A method for calculating loss rate of an effective kill zone in air defense

Abstract

The present application relates to a kind of loss rate calculation method of effective killing zone of air defense, belong to the technical field of killing zone characteristics of air defense weapon system.A kind of loss rate calculation method of effective killing zone of air defense, comprising the following steps: one, establish the killing airspace model of air defense weapon system two, determine the killing zone of killing airspace in step one is divided into vertical plane killing zone and horizontal plane killing zone;Vertical plane killing zone is the vertical section of killing zone with the direction of air route shortcut being zero;Horizontal plane killing zone is the horizontal section made by target when air raid with height H;Three, establish the numerical model of vertical plane killing zone the killing zone of air defense weapon system can be represented by a cluster of vertical killing zones with equal interval between air route shortcuts;Four, determine the loss rate calculation method of killing zone according to the height of each shelter and the distance between the position of each shelter and air defense weapon system to determine the loss rate of vertical killing zone affected by shelter, then the sum of loss rate is obtained.

Description

TECHNICAL FIELD

[0001] The present application relates to a kind of loss rate calculation method of effective killing area of air defense, belong to missile weapon system application technical field. BACKGROUND

[0002] When coastal key point air defense weapon system faces sea attacking target, usually because of many sea islands, coastal mountainous terrain, radar shelter angle is large, there are many detection blind areas, resulting in the effective killing area of air defense weapon system is smaller than the theoretical killing area.Especially in the modern air attack and counter air attack combat conditions, various low altitude, super low altitude penetration long-range missiles and third-generation, fourth-generation aircrafts and other attacking targets take sea flight, resulting in the effective killing area of air defense weapon system is greatly influenced.

[0003] At present, the research on effective killing area of air defense weapon system mainly involves air defense radar shelter problem, according to the performance parameters of air defense weapon system, the shelter judgment condition of attacking target is analyzed, so as to deduce the calculation method of flying time of attacking target in shelter area, but there is no quantitative analysis of the influence of shelter problem on killing area of air defense weapon system, and there is no system to give the calculation method of killing area loss rate, so that the defense efficiency of air defense weapon system is not accurate when calculating. SUMMARY

[0004] The purpose of the present application is to solve the influence of radar shelter problem on air defense weapon system by quantitative analysis, to build a killing area loss rate model of air defense weapon system according to the radar shelter of air defense weapon system, target attacking height and other conditions, and to give a calculation method of effective killing area loss rate of air defense.Using this method can effectively calculate the killing area loss rate of air defense weapon system caused by shelter in sea key point, and give the comprehensive defense efficiency of air defense weapon system.

[0005] In order to solve the above problems, a kind of loss rate calculation method of effective killing area of air defense is realized by the following technical scheme:

[0006] A kind of loss rate calculation method of effective killing area of air defense, which is characterized by the following steps:

[0007] I. Establish the killing airspace model of air defense weapon system

[0008] The killing airspace of air defense weapon system refers to the airspace of anti-missile weapon system damaging the target with not less than a given probability value;

[0009] Described by horizontal plane killing area and vertical plane killing area determined by far boundary, near boundary, high boundary, low boundary and side boundary;

[0010] In the rectangular coordinate system, the killing airspace of air defense weapon system is a region surrounded by the curved surface ABCD, KLNM, ABFE, CDMN, EFLK, BCNLF, ADMKE in space;

[0011] Wherein, the weapon system is located at the origin point O of the coordinate system, the S axis is related to the incoming target, its direction is parallel to and opposite to the horizontal projection of the velocity vector of the incoming target; the H axis is perpendicular to the horizontal plane and positive upward, and the P axis forms a right-handed rectangular coordinate system with the S and H axes; the far boundary ABCD is a partial spherical surface with the origin point O and the maximum killing slant range as the radius; the near boundary KLNM is a partial spherical surface with the origin point O and the minimum killing slant range as the radius; the high boundary ABFE is parallel to the SOP plane, and the distance from the high boundary ABFE to the SOP plane is the maximum height of the killing zone; the low boundary CDMN is parallel to the SOP plane, and the distance from the low boundary CDMN to the SOP plane is the minimum height of the killing zone; the high near boundary EFLK is determined by the maximum radar depression angle θ of the weapon system; the side boundary BCNLF and ADMKE are perpendicular to the POS plane, and the included angle between the side boundary BCNLF and the SOH is the maximum course angle of the weapon system .

