Publication number | USH2255 H1 |

Publication type | Grant |

Application number | US 12/152,122 |

Publication date | Jun 7, 2011 |

Filing date | Apr 24, 2008 |

Priority date | Apr 26, 2007 |

Also published as | US8176834 |

Publication number | 12152122, 152122, US H2255 H1, US H2255H1, US-H1-H2255, USH2255 H1, USH2255H1 |

Inventors | Michelle R. Arevalo, Geoffrey Bland |

Original Assignee | The United States Of America As Represented By The Secretary Of The Navy |

Export Citation | BiBTeX, EndNote, RefMan |

Patent Citations (6), Referenced by (2), Classifications (10), Legal Events (1) | |

External Links: USPTO, USPTO Assignment, Espacenet | |

US H2255 H1

Abstract

A method is provided for determining fratricide probability of projectile collision from a projectile launcher on a platform and an interception hazard that can be ejected or launched from a deployment position. The platform can represent a combat vessel, with the projectile launcher being a gun, the interception hazard being a missile, and the deployment position being a vertical launch cell. The projectile launcher operates within an angular area called the firing zone of the platform. The method includes determining the firing zone, calculating an angular firing area, quantifying a frontal area of the interception hazard, translating the resulting frontal area across a flight trajectory, sweeping the projectile launcher to produce a slew angle, combining the slew and trajectory, and dividing the combined interception area by the firing area. The firing and interception areas are calculated using spherical projection.

Claims(15)

1. A method for determining fratricide probability of projectile collision from a projectile launcher on a platform and an interception hazard ejectable from a deployment position, the method comprising:

determining a firing zone of the platform, said firing zone presenting an area through which the projectile launcher operates;

calculating an angular firing zone area from said firing zone that extends from the projectile launcher;

quantifying a frontal area of the interception hazard to produce an intercept area with respect to the projectile launcher;

translating said frontal area across a flight trajectory of said intercept area to produce a path area; and

determining the fratricide probability for said deployment position from dividing said path area by said angular firing zone area.

2. The method according to claim 1 , wherein the platform is a combat vessel, the projectile launcher is a gun, the interception hazard is a missile, and the deployment position is a vertical launch cell.

3. The method according to claim 1 , wherein calculating said angular firing zone further includes calculating an integral for a rectangular solid angle as:
${\Omega}_{\mathrm{rectangle}}={\int}_{{\varphi}_{1}}^{{\varphi}_{2}}{\int}_{{\theta}_{1}}^{{\theta}_{2}}\mathrm{cos}\text{\hspace{1em}}\varphi \text{\hspace{1em}}d\theta \text{\hspace{1em}}d\varphi ,$

where θ_{1 }and θ_{2 }are azimuth bounds and φ_{1 }and φ_{2 }are elevation bounds of said firing zone.

4. The method according to claim 1 , wherein quantifying said frontal area further includes:

discretizing a perspective view of the interception hazard into discrete spatial points, each point having a coördinate position in relation to the projectile launcher;

evaluating said points as a contiguous group of triangular plates, each plate being represented by triangular points of said spatial points, said each triangular plate forming a triangular solid angle Ω_{triangle }determined by:
${\Omega}_{\mathrm{triangle}}=2\text{\hspace{1em}}\mathrm{arc}\text{\hspace{1em}}\mathrm{tan}\left(\frac{\left[\overrightarrow{a}\text{\hspace{1em}}\overrightarrow{b}\text{\hspace{1em}}\overrightarrow{c}\right]}{\mathrm{abc}+\left(\overrightarrow{a}\xb7\overrightarrow{b}\right)c+\left(\overrightarrow{a}\xb7\overrightarrow{c}\right)b+\left(\overrightarrow{b}\xb7\overrightarrow{c}\right)a}\right),$

where scalar magnitudes a, b, c represent distances and tensors {right arrow over (a)}, {right arrow over (b)}, {right arrow over (c)} represent vectors between respective said triangular points and the projectile launcher; and

summing said each triangular solid angle to produce said frontal area as an intercept solid angle Ω_{ordnance}.

5. The method according to claim 1 , wherein determining the fratricidal probability further includes dividing an intercept solid angle determined from discretizing said path area by a firing solid angle determined from azimuth bounds and elevation bounds of said firing zone as:
${p}_{f}=\frac{{\Omega}_{\mathrm{ordnance}}}{{\Omega}_{\mathrm{firingzone}}},$

where P_{f }represents fratricidal probability, Ω_{ordnance }represents said intercept solid angle, and Ω_{firingzone }represents said firing solid angle.

