CN108829635A - The calculation method in the motor-driven area of enemy plane in a kind of surface ship air-defense - Google Patents

The calculation method in the motor-driven area of enemy plane in a kind of surface ship air-defense Download PDF

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CN108829635A
CN108829635A CN201810192184.4A CN201810192184A CN108829635A CN 108829635 A CN108829635 A CN 108829635A CN 201810192184 A CN201810192184 A CN 201810192184A CN 108829635 A CN108829635 A CN 108829635A
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CN108829635B (en
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龙飞
孙永侃
姚晓白
张永
邓可
郭久智
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Dalian Naval Vessels College Navy P L A
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Abstract

The invention belongs to defend algorithmic technique field, and in particular to the calculation method in the motor-driven area of enemy plane in a kind of surface ship air-defense.The calculation method in the motor-driven area of enemy plane, includes the following steps in a kind of surface ship air-defense：The first step, the foundation of algorithm coordinate system；Second step, the algorithm classification in the motor-driven area of enemy plane, with the variation of enemy and we's distance, the shape and its calculation method in the motor-driven area of enemy plane are divided into 3 kinds of situations；Third step, the calculating in the motor-driven area of enemy plane in the case of 3 kinds.Calculation method proposed by the present invention accurately calculates the region shape in the motor-driven area of enemy plane, it can be directly as air-defense demand analysis and the foundation of troops collocation, and can become to fight and prepare the critical function point of software, effectively auxiliary commander is formed to the air-defense battle plan of science.

Description

The calculation method in the motor-driven area of enemy plane in a kind of surface ship air-defense
Technical field
The invention belongs to defend algorithmic technique field, and in particular to the motor-driven area of enemy plane in a kind of surface ship air-defense Calculation method.
Background technique
During surface ship air-defense is fought, enemy is that our surface ship faces using enemy plane transmitting air to ship missile attack Prevailing air threaten one of.For the threat, we can take two kinds of air-defense modes of operation：Mode one defends enemy plane. The enemy plane to attack is resisted using air arm's interception, region or short-range air-defense naval vessels.Mode two, anti-air to ship missile of resisting the enemy.Use area Enemy's air to ship missile that domain or short-range air-defense naval vessels are resisted to attack.
The motor-driven area of enemy plane, when referring to that enemy implements attack using air to ship missile, the possible flight range of enemy plane.Enemy plane can be with It takes off from the threat source of the types such as airport or aircraft carrier, we carries out preparing in advance and decision as the occasion requires for air-defense operation When, it is necessary to the motor-driven area for accurately grasping enemy plane just can be carried out effective defence demand analysis and troops collocation, form science Interception resist battle plan.
Summary of the invention
The present invention provides a kind of calculation methods in the motor-driven area of enemy plane in surface ship air-defense, to surface ship to sky In defensive operation, enemy using enemy plane transmitting air to ship missile attack when the motor-driven area of enemy plane computational problem, carried out demand analysis, Algorithm establishment of coordinate system, the classification of enemy and we position situation situation, define the area in the motor-driven area of enemy plane in each case on this basis Domain shape, and study and establish corresponding algorithm model.
Technical solution of the present invention：
The calculation method in the motor-driven area of enemy plane, includes the following steps in a kind of surface ship air-defense：The first step, algorithm are sat Mark the foundation of system
Establish plane right-angle coordinate xOy；If our surface ship position is point W, enemy plane field or opposes aircraft carrier position For point O, enemy and we's distance is d=| OW |, enemy plane combat radius is R, and enemy's air to ship missile maximum range is r, then opposing attack distance is R + r, using point O as origin, OW is that x-axis is positive, if OW is rotated by 90 ° counterclockwise as y-axis forward direction.
Wherein：
Circle Ω1For enemy's combat radius circle, center of circle O, radius R；
Circle Ω2For enemy's attack circle, center of circle O, radius R+r；
Circle Ω3Circle, center of circle W, radius r are attacked for enemy's air to ship missile.
