External Ballistics Calculator
A Ballistic Spreadsheet
This free download from Owen Guns will give a lot of answers to ballistic questions by shooters who have a computer with either Excel or OpenOffice.org installed. To obtain a copy of the FREE Ballisctics Calculator, please send an email to owenguns@spiderweb.com.au with the subject line “Ballictics Calculator”.
By entering values for any practical combination of MV (or velocity at a nominated range), Ballistic Coefficient, Bullet Weight, Sight Height (scope above bore), a desired Zero Range, and the actual target ranges you are interested in, the spreadsheet will instantaneously display ballistic predictions at those ranges. Remaining velocity and kinetic energy, drop from line of departure, bullet path above or below line of sight, and the bullets time of flight are given in metric and Imperial units. If you also care to nominate a crosswind speed in metres per second, deflection at each nominated range will be given, in metres, inches, and MoA, along with the wind strength equivalent in Km/h, MPH, or Knots.
Inputs for range can be entered in metres, yards or both and output can be selected to display either or both in combination with the predictions for those ranges also in the desired measurement units for printout.
A lot of questions can be answered by working the process backwards. For instance published ballistics for factory ammo are based on a MV that is often higher than shooters find when they test the ammo in a shorter barrel over a chronograph. In this case the implied BC of the factory projectile can be found by getting the spreadsheet (usually in the “G1” drag model worksheet) to mimic the published ballistics. This is done by nominating the same MV and increasing or decreasing the BC value as required to obtain the same remaining velocity at the furthest range given. If the manufacturer also used the G1 drag model (the de facto standard) the remaining velocity at intermediate ranges should match also. With the BC found this way you then simply nominate the actual chronographed velocity and the range of the midpoint of the screens (the Range X input), and you’ll get a set of more realistic downrange predictions at any of the ranges that you want.
Other calculations such as finding how hard a particular bullet has to be driven to deliver a desired amount of kinetic energy at a certain range can also be worked in reverse by trial fitting the MV. It is possibly even more interesting to find where the other Zero Range is. The usually nominated Zero Range, at 200 metres for instance, is where the bullet falls back across the line of sight after which it hits ever lower as range increases. But where does the bullet first cross the line of sight as it climbs from the muzzle, which is, for practical purposes, at the “sight height” distance below? By trial and error on one of the range input cells you’ll soon find this other point where the bullet crosses the line of sight and the bullet path value comes up “0.0”, the short range zero.
Currently there are numerous ballistic programs available for PCs but the better ones cost money and may offer little advantage in practical terms over this free file (BallisticSS.xls) that adapts common spreadsheet software to the same purpose. BallisticSS has an advantage of its’ own in that the output can be shuffled in different combinations of columns containing the most useful values for the job at hand. For instance you could show just Bullet Path data in the desired units for uncluttered use in the field. Or you might include a “Remaining Energy” column if theoretical comparisons are to be made about target damage. Being able to nominate any particular shooting distance (range) is also likely to be an advantage over some bought programs that are restricted to even increments of range.
Hatcher’s Notebook, first published in 1947 describes how drag functions work, It also describes how to construct a table of space (range) and time values from them corresponding to decrements in velocity. These decrements are caused by the atmospheric drag acting on the standard projectile at a standard pressure, temperature, and humidity. Applying a particular bullets’ BC as a factor to space and time intervals for the standard projectile (which has a BC of 1.0 ) allows predictions to be made for the bullet of known BC. Things have moved on since those pre-computer days. The same principles apply but the application is so much easier that there is no reason not to follow ones’ curiosity about practical ballistic questions.
There are sources, on the internet, for retardation functions for all the commonly known drag models including the one for Krupp’s 1881 standard projectile the, basis of Mayevski’s work that was then adapted to Imperial units by Ingalls for his table published in Hatcher’s Notebook.
The third edition, second printing of Hatcher’s Notebook, lists retardation functions (in log form) on page 559 and the method of finding drag at a particular velocity, and thereby the distance and time increments as velocity decreases on pages 565 to 567. With the power of spreadsheet software you can make a three column table for velocity in 1 fps decrements with corresponding distance and time increment, (3600 rows in the case of Ingalls) in a matter of minutes. A whole new ballgame from the days when Julian S.Hatcher’s book was first published in 1947….After creating such a table on a spreadsheet there remains the task of extracting and processing data from such long columns. This turns out to be a breeze as soon as the LOOKUP function is applied.
As well as the Krupp-Mayevski-Ingalls version Hatcher’s book also gives the retardation functions for the British 1909 tables so tables for this model can also be easily replicated on a spreadsheet in the same quick and easy manner. Hatcher mentions the origin of the now widely used G1 model but does not list it’s retardation functions. These are available by Google search which leads towww.snipercountry.com/ballistics/index.html.One advantage of the G1 model is that it covers velocities above 4230 fps. Just how far above is uncertain but BallisticSS applies the top retardation function to over 5000 fps with the idea that at least it would provide some approximations at that extreme level. Another advantage is that the G1 drag model is now by far the most popular one in the sporting arms industry.
Presently the spreadsheet will calculate results by the G1, Ingalls, and British 1909 models, each on its’ own separate worksheet. All three are similar, having a standard projectile of the same sectional density, but are apparently different enough in form factor (or accuracy of original test data) to require slightly different Ballistic Coefficients to be determined for a particular bullet. A fourth worksheet called “G1 Sierra” is included. It is the same as G1 except there is provision for inputting various values for BC in different brackets of the velocity spectrum in the manner advocated by the bullet maker Sierra. Based on their own tests they publish these varying BC values for the bullets they make. So why not use them if it will improve accuracy in the calculated data?
Lots of other commercially available bullets have their BC stated by their manufacturer in either the Ingalls or G1 model, mostly G1 nowadays. If a bullet’s BC in one drag model is known it is simple to arrive at a figure in another by trial guessing it till you get the same velocity drop over the same distance. Likewise, as explained above, a BC can be found from manufacturers published ballistics for factory loaded cartridges. This will enable the calculation of better info if your rifle or pistol produces a different MV than the one published. This will usually be the case, especially if your gun has a different barrel length than the factory test gun.
Regardless of which drag model is used to find remaining velocities (and time of flight), the subsequent calculations for Kinetic Energy, Drop, Bullet Path, and Cross Wind Deflection are all done with the same formulas that are normally used to produce published ballistics. In addition to the worksheets for each of the drag models mentioned there is a supplementary worksheet that provides an easy way to calculate an unknown BC from a known SD and shrewdly estimated Form Factor, or to use a known BC to calculate a Form Factor etc.. there is also provision for calculating a change in the value of a BC due to temperature and or barometric pressure varying significantly from standard conditions.
The file BallisticSS-20090906.xls runs in the popular Microsoft Excel. If you don’t have that software check out OpenOffice.org which is free and includes spreadsheet software that will also handle the .xls format.
As supplied the area to the left of column “S” in the various drag model worksheets is “protected” with only the red numbers and text changeable as user inputs. This avoids accidentally disrupting cells with formulas or fixed data. “Protected” status can be removed without a password via the “Tools” menu if constructive changes are needed. Save an original version somewhere in case your modifications don’t turn out well.
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