==================== +----+ | | | | | +--+ --+ | | | -+| | | +--| | | | || | | | | | | +---|+ +--+ +--+ + + +- ver 2.09 ==================== SMALL ARMS EXTERIOR BALLISTICS FOR IBM PC's and COMPATIBLES ---- Benjamin W. Hartley Forest Park Estates #103 Jaffrey, NH 03452 [Voice#: (603) 532-6248] +------------------------------------------------------------------+ | _______ | | ____|__ | (R) | | --| | |------------------- | | | ____|__ | Association of | | | | |_| Shareware | | |__| o | Professionals | | -----| | |--------------------- | | |___|___| MEMBER | | | | | | This program is produced by a member of the Association of | | Shareware Professionals (ASP). ASP wants to make sure that the | | shareware principle works for you. If you are unable to resolve | | a shareware-related problem with an ASP member by contacting the | | member directly, ASP may be able to help. The ASP Ombudsman can | | help you resolve a dispute or problem with an ASP member, but | | does not provide technical support for members' products. Please | | write to the ASP Ombudsman, 545 Grover Road, Muskegon, MI 49442, | | or send a CompuServe message to: ASP Ombudsman 72050,1433. | | | +------------------------------------------------------------------+ (This is ASCII-formatted QBALL.DOC, the On-disk documentation.) "QBALL" -- Source code, executable files, and documentation are (c) 1992 by Benjamin W. Hartley. All rights reserved. [ QBALL -- Exterior Ballistics -- ii ] TABLE OF CONTENTS ----------------- Dedication, Disclaimer, License, Copyright Information..........i Table of Contents..............................................ii Introduction..................................................iii About Shareware................................................iv Chapter page ------- ---- 1. Getting started..............................................1 1.1 Files required......................................1 1.2 Will It Work ?......................................1 1.3 Copying the program.................................2 1.4 Printing the documentation..........................2 1.5 General Instructions................................3 1.6 Starting QBALL......................................4 2. Computing ballistic or gun data..............................7 2.1 Preliminary data entry..............................7 2.2 Computing and displaying a range table..............8 2.3 Displaying graphics................................11 2.4 Changing input data................................16 2.5 Other ballistic procedures.........................17 3. Inferring ballistic coefficients............................22 3.1 First Run: r1 = 0..................................23 3.2 Second Run: r1 = 25................................24 4. Printing tables.............................................25 4.1 Printer warnings...................................25 4.2 Screen dumps.......................................25 4.3 Printer setup......................................25 4.4 Print functions....................................25 4.5 Typical printed output.............................26 5. Configuring display and default starting values.............27 5.1 The Configuration Menu.............................27 5.2 Switch toggles (set defaults)......................27 5.3 Configuring display colors.........................28 5.4 Using the values you've set........................28 5.5 Some other considerations..........................28 Some Afterthoughts and Some Wrinkles...........................30 Appendices:-- A. Glossary....................................................33 B. Example of Ballistic Coefficient from Tabular Data..........39 C. Example QBALLSAV.* file.....................................41 D. Selected bibliography.......................................43 E. Error analysis..............................................44 F. Error Messages, Default Starting Values.....................47 G. Enhancement form............................................53 H. Registration form...........................................55 [ QBALL -- Exterior Ballistics -- iv ] About Shareware --------------- Shareware distribution gives users a chance to try software before buying it. If you try a Shareware program and continue using it, you are expected to register. Individual programs differ on details -- some request registration while others require it, some specify a maximum trial period. With registration, you get anything from the simple right to continue using the software to an updated program with printed manual. Copyright laws apply to both Shareware and commercial software, and the copyright holder retains all rights, with a few specific excep- tions as stated below. Shareware authors are accomplished programmers, just like commercial authors, and the programs are of comparable quality. (In both cases, there are good programs and bad ones!) The main difference is in the method of distribution. The author specifi- cally grants the right to copy and distribute the software, either to all and sundry or to a specific group. For example, some authors require written permission before a commercial disk vendor may copy their Shareware. Shareware is a distribution method, not a type of software. You should find software that suits your needs and pocketbook, whether it's commercial or Shareware. The Shareware system makes fitting your needs easier, because you can try before you buy. And because the overhead is low, prices are low. Shareware also has the ultimate money-back guarantee -- if you don't use the product, you don't pay for it. QBALL is a "shareware program" and is provided at no charge to the user for evaluation. Feel free to share it with your friends, but please do not give it away altered or as part of another system. The essence of "user-supported" software is to provide personal computer users with quality software without high prices, and yet to provide incentive for programmers to continue to develop new products. If you find this program useful and find that you are using QBALL and con- tinue to use QBALL after a reasonable trial period, you must make a registration payment of $25.00 to the author. The $25.00 registration fee will license one copy for use on any one computer at any one time. You must treat this software just like a book. An example is that this software may be used by any number of people and may be freely moved from one computer location to another, so long as there is no possibility of it being used at one location while it's being used at another, just as a book cannot be read by two different persons at the same time. Commercial users of QBALL must register and pay for their copies of QBALL within 30 days of first use or their license is withdrawn. Site- License arrangements may be made by contacting the author. [ QBALL -- Exterior Ballistics -- 1 ] Chapter 1 --------- Getting Started """"""""""""""" 1.1 Files Required. -------------- QBALL is initially distributed with the following files: QBALL EXE -- The QBALL executable file. QBALL FON -- The QBALL graphics font file. QBALLODD DOC -- Odd-numbered documentation pages. QBALLEVN DOC -- Even-numbered documentation pages. QBREADME BAT -- Prints short intro on screen. QBALLENH DOC -- The QBALL enhancement form. QBALLREG DOC -- The QBALL registration form. WARRANTY DOC -- What's covered and for how long. LICENSE DOC -- "Thou shalt and thou shalt not..." USERPACK LST -- A files list like this one. (Note: Registered copies of QBALL are distributed in non-compressed format, with no *.DOC files) The only absolutely, positively, gotta-have files are QBALL.EXE. and QBALL.FON. The documentation is helpful, but you can get by without it. The rest qualify as "nice to have." 1.2 Will It Work ? -------------- In its present incarnation, QBALL is written in and compiled as a stand-alone .EXE file using Microsoft Professional Development System, version 7.1. QBALL was written on a Gateway 2000 AT clone, with an 80286 process- or, AMI BIOS, MS-DOS 5.0 with 4DOS 4.0 command processor, 5 1/4" (1.2 meg) and 3 1/2" (1.44 meg) floppy drives, 40 megabyte hard-disk, and Samsung CM4531 EGA monitor. No coprocessor was used. QBALL Version 2.09 does not include any routines from third parties. QBALL should function on any PC-DOS or MS-DOS compatible computer, and will detect the presence of a CGA or EGA card/monitor. If no graphic equipment is installed, QBALL internally disables its graphics routines. The purely tabular routines, however, remain usable. [ QBALL -- Exterior Ballistics -- 3 ] 1.5 General instructions. -------------------- Selecting menu options. Press the key corresponding to the letter which is highlighted/bracketed in that option. For example, to choose option

, press upper- or lower-case "P." QBALL's menus are not case sensitive. If the option does not appear, or appears in low- intensity color, QBALL will "beep", and do nothing further. Response to "Y or N". Press upper- or lower-case "Y" or "N". (The default for "Y" is [Enter].) If any other character is pressed, QBALL will "squeak" and do nothing further. ESC key. "ESC" will "back out" of data entry, and will "back up" from a displayed menu. Each menu specifies where "ESC" will take you. There is one exception: "Quit to DOS" requires that you press "Q", confirm with "Y," and respond to one further prompt. Data entry and error trapping. Type the value or string to be used and press [Enter]. If a value already appears, press [enter] to accept it, or overtype to change. QBALL will not accept the wrong data type; out-of-range values will produce an error message. Use the [Backspace] key to edit your entries before entering them. If there is a "standard value" for the data, that value is displayed on the prompt line in [brackets]. Swap Units option. The unit of range measure may be swapped back and forth between Yards and Meters using the "New Input Data" menu. As distributed, QBALL defaults to "Yards"; this may be changed using the configuration routines. Noises. QBALL will "squeak" upon erroneous data value entry, and "chirps" upon completion of a computation, or upon invocation of wap units. QBALL defaults to sounds "on"; sounds may be toggled "off" for peace and quiet. A "flash" replaces noises in quiet mode. Graphics. Given a CGA or an EGA card/monitor, graphics are always enabled. You may suppress display of the graphics grid, but there is no provision for toggling graphics completely "off." Print options. ENSURE that your printer is on/on-line if you want hard copy; QBALL will detect whether or not your printer is on, but not "paper out"! You may disable the "print" function if desired. Help. Press the [F1] key to display help in contrasting video. Help displays are erased in ten seconds, or press any key to exit help. Redirection of data output. QBALL does not support redirection of data output, e.g., to a disk file, except as otherwise provided within the graphics and computations routines. [ QBALL -- Exterior Ballistics -- 5 ] Having pressed a key, the screen clears, and the following screen is displayed: ++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ > Ballistic Computations: Typical Firearm < +=====================================+ | *** M A I N ME N U *** | | --------------------------------- | | ompute Ballistic or Gun Data | | Infer allistic Coefficient | | Use tilities / Configure QBALL | | ew or Changed Input Data | | --------------------------------- | | uit -- Return to DOS | +=====================================+ ----------------------------------------------------------------+ [ MV: ][ C1: ][ Wt: ][ Met: 59d 0' 29.53" 78% ]| | | | | | | | | | | Muzzle Ballistic Bullet Metro -- | Velocity Coefficient Weight, Temperature, degrees F. | (FPS) (grains) Gun Altitude, feet | Barometric Pressure, "Hg | Relative Humidity, percent | | +---------------+ | (Please make note of the information) +-------------- (contained in the "Information Line",) [ H: 1.00][Yds] (here shown "folded". The "Informa-) | | (tion" or "Info Line" is updated if) | | (changes are made to any of the in-) Sight Range (formation it shows. Note that some) Height Units (of the items are blank; values will) (inches) (Inverse) (be filled in presently. ) ++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ Go on to the next page... [ QBALL -- Exterior Ballistics -- 7 ] Chapter 2 --------- Computing Ballistics or Gun Data """""""""""""""""""""""""""""""" 2.1 Preliminary data entry. ---------------------- Before doing anything else, we're going to have to enter some in- formation for QBALL to chew on. QBALL will ask you for data which it does not already have. The items of information for which QBALL will prompt you are, in order, (with suggested practice entries): a. The ballistic coefficient (C1) for the projectile in question . . . . . . . . . . . .250 (The leading decimal point is automatic.) b. The bullet weight in grains . . . . . . . . . 125 c. Whether or not to use the displayed metro . . "Y" (QBALL will default to "Standard Metro"; you) (can use nonstandard metro, but, just to keep) (things simple, stay with standard metro for) (now. Press "Y" or [Enter]. ) d. The muzzle velocity . . . . . . . . . . . . . 