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[ QBALL -- Exterior Ballistics -- i ] ===================== D E D I C A T I O N --------------------- QBALL was inspired by the many computer programs published in The American Rifleman, and is respectfully dedicated to their author: William C. Davis, Jr. ==================== DISCLAIMER ---------- The application described in this documentation, this documentation itself, and all programs and/or files written or modified by the application are supplied "as is." Responsibility for determining its suitability for any purpose rests solely with the user. The au- thor will not be held responsible for injury or damages resulting from the use of the application; all remedies rest solely with the user. The application is distributed without any warranties, express or implied, with this SINGLE exception: copies of the pro- gram files distributed on author-supplied disks will be replaced if the disk(s) prove defective. +=================================================================+ | LIMITED LICENSE | | =============== | | Individual users may make copies of the program files for | | backup and personal use. Individual users are also encouraged | | to distribute copies to others, provided that all files are so | | distributed in their entirety and without modification. | | Computer clubs may make copies for distribution, with the | | same provisions, and also provided that no fee in excess of a | | reasonable copying/media fee is charged. (Reasonable is taken | | to mean $10.00). | | Commercial distribution by "library" companies is subject | | to the same conditions imposed upon computer clubs. | +=================================================================+ +=================================================================+ | QBALL is distributed as user-supported software, ("Shareware"), | | and should be registered. See Appendix G for registration form. | +=================================================================+ COPYRIGHT INFORMATION --------------------- IBM, PC-DOS are trademarks of International Business Machines. MS-DOS, QuickBASIC, GW-BASIC are copyright, Microsoft, Inc. GRAFWIZ, PBCLONE, PTCLONE are copyright, Thomas G. Hanlin III. --------------------- [ QBALL -- Exterior Ballistics -- iii ] INTRODUCTION ------------ QBALL is a menu-driven application for the rapid computation of ballistic values for small arms projectiles. QBALL will quickly compute point-of-impact data, velocity and energy levels, trajectories relative to line-of-sight, and times of flight. Additional routines permit the calculation of ballistic coefficients, point-blank range, wind deflection corrections, sectional densities, impact variations for non-horizontal fire, and free recoil energy. Printing routines provide for the production of hard copy where appropriate. Starting values to which the program will default may be modified using the built-in configuration routines. It is assumed that QBALL users will have some knowledge of exter- ior ballistics. QBALL is not intended as a means of learning the subject; several of the references in the Bibliography contain basic introductions to ballistics. Study of the references will amply repay the effort involved. QBALL uses the "G1" drag function for computation of trajectory and other values. Appendix D of this documentation compares values from selected published tables with values calculated using QBALL. Warning! QBALL users are cautioned that data computed using the routines contained herein should be used as guides to the determ- ination of ballistic performance! Should the user be engaged in reloading small arms ammunition, it is incumbent upon the user to verify the values obtained using QBALL with a standard published reloading manual. Several such manuals are listed in Appendix C. The application title, "QBALL" does not in any way refer to the game of billiards; it's short for "Quick BALListics." Seemed appro- priate, somehow: QBALL's written in QuickBASIC. If you find QBALL of use, but would like it to do something that it doesn't do now, or have suggestions to improve what it does already, you are invited to send in a copy of the Enhancement Form. While no promises are made that your suggestion will be incorporated, the first person suggesting an improvement which is subsequently implemented will receive a free copy of the first release in which that improvement is implemented. The latest version of QBALL is available from the author for a $25.00 registration fee. Registration entitles the user to the most recent version with one free upgrade, and a 3-hole punched printed manual. The QuickBASIC 4.50 source code is available to registered users for $50.00. You may register and obtain the source code at the same time for $60.00. [ QBALL -- Exterior Ballistics -- 2 ] 1.3 Copying the program files. ------------------------- It is a good idea to make a copy of the original QBALL files, and keep it in a safe place. Run QBALL from copies of the original! Make