[0012] II. Determine the killing zone of the killing airspace in step I

[0013] The killing zone is divided into vertical plane killing zone and horizontal plane killing zone;

[0014] The vertical plane killing zone is a vertical cross section of the killing zone made in the direction of the course shortcut being zero;

[0015] The vertical plane killing zone , is the far boundary of the killing zone, is the near boundary of the killing zone, is the high boundary of the killing zone, is the low boundary of the killing zone, is the maximum high-low angle.

[0016] The horizontal plane killing zone is a horizontal cross section made by the target when it attacks with the height H;

[0017] The horizontal killing zone , is the maximum course angle, is the maximum course shortcut of the far boundary of the killing zone, is the maximum course shortcut of the near boundary of the killing zone.

[0018] III. Establish the numerical model of the vertical plane killing zone

[0019] The killing zone of the air defense weapon system can be represented by a cluster of vertical killing zones with equal interval of course shortcuts:

[0020] For different course shortcuts, the vertical killing zone has four cases:

[0021] A. When hour,

[0022] The near boundary (MK) and far boundary (AD) of the kill zone can be approximated by the near boundary of the kill zone. and distant world An arc with radius MD and EA are the lower boundaries of the kill zone. and Gao Jie AE is the oblique near boundary, which is determined by the maximum elevation angle θ of the weapon system radar;

[0023] The coordinates of each feature point are as follows: , , , , ;

[0024] B, when hour,

[0025] The coordinates of each feature point are as follows: , , , , ; ;

[0026] C. When At that time, the incoming target's trajectory flew out along the side of the kill zone, and the coordinates of each feature point in the kill zone are as follows: , , , , ;

[0027] D. When At that time, the incoming target's trajectory flew out along the side of the kill zone and did not cross the oblique near-boundary of the kill zone. The coordinates of each feature point in the kill zone are as follows: , , , ;

[0028] IV. Determining the Calculation Method for Kill Zone Loss Rate

[0029] Based on the height of each shelter and the distance between each cover location and the air defense weapon system To determine the loss rate of the vertical kill zone affected by the shielding, and then calculate the sum of the loss rates;

[0030] Assume an incoming target's trajectory is within the vertical kill zone, and its flight altitude is... Flight speed is Air defense weapon system missile flight speed The system finds that the reaction time from the target to the first interception missile is ;

[0031] The loss rate of the kill zone is calculated to analyze the vertical kill zone, and the coordinates of each feature point are marked as , , , , .

[0032] A. When the height of the shelter :

[0033] When , the shelter is too close to the air defense weapon system, the air defense weapon system missile has not reached the near boundary of the kill zone, the incoming target has flown out of the kill zone, and cannot cause effective damage to the incoming target, the loss rate of the kill zone is 100%;

[0034] When , after the incoming target flies over the height of the shelter , the radar immediately searches and captures the target to complete the shooting element solution, and immediately launches the missile, then the farthest missile will encounter the target on the line, that is, the height of the shelter The range of influence on the vertical kill zone is , that is, the height of the shelter The loss rate in the vertical kill zone is The area of the vertical kill zone

[0035] ,

[0036] According to Green's formula, we have

[0037] ,

[0038] where ,

[0039] The directed circular arc , , ,

[0040] The directed circular arc .

[0041] The area of the entire vertical kill zone is

[0042] ,

[0043] The area of the vertical kill zone lost due to the shelter is

[0044] ,

[0045] The loss rate of the vertical kill zone affected by the shelter is:

[0046] ;

[0047] When , the shelter does not constitute a shelter for the incoming target, and the loss rate of the kill zone is 0.