2300 Enter values at the appropriate places when prompted. (Try enter- ing an impossible value or two, and see what happens.) Here are some "impossible" values to try: Ballistic Coefficient: 1.000; Bullet Weight: 0; Muzzle Velocity: 4700 FPS. A complete list of QBALL's error messages is in Appendix E, with the most common causes for their display. For purposes of this tutorial, the gun/bullet is identified as "Typical Firearm." This may be changed using the "ew or Changed" menu option. Continue with "Typical Firearm" for the time being. [ QBALL -- Exterior Ballistics -- 9 ] Take a close look at the menu: it is telling you that the range at which you wish to be zeroed must be set. Press "et Zero..." and enter: "150" -- without the quotes, of course. (Until you set a zero range, "Range able..." won't do anything.) Back where we started, eh? Take a closer look. +=================================+ | *** Computations Menu *** | | ------------------------------ | | et/Reset Current Zero Range | | Range able (0 = 150 Yards) | | ther Ballistics Procedures | | ew or Changed Input Data | | ------------------------------ | | to M A I N M E N U | +=================================+ The zero range for your range table is now set. In future, if QBALL has been provided a zero range, it will be displayed in the computa- tions menu. If no valid zero range exists, then the phrase "Range able (0 MUST BE SET)" will be displayed in low intensity color instead. One of the useful tables that QBALL will generate is a range table from zero to a designated range with a fixed range increment. Press "T" and enter the following data when prompted: Range for this procedure..........: 200 Range Increment...................: 25 QBALL will clear the screen and display the following table, (here shown in somewhat compressed format): Range Table, Zeroed at Highlighted Range ---------------------------------------- Range R e m a i n i n g Total Path/Sight Line Defl'n Time Yards Velocity Energy Drop M.O.A. Inches 10 MPH Flght ----- ----------------- ----- --------------- ------ ----- 0 2300 1468 0.0 0.0 -1.0 0.0 0.000 25 2218 1365 0.2 1.5 0.4 0.1 0.033 50 2138 1268 0.9 2.7 1.3 0.5 0.068 75 2059 1176 2.0 2.4 1.8 1.0 0.104 100 1982 1090 3.6 1.7 1.7 1.8 0.141 125 1906 1008 5.8 1.0 1.2 2.8 0.179 [ 150 1832 932 8.6 0.0 0.0 4.1 0.219 ] 175 1761 861 12.0 -1.1 -1.9 5.8 0.261 200 1693 795 16.2 -2.2 -4.5 7.7 0.305 ----------------------------------- ===> Press any key <=== [ QBALL -- Exterior Ballistics -- 11 ] 2.3 Displaying Graphics. (Available in EGA and CGA flavors) ------------------- You should at this time be looking at a graphic representation of the projectile's trajectory as viewed from the side. Note the empha- sized line indicating the line of sight, and the curved line which delineates the bullet's path from the muzzle (0) to the maximum range (200). (Use a pencil to draw a smooth curve through the five #-signs to delineate the bullet's path on this schematic representation.) +-------+-------+--------+-------+--------+--------+-------+-------+ | | | | | | | | | I| | | | | | | | | | +5 ---+-------+--------+-------+--------+--------+-------+---- +5| N| | | | | | | | | | | | | # | | | | | C| 0 --#+-------+--------+-------+--------+--------#-------+----- 0| # | | | | | | | | H| | | | | | | | # | -5 ---+-------+--------+-------+--------+--------+-------+---- -5| E| | | | | | | | | | | | | | | | | | S|-10 ---+-------+--------+-------+--------+--------+-------+--- -10| | | | | | | | | | | | | | YARDS | | | | |-15 ---+-------+--------+-------+--------+--------+-------+--- -15| | 25 50 75 100 125 150 175 | +-------+-------+--------+-------+--------+--------+-------+-------+ | [ "Fine Print" -- remaining velocity and energy, current round ] | +------------------------------------------------------------------+ | > Current < > Previous < +=========================+| | Max Ht : 1.8" @ 86 | *** Graphics Menu *** || | Min Ht : -4.5" @ 200 | --------------------- || | MuzVel : 2300 FPS | rid Toggle On/Off || | TermVel: 1693 FPS | ave Current Data || | BCoeff : .250 | ecall Saved Data || | ZeroRg : 150 Yards | --------------------- || | Metro : Standard | ape to Choose Next || +---------------------------------------+-------------------------++ The information provided is pretty much self-explanatory. (The "fine print" below the display indicates the velocity and energy of the CURRENT round at the appropriate range.) the menu options, i.e., rid, ave, and ape, allow you to toggle the background grid on and off, save trajectory data to disk, and quit the graphics rou- tine, respectively. Press "G" to see what happens; the screen is redrawn without the background grid lines. Press "G" again to re-display the grid lines. (In its default configuration, QBALL will display the grid.) [ QBALL -- Exterior Ballistics -- 13 ] Note that the range at which zeroed, 150 yards, is still set. Step through the process of developing a range table by entering a maximum range (200), and the range increment (25). Press "G" at the "Choose Next Output" Menu. In addition to the graph, this should be displayed: (Again, use a pencil to draw a smooth curve connecting the X's in this schematic diagram.) +-------+-------+--------+-------+--------+--------+-------+-------+ | | | | | | | | | I| | | | | | | | | | +5 ---+-------+--------+-------+--------+--------+-------+---- +5| N| | | | | | | | | | | | | X | | | | | C| 0 ---X-------+--------+-------+--------+--------X-------+----- 0| X | | | | | | | X H| | | | | | | | | | -5 ---+-------+--------+-------+--------+--------+-------+---- -5| E| | | | | | | | | | | | | | | | | | S|-10 ---+-------+--------+-------+--------+--------+-------+--- -10| | | | | | | | | | | | | | YARDS | | | | |-15 ---+-------+--------+-------+--------+--------+-------+--- -15| | 25 50 75 100 125 150 175 | +-------+-------+--------+-------+--------+--------+-------+-------+ | [ "Fine Print" -- remaining velocity and energy, current round ] | +------------------------------------------------------------------+ | > Current < > Previous < +=========================+| | Max Ht : 1.5" @ 86 | *** Graphics Menu *** || | Min Ht : -3.5" @ 200 | --------------------- || | MuzVel : 2500 FPS | rid Toggle On/Off || | TermVel: 1858 FPS | ave Current Data || | BCoeff : .250 | ecall Saved Data || | ZeroRg : 150 Yards | --------------------- || | Metro : Standard | ape to Choose Next || +---------------------------------------+-------------------------++ Now press and <0> (that's "zero") to retrieve the trajectory data you saved previously. You should get a display as shown on the next page. (Again use a pencil to connect the X's and the # signs with smooth curves. Note that the "X" curve is flatter than the "#" curve.) [ QBALL -- Exterior Ballistics -- 15 ] +=========================+ > Current < > Previous < | Graphics Menu | Max Ht : 1.5" @ 86 +-------------------------+ Min Ht : -3.5" @ 200 | rid Toggle | MuzVel : 2500 FPS | ave Current Data | TermVel: 1858 FPS | On Disk: <0> thru <1> | BCoeff : .250 +-------------------------+ ZeroRg : 150 Yards | ape to Choose Next | Metro : Standard +=========================+ QBALL lets you save up to 16 "QBALLSAV" files, 0 through 15; the Graphics Menu