6. A method for determining fratricide probability of projectile collision from a projectile launcher on a platform and an interception hazard ejectable from a deployment position, the method comprising:

determining a firing zone of the platform, said firing zone presenting an area through which the projectile launcher operates;

calculating an angular firing zone area from said firing zone that extends from the projectile launcher;

quantifying a frontal area of the interception hazard to produce an intercept area with respect to the projectile launcher;

translating said frontal area across a flight trajectory of said intercept area to produce a path area;

angularly sweeping the projectile launcher to produce a slew angle;

superimposing said slew angle over said path area to produce a combination area; and

determining the fratricide probability for said deployment position from dividing said combination area by said angular firing zone area.

7. The method according to claim 6 , wherein the platform is a combat vessel, the projectile launcher is a gun, the interception hazard is a missile, and the deployment position is a vertical launch cell.

8. The method according to claim 6 , wherein calculating said angular firing zone further includes calculating an integral for a rectangular solid angle as:
${\Omega}_{\mathrm{rectangle}}={\int}_{{\varphi}_{1}}^{{\varphi}_{2}}{\int}_{{\theta}_{1}}^{{\theta}_{2}}\mathrm{cos}\text{\hspace{1em}}\varphi \text{\hspace{1em}}d\theta \text{\hspace{1em}}d\varphi ,$

where θ_{1 }and θ_{2 }are azimuth bounds and φ_{1 }and φ_{2 }are elevation bounds of said firing zone.

9. The method according to claim 6 , wherein quantifying said frontal area further includes:

discretizing a perspective view of the interception hazard into discrete spatial points, each point having a coördinate position in relation to the projectile launcher;

evaluating said points as a contiguous group of triangular plates, each plate being represented by triangular points of said spatial points, said each triangular plate forming a triangular solid angle Ω_{triangle }determined by:
${\Omega}_{\mathrm{triangle}}=2\text{\hspace{1em}}\mathrm{arc}\text{\hspace{1em}}\mathrm{tan}\left(\frac{\left[\overrightarrow{a}\text{\hspace{1em}}\overrightarrow{b}\text{\hspace{1em}}\overrightarrow{c}\right]}{\mathrm{abc}+\left(\overrightarrow{a}\xb7\overrightarrow{b}\right)c+\left(\overrightarrow{a}\xb7\overrightarrow{c}\right)b+\left(\overrightarrow{b}\xb7\overrightarrow{c}\right)a}\right),$

where scalar magnitudes a, b, c represent distances and tensors {right arrow over (a)}, {right arrow over (b)}, {right arrow over (c)} represent vectors between respective said triangular points and the projectile launcher; and

summing said each triangular solid angle to produce said frontal area as an intercept area Ω_{ordnance}.

10. The method according to claim 6 , wherein determining the fratricidal probability further includes dividing an intercept solid angle determined from discretizing said combination area by a firing solid angle determined from azimuth bounds and elevation bounds of said firing zone as:
${p}_{f}=\frac{{\Omega}_{\mathrm{ordnance}}}{{\Omega}_{\mathrm{firingzone}}},$

where P_{f }represents fratricidal probability, Ω_{ordnance }represents said intercept solid angle, and Ω_{firingzone }represents said firing solid angle.

11. A system for determining fratricide probability of projectile collision from a projectile launcher on a platform and an interception hazard ejectable from a deployment position, said system comprising:

a firing determiner for determining a firing zone of the platform, said firing zone presenting an area through which the projectile launcher operates;

a calculator for calculating an angular firing zone area from said firing zone as extending from the projectile launcher;

a quantifier for quantifying a frontal area of the interception hazard to produce an intercept area;

a translator for translating said frontal area across a flight trajectory of said intercept area to produce a path area;

a sweeper for angularly sweeping the projectile launcher to produce a slew angle;

a superpositioner for superimposing said slew angle over said path area to produce a combination area; and

a probability determiner for determining the fratricide probability for said deployment position from dividing said combination area by said angular firing zone area.

12. The system according to claim 11 , wherein the platform is a combat vessel, the projectile launcher is a gun, the interception hazard is a missile, and the deployment position is a vertical launch cell.

13. The system according to claim 11 , wherein said calculator operates to further calculate an integral for a rectangular solid angle as:
${\Omega}_{\mathrm{rectangle}}={\int}_{{\varphi}_{1}}^{{\varphi}_{2}}{\int}_{{\theta}_{1}}^{{\theta}_{2}}\mathrm{cos}\text{\hspace{1em}}\varphi \text{\hspace{1em}}d\theta \text{\hspace{1em}}d\varphi ,$

where θ_{1 }and θ_{2 }are azimuth bounds and φ_{1 }and φ_{2 }are elevation bounds of said firing zone.

