Exbal Topics

 


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 mil-radian. The mil-radian is defined a 1/1000th of a radian. There are 2 pi radians (6283 mil-radians) in a circle. Early in the 20th 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 mil-radian 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 mil-radian. The mil-radian is defined a 1/1000th of a radian. There are 2 pi radians (6283 mil-radians) in a circle. Early in the 20th 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 mil-radian 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.

Mil Dots

Mil-dot Reticles:

To make things even more complicated there are two systems that use mil-radians. Both the US Army and US Marine Corps use scopes equipped with cross-hairs that have dots spaced one mil-radian 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 mil-dot scopes available.

Mil-dot Reticle:

Military shooters are trained to use the mil-dots to estimate target distance.  By measuring the height or width of a known (or approximately known target size) in mil-radians using the reticles, the target distance can be calculated as follows.

R = range in meters, H = target size in meters, M = mil-radians 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 mil-dot 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 = mil-radians of image size:

            R = 25.4 * H / M

 R = range in yards, H = target size in inches, M = mil-radians of the image measure in the scope:

            R = 27.78 * H / M

R = range in yards, H = target size in feet, M = mil-radians 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.

Ballistic Reticle

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 NP-R2 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.

Re-establishing 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 re-entering 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.perry-systems.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.

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