sure that you copy both QBALL.CFG and QBALL.EXE to the same directory, or onto the same disk. QBALL.EXE will look for its associated .CFG file in the current directory. (Running the configuration routine writes the resulting .CFG file to the current directory.) If QBALL.CFG is not found, QBALL.EXE will default to its own internal values, so lacking the .CFG file is not fatal. (Just neater to put 'em both in the same place!) Put QBALL.DOC, QBALL.ODD, and QBALL.EVN wherever you can get at them. 1.4 Printing the documentation. -------------------------- QBALL.DOC is formatted to print with a wide-enough left margin to allow for puching to fit a 3-ring binder. There is no need to set your printer to print the IBM graphics set as in earlier editions; this version of the on-disk documentation uses only the low-order characters. You need not set your printer to skip perforations in fanfold paper; the document file contains the appropriate form-feed control characters. QBALL.DOC is an approximately 125K file. (That's 50 pages; plan your paper and time requirements accordingly!) There are two ways of printing the documentation: one is to copy "QBALL.DOC" to your printer; otherwise, copy "QBALL.ODD" to your printer, then flip the paper over, and copy "QBALL.EVN" on the backs of the same sheets. The second option saves paper, but requires that you do a bit more work. In either case, log into the directory or onto the disk where you've put QBALL.DOC, and enter the following: COPY QBALL.[DOC][ODD][EVN] PRN (Now go do something else. Each pass) (using the ODD/EVN option takes about) (25 minutes to print at 10 cpi, near-) (letter quality; a single pass takes) (just about double that. If you're in) (a real rush, print in draft mode... ) [ QBALL -- Exterior Ballistics -- 4 ] 1.6 Starting QBALL -------------- Log into the directory or onto the disk where you've put QBALL.EXE and QBALL.CFG, and type: QBALL (+ [Enter]). The next thing you'll see is this screen, here somewhat modified to permit printing it without using graphics characters: +++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ +=====================================================================+ | +=======+ + + + | | | | | | | | | | | | +===+ | | | | | | +===+ +===+ | | | | | =+ | | | | | | | | | +=====|=+ +===+ +===+ + + | | += Reg #0000SW | | [ Exterior Ballistics for PC's & Compatibles ] | | [ Using G1 Drag Functions -- version 2.0 ] | | [ Copyright (c) 1991 - Benjamin W. Hartley ] | +=====================================================================+ Welcome to computer ballistics with QBALL! QBALL provides small arms trajectory data quickly and accurately. Users are encouraged to verify QBALL data with a standard reloading handbook! The author will NOT be responsible for the misuse or misapp- lication of QBALL-generated data. ===> press any key <=== (-SAV) ++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ QBALL "honked" at you, didn't it? That simply means that QBALL could not find a specialized *.INI file; there isn't any right now, but you'll be writing one later. If you heard two tones, the opening screen should also be displaying "(-CFG)," indicating that QBALL.CFG wasn't found, either, and QBALL started with its internal default values. Two pieces of information which you should note from the initial screen: the Version, and the Registration Number. When you register your copy of QBALL, please include these numbers on your order. Press any key to continue. [ QBALL -- Exterior Ballistics -- 6 ] The most frequent use for QBALL will be the production of ballis- tics tables for a specific cartridge/load. With the menu shown on the screen, pressing "C" will open the menu for computation of ballistic or gun data. More information about using this option is contained in Chapter 2. If you wish to infer a ballistic coefficient, then press "B". More information is to be found in Chapter 3. "Change <D>isplay...", "D" provides a means to set display col- ors, the status of the printer and noise switches, and the values to which QBALL will default upon start-up. See Chapter 5 for more information about configuring QBALL. "<N>ew or Changed..." goes to a secondary menu which allows entry or modification of input data. We'll try this one a bit later. "Quit" -- press "Q" to return to DOS. QBALL will ask you to confirm that you indeed wish to quit. Press "Y" to return to DOS or press "N" to continue using QBALL. For right now, press "C" to compute ballistic data and to do the "tutorial" which follows. Go on to Chapter 2, page 7. [ QBALL -- Exterior Ballistics -- 8 ] 2.2 Computing and displaying a range table. -------------------------------------- Assuming everything is going as it's supposed to go, the screen will clear, and you'll be presented with this screen: ++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ > Ballistic Computations: Typical Firearm < +=================================+ | *** Computations Menu *** | | ------------------------------ | | <S>et/Reset Current Zero Range | | Range <T>able (0 MUST BE SET) | | <O>ther Ballistics Procedures | | <N>ew or Changed Input Data | | ------------------------------ | | <ESC> to M A I N M E N U | +=================================+ ---------------------------------------------------------------+ [ MV: 2300 ][ C1: .250 ][ Wt: 125 ][ Met: 59° 0' 29.53" 78% ]| | (Note: Info line shown) +---------------------+ ( "folded". ) +--------------- [ H: 1.00 ][Yds] ++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ AHA! All the spaces on the Info Line now have values in them, some of which you just entered, and some of which are the QBALL de- fault (or starting) values. "<O>ther Ballistics Procedures" are described in Chapter 5. As you can see, you can change the Input Data by using option "N" on this menu; for now, continue with what you've got. "ESC" will "back up" one menu; try it and see. Then remember to press "C" to get back here. The other two options are described in the following section. (From here on, the Screen Header line, which ) (tells you what cartridge/bullet you're deal-) (ing with, and the Info Line will be omitted) ( from the printed examples. ) [ QBALL -- Exterior Ballistics -- 10 ] This table is interpreted as follows: if, for example, a bullet having the given ballistic characteristics is fired at the given muzzle velocity, then, at a range of, say, 200 yards, it will retain 1693 FPS velocity, 795 ft-lbs of energy, will have dropped 16.2 inches below the line of departure, will have risen to a maximum of 1.8" above the line of sight, will have been blown 7.7" sideways by a 10 MPH crosswind, and will have taken 0.305 seconds to travel 200 yards downrange from the muzzle. Additionally, the height of the bullet above or below the sight line in both minutes of arc and inches is given at each listed range. Note that the tables displays "0.0" at 150 yards, the zero range. In similar fashion, data may be read from the table for each of the listed ranges. Should you try this procedure with a larger range, or a smaller range increment, QBALL will display as many lines as will fit on the screen, and display a prompt like this: ----------------------> More <-------------------. Press any key to continue with the next part of the table. The hardcopy print routines recompute the tabular data, so there is no need to be concerned with information which has scrolled off the screen. Put a marker in this page, and return to it to experiment later. Press "Y" to display graphics...(and turn the page). [ QBALL -- Exterior Ballistics -- 12 ] And here it is; you can access this menu from either the compu- tations menu, or the main menu. +=================================+ | *** New Input Data Menu *** | | ----------------------------- | | <C>artridge/Bullet Identifier | | Muzzle <V>elocity | | allistic Coefficient | | Bullet <W>eight | | <M>etro (dFnt 'Alt "Hg %RH) | | Sight <H>eight | | Yds/Mets <S>wap (Now Yards) | | ----------------------------- | | <ESC> to Computations Menu | +=================================+ In this instance, press "V" to change the muzzle velocity, and enter "2500" when prompted. You'll be returned to this menu; it is possible, but not recommended, to change more than one item of input data at a time. Note that the info line now reflects the new muzzle velocity. Press "ESC" to return to the computations menu. Now step through the process of setting the zero range (150), the maximum range for the range table (200), and the range increment (25). When prompted for graphics, press "Y." The information block now looks like this: +============================================+ | Current Previous | | Max Ht: 1.5" @ 86 mmediate | | Min Ht: -3.5" @ 200 <none> | | MuzVel: 2500 FPS | | BCoeff: .250 | | ZeroRg: 150 Yards | | Metro : Standard | | * = MaxHt | +==<Q>uit <S>ave <G>rid======================+ Now press "I" to display a graphic representation of the mmed- iately-previous trajectory data. Here's the new information block: +============================================+ | Current Previous | | Max Ht: 1.5" @ 86 1.8" @ 86 | | Min Ht: -3.5" @ 200 -4.5" @ 200 | | MuzVel: 2500 FPS 2300 | | BCoeff: .250 .250 | | ZeroRg: 150 Yards 150 Yards | | Metro : Standard Standard | | * = MaxHt * = MaxHt | +==<Q>uit <S>ave <G>rid======================+ [ QBALL -- Exterior Ballistics -- 14 ] At this point, either print the range table, or skip the print, and return to the computations menu, and we'll take a more detailed look at the "New or Changed Input Menu." 2.4 Changing Input Data. ------------------- Here's the "New or Changed Input Menu" again. +=================================+ | *** New Input Data Menu *** | | ----------------------------- | | <C>artridge/Bullet Identifier | | Muzzle <V>elocity | | allistic Coefficient | | Bullet <W>eight | | <M>etro (dFnt 'Alt "Hg %RH) | | Sight <H>eight | | Yds/Mets <S>wap (Now Yards) | | ----------------------------- | | <ESC> to Computations Menu | +=================================+ Let's see what each option does. Cartridge or Bullet