Sight
Adjustments:
Scopes
and target aperture sights are equipped with adjustment knobs for windage
and elevation. The common unit of measure for sight adjustments is the
minute of angle. A minute of angle (MOA) is defined as follows  there
are 360 degrees in a circle and there are sixty minutes in each degree.
If a minute of angle is extended to 100 yards it will be 1.047 inches
high. In order to simplify things some manufactures refer to a minute of
angle as 1 inch at 100 yards. However the shooter needs to be aware that
there is a five percent error in this simplification. At 1000 yards this
amounts to 10.47 inches versus 10 inches for each MOA. For the long range shooter this can be
a problem. For example the 308 Win has a trajectory of approximately 400
inches at 1000 yards when sighted in at 100 yards. A five percent error
at this distance is 20 inches. This is really significant if the target
is a 12 inch steel plate.
Another unit of measure used by the military is the milradian. The
milradian is defined a 1/1000^{th} of a radian. There are 2 pi
radians (6283 milradians) in a circle. Early in the 20^{th}
century, the Infantry adopted the system but defined the “Mil” as 6280
Mils in a circle. Shortly after that the Artillery decided to refine the
system and divided a circle into 6400 mils. Thus a true milradian is
equal to 3.4377 MOA, the Infantry Mil is 3.439 MOA, and the Artillery
version is 3.375 MOA. The difference between the two versions of the
“mil” is about two percent. For the example above this translates to an
error of eight inches.
Sight
Adjustments:
Scopes
and target aperture sights are equipped with adjustment knobs for windage
and elevation. The common unit of measure for sight adjustments is the
minute of angle. A minute of angle (MOA) is defined as follows  there
are 360 degrees in a circle and there are sixty minutes in each degree.
If a minute of angle is extended to 100 yards it will be 1.047 inches
high. In order to simplify things some manufactures refer to a minute of
angle as 1 inch at 100 yards. However the shooter needs to be aware that
there is a five percent error in this simplification. At 1000 yards this
amounts to 10.47 inches versus 10 inches for each MOA. For the long range shooter this can be
a problem. For example the 308 Win has a trajectory of approximately 400
inches at 1000 yards when sighted in at 100 yards. A five percent error
at this distance is 20 inches. This is really significant if the target
is a 12 inch steel plate.
Another unit of measure used by the military is the milradian. The
milradian is defined a 1/1000^{th} of a radian. There are 2 pi
radians (6283 milradians) in a circle. Early in the 20^{th}
century, the Infantry adopted the system but defined the “Mil” as 6280
Mils in a circle. Shortly after that the Artillery decided to refine the
system and divided a circle into 6400 mils. Thus a true milradian is
equal to 3.4377 MOA, the Infantry Mil is 3.439 MOA, and the Artillery
version is 3.375 MOA. The difference between the two versions of the
“mil” is about two percent. For the example above this translates to an
error of eight inches.

Mildot Reticles:
To make things even more complicated there are two systems that use
milradians. Both the US Army and US Marine Corps use scopes equipped
with crosshairs that have dots spaced one milradian apart on both
the vertical and horizontal axis.


The
dots on the US Army scopes are circular and are 0.75 MOA (.22 mil) in
diameter. The dots on the Marine scopes are oblong. They are 0.25 mils
(.86 MOA) long . There are commercial versions of both US Army and US
Marine Corps mildot scopes available.
Mildot Reticle:
Military
shooters are trained to use the mildots to estimate target
distance. By measuring the height
or width of a known (or approximately known target size) in milradians
using the reticles, the target distance can be calculated as follows.
R
= range in meters, H = target size in meters, M = milradians of image
size:
R
= 1000 * H / M
Military
shooters are trained to know that the common male torso is 39 inches from
crotch to top of head. This is very close to exactly one meter. The above formula reveals a lot about
the genesis of the mildot system. This formula then becomes R = 1000 / M
for a one meter target size.
All of the following formulae are equivalent to the one above for
estimating range.
R =
range in meters, H = target size in inches, M = milradians
of image size:
R = 25.4 * H / M
R
= range in yards, H = target size in inches, M =
milradians of the image measure in the scope:
R = 27.78 * H / M
R =
range in yards, H = target size in feet, M = milradians of
the image measure in the scope:
R = 333.3 * H / M
Ballistic Reticles:
A
tool that is becoming popular for long range shooters is the
"ballistic reticle". It consists of the normal vertical and
horizontal crosshairs plus a series of horizontal reference bars. In the
figure below, a ballistic reticle with four horizontal reference bars is
shown.

