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. ii QBALL COPYRIGHT INFORMATION IBM, PC-DOS, and OS/2 are trademarks of International Business Machines. 4DOS is (C)1988-91 Rex C. Cohn and J. P. Software, Inc. MS-DOS and Professional Development System are (C)Microsoft, Inc. Universal INSTALL is (C)1994 The GoodSoft Corp. GX Kernel and GX Printer are (C)1990-94 Genus Microprogramming, Inc. Video Display Editor (VDE) is (C)1987-1993 Eric Meyer All other copyrights and trademarks are the property of their respective holders. MISCELLANEOUS INFORMATION Composition in Plain-vanilla ASCII format using Video Display Editor v1.71a by W O R D S M I T H Jaffrey, New Hampshire ---------- Some screen dump graphics developed using PRN2FILE, by Tom Kihlken (C)1988 Paul Somerson and Ziff Communications Company. iv QBALL TABLE OF CONTENTS (continued). Chapter Page 3. Inferred Ballistics Data . . . . . . . . . . . . . . . . . .37 3.1 Inferring a Ballistic Coefficient. . . . . . . . . . . .37 Ballistic Coefficient, R1 = 0 . . . . . . . . . . . . .38 Ballistic Coefficient, R1 = 25. . . . . . . . . . . . .39 3.2 Inferring a Muzzle Velocity. . . . . . . . . . . . . . .41 Muzzle Velocity Using the Bullet Drop Method. . . . . .41 Muzzle Velocity from One Downrange Velocity . . . . . .44 4. Printed Output and Printer Configuration . . . . . . . . . .45 4.1 Printer Warnings . . . . . . . . . . . . . . . . . . . .45 4.2 Screen Dumps (Shift-PrintScr). . . . . . . . . . . . . .45 4.3 Printer Setup. . . . . . . . . . . . . . . . . . . . . .45 4.4 Configuring QBALL for Traj'y Grfx, One Parallel Port . .46 4.5 Configuring QBALL for Traj'y Grfx, Multiple Ports. . . .48 4.6 Common Printer Problems. . . . . . . . . . . . . . . . .49 5. Configuring Display and Defaults, Using Utilities. . . . . .51 5.1 The Utilities and Configuration Menu . . . . . . . . . .51 5.2 Choose Units and Options, Toggle Switches, Choose Printer Port . . . . . . . . . .51 Setting Unit System and Optional Units. . . . . . . . .51 Toggling Graphics Grid Display and Noises . . . . . . .53 Printer Enablement and Using Other Available Parallel (Printer) Ports. . .53 5.3 Configuring Screen Colors. . . . . . . . . . . . . . . .54 5.4 Using the Values You've Set. . . . . . . . . . . . . . .54 5.5 Invoking a DOS Shell . . . . . . . . . . . . . . . . . .55 5.6 Reading a Saved Range or Slant Fire Table. . . . . . . .56 6. Recalling Saved Trajectory Data. . . . . . . . . . . . . . .57 Appendices. . . . . . . . . . . . . . . . . . . . . . . . . . .59 Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . .77 LIST OF FIGURES Figure Page 1. Opening Screen . . . . . . . . . . . . . . . . . . . . . 3 2. Main Menu Display. . . . . . . . . . . . . . . . . . . . 4 3. Metric Units Information Line. . . . . . . . . . . . . . 4 4. A Clean Sweep Prompt . . . . . . . . . . . . . . . . . . 5 5. Required Data Entry. . . . . . . . . . . . . . . . . . . 7 6. Computations Menu. . . . . . . . . . . . . . . . . . . . 8 7. Partial Computations Menu, Valid Zero Set. . . . . . . . 8 8. Range Data Entry Window, All Data Set. . . . . . . . . . 9 9. Typical Range Table. . . . . . . . . . . . . . . . . . . 9 10. Partial Range Table. . . . . . . . . . . . . . . . . . .10 11. Typical Range Table (Metric Measure) . . . . . . . . . .11 vi QBALL LIST OF FIGURES (continued) Figure Page 60. Bullet Drop Method Schematic . . . . . . . . . . . . . .41 61. Muzzle Velocity from Bullet Drop Display . . . . . . . .42 62. Measurements to Find Group Center. . . . . . . . . . . .43 63. Muzzle Velocity from One Downrange Velocity. . . . . . .44 64. Choosing a Printer Make. . . . . . . . . . . . . . . . .46 65. Choosing a Printer Model . . . . . . . . . . . . . . . .47 66. Confirming Reconfiguration . . . . . . . . . . . . . . .47 67. Assigning a Driver to a Parallel Port. . . . . . . . . .48 68. Assignment Status and "Another?" Prompt. . . . . . . . .48 69. Utilities Menu . . . . . . . . . . . . . . . . . . . . .51 70. Units, Switches & Printer Menu . . . . . . . . . . . . .51 71. Selecting English Unit System Options. . . . . . . . . .52 72. Selecting Metric Unit Sysytem Options. . . . . . . . . .52 73. Printer Settings Menu. . . . . . . . . . . . . . . . . .53 74. Error Message, Parallel Port Not Detected. . . . . . . .53 75. Configuring Display Colors Screen. . . . . . . . . . . .54 76. DOS Prompt in Shell. . . . . . . . . . . . . . . . . . .55 77. Already Loaded Error Message . . . . . . . . . . . . . .55 78. Loading Range Table Reader Utility . . . . . . . . . . .56 79. Saved Tables Found by RRTABLE. . . . . . . . . . . . . .56 80. Typical RRTABLE Display. . . . . . . . . . . . . . . .56.1 81. "Long Table" Menu Line . . . . . . . . . . . . . . . .56.1 82. Recall Trajectory Data Display and Menu. . . . . . . . .57 83. Recall Trajectory Data Menu and Choice Box . . . . . . .57 84. Graphics Display, Saved Trajectory File. . . . . . . . .58 LIST OF TABLES 1. Free Recoil Velocity and Energy, Selected Weapons. . . .28 2. Metric Data Limits . . . . . . . . . . . . . . . . . . .36 3. Unit System Conversion Factors . . . . . . . . . . . . .36 4. Decimal Equivalents, 1/64 Inch Measure . . . . . . . . .43 B.1. Data from Gun Digest Ballistic Table . . . . . . . . . .67 B.2. Data Using Inferred C1 . . . . . . . . . . . . . . . . .67 B.3. Trajectory Data, Speer Manual #11. . . . . . . . . . . .67 B.4. Trajectory Data, Inferred Muzzle Velocity. . . . . . . .68 B.5. Inferred vs Known Muzzle Velocity Results. . . . . . . .68 B.6. Remaining Velocities with Given Inputs . . . . . . . . .68 B.7. Trajectory Comparisons . . . . . . . . . . . . . . . . .69 B.8. Inferred Muzzle Velocity, Various Bullet Drops . . . . .70 B.9. Comparing Inferred vs Nominal Muzzle Velocity. . . . . .70 B.10. QBALL and Sierra Ballistics . . . . . . . . . . . . . .71 B.11. QBALL and BALCALC . . . . . . . . . . . . . . . . . . .71 B.12. QBALL and BALTEC. . . . . . . . . . . . . . . . . . . .72 B.13. QBALL and Barnes Ballistics . . . . . . . . . . . . . .72 D.1. Input Data for a Typical Air Rifle . . . . . . . . . . .75 D.2. QBALL Range Table for a Typical Air Rifle. . . . . . . .76 D.3. INGALLS Range Table for a Typical Air Rifle. . . . . . .76 viii QBALL OBTAINING THE LATEST SHAREWARE EDITION The most current Shareware Edition of QBALL -- functionally the same as the same-numbered Registered Edition -- is available direct from the author for a $7.50 materials and postage fee, and on the following electronic services and BBS. (Unless otherwise noted, look for filename QBALLnnn.ZIP, or use the search keyword "ballistics.") Attention to Details BBS, 909-681-6221, 1200/2400 8N1. Break RBBS, 703-680-9269, 1200/2400 8N1. CompuServe Outdoor Forum, Firearms Library, filename QBALnn.ZIP. Consultant BBS, 718-837-3236, 1200/2400 8N1. Data Exchange BBS, 318-239-2122, 1200/2400 8N1. EXEC-PC BBS, 414-789-4210, 1200/2400 8N1, Files/Mahoney Collection. GEnie IBMPC Roundtable library. Interstellar Express BBS, 614-436-5448, 1200/2400 8N1. Knightec BBS, 519-940-0007, 1200/2400 8N1. MicroData BBS, 509-482-2016, 1200/2400 8N1. SPACE BBS, 415-323-4193, 1200/2400 8N1. Twilight Zone BBS, 715-652-2758, 1200/2400 8N1. V-I-S-I-O-N BBS, voice: 410-461-6430, 14400 only - call for BBS #. The author provides QBALL directly to these services and BBS. Downloads from other sources may not be complete and functional -- caveat emptor! Other vendors to whom the author provides QBALL directly include, but are not limited to: *** Diskette Libraries: Micro Magic, PO Box 598, Nedlands, W.A. 6009 AUSTRALIA Public (software) Library, PO Box 35705, Houston, TX 77235-5705 Somewhere in Time Software, 485 Grant Ave., Copiague, NY 11726 Talon Shareware, 2770 Jane St. #415, Downsville, Ont M3N-2J1 CANADA Windchimes Shareware, PO Box 2100, Juniper, FL 33468-2100 *** CD-ROM Suppliers: Association of Shareware Professionals - address on cover CSD Software, 6754 Tara Blvd. Suite B-1, Jonesboro, GA 30236-1432 EMS Professional Shareware, 4505 Buckhurst Ct., Olney, MD 20832- 1830 JCS Marketing/Distribution, PO Box 1216, Lakeville, MN 55044 UAV Corporation, PO Box 7647, Charlotte, NC 28241 Diskette Libraries will almost certainly have the latest QBALL Shareware Edition; CD-ROM Suppliers should, but may have an older edition in stock. . . 2 Getting Started QBALL 1.5 General Instructions. Selecting Menu Options. Press the key corresponding to the letter which is highlighted or bracketed in the menu option. For example, to choose option , press upper- or lower-case "P." The QBALL menus are not case sensitive. If an option does not appear, or appears in low-intensity characters, QBALL will ignore the key press. Response to "([Y] or N)." Press <Y>, <y> or <enter> for "yes," <N> or <n> for "no." QBALL ignores any other key. <ESC>ape Key. <ESC>ape will back out of data or text entry, or will back up one menu level if a menu is displayed on the screen. Data Entry and Error Trapping. Type the value to be used, then press <enter>. If a value already appears in the entry box, press <enter> to accept it, or overtype to change it. QBALL will not accept the wrong data type, and out-of-range values will produce an error message. You may use the <backspace> key to edit the data value before entering it, or <ESC>ape to the previous menu. Text Entry. Use the usual editing keys: backspace, insert/de- lete, home/end, left/right arrows to edit descriptive text. The length of the text box is the maximum text length that QBALL will accept. Press <enter> to accept what is shown, or <ESC>ape to abort text entry. Caution: ensure that all extraneous characters have been edited out...QBALL will use the text exactly as shown. Help. Limited help is available during data and text entry, and when tables are displayed. Press <F1> to invoke help, any other key to clear the help message. Unit System Options. QBALL can display ballistics data using English units: yards, pounds, etc.; or Metric units: meters, kilograms, etc. The unit system may be toggled using the alt-[U] hotkey while range tables are displayed. As distributed, QBALL defaults to English units; this may be changed using the configuration routines. Graphics. Graphics are always enabled. You may toggle the graphics display grid on or off at any time when graphics are displayed, or use the configuration routines to change the default display. As distributed, QBALL defaults to graphics grid "on." Printer Options. Ensure that your printer is on, on-line, and has sufficient paper loaded if you want hard copy. QBALL will detect up to three parallel printers and their on/on-line status. but will not detect "paper out". The QBALL distribution default is "LPT1:/enabled." Change these using the configuration routines. Redirection of Data Output. Except as provided by the hardcopy printing and the save-to-file routines, QBALL does not support redirection of data output, e.g., to a disk file. 4 Getting Started QBALL The screen is swept clear, and the following Main Menu is dis- played: >> Ballistic Computations, Typical Firearm << ======================================= | *** M A I N M E N U *** | | --------------------------------- | | <C>ompute Ballistic or Gun Data | | nfer BC or MV from Firing Data | | Use tilities/Configure QBALL | | <R>ecall Saved Trajectory Data | | --------------------------------- | | <Q>uit -- Return to