14. The system according to claim 11 , wherein said quantifier operates to further:

discretize a perspective view of the interception hazard into discrete spatial points, each point having a coördinate position in relation to the projectile launcher;

evaluate said points as a contiguous group of triangular plates, each plate being represented by triangular points of said spatial points, said each triangular plate forming a triangular solid angle determined by:
${\Omega}_{\mathrm{triangle}}=2\text{\hspace{1em}}\mathrm{arc}\text{\hspace{1em}}\mathrm{tan}\left(\frac{\left[\overrightarrow{a}\text{\hspace{1em}}\overrightarrow{b}\text{\hspace{1em}}\overrightarrow{c}\right]}{\mathrm{abc}+\left(\overrightarrow{a}\xb7\overrightarrow{b}\right)c+\left(\overrightarrow{a}\xb7\overrightarrow{c}\right)b+\left(\overrightarrow{b}\xb7\overrightarrow{c}\right)a}\right),$

where scalar magnitudes a, b, c represent distances and tensors {right arrow over (a)}, {right arrow over (b)}, {right arrow over (c)} represent vectors between respective said triangular points and the projectile launcher; and

sum said each triangular solid angle to produce said frontal area.

15. The system according to claim 11 , wherein said probability determiner operates to further divide an intercept solid angle determined from discretization of said combination area by a firing solid angle determined from azimuth bounds and elevation bounds of said firing zone as:
${p}_{f}=\frac{{\Omega}_{\mathrm{ordnance}}}{{\Omega}_{\mathrm{firingzone}}},$

where P_{f }represents fratricidal probability, Ω_{ordnance }represents said intercept solid angle, and Ω_{firingzone }represents said solid angle.

Description

Pursuant to 35 U.S.C. §119, the benefit of priority from provisional application 60/928,671, with a filing date of Apr. 26, 2007, is claimed for this non-provisional application.

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.

The invention relates generally to ordnance fratricide probabilities. In particular, techniques are presented to enable systematic and comparative fratricidal interceptions from concurrently conflicting weapons systems.

Weapon fratricide represents a long-standing safety concern for weapon systems. Fratricide is defined as an attack on friendly forces by other friendly forces. Calculating the probability of fratricide has proven to be technically challenging. Manual resources devoted to these efforts yield limited results due to their time-consuming nature and the simplifying assumptions necessary to render the mathematical calculations tractable on a reasonable scale.

Conventional fratricide probability techniques yield disadvantages addressed by various exemplary embodiments of the present invention. In particular, conventional systems introduce errors that expand exponentially with increasing field coverage. Additionally, the absence of systematic characterization of the gun-restriction firing zone and ordnance that present interception hazards render manual calculations tedious and time-consuming.

Various exemplary embodiments provide a method for determining fratricide probability of projectile collision from a projectile launcher on a platform and an interception hazard that can be ejected or launched from a deployment position. The platform can represent a combat vessel, with the projectile launcher being a gun, the interception hazard being a missile, and the deployment position being a vertical launch cell. The projectile launcher operates within an angular area called the firing zone of the platform.

The method includes determining the firing zone, calculating an angular firing area, quantifying a frontal area of the interception hazard, translating the resulting frontal area across a flight trajectory, sweeping the projectile launcher to produce a slew angle, combining the slew and trajectory, and dividing the combined interception area by the firing area. The fire and interception areas are calculated using spherical projection.

Various exemplary embodiments calculate the angular firing zone by an integral for a rectangular solid angle as:

where θ_{1 }and θ_{2 }are azimuth bounds and φ_{1 }and φ_{2 }are elevation of the firing zone. Calculating the interception hazard includes discretizing a perspective view of the interception hazard into discrete spatial points, evaluating those points as a contiguous group of triangular plates, and summing all of the triangular solid angles to produce the frontal area.

Triple points can represent each triangular plate to form a triangular solid angle determined by:

where scalar magnitudes a, b, c represent distances and tensors {right arrow over (a)}, {right arrow over (b)}, {right arrow over (c)} represent vectors between respective points and the projectile launcher, and summing each triangular solid angle to produce the frontal area.

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:

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.

Various exemplary embodiments describe the development of techniques for calculating fratricide probabilities between a gun projectile and other ship-fired ordnance. These embodiments provide flexibility to analyze any combination of ship, layout, gun, and surface-launched ordnance system. Various collected data are mathematically manipulated to calculate the probability of fratricide using solid angle geometry. These calculations account for ordnance fly-out paths as well as gun-slewing action. This development aids and improves accurate prediction of fratricide potential of a weapon system safety engineer between various shipboard weapons systems and to thereby quantify the risk of personnel injury and equipment damage.