accesses the saved files using "0" through "9: and "A" through "F". (Quick introduction to hexadecimal, anyone?) An example of "QBALLSAV" is to be found in Appendix C., page 41. Should the display become cluttered with too many trajectory plots, you may erase all but the "Current" plot by toggling the grid. "QBALLSAV.INI" now exists in the current directory, along with two sets of saved trajectory data: "QBALLSAV.0" and "QBALLSAV.1." The *.INI file keeps track of how many sets of trajectory data have been saved. When you decide to quit QBALL, you will be prompted to either retain or delete the saved-trajectory data. It is recommended that you press "N" at that point, at least until you have played with QBALL awhile. (Answering "N" erases all the "QBALLSAV" -- that is, the trajectory data -- files, including "*.INI.") You cannot erase saved Range Tables from within QBALL, unless you invoke the "DOS shell." NOTE: don't confuse "Save Current Data," which saves the data used to plot a previous trajectory, and "Save Range Table," which makes a disk file identical in content to the hardcopy output. QBALL starts numbering Range Tables at "1" (one), and does not keep track of tables saved during previous sessions. If not renamed or moved, saved range tables are overwritten. All saved range tables are named "RGTABLE.n," where n is a number. Now press "ESC" to return to the "Choose Next Option" menu. [ QBALL -- Exterior Ballistics -- 17 ] Sight Height. Allows fine-tuning QBALL to a specific weapon. The supplied sight height of 1.00 inches is a "generic" value, and should be changed to reflect the actual sight height. Acceptable values are -2 to +5 inches. QBALL rounds sight heights to 0.01 inches. Swap Units. This option toggles QBALL between yards and meters, and will cause QBALL to make all range calculations in the chosen unit of measure. Note well, however, that while computations using meters are accurate, they may produce some rather strange looking displays; specifically, the range increment may not appear as expected. This is unavoidable, as meters and yards do not take kindly to being convert- ed, one to the other. You may return to "yards" by swapping units again. Note that only ranges are affected; heights and deflections will still be displayed or printed in inches, and velocities will continue to be shown in feet per second (FPS). (A rough approximation to convert inches) (to centimeters is to multiply all inches) (dimensions by 2 1/2. (A more accurate) (multiplier = 2.54.) Now, If you're a real) (glutton for punishment, you can divide) (velocities in FPS by 3.28083 to obtain) (velocities in Meters per second. QBALL,) (however, will not perform either of these) (conversions for you. ) 2.5 Other Ballistic Procedures. -------------------------- Five "other ballistic procedures" are described in this section. The first two, point-blank range and wind vector corrections, directly interface with the range table/graphics procedures; slant angle of fire, sectional density, and free recoil may be invoked for the infor- mation they produce. From the computations menu, press "O" to access the "Other Procedures Menu:" +===============================+ | * Other Procedures Menu * | | --------------------------- | |

oint-blank Range | | ind Vector Corrections | | Slant ngle of fire | | ectional Density | | ree Recoil of Gun | | --------------------------- | | to Computations Menu | +===============================+ NOTE: All the examples in section 2.5 assume that you're still using the input data as shown on page 7. [ QBALL -- Exterior Ballistics -- 19 ] Wind Vector Corrections. ----------------------- One of the columns in the range table gives the wind deflection, in inches, for a 10 MPH "pure" crosswind. To compute the deflection for other windspeeds and directions, press "W", and enter the wind speed (in MPH), and the direction from which the wind is blowing, relative to the line of sight, from 0 to 360 degrees. (O degrees is considered as pure headwind, 180 degrees as pure tailwind.) QBALL will compute the vector effects of the wind values entered, and will display them as shown: +++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ ------------------------------ Wind velocity [ 10 MPH ] 20 Wind direction [ 270d ] 135 ------------------------------ Range wind = 21 feet per second Cross wind = 14 miles per hour Crosswind correction = -1.40 Use crosswind correction factor in tables ? ([Y] or N) +++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ A "Y" response will cause the deflection values in the range table to be displayed for the computed crosswind; in this case, 14 MPH. QBALL takes crosswinds from left to right as positive; from right to left, as negative. No correction is applied for the range wind, as that effect becomes significant only at very long range, with a low muzzle velocity, and small ballistic coefficient. (Try entering a new muzzle velocity using the range wind correction and see.) Should you wish to return to the default wind values, enter the values appearing on the prompt line in [brackets]. [ QBALL -- Exterior Ballistics -- 21 ] Free Recoil Energy. ------------------ We all know that a firearm "kicks." Simple Newtonian physics, right? But how hard does it kick? One way to compare absolute num- bers, and without getting into the mare's nest of "actual" versus "perceived" recoil, is to compare the recoil velocity and energy im- parted to the weapon upon firing. Press "F," and enter the powder weight in grains. The example uses 38 grains powder weight, which seems to be a fair "average" powder weight from several random exam- ples taken from the SPEER Reloading Manual. You must also enter the weapon's weight, in either pounds and decimal fractions of a pound or in pounds and ounces. For an 8 1/2 pound rifle, for example, enter either "8.5" or "8 8". The result is displayed: ------------------------------ Gun Recoil Velocity: 7.83 FPS Free Recoil Energy : 8.11 Ft# ===> press any key <=== Unfortunately, these figures are relatively meaningless without some basis for comparison. Here are three for starters, all data computed using QBALL: --------- G U N -------- 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 The ammunition specified is a "best estimate" using published Winchester data for velocities and bullet weights, and powder weights from the HORNADY HANDBOOK. The weapon weights were taken from the 1991 edition of GUN DIGEST. [ QBALL -- Exterior Ballistics -- 23 ] 3.1 First Run: r1 = 0 ----------------- When prompted for the "first range," press "enter;" for "second range," enter "100." The following screen will be displayed. Enter the appropriate velocity values as shown. QBALL will quickly return the value of the ballistic coefficient, and ask if you wish to calcu- late