1 in
Table 2.3-1, the difference between the initial velocity (2742 fps)
and the final velocity (2549 fps) is 193 fps, which is about 7 percent
of the initial velocity. In this situation the BC value derived
for each round characterizes the bullet performance in the range
between the initial and final velocities. An alternative point of
view is that the BC value is valid for a velocity that is midway
between the initial and final velocity values. Thus, for round 1
in Table 2.3-1 the BC value 0.4583 is considered valid for a velocity
of 2646 fps. This point of view is justified because the difference
between the initial and final velocities is a small fraction of
the initial velocity. We use this approach when we measure BC values.

Another situation that sometimes arises
is that a single BC value is needed for a certain hunting or target
shooting situation. For example, if you are a hunter and use a particular
cartridge load for certain game, and you use a bullet for which
the BC is not known, you may need a single value of BC valid for
range distances out to a maximum of 400 yds. You can use the procedure
explained above to measure an effective BC by placing the initial
velocity chronograph near the muzzle of your rifle and the final
velocity chronograph 400 yds downrange (carefully measured). This
BC value will serve for all ballistic calculations, such as finding
effects of changing altitude, changing weather, winds, uphill/downhill
shooting, etc. However, you must think of this BC as valid for (a)
the muzzle velocity of your cartridge and (b) a range distance of
no more than 400 yards. If you change either of these parameters,
the BC value may not be valid for accurate trajectory calculations.

5. BC values determined by using Sierra’s
Infinity software using the process described are referenced to
sea level standard atmospheric conditions. We have made the point
in previous editions of the Sierra Reloading Manuals that measured
BC values must be reduced to sea level altitude and standard atmospheric
conditions at sea level, and we explained how to perform the necessary
calculations. This is effectively done in the Sierra Infinity program
(and we believe it is done also in other ballistic software programs).
When using Infinity, simply enter the altitude, temperature, barometric
pressure, and relative humidity at the firing point when beginning
the computations. The BC used by Infinity for each round fired then
is assumed to be the value for sea level standard conditions. Thus
when the calculated velocity or time of flight values equal the
measured values (after being corrected for the defined altitude,
pressure, etc. during computations) the input BC is referenced to
sea-level standard atmospheric conditions. Note that the barometric
pressure entered into Infinity is from a barometer at the range
or a local weather report. It is NOT the absolute pressure for the
range altitude. The absolute pressure necessary for trajectory computations
is calculated within Infinity from the altitude and atmospheric
data for the firing point.

6. Protect the chronographs from stray
bullets. This is a practical consideration
when measuring ballistic coefficients. It is extremely embarrassing
(especially when the equipment does not belong to you) and very
expensive when a stray bullet destroys a screen or an electronics
enclosure. The final velocity chronograph is especially vulnerable
because it is far from the muzzle. We use a paper target at the
downrange location before the final velocity chronograph is moved
into position, and fire several shots to make sure the rifle is
properly sighted to put bullets through the “window” in
the screen. Then, the final velocity chronograph is moved into position
for the firing tests. At Sierra’s test range, armor plates
also are used to protect the structure and electronics of both chronographs.
Even though all firing is done from machine rests, these plates
bear the scars of some accidental stray bullets.