[0048] B. When the shelter height :

[0049] If the shelter height In the low boundary and high boundary , the nearest discovery distance of the target no higher than the shelter height is the position of , and if the target is higher than the shelter height , the discovery target line is ;

[0050] After discovering the target, the radar immediately captures the target to complete the shooting element solution, and immediately launches the missile. The farthest missile will encounter the target on the broken line line, that is, the shelter height The affected range of the kill zone is the polygon range, that is, the kill zone loss rate in the shelter height sector exists;

[0051] The area of the entire vertical kill zone is:

[0052] ,

[0053] Assuming the coordinates of the characteristic points of the vertical kill zone are: , , , , , , ,

[0054] The coordinates of the characteristic points on the encounter line are: , ;

[0055] The area of the vertical kill zone lost due to the shelter:

[0056] ,

[0057] Among them:

[0058] ,

[0059] Therefore:

[0060] ,

[0061] Therefore, the loss rate of the vertical kill zone is:

[0062] ;

[0063] C. When the height of the shelter is :

[0064] At this time, the air defense weapon system does not have the ability to intercept the target, and the loss rate of the kill zone is 100%;

[0065] D. The overall loss rate of the kill zone in the combat sector

[0066] The overall loss rate of the kill zone in the combat sector is assumed to be , if there are shelters that affect the kill zone in the sector, the sheltered sector angles are , the loss rate of the kill zone in the range can be calculated respectively using the method of calculating the loss rate of the vertical kill zone. The overall loss rate of the kill zone in the sector is The calculation formula is:

[0067] .

[0068] The method provides a calculation formula for calculating the characteristic points of the kill zone boundary of the air defense weapon system, and according to the influence of the radar on the shelter, the loss rate calculation formula of the kill zone of the air defense weapon system is analyzed and given. Through the technical scheme of the present application, the calculation formula of the characteristic point coordinates of the vertical kill zone boundary of the air defense weapon system is given, and according to the flight height of the target and the influence of the shelter on the air defense radar, an effective area calculation method for calculating the loss of the vertical kill zone of the air defense weapon system is proposed, and the loss rate calculation formula of the kill zone of the air defense weapon system is further given, which provides certain theoretical support for the deployment of coastal important air defense and anti-missile weapon systems. BRIEF DESCRIPTION OF DRAWINGS

[0069] Figure 1 : Schematic diagram of the kill airspace model of the air defense weapon system;

[0070] Figure 2 : Figure 1 Schematic diagram of the vertical plane kill zone;

[0071] Figure 3 : Figure 1 Schematic diagram of the horizontal plane kill zone;

[0072] Figure 4 : schematic diagram of vertical plane kill zone at t = 0;

[0073] Figure 5 : schematic diagram of vertical plane kill zone at t = 0;

[0074] Figure 6 : schematic diagram of vertical plane kill zone at t = 0;

[0075] Figure 7 : schematic diagram of vertical plane kill zone at t = 0;

[0076] Figure 8 : shelter height greater than schematic diagram of kill zone loss range at t = 0;

[0077] Figure 9 : shelter height within schematic diagram of kill zone loss range at t = 0. DETAILED DESCRIPTION

[0078] The specific embodiments of the present application are described below with reference to the accompanying drawings, which are used to further explain the constitution of the present application.

[0079] Example 1. A method for calculating the loss rate of an effective kill zone of air defense, comprising the following steps:

[0080] I. Establish a kill airspace model of an air defense weapon system

[0081] The kill airspace of an air defense weapon system refers to the airspace in which a missile defense weapon system can damage a target with a given probability value;

[0082] The horizontal plane kill zone and the vertical plane kill zone determined by the characteristic parameters such as the far boundary, the near boundary, the high boundary, the low boundary, and the side boundary are used for description;

[0083] In the rectangular coordinate system, the kill airspace of an air defense weapon system is surrounded by the curved surfaces ABCD, KLNM, ABFE, CDMN, EFLK, BCNLF, ADMKE in space, as shown in Figure 1 ;

[0084] Wherein, the weapon system is located at the coordinate system origin point O, the S axis is related to the incoming target, the direction is parallel to the horizontal projection of the incoming target velocity vector and is opposite; the H axis is perpendicular to the horizontal plane and is positive upward, the P axis forms a right-handed rectangular coordinate system with the S and H axes; the far boundary ABCD is a partial sphere with O as the origin and the maximum killing slant range as the radius; the near boundary KLNM is a partial sphere with O as the origin and the minimum killing slant range as the radius; the high boundary ABFE is parallel to the SOP plane and the distance from the SOP is the maximum height of the killing zone; the low boundary CDMN is parallel to the SOP plane and the distance from the SOP is the minimum height of the killing zone; the high near boundary EFLK is determined by the maximum radar depression angle θ of the weapon system; the side boundary BCFNLF, ADMKE is perpendicular to the POS plane and the included angle with SOH is the maximum course angle of the weapon system .

