Table of Contents  

  1. Foreword by the author.
  2. Brief comments on the history of external ballistics.
  3. What this program can do for the shooter, sportsman, and the researcher.
  4. How to enter the program and input data.
  5. How to use the program to answer specific questions.
  6. Frequently asked questions.
  7. Information on program updates and technical support.  
  8. Glossary of key terms.


CHAPTER ONE:  Foreword by the author.

    Thank you for buying “Modern Ballistics”.  You have purchased a very powerful ballistic tool that will give you the answers to your shooting questions.  These answers are accurate, and based upon formulas that are the results of extensive testing in the field as well as in the laboratory.  Thanks to centuries of dedicated research the primary questions regarding the bullets flight are solved.  The modern shooter and researcher have at their fingertips proven information of a quality that was unheard of as recently as 20 years ago.  Please study this manual carefully.  Like any powerful program there is a learning curve to mastering “Modern Ballistics”.  However, in a short period of time the program will be working for you.   Every effort has been made to make “Modern Ballistics” a powerful and enjoyable program for you to use. 

Have a good time and good shooting!

CHAPTER TWO:  Brief comments on the history of external ballistics.

    The study of ballistics has been one of the longest and most intensive studies of mankind.  Far before any written history existed, the study of objects in flight has been of vital concern to humans.  Mastering standard ballistic questions has been a matter of personal survival and intellectual curiosity for many centuries before the written word was available.  To predict the flight and the force of air borne projectiles has occupied many of the finest scientific minds that have ever lived.   It would be impossible to acknowledge all those that have worked on external ballistics.  However, it is possible to point out some of the brightest stars so that the modern shooter can be aware of the quality of minds that have studied ballistics.  Many argue that scientific efforts on ballistics began with the Italian physicist Niccolo Tartaglia who died in 1557.  His primary accomplishment was to prove that trajectory is curved and he proposed that maximum range could be obtained if the departure angle was 45 degrees.  It remained for the great Galileo (1642) to prove that the curve that a projectile took was a special curve called a parabola.  Galileo also showed that Tartaglia’s belief that the maximum range could be obtained at a 45 degree departure angle was wrong.  In a vacuum, Tartaglia would have been right, but in our atmosphere the maximum range is obtained near the 32 degree angle. 

    Sir Isaac Newton (1727) was probably the greatest scientist that the world has ever seen.  His work on ballistics was mostly concerned with air resistance.  His calculations were mainly concerned with low speed projectiles and his conclusions about the effect of “drag” on bullets were wrong at the higher speeds.  The preeminence of Newton actually delayed scientific advance for several decades.  The main breakthrough in external ballistics was the discovery of the ballistic pendulum which was the first practical (but crude) chronograph.  The ballistic pendulum was developed by Benjamin Robins in 1742.  The ballistic pendulum was a device that swung through a measured arc when struck by a fired bullet.  The pendulum showed that Newton had to be wrong about the speed loss of a bullet in flight.  The measured speeds were much lower than Newton predicted.  Therefore the “drag” on the bullet in flight had to be much greater than previously thought.  Indeed, the figures showed that the power of drag was over 80 times the power of gravity.  This was a shocking conclusion to the scientific world.  However, true science follows the evidence.  In time, it became very clear that Robins was right.  The force of drag was as great of a force as the tests of Robins showed. 

    The study of “drag” became the focus of an international effort to predict the characteristics of a projectile in flight.  The powerful industrial firm of Krupp in Germany conducted many important studies between 1881 and the beginning of World War 11.  Likewise, the Gavre Commission in France published a great deal of data between 1873 and 1898.  Intellectual contributions came from all over the world.  Men like Maysvski from Russia and Ingalls from the United States constructed ballistic tables that added to the growing body of ballistic information.   World War 11 pushed ballistic research to unheard of heights as the complexity of high altitude bombing, advanced artillery, and long range small arms fire greatly increased.

   The pace of knowledge concerning external ballistics increased at tremendous speed with the invention of the computer.  The computer made very complex computations a matter of seconds instead of days or even years by very tedious former hand methods.   Test data could be complied in minutes in spite of incredible mathematical complexities.  All types of physical interactions were mathematically resolved at a speed that was inconceivable to the recent past.   The program “Modern Ballistics” that you have in front of you is a result of all this human effort and investment.  You now have a tool that can easily explore questions that were only dreams of the many people who lived before you.   The accuracy and the power of this affordable program called “Modern Ballistics” would have awed the greatest minds that ever lived.  “Modern Ballistics” will answer nearly any question that you have about a bullets flight. You can use this program with the confidence that the answers are correct and that the hard work is truly over.

CHAPTER THREE:  What this program can do for the shooter, sportsman, and the researcher.

