U.S. patent application number 16/239105 was filed with the patent office on 2020-03-19 for ballistic wind correction to improve artillery accuracy.
This patent application is currently assigned to United States of America, as represented by the Secretary of the Navy. The applicant listed for this patent is William Arthur Kenney. Invention is credited to William Arthur Kenney.
Application Number | 20200088498 16/239105 |
Document ID | / |
Family ID | 69772402 |
Filed Date | 2020-03-19 |
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United States Patent
Application |
20200088498 |
Kind Code |
A1 |
Kenney; William Arthur |
March 19, 2020 |
Ballistic Wind Correction to Improve Artillery Accuracy
Abstract
A computer-implemented method is provided for implementing wind
correction for a projectile launching gun aiming at a target on a
gun fire control system on an aircraft. The fire control method
includes obtaining first physical parameters; executing a
ballistics model to obtain a flight path of the projectile;
obtaining number of points for wind direction and velocity across
altitudes; executing a tracker model to obtain tracker location and
initial gun state; obtaining closure tolerance and
cross-correlation factor; modeling wind prediction to obtain a
predicted wind column; incorporating the predicted wind column for
wind column prediction for a projectile effect; and applying the
projectile effect to the fire-control processor to adjust aiming
the gun. The first physical parameters include wind column, gun
state, ammunition type and aircraft flight conditions. The
ballistics model obtains a flight path of the projectile based on
the first physical parameters. The tracker model is based on the
number of points and the flight path. The wind prediction is based
on the closure tolerance, the cross-correlation factor, the tracker
location and the initial gun state. The wind direction and velocity
are obtained from multiple measurements or alternatively from a
single-point measurement.
Inventors: |
Kenney; William Arthur;
(Spotsylvania, VA) |
|
Applicant: |
Name |
City |
State |
Country |
Type |
Kenney; William Arthur |
Spotsylvania |
VA |
US |
|
|
Assignee: |
United States of America, as
represented by the Secretary of the Navy
Arlington
VA
|
Family ID: |
69772402 |
Appl. No.: |
16/239105 |
Filed: |
January 3, 2019 |
Related U.S. Patent Documents
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Application
Number |
Filing Date |
Patent Number |
|
|
62730745 |
Sep 13, 2018 |
|
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Current U.S.
Class: |
1/1 |
Current CPC
Class: |
F41G 3/22 20130101; F41G
3/142 20130101; F41G 3/08 20130101; F41G 5/18 20130101; F41G 3/10
20130101 |
International
Class: |
F41G 3/08 20060101
F41G003/08; F41G 3/22 20060101 F41G003/22; F41G 3/10 20060101
F41G003/10 |
Goverment Interests
STATEMENT OF GOVERNMENT INTEREST
[0002] The invention described was made in the performance of
official duties by one or more employees of the Department of the
Navy, and thus, the invention herein may be manufactured, used or
licensed by or for the Government of the United States of America
for governmental purposes without the payment of any royalties
thereon or therefor.
Claims
1. A computer-implemented wind correction method on a fire-control
processor operated by a gun aiming system on an aircraft for a
projectile launching gun aiming at a target, said method for said
processor comprising instructions for: obtaining first physical
parameters for wind column, gun state, ammunition type and aircraft
flight conditions; executing a ballistics model to obtain a flight
path of the projectile based on said first physical parameters;
obtaining number of points for wind direction and velocity across
altitudes; executing a tracker model to obtain tracker location and
initial gun state based on said number of points and said flight
path; obtaining closure tolerance and cross-correlation factor;
modeling wind prediction based on said closure tolerance, said
cross-correlation factor, said tracker location and said initial
gun state to obtain a predicted wind column; incorporating said
predicted wind column or wind column prediction for a projectile
effect; and applying said projectileeffect to the fire-control
processor to adjust aiming the gun.
2. The method according to claim 1, wherein said aircraft flight
conditions include attitude, bank angle and speed of the
aircraft.
3. The method according to claim 1, further including: obtaining
type, speed and direction of wind; and executing a wind model to
obtain said wind column based on said wind type, said wind speed
and said wind direction.
4. The method according to claim 1, further including: obtaining
attitude, bank angle and speed of the aircraft; and executing an
aircraft model to obtain aircraft flight conditions based on said
attitude, said bank angle and said speed of the aircraft.
5. The method according to claim 1, wherein said wind direction and
velocity are obtained from multiple measurements.
6. The method according to claim 1, wherein said wind direction and
velocity are obtained from a single-point measurement.
Description
CROSS REFERENCE TO RELATED APPLICATION
[0001] Pursuant to 35 U.S.C. .sctn. 119, the benefit of priority
from provisional application 62/730,745 with a filing date of Sep.
13, 2018, is claimed for this non-provisional application.
BACKGROUND
[0003] The invention relates generally to wind correction for
ballistic projectiles. In particular, the invention relates to
incorporation of multiple data points to compensate for errors from
wind effects on ballistic trajectories.
SUMMARY
[0004] Conventional wind corrections for ballistic flight
predictions yield disadvantages addressed by various exemplary
embodiments of the present invention. In particular, various
exemplary embodiments yield wind corrections based on ballistic
influence from empirical wind profiles. These embodiments provide a
computer-implemented method for implementing wind correction for a
projectile launching gun aiming at a target is provided on a gun
fire control system on an aircraft. The fire control method
includes obtaining first physical parameters; executing a
ballistics model to obtain a flight path of the projectile;
obtaining number of points for wind direction and velocity across
altitudes; executing a tracker model to obtain tracker location and
initial gun state; obtaining closure tolerance and
cross-correlation factor; modeling wind prediction to obtain a
predicted wind column; incorporating the predicted wind column for
wind column prediction for a projectile effect; and applying the
projectile effect to the fire-control processor to adjust aiming
the gun.
[0005] The first physical parameters include wind column, gun
state, ammunition type and aircraft flight conditions. The
ballistics model obtains a flight path of the projectile based on
the first physical parameters. The tracker model is based on the
number of points and the flight path. The wind prediction is based
on the closure tolerance, the cross-correlation factor, the tracker
location and the initial gun state. The wind direction and velocity
are obtained from multiple measurements or alternatively from a
single-point measurement.
BRIEF DESCRIPTION OF THE DRAWINGS
[0006] These and various other features and aspects of various
exemplary embodiments will be readily understood with reference to
the following detailed description taken in conjunction with the
accompanying drawings, in which like or similar numbers are used
throughout, and in which: [need hardware diagram]
[0007] FIG. 1 is a schematic view of a Wind Corrected Orbit;
[0008] FIG. 2 is a flowchart view of a Model Architecture
Diagram;
[0009] FIG. 3 is a plan frontal view of an aircraft's Free-Body
Diagram;
[0010] FIG. 4 is a tabular view of Nominal, Static, Initial State,
Variable and Range Values (Tables 1, 2, 3 and 4);
[0011] FIG. 5 is a graphical view of transient Radial Wind Error
with CCCC=1.0;
[0012] FIG. 6 is a set of graphical views of Wind Errors for
different CCCC values;
[0013] FIG. 7 is a graphical view of a Radial Wind Errors with
Closure Tolerance;
[0014] FIG. 8 is a tabular view of a curve-fitting constants,
iteration change, variables and ranges (Tables 5 and 6);
[0015] FIG. 9 is a graphical view of Outliers at CCCC=1.05;
[0016] FIG. 10 is a graphical view of Wind Profile I;
[0017] FIG. 11 is a graphical view of Model Representations for
Wind Profile I;
[0018] FIG. 12 is a graphical view of Ballistic Winds for Wind
Profile I;
[0019] FIG. 13 is a graphical view of Wind Profiles I through
4;
[0020] FIG. 14 is a graphical view of Wind Profiles 5 through
8;
[0021] FIG. 15 is a flowchart view of Wind Profiles 9 through
12;
[0022] FIG. 16 is a graphical view of Wind Profiles 13 through
16;
[0023] FIG. 17 is a flowchart view of a Multipoint Wind Prediction
Model Architecture;
[0024] FIG. 18 is a graphical view of Initial Raw Wind Speed
Prediction;
[0025] FIG. 19 is a graphical view of Filtered Wind Speed
Prediction;
[0026] FIG. 20 is a graphical view of Final Multipoint Wind
Prediction;
[0027] FIG. 21 is a graphical view of Comparison of Single-point
and Multipoint Models;
[0028] FIG. 22 is a graphical view of a Modeled Wind Errors Off of
Measured Winds;
[0029] FIG. 23 is a tabular view of East Wind Prediction Standard
Deviation (Table 7);
[0030] FIG. 24 is a tabular view of North Wind Prediction Standard
Deviation and State Variation Ranges (Tables 8 and 9);
[0031] FIG. 25 is a graphical view of Example Impact
Dispersion;
[0032] FIG. 26 is a graphical view of Radial Miss for Varying State
Variables;
[0033] FIG. 27 is a flowchart view of a conventional gun weapon
System Architecture; and
[0034] FIG. 28 is a flowchart view of an exemplary gun weapon
System Architecture.
DETAILED DESCRIPTION
[0035] In the following detailed description of exemplary
embodiments of the invention, reference is made to the accompanying
drawings that form a part hereof, and in which is shown by way of
illustration specific exemplary embodiments in which the invention
may be practiced. These embodiments are described in sufficient
detail to enable those skilled in the art to practice the
invention. Other embodiments may be utilized, and logical,
mechanical, and other changes may be made without departing from
the spirit or scope of the present invention. The following
detailed description is, therefore, not to be taken in a limiting
sense, and the scope of the present invention is defined only by
the appended claims.
[0036] In accordance with a presently preferred embodiment of the
present invention, the components, process steps, and/or data
structures may be implemented using various types of operating
systems, computing platforms, computer programs, and/or general
purpose machines. In addition, artisans of ordinary skill will
readily recognize that devices of a less general purpose nature,
such as hardwired devices, may also be used without departing from
the scope and spirit of the inventive concepts disclosed herewith.
General purpose machines include devices that execute instruction
code. A hardwired device may constitute an application specific
integrated circuit (ASIC), a field programmable gate array (FPGA),
digital signal processor (DSP) or other related component.
[0037] The disclosure generally employs quantity units with the
following abbreviations: length in meters (m), mass in kilograms
(kg), time in seconds (s), angles in milli-radians (mrad) or
degrees (.degree.), and force in newtons (N).
[0038] Chapter I--Introduction: Using new round tracking
capabilities, one can track a fired ballistic projectile or round.
From these tracking data, an improved ballistic wind prediction can
be made that is superior to previous methods of ballistic wind
prediction due to the increased data from the round tracker. This
improved ballistic wind prediction can then be used to correct gun
fire-control modeling of the round in flight and produce a better
firing-solution to increase gun fire accuracy.
[0039] This topic is being pursued because of the inability of
current United States Air Force (USAF) AC-130 gun-ships to correct
for winds in a detailed manner. Conventional methods of wind
prediction are low fidelity and tend to lose validity provided the
aircraft and gun change state so as to alter the time of flight of
the round. The method employed in exemplary embodiments greatly
reduces the effects of state changes on the impact prediction.
Incorporation of the exemplary techniques on the AC-130 via a
fire-control (FC) processor for aiming the gun enables improved
ballistic wind prediction, which leads to better firing solutions,
which augments overall performance by ability to predict detailed
ballistic winds that more closely match the true winds acting on
the round. Exemplary embodiments reduce not only the bias on
impacts due to the wind effects but also reduce dispersion induced
by changing the state of the aircraft and gun.
[0040] Conventional ballistic wind prediction methods rely on
knowing only the final impact of the round. As such, the ballistic
wind generated is a single value ballistic wind, holding a constant
wind speed and direction at all altitudes. This type of wind
prediction is only valid in gun fire states dose to state where the
wind prediction was made. For a gun fired in a state different from
the prediction state, the ballistic wind is likely to be incorrect.
This inaccuracy in the ballistic wind leads to incorrect
fire-solution angles being used to fire the gun, causing rounds to
impact away from the intended target. This has two effects. First,
more rounds are needed to ensure effect on target. Second, the gun
weapon system is less usable close to blue (friendly) forces due to
the increased chance of rounds impacting far off the target and
threatening collateral damage.
[0041] USAF AC-130 gun-ships have been in operation since the
Vietnam War and have seen frequent use during recent conflicts.
They are able to employ gun weapon systems from above a target in a
manner that maximizes possible time on target. When firing, the gun
operators must deal with miss distances caused by winds acting on
the projectile in flight. Operators currently perform a "tweak" to
predict a ballistic wind affecting fired rounds that is then
incorporated in the fire-control to correct for the real winds and
bring shots onto target. This correction, a single-point wind
prediction, is made using only the initial state of the gun and
aircraft and the final impact location. This disclosure explores
the possibility of using a round tracking sensor to track a
projectile as it falls and produce a multipoint ballistic wind that
would be better at correcting for the true winds than a
single-point ballistic wind.
[0042] An exemplary algorithm for a multipoint wind prediction
method is described and validated by executed simulation with a
single-point prediction method against measured wind profiles. The
results of the single-point and multipoint ballistic winds are
compared to the measured winds to test for a goodness of fit. The
results are also tested for stability; that when used the ballistic
wind remains valid even when the aircraft and gun change state from
the initial state when the ballistic wind was predicted. The
results show that a multipoint ballistic wind that is a better fit
and more stable ballistic wind than a single-point ballistic wind
is possible using the exemplary algorithm presented. Also, the
multipoint ballistic wind can be produced with very few data points
along the trajectory of the projectile.
[0043] When firing a gun, winds tend to be the largest
uncontrollable error contributor to final impact miss distance.
Most other errors, such as aiming and accounting for projectile
physical parameters, can be minimized prior to firing. The winds
and their effects on the round throughout its flight cannot be
known before firing. This is true regardless of the type of
gunfire, be it stationary and ground based or in motion on an
orbiting aircraft. For a stationary gunner, winds and other errors
can be corrected for by applying an offset to the pointing angles
of the gun, called "Kentucky Windage" as a simplifying assumption.
This type of correction assumes that all errors observed on one
shot acts the same on the next shot. For examp le, assuming wind
and other errors combine to force a round to impact high and to the
right of a target, then a stationary gunner can apply Kentucky
Windage to the shot by aiming low and to the left of the
target.
[0044] For moving gunners this type of correction does not apply,
especially for an orbiting gun-ship such as the USAF AC-130
gun-ships. When circling a target error effects that manifest
themselves in different frames of reference mixes in such a way
that Kentucky Windage cannot be used to correct the errors. A
method of separating the errors into their specific reference
frames and accounting for each error source individually is,
needed. Correcting the wind error when firing from an orbiting
gun-ship has been addressed in each iteration of the AC-130 gun FC
system. Each model's operators have had a method of correcting the
observed wind induced miss distance suited to their specific method
of FC, whether by changing the orbit center or using a "tweak" by
estimation.
[0045] However, little literature exists on these methods. The
Technical Orders (TO) for past gun-ships describe in general terms
either the method of correction via changing the orbit center or
the intent of the correction via a tweak. Research into the exact
methods of predicting a ballistic wind have not been published in a
publicly accessible database. Whether this is due to protection of
intellectual property or classification of the method is not dear.
Conventional methods attempt to predict a ballistic wind using only
the initial firing conditions and the final impact of the round.
This can be done to correct for the wind effects on the round,
though the ballistic wind predicted can lose validity over time and
as the aircraft changes state. A single-point ballistic wind is
computationally easy to calculate. The prediction requires no more
hardware than would already be available for normal operations of a
gun FC system: a method of measuring the aircraft and gun state and
a sensor to detect and locate the round's impact.
[0046] The single-point ballistic wind has been in operation for
years on USAF AC-130 gun-ships. This conventional method is trusted
and has been shown to be effective. The limitations are well known.