another round. Responding "Y" clears the velocity inputs, and you'll be prompted for another velocity pair. In this case, press "N." (In all probability, you're working from published tables, and using the same numbers twice would be superfluous.) ++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ *** Inferring a Ballistic Coefficient *** ----------------------------------------- Metro: as displayed Relative Air Density = 1.000; Sonic Velocity = 1.000 ----------------------------------------- For Round Number 1 First Velocity (Ft/Sec) 2300 Second Velocity (Ft/Sec) 1982 For Standard Atmosphere, C1 = .250 Calculate another Round? ([Y] or N) [ Lower & Upper Ranges (yards) [0] & 100 ] ++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ The center of the screen will clear, and the following information is displayed: ----------------------------------------- Average C1 for 1 round = .250 Between Mean Velocities 2300 and 1982 Calculated Muzzle Velocity = 2300 ----------------------------------------- QBALL will ask if you wish to print the table. For now, press "N" to return to the main menu. Note that the muzzle velocity and the computed ballistic coefficient are now shown in the information line. If you so desired, you could go on to compute ballistic or gun data, but let's try the infer ballistic coefficient routine again, with r1 set to something other than zero. (You should be at the main menu; press "B.") [ QBALL -- Exterior Ballistics -- 25 ] Chapter 4 --------- Printing Tables """"""""""""""" 4.1 Printer warnings. ---------------- QBALL will detect "device fault" if your printer is off or off-line. You must, however, ensure that paper is installed and the necessary printer setup has been accomplished BEFORE you try to print ANY QBALL output! (QBALL does not detect "paper out.") 4.2 Screen dumps. ------------ You may print a screen's worth of information using the Shift-PrtScr key combination. This is NOT recommended, however, as you will lose any information which has scrolled past on the screen. 4.3 Printer setup. ------------- You need not set up your printer to skip perforations in fanfold paper; QBALL keeps track of the number of lines printed and issues a formfeed when appropriate. Continuation pages are sequentially num- bered, and the appropriate column headers are printed on them. Nor need you set your printer to indent from the left margin. At first, it is best to use a printer setup of "left margin = 0," as QBALL is set up to indent each table it prints. (The indents may be changed using your own printer utilities, if desired.) You may also toggle the print option "off," in which case, the

rint menu options are disabled. This feature is useful if you are sure that you won't want printouts, or if you have no printer. QBALL defaults to printer "on," and enables the print option. 4.4 Print functions. --------------- You may obtain hard copy from the "Choose Next Output" menu, if enabled, or from this prompt: Print this table? (Y or N). Press "Y" to print the table. The prompt will be replaced with then statement "Printing table" in highlighted text. If you have a printer with a sizable buffer, QBALL will return you to the previous menu quite quickly. If not, QBALL will finish printing out the table, then return you to the previous menu. [ QBALL -- Exterior Ballistics -- 27 ] Chapter 5 --------- Configuring display and default starting values """"""""""""""""""""""""""""""""""""""""""""""" 5.1 The Configuration Menu. ---------------------- You may wish to change some or all of QBALL's start-up data. Press "U" at the main menu, to display this "Utilities Menu:" +=============================+ | *** Utilities Menu *** | | ------------------------- | | Toggle witches | | Change Display olors | | rite QBALL.INI Data | | Invoke a OS Shell | | ------------------------- | | to M A I N M E N U | +=============================+ 5.2 Toggle Switches. --------------- Press "S" to display this "Switch Toggle Menu." Pressing the appropriate key toggles that particular item; the current setting is reflected immediately; QBALL uses that setting until again changed. +================================+ | *** Switch Toggle Menu *** | | ---------------------------- | | Yds/Mets wap (Now Yards) | | Graphics rid (Now ON) | |

rinter on/off (Now ON) | | oises on/off (Now ON) | | ---------------------------- | | to Utilities Menu | +================================+ You may also toggle the unit of range measure between yards and meters from the "New/changed Input Data" menu, which is accessed from the main menu and the computations menu. If you toggle the printer off, all "Print This Table" prompts are suppressed, and "====> Press any key <====" is displayed instead. If noises are toggled off, they are replaced with a short-duration "flash" in the lower right corner of your screen. Toggling the graphics grid merely changes the appearance of the first display of "pictures;" you will retain the option of changing that appearance with the Graphics Menu's "rid..." option. [ QBALL -- Exterior Ballistics -- 29 ] Upon invocation of the "Write QBALL.INI Data," the new .INI data will also include the values of these items which are currently in effect. This allows you to "tailor" your copy of QBALL to match your own con- ditions: your weapon, and the actual (or anticipated) metro which is encountered at your own firing range. QBALL no longer uses a separate *.INI file, but writes the initial- zation data in binary format to the very end of QBALL.EXE. (This means that the file date on your copy of QBALL.EXE will change every time you invoke "rite QBALL.INI Data." It's supposed to.) Specific times you might very well want to use metro values other than standard are, for example, if your range is not at sea level, or if you're shooting during the summer, when the temperature might very well exceed 59 deg.F. You can configure QBALL to start with the alti- tude of your range, or an expected temperature, without the hassle of changing the values after start-up. In similar fashion, you may configure QBALL to start with the name of your own weapon, say, "Ruger M77 .270" and the actual measured height of that weapon's sight, say, 1.25 inches. [ QBALL -- Exterior Ballistics -- 31 ] Now, if you are going to save a lot of range tables, all bets on disk space are off! For example, the range table for a maximum range of 500 yards with a range increment of 1 yard is over 43,000 bytes long. For that reason, you might want to hold off on writing too many of 'em. One other wrinkle -- previously mentioned, but it bears repeating -- is that QBALL starts numbering RANGE TABLES from #1 in each session. Between sessions, either rename the RGTABLE files, or move 'em some- where else where they won't get overwritten. You could, of course, write a batch file to take care of this; something like the following: REN RGTABLE.