An Algorithm of Enemy Flight Area in Fleet Air Defense

Aiming at the algorithm of the enemy flight area when the enemy launches air-to-ship missiles in fleet air defense, this paper analyzes the position situation of both parties. On the basis of the analysis, it describes the shape of the enemy flight area, and establishes the calculation model. Finally, a demonstration verification program is developed and the application examples in various cases are given. This algorithm can not only accurately calculate the enemy flight area, but effectively assist the commander to form scientific air defense plans.


INTRODUCTION
In fleet air defense, one of the main air threats for our fleet is the attack of air-to-ship missiles from the enemy aircrafts. In response to the threat, there are two modes of air defense. One mode is resisting the enemy aircrafts. Naval aviation and regional/close range air defense ships are used to intercept and resist the incoming enemy aircrafts. The other mode is resisting the hostile air-toship missiles. Regional/close range air defense ships are used to combat the incoming hostile air-to-ship missiles [1].
This paper focuses on determining the enemy flight area, which is a key issue for the mode of resisting the enemy aircrafts. Enemy flight area refers to the possible flight area for the enemy aircrafts when using air-to-ship missiles to carry out attacks. The enemy aircrafts may take off from threat sources such as airports or aircraft carriers. Our party must accurately grasp the flight area of the enemy aircrafts as preplanning the air defense and making emergency decisions, so as to carry out effective defense demand analysis and force assignment, and form scientific interception and resistance plans [2].

Establishment of Plane Rectangular Coordinate System
Grasping the enemy aircraft's projection on the sea surface is adequate to formulate air defense plan in practice, so the plane rectangular coordinate system is established. The initial condition is that the location of our fleet is Point , and the enemy airport or aircraft carrier locates in Point , with a distance of in between. The enemy aircraft's combat radius is , and the maximum range of the enemy air-to-ship missile is . So the enemy's attack distance is . The coordinate system established is shown in Figure 1: Point is the original point, is the Axis forward. Let's rotate 90 degrees counter clockwise and get The Circle is the enemy combat radius circle, with the center , and the radius ; the Circle is the enemy attack circle, with the center , and the radius ; the Circle is the enemy air-to-ship missile attack circle, with the center , and the radius .

Establishment of Plane Rectangular Coordinate System
With the change of the distance between both parties, the shapes of enemy flight area and their algorithms are divided into 3 cases. Case 1: our party locates inside the enemy attack circle, and outside the enemy combat radius circle, that is ; Case 2: our party locates inside the enemy combat radius circle, and is beyond the maximum range of the enemy air-to-ship missile, that is ; Case 3: our party locates inside the enemy combat radius circle, and is within the maximum range of the enemy air-to-ship missile, that is .

Auxiliary geometric figure
The maximum value of the sum of the distance between the enemy aircraft's flight distance and the enemy air-toship missile is of fixed value , so partial boundary of the enemy flight area conforms to the geometric characteristics of an ellipse [3][4] . As in Figure 2

Description of the shape of the enemy flight area
The shadow part in Figure 2 is the enemy flight area , which should meet the following conditions at the same time. First, being inside or on the enemy combat radius circle . Second, being inside or on the Ellipse . Third, the enemy aircrafts do not reverse the flight during the attack, that is, Area is excluded. Therefore, is: The geometric properties of Case 2 and Case 1 are basically the same, with only an area added. With the change of , which is the distance between the enemy and our party, the area is divided into two cases: Case 2.1: When , schematic diagram of the calculation of enemy flight area is as shown in Figure  3. Case 2.2, when , schematic diagram of the calculation of enemy flight area is as shown in Figure 4.

Description of the shape of the enemy flight area
The shadow parts in Figure 3 and Figure 4 are the enemy flight area , that is , on the basis of , Sector is superimposed. Therefore, is :

Calculation Model of Case 3
According to the rule that the enemy aircrafts do not reverse the flight during the attack, and the analysis of Case 2, in Case 3, the sector angle of Sector is defined as , and properly include

APPLICATION EXAMPLE OF THE CALCULATION MODEL OF THE ENEMY FLIGHT AREA
In order to test the algorithm of enemy flight area, a demonstration verification program is developed using Qt [5][6]. It can be used to calculate the enemy flight area under various combination of combat radius of the enemy aircraft, maximum range of the enemy air-to-ship missile, and distance between both parties.
Here is a set of assumed numeric values for calculating the enemy flight areas in various cases. It is known that the position of our fleet is Point ; the position of the enemy airport or aircraft carrier is Point ; the operational radius of the enemy aircraft is 1300km; the maximum range of the enemy air-to-ship missile is 230km; assume that the distance between the enemy and our party is 1500km, 1125km, 600km and 175km, respectively corresponding to Case 1, Case 2.1, Case 2.2 and Case 3, then the enemy flight area are calculated, and described with shadow areas shown in Figure 6-9.

CONCLUSION
Aiming at the algorithm of the enemy flight area when the enemy launches air-to-ship missiles with aircrafts in fleet air defense, this paper carries out military requirement analysis and classification of position situation of both parties. On this basis, it describes the shape of the enemy flight area in various cases, and establishes the calculation model. Finally, a demonstration verification program is developed and the application examples in various cases are given. The calculation model established in this paper, which is able to accurately calculate the shape of the enemy flight area, can be directly used as the basis for the analysis of defense demand and the assignment of forces. Besides, this calculation model will become an important function point of the operational planning software to effectively assist the commander to form scientific air defense plans.