  1. Generate a bullet trajectory.

  2. Allow the shooter to change his zero.

  3. Calculate a “dead-on” range.

  4. Calculate velocity and energy losses with increasing range.

  5. Generate probabilities of hits at a given range.

  6. Simulate target sizes and sight picture with either scope or iron sights.

  7. Calculate the effects of wind by either deterministic or probabilistic methods.

  8. Automatically measure target group size by several methods.

  9. Simulate a firing rifle by randomly shooting five or ten shot groups.

  10. Predict the probabilities of shooting a given group size with a given rifle.

  11. Allow the user to use, save, or print the resulting data of the program.

  12. Allow the shooter to find his actual zero with limited data at a known range.

Now we will briefly but thoroughly examine each use.

  1.  Generate a bullet trajectory.
    This has been the most basic purpose of centuries of ballistic work.  It simply tells the shooter where the bullet is at any given point.  If the shooter is sighted in at any given range the program will tell him where the bullet is at any other range.

  2. Allow the shooter to change zero.
    This function answers another basic ballistic question.  It tells the shooter how to adjust his sights to hit point of aim at a new desired zero.  It also shows the bullets path on this new trajectory.

  3. Calculate a “dead-on” range.
    This important function tells the shooter what distance his zero range should be in order to take full advantage of his rifles ballistics.  The shooter decides how high above or below the line of sight that the bullet can be and still not miss the target.   The computer calculates this range instantly. 

  4. Calculate velocity and energy losses with increasing range.
    As the velocity of the bullet becomes less, it is true that the terminal energy becomes less.  This function is easily shown by the computer.

  5. Generate probabilities of hits at a given range.
    This is a very important and unique function of “Modern Ballistics”.  The shooter gives the computer the required data about the given cartridge, given conditions, and given firearm characteristics.  With this data the computer can tell the shooter his probabilities of hitting a given target at a given range.  This allows the shooter to obtain results from his computer that cannot easily be gotten on the range.  A very valuable function of “Modern Ballistics”. 

  6. Simulate target sizes and sight picture with either scope or iron sights.
    This is a powerful visual tool for the shooter.  It gives him/her the perspective of the target size in relationship with his sighting equipment.  This is a valuable training aid.

  7. Calculate the effects of wind by either deterministic or probabilistic methods.
    The program allows the shooter to input the speed of the wind, the angle of the wind, and a variable factor to allow for judgment errors of wind velocity.  This will allow the computer to plot the results of the combined effects.  These results plainly show the cumulative results of shooting a group under these conditions.

  8. Measure target group size by several methods.
    “Modern Ballistics” will allow you to enter data from targets that you have shot at the range.  The computer then allows you to select which measuring method that you prefer to use.  The computer will then do the mathematics automatically and give you the exact results of that measurement. “Modern Ballistics” will also perform the mathematics of group measuring on groups that the computer itself randomly “fires”.   The available measuring choices are as follows:

    Extreme Spread.  This is the distance between the two furthest shots.
    Vertical & Horizontal Spread.  This is the distance between the furthermost horizontal shots and the furthermost vertical shots.
    Average Vertical & Horizontal Spread.  A better statistical measure.
    Average Group Radius.  A very good method of measuring accuracy.  This provides a “statistically significant” number.

  9. Simulate a firing rifle by randomly shooting five or ten shot groups.
    This is an incredible feature of the “Modern Ballistics” program.  This feature turns the computer into a simulated rifle.  You select the characteristics of cartridge, astrosphere conditions, and the firearm.  Then you tell the computer to randomly “fire” a given number of five or ten shot groups at a given range.  The user can fire random shots one at a time by clicking on the "Fire" button.  However, if the shooter does not elect to “fire” each shot the computer can randomly fire them. The simulated targets will then be displayed on your computer screen.  The computer can then measure the simulated targets in whatever manner you desire.  This allows the user to save hundreds of dollars by obtaining data quickly, accurately, and inexpensively.  The experimental possibilities of this feature are almost limitless.   You as a shooter can explore shooting questions in the comfort of your home regardless of the weather at the range.  The results are scientifically valid and enable the shooter to perform experiments with a precision that is not possible on the range.

  10. Predict the probabilities of shooting a given group size with a given rifle.
    This is another “Modern Ballistics” exclusive.  This function allows the shooter to ask the computer how many groups with a given rifle he would have to shoot to obtain a group of another size.  For example, if you had a rifle that shoots 12 inch groups at 1000 yards.  How many groups would you have to shoot before the rifle would give you a group that was seven inches or smaller?  This is a function of probability.  “Modern Ballistics” will answer this type of question effortlessly.  You may see that any given rifle is just not statistically capable of giving you that “dream” group.