In the context of this disclosure, fratricide involves intersection of ordnance on one's own ship (ownship ordnance) with other ownship ordnance. Collision of such ordnance can cause an energetic reaction leading to catastrophic damage and/or death. One such tragic example occurred on Jul. 29, 1967 aboard the U.S.S. Forrestal (CV-59) in which an accidentally launched Zuni rocket struck a bomb-laden A-4 Skyhawk causing a conflagration that cost 134 lives, many of whom from thermal cook-off of exposed munitions. This analysis procedure aids in the determination of the probability of such an incident to advise proper authorities of the level of risk associated with this hazard and institute appropriate mitigation measures.

Conventionally, fratricide analysis is performed manually. Various exemplary embodiments describe development and utilization of an automated Fratricide Probability Calculator (FPC), which more precisely calculates fratricide probabilities for user defined ship classes and layouts, as well as various gun weapon systems (i.e., projectile launcher) and missile launching systems (e.g., potential interception hazard).

Conventional analytical efforts have incorporated cylindrical modeling to calculate the probability. Preferably, spherical modeling can provide more accurate results by taking into consideration the various fly-out paths as well as various slewing actions of the gun. The FPC can employ this spherical modeling along with other enhancements to provide an automated capability to provide quick and accurate probabilities of fratricide for a myriad of weapon systems combinations.

The calculation of fratricide probability can be analogized as a ratio of the total amount of area being presented by a target relative to the total area available in which the gun can fire. A blindfolded person randomly throwing darts at a dart board on a wall represents a hypothetical example. Assuming that the person can only strike within the boundaries of the wall, for a dart board that represents one-tenth the presented area of the wall, the chances that the person hits the board is ten-percent (10%). The calculation of fratricide probability introduces greater complexity than the simple random dart-throwing analogy assumes, particularly for combat vessels (e.g., naval ships) with intricate restrictions depending on positions of superstructure components, antenna masts, etc.

**100** of cylindrical collision modeling to calculate fratricide probability. The modeling steps begin with gun firing zone determination **110**, and proceeds to missile sector determination **120**. The model continues to distance calculation **130** between the missile center and the gun and field-of-fire calculation **140**. The model follows by determining height calculation **150** of the exposed missile, and proceeds with probability calculation **160** of fratricide for each missile cell. The model concludes by repeating these procedures for final determination **170** of maximum and average probabilities are determined for the entire system.

First Step **110**: The model determines the gun firing zones for a warship or other combat vessel from the gun-mount view over a missile system that contains a plurality of missiles. The gun firing zone is defined as the region within which the gun can fire without striking any portion of the ship. Irrespective of type or class, each ship possesses a unique layout and therefore different firing zones from other ships. The gun firing zones are defined in terms of their azimuth and elevation boundaries. For the example described herein, the entire gun firing zone can be divided into separate sectors, depending on the minimum elevation angles.

Second Step **120**: The model identifies which sector to which each missile corresponds. Aegis-equipped warships house vertically containerized missiles launched from cells.

Third Step **130**: The model calculates the distance R between the center of each missile cell and the gun. This determination can be performed using the Pythagorean Theorem using orthogonal rectangular coördinates.

Fourth Step **140**: The model calculates the field-of-fire area A_{f }above each missile cell using cylindrical geometry. Spherical geometry techniques are discussed subsequently.

For a cylindrical geometry as an example, eqn (1) can be used as a function of distance R. The parameters to be determined include the firing azimuth arc Δθ_{f }and the height H_{f }of the field-of-fire above the missile cells. The azimuth arc Δθ_{f }in eqn (2) is based on azimuth boundary difference from port to starboard swing of the gun mount. The firing height H_{f }in eqn (3) is based on the relative angular difference between elevation and depression bounds. These equations are provided below:

where θ_{1 }and θ_{2 }are the respective port and starboard azimuth bounds (in degrees) and φ_{1 }and φ_{2 }are the respective elevation and depression bounds.

Fifth Step **150**: The model calculates the exposed missile height H_{m }in the field-of-fire over each missile cell. For vertical length values of the missile exceeding the firing height of eqn (3), the exposed missile height H_{m }is assigned to equal the field-of-fire height H_{f }over the missile cell. Otherwise, the exposed missile height H_{m }equals the vertical length of the missile.

Sixth Step **160**: The model calculates the probability of fratricide for each missile cell. The missile area A_{m }can be calculated based on the exposed missile height H_{m }and the width of the missile W_{m }in eqn (4). The fratricide probability P_{f }can then be calculated based on the missile area A_{m }and the total field-of-fire area A_{f }in eqn (5). The equations are shown below:

where the total field-of-fire A_{f }is determined in eqn (1).

Seventh Step **170**: The model extends these calculations to determine the maximum and average of all the missile probabilities for the entire missile system. This involves determining the overlapping regions between gun slew and missile firings over the entire combat vessel.