Second step, the algorithm classification in the motor-driven area of enemy plane
With enemy and we's distance | OW | variation, the shape and its calculation method in the motor-driven area of enemy plane be divided into 3 kinds of situations, corresponding | OW | value range is as follows：
Situation 1, we is located in enemy's attack circle, enemy's combat radius circle is outer, i.e. R<|OW|<R+r；
Situation 2, we is in enemy's combat radius circle, enemy and we's distance exceeds enemy's air to ship missile maximum range, i.e. and r≤| OW | ≤R；
Situation 3, we is located in enemy's combat radius circle, enemy and we's distance is without departing from enemy's air to ship missile maximum range, i.e., | OW |< r。
Third step, the calculating in the motor-driven area of enemy plane
The algorithm of 3.1 situations 1
3.1.1 it is oval to establish auxiliary
Enemy plane transmitting air to ship missile is when attacking our surface ship, enemy plane flying distance and enemy's air to ship missile flying distance it The maximum value of sum is definite value R+r.
Establish auxiliary ellipse P, focus O, W, a length of R+r of long axis；Point A, B are ellipse P and circle Ω1, circle Ω3Intersection point, point C, D is the intersection point of ellipse P and y-axis.
3.1.2 the motor-driven area J of enemy plane under calculated case 11
(1) circle Ω1Equation
x2+y2=R2
(2) equation of ellipse P
Wherein：Major semiaxis a=(R+r)/2；Semi-minor axis
(3) coordinate of point A, B
Point A, B are circle Ω1, circle Ω3, ellipse P intersection point, wherein round Ω3Equation be：
(x-d)2+y2=r2
Simultaneous justifies Ω1, circle Ω3, ellipse P equation can acquire the coordinate of point A, B：
Point A coordinate,
Point B coordinate,
(4) coordinate of point C, D
For point C, D on oval P, the abscissa of C point is xC=0；The abscissa x of D pointD=0, the equation for substituting into ellipse P can be asked The coordinate of invocation point C, D：
Point C coordinate,
Point D coordinate,
Enemy plane motor-driven area J when situation 11, while meeting following condition：First, not in combat radius circle Ω1Outside；Second, no Outside oval P；Third, enemy plane does not include region Q without reversed motor-driven when attack1；Therefore, enemy plane motor-driven area when situation 1 J1For：
J1=Ω1∩P-Q1
Wherein, Q1The region surrounded for line segment CD and arc CD.
The algorithm of 3.2 situations 2
With enemy and we's distance | OW | variation, the shape in the motor-driven area of enemy plane is divided into two kinds of situations：
Situation 2.1, R-r≤| OW |≤R；
Situation 2.2, r≤| OW |<R-r.
3.2.1 establishing auxiliary covering of the fan
Establish auxiliary covering of the fanStraight line OA1、OB1With circle Ω3It is tangent, and with circle 01Point A is intersected at respectively1、B1, with Oval P intersects at point C respectively1、D1, wherein ellipse P focus is O, W, a length of R+r of long axis.Through geometric characteristic analysis, our water surface Naval vessels are in circle Ω1Interior, enemy plane is in covering of the fanIt is interior motor-driven, it can emit air to ship missile and implement attack.
3.2.2 the motor-driven area J of enemy plane under calculated case 22
(1) circle Ω1Equation
x2+y2=R2
(2) equation of ellipse P
Wherein：Major semiaxis a=(R+r)/2；Semi-minor axis
(3) coordinate of point A, B
When situation 2.1, circle Ω1, circle Ω3, ellipse P intersect at point A, B；
When situation 2.2, circle Ω1, circle Ω3, ellipse P it is non-intersecting.
