6.0 Sierra’s Infinity Exterior Ballistics Software
This section presents an overview description of Sierra’s Infinity software for personal computers. The description includes key features, modes of operation, and tables and graphs which the program provides.
Features of Infinity
Infinity incorporates a number of significant features. They include: • Provisions for determination of a reference trajectory for each of five bullets on a sight-in range which may either be level or not level.
• Atmospheric corrections along the bullet trajectory for uphill or downhill shooting.
• An extensive Database which contains the necessary information (Ballistic Coefficients and applicable velocity ranges) for the bullets of all leading manufacturers.
The Exterior Ballistics Section of our previous manuals has given you a brief history of Ballistics, the significant factors that affect the flight of a bullet and how those factors are used in determining how the bullet “flies.” We have used all of these factors and the most accurate mathematical methods available in developing Infinity and the information that it computes and prints. Our intent has been to develop software that computes information to be used by both the serious competitive shooter and the “once-a-year” hunter. We hope we have succeeded in making this information truly useful to you.
The Sierra Ballistics Program, Infinity, computes all essential elements of a small arms trajectory for any bullet that has a Ballistic Coefficient referenced to the “G1” drag function and for any set of firing conditions. The program has eight computational modes of operation, and it performs these operations on any one of five selectable (active) bullets at any time. In the first operation, the Trajectory computation operation, it computes downrange, vertical, and crossrange positions and downrange, vertical, and crossrange velocities in slant range coordinates referenced to the extended bore line of the gun. That is, it performs the trajectory computations for level or non-level shooting and refers the data to the direction in which the shooter is pointing the bore of the gun. It also computes time of flight, energy, momentum and wind deflections. It does these computations for specifiable atmospheric conditions, altitudes and wind conditions. This operation permits the selection of 10 different tabular printout formats. There are ten individual tabular printouts that are available to the user in the normal Trajectory operation. The Uphill-Downhill and Trajectory Variations operations present two additional tabular printouts that are similar to the basic trajectory table but show the parameter changes resulting from the changed shooting conditions. The remaining operations provide unique textual or tabular material that relate to that particular operation. We recommend that you select your favorite bullet and run trajectories with each of the tabular modes to examine the data on each.
The second operation in the Operations menu computes Point Blank Range for a game animal (or target such as a silhouette) for the case where a gun is already zeroed at a specific range. The third operation computes the Maximum Point Blank Range for a given game animal and the necessary zero range to use to achieve this maximum.
The fourth operation, Uphill-Downhill, computes the bullet path difference for the case of zeroing in on a reference range and then shooting later at an elevated or depressed firing angle. This is an important situation for hunting.
The fifth operation, Calculate Zero, calculates the zero range for the case in which a gun shoots high by a measured amount on a target at a measured distance from the muzzle. This is an important situation for many hunters and target shooters.
The sixth operation calculates the Maximum Range of a bullet along a given slope angle, which can be chosen as positive (uphill), zero (level fire), or negative (downhill). This operation also calculates the elevation angle of the muzzle (referenced to level) to reach the maximum range along the chosen slope.
The seventh operation, Vertical Fire, utilizes a special case of the equations of motion to calculate the maximum altitude that a bullet can reach if fired vertically.
The eighth operation, Trajectory Comparisons, is designed to answer a variety of “what if” questions. It calculates variations from a reference (or baseline) bullet trajectory caused by variations in shooting conditions. This operation is very useful to determine sensitivities of trajectory parameters to changes in shooting conditions. It permits the user to determine the trajectory characteristics of varying bullet and environmental parameters without destroying the initial trajectory parameters.
Although the program operates in normal English units to accommodate the G1 Drag function, it handles full metric input and output units, or mixed mode units for some of the current shooting games where ranges are in metric units and all other values are in English units. The Units mode is selectable on the Trajectory Parameters panel of the Trajectory operation.