* KEEPTBL.* (or, for the brave:) COPY RGTABLE.* [d:\]*.* DEL RGTABLE.* Call this RTNAME.BAT or some such, and run it from the DOS prompt, or from within QBALL using the "Shell to DOS" feature. Just make sure that the *.BAT file is in the same directory with the Range Table files, or where it will be picked up by your computer's PATH. [ QBALL -- Exterior Ballistics -- 33 ] Appendix A ---------- Glossary """""""" ABSOLUTE ZERO - Properly, that temperature at which all molecular mo- tion ceases. For practical purposes, -459.67 degrees Fahrenheit, or 0 degrees Rankine. AIR DENSITY - The mass (weight) of a unit volume of air. AIR RESISTANCE - The retardation of a bullet's forward flight due to the atmosphere. ALTITUDE - The vertical distance above or below sea level. Altitudes above sea level are taken as positive; those below, as negative. BALLISTICS - The study of moving projectiles. Commonly, what is meant is "exterior" ballistics: that portion of the bullet's flight between the muzzle and the target. BALLISTIC COEFFICIENT - The ratio of the sectional density of a pro- jectile to its coefficient of form. A measure of how well a bullet re- tains its velocity. Commonly supplied by reloading manufacturers, or it may be derived from their ballistic tables. In QBALL, the ballis- tic coefficient is always taken at standard metro. The program cor- rects for nonstandard conditions, but does not display the corrected ballistic coefficient(s). See STANDARD METRO BALLISTIC EFFICIENCY - The relative ability of a bullet in flight to overcome air resistance. BORE - The inside of a firearm's barrel. In rifled firearms, the bore diameter is the original dimension of the barrel before the rifling grooves are cut or swaged in it. Bore diameter may also be taken as the transverse dimension between the lands of the rifling. See LANDS BRASS - Alloy of copper and zinc commonly used in the fabrication of cartridge cases. Also, one or more cartridge cases containing neither powder, nor primer, nor bullet. BULLET - The actual projectile in small arms ammunition. Commonly corrupted to mean the entire cartridge. BULLET WEIGHT - Weight of the actual projectile, usually stated in grains. See GRAIN [ QBALL -- Exterior Ballistics -- 35 ] GRAIN - A unit of weight equal to 1/7000 of a pound. 437.5 grains equal one ounce. May also refer to an individual particle, or ker- nel, of powder. In cartridge specifications, always refers to the weight, never to individual particles. GROOVES - Spiral impressions cut or swaged lengthwise through a bore to impart spin to projectiles. See LANDS. GROUP - The pattern made, at the target, by a number of shots fired at a single point of aim and (usually) a common sight setting. Usually measured from center-to-center of the two most widely spaced holes. GUN - In popular usage, refers to firearms, generally. HANDGUN - A firearm designed to be held and fired with one hand. HOLD OFF - The distance a shooter must shift his point of aim to the left or right to compensate for wind deflection. HOLD OVER - The distance a shooter must raise his point of aim to be on target when his firearm is zeroed at a lesser range. HORIZONTAL FIRE - That type of fire occurring when the barrel of the firearm is not elevated significantly above the horizontal. Generally may be 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 - Colloquial term for metallic sights. LANDS - Those portions of a rifled bore not cut away by rifling grooves. See GROOVES 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 melt- ing point which forms the basis for many bullets. LINE OF DEPARTURE - An imaginary line formed by extending the axis of a firearm's bore in a downrange direction. 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. MASS - Properly, the weight of an object divided by the acceleration due to gravity. Commonly taken to mean "weight." [ QBALL -- Exterior Ballistics -- 37 ] 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 as 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, golfball 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 divid- ed by the density of air at standard metro, expressed as a dimension- less 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, expressed as a di- mensionless decimal fraction, e.g., 1.000. REMAINING ENERGY - A projectile's energy in foot-pounds at a given range. REMAINING VELOCITY - A projectile's velocity in FPS at a given range. ROUND - One complete cartridge. Also used to refer to the sequential number of a shot in a number of shots, as "Round #3." SCOPE - optical, as opposed to metallic, sights. Generally compounded as in "scope sight", "scope equipped", "scoped." SIGHT HEIGHT - The measured vertical distance between the horizontal centerline of the sights and the axis of the bore. SIGHTING IN - The process of firing to determine point of impact at a given range and adjusting the sights so that the point of impact has the desired relationship to the point of aim. See also ZERO. SIGHT RADIUS - The distance between the rear and the front sight, on those weapons equipped with metallic sights. SONIC VELOCITY - The speed of sound through air. STANDARD MET - Atmospheric conditions as follows: Temperature is 59 degrees Fahrenheit, barometric pressure is 29.53 inches mercury, gun altitude is zero (sea level), and relative humidity is 78 percent. Firing tables are usually corrected to standard met conditions. STP - Standard Temperature and Pressure. See STANDARD MET. [ QBALL -- Exterior Ballistics -- 39 ] Appendix B ---------- Example of Ballistic Coefficient from Tabular Data """""""""""""""""""""""""""""""""""""""""""""""""" The following table summarizes the determination of a ballistic coefficient using tabular values. The table data is as published in the 1990 GUN DIGEST, page 229. +-----------------------------------------------------+ | From Gun Digest Table for 30-06 Spfd, 180 gr bullet:| | | | Range in Yards | | ------------------------------------ | | Muz 100 200 300 400 | | ------------------------------------ | | Velocity 2700 2469 2250 2042 1846 | | Energy 2913 2436 2023 1666 1362 | | Trajectory -1.5 2.5 0.0 -9.3 -27.0 | +-----------------------------------------------------+ Table B1. Data Taken From Published Table. Using the routines to infer a ballistic coefficient, plugging in 100 and 200 yards for the required ranges, and using the associated velocities, QBALL reports that C1 (the ballistic coefficient) is equal to 0.384. Returning to the main menu, selecting the ballistic computations option, and entering the appropriate values for muzzle velocity and bullet weight and zero range, QBALL produces the data shown in Table B2. +-----------------------------------------------------+ | QBALL Data Table for 30-06 Spfd, 180 gr bullet: | | | | Range in Yards | | ------------------------------------ | | Muz 100 200 300 400 | | ------------------------------------ | | Velocity 2700 2470 2251 2043 1846 | | Energy 2913 2437 2024 1668 1362 | | Trajectory -1.5 2.1 0.0 -9.0 -26.2 | +-----------------------------------------------------+ Table B2. Data Calculated Using QBALL. The maximum variations are: Velocity, 1 FPS; Energy, 2 FtLbs; and Trajectory 0.8 inches. QBALL, therefore, can produce results in sub- stantial agreement with published data. It may be found that QBALL's computation of ballistic coefficient from tabular data does not exactly agree with the value known to be correct. A series of successive approximations can compensate for QBALL's built-in roundoff characteristics, and the small errors re- sulting from them. [ QBALL -- Exterior Ballistics -- 41 ] Appendix C ---------- Example QBALLSAV.