  11. Allow the user to use, save, or print the resulting data of the program. 
    This allows the shooter to have hard copy and/or manipulate his data.

  12. Allow the shooter to find his actual zero with limited data at a known range.  
    You fire a group at 100 yards and it's six inches high.  At what range will be zeroed?  Where will it be six inches low?  "Modern Ballistics" will tell you.

CHAPTER FOUR:  How to enter the program and input data.

    To enter the program the user clicks on start, then clicks on programs, then clicks on “Modern Ballistics”. You are now in the program.  On the title bar will appear MBall-(MBALL1).   Take a few minutes to study the screen.  Do not be disturbed if some of the terms appear unknown to you.  All these terms are explained in the glossary.  Ballistics like any body of knowledge has developed its own vocabulary over the years.  The important thing to realize is that the power of the program can only be used based on the information that you give it about your specific cartridge characteristics, specific physical conditions, and the specific capacity of your rifle.

      To give the computer these vital bits of information the user must click on the word “edit” on the menu bar.  The edit command will drop down three fields.  These fields are listed as cartridge, conditions and firearm.  When the user clicks on cartridge he will see a screen that asks you to give the computer specific data on your cartridge.  Place your curser on each field.  Enter the correct information in each field and when the fields are filled then press enter.  Each field should be basically self-explanatory.  Place close attention to the field that asks you to enter a five-shot group size.  This is based on the known accuracy of your specific rifle.  For example, if your rifle averages one inch at 100 yards then the correct entry in that queried field is “1”.  The numerical “1” standing for one minute of angle.  If your rifle averages ½ inch groups at 100 yards then the correct entry is “.5”.  This is approximately ½ minute of angle.    Go through the same procedure on the “Conditions” and “Firearm” items.

       The “firearm” item can be a little tricky.  The computer is going to ask you for the “indicated sight angle” Be sure to take your time and look up what the term means.  For now, it might be easier to just press “calculate” immediately to the right of the indicated sight angle box.  When you hit “calculate” the computer is going to ask you for your “range” and your “height”.  Let us just assume that you are interested in zeroing your rifle to hit dead on at 300 yards.  This requires that you enter 300 in the range box.  Three hundred yards is now your point of aim/point of impact commonly called the rifle “zero”.  Put “0” in the height box.  Push “okay” twice and the page disappears.  You will now be returned to the home document. 

     Make sure that you pay close attention to the “View” radio buttons.  The choices are table, graphic, and target.  The most conventional views are “Table” and “Graphic”.  The purpose of these points of view will become clear as you play with the program.  The “target” view is very unique.  This view allows the user to see the target from the perspective of the rifle sights.  The “target” view displays the variation in bullet hits due to the rifle accuracy, wind factors, and muzzle velocity variations.  By changing these factors you can see the size and shape of the resulting target.  The target will reflect the different probabilities of hits that are calculated by “Modern Ballistics”. 

     For our specific example, make sure the selected button is in “Table”.  All the data on the “table” page reflects the results of your 300 yard zero and all the constants that you previously entered.  It is a good idea to print that page for a practice reference.  Play with the computer by changing various characteristics of different loads, different conditions, and different firearm characteristics.  By comparing the screen with your printed reference you will be able to see how “Modern Ballistics” gives you new answers to new conditions.  In addition, explore the “graphic” and the “target” options.  The speed and power that these calculations are performed is truly remarkable.

    Pay particular note to the box that says “independent variable”.  The fall down menu shows 23 variables.  These variables in turn will change the lower row that is called “independent variable values”.  Explore the results of changing variables and carefully study the changing data fields.  By a careful study of the glossary and the screens you will soon be accessing ballistic information with confidence. 

   The user can edit this data for the individual document being worked on or they can select the data from sets that have been stored on disk.  There are also sets of data supplied with the program for some common cartridges and the user may create new ones that specifically match his/her needs and situation.  These are called “Factory Defined” and “User defined” cartridges, conditions, and firearms.  A document containing a set of one cartridge, one set of conditions, and one firearm can be stored on disk as a .BAL (ballistics) document.  The document can be opened again at a later time to view the exact data set and the specific view of that data that you were working with last time.  To get the full benefit of “Modern Ballistics” you will have to study, practice, and simply explore.  Perhaps a simple cheat sheet will help you remember how to get started.  Let us assume that you want a 300 yard zero.

Start your computer.

Press “Start”

Go to “Programs”

Select “Modern Ballistics”

Go to “Edit”

Go to “Cartridge”. Fill the slots, and hit “enter”

Go to “ Conditions”. Fill the slots, and hit “enter”. 

Go to “Firearm”.  Go to “calculate”.  Enter 300 in the range box.  Enter zero in the height box.

 Press “okay” twice.

You are now at the “home” document.  Make sure that the Table radio button is selected which is located next to the “View” heading. 