The program calculates all basic trajectories in 1-yard (or meter) increments to the specified Maximum Range specified on the Trajectory Parameters sidebar or to a maximum of 8000 yards (meters). The printout values, zero ranges and maximum ranges can be any multiple of one yard (or one meter). The printout ranges will be multiples of the Range Increment specified on the Trajectory Parameters panel with the exception of the Silhouette tables. All computed values for maximum range, point blank range, etc. are computed to one yard. In order to prevent computational overflow in the equations, we have included a computational limit when the bullet drop reaches a value which exceeds 9 feet within 3 feet of downrange travel. A special note on the table will be printed when this limit is exceeded, and the Maximum Range value in the Trajectory Parameters panel will be set to this number.
The only operating restrictions we have placed on the user are ones that are necessary for proper mathematical and program function. It is incumbent upon the user to assure that his operational conditions are what he desires prior to computation. It is easy, for example, to run a trajectory at an altitude of 10000 feet and a non-standard temperature condition with a vertical wind of 20 miles per hour when what is really wanted is a trajectory at 1000 feet altitude with no winds. While we have tried to print all conditions on the outputs, the results can be misinterpreted if the user is lax or in a hurry when computing. It is easy, of course, to correct the input value and re-run the calculation.
The basic means of navigating the software and the functions of each operation will be discussed briefly below in order to get you started. Any restrictions on your use should be self-explanatory with error messages requesting different input or by having the controls visible only when they are applicable.
When you first start the program, a title displays the necessary credits while the initial information for the screens and computations loads. The time-consuming operation during this period is the loading of the information computed during the last session. (On Initial start-up, we provide a pre-computed data set using the Sierra Bullets we love the most.) This data set contains the complete trajectory information, including the bullet trajectory and environmental parameters with which each trajectory was computed, for the five active bullets last used in the program. Thus, the user can resume operations where the last session ended.
Once these data have been loaded, the initial screen appears with the menu and toolbars. The program initializes in the Trajectory operation showing the Trajectory Parameters panel on the right side of the monitor and with the Current Bullet from the last session highlighted in the Active Bullets window. The Menu bar operates just as the normal MS Windows or MS Office menu bar in that left clicking on a menu item drops down the sub-menu items that can be performed. An example of this can be found by left clicking on the Operations menu item to drop down the available operations (Trajectory Calculation, Point Blank Range Calculation with a Given Zero, Maximum Point Blank Range Calculation, Elevated Fire, Calculate Zero, Maximum Range Calculation, Vertical Fire and Trajectory Comparison). Right-clicking the mouse with the cursor located anywhere on the left panel of the screen and outside a defined window will bring up the same Operations in a panel on the screen. A similar function (Right-Click) has been included in the right panels to switch between the Trajectory Parameters panel and the Environment Parameters panel. The user may select any of these operations to perform.
If the user has selected a new bullet or has not run a baseline trajectory on a new bullet and one is required for the commanded operation, the baseline trajectory will be run automatically prior to performing the commanded operation. The baseline trajectory will be run using the values specified in the Trajectory Parameters and Environment Parameters panels located on the right portion of the screen. Thus, the user should review these panels when a new bullet is loaded to assure they are consistent with the bullet.
While selecting and loading a new bullet from the Load Bullet menu item should be self-explanatory, it should be noted that loading a new bullet replaces the currently selected (highlighted) bullet. With the exception of the parameters unique to the specific bullet (and a typical muzzle velocity) the new bullet will receive the same trajectory and environmental parameters that were present for the bullet being replaced. For example, if the bullet being replaced was run with a 1000 yard maximum range, the bullet replacing it will also have a 1000 yard maximum range. This may be undesirable for a bullet like the .458 diameter 300 gr. Flat Nose for the .45-70.
Placing the cursor on any individual button on the toolbar just below the menu bar will bring up a label that defines the button’s functions. Reading from the left, the first button will permit editing a custom bullet. The second will print. The third is reserved for a Print Preview function. The fourth button will return to the chart (table) mode when available, and the fifth button will switch from the chart mode to graphics output when available. The sixth button will hide/show the data entry panels for those users with 640 x 480 screens to permit viewing of the entire output box. Note that a trajectory must be calculated prior to utilizing the graphics output mode. The next command buttons are only effective in the graphics mode to add/remove the trace label box, add/remove grids, add/remove labels on the graph, and zoom the graph.
