The Model Scope Adjustments
Chronograph Distance Calculation of Scope Corrections from Target Data Scope Calibration and Cant Analysis
Rifle Geometry
While many trajectory tables and other tools have either a predefined difference
between LOS and bore line (tables are typically done for one such Scope Height), we are
not aware of any that use this for other than error from LOS calculations. On Target
uses this information to calculate the angle between the plane of the bore and the plane
of LOS when a Sight in Range is defined. While very small (0.0526054 degrees for
John's BAR on the Preview page), this angle determines the velocity component in the
vertical direction. Since those that deal in "trajectory" solutions
utilize the well known G1 model for calculations, this angle is never known.
The Barrel length for the rifles you define is a part of the Rifle Definition.
This allow On Target to calculate the actual muzzle velocity for the rifle from
cartridge data which has its own barrel length used by the manufacturer in specifying the
velocity.
On Target is not "bullet" based...it is Rifle based. You must define
the geometry of your rifle in order to understand how it will perform. While
obviously exaggerated, the diagram below clearly shows how this angle is affected by both
scope height and sight in range.
For years, the G1, and sometimes G5 and G7, tables have
been used to define the trajectory of a bullet. In fact, published Ballistic
Coefficients are based on the G1 model. Some manufacturers will provide data for
their bullets giving the G1 based Ballistic Coefficient for different velocities. On
Target utilizes a proprietary model that calculates bullet dynamics every 100 microseconds
of simulated flight. The model incorporates factors that continuously compute
aerodynamic forces as a function of atmospheric conditions and velocity. The result
is a continuously adapted Ballistic Coefficient.
The use of this sophisticated model has two profound
results:
Precision is not compromised.
Don't try to run on an old
486!
Not enough MIPS.
The number of factors that will affect a bullets
trajectory are large. They include buoyancy, gravitational changes due to latitude
and altitude, coriolis changes due to latitude, humidity, air density, temperature, etc.
Any factor of significance is incorporated in On Target's unique model.
Since On Target computes the angle between the plane of the bore and the plane of
LOS, and uses this as the basis for all calculations, changing this angle by adjusting the
MOA (clicks) on the scope allows On Target to calculate the impact of such changes.
Actually, when a shooting objective is defined (say, dead-on at 400 yards or
perhaps a maximum error of 3 inches), On Target will increment/decrement the MOA
using the precision of your scope
and run its model until the objective is achieved. The equations used in this
sophisticated model do not lend themselves to closed form solution, thus each shooting
objective can result in millions of calculations being performed to determine a unique
solution. Fortunately, PC's can accommodate this need with ease today. Ten
years ago during the early development of On Target's model, engineers would wait 10-15
minutes for a result. Today, this is measured in fractions of a second.
The linear change at a given range for one MOA change in your scope is a function of
the basic geometry of the rifle, the cartridge being fired, the BC of the bullet and
atmospheric conditions. It is not a constant, though some assume it is. Change
your scope clicks and the velocity in the vertical direction changes, changing the
velocity in the horizontal direction. The bullet arrives at a fixed location after a
different TOF (time of flight), and with a different rate of change in the vertical plane.
So, how many clicks per inch...the model must shoot under these new conditions to
find out!
While cartridge manufacturers have done an outstanding job of producing cartridges
with minimal variation in either BC or muzzle velocity, these variations are not zero.
Published muzzle velocities are also based on a "typical" rifle, as they
must be. While fine for most shooting objectives, precision long distance shooting
requires that the muzzle velocity be accurately determined for a cartridge/rifle pair.
I have been told that there are two kinds of people that have chronographs:
those that have shot them and those that have not used them. For that reason,
we tend to place our chrono close to the muzzle. However, muzzle blast will cause
both damage and erratic reading from the chrono, so we adopt something between 10-30 feet
as a reasonable distance.
Assume we are at the 10 yard point. What we are really measuring is the
velocity in the plane of the chronograph, not the total velocity, and we are measuring it
after the bullet has slowed down for 10 yards. While the former error is
insignificant except in the cases of obscure scope heights, the latter can...and
does...introduce errors ranging from 0.5% to 1.5%. Although small, these errors will
compound should one attempt to use, say G1, to determine a BC. On Target utilizes
your defined distance to the chrono and rifle geometry to calculate what the velocity
would have been at the muzzle...not 10 yards away! This seemingly minor error can
result in a totally missed target at long ranges if not considered in the computations.
By use of its sophisticated model, and knowledge of your rifle geometry, On Target
is able to determine the precise scope adjustments required to move your point of impact
(POI) to the bullseye! It does not store any "standard" for the affect of
scope changes at a given range. This is calculated by On Target for your rifle,
cartridge and conditions.
A statistical analysis is performed on your entered shot pattern. If On Target
detects shots outside a statistical limit, it will identify them, and ask the shooter if
they want to eliminate those shots from the resultant corrections computations. It
will then utilize its model, making adjustments equal to your scope resolution, until
errors from dead-on are minimized.
This feature of On Target allows you to
determine the actual change in Minutes of Angle that result from a specified change in
your scopes elevation setting.
It functions by first having the shooter enter a
shot pattern from target data. Any range less than 200 yards can be used, but we suggest
50 yards due to wind effects. On Target will then determine the statistical center
point of that group.
The shooter than sets a number of click/divisions
of adjustment in his scope elevation. If the original group was high relative to bullseye,
he would move his point of impact down, say 4 MOA (16 clicks on a ¼ MOA/click scope), and
shoot another group. After entering this group pattern and the number of clicks the
elevation was moved, On Target will calculate (based on the cartridge, rifle and
range) the actual resolution of the scope.
If the analysis indicates that the rifle was
Canted, On Target will give a message stating which direction the rifle appears to
be canted.
This feature is initiated by clicking on the
Calculate menu item, and then clicking on Scope Calibration.
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