Firing zones for an exemplary combat vessel can be visualized along an elevation view (such towards the bow) and a plan view (from above) in **200** with abscissa **210** and ordinate **220** demarcating angular degrees. The abscissa **210** represents azimuth from the longitudinal ship axis, with port extending positively from 0° and starboard extending negatively from 360°. The ordinate **220** represents elevation from −30° (depression) to +90° (vertical). A ship horizon outline **230** from the gun's perspective demarcates definitive regions. The region below the outline **230** denotes a restrictive “cutout” area **240**, whereas the region above the outline **230** denotes a firing area **250**.

Missile cells **260** are disposed within the restrictive area **240**. An example missile profile **265** features a Standard-Missile-2 adjacent to the cells **260**, which represent the Vertical Launcher System (VLS) that houses these missiles before launch. The example surface-to-air missile **265** in profile represents an interception hazard against which probability of collision may be calculated.

A firing zone **270** denotes portions of the angular window through which the gun may aim. This zone **270** may be subdivided into substantially rectangular sectors **271**, **272**, **273**, **274** and **275** as plotted along the azimuth-quantifying abscissa **210** and the elevation-quantifying ordinate **220**. The firing zone **270** (or its individual sectors) may be quantified by an azimuth **280** and by an elevation **290**.

**300** with the ship outline **230** and missile cell positions **260**. From this perspective, the sectors **271**, **272**, **273**, **274** and **275** represent arcs across angles plotted along the abscissa **210**. The gun's vantage is denoted by a central position **310**, with the radial limits of the sectors denoted by an arc **320**, and the direction of the ship's bow denoted by arrow **330**.

Cylindrical Modeling Limitations: Although cylindrical modeling can be appropriate for an exemplary analysis, this geometry introduces error as elevation increases. This effect can be observed in **400** shown. Three-dimensional orthogonal axes are illustrated in the axial X direction **410**, the vertical Y direction **420** and the lateral Z direction **430**, with a center position **440** as the origin. A cylinder **450** and a sphere **460** extend about the center **440** as origin. Spherical and cylindrical projections radiate from the origin, visibly displaying respectively a cylindrical four-cornered region **470** and a spherical four-cornered region **480**. As the elevation (or latitude) increases (i.e., diverges from 0°), the cylindrical region **470** distorts further in relation to the spherical region **480**.

**500** of projection error in relation to elevation angle. The abscissa **510** represents angle of elevation (in degrees). The left ordinate **520** represents percent error, and the right ordinate **530** represents surface area error (in non-defined exemplary units). A legend **540** identifies the plotted lines. Line **550**, as measured against the left ordinate **520**, exhibits exponential increase in error with increasing elevation. The area lines **560**, **570** are comparable against the right ordinate **530**. The cylindrical area value **560** increases exponentially, whereas the spherical area value **570** appears monotonic.

As observable in the _{f }that increases asymptotically.

Spherical Modeling Method: The FPC provides a tool that can quickly and accurately calculate the probability of fratricide between a gun and another weapon system. This tool enables automation of the process to be executable on a standard desktop computer, thereby enabling analysis of any combination of ship type, layout, gun, and ship launched ordnance system while considering the three dimensional relationship between the gun and other ordnance.

Analysis efforts focus on ship-launched missiles, due to the criticality and detrimental effects of the fratricide mishap. However, ordnance also includes ship self-defense weapons and gun projectiles. In special cases, a gun barrel may also be modeled as the ordnance to be examined. Consideration can be given to the vulnerability of the ordnance as well as the total elapsed time in which the missile is within the field-of-view of the gun.

For the purpose of alterations and reproducibility, the operator is assumed to be able to create and save a database of ordnance, gun, ship types, and layouts, as well as missile motion parameters and gun firing scenarios. Additional fidelity in the predictions can be gained through the use of Monte Carlo scenarios in which combinations of variables could be modified with respect to one another.

Parameter Inputs: The main inputs are the gun firing zones, gun firing parameters, physical dimensions of the ordnance, and ordnance flyout parameters, including trajectory. The gun firing zones are defined in terms of their azimuth and elevation boundaries as depicted in

The gun firing parameters are defined by the path along which the gun is trained and the duration of time the gun fires a round. For simplicity, the path can be defined as a straight line between starting and ending coördinates (azimuth and elevation). The duration can be defined as either a period of time or a single shot. For simplicity in these examples, the passage of the ordnance between two rounds can be neglected.