Circle Ω3Equation be：
(x-d)2+y2=r2
When situation 2.1, simultaneous circle Ω1, circle Ω3, ellipse P equation can acquire the coordinate of point A, B：
Point A coordinate,
Point B coordinate,
(4) coordinate of point C, D
For point C, D on oval P, the abscissa of C point is xC=0；The abscissa x of D pointD=0, the equation for substituting into ellipse P can be asked The coordinate of invocation point C, D：
Point C coordinate,
Point D coordinate,
(5) point A1、B1Coordinate
Straight line OA1、OB1Equation：
± kx-y=0
Point F (d, 0) arrives straight line OA1、OB1Distance be r, can acquire accordingly
Simultaneous justifies Ω1Equation can acquire point A1、B1Coordinate：
Point A1Coordinate,
Point B1Coordinate,
Enemy plane motor-driven area J when situation 22, while meeting following condition：First, not in combat radius circle Ω1Outside；Second, In oval P or in covering of the fanIt is interior；Third, enemy plane does not include region Q without reversed motor-driven when attack1；
Therefore, enemy plane motor-driven area J when situation 22For：
Wherein：Q1The region surrounded for line segment CD and arc CD；
When situation 2.1, J2Opposite Ω1∩P-Q1Increase Q2∪Q3, wherein Q2For line segment A1D1, arc AD1, arc AA1It surrounds Region, Q3For line segment B1C1, arc BC1, arc BB1The region surrounded；
When situation 2.2, J2Opposite Ω1∩P-Q1Increase Q4, wherein Q4For line segment A1D1、B1C1, arc A1B1、C1D1It surrounds Region.
The algorithm of 3.3 situations 3
3.3.1 establishing auxiliary covering of the fan
Establish auxiliary covering of the fanStraight line OA1、OB1With circle Ω1Point A is intersected at respectively1、B1, not according to enemy plane when attacking Carry out reversed motor-driven rule, point A1On y-axis negative sense, point B1Y-axis forward.Through geometric characteristic analysis, our surface ship In circle Ω1Interior, enemy plane is in covering of the fanIt is interior motor-driven, it can emit air to ship missile and implement attack.
3.3.2 the motor-driven area J of enemy plane under calculated case 33
(1) circle Ω1Equation
x2+y2=R2
(2) point A1、B1Coordinate
Utilize circle Ω1Equation can acquire point A1、B1Coordinate：
Point A1Coordinate,
Point B1Coordinate,
Enemy plane motor-driven area J when situation 33, while meeting following condition：First, not in combat radius circle Ω1Outside；Second, In oval P or in covering of the fanIt is interior；Third, enemy plane does not include region Q without reversed motor-driven when attack1；Therefore, may be used Establish J3Formula be：
Wherein：Oval P focus is O, W, a length of R+r of long axis；Q1The region surrounded for line segment CD and arc CD.
Through geometric characteristic analysis, covering of the fanIt really include P-Q1, and really it is contained in Ω1.Therefore, enemy plane is motor-driven when situation 3 Area J3For：
Beneficial effects of the present invention are：Calculation method proposed by the present invention accurately calculates the region shape in the motor-driven area of enemy plane Shape, can be directly as air-defense demand analysis and the foundation of troops collocation, and can become to fight and prepare the important function of software Energy point effectively auxiliary commander will form scientific air-defense battle plan.
Detailed description of the invention
Attached drawing 1 is algorithm coordinate system.
Attached drawing 2 is the motor-driven area J of enemy plane in situation 11。
Attached drawing 3 is the motor-driven area J of enemy plane in situation 2.12.1。
Attached drawing 4 is the motor-driven area J of enemy plane in situation 2.22.2。
Attached drawing 5 is the motor-driven area J of enemy plane in situation 33。
Attached drawing 6 is the motor-driven area's example of enemy plane in situation 1, d=1300km.
Attached drawing 7 is the motor-driven area's example of enemy plane in situation 2.1, d=875km.
Attached drawing 8 is the motor-driven area's example of enemy plane in situation 2.2, d=450km.
Attached drawing 9 is the motor-driven area's example of enemy plane in situation 3, d=200km.
Specific embodiment
Below in conjunction with attached drawing and technical solution, a specific embodiment of the invention is further illustrated.
