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BALLISTIC is a program used to calculate bullet trajectories, remaining energy, velocities, etc., for small arms. It will generate ballistic tables, calculate point blank range, and many other useful functions. Several may be plotted vs. range on systems with VGA, EGA, CGA, MCGA or Hercules graphics adapters. A built-in database makes storage of personal data easy. The purpose of this program is NOT to teach the fundamentals of reloading small arms ammunition, 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 is supplied. This program is very thorough and complete. The documentation is over 35 pages long and extremely informative. It discusses the variables considered in calculations, how they are to be derived, and why they are so important. The appendix even has definitions on key words, making BALLISTIC a fine learning tool.
B A L L I S T I C Version 4.00 Copyright 1988, 1989 by William R. Frenchu All Rights Reserved. WARNING Reloading small arms ammunition can be a DANGEROUS pastime. The purpose of this program is NOT to teach the principles of this fascinating hobby. It is, rather, to aid the hobbyist in as- sessing the performance of the ammunition he has produced. It is assumed from the outset that the user of this program is ac- quainted with basic reloading techniques. (For review, a list of references may be found in Appendix B of this document.) DO NOT ATTEMPT TO PRODUCE AMMUNITION FOR YOURSELF 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. User Supported Software (Shareware) These programs (and their documentation) are copyrighted mate- rial. Non-registered users of BALLISTIC are granted a limited license to use the complete package for a trial period, to deter- mine if it suits their needs. See Appendix F for further infor- mation (and the usual pitch for cash). COPYRIGHT NOTICE ---------------- BALLISTIC v4.00 is Copyright 1988, 1989 by William R. Frenchu. GENTABLE v4.00 is Copyright 1988, 1989 by William R. Frenchu. READTABLE v4.00 is Copyright 1988, 1989 by William R. Frenchu. This document is Copyright 1988, 1989 by William R. Frenchu. None of the programs listed above (or their documentation) may be copied, in part or in whole, except as provided in the License in the following pages. Disclaimer Although every reasonable care was taken to insure the accuracy of these programs and their documentation, they are provided "AS IS" and without warranties as to performance of merchant- ability or any other warranties whether expressed or implied, including, but not limited to warranty of fitness for a partic- ular 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. In no event will the author be liable for any damages (or injury) arising out of the use of or inability to use this program. Trademarks The several product names found throughout this manual are trade- marks of various companies. LICENSE ------- The "BALLISTIC software package" (hereafter referred to as the Package) includes the executable versions of BALLISTIC 4.00 and GENTABLE 4.00, and this document. Source code for these programs is specifically excluded. (READTABLE is an optional program available only to registered users. See Appendix E.) The Package is not, nor has it ever been, public domain or free software. The Package is distributed under the User Supported Software concept. Non-registered users (private, governmental OR commer- cial) are granted a limited license to use the Package for a 30 day trial period, to determine if it suits their needs. This license further allows registered OR non-registered users to make and distribute copies of the Package for the purpose of allowing others to try it, provided the following restrictions are met: 1. The Package must include unmodified copies of all files and documentation. 2. The Package may not be included with any other product for any reason without a license from the author. 3. No charge or payment may be levied or accepted for the Package beyond a small media fee. Bulletin Board System Operators (sysops) may post the Package on their BBS for downloading without written permission so long as no SPECIAL fees are necessary to access the files. (A fee for general access to the BBS or charge for connect time is specifi- cally allowed.) Distributors of User Supported and Public Domain Software MUST additionally obtain permission in writing from William R. Frenchu before distributing the Package. Permission is almost always granted. Any other use of Package, or use past the 30 day trial period requires registration. Appendix F contains information on registration. TABLE OF CONTENTS ----------------- 1. ABOUT THE PROGRAM A. General ............................................... 1 B. Program Files ......................................... 1 C. System Requirements ................................... 1 D. Program Limitations ................................... 2 E. Communicating with BALLISTIC .......................... 2 F. What's New ............................................ 2 G. The Future ............................................ 3 H. Acknowledgments ....................................... 3 2. INSTALLATION A. Shareware Copies....................................... 5 B. All Users ............................................. 5 C. The Configuration File ................................ 5 D. Using the Pre-programmed Functions .................... 5 3. CALCULATING A BALLISTIC TABLE A. Command Line Arguments ................................ 8 B. Calculating a Ballistic Coefficient ................... 8 C. The Ballistic Table ................................... 9 D. Sight (Trajectory) Tables ............................. 9 E. Plotting the Trajectory ............................... 10 4. OTHER MAIN MENU FUNCTIONS A. Modifying the Ballistic Coefficient ................... 11 B. Changing the Cross Wind Value ......................... 11 C. Changing the Input Function Table ..................... 11 D. Miscellaneous Functions Menu .......................... 11 E. Database Function Menu ................................ 11 5. THE MISCELLANEOUS FUNCTIONS MENU A. Calculating Recoil .................................... 13 B. Calculating Minimum Twist ............................. 13 C. Calculating the Point Blank Range ..................... 14 D. Correction from Instrumental to True Muzzle Velocity .. 14 E. Calculation of Velocity Statistics .................... 14 F. Calculation of Target Statistics ...................... 15 6. DATABASE FUNCTIONS A. Internal or External Databases ........................ 16 B. Display Database ...................................... 16 C. Search Database ....................................... 16 D. Delete Record from Database ........................... 17 E. Add Record to Database ................................ 17 F. Print Reloading Label ................................. 17 G. Select Database File .................................. 17 H. Internal Database Structure ........................... 17 I. External Database Return Values ....................... 18 7. GRAPHICS MODE FUNCTIONS A. Changing the Axes ..................................... 19 B. Saving and Restoring Plot Data ........................ 19 C. Graphics Cursor ....................................... 19 D. Hardcopy of Graphic Data .............................. 19 E. Plotting Other Functions .............................. 20 F. Miscellaneous Graphics Commands ....................... 20 8. THE BALLISTIC TABLE A. The Table Header ...................................... 21 B. Functions of Merit .................................... 21 C. Energy ................................................ 22 D. Momentum .............................................. 22 E. Maximum Ordinate ...................................... 22 F. Deflection ............................................ 22 G. Drop .................................................. 23 H. Lead .................................................. 23 I. Time of Flight ........................................ 23 J. Trajectory ............................................ 23 9. THE CONFIGURATION FILE A. Using the Configuration File .......................... 25 B. Allowable Parameters .................................. 25 10. SOURCES OF DATA A. Altitude .............................................. 27 B. Ballistic Coefficient ................................. 27 C. Bullet Weight, Length and Caliber ..................... 27 D. Gun and Powder Weight ................................. 27 E. Specific Gravity of Bullet Alloy ...................... 28 F. Temperature, Atmospheric Pressure and Wind ............ 28 G. Velocity .............................................. 28 Figures .................................................... 30 Appendix A, Glossary ....................................... 35 Appendix B, Information Sources ............................ 38 Appendix C, Coefficients for Several Factory Cartridges .... 40 Appendix D, Specific Gravities of Bullet Alloys ............ 43 Appendix E, Using Other Standard Functions ................. 