Engel Ballistic Research

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 0.0".

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.

Basics of Ballistics

Near-Zero and Far-Zero

Sight Height and Factory Ballistic Data

Point Blank Diameter and Range

Aerodynamic Drag and the Ballistic Coefficient