Sierras Infinity Exterior Ballistics Software
This section presents an overview description
of Sierras Infinity software
for personal computers. The description includes key features, modes
of operation, and tables and graphs which the program provides.
Features of Infinity
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
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
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
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 buttons 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.
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.
Zero operation is designed to answer
the question Im sighted in x inches high
at Y yards. Whats 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.
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.
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.
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