A “collision” occurs if the gun points at the ordnance at any time while firing. The physical dimensions of the ordnance may be loaded into the program via a Computer Aided Drafting (CAD) file, while the ordnance's flyout parameters can be modeled as a series of orthogonal coördinates related to the position of the ordnance over a series of time-steps. Additional accuracy can be added by incorporating gun-firing probability zones and ordnance vulnerability maps into the calculation.

Description of Mathematical Method: One significant difference between cylindrical and spherical modeling involves the absence of a physical surface to yield an area of the gun firing zone against which to compare to the target's area facing the gun. The target as described herein represents a fratricide hazard, although these principles can be extended to intended interception scenarios.

Therefore, a sounder approach compares the angular area of the target to that of the firing zone presented to the gun. Angular areas, called solid angles Ω, are measured in steradians, in the same manner that standard angles can be measured in radians. The solid angle of a sphere equals 4π steradians. The calculation of angular areas includes two different geometries: rectangular and triangular solid angles.

**600** of a four-corner angular area projected onto a spherical surface. The three-dimensional coördinates for the X, Y and Z axes correspond to labels in **440** and the sphere **460**. In the X-Z horizontal plane, a first azimuth line **610** extends from the origin **440** forming a port-side azimuth angle θ_{1 }as the first port azimuth form the X axis **410**. Another second azimuth line **620** extends from the origin **440** forming a starboard-side azimuth angle θ_{2 }as the second starboard azimuth from the X axis **410**. In the X-Y vertical plane, a first elevation line **630** extends from the origin **440** forming a depression angle φ_{1 }as the first elevation from the X axis **410**. Another second elevation line **640** extends from the origin **440** forming an elevation angle φ_{2 }as the second elevation from the X axis **410**.

The first pair of azimuth lines **610**, **620** provides lesser and greater longitudinal boundaries **650**, **660**. The second pair of elevation lines **630**, **640** produces lower and higher latitude boundaries **670**, **680**. These curved boundaries **650**, **660**, **670** and **680** produce a rectangular solid area **690** or shadow denoted as Ω_{rectangle }that maps onto the sphere **460**. The rectangular solid angle **690** can be calculated from the azimuth and elevation boundaries corresponding to the integral solution of eqn (6):

where θ_{1 }and θ_{2 }are the azimuth bounds **650**, **660** and φ_{1 }and φ_{2 }are the elevation bounds **670**, **680**. These boundaries can be used to constitute an area representing a solid angle Ω_{firingzone }for the firing zone.

**700** of three-corner angular areas projected onto spherical and Cartesian surfaces. The three-dimensional coördinates for the X, Y and Z axes correspond to labels in **440** and the sphere **460**. In the X-Z plane, a first horizontal line **710** extends from the X-axis **410** in the Z direction, and a second horizontal line **715** extends from the Z-axis **430** in the X direction. Similarly, third and fourth horizontal lines **720**, **725** respectively extend in the Z and X directions, with fifth and sixth horizontal lines **730**, **735** also extending in like manner.

In the X-Y plane, a first vertical line **740** extends from the intersection of horizontal lines **710**, **715** in the Y direction reaching to point a. Correspondingly, a first radial line **745** extends from the origin **440** to point a. Similarly, second vertical and radial lines **750**, **755** respectively extend in the Y and radial directions to point b, with third vertical and radial lines **760**, **765** also extending in like manner to point c.

The radial lines **745**, **755**, **765** extending from the origin **440** intersect through the surface of the sphere **460** to bound a triangular solid angle **770** or shadow labeled Ω_{triangle}. These radial lines extend to points a, b and c to form a flat Cartesian triangle **780** beyond the sphere **460**. Calculating the triangular solid angles involves the magnitudes of the three points of the triangle **780** in three-dimensional orthogonal space (e.g., Cartesian, polar, etc.). This can be expressed as eqn (7):

where a, b, c represent the scalar magnitudes (corresponding to the radial lengths of the lines **745**, **755** and **765**), and the tensors {right arrow over (a)}, {right arrow over (b)}, {right arrow over (c)} represent the directional vectors from the origin **440** to their respective points.

Because the gun firing zone **270** in **280**, **290**, the total angular area of the zone **270** equals the sum of rectangular solid angles dictated by these bounds (represented by the sections **271** through **275**). The ordnance's dimensions and location can be mathematically defined as a series of points in space similar to points a, b, c in

Consequently, the techniques described herein prefer the triangular method to solve for the solid angle of the ordnance. This can be accomplished by dividing the ordnance into a series of triangles in space (known as “meshing” in finite element modeling) and then adding the solid angles of each individual triangle for a combined profile, such as by Ω_{ordnance}=ΣΩ_{triangle }by summation.