The ballistic wind values can be invalid for an aircraft changing
state from the time of the original calculation to the time of
fire, even if only changing the altitude of the aircraft. A more
flexible and stable method of modeling the winds would improve
overall gun accuracy. A multipoint ballistic wind prediction is
possible, though not with technology conventionally operable on the
AC-130 gun-ships. In order to create a multipoint ballistic wind,
the location and speed of the round must be known at various
locations along the projectile's flight path.
[0047] Round tracking sensors exist and could be used to provide
this telemetry data to an FC system. Could a round tracking system,
be implemented to allow for the calculation of a more stable
ballistic wind? This research tests the hypothesis that a more
stable ballistic wind profile can be calculated using data from a
round tracking sensor. The multipoint ballistic wind prediction can
be made with very few data points and can be done in a way that is
suited to a tactical application of the algorithm. A tactically
employable algorithm can be developed to predict more dynamic
ballistic wind profiles would increase the accuracy of the gun
weapon system. Assuming that the system would track each round
fired, winds could be predicted for each round individually. Using
the winds from the most recently fired round the FC system could
improve the firing solution for the subsequent round. This does not
lead to first round accuracy but introduces the possibility of
greatly improved accuracy for all following rounds. The disclosure
for exemplary embodiments is divided into seven chapters, including
this Introduction. Chapter II explains the current state of the
systems to be modeled for this research. The conventional
state-of-the-art for aircraft flight, the FC system, wind
correction method, and projectile tracking systems are described.
Chapter III describes the models designed and implemented to
recreate the relevant parts of the real-world systems described in
Chapter II.
[0048] The modeling assumptions and limitations are presented along
with the expected input and output. Validation of the individual
models is discussed, though the validation criteria and results are
not presented. Two factors controlling the performance of the wind
prediction model are tuned and the results are discussed in Chapter
IV. Chapter V uses the models to simulate the current wind
prediction method, a single-point wind correction. Real measured
winds are used and the wind prediction model finds a single value
ballistic wind to account for the effects of the measured winds.
Chapter VI uses the same measured winds and initial conditions used
in Chapter V to predict a ballistic wind based on multiple points
along the flight path of the round. The multipoint wind prediction
method is described and the results of the simulation runs are
presented.
[0049] Assuming the above hypothesis is correct, then the wind
predictions from Chapter VI should prove to be more stable than the
wind predictions made in Chapter V. Chapter VI investigates the
closeness of the predicted winds to the true winds to indicate
which ballistic wind method performs better. The ballistic winds
are also tested as the state of the aircraft and gun are changes to
see which ballistic wind method performs better, allowing less
error into the impact prediction. Chapter VII presents the
conclusion to the research. Along with summing up the results
presented, recommendations are presented for future experiments or
analysis and a discussion of some of the remaining limitations on
an FC system using the multipoint wind prediction method described
in Chapter VI.
[0050] Chapter II--State of the Art: This research is focused on
determining whether increased knowledge of a ballistic projectile's
location in flight can be used to make ballistic wind predictions
that closely match the true winds acting on the projectile.
Specifically, this disclosure examines at a weapons platform that
relies on wind predictions to improve weapon effectiveness; USAF
AC-130 gun-ships. In order to establish a framework developed in
Chapter III for the models and simulation, this section reviews the
conventional state of technology of the modeled systems and
subsystems.
[0051] This description is by no means exhaustive, but provides
adequate details and background data to enable the design and
implementation of models to recreate the system of interest. A
brief description of USAF fixed-wing gun-ships is presented,
describing the theory of operations and the flight profile used
during a weapons engagement. Gun weapon systems require an FC
system to properly point the gun so that rounds fired strikes the
desired target Features of an FC are detailed and errors common to
FC systems are discussed. One of the most common and largest errors
experienced by FCs is the effect of wind on the projectile.
Existing methods to predict the effects of wind and account for
them to improve impact accuracy are described. Finally, various
round tracking systems and their configurations are detailed.
[0052] Section II.1--Side-Firing Gun-ships: Shortly after the first
flight by the Wright brothers in 1903, airplanes were adopted for
military use. In 1909, the US Army Signal Corps purchased and used
the first military aircraft. Early uses included both combat and
non-combat roles. The first recorded deployment of a gun on a
military airplane occurred in 1915 when French pilot Roland Garros
used a forward firing machine-gun to engage enemy aircraft. For
engaging ground targets, some early aviators carried rifles in
flight that they would fire sideways out of the cockpit. In the
1920s both the Americans and the French mounted side-firing guns on
various aircraft, though there was no specific tactic developed to
employ such weapons.
[0053] One of the problems faced with all air-to-ground engagements
is the aircraft's typically short time to engage the target.
Strafing a target or engaging in a fly-by attack allows for a short
period of time where weapons can be brought to bear on a target. A
pilot then must turn the aircraft and reacquire the target before
they can reengage. Pilots both military and civilian had developed
a maneuver called the "pylon turn" by the 1920s. The pylon turn is
a maneuver where the pilot turns the aircraft at a constant bank
angle. This has the effect of pulling the aircraft into a roughly
circular turn around a stationary ground location. Pilots had
developed the pylon turn maneuver for airplane racing.
[0054] Military aviators saw the advantage of combining side-firing
weapons with a coordinated pylon turn. The tactic was initially
tested in 1926 by the US Army and developed from there into the
side-firing fixed wing gun-ships used today. A pylon turn is
defined by the bank angle of the aircraft, the aircraft's speed,
and the altitude of flight. There values are called the "nominals"
and they control the geometry of the pylon turn. With a given set
of nominals the total range from the gun to the target, the slant
range, can be calculated. Nominals can be chosen to achieve a
specific slant range.
[0055] There are many advantages to using side-firing weapons in a
pylon turn. From a combat perspective the primary advantage is
increased weapon time on target. A pylon turn can be executed
around a specific target or target area that enables the weapon to
be trained on the target for the duration of the orbit. Side-firing
weapons employed without using a pylon turn and forward firing
weapons have a limited time to engage before the aircraft has
passed the target and must turn to reengage. Along with increasing
the time available to fire at the target, the pylon turn reduces
the apparent target motion relative to the aircraft. Provided the
pylon turn is properly executed, a target can be placed at the
center of the orbit. From the perspective of an observer on the
aircraft, a target at the center of the orbit appears stationary.
Even though the aircraft is in motion the target appears stationary
relative to the aircraft facilitating target engagement.
[0056] The idea of combining side-firing guns with aircraft
executing a pylon turn was first tested in 1926 but was not pursued
by the US military at that time. During World War II the US
military proposed using a side-firing gun on an aircraft to engage
submarines, but again the tactic was not pursued. Not until the
Vietnam War did the US military operate a true side-firing gun-ship
executing a pylon turn. Pylon turns are the standard flight profile
for modern USAF AC-130 gun-ships. The side-firing guns can be
trained on targets throughout the orbit and engage for extended
periods without losing sight of the target. Pilots select nominals
to fly in order to hold a specific slant range around a target. The
nominals determine the geometry of the orbit and the target-to-gun
system. The selection of the nominals varies based on pilot
preference and mission needs.
[0057] Section II.2--Gun Fire Control: When a gun-ship engages a
target with its guns, a firing solution must be calculated. The
firing-solution is a set of gun pointing angles (azimuth and
elevation) that enables a round fired by the gun to impact the
intended target. The firing-solution takes into account the current
state of the aircraft and target location. For modern gun weapon
systems, the FC (as a system processor) calculates the
firing-solution. The FC ties together different data sources
available on the gun-ship and uses those data to compute the
firing-solution. The specific operations and functions of a given
FC may vary based on hardware and software design considerations,
but the common functions are as follows. [0058] (1) obtain target
location data from a sensor system. [0059] (2) convert the target
location from a sensor-relative frame of reference to a
gun-relative frame of reference. [0060] (3) use ballistic model to
predict a set of azimuth and elevation gun angles that enables a
ballistic projectile to impact the target location. [0061] (4) move
the gun into position to match firing-solution. [0062] (5) fire the
gun.
[0063] Each of the above steps involves many hardware;components
providing input data on the state of the gun, target, and aircraft
as well as software algorithms to calculate the required pointing
angles and control the gun weapon system. A full discussion of such
FCs is beyond the scope of this research. Pertinent to this
research are the possible errors in the firing-solution generated
by the FC.
[0064] Failure of the round to strike the intended target indicates
an error in the firing-solution. The error is judged by the
characteristics of how the round missed the target. There are many
sources of possible error in the FC and its generated
firing-solution. A full list of the error sources depends on the
specific configuration and design of the system, but some common
error sources are poor ballistic modeling, mechanical errors
controlling the pointing of the gun, incorrect targeting data,
winds, and production tolerances for the ammunition. During the
development of the FC system, concerted efforts reduced any errors
that can be eliminated a priori based on gaining more knowledge of
the FC. For example, the initial velocity of the round is found
through testing and is treated as an input to the FC.
[0065] Each round has a different initial velocity, which cannot be
known before firing. The initial velocities measured during testing
result in a distribution of possible values. The average initial
velocity value is used in the FC, thus accounting for an epistemic
error that would exist even assuming the initial velocity had not
been measured at all. The variability in the initial velocity still
exists as an aleatory error that cannot be corrected. All errors in
the system can be described as causing either a bias or dispersion
on the round impacts. A bias error causes round impacts to be
offset from the intended target in a repeatable and predictable
way. Dispersion errors cause the rounds to impact within a "cloud"
or region but not a single repeatable location.
[0066] When firing from an orbiting aircraft, impacts can be
tracked in two frames of reference: a platform relative frame and a
world relative frame. Biasing effects manifest in one of these two
frames as a roughly static offset. Because the aircraft is
orbiting, a bias in one frame appears to drift in the other frame
in a predictable way based on the heading of the aircraft at time
of fire. The platform relative frame of reference is fixed to the
aircraft. Regardless of the aircraft orientation, the Y-axis of the
platform relative frame is oriented with the positive direction
pointing vertical and parallel to the gravity vector at the
aircraft.
[0067] The X-axis, called the downrange (DR) direction, points with
the positive direction to the left side of the aircraft orthogonal
to the Y-axis. The Z-axis, called the cross-range (CR) direction,
completes the right-handed system and points with the positive
direction to the nose of the aircraft. When discussing errors in
round impacts away from the target, the origin of the platform
relative frame is assumed to be at the intended target. Platform
relative biases are roughly static as observed from the aircraft.
These bias errors can be corrected by applying a static offset to
the gun pointing angles. This correction can be held through the
entire orbit. Examples of platform relative bias include gun barrel
misalignments, poor ballistic modeling, and inaccuracies in the
body description and physical properties of the round being
fired.
[0068] The world relative reference frame is a local East-North-Up
(ENU) reference frame. When discussing errors in impacts, the
origin of the world relative frame is at the target. The X-axis
points positive to the East, the Y-axis points positive to the
North, and the Z-axis completes the orthogonal system pointing
positive upwards parallel to the gravity vector. World relative
biases are static as observed from the ground. A world relative
bias causes all shots to fall in roughly the same direction in East
and North relative to the target. These biases can also be
corrected by applying an offset to the gun pointing angles. The
offset is not static and changes as the aircraft orbits the target
location.
[0069] Winds account for the world relative bias affecting the
flight of ballistic projectiles. Dispersion effects also manifest
in specific frames depending on the cause of the error. Given the
nature of dispersive errors, they cannot be separated into a
specific frame of reference. The dispersion appears as "noise" on
the impacts regardless of the frame of reference they are rendered
in. In flight, attempts can be made to correct for biases that
could not be corrected for on the ground. To detect and remove
biases in both the platform and world reference frame multiple
shots must be taken at headings around the orbit. This is required
to decouple world relative bias from platform relative bias. Once
the shot data are collected and decoupled the appropriate
corrections can be made to the pointing angles of the gun to remove
any platform or world relative bias.
[0070] Section II.3--Correcting for Winds: Winds affect the flight
of a projectile in two ways, as a bias and as a dispersion in the
observed impacts. The wind's average effect on the projectile
causes a world relative bias, moving the impact of the round to a
roughly constant location as measured in meters East and North of
the target. While there is no such thing as a true average wind,
there is a component of the wind column that changes very slowly
over time, which is generally regarded as the average wind.
[0071] The average wind speed column, if known, does not capture
all of the wind effects. The wind's dispersive effect on the round
is due to the variability of the winds over time and unpredictable
gusts that occur after the round is fired. Gusts and variability in
wind speeds close to the ground always cause dispersion on the
impacts that cannot be accounted for a priori. One can account for
the offset in the impacts due to the average wind column.
Historically, two different ways have been used to correct for wind
effects with weapon systems: wind-corrected orbits and ballistic
wind adjustment. Each method relies on knowing only two points, the
initial firing conditions and the final impact, to correct the
impacts. When firing from a pylon turn, the target is usually at
the center of the orbit to maximize weapon time on target and
minimize the need to change gun pointing angles to fire on a
target.
[0072] FIG. 1 illustrates a diagram view 100 of orbit paths of an
aircraft, such as the AC-130. An orbit path 110 is shown as a solid
circle with a target center 120 shown as a triangle that identifies
a target subject to attack. A wind-corrected orbit path 130 to
adjust the aim point is shown as a dash circle with an impact
center 140 shown as a cruciform. The impact center 140 denotes the
impact site due to wind shifting the projectiles fired from the
aircraft while in ballistic trajectory flight.
[0073] Assuming winds are present and causing the impacts to fall
in a roughly constant location East and North relative to the
intended target 120, the orbit path 110 can be offset to correct
for this miss. Adjusting the center point of the orbit by the same
magnitude as the average wind induced miss distance in the opposite
direction causes shots fired at the center of the orbit to impact
on the original target shown in view 100 as a wind-corrected orbit
path 130. The target 120 is no longer in the center of the orbit
path 110 but the gun is still aimed as though the target was
located at the center 120. Offsetting the impact center 140 was
commonly used in older gun-ships because it did not require
extensive ballistic calculations or fully trainable gun
systems.
[0074] Modern FC and gun weapon systems are capable of
recalculating ballistic solutions and training the guns
automatically to account for offsets required to bring missed
impacts back on target. This method, referred to as a "tweak" in
this context, also encompasses correcting for alignment offsets as
well as the winds. The wind correction result of the tweak
algorithm is a "ballistic wind." The ballistic wind is not a
measure of the true winds affecting the round in flight. Ballistic
winds are an approximation of the winds from the tip of the barrel
to the ground level that would account for the observed wind
induced miss distance. A ballistic wind is a single wind speed and
direction value, which is assumed to apply for the entire flight
path of the projectile.
[0075] The tweak process finds the ballistic wind that best
accounts for the observed world relative bias in any impact data.
Multiple shots are taken and the miss distances are recorded. Using
the impact data, a search algorithm is used to iterate over a
search space of possible wind vectors. The wind model is then
applied to the ballistics model 260 in the FC 290. Applying the
winds in the ballistics model 260 under the initial firing
conditions, an impact is predicted. The algorithm varies the
parameters of the wind model to reduce the difference in the
observed impacts the predicted impacts with ballistic winds
applied. The ballistic winds predicted by the tweak are valid only
for a period of time. This period varies based on the wind itself;
no clear time limit exists. For calm winds that are slow to change
when the ballistic wind is calculated, the tweak results may be
valid for a long period. For highly dynamic true winds that change
rapidly, then the tweak results may become "stale" in a short
period.
[0076] Section II.4--Tracking Projectiles: Technology exists to
track a projectile in flight. Such round tracking technologies fall
broadly into two categories: internal trackers and external
trackers. Internal trackers, also known as telemetry rounds,
contain hardware to detect or measure their location and relay that
data back to a base station. Telemetry rounds contain some form of
global positioning system (GPS) or Inertial Navigation Unit used to
measure the location of the round in flight. The round then
transmits that information to a base station that records the
information.