DOS | --------------------------------------- MV: | C1: | G: | Metro: 59d 0' 29.53" 78% | H: 1.00 |E ^ ^ ^ ^ ^ ^ -------- | ------ ------------------------- ------ ------- Muzzle | Bullet Meteorological Conditions Sight Unit Velocity | Weight Temperature, dF or dC Height System FPS | Grains Gun Altitude, ft or met inches English or | or Bar. Press., inch or mm or or MpS | Grams Rel. Humidity, % cm Metric | ----------- Ballistic Coefficient Figure 2. Main Menu Display. The Main Menu is QBALL's central dispatcher, from which all of the QBALL routines are accessed. Also displayed on this screen, at the top, is what you're doing ("Ballistic Computations") and the weapon name ("Typical Firearm"). At the very bottom of the screen is the information (info) line, which is displayed at all times, and is updated whenever any of the information is changed. This example shows the as-distributed QBALL default values: standard metro, 1 inch sight height, and English units. If QBALL is configured to use Metric units at startup, the info line looks like this, using the as-distributed default values: MV: | C1: | G: | Metro: 15d 0m 750mm 78% | H: 2.54 |M Figure 3. Metric Units Information Line. There are some blanks on the information line as no specific ammunition data has been entered for QBALL to work on. You'll get to fill in the blanks in Chapter 2, Computing Ballistic or Gun Data. 6 Getting Started QBALL 1.7 Uninstalling or Removing QBALL. If you have been running QBALL from a high-density floppy, un- installation is simplicity itself: exit QBALL and remove the QBALL disk from its drive. Removing QBALL from a hard disk is more involved, but not ser- iously so. It's simply a matter of deleting files and removing the QBALL directory. Here's how to go about it. a. Get to a bare DOS prompt like this: C:\>_ (If you're running "Windows" or "OS/2" exit the "Windows" or "OS/2" session.) b. Change to the drive upon which you installed QBALL: [drive:] + <enter>. (If you used the INSTALL defaults, [drive:] is "C:".) c. Change to the QBALL directory: [CD QBALLdirectory] + <enter>. (If you used the INSTALL defaults, QBALLdirectory is "QBALL330.") d. (Optional) To make a backup copy of the QBALL files, insert a blank formatted high-density disk into the appropriate [drive:] and type: COPY *.* [drive:] + <enter>. (If you've not saved range tables, the files should fit on one high-density disk.) e. Type this command: DEL *.* + <enter>. (You'll be asked to confirm the deletion; type Y + <enter>. f. Change to the parent directory: type CD.. + <enter>. g. Remove the QBALL directory: type RD [QBALLdirectory] + <enter>. QBALL uninstallation is now complete. Reinstallation may be accomplished using the distribution disk and INSTALL, or make an appropriate directory and copy the files from your backup disk to that directory. See your operating system documentation for details about making a directory, probably under MD or MKDIR. If you're running "Windows," "OS/2," or a similar "graphical user interface," you may have to perform some other operations. Please refer to your operating system documentation for details. 8 Computing Ballistic Data QBALL 2.2 Computing and Displaying Range Tables. When all the required information is available, QBALL displays the Computations Menu. > Ballistic Computations, Typical Firearm < ======================================= | *** Computations Menu *** | | --------------------------------- | | Range <T>able (0 must be set) | | Set or Reset Current <Z>ero Range | | <O>ther Ballistics Procedures | | <N>ew or Changed Input Data | | --------------------------------- | | <ESC> to M A I N M E N U | --------------------------------------- MV:2700 | C1:.300 | G:180 | Metro:59d 0' 29.53" 78% | H:1.00 |E Figure 6. Computations Menu. At this point, you may perform some other procedures, change some or all of the input data, or simply return to the Main Menu by pressing the appropriate key: <O>, <N>, or <ESC>, respectively. <O>ther procedures are fully described in section 2.12; <N>ew or Changed Input Data, in section 2.13. Press <T> to develop a range table. Since no valid zero range has been set, QBALL will prompt you for the zero range, and for the maximum range for the table and the range increment. Enter the following data in yards when prompted in the input box: a. Zero Range . . . . . . . . . . . . . . . . 250 b. Maximum Range. . . . . . . . . . . . . . . 300 c. Range Increment. . . . . . . . . . . . . . 50 QBALL allows zero and maximum ranges of 1760 yards (1 mile) and range increments of 1 yard to the maximum range set; all remain in effect until changed. Valid zero ranges are displayed in the Com- putations Menu thus: ======================================= | *** Computations Menu *** | | --------------------------------- | | Range <T>able (0 = 250 yards) | - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - --------------------------------------- Figure 7. Partial Computations Menu, Valid Zero Set 10 Computing Ballistics Data QBALL Consider the following, extracted from the Range Table shown in Figure 9: |Range R e m a i n i n g Drop Path/Sight Line 10 MPH Time | |Yards V: FPS E: Ft-Lbs Inches M.O.A. Inches Inches Flght | |----- ----------------- ------ --------------- ------ ----- | - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - | 200 2133 1819 11.19 1.52 3.18 4.93 0.250 | Figure 10. Partial Range Table. A bullet having the given ballistic characteristics, fired at the given muzzle velocity, with the given height of sight and metro conditions, will, at 200 yards range, retain 2133 FPS velocity and 1819 foot-pounds of energy, will have dropped 11.19 inches from the line of departure, will be 1.52 minutes of arc (MOA)/3.18 inches above the line of sight, will have been blown sideways 4.93 inches by a 10 miles-per-hour cross wind, and will have taken 0.250 seconds to travel the 200 yards downrange from the muzzle. 2.3 Range Tables Too Long to Display. QBALL can develop and display range tables which will not fit on one screen. If this is the case, you may use the <Home>/<End>, <PgUp>/<PgDn>, and the arrow keys to browse through the table. For tables which do not fit on a single screen, you may also use the following keys to display the indicated lines: <Z> The zeroed range; <M> The range at which the maximum ordinate occurs; alt-<M> The range at which the bullet is the same distance below the line of sight; <R> Find a user-specified range in the table. That range is marked with a | | combination; alt-<R> Erases the | | marks from the display. If possible, the requested data line will be vertically centered in the range table display. If you use <R> to find a range that is not specifically displayed, the next lower and next higher displayed ranges are marked with | |. (Put a bookmark here, and return to this section later to experiment with lengthy range tables.) 2.4 Alternate Unit System Display (alt-U hotkey). At any time that QBALL displays a range table, you may redis- play the current data in the alternate measurement system by pressing alt-U. For example, if you've developed a table using English units, the redisplay will be in Metric units; if in Metric units, the redisplay is in English units. The currently-displayed measurement system is used until it is again toggled. 12 QBALL -===| Unit Conversion... |======--\ The calculator choice box ||~~~Yards -> Meters~~~~~~~~~~~|, \ is always initially displayed +| Feet/Sec -> Meters/Sec |--\ at the upper left, but its || Foot-Pounds -> Meter-Kg |Dr\ position may be changed using || Inches -> Centimeters |nc\ the <home>, <end>, <pgUp> and || Grains -> Grams |--\ <pgDn> keys. The chosen posi- || dFahrenheit -> dCelsius | 0\ tion remains in effect for || Feet -> Meters | 0\ the duration of the QBALL run || Inches -> Millimeters | 0\ or until you change it. || Miles/Hr -> Meters/Sec | 0\ || Pounds -> Kilograms | 1\ In the example shown to |---------- Metric -> ---------- 2\ the left, Metric conversion | 125 2337 2061 4\ may be performed. (Which sys- \\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\ tem pops up depends upon the system you're using when you Figure 12. Conversion Calculator invoke the calculator. The Displayed, English Base Units. from-to unit is shown on the screen in a highlight bar. Press <pgDn> and the \\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\ <right> key. The box moves \ 2.94 0.77 0.00 0.028 | to the lower right corner, \ 4===| Unit Conversion... |======= | and metric-to-english sys- \ 4|~~~Meters -> Yards~~~~~~~~~~~~| | tem conversion may be done. \ 3| Meters/Sec -> Feet/Sec | | \ 3| Meter-Kg -> Foot-pounds | | Note the metric energy \ 3| Centimeters -> Inches |+| unit shown figures 12 and \ 2| Grams -> Grains | | 13: Meter-Kg. Had QBALL \ 2| dCelsius -> dFahrenheit | | been configure to use the \ 1| Meters -> Feet |<| joules option, then joules \--| Millimeters -> Inches |-- would appear in both. | Meters/Sec -> Miles/Hr | | Kilograms -> Pounds | Now press <home>, the --------- <- English ----------- <left> key, and use <up>/ <down> to move the high- Figure 13. Conversion Calculator light bar. Press <enter> to Displayed, Metric Base Units. select the highlighted con- version. Use the keypad or the \--===| Unit Conversion... |=======-- regular number keys, type \t | ---| Convert... |---------- | | in the quantity to be con- \--| | Yards -> Meters | |-+ verted, and press <enter>. \Pa| +-------------------------+ | | \M.| | | | | Here, yards-to-meters \--| | Yards: 136.75 | | | was selected; 136.75 was \ | | | | | entered, and the result is \ | | = 125.04 Meters | |:| as shown: 125.04 meters. \ 2| | | | | \ 4| | | | | Press any key to clear \ 4| -----> press any key <----- | | the result box. You may now \ 3---------- Metric -> ----------- | do more conversions, or \\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\ press <ESC>ape to exit the calculator and return to Figure 14. Result Box Displayed. what you were doing. 14 Computing Ballistics Data QBALL Depending in part upon how long the range table is, how fast your printer can print, and the size of the printer or other buffer, the range table is printed, and you are returned to the Range Table Output menu. If you want another hardcopy, simply press to repeat the process. The range table you've printed should look like this, making due allowance for print sizes, fonts, and "compression" shown here. ======================================== Ballistic Computations = Typical Firearm ======================================== Muzzle Velocity = 2700 FPS Ballistic Coef'nt = .300 Bullet Weight = 180 grains Sectional Density = n/a Temperature = 59 degF. Altitude at gun = 0 feet Barometric Pressure = 29.53 inches Hg Relative Humidity = 78 % ======================================== Range Table, Zeroed at 250 Yards ------------------------------------------------------------ Range R e m a i n i n g Drop Path/Sight Line 10 MPH Time Yards V: FPS E: Ft-Lbs Inches M.O.A. Inches Inches Flght ----- ----------------- ------ --------------- ------ ----- [ DATA OMITTED -- see Figure 9 ] ------------------------------------------------------------ ---------------------------------------- | -= SYMBOL KEY =- | | Range at which zeroed: [ ----- ] | | Range for max height: + ----- + | | Range MINUS max height: - ----- - | | Crossing(s) of LOS: : ----- : | | Found/marked ranges: | ----- | | | Maximum Range: > ----- < | ---------------------------------------- . . . = Last Page = Figure 17. Typical Printed Range Table. Should the range table be too long to fit on one page, page breaks, page numbers and appropriate column headers are included in the printed output. Pages other than the last page will show the word = more = at the bottom of each section. The last page will always include the Symbol Key shown, and the words = Last Page =. There is no need to set the left margin on your printer: the range table is printed with a (small) left margin. The QBALL printing routines have been found to work properly on dot-matrix and laser printers working at a character pitch of 10 cpi. You can, of course, use a finer character pitch, if desired. 