A method for calculating damage probability and determining optimal opening distance of ammunition based on AHEAD ammunition

Abstract

A method for calculating damage probability of AHEAD ammunition and determining optimal opening distance of ammunition comprises the following steps: measuring error parameters of a weapon; calculating shooting error of ammunition on a bullet-facing surface; calculating equivalent area of a target on the bullet-facing surface; determining corresponding opening distance according to opening time of ammunition at the moment of leaving the muzzle; calculating error of ammunition in the flight direction; obtaining the number of bullets contained in the ammunition and bullet dispersion half-cone from the ammunition parameters; calculating opening distance of the ammunition under the condition of known target bullet-facing area and bullet hit number; determining a damage probability calculation model of the ammunition, and calculating damage probability according to specific parameters; and determining optimal opening distance corresponding to the maximum damage probability of the ammunition through the method of traversing opening distance according to the damage probability calculation model. The application improves the accuracy of damage probability of each AHEAD ammunition, and can calculate the optimal opening distance of the ammunition when the maximum damage probability is reached.

Description

Technical Field

[0001] This application relates to the field of system performance analysis technology, and in particular to a method for calculating the damage probability of AHEAD ammunition and determining the optimal ammunition opening distance. Background Technology

[0002] The increasing diversity and complexity of aerial threats place higher demands on the effectiveness of air defense systems. Anti-aircraft artillery systems continue to play a vital role due to their rapid response and cost-effectiveness. To effectively counter low, small, and slow-moving aerial targets, traditional anti-aircraft artillery ammunition has been gradually replaced by AHEAD (Advanced Hit Efficiency and Destruction) ammunition. AHEAD ammunition, through its unique design, can form a dense fragment cloud in front of the target, significantly improving interception efficiency and the probability of damage. The core advantage of AHEAD ammunition lies in its intelligent fuse system and optimized fragment distribution. The electronic time fuse can precisely control the timing of activation based on real-time target data, while the fragment cloud design aims to maximize the damage area to the target. However, the destructive effectiveness of AHEAD ammunition is not fixed; it is affected by various factors, including hatch opening distance, fragment dispersion, and target characteristics.

[0003] However, the publicly available literature on calculating the damage probability of AHEAD munitions, exemplified by the paper "Research on the Influence of Opening Distance on Damage Effectiveness of Advanced Hit and High-Efficiency Damage Munitions," only considers the error factor of the munition on the target's attack surface when considering the opening point of the munition. This means the firing error is only reflected in a two-dimensional plane, ignoring the time error in the munition's flight direction. When calculating the firing error, most literature assumes that the firing errors in the X and Y directions on the target's attack surface follow a Gaussian distribution in a rectangular coordinate system. Consequently, when considering the target's projected area, it can only be approximated as a rectangle or square, accepting a significant error in the target's projection on the attack surface. Furthermore, the damage probability of rapid-fire weapons based on AHEAD munitions needs to consider both the hit probability and the bullet damage probability corresponding to different numbers of bullets hitting the target. Therefore, existing methods for calculating the damage probability of AHEAD munitions contain significant approximation errors. Summary of the Invention

[0004] This application provides a method for calculating the damage probability of AHEAD ammunition and determining the optimal ammunition opening distance, which can be used to solve the technical problem that the existing methods for calculating the damage probability of AHEAD ammunition have large approximation errors.

[0005] This application provides a method for calculating the damage probability of AHEAD ammunition and determining the optimal ammunition opening distance, the method comprising the following steps:

[0006] Step 1: Measure the weapon's error parameters; these parameters include firing data errors. Follow-up error Stable platform error Systematic errors Projectile dispersion error Ammunition flight time error ;

[0007] Step 2: Calculate the firing error of the ammunition on the attack surface. ;

[0008] Step 3: Calculate the equivalent area of ​​the target on the incoming surface. ;

[0009] Step 4: Determine the corresponding magazine opening distance based on the pre-set magazine opening time at the instant the ammunition leaves the muzzle. ;