* File """"""""""""""""""""""" The following table represents, in part and in somewhat compress- ed form, one of the QBALLSAV files produced using the data entered in Chapter 2. The first column is the range; the second, the trajectory height relative to the sight line. Note that the range increment is 1/100 of the maximum range. (This is for EGA; CGA uses 1/50.) ---------- Yards 0.0 -1.00 2.0 -0.89 4.0 -0.78 //////////////////////////////////////////////// ... major portion of data omitted //////////////////////////////////////////////// 196.0 -3.17 198.0 -3.36 200.0 -3.55 2500 .25 150 1.49034 -3.548949 86 200 166.53 01-09-1992 / 12:00:00 / Typical Firearm Misc Info: Wt Tmp Alt BPr Hum SHt 125 59 0 29.53 78 1 [ end QBALLSAV.0 ] ------------------------------------- Key to values listed at end of table: ------------------------------------- First line: [Muzzle velocity] [Ballistic Coefficient] [Zero Range] [Max Height] [Min Height] [Range at Max Height] Second line: [Max Range] [Metro constant] [Date/Time/Identifier] Third and fourth lines: [Bullet weight] [Temperature] [Gun altitude] [Barometric Pressure] [Relative humidity] [Sight height] Fifth line: End of file indicator with Filename and number ===================================== The metro constant in line 2 keeps track of whether this trajec- tory data was computed using standard or nonstandard met. It is the sum of the four metro values: temperature, altitude, barometric pres- sure, and relative humidity. [ QBALL -- Exterior Ballistics -- 43 ] Appendix D ---------- Selected bibliography """"""""""""""""""""" Davis, William C., Jr. "Ballistics on the Home Computer," American Rifleman, CXXXI, 6 (June, 1983), p. 36. Davis, William C., Jr. "Ballistics on A Pocket Calculator," American Rifleman, CXXXV, 6 (June, 1987), p. 42. Davis, William C., Jr. "Calculate Ballistic Coefficients," American Rifleman, CXXXVII, 3 (March, 1989), p. 44. Davis, William C., Jr. "What Is The Ballistic Coefficient?," American Rifleman, CXXXVII, 3 (March, 1989), p. 12. HODGDON BASIC DATA MANUAL, Shawnee Mission: Hodgdon Power Company, Incorporated, 1987 Ramage, C. Kenneth (ed.). LYMAN RELOADING HANDBOOK. 46th ed. Middlefield: Lyman Products Corporation, 1982. Reiber, Ron L., and Heers, Edward A. (eds.). HORNADY HANDBOOK OF CARTRIDGE RELOADING, RIFLE-PISTOL. 3d ed. Grand Island: Hornady Manufacturing Company, 1980. SPEER RELOADING MANUAL #11, Lewiston: Omark Industries, Incorp- orated, 1987 Warner, Ken (ed.). GUN DIGEST, 1990. Northbrook: DBI Books, 1989. Warner, Ken (ed.). GUN DIGEST, 1991. Northbrook: DBI Books, 1989. WINCHESTER PRODUCT INFORMATION AND BALLISTICS GUIDE, East Alton: Winchester/Olin Corporation, 1989 [ QBALL -- Exterior Ballistics -- 45 ] An examination of the data in Table D1 indicates that computa- tion of remaining velocities using QBALL will be, on average, 0.47% high relative to the Speer data, and 0.42% low relative to the Hornady data. The Hornady data, however, must be considered suspect, as the actual ballistic coefficients available in the Hornady table do not exactly match those specified. Even so, it would appear that QBALL's velocity results are certainly within one or two percent of published data. In practical terms, there is probably one or two percent vari- ation in velocity between successive rounds in a string, if not more. QBALL, it would appear, can produce velocity figures which are accu- rate enough for practical purposes. Trajectory comparisons are presented in the following table. +----------------------------------------------------------------+ | Trajectory Comparisons - Conditions as Shown | | ============================================== | | [ All at Standard Met ] | +----------------------------------------------------------------+ | Range = 250 yards, zeroed at 50 yards; C1 =.12, MuzVel = 2100 | | | | Inches above/below line of sight at...(yards) | | --------------------------------------------- | | Muzzle 50 100 150 200 250 | | ------ --- ---- ---- ---- ---- | | QBALL -1.5 0.0 -1.3 -6.4 -16.9 -34.3 | | SPEER -1.5 0.0 -1.3 -6.4 -17.0 -34.7 | | HORNADY -1.5 0.0 -1.2 -6.3 -16.7 -33.2 | +----------------------------------------------------------------+ | Range = 400 yards, zeroed at 200 yards; C1 =.26, MuzVel = 2500 | | | | Inches above/below line of sight at...(yards) | | --------------------------------------------- | | Muzzle 100 200 300 400 | | ------ ---- ---- ---- ---- | | QBALL -1.5 2.9 0.0 -13.0 -39.5 | | SPEER -1.5 3.0 0.0 -13.0 -39.6 | | HORNADY -1.5 3.0 0.0 -13.1 -39.7 | +----------------------------------------------------------------+ | Range = 400 yards, zeroed at 200 yards; C1 =.50, MuzVel = 3300 | | | | Inches above/below line of sight at...(yards) | | --------------------------------------------- | | Muzzle 100 200 300 400 | | ------ ---- ---- ---- ---- | | QBALL -1.5 1.1 0.0 -5.2 -15.2 | | SPEER -1.5 1.1 0.0 -5.2 -15.2 | | HORNADY -1.5 1.1 0.0 -5.3 -15.7 | +----------------------------------------------------------------+ (Key: MuzVel = Muzzle Velocity C1 = Ballistic Coefficient) Table D2. Trajectory Comparisons Under Specified Conditions. [ QBALL -- Exterior Ballistics -- 47 ] Appendix F ---------- Error messages and default starting values """""""""""""""""""""""""""""""""""""""""" Error Messages -------------- Following are all the QBALL error messages, with a description of the circumstances under which they will be encountered. +----------------------+ | .INI File Not Found | +----------------------+ QBALLSAV.INI not found. Either it doesn't exist, or QBALL.EXE and *.INI are not in the same directory/on the same disk. (On a fast enough machine, you probably won't see this one.) +------------------------------------------------+ | Not Enough Velocity Remains - Input Greater MV | +------------------------------------------------+ QBALL is unable to complete a computation because the remaining velocity is