[0085] II. Determine the killing zone of the killing space in step I

[0086] The killing zone is divided into vertical plane killing zone and horizontal plane killing zone;

[0087] The vertical plane killing zone is a vertical section of the killing zone in the direction of the course shortcut, as shown in Figure 2 ;

[0088] The vertical plane killing zone , is the far boundary of the killing zone, is the near boundary of the killing zone, is the high boundary of the killing zone, is the low boundary of the killing zone, is the maximum height-low angle.

[0089] The horizontal plane killing zone is a horizontal section made by the target when it attacks at the height H, as shown in Figure 3 ;

[0090] The horizontal killing zone , is the maximum course angle, is the maximum course shortcut of the far boundary of the killing zone, is the maximum course shortcut of the near boundary of the killing zone.

[0091] III. Establish the numerical model of the vertical plane killing zone

[0092] The killing zone of the air defense weapon system can be represented by a cluster of vertical killing zones with equal interval of course shortcuts:

[0093] For different course shortcuts, the vertical killing zone has four cases:

[0094] A, when ,

[0095] The near boundary (MK) and far boundary (AD) of the kill zone can be approximated by the near boundary of the kill zone. and distant world An arc with radius MD and EA are the lower boundaries of the kill zone. and Gao Jie AE is the oblique near boundary, determined by the maximum elevation angle θ of the weapon system radar, such as... Figure 4 As shown;

[0096] The coordinates of each feature point are as follows: , , , , .

[0097] B, when hour,

[0098] The coordinates of each feature point are as follows: , , , , ; ,like Figure 5 As shown;

[0099] C. When At that time, the incoming target's trajectory flew out along the side of the kill zone, and the coordinates of each feature point in the kill zone are as follows: , , , , ,like Figure 6 As shown;

[0100] D. When At that time, the incoming target's trajectory flew out along the side of the kill zone and did not cross the oblique near-boundary of the kill zone. The coordinates of each feature point in the kill zone are as follows: , , , ,like Figure 7 As shown;

[0101] IV. Determining the Calculation Method for Kill Zone Loss Rate

[0102] Based on the height of each shelter and the distance between each cover location and the air defense weapon system To determine the loss rate affected by cover within the vertical kill zone, we then calculate the sum of the loss rates. Assume an incoming target's flight path is within the vertical kill zone, and its flight altitude is [missing information]. Flight speed is Air defense weapon system missile flight speed , the system finds that the reaction time of the target to the launch of the first interceptor missile is ;

[0103] The loss rate of the kill zone is calculated to show the vertical kill zone Figure 8 Analysis is carried out, and the coordinates of each feature point are marked as , , , , ;

[0104] A. When the height of the shelter :

[0105] When , the shelter is too close to the air defense weapon system, the air defense weapon system missile has not reached the near boundary of the kill zone, the incoming target has flown out of the kill zone, and cannot cause effective damage to the incoming target, with a kill zone loss rate of 100%;

[0106] When , the effect of the shelter on the kill zone is shown in Figure 8 ;

[0107] After the incoming target flies over the height of the shelter , the radar immediately searches and captures the target to complete the shooting element solution, and immediately launches the missile, which will encounter the target on the line at the farthest, i.e., the height of the shelter has an impact on the vertical kill zone within the range of , , i.e., the height of the shelter within the vertical kill zone, the area of the vertical kill zone is:

[0108] ,

[0109] According to Green's formula, we have:

[0110] ,

[0111] wherein: ,

[0112] Directed circular arc , , ,

[0113] Directed circular arc ,

[0114] The area of the entire vertical kill zone is:

[0115] ,

[0116] The area of vertical kill zone lost due to the shelter:

[0117] ,

[0118] The loss rate of vertical kill zone affected by the shelter is:

[0119] ;

[0120] When , the shelter does not constitute a shelter for the incoming target, and the loss rate of the kill zone is 0.