[0010] Step 5: Calculate the error of the ammunition in its flight direction. ;

[0011] Step 6: Obtain the number of bullets contained in one AHEAD ammunition from the ammunition parameters. and the bullets scattered at a half-cone angle ;

[0012] Step 7: Calculate the ammunition magazine opening distance under the given conditions of target area and number of bullet hits. ;

[0013] Step 8: Based on the firing error of the ammunition on the attack surface Error in the flight direction of the ammunition The model for calculating the damage probability of ammunition is determined by considering the number of bullets that hit the target and the corresponding target damage probability (obtained from target vulnerability analysis), and the damage probability is calculated based on the specific parameters.

[0014] Step 9: Based on the damage probability calculation model, determine the optimal opening distance for the ammunition to reach the maximum damage probability by iterating through the opening distances.

[0015] Furthermore, the shooting parameter errors mentioned in step 1 Follow-up error Stable platform error Systematic errors Projectile dispersion error and the error in the flight time of the ammunition The error parameters are in the following forms:

[0016] ,

[0017] in For shooting parameters error The mean square error in the radial direction and the mean square error in the angular direction These are the following errors The mean square error in the radial direction and the mean square error in the angular direction These are the stable platform errors. The mean square error in the radial direction and the mean square error in the angular direction These represent the root mean square error of the projectile dispersion in the radial direction and the root mean square error in the angular direction, respectively; systematic error. A constant value in the radial direction ; This represents the mean square error of the launch time.

[0018] Furthermore, the shooting error in step 2 Determined by the following method:

[0019] Root mean square of shooting error in the radial direction It is determined by the following method:

[0020]

[0021] The root mean square error of the shooting error in terms of angle is determined by the following method:

[0022]

[0023] Shooting error The probability distribution function in polar coordinates takes the following form:

[0024]

[0025] in Let be a random variable in the probability density function of shooting error.

[0026] Furthermore, the equivalent area of ​​the target's attack surface of the ammunition described in step 3. Determined by the following method:

[0027] Based on the spatial relationship between the weapon and the target in a Cartesian coordinate system at the time of firing, and given the target's projected area, the equivalent area of ​​the target on the attack surface can be obtained. .

[0028] Furthermore, the error in the flight direction of the ammunition described in step 5. Determined by the following method:

[0029] Based on the ammunition's flight time error Ammunition opening distance and the muzzle velocity of the projectile provided by the corresponding weapon firing table. ,Sure The mean square error is:

[0030]

[0031] It follows a Gaussian distribution with a mean of 1 / 2. The root mean square error of the ammunition in its flight direction is The probability density distribution function is:

[0032] .

[0033] Furthermore, in step 7, the ammunition opening distance... Determined by the following method:

[0034]

[0035] in, The number of bullets that hit the target, i.e., the number of hits. The magazine opening distance corresponding to firing ammunition.

[0036] Furthermore, the probability of damage from the ammunition described in step 8. Determined by the following method:

[0037] Target hit The probability of damage from firing a bullet is

[0038]

[0039] The probability of damage from a single AHEAD round is:

[0040]

[0041] in, The number of bullets that hit the target, with a value of ; The maximum number of bullets that can hit the target corresponding to the probability of target destruction; Target hit The probability of damage from a bullet; and These represent the target hit. hair and The magazine opening distance corresponding to the launch site; Indicates target hit The corresponding magazine opening distance for firing projectiles; and Then the target is hit. Firing bullets and hitting targets The probability of damage corresponding to each bullet fired is calculated based on target vulnerability analysis and bullet-target rendezvous parameters, as shown in the table below:

[0042] Table 1. Probability of Damage to Target with Different Numbers of Bullets

[0043]

[0044] in, This indicates that when the number of bullets hitting the target exceeds a certain threshold, the probability of a bullet damaging the target reaches a fixed value, which is the maximum probability of a single AHEAD bullet damaging the target.