The calculation method in the motor-driven area of enemy plane, includes the following steps in a kind of surface ship air-defense：The first step, algorithm are sat Mark the foundation of system
Establish plane right-angle coordinate xOy；If our surface ship position is point W, enemy plane field or opposes aircraft carrier position For point O, enemy and we's distance is d=| OW |, enemy plane combat radius is R, and enemy's air to ship missile maximum range is r, then opposing attack distance is R + r, using point O as origin, OW is that x-axis is positive, if OW is rotated by 90 ° counterclockwise as y-axis forward direction.
Wherein：
Circle Ω1For enemy's combat radius circle, center of circle O, radius R；
Circle Ω2For enemy's attack circle, center of circle O, radius R+r；
Circle Ω3Circle, center of circle W, radius r are attacked for enemy's air to ship missile.
Second step, the algorithm classification in the motor-driven area of enemy plane
With enemy and we's distance | OW | variation, the shape and its calculation method in the motor-driven area of enemy plane be divided into 3 kinds of situations, corresponding | OW | value range is as follows：
Situation 1, we is located in enemy's attack circle, enemy's combat radius circle is outer, i.e. R<|OW|<R+r；
Situation 2, we is in enemy's combat radius circle, enemy and we's distance exceeds enemy's air to ship missile maximum range, i.e. and r≤| OW | ≤R；
Situation 3, we is located in enemy's combat radius circle, enemy and we's distance is without departing from enemy's air to ship missile maximum range, i.e., | OW |< r。
Third step, the calculating in the motor-driven area of enemy plane
The algorithm of 3.1 situations 1
3.1.1 it is oval to establish auxiliary
Enemy plane transmitting air to ship missile is when attacking our surface ship, enemy plane flying distance and enemy's air to ship missile flying distance it The maximum value of sum is definite value R+r.
Establish auxiliary ellipse P, focus O, W, a length of R+r of long axis；Point A, B are ellipse P and circle Ω1, circle Ω3Intersection point, point C, D is the intersection point of ellipse P and y-axis.
3.1.2 the motor-driven area J of enemy plane under calculated case 11
(1) circle Ω1Equation
x2+y2=R2
(2) equation of ellipse P
Wherein：Major semiaxis a=(R+r)/2；Semi-minor axis
(3) coordinate of point A, B
Point A, B are circle Ω1, circle Ω3, ellipse P intersection point, wherein round Ω3Equation be：
(x-d)2+y2=r2
Simultaneous justifies Ω1, circle Ω3, ellipse P equation can acquire the coordinate of point A, B：
Point A coordinate,
Point B coordinate,
(4) coordinate of point C, D
For point C, D on oval P, the abscissa of C point is xC=0；The abscissa x of D pointD=0, the equation for substituting into ellipse P can be asked The coordinate of invocation point C, D：
Point C coordinate,
Point D coordinate,
Enemy plane motor-driven area J when situation 11, while meeting following condition：First, not in combat radius circle Ω1Outside；Second, no Outside oval P；Third, enemy plane does not include region Q without reversed motor-driven when attack1；Therefore, enemy plane motor-driven area when situation 1 J1For：
J1=Ω1∩P-Q1
Wherein, Q1The region surrounded for line segment CD and arc CD.
The algorithm of 3.2 situations 2
With enemy and we's distance | OW | variation, the shape in the motor-driven area of enemy plane is divided into two kinds of situations：
Situation 2.1, R-r≤| OW |≤R；
Situation 2.2, r≤| OW |<R-r.
Identical as the principle of situation 1, the segment boundary in the motor-driven area of enemy plane meets elliptical geometrical property.
3.2.1 establishing auxiliary covering of the fan
Establish auxiliary covering of the fanStraight line OA1、OB1With circle Ω3It is tangent, and with circle Ω1Point A is intersected at respectively1、B1, with Oval P intersects at point C respectively1、D1, wherein ellipse P focus is O, W, a length of R+r of long axis.Through geometric characteristic analysis, our water surface Naval vessels are in circle Ω1Interior, enemy plane is in covering of the fanIt is interior motor-driven, it can emit air to ship missile and implement attack.