[0077] Telemetry rounds require changes to the projectile itself to
enable the inclusion of the necessary hardware and are commonly
inert. Any explosive warhead being removed to enable the inclusion
of the tracking hardware. These rounds are often used in
experiments where the terminal effects of the round are not under
study. Because of the changes, telemetry rounds may not be
representative of the rounds intended for tactical use.
[0078] External trackers are sensors that track the round in flight
without needing the round itself to transmit a signal to the
tracker system. There are a variety of methods used to track
projectiles in flight. A rigid body system measures a direct range
and pointing angles to the projectile from a known sensor location.
A Doppler system pings the projectile with a radio or microwave
signal and finds the round's velocity based on the Doppler shift of
the return signal. The round's velocity is integrated over time to
predict the position of the projectile. Sensor array systems exist
that rely on the pointing angles of multiple sensors pointing at
the round in flight and triangulation to find the location of the
round. For each external system, some form of sensor must be used.
These all rely on reflected electromagnetic radiation to detect and
locate the round. The specific sensor configuration used depends on
the composition material the round.
[0079] Light Detection and Ranging (LIDAR) systems can be used to
track a round provided a portion of the round is painted so as to
reflect LIDAR signals. Radar tracking functions with any round in
current use as they are all metal jacketed, though round size is a
limitation. Tracer rounds, those with base-burners, can be tracked
with infrared or electro-optical sensors. Regardless of the method
of tracking the round used, the tracker itself must measure or
calculate the location of the round in some reference frame
relative to some origin point. The frame and the target point are
arbitrary. The only firm requirement is that the data be of such a
form that they can be translated into a frame relevant to the
weapon system.
[0080] Chapter III--Models: In Chapter II, the system of interest
was described. This research investigates the incorporation of a
round tracking system to predict a ballistic wind to reduce wind
induced bias errors on projectiles fired from an AC-130 gun-ship.
In order to simulate firing from an AC-130 gun-ship and attempt to
correct for the wind effects on a projectile, a series of models
were developed to recreate the systems described in Chapter II. A
model is required to simulate the flight conditions of the aircraft
at the time of fire. Chapter III describes the simplifying
assumptions made in developing the model and also details the
equations employed and the required input to the model. Early in
the simulation design, the assessment was made that modeling the
entire FC would greatly increase the complexity of the system,
introducing greater chances for errors without increasing the level
of fidelity of the simulation.
[0081] Instead of modeling the entire FC 290, a ballistics model
260 for use thereby, was developed to simulate the flight of ;a
projectile. Section III.2 presents the design consideration made,
the assumption inherent to the model, and the required input
parameters. Section III.3 describes modeling the wind. A method is
required that models a consistent wind both for developmental
testing and for simulation of the ballistic wind predictions. Along
with the winds, the developed model simulates the data supplied by
a round tracking sensor. The modeling assumptions are fairly broad;
the resultant model described in Section III.4 is designed to give
the proper output expected from a round tracking system. Finally,
Section III.5 describes a method of wind prediction and details a
model. The internal algorithm is described along with the expected
inputs and outputs to allow the wind prediction model to interact
with the other models and their data.
[0082] The high-level architecture of the resulting simulation
software is shown in FIG. 2, in which one can observe what the
expected inputs into each of the sub-models is and what data are
being sent to the other models. All messages are sent via multicast
network messages. FIG. 2 shows a flowchart view 200 of a Model
Architecture Diagram. Inputs include wind characteristics 210, gun
and ammunition characteristics 215, number of points 220 for wind
data, aircraft characteristics 225, and iteration parameters 230,
Wind characteristics 210 include type, speed and direction. Gun and
ammunition characteristics 215 include state and type. Aircraft
characteristics 225 include speed, bank angle and altitude.
Iteration parameters 230 include closure tolerance and
cross-correlation factor. Processes include wind model 240 to
produce a wind column 245, aircraft model 250 to produce altitude,
bank and speed 255, ballistics model 260 to produce a round's
complete flight path 265, tracker model 270 to produce a tracker
location and initial gun state 275, and wind prediction model 280
to produce a predicted wind column 285 for the FC 290. One can note
that characteristics 225 and 255 are not distinct in this context,
but shown as separate for sake of completeness. For a more refined
model the of AC-130, then characteristics 255 would include
additional information beyond a "pass through" of the nominal
data.
[0083] The wind model 240 receives wind characteristics 210. The
aircraft model 250 receives aircraft characteristics 225. The
ballistic model 260 receives gun and ammunition characteristics
215, wind column 245 along with altitude, bank and speed 255 to
produce the flight path 265. The tracker model 270 receives the
number of points 220 and the flight path 265 to produce the tracker
location 275. The wind prediction model 280 receives the iteration
characteristics 230 and the tracker location 275 to produce the
predicted wind column 285. The number of points 220 represents an
integer setting to specify to the tracker model how many measured
location/velocity data points to simulate for the rounds.
[0084] This design configuration ensures that the method of
communication is as close as possible to that in a real tactical
application of these systems. Also, by limiting the interactions of
the various models to only those inputs and outputs shown in view
200, one can ensure that the wind prediction model 280 would only
have access to those data that a hardware round tracking sensor
would provide. This control of network messages prevents the chance
of the wind prediction model 280 having knowledge of the underlying
winds that would not truly be available to a wind prediction
system.
[0085] Section III.1--Aircraft State: This research focuses on
projectiles fired from aircraft executing a pylon turn. The
aircraft motion in a pylon turn is a direct contributor to the
state of the projectile at time of fire. The orientation of the
aircraft and the speed of the aircraft are factors that must be
accounted for when attempting to predict the motion of a projectile
fired from the aircraft. A fully descriptive model of the
aircraft's motion in flight is not needed for this analysis. For
these purposes and timescales, the firing of a gun is a virtually
instantaneous event from the moment of trigger to the time the
round exits the barrel. The motion of the aircraft after the time
of fire has no effect on the flight of the round. The motion of the
aircraft before the round exits the barrel is only important in
that it imparts a velocity to the round. This enables a simplified
model of the aircraft's motion and state to be used. When modeling
the ballistics of a projectile fired from the aircraft very few
factors of the aircraft's state need to be considered. The model
used here is as simple as possible to model an aircraft in a pylon
turn and supply the needed inputs to the ballistics model.
[0086] Section III.1.1--Assumptions: The model assumes that the
acceleration due to gravity is constant at all altitudes and
latitudes. This is not strictly true--see eqns. (10) and (11). For
the purpose of modeling the flight of the aircraft, the small
changes in gravity due to changes in latitude or altitude alters
the geometry of the orbit only slightly. This change does not
affect the quality of the ballistics model 260 or the applicability
of winds to the flight of the projectile. As such, the dynamic
nature of the gravitational acceleration can be neglected.
[0087] This model further assumes that the geometry of the orbit is
controlled only by those forces acting normal to the direction of
travel of the aircraft. The forward motion of the aircraft is only
used to apply a velocity to the system. Any forces acting in that
direction, such as drag on the aircraft, are ignored. Similarly,
any orientation of the aircraft off of the ideal nominals is
assumed to be zero. The aircraft in this model experiences no
pitching and no yawing between the velocity vector and the heading
vector. One can assume that no winds aloft affect the flight of the
aircraft. This is not realistic, but the aircraft dynamics in a
winded orbit 130 do not directly affect the applicability of the
winds to the ballistic prediction.
[0088] Section III.1.2--Model Description: With the assumptions
applied, the geometry of the orbit is controlled by few factors. A
free-body diagram of the remaining forces is shown in FIG. 3 as
elevation view 300 of simplified forces of flight on an aircraft
310, which can be used to illustrate the system. The two most
consequential forces acting on an aircraft 310 are lift and
gravity. Gravity constantly pulls the aircraft 310 downward
relative to the local geographic reference frame. Lift constantly
pulls the aircraft upward normal to the wings of the aircraft 310.
When the aircraft 310 is banked the lift vector can be decomposed
into a vertical and horizontal force.
[0089] To keep the aircraft 310 flying at a constant altitude, the
vertical component of lift must equal the force of gravity acting
on the aircraft, such that
{right arrow over (F)}.sub.lift,y={right arrow over
(F)}.sub.gravity. (1)
Newton's second law states:
{right arrow over (F)}.sub.gravity=m {right arrow over (g)},
(2)
where m is aircraft mass in kilograms (kg) and g is gravitational
acceleration in meters-per-second (m/s.sup.2). For flat and level
aircraft flight, the forces are balanced and no horizontal
component exists. For a banked aircraft, the airspeed over the
wings must be high enough that the lift force's vertical component
can balance out the gravity force.
[0090] There is a remaining horizontal component to the scalar lift
force when banked:
F.sub.lift,x=mg tan(.beta.), (3)
where .beta. is the bank angle of the aircraft. This horizontal
component of lift acts a centripetal force on the aircraft. To hold
a constant turn radius, this force must balance with a centrifugal
force. Substituting, one obtains:
F lift , x = m g tan ( .beta. ) = m v 2 R , ( 4 ) ##EQU00001##
where V is the airspeed of the aircraft in meters-per-second (m/s)
and R is the turn radius of the orbit in meters (m). Rearranging
one can find an equation to determine the turn radius of the
orbit
R = v 2 g tan ( .beta. ) , ( 5 ) ##EQU00002##
which matches the pilot guidance for choosing flight nominals used
by AC-130 pilots.
[0091] Section III.1.3--Model Factors and Parameters: Inputs into
the flight model are limited to the nominals. Pilots select a
desired turn radius eqn. (5) to the intended target for an
engagement. Based on this desired range to target a set of flight
nominals are chosen. The variables from eqn. (5) are the flight,
nominals, which along with the altitude of the aircraft control the
shape of the orbit and the slant range to target. Note that FIG. 4
provides tabular views 400 for Table 1 as 410 for flight nominals,
Table 2 as 420 for static values, Table 3 as 430 for projectile
state data and Table 4 as 440 for variables and ranges.
[0092] The derivation above serves to demonstrate that the only
state variables needed to describe the aircraft for this simulation
are the list of nominal in Table 1 as 410.
[0093] Section III.1.4--Model Verification and Validation: The
implementation of the model was verified through code inspection
and unit testing. Code inspection was performed to ensure that the
equations were properly coded, and that the inputs and outputs were
of the proper form. Unit testing checked that known inputs produced
expected outputs from the code. Similarly, the inputs and outputs
were validated against an independently generated list of nominals.
This Table 1 of nominals 410 is used to select effective nominals
for weapon use in tactical situations and generated for use in
tactical operations. The tabulations enable a pilot to select a
desired turn radius and slant range and show the required nominals
to achieve those range values. The results of the model for this
simulation match the expected results from the independently
generated tabular list.
[0094] Section III.2--Ballistics: The forces acting on a projectile
in flight are well known and studied in the fields of physics and
aeronautical engineering. When implementing a ballistic model to
describe the motion of a spinning projectile in flight, the number
of degrees-of-freedom (DOF) must be selected for the model. The
number of DOF chosen controls the complexity of the model. When
dealing with exterior ballistics, the DOF refer only to those
possible motions of the round that are physically modeled. The
maximum DOF in a ballistics model 260 is six.
[0095] This 6-DOF model would account for motion in all three
spatial directions (as determined by the frame of reference chosen)
and rotation about all three orientation angles (roll, pitch, and
yaw). Typically, 6-DOF ballistics models are high-fidelity models
used to study the body orientation of the round in flight or to
model flight control and guidance on a round. One can simplify an
exterior ballistics problem to a model with four-DOF (4-DOE). A
4-DOF model describes the motion of the round in all three spatial
dimensions and allows for the rotation of the round around its
central body axis. A 4-DOF model does not model the yawing and
pitching motion of a projectile in flight as a true physical moment
acting on the round's body. Instead, a 4-DOF ballistic model
simplifies the yawing and pitching motions into a single term, the
yaw of repose. The yaw of repose approximation assumes that the
precession and nutation of the round early in its flight are very
small magnitude and have no effect on the trajectory.
[0096] After the precession and nutation have settled out, the
spinning of the round causes a yawing and pitching of the central
axis of rotation for the round off of the velocity vector of the
round. The Modified Point-Mass (MPM) model, a type of 4-DOF
ballistic model, assumes that the yawing and pitching angles
between these vectors can be combined into a single angular offset.
This total angular offset is the yaw of repose, a steady state
yawing and pitching of a gyroscopically stable round. For this
analysis, the exterior ballistics model 260 designed and
implemented is a version of the MPM 4-DOF model. The 4-DOF model
was chosen as a basis for this research due to ease of coding and
the general popularity of the model in both academic and defense
applications.
[0097] Section III.2.1--Assumptions: The ballistics of the round is
modeled with a 4-DOF model. The physical forces to be modeled can
be restricted to drag, lift, Magnus, and gravity. The model
terminates upon prediction of the round impacting the ground. This
implementation of the ballistic model assumes a flat Earth. The
purpose of the analysis is to study the effects of winds on the
trajectory of the projectile. The curvature of the Earth, whether
spherical, ellipsoidal, or flat would have no effect on the
predicted trajectory of the round. The atmosphere is modeled using
the International Civilian Aviation Organization (ICAO) standard
atmosphere. The ICAO atmospheric model is used to find the air
density and speed of sound at varying altitudes.
[0098] The ICAO atmosphere model assumes that any variations in air
density or speed of sound due to variations in wind speed will be
small and have little effect on the trajectory of the round when
compared to the effect of the wind itself. The implemented model
assumes that there are winds acting on the round. The winds act in
a horizontal plane, specifically the DR/CR plane of the gun frame.
Vertical winds are assumed to be nonexistent. The actual model
generating the wind values is separate from the modeling of the
ballistics and is described in Section III.3. The model does not
include the Coriolis force on the round as the total effect is
assumed to be small.
[0099] Section III.2.2--Equations of Motion: The model used in this
research is based on the ballistic model used in the NATO Armaments
Ballistic Kernel. This model is a 4-DOF MPM that models the forces
acting on the round in a frame of reference aligned to the gun. A
common term appears in many of the equations of motion. For ease of
notation, and comptation, this term is simplified by the following
relation:
Q = ( .pi. .rho. d 2 8 m ) , ( 6 ) ##EQU00003##
where Q is the common term, d is projectile diameter in meters (m),
m is projectile mass in kilograms (kg), .rho. is atmospheric
density in kilograms-per-cubic-meter (kg/m.sup.3). The drag force
is modeled by the following:
{right arrow over
(D)}=-Q(C.sub.D.sub.9+C.sub.D.sub..alpha..sub.2.alpha..sub.e.sup.2)v{righ-
t arrow over (v)}, (7)
where C.sub.D.sub.0, is dimensionless zero-yaw drag coefficient,
C.sub.D.sub..alpha..sub.2, is dimensionless quadratic drag force
oefficient, .alpha..sub.e is the projectile's magnitude of yaw of
response in radians, v is the velocity magnitude and {right arrow
over (v)} is velocity vector of the projectile relative to the air
in meters-per-second (mIs).
[0100] The lift force is modelled by the following:
{right arrow over
(L)}=Q(C.sub.L.sub..alpha.+C.sub.L.sub..alpha..sub.3.alpha..sub.e.sup.2)|-
v|.sup.2{right arrow over (.alpha.)}.sub.e, (8)
where C.sub.L.sub..alpha. is dimensionless lift force coefficient,
C.sub.L.sub..alpha..sub.3 is dimensionless cubic lift force
coefficient and {right arrow over (.alpha.)}.sub.e is the
projectile's yaw repose vector in radians. The Magnus force is
modeled on the following:
{right arrow over (M)}=-QdpC.sub.mag-f({right arrow over
(.alpha.)}.sub.e.times.{right arrow over (v)}), (9)
where p is the axial spin rate of the projectile around the body
axis of symmetry in radians-per-second, and C.sub.mag-f is
dimensionless Magnus force coefficient.