Identifier. This option allows you to change the designation of the cartridge, bullet, or firearm with which you are working. Press "C" and enter a string of characters. (If you press enter at the prompt, it returns "Typical Firearm.") Muzzle Velocity. This, as has been seen, changes the muzzle velocity to be used. QBALL accepts velocities from 300 FPS to 4500 FPS, inclusive. Ballistic Coefficient. This allows changing the ballistic coeff- icient to be used, perhaps reflecting a different bullet or cartridge. QBALL will accept values greater than zero and less than or equal to unity (one). Bullet weight. Allows changing the bullet weight. Acceptable values are any number greater than zero. Metro. This one's got four parts; you are required to either confirm or change each of temperature, gun altitude, barometric pres- sure, and relative humidity. Pressing "Enter" at each input prompt uses "standard" metro. Acceptable values are as follows: a. Temperature : -50 to +125 Fahrenheit. b. Gun Altitude : -800 to 10000 feet. c. Barometric Pressure : 25 to 35 inches of mercury. d. Relative Humidity : 0 to 100 percent. [ QBALL -- Exterior Ballistics -- 16 ] Point-Blank Range. ----------------- The "point-blank range" for any weapon / ammunition combination may be defined as that range for which the trajectory deviates not more than a specified amount from the line of sight, either above it or below it. Press "P" to access the point-blank range determination routine. When prompted, enter maximum deviation = 3 (for 3 inches above and below the line of sight). The screen will look something like this: +++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ Determination of Point Blank Range ---------------------------------- Maximum Deviation 3 ---------------------------------- Trial Zero Range = 512 Yards +++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ After a pause, during which the trial zero range will change several times, the following will be displayed: ---------------------------------- Point Blank Zero Range = 179 Maximum Range = 207 ---------------------------------- ===> press any key <=== When you "press any key" you are returned to the computations menu, where you will observe that the zero range has been set to 179. You may now go ahead and develop a range table for this weapon/ammuntion combination, using that computed zero range. It is recommended that you use a range increment which will give you trajectory heights at even multiples of 50 yards. If you do so, you'll know how high to sight in your weapon at, say, 100 yards so as to be zeroed at 179, thus assuring a maximum deviation of 3 inches from the line of sight out to 207 yards. (The graphics routine, if invoked, will draw a horizontal line on the screen at scale 3 inches above and below the line of sight. These lines will continue to be displayed until you change the zero range.) And what does all this do for you? Well, with this "point-blank" zero, you can hold "dead-on" out to slightly more than 200 yards, and be assured that the bullet will strike no more than 3 inches high or low at any point along its path. Beats estimated holdover, don't you think? [ QBALL -- Exterior Ballistics -- 18 ] Slant Angle of Fire. ------------------- Virtually all firing tables and ballistics computations programs, QBALL among them, assume that the angle of fire in use is relatively close to horizontal. It is known, however, that firing "upslope" or "downslope" will effect the strike of the bullet: it will hit high relative to point of aim in both cases. How high? Press "A," and enter a maximum range of 400, a range increment of 100, and a vertical angle of 25 degrees. The following table will be displayed: +++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ Hits High for Slant Fire, 25d Above or Below Horizontal ----------------------------- Range True Hits Yards Drop High ----- ----- ----- 0 0.00 0.00 100 3.64 0.34 200 16.23 1.52 300 40.99 3.84 400 82.94 7.77 ----------------------------- ===> press any key <=== +++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ The table tells you that this weapon / ammunition combination, fired at a vertical angle of 25 degrees above or below the horizontal, will hit high by the specified distance for each listed range. The effect is relatively small for small vertical angles, but can become great enough to be of real concern, especially at relatively long ranges and at large vertical angles. Try several examples and see. (A clear exposition of the geometry of this problem may be found in the LYMAN Manual, listed in the bibligraphy.) Sectional Density. ----------------- The sectional densities of two or more particular bullets may be used to compare their relative penetrating power. Sectional density is defined as the weight of the bullet in pounds divided by the square of its diameter in inches. Press "S," and enter the bullet diameter in either inches or millimeters. QBALL assumes that any value you enter which is greater than "1" is in millimeters, and