Fratricide Probability Calculation Using Spherical Geometry
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Solution Overview
Problem
Conventional methods for calculating fratricide probabilities in weapon systems are time-consuming and prone to errors due to simplifying assumptions and the lack of systematic characterization of firing zones and ordnance interception hazards, especially as field coverage increases.
Innovation Solution
The development of a method using spherical geometry to calculate fratricide probabilities by determining the firing zone, quantifying the frontal area of interception hazards, and combining these with slewing actions of the projectile launcher, employing integral calculations for rectangular solid angles and triangular plate summations to provide accurate and automated probability assessments.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Ease of manufacture
If manual calculations are used to determine fratricide probability, then the calculation process can be performed with simple tools, but the calculation becomes time-consuming and yields limited results
Solution Approach 1:
The patent replaces manual mechanical calculation methods with an automated computer-based system that uses mathematical models and algorithms to calculate fratricide probability. The system automatically processes weapon system data, performs spherical geometry calculations for firing zones, and generates probability assessments without manual intervention, thereby eliminating the time-consuming nature of manual calculations while maintaining accuracy.
Solution Approach 2:
The patent creates a computational model that replicates the complex geometric and probabilistic relationships of weapon systems. By copying the physical firing zones, trajectories, and hazard areas into a mathematical representation using spherical coordinates and solid angle calculations, the system enables rapid automated computation that would be impractical to perform manually.
2Productivity
If conventional fratricide probability techniques are used, then the initial calculation can be completed, but errors expand exponentially with increasing field coverage
Solution Approach 1:
The patent applies spherical geometry to accurately model firing zones and hazard areas in three-dimensional space. By using spherical coordinates and calculating solid angles on a spherical surface, the system maintains geometric accuracy across the entire field of fire, preventing the exponential error expansion that occurs with planar approximations when coverage area increases.
Solution Approach 2:
The patent transitions from two-dimensional planar calculations to three-dimensional spherical geometry to represent firing zones and hazard volumes. This dimensional change allows accurate modeling of curved trajectories, angular constraints, and spatial relationships that cannot be properly represented in flat geometry, thereby maintaining reliability as field coverage expands.
3Ease of operation
If simplifying assumptions are made in fratricide calculations, then the mathematical calculations become tractable, but the results become less accurate
Solution Approach 1:
The patent changes the mathematical parameters from simplified Cartesian coordinates to spherical coordinates, and from area-based calculations to solid angle-based calculations. This parameter transformation enables the system to handle complex three-dimensional geometry and angular constraints without requiring simplifying assumptions, maintaining both computational tractability and measurement precision through appropriate mathematical formulation.
Data Source
AI summary
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.