16 Computing Ballistics Data QBALL 2.9 Slant Fire Effects. Published firing tables generally deal with horizontal fire, which, for use on a level firing range, is all that is required. If, however, the line of sight (LOS) is significantly elevated or depressed, the point of impact is found to be higher than expect- ed. Figure 20 schematically represents the effect of elevating the line of sight significantly above the horizontal. . Consider first the . case of horizontal | fire, assuming a sight | height of 0 (zero) . | inches. The line of a1 d1 sight is indicated by | the line labeled LOS; . | the line of departure, | by LOD. A bullet fired D | at point O travels the . b b -- path O-a-a-a-a and HH crosses LOS at the O rightmost a, the zero . b -- . range for horizontal a1. | fire. The correspond- L .(e) | ing bullet drop d is . .D | equal to the vertical b .O aa(d) distance aa between LOD .L | and LOS at range Oa. . . a | Now consider the case .a a | of an elevated angle . | of fire, or slant O_________________________________a___ fire. The line of LOS sight is indicated by the lower of the two Figure 20. Slant Fire Schematic. lines labeled LOD; the line of departure, by the upper LOD. The slant range Oe is taken as equal to the horizontal range Oa. A bullet fired from point O travels the path O-b-b-b-b. Since bullet drop is time- dependent, the drop d1 at range Ob is equal to drop d. The distance a1a1, taken at 90 degrees to LOS, is equal to aa. Thus, the bullet path is a distance HH above the line of sight, or "hits high" by this amount. The quantity hh is calculated using the relation: HH = D x ( 1 - COS ( LOS elevation angle )) Slant fire effects are the greatest under two conditions: 1. The LOS elevation angle is large; and, 2. The time of flight is relatively long. Since time of flight is dependent upon muzzle velocity and ballistic coeffi- cient, under those conditions where either one or both are relatively small, HH will be found to be relatively large. 18 Computing Ballistics Data QBALL QBALL can develop and display slant fire tables which will not fit on one screen. If this is the case, you may use the <Home> /<End>, <PgUp>/<PgDn>, and the arrow keys to browse through the table. You may also use the following keys to display the indicated lines applicable to horizontal fire: <Z> The zeroed range; <M> The range at which the maximum ordinate occurs; alt-<M> The range at which the bullet is the same distance below the line of sight; <R> Find a user-specified range in the table. That range is marked with a | | combination; alt-<R> Erases the | | marks from the display. If possible, the requested data line will be vertically cen- tered in the slant fire table display. If you use <R> to find a range that is not specifically displayed, the next lower and next higher displayed ranges are marked with | |. Press <ESC>ape to display the Slant Table Output Menu. ======================================= | *** Slant Table Output *** | | -------------------------------- | | <R>edisplay Slant Fire Table | | Change <V>ertical Displacement | | rint Slant Fire Table | | <S>ave Slant Fire Table to File | | -------------------------------- | | <ESC> to Range Table Output Menu | --------------------------------------- Figure 24. Slant Table Output Menu. At this point, you may <ESC>ape to the Range Table Output Menu if, for example, you wish to change the range or other input data. You may also redisplay the slant fire table - press <R> - which will put you back in the slant fire table at the same place you were when you <ESC>aped from it. rint Slant Fire Table and <S>ave Slant Fire Table to File are discussed in section 2.11 and section 2.12, respectively. QBALL allows you to Change <V>ertical Displacement type and size. In the preceding example, you entered an angular vertical displacement, i.e., the LOS was elevated above the horizontal. In most cases, angular vertical displacements will be easier to estimate, but you may develop a slant fire table if you know the linear vertical displacement. If you are using English units, the QBALL default, linear vertical displacements are taken in feet; if using Metric units, linear vertical displacement are taken in meters. The maximum linear vertical displacement in both cases is 1.73 times the zero range. In the present example, the maximum linear vertical displacement is (1.73 x 250 x 3) = 1287 feet. 20 Computing Ballistics Data QBALL The slant fire table you've printed should look like Figure 27, making due allowance for print sizes and fonts. Should the slant fire table be too long to fit on one page, page breaks, page numbers and appropriate column headers are included in the printed output. Pages other than the last page will show the word = more = at the bottom. The last page will always include the Symbol Key shown, and the words = Last Page =. There is no need to set the left margin on your printer: the slant fire table is printed with a (small) left margin. The QBALL printing routines have been found to work properly on dot-matrix and laser printers working at a character pitch of 10 cpi. You can, of course, use a finer character pitch, if desired. ======================================== Ballistic Computations = Typical Firearm ======================================== Muzzle Velocity = 2700 FPS Ballistic Coef'nt = .300 Bullet Weight = 180 grains Sectional Density = n/a Temperature = 59 degF. Altitude at gun = 0 feet Barometric Pressure = 29.53 inch Hg Relative Humidity = 78 % =================================================== =Remarks = [ Forty characters allowed for remarks ] =================================================== Slant Fire Table, Impact 433 feet Above or Below Gun --------------------------------------------------------- For Horizontal Fire For Slant Fire Hits Range in +/- LOS Slant Range in +/- LOS High ------- ---------- ----------- ---------- ------ 0 -1.00 0 -1.00 0.00 : 13.60 0.00 : 13.60 0.01 0.01 50 2.22 50 2.31 0.08 100 4.12 100 4.47 0.34 + 136.78 4.56 + 136.78 5.23 0.66 150 4.51 150 5.31 0.81 200 3.18 200 4.68 1.50 [ 250.00 0.00 ] 250.00 2.44 2.44 - 294.14 -4.56 - 294.14 -1.05 3.51 > 300 -5.31 < 300 -1.64 3.67 --------------------------------------------------------- ---------------------------------------- | -= SYMBOL KEY =- | | Range at which zeroed: [ ----- ] | | Range for max height: + ----- + | | Range MINUS max height: - ----- - | | Crossing(s) of LOS: : ----- : | | Found/marked ranges: | ----- | | | Maximum Range: > ----- < | ---------------------------------------- : = Last Page = Figure 27. Typical Printed Slant Fire Table. 22 Computing Ballistics Data QBALL 2.11 Displaying a Trajectory Graphic. You may graphically display the trajectory data which has been computed. Press <G> to display the following graphics screen. > Trajectory Display, Typical Firearm < --+-------------------------------------------------------------- ////////////////// (Portion of screen omitted)/////////////////// | | | |N| +4 x x +4 | | | x | | | +2 x +2 | |C| | | |--0----|---------|-----------|----------|----------x------0--| | x | |H| -2 Use a pencil, draw a smooth -2 | | | curve connecting the "x's". | | | -4 -4 | |E| x | | -6 -6 | | | | |S| -8 YARDS -8 | | | 50 100 150 200 250 | --+-------------------------------------------------------------- | Vel 2551 2407 2268 2133 2003 | | Eng 2601 2315 2055 1819 1603 | ----------------------------------------------------------------- Current ========================= ------- | *** Graphics Menu *** | Max Ht: 4.56 @ 137 Yds | --------------------- | Min Ht:-5.31 @ 300 Yds | Toggle <G>rid (Now on)| C1/Wt : [ As Shown ] | <S>ave Current Data | M/TVel: 2700/1877 FPS | <R>ecall <1> | M/TEng: 2913/1408 Ft# | rint Graphic Screen| ZeroRg: 250 Yds | --------------------- | Metro : [ As Shown ] | <ESC> to Rg Tble Out | ------------------------- MV: 2700| C1: .300 |G: 180 | Metro: 59d 0' 29.53" 78% | H: 1.00|E Figure 30. Typical Trajectory Graphics Display. The upper part of the screen represents your firing range as viewed from the side: the firing point is at the left, the point of impact, at the right. Each range increment is indicated by a vertical line, numbered across the bottom. The horizontal lines, numbered at both left and right, indicate the bullet's position relative to the line of sight (LOS), which is indicated by the emphasized line numbered 0-0. The maximum ordinate is indicated by the circle on the curved trajectory. The velocity and energy re- maining at each incremental range is printed below the grid. The information block at the bottom left includes the maximum and minimum heights and the ranges at which they occur, the muzzle and terminal velocities and energies, the ballistic coefficient and bullet weight, the zero range, and the metro currently in use. 24 Computing Ballistics Data QBALL Here, the recalled trajectory data is displayed in a contrast- ing color, and the ballistic coefficient, bullet weight, and the metro are what was saved to disk. You may press <G> at any time to redraw the screen without the background grid lines. To redisplay the grid, press <G> again. As supplied, QBALL defaults to grid "on;" you may change this with the configuration routines. Should you recall a number of saved trajectory files, and the screen is becoming cluttered, press <G> to erase all but the current data. (Press <G> again to redraw the background lines.) If the rint Graphics Screen option is displayed in normal video, your printer is on, on-line, has sufficient paper, and has been properly configured, you may press to print the trajec- tory screen, in your choice of ortrait or <L>andscape orienta- tion. Please read Chapter 4 regarding printer setup! QBALL prints the trajectory curve portion of the display at the resolution determined by the printer driver you used to configure QBALL. The information blocks are printed using your printer's default typeface and pitch. The information line is omitted in both orientations. (You may wish to experiment with third-party screen capture utilities and graphics editing programs.) 