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B A L L I S T I C Version 3.20 (C) Copyright 1988 by William R. Frenchu DISCLAIMER Reloading small arms ammunition can be a DANGEROUS pastime. The purpose of this program is NOT to teach the fundamentals of this fascinating hobby but rather to aid the hobbyist in assessing the performance of the ammunition he has produced. It is assumed from the outset that the user of this program is acquainted with basic reloading techniques. For review, a list of references wherein may be found the necessary instruction is included in Appendix B of this document. DO NOT ATTEMPT TO PRODUCE AMMUNITION FOR YOUR- SELF OR OTHERS UNTIL YOU ARE COMPLETELY FAMILIAR WITH ALL THE FUNDAMENTALS OF RELOADING. ALWAYS START WITH THE MINIMUM LOAD AND WORK SLOWLY UP TO (NEVER EXCEED) THE MAXIMUM LISTED LOAD. Although every reasonable care was taken to insure the accuracy of this program, it is provided "AS IS" and without warranties as to performance of merchantability or any other warranties whether expressed or implied, including, but not limited to warranty of fitness for a particular purpose. Good data processing procedure dictates that any program be tested with non-critical data before relying on it. The user must assume the entire risk of using the program. The author will assume NO responsibility for any damage or injury that may occur. User Supported Software This program may be copied and freely distributed for any non- commercial use provided all accompanying files and documentation are included WITHOUT MODIFICATION. See Appendix E for further information (and the usual pitch for cash). TABLE OF CONTENTS ----------------- 1. About the Program ....................................... 1 A. General ............................................... 1 B. Program files ......................................... 1 C. System requirements ................................... 1 D. Program limitations ................................... 1 E. Notation .............................................. 2 F. What's new ............................................ 2 G. The future ............................................ 2 H. Acknowledgments ....................................... 3 2. Using the Program ....................................... 4 A. Starting the program .................................. 4 B. Command line arguments ................................ 4 C. Calculating the ballistic coefficient ................. 5 D. The ballistic table ................................... 5 E. Sight (trajectory) tables ............................. 5 F. Plotting the trajectory ............................... 6 G. Modifying the ballistic coefficient ................... 7 H. Changing the cross wind value ......................... 7 I. Changing the input function table ..................... 7 J. Miscellaneous functions menu .......................... 7 K. Calculating recoil .................................... 8 L. Calculating minimum twist ............................. 8 M. Calculating the point blank range ..................... 9 N. DOS shell ............................................. 9 O. Instrumental velocity correction ...................... 9 P. Velocity statistics ................................... 9 Q. Target statistics ..................................... 10 3. The Ballistic Table ..................................... 11 A. The table header ...................................... 11 B. Energy ................................................ 11 C. Momentum .............................................. 11 D. Maximum height ........................................ 12 E. Deflection ............................................ 12 F. Drop .................................................. 12 G. Lead .................................................. 12 H. Time of flight ........................................ 12 I. Trajectory ............................................ 13 4. The Configuration File .................................. 14 A. Using the configuration file .......................... 14 B. Allowable parameters .................................. 14 5. Sources of Data ......................................... 16 A. Altitude .............................................. 16 B. Ballistic coefficient ................................. 16 C. Bullet weight, length and caliber ..................... 16 D. Gun and powder weight ................................. 16 E. Specific gravity of bullet alloys ..................... 17 F. Temperature, atmospheric pressure and wind ............ 17 G. Velocity .............................................. 17 6. Using GENTABLE and READTABLE ............................ 19 A. Using the pre-programmed functions .................... 19 B. Creating custom function tables ....................... 19 C. Checking the function file ............................ 20 Figures .................................................... 21 Appendix A, Glossary ....................................... 26 Appendix B, Information Sources ............................ 29 Appendix C, Coefficients for Several Factory Cartridges .... 30 Appendix D, Specific Gravities of Bullet Alloys ............ 33 Appendix E, User Supported Software ........................ 34 Registration Form .......................................... 35 1. ABOUT THE PROGRAM A. General BALLISTIC is a Turbo C (v1.5) program written to generate ballistic tables for shooters. Given certain easily obtainable data, it calculates such useful information as the ballistic coefficient and sectional density, remaining velocity, energy, momentum, drop, wind deflection, maximum height, time of flight and lead (for a moving target) at a given range. In addition, it can be used to determine the amount of recoil generated by a cartridge and gun, estimate the minimum twist necessary for bul- let stabilization, calculate point blank ranges generate target and velocity statistics, and produce trajectory tables for est- imating "holdover". Finally, BALLISTIC will produce a plot of the bullet's trajectory versus range. It does all this by comparing the bullet in question to a "standard bullet" with a well known trajectory. As this data is calculated before use by a separate program (GENTABLE), the user's ballistic tables are produced very quickly. B. Program files The following files should be included in any distribution of BALLISTIC: BAL-GEN.EXE -GENTABLE :Creates ballistic function tables. BAL-READ.EXE -READTABLE :Optionally checks function table. BAL-READ.ME! -Describes version, etc. BALISTIC.EXE -BALLISTIC :Executable file. BALISTIC.DOC -This file. BALISTIC.REV -BALLISTIC Revision history. C. System Requirements BALLISTIC should run on most IBM BIOS-compatible computers using PC/MS-DOS 3.0 or above. It requires 256k of free memory and at least one disk drive. Non-graphic functions are directed to the default display. Graphic output (for Shareware versions) requires a VGA, MCGA, EGA, CGA or Hercules compatible display card. Registered versions can be supplied that support the higher resolution modes of the AT&T (400 line), Toshiba 3100, IBM 8514, PC-3270 or Everex EGA+. BALLISTIC has been tested and found to operate properly on the following systems: PC/XT with Hercules monochrome or ATI "EGA Wonder" adapter PC/AT with CGA or EGA adapter PS/2 System 30 with VGA adapter NEC MultiSpeed Portable BIOS Model G (V40 CPU) AT&T 6300 Compaq Plus with Compaq CGA-type adapter Compaq DeskPro 386 with Compaq EGA-type adapter D. Program limitations Any program of this type will have certain limitations re- garding its use and accuracy and BALLISTIC is no exception. These discrepancies between actual and calculated performance arise BALLISTIC v3.20 - (C) Copyright 1988 W.R. Frenchu Page 1 primarily because of the inability of the user to measure input values exactly and certain approximations the program uses in its calculations. Assuming that the input values are known to 1% the average user should find agreement with published data to be 1-2% for all velocity and trajectory calculations. The recoil section, due to the more approximate nature of the calculation, shouldn't be considered more than 10-15% accurate. In any case, while the numbers produced by the program are believed to be accurate enough for all practical purposes, they are meant only as a guide to ammunition performance. How a particular load performs with a given gun can ONLY be determined by actual firings. While Ingalls' ballistic table is historically the most commonly used for this sort of work, several others are likely to be encountered. (Many manufacturers, for instance, favor the "G1" table.) For the types of bullets most often used by reloaders the results will be very similar regardless of the table used. In- deed, the variation between handloads or factory ammunition ran- domly selected from the same lot will probably be greater than the discrepancies noted between different tables over normal shooting ranges. For best results, one should try to use the same input function to produce the table that was initially used to calculate the ballistic coefficient. However, this isn't always possible, as in the case where a published coefficient was cal- culated using a table to which the program doesn't have access. E. Notation Throughout this document, keys to be pushed in response to program prompts are enclosed in angle brackets. For example, "press <1>" means to press number 1 on the keyboard. For "press <ENTER>", use the key labeled either "return" or "enter". "En- tering" a value will require that the <ENTER> key be pressed when finished, i.e., to "enter 10" press <1><0><ENTER>. F. What's New There have been several additions to the program since ver- sion 3.10. Some of these include: 1. Added sectional density calculation to table. 