**800** of a missile in three-dimensional space divided into triangular surfaces. The three-dimensional coördinates for the X, Y and Z axes correspond to labels in **440** and the sphere **460**. The combined set of triangles representing the missile provides lower and upper boundary lines **810**, **820** demarcating the missile's axial length. The missile solid area **830** or shadow projects a region labeled Ω_{ordnance }on the sphere **460** corresponding to the missile frontal area **840** in space beyond.

As mentioned previously, the resultant fratricide probability P_{f }equals the ratio of solid angles between the ordnance and firing zone, as expressed in eqn (8):

where Ω_{ordnance }represents the solid area **830** of the missile and Ω_{firingzone }represents the solid area **840** of the gun firing zone **270**.

For a single shot from the gun, the fratricide probability can be readily determined. However, determining a fratricide probability solution becomes more complicated for either when a gun is slewing or is firing over an extended time interval, because the relative motion between the gun and the ordnance must be accounted for. (Either example may represent a high-speed missile intercept and/or avoidance scenario.) In the case of ordnance motion, a solid angle shadow extending over the entire firing duration can be modeled.

A collision (interception of the ordnance) occurs in consequence to a gun firing continuously at any single point in its firing zone, with the ordnance traveling through the gun-firing line. Continuous firing in this context means that intervals yield distances between bullets (or other gun-launched projectile) is smaller than the missile's smallest dimension.

**900** of a missile passing through three-dimensional space. The three-dimensional coördinates for the X, Y and Z axes correspond to labels in **440** and the sphere **460**. Representation of the missile **265** is shown by projection on the sphere **460** and in space. Lower and upper boundary lines **910**, **920** define the missile path **930** along a time interval that corresponds to the gun-accessible portion of the trajectory. The gun firing zone **270** can be projected on the sphere **460** as a solid area **940** representing a region labeled Ω_{firingzone }and outlined by a firing boundary **945**.

Intersection of the sphere **460** by the boundary lines **910**, **920** projects a smaller solid area **950** representing a region labeled Ω_{ordnancepath}. The fratricide probability P_{f }of eqn (8) can be revised accordingly by substituting the trajectory solid angle Ω_{ordnancepath }for the original ordnance solid angle Ω_{ordnance }in the numerator.

For a slewing gun, the ordnance is likewise in relative motion to the gun's aim point **310**, corresponding to the spatial origin **440**. This motion creates a distortion of the ordnance's shadow as solid angle **830** on the sphere **460**. While the gun motion creates a greater solid angle for the ordnance, the solid angle **940** of the firing zone labeled Ω_{firingzone }remains unchanged. The solid angle of the firing zone projection **940** is based on the ship outline **230**, whereas the solid angle of the ordnance **830** and/or its path **950** is measured relative to the gun aim vantage **310**.

**1000** of a missile passing through three-dimensional space as the gun slews. Pivoted at the origin **440**, the gun swings along an arc path **1010** that projects within the firing zone solid area **940**. Integration of the slewing arc **1010** and missile path bounded by lines **910**, **920** yields a combination ordnance-travel and gun-slewing solid angle **1020** labeled as Ω_{ordnance-and-slew}, thereby increasing fratricide probability with proportional increase of the numerator term.

**1100** of spherical collision modeling to calculate fratricide probability as a summary to these techniques described. The modeling steps begin with gun firing zone determination **1110**, and proceeds to discretization of the missile's profile **1120**. The model continues to determine the missile's trajectory path **1130** from its launch cell, and the angular sweep of the gun's slew **1140**.

The model follows by determining the solid angle of the combined path and sweep **1150**, and proceeds with probability calculation **1160** of fratricide for each launch cell. The model concludes by repeating these procedures for final determination **1170** of maximum and average probabilities are determined for the entire system.

First Step **1110**: The model determines the gun firing zones for a ship from the gun-mount view over the missile system. The gun firing zones are defined in terms of their azimuth and elevation boundaries, thereby enabling their boundaries as shown in _{firingzone}.

Second Step **1120**: The model discretizes the elevation-view frontal profile of the missile **265**, such as into triangular plates **840** as determined by eqn (7). The boundaries of these plates can be represented as shown in **310**.

Third Step **1130**: The model calculates the missile's trajectory path **930** from its launch cell. This can be accomplished by translating the discrete points representing the missile across its trajectory flight path to produce a solid angle Ω_{ordnancepath }for the ordnance path **950** mapped onto the sphere **460**.

Fourth Step **1140**: The model calculates the angular sweep of the gun's slew. This can be accomplished by mapping the gun-slewing sweep **1010** swept from the center **440** onto the sphere **460**.