44 1. Creating Custom Function Tables ....................... 44 2. Checking the Function File with READTABLE ............. 44 Appendix F, User Supported Software (Shareware) ............ 46 Registration Form .......................................... 47 1. ABOUT THE PROGRAM A. General BALLISTIC is a Turbo C (v2.0) program written to generate ballistic tables for shooters. Given easily obtainable data, it calculates such useful information as the ballistic coefficient and sectional density, remaining velocity, energy, momentum, drop, deflection, maximum ordinate, time of flight and lead (for moving targets) at a given range. In addition, it can determine the recoil, estimate the minimum rifling twist, calculate point blank range, generate statistics, and produce trajectory tables for estimating holdover. Several of the values calculated by BAL- LISTIC may be displayed not only in tabular form, but also graph- ically as a function of range. B. Program Files The following files should be included in any distribution of BALLISTIC: BAL-GEN.EXE -GENTABLE :Creates ballistic function tables. BAL-READ.ME! -Describes version, etc. BALISTIC.EXE -BALLISTIC :Executable file. BALISTIC.DOC -This file. Registered users may additionally receive: BAL-READ.EXE -READTABLE :Optionally displays function tables. BALISTIC.REV -Program revision history. *.DB -BALLISTIC databases of commercial components. CHECK_DB.COM -Checks format of user created databases. BAL400-?.C -C Source code (extra cost) 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 non-registered versions) requires a VGA, MCGA, EGA, CGA or Hercules compatible display adapter. Registered versions can be supplied that support the higher resolution modes of several additional displays. (See file BAL-READ.ME! for the current list.) BALLISTIC 4.00 has been tested and found to operate properly on the following systems: PC/XT with Hercules monochrome or ATI "EGA Wonder" adapter PS/2 System 30 with MCGA adapter Compaq Plus with Compaq CGA-type adapter Compaq DeskPro 386 with Compaq EGA-type adapter Compaq DeskPro 386s with Compaq VGA-type adapter Panasonic Executive Partner (8086 with CGA type display) Version 2.0 of Turbo C appears to use a new method to check for available graphics adapters. This may cause BALLISTIC to crash some of the less compatible clones. (The Panasonic Executive Partner is an example of this.) In most cases, this will be solved by using the configuration file or command line to force BALLISTIC to use BIOS calls for video I/O. See section 3A (com- mand line) or 9 (configuration file) for more detailed instruc- tions. BALLISTIC v4.00 - Copyright 1988, 1989 by W.R. Frenchu Page 1 D. Program Limitations Any program of this type will have certain limitations on its use and accuracy. BALLISTIC is no exception. Discrepancies between actual and calculated performance arise primarily because of approximations the program uses in its calculations. An additional source of error is the inability of the user to measure input values exactly. Assuming that the input values are known to 1% the average user should find agreement with published velocity and trajectory data to be 1-2%. The recoil calculation, due to its more approximate nature, 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 parti- cular load performs with a given gun can only be determined by actual firings. BALLISTIC works by comparing the user's bullet to a "stan- dard projectile" with a well known trajectory. Since the standard data is calculated before use by a separate program (GENTABLE), the user's ballistic tables can be produced very quickly. For best results, one should try to use the same standard function to produce the table that was initially used to calcu- late the ballistic coefficient. This may not always be possible, as in the case where a published coefficient was calculated using a drag function to which the program doesn't have access. E. Communicating with BALLISTIC Throughout this document, single keys pressed in response to program prompts are enclosed in angle brackets. For example, "press <1>" means to press the key labeled "1" on the keyboard. For "press <ENTER>", use the key marked either "return" or "enter". When the document requires that a value be "entered", the <ENTER> key must be pressed when finished, e.g., to "enter 10" press <1><0><ENTER>. Prior to hitting the <ENTER> key, values may be edited using any of the appropriate cursor keys, including <HOME>, <END>, <INSERT> and <DELETE>. Improper entries on previous 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. File names each have an associated default extension which need not be entered. For input filenames, a directory of matching files may be displayed by entering a name containing the usual DOS wildcards, "?" or "*". (This option is NOT implemented in graphics mode.) Input filenames will be checked for existence before they are accepted. Several function keys have been implemented in version 4.00. These keys will always perform the same functions, even when similar menu choices are available. "F1" currently provides help when in graphics mode. (The author's plan is to use this key to provide "context sensitive" help in a future release.) "F5" will execute a "shell to DOS" function from anyplace EXCEPT graphics mode. "F9" will perform a "selective" print screen function, i.e., it will print that part of the screen containing the cur- rent calculations, without the titles, etc. "F10" will perform a form feed. F. What's New There have been several additions to the program since ver- BALLISTIC v4.00 - Copyright 1988, 1989 by W.R. Frenchu Page 2 sion 3.20. Some of these include: 1. Added database functions for storage and retrieval of ballistic input values. Both internal and external databases are supported. 2. Added angle of departure feature to trajectory menu. 3. Added ability to plot energy, velocity, momentum or deflection as a function of range. 4. Added choice of several "functions of merit" to the original IPSC power function. 5. Added graphics cursor with coordinate display. 6. Added "print to file" option for tables. 7. Maximum range has been extended. 8. Minimum bullet weight is now 1 grain. 9. Minimum bullet diameter is now 0.08" (#9 shot). 10. Users can now print input data and results of calcula- tions performed in miscellaneous functions menu. 11. When modifying atmospheric data, the standard values may be accepted by pressing <SHIFT-RETURN>. 12. HP Paintjet and C. Itoh 8510A printers are now sup- ported in graphics mode. As a result of these (and other) changes, plot files saved under previous versions of BALLISTIC are incompatible with the new release. G. The Future The author is the first to admit that BALLISTIC isn't per- fect (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 calculations based on dis- tances given in meters OR yards would be a welcome improvement. Additional features the author is considering include context sensitive help. The author is interested in adding new drag function tables if reliable data can be found. He is currently on the lookout for listings of the "J", "G5" or "G7" drag functions. Also of inter- est is additional specific gravity data for commonly used bullet casting alloys, and information on the types of materials used in non-lead bullet designs (e.g., bronze and steel). Finally, a description of the Relative Incapacitation Index (RII) would help round out the merit function selections. 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: Jim Kreiser Hugh Roberts James Roberts Donald Terwilliger Special thanks are due to the author's wife and family, BALLISTIC v4.00 - Copyright 1988, 1989 by W.R. Frenchu Page 3 Susan, Billy and Karen, for understanding (or at least putting up with!) the author's wild mood swings, ranting and raving as var- ious parts of BALLISTIC (which were working just fine yesterday!) stopped working for no apparent reason. Thank you. BALLISTIC v4.00 - Copyright 1988, 1989 by W.R. Frenchu Page 4 2. INSTALLATION BALLISTIC is available in two formats. The shareware version is a packed or archive type file (typically with a .ZIP exten- sion) which the user has most often downloaded from a computer bulletin board system. The registered version may be supplied already "unpacked" on one 3.5" or two 5.25" diskettes directly from the author. The installation procedure for both formats is similar. Briefly, the executable files are installed on a working disk, the system graphics printer is chosen, and a standard function file is created. A. Shareware Copies Those users starting with a packed file should create their own "distribution diskette" by formatting a blank floppy, then unpacking all the files directly to the new diskette. This floppy is identical to "disk 1" of the registered version. B. All Users The first step should be to print (and read!) the documen- tation file from "disk 1". (3.5" disk users receive "disk 1" and "disk 2" on a single diskette.) This may be done with either of the DOS commands: PRINT BALISTIC.DOC or: TYPE BALISTIC.DOC >PRN (The documentation is an ascii file formatted for 66 lines of 80 characters each per page.) The second step is the creation of a "working diskette" (or directory). If installing to a hard disk, this may be done by simply creating an appropriate sub-directory and copying all the files from the distribution diskettes. If installing to a floppy disk based system, the working diskette is created by copying ONLY the files BALISTIC.EXE and BAL-GEN.EXE from "disk 1". This is necessary in order to leave enough room to create the .TAB files later. Finally, the distribution diskettes should be stored in a safe place, away from electric or magnetic fields and extremes of temperature. C. The Configuration File Certain program default values may be changed by creating an ascii file called BALISTIC.CFG. (Detailed instructions and allow- able parameters are described in section 9.) It is recommended that the user determine the proper value for PTYPE (the system graphics printer) at this time. (The default value is NO PRIN- TER.) The author suggests that other parameters be left at their default values until installation is complete, and the user is satisfied with the program's operation. D. Using the Pre-programmed Functions Before running BALLISTIC for the first time, a file con- taining the "standard" drag values the program will use during its calculations must be produced. BALLISTIC v4.00 - Copyright 1988, 1989 by W.R. Frenchu Page 5 Although Ingalls' table was historically the most often used for this sort of work, several others are likely to be encoun- tered today. Many manufacturers, for instance, favor the "G1" table. For the types of bullets typically used by reloaders the results will be very similar regardless of the table employed. Indeed, the variation between handloads or factory ammunition randomly selected from the same lot will probably be greater than the discrepancies noted between different tables over normal shooting ranges. GENTABLE Version 4.00 makes the following functions avail- able: FUNCTION VELOCITY ATMOSPHERIC max. min. temp. pressure British 1909 4000 300 59 29.53 Brit. 1929 Round Shot 1900 300 59 29.53 "G1" 4095 300 59 29.53 Ingalls' 3600 300 60 30.00 Ingalls' (extended) 4095 300 60 30.00 The G1, British 1909 and Ingalls' functions are practically identical until low velocities are reached. All are well suited to calculations involving typical hunting or pistol bullets, i.e., rounded or slightly pointed spitzers. Results for sharply pointed spitzers and boattails may not be as accurate with these functions as they might with some others. Less accurate results will also be obtained if ballistic coefficients calculated with one set of functions are used with another, e.g., using the coefficients listed in Appendix C (calculated with Ingalls' table) with the British 1909 tables. (Descriptions of the differ- ences between the functions, and the projectiles used to deter- mine them, may be found in HATCHER'S NOTEBOOK.) The extended Ingalls' table is simply the standard table continued to the maximum allowable program velocity following the method used in Hatcher. Since the values above 3600 fps are extrapolated, they will 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. 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. The Round Shot table should be of special interest to those using black powder arms and shotguns. To the author's knowledge, however, no ballistics have been published using these tables. Consequently, ballistic coefficients are unavailable. The author recommends that the user "roll his own" by assuming a coefficient of form equal to 1.00 and using the formula: M B.C. = --------- i * d * d where M is the bullet mass (not weight) in pounds, i is the coefficient of form, and d is the bullet diameter in inches. 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 and be prompted for the number of the drag function he desires. The program will next prompt for a filename to contain the new data. After this data BALLISTIC v4.00 - Copyright 1988, 1989 by W.R. Frenchu Page 6 has been entered, GENTABLE will create the new function file, overwriting any previous file with that name. Users planning the routine use of more than one function should probably create them all ahead of time, giving them de- scriptive file names. The one to be used most often should be copied to BALISTIC.TAB. GENTABLE will accept two arguments 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. The "-H" flag will display a short help screen. Once a drag function file has been generated, BALLISTIC is ready to run. A minimum working disk need only include the files BALISTIC.EXE and BALISTIC.TAB. (If the graphics printer or other defaults require changing, BALISTIC.CFG must also be on the working disk.) This should leave sufficient room for the program to write plot and table files, and for the user to create a fair sized database of his most currently used loads. BALLISTIC v4.00 - Copyright 1988, 1989 by W.R. Frenchu Page 7 3. CALCULATING A BALLISTIC TABLE 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 for all required data. Values entered (or calculated) in one part of the program become the default for all other sec- tions. This default data is displayed during the prompts. To accept the displayed value press <ENTER>. To change it, simply enter the new data over the old. The output values calculated by BALLISTIC (the ballistic and trajectory tables) will be discussed in depth in section 8. A. Command Line Arguments BALLISTIC is started by simply typing its filename (BALISTIC) at the DOS prompt, optionally following it with one or more of the following arguments: "-BIOS" will cause all video output to be performed using BIOS calls rather than direct screen writes. This will significantly slow screen I/O, but may be necessary with computers that are not 100% IBM compatible. "-F" followed (with NO spaces) by the name of a BALLISTIC drag function file, will cause that file to be loaded instead of the default. For example, -FG1.DAT would cause the program to load the file called G1.DAT instead of the BALISTIC.TAB. "-H" (Help) will display a brief help screen, including a description of these arguments, then stop. "-NOCHECK" causes the initial check of the function file to be skipped. This may be useful on machines without a math coprocessor. Upon startup, BALLISTIC will attempt to read the configu- ration file (BALISTIC.CFG, see Section 9), then load the default function file (either BALISTIC.TAB or that file specified with the "-F" option). If the default file is not found in the current directory, the user will be prompted for the name of an alternate. The de- fault file type is ".TAB". (To use a name with no extension enter "filename." with the trailing period.) BALLISTIC will read the function file, make a brief check to determine its validity (a checksum procedure), and present the user with the main menu. (Fig. 1) B. 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 in one of the sources described in section 10B, 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 calculated value of the effective ballistic coefficient (as well as the coefficient at standard conditions for the table chosen) will be displayed. (Fig. 2). Having determined a coefficient, BALLISTIC BALLISTIC v4.00 - Copyright 1988, 1989 by W.R. Frenchu Page 8 can now calculate the table. Pressing the <ENTER> key will redisplay the main menu, then <1> will bring up the input screen. C. The Ballistic Table Figure 3 shows sample input data for main menu choice 1, calculating the ballistic table. Since the initial velocity, range and ballistic coefficient have been entered or calculated on a prior screen, they needn't be re-typed unless a different value is desired. The bullet diameter prompt should be answered with the ac- tual bore diameter in inches although input of the firearm's nominal caliber (with leading decimal point, e.g., .22) is often close enough. 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.) In this example, entering a range value of 500 will create a table to 500 yards based on the performance noted over the first 100. If a value of zero had been entered for the range, it would have caused the program to switch to "metallic silhouette mode". The user would then be prompted for his choice of standard rifle or pistol silhouette target distances (rounded to the nearest yard). As long as the input value for range remains zero, these alternate ranges will be used. The final necessary data item is the number of intervals into which the total range should be divided. The maximum number allowed is the smaller of 50 or the total range (in yards). This value is assumed to be four when operating in silhouette mode. Data entry is concluded with an optional table title. 