[0101] The gravity force is modeled by the following:
g .fwdarw. = - g 0 [ X 1 R 1 - 2 X 2 R X 3 R ] , ( 10 )
##EQU00004##
where R is the radius of the earth assuming a spherical model of
R=6.35676610.sup.6 is the strength of the gravity vector at the
origin of the gun frame:
g.sub.0=9.80665(1-0.0026 cos(2.phi.)), (11)
where .phi. is the geodetic latitude of the origin of the gun
frame.
[0102] The total acceleration acting on the projectile at any given
time is calculated using the following:
{dot over (u)}={right arrow over (D)}+{right arrow over (L)}+{right
arrow over (M)}+{right arrow over (g)}, (12)
where {dot over (u)} is the total acceleration of the projectile
with respect to the gun frame, {right arrow over (D)} is
acceleration due to drag force in eqn. (7), {right arrow over (L)}
is acceleration due to lift force in eqn, (8), is acceleration due
to Magnus force in eqn. (9), and {right arrow over (g)} is
acceleration due to gravity in eqn. (10). The spin of the
projectile around its centerline of symmetry is the only rotational
motion physically modeled in the 4-DOF model. The temporal change
in spin acceleration is modeled by the following:
p . = .pi. .rho. d 4 p v C spin 8 I x , ( 13 ) ##EQU00005##
where C.sub.spin is dimensionless spin damping moment coefficient
and I.sub.x is the axial moment of inertia in
kilogram-meters-squared.
[0103] The yaw of repose is modeled by the following:
.alpha. .fwdarw. = 8 I x p ( v ~ .times. u ~ . ) .pi. .rho. d 3 ( C
M a + C M a 3 .alpha. e 2 ) v 4 , ( 14 ) ##EQU00006##
where p is current axial spin rate of the projectile in
radians-per-second (rad is the current acceleration vector in
meters-per-second-cubed (m/s.sup.3), C.sub.M.sub..alpha. is the
dimensionless overturning moment coefficient, and
C.sub.M.sub..alpha..sub.3 is the dimensionless cubic overturning
moment coefficient. In eqns. (7) and (8), the higher order terms
that depend on the yaw of repose are dropped. For example, the
equation for drag can be expanded to include a quartic drag force
effect due to the yaw of the projectile. This and other similar
contributions from higher power terms of the yaw of repose are
assumed to be zero. An earlier study has determined that the
Modified Point-Mass model is able to predict the flight path of a
round accurately provided the yaw of repose predicted in flight is
0.6 mrad or less. A yaw of repose with such a small magnitude has a
negligible effect given the form of the quartic drag force term
C.sub.D.sub..alpha..sub.4.alpha..sub.e.sup.4.
[0104] Section III.2.3--Model Factors and Parameters: The 4-DOF
model used requires input parameters to model a specific ammunition
type. For this analysis, the PGU-13 A/B round type is used for all
simulated shots. This round type is used in many air-to-ground
systems. The round description, including the aeroballistic
coefficients and the physical constants, are taken from the
Projectile Design and Analysis System (PRODAS) software suite. Each
round type has a set of physically measurable properties that do
not change relative to the air mass the round is traveling through.
These values are listed in Table 2 as 420 in FIG. 4.
[0105] As the round travels through the air, the round interacts
with the mass of air differently depending on the speed of the
round relative to the speed of sound in the air mass. Each of the
equations of motion above includes dimensionless coefficients that
tune the equations to the round type selected. The values of these
coefficients are the aeroballistic coefficients of the round
indexed by Mach value and solved for in each iterative step as part
of the ballistics model. To simulate the flight of the projectile
the state of the gun at time of fire is needed. These inputs
include the altitude of the gun, the latitude of the gun, the
current speed of the gun, and the gun's inertial pointing angles.
For this simulation, the altitude, latitude, and speed of the gun
are taken as inputs from the aircraft model 250 in Chapter III.
[0106] Section III.2.4--Model Verification and Validation: The
ballistic model implemented for this research was verified and
validated to ensure accuracy. The model was verified via code
review and unit testing. Code inspection verified that the
ballistics model 260 in the code matched the documented model, A
feature added to the model enables an operator to turn on or off
individual forces and moments. This facilitates unit testing of the
model in a "build-up" manner; adding forces into the system and
confirming that they act as expected. Testing confirmed that each
force was acting as expected resulting in the motion associated
with that force.
[0107] Where possible, the results were verified against
theoretical results (such as when gravity is the only acting
force). Testing verified that the model is correct to within the
limits of the documented model and the algorithms used in its
implementation. The flight path predictions made by the model were
validated by comparison to other validated models. The PRODAS
software has a built-in 4-BOF ballistics model 260 and support for
many ammunition types. Both PRODAS and the 4-DOF model developed
for this research were used to produce surface-fire range tables
with the same ammunition. The predicted DR and CR impact locations
matched between the PRODAS table and the one generated the 4-DOE
developed for this analysis.
[0108] PRODAS is considered valid due to extensive testing and wide
acceptance of the modeling suite for ballistics analysis. The
research model was similarly validated against the ballistics model
260 used in tactical code for AC-130 gun-ships. The predicted final
state of the round produced by the models was compared over
two-thousand random starting conditions. The model developed for
this research produced predicted impacts that match the tactical
code's predicted impacts to within machine truncation limitations.
The tactical code is considered valid due to years of successful
use engaging hostile forces in combat situations and validation
during testing at Dahlgren.
[0109] Section III.3 Wind Modeling: Two different wind models 240
were used in this research: a static wind model and a measured wind
model. During simulation, the static wind model was used both for
code development and validation and to simulate the ballistic wind
that results from the current method of wind prediction in AC-130
tactical systems in Section II.3. The measured wind model
introduces dynamic winds closer to reality than the static wind
model. The wind models 240 were applied to the ballistics model 260
in Section III.2 in separate simulations and modify the velocity of
the round relative to the air stream in the equations of
motion.
[0110] Section III.3.1--Assumptions: Both models assumed that the
vertical wind speed is 0.0 m/s. The vertical winds tend to be very
low so this assumption does not cause any large errors. Wind
measuring systems commonly use vertical winds as a validation; low
to nonexistent vertical winds are considered an indication that the
measuring system is functioning as expected. Both models also
assume that the winds do not change over time. Again, this is not
strictly true, but for the sake of analysis the winds are held
constant.
[0111] Section III.3.2--Model Description: Static winds can be
generated with speed up to 100.0 m/s in any direction. The 100.0
m/s limit is close to the highest observed wind speed. This highest
observed value was chosen as the limit to test the system in as
broad a range as possible. The static wind column generated by the
model has the same wind speed and direction at all altitudes.
Measured winds are produced off of meteorological balloon data.
This met balloon data is actual data that was recorded during
previous testing at the Naval Surface Warfare Center, Dahlgren VA.
The wind speed and direction at altitudes are modified only to add
a wind speed of 0.0 m/s at the ground. For both models, the
vertical winds are 0.0 m/s.
[0112] Section III.3.3--Model Factors and Parameters: The wind
speed and direction of the static wind column can be set either
programmatically or using configuration settings. Measured wind
columns are chosen based on which set of met balloon data are to be
used. Once chosen, no other user input to the wind model 240 is
required.
[0113] Section III.3.4--Model Verification and Validation: The wind
models 240 were validated by inspecting the results of the applied
winds on the impact predicted by the ballistic model. When applying
a static wind, the predicted final impact of the round moves in the
direction expected and by the rough magnitude expected. One cannot
directly predict how far a given wind pushes a round without using
the ballistic model. The validation tests confirmed that larger
wind magnitudes moved the round farther than smaller magnitude
winds. The format of the data output by the wind model 240 for the
measured winds was verified to match the format used by the static
model. The measured winds can be applied to the ballistics model
260 and testing confirmed that the final impact was moved by the
winds. Given the dynamic nature of the measured winds, one cannot
validate based on direction or magnitude of the induced impact miss
distance.
[0114] Section III.4--Tracker Model: The technology to track a
round in flight exists. Different methods and devices exist to
track the round. Regardless of the method the expected output data
from a tracking system is the same. A acking system must detect the
round and provide relevant position and velocity data about the
round in a relevant reference frame. The exact method of detection
and measurement is not relevant to this process. Instead, what
matters is the ability to use the resulting positional and velocity
data. Given this, the model developed for the tracker model 270
ignores the specific methods and any idiosyncrasies they may have
and focuses on the production of valid tracking data for the
projectile in flight.
[0115] Section III.4.1--Assumptions: The tracker model 270 assumes
that any round tracking device used in a tactical application would
report the position and velocity of the round (i.e., gun-launched
projectile). A real-world application of the tracker can be assumed
to be a separate piece of hardware from the rest of the gun FC
system. As a separate configuration item, any model meant to
recreate the tracker output must be a separate software process.
This controls the availability of data in the system. All data
coming into or out of the tracker model 270 are controlled by
defined network messages. The messages sent by the tracker model
270 are limited. Any real tracker hardware would have to share
network bandwidth with other devices. This limits the size of the
message that can be sent by the tracker to the wind prediction
model. Attempting to send a flight path for a projectile that
contains thousands of data points may bog down a network and
prevent other traffic from reception. The tracker model 270 is
further assumed to incorporate the full predicted ballistic flight
path with winds applied. The tracker model 270 must know the entire
path and then down-select the data points to produce a smaller
track.
[0116] Section III.4.2--Model Description: The tracker model 270
uses the predicted flight path of the round produced by the
ballistics model 260 with winds generated by the wind model 240
applied. The trajectory of the round is produced by the ballistics
model 260 to a granularity controlled only by the integration time
step chosen. The tracker model 270 incorporates the full trajectory
to generate a "tracked" flight path.
[0117] The operator can configure the number of data points in the
track. The data are then used to populate a message that is sent
over a multicast network. The messages generated by the tracker
model 270 contain the positions and velocities of the round in
flight and the initial gun state. The initial gun state data
include the ammo type, initial geographic position, aircraft speed,
aircraft course, and the inertial azimuth and elevation of the
barrel of the gun. Additionally, a value is included to indicate
the number of tracked positions in the message. The tracker
positions are included as an array of latitude, longitude, and
altitude values for the number of selected data points.
[0118] Section III.4.3--Model Factors and Parameters: For the
purposes of all simulation in this research the number of data
points produced by the tracker model was set to ten. This number
was selected to test the possible improvement seen when tracking
comparatively few data points. The tracker model 270 relies on the
ballistics model 260 and the wind model 240. The ballistics and
wind models each have their own inputs and controls. The tracker
model 270 does not control the parameters of these other models.
Network messages can be sent to the tracker model 270 to produce
and send tracks.
[0119] Section III.4.4--Model Verification and Validation: Model
verification was performed to ensure that the tracker model would
run as expected and send the network message expected. Testing
confirmed that the tracker model produced an array of positions on
command and sent those points in a message of the expected size to
the wind prediction model. The tracker model's output was validated
by inspection. Multiple ballistic flyouts were generated with
random initial conditions and wind column applied. The resulting
full trajectory was recorded. The trajectory was then processed
with the tracker model that produced an array of points simulating
the tracker results. The tracker model produced the proper number
of positions as selected for each run. The positions in the tracker
data were compared to the full trajectory. The tracker values
matched the full trajectory values.
[0120] Section III.5--Wind Prediction Model: Wind effects on the
round result in both an epistemic and aleatory error in the
predicted flight path and final impact of the round. Winds pushing
on the round cause the round to miss the intended target. This
error is not accounted for in the initial pointing angles of the
gun. Were the winds from the starting point of the round in flight
to the ground perfectly known, they could be input in the
ballistics model 260 and their effect could be accounted for when
predicting the pointing angles needed to get a round to impact a
target. The epistemic nature of the error caused by winds arises
from the fact that winds are slow to change. The wind column varies
over time, but the ballistic effect of the wind is generally the
same over short periods of time. This has enabled successful
prediction of ballistic winds in tactical applications in the
past.
[0121] Section III.5.1--Assumptions: The wind column can be
predicted based on the observed location and velocity of the round
in flight. The model described herein assumes the absence of errors
other than unaccounted for winds affecting the flight of the round.
This is invalid in the real world, but the other errors tend to
manifest themselves in the platform relative frame of reference
whereas the wind errors manifest themselves in the world relative
reference frame.
[0122] Methods exist to separate the platform relative errors from
the world relative errors. Here one can assume that all platform
relative errors have been accounted for, leaving only the wind
induced errors. The exemplary model is not intended to solve for
the true winds. Rather, the model solves for ballistic winds
between the initial point and the final location used. This final
location can be anywhere along the trajectory of the round
including the final impact on the ground. The smaller the distance
between the initial and final points, the closer the predicted wind
should be to the actual winds acting on the round.
[0123] Section III.5.2--Model Description: The wind prediction
model 280 predicts winds using a two-dimensional bisecting search
algorithm. Using a set of initial conditions for the round and a
final winded location winds are iteratively applied to the
ballistics model 260 to find a set of East and North winds that
push the predicted final location of the round towards the winded
location. The model has predicted the correct ballistic winds when
the distance between the predicted final location and the winded
location is smaller than some specified distance, expressed as the
closure tolerance. In various locations in this disclosure the
successful termination of this search algorithm is referred to as
"closure" on the solution. This means that the search algorithm has
converged on to the correct answer. The search algorithm was
modified for this application from its standard form. A standard
bisecting search converges on the correct solution poorly when the
axes of the search space are not fully aligned with the axes of the
metric being closed on.
[0124] Here, the search space is defined over a range of possible
East and North winds. The model searches through that space to
minimize a DR and CR miss distance in the gun reference frame. The
East/North winds can be rotated into the gun frame to act on the
rounds as a combination of headwind and crosswind. Assuming perfect
alignment of the headwind/crosswind effects on the round, then a
headwind would only affect the DR portion of the projectile's
flight, and the crosswind would only affect the CR portion of the
projectile's flight. The total DR and CR motion of the round are
not independent, however, They are cross correlated; each depending
on the total time of flight of the round.
[0125] For example, a round in flight experiencing a headwind has
more drag applied to it resulting in a reduced time of flight. This
reduced time of flight gives the CR forces (Magnus and lift) less
time to act on the round, reducing the total CR deflection even
though there is no cross-wind. A bisecting search does not account
for this cross-correlation. The search algorithm was modified for
this application to account for the cross-correlation. The standard
form of the bisecting search limits each search axis by one-half on
each iteration through the search.
[0126] The modified method applies a multiplicative increase onto
the resulting limited search space. This has the effect of "bumping
out" the limited search space on each iteration and reduces the
chance that the winded location ends up outside of the search space
due to cross correlation. The wind prediction model 280 yields a
ballistic wind valid for that range of altitudes between the
initial and final points supplied to the model. To be employed, the
closure tolerance and cross-correlation correction coefficient
(CCCC) values must be set appropriately--see Chapter IV.
[0127] Section III.5.3--Model Factors and Parameters: In order to
predict a wind vector, the wind prediction model 280 requires the
initial state of the projectile and a final location for the
projectile. The initial state of the projectile includes the
following in Table 3 as 430 in FIG. 4. The search space is limited
to .+-.100.0 m/s of wind speed in both the East and North
directions. This speed is likely excessive for this analysis and
any practical application. This was chosen because such values are
significantly higher than almost any true winds that would be
encountered. At worst, starting a search space wider than needed
increases the number of iterations needed to close on the ballistic
winds. In a practical application of this wind prediction model 280
the search space can be set narrower to reduce the number of
calculations performed.