2. Added calculation for correction of instrumental velocity to true muzzle velocity. 3. Added calculation of velocity statistics, including mean, extreme spread, and standard deviation. 4. Added calculation of target statistics, including group center, group size and indication of "true flyers". 5. Added Epson FX80 support for graphics screen dump. 6. Fixed bug in DOS Shell command. 7. Added helix angle calculation to twist section. 8. Added multiple plot save and restore. G. The Future BALLISTIC isn't perfect (or even necessarily finished). It is hoped, for instance, that future releases will incorporate a "Powley Computer" type computation for estimating the powder charge necessary for a given velocity. The ability to make calcu- lations based on distances given in meters or yards would also be a welcome improvement, as would an on-line database relating to commercially loaded cartridges. Additional features the author is BALLISTIC v3.20 - (C) Copyright 1988 W.R. Frenchu Page 2 considering include: context sensitive help, reading/writing load data to dBase III or Lotus 123/Symphony compatible files, and plotting of functions other than trajectory (i.e., energy or momentum vs. range). The author is interested in adding new function tables if reliable data can be found. He is currently on the lookout for a copy of BRITISH TEXTBOOK OF SMALLARMS or listings of the "J" or "G5" tables. Also of interest is additional specific gravity data for commonly used bullet casting alloys, and information on the types of materials being used in the "new" non-lead bullet de- signs (i.e., bronze) AND the "old" ones (steel). All things will come to those users who wait (and support BALLISTIC with the voluntary contribution!) All in all, BALLISTIC seems likely to fill the needs of many shooting buffs. Included in the documentation is a section listing sources for further reading on small arms ballistics and reloading. The local gun shop or public library may have others. READ some of them!.. AND the disclaimers. Then enjoy the program. H. Acknowledgments The author is indebted to the following people for their help, support, and the many suggestions they made. Without dedi- cated users such as these, the program would never have reached its current level of sophistication: Bart Carfizzi Hugh Roberts Jim Kreiser James Roberts Donald Terwilliger Dave Zarodnansky Special thanks, of course, are due to the author's wife and family, Susan, Billy and Karen, for understanding (or at least putting up with!) the author's wild mood swings, ranting and raving as various parts of BALLISTIC (which were working just fine yesterday!) stopped working for no apparent reason. Thank you. BALLISTIC v3.20 - (C) Copyright 1988 W.R. Frenchu Page 3 2. USING THE PROGRAM The goal in writing BALLISTIC was to produce a program which was at once versatile and relatively easy to use. While there is still room for improvement, some success in both of these direc- tions has been achieved. The program is primarily menu driven and prompts whenever input data is required. Additionally, data en- tered (or calculated) in one section of the program need not be re-entered unless the user wants to change the value. Data the program knows about are displayed during the prompts. To accept the displayed value press <ENTER>. To change it, simply type the new data over the old, then press <ENTER>. (The table title and uphill/downhill shooting angle must ALWAYS be entered expli- citly.) To correct typing errors on the current line, use the <BACKSPACE> key, NOT the <DELETE> key. Improper entries on pre- vious lines can be corrected by using the <ESC> key to "back up" to the bad line, then retyping the data. In most cases, obviously improper data will be refused and an acceptable range displayed. Input filenames will be checked for existence before they are accepted. A. Running the Program for the First Time Prior to running BALLISTIC for the first time, the file containing the function table required by the program must be created using GENTABLE (v3.00 or above, see Section 6). This file will contain the version number of the GENTABLE used to produce it, the function name, some atmospheric data, the maximum and minimum velocity and S and T value pairs. Once this file has been created (and optionally checked using READTABLE) BALLISTIC can be invoked. Only BALISTIC.EXE and a function file need actually be present on the disk when running the program. B. Command Line Arguments BALLISTIC is started by simply typing its filename (BALISTIC) at the DOS prompt, optionally following it with one or both of the following arguments. "-BIOS" will cause all video output to be done using BIOS calls rather than direct screen writes. This will significantly slow screen I/O, but may be necessary in cases where the computer being used isn't 100% IBM compatible, or when the program is being operated remotely. The second argument, "-F" followed (with NO spaces) by the name of a BALLISTIC function file, causes the named function file to be loaded instead of the default file BALISTIC.TAB. BALLISTIC will first attempt to read the configuration file (BALISTIC.CFG, see Section 4), then search for the default func- tion file (either BALISTIC.TAB or the command line specified file), prompting the user for the name of an alternate if it's not found. The default file type is ".TAB" which need not be entered. (To enter a filename with no extension enter "filename." with the trailing period.) BALLISTIC will next read the function file, make a check to determine its validity (a simple checksum procedure), and present the user with the main menu. (Fig. 1) BALLISTIC v3.20 - (C) Copyright 1988 W.R. Frenchu Page 4 C. Calculating a Ballistic Coefficient The first step in developing a ballistic table is to deter- mine the ballistic coefficient. If this value cannot be found explicitly in one of the sources described in section 5B, main menu choice 2 may be used to calculate it. Press <2> and the program will prompt for an initial and final velocity, the range and some atmospheric data. After this has been entered, the cal- culated value of the effective ballistic coefficient (as well as the coefficient at standard conditions for the function chosen) will be displayed on the screen (Fig. 2). Having found the coef- ficient, BALLISTIC can now calculate the table. Press the <ENTER> key to redisplay the main menu then <1> to bring up the input section. D. The Ballistic Table Figure 3 shows the input data for main menu choice 1, cal- culating the ballistic table. Since the initial velocity, range and ballistic coefficient have been entered or calculated on a prior screen, these values needn't be re-entered unless a dif- ferent value is required. In this case, entering a range value of 500 will create a table to 500 yards based on the performance noted over the first 100. Entering a value of zero for the range will cause the program to switch to metallic silhouette mode. The user will then be prompted for his choice of standard silhouette rifle or pistol ranges rounded to the nearest yard. As long as the input value for range remains zero these alternate ranges will be used. The bullet diameter prompt should be answered with the actual diameter in inches although input of the firearm's nominal caliber (with leading decimal point, i.e., .22) is often close enough. The final necessary data item is the number of intervals into which the total range should be divided. The max- imum number allowed is the smaller of 50 or the total range (in yards). Data entry is concluded with an optional table title. Throughout the program, entering a value of 0.0 for the "effective" ballistic coefficient, will cause the program to re- prompt for the value of the coefficient at STP. The "effective" value will then be calculated from the STP value using the cur- rent values of temperature and pressure. (Temperature and pres- sure may be changed from either main menu choice 3, or the con- figuration file.) Figure 4 shows the table itself and the program's prompt for generation of a sight table. At this point, should it be desir- able to get a printed copy, press <1>. The program will redirect ballistic table output to the system's LST: device and return to the prompt. A form feed (page eject) can be sent to the printer by pressing <2>. The "New Data" choice, <4>, will return the user to the data entry screen to calculate another ballistic table, while "Main Menu" (<5> or <ESC>) will jump directly back to the program's initial screen. E. Sight (Trajectory) Tables. Sight (trajectory) tables can be produced by pushing <3> in response to the prompt at the bottom of the ballistic table. The program will require that distance for which the weapon is "sighted in" (this value need NOT have appeared in the range BALLISTIC v3.20 - (C) Copyright 1988 W.R. Frenchu Page 5 column of the original ballistic table), the height of the sight above the centerline of the bore, and any angular correction for uphill or downhill shooting. In silhouette mode, entering a value of zero for the targeted range will cause the prompt to take the form of which silhouette (chicken, pig, turkey or ram) the weapon is zeroed for. The user should respond with the first letter of the appropriate target. Output of this table can be diverted in exactly the same manner as the ballistic table. Pressing <3> allows the user to enter new data for another sight table (using the current ballistic conditions), and <5> (or <ESC>) returns to the ballistic table and prompt. F. Plotting the Trajectory. Pressing <4> at the sight table prompt will present the user with a graphic representation of the bullet's trajectory on sys- tems with an appropriate graphics card. Range, in yards will be indicated along the bottom, with