Ballistics (from Perry-Systems.com )
Ballistics is the study of the path of a projectile and how it is affected by external factors (gravity, air resistance, wind, etc). Exterior ballistics is the sub category that pertains to rifle and pistol bullets that are fired at a relatively low angle relative to horizontal and have no means of propulsion after leaving the muzzle. Trajectory is a primary measurement of concern. It is the position of a bullet in relation to the line of sight (aim point) at any point along its flight path. When the bullet is above the line of sight, the trajectory is positive. When it is below the line of sight, the trajectory is negative. Trajectory is extremely important to the hunter or target shooter because it determines where the bullet will strike compared to the point of aim. The error in point of impact vs point of aim can be much larger than one might first imagine. This lesson is quickly learned here in South Texas where long shots are not uncommon. Ballistic coefficient is a measure of how well a bullet is able to overcome air resistance compared to other bullets. The higher the ballistic coefficient, the less air resistance impedes the forward motion of the bullet. A standard bullet was developed by military ordinance personnel who first studied the flight of projectiles (ballistics). It is a one pound projectile (bullet) that is one inch in diameter and has a semipointed shape. This standard projectile was defined as having a ballistic coefficient of 1.0000. The ballistic coefficient of other bullets are determined by the ratio of how far they must travel to lose the same amount of velocity as the standard projectile. Most hunting and target bullets have a ballistic coefficient less than one simply because they are not as long and heavy as the standard projectile and can not "punch" a hole through air as easy as the standard projectile does. Although some of the "very low drag" target bullets are getting pretty close. There are some heavy 50 caliber target bullets that actually have a ballistic coefficient greater than one.
3. Sight-in distance - when a bullet leaves the muzzle towards the target, it spends about half the time rising and the other half of the time falling. When a target is beyond the sight-in distance, the bullet will strike below the point of aim. When the target is closer than the sight-in distance, the bullet will strike above the point of aim. The two trajectory curves below illustrate this concept.
4. Air resistance - is not constant. It is directly related to air density which depends on altitude, temperature, pressure, and moisture content. Increased altitude, temperature, and moisture content will reduce air resistance so that the trajectory will be "flatter". Increased pressure will increase air resistance.
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1.
Multiple
Ballistic
Coefficients
Ballistic coefficients are determined by velocity tests that the manufacturers conduct. The rates of loss are compared to the Ingall's G1 tables to establish a ballistic coefficient. The standard projectile used for building the model used in the Ingall's tables is a one pound, one inch diameter, two caliber ogive point. The aerodynamic shape of more efficient target bullets is different than the standard projectile so that the loss data does not fit the entire velocity range. However, by using several ballistic coefficients to cover the entire velocity range a very good fit can be obtained. This is illustrated by the following example of a Sierra 30 caliber 168 grain MatchKing bullet:
2.
Ballistic Coefficient
Lower Velocity Limit
Velocity Range
0.462
2600
> 2600 fps
0.447
2100
2600 to 2100 fps
0.424
1600
2100 to 1600 fps
0.405
0
< 1600 fps
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Wind
Data
Wind data consists of two components, a magnitude (velocity), and an approach direction. The convention used by Exbal is that the line of sight is zero degrees. A wind approaching from the 3 o'clock position has an angle of 90 degrees.
3. Atmospheric Pressure Atmospheric pressure is determined by measuring the ambient, absolute pressure with a barometer. A mercury barometer is the standard scientific method for measurement. If the altitude is above sea level, barometric pressure readings are commonly "corrected" for sea level for reporting purposes to establish a common basis. When you hear a weather report for example, the barometric pressure is corrected for sea level. Another source for atmospheric pressure data is an electronic pressure gauge. These devices report the absolute pressure and do not correct for sea level. The Exbal program allows you to use either of these conventions. The "pressure at sea level" box is for corrected readings and the "pressure at altitude" is for uncorrected readings. If you specify pressure at sea level, the program will automatically calculate the pressure at altitude, and vice versa. If you are equipped with an electronic pressure gauge, thermometer, wind velocity meter, and Exbal loaded on a lap top computer, you will have a definite advantage at the range. 4. Separate Sight-in and Range Conditions A unique feature of Exbal is the ability to establish separate sight-in and range conditions. This is illustrated by the following example: Sight-in Conditions
Range Conditions
Location
Corpus Christi, TX
DuBois, WY
Altitude
30 ft
7500 ft
Temperature
80 degrees F
40 degrees F
Muzzle Velocity
3100 fps
3050 fps
Relative Humidity
78%
78%
Pressure corrected to sea level
29.53 inches Hg
29.53 inches Hg
Pressure at altitude
29.53 inches Hg
22.70 inches Hg
This example corresponds to some very practical considerations when preparing for a hunting trip or a match at a different location where there may not be an opportunity to sight-in. First, there is a significant change of altitude and temperature. Notice that with the change in altitude there is a change in atmospheric pressure at that altitude. Finally, there is a decrease in velocity because the powder being used is temperature sensitive (some powders are not). All of these factors affect the trajectory of the bullet. At two hundred yards or less, it probably won't make much difference. Beyond that, the difference in atmospheric conditions becomes increasingly more important as the distance to the target increases. At one thousand yards, these differences would mean 30 inches or 3 minutes of angle for a 300 Winchester Magnum. To a competitor, this is enormous. Exbal gives you the capability to pinpoint the trajectory calculations to give you a cutting edge advantage. 5. Interface to Excel Exbal has the ability to load an Excel spreadsheet with the ballistic calculation results. In the default case, a spreadsheet with six sheets is used. After the first sheet is loaded with calculations, you can click on the tab for sheet 2 and run another calculation. When you load the Excel spreadsheet this time, the results will go into sheet 2. This process can be repeated for all six sheets. If you need more, there is an option to set the maximum number of sheets in the workbook. This interface provides all the power of Excel to analyze data, create graphic displays, etc.