[0128] There is the possibility of the search algorithm failing to
find a ballistic wind that can account for the observed location of
the round. This can occur when the required ballistic wind exceeds
the limits of the search space or if the search fails to account
for the cross-correlation of the data as described above. One
should prevent such a failure from occurring by properly tuning the
model parameters. To further ensure that the model as coded does
not continue to search for a solution without possible convergence,
an explicit fifty iteration limit is imposed on the search
algorithm.
[0129] Section III.5.4--Model Verification and Validation: The wind
prediction model 280 was both verified and validated through
extensive testing. The model was run with single-point impact data
with random winds to calculate a ballistic wind for the entire wind
column. Testing confirmed that the wind prediction model 280 was
able to consistently predict the winds based on an input tolerance
to the tweak closure. Adjusting this tolerance to require that the
predicted wind-induced impact to be closer to the observed sample
impact forced the wind prediction to be closer to the actual
applied winds. The reverse was also observed; increasing the
tolerance allowed the predicted wind to be less accurate when
compared to the applied winds.
[0130] This verified that the tweak process not only found the
correct wind values, but that the tolerance control applied to the
tweak closure performed as expected. For some test conditions, the
tweak model failed to predict winds correctly due to the
cross-correlation of the data. Increasing the CCCC value enables
the search algorithm to account for the cross-correlation between
headwind/crosswinds and the DR/CR effect on the final impact. The
details of the setting of the CCCC for the tweak closure are
detailed in Chapter IV.
[0131] Chapter IV--Tuning Wind Prediction Model Parameters: After
coding the models described above, values had to be chosen for the
CCCC (introduced in Section III.5.2) on the wind prediction search
algorithm and the wind prediction closure tolerance. The CCCC must
be tuned to enable the wind prediction model 280 to correctly
predict the wind speed values. As described above, a headwind
acting on a round has both a DR and CR effect on the final impact.
Similarly, a crosswind acting on a round affects both directions of
travel. This cross-correlation can cause the wind prediction model
280 to converge to an incorrect set of wind speeds. This
cross-correlation can be corrected by rotating the impact data from
the DR/CR frame to a headwind/crosswind frame.
[0132] The exact nature of the rotation and value needed depends on
the entire state of the round and the winds at time of fire. This
calculation is complicated and assumes knowledge of the winds that
the modeler would not have. A simpler solution is to increase the
size of the search space on each iteration enough to cover the
cross-correlation. The exact value of the CCCC was chosen to enable
the wind prediction to solve for the correct wind values while
still collapsing the search space quickly. Small values for the
CCCC may still permit the cross-correlation to prevent the wind
prediction model 280 from converging on the correct values. Large
values for the CCCC might eliminate the problems caused by
cross-correlation, but require more iterations of the search
algorithm to complete the search due to the size of the search
space after each iteration.
[0133] The wind prediction tolerance controls when the wind
prediction model 280 terminates its search. This setting is a
distance; provided the predicted winds permit a round to fall
within the specified distance of the measured impact, then the wind
prediction is said to be good and the search terminates. The
accuracy of the wind prediction is controlled by the tolerance
chosen. Using a large distance for the tolerance enables the
predicted winds to be farther off of the actual winds. Using a
small distance for the tolerance induces the predicted winds to be
closer to the actual winds. But, choosing a tolerance too small
causes the wind prediction model 280 to take longer to converge on
the correct solution, sacrificing speed for accuracy.
[0134] Additionally, setting the tolerance to a very small value
may not be practical. There is a limitation to the ability to
measure the impact location of a round. For a precision on the
measured impact location of .+-.0.1 m, then in closing to a
tolerance less than .+-.0.1 m, the FC 290 attempts to converge to
an inaccurate location. For these purposes, the round has an
assumed specific diameter of 0.03 m. Closing with a tolerance of
0.015 m is sufficient to insure that the round would hit the
target. Conversely, setting the tolerance to a very small value may
force the wind prediction to be more stable and less susceptible to
changes in state. As shown below, at shorter times of flight the
tolerance has a strong effect on the accuracy of the wind
prediction and its validity when used at different slant ranges.
This may force the tolerance to be a smaller value than practical
considerations would suggest.
[0135] Section IV.1--Simulation. Description: The same type of
simulation was used to tune both the wind prediction closure
tolerance and the CCCC values. A stochastic simulation with 500
runs was performed. A stochastic simulation was used in this
simulation to give better coverage of the possible range of flight
nominals and gun state. Given the possible variations in initial
state over all of the initial state variables, using a stochastic
method that randomly generates the state variable values at each
run helps to ensure that the testing better covers the total range
of possible values.
[0136] In a real-world setting, a wind prediction system like the
one modeled here would have to be able to perform under any initial
conditions within an expected range. A stochastic simulation is the
easiest way to recreate that type of environment. The simulation
used a static wind column. The static wind column has the same wind
speed and direction for all altitudes. This is not a realistic
model of the wind, but the assumption is useful for testing and
tuning the models. Additionally, the static wind column is a common
model used to correct wind errors applied to guns. This type of
wind model 240 when applied to a specific gun and round type is
referred to as ballistic winds, an averaging of the effects of the
real winds into a single set of wind values.
[0137] The wind speeds are randomly generated for each simulation
run. The possible value for the east and north winds is taken from
a uniform distribution of .+-.100.0 m/s. This speed limitation is
based on the highest measured surface wind speed. The highest
possible wind speed in this simulation is 141.4 m/s, which would be
applied as a constant wind over the flight of the round. This
ballistic wind is unrealistic. Category-5 hurricanes have a
sustained wind speed of at least 70.0 m/s. The upper limit for the
wind speed in this simulation is specifically set to exceed the
maximum possible to ensure that the models are stable and valid at
higher speeds. A good wind prediction model 280 should be capable
of calculating wind speeds even when they fall outside of the
expected range of real wind speeds. The flight nominals of the
aircraft were varied randomly as well. The flight model of the
aircraft and the modeling of the gun pointing reduce the number of
settable variables. The values for each variable were selected from
a uniform random distribution between the values shown in Table 4
as 440 in FIG. 4.
[0138] The simulation was executed as a stochastic simulation to
ensure that the possible combinations of initial state were covered
as well as possible. The ranges selected for all of the variables
include but are not limited to those possible values see in actual
gunfire missions. At each set of randomly generated initial
conditions and winds a single ballistic flyout is run, creating a
winded impact location. This winded impact location and the initial
gun and aircraft state are then used by the wind prediction model
280 to predict a ballistic wind that accounts for the observed
offset of the impact from the expected no-wind impact location. One
can expect that the predicted winds to closely match the static
wind model values used in each run.
[0139] Section IV.2--Initial Tuning of Cross-Correlation Correction
Coefficient: Multiple sets of simulation data were collected to
analyze the effect of changing the CCCC value on the wind
prediction model's ability to close on the proper wind speeds. For
each of the data sets the wind prediction closure tolerance was set
to 10.sup.-16 m. This value was selected because it would force the
wind prediction model 280 to terminate on maximum number of
iterations, or fifty iterations, through the wind search space.
This reduced the possibility that any errors in the wind prediction
are from the closure tolerance. Any errors that are outliers from
the rest of the data set are due to the cross-correlation as
described above. The initial run set the CCCC equal to 1.0, meaning
the wind prediction model 280 was not trying to account for the
cross-correlation. The east and north winds predicted for each run
are then compared to the applied winds for that run and a radial
wind error is computed. That radial wind error is plotted against
the time of flight for the round in each run in FIG. 5 for Radial
Wind Error with CCCC=1.0.
[0140] In particular, FIG. 5 illustrates a graphical view 500 of
transient Radial Wind Error for CCCC=1.0. Time of flight 510 in
seconds (s) represents the abscissa and radial wind error 520 in
meters-per-second (m/s) denotes the ordinate. Most points lie near
errors less than 0.05 m/s, but several outliers approach 1.0
m/s.
[0141] Most of the runs have a very low error, so low that the
scale of the plot obscures the exact magnitude. Of note are the few
data points that show runs with higher radial wind errors. These
errors remain after the wind predictor model had completed fifty
iterations through the bisecting search algorithm. They are due to
the unaccounted for cross-correlation. More data were generated
increasing the CCCC value by 0.01 for each up to CCCC=1.1. Data
sets for CCCC values up to 1.07 are shown in FIG. 6 as Wind errors
versus time of flight at varying values of CCCC.
[0142] FIG. 6 illustrates a graphical view 600 of Radial Wind Error
plots for several CCCC values, with flight time 510 as the abscissa
and radial wind error 520 as the ordinate, albeit with varying
scales. For CCCC values of 1.05 and higher, the outliers have been
eliminated from the radial wind errors. This indicates that the
CCCC value is sufficiently high to account for the observed
cross-correlation between the DR/CR impacts of the round and the
headwind/crosswind effects on the round.
[0143] Section IV.3--Tuning the Wind Prediction Closure Tolerance:
The wind prediction model's closure tolerance was investigated
next. The CCCC value used during the data generation for this
portion was 1.1. This value is higher than the apparent lower
possible value of 1.05 found in Section IV.2. The higher CCCC value
was chosen for this portion of the research to ensure that the
cross-correlation problem would not affect the results as the
number of data points generated in each set increased. The number
of data points generated in each run was increased from 500 to
5000. The simulation was run as described above and radial wind
errors were calculated. An initial data set was generated with a
closure tolerance of 0.01 m. The results are plotted in FIG. 7 as
Radial wind errors over time of flight with closure tolerance of
0.01 m.
[0144] FIG. 7 illustrates a graphical view 700 of transient Radial
Wind Error for CCCC=1.07. Time of flight 710 in seconds (s)
represents the abscissa and radial wind error 720 in
meters-per-second (m/s) denotes the ordinate. The errors reach a
peak near 0.01 m/s at about 2 s in flight and asymptotically
decrease thereafter.
[0145] Note the shape of the curve to the data, which is expected.
Consider the situation where a round is fired from a very short
distance. With a low time of flight, the winds have very little
time to affect the round and changes its trajectory. A round with a
longer time of flight has a longer time for the winds to affect the
trajectory. This means predicting winds for rounds with a longer
time of flight requires more accuracy to meet a closure tolerance
than such predictions would require for rounds with shorter times
of flight.
[0146] This relationship established a baseline for the validity of
the wind correction as the time of flight of the round changes. A
prediction made based on firing at a lower time of flight can have
more error in it than one made at a longer time of flight and still
fall within tolerance. For a prediction made at a lower time of
flight, the aircraft ascends and attempts to fire accurately using
the prior wind prediction. Under these circumstances, the round
might fall outside of the tolerance based only on the effects of
the wind prediction errors playing out over a longer time of
flight.
[0147] This simulation was repeated with varying closure tolerances
and a pattern was observed. All of the data sets showed the same
curved pattern as in FIG. 7. The edges of the curves for each data
set were isolated and trend-lines calculated to fit the maximum
edge of each of the curves. The best fit was achieved with a power
curve:
y=ax.sup.b, (15)
where the fitting constants and b found at varying wind prediction
tolerances, showed a clear relationship to each other. FIG. 8
provides tabular views 800 including Table 5 with curve-fit
constants for eqn. (15) as 810 and Table 6 iteration variation with
CCCC as 820.
[0148] Based on the pattern in the fitting constants a generalized
equation was expressed to describe the relationship between the
maximum possible wind error and the time of flight of the round
that would fall within a specified closure tolerance:
.epsilon..sub.wind.ltoreq.4.374563d.sub.tol.tau..sup.-1.36009,
(16)
where .epsilon..sub.wind is the radial wind error in
meters-per-second d.sub.tol is the wind prediction tolerance in
meters (m), .tau. is the time of flight in seconds (s) and the
fitting parameter values are set based on the data in Table 5 as
810 in FIG. 8. For practical considerations, the closure tolerance
never needs to predict a wind that would move the round any closer
to the measured impact than one-half of the width of a man-sized
target. This would ensure a direct hit onto the target assuming
that all other errors were accounted for at the time of fire. Based
on small-arms target practice standards, the width of a man-sized
target is 0.45 m.
[0149] FIG. 9 illustrates a graphical view 900 of transient Radial
Wind Error for CCCC=1.05. Time of flight 910 in seconds (s)
represents the abscissa and radial wind error 920 in
meters-per-second (m/s) denotes the ordinate. Most errors reach
remain below 0.01 m/s with scattered outliers an order of magnitude
higher. The longest predicted time of flight of 40.0 s was used.
Knowing the time of flight and the closure tolerance the above
equation can be used to find an upper bound to the wind prediction
error. This upper bound can then be used at a lower time of flight,
in this cas 5 s, to calculate a closure tolerance, given:
a d 1 .tau. 1 b .gtoreq. wind .ltoreq. a d 2 .tau. 2 b , ( 17 ) d 1
.tau. 1 b = d 2 .tau. 2 b , and ( 18 ) d 1 .tau. 1 b .tau. 2 b = d
2 , ( 19 ) ##EQU00007##
resulting in the numerical value for distance in meters:
( 0.225 ) 40.0 - 1.36009 2.5 - 1.3009 = d 2 = 5.182 10 - 3 m . ( 20
) ##EQU00008##
This closure tolerance, 5.182 mm, is enough to ensure that a wind
prediction calculated based on shots with a time of flight of 2.5 s
still results in rounds impacting within 0.225 m assuming a time of
flight of 40.0 s.
[0150] Section IV.4--Final Tuning of Tolerance and CCCC: In Section
IV.2, the CCCC was investigated and a range of possible values was
determined. Those data showed that a CCCC value of 1.05 or larger
was sufficient to remove the outliers due to cross-correlation
between the head/crosswinds and the DR/CR impacts of the round when
a sample of 500 data points is used. The wind prediction closure
tolerance was set to a small value, 10.sup.-16 m, to ensure that
the wind prediction went through as many cycles as possible.
[0151] Based on the closure tolerance tuning in Section IV.3, the
CC was reexamined. The sample size was increased from 500 shots to
5000 shots to cover more initial states of the gun and aircraft.
There may be states that were not covered with five-hundred sample
shots that would show the same outliers seen with lower CCCC
values, The stochastic nature of the data generation was controlled
to ensure that the same states were generated for each CCCC value
and that the first five-hundred states tested matched the states in
the prior analyses. New data sets were generated with CCCC values
ranging from 1.05 to 1.1 in steps of 0.01. The goal of the analysis
involved finding a CCCC setting that eliminates the
cross-correlation outliers, while minimizing the number of
iterations the wind prediction model 280 executes to close to
within the specified tolerance.
[0152] At each CCCC value, the number of iterations to close was
recorded and compared to subsequent runs. The expectation is that
larger CCCC values open the search space and lead to more
iterations overall. Runs with CCCC=1.05 revealed outliers in FIG. 9
runs beyond number five-hundred. Outliers at CCCC=1.05 with
five-thousand samples. These three data points indicate that a
larger CCCC value is required to reduce the chances of seeing a
failure to close properly due to cross-correlation. At CCCC=1.06 no
outliers were apparent from the data. This held true for all CCCC
values larger than 1.05 investigated. The numbers of iterations
required for the wind prediction to close to within the specified
tolerance at a given CCCC were compared against the number of
iterations required at CCCC=1.06 in Table 6 as 820 in FIG. 8. No
benefit was observed with CCCC values greater than 1.06. The number
of iterations required by the wind prediction model 280 increased
on average as the CCCC value increased, though the increase was
small.
[0153] Section IV.5--Conclusion: Initial runs of the simulation
confirmed that the wind prediction model 280 performed as expected.