tic marks appearing at distances corresponding to the entries in the ballistic table. Dotted lines will appear vertically at the distance for which the weapon is zeroed and horizontally at the line of sight. The trajectory (in inches above or below the line of sight) is indicated on the left scale. Pressing <A> (for axes) will allow the user to set a "viewport". The program will prompt for starting and ending range, and the maximum and minimum trajectory, then plot only that portion of the trajectory that falls in the described "win- dow". Pressing <S> (for start) will reset the plot to the initial (program chosen) limits. <G> will toggle the appearance of a grid on the plot and <H> will provide a short help screen. If <W> is pressed, trajectory data (for the current range viewport ONLY) will be written to a file. The user will first be prompted for a filename and any existing file with that name will be overwritten. (There is NO default extension.) ONLY the trajec- tory plotted with a solid line will be saved to the file. This data may be "merged" with the current trajectory plot at any time by pressing <R>. When read back, it will be scaled and plotted using a dotted line to distinguish it from the current plot. The number of files that can be read back is limited only by the user's ability to tell them apart on the graphics screen. Hardcopy of the plot (actually, a screen dump) may be ob- tained by pressing if an appropriate graphics printer is present. (Supported printers are discussed in the configuration file section under PTYPE.) Depending on the display adapter and printer, this may require several minutes. (A typical EGA gra- phics screen dump is about 30k, roughly the size of a ten page document, and takes just as long to print.) Printing may be aban- doned at any time by pressing a key. Users with a printer not listed may want to try using the <PRINT SCREEN> key which will usually require that the program GRAPHICS.COM (from the DOS sys- tem diskette) be run before BALLISTIC is started. Neither method will work with all display and printer combinations. (Registered users may, of course, contact the author and request support for their particular printer.) Pressing <X> or the <ESC> key will return the user to the sight table prompt. From the sight table press <5> (or <ESC>) to return to the ballistic table, (Figure 4 again) then a <5> (or <ESC>) to return to the main menu. BALLISTIC v3.20 - (C) Copyright 1988 W.R. Frenchu Page 6 G. Modifying the Ballistic Coefficient Those living at high altitude or in areas of extreme temp- erature will want to adjust published (sea level) values of the ballistic coefficient to more accurate local values. Main menu choice 3 may be used to accomplish this (Figure 5). The program will need to know the altitude, barometric pressure and temper- ature in addition to the value of the ballistic coefficient at STP (Standard Temperature and Pressure, the published value). Bear in mind that these meteorological values (especially temper- ature) ALSO affect the initial velocity of a given load. This effect is beyond the ability of this program to calculate but descriptions of it may be found in many reloading manuals. H. Changing the Cross Wind Value and Angle Menu choice 3 also allows for adjustment of the speed of the cross wind used to calculate wind deflection. By default, the program sets this value to 10 miles per hour, blowing directly across the path of the bullet (0 degrees). It should be noted that deflection is a linear function, i.e., a 5 mph wind will deflect a bullet by exactly half the amount of a 10 mph wind. The angle of the cross wind may be changed here as well. In program coordinates, 0 degrees (the default) is blowing directly across the bullet's path, either left to right or right to left. 90 degrees would be either a head or tail wind with no cross wind component. These values are used ONLY for calculating deflection. Their effect on other aspects of the trajectory is currently ignored. I. Changing the Input Function Table Starting with version 2.00, it is possible to switch input function tables without restarting the program. Pressing <4> from the main menu will cause a prompt for the new file name. If a filename containing wildcard characters ("*" or "?") is entered, the directory of all matching filenames will be displayed. As noted in section A, the default table type is ".TAB" which need not be entered. Simply press <ENTER> to abort and return to the main menu. This option doesn't alter the fact that BALISTIC.TAB (or the filename supplied with the "-F" command line option) will be searched for (and loaded if present) when the program is first started. It is provided only for users who routinely use more than one function table. Even so, program startup will be simpli- fied if the table most commonly used is copied to BALISTIC.TAB. It should be noted here that loading a new function file will not reset the temperature and pressure to the defaults for the new table. Thus, some care should be taken if switching be- tween two tables that use different standard conditions. J. Miscellaneous Functions Menu Pressing <5> at the main menu prompt will present the user with the miscellaneous functions menu. From this menu the user may elect to calculate recoil, shot statistics, the minimum ne- cessary twist for bullet stabilization, or the point blank range for a given target size. BALLISTIC v3.20 - (C) Copyright 1988 W.R. Frenchu Page 7 K. Calculating Recoil The recoil energy and velocity of a weapon can be calculated using miscellaneous menu choice 1, provided its weight and the weight of the powder charge are known (Figure 6). This number can be deceptive as the perception of recoil by different shooters is VERY subjective. In addition to the physics involved, there must be some consideration given to the fit of the gun to the individ- ual, shape and material of the stock or grips, etc. Many shooters, for instance, fear the recoil of a 12 gauge shotgun even with target loads while thinking nothing of using a 6 pound 30-06 despite the fact that the "calculated" recoil can be quite similar. Such recoil is often in the eye (or shoulder) of the beholder. This section also calculates whether a "muzzle brake" type device will be useful in reducing felt recoil by allowing the user to determine the rough percentage of recoil caused by the bullet itself (which a muzzle brake cannot affect). The value indicated is the level to which recoil energy would be reduced if there were no powder at all. This is a crude estimate of what a shooter might achieve with a perfect brake. (Bear in mind, how- ever, that NO muzzle brake is 100% effective and the actual amount of reduction will be less.) The recoil calculation used by BALLISTIC is a very rough approximation, similar to that discussed in the March 1988 Amer- ican Rifleman. It would be extremely challenging to write a com- pletely accurate description of the recoil process. It would also be very difficult to use as many variables are involved in- cluding, but not limited to bore cross sectional area, length of barrel, atmospheric pressure and temperature, type of powder, loading density, etc. The values calculated here should not be considered accurate to more than 10-15%. Barrel/powder combina- tions that produce excessive muzzle flash will be even less accu- rate. L. Calculating Minimum Twist The slowest twist that will stabilize a bullet in flight may be calculated using miscellaneous menu choice 2. The formula used here is the approximation credited to Sir Alfred George Greenhill in 1879. Necessary input data includes the bullet's diameter and length in inches and specific gravity. The default value for specific gravity is the average density of a typical jacketed bullet. Also listed on the input screen (for reference) is the specific gravity of pure lead. Specific gravities (or densities) of other bullet alloys seem difficult to find. It should be pointed out that these specific gravities can NOT be added algeb- raically. That is, an alloy containing 50% lead and 50% tin will NOT have a specific gravity that is the average of the two pure metals. Appendix D of this document contains specific gravity data for a small selection of common alloys. The angle made by the rifling grooves and the axis of the bore is known as the "helix angle". As some European manufac- turers describe the twist using this value rather than the custo- mary "1 turn in xx inches", BALLISTIC provides both numbers. It has been pointed out to the author, that this approxima- tion was originally intended for use with artillery projectiles. More recent findings indicate that, for typical small arms am- BALLISTIC v3.20 - (C) Copyright 1988 W.R. Frenchu Page 8 munition, a Greenhill number smaller than the default of 150.0 (100 has been suggested) may be appropriate especially under adverse atmospheric conditions such as rain and snow. A discus- sion may be found in the June 1988 issue of Rifle. ("Shooting the Kalashnikov", pp. 28 - 31.) This number may be "permanently" changed using the configuration file. M. Calculating the Point Blank Range Given the velocity, sight height and ballistic coefficient, a point blank range may be determined for a specific target size. The point blank range is the maximum range for which a bullet can be counted upon to strike a target by simply aiming the weapon directly at it. For example, given a 6 inch target, a point blank range may be calculated so that the bullet is always less than 3 inches (above or below) from the line of sight. BALLISTIC will calculate this distance for a given target size and tell the user for what range the weapon should be sighted and what trajectory the bullet will have at 100 yards. (If the targeted range is less than 100 yards, the