2.14 Other Ballistic Procedures. Five other ballistic procedures are described in this section: determination of point-blank ranges, finding a most-probable zero for a given range and trajectory height, wind vector corrections for other than "standard" 10 MPH left-to-right crosswinds, bullet sectional densities (if not already entered using bullet lookup), and your weapon's free recoil velocity and energy. Point-blank range, most probable zero and wind vector corrections directly affect the range and graphics graphics displays. Sectional density and gun free recoil are informational in nature, only. With the Computations Menu displayed on the screen, press <O> to access the Other Procedures Menu. =================================== | *** Other Procedures Menu *** | | ----------------------------- | | oint-blank Range | | <Z>ero for Range and Height | | <W>ind Vector Corrections | | <S>ectional Density | | Weapon <F>ree Recoil | | ----------------------------- | | <ESC> to Computations Menu | ----------------------------------- Figure 34. The Other Ballistics Procedures Menu. 26 Computing Ballistics Data QBALL Press <T> to develop a range table using this zero range. The data entry box displays the calculated maximum range and the range increment which was previously used. You may change either if you wish, but for this example, simply press <enter> twice. The following range table is displayed. --------------------------------------------------------------- | Range Table, Zeroed at 278.5 Yards | |-------------------------------------------------------------| |Range R e m a i n i n g Drop Path/Sight Line 10 MPH Time | |Yards V: FPS E: Ft-Lbs Inches M.O.A. Inches Inches Flght | |----- ----------------- ------ --------------- ------ ----- | | 0 2700 2913 0.00 -- -1.00 0.00 0.000 | |: 11.92 2664 2836 0.03 0.00 0.00 0.00 0.013:| | 50 2551 2601 0.62 5.19 2.72 0.28 0.057 | | 100 2407 2315 2.56 4.88 5.11 1.11 0.117 | | 150 2268 2055 6.02 3.81 5.98 2.66 0.182 | |+151.38~~2264~~~~~~2048~~~~6.14~~3.77~~~~~~5.98~~~2.71~0.184+| | 200 2133 1819 11.19 2.45 5.15 4.93 0.250 | | 250 2003 1603 18.21 0.94 2.46 7.86 0.322 | | 278.50 1930 1489 23.14 0.00 0.00 9.89 0.366 | | 300 1877 1408 27.36 -0.75 -2.35 11.61 0.399 | |-326.73~~1812~~~~~~1312~~~33.31~-1.75~~~~~-5.98~~14.07~0.443-| --------------------------------------------------------------X Figure 37. Range Table Using Point Blank Zero. Note that this range table has too many lines to display all at once. To view the end of the table, press either <PgDn> or <end>. Also note that the appropriate maximum and minimum height data lines are here shown ~~~~~~~ ; they are indicated with "+ +" and "- -" on your screen. You may go on to save, print, or display a graphic of this range table, or develop a slant fire table based on this input data. 28 Computing Ballistics Data QBALL You may go on to save, print, or display a graphic of this range table, or develop a slant fire table based on this input data. QBALL may be unable to determine the most probable zero from apparently valid data, generally with small ranges and large heights. Try this procedure with a range of 25 yards, and a height of 40 inches. The following is displayed: ===| Warning... |======================================= | Cannot determine a valid zero range from given data. | | * Input a smaller height or a greater range. | | * You may wish to increase the muzzle velocity, | | the ballistic coefficient, or both. | -------------------------------------------------------- Figure 40. Probable Zero Warning Message. Press any key to return to the Computations Menu. You may then press <Z> to use this procedure again; overtype the new data as shown above in Figure 38. **** Wind Vector Corrections. QBALL is set up to account for 10 MPH crosswinds blowing from left to right. Real world crosswind, however, is seldom so accommodating as to blow from left to right at precisely 10 MPH. With the Other Procedures Menu displayed, press <W> to correct for a nonstandard wind speed and direction. Enter a new wind velocity of 20 MPH, and a wind direction of 235 degrees - from the left rear of the firing point. (The figures in [brackets] are the QBALL default values.) ---| Cross Wind Corrections... |----------------- | | | Wind Velocity: [10 MPH] 20 | | Wind direction: [270d] 235 | | | | Range wind = 16 feet per second | | Cross wind = 16 miles per hour | | Crosswind correction = 1.6 | | | | Use this correction in tables? ([Y] or N) | | | ------------------------------------------------- Figure 41. Entering Wind Vector Correction Data. While QBALL computes the range wind, its effect is small, and is neglected. Press <Y> or <enter> to use the correction, or <N> or <ESC>ape to use the previous wind velocity and direction. 30 Computing Ballistics Data QBALL Sectional density is shown in printed and saved table headers; QBALL has no specific routine which uses it, nor is it displayed anywhere other than as shown in Figure 43. **** Free Recoil Velocity and Energy. All firearms "kick." But HOW HARD? QBALL can find the recoil velocity and energy imparted to the weapon upon firing. At the Other Procedures Menu, press <F>. Enter a powder weight between 1 and 200 grains, and a weapon weight between 1 ounce and 30 pounds. (Enter weapon weights as <pounds>.<decimal pounds>, or as <pounds><space><ounces>.) ---| Finding Gun Free Recoil... |---------------- | | | Powder weight (grains) 38 | | Weapon weight (pounds) 8.5 | | | | Weapon recoil velocity = 11 FPS | | Weapon recoil energy = 16.4 Ft-lbs | | | | Use for comparative purposes only! | | | ----------> press any key to continue <---------- Figure 44. Determining Free Recoil Velocity and Energy. These figures are relatively meaningless without some basis for comparison. Here are three examples, all computed using QBALL. ---------------------------------------------------- | | Weapon | | Selected Weapon, Caliber, |-------------------| | and Load | Velocity | Energy | | | FPS | Ft-Lbs | |------------------------------+----------+--------| | 1. Ruger M77R (6.75 pounds) | | | | .22-250 Remington | 7.86 | 6.49 | | Muz Vel = 3680 | | | | Bul Wt = 55 | | | | Pow Wt = 36 | | | | 2. Marlin 336CS (7 pounds) | | | | .30-30 Winchester | 10.67 | 12.39 | | Muz Vel = 2390 | | | | Bul Wt = 150 | | | | Pow Wt = 35 | | | | 3. M1 Garand (9.5 pounds) | | | | .30-'06 Springfield | 10.88 | 17.47 | | Muz Vel = 2700 | | | | Bul Wt = 180 | | | | Pow Wt = 50.5 | | | ---------------------------------------------------- Table 1. Free Recoil Velocity and Energy, Selected Weapons. 32 Computing Ballistics Data QBALL **** Weapon Identifier. Press <W> to change the weapon identifier. Enter the new ident- ifier in the entry box, using the standard editing keys. When it is exactly as you want it, press <enter>. You may save the new identifier for use as the startup default; see Chapter 5. ---| Enter New/Changed Weapon ID... |------------ | _______________ | | Typical Firearm_______________| | | | ------------------------------------------------- Figure 47. Entering a Weapon Identifier. **** Bullet Identifier. If you have entered a new weapon identifier, or if you press , you may change the bullet identifier, i.e., its diameter, maker and type. If no bullet identifier is available, QBALL displays "[]" in the entry box. If a bullet identifier is shown, and you don't want to use it, enter "[]" in the entry box. Enter the new identifier in the entry box, using the standard editing keys. When it is exactly as you want it, press <enter>. ---| Enter New/Changed Bullet ID... |------------ | __________ | | []__________| | | | ------------------------------------------------- Figure 48. Entering a Bullet Identifier. **** Muzzle Velocity. Press <V>, and enter a new muzzle velocity, from 200 FPS to 4500 FPS, inclusive. **** Ballistic Coefficient. Press <C>, and enter a new ballistic coefficient (C1). C1 must be greater than 0.0000 and less than 1.0000; QBALL automatically adds the leading decimal point. If [Lookup] appears on the prompt line, you may use bullet lookup: see section 2.16. **** Bullet Weight. Press <G>, and enter a new bullet weight from 0.1 to 999 grains, inclusive. For bullet weights less than 50 grains, 1/10- grain increments are allowed, e.g., 17.6. If [Lookup] appears on the prompt line, you may use bullet lookup: see section 2.16. 34 Computing Ballistics Data QBALL 2.16. Bullet Lookup You may use the QBALL bullet lookup facility if the term [Lookup] appears on the prompt line when entering either the ballistic coefficient or the bullet weight. [Lookup] appears only if AMMO.DAT and either D.NDX or M.NDX is present on/in the current disk/directory. QBALL defaults to D.NDX - sort by diameter - if both index files are present. Press <L> to use the bullet lookup facility. A bullet listing is "windowed" over the data entry screen. > Ballistic Computations, Typical Firearm < ---| Enter Required Initial Data... |------------ | | | | ===| Bullet Lookup... |=================================== | | Mak Dia Wt C1 Type Remarks: 1 of 505 | | | --- ---- ---- ----- -------- -------------------- | | |~HDY~~.172~~~~25~~.190~~~HP~~~~~~~~1710~~~~~~~~~~~~~~~~ | | | HDY .222 40 .100 JET 2210 | | | SRA .223 40 .125 HORNET 1100 | | | SPR .223 40 .145 SPIRE 1005 | | | SRA .223 45 .153 HORNET 1110 |---- | SPR .223 45 .166 SPITZ 1011 | | HDY .223 45 .191 HORNET 2220 | | SRA .224 40 .124 HORNET 1200 | | SPR .224 40 .144 SPIRE 1017 | | SRA .224 40 .160 HP 1385 | ---------------------------------------------------------- PgUp PgDn (up) (dn) Home End [ESC] Figure 51. Bullet Lookup Window, Sorted by Diameter. Use the <PgUp>/<PgDn>, <Home>/<End>, <arrow> keys to move the highlight bar, and press <enter> to choose the highlighted bullet. You may press <S> to search for a specific diameter or maker, depending on the indexing key. If you change your mind, and decide not to use bullet lookup, simply press <ESC>ape. If both *.NDX files are present, you may resort the list by pressing <M>; the list is redisplayed, sorted by maker. Press <D> to resort by diameter. With the highlight bar positioned as shown ~~~~thus~~~~, press <enter>. QBALL reads the data for bullet #1 of 505 bullets: the Mak(er), Dia(meter), Weight, C1 (Ballistic Coefficient), and Bullet Type. The screen header and information line are changed, as shown in Figure 52, next page. 36 Computing Ballistics Data QBALL The following table contains the maximum and minimum allowable Metric system values when using QBALL configured for Metric measure. ------------------------------------------------------------ | Data Item to Allowable Unit of Default or | | Enter Min Max Measure Standard | | ------------ --------- ------- ---------- | | Muzzle Velocity 61 1371 MpS | | Ballistic Coefficient .001 .999 [dimensionless] | | Metro (Weather) | | Temperature -45.5 51.6 deg C. 15 deg C. | | Gun Altitude -399 8847 meters 0 meters | | Barometric Pressure 635 889 mm 750 mm | | Relative Humidity 0 100 % 78 % | | Bullet Weight .065 64.8 grams (1-999 grains)| | Bullet Diameter 4.32 19.05 mm | | Gun Weight .03 13.6 kg | | Powder Weight .065 12.95 grams | | Sight Height -5.08 25.4 cm 2.54 cm | | Maximum Range 1 1609 meters | | Wind Velocity 0 103.2 MpS 4.7 MpS | | Wind Direction 0 360 deg arc 270 deg | | Point-blank Deviation .25 101 cm | ------------------------------------------------------------ Table 2. Metric Data Limits. The following table contains unit system conversions from English to Metric and from Metric to English system measure. ------------------------------------------------------------ | English to Metric Metric to English | | ----------------- ----------------- | | 1 inch = 25.4mm = 2.54cm 1cm = 0.0394 inches | | 1 foot = 30.48 cm = 0.3048m 1m = 3.2808 feet | | 1 yard = 0.9144m 1m = 1.0936 yards | | 1 mile = 1609.34m = 1.60934km 1km = 0.6214 miles | | 1 MPH = 0.447039 MpS 1 MpS = 2.2369 MPH | | 1 pound = .4537kg = 453.7g 1kg = 2.204 pounds | | 1 ounce = 28.358g 1g = .0353 ounces | | 1 grain = 0.0649g 1g = 15.4 grains | | 1 FtLb = 0.1384 MetKg 1 MetKg = 7.223 FtLbs | | 1 FtLb = 1.3558 Joules 1 Joule = .7376 FtLbs | | 1 deg F.