Calculating Weapon Fratricide Probability Between Two Weapon Systems

by Michelle Arevalo and Geoffrey Bland, Dahlgren, Virginia

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Introduction
Fratricide is defined as an attack on friendly forces by other friendly forces [Ref. 1]. Throughout this document, fratricide is used in the context of ownship ordnance intersecting with other ownship ordnance, the collision of which would result in an energetic reaction leading to significant damage and/or death. Previously, this analysis was conducted manually without the benefit of a tool. This resulted in the determination of the probability of such an occurrence, thus advising the appropriate authorities of the level of risk associated with this hazard and any appropriate mitigations.

This paper makes a case for the development and utilization of an automated Fratricide Probability Calculator (FPC), which will more precisely calculate fratricide probabilities for user-defined ship classes and layouts, as well as various gun weapon systems and missile-launching systems. Earlier analytical efforts used cylindrical modeling to calculate the probability. If other ship-launched ordnance were to be examined, then the use of spherical modeling would provide more accurate results by taking into consideration the various fly-out paths as well as various slewing actions of the gun. The FPC would use this spherical modeling, along with other enhancements, to provide an automated capability to provide quick and accurate probabilities of fratricide for myriad weapon systems combinations.

Analysis
Cylindrical Modeling Method: The calculation of fratricide probability in its most basic form can be thought of 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 simple example is that of a blindfolded person randomly throwing darts at a dartboard on a wall. Assuming that the person can only hit within the boundaries of the wall, if the dartboard is one-tenth the presented area of the wall, the person has a 10 percent chance of hitting the board. While this is a simple example, the calculation of fratricide probability introduces greater complexity. Cylindrical modeling can be used to calculate fratricide probability using the steps outlined in Table 1.

Table 1 — Cylindrical Modeling Steps.

Step	Description	Equations
1	Determine the gun cutout zones for each ship from the gun mount view over the missile system containing multiple missiles.1 The gun cutout zone is defined as the region in which the gun can fire. Each ship, regardless of type or class, has a different layout and, therefore, different cutout zones. The gun cutout zones are defined in terms of their azimuth and elevation boundaries. The entire gun cutout zone was divided into separate sectors, depending on the minimum elevation angles, and then color coded (Figure 1).
2	Determine which sector each missile falls under. As can be seen in Figure 2, the missiles are located in only three of the five sectors, sectors 2, 3 and 4. If a missile cell fell under two sectors, the cell was placed in the sector that contained 50 percent or more of the cell for calculation purposes.
3	Calculate the distance between the center of each missile cell and the gun using the Pythagorean Theorem.
4	Calculate the field of fire above each missile cell. Equation 1 shows this calculation using the distance, R, calculated in Step Three, the firing arc (Eqn. 2) and the height (Eqn. 3), H, of the field of fire over the missile cell.	(1) (2) (3)
5	Calculate the exposed missile height in the field of fire over each missile cell. If the height of the missile was greater than the height calculated in Eqn. 3, then the exposed missile height was equal to the height of the field of fire over the missile cell. Otherwise, the exposed missile height was equal to the height of the missile.
6	Calculate the probability of fratricide for each missile cell. This is done by calculating the missile area (Eqn. 4), which is then used to calculate the probability (Eqn. 5).	(4) (5)
7	Calculate the maximum and average of all the missile probabilities for the entire missile system.

Figure 1 — Gun Perspective of Firing Cutout Zones.

Figure 2 — Missile to Sector Determination.

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