trajectory at 25 yards will be given in- stead.) This figure may be used to sight the weapon when the targeted range is either unrealistically far away, or an unusual number of yards. For instance, in the example screen, sighting the weapon 2.9 inches high at 100 yards will allow the shooter to hit a 6 inch target out to 257 yards, without allowing for any holdover. However, the bullet will only strike the CENTER of the target at 219 yards. It should be noted that the point blank range is ALWAYS calculated for an uphill/downhill angle of zero degrees. As before, entering a value of zero for the "effective" ballistic coefficient will re-prompt for the STP value. N. DOS Shell (Escape to DOS) Users operating under MS/PC-DOS version 3.00 or higher have the option of shelling out to DOS from the main menu. The only other requirement for this option is that there be a copy of COMMAND.COM in the place indicated by the COMSPEC environment variable. O. Correction from Instrumental to True Muzzle Velocity When bullet velocities are measured by chronograph, it is necessary to set the first (or start) screen far enough away from the muzzle to avoid blast effects. The second (or stop) screen must be set a fixed distance from the first so the elapsed time between the two can be measured. Unfortunately, the speed calcu- lated under these conditions is NOT the actual muzzle velocity, but rather the average speed of the bullet over the interval between the two screens. While the difference is usually small, it is possible to make the correction to the true muzzle velo- city, provided the screen distances and the ballistic coefficient are known. Miscellaneous menu choice 4 provides for this calcu- lation. P. Calculation of Velocity Statistics Not all bullets from the same lot will leave the barrel of a gun at exactly the same speed. Some statistical variation is also to be expected in the measurement of any physical quantity. Anal- BALLISTIC v3.20 - (C) Copyright 1988 W.R. Frenchu Page 9 ysis of a string of measured velocities (up to 25) may be accomp- lished using miscellaneous menu choice 5. Output data includes the maximum and minimum velocity values (and extreme spread), the average velocity for the string, and the standard deviation of the sample. BALLISTIC updates these values as each point is en- tered, allowing the user to determine the effect of each shot on the statistics. Pressing <ESC> at the prompt for "Next Velocity" will display the statistics menu, allowing the user to correct or delete the entry list. From here, pressing <5> (or <ESC>) will return to the miscellaneous menu. A complete discussion of statistics is beyond the scope of this document, but it should be noted that standard deviation of a velocity string is a measure of data or sampling scatter, and NOT necessarily an indication of the target accuracy of a part- icular load. (Accurate loads will, however, tend to have lower standard deviations.) Examination of the standard deviation can indicate whether a particular measurement should be included in the average. For example, in a string of 10 shots or less, it is usually safe to delete any velocity that deviates by more than 2 standard deviations from the average as a statistical anomaly. BALLISTIC will mark each shot that exceeds the current average value by more than one standard deviation (SD). A single star (*) indicates difference of more than one but less than two SD. Two stars (**) indicate a value more than 2 SD from the mean. Q. Calculation of Target Statistics BALLISTIC will also provide some statistical analysis of targets, including group center, group size and an indication of "true flyers". This section is most easily used when the x,y coordinates of each shot can be read directly from one of the "sighting in" targets, commonly supplied by some firearms manu- facturers. (These targets are marked off in small squares rather than the concentric circles used for "bullseye" shooting.) Enter the coordinates of each shot (up to 10 total) and the program will display the x,y coordinates of the group center, and the size of the group as measured across the two shots farthest apart. As with the velocity statistics section, pressing <ESC> in response to a coordinate prompt will cause the statistics menu to be displayed. "Flyers" will be marked in a manner similar to that used for velocity statistics. A single star will indicate that the shot exceeds one standard deviation from the group center in the x direction, the y direction or both. Two stars indicates a devia- tion of more than 2 SD from the current group center. BALLISTIC v3.20 - (C) Copyright 1988 W.R. Frenchu Page 10 3. THE BALLISTIC TABLE The primary purpose of BALLISTIC is to produce a "ballistic table" showing the remaining velocity at given ranges. The pro- gram is also capable of supplying a wealth of additional infor- mation derived from these values. (Refer to Fig. 4) A. The Table Header The ballistic table header merely provides a "data echo" of the conditions used to produce the accompanying table. In addi- tion to the table title and other user supplied data, two calcul- ated values are displayed here. Sectional density of the bullet is defined as the weight of the projectile in pounds, divided by the square of its diameter (in inches). Sectional density can provide the reloader with a handle on two important pieces of information. First, it provides a measure of how fast a bullet can be safely "pushed". Certainly for a given caliber, bullets with a high sectional density should not be loaded to as high a velocity as bullets with a low value. Secondly, a bullet with high sectional density will tend to have greater penetration than a projectile with a smaller value. An excellent discussion of sectional density and its relation to hunting bullets may be found in June 1988 issue of The American Rifleman. ("From the Loading Bench: Sectional Density Counts", page 16) The IPSC Power Factor is a number used by the International Practical Shooting Confederation to determine whether a comp- etitor's handgun load is to be scored as "major" or "minor" cal- iber. It can be calculated by multiplying the bullet weight in grains by the initial velocity and dividing by 1000. Any load whose power factor is over 175 is scored as major. Factors be- tween 125 and 175 are scored as minor caliber. Loads with a power factor of less than 125 are not legal for IPSC competition. B. Energy The kinetic energy of a moving body is described by 1/2 times the mass of the body multiplied by the square of its vel- ocity. It may be thought of as the amount of work the bullet is able to do on its target. The unit (foot-pounds) is the amount of work necessary to lift an object weighing 1 pound to a height of 1 foot. Many hunters feel this quantity is a good one to use when determining the suitability of a given load for a particular game animal as (under certain conditions) it is probably related to the "killing power" of a projectile. One cannot rely entirely on this simplified picture, however, as terminal ballistics is also concerned with bullet and target construction. C. Momentum As, in any collision of moving bodies, momentum is com- pletely conserved, it may be thought of as the "striking" or "knockdown" power of a projectile. This can be slightly mis- leading, however, as the conservation applies only to the total "system" of particles. If, for example, the bullet completely penetrates the target, it may retain a large portion of its orig- BALLISTIC v3.20 - (C) Copyright 1988 W.R. Frenchu Page 11 inal momentum, transferring to the target only that part it act- ually lost. It is defined as the mass of a body times its vel- ocity. D. Maximum Height The maximum height calculated by BALLISTIC is the greatest distance that a projectile will pass above a straight reference line drawn from the muzzle to its current position at any given range. (Many books refer to this number as the maximum ordinate.) It is NOT the same as the mid-range trajectory which is defined as the bullet's trajectory (above the line of sight) exactly half way to the indicated range. Typically, the maximum height occurs slightly after the half way point and is very slightly larger. For average shooting conditions, however, the two values may be taken as equal without causing any great error. E. Deflection Deflection, as used in BALLISTIC, is the amount of sideways motion which can be attributed to the action of a crosswind on the projectile. This value is directly proportional to wind speed, that is, if the wind at the site is 5 m.p.h. and the fig- ures calculated are for 10 m.p.h., simply divide the table values by 2. Deflection should not be confused with drift, the sideways motion caused by the bullet's spin. Deflection is typically a much larger figure. For example, at 1000 yards the drift of a .30 caliber service bullet is only about 7 inches. Compare this value with the roughly 175 inches of deflection produced by the same bullet in a 10 mph cross wind. F. Drop From the instant a bullet leaves the barrel, gravity and air resistance conspire to bend its path from that along which it was originally projected (the bore line, NOT the line of sight). A bullet's drop is the distance it has fallen away from that ini- tial path, known as the line of departure. This is that quantity to which shooters refer when speaking about the "flatness" of a particular loading. G. Lead Lead is primarily of interest to those who hunt. By now, most experienced hunters will have realized that aiming directly at an animal running across the path of the bullet is almost guaranteed to produce a miss. By the time the bullet has gotten to the point of aim, the animal is somewhere else. The trick, then, is to know how far ahead of the target one needs to aim