It
should be noted that the four bars are not equally spaced. In fact they are spaced so that the
each of the bars represents a meaningful target distance. For
example, 300, 400, 500, and 600 yards in the case of a cartridge such
as the 7mm Rem Mag.
The ballistic reticle has been of greater interest to long range
hunters. However proponents of
the system are refining it for military applications.
Another variety of the ballistic reticle is a series of reference
bars spaces at increments of one or two minutes of angle. The
Nightforce NPR2 reticle is such a reticle and is popular with long
range shooters.


A
shooter equipped with a range finding device and a Palm version of Exbal
can determine which crossbar should be used for sighting on targets at
extended distances.
The PC
version of Exbal has an option that performs the calculation require to
analyze and optimize the set up of a ballistic reticle.
Sighting in at one
location, shooting at another:
A classic dilemma is faced by the hunter or competitor who practices
at one elevation and has to hunt or compete at another. Yesterday I talked to a Palma shooter
who lives near Dallas and was getting ready for a match at the NRA range
in New Mexico. Dallas is
approximately 500 feet in elevation, and the NRA range is at
approximately 6000 feet.
Reestablishing sight in at a new location may not be convenient and can
be a big mistake if rushed and not done properly. There are two primary factors that will
affect the trajectory of a bullet fired at two different locations. First
there is a difference in air density (measured by air pressure) at the
two locations. The bullet will loose velocity slower in less dense air so
the trajectory will be flatter at higher altitudes. A second significant
effect is that muzzle velocity may be impacted by temperature, depending
on the powder used. Both of these factors will impact the time of flight
and consequently how much the bullet drops.
Exbal has an option to analyze trajectory based on one set of conditions
for sight in and another set of conditions in the field (or range). The program will perform one set of
calculations to determine what the angle of departure (angle between line
of sight and line of bore) is at sight in. It uses the same angle of departure but
does the calculations based on atmospheric conditions and muzzle velocity
in the field. Once again, the Palm version can be used on the spot. If that is not convenient, a reference
card(s) can be created by using the Excel output option on the PC version
of Exbal.
One long range shooter friend of mine uses the Palm version, a laser
range finder, and a Kestral 4000 which provides wind speed measurements,
temperature and atmospheric pressure.
Using the Excel Output option to extend ballistic calculations:
One of things that inspired the development of the interface to Excel
was that I was perpetually copying data from Exbal calculations and then
reentering it in Excel so I could create reference cards. The Excel
output option causes Exbal to load a spreadsheet with all of the user
input data and the ballistic calculation results. Then it is easy to cut and paste the
information to create a table that can be printed and laminated for a
reference card.
Another use is to plot the ballistic calculation results to compare
cartridges, loads, etc.
It is also possible to perform additional calculations in Excel. When I was developing a web page http://www.perrysystems.com/reticle_analysis.htm
regarding the analysis of ballistic reticles, I wanted to show the +/
four inch point blank ranges for each of the reference bars. Using the
output to Excel, I inserted four columns to the trajectory table. In each
of the columns I subtracted the MOA of holdover for each the four bars
from the trajectory result of the main cross hair. It was easy to see
where each of the four bars was four inches high and four inches low.
That’s how I developed the bar graph.
