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
3. The method according to
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
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:
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
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
8. The method according to
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
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:
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
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
13. The system according to
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
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:
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
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:
Triple points can represent each triangular plate to form a triangular solid angle determined by:
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. First Step Second Step Third Step Fourth Step 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 Fifth Step Sixth Step Seventh Step 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 Missile cells A firing zone 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 As observable in the 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. The first pair of azimuth lines In the X-Y plane, a first vertical line The radial lines Because the gun firing zone 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 As mentioned previously, the resultant fratricide probability P 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. Intersection of the sphere For a slewing gun, the ordnance is likewise in relative motion to the gun's aim point The model follows by determining the solid angle of the combined path and sweep First Step Second Step Third Step Fourth Step Fifth Step Sixth Step Seventh Step 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 This capability incorporates into the fratricide probability calculation weighting factors to the solid angle depending on the corresponding probability zone. 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. 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. Patent Citations
Referenced by
Classifications
Legal Events
Rotate |