so that bullet and target arrive in the same place at the same time. In BALLISTIC, the units used for this figure are "inches per m.p.h. of target speed" and are used as follows. Imagine a target moving 10 m.p.h. across the path of the bullet at a distance of 100 yards. Examining the table (Fig. 4) produces a value of 2.0 in/m.p.h. at that distance, so the appropriate target lead would be (10 m.p.h.) times (2.0 in/m.p.h.) or 20.0 inches. Wind speed is NOT taken into account during the calculation of lead. H. Time of Flight Time of flight is simply that; the amount of time, in sec- BALLISTIC v3.20 - (C) Copyright 1988 W.R. Frenchu Page 12 onds, necessary for a bullet to travel the distance from the muzzle to the indicated range. I. Trajectory Loosely speaking, trajectory is simply the path of any moving projectile. BALLISTIC provides both tabular and graphic representations of this path, relative to the weapon's line of sight, i.e., the line drawn directly from the sights (either "iron" or telescopic) to the target. It should be noted, that the actual trajectory of a small arms bullet coincides with the line of sight at only two places. Once, a few yards from the muzzle, (when its motion relative to the line of sight is upward) and again at the targeted (or "sighted in") distance (when it crosses in a downward direction). Trajectory may be described in several ways, but the two most common are "inches" and "minutes of angle". When expressed in inches it is the actual distance of the projectile above or below the line of sight. This value may be converted to the necessary angular correction (minutes of angle, or M.O.A.) by applying the conversion factor of 1 M.O.A. = 1.047 inches/100 yds. This value is particularly useful as most sight adjustments are calibrated in minutes of angle. Target scopes are usually calibrated at 1/4 minute per "click", while iron sights may be as much as 1 minute per click. (In this notation, minutes do NOT refer in any way to units of time, but rather to 1/60th of an angular degree.) BALLISTIC provides both systems in its traj- ectory tables. When the uphill/downhill angle is not equal to zero, the bullet will follow a higher trajectory than it would during level firing. That is, shooting either uphill or downhill will cause the bullet to shoot higher than it is aimed. Under these condi- tions, the projectile doesn't make a second crossing of the line of sight until AFTER the targeted distance. The term "level firing" used here may be slightly misleading. Almost all small arms are sighted so the initial angle of the bullet's departure is very slightly up. (This angle is known as the "angle of depar- ture", and for a typical rifle, is less than one degree.) Firing uphill or downhill usually produces a tilt that dwarfs this small value, so for practical purposes, the uphill/downhill angle used in the program may be thought of as the angle of departure, rounded to the nearest degree. BALLISTIC v3.20 - (C) Copyright 1988 W.R. Frenchu Page 13 4. THE CONFIGURATION FILE Version 3.20 of BALLISTIC will allow certain program de- faults to be overridden with the aid of the configuration file BALISTIC.CFG. This option was originally provided for users in the CP/M environment. The file is searched for only in the cur- rent directory when BALLISTIC is first started and is NOT neces- sary for the operation of the program. A. Using the configuration file The configuration file is an ascii text file each line of which contains the name of the parameter to be changed, one or more spaces, and the new value. Parameters listed as "must be integer" may NOT contain a decimal point or exponential notation. Certain parameters may only accept ON and OFF (or similar string choices) as values. Entries are NOT case specific. The following file would turn off the bell, set the default altitude to 2000 feet and set the video write mode to BIOS: BELL OFF Altitude 2000 video bios B. Allowable parameters The following parameters are allowable for BALLISTIC v3.20: ALTITUDE - The altitude to be used in the ballistic table and ballistic coefficient calculations. May be REAL. The default value is zero. BELL - Controls whether the console bell is rung for errors detected by the program. Allowable values are ON and OFF. The default is BELL ON. BKG - Determines the background text screen color. Allow- able values are 0 through 7. Must be INTEGER. The de- fault value is 0. This parameter is illegal for systems having only a monochrome text/graphics card. Following are the colors corresponding to each value: 0 - Black 4 - Red 1 - Blue 5 - Magenta 2 - Green 6 - Brown 3 - Cyan 7 - Lt. Gray COLOR - The text color. Default is 7. See BKG for a des- cription of allowable values and restrictions. GREENHILL - This option specifies a new Greenhill number for use in the minimum twist calculation. Acceptable values range from 75.0 to 200.0. The default is 150.0. GRID - This option informs the program whether the grid should initially appear in the Plot function. This may BALLISTIC v3.20 - (C) Copyright 1988 W.R. Frenchu Page 14 also be toggled from the Plot function itself. Allow- able values are ON and OFF. PRESSURE - The atmospheric pressure used for the ballistic table and ballistic coefficient calculations. May be REAL. The default value is dependent on the function file chosen. PRINTER - Line width in characters of the system printer. Must be an INTEGER value from 80 to 200. Default is 80. PTYPE - Type of graphics printer connected to system. This option is only used by the graphic screen dump routine. Default is 1, for the HP Laserjet. Currently supported values are: 1 - Hewlett Packard Laserjet 2 - Star SG-10 (in IBM mode) 3 - IBM Proprinter 4 - IBM Graphics Printer 5 - Epson FX-80 TEMPERATURE - The temperature to be used for ballistic table and ballistic coefficient calculations. May be REAL. The default value is dependent on the function file chosen. VIDEO - Determines the method used to write to the screen. Allowable values are BIOS and DIRECT. BIOS causes all output to be done through the use of system BIOS calls. This mode may be useful for computers/graphics adapters that are not 100% compatible with the IBM PC family. It does, however, significantly slow output. Using the DIRECT option causes all screen output to be written directly to video memory. Default is DIRECT. BALLISTIC v3.20 - (C) Copyright 1988 W.R. Frenchu Page 15 5. SOURCES OF DATA Much of the data necessary for ballistic calculations is readily available. Even the ballistic coefficient can usually be calculated from the information at hand. Following are suggested sources for specific input data to the program. A. Altitude The calculation doesn't depend on altitude directly, but rather on the way air temperature and pressure vary with alti- tude. The program uses this value to determine what the "stan- dard" temperature and pressure are for a given ballistic func- tion. Users can look up the actual altitude of their location in an almanac or one of the U.S. Department of the Interior "Quad- rangle Maps" available at many sporting goods or camping stores. Either jot it down near the computer so it can be entered when the program is run or add it to the configuration file as de- scribed in section 4. B. Ballistic Coefficient This will probably be the most difficult number to find. Those who reload will usually be able to get this value from the manufacturer of their bullets. (Speer and Sierra, for instance, print this data in their reloading manuals.) The value for other bullets may sometimes be estimated by comparing bullet shapes, provided the bullet is of the same caliber. Comparing the bullet in question to a specially prepared chart of shapes is often more accurate. The DuPont Company at one time produced a series of these and other useful charts, called "A Short Cut To Ballis- tics". The complete set is supplied with Ackley's handbook and the specific chart for estimating ballistic coefficients is re- printed in HATCHER'S NOTEBOOK. The program itself will calculate the ballistic coefficient in certain cases. Both the initial and remaining velocity at a given range must be known. This data is available for factory loaded ammunition in manufacturers' literature and sources such as SHOOTERS BIBLE. (A short section of coefficients for several factory loadings calculated using this program and Ingalls' table may be found in Appendix C.) C. Bullet Weight, Length, and Caliber These are easy. On factory-loaded ammunition or components, bullet weight (in grains) and caliber will be written on the box. Those who cast their own bullets will need to weigh several sam- ples prepared with the actual alloy used. Take the average of half a dozen or so and use that value. A sufficiently accurate value for bullet length may be found with a ruler. D. Gun, Powder Weights These two are needed only to calculate the amount of recoil generated by a given load. The weight of a rifle can usually be found accurately enough on a bathroom-type scale. Actual weights of most firearms can be found in manufacturers' literature as well as in such sources as SHOOTER'S BIBLE, GUN DIGEST, and pro- BALLISTIC v3.20 - (C) Copyright 1988 W.R. Frenchu Page 16 duct reviews in many magazines. Don't forget to add in the weight of scopes, slings, custom stocks or any other accessories. Powder weights will be known if performing calculations for handloads. If using factory loads, try estimating by comparing to available reloading data. Find a load that moves a bullet of similar construction (jacketed, soft lead, etc.) to about the same muzzle velocity. E. Specific Gravity This value is only required for calculating the minimum necessary twist for stabilization. Two more or less standard values are 11.34 for pure lead, and 10.90 for a typical