It was able to close on a single-point wind value to within the
specified tolerance, verifying the model's functionality. Tuning
tests were performed to find and set the values of the
cross-correlation correction coefficient and the wind prediction
closure tolerance. The CCCC was set to 1.06. This setting was
sufficient to eliminate all outliers in a five-thousand sample data
set. The closure tolerance was set to 5.182.times.10.sup.-3 m. This
value was selected based on the behavior of the data showing the
relationship between radial errors in the wind prediction based on
the time of flight of the projectile. This tolerance was selected
to ensure that the effects of changes in state that would affect
the time of flight of a round would induce no more than 0.225 m of
possible miss distance so to poor wind prediction.
[0154] Chapter V--Single-Point Prediction of Ballistic Winds: The
single-point wind prediction model 280 can be used with a constant
value wind model, as shown in Chapter IV, or instead can be used
against a measured wind model. When tested with a constant wind
model, the wind prediction model 280 generates a wind speed and
direction (or East and North wind speeds) that matches the constant
wind model speed and direction to within an error tolerance based
on the closure tolerance distance used in the wind prediction model
280 as described by eqn. (16).
[0155] In this chapter, single-point wind predictions are made at
varying initial states using multiple measured wind models. These
data are used as a baseline of current wind prediction
capabilities. Subsequent sections incorporate these single-point
ballistic wind predictions to compare to wind predictions made
using data from a round tracking sensor.
[0156] Section V.1--Simulation Description: For this simulation
sixteen measured winds were used as the winds applied to the round
in flight. These winds were measured using a radiosonde
meteorological balloon. The measurements were taken on different
four different days at the Naval Surface Warfare Center at
Dahlgren, Virginia. Wind Profile 1 provides a sample wind profile
showing the East and North wind speeds with respect to altitude.
FIG. 10 illustrates a graphical view 1000 of Wind Profile 1. Plot
1010 provides East wind speed 1020 (m/s) as the abscissa, with
altitude 1030 in kilometers (km) as the ordinate. The staggering
line 1040 shows East wind variation as altitude increases. Plot
1050 provides North wind speed 1060 (m/s) as the abscissa, with
altitude 1030 in kilometers (km) as the ordinate. The staggering
line 1070 shows North wind variation as altitude increases.
[0157] A stochastic simulation was run with each of the sixteen
wind profiles. Each simulation consisted of ballistic impact
predictions made with five-thousand different initial conditions.
The gun altitude, aircraft speed, and total gun depression angle
were generated for each of the runs from a uniform distribution
with the limits shown in Table 4 as 440 in FIG. 4. The random
number generator seed was controlled to ensure that the same
five-thousand states were used with each wind profile. The
five-thousand states also matched the states used in the analysis
in Chapter IV.
[0158] At each of the five-thousand initial states a ballistic
flyout was performed with measured winds applied. The winded impact
location of the round was recorded. The initial state and the
winded impact location were used by the wind prediction model 280
to generate ballistic wind that would account for the observed
offset of the winded impact location from the expected no-wind
impact location. The closure tolerance used for all simulation runs
was 5.182.times.10.sup.-3 m, as used in Chapter IV. The result is a
ballistic wind that holds the same speed and direction from the
ground up to the altitude of the gun at time of fire.
[0159] Section V.2--Results: The wind, prediction model 280 was
able to solve for a ballistic wind on all five-thousand runs for
each of the sixteen Treasured wind profiles. This was verified in
two ways: First, the total number of iterations required to close
on a ballistic wind to within the closure tolerance was recorded
for each run. The maximum possible number of iterations permitted
by the model for each attempt at finding a ballistic wind was
fifty. The minimum number of iterations used for any of the runs
was ten; the maximum was twenty-two. These values are well below
the maximum of fifty runs allowed.
[0160] Had the wind prediction model 280 failed to close to within
the closure tolerance distance specified, then the model would have
continued to iterate through the search space until the search
reached the maximum number of iterations. The fact that no run ever
required close to fifty iterations to complete indicates that the
wind prediction model 280 successfully closed on a ballistic wind.
Second, each ballistic wind prediction was tested to ensure that
the resulting impact fell within the closure tolerance of the
initial winded impact used as input to the wind prediction model.
The ballistic wind result was applied to the round in flight and
another ballistic flyout was performed. The new impact location was
compared with the initially generated winded impact location and
the distance between them was calculated. For all eighty-thousand
data runs the distance between the new impact location and the
original winded impact location was within the closure
tolerance.
[0161] Displaying the results of all eighty-thousand runs is
difficult. Even limiting the data to a single wind profile out of
the sixteen tested profiles does not help as each profile was used
to test five-thousand different initial states. To better
investigate the data, one can more simply select a few ballistic
wind profiles based on states at varying altitudes and plot those
against the measured wind profiles. An example of the wind
prediction is presented in FIG. 11 for three sample states out of
the set of five-thousand for Wind Profile 1.
[0162] FIG. 11 illustrates a graphical view 1100 of Three
Representative Ballistic Wind with Wind Profile 1. Plot 1110
provides East wind speed 1120 (m/s) as the abscissa, with altitude
1130 (km) as the ordinate. The vertical lines 1140 terminated by
dots show East wind predictions. Plot 1150 provides North wind
speed 1160 (mIs) as the abscissa, with altitude 1130 (km) as the
ordinate. The vertical lines 1170 terminated by dots show North
wind predictions. For comparison, the staggered lines 1040 and 1070
represent the respective East and North wind speeds as measured at
varying altitudes. The vertical lines 1140 and 1170 represent the
ballistic wind predicted for a given simulated firing event. The
East and North wind speeds are constant through the entire wind
profile from the initial altitude to the ground for these ballistic
winds. An inspection of the results shows that the ballistic wind
profile tends to fall close to the average of the wind speeds from
the starting altitude to the ground at 0.0 m.
[0163] For example, the highest altitude ballistic wind profile for
the North wind speed has a value of -4.41 m/s. The average wind
speed from that same altitude to the ground is -5.41 m/s. The
values are close but not exact. This is expected due to the
physical effects of the wind on the round, which changes based on
the speed of the round. The state of the round, such as the air
speed of the round, changes as the altitude decreases. The change
in air speed relative to the speed of sound causes the ballistic
wind diverge from the average wind speed due to the increased drag
force experience in the transonic region of flight.
[0164] A visual inspection also shows that the values make
intuitive sense. The measured winds have regions were wind speeds
fall on either side of the predicted ballistic wind speed. This
indicates that the ballistic wind profile is an attempt at
balancing out the effects of the dynamic measured wind profile with
a single value. The East wind speed graph has all three wind
predictions grouped closely together. Visual inspection of the
measured East wind shows that the wind speeds at almost all
altitudes were between 5 m/s and 10 m/s. One can expect that the
predicted values would fall in that band of wind speeds, which is
what the results show. Plotting similar data for all five-thousand
ballistic winds for a given measured wind profile would do little
more than fill the graph with vertical lines. A graph that shows
only the top, of the ballistic wind profile is more readable. The
points on such a graph in FIG. 12 five-thousand Ballistic Winds
with Wind Profile 1 represent the entire ballistic wind, but are
only shown at the initial altitude for the initial prediction.
[0165] FIG. 12 illustrates a graphical view 1200 of five-thousand
Ballistic Wind points with Wind Profile 1. Plot 1210 provides East
wind speed 1220 (m/s) as the abscissa, with altitude 1230 (km) as
the ordinate. The curved spread of points 1240 show East wind
predictions. Plot 1250 provides North wind speed 1260 (m/s) as the
abscissa, with altitude 1230 (km) as the ordinate. The curved
spread of points 1270 show North wind predictions. For comparison,
the staggered lines 1040 and 1070 represent the respective East and
North wind speeds as measured at varying altitudes.
[0166] The ballistic winds are expected to change as the altitude
changes. Changing the altitude of the initial fire changes the
amount of atmosphere that the round flies through, The, ballistic
wind necessarily changes based on certain portions of the measured
wind profile being included or excluded by the starting altitude.
The ballistic winds are not the same at the same altitude. The
spread of the points at a given altitude indicates that some factor
other than altitude is causing a change in the expected wind
effects on the round in flight. The gun elevation, which was also
permitted to vary for the data points shown, and the dynamics of
the measured wind profile itself are the factors that cause the
spread in the ballistic winds at a given altitude.
[0167] Gun elevation changes the slant range to the impact location
and the time of flight of the round. The measured winds have a
different effect on a round that takes longer to reach the ground
than on another round with a shorter time of flight. For a round
fired from the same altitude, the measured winds affecting the
round are the same but the state of the round varies in other ways.
Rounds with a longer time of flight have a lower airspeed at each
altitude than rounds with a lower time of flight. The equations of
motion used to model the flight of the round depend on airspeed to
calculate the forces acting on the round. Thus, even though the air
column is the same for both steep and shallow shots, the round
experiences those winds differently, which leads to a different
prediction of the ballistic wind.
[0168] The dynamics of the measured wind also affect the spread in
ballistic wind predictions. The East winds in FIG. 12 show little
variation from about 5500 m to 250 m of altitude. This leads to a
very narrow spread in the speeds of the predicted ballistic winds
in that band of altitudes. The measured North wind speeds show more
variation that leads to a greater spread in the ballistic winds at
a given altitude. This same feature hold for all sixteen tested
wind profiles, as can be seen in FIGS. 13 through 16.
[0169] FIG. 13 illustrates graphical views 1300 of East and North
wind speed variations with altitude. Plots 1310 and 1320 provides
East and North wind speeds for Wind Profile 1. Plots 1330 and 1340
provides East and North wind speeds for Wind Profile 2. Plots 1350
and 1360 provides East and North wind speeds for Wind Profile 3.
Plots 1370 and 1380 provides East and North wind speeds for Wind
Profile 4. For these four plots, the wind speed 1220 (m/s) is the
abscissa, with altitude 1230 (km) is the ordinate, with the
staggered lines denoting the wind velocity variation with altitude,
and the curved spread denoting the ballistic wind predictions.
[0170] FIG. 14 illustrates graphical views 1400 of East and North
wind speed variations with altitude with similar abscissa and
ordinate scales as views 1300. Plots 1410 and 1420 provides East
and North wind speeds for Wind Profile 5. Plots 1430 and 1440
provides East and North wind speeds for Wind Profile 6. Plots 1450
and 1460 provides East and North wind speeds for Wind Profile 7.
Plots 1470 and 1480 provides East and North wind speeds for Wind
Profile 8.
[0171] FIG. 15 illustrates graphical views 1500 of East and North
wind speed variations with altitude with similar abscissa and
ordinate scales as views 1300. Plots 1510 and 1520 provides East
and North wind speeds for Wind Profile 8. Plots 1530 and 1540
provides East and North wind speeds for Wind Profile 10. Plots 1550
and 1560 provides East and North wind speeds for Wind Profile 11.
Plots 1570 and 1580 provides East and North wind speeds for Wind
Profile 12.
[0172] FIG. 16 illustrates graphical views 1600 of East and North
wind speed variations with altitude with similar abscissa and
ordinate scales as views 1300. Plots 1610 and 1620 provides East
and North wind speeds for Wind Profile 13. Plots 1630 and 1640
provides East and North wind speeds for Wind Profile 14. Plots 1650
and 1660 provides East and North wind speeds for Wind Profile 15.
Plots 1670 and 1680 provides East and North wind speeds for Wind
Profile 16.
[0173] Section V.3--Conclusion: From the data as described, one can
deduce that the wind prediction model 280 can find a single-point
ballistic wind that accounts for the miss distance when a measured
wind is applied to the round. In Chapter IV the wind prediction
model 280 was tested using a static wind model. Here dynamic winds
based on real winds as measured by a meteorological balloon were
used to induce a miss distance in the final impact. The miss
distance and the initial state were used to predict a ballistic
wind to correct for the cumulative effect of the measured
winds.
[0174] In Chapter IV, one could expect that the ballistic winds
would match the randomly generated winds to within some error
metric. In this section, the ballistic winds do not match the input
winds due to the nature of the wind model 240 used to generate the
ballistic wind. Features of the ballistic wind were used to confirm
that the results were correct. The predicted speeds of the
ballistic winds are mostly controlled by the measured wind speeds
used as inputs. The speeds of the ballistic wind also vary based on
the state of the gun at the time of fire. The initial altitude is a
strong controller. This is evident from the East and North speed
predictions changing as the altitude changes. The initial altitude
is not the only controller, though. The spread in ballistic wind
values at a given altitude indicate that something else beyond the
altitude is affecting the ballistic wind. The gun elevation, which
controls the time of flight of the round, changes the state of the
round at a given altitude. This difference in state leads to
different interactions with the atmosphere.
[0175] The ballistic wind prediction changes based on the time of
flight and the variability of the atmosphere. Based on the
variations in the ballistic wind values seen in the graphs, one can
expect that predictions remain valid provided the gun does not
change state greatly. This is not a reasonable expectation in
flight. Any state change that causes a round to have a different
time of flight than the firing event used to make the wind
prediction may render the ballistic wind invalid, or at the very
least less valid. The data generated in this section are used as a
point of comparison in subsequent sections. The results of a
multipoint ballistic wind prediction method are compared to this
single-point data to determine which method better models the winds
and be less prone to errors induced by changes in state.
[0176] Chapter VI--Multipoint Wind Prediction: The single-point
wind prediction method was shown to work as expected and make
ballistic wind predictions that account for the observed wind
induced miss distance to within the closure tolerance. The method
can be used to predict winds under varying initial gun and aircraft
states. Results from the Chapter V show that the ballistic wind
speeds vary based on the initial conditions at the time of fire
even when fired through the same wind column. During a live-fire
event, the state of the gun and aircraft is constantly changing.
This change in state may reduce the ability of the single-point
ballistic wind speeds to correct for the actual wind effects.
[0177] This possibility is due to the limited number of data points
being incorporated to predict the winds, using only the initial and
final locations of the projectile. A method that incorporates more
data, if available, is expected to generate a predicted wind that
better matches the true winds acting on the round. This chapter
proposes a method to model winds accurately based on increased
information about the round in flight. A round tracking sensor is
modeled to produce location and velocity data about the projectile.
This information is used to generate a prediction of the wind
speeds acting on the round. The closeness of the multipoint wind
predictions is compared to the measured wind profiles. The metrics
derived are then compared to similar metrics calculated using the
single-point wind prediction. Based only on closeness of fit, the
multipoint wind prediction method produces wind predictions that
are a much closer match to the true winds than the single-point
wind prediction method.
[0178] Section VI.1--Point Data Generation: The previous analysis
of the single-point wind prediction only used the initial firing
state and the final impact location to make a wind prediction. For
the multipoint wind prediction, a round tracking sensor is modeled
to provide data for the path of the round in flight. This track
sensor model runs as a separate process for the simulation. This
process uses the ballistics model, applying the measured winds to
produce an offset impact and a full trajectory of the round in
flight. Based on user configuration settings the track sensor model
produces a data set with a specified number of locations and
velocities for the round in flight. These data points are sent via
a network message to the wind prediction model. The design and
execution of the track sensor model is intended to isolate any
possible information about the measured winds being applied to the
ballistic model. The wind prediction model 280 has no information
about the underlying winds in the system.
[0179] Section VI.2--Determining Wind Prediction Parameters: For
this research the track sensor model was configured to generate
data for eleven points along the flight path of the projectile. The
first point is always the initial location of the round as it exits
the barrel. The last point is always the impact location. The other
nine data points are evenly spaced along the flight path of the
round. The spacing is based on the time of flight of the round, not
the distance traveled or the altitude of the round at a given
point. This leads to ten intervals bounded by eleven points with
the same time of flight in each interval. The number of data points
chosen for the track sensor is purposefully set to a low number.
The intent is to show that even with fairly sparse data, only
eleven points, the wind prediction can be improved when compared to
the single-point method. There is nothing to prevent further
investigation with progressively larger numbers of tracked
locations.