= 0.555 deg C. 1 deg C.= 1.8 deg F. | | temp F. = 32 + (1.8 x C.) temp C. = (F. - 32) / 1.8 | ------------------------------------------------------------ Table 3. Unit System Conversion Factors 38 Inferred Ballistics Data QBALL You may use nonstandard metro when inferring a ballistic coefficient, should you have developed you own velocity data from live firing. Metro conditions may be changed prior to entering velocity data. QBALL reports ballistic coefficients adjusted to standard conditions. You may enter as many as ten (10) V1/V2 pairs. QBALL displays each velocity, the average V1 and V2, and the ballistic coeff- icient computed based upon the last V1/V2 pair. (If there are three or more V1/V2 pairs, QBALL also reports the standard deviation.) If R1 is greater than zero; i.e., you're not working with a muzzle velocity, QBALL reports a calculated muzzle velocity. The following examples demonstrate the process twice: once with R1 set to "zero", and once with R1 set to 25; R2 is set to 100 in both cases. **** Ballistic Coefficient, R1 = 0. This procedure may be used if, for example, you have published trajectory and velocity/energy data provided by an ammunition manufacturer, but not the ballistic coefficient. The velocity data used here is the same as that shown in Figure 9, on page 9. When prompted for "Shorter Range," enter "0" or press <enter>; enter "100" for "Longer Range." Press "Y" or <enter> when prompted for metro. --------------------- -| Ballistic Coefficient, 2 Velocities... |-| # V1 V2 | | |+-------------------+ | Enter range data in yards: || 1 | | || 2 | | Shorter Range [0=muzzle]: 0 || 3 | | Longer Range : 100 || 4 | | || 5 | | Use Displayed Metro? ([Y] or N) || 6 | | || 7 | | || 8 | | || 9 | | ||10 | | |+-------------------+ | ||Av | | Ranges: Muzzle & 100 yards ||sV | | ||C1, Last Pair: | ----------------------------------------------------------------- Figure 56. Entering Range and Metro Data. Since R1 = 0, QBALL will ask for the muzzle velocity; enter "2700." When asked for "Velocity, longer range," enter "2407." QBALL displays the two velocities, their averages, and the ballistic coefficient based upon them. You are also prompted for another velocity pair. Since you're working from tabular data, another pair is superfluous; press <N>. 40 Inferred Ballistics Data QBALL --------------------- -| Ballistic Coefficient, 2 Velocities... |-| # V1 V2 | | |+-------------------+ | || 1 2625.0 2407.0 | | Using 3 rounds, QBALL finds: || 2 2625.0 2407.0 | | || 3 2625.0 2407.0 | | Between ranges 25 and 100 yards, || 4 | | || 5 | | Avg Higher Velocity 2625 FPS || 6 | | Avg Lower Velocity 2407 FPS || 7 | | Ballistic Coefficient .301(sC1 .000)|| 8 | | || 9 | | Calculated Muzzle Velocity = 2700 FPS ||10 | | |+-------------------+ | ||Av 2625.00 2407.00| | ||sV 0.58 0.58 | | ||C1, Last Pair: .301| -------> press any key to continue <----------------------------- Figure 58. Ballistic Coefficient, Three Rounds, R1 > 0. Press any key, or wait 60 seconds for QBALL to continue auto- matically. If all the required initial data is now available, you'll be returned to the Computations Menu, otherwise, QBALL asks for the data it needs. Granted, in this case, the ballistic coefficient doesn't exactly match what we started with, i.e., we started with 0.300, and ended up with 0.301. If, however, you develop a range table using the input data from chapter 2 with C1 = 0.301, you'll find that the differences are well within the QBALL round off errors. Try it and see. Under other conditions, you may find that the calculated muzzle velocity doesn't quite match, either. The difference will be small, and you may use all calculated muzzle velocity and ballis- tic coefficient data and expect excellent practical accuracy. ------------------------------------------------------------------ | Only one chronograph? | | --------------------- | | If you have only one chronograph, you could fire a string of | | say, five rounds at one range, then five more at a different | | range, thus getting two different sets of velocity data. One | | major disadvantage is that metro conditions may change between | | the two strings. You'd also be playing pretty "fast and loose" | | with the statistics involved. (The reliability of data so ob- | | tained might be a bit shaky, but better questionable data than | | no data at all!) | ------------------------------------------------------------------ 42 Inferred Ballistics Data QBALL Zero your weapon at a range between 50 and 100 yards; the greater the zero range, the more accurate the results. Without changing your weapon's sight settings, fire a string of three to five rounds at a range at least twice the zero range. Find the group center, and measure its vertical displacement from the point of aim. This is D, the vertical difference. In most cases, the group center will be below the point of aim, but with high velocities, it may be above the point of aim. For this example, QBALL was used to generate a typical bullet drop. (The input data from chapter 2 was used.) The zero range was set to 50 yards; the maximum range, to 100 yards. The vertical distance D at 100 yards was found to be 0.33 inches below the line of sight. At the Infer MV using menu, press <D>, and enter (or confirm) the data as prompted. > Ballistic Computations, Typical Firearm < ---| Muzzle Velocity, Bullet Drop Method... |---- | | | Ballistic coefficient .300 | | Range for zero drop: 50 | | Range to point of impact: 100 | | Impact Height Difference .33 | | (Impact is below Line of Sight) | | Metro As displayed | | | | Calculated Muzzle Velocity = 2695 FPS | | | ----------> press any key to continue <---------- MV: |C1: .300|G: |Metro: 59d 0' 29.53" 78%|H: 1.00|E Figure 61. Muzzle Velocity from Bullet Drop Display. In this case, the calculated muzzle velocity, 2695 FPS, does not match what we started with, 2700 FPS. How much difference does 5 FPS make? Given a zero range of, say, 250 yards, and a maximum range of 300 yards, the differences are inconsequential: 0.06 inch trajectory variation, and 0.001 seconds difference in time of flight at 300 yards. There might be - almost certainly would be - that much variation between two successive rounds in any given string. It bears repeating that this method is extremely sensitive to errors in vertical distance measurement. One or two hundredths of an inch can make a big difference; a thousandth or two gives some variation. In the example just given, if the vertical distance is taken as 0.325 inches, rather than 0.33, the resulting calculated muzzle velocity is 2699 FPS. 44 Inferred Ballistics Data QBALL **** Muzzle Velocity from One Downrange Velocity. A chronograph may be used to measure a bullet's downrange velocity, but two things must be kept in mind. First, no matter how close to the muzzle the chronograph is placed, the measured velocity is inevitably less than the muzzle velocity. Second, there is a minimum safe distance at which the chronograph should be placed. QBALL provides a means to determine the muzzle velocity from a velocity measured at a relatively short range. This process is variously known as "back-computing muzzle velocity" and "correct- ing for instrument(al) error/variation." Select One Downrange <V>elocity from the Infer MV using menu. QBALL will ask for a ballistic coefficient, the range, the chronographed short-range velocity, and will prompt for metro. QBALL can use any range from 1 to 100 yards/meters. For safety's sake, however, a minimum range of 3 yards/meters is suggested. This example assumes that the chronograph is placed 5 yards (15 feet) in front of the muzzle. Using the initial data from chapter 2, the remaining velocity at 5 yards is found to be 2685 FPS. Figure 63 illustrates the data entry and result. > Ballistic Computations, Typical Firearm < ---| Muzzle Velocity, 1 Downrange Velocity... |-- | | | Ballistic coefficient .300 | | Range to chronograph: (Yards) 5 | | Downrange velocity: (FPS 2685 | | Metro As displayed | | | | Calculated Muzzle Velocity = 2700 FPS | | | ----------> press any key to continue <---------- MV: |C1: .300|G: |Metro: 59d 0' 29.53" 78%|H: 1.00|E Figure 63. Muzzle Velocity from One Downrange Velocity. Press any key, or wait 60 seconds for QBALL to continue auto- matically. If all the required initial data is now available, you'll be returned to the Computations Menu, otherwise, QBALL asks for the data it needs. 46 Printed Output and Printer Configuration QBALL 4.4 Configuring QBALL for Trajectory Graphics, One Parallel Port. First, ensure that all the following: QBALL.EXE PRCONFIG.EXE and PRINTERS.DAT are on/in the same disk/directory. Note that if you're using 5 1/4 inch disks, they must be high- density floppies; the required files will not fit on a single 360k disk! 3 1/2 inch floppies of either density will work. Log onto/into the disk/directory where the files reside, and type: PRCONFIG (+ <enter>) (You may also invoke PRCONFIG from within QBALL's DOS shell.) Some start-up messages are displayed, followed by this screen: > QBALL Graphics Printer Selection < ===| Printer Makers... |=========== | C.Itoh | | Dataproducts | | Datasouth | | DEC | | Desktop | | Decision Data | | Diablo | | Diconix | | Dynax-Fortis | |~~Epson~~~~~~~~~~~~~~~~~~~~~~~~~~| | Everex | | Facit | | Fortis | | Fujitsu | | GCC | | General Parametrics | ----------------------------------- PgUp PgDn <up><dn> Home End [ESC] Found: 707 printers by 91 makers. Figure 64. Choosing a Printer Make. Use the <PgUp>/<PgDn>, arrow, or the <Home>/<End> keys to position the highlight bar over the name of your printer, and press <enter> to select it. You may also exit from this utility without choosing anything by pressing <ESC>ape. In this example, Epson printers are to be used. Press <enter>. 