less than 300 FPS. +--------------------------------+ | Enter Range greater than zero | +--------------------------------+ QBALL will not accept a range of "zero." +-------------------------------------+ | Enter 0 < Range Increment <= Range | +-------------------------------------+ You're trying to enter a range increment of zero, or to enter a range increment greater than the maximum range chosen. +------------------------------------+ | Enter 300 <= Velocity <= 4500 FPS | +------------------------------------+ You're trying to enter a velocity less than 300 or greater than 4500 FPS. +-----------------------------------+ | Enter -50 <= Temperature <= +125 | +-----------------------------------+ You're trying to enter a temperature value which is out of range. (If you really need this program to operate at Arctic/Saharan temperatures, let me know! I'll customize one for you.) [ QBALL -- Exterior Ballistics -- 49 ] Error Messages (continued) -------------- +-----------------------------------+ | Enter Second Range > First Range | +-----------------------------------+ In inferring ballistic coefficients, you're attempting to enter a second range which is smaller than the first range you have entered. +---------------------------------------+ | Inferred C1 exceeds 1.00 - check data | +---------------------------------------+ Input data is probably incorrect; ballistic coefficients cannot, by definition, exceed unity. +------------------------------------+ | Enter 1 <= Powder Weight < 200 gr | +------------------------------------+ You're attempting to enter a zero propellant weight in the determination of recoil. +-------------------------------------+ | Enter 1 oz <= Gun Weight <= 30 lbs | +-------------------------------------+ You're attempting to enter a value which is out of range. +-----------------------------------------+ | Enter Lbs + [space] + 0 <= Ounces < 16 | +-----------------------------------------+ QBALL can't figure out how much your weapon weighs in the determination of recoil. +------------------------------------------------+ | Enter Sight Height <= Maximum Deviation <= 40 | +------------------------------------------------+ In determining point blank range, the maximum deviation must exceed the sight height, and may not exceed 40 inches. +----------------------------+ | Enter Bullet Diameter > 0 | +----------------------------+ In determining a sectional density, the bullet must have a diameter. +-----------------------------------------+ | Maximum Deviation Reset to Sight Height | +-----------------------------------------+ In determining point blank range, the maximum deviation cannot be less than the sight height. (Sorry.) [ QBALL -- Exterior Ballistics -- 51 ] Default Starting Values ----------------------- QBALL uses information stored at the tail end of QBALL.EXE to set its display colors and several of the values with which it starts. As supplied, that data is as follows: "Typical Firearm",15,10,7,1,7,"Yards ","Meters",1, -1,59,0,29.53,78,1,-1,-1 Taking these in order, the individual entries result in the following: "Typical Firearm" ... Cartridge/bullet identifier 15 ... Foreground (text) color ( = HI white) 10 ... Highlighted text color ( = HI green) 7 ... Title/Info line color ( = white ) 1 ... Background color ( = blue ) 7 ... Help display background ( = white ) "Yards " ... Unit of range measure (trailing space necessary) "Meters" ... Alternate unit of range measure 1 ... Sight height in inches -1 ... Noises on or off ( = on ) 59 ... Air temperature, degrees Fahrenheit 0 ... Gun altitude in feet 29.53 ... Barometric pressure in inches of mercury 78 ... Relative humidity, in percent 1! ... Relative air density at given metro -1 ... Graphics grid on or off ( = on ) -1 ... Print prompt on or off ( = on ) (The metro values are for the STANDARD atmosphere) Should you be VERY brave, you can modify this data with any disk file editor; DEBUG, for example. THIS IS NOT RECOMMENDED! (Better by far to use the QBALL configuration routines!) (There are those who would say that) (manually modifying a program's .INI) (data isn't brave; it's foolhardy!) [ QBALL -- Exterior Ballistics -- 53 ] Appendix G ---------- Suggested Enhancements """""""""""""""""""""" Version of QBALL you are using? (appears in the box on screen one)______________ What should QBALL do that it doesn't do now? _____________________ __________________________________________________________________ __________________________________________________________________ __________________________________________________________________ What does QBALL do now, but could do better? _____________________ __________________________________________________________________ __________________________________________________________________ __________________________________________________________________ Other comments, requests, gripes? ________________________________ __________________________________________________________________ __________________________________________________________________ __________________________________________________________________ (continue on reverse) If you are the first to suggest an improvement which is subse- quently implemented, you'll receive a free copy of the first release incorporating your suggestion. It will take awhile, so please be patient. Your name ___________________________________________ Street ___________________________________________ City/State/Zip ______________________________________ Remove this page, fold, tape it shut, stamp, and mail. (Make sure that the address block is plainly visible!) [ QBALL -- Exterior Ballistics -- 55 ] Appendix H ---------- Registration Form """"""""""""""""" User Questionnaire (optional) ----------------------------- Version and Registration number of QBALL you have now? (appears in the box on screen one) V:________Reg#:__________ Where did you initially obtain QBALL? (Bulletin Board, CompuServe, etc.)__________________________ Do you use other ballistics programs?_____ Which one(s)?________ _________________________________________________________________ Order Form ---------- Please send the following (check appropriate box): +--+ | | Register QBALL (most recent release) with | | source code and manual @$60.00: $____.___ +--+ +--+ | | Register QBALL (most recent release) with | | manual @25.00: $____.___ +--+ TOTAL ENCLOSED: $____.___ +--+ +--+ Format: 5 1/4" 360k | | 3 1/2" 720k | | +--+ +--+ Your name ___________________________________________ Street ___________________________________________ City/State/Zip ______________________________________ Please make checks payable in US funds drawn upon a US bank, or use USPS money orders payable to Benjamin W. Hartley, and mail to: Benjamin W. Hartley Forest Park Estates #103 Jaffrey, NH 03452