Fifth Step **1150**: The model determines the solid angle of the combined path and sweep. The mapped area **1020** in _{ordnance-and-slew }formed by the combined missile path and gun slew. This can be accomplished by translating the discrete points representing the ordnance path from the third step **1130** across the sweep of the slewing gun in the fourth step **1140** to determine the boundary limit points within the firing zone area **940** that define the region in which the gun can fire into the missile's trajectory.

Sixth Step **1160**: The model calculates the probability of fratricide for each of the missile cells **260** using eqn (8) with Ω_{ordnance }representing the path-and-slew solid angle **1020** of the fifth step **1150** and Ω_{firingzone }representing the solid area **940** of the gun firing zone **270** of the second step **1120**. Alternatively for circumstances neglecting gun slew, eqn (8) can employ Ω_{ordnance }as representing only the ordnance path solid angle **950** of the third step **1130**.

Seventh Step **1170**: The model extends these calculations to determine the maximum and average of all the missile probabilities for the entire missile system. This involves determining the overlapping regions between gun slew and missile firings over the entire combat vessel.

Additional precision of the fratricide probability may be achieved by including gun fire probability zones into the calculation. These are simply areas of the gun firing zone **270** in which the probability of firing may vary. Such an example would be a gun that fires seven-five-percent (75%) of the time between −5° and +10° elevation and the remainder above this region within the firing zone **270**.

This capability incorporates into the fratricide probability calculation weighting factors to the solid angle depending on the corresponding probability zone. **1200** of a missile passing through three-dimensional space. The projected firing zone solid area **940** is shown subdivided into a lower zone portion **1210** and an upper zone portion **1220**. Within each lower and upper portion, the gun respectively fires 75% and 25% of the total operational time.

These techniques may also be applied to ordnance vulnerability in the same manner as for determining gun-fire probability zones increase precision. A round penetrating the warhead significantly increases the chance for fratricide whereas hitting a fin or another inert component may not. **1300** that can be included to feature an ordnance vulnerability map. Similar to the gun fire probability, ordnance vulnerability (calculated by the ordnance designers) can be included in the fratricide probability calculation by adding and subtracting weighting factors to the solid angle.

**1310** with hypothetical graduated gray-scale levels corresponding to vulnerability. These exemplary vulnerabilities are characterized as a first level **1315** for 100%, a second level **1320** for 90%, a third level **1325** for 75%, a fourth level **1330** for 40% and a fifth level **1335** for 10%. A missile profile representation **265** includes regions having gray-scale shading that corresponds to the associated vulnerability level. These regions include the nose **1340**, an integration connector **1345**, radial flanks **1350**, mid-section **1355**, aft fin guidance **1360** with pivotable cruciform fins **1365**, propellant section **1370** and aft propulsion nozzle **1375**. Artisans of ordinary skill will recognize that this model is exemplary only.

Further accuracy can be added by running Monte Carlo scenarios. The technique enables comparative analysis of multiple firing times, slewing paths, and ordnance flyout courses against one another. The resultant fratricide probabilities can then be averaged together to achieve a more confident result.

Development of the Fratricide Probability Calculator adds significant capability in determining the fratricide probability between two shipboard weapon systems. Inclusion of spherical modeling of the ship environment leads to a better representation of the relationship between the gun and the ordnance. The technique facilitates a mathematical determination of the effects of a complicated ordnance fly-out path and slewing gun on the fratricide probability. Thus, these techniques generate higher fidelity probabilities and expand the variables that can be analyzed.

While certain features of the embodiments of the invention have been illustrated as described herein, many modifications, substitutions, changes and equivalents will now occur to those skilled in the art. It is, therefore, to be understood that the appended claims are intended to cover all such modifications and changes as fall within the true spirit of the embodiments.

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Referenced by

Citing Patent | Filing date | Publication date | Applicant | Title |
---|---|---|---|---|

US8176834 * | Jun 7, 2011 | May 15, 2012 | The United States Of America As Represented By The Secretary Of The Navy | Determination of weapons fratricide probability |

US8776664 | Jan 11, 2012 | Jul 15, 2014 | The United States Of America As Represented By The Secretary Of The Navy | Determination of weapons fratricide probability |

Classifications

U.S. Classification | 235/404, 89/134 |

International Classification | G06G7/80, F41A17/08 |

Cooperative Classification | F41A17/08, F41G3/04, F41G7/007 |

European Classification | F41G3/04, F41G7/00F, F41A17/08 |

Legal Events

Date | Code | Event | Description |
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Apr 24, 2008 | AS | Assignment | Free format text: ASSIGNMENT OF ASSIGNORS INTEREST;ASSIGNORS:AREVALO, MICHELLE R.;BLAND, GEOFFREY A.;REEL/FRAME:020985/0941 Effective date: 20080418 Owner name: NAVY, UNITED STATES OF AMERICA, REPRESENTED BY SEC |

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