makes the con- version to inches. The dimension may be taken as the bore diameter of the weapon you are considering. This routine reports the sectional density of the bullet under consideration. This value is included in the Range Table printed header, but there is no specific routine to print just this value. [ QBALL -- Exterior Ballistics -- 20 ] Chapter 3 --------- Inferring ballistic coefficients """""""""""""""""""""""""""""""" From time to time, it may be desired to determine the ballistic coefficient of a particular bullet, and the available tables do not include that data. Select "Infer allistic Coefficient" at the main menu. (You will be encouraged to read this section of the manual, if you haven't done so already.) Press "Y" to continue with the routine. QBALL will ask for several pieces of information: basically, two ranges, and two velocities. This diagram will help you visualize the setup. |---[r1]----| ( >>>>>>> = bullet path ) |-----------[r2]----------| Gun >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> v@1 v@2 r1 = range, muzzle to first range r2 = range, muzzle to second range v@1 = velocity at first range v@2 = velocity at second range It is possible for r1 to equal zero; in that case, of course, v@1 would equal the muzzle velocity. (This is the only time that QBALL will allow you to enter a range of zero; "zero" is the default value for r1.) The routine for inferring a ballistic coefficient allows use of non-standard metro, should you have developed your own velocity data from live firing. You may change the metro conditions to be used before beginning to enter velocity data. The ballistic coefficient reported, however, is adjusted to standard metro conditions in all cases. You may enter as many as ten (10) individual range/velocity pairs. The average v@1, v@2, and ballistic coefficient are reported. If r1 is greater than zero, i.e., you are not working with a muzzle velocity, QBALL reports an inferred muzzle velocity. Let's work through the process. Refer to the table on page 9, and either copy the range and velocity figures, or run the range table routines and produce hard copy. We'll do this twice: once, with r1 set to 0, and once more with r1 set to 25; r2 will be set at 100 in both cases. [ QBALL -- Exterior Ballistics -- 22 ] 3.2 Second Run: r1 = 25 ------------------- Enter "first range" = 25 and "second range" = 100. When prompted for the velocities, enter 2218 and 1982. You should end up with the following display: ++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ For Round Number 1 First Velocity (Ft/Sec) 2218 Second Velocity (Ft/Sec) 1982 For Standard Atmosphere, C1 = .250 Calculate another Round? ([Y] or N) [ Lower & Upper Ranges (yards) 25 & 100 ] ++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ Again, press "N;" you don't want to calculate another round. The center of the screen will clear, and, after a short time for computa- tions, the following information is displayed: ----------------------------------------- Average C1 for 1 round = .250 Between Mean Velocities 2218 and 1982 Calculated Muzzle Velocity = 2300 ----------------------------------------- Press "N" to skip printing the table, and return to the main menu. Again note that the information line shows the calculated muzzle velocity and the inferred ballistic coefficient. You may now go on to calculate ballistic data using the values obtained using this routine; QBALL will continue to use this data until changed. This may have seemed like an exercise in futility: we did, after all, know what the ballistic coefficient was in the first place. Suppose, however, you have a ballistics table from, say, Winchester- Western, which includes only velocity data? Inferring a ballistic coefficient based on the published velocity figures will allow you to make your own "custom" firing table for a particular factory round. (Most ammunition manufacturers are noticeably reticent when it comes to some ballistics data.) Additionally, should you be reloading your own ammunition, and have access to two chronographs, you could make a custom firing table for your own custom ammunition. [ QBALL -- Exterior Ballistics -- 24 ] 4.5 Typical Printed Output. ---------------------- QBALL will print a "standard header" and a table title at the top of each table the first time you respond "Y" to the printer prompt. If the input data remains unchanged, QBALL will not print the standard header, but will print the table title. If one or more items of input data are changed, QBALL again prints the standard header, which looks like this: ====================================================== >>> Ballistic Computations for the Typical Firearm <<< ------------------------------------------------------ Muzzle Velocity = 2300 FPS Ballistic Coefficient = .250 Bullet Weight = 125 Gr Sectional Density = n/a Temperature = 59 deg F Altitude = 0 Feet Barometric Pressure = 29.53" Relative Humidity = 78% ------------------------------------------------------ For printed data