[0180] This investigation shows that improvements are seen with few
data points; any extra data only further improve the wind
predictions increase the overall reliability of the prediction. The
multipoint method makes a wind prediction within each interval in
the track data. The time of flight of the round in each interval
has the potential to be much shorter than the shortest time of
flight simulated with the single-point wind prediction method. As
was shown in Chapter IV, the closure tolerance for the wind
prediction and the time of flight of the round control the maximum
possible radial wind error. This relationship is expected to hold
for each interval of the multipoint wind prediction. This reduced
time of flight increases the possible wind prediction error. To
reduce the possible maximum wind error, the closure tolerance was
reduced to 0.00001 m for all of the runs.
[0181] Section VI.3--Multipoint Wind Prediction Method: FIG. 17
illustrates a flowchart view 1700 of Multipoint Wind Prediction
Model Architecture. The process initiation begins with start 1705,
followed by receipt of round track data points 1710. This initiates
process loop 1720 at an iteration interval leading to calculation
of ballistic wind 1730 between the current interval and the next
interval. The process continues to recordation of ballistic wind at
altitude 1740, followed by correction of predicted round velocity
1750 to match measured values.
[0182] Next a query 1755 determines whether the iteration steps
reach a termination value. If not, the operation returns to the
calculation 1730. Otherwise, the operation proceeds to a filter
predicted wind profile 1760 and then to set wind speed to zero
velocity at zero altitude 1770. This follows an output wind profile
1790 and then termination 1795. The multipoint wind prediction
model 280 uses the same wind prediction closure method as the
single-point wind prediction. The single-point wind prediction
model 280 takes into account only initial state of the gun and the
final impact location to predict a ballistic wind that accounts for
the wind induced miss distance. The multipoint model performs the
same ballistic wind prediction but between measured points along
the flight path of the round. A diagram of thealgorithm used in
this analysis is presented in FIG. 17.
[0183] The wind prediction model 280 receives information about the
position and velocity of the round at various points along its
flight path ordered by the altitude of the round from the track
sensor model. Starting with the initial state of the round and gun
and the first measured position of the round along its flight path,
the wind prediction model 280 find a ballistic wind that accounts
of the observed difference between the round location and the
predicted location had there been no wind. This ballistic wind is
considered to be valid only between the two points for which
calculations were conducted. The wind prediction is recorded at the
given altitudes. The predicted state of the round at the first
measured location is used in the next iteration.
[0184] The round tracking model assumes that the position and the
velocity of the round are measured, but the accelerations of the
round are not known and must be predicted using the ballistics
model. The position, orientation, spin rate, and accelerations of
the round are taken from the ballistics model prediction at the end
of the wind prediction model search. The velocity of the round is
set to the velocity measured by the track sensor for the round at
that location. The process continues by finding a ballistic wind
that would account for the measured location between the next two
points in the track data to the end of the tracked data list.
[0185] FIG. 18 illustrates a graphical view 1800 of Initial Raw
Wind Speed Predictions of resulting raw data for Wind Profile 1
that require further processing. Plot 1810 provides East wind speed
1820 (m/s) as the abscissa, with altitude 1830 (km) as the
ordinate. Vertical line segments 1840 terminating in dots show East
wind predictions. Plot 1850 provides North wind speed 1860 (m/s) as
the abscissa, with altitude 1830 (km) as the ordinate. Vertical
line segments 1870 terminating in dots show North wind predictions.
For comparison, the staggered lines 1040 and 1070 represent the
respective East and North wind speeds as measured at varying
altitudes. The predicted North wind speeds in segments 1870 fit
fairly well to the real winds. The East wind speeds in segments
1840 do not appear to fit well at all. This was seen in many of the
wind predictions when the applied measured winds were comparatively
static. The measured wind speed data has a roughly constant overall
trend from 4000 m almost until the ground. There are small
oscillations in the data off of a roughly constant value, but there
is no large-scale trend to the data when compared to the North wind
speed data.
[0186] The wide oscillations seen in the raw ballistic winds in the
East direction are an artifact of the prediction error expected.
The time of flight between the data points is small, enabling the
wind prediction model 280 to have a high error in the predicted
ballistic winds in a given interval. This wind error changes the
accelerations in the state of the round at the end of that
interval. The error in the accelerations and slight error in
position allowed for by the closure tolerance with both affect the
wind prediction in the next interval. Assuming the actual winds
acting on the round do not change largely in the following
interval, the wind prediction model 280 will "chase" the errors in
the acceleration and position and overcompensate for the effects of
the wind in the wrong direction. This effect compounds over time
leading to the large oscillations observed. Once the entire path of
the round has been processed for raw ballistic wind predictions,
the data are filtered.
[0187] In the disclosed research, the data were analyzed through a
running average filter with a sliding window of two data points.
FIG. 19 illustrates a graphical view 1900 of Filtered Wind Speed
Predictions for Wind Profile 1. Plot 1910 provides East wind speed
1920 (m/s) as the abscissa, with altitude 1930 (km) as the
ordinate. Vertical line segments 1940 terminating in dots show East
wind predictions. Plot 1950 provides North wind speed 1960 (m/s) as
the abscissa, with altitude 1930 (km) as the ordinate. Vertical
line segments 1970 terminating in dots show North wind predictions.
For comparison, the staggered lines 1040 and 1070 represent the
respective East and North wind speeds as measured at varying
altitudes. This filter eliminates the oscillation seen in the
predicted values for the East wind speed in segments 1940. The wind
speed at ground level was set to 0.0 m/s. Though the winds
immediately above the ground level may be non-zero at the ground,
there is no wind.
[0188] The last step in processing the raw ballistic winds into
final form is to assume that the wind speeds are linearly
interpolated between the actual data points. From the graphs one
can assume that the wind speed is constant from the initial point
in the interval to the end of the interval. The ballistic wind then
immediately jumps to the single value of the next interval.
Instead, one can assume that the ballistic wind speed predicted
only applies at the start of an interval. The wind speed at the end
of each interval is assumed to be the wind speed at the start of
the next interval. Any values between these points are modeled
using a linear interpolation between the points as shown in FIG.
20--Final Multipoint Wind Prediction.
[0189] FIG. 20 illustrates a graphical view 2000 of Final
Multipoint Wind Prediction for Wind Profile 1. Plot 2010 provides
East wind speed 2020 (m/s) as the abscissa, with altitude 2030 (km)
as the ordinate. Contiguous multipoint line 2040 connected by dots
show East wind predictions. Plot 2050 provides North wind speed
2060 (m/s) as the abscissa, with altitude 2030 (km) as the
ordinate. Contiguous multipoint line 2070 connected by dots show
North wind predictions. For comparison, the staggered lines 1040
and 1070 represent the respective East and North wind speeds as
measured at varying altitudes.
[0190] Section VI.4--Simulation Description: The simulation was
performed similar to the previous sections. A set of five-thousand
random initial states were generated and incorporated. The random
seed for these five-thousand states was controlled to ensure that
the states would match previous runs and would be the same for each
of the wind profiles used. For each of the five-thousand initial
states, a measured wind profile was applied and the ballistic model
was then used to generate an impact location, This was repeated
with all sixteen measured wind profiles.
[0191] The Monte Carlo nature of the simulation, with five-thousand
randomly generated initial states, was selected to ensure that the
possible range of states was covered with a reduced chance of
biasing results based on selection of initial state. To limit the
initial states to a possible subset of states or to do a parametric
search through the allowed ranges of the initial state variables
may cause the analysis to miss some aspect of the system. By
performing a stochastic analysis the chances of missing an effect
due to excluding a combination of initial state values via a
strictly controlled selection process is reduced.
[0192] For each initial state, the full track of the projectile was
recorded from the ballistics model 260 and input to the track
sensor model. From this track data, ten evenly spaced points along
the path are selected that, with the initial location of the round
at time of fire, form the eleven points used to make the ballistic
wind prediction. The spacing of these points was controlled by the
total time of flight of the round, dividing the total time into ten
evenly spaced segments with the tracked points making up the end
points of those segments. The points were not selected based on
altitude or position. For each of the five-thousand random runs
with a given measured wind profile a multipoint ballistic wind
profile was generated using the setting referenced in Section VI.2
and using the method described in Section VI.3.
[0193] Section VI.5--Results: With five-thousand initial states and
sixteen different wind profiles, eighty-thousand individual runs
were completed. All eighty-thousand runs completed successfully,
producing ballistic wind profiles that account for the measured
winds and correct the impact miss distance to within the specified
closure tolerance.
[0194] Section VI.6--Analysis of Results: The goal of this research
is to investigate the efficacy of wind predictions made using
multiple measured locations along the flight path of the round. The
best manner to judge a predicted ballistic wind is to apply the
results in a simulated ballistic flyout to determine whether or not
the ballistic winds correct for the observed impact miss distance.
The wind prediction model 280 already accounts for this kind of
analysis. The ballistic wind prediction is controlled by the
closure tolerance. Wind predictions are checked at time of
calculation to ensure that they generate an impact within the
closure tolerance when applied to a ballistic flyout. As a check on
the multipoint wind prediction compared to the single-point, the
fit of the wind model to the measured winds can, be used as an
analog to the correctness of the wind prediction.
[0195] A perfect wind prediction model 280 would match the measured
winds exactly. Expectation of perfect matching by a modeled wind
profile to match the measured winds is not practical. One can
reasonably expect that a valid ballistic wind model matches the
true winds closely. The closeness of fit is measured by examining
the standard deviation of the predicted wind model 240 off of the
measured wind speeds at all altitudes. The standard deviation
metric was calculated for both the single-point results and the
multipoint model results for all five-thousand initial states. The
results for each of the sixteen different wind profiles were kept
separate. Using the above wind prediction as an example and
comparing to the single-point wind prediction, the differences and
quality of fit are visually apparent in FIG. 21--Comparison of
Single-point and Multipoint Models.
[0196] FIG. 21 illustrates a graphical view 2100 of Comparison of
Single-point and Multipoint Models similar to view 2000 for Wind
Profile 1. Plot 2110 provides East wind speed 2120 (m/s) as the
abscissa, with altitude 2130 (km) as the ordinate. Vertical line
2140 denotes a single-point East wind prediction. Plot 2150
provides North wind speed 2060 (m/s) as the abscissa, with altitude
2130 (km) as the ordinate. Vertical line 2170 denotes a
single-point North wind prediction. For comparison, the multipoint
lines 2040 and 2070 connected by dots show the respective East and
North wind predictions, and the staggered lines 1040 and 1070
represent the respective East and North wind speeds as measured at
varying altitudes. The multipoint lines 2040 and 2070 follow
respective the staggered lines 1040 and 1070. The measured wind
speeds applied to the round in flight follow more closely than the
single-point values.
[0197] There are variations in the measured winds that are not
captured by either of the wind prediction methods. This is a
limitation caused by the use of only ten data points along the
trajectory of the round. To provide, a quantitative measure of the
closeness of the predicted data to the actual data, the difference
between the measured wind speed and the predicted wind speed was
calculated at each included altitude in the measured wind speed for
both wind prediction methods and in both the East and North
directions.
[0198] FIG. 22 illustrates graphical views 2200 of Modeled Wind
Errors Off of Measured Winds. East wind plot 2210 shows altitude
2210 (km) denoted by the abscissa and East wind error 2220 (m/s),
with trace predictions for single point 2230 and filtered
multipoint 2240. North wind plot 2250 shows altitude 2260 (km)
denoted by the abscissa and East wind error 2270 (m/s), with trace
predictions for single point 2280 and filtered multipoint 2290. For
both East and North wind directions, single-point trace predictions
feature higher errors than filtered multipoint traces, but
otherwise follow in similar manners.
[0199] The standard deviations of the residuals, shown in FIG.
22--Modeled Wind Errors Off of Measured Winds, were calculated to
test the goodness of the, fit of the predicted winds to the
measured winds. For the East winds, this single-point wind
prediction 2230 had a standard deviation of 2.44 m/s, and the
multipoint wind prediction 2240 had a standard deviation of 1.38
m/s. For the North winds the single-point wind prediction 2280 had
a standard deviation of 3.28 m/s, and the multipoint wind
prediction 2290 had a standard deviation of 0.973 m/s. The
multipoint wind prediction 2290 has a lower standard deviation that
the single-point wind prediction 2280, indicating that the data
multipoint prediction move closely matches the measured winds.
[0200] FIG. 23 provides a tabular view 2300 including Table 7 with
East wind prediction standard deviations as 2310. FIG. 24 provides
tabular views 2400 including Table 8 North wind prediction standard
deviations as 2410 and Table 9 state variables and distributions as
2420. Tables 7 and 8 compare minimum, mean and maximum standard
deviations for single-point and multipoint winds in relation to
their respective wind directions.
[0201] This same metric was calculated for all five-thousand wind
predictions made with all sixteen measured wind sets shown in FIGS.
13 through 16. The results are summarized in Tables 7 as 2310 in
FIGS. 23 and 8 as 2410 in FIG. 24, respectively. For all sixteen
measured wind profiles, the multipoint wind predictions had a lower
standard deviation off of the measured winds than the single-point
wind predictions. This indicates that the multipoint wind
prediction provides results as expected; that the winds predicted
by the multipoint method more closely match the true underlying
winds. One can expect that a wind prediction that more closely
matches the true winds would be more stable for predicting impact
locations as the initial state of the system changes.
[0202] Section VI.7--Changing State: An additional simulation was
performed to compare the results of the single-point ballistic wind
prediction to the results of the multipoint ballistic wind
prediction as the state of the aircraft and gun are changed from
the state in which the prediction was made. A random set of fifty
initial states for the aircraft and gun were chosen. A single-point
and multipoint ballistic wind profile was predicted using those
fifty initial states with all sixteen measured wind profiles.
[0203] The process changed the initial state of the gun and
simulated a ballistic flyout. The aircraft altitude, speed, and
total gun depression were allowed to vary based on a uniform random
distribution with bounds detailed in Table 9 as 2420 in FIG. 24.
Because the assumption that changes in the state of the aircraft
and gun tend to cluster around the initial state is unwarranted, a
uniform continuous distribution was selected to model these
variations. The uniform distribution offers an equal probability of
occurrence to all values in the range specified and does not favor
values closer to the initial state.
[0204] Monte Carlo simulation was preferred over parametrically
stepping through the ranges for each state variable because the
effects of coupling between the state variable and the ballistic
winds are not known. A parametric search could miss an effect from
incorrect value selection. The measured winds were applied, and an
impact location was generated. This impact was treated as "truth"
data. Similar impacts were generated using both the single-point
and the multipoint ballistic wind model. The state of the gun and
aircraft was then changed and the data generation repeated to
collect a total of one-hundred impacts around the original state
where the ballistic winds were calculated. After all one-hundred
variations off of the original state had been used, a new original
state was selected along with the single-point and multipoint
ballistic wind profiles for that state. The process was repeated
for each original state, generating one-hundred variations off of
the original state.
[0205] Section VI.7.1--Results: To analyze the usefulness of a
ballistic wind as the state changes, the total magnitude of the
impact miss distance was calculated. The impact location predicted
using the measured winds was compared to the impact location
predicted with the ballistic wind and a difference was calculated
in the DR and CR directions to find a miss distance. The DR
component of the miss distance was converted to be normal to the
line-of-sight from the gun to the target. This eliminates the
skewing of the impact data in the DR direction due to conic
projection to the simulated surface of the Earth. The DR and CR
miss distances were then converted to an angular miss instead of a
linear miss distance.
[0206] FIG. 25 illustrates a graphical view 2500 of Example Impact
Dispersion under varying states, showing the resulting data for one
initial state and wind profile. The diagonal scatter impacts 2530
are based on the multipoint ballistic wind and the near vertical
scatter impacts 2540 are based on the single-point. The DR and CR
angular miss distances were then combined into a single radial miss
distance. For this analysis, the direction of the miss is less
important than the total distance. For a given original state, the
maximum radial miss distance for a given ballistic wind method out
of the hundred varied states was found. The radial miss distance
for the single-point and multipoint ballistic winds were compared
to find which method had the lowest radial miss distance under the
same change in state. As expected, the multipoint ballistic wind,
with its closer fit to the measured wind, has less miss distance
induced by a changing state than the single-point ballistic
wind.