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 table can be written to an ASCII file (for inclusion by a word processor or later printing) by pressing <3>. The program will prompt for a filename, which may exist. (Default extension is .OUT.) The file will in NO case be overwritten. If it is already present, the data will be appended. If the file does not exist, BALLISTIC will create it. The "New Data" choice, <5>, will return the user to the data entry screen to calculate another ballistic table. "Main Menu" (<6> or <ESC>) will jump directly back to the program's initial screen. D. Sight (Trajectory) Tables Sight tables can be produced by pushing <4> 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 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 tar- geted range will cause the prompt to take the form of which sil- BALLISTIC v4.00 - Copyright 1988, 1989 by W.R. Frenchu Page 9 houette (chicken, pig, turkey or ram) the weapon is zeroed for. The user should respond with the first letter of the appropriate target. If the program is not in silhouette mode, entering a range of zero for the targeted range will cause the program to reprompt for the bullet's angle of departure (in decimal degrees). Output of this table can be diverted in exactly the same manner as the ballistic table. Pressing <5> allows the user to enter new data for another sight table (using the current bal- listic conditions), and <6> (or <ESC>) returns to the ballistic table and prompt. E. Plotting the Trajectory Pressing <4> at the sight table prompt will present the user with a graphic representation of the bullet's trajectory. Range, in yards, will be shown along the bottom, with tic marks ap- pearing at distances corresponding to the entries in the ballis- tic 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. (Additional commands available in graphics mode are discussed in section 7.) Pressing <X> (or <ESC>) will return the user to the sight table prompt. BALLISTIC v4.00 - Copyright 1988, 1989 by W.R. Frenchu Page 10 4. OTHER MAIN MENU FUNCTIONS A. Modifying the Ballistic Coefficient Those living at high altitude or in areas of extreme temper- ature 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 tempera- ture in addition to the value of the ballistic coefficient at STP (Standard Temperature and Pressure, the published value). One should bear in mind that these meteorological values (especially temperature) 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. B. 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. It should be noted that deflection is linear with wind speed, 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. C. Changing the Input Function Table Starting with version 2.00, it is possible to change func- tion tables without restarting the program. Pressing <4> from the main menu will cause a prompt for the new file name. As noted in subsection A, the default extension is ".TAB" which need not be entered. Users should remember that to enter a filename with no extension, the trailing period is required. Simply press <ESC> to abort the function 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 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 simplified if the table most commonly used is copied to BALISTIC.TAB. 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 between two tables that use differ- ent standard conditions. D. 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 choose to calculate recoil, shot statistics, the minimum ne- cessary twist for bullet stabilization, or the point blank range for a given target size. These functions will be discussed in section 5 of this document. E. Database Function Menu Pressing <6> at the main menu prompt will cause the program BALLISTIC v4.00 - Copyright 1988, 1989 by W.R. Frenchu Page 11 to enter the database section. Both internal and external data- bases are supported. When entered, the program looks in the current directory to see if an executable file (.BAT, .COM, or .EXE) called BAL-DBF exists. If it does (and if sufficient memory is installed), control passes to that program. If not, the internal database is invoked. Section 6 will explain the func- tions available there in greater detail. BALLISTIC v4.00 - Copyright 1988, 1989 by W.R. Frenchu Page 12 5. THE MISCELLANEOUS FUNCTIONS MENU Several interesting calculations not as often needed by the shooter have been grouped together in the miscellaneous functions menu. A. 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" will be useful in reducing felt recoil by allowing the user to deter- mine the rough percentage of recoil caused by the bullet itself (which a muzzle brake cannot affect). The value produced 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, however, that NO muzzle brake is 100% effective and the actual amount of reduction will be less.) The recoil calculation used by BALLISTIC is a rough approxi- mation, similar to that discussed in the March 1988 American Rifleman. It would be extremely challenging to write a completely accurate description of the recoil process. It would also be very difficult to use as many variables are involved including, but not limited to bore cross sectional area, length of barrel, at- mospheric pressure and temperature, type of powder, loading den- sity, etc. The values calculated here should not be considered accurate to more than 10-15%. Barrel/powder combinations that produce excessive muzzle flash will be even less accurate. B. 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 den- sity 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. The user should be aware that these specific gravities can NOT be added algebraically. That is, an alloy con- taining 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 cus- tomary "1 turn in xx inches", BALLISTIC provides both numbers. BALLISTIC v4.00 - Copyright 1988, 1989 by W.R. Frenchu Page 13 The author has been informed that this approximation was originally intended for use with artillery projectiles. More recent findings suggest that, for typical small arms ammunition, a Greenhill number smaller than the default of 150.0 may be ap- propriate, especially under adverse atmospheric conditions such as rain and snow (100 has been recommended). A discussion may be found in the June 1988 issue of Rifle. ("Shooting the Kalashni- kov", pp. 28 - 31.) This number may be "permanently" changed using the configuration file. C. 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 its center. For example, given a 6 inch target, a point blank range may be calculated so the bullet is always less than 3 inches above or below 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, the maximum point blank range 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.) BALLISTIC always calculates the point blank range for an uphill/downhill angle of zero degrees. As during previous input screens, entering a value of zero for the "effective" ballistic coefficient will cause the program to re-prompt for the STP value. D. 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 veloc- ity, provided the screen distances and the ballistic coefficient are known. Miscellaneous menu choice 4 provides for this calcula- tion. E. Calculation of Velocity Statistics Not all bullets from the same load 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. Analysis of a string of measured velocities (up to 25) may be accomplished using miscellaneous menu choice 5. Output data in- cludes 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 entered, allowing the user to determine the effect of each shot on the statistics. Pressing <ESC> at the prompt for BALLISTIC v4.00 - Copyright 1988, 1989 by W.R. Frenchu Page 14 "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 partic- ular load. (Accurate loads will, however, tend to have lower standard deviations.) Examination of the standard deviation can show 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. F. Calculation of Target Statistics BALLISTIC will also provide some statistical analysis of targets, including group center, group size and an evaluation of "true fliers". 