Regional Ship-to-Air Missile Ship Maneuvering Cover Model

— In view of the problem of a regional ship-to-air missile ship covering an adjacent ship, considering the locations of the ships, the required azimuth angle of a regional ship-to-air missile ship covering an adjacent ship, the maximum azimuth angle of a regional ship-to-air missile ship instantaneously covering an adjacent ship, and the remote distance of the regional ship-to-air missile launch area, a model of a regional ship-to-air missile ship longitudinally and laterally maneuvering to cover an adjacent ship was proposed, which provides a model basis for a regional ship-to-air missile ship longitudinally and laterally maneuvering to cover an adjacent ship.


I. INTRODUCTION
When a regional ship-to-air missile ship covers an adjacent ship, it can perform longitudinal and lateral maneuvers to cover the adjacent ship.
At present, the main relevant research are as follows: mainly analyze and determine the air defense ship cover sector, mainly analyze and determine the air defense weapon cover angle, mainly evaluate the minimum configuration number parameter of the regional air defense ship, adopt the comprehensive evaluation method to optimize the cover target scheme, mainly determine the air defense fire unit distance, etc.
The above research results do not consider factors such as the locations of the ships, the azimuth angle required by a regional ship-to-air missile ship to cover an adjacent ship, the maximum azimuth angle of a regional ship-to-air missile ship to cover an adjacent ship instantaneously, and the far boundary distance of the ship-to-air missile launch area. Therefore, this paper proposes a regional ship-to-air missile ship maneuvering model to cover an adjacent ship in the longitudinal and lateral directions, which takes into account such factors as the positions of ships, the azimuth angle required by a regional ship-to-air missile ship to cover an adjacent ship, the maximum azimuth angle of a regional shipto-air missile ship to cover an adjacent ship instantaneously, and the far-off distance of the ship-to-air missile launch area. It can quantitatively provide a model basis for a regional shipto-air missile ship to cover an adjacent ship in longitudinal and lateral maneuvers.
In Fig. 1, point O is the position of an adjacent ship. The required azimuth range for a single regional ship-to-air missile ship to cover an adjacent ship refers to the required azimuth range for the regional ship-to-air missile ship to cover the adjacent ship, that is, the azimuth range formed by two straight lines, OJ2 and OJ3, with point O as the starting point. Angle H is the azimuth angle required by the regional ship-to-air missile ship to cover the adjacent ship, straight line OJ2 is the azimuth angle line that the regional ship-to-air missile ship needs to cover the adjacent ship, and straight line OJ3 is the azimuth angle line that the regional ship-to-air missile ship needs to cover the adjacent ship. The straight line OJ1 is the reference line, and the angle B is the azimuth angle of the minimum demand angle line for the ship-to-air missile ship to cover the adjacent ship in the area. The Y1 circle is the fire circle of the ship-to-air missile of the adjacent ship, which is a circle with point O as the center and radius E1. E1 is the distance from the ship-to-air missile launch area of the adjacent ship. Point A1 is the instantaneous position of the regional ship-to-air missile ship, and circle A1 is the instantaneous fire circle of the regional ship-to-air missile ship, which is a circle with point A1 as the center and radius E2. E2 refers to the distance from the ship-to-air missile launch area in the area. R is the distance between the point O and the point A1.
Jihua Dou, Jiaqi Zou, and Yuliang Sun The maximum azimuth angle at which the regional shipto-air missile ship can cover the adjacent ship instantaneously refers to the maximum azimuth angle at which the regional ship-to-air missile ship can cover the adjacent ship instantaneously, which is set as angle U. It is determined by the instantaneous fire circle of the regional ship-to-air missile ship and the ship-to-air missile fire circle of the adjacent ship, that is, the maximum azimuth angle U formed by the straight line OJ2 and the straight line OJ4, which constitutes the covering closed area when the regional ship-to-air missile ship instantaneously covers the adjacent ship at the point A1. That is, when the regional ship-to-air missile ship instantaneously covers the adjacent ship at point A1, the circle A1 is tangent to the straight line OJ2 and the straight line OJ4, and the tangent intersections are also at point C1 and point C2 respectively. The intersection points of circle X1 and circle Y1 are also at point C1 and point C2, respectively, forming a covering closed area formed by line segment OC1, line segment OC2 and circle X1. This covering closed area is the largest closed area where the regional ship-to-air missile ship can instantaneously cover the adjacent ship at point A1. The maximum azimuth angle of the covering closed area to point O is the maximum azimuth angle U that the regional ship-toair missile ship can instantaneously cover the adjacent ship at point A1. R is given in (1), U is given in (2).