There you are!  Your data is now before you.  It will get easier to find your way around the program as you play with the program.

CHAPTER FIVE:  How to use the program to answer specific questions.

1.      Creating a “zero” for your rifle.  This was used as an earlier example. Just go back to chapter four.

2.      Going from one “zero” to a new “zero”.  

    This is a very common question and the “Modern Ballistic” program will do this for you easily. Let us take for a given that the rifle is already sighted in for a zero of 300 yards.  Remember you used the same constants listed below.   In addition, let us assume the following constants.

  1. .300 Winchester

  2. SA Offset 0.00

  3. Mass 168

  4. Incline 0

  5. Temp 59

  6. M.V. 3100

  7. Sight HT 1.50

  8. Wind (mph) 5

  9. Alt. 3200

  10. M.V. SDev 15.0

  11. Gravity 32.17

  12. Wind error 2

  13. Shots per group 5

  14. B.C. .462

  15. Barometer 29.53

  16. Wind (deg.) 45

  17. Bullet accuracy (moa) 1.00

     The home document with the Table radio button selected will show an “indicated SA (moa) of 3.23 inches under the 100 yard zero (yds) column.  This means that your rifle shoots 3.23 inches high at 100 yards in order to hit exactly dead on at 300 yards.  Let us assume that you now want a 500 yard zero.  If you look under the 500 yard column you will notice that it says that 9.84 minutes of total adjustment is needed to be dead on at 500 yards.  Since you already have 3.23 moa on your scope you need to “click” up the difference to get to 9.84 minutes.  In short, you need to go “up” 6.61 minutes to be dead on at 500 yards.  If your scope has quarter minute “clicks” then you would need to take 4 ( 4 clicks to a minute in a quarter click scope) times 6.61 minutes.  Twenty Six clicks “up” puts you dead on at 500 yards.  This is all really a great deal easier than it may appear at the moment.  The same method will work to convert any given “zero” to a new desired “zero”.   You can also use the independent variable of Zero to do this.  Some people find the latter method easier.

3.  Simulate hit probability at your new “zero”.

     Now that you have a new zero, you may want to see how accurate your rifle is at the new range with your listed conditions.  This a very simple task for the “Modern Ballistic” program.  Under your view options on the home page simply select the target view radio button.  Let us assume that your target at the range is a 10 inch circle.  Under the target size box put width 10 and the height 10.  Hit the “enter” button.  You will now see a round target and your simulated group.  Note to the right that you have a 100% hit probability with the constants that you have given the computer.  Just for fun, change your target size to 5 inches in both the height and width boxes.  Hit enter.  Note that your hit probability dropped to 20% if you count a hit as a touching bullet.  Notice that reducing the target by 50% reduced the hit probability to 20% (not to 50% that some shooters might think).   Mathematics has many surprises for the unwary.  Your “Modern Ballistics) program will educate you to more bullet flight reality than a lifetime on the range.

4.  Estimate the probabilities of shooting a given group size with a given rifle.

    This is very computationally intensive and is turned off by default. To enable it go to 'Edit', 'Conditions', and click on 'Enabled' in the 'Desired Groups' group box.

    This is an interesting and educational function that is exclusive to “Modern Ballistics”.  Let us assume that you still have the 500 yard zero used in the last example.  With your view set on “table” you will note under the 500 yard column that your rifle is shooting 1.21 moa.  Since you are shooting at five hundred yards you can easily convert the 1.21 moa to group size.  Simply multiply 1.21 by 5 (five is for five units of 100 yards each) which gives you group size at 500 yards of 6.05 inches.  You have a rifle capable of shooting 5 shot- six inch groups at 500 yards.  That is a quite accurate rifle in reality.  However, you are interested in knowing how many groups you would have to fire with the given rifle to shoot a five, four, or even a 3 inch group.  One way to get this answer would be to go to the range and shoot 500 groups.  This would give you a good statistical base.  It would also be very expensive.  The “Modern Ballistic” program can do this task for you in moments at a nearly zero cost.   From the home document, simply click on “independent variable”.  Select “desired group (moa)”.   This is going to bring up a row that features the symbols of “Groups <= desired”.  In English this means the percentage of groups fired that are less or equal to the minutes of angle in the independent variable fields.  With your existing constants you will see that you should be able to get 6% of your groups under .5 minutes of angle.  A minute of angle at 500 yards is about five inches.  Therefore about 6% of a large sampling (in this case 500 groups fired) will be three inches or smaller.  Therefore you could expect about 30 groups out of 500 groups to be three inches or under. 