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 manufac- turers. (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 furthest apart. As with the velocity statistics section, pressing <ESC> in response to a coordinate prompt will cause the statistics menu to be displayed. Each shot will be marked for geometric standard deviations in a manner similar to that used for velocity statistics. A sin- gle star will indicate that the shot exceeds one SD from the group center in the x direction, the y direction OR both. Two stars indicates a deviation of more than 2 SD from the current group center. Shots which lie outside of 2 SD from the group center, especially in the absence of other "wide" shots, can usually be safely labeled "fliers". BALLISTIC v4.00 - Copyright 1988, 1989 by W.R. Frenchu Page 15 6. DATABASE FUNCTIONS While writing BALLISTIC, the author was convinced that some kind of database feature would prove extremely useful. The prob- lem confronting him was what kind of database to provide. The established databases, like dBase III+ or Symphony, might be preferred by users with access to them, but those without them would then be left out in the cold. Clearly some type of internal database was necessary. Ideally, it would be able to read ex- isting database files. The solution was to provide both options. Version 4.00 of BALLISTIC incorporates a rudimentary database program, using a simple ascii file format for storage. Users without access to a more comprehensive database program can use this feature to build up their own library of ballistic information. Those fortunate enough to have access to one of the more powerful commercial database managers have two options. They may use the "report generation" features of their databases to create a BALLISTIC compatible database, or they can choose to ignore the built in feature and have BALLISTIC run their program directly. (BALLISTIC will remain in memory.) On exiting from the external program, BALLISTIC will attempt to read a file containing the updated parameters returned by their program. A. Internal or External Databases Upon pressing the <6> key from the main menu, BALLISTIC attempts to determine which of its database options to execute. It first searches (in the current directory ONLY) for a file called BAL-DBF.BAT, a batch file that will start up the users database program. If that file cannot be found, it will attempt to run either BAL-DBF.COM or BAL-DBF.EXE. If none of these files exist, the program executes the internal database. If the internal database is activated, and the program cannot find the datafile, only options 5 and 6 (Print Label and Select Database) will be active. If the database is found, but contains no records, option 4 (Append Record to Database) will be operational as well. B. Display Database Assuming the internal database has been selected, and an appropriate database file was found, menu choice 1 will allow the user to display individual records on the screen. Several "sub- options" will be available. Pressing <1> or <2> (or the arrow cursor keys) will display the previous or next record, respec- tively. If the user already knows which record is of interest, choice 3 will allow him to proceed directly to that record num- ber. The <HOME> and <END> keys will at all times take the user to the first or last record in the current dataset. Choice 4 (Accept data) will read the currently displayed record into BALLISTIC. If the record contains muzzle velocity and another velocity recorded at a given distance, the program will ask the user if the ballistic coefficient should be calculated for the current drag function. C. Search Database Database menu choice 2 will allow the user to perform a text search of the records. Upon entering the search subroutine, the BALLISTIC v4.00 - Copyright 1988, 1989 by W.R. Frenchu Page 16 user will be prompted for a search string, and the search will begin with the last record displayed. Record movement keys are similar to those discussed in the previous section, with the addition of choice 4 (New Key) which will allow the user to specify a new search key. The <HOME> and <END> keys will initiate a forward or reverse search from either end of the database. D. Delete Record from Database Database menu choice 3 will allow the user to delete a record from the current database. Records may be displayed as described in section B, and the currently displayed record de- leted by pressing <4>. The first time the database is changed, whether by appending or deleting a record, the original database file is backed up by copying it to <database filename>.BAK. If the user should decide that an error was made, the backup file can be recopied or re- named. E. Add Record to Database This option (number 4 from the Database menu) will append a new record to the end of an existing database. The user will be prompted for all the necessary data, using the current program values as the default. F. Print Reloading Label Pressing <5> from the Database menu will present the user with a function virtually identical to the Display option. The primary difference is that sub-option 4 will now direct the record's image to the printer, for including in boxes of reloaded cartridges. G. Select Database File Option 6 (Select Database File) will allow the user to choose a new database file for use. After being prompted for a name, the program will attempt to open the file and read the header record. If the file does not exist, the user is given the option of creating it. Since the performance of several of the database functions degrades as file size gets larger, this option allows the user to keep several smaller databases available, and switch between them as necessary. H. Internal Database Structure Data files for the internal database may be created using BALLISTIC itself, the "report" option of most commercial data- bases, or any ascii word processor. Each line must be EXACTLY 120 characters long, not counting the CR/LF pair used as a termina- tor. The first line should contain (starting in the left column, WITHOUT leading spaces) the number of records contained in the database, a space, the version number of BALLISTIC (4.00), an- other space, and a database comment. If necessary, it must be padded with blanks on the right to bring the total line length to 120 characters. Second and subsequent lines will consist of a chart title or load comment exactly 79 characters long (padded with blanks if necessary), followed (starting in column 80) by: Bullet Weight (integer, bullet weight in grains) Caliber (real, bullet diameter in inches) Initial Velocity (real, f.p.s) Final Velocity (integer, f.p.s) BALLISTIC v4.00 - Copyright 1988, 1989 by W.R. Frenchu Page 17 Range (integer, range for final velocity in yds.) Bal. Coeff. (real, ballistic coeff. at STP, can be 0) Powder Weight (real, powder weight in grains, can be 0) Again, the values must be separated by at least one space. The whole line must be exactly 120 characters long, not counting the terminating CR/LF pair. I. External Database Return Values The values from an external database program can be imported into BALLISTIC through the file BALISTIC.RET. The external pro- gram should create this ascii file containing the following information: (Line 1) Chart title or comment (79 characters max., ending in CR/LF) (Line 2 - Each entry separated by a space, line ends with CR/LF) Bullet Weight (integer, bullet weight in grains) Caliber (real, bullet diameter in inches) Initial Velocity (real, f.p.s) Final Velocity (integer, can be zero) Range (integer, range for final velocity in yds.) Bal. Coeff. (real, ballistic coeff. at STP, can be 0) Powder Weight (real, powder weight in grains, can be 0) (Maximum length of Line 2 must be less than 79 characters) BALLISTIC v4.00 - Copyright 1988, 1989 by W.R. Frenchu Page 18 7. GRAPHICS MODE FUNCTIONS It is possible to display several useful bullet character- istics graphically (as a function of range). Graphics mode is entered by pressing <4> from the trajectory table prompt. The following commands are available to users only while in graphics mode. A. Changing the Axes Pressing <A> (for axes) will allow the user to set a "view- port" in the current graphics display. The program will prompt for starting and ending range, and the maximum and minimum ordi- nate then plot only that portion of the chosen function that falls in the described "window". The minimum and maximum allow- able range values are 0 and the maximum table range, respec- tively. Pressing <S> (for start) will reset the plot to the ini- tial (program chosen) limits. B. Saving and Restoring Plot Data If <W> is pressed, graphics 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 current data (plotted with a solid line) will be saved to the file. This data may be "merged" with the current graphics plot at any time by pressing <R>. When read back, it will be scaled and plotted using a different color (if available) to distinguish it from the current plot. The number of files that can be read back is lim- ited only by the user's ability to tell them apart on the gra- phics screen. Data types CANNOT be mixed, i.e., the user cannot read a trajectory plot onto an energy display. C. Graphics Cursor The coordinates of a given point (to the nearest pixel) can be displayed with the graphics cursor feature. Pressing <C> in graphics mode toggles the appearance of a small, cross shaped cursor, and two boxes at the top of the plot containing the co- ordinates of the displayed point. The current function value will be on the left and range (in yards) will be on the right. The cursor may be moved around the screen (one pixel at a time) through use of the the cursor keys. Holding the <SHIFT> key down while manipulating the cursor keys will cause faster move- ment (about 16 pixels). Increased (apparent) resolution can be obtained by using the <A>xes command to expand the screen around the region of inter- est. (This actually just makes each pixel represent a smaller area.) D. Hardcopy of Graphic Data A hardcopy of the plot (actually, a screen dump) may be produced by pressing <P> if an graphics printer is present. (Sup- ported 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 graphics screen dump is about 30k, roughly the size of a ten page document, and takes as long to print.) Printing may be abandoned at any time by pressing a key. BALLISTIC v4.00 - Copyright 1988, 1989 by W.R. Frenchu Page 19 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 system diskette) be run before BALLIS- TIC 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.) E. Plotting Other Functions When the plotting command is first issued, a plot of the bullet's trajectory versus range is immediately generated. Plots of several other parameters as a function of range are also available. Pressing <V> will present the user with a plot of velocity, <M> with momentum, <D> with deflection and <E> with the bullet's kinetic energy. The original trajectory plot may be restored by pressing <T>. F. Miscellaneous Graphics Commands Pressing <X> or the <ESC> key will return the user to the sight table prompt. <G> will toggle the appearance of a grid on the plot and <H> will provide a short help screen. BALLISTIC v4.00 - Copyright 1988, 1989 by W.R. Frenchu Page 20 8. 