Basics of Ballistics
Near-Zero and Far-Zero
A common misconception is that a bullet will rise for a while
after firing from a horizontal barrel. In fact, a bullet
fired from a horizontal barrel will fall
towards the earth at the same rate as a bullet dropped from the hand
at the instant of firing. The origin of the misconception is that in order
to have the bullet cross the line of sight downrange, the barrel and sights
must be misaligned such that the barrel is angled upwards relative to the
sights. As a result, the bullet is "lobbed" towards the target and crosses the
line of sight at two points, the near-zero and the far-zero.
This is illustrated by the following figure:
The angles in the figure have been grossly exaggerated for clarity.
It can be seen that the bullet is rising as it crosses the near-zero
and falling as it crosses the far-zero.
Unless you sight your rifle in at very short range,
it is likely that the x-ring of your target is at the far-zero of the
trajectory. Also illustrated are the differences between the line of
departure (which extends from the barrel), the line of sight (which
extends from the scope or other sighting apparatus), and the trajectory.
The WBC calculates the drop from line of sight based on a far
zero that you set equal to the distance at which you sight in the rifle.
The WBC will also tell you the corresponding near-zero.
Sight Height and Factory Ballistic Data
Because everyone may have a different far-zero setting
and their sights may be mounted at various heights above the barrel,
the most consistent way to tabulate the trajectory of a
projectile is to measure the amount of drop from the
line of departure at various ranges (true drop).
In practice, the true drop is of little use to the shooter since he or
she is concerned with the drop from the line of sight, the apparent drop.
As a result, ballistics tables generally assume a certain far-zero setting
and sight height and then tabulate the apparent
drop from the line of sight. You can determine the assumed far-zero setting
because the bullet drop will be zero at that range. However, not all tables,
including most of the tables I used to generate the graphs in
the Web Ballistics Library, mention the
assumed sight height. If that information was available when I graphed the
data, it was indicated as the bullet drop at a range of zero on
the graph. If the information was unavailable, the zero yard drop was set to
The Web Ballistics Computer allows you to specify a
sight height and adjusts the trajectory accordingly. In the case of
optical sights, the sight height is measured from the center of the bore
to the center of the objective (front) lens of the sight. Iron sights
are measured from the center of the bore to the top of the front sight.
Point Blank Diameter and Range
The difference between the line of sight and the path that the
bullet takes is constantly changing as the bullet moves downrange. However,
you may not care about the exact trajectory as long as the bullet strikes
close to the point of aim. The point-blank diameter defines what's close
and what's not. Different ballistics software packages use different
definitions of "point blank". My software defines the point blank diameter
as the farthest total distance the bullet can deviate from the point
of aim as it flies towards the target.
This is illustrated in the figure above as the
vertical line dropped from the high point of the trajectory.
The range at which the difference between
the high point and the apparent drop equal the point blank diameter is
the point blank range.
For instance, say you're hunting a deer and you know that
its vital area is about 5" across. You look up the ballistics for your
factory load and find that the bullet is 1.5" high at 100 yards and is
3.5" inches low at 250 yards. Since you know that the bullet will fall
within 5 inches of point of aim at any distance out to 250 yards, this is
defined to be the point blank range.
Note that the point blank range is not the distance at which the drop is 5
inches because the bullet is above the line of sight earlier in flight.
Mine is a conservative definition, allowing you to grossly misjudge the
range to the target and still put the bullet within the point blank diameter,
regardless of whether you shoot a bullet with a curved or flat trajectory.
For extremely curved trajectories, the bullet
may exceed the point blank diameter before it reaches the high point of
the trajectory, in which case the point blank range will be shorter than
the far zero. The Web Ballistics Computer can find the point blank range
regardless of the curvature of the trajectory.
It doesn't assume that you're aiming at the center of a "circle of uncertainty",
just that the bullet will strike within a given distance from the point of aim.
Beyond point blank range, you'll have to take into account the trajectory of
the bullet in order to hit the zone you've specified by "holding over"
the required amount.
The Web Ballistics Computer can account for the effects of
altitude and temperature on the flight of the bullet but it cannot
account for the fact that powder burns more slowly on cold days
or that your barrel is dirty. For this reason, it bears repeating that
you should test fire your rifle at various distances to determine its
performance (and yours) before a hunt.
Aerodynamic Drag and the Ballistic Coefficient
The aerodynamic drag that a bullet experiences depends heavily on
its velocity. If the drag is graphed against velocity, the curve will
have a similar shape for all similarly shaped bullets, though it's easy
to imagine that a larger bullet will experience more drag than one of the
same shape but smaller size. Since the shape of the drag curves are similar,
the two curves can be related by multiplying or dividing by a single number. The ballistic coefficient is that number, and it relates the
drag of bullets that have similar shapes to one another. Unfortunately,
most of the ballistic coefficients you find published today are in error.
This is because the original bullet used as a reference was of a very different
shape than those commonly used today. To deal with this, some companies
publish several different ballistic coefficients for a given bullet,
depending on the velocity range. Of course, this completely defeats the purpose
of the ballistic coefficient.
If you don't know the ballistic coefficient of your bullet,
the Web Ballistic Computer will allow you to choose from one of
four shape classes. It will then calculate an approximate ballistic
coefficient based on the bullet shape, diameter, and weight.