tables, QBALL recomputes each line of data which appears or has appeared on the screen, so information which has scrolled off the screen may be printed. (This might occur, for exam- ple, if you've used a large range, and a small range increment.) In most data table cases, the format of the printed output is virtually identical to the screen display. And here's the printed output for the "Infer Ballistic Coeffi- cient" routine, using some of the same data we used in chapter 3: ============================================================ >>> Inferring Ballistic Coefficient for: Typical Firearm <<< ------------------------------------------------------------ Given the following meteorological conditions: Temperature..........: 59 deg F Barometric Pressure....: 29.53"Hg Relative Humidity....: 78 % Gun Altitude...........: 0 Feet Relative Air Density.: 1.000 Relative Sonic Velocity: 1.000 and the number of rounds shown, the ballistic coefficient (C1) was computed using the veloci- ties indicated. ---------------------------------------------- Round V1 V2 C1 ----- ---- ---- ---- 1 2300 1982 .250 ---------------------------------------------- Average C1 for 1 round = .250 Between Mean Velocities 2300 and 1982 Calculated Muzzle Velocity = 2300 ============================================== [ QBALL -- Exterior Ballistics -- 26 ] 5.3 Configuring display colors. -------------------------- Press "C". A special color configuration screen will appear. Pressing the appropriate keys will "step" through the available colors for background ("B"), main body text ("foreground," "F"), Highlighted text ("highlight," "H"), and for the Title/Info line ("low intensity," "L"). When you've found a combination that you like, press "ESC" to use the display colors you have chosen, and return to the configura- tion menu. Note that the currently chosen and the default color values are displayed at the bottom of the color configuration screen. If you get in a muddle, and want to start over again, press "D" to return to the default color settings. 5.4 Using the values you've set. --------------------------- Having set the display colors and toggles as you like them, and <ESC>-ing to the main configuration menu, you may: Use <T>his session only... ...or <W>rite QBALL.CFG File If you're sure of the values you've entered, press "W" to write a new QBALL.CFG file to the current directory. (And remember, if you change your mind, there's nothing to stop you from running Configur- ation again.) If you'd like to use the values for this session only, perhaps to see how they work out, press "T". ("ESC" has the same effect as "T" in this case.) If you decide later to save your "temporary" setup, choose "D" from the main menu, then choose "W" immediately from the configuration menu. QBALL doesn't care if there's a delay between choosing configuration values and writing an *.CFG file; it will quite cheerfully write a *.CFG file using whatever values are in effect at the time the "W" option is chosen. [ QBALL -- Exterior Ballistics -- 28 ] --------- N O T E S --------- [ QBALL -- Exterior Ballistics -- 30 ] CALIBER (or CALIBRE) - Technically, the diameter of the barrel mea- sured across the lands. In practice, the diameter of the bullet. A measure of length equal to bore diameter; thus, a "fifty caliber" barrel would be 50 bore diameters long. CARTRIDGE - Fixed ammunition, including case, powder, primer, and bullet, for small arms. See ROUND. CHAMBER - The breech, or rearmost portion of the barrel, which con- tains 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 and line of departure. Typically tabulated as ninety degrees, or "pure" crosswind with no range vector. QBALL takes left-to-right wind as positive. DRIFT - Technically, the distance a bullet will travel horizontally due to its spin. This effect is usually quite small, amounting to about 7 inches at 1000 yards for the military M2 Ball (.30-'06) car- tridge. Often confused with wind deflection. See WIND DEFLECTION. DEFLECTION - See wind deflection. 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. DROP - The distance a bullet will fall due to the influence of grav- ity. Measured from the line of departure, not the line of sight. ELEVATION - Vertical sight adjustment. Also, the (usually small) angle between the axis of a firearm's bore and the horizontal. ENERGY - Here, the kinetic energy of a moving bullet, usually given in ft-lbs. Equal to one half the mass of the bullet in pounds multi- plied by the square of the velocity in feet per second. F.P.S. - Feet per second. A unit of velocity. Also abbreviated as FPS and Ft/Sec. FT.