jacketed bullet. Other values are very difficult to find in the litera- ture. Hatcher, describes a fairly simple way to measure this quantity, but the two values above should be sufficiently accu- rate for most practical purposes. Appendix D of this document contains a short compilation of specific gravity data for some common Lead/Tin/Antimony alloys. These were taken primarily from volume one of the American Soci- ety of Metals METALS HANDBOOK. F. Temperature, Atmospheric Pressure, Wind Speed and Direction Suitably accurate values for temperature and pressure can be obtained from a weather report or newspaper. As with altitude, the calculation isn't terribly sensitive to these factors, so unless the range is in the Sahara Desert or Antarctica they can probably be ignored. (It CAN be interesting to set up a ballistic table and vary them just to see what happens... Experiment!) The same suggestion applies; try the program with and without cor- recting and see if the difference is big enough to realistically notice. Bear in mind that this program examines the effect of these variables only on the ballistic coefficient. Temperature, for instance, will also change the initial velocity of a load, a factor beyond the ability of this program to calculate. (Tables describing this effect can be found in both the Speer reloading manual and Ackley's handbook.) Temperature and pressure are also valid parameters for use in the configuration file. (Section 4) Wind direction can only be estimated at the actual shooting site. Zero degrees indicates a wind blowing across the bullet's path to either the right or left. Ninety degrees indicates a wind blowing either directly behind or directly into the bullet's path. As this value is only used for calculating wind deflection, a signed value isn't necessary. Also, since deflection is linear with wind speed, leaving the value set for the default 10 mph allows for easy interpolation at the range. G. Velocities Muzzle velocities of most factory ammunition can be found in periodicals such as the SHOOTER'S BIBLE. Those who reload are aware that estimated or reported velocities are usually listed with the loading data for a particular cartridge. The most effective way to find the velocity for a completely unknown load is, of course, the chronograph. Unfortunately, few people have access to one and their price puts them beyond the reach of the casual buyer. (The author once built an inexpensive attachment that allowed a Commodore-64 home computer to be used BALLISTIC v3.20 - (C) Copyright 1988 W.R. Frenchu Page 17 as a simple chronograph, but its usefulness was limited since a source of house current was still needed nearby... also, the C-64 isn't exactly portable. The technique SHOULD be adaptable to many other home computers and the author would be happy to discuss the project with registered users.) Ackley, in his book HANDBOOK FOR SHOOTERS AND RELOADERS, describes a simple "ballistic pendulum" that can be used to estimate projectile velocities. No external power is necessary; it relies on the kinetic energy of the bullet to swing a heavy mass. BALLISTIC v3.20 - (C) Copyright 1988 W.R. Frenchu Page 18 6. USING GENTABLE AND READTABLE A. Using the pre-programmed functions Before running BALLISTIC for the first time a file con- taining the chosen set of function values the program will use during its calculations must be produced. GENTABLE Version 3.00 makes the following functions available: FUNCTION VELOCITY ATMOSPHERIC max. min. temp. pressure British 1909 4000 0 59 29.53 "G1" 4094 300 59 29.53 Ingalls' 3600 0 60 30.00 Ingalls' (extended) 4094 0 60 30.00 The British 1909 and Ingalls' functions are practically identical until low velocities are reached. Both are well suited to calculations involving typical hunting or pistol bullets, i.e., rounded or slightly pointed (roughly two caliber radius) spitzers. Results for sharply pointed spitzers and boattails will not be as accurate with these functions as they might be with some others. Less accurate results will also be obtained if bal- listic coefficients calculated with one set of functions are used with another, i.e., using the coefficients listed in Appendix C (calculated with Ingalls' table) with the British 1909 tables. The extended Ingalls' table is simply the standard table continued to the maximum allowable program velocity following the method used in Hatcher. As values above 3600 are extrapolated, they may not be as accurate as those below. Many of the companies producing reloading components feel that the G1 table is the best choice for all around use. Indeed, most of the major ammunition manufacturers seem to use the G1 drag function for calculating their own "factory" ballistics and duplication of these tables is most easily accomplished using this selection. This function is used by SAAMI in calculating the tables they supply to the manufacturers as well. GENTABLE is started by typing its name (BAL-GEN) at the DOS prompt, optionally following it with a command line argument. The user will be presented with a short menu to which he should res- pond with the number of the function he desires. The program will next prompt for a filename to contain the new data, then create the table, overwriting any previous file with that name. Users that plan to routinely use more than one table should probably create them all ahead of time, renaming them to something more descriptive. Copy the one used most often to BALISTIC.TAB. GENTABLE will accept only one argument on the command line. If the flag "-BIOS" is used all video output will be sent to the screen via BIOS calls. The default is to write directly to screen memory. B. Creating custom function tables The user is not limited to using the functions produced by GENTABLE. Tables may be produced by any program or language that stores numbers in IEEE format, including Microsoft C v5.0 or BALLISTIC v3.20 - (C) Copyright 1988 W.R. Frenchu Page 19 Quick C. (There will be a problem calculating checksums when using Microsoft 5.0 unless the -Op optimization is used.) The file format and data types used are as follows: 1. Truncated revision number for version of GENTABLE used multiplied by -1. (int) 2. The table name. (char[32]) 3. Standard temperature for table data. (double) 4. Standard pressure for table data. (double) 5. Maximum velocity in table (<=4094). (unsigned) 6. Minimum velocity in table. (unsigned) 7. S_table, T_table pairs as described in HATCHER'S NOTEBOOK for velocities (max >= v >= 0). (float) 8. Checksum calculated as the sum of (S_table - T_table) values. (float) C. Checking the function file After creating the function file it may be optionally checked with READTABLE. READTABLE was originally written as a debugging aid and is included only to satisfy user's curiosity as to what is contained in a ballistic function table. It might also be of some use to those contemplating creation of their own func- tion files. Once started, it prompts the user for the name of the function file to be examined, displays the header information, then prints the values to the screen. The speed of the display may be altered by pressing either the <-> or <+> keys. Pressing any other key will cause the display to pause at the next value. Once paused, pressing <ESC> causes execution to abort. Any other key will cause the program to resume. As with GENTABLE, READTABLE is started by typing its name (BAL-READ) at the DOS prompt, optionally followed by any of the following flags: -BIOS - Causes the program to perform all writes using BIOS calls. This will significantly slow output. -F - (From) - Start listing the table to the screen with the value immediately following the argument, i.e., -F2000 will start the listing at 2000 fps. -T - (To) - End the listing at the value following this argu- ment. -N - (Noprint) - Don't print the table, calculate the check- sum only. -G - (Graphics) - Don't use the IBM graphic character set. (Use ASCII characters instead.) Flags requiring numeric arguments should NOT have a space between the flag and input value. BALLISTIC v3.20 - (C) Copyright 1988 W.R. Frenchu Page 20 --====-- (C) Copyright 1988 by W.R. Frenchu - MAIN MENU - 1 ........... Calculate Ballistic Table. 2 ..... Calculate Ballistic Coefficient. 3 ....... Adjust Atmospheric Conditions. 4 ........... Select New Function Table. 5 ............. Miscellaneous Functions. 6 ........................... DOS Shell. 7 .................... Return to System. Your Choice ? 1 ---------------------( Fig. 1 - MAIN MENU )---------------------- --====-- (C) Copyright 1988 by W.R. Frenchu - CALCULATE BALLISTIC COEFFICIENT - Please input: Initial velocity ....(fps) 2820 Final velocity ......(fps) 2507 Range .............(yards) 100 Altitude ............(ft.) 0 Temperature ......(deg. F) 59.0 Atmos. pressure ..(in. Hg) 29.53 Effective Bal. Coeff. = 0.288 (Bal. Coeff. at STP = 0.288 -------( Fig 2. - Calculating the Ballistic Coefficient )------- BALLISTIC v3.20 - (C) Copyright 1988 W.R. Frenchu Page 21 --====-- (C) Copyright 1988 by W.R. Frenchu - CALCULATE BALLISTIC TABLE - Please input: Initial velocity ........(fps) 2820 Bullet weight ........(grains) 165 Bullet diameter .........(in.) 0.308 Effective Bal. Coeff. ........ 0.288 Range .................(yards) 500 Number of intervals ..(50 max) 10 Chart title ? .308 Winchester - 165 gr. Spire pt. -----------------( Fig. 3 - MAIN MENU choice 1 )----------------- .308 Winchester - 165 gr. Spire pt. (Calculated using G1 table) Bullet weight ......... 165 grains Bullet Caliber ........ 0.308 Sectional Density ..... 0.248 IPSC Power Factor ..... 465.3 Effective Bal. Coeff... 0.288 Bal. Coeff. at STP .... 0.288 Cross wind ............ 10.0 m.p.h. Altitude .............. 0 Ft. Atmospheric pressure .. 29.53 in. Temperature ........... 