[0121] B. When the shelter height :

[0122] If the shelter height In the low boundary and high boundary , the nearest discovery distance of the target no higher than the shelter height is , and if the target is higher than the shelter height , the discovery target line is , as shown in Figure 9 ;

[0123] After discovering the target, the radar immediately captures the target to complete the shooting element solution, and immediately launches the missile. The farthest missile will encounter the target on the broken line line, that is, the shelter The range of influence on the kill zone is a polygon range, that is, the kill zone loss rate in the shelter sector.

[0124] Where the area of the entire vertical kill zone is still:

[0125] ,

[0126] Assume that the coordinates of each feature point of the vertical kill zone are: , , , , , , ,

[0127] The coordinates of the feature points on the encounter line are: , ,

[0128] From Figure 9 , the area of the vertical kill zone lost due to the shelter is:

[0129] ,

[0130] Wherein:

[0131] ,

[0132] Thus:

[0133] ,

[0134] Therefore, the loss rate of the vertical kill zone is:

[0135] ;

[0136] C. When the height of the shelter :

[0137] At this time, the air defense weapon system does not have the ability to intercept the target, and the loss rate of the kill zone is 100%;

[0138] D. The overall loss rate of the kill zone in the combat sector

[0139] The overall loss rate of the kill zone in the combat sector

[0140] Suppose that in the main firing range of a certain position, the sector angle is , and there are shelters that affect the kill zone in the sector, with sheltered sector angles of , the loss rate of the kill zone in this range can be calculated respectively using the method of calculating the loss rate of the vertical kill zone. The overall loss rate of the kill zone in the sector is The calculation formula is:

[0141] .

[0142] Suppose that 6 sets of air defense weapon systems are deployed in a coastal location, and the loss rate of the kill zone and the main combat direction angle of each air defense weapon system are shown in Table 1:

[0143] Table 1 Calculation formula of overall kill efficiency of coastal location deployment scheme

[0144] .