3.2.2 the motor-driven area J of enemy plane under calculated case 22
(1) circle Ω1Equation
x2+y2=R2
(2) equation of ellipse P
Wherein：Major semiaxis a=(R+r)/2；Semi-minor axis
(3) coordinate of point A, B
When situation 2.1, circle Ω1, circle Ω3, ellipse P intersect at point A, B；
When situation 2.2, circle Ω1, circle Ω3, ellipse P it is non-intersecting.
Circle Ω3Equation be：
(x-d)2+y2=r2
When situation 2.1, simultaneous circle Ω1, circle Ω3, ellipse P equation can acquire the coordinate of point A, B：
Point A coordinate,
Point B coordinate,
(4) coordinate of point C, D
For point C, D on oval P, the abscissa of C point is xC=0；The abscissa x of D pointD=0, the equation for substituting into ellipse P can be asked The coordinate of invocation point C, D：
Point C coordinate,
Point D coordinate,
(5) point A1、B1Coordinate
Straight line OA1、OB1Equation：
± kx-y=0
Point F (d, 0) arrives straight line OA1、OB1Distance be r, can acquire accordingly
Simultaneous justifies Ω1Equation can acquire point A1、B1Coordinate：
Point A1Coordinate,
Point B1Coordinate,
Enemy plane motor-driven area J when situation 22, while meeting following condition：First, not in combat radius circle Ω1Outside；Second, In oval P or in covering of the fanIt is interior；Third, enemy plane does not include region Q without reversed motor-driven when attack1；
Therefore, enemy plane motor-driven area J when situation 22For：
Wherein：Q1The region surrounded for line segment CD and arc CD；
When situation 2.1, J2Opposite Ω1∩P-Q1Increase Q2∪Q3, wherein Q2For line segment A1D1, arc AD1, arc AA1It surrounds Region, Q3For line segment B1C1, arc BC1, arc BB1The region surrounded；
When situation 2.2, J2Opposite Ω1∩P-Q1Increase Q4, wherein Q4For line segment A1D1、B1C1, arc A1B1、C1D1It surrounds Region.
The algorithm of 3.3 situations 3
3.3.1 establishing auxiliary covering of the fan
Establish auxiliary covering of the fanStraight line OA1、OB1With circle Ω1Point A is intersected at respectively1、B1, not according to enemy plane when attacking Carry out reversed motor-driven rule, point A1On y-axis negative sense, point B1Y-axis forward.Through geometric characteristic analysis, our surface ship In circle Ω1Interior, enemy plane is in covering of the fanIt is interior motor-driven, it can emit air to ship missile and implement attack.
3.3.2 the motor-driven area J of enemy plane under calculated case 33
(1) circle Ω1Equation
x2+y2=R2
(2) point A1、B1Coordinate
Utilize circle Ω1Equation can acquire point A1、B1Coordinate：
Point A1Coordinate,
Point B1Coordinate,
Enemy plane motor-driven area J when situation 33, while meeting following condition：First, not in combat radius circle Ω1Outside；Second, In oval P or in covering of the fanIt is interior；Third, enemy plane does not include region Q without reversed motor-driven when attack1；Therefore, may be used Establish J3Formula be：
Wherein：Oval P focus is O, W, a length of R+r of long axis；Q1The region surrounded for line segment CD and arc CD.
Through geometric characteristic analysis, covering of the fanIt really include P-Q1, and really it is contained in Ω1.Therefore, enemy plane machine when situation 3 Dynamic area J3For：
To examine the motor-driven area's algorithm of enemy plane, demonstration and verification program is developed using Qt, may be implemented to calculate any enemy plane work Fight the motor-driven area of enemy plane of radius, enemy air to ship missile maximum range, enemy and we under combined situation.