-LBS. (Also FtLbs, Ft#) - Foot pounds. A unit of energy equal to the effort required to lift one pound, one foot. FORM FACTOR - A multiplier which relates a bullet's shape to that of the standard projectile used to prepare a particular ballistic table. [ QBALL -- Exterior Ballistics -- 32 ] MAXIMUM HEIGHT - The highest vertical distance above a line from the muzzle to the bullet's current position. Sometimes confused with midrange trajectory since it typically occurs about halfway between the muzzle and the target. Maximum height is usually somewhat higher and occurs somewhat further downrange than the midrange trajectory. METALLIC SIGHTS - Sights on a firearm which contain no optical ele- ments. MET - An abbreviation for "meter"; also, a super-abbreviation of "Meteorological Conditions." See METER, METRO, STANDARD MET METER (also METRE) - A unit of length measure equal to 39.37 inches, 3.28083 feet, or 1.09361 yards. METRIC - Having reference to length measurements based upon the meter, its subdivisions, or its multiples. METRO - Short for Meteorological Conditions; the air temperature, bar- ometric pressure, gun altitude, and relative humidity existing at the place and time of firing. See STANDARD MET. MIDRANGE TRAJECTORY - The height of the trajectory at a point halfway between the firearm's muzzle and the point of aim. M.O.A. - Minute of Arc. Equal to 1/60 of an angular degree. At 100 yards, 1 M.O.A. is approximately 1.047 inches. MUZZLE - The foremost point of a firearm's barrel; that part of a firearm closest to the target. MUZZLE ENERGY - Foot-pounds of energy developed by a moving projectile at the firearm's muzzle. MUZZLE VELOCITY - The speed of a projectile at the firearm's muzzle, generally expressed in FPS. N.R.A - National Rifle Association. If you shoot, you SHOULD belong to this organization. OGIVE - The curve of a bullet's forward portion. Also, the radius of this curve, usually expressed in calibers. POINT-BLANK RANGE - That range for which the bullet's path varies from the line of sight by no more than a specified amount for the entire trajectory from the muzzle to that range. 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. [ QBALL -- Exterior Ballistics -- 34 ] TARGETED RANGE - That distance furthest from the muzzle where the path of the bullet crosses the line of sight. (The "sighting in" distance.) TIME OF FLIGHT - The time necessary for a bullet to travel from the muzzle of a firearm to a given range. TRAJECTORY - The path of a moving projectile. Often expressed as the number of inches above or below the line of sight. WINDAGE - Horizontal, lateral sight adjustment. Also, the sight adjustment required to compensate for crosswind effects at a given range. WIND DEFLECTION - The amount of a projectile's horizontal lateral motion attributable to the action of the wind. Often mistakenly called drift. See DRIFT, WINDAGE YAW - Normally, a situation in which a bullet rotates on its axis at a small angle to the line of flight. ZERO - The sight setting at which point of impact and point of aim coincide at a given range. Also, the process of determining that sight setting. See also SIGHTING IN. [ QBALL -- Exterior Ballistics -- 36 ] Suppose you have determined a ballistic coefficient from pub- lished data, say, the Ballistics Section of "Gun Digest." Having the ballistic coefficient, use that figure to calculate a table showing the same data as the published table. If, for example, the resulting velocities are too high, then reduce the ballistic coefficient that you're using to, say, 90% of the value QBALL has reported. Recompute the table. If the resulting velocities are now low relative to the published data, increase the second ballistic coefficient to 95% of the value originally used. In similar fashion, continue to refine the value of ballistic coefficient until the QBALL results agree as closely as possible with the published data. In general, however, the process of successively refining a ball- istic coefficient will prove unnecessary. The very small variations introduced by differences between successive bullets in a string, variations in muzzle velocity, and, possibly, rapidly changing metro render the process of successive refinement superfluous. [ QBALL -- Exterior Ballistics -- 38 ] H O U S E K E E P I N G - - - - - - - - - - - - It is STRONGLY recommended that you either erase or rename all QBALLSAV files after each session. QBALL has no way of knowing whether saved trajectory data is from the session in progress or a previous session. There are two ways of going about this. First, at the DOS prompt, enter: DEL QBALLSAV.* This is the simplest way, and avoids confusing QBALL in a later ses- sion. (Yes, QBALL gets confused easily.) Second, and if you want to keep the trajectory data for later examination, at the DOS prompt, enter this: DEL QBALLSAV.INI and REN QBALLSAV.* QBALLOLD.* This preserves the data and gets rid of QBALLSAV.INI, but the current directory or the current disk may end up jammed with old data. One further hint: EACH QBALLSAV.00n file uses 5800 bytes of disk space, and the .INI file uses 3 bytes. That's a LOT of disk sectors; make sure you've got sufficient space in the current directory/on the current disk for better than 60K worth of files! QBALL will "hang" if there's an error writing to disk. [ QBALL -- Exterior Ballistics -- 40 ] Appendix E ---------- Error analysis """""""""""""" How accurate are the results obtained with QBALL? 