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 informa- tion 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 cal- culated 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) B. Functions of Merit There is great interest in a simple calculation that would allow shooters to rank quantitatively the terminal performance of their loads. Given the difficulty of obtaining reliable scien- tific data on stopping power (the subjects tend to object...), a universally accepted description of it has been a Holy Grail among gun gurus for practically as many years as there have been cartridges. (It has been the author's observation that many shooters find a gun that they like FIRST, THEN try to justify it with the calculation that makes their choice look best!) In the interest of peace and harmony, the user may choose one of six "functions of merit" to be displayed in the header. These are, IPSC Power Factor, Tappen WAVE Function, Taylor Knock Out, Josse- rand Energy Transfer, Hatcher RSP or Coefficient of Form (i). The user can specify his particular choice with BALISTIC.CFG (section 9). Default is the Coefficient of Form (which plays no favor- ites). All functions are determined using the muzzle velocity rather than velocity at range. The coefficient of form relates the shape of the bullet in question to the shape of the projectile used in constructing the drag function. The IPSC Power Factor is a number used by the International Practical Shooting Confederation to determine whether a compet- itor's handgun load is to be scored as "major" or "minor" cali- ber. It is 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 between 125 and 175 are scored as minor caliber. Loads with a power factor of less than 125 are not legal for IPSC competition. Taylor Knock Out was devised by John Taylor to describe his experiences with bullet performance in large game. It's defined BALLISTIC v4.00 - Copyright 1988, 1989 by W.R. Frenchu Page 21 as bullet weight (in pounds) times velocity times the bullet diameter in inches. (See "African Rifles and Cartridges" by John Taylor for a more thorough description.) General Julian Hatcher, following his involvement in the Thompson-LaGarde experiments in wound ballistics, established a widely used scale he called the Relative Stopping Power (RSP). A simplified version has been credited to Mel Tappan in his book SURVIVAL GUNS. Called the WAVE factor, (for Weight, Area, Velo- city and Efficiency) it is typically about 1/2 the actual RSP listed by Hatcher. Defined (as the name implies) as the product of weight, area, and velocity divided by 1000, it is frequently modified by a rather arbitrary bullet shape factor (the effici- ency). Hatcher gave a "slightly flat pointed" bullet an effici- ency of 1.0, and scaled everything else from 0.9 (for round nosed bullets) to 1.25 (for semi-wadcutters or jacketed hollow points). Tappen also adopted this factor. In the value provided by BALLIS- TIC the efficiency is ALWAYS assumed to be 1.0 and any scaling for bullet shape must be done by the user. Recently popular, (although first described some time ago) is the concept of "energy transfer" or "energy dump" as an ap- proximation of stopping power. The Josserand Energy Transfer Function provided by BALLISTIC is defined as the product of area and kinetic energy. C. 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 veloc- ity. It may be thought of as the amount of work the bullet can do on its target. The unit (foot-pounds) is the amount of work nec- essary to lift an object weighing 1 pound to a height of 1 foot. Many hunters feel this quantity is good 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 simpli- fied picture, however, as terminal ballistics is also concerned with bullet and target construction. D. Momentum As, in any collision of moving bodies, momentum is con- served, it may be thought of as the "striking" or "knockdown" power of a projectile. This can be slightly misleading, however, as the conservation applies only to the total "system" of par- ticles. If, for example, the bullet completely penetrates the target, it may retain a large portion of its original momentum, transferring to the target only that part it actually lost. It is defined as the mass of a body times its velocity. E. Maximum Ordinate The maximum ordinate 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. 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. It is also slightly different from the maximum height (which is also referenced to the line of sight). F. Deflection Deflection 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 BALLISTIC v4.00 - Copyright 1988, 1989 by W.R. Frenchu Page 22 wind at the site is 5 m.p.h. and the figures 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 m.p.h. cross wind. G. 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. H. 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 got 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 bullet and target arrive in the same place at the same instant. 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 proper target lead would be (10 m.p.h.) times (2.0 in./m.p.h.) or 20.0 inches. Wind speed (deflection) is NOT taken into account during the calculation of lead. I. Time of Flight Time of flight is simply that; the amount of time, in se- conds, necessary for a bullet to travel the distance from the muzzle to the indicated range. J. Trajectory Loosely speaking, trajectory is the path of a moving projec- tile. 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. The user should note 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 rela- tive to the line of sight is upward) and again at the targeted (or "sighted in") distance (when it crosses in a downward direc- tion). 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 ne- cessary angular correction (minutes of angle, or M.O.A.) by ap- plying 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 cali- brated at 1/4 minute per "click", while iron sights may be as much as 1 minute per click. (In this notation, minutes do NOT BALLISTIC v4.00 - Copyright 1988, 1989 by W.R. Frenchu Page 23 refer in any way to units of time, but rather to 1/60th of an angular degree.) BALLISTIC provides both systems in its trajec- tory tables. Shooting at a target 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. Most 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 departure", and for a typical rifle, is less than one degree.) Firing uphill or downhill usually produces a tilt that dwarfs this small value. BALLISTIC v4.00 - Copyright 1988, 1989 by W.R. Frenchu Page 24 9. THE CONFIGURATION FILE Version 4.00 of BALLISTIC will allow certain program de- faults to be overridden with a configuration file, BALISTIC.CFG. The file is searched for ONLY in the current directory when BALLISTIC is first started and is NOT necessary for operating the program. A. Using the Configuration File The configuration file is a user-created, 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 exponen- tial 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 v4.00: 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 default 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 de- scription of allowable values and restrictions. FUNCTION - The "function of merit" to be displayed in the table header. Default is 0, for Coefficient of Form. The choices are described in more detail in section 8B. Acceptable values are: 0 - Coefficient of Form 1 - IPSC Power Function 2 - Taylor Knock Out (TKO) Value 3 - Tappen WAVE Function 4 - Josserand Energy Transfer Function 5 - Hatcher Relative Stopping Power (RSP) BALLISTIC v4.00 - Copyright 1988, 1989 by W.R. Frenchu Page 25 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 also be toggled from the Plot function itself. Allow- able values are ON and OFF. PCHECK - The type of printer check to be performed by BALLISTIC before printing tabular data. Non-IBM printers and computers may have trouble with the BIOS level check. Default is 2. Acceptable values are: 0 - Don't perform any check 1 - Perform BIOS check of printer 2 - Prompt for user check 3 - Perform both checks PRESSURE - The atmospheric pressure used for the ballis- tic table and ballistic coefficient calculations. May be REAL. The default value is dependent on the func- tion 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 0, for no graphics printer. Cur- rently supported values are: 0 - No graphics printer 1 - Hewlett Packard LaserJet 2 - Star SG-10 (in IBM mode) 3 - IBM Proprinter 4 - IBM Graphics Printer 5 - Epson FX-80 6 - C. Itoh 8510A 7 - Hewlett Packard PaintJet 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. TCHECK - Determines whether the program performs a check sum test of the function file after reading it. De- fault value is ON, allowable values are ON or OFF. 