Our known surface ship position is point W, and enemy plane field or enemy aircraft carrier position are point O, and enemy plane combat radius R takes 1100km, enemy air to ship missile maximum range r take 280km, corresponding situation 1, situation 2.1, situation 2.2, situation 3, and enemy and we's distance d divides 1300km, 875km, 450km, 200km are not taken, the motor-driven area J of enemy plane is calculated1、J2.1、J2.2、J3, as a result such as Fig. 6 to Fig. 9 institute The shadow region shown.

Claims (1)

1. the calculation method in the motor-driven area of enemy plane in a kind of surface ship air-defense, which is characterized in that include the following steps：
The first step, the foundation of algorithm coordinate system
Establish plane right-angle coordinate xOy；If our surface ship position is point W, enemy plane field or enemy aircraft carrier position are a little O, enemy and we's distance are d=| OW |, enemy plane combat radius is R, and enemy's air to ship missile maximum range is r, then opposing attack distance is R+r, Using point O as origin, OW is that x-axis is positive, if OW is rotated by 90 ° counterclockwise as y-axis forward direction；
Wherein：
Circle Ω1For enemy's combat radius circle, center of circle O, radius R；
Circle Ω2For enemy's attack circle, center of circle O, radius R+r；
Circle Ω3Circle, center of circle W, radius r are attacked for enemy's air to ship missile；
Second step, the algorithm classification in the motor-driven area of enemy plane
With enemy and we's distance | OW | variation, the shape and its calculation method in the motor-driven area of enemy plane be divided into 3 kinds of situations, corresponding | OW | take It is as follows to be worth range：
Situation 1, we is located in enemy's attack circle, enemy's combat radius circle is outer, i.e. R<|OW|<R+r；
Situation 2, we is in enemy's combat radius circle, enemy and we's distance exceeds enemy's air to ship missile maximum range, i.e. and r≤| OW |≤R；
Situation 3, we is located in enemy's combat radius circle, enemy and we's distance is without departing from enemy's air to ship missile maximum range, i.e., | OW |<r；
Third step, the calculating in the motor-driven area of enemy plane
The algorithm of 3.1 situations 1
3.1.1 it is oval to establish auxiliary
When enemy plane transmitting air to ship missile attacks our surface ship, enemy plane flying distance and the sum of enemy's air to ship missile flying distance Maximum value is definite value R+r；
Establish auxiliary ellipse P, focus O, W, a length of R+r of long axis；Point A, B are ellipse P and circle Ω1, circle Ω3Intersection point, point C, D For the intersection point of oval P and y-axis；
3.1.2 the motor-driven area J of enemy plane under calculated case 11
(1) circle Ω1Equation
x2+y2=R2
(2) equation of ellipse P
Wherein：Major semiaxis a=(R+r)/2；Semi-minor axis
(3) coordinate of point A, B
Point A, B are circle Ω1, circle Ω3, ellipse P intersection point, wherein round Ω3Equation be：
(x-d)2+y2=r2
Simultaneous justifies Ω1, circle Ω3, ellipse P equation can acquire the coordinate of point A, B：
Point A coordinate,
Point B coordinate,
(4) coordinate of point C, D
For point C, D on oval P, the abscissa of C point is xC=0；The abscissa x of D pointD=0, the equation for substituting into ellipse P can acquire a little C, the coordinate of D：
Point C coordinate,
Point D coordinate,
Enemy plane motor-driven area J when situation 11, while meeting following condition：First, not in combat radius circle Ω1Outside；Second, not ellipse Outside circle P；Third, enemy plane does not include region Q without reversed motor-driven when attack1；Therefore, enemy plane motor-driven area J when situation 11For：
J1=Ω1∩P-Q1
Wherein, Q1The region surrounded for line segment CD and arc CD；
The algorithm of 3.2 situations 2