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. Two ques- tions were to be answered: first, how well do velocity figures compare between the three sources?; second, are the trajectories found by the different sources comparable? Some difficulty was experienced in the choice of ballistic coeff- icients and velocities due to the differences between the two pub- lished sources. Speer, for example, rounds all ballistic coefficients to two decimal places, while Hornady carries three. In addition, when comparable values of ballistic coefficients could be found, the Horn- ady tables quite often did not have the spread of velocities available in the Speer manual. The following table summarizes as-comparable-as-possible data from all three sources. While severely limited, the data shows that the results obtained from QBALL are in substantial 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 | | | +----------------------------------------------------------------+ (Key: MuzVel = Muzzle Velocity C1 = Ballistic Coefficient) Table D1. Remaining Velocities With Given Inputs. Note should be made that the Hornady ballistic coefficients were actually .122, .259, and .496 for the three sets of data shown. This accounts for the apparent "high-on-low" spread of values seen here. QBALL was run with the bal- listic coefficients as shown. [ QBALL -- Exterior Ballistics -- 42 ] A close examination of the data in Table D2 shows that there is very close agreement between the QBALL results and the published data. The greatest variation is at the greatest ranges; this is to be ex- pected. Since the ballistic coefficients used in obtaining data from the Hornady tables are not exactly those chosen as typical, being "high-on-low" respectively, it is also expected that the resulting bullet strikes will be too small, "on", and too large. There is, how- ever, substantial agreement between the QBALL results and the data from both published tables. The actual bullet strike differences be- tween QBALL's results and the published tabular data is two or three tenths of an inch. This indicates that QBALL is capable of excellent practical accuracy. (One and one half inches at 400 yards) (is equal to three-eighths minutes-of-) (arc -- that's 22 1/2 SECONDS of arc!!) (If your rifle will group as tight as) (this -- let alone tighter -- you have) (an exceptional rifle, indeed! ) [ QBALL -- Exterior Ballistics -- 44 ] Error Messages (continued) -------------- +-----------------------------------+ | Enter -50 <= Temperature <= +125 | +-----------------------------------+ Attempting to enter a temperature value which is out of range. (In metro data entry, [enter] uses the STANDARD met value: 59°F.) (If you really need this program to operate with Arctic/Saharan temperatures, let me know! I'll custom- ize one for you.) +--------------------------------------+ | Enter 0 <= Relative Humidity <= 100 | +--------------------------------------+ Attempting to enter a relative humidity value which is out of range. (In metro data entry, [enter] uses the STANDARD met value: 78%.) +--------------------------------------+ | Enter 25 < Barometric Pressure < 35 | +--------------------------------------+ Attempting to enter a barometric pressure value which is out of range. (In metro data entry, [enter] uses the STANDARD met value: 29.53" Hg.) +------------------------------------+ | Enter -800 < Gun Altitude < 10000 | +------------------------------------+ Attempting to enter a gun altitude value which is out of range. (In metro data entry, [enter] uses the STANDARD met value: 0 feet - sea level.) +--------------------------+ | Enter Bullet Weight > 0 | +--------------------------+ Pressing [enter] when bullet weight is prompted for; alter- natively, you're attempting to enter a zero bullet weight. +-------------------------------------+ | Enter -2.0 <= Sight Height <= +5.0 | +-------------------------------------+ Pressing [enter] when sight height is prompted for; alter- natively, attempting to enter a value which is out of range. +------------------------------------------+ | Enter Second Velocity < First Velocity | +------------------------------------------+ In inferring ballistic coefficients, attempting to enter a downrange velocity which is larger than the velocity closer to the muzzle. (Rocket-assisted bullet, maybe?) [ QBALL -- Exterior Ballistics -- 46 ] If, for some reason, QBALL.EXE cannot find QBALL.CFG (either QBALL.CFG doesn't exist, or it's not in the current directory) QBALL will start with its default values, which are made available inter- nally through an error-trapping routine. Should you be VERY brave, you can modify QBALL.CFG with any text editor which will produce plain vanilla ASCII files. THIS IS NOT RECOMMENDED; better by far to use the QBALL configuration routines. (There are those who would say that) (using a text editor to modify a .CFG) (file isn't brave; it's foolhardy!) [ QBALL -- Exterior Ballistics -- 48 ] Continue comments, if desired