    However, we were interested into going down to a three inch group probability.  Therefore change the dependent variable boxes with .2 units starting from the left.  Therefore the order is .02, .04, .06, .08, and 1.  For round numbers let us assume that a minute of angle at five hundred yards is five inches.  Therefore, .2 equals 1.2 inches, .4 equals 2.4 inches, .6 equals 3.6 inches, .8 equals 4.8 inches, and l equals six inches.  You can see under the .2 column that you have zero chance to shoot a five shot group under 1.2 inches at 500 yards with this rifle.  However, you have a two percent chance to shoot a 2.4 inch group or better at 500 yards.  This in absolute terms would be 2% of 500 groups which equals 10 groups.  Your odds get much better at 3.6 group size.  You have a 12% chance of shooting groups 3.6 inches or better. In absolute numbers this would be 60 groups.  You can easily see that .8 and 1 inch groups are much easier to obtain. 28% and 52% respectively.  The program is currently being directed to generate larger numbers in order to see how large the sampling would have to be to give you that “dream” one inch group at 500 yards.  In all probability you will need a great deal of time, money, and opportunity.  Whatever the facts are, you can obtain the facts from “Modern Ballistics”.

5.       Calculate a dead-on range.

     This is an important function for many practical reasons.  Range estimation has always been a big problem in shooting.   The bullets flight is a type of a curve.  It is important that the shooter matches that curve to his target size in order to receive full benefit from the capacity of his rifle.  Through the use of “Modern Ballistics” the shooter can easily learn the optimum range to zero his rifle in relationship to the size of his target.  The simple goal is to sight the rifle in such a manner as to extend the range that the shooter can hold “dead-on” without fear of missing his target.   Suppose the hunter is sighting his rifle in for the purpose of hunting deer.  Let us agree that the hunter does not want his bullet to rise more than five inches above his line of sight nor allow the bullet to fall more than five inches below his line of sight.   Let us go to the program to answer this question.

    You should still have the 500 yard zero from the last example with all the same constants.  At this point, simply go to the “P.B. Size in inches” in the independent variable drop down menu. Under “dependent variables” look at the number 10.  This means that the bullet requirements are such that it cannot have a total spread greater than 10 inches. In other words, it is not desirable for the bullet to go higher than five inches above the line of sight nor five inches below the line of sight.  Therefore, if you zero your rifle in at 318.7 yards you will have a point blank range of 376 yards.  You can hold dead on your deer anywhere out to 376 yards and you should make your hit.

     “Modern Ballistics” also calculates how to obtain a 318 yard zero when the shooter only has access to a shorter range.  The user has to go to “Edit>firearm>calculate sight angle offset.  The sight angle calculator will ask you the range.  Put 318 yards in this box and leave the height in inches at zero.  Hit the “okay button” twice.  In the independent variable box hit “range” then enter.  In your independent variable values under the 100 yard box you will see “ 2.93 inches”.  If you sight your rifle in to be 2.93 inches high at 100 yards then you will be zeroed at 318 yards.

6.       Calculate how much to hold over or under a target to hit it?

      There are many situations where the shooter does not have time to adjust his scope to change “zeros”.  There may be hunting or even target situations where it is easier (or necessary) to “hold off”.  Typically the problem is time.  The target shooter may “hold off” in switching wind conditions.  Likewise, the hunter may want to take a shot in conditions that do not allow for a leisurely sight adjustment.  In addition, many rifle scopes do not have “click” adjustments.  Typically rifle scopes that do not have click adjustment use friction adjustments to roughly (very roughly in cases) make moa adjustments.  Having said these things it is important to understand that “holding off” is nearly always a second best choice.  Most experienced shooters will make every effort to change their zero if time permits.  Taking “clicks” and then aiming precisely is the standard practice of masters.  Nevertheless, “Modern Ballistics” can help the shooter by showing him how many inches the bullet rises and falls in relationship with his line of sight throughout its trajectory.    This relationship is based upon the actual “zero” of the rifle.  All the user has to do is to set the independent variable to “range” and look at the dependent variable “height (inches)”.  This line clearly shows the bullets path as it rises (positive numbers) and as the bullet descends (negative numbers).  These numbers clearly tell the shooter where to “hold” if time or convenience does not permit changing zeros.

7.  Where is my zero point?

    This is a very necessary feature of “Modern Ballistics”.  Let us assume that you are shooting at 100 yards.  Further assume that you have shot a group that is 6.75 inches high at the 100 yard target.  At this point you might want to know your true “zero” and all the characteristics of your rifle with that trajectory.  This is a very simple task.  Go to “edit” then click on firearm.  Where is asks for indicated sight angle just click on “calculate” to the immediate right.  Put 100 yards in the range box (yards).  This is your first “known”; you are shooting at 100 yards.  Then put 6.75 inches in your height box.  This is your second “known”.  Then click “okay” twice.  This brings you back to the “home” page.  Make sure that “table” is dotted under the “View” window.  At that point go to “independent variable” and then click on “range (yds)”. At this point hit “enter”.  You are back to the “home” page.  Look at the “constants” section.  The third column on the top row read “Zero (yds)”.  Your exact zero is 443.5 yards.  Thanks to “Modern Ballistics” you have the easy answer in a few moments.