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Ballistic Reticle Analysis 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. Each of the horizontal reference bars can be used for sighting at different target distances. To illustrate this concept the following table shows how the Ballistic Plex reticle performs with a 7mm Rem Mag, 140 gr Nosler Ballistic Tip, at 3200 fps.
Vertical Sight Reference
Sight In Distance
+/- 4-inch Range
Sight-in (Main Cross-Hair)
135 Yards
0 to 241 Yards
Bar Number 1 (1.54-inches hold-over at 100 Yards
235 Yards
0 to 303 Yards
Bar Number 2 (4.51-inches hold-over at 100 Yards
378 Yards
322 to 419 Yards
Bar Number 3 (7.52-inches hold-over at 100 yards)
500 Yards
467 to 528 Yards
Bar Number 4 (11.06-inches hold-over at 100 yards)
624 yards
602 to 644 Yards
The Sight In distance in the table above is the exact distance at which the bullet will strike exactly at the point of aim using the corresponding reference bar. The data shown in this example was determined by computing the optimum sight in distance so that Bar # 3 will be right on at 500 yards. Notice that Bar # 2 is very close to being on at 400 yards, and Bar # 4 is very close to being on at 600 yards. This example is a very practical configuration for the long range hunter. At longer distances (Bars # 2, 3, and 4) the accuracy of the sight reference bar is very important. Bar # 2 will be on at 378 yards, 4 inches high at 322 yards, and 4 inches low at 419 yards. Likewise Bar # 3 will be on at 500 yards with a +/- 4 inch range of 467 to 528 yards. Bar # 4 will be on at 624 yards with a +/4 inch range of 602 to 644 yards. At shorter distances, the main cross hair can be used to 241 yards where it will be 4 inches low. Bar # 1 can be used to 303 yards where it will be 4 inches low.
The above discussion outlines an optimum sight in strategy. This coupled with practice to identify target distances and how to hold between reference bars will lead to a very useful way for a shooter to adapt to targets at extended distances. Once mastered, this technique is much faster than making external scope adjustments.
Exbal Ballistic Reticle Analysis quickly performs the calculations that will help you understand your ballistic reticle and to optimize its performance. This option has preprogrammed setups for the Ballistic Plex (Burris), the NP-R2 (Nightforce), and standard mil dot reticles. Other reticle continue to be added and custom configurations can easily be specified by the user. It should be noted that the column entitled +/- 4 inch range was determined using the Output to Excel feature once an optimum sight in distance was determined.
The basic concept is that the program will use the "holdover" value associated with each reference bar to calculate the distances at which the bullet will strike a "point blank range" target. The point blank target is defined by a circle whose diameter is specified by the user. There is the Zero range at which the bullet would strike the center of the target. Secondly there is the "MIN" range at which the bullet would strike at the top of the circle. And finally there is a "MAX" range at which the bullet would strike at the bottom of the circle. The reticle specifications for four different reticles are pre-defined. The user has the option of specifying any other reticle configuration. These specifications consist of holdover values for each bar or dot along the verticle axis and a units of measure - Minutes of Angle (MOA), Inches per hundred yards (IPHY), of Mil Radians (MILS). Finally there are specifications to define the scope being used. They consist of the maximum power and the reticle location. A reticle located in the first focal plane grows or shrinks along with image size when the power is changed. This is common in the Eurpoean scopes. A reticle located in the second focal plane stays the same size as the power and image size changes. This is common in American scopes. When the second focal plane location is specified, Exbal calculates the actual holdover values that correspond to the actual (operating) power setting. A power factor is also shown, it is the ratio of the operating power to the maximum power. (Note: The power factor can be used to adjust "come ups" computed for the main cross hair when the scope is not at full power setting.) There are two optimize functions. The first determines the sight in distance (main cross hair) so that that a specified reference bar or dot will strike the center of the circle at a distance specified by the user. For scopes with reticles located in the second focal plane there is an additional option to determine the power setting needed so that a specified reference bar or dot will strike the center of the circle at a distance specified by the user.