III. A MODEL OF LONGITUDINAL MANEUVER FOR A SINGLE REGIONAL SHIP-TO-AIR MISSILE SHIP TO COVER AN ADJACENT SHIP On the basis of Fig. 1, when the required azimuth angle H of the regional ship-to-air missile ship for covering the adjacent ship is smaller than the maximum azimuth angle U of the instantaneous covering the adjacent ship, (see Fig. 2). The straight line OJ4 is the center line of the angle range of the adjacent ship covered by the regional ship-to-air missile ship. When the regional ship-to-air missile ship covers the adjacent ship, the regional ship-to-air missile ship can make longitudinal maneuvers on the straight line OJ4. Set a point A2 on the straight line OJ3, and the point A2 is the instantaneous position of the regional ship-to-air missile ship. The X2 circle is also the instantaneous fire circle of the regional ship-to-air missile ship, which is a circle with point A2 as the center and radius E2. The Y1 circle and the X2 circle intersect on the straight lines OJ2 and OJ3, The Y1 circle and the X2 circle intersect on the straight line OJ2 at point C3, and the Y1 circle and the X2 circle intersect on the straight line OJ3 at point C5. It constitutes the covering closed area formed by the line segment OC3, the line segment OC5 and the circle X2 that is the closest to point O when the regional ship-to-air missile ship instantaneously covers the adjacent ship at point A2. This covered area is the closest closed area when the regional ship-to-air missile ship can instantaneously cover the required azimuth angle H of the adjacent ship. Set point A3 on the straight line OJ3, and point A3 is the instantaneous position of the regional ship-to-air missile ship. The X3 circle is the instantaneous fire circle of the regional ship-to-air missile ship, which is a circle with point A3 as the center and radius E2. The X3 circle is tangent to the straight line OJ2 and the straight line OJ3, and the tangent intersections are points C4 and C6 respectively. It constitutes the covering closed area farthest from point O, formed by the line segment OC4, the line segment OC6 and the circle X3, when the regional shipto-air missile ship instantaneously covers the adjacent ship at point A3. This covered closed area is the farthest closed area when the regional ship-to-air missile ship can instantaneously cover the required azimuth angle H of the adjacent ship. The intersection of the straight line C3C5 and the straight line OJ4 is a point C7.
Therefore, the regional ship-to-air missile ship can make longitudinal maneuvers on the straight line OJ4 to cover the adjacent ship, and its longitudinal maneuvering range is the line segment A2A3 from point A2 to point A3. |OA2| is given in (3).
The distance between point A2 and point O is | " | and the relative angle is + 0.5 . The distance between point A3 and point O is | # |, and the relative angle is + 0.5 . | # | is given in (4). Fig. 2. A schematic diagram of a regional ship-to-air missile ship's longitudinal maneuver for covering an adjacent ship. On the basis of Fig. 1, when the required azimuth angle H of the regional ship-to-air missile ship for covering the adjacent ship is greater than or equal to the maximum azimuth angle U of instantaneously covering the adjacent ship, see Fig. 3. Point A4 is also the instantaneous position of the shipto-air missile in the area. The X4 circle is also the instantaneous fire circle of the regional ship-to-air missile ship, which is a circle with point A4 as the center and radius E2. The X4 circle is tangent to the straight line OJ3, and the tangent intersection point is point C9. The angle H1 is the included angle between the straight line OA1 and the straight line OA4. When the regional ship-to-air missile ship covers the adjacent ship, it needs to implement lateral maneuvers in Fig.  3. That is, the regional ship-to-air missile ship can make a lateral maneuver on the arc S with the point O as the center and the radius R, and the lateral maneuver range is the arc segment from the point A1 to the point A4. The azimuth angle of the arc segment with respect to the point O is H1. It constitutes a covering closed area formed by the line segment OC1, the line segment OC9 and the instantaneous fire circle of the regional ship-to-air missile ship when the regional ship-to-air missile ship covers the adjacent ship in this arc segment. The covering closed area is the closed area when the regional ship-to-air missile ship can instantaneously cover the required azimuth angle of the adjacent ship. Where the distance between the point A1 and the point O is R and the relative angle is given in (5).
The distance between point A4 and point O is R and the relative angle is given in (6). H1 is given in (7). Fig. 3. A schematic diagram of a regional ship-to-air missile ship's lateral maneuver for covering an adjacent ship.

V. CONCLUSION
On the basis of considering the positions of the ships, the required azimuth angle of the regional ship-to-air missile ship to cover the adjacent ship, the maximum azimuth angle of the regional ship-to-air missile ship to instantaneously cover the adjacent ship, and the far distance of the ship-to-air missile launch area, the longitudinal and lateral maneuvering cover model for a regional ship-to-air missile ship to cover an adjacent ship is proposed in this paper, which provides a basis for the regional ship-to-air missile ship to cover adjacent ship in the longitudinal and lateral maneuvers.