48 Printed Output and Printer Configuration QBALL 4.5 Configuring QBALL for Trajectory Graphics, Multiple Ports. If your computer is equipped with up to three parallel ports, you may assign a specific graphics printer driver to each port. QBALL detects which ports are available "beyond" LPT1, i.e., LPT2 and/or LPT3. The remainder of this section assumes that both LPT2 and LPT3 are available on your equipment. Up to the point that you choose a printer driver, PRCONFIG works just as it does for single parallel ports. With multiple ports available, however, when you choose a printer model, the following is displayed: ============================================================= | QBALL shows "P_HOLDER" assigned to LPT1: | | "P_HOLDER" assigned to LPT2: | | "P_HOLDER" assigned to LPT3: | +-----------------------------------------------------------+ | | | You have selected: EPSON2VH.PRD | | | | Assign EPSON2VH.PRD to LPT<1>: LPT<2>: LPT<3>: | | | ------------------------------------------------------------- Figure 67. Assigning a Driver to a Parallel Port Press <1>, <2>, or <3> to assign the chosen printer driver to the corresponding parallel port. You may also press <ESC>ape to exit PRCONFIG, and make no changes to the QBALL internal driver assignments. Assume in this case, you want the chosen driver assigned to LPT1; press <1>. The following is displayed: __ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ __ | | | Assigning EPSON2VH.PRD to LPT1: | | | | Make another assignment? ([Y] or N) | | | __|_ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _|__ Figure 68. Assignment Status and "Another?" Prompt. Press <Y> or <enter> to make another assignment, or <N> to exit PRCONFIG. If <Y>/<enter> is pressed, PRCONFIG returns to the Printer Maker Selection screen. Choose an appropriate make and model of printer, and assign the printer driver to the desired parallel port. 50 Printed Output and Printer Configuration QBALL Don't forget to write the printer driver's name to the QBALL startup data; press <Y> or <enter> when PRCONFIG so prompts you. Note that all these alternatives specify "lowest available resolution." If you want a higher-resolution printout, then simply choose the next higher resolution and try it. **** Something Prints. This is probably the most maddening demon to track down and exorcise. Here are some symptoms and suggestions. The printout begins fine, then breaks down and prints garbage. This is often caused by a hardware problem which prevents the printer from reporting a buffer full condition. Replace the printer cable with a new one less than eight feet long, bypassing any external print buffers and printer switches. The printout has extra line feeds. This usually occurs on older printers or on IBM graphics printers. The printer has probably missed or misinterpreted the line spacing command. Make sure the printer is on-line before attempting to print. If you're using an IBM printer, choose an IBM driver. The printout is jagged. The printer itself cannot print at the called-for resolution. Choose a lower-resolution driver. A black-and-white printout omits colors (usually yellow), or some areas of the printout have a shaded background. Configure the QBALL screen colors to black-and-white. Either start QBALL with the command QBALL /b or use the screen color routines in the built-in utilities as described in Chapter 5. The printout is on multiple pages. This may caused by the same problem that causes the printer to start out fine, then begin printing garbage. Replace the printer cable with a new one less than eight feet long, bypassing any external print buffers and printer switches. A laser printer may not have sufficient built-in memory to print at the called-for resolution. Choose a lower-resolution driver, or add memory to your printer. ----------------------------------------------------------------- | The material on pages 49 and 50 is adapted from documentation | | provided by Genus Microprogramming, Inc., 1155 Dairy Ashford, | | Suite 200, Houston, TX 77079-3012. Acknowledgment is made for | | this and other Genus Microprogramming material. | ----------------------------------------------------------------- 52 Configuring Display and Defaults, Using Utilities QBALL Press to choose the measurement system and optional units. ===================================== | *** Unit System & Options *** | | ------------------------------- | | Unit System : <E>nglish X | | <M>etric | | Wind Velocity : Mle/Hr X | | K<N>ots | | Bullet Weight : <G>rams X | | G<R>ains | | Energy Unit : Met-<K>g X | | <J>oules | | ------------------------------- | | <ESC> to Switches and Printer | ------------------------------------- Figure 71. Selecting English Unit System Options. The as-supplied unit system and units are indicated by "X" in Figure 71. The unit system and wind velocity choices are shown in normal video; weight and energy are subdued. Press or <N> to choose wind velocity in statute miles-per-hour or knots. Now press <M> to activate metric units, and bullet weight and energy measure choices, which are now displayed in normal video. ===================================== | *** Unit System & Options *** | | ------------------------------- | | Unit System : <E>nglish | | <M>etric X | | Wind Velocity : Mle/Hr X | | K<N>ots | | Bullet Weight : <G>rams X | | G<R>ains | | Energy Unit : Met-<K>g X | | <J>oules | | ------------------------------- | | <ESC> to Switches and Printer | ------------------------------------- Figure 72. Selecting Metric Unit System Options. Note "X" next to <M>etric, Figure 72. Press <G> or <R> to select the bullet weight unit; <K> or <J>, the energy units. Press <ESC>ape to return to the Switches and Printer menu. QBALL writes the choices indicated by "X" to its startup data. In this case, QBALL will start up using metric units, grams, and Met- Kg. Using the alt-U hotkey at range table display will display crosswinds in statute miles-per-hour. 54 Configuring Display and Defaults, Using Utilities QBALL 5.3 Configuring Screen Colors. At the Utilities Menu, press <C> to display this special color choice screen. > Configuring QBALL Screen Display < =============================== | Press [K]ey to increment: | | | | [F] - Foreground | | [H] - Highlight color | | [I] - Info Line color | | [B] - Background color | | [L] - Help Background | | | | press <ESC> to end... | ------------------------------- [ Now set - FG = 15 HiLite = 10 Info = 7 BG = 1 Help = 6 ] [ [D]efault - FG = 15 HiLite = 10 Info = 7 BG = 1 Help = 6 ] [ Blk/[W]ht - FG = 7 HiLite = 15 Info = 7 BG = 0 Help = 0 ] MV: 2700| C1: .300| G: 180| Metro: 59d 0' 29.53" 78%| H: 1.00 |E Figure 75. Configuring Display Colors Screen. Press the appropriate key to step through the available colors for the [B]ackground; main body text, [F]oreground; [H]ighlighted text; the title and [I]nfo lines; and the he[L]p window background color. The chosen colors are immediately displayed so that you can see what they look like. When you've found an appealing combina- tion, press <ESC>cape to use that combination henceforth. You may also press [W] to use a black-and white display. You may find this advisable if you want to print trajectory graphics. If you get in a muddle, and want to start over, press [D] to return to the as-supplied default color settings. 5.4 Using The Values You've Set. Having set the display colors and toggles as you like them, and with the Utilities Menu displayed, you may either <W>rite QBALL initialization data, or you may <ESC>ape to the Main Menu. If you'd like to use the values for this session only, perhaps to see how they work out, then press <ESC>ape. If you later decide to save your "temporary" setup, choose from the Main Menu and <W> from the Utilities Menu. QBALL doesn't care if there's a delay between choosing and saving configuration data, and will save what's in effect at the time the <W>rite option is chosen. 56 Configuring Display and Defaults, Using Utilities QBALL 5.6 Reading a Saved Range or Slant Fire Table. If at least one saved range table or slant fire table, and RRTABLE.EXE is present in the current directory, you may view or print that table using the RRTABLE utility. If there are no saved tables, or RRTABLE is absent, the <R> option will not appear. RRTABLE may also be invoked directly from the command line without starting QBALL. Assuming that you saved the range table, the slant fire table, or both which were developed in chapter 2, the <R> option appears. The remainder of this section assumes that both were saved, and that you are running RRTABLE from within QBALL. With the Utilities Menu displayed, press <R>. The following is displayed: ================================= | *** Utilities Menu *** | | -------------------------- | | Toggle <S>witches | |===============================| || || || Loading Range Table Reader || || || |-------------------------------| | <ESC> to M A I N M E N U | --------------------------------- Figure 78. Loading Range Table Reader Utility. QBALL starts RRTABLE.EXE, which finds all the files in the current directory with an "Rnn" extension; RRTABLE displays the following: > Range Table Reader - accompanies QBALL v3.00 < . . . ===| 2 QBALL-generated Range Tables found... |=================== | FILENAME.R01 FILENAME.R02 | ----------------------------------------------------------------- Enter <01> thru <02> to read table ("0" exits): . . . Figure 79. Saved Tables Found by RRTABLE. You may exit without doing anything further by pressing <0> (zero) (+ <enter>); you are returned to the QBALL Utilities Menu. 56.2 Configuring Display and Defaults, Using Utilities QBALL This page is for notes. 58 Recalling Saved Trajectory Data QBALL If, however, you want to use the selected file's data, you may press <G> to display a trajectory graphic, or <D> to use the file's data as the QBALL input data. Choosing <D> will take you directly to the Computations Menu; <G> displays this graphic: > Trajectory Display, Typical Firearm < --+-------------------------------------------------------------- ////////////////// (Portion of screen omitted)/////////////////// | | | |N| +4 x x +4 | | | x | | | +2 x +2 | |C| | | |--0----|---------|-----------|----------|----------x------0--| | x | |H| -2 Use a pencil, draw a smooth -2 | | | curve connecting the "x's". | | | -4 -4 | |E| x | | -6 -6 | | | | |S| -8 YARDS -8 | | | 50 100 150 200 250 | --+-------------------------------------------------------------- | Vel 2551 2407 2268 2133 2003 | | Eng 2601 2315 2055 1819 1603 | ----------------------------------------------------------------- Current ========================= ------- | *** Graphics Menu *** | Max Ht: 4.56 @ 137 Yds | --------------------- | Min Ht:-5.31 @ 300 Yds | Toggle <G>rid (Now on)| C1/Wt : [ As Shown ] | <S>ave Current Data | M/TVel: 2700/1877 FPS | <R>ecall <1> thru <2> | M/TEng: 2913/1408 Ft# | rint Graphic Screen| ZeroRg: 250 Yds | --------------------- | Metro : [ As Shown ] | <ESC> to Computations | ------------------------- MV: 2700| C1: .300 |G: 180 | Metro: 59d 0' 29.53" 78% | H: 1.00|E Figure 84. Graphics Display, Saved Trajectory Data. This is the same graphic you developed in Chapter 2. At this point, you may <R>ecall and display the data from SAMPLE.TJ1, or rint this screen (if QBALL has been properly configured). Note that the data read from FILENAME.TJ2 has been set as the current input data, which QBALL will use until you change it. You may do this using the New/Changed Data Input routines, you may <ESC>ape back to the Main Menu, <R>ecall another trajectory, and reset all the input data at once, or you may use "clean sweep" at the Main Menu (press <C> + <N>). . 60 Appendix A - Glossary QBALL bullet weight - Weight of the actual projectile, usually stated in grains (English measure), or in grams (Metric measure). See also: grain, gram. caliber - For small arms, the diameter of the bore measured across the lands. In practice, the diameter of the bullet. In artil- lery and naval gun usage, a measure of length equal to bore diameter; thus, a "fifty caliber" barrel would be 50 bore dia- meters long. cartridge - Fixed ammunition, including case, powder, primer, and bullet, for small arms. See also: round, shell. case - The usually brass, sometimes aluminum or soft steel compo- nent of a cartridge which contains the powder, primer, and bullet prior to firing. See also: brass. centimeter - In Metric measure, 1/100 of a meter. Approximately 0.0394 inches. chamber - The breech, or rear most portion of the barrel, which contains and supports the cartridge prior to, during, and immediately following firing. coefficient of form - A number relating the ballistic efficiency of a given bullet shape to the shape of the projectile used to calculate the ballistic table. C1 - Formula symbol for ballistic coefficient. cross wind angle - The angle between the wind direction and the line of departure. Typically tabulated as ninety degrees, or "pure" crosswind with no range vector. deflection - See: wind deflection. degree - 1: Angular measure equal to 1/360 of a full circle. 