CHAPTER SIX:  Frequently asked questions.

Q: What is this sight angle stuff?

A: The primary way to use this program is by changing the angle of your sights relative to the bore of your rifle barrel.  The purpose of this adjustment is to achieve a point of impact at your precise point of aim.  Much of the mathematics for Modern Ballistics came from the book “Modern Practical Ballistics” by Arthur J. Pejsa.  Mr. Pejsa is a well known authority on aerodynamic flight with a career of experience in space and military applications.  The sight angle method is extremely accurate, extremely fast, and extremely versatile.  For example, most people know that the zero of your rifle will change when you shoot at a different location.  But what most people do not know is that this change is very predictable.  The change is not due to a change in adjustment.  It is due to a change in the conditions.  Altitude and temperature being the biggest factors.  Assuming that your muzzle velocity is constant with temperature you can predict with great accuracy how your rifle zeroed at sea level at 60 degrees F will perform on the high desert at 6000 feet above sea level and 80 degrees F.  This is because the sight angle, the angle between the sights and the axis of the barrel has not changed.  The zero changed because of the physical conditions changed and because you can measure those changes you can predict the new zero.  It is important that the user of this program make every effort to understand the “sight angle” concept of external ballistics.  This concept is the conceptual heart of “Modern Ballistics”.  This method is often referred to as “taking clicks” by experienced shooters.  Nearly all rifle scopes are calibrated in minutes of angle (moa).  In addition, nearly all rifle scopes divide a minute of angle into fractional adjustments in the rifle scope.  The most common adjustments are quarter minute clicks (.250 per “click” as a unit of adjustment) or half minute clicks (.500 per click as a unit of adjustment).  It is important to remember that one MOA is approximately one inch at 100 yards.  Discussion of MOA is given in greater depth in the glossary.

Q: How do I get accuracy data for my bullets?

A: It is more than just the bullet that affects accuracy.  It is the entire firing system.  “Modern Ballistics” assumes the statistics of accuracy can be broken down into three areas.  These areas are:
  1. The effects of the wind.
  2. Variations in muzzle velocity.
  3. The inherent accuracy of the bullets in your rifle with you as the shooter.

The program further assumes that each of these variables is distributed in a “normal” bell curve.  A bell curve distribution is normal unless there is something that is not consistent.  A mechanical problem with the rifle could give a distribution that is not “smooth”.  By the same token there might be an abnormal distribution of data if the shooter is using two different lots of ammunition. For example, one lot of ammunition might average 50 fps slower than another lot.

 “Modern Ballistics” assumes that you give it wind data that is within a 90% confidence level.  For example, let us assume that you judge  the wind at your location to be between 6 and 8 miles per hour.  Your confidence level in your estimation of the wind is such that you believe that 90% of the time your judged wind velocity is correct. Based on this example you should enter a wind speed of 7 mph with an error spread of 2 mph.  If the wind is quite erratic you might change the error spread figure to 6mph to cover a situation that might have a wind spread from 4mph to 10mph.

Your figures on the variation in muzzle velocity should be based on the results of testing that rifle with a chronograph.  The preferred figure to enter into the program is “standard deviation”.  If your chronograph does not express standard deviation then click on “edit” then “cartridge” and then “calculate”.  “Modern Ballistics” will calculate the standard deviation for you. 

The accuracy of the rifle itself is determined by the size of 5 shot groups.  It is important to get the best data possible.  This data is obtained by shooting under the very best conditions possible.  A windless day in the evening is one of the best times.  Put up a target with five separate aiming points.  Shoot one shot at each target.  If you shoot across your chronograph at the same time then you can be getting data on velocity at the same time you are getting data on accuracy.  Shoot one shot at each of the five targets.  Carefully measure the horizontal (X) error and the vertical error (Y) of each shot from the exact center of the aiming point.  The program is going to create a measure of accuracy based on your group size.  Do not be concerned that your group is not actually centered at your aiming point.  You are concerned at the moment with only determining the accuracy of your rifle based on its group size.  You will later center your group to your point of aim.  That is merely a matter of sight adjustment.   If you do not have five shots to express your accuracy, the computer allows you to enter what you do have for shots.  The computer itself will generate the five shot group.  The same function holds true if you enter more than five shots.  The computer will make the proper adjustments to give you the equivalent for a five-shot group.  

CHAPTER SEVEN: Information on program updates and technical support.