The Trajectory operation is designed to calculate the baseline trajectory of a selected bullet. It handles an elevated fire case where the shooting range is not level. It will handle up to +/- 65 degrees. The results are stored into the current bullet locations as the baseline trajectory for that bullet. You may change the information as defined on either the Trajectory Parameters panel or the Environment Parameters panel as you desire. However if you change anything, you must left-click the Accept Data control to make the change effective. You must then left-click the Calculate control to calculate the trajectory.
There are two operations associated with Maximum Point Blank Range. The first calculates the Maximum Point Blank Range of your weapon as you have zeroed it. That is, given that you choose a vital zone for your target or game animal and you have zeroed your gun in for a specific range, this operation will calculate whether your zero is such that the bullet will rise farther than one-half the vital zone height above your line of sight prior to reaching your specified zero range (point blank zero less than your zero range), and when it will be more than one-half the vital zone height below your line of sight at ranges farther than your zero. It will also determine if your zero range is less than the zero range for maximum point blank range. In either case, the maximum point blank range is determined for your gun as sighted.
The second operation associated with Maximum Point Blank Range determines what the optimum zero range is to maximize the point blank range of your particular bullet given any reasonable vital zone height. We arbitrarily determined a limit of 36 inches for the vital zone height assuming that some hunters might be going after the few elephants left! The operation is performed on your selected bullet and its baseline trajectory.
The Uphill-Downhill operation calculates the difference between your reference trajectory (which may have been computed for a non-level range) and the elevated (or depressed) firing angle. The printout will define the bullet path difference directly as a separate column in the tabular output. The remaining values in the table (remaining velocity, energy etc.) are based on the new trajectory at the new elevation angle so that the remaining differences at the elevation angle can be calculated from the reference trajectory output data. The reference trajectory is not destroyed so repetitive trajectories can be run without changing the reference trajectory.
The Calculate Zero operation is designed to answer the question “I’m sighted in “x” inches high at “Y” yards. What’s my zero range? The program permits measured bullet path height input to .01 inches (for those purists who believe that they can reliably determine the centroid of their group to .01 inches) and range increments of 1 yard out to 1000 yards. Only positive (above the line of sight) values are accommodated.
The Maximum Range operation computes the maximum range of your selected bullet given the environmental conditions of your site (altitude, temperature, pressure and humidity), a reference slope angle, and the muzzle velocity of your bullet. The reference slope angle is designed to support determining whether the bullet will clear an object or not. The Maximum Range is determined with respect to this slope. A zero–degree value is level fire. The program outputs the maximum range along the reference slope and the bore elevation angle with respect to level (horizontal direction) necessary to achieve it.
The Vertical Fire operation determines the maximum altitude that the selected bullet will reach given the muzzle velocity, firing point altitude, and environmental conditions defined by the user. This is a special algorithm for vertical fire. Since winds may vary in direction and magnitude at different altitudes (and almost always do!), there is no provision for wind. The program outputs maximum altitude in feet (or meters) above sea level, maximum height above the firing point, time of flight to the maximum point, and the environmental conditions at the firing point.
The Trajectory Comparisons operation permits graphic comparison of up to five bullets. The values that can be compared graphically are remaining velocity, remaining energy, drop, bullet path and wind drift. Only trajectories with like computational units (English or Metric) can be compared. Since the graphs are plotted in 1-yard (or meter) increments, printout range increments, maximum ranges and zeros need not be the same. The zoom function clearly makes the value labels on each plot more readable, although for closely matched bullets it still requires some interpretation.
The Trajectory Variations menu item permits a “what if” function. It is much the same as the Uphill-Downhill operation in that the reference trajectory is preserved for all calculations. The output table gives a specific bullet path difference column for the difference between the reference trajectory and the trajectory computed with the variations input data. The values in the body of the table are for the trajectory with the variations included. Note that there are four panels of information that can be varied to observe the effects on the bullet trajectory. Graphic output is available showing the velocities for both the reference and the variations trajectory. Those of us who hunt at altitudes and in weather conditions other than those at which we sight-in, use this operation to get an accurate feel for where the rifle shoots under real conditions.