[0207] Section VI.7.2--Analysis of Results: Testing one-hundred
changes in initial state for each of the fifty initial states using
all sixteen wind profiles resulted in eight-hundred different
maximum radial miss distance for the single-point and multipoint
ballistic wind profiles. A histogram was generated to see what the
predicted distribution of miss distances was for each ballistic
wind prediction method.
[0208] FIG. 26 illustrates graphical views 2600 of four
plots--Single-point, Multipoint and Comparative Radial Miss
Distance varying all state variables with Instances where
single-point method appears more stable varying all state
variables. Single-point Radial Miss Distance plot 2610 features
vertical bars with maximum radial miss 2620 in milliradians (mrad)
as the abscissa and bin count 2625 as the ordinate. Multipoint
Radial Miss plot 2630 features vertical bars with maximum radial
miss 2640 (mrad) as the abscissa and bin count 2645 as the
ordinate. Difference plot 2650 features vertical bars with radial
miss difference 2660 (mrad) as the abscissa and bin count 2665 as
the ordinate. Instances plot 2670 features vertical bars with wind
profile number 2680 as the abscissa and bin count 2685 as the
ordinate,
[0209] For the single-point plot 2610 ballistic wind the radial
miss distances are low, but the greatest number of data points is
not at 0.0 mrad. The maximum single-point radial miss distance
predicted was 2.1068 mrad. The multipoint radial miss distance plot
2630 was also not clustered at 0.0 mrad. The maximum multipoint
radial miss distance predicted was 0.3069 mrad. The changing of the
aircraft and gun state from the ballistic wind prediction induces
less error for using a multipoint ballistic wind in plot 2630 as
compared to a single-point ballistic wind in plot 2610. This is
expected based on the results above in Section VI.6. A comparison
of the radial miss distances in plot 2650 under the same conditions
is needed to judge whether one ballistic wind method is always
better than the other.
[0210] Despite the multipoint ballistic wind appearing to have a
much lower radial miss distance, it might not always be better than
the single-point method. The maximum radial miss distances for the
multipoint ballistic wind were subtracted from the maximum radial
miss distances for the single-point ballistic wind. Very few
negative points exist in the comparison data in plot 2650.
Differences between single-point and multipoint stability varying
all state variables. This means that the multipoint ballistic wind
was more often more stable relative to changes in all three state
variables when compared to the single-point method. There are
twenty-nine negative data points, instances where the single-point,
ballistic wind appears to be more stable than the multipoint
ballistic wind. The largest negative magnitude was -01165 mrad for
Wind Profile 14.
[0211] Instances plot 2650 illustrates conditions in which
single-point method appears more stable varying all state
variables. The largest number of instances where the single-point
ballistic wind appears more stable occurred for wind profiles 14
and 16 in FIG. 16. Examining Tables 7 and 8 in respective FIGS. 23
and 24, one expects that wind profiles 14 and 16 have some
instances where the single-point ballistic wind is slightly better
than the multipoint method. The minimum, mean, and maximum standard
deviations of the single-point ballistic wind profiles for wind
profiles 14 and 16 are all low in comparison to the other wind
profiles. This indicates that the single-point method did better at
fitting wind profiles 14 and 16 than the others.
[0212] Section VI.8--Gun System Implementation: Correction of
ballistic trajectory from wind displacement includes incorporation
into a projectile launching gun system. To this effect,
instrumentation and response devices can be adjusted to achieve
this benefit.
[0213] FIG. 27 illustrates a flowchart view 2700 of a conventional
gun weapon System Architecture 2710. A targeting sensor 2720
provides target location data 2725 to a fire control computer 2730
for target aiming. The computer 2730 in turn provides a firing
solution 2735 of azimuth and elevation to a mount control computer
2740 for adjusting pointing orientation of a gun. The computer 2740
provides motor rates 2745 for operating motors 2750 to impose
torque 2755 to a gun mount 2760. The computer 2740 receives
feedback 2765 of the measured mount position data, azimuth and
elevation from the gun mount 2760 for correcting the gun's aim.
[0214] FIG. 28 illustrates a flowchart view 2800 of an exemplary
gun weapon System Architecture 2810 that incorporates the benefits
provided by the claimed wind correction technique. The exemplary
Architecture 2810 incorporates the hardware components and
processes of the conventional Architecture 2710, but also including
an exemplary wind adjustment module 2820. This includes a round
tracking sensor 2830 for determining bullet trajectories for rounds
fired from the gun, and submits 2835 measured round location and
velocity to a ballistic wind calculation computer 2840, which
provides firing solution adjustment, azimuth and elevation 2845 to
the mount control computer 2740 for fine-tuning the torque 2755
applied by the motors 2750 to the gun mount 2760, thereby improving
accuracy in firing at the acquired target,
[0215] Section VI.9--Summary: In this section, a method of
multipoint wind predictions was proposed and tested. With very few
data points, the multipoint method can generate a wind prediction
that closely matches the measured winds applied to the round. By
analyzing the standard deviation of the differences between the
measured winds and the two ballistic wind profiles, the closeness
of the ballistic wind to the actual winds can be calculated. The
results indicate that the multipoint ballistic wind more closely
fit the measured wind profiles than the single-point ballistic
wind.
[0216] The two ballistic wind methods were also tested under
changing initial state of the aircraft and gun. This ballistic
wind, whether a single-point and multipoint ballistic wind, is
tuned based on the state of the gun and aircraft at the time of
fire. Anything that changes the state of the system may invalidate
the ballistic wind profile. Using the ballistic wind in a different
state may lead the ballistic model to predict an impact that does
not match the impact using the true winds. Ideally, a ballistic
wind would be insensitive to changes in state. A simulation was run
to test the radial miss distance induced by changing the state of
the aircraft and gun from the state when the ballistic wind was
generated.
[0217] The results showed that the multipoint ballistic wind was
able to accept a change in the aircraft and gun state and maintain
a lower maximum radial miss distance than the single-point
ballistic wind. The multipoint ballistic wind did not always have
the lower radial miss distance, however. There were instances where
the single-point ballistic wind appeared to perform better under
changing states, though the difference in the maximum radial miss
distance between the two methods in these few instances was
small.
[0218] Overall, the multipoint ballistic wind performed better than
the single-point ballistic wind. For the data collected, the
largest multipoint miss distance induced was 0.3069 mrad. The
largest single-point miss distance induced was 2.1068 mrad. The
data indicate that a multipoint ballistic wind based only on ten
tracked points of the round in flight enables a more consistent
impact prediction as the aircraft and gun state changes than the
single-point ballistic wind.
[0219] Chapter VII--Conclusion: A successful method of making
multipoint ballistic wind predictions was developed and tested as
part of this research. The multipoint prediction method presented
in this disclosure is based on a repetition of the single-point
wind prediction between all available tracked locations of the
round. The single-point wind prediction method is itself based on a
bisecting search, a relatively simple search algorithm used to find
an optimal value to minimize an error metric. The multipoint wind
prediction method being a series of bisecting searches renders the
programming of the algorithm easier and less prone to errors,
indicating utility for tactical applications. The multipoint
prediction method can predict ballistic winds that closely fitted
the true measured winds using few data points for the tracked
round, only ten points along the flight path and the initial firing
conditions. The multipoint wind predictions are all much closer to
the measured winds applied the round than the same single-point
wind predictions. This result may seem trivial, but recall that the
use of a ballistic wind does not require that it match the
underlying real winds acting on the tracked round. The ballistic
wind only has to cover for the physical effects on the round.
[0220] One can assume and hope that the multipoint ballistic winds
closely match the underlying measured winds. The analysis of the
fit of both ballistic wind models to the true winds showed that the
multipoint more closely matched the true winds in all cases.
Testing the stability of the single-point and multipoint wind
models showed that the multipoint wind was almost always the more
stable method. Changing the aircraft and gun state had less of an
effect on the accuracy of the predicted impacts when a multipoint
ballistic wind was used than seen when a single-point ballistic
wind was used. The highest error caused by changing state was
slightly over 2.1068 mrad using a single-point ballistic wind. The
highest using a multipoint ballistic wind was slightly over 0.3069
mrad. This is within the manufacturers stated dispersion of the
ammunition used in this simulation, meaning that this extra miss
distance due to changing state is not likely to be discernable
given the imprecision of the round itself. For some of the wind
profiles used, a few simulation runs indicated that the
single-point ballistic wind would be more stable than the
multipoint ballistic wind.
[0221] Out of eight-hundred runs, only twenty-nine of them showed
that the single-point ballistic wind was more stable. The slight
improvement on the stability metric with the single-point, 0.1165
mrad better than the multipoint, is also well below the nominal
dispersion of the round type. Further investigation of the
instances where the single-point method was more stable revealed
that the stability was due to the almost static nature of the
measured wind profiles being tested. Wind Profiles 14 and 16 had
very low wind speeds in both the East and North directions and the
wind speeds in one of the directions had a clear average trend with
small variations off therefrom. This is the ideal case for the
single-point ballistic wind.
[0222] Examining the standard deviation values calculated as a
closeness of fit of the single-point ballistic wind to the true
winds, Tables 7 and 8 in FIGS. 23 and 24, wind profiles 14 and 16
have a very low standard deviation when compared to the other wind
profiles, meaning that the single-point ballistic wind model was
able to fit those winds more closely than the other wind profiles.
None of this invalidates or reduces the usefulness of the
multipoint ballistic wind. The slight improvement using the
single-point ballistic wind is within the dispersion of the round.
The results point to the fact that under a roughly static set of
wind speeds, both the single-point and multipoint methods should
converge towards each other.
[0223] Chapter VII--Epilogue: Expectations and Future Research may
augment the previous analysis from wind measurements.
[0224] Section VIII--Secondary Results: The relationship between
the radial wind error and the time of flight was unexpected, though
this makes sense on further review. As observed in eqn. (16), the
lower the time of flight the higher the maximum radial error in the
wind prediction can be off of the true wind. The predicted
ballistic wind is still expected to correct the round's impact to
be within the closure tolerance on the wind prediction model's
search, but the actual value of the predicted wind can be wrong. At
lower times of flight, the error can be larger because the wind
does not have as much time to influence the flight of the round. At
longer times of flight, the radial error must be lower to achieve
the same closure tolerance because the wind has a longer time to
act on the round.
[0225] Another secondary result of note is that changes to the
total gun elevation are strong contributors to the instability of
the ballistic wind predictions. In light of the relationship shown
in eqn. (16), this result is not surprising. Changing the elevation
has a large effect on the time of flight of the round. Small errors
in the ballistic winds can lead to large miss distances by simply
changing the elevation of the gun. Also of note is that the
multipoint wind prediction was able to do so well with only ten
points along the path of the projectile. Even at higher altitudes
maximum distance between the data points, the multipoint wind
prediction model could generate a ballistic wind demonstrated to be
more stable than the single-point method.
[0226] Section III.2--Future Research: The research in this
disclosure shows the possible benefits to be gained by using a
round racking sensor as part of an FC system. The data can be used
to model the winds accurately and in a stable manner as the
aircraft state changes. Increasing the fidelity of the simulation
could provide better indications of the total possible improvements
that could be seen from using a round tracking sensor to predict
the ballistic winds.
[0227] Section VII.2.1--Full Fire-Control Simulation: This
exemplary analysis assumed that a full simulation of an FC 290 was
not needed and that a ballistics model 260 would suffice. This
constitutes a valid assumption to limit the complexity of the
system for simulation while leaving some questions unanswered. This
analysis had a target determined by randomly selected gun pointing
angle and aircraft state to ascertain the effect multipoint wind
prediction model would have on these pointing angles? An assumption
was made that the winds would cause a round to miss a target, and
that modeling the winds would enable the round to hit the target.
In reality, the target exists external to the FC 290 and is not
determined by the gun or aircraft state. The gun and aircraft
states 215 and 225 are calculated by the FC 290 to engage that
target. Winds are used as part of the calculation of the gun
pointing angles by the FC 290. By predicting and using a ballistic
wind in the FC 290 and by changing the state of the aircraft 225
relative to the target, the gun pointing angles change to bring the
round back on target.
[0228] Section VII.2.2--Full Pylon Turn Orbits: The analysis
assumed that the orbit of the aircraft 310 was sufficiently modeled
by a stationary aircraft at the time of fire. This makes the target
static relative to the aircraft, which isn't always the case. This
also causes the gun to fire the same way into the winds for each
shot simulated. In reality, the aircraft 310 is orbiting a path
110. This causes a target to change location relative to the
aircraft 310 unless perfectly aligned with center 120 in orbit path
110. Changing target location alters the gun elevation over time.
As seen in Chapter VI, changing the state of the aircraft and gun
can have an effect on the possible errors in impacts that result
from using ballistic wind predictions. Investigating the effect of
full pylon turns combined with a full model of the FC 290 can
provide a good indication of whether the multipoint ballistic wind
model introduces any instabilities to the gun pointing angles at
the time of flight of the round changes in different parts of the
orbit.
[0229] Section VII.2.3--More Tracked Data Points: The exemplary
analysis assumes that the round tracking sensor provides ten data
points along the flight path of the round. This is a very low
value. What are the benefits of adding more values? Or, conversely,
what is the effect of having fewer values? A parametric analysis of
the number of data points required to achieve a certain level of
stability would help to inform future work into developing the
necessary hardware and software to integrate a round tracking
sensor.
[0230] Section VII.2.4--Combined Errors: Other errors are neglected
for this analysis. In a real system, these errors would manifest
themselves and complicate the wind prediction. These errors would
have to be sorted and minimized in their specific frames of
reference to enable the correction of the world-relative errors
with a ballistic wind prediction. A fuller simulation that accounts
for the platform relative errors, such as sensor and gun
misalignment, errors in the ammunition description, and limitations
in ballistics modeling, could reveal possible complications for a
round tracking sensor integrated into the FC 190 of an aircraft
310. Any method for decoupling errors into their proper frames of
reference entails uncertainties that can affect the ability of the
multipoint wind prediction model to properly close on the ballistic
wind.
[0231] Section VII.2.5--Wind Vector Field: This disclosure shows
the possibility of correctly predicting a ballistic wind profile
that closely matches the underlying winds. These ballistic wind
profiles can be used to correct wind errors in subsequent firings.
These winds are only valid for the round used to predict them,
however, and may not be the best ballistic wind to apply to later
rounds. The validity of the ballistic wind depends on the
variations of the true winds over both time and space. The winds
that are acting at one location in the orbit may not be
representative of the winds acting at other locations. Further, the
true winds are expected to vary over time, possibly reducing the
usefulness of the winds predicted at any location in the orbit.
This research presents an opportunity to research the creation of a
model of a wind vector field that covers the entire orbit.
Combining the individual ballistic winds may be possible to
describe not only the winds at a single location in the orbit but
around the entire orbit. Such a model could enable, accurate
predictions of the ballistic winds as they change over time. A
change in the ballistic winds at one location in the orbit from an
earlier ballistic wind could be used to predict a change in the
ballistic winds at other locations in the orbit.
[0232] Section VII.2.6--Tuning Ballistic Model: The prediction of a
multipoint ballistic wind enables the tuning of the ballistics
model 260 for different round types. A ballistics model 260 can be
poorly calibrated for the round type being fired and still enable a
usable prediction of the round's flight. Calibrating or tuning, the
model requires a source of truth data to compare the model against.
A multipoint ballistic wind can be used as the truth data, enabling
improved calibration of the ballistics model 260 for all round
types. The process of calibrating would, requir