Claims

1. A method for calculating the loss rate of the effective kill zone in air defense, characterized in that: The method comprises the following steps: I. Establishing a killing airspace model of the air defense weapon system The killing airspace model of the air defense weapon system is described by horizontal plane killing zones and vertical plane killing zones determined by five characteristic parameters of far boundary, near boundary, high boundary, low boundary and side boundary; The killing airspace model of the air defense weapon system is a region surrounded by curved surfaces ABCD, KLNM, ABFE, CDMN, EFLK, BCNLF and ADMKE in the space under the rectangular coordinate system; Wherein, the weapon system is located at the coordinate system origin point O, the S axis is related to the incoming target, the direction is parallel to the horizontal projection of the incoming target velocity vector and is opposite; the H axis is perpendicular to the horizontal plane and is positive upward, the P axis forms a right-handed rectangular coordinate system with the S and H axes; the far boundary ABCD is a partial sphere with O as the origin and the maximum killing slant range as the radius; the near boundary KLNM is a partial sphere with O as the origin and the minimum killing slant range as the radius; the high boundary ABFE is parallel to the SOP plane and the distance from the SOP is the maximum height of the killing zone; the low boundary CDMN is parallel to the SOP plane and the distance from the SOP is the minimum height of the killing zone; the high near boundary EFLK is determined by the maximum radar depression angle θ of the weapon system; the side boundary BCNLF and ADMKE are perpendicular to the POS plane and the included angle with SOH is the maximum course angle of the weapon system ; II. Determining the killing zones of the killing airspace in step I The killing zones are divided into vertical plane killing zones and horizontal plane killing zones; In the plane rectangular coordinate system, the vertical plane killing zone is a vertical cross section of the killing zone in the direction of the zero shortcut; Vertical plane kill zone , is the far boundary of the kill zone, is the near boundary of the kill zone, is the high boundary of the kill zone, is the low boundary of the kill zone, is the maximum high-low angle; The horizontal plane killing zone is a horizontal cross section made by the target when it attacks at the height H; horizontal kill zone , is the maximum course angle, is the maximum course shortcut of the far boundary of the kill zone, is the maximum course shortcut of the near boundary of the kill zone; III. Establishing a numerical model of the vertical plane killing zone The killing zone of the air defense weapon system is represented by a cluster of vertical killing zones with equal intervals between the shortcuts; IV. Determining the calculation method of the loss rate of the killing zone According to each shelter height and each shelter position and distance from the antiaircraft weapon system to determine the loss rate of the vertical kill zone affected by the shelter, and then sum the loss rates; When the height of the shelter is: When The shelter is too close to the air defense weapon system, the air defense weapon system missile has not reached the near boundary of the killing area, the attacking target has flown out of the killing area, and the attacking target cannot cause effective killing, and the loss rate of the killing area is 100%. When time, At the height of the target passing the shelter After the radar immediately searches and captures the target, completes the shooting data solution, and immediately launches the missile, the farthest missile will encounter the target Online and target encounter, that is, the height of the shelter The impact range of the vertical kill zone is Range, That is, the height of the shelter Loss rate in the vertical kill zone; When the shelter does not constitute a shelter for the incoming target, and the kill zone loss rate is 0; When the height of the shelter is: If the height of the obstruction In the lower boundary and Gao Jie Inside, it should not be higher than the height of the covering. The closest target is the one that is found. If the position is higher than the height of the shield. The target, its target line is ; After finding the target, the radar immediately captures the target to complete the shooting data solution, and immediately launches the missile, and the farthest missile will be in the broken line Online and target encounter, that is, the height of the shelter The impact range of the kill zone is a polygon Range, That is, there is a shelter height The loss rate of the kill zone in the sector; When the height of the shelter The anti-air weapon system has no interception ability to the attacking target, and the loss rate of the killing area is 100%.

2. The method of claim 1, wherein: In step III, for different shortcuts, the vertical killing zone has four cases: A. When time, The near boundary MK and the far boundary AD of the kill zone can be approximated as circular arcs with radii and The low boundary MD and the high boundary EA of the kill zone are and The slant near boundary AE is determined by the maximum radar depression angle θ of the weapon system, The coordinates of the characteristic points are respectively: ， ， ， ， ； B. When time, The coordinates of the characteristic points are respectively: ， ， ， ， ； ； C. When the target heading path flies out along the side of the kill zone, the coordinates of each feature point of the kill zone are as follows: , ， ， ， ； D. When the incoming target heading path flies out along the side of the kill zone and does not cross the oblique near-boundary of the kill zone, the coordinates of each feature point of the kill zone As follows: , , , .

3. The method according to claim 1 or 2, wherein: In step four: when the height of the shelter , is The coordinates of each feature point of the vertical killing zone are: , , , , , , , The coordinates of the feature points encountered by the ray are then given by: , , Vertical kill zone The area of: ， According to the Green formula, we have: ， wherein: , Directed circular arc , , , Directed circular arc , The area of the whole vertical killing zone is: ， The area of the vertical killing zone lost due to the shelter is: ， The loss rate of the vertical killing zone affected by the shelter is: 。 4. The method of claim 3, wherein: In step four: when the height of the shelter is: The area of the whole vertical killing zone is: ， Assume that the coordinates of the feature points of the vertical kill zone are: , , , , , , , The coordinates of the characteristic points on the encounter line are: ， The area of the vertical killing zone lost due to the shelter is: ， Wherein: ， Thus, ， Therefore, the loss rate of the vertical killing zone is: 。 5. The method of claim 4, wherein: In step IV, The overall loss rate of the killing zone in the combat sector Suppose the sector angle of the main firing range of a certain position is , if there are shelters that have influence on the kill zone in the sector, and the sheltered sector angles are , the loss rates of the kill zone in the range can be calculated respectively by using the method of calculating the vertical loss rate of the kill zone, and the loss rates are , then the calculation formula of the overall loss rate of the kill zone in the sector is: ​ 。

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