59.0 F Range Velocity Energy Momentum Mx. Ht. Defl. Drop Lead Time yards f.p.s. ft-lb. lb.-sec. in. in. in. in/mph sec. 0 2820 2913.2 2.0661 0.0 0.0 0.0 0.0 0.000 50 2661 2593.5 1.9494 0.1 0.3 0.6 1.0 0.055 100 2507 2302.4 1.8368 0.6 1.1 2.4 2.0 0.113 150 2358 2037.4 1.7278 1.5 2.6 5.5 3.1 0.175 200 2215 1797.1 1.6228 2.8 4.8 10.3 4.2 0.240 250 2076 1579.4 1.5213 4.7 7.8 16.8 5.5 0.310 300 1942 1382.2 1.4231 7.2 11.6 25.3 6.8 0.385 350 1814 1205.8 1.3292 10.5 16.3 36.2 8.2 0.465 400 1693 1050.3 1.2406 14.7 22.0 49.7 9.7 0.550 450 1578 912.5 1.1563 20.0 28.8 66.2 11.3 0.642 500 1470 791.2 1.0767 26.7 36.7 86.2 13.0 0.741 1=Print 2=Form Feed 3=Sight Table 4=New Data 5=Main Menu ? 3 ------------( Fig. 4 - The completed ballistic table )----------- BALLISTIC v3.20 - (C) Copyright 1988 W.R. Frenchu Page 22 --====-- (C) Copyright 1988 by W.R. Frenchu - ADJUST ATMOSPHERIC CONDITIONS - (Modify ballistic coefficient) Please input: Bal. Coeff. at STP ........ 0.288 Altitude .............(ft.) 5000 Temperature .......(deg. F) 41.2 Atmos. pressure ...(in. Hg) 25.44 Wind speed ........(m.p.h.) 10.0 Angle from broadside (deg.) 0 Effective Ballistic Coefficient = 0.323 --------( Fig. 5 - Modifying the ballistic coefficient )-------- --====-- (C) Copyright 1988 by W.R. Frenchu - CALCULATE RECOIL - Please input: Initial velocity .....(fps) 2820 Weight of gun ........(lbs) 9.50 Weight of bullet ..(grains) 165 Weight of powder ..(grains) 42.0 Recoil Velocity = 9.5 fps Recoil Energy = 13.4 ft-lbs (Recoil due to bullet = 7.2 ft-lbs or 54%) -----------------( Fig. 6 - Recoil calculation )---------------- BALLISTIC v3.20 - (C) Copyright 1988 W.R. Frenchu Page 23 --====-- (C) Copyright 1988 by W.R. Frenchu - CALCULATE POINT BLANK RANGE - Please input: Initial velocity ............(fps) 2820 Sight height .............(inches) 0.90 Max. dist. from sight line ..(in.) 6.00 Effective Bal. Coeff. ............ 0.288 Targeted range for +/-3.00 inch path is 219 yds. Point-blank range is 257 yds. (100 yd. trajectory = +2.9 in.) -----------( Fig. 7 - Calculating Point Blank Range )----------- --====-- (C) Copyright 1988 by W.R. Frenchu - CALCULATE TWIST - Please input: Bullet diameter ......(in.) 0.308 Bullet length ........(in.) 1.20 Greenhill number .......... 150.0 Spec. gravity of bullet ... 10.90 Slowest twist allowing for stabilization is 1 turn in 11.9 inches. (Helix angle = 4.7 degrees) ------------------( Fig. 8 - Calculating twist )---------------- BALLISTIC v3.20 - (C) Copyright 1988 W.R. Frenchu Page 24 --====-- (C) Copyright 1988 by W.R. Frenchu - CALCULATE TRUE MUZZLE VELOCITY - Please input: Distance to first screen ..(ft.) 3.00 Distance between screens ..(ft.) 1.00 Instrumental velocity .....(fps) 2820 Effective Bal. Coeff. .......... 0.288 Actual Muzzle Velocity = 2824 fps ---( Fig. 9 - Calculating muzzle velocity from instrumental )--- --====-- (C) Copyright 1988 by W.R. Frenchu - CALCULATE VELOCITY STATISTICS - 1 - 2820.0 6 - 2852.0 2 - 2825.0 7 - 2827.0 3 - 2830.0 8 - 2818.0 4 - 2835.0 5 - 2850.0 Maximum = 2852.0, Minimum = 2818.0, Extreme Spread = 34.0 Average Velocity = 2832.1, Sample Standard Deviation = 12.8 1=Clear All 2=Delete 3=Correct 4=Add Entries 5=Exit ? 4 ----------( Fig. 10 - Calculating velocity statistics )---------- BALLISTIC v3.20 - (C) Copyright 1988 W.R. Frenchu Page 25 Appendix A Glossary BALLISTICS - The study of moving projectiles. Commonly, what is meant is "exterior" ballistics, that portion of the bullet's flight between muzzle and target. "Interior" ballistics refers to the portion between primer ignition and free flight and "terminal" ballistics to what happens when the bullet strikes its target. BALLISTIC COEFFICIENT - The ratio of the sectional density of a projectile to its coefficient of form. A measure of how well a bullet retains its velocity. Commonly supplied by re- loading manufacturers, or it may be derived from their bal- listic tables. Two types are used by the program. The STP value is that which the bullet would have at the standard temperature and atmospheric pressure for the table being used. The "effective" value is the STP value modified for the actual atmospheric conditions. BULLET - The actual projectile in small arms ammunition. Commonly corrupted to mean the entire cartridge. BULLET WEIGHT - Weight of the actual projectile. Usually given in grains. CALIBER - Technically, the diameter of the barrel measured across the lands. In practice, the diameter of the bullet. CARTRIDGE - Fixed ammunition, including case, powder, primer, and bullet, for small arms. COEFFICIENT OF FORM - A number relating the ballistic efficiency of a given shape to the shape of the projectile used to calculate the ballistic table. CROSS WIND ANGLE - The angle between the wind and line of de- parture. DRIFT - Technically, the distance a bullet will travel horizon- tally due to its spin. This effect is usually quite small, amounting to about 7 inches at 1000 yards for a military M2 (30-06) cartridge. Often confused with wind deflection. DEFLECTION - See wind deflection. DROP - The distance a bullet will fall due to the influence of gravity. Measured from the line of departure, not the line of sight. ENERGY - Here, the kinetic energy of a moving bullet, usually given in ft-lbs. Equal to one half the mass of the bullet multiplied by the square of the velocity. F.P.S. - Feet per second. A unit of velocity. BALLISTIC v3.20 - (C) Copyright 1988 W.R. Frenchu Page 26 FT.-LBS. - Foot pounds. A unit of energy equal to the effort required to raise one pound to a height of one foot. GRAINS - A unit of weight equal to 1/7000 of a pound. INGALLS' TABLES - A set of ballistic tables first calculated by Col. J. M. Ingalls in 1918. Probably the most widely used tables for small arms calculations. Other tables commonly used include the British tables of 1909, 1929, Winchester's G tables and the Ordnance Department's J table. I.H.M.S.A. - International Handgun Metallic Silhouette Assoc- iation. I.P.S.C - International Practical Shooting Confederation. LEAD - How far ahead of a moving target a shooter must aim to be assured of hitting it. In BALLISTIC, the lead is given in inches/m.p.h. of target speed. If the entry in the table is "1.2", the lead for a target moving at 5 m.p.h., (perpen- dicular to the bullet's path) would be (5 * 1.2) 6.0 inches. Wind speed is NOT taken into account in this calculation. LINE OF DEPARTURE - An imaginary line formed by extending the muzzle of the weapon. It coincides with the bullet's path only while the bullet is actually in the barrel. LINE OF SIGHT - An imaginary line from the center of the sights to the point of aim. The bullet typically crosses this line only twice; once, a few yards from the muzzle, and again at the targeted distance. MAXIMUM HEIGHT - The highest vertical distance above a line from the muzzle to the bullet's current position. Sometimes con- fused with the mid-range trajectory due to the fact that it typically occurs about halfway between muzzle and target. Maximum height is usually somewhat higher and occurs slightly later than the MRT. M.O.A. - Minute of Angle. Equal to 1/60 of an angular degree. At 100 yards, 1 M.O.A. is approximately 1.047 inches. MOMENTUM - Equal to the mass of a bullet multiplied by its velo- city. Indicative of the striking or knockdown power of a projectile. N.R.A - National Rifle Association. If you shoot, you SHOULD belong to this organization. POINT-BLANK RANGE - That range for which the bullet's path doesn't vary from the line of sight by more than a given amount. POWER FACTOR - A number used in IPSC competition to determine whether a handgun cartridge may be scored as a "major" or "minor" caliber. Defined as the bullet weight (in grains) BALLISTIC v3.20 - (C) Copyright 1988 W.R. Frenchu Page 27 divided by 1000 and multiplied by the velocity. Cartridges with a power factor equal to or greater than 175 are con- sidered "major". Cartridges ranking between 125 and 175 are "minor" and those below 125 are not legal for IPSC compe- tition. S.A.A.M.I - Sporting Arms Ammunition Manufacturers Institute. SECTIONAL DENSITY - The weight of a projectile (in pounds) di- vided by the square of its diameter (in inches). SIGHT HEIGHT - The measured distance between the centerlines of the sights and muzzle of a gun. SPECIFIC GRAVITY - The ratio of the mass of a material to that of an equal volume of water. TARGETED RANGE - That distance where the path of the bullet crosses the line of sight. (The "sighting in" distance.) TIME OF FLIGHT - The time necessary for a bullet to travel from the muzzle of a gun to a given range. TRAJECTORY - The path of a moving projectile. Here, the number of inches above or below the line of sight. TWIST - Here, the rate of twist in the rifling of a gun barrel. The minimum amount of twist necessary to stabilize a bullet in flight can be determined from its length, density, and caliber. Usually expressed as "1 turn in xx inches" where xx may range from about 8 inches up to over 30. "Faster" twist translates to a smaller number. Minimum twist is the "slowest" twist that will stabilize a given bullet. WIND DEFLECTION - The amount of horizontal motion attributable to the action of the wind. Often mistakenly called drift. BALLISTIC v3.20 - (C) Copyright 1988 W.R. Frenchu Page 28 Appendix B Information Sources BALLISTICS: Any intermediate physics (mechanics) text. BALLISTICS ON THE HOME COMPUTER. American Rifleman, June 1983 BALLISTICS ON YOUR POCKET CALCULATOR. American Rifleman, June 1987 BALLISTIC TABLES AND HOW TO USE THEM. American Rifleman, December 1963 CALCULATING RECOIL. American Rifleman, March 1988 EXPLORING BALLISTICS WITH YOUR COMPUTER, Byte Magazine September 1980 EXTERIOR BALLISTICS, McShane, Kelly and Reno, University of Denver Press, 1953 HATCHER'S