The program is updated on a near continuous basis in response to customer input.  If you find a bug or would like to see a new feature added please send an email to find out the current status and what has been changed since the last version that you received.  Within your license period updates are free but you have to ask for them.

Support is one of the biggest costs of a software business.  Modern Ballistics is a labor of love, not something that will make anyone rich or even provide a living for someone.  For this reason support, except in the rarest of circumstances, will be by email only.  Support will be limited to five support issues (each of which may involve several email exchanges) the first month, and two issues per any given calendar month for the remainder of the license.  Typically you will receive a response within a few hours.  In extreme cases of family vacation, etc., it may take up to one week.  The email address is


Altitude:  Elevation above mean sea level in feet.

Ballistic Coefficient (.B.C.):  A bullet’s Ballistic Coefficient is a measure of its ability to go through the air without losing velocity.  Larger ballistic coefficient numbers are better than smaller numbers.  A bullet with a ballistic coefficient of .550 has better wind bucking ability than a bullet with a ballistic coefficient of .475 assuming that both bullets have the same velocity.  Typical numbers are from .084 for a 15 grain .172 caliber bullet to 1.0 for a heavy boat-tailed .50 BMG round.  This program will process this number if it is between .01 and 10.0.  Modern Ballistics will calculate this number for the user from the Edit/Select>Cartridge, “Calculate via velocity” or “Calculate via drop” dialogs.  The use of “Calculate via velocity” is the preferred option because it is not affected by the accuracy of the bullet, gun, or shooter.

Barometer:  An instrument that measures barometric pressure in inches of mercury.

Bullet Accuracy:  This is the inherent accuracy of a particular bullet in a particular gun ignoring the errors due to muzzle velocity and wind variations.  Accuracy is typically defined by group size at a given range in inches or in minutes of angle.

“Modern Ballistics” will calculate this number for the user from the Edit/Select> Cartridge> “Calculate via shots”.  Another option is for the user to use the “Calculate via groups” dialog.  The “Calculate via shots” is preferred because it takes into account the exact muzzle velocity for each shot.

Drop:  The distance the bullet falls in the vertical direction during its trajectory.  This differs from height because the height is measured from the line of sight of the scope or other sights.  The line of sight as viewed through the firearm sight and the axis of the bore are usually at an angle to each other.  It is also important to remember that drop is independent of “incline”.  As a result, if the gun is fired straight up, the drop will be the same as if the gun was fired horizontally.  See also “Height” and “Sight Angle”.

Gravity:  The attraction between material bodies.  The acceleration of a falling object due to mass of the planet measured in feet per second per second.

Incline:  The angle of the line of sight (through the rifle scope) relative to the horizontal.

Indicated S.A. :  see “Sight Angle Indicated”.

Mass:  Mass is weight in pounds divided by the acceleration of gravity (32.17 feet per second per second).  Mass is a better measurement for the bullets and gunpowder (although it is a more difficult measure to use).  The units of mass in “Modern Ballistics” are always in grains.  There are 7000 grains in a pound at standard gravity.

Mil (s):  Short for milliradian- a unit of angle.  There are one thousand milliradians in one radian.  There are two pi radians in a complete circle.  A mill is a very convenient unit for some types of measurement.  For example:  A two yard tall object at 1000 yards will measure two mils high, four mils, at 500 yards, or eight mils at 250 yards.  This allows for a scope with a mil-dot reticule to be used for angle finding.  Mil-dot reticules often have windage and elevation holdover expressed in mils.

Midrange:  The range at which the bullet is at its maximum height during its trajectory.  This is also known as midrange height.  Midrange is not equal to the midpoint of the range to the target.

Midrange Height:  The maximum distance of the bullet above the line of sight during its trajectory.

Minutes of Angle:  See MOA

MOA:  Minutes of Angle.  This is a unit of measurement for an angle.  One MOA is equal to 1/60th of a degree.  At one hundred yards one MOA is 1.0472 inches, or 2.0944 at two hundred yards.  Frequently this is rounded off to one inch at one hundred yours or two inches at two hundred yards and these figures are usually close enough.

Muzzle Velocity (M.V.):  Velocity of the bullet as it leaves the barrel of the gun.  “Modern Ballistics” can help arrive at this figure in several ways.  If the B.C. is known, the muzzle velocity can be estimated from the chronograph velocity and the distance from the muzzle to the chronograph.  Modern Ballistics will calculate this number for the user from the Edit/Select, Cartridge , “Calculate via chrono”,  “Calculate via drop”, Velocity Sdev “Calculate” or 5-shot Group Size “Calculate via shots” dialogs.  The “Calculate via drop” is the least desirable method because it is affected by bullet accuracy, BC estimation error, wind, and shooter error.