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 v4.00 - Copyright 1988, 1989 by W.R. Frenchu Page 26 10. 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 9. 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. BALLISTIC will itself calculate the coefficient in certain cases. Both the initial and remaining velocity at a fixed range must be known. This data is available for factory loaded ammuni- tion 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 and 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- duct reviews in many magazines. The user shouldn't forget to add in the weight of scopes, slings, custom stocks or any other accessories. BALLISTIC v4.00 - Copyright 1988, 1989 by W.R. Frenchu Page 27 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 of Bullet Alloy 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 So- ciety of Metals METALS HANDBOOK. F. Temperature, Atmospheric Pressure, Wind 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 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 9) 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 describes 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. Velocity 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 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 regis- tered users. Ackley, in his book HANDBOOK FOR SHOOTERS AND RELOADERS, BALLISTIC v4.00 - Copyright 1988, 1989 by W.R. Frenchu Page 28 describes a simple "ballistic pendulum" that can be used to esti- mate projectile velocities. No external power is necessary; it relies on the kinetic energy of the bullet to swing a heavy mass. BALLISTIC v4.00 - Copyright 1988, 1989 by W.R. Frenchu Page 29 --==< B A L L I S T I C v4.00 >==-- Copyright 1988, 1989 by W.R. Frenchu All Rights Reserved. - MAIN MENU - 1 ........ Calculate Ballistic Table. 2 .. Calculate Ballistic Coefficient. 3 .... Adjust Atmospheric Conditions. 4 ........ Select New Function Table. 5 .......... Miscellaneous Functions. 6 ............... Database Functions. 7 ................. Return to System. Your Choice ? 1 ---------------------( Fig. 1 - Main Menu )---------------------- --==< B A L L I S T I C v4.00 >==-- Copyright 1988, 1989 by W.R. Frenchu All Rights Reserved. - CALCULATE BALLISTIC COEFFICIENT - Please input: Initial velocity ....(fps) 2820 Final velocity ......(fps) 2520 Range .............(yards) 100 Altitude ............(ft.) 0 Temperature ......(deg. F) 59.0 Atmos. pressure ..(in. Hg) 29.53 Effective Bal. Coeff. = 0.301 (Bal. Coeff. at STP = 0.301) -------( Fig 2. - Calculating the Ballistic Coefficient )------- BALLISTIC v4.00 - Copyright 1988, 1989 by W.R. Frenchu Page 30 --==< B A L L I S T I C v4.00 >==-- Copyright 1988, 1989 by W.R. Frenchu All Rights Reserved. - CALCULATE BALLISTIC TABLE - Please input: Initial velocity ...........(fps) 2820 Bullet weight ...........(grains) 147 Bullet diameter ............(in.) 0.308 Effective Bal. Coeff. ........... 0.301 Range ....................(yards) 100 Number of intervals .....(50 max) 10 Chart title (79 chars. max) ? 7.62 NATO - 147gr FMJ ------------------( Fig. 3 - Main input screen )----------------- 7.62 NATO - 147gr FMJ (Calculated using G1 table) Bullet Weight ......... 147 grains Bullet Caliber ........ 0.308 Sectional Density ..... 0.221 Coefficient of Form ... 0.735 Effective Bal. Coeff... 0.301 Bal. Coeff. at STP .... 0.301 Cross wind ............ 10.0 m.p.h. Altitude .............. 0 Ft. Atmospheric pressure .. 29.53 in. Temperature ........... 59.0 F Range Velocity Energy Momentum Mx. Ord. Defl. Drop Lead Time yards f.p.s. ft-lb. lb.-sec. in. in. in. in/mph sec. 0 2820 2595.4 1.8407 0.0 0.0 0.0 0.0 0.000 10 2789 2538.8 1.8205 0.0 0.0 0.0 0.2 0.011 20 2758 2483.3 1.8005 0.0 0.0 0.1 0.4 0.022 30 2728 2428.8 1.7806 0.1 0.1 0.2 0.6 0.032 40 2698 2375.2 1.7609 0.1 0.2 0.4 0.8 0.044 50 2668 2322.6 1.7413 0.1 0.3 0.6 1.0 0.055 60 2638 2270.9 1.7218 0.2 0.4 0.8 1.2 0.066 70 2608 2220.1 1.7024 0.3 0.5 1.1 1.4 0.077 80 2579 2170.3 1.6832 0.4 0.7 1.5 1.6 0.089 90 2549 2121.3 1.6641 0.5 0.9 1.9 1.8 0.101 100 2520 2073.1 1.6451 0.6 1.1 2.4 2.0 0.113 1=Print 2=Form Feed 3=File 4=Sight Table 5=New Data 6=Main Menu ? 4 ------------( Fig. 4 - The completed ballistic table )----------- BALLISTIC v4.00 - Copyright 1988, 1989 by W.R. Frenchu Page 31 --==< B A L L I S T I C v4.00 >==-- Copyright 1988, 1989 by W.R. Frenchu All Rights Reserved. - ADJUST ATMOSPHERIC CONDITIONS - Please input: Bal. Coeff. at STP ........ 0.301 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 = 0.337 --------( Fig. 5 - Modifying the ballistic coefficient )-------- --==< B A L L I S T I C v4.00 >==-- Copyright 1988, 1989 by W.R. Frenchu All Rights Reserved. - CALCULATE RECOIL - Please input: Initial velocity .....(fps) 2820 Weight of gun ........(lbs) 9.50 Weight of bullet ..(grains) 147 Weight of powder ..(grains) 43.0 Recoil Velocity = 8.8 fps Recoil Energy = 11.5 ft-lbs (Recoil due to bullet = 5.7 ft-lbs or 50%) -----------------( Fig. 6 - Recoil calculation )---------------- BALLISTIC v4.00 - Copyright 1988, 1989 by W.R. Frenchu Page 32 --==< B A L L I S T I C v4.00 >==-- Copyright 1988, 1989 by W.R. Frenchu All Rights Reserved. - CALCULATE POINT BLANK RANGE - Please input: Initial velocity ...........(fps) 2820 Sight height ............(inches) 0.90 Max. dist. from sight line .(in.) 3.00 Effective Bal. Coeff. ........... 0.301 Targeted range for +/-3.00 inch path is 220 yds. Point-blank range is 258 yds. (100 yd. trajectory = +2.9 in.) -----------( Fig. 7 - Calculating Point Blank Range )----------- --==< B A L L I S T I C v4.00 >==-- Copyright 1988, 1989 by W.R. Frenchu All Rights Reserved. - 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 v4.00 - Copyright 1988, 1989 by W.R. Frenchu Page 33 --==< B A L L I S T I C v4.00 >==-- Copyright 1988, 1989 by W.R. Frenchu All Rights Reserved. - 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. ........... 0.301 Actual Muzzle Velocity = 2824 fps ---( Fig. 9 - Calculating muzzle velocity from instrumental )--- --==< B A L L I S T I C v4.00 >==-- Copyright 1988, 1989 by W.R. Frenchu All Rights Reserved. - 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 v4.00 - Copyright 1988, 1989 by W.R. Frenchu Page 34 Appendix A Glossary BALLISTICS - The study of moving projectiles. Commonly, what is meant is "exterior" ballistics, that is, the portion of the bullet's flight between muzzle and target. "Interior" ballis- tics 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 reloading manufacturers, or it may be derived from their ballistic ta- bles. 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 cal- culate the ballistic table. CROSS WIND ANGLE - The angle between the wind and line of depar- ture. 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. FT.-LBS. - Foot pounds. A unit of energy equal to the effort required to raise one pound to a height of one foot. BALLISTIC v4.00 - Copyright 1988, 1989 by W.R. Frenchu Page 35 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 ta- bles and the Ordnance Department's J table. I.H.M.S.A. - International Handgun Metallic Silhouette Associa- tion. 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., (perpendicul- ar 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 ORDINATE - The highest vertical distance above a line from the muzzle to the bullet's current position. Sometimes confused with the maximum height (which is referenced to the line of sight). 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 veloc- ity. Indicative of the striking or knockdown power of a pro- jectile. 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) divided by 1000 and multiplied by the velocity. Cartridges with a power factor equal to or greater than 175 are consid- ered "major". Cartridges ranking between 125 and 175 are "minor" and those below 125 are not legal for IPSC competi- tion. 