NOTEBOOK, Julian S. Hatcher, Harrisburg: Stackpole Books, 1962 TRAJECTORY COMPUTATION SYSTEM FOR DIGITAL COMPUTER, SAAMI publications, 1976 RELOADING: CARTRIDGES OF THE WORLD, J.T. Amber, Northfield: Digest Books, 1972 COMPLETE GUIDE TO HANDLOADING, Philip B. Sharpe, New York: Funk & Wagnells Co., 1953 HORNADY HANDBOOK OF CARTRIDGE RELOADING, RIFLE-PISTOL, Grand Island: Hornady Manufacturing Co., 1973 HANDBOOK FOR SHOOTERS AND RELOADERS, VOL I & II, P.O. Ackley, Salt Lake City: Publisher's Press, 1965 LYMAN RELOADING HANDBOOK #46, Middlefield: Lyman Products for Shooters, 1970 NRA HANDLOADER'S GUIDE, Wash. D.C.: The National Rifle Association of America, 1969 PRINCIPLES AND PRACTICE OF HANDLOADING, Georgetown: Small Arms Technical Publishing Co., 1954 SIERRA BULLETS RELOADING MANUAL, Santa Fe Springs: Sierra Bullets, 1971 SPEER RELOADING MANUAL #10, Lewiston: Speer, Inc., 1979 STATISTICS: DATA REDUCTION AND ERROR ANALYSIS FOR THE PHYSICAL SCIENCES, Philip R. Bevington, New York: McGraw-Hill Co., 1969 ASSOCIATIONS: THE NATIONAL RIFLE ASSOCIATION - 1600 Rhode Island Ave. NW, Washington, D.C. 20036 S. A. A. M. I. (SPORTING ARMS AMMUNITION MANUFACTURERS INSTITUTE) - PO Box 838, Branford, Conn. 06405 BALLISTIC v3.20 - (C) Copyright 1988 W.R. Frenchu Page 29 Appendix C Ballistic Coefficients for Factory Bullets The coefficients listed here were calculated from tables found in SHOOTER'S BIBLE No. 75 (1984) using the program and Ingalls' function. No attempt was made to include every load, instead, representative loads for each caliber were chosen. Part 1 - Centerfire Pistol and Revolver Cartridge Bullet Coefficient Manufacturer ================================================================ .25 ACP 50 FMC .174 F .25 ACP 50 FMC .097 R,W .380 ACP 85 STHP .105 W .380 ACP 90 JHP .073 F .380 ACP 95 FMC .082 F,R,W 9 mm 95 JHP .101 F,R,W 9 mm 115 FMC .128 W 9 mm 115 JHP .131 R,F 9 mm 115 STHP .131 W 9 mm 123 FMC .140 F .38 SPEC. 110 STHP .147 W .38 SPEC. 148 WC .062 F,R,W .38 SPEC. 158 LRN .162 F,R,W .357 MAG. 110 JHP .093 F,R,W .357 MAG. 125 JHP .122 F,R,W .357 MAG. 158 JSP .135 F,R,W .44 MAG. 180 JHP .120 F,R .44 MAG. 210 STHP .125 W .44 MAG. 220 MCP .193 F .44 MAG. 240 JHP .156 R .44 MAG. 240 LGC .139 R .45 ACP 185 MCWC .082 R,W .45 ACP 185 JHP .152 F .45 ACP 185 STHP .137 W .45 ACP 230 FMC .165 R,W .45 COLT 225 STHP .167 W .45 COLT 225 SWCHP .172 F .45 COLT 250 LRN .157 R --------------- ABBREVIATIONS Manufacturers: F=Federal, R=Remington, W=Winchester Bullets: FMC=Full Metal Case, STHP=Silver Tip Hollow Point, JHP=Jacketed Hollow Point, MCWC=Metal Case Wadcutter, WC=Wad- cutter, LRN=Lead Round Nose, LGC=Lead Gas Check, JSP=Jacketed Soft Point, MCP=Metal Case Profile, SWCHP=Semiwadcutter Hollow Point BALLISTIC v3.20 - (C) Copyright 1988 W.R. Frenchu Page 30 Part 2 - Centerfire Rifle Cartridge Bullet Coefficient Manufacturer ================================================================= .22-250 REM. 55 PSP .231 F,W .22-250 REM. 55 PSP .253 R .223 REM. 55 FMC .207 R .223 REM. 55 FMC .278 W .223 REM. 55 MCBT .350 F .243 WIN. 80 SP .259 F,R,W .243 WIN. 100 PSP .371 F,R,W .270 WIN. 130 PSP .378 F,W .270 WIN. 130 PSP .345 R .270 WIN. 150 SP .267 F,R .270 WIN. 150 PSP .356 W 7mm MAUSER 140 PSP .433 F,R 7mm MAUSER 175 SP .280 F,W 7mm REM.MAG. 150 PSP .354 F,R,W 7mm REM.MAG. 175 PSP .453 F,R,W .30 CARBINE 110 FMC .180 F,W .30 CARBINE 110 FMC .164 R 30-30 WIN. 150 SP .221 F,W 30-30 WIN. 150 SP .195 R 30-30 WIN. 170 SP .259 F,R,W 30-06 150 PSP .329 F,R,W 30-06 180 PSP .398 F,R,W 30-06 200 BTSP .592 F 30-06 220 SP .299 R,W .300 WIN.MAG. 180 PSP .462 F,R,W .308 WIN. 150 PSP .323 F,R,W .308 WIN. 180 PSP .390 F,R,W .35 REM 200 SP .193 F,R,W .45-70 300 JHP .302 F,W .45-70 405 SP .269 R --------------- ABBREVIATIONS Manufacturers: F=Federal, R=Remington, W=Winchester Bullets: FMC=Full Metal Case, PSP=Pointed Soft Point, SP=Soft Point, BTSP=Boat Tail Soft Point, MCBT=Metal Case Boat Tail BALLISTIC v3.20 - (C) Copyright 1988 W.R. Frenchu Page 31 Part 3 - Rimfire Cartridge Bullet Coefficient Manufacturer ================================================================== .22 LR "VIPER" 36 TC .110 R .22 LR "YELLOW JACKET" 33 TCHP .101 R .22 LR HV 40 LRN .128 R .22 LR HV 36 LHP .115 R .22 LR TARGET 40 LRN .136 R .22 LONG 29 LRN .095 R .22 SHORT 29 LRN .098 R .22 SHORT 27 LHP .091 R .22 SHORT TARGET 29 LRN .097 R .22 WIN. MAG. 40 JHP .108 W .22 WIN. MAG. 40 FMC .108 W .22 LR "XPEDITER" 29 LHP .079 W .22 LR "H.P." 37 LRN .117 W .22 LR "DYNAPOINT" 40 LDP .127 W .22 LR "T22" 40 LRN .135 W .22 LR 40 LRN .127 W .22 LONG 29 LRN .095 W .22 SHORT "H.P." 27 LRN .091 W .22 SHORT "T22" 29 LRN .097 W .22 SHORT 29 LRN .098 W .22 LR "HI POWER" 40 LRN .126 F .22 LR "HI POWER" 38 LHP .122 F .22 LR "CHAMPION" 40 LRN .135 F .22 LONG "HI POWER" 29 LRN .094 F .22 SHORT 29 LRN .100 F .22 SHORT 29 LHP .092 F --------------- ABBREVIATIONS Manufacturers: F=Federal, R=Remington, W=Winchester Bullets: LRN=Lead Round Nose, LHP=Lead Hollow Point, LDP=Lead Dynapoint, FMC=Full Metal Case, TC=Truncated Cone, TCHP= Trun- cated Cone Hollow Point BALLISTIC v3.20 - (C) Copyright 1988 W.R. Frenchu Page 32 Appendix D Specific Gravities of Bullet Alloys Part 1 - Lead/Tin/Antimony Alloys Percent Composition Specific Gravity Trade or Pb Sn Sb of alloy Common Name ================================================================= 100 11.340 pure lead 100 7.298 pure tin 100 6.62 pure antimony 30 70 8.32 soft solder 37 63 8.42 eutectic solder 50 50 8.89 50-50 solder 75 10 15 9.73 lead babbit-SAE 14 80 20 10.20 20-80 solder 80 5 15 10.04 alloy 8 83 2 15 10.09 alloy 10 85 15 10.28 alloy 11 85 5 10 10.24 lead babbit-SAE 13 91 9 10.66 9% antimonial lead 92 8 10.74 8% antimonial lead 94 6 10.88 hard lead (bullets) 95 5 11.00 5-95 solder 96 4 11.04 hard lead 99 1 11.27 1% antimonial lead 92 8 7.28 white metal Part 2 - Other Alloys Composition Specific Gravity Trade or of alloy Common Name ================================================================= 100 Cu 8.96 pure copper 100 Fe 7.87 pure iron 95 Cu, 5 Zn 8.86 gilding 90 Cu, 10 Zn 8.80 commercial bronze 70 Cu, 30 Zn 8.53 cartridge brass 98.75 Cu, 1.25 Sn 8.89 1.25% phos. bronze 90 Cu, 10 Sn 8.78 10% phosphor bronze 97 Cu, 3 Si 8.53 silicon bronze (A) 98.5 Cu, 1.5 Si 8.75 silicon bronze (B) 99.5 Fe,.06 C,.38 Mn,.01 Si 7.87 .06% carbon steel 99.0 Fe,.23 C,.64 Mn,.11 Si 7.86 .23% carbon steel 98.7 Fe,.44 C,.69 Mn,.20 Si 7.84 .435% carbon steel --------------- SOURCES: Metals Handbook, Vol. 1, "Properties and Selection of Metals" (8th ed.), American Society for Metals Metal and Alloys Data Book, Samuel L. Hoyt BALLISTIC v3.20 - (C) Copyright 1988 W.R. Frenchu Page 33 Appendix E User Supported Software User Supported Software is based on the premise that if a someone gets a chance to try out a program, likes it, and finds he uses it on a regular basis, he will voluntarily contribute to the support of that program. (Where else do you get the oppor- tunity to check out a product BEFORE you buy it?) Users are en- couraged to copy and distribute User Supported Software for non- commercial purposes. Commercial users should be aware that the author of the program often retains commercial rights. BALLISTIC is being distributed as User Supported Software. If after an initial trial period you find you're using BALLISTIC and you like it, please send the registration form, check (and diskette if indicated) to: William R. Frenchu 79 Taylor Terrace Hopewell, NJ 08525 (Please label the diskette with your name and address.) Contributors will receive a copy of the latest revision of the program, as well as the TURBO C source code. In addition, they will be informed by mail of any major updates or improve- ments. Major revisions will probably not be undertaken without a positive user response. If you have any questions, problems or suggestions about the program, (or need support for a special printer, etc.) please contact the author. All commercial rights to BALLISTIC are reserved by the author. Anyone wishing to make any commercial use of this program (or the tables it produces) is urged to contact the author at the above address. This includes people who use the program in any commercial or governmental environment. Site and commercial li- censes are available at very reasonable rates. Non-commercial users are encouraged to make and distribute as many UNMODIFIED copies as they like, provided the following files are included: BAL-GEN.EXE BAL-READ.EXE BAL-READ.ME! BALISTIC.EXE BALISTIC.DOC BALISTIC.REV Comments or suggestions may be left for the author (Bill Frenchu) at any of the following places: Bullet 'n Board BBS (703)-971-4491 Road To Utopia BBS (609)-799-5418 (CoSysop) CompuServe 74575,61 BALLISTIC v3.20 - (C) Copyright 1988 W.R. Frenchu Page 34 REGISTRATION FORM FOR BALLISTIC v3.20 Name _____________________________________ Date _______________ Mailing Address: Street __________________________________ Phone ______________ City ________________________ State ___ Zip ________________ Computer type (& BIOS)________________________ Printer __________ Display and adapter type ________________________________________ Where did you find out about BALLISTIC? _________________________ (If CompuServe, please list forum.) Please register my copy of BALLISTIC and send the latest version (as well as the TURBO-C source code) to the above address. _____ I've enclosed $15.00 and a 5 1/4" DSDD (360k) or 3.5" (720k) diskette. (No 1.2 or 1.44 Meg diskettes please!) _____ I've enclosed $20.00. Please send 5 1/4" 3.5" (circle) The author is always trying to improve BALLISTIC. You can help! Comments about BALLISTIC v3.20: Comments about the documentation: Suggestions for future versions of BALLISTIC: Types of shooting you do (How will you use BALLISTIC?): Mail to: William Frenchu, 79 Taylor Terrace, Hopewell, NJ 08525