Muzzle Velocity Standard Deviation (MV Sdev):  A measure of the variation in the muzzle velocity.  This measure of the variation takes into account every shot fired but does give emphasis to the extreme variations.  Modern Ballistics will calculate this number for the user from the Edit/Select/, Cartridge, Velocity Sdev “Calculate” or 5-shot Group Size “Calculate via shots” dialog.

Near zero or Near Zero Range:  The range at which the bullet crosses the line of sight in the vertical direction on the ascending portion of the trajectory.  This is in contrast to the Zero where the bullet crosses the line of sight as it is descending.  For normal rifle velocities and Sight Heights it is rare to achieve a Near Zero exceeding one hundred yards.

Point Blank Range:  The maximum distance that an object of Point Blank Size will be hit when the sights are aimed at its center.  For example, if the Point Blank Size is six inches and the Point Blank Range is 230 yards, then the Midrange Height is three inches and the bullet is three inches low at 230 yards.  The Zero will always be something less than the Point Blank Range.

PF (Power Factor):  A measure of momentum.  This measure is mostly used in the pistol world.  It is arrived at by taking the velocity of the bullet in fps times the mass of the bullet in grains divided by 1000.  Hence a 200 grain bullet traveling at 1000 fps would have a PF of 2000.  It is generally considered you need a PF of 190 or greater to knock a bowling pin off of a table cleanly. 

Range:  Distance from the muzzle to the target.  Usually measured in yards.

Sight Angle:  The angle between the sights and the axis of the barrel in MOA.  Because of limitations of some scopes this is broken down into Sight Angle Indicated and Sight Angle Offset.  The relationship between these three quantities is:  Sight Angle=Sight Angle Indicated- Sight Angle Offset.

Sight Angle Indicated:  The sight angle shown on the scope in MOA for some scopes, possibly with the addition of a shim or angled base this can be the actual Sight Angle.  For others there is a Sight Angle Offset that must be subtracted to get the true sight angle.  Also because of vibration and other variations from load to load the effective Sight Angle of the gun can vary.  By setting the Sight Angle Offset in the program to something slightly different and appropriate for each load you can have the program generate scope setting for various loads that will read correctly on your scope without obnoxious adjustments.  See also Sight Angle and Sight Angle Offset.

Sight Angle Offset:  The angle subtracted from your scope setting will give you the effective Sight Angle for that firearm and load.  See also Sight Angle and Sight Angle Indicated.

Sight Height:  The distance from the centerline of the bore to the optical center of the sight at the muzzle.  For iron-sighted firearms this is usually from the top of front sight to the center of the bore.  For scoped firearms the number is usually insignificant depending on the setting for the scope.  For most calculations the distance from the center of the bore to the center of the scope at the receiver is good enough.  An easy way to get this measure is to put a cleaning rod down the bore and measure from the center of the rod to the center of the scope.  The scope height is typically measured in units of inches.  Typical measured values are from 0.5 to 3.5 inches.

Shots Per Group:  The number of shots the shooter takes at a single target.  Typically the resulting measure is used to describe accuracy of a given firearm/cartridge combination.  As the number of shots increase in any given group, the size of the group will get larger.  Modern Ballistics calculates the effect of changing the number of shots in a group from data obtained from a different group with a different number of shots.  For example, “Modern Ballistics” will calculate the probable size of a ten shot group from a known five shot group.  This can be done in several ways.  From the Edit/Select, Conditions dialog the shots per group may be changed or one can select either table or graphic view and set the independent variable to be “Shots Per Group”.

Temperature:  A measure of the hotness or the coldness of the air.  This measure affects the density and hence the drag of the bullet as it passes through the atmosphere.

Windage:  The horizontal movement of the bullet due to cross winds.  This offset may be measured in MOA, Mils, or inches.

Wind Error.  The extreme spread (90 % confidence) of the variation in wind estimates.  For example, if on the average, 90% of the time the wind is between 9 and 11 miles per hour the wind error would be two miles per hour.

Wind Speed:  The velocity of the wind through which the bullet must travel.

Wind Direction:  The angle of the wind to the path of the bullet.  Perpendicular winds (90 degrees) have more effect than winds blowing parallel ( 0 degrees) to the path of the bullet.

Zero or Zero Range:  The range at which the bullet crosses the light of sight in the vertical plane on the descending portion of the trajectory.  In a normal horizontal trajectory the bullet crosses the line of sight twice.  Once on the ascending leg of the trajectory when the bullet first crosses the light of sight (Near Zero) and second when the bullet is descending.  Where the bullet crosses the line of sight on the descending part of the trajectory is called the zero or the zero range.  The bullet path through the line of sight twice is due to the relationship of the rifle bore to the line of sight.

Last update: 05/26/2008