Patent Grant
8176834
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: Ωrectangle=∫φ
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 stewing 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 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 coordinates.
Fourth Step 140: The model calculates the field-of-fire area A, 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 Δθf and the height Hf of the field-of-fire above the missile cells. The azimuth arc Δθf in eqn (2) is based on azimuth boundary difference from port to starboard swing of the gun mount. The firing height Hf in eqn (3) is based on the relative angular difference between elevation and depression bounds. These equations are provided below:
Δθf=θ2−θ1 (2)
Hf=R tan(Δφf),∃Δφf=φ2−φ1, (3)
where θ1 and θ2 are the respective port and starboard azimuth bounds (in degrees) and φ1 and φ2 are the respective elevation and depression bounds.
Fifth Step 150: The model calculates the exposed missile height Hm 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 Hm is assigned to equal the field-of-fire height Hf over the missile cell. Otherwise, the exposed missile height Hm equals the vertical length of the missile.
Sixth Step 160: The model calculates the probability of fratricide for each missile cell. The missile area Am can be calculated based on the exposed missile height Hm and the width of the missile Wm in eqn (4). The fratricide probability Pf can then be calculated based on the missile area Am and the total field-of-fire area Af in eqn (5). The equations are shown below:
Am=HmWm (4)
where the total field-of-fire Af 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
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.
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 coordinates (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 coordinates 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 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 Ωrectangle 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):
Ωrectangle=∫φ
where θ1 and θ2 are the azimuth bounds 650, 660 and φ1 and φ2 are the elevation bounds 670, 680. These boundaries can be used to constitute an area representing a solid angle Ωfiringzone for the firing zone.
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 Ωtriangle. 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
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 Ωordnance=ΣΩtriangle by summation.
As mentioned previously, the resultant fratricide probability Pf equals the ratio of solid angles between the ordnance and firing zone, as expressed in eqn (8):
where Ωordnance represents the solid area 830 of the missile and Ωfiringzone 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.
Intersection of the sphere 460 by the boundary lines 910, 920 projects a smaller solid area 950 representing a region labeled Ωordnancepath. The fratricide probability Pf of eqn (8) can be revised accordingly by substituting the trajectory solid angle Ωordnancepath for the original ordnance solid angle Ωordnance 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 Ωfiringzone 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.
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
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
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 Ωordnancepath 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
Sixth Step 1160: The model calculates the probability of fratricide for each of the missile cells 260 using eqn (8) with Ωordnance representing the path-and-slew solid angle 1020 of the fifth step 1150 and Ωfiringzone 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 Ωordnance 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.
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.
The invention is a Continuation, claims priority to and incorporates by reference in its entirety U.S. patent application Ser. No. 12/152,122 filed Apr. 24, 2008 titled “Determination of Weapons Fratricide Probability” assigned Navy Case 98713 and issued as Statutory Invention Registration H002255, which pursuant to 35 U.S.C. §119, claims the benefit of priority from provisional application 60/928,671, with a filing date of Apr. 26, 2007.
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.
| Number | Name | Date | Kind |
|---|---|---|---|
| 3618456 | Mindel | Nov 1971 | A |
| 4164165 | Bean et al. | Aug 1979 | A |
| H2255 | Arevalo et al. | Jun 2011 | H |
| Number | Date | Country | |
|---|---|---|---|
| 60928671 | Apr 2007 | US |
| Number | Date | Country | |
|---|---|---|---|
| Parent | 12152122 | Apr 2008 | US |
| Child | 13134487 | US |