2: Unit of measure in any of several systems of temperature measurement. downrange - Refers to the position of objects in space relative to the direction of fire; point of aim and point of impact, for example, are by definition downrange. drift - Properly, the distance a bullet will travel laterally due to its spin. This effect is usually quite small, amounting to about 7 inches at 1000 yards for military M2 Ball (.30-'06) ammunition. Often confused with wind deflection. See also: wind deflection. drop - The distance a bullet will fall due to the influence of gravity. Drop is measured from the line of departure, not the line of sight. 62 Appendix A - Glossary QBALL horizontal fire - That type of fire occurring if the weapon's bar- rel is not elevated significantly above or below the horizon- tal. Generally taken as 1 degree of arc or less. 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 ballistics calculations. iron sights - In popular usage, metallic sights. kilogram - In Metric measure, the mass of 1000 cubic centimeters of water at a temperature of 4 degrees C. Approximately 2.204 pounds, 35.264 ounces, or 15,400 grains. lands - Those portions of a rifled bore not cut away by rifling grooves. See also: grooves, rifling. lead - (leed) How far ahead of a moving target a shooter must aim to be assured of hitting it. lead - (led) Soft, dense, silvery-gray metal with relatively low melting point which forms the basis for many bullets. line of departure (also LOD) - An imaginary line formed by ex- tending the axis of a firearm's bore in a downrange direction. line of sight (also LOS) - An imaginary line from the shooter's eye through the center of the sights to the point of aim. The bullet typically crosses this line only twice; once near the muzzle, and once at the targeted distance. mass - Properly, the weight of an object divided by the acceler- ation due to gravity. Commonly taken to mean "weight." maximum height - The greatest vertical distance the bullet rises above the line of sight. Sometimes confused with midrange traj- ectory since it typically occurs about halfway between muzzle and target. Maximum height is usually somewhat higher and occurs somewhat further downrange than the midrange trajectory. See also: midrange trajectory. maximum range - The horizontal distance measured from the fire- arm's muzzle to the point of impact. metallic sights - Sights containing no optical elements. met - 1. An abbreviation for "meter." 2. An abbreviation for "Met- eorological Conditions." See also: meter, metro, standard met. meter (also metre) - In Metric measure, the fundamental unit of linear measurement. Approximately equal to 39.37 inches, 3.28083 feet, or 1.09361 yards. 64 Appendix A - Glossary QBALL point of aim - That downrange point with which a firearm's sights are aligned. point of impact - That point which a bullet actually strikes. In most cases, considered in relation to point of aim. powder - The propellant material used in firearms. Usually not in powder form, but in the form of small rods, spheres, or flakes. primer - Impact-sensitive component of a cartridge which ignites the powder charge upon being struck by the firing pin or the striker of a firearm. projectile - A bullet, shell, golf ball, rock, or other object shot, hit, thrown, or hurled in space; a projectile receives a single impetus, and continues in motion by its own inertia. A bullet is not properly a projectile until it is in motion. relative air density - The density of air at the measured metro divided by the density of air at standard metro, expressed as a dimensionless decimal fraction; e.g., 1.000. relative sonic velocity - The velocity of sound at the measured metro divided by the velocity of sound at standard metro, ex- pressed as a dimensionless decimal fraction; e.g., 1.000. remaining energy - A projectile's energy in FtLbs or MetKg at a given range. See also: FtLbs, MetKg. remaining velocity - A projectile's velocity in FPS or MpS at a given range. See also: FPS, MpS. revolver - Handgun which sequentially aligns each of several rounds with a single barrel to achieve multi-shot capability. rifle - Firearm equipped with a rifled barrel, designed to be fired by a single individual, using both hands, from the shoulder. rifling - The spirally-cut or swaged grooves in a firearm's bore, taken collectively with the resulting lands, which impart a stabilizing spin to the bullet. See also: grooves, lands. round - 1. One complete cartridge. 2. The sequential number of a shot in a number of shots; e.g., "Round #3." scope - Optical or telescopic, as opposed to metallic, sights. second - 1: 1/60 of an angular minute. 2: 1/60 of a minute of time. shell - 1. In artillery and naval usage, a projectile containing a high explosive and obtaining its effect from the detonation of that explosive. 2. One complete cartridge for a shotgun, or commonly, one complete cartridge of any kind. 66 Appendix A - Glossary QBALL string - A number of rounds fired at a common point of aim, often for the purposes of sighting in or zeroing a firearm. targeted range - That distance furthest from the muzzle where the path of the bullet crosses the line of sight. (The "sighting in" distance, or "zero range.") terminal energy - The remaining energy at the point of impact. See also: remaining energy, point of impact. terminal velocity - The remaining velocity at the point of impact. See also: remaining velocity, point of impact. time of flight - The time necessary for a bullet to travel from the muzzle of a firearm to its point of impact or to any inter- mediate range. total drop - The bullet's vertical distance below the line of departure taken at the maximum range. trajectory - The path of a moving projectile. Often expressed as the number of linear units above or below the line of sight. trajectory, effects on - Generally, trajectory is affected by: 1. muzzle velocity; 2. ballistic coefficient; 3. air density, which is generally determined by air temperature and pressure, relative humidity, and gun altitude; 4. elevation of the line of sight. In slant fire, there is a small retardation or ac- celeration force due to the gravity vector, but this is usually ignored. Bullet weight generally has no effect upon trajectory, except in those cases involving extreme elevation angles of the line of sight. windage - 1. Lateral sight adjustment. 2. The sight adjustment re- quired to compensate for crosswind effects at a given range. wind deflection - The size of a projectile's horizontal lateral motion attributable to the action of crosswind wind vector. Often mistakenly called drift. See also: drift, windage. yaw - Normally, a situation in which a bullet rotates on its axis at a small angle to the line of flight. zero - 1. The sight setting producing coincidence of point of im- pact and point of aim at a given range. 2. The process of determining that sight setting. See also: sighting in. zero range - That range furthest from the muzzle at which the point of aim and point of impact coincide. 68 Appendix B - Miscellaneous Information QBALL Using the zero range of 50 yards, a vertical difference of 0.2" below line of sight at 100 yards, and standard metro, QBALL infers the muzzle velocity to be 2411 FPS. QBALL reports this trajectory data using the inferred muzzle velocity: ------------------------------------------------------- | Calculated using QBALL. 180 gr bullet, C1=.30 | | Range in Yards | | --------------------------------------- | | Muz 50 100 150 200 250 | | --------------------------------------- | | Velocity 2411 2272 2137 2006 1880 1761 | | Energy 2323 2062 1825 1609 1413 1239 | | Trajectory -1.50 0.00 -0.20 -2.27 -6.47 -13.23 | ------------------------------------------------------- Table B.4. Trajectory Data, Inferred Muzzle Velocity. The maximum differences are: ------------------------------------------------------- | QBALL vs Speer. Speer data taken as standard. | | Range in Yards | | --------------------------------------- | | Muz 50 100 150 200 250 | | --------------------------------------- | | Velocity 0.5% 0.6% 0.7% 0.8% 0.9% 1.1% | | Energy 0.9% 1.1% 1.4% 1.7% 1.8% 1.1% | | Trajectory 0" 0" 0" .03" .23" .27" | ------------------------------------------------------- Table B.5. Inferred vs Known Muzzle Velocity Results. Error Analysis -- Velocity and Energy. Results from several QBALL runs were compared with comparable data from two sets of published tables: the Speer Reloading Manual #11, and the Hornady Handbook of Cartridge Reloading, 3d Edition. The following table summarizes as-comparable-as-possible velo- city data from all three sources. The data shows QBALL to be in general agreement with the two published sources. -------------------------------------------------------------- | Remaining Velocity, Conditions as Shown | | ======================================= | | [ Range = 200 yards, Standard Met ] | +------------------------------------------------------------+ | MuzVel = 2100 MuzVel = 2500 MuzVel = 3300 | | C1 = .12 C1 = .26 C1 = .50 | | --------------- --------------- --------------- | | QBALL 1112 1879 2899 | | SPEER 1102 1872 2895 | | HORNADY 1126 1875 2892 | -------------------------------------------------------------- Table B.6. Remaining Velocities with Given Inputs. Note that the Hornady ballistic coefficients were actually .122, .259, and .496, thus, the "high-on-low" value spread. 70 Appendix B - Miscellaneous Information QBALL Error Analysis -- Inferred Muzzle Velocity. Table B.8 summarizes the muzzle velocities obtained using a range of values for the bullet drop. Table B.9 summarizes the expected variation in "final" data. ------------------------------------------------- | -LofS Velocity -LofS Velocity | | ----- --------- ------ --------- | | 0.25 2781 --> 0.320 2705 | | 0.26 2769 | 0.321 2703 | | 0.27 2757 | 0.322 2702 | | 0.28 2745 | 0.323 2701 | | 0.29 2735 | 0.324 2700 | | 0.30 2724 | 0.325 2699 | | 0.31 2714 | 0.326 2699 | | 0.32 2704 ---- 0.327 2698 | | 0.33 2695 ---- 0.328 2697 | | 0.34 2686 | 0.329 2696 | | 0.35 2677 --> 0.330 2695 | ------------------------------------------------- Table B.8. Inferred Muzzle Velocity, Various Bullet Drops. ------------------------------------------------------------ | USING THE "NOMINAL" MUZZLE VELOCITY | |Range R e m a i n i n g True Path/Sight Line Defl'n Time | |Yards Velocity Energy Drop MOA Inches 10 MPH Flght| |----- ----------------- ---- --------------- ------ -----| | 0 2700 2913 0.00 -- -1.00 0.00 0.000| | 25 2625 2754 0.15 1.42 0.37 0.08 0.028| | 50 2551 2601 0.62 2.73 1.43 0.28 0.057| | 75 2479 2455 1.42 2.74 2.15 0.63 0.087| | 100 2407 2315 2.56 2.42 2.53 1.11 0.117| | 125 2337 2182 4.09 1.93 2.53 1.79 0.149| | 150 2268 2055 6.02 1.35 2.12 2.66 0.182| | 175 2200 1934 8.38 0.70 1.28 3.71 0.216| | 200 2133 1819 11.19 0.00 0.00 4.93 0.250| +----------------------------------------------------------+ | USING MUZZLE VELOCITY INFERRED FROM BULLET DROP | |Range R e m a i n i n g True Path/Sight Line Defl'n Time | |Yards Velocity Energy Drop MOA Inches 10 MPH Flght| |----- ----------------- ---- --------------- ------ -----| | 0 2695 2903 0.00 -- -1.00 0.00 0.000| | 25 2620 2743 0.15 1.44 0.38 0.08 0.028| | 50 2546 2591 0.62 2.75 1.44 0.28 0.057| | 75 2474 2446 1.42 2.76 2.16 0.63 0.087| | 100 2402 2306 2.57 2.43 2.55 1.11 0.118| | 125 2332 2174 4.10 1.94 2.54 1.79 0.149| | 150 2263 2047 6.05 1.36 2.13 2.67 0.182| | 175 2195 1926 8.42 0.70 1.29 3.72 0.216| | 200 2129 1811 11.23 0.00 0.00 4.94 0.251| ------------------------------------------------------------ Table B.9. Comparing Inferred vs Nominal Muzzle Velocity. 