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). BALLISTIC v4.00 - Copyright 1988, 1989 by W.R. Frenchu Page 36 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 cali- ber. Usually expressed as "1 turn in xx inches" where xx may range from about 8 inches up to over 30. "Faster" twist trans- lates 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 v4.00 - Copyright 1988, 1989 by W.R. Frenchu Page 37 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 METALLIC CARTRIDGE RELOADING, Edward A. Matunas: DBI Books SHOOT WITH A COMPUTER, Outdoor Life, January 1989 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 HANDBOOK FOR SHOOTERS AND RELOADERS, VOL I & II, P.O. Ackley, Salt Lake City: Publisher's Press, 1965 HODGDON POWDER DATA MANUAL #25, Shawnee Mission, KS: Hodgdon Powder Co. Inc., 1987 HORNADY HANDBOOK OF CARTRIDGE RELOADING, RIFLE-PISTOL, Grand Island: Hornady Manufacturing Co., 1973 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 BALLISTIC v4.00 - Copyright 1988, 1989 by W.R. Frenchu Page 38 ASSOCIATIONS: AMERICAN SHOOTING SPORTS COALITION, INC. - P.O. Box 1447, Ft. Washington, PA 19034 FIREARMS COALITION (Neal Knox Associates) - Box 6537, Silver Springs, MD 20906 GUN OWNERS OF AMERICA - 8001 Forbes Place (Suite 102), Springfield, VA 22151 INTERNATIONAL HANDGUN METALLIC SILHOUETTE ASSOCIATION - Box 1609, Idaho Falls, ID 83401 NATIONAL ASSOCIATION TO KEEP & BEAR ARMS - P.O. Box 78336, Seattle, WA 98178 NATIONAL FIREARMS ASSOCIATION - P.O. Box 160038, Austin, TX 78716 NATIONAL RIFLE ASSOCIATION - 1600 Rhode Island Ave. NW, Washington, D.C. 20036 S. A. A. M. I. (SPORTING ARMS AMMUNITION MANUFACTURERS INSTITUTE) - P.O. Box 838, Branford, Conn. 06405 SECOND AMENDMENT FOUNDATION - 12500 N.E. Tenth Place, Bellvue, WA 98005 BULLETIN BOARDS/INFORMATION SERVICES: BULLET'N BOARD BBS - Tanya Metaska, Sysop - (703) 971-4491 BBS of the Firearms Coalition. Legal updates, firearms programs, Reload conference. COMBAT ARMS BBS - Richard Bash, Sysop - (415) 537-1777 BBS of Combat Arms Gun Shop. Many firearms, legal, and aviation programs. National Firearms Echo. COMPUSERVE INFORMATION SERVICE - (check local numbers) Outdoor forum (firearms and NRA conferences) LOTS of useful information. POLYMATH ONE BBS - D.G. Gabrial, Sysop - (609) 394-2608 BALLISTIC support board. PCRelay Firearms Echo. BALLISTIC v4.00 - Copyright 1988, 1989 by W.R. Frenchu Page 39 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 v4.00 - Copyright 1988, 1989 by W.R. Frenchu Page 40 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 v4.00 - Copyright 1988, 1989 by W.R. Frenchu Page 41 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 v4.00 - Copyright 1988, 1989 by W.R. Frenchu Page 42 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 v4.00 - Copyright 1988, 1989 by W.R. Frenchu Page 43 Appendix E Using Other Standard Functions 1. 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 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: 1. Truncated revision number for version of GENTABLE used multiplied by -1. (int) 2. The complete revision number. (float) (Added in v4.0) 3. The table name. (char) 4. Standard temperature for table data. (double) 5. Standard pressure for table data. (double) 6. Maximum velocity in table (<=4094). (unsigned) 7. Minimum velocity in table. (unsigned) 8. S_table, T_table pairs as described in HATCHER'S NOTE- BOOK for velocities (max >= v >= 0). (float) 9. Checksum calculated as the sum of (S_table - T_table) values. (float) 2. Checking the Function File with READTABLE After creating the function file, registered users may (op- tionally) check it with READTABLE. Since BALLISTIC makes its own brief check, this step is usually unnecessary. READTABLE was originally written as a debugging aid and is provided 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 function 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. "-G" (Graphics) - Don't use the IBM graphic character set. (Use ASCII characters instead.) "-H" (Help) - Display a short help screen listing these flags. "-T" (To) - End the listing at the value following this argument. BALLISTIC v4.00 - Copyright 1988, 1989 by W.R. Frenchu Page 44 "-N" (Noprint) - Don't print the table, calculate the checksum only. Flags requiring numeric arguments should NOT have a space between the flag and input value. BALLISTIC v4.00 - Copyright 1988, 1989 by W.R. Frenchu Page 45 Appendix F User Supported Software (Shareware) User Supported Software is based on the premise that if someone gets a chance to try out a program, likes it, and finds he uses it on a regular basis, he will contribute to the support of that program. Users who take the trouble to register know they are helping to make sure that high quality software like BALLIS- TIC continues to be sold in this low cost way. BALLISTIC is being distributed as User Supported Software. Registration allows you to continue using BALLISTIC after the initial 30 day trial period. Registered users get mailed notifi- cation of future BALLISTIC releases, and are eligible for low cost (or free) upgrades. Additionally, registered users may obtain support for special printers, video cards, etc. Registration of BALLISTIC costs $15.00. For $30.00, you receive registration, a disk containing the current version of the BALLISTIC package, READTABLE, CHECK_DB, a printed copy of the manual, and whatever BALLISTIC compatible databases the author has acquired. (Currently available: Sierra, Nosler, Speer and Hornady reloading components, and CCI and Federal handgun car- tridges.) Source code for version 4.00 is available (to registered users only) for an additional $50.00. (This price does NOT in- clude registration.) Checks and money orders are accepted for payment, as well as corporate purchase orders. A registration (order) form appears on the following page. Comments or suggestions may be left for the author (Bill Frenchu) at any of the following places: Bullet 'n Board BBS (703) 971-4491 Polymath One BBS (609) 394-2608 (Co-Sysop) CompuServe 74575,61 (E-Plex or Outdoor Forum) PCRelay Firearms Echo (routed mail to ->POLYMATH) Corporations and Institutions Please contact the author for information on licensing mul- tiple copies of BALLISTIC. (Site licenses are available at very reasonable rates.) Under no circumstances may an unregistered copy of BALLISTIC be used in a corporate, institutional or gov- ernment environment. BALLISTIC v4.00 - Copyright 1988, 1989 by W.R. Frenchu Page 46 BALLISTIC 4.00 REGISTRATION FORM Name _____________________________________ Date _______________ Mailing Address: Street __________________________________ Phone ______________ City ________________________ State ___ Zip ________________ Computer/DOS (& BIOS) _____________________ Printer ____________ Display/adapter type _______________________ Co-processor? ______ Where did you find out about BALLISTIC? _________________________ ================================================================= Quan Item Each Total ____ BALLISTIC v4.00 - Registration ONLY $15.00 _____ (No diskette or manual) ____ BALLISTIC v4.00 - "Deluxe" Registration $30.00 _____ (Includes current version of BALLISTIC, databases, aux. files, and manual.) Diskette size: ___ 5.25" ___ 3.5" ____ Version 4.00 source code. (Turbo C v2.0) $50.00 _____ Must be registered user. (Price does NOT include registration.) TOTAL ===== ================================================================= The author is always trying to improve BALLISTIC. You can help! Comments about BALLISTIC v4.00 (and documentation): Suggestions for future versions of BALLISTIC: Types of shooting you do (or how will you use BALLISTIC?): Have you used any other ballistic programs? Which ones? Mail to: William Frenchu, 79 Taylor Terrace, Hopewell, NJ 08525
Disk No: 1802 Disk Title: Ballistic PC-SIG Version: S2 Program Title: Ballistic Author Version: 4.00 Author Registration: $15.00 basic or $30.00 deluxe. Special Requirements: None. BALLISTIC is a program used to calculate bullet trajectories, remaining energy, velocities, etc., for small arms. It will generate ballistic tables, calculate point blank range, and many other useful functions, even plot trajectory vs. range on systems with VGA, EGA, CGA, MCGA or Hercules graphics adapters. The purpose of this program is NOT to teach the fundamentals of reloading small arms ammunition, 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 is supplied. This program is very thorough and complete. The documentation is over 35 pages long and extremely informative. It discusses the variables considered in calculations, how they are to be derived, and why they are so important. The appendix even has definitions on key words, making BALLISTIC a fine learning tool. PC-SIG 1030D East Duane Avenue Sunnyvale Ca. 94086 (408) 730-9291 (c) Copyright 1989 PC-SIG, Inc.
╔═════════════════════════════════════════════════════════════════════════╗ ║ <<<< Disk #1802 BALLISTIC >>>> ║ ╠═════════════════════════════════════════════════════════════════════════╣ ║ ║ ║ To start program, type: BALISTIC (press enter) ║ ║ ║ ║ To print documentation, type: COPY BALISTIC.DOC PRN (press enter) ║ ║ ║ ╚═════════════════════════════════════════════════════════════════════════╝ (c) Copyright 1990, PC-SIG Inc.
Volume in drive A has no label Directory of A:\ BAL-READ ME! 3647 11-15-89 BALISTIC DOC 136404 11-15-89 BALISTIC EXE 127479 11-15-89 BAL-GEN EXE 33507 11-15-89 BALISTIC DB 4480 11-15-89 GO BAT 38 1-01-80 1:37a GO TXT 732 7-11-90 12:58a FILE1802 TXT 2443 7-12-90 3:24p 8 file(s) 308730 bytes 9216 bytes free