With enemy and we's distance | OW | variation, the shape in the motor-driven area of enemy plane is divided into two kinds of situations：
Situation 2.1, R-r≤| OW |≤R；
Situation 2.2, r≤| OW |<R-r；
3.2.1 establishing auxiliary covering of the fan
Establish auxiliary covering of the fanStraight line OA1、OB1With circle Ω3It is tangent, and with circle Ω1Point A is intersected at respectively1、B1, with ellipse P intersects at point C respectively1、D1, wherein ellipse P focus is O, W, a length of R+r of long axis；We is justifying Ω by surface ship1Interior, enemy plane exists Covering of the fanIt is interior motor-driven, it can emit air to ship missile and implement attack；
3.2.2 the motor-driven area J of enemy plane under calculated case 22
(1) circle Ω1Equation
x2+y2=R2
(2) equation of ellipse P
Wherein：Major semiaxis a=(R+r)/2；Semi-minor axis
(3) coordinate of point A, B
When situation 2.1, circle Ω1, circle Ω3, ellipse P intersect at point A, B；
When situation 2.2, circle Ω1, circle Ω3, ellipse P it is non-intersecting；
Circle Ω3Equation be：
(x-d)2+y2=r2
When situation 2.1, simultaneous circle Ω1, circle Ω3, ellipse P equation can acquire the coordinate of point A, B：
Point A coordinate,
Point B coordinate,
(4) coordinate of point C, D
For point C, D on oval P, the abscissa of C point is xC=0；The abscissa x of D pointD=0, the equation for substituting into ellipse P can acquire a little C, the coordinate of D：
Point C coordinate,
Point D coordinate,
(5) point A1、B1Coordinate
Straight line OA1、OB1Equation：
± kx-y=0
Point F (d, 0) arrives straight line OA1、OB1Distance be r, can acquire accordingly
Simultaneous justifies Ω1Equation can acquire point A1、B1Coordinate：
Point A1Coordinate,
Point B1Coordinate,
Enemy plane motor-driven area J when situation 22；Meet following condition simultaneously：First, not in combat radius circle Ω1Outside；Second, in oval P It is interior or in covering of the fanIt is interior；Third, enemy plane does not include region Q without reversed motor-driven when attack1；
Therefore, enemy plane motor-driven area J when situation 22For：
Wherein：Q1The region surrounded for line segment CD and arc CD；
When situation 2.1, J2Opposite Ω1∩P-Q1Increase Q2∪Q3, wherein Q2For line segment A1D1, arc AD1, arc AA1The region surrounded, Q3For line segment B1C1, arc BC1, arc BB1The region surrounded；
When situation 2.2, J2Opposite Ω1∩P-Q1Increase Q4, wherein Q4For line segment A1D1、B1C1, arc A1B1、C1D1The region surrounded；
The algorithm of 3.3 situations 3
3.3.1 establishing auxiliary covering of the fan
Establish auxiliary covering of the fanStraight line OA1、OB1With circle Ω1Point A is intersected at respectively1、B1, according to attack when enemy plane without Reversed motor-driven rule, point A1On y-axis negative sense, point B1Y-axis forward；We is justifying Ω by surface ship1Interior, enemy plane is being fanned FaceIt is interior motor-driven, it can emit air to ship missile and implement attack；
3.3.2 the motor-driven area J of enemy plane under calculated case 33
(1) circle Ω1Equation
x2+y2=R2
(2) point A1、B1Coordinate
Utilize circle Ω1Equation can acquire point A1、B1Coordinate：
Point A1Coordinate,
Point B1Coordinate,
Enemy plane motor-driven area J when situation 33, while meeting following condition：First, not in combat radius circle Ω1Outside；Second, in oval P It is interior or in covering of the fanIt is interior；Third, enemy plane does not include region Q without reversed motor-driven when attack1；Therefore, J can be established3 Formula be：
Wherein：Oval P focus is O, W, a length of R+r of long axis；Q1The region surrounded for line segment CD and arc CD；
Covering of the fanIt really include P-Q1, and really it is contained in Ω1；Therefore, enemy plane motor-driven area J when situation 33For：
It calculates and completes.
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