72 Appendix B - Miscellaneous Information QBALL ---------------------------------------------------------- | Program: BALTEC. | | Input Data: | | Ballistic Coefficient (C1)....... .295 | | Bullet Weight.................... 130 grains | | Zero Range....................... 200 yards | | Maximum Range.................... 600 yards | | Range Increment.................. 50 yards | | Sight Height..................... 0.9 inches | | Crosswind........................ 10 MPH | | Metro............................ Standard | +--------------------------------------------------------+ | QBALL vs BALTEC Results | | Remaining Velocity............... 0 FPS | | Remaining Energy................. 0 FtLb | | Total Drop....................... 0.04 inches | | Path/Sight Line.................. 0.04 MOA/0.03 in | | Time of Flight................... 0 seconds | ---------------------------------------------------------- Table B.12. QBALL and BALTEC. Available in BALTEC, unavailable in QBALL: Bullet Momentum. ---------------------------------------------------------- | Program: Barnes Ballistics. (Barnes Bullets, Inc.) | | Input Data: | | Ballistic Coefficient (C1)....... .295 | | Bullet Weight.................... 130 grains | | Zero Range....................... 200 yards | | Maximum Range.................... 600 yards | | Range Increment.................. 100 yards | | Sight Height..................... 0.9 inches | | Crosswind........................ - no wind - | | Metro............................ Standard | +--------------------------------------------------------+ | QBALL vs Barnes Ballistics | | Remaining Velocity............... 1 FPS | | Remaining Energy................. 1 FtLb | | Total Drop....................... - - - - - | | Path/Sight Line.................. 0.058 inches | | Time of Flight................... 0.0025 seconds | ---------------------------------------------------------- Table B.13. QBALL and Barnes Ballistics. Available in BARNES BALLISTICS, unavailable in QBALL. Tabular comparison. As can readily be seen from the preceding tables, QBALL is in substantial (not to say "bang on"--pun intended) agreement with several other computer ballistics programs. Other sources with which QBALL is in substantial agreement include the Winchester Product Information and Ballistics Guide (1989), and the Remington Firearms and Ammunition Catalog (1990). 74 Appendix C - Selected Bibliography QBALL Warner, Ken (ed.). Gun Digest, 1990. 44th ed. Northbrook: DBI Books, 1989. --. Gun Digest, 1991. 45th ed. Northbrook: DBI Books, 1990. --. Gun Digest, 1992. 46th ed. Northbrook: DBI Books, 1991. --. Gun Digest, 1993. 47th ed. Northbrook: DBI Books, 1992. --. Gun Digest, 1994. 48th ed. Northbrook: DBI Books, 1993. --. Gun Digest, 1995. 49th ed. Northbrook: DBI Books, 1994. Winchester Ammunition Product Guide. East Alton: Winchester/Olin Corp., 1993. Winchester Product Information and Ballistics Guide. East Alton: Winchester/Olin Corp., 1989. Winchester Reloading Components Catalog. East Alton: Winchester Group, Olin Corp., 1992. 76 Appendix D - Low Velocity Applications QBALL Using this input data, QBALL computes the following range table, shown here in part, and in printed format. QBALL Range Table, Zeroed at 30 Yards ------------------------------------------------------------ Range R e m a i n i n g Drop Path/Sight Line 10 MPH Time Yards V: FPS E: Ft-Lbs Inches M.O.A. Inches Inches Flght ----- ----------------- ------ --------------- ------ ----- 0 579 14 0.00 -- 0.00 0.00 0.000 20 450 8.3 2.47 7.59 1.59 2.50 0.118 [ 30.00 394.7 6.4 6.08 0.00 0.00 5.88 0.189 ] 40 345.4 4.9 11.98 -9.24 -3.87 11.13 0.270 60 260.9 2.8 32.72 -32.72 -20.55 27.11 0.465 80 188.5 1.5 65.93 -59.34 -49.70 47.84 0.686 100 124.2 0.6 110.68 -86.34 -90.40 71.70 0.926 > 108.00 100.2 0.4 131.39 -96.83 -109.49 81.91 1.025 < ------------------------------------------------------------ Table D.2. QBALL Range Table for a Typical Air Rifle. Using the Ingalls Ballistics Tables and the procedures found in Hatcher's Notebook, the following set of data is computed. (Drop is corrected to allow for air resistance.) INGALLS Range Table, Zeroed at 30 Yards -------------------------------------------------------------- Range R e m a i n i n g Drop Path/Sight Line 10 MPH Time Yards V: FPS E: Ft-Lbs Inches M.O.A. Inches Inches Flght ----- ----------------- ------ --------------- ------ ----- 0 579 14 0.00 +-----------------------+ 0.000 20 437 7.8 2.52 |Not computed. Path is| 0.120 [ 30.00 380.1 5.9 6.25 |dependent on drop; wind| 0.193 ] 40 336.5 4.7 11.46 |deflection, on time of | 0.266 60 249.5 2.6 35.48 |flight. For comparison | 0.488 80 188.5 1.5 80.47 |purposes, this data is | 0.765 100 142.5 0.8 ~175 |superfluous. | 1.131 > 108.00 127.1 0.7 ~232 +-----------------------+ 1.313 < -------------------------------------------------------------- Table D.3. INGALLS Range Table for a Typical Air Rifle. As can be seen, there isn't very good agreement between the two data sets. Consider, however, that the comparison is being made between two sets of very questionable data, i.e., neither the Ing- alls Table method nor QBALL are particularly reliable at extremely low velocities. With all of the foregoing in mind, you may use QBALL for low- velocity applications, but your results will be, at best, suspect. For this reason, it is recommended that experimental shooting be conducted to confirm - or deny - the validity of low-velocity data. . 78 Index QBALL [D] continued gun weight in. . . . . . 30 powder (propellant) wt in 30 DEDICATION. . . . . . . . . . i valid data limits. . 30, 36 Defaults changing . . . . . . . 51ff G filename, range table. . 15 Glossary. . . . . . . . . . 59 filename, slant fire tbl 21 Graphics filename, traj graphic . 23 auto-detect. . . . . . . 4 metro. . . . . . . . . 4, 36 displaying . . . . . . 22ff sight height . . . . . 4, 36 printing . . . . . . . . 24 unit system. . . . . . . . 4 recalling. . . . . . . . 57 DISCLAIMER. . . . . . . . . . i saving . . . . . . . . . 23 Distribution. . . . . . . . . i Group center, finding . . . 43 DOS Shell Gun weight Already Loaded! message. 55 in free recoil/velocity. 30 exiting. . . . . . . . . 55 valid data limits. . .30, 36 invoking . . . . . . . . 55 PRCONFIG in. . . . . . . 46 H prompt in. . . . . . . . 55 Hardware chronograph(s) . .37, 40, 44 E graphics auto-detect . . . 4 Editing parallel ports . . . . 46-48 Data entries . . . . 3, 31ff required/suggested . . . . 4 General. . . . . . . . . . 3 Header line see Screen header Text entries . . . . 3, 31ff Help see also Remarks accessing cntxt-sensitive. 2 Error analysis. . . . . . .68ff from author. . . . . . . ix Exiting Hotkeys DOS Shell. . . . . . . . 55 alt-[C]alculator . . . . 11 QBALL. . . . . . . . . . . 5 alt-[U]nit system swap . 10 F I Files Inferred ballistic coefficient copying. . . . . . . . . . 4 Using 1 downrg velocity 38 distribution . . . . . . . 4 Using 2 downrg velocities 39 naming . . . . . 15, 21, 23 Inferred data, examples . . .67 PRCONFIG.EXE . . . . . . 46 Infer MV using menu . . . . .41 PRINTERS.DAT . . . . . . 46 Inferred muzzle velocity QBALL.EXE. . . . . . . . . 4 Bullet drop method . . . .41 QBSHELIT.BAT . . . . . . 55 One velocity method. . . .44 required . . . . . . . . . 4 Information (Info) line . . . 4 RRTABLE.EXE. . . . . . . 56 INSTALL . . . . . . . . . . . 1 trajectory graphic . . . 23 Installation. . . . . . . . . 1 Filenames see also Uninstall entering . . . . . . 15, 21 INTRODUCTION. . . . . . . . .ix graphics (*.TJ?) . . . . 23 in range tables. . . . . 15 L in slant fire tables . . 21 LIMITED LICENSE . . . . . . . i special note, *.R?? files 21 Load From a Disk . . . . . .ix FIX.BAT . . . . . . . . . . 55 [L]ookup see Bullet [L]ookup Fraction table. . . . . . . 43 Low-velocity applications . .75 Free recoil vel/egy examples 30 LPT1 (2,3) see Parallel ports 80 Index QBALL R display . . . . . . . 17, 19 Range, generally printing. . . . . . . . . 19 entering . . . . . . . . . 8 reading . . . . . . 21, 55ff valid data limits. . . 8, 36 remarks in. . . . . . 19, 21 Range increment saving. . . . . . . . . . 21 entering. . . . . . . . . .8 Stand-alone programs in graphics display . . . 22 PRCONFIG.EXE . . . . . . 46 valid data limits . . . . .8 RRTABLE.EXE . . . . . . . 56 Range, zero Starting QBALL entering. . . . . . . . . .8 Already Loaded! message . 55 finding probable. . . . . 27 monochrome. . . . . . . . 3 valid data limits . . . . .8 Suggestions Range tables procedure . . . . . . . . ix data entry . . . . . . . . 8 rewards for . . . . . . . ix display. . . . . . . . . . 9 Switches & Printer Menu interpretation . . . . . 10 Graphics grid on/off. . . 53 printing . . . . . . . . 13 Noises on/off . . . . . . 53 reading. . . . . . 15, 55ff Printer settings. . . 51-52 remarks in . . . . . 13, 15 System of measure saving . . . . . . . . . 13 Configuration . . . . 51-52 Reading saved table . . . . 55 Optional units. . . . . . 52 Registration fee, benefits. ix Toggle. . . . . . . . 10, 52 Remarks in printed/saved range, slant fire table 13,15,19,21 T Removing QBALL see Uninstall Tables too long RRTABLE.EXE . . . . . . 15, 55 for one screen 10, 18 Toggling switches S Graphics grid display . . 53 Saving Noises. . . . . . . . . . 53 Range tables . . . . . . 15 Printer enable status . . 53 remarks in. . . . . . 15 Trajectory from Range, Height Slant fire tables. . . . 21 see Most Probable Zero remarks in . . . . . . . 21 Trajectory graphics Trajectory graphics. . . 23 displaying . . . . .22ff, 58 Screen Colors printing . . . . . . . . 24 choosing . . . . . . . . 54 see also PRCONFIG.EXE saving . . . . . . . . . 54 recalling. . . . . . . . .57 Screen Header saving . . . . . . . . . .23 default. . . . . . . . . . 4 U graphics . . . . . . . . 22 Uninstall/remove QBALL. . . . 6 weapon identifier. . . . . 4 Unit Conversion Factors Shareware Table 36 about... . . . . . . . vii Unit System availability . . . . . viii Configuration. . . . . . 51 distribution . . . . i, vii Coversion Factors. . . . 36 obtaining latest . . . viii Optional Units . 11, 35, 52 Sight height English wind velocity 52 changing . . . . . . . . 33 Metric bullet energy. 52 default. . . . . . . . . . 7 Metric bullet weight. 52 valid data limits. . 33, 36 Toggling . . . . . . . . 10 Slant fire effects. . . . . 16 Uphill/downhill see Slant fire Slant fire tables data entry. . . . . . 17, 19 [U] continues Thanks for trying QBALL !