[0045] Furthermore, based on the damage probability calculation model, the optimal opening distance for the ammunition to achieve the maximum damage probability is determined by iterating through the opening distances, including:

[0046] The optimal breech-opening distance mentioned in step 9, and the programmability of AHEAD ammunition, are reflected in the configurable breech-opening distance. This involves iterating through the breech-opening distances, i.e., traversing the range of breech-opening distances. Based on the required calculation accuracy (e.g., with an interval of 0.01), the damage probability calculation model given in step 8 is used to calculate the damage probability corresponding to all opening distances. The maximum damage probability corresponds to the optimal opening distance.

[0047] Furthermore, if the shooting error And the error in the flight direction of the ammunition If a random distribution other than a Gaussian distribution is followed, it is set as the actual distribution.

[0048] Compared with the prior art, the significant advantages of this application are: (1) Based on the characteristic that the bullets are distributed in a flat conical shape, the shooting error of the weapon is expressed in polar coordinates. For targets with a small projected area on the incoming surface, or after dividing large targets into small targets, the model error is reduced; (2) This application takes into account the error of the projectile in the flight direction, making the method for determining the damage probability of AHEAD ammunition more accurate; (3) Based on the damage probability calculation model of AHEAD ammunition, the optimal ammunition opening distance corresponding to the maximum damage probability of the weapon system can be accurately obtained. Attached Figure Description

[0049] Figure 1 A schematic diagram of the model provided for an embodiment of this application;

[0050] Figure 2 A graph showing the relationship between ammunition opening distance and damage probability provided in an embodiment of this application. Detailed Implementation

[0051] To make the objectives, technical solutions, and advantages of this application clearer, the embodiments of this application will be described in further detail below with reference to the accompanying drawings.

[0052] The embodiments of this application will now be described in conjunction with the accompanying drawings.

[0053] This application provides a method for calculating the damage probability of AHEAD ammunition and determining the optimal ammunition opening distance, the method comprising the following steps:

[0054] Step 1: Measure the weapon's error parameters; these parameters include firing data errors. Follow-up error Stable platform error Systematic errors Projectile dispersion error Ammunition flight time error ;

[0055] Step 2: Calculate the firing error of the ammunition on the attack surface. ;

[0056] Step 3: Calculate the equivalent area of ​​the target on the incoming surface. ;

[0057] Step 4: Determine the corresponding magazine opening distance based on the pre-set magazine opening time at the instant the ammunition leaves the muzzle. ;

[0058] Step 5: Calculate the error of the ammunition in its flight direction. ;

[0059] Step 6: Obtain the number of bullets contained in one AHEAD ammunition from the ammunition parameters. and the bullets scattered at a half-cone angle ;

[0060] Step 7: Calculate the ammunition magazine opening distance under the given conditions of target area and number of bullet hits. ;

[0061] Step 8: Based on the firing error of the ammunition on the attack surface Error in the flight direction of the ammunition The model for calculating the damage probability of ammunition is determined by considering the number of bullets that hit the target and the corresponding target damage probability (obtained from target vulnerability analysis), and the damage probability is calculated based on the specific parameters.

[0062] Step 9: Based on the damage probability calculation model, determine the optimal opening distance for the ammunition to reach the maximum damage probability by iterating through the opening distances.

[0063] Furthermore, the shooting parameter errors mentioned in step 1 Follow-up error Stable platform error Systematic errors Projectile dispersion error and the error in the flight time of the ammunition The error parameters are in the following forms:

[0064] ,

[0065] in For shooting parameters error The mean square error in the radial direction and the mean square error in the angular direction These are the following errors The mean square error in the radial direction and the mean square error in the angular direction These are the stable platform errors. The mean square error in the radial direction and the mean square error in the angular direction These represent the root mean square error of the projectile dispersion in the radial direction and the root mean square error in the angular direction, respectively; systematic error. A constant value in the radial direction ; This represents the mean square error of the launch time.

[0066] Furthermore, the shooting error in step 2 Determined by the following method:

[0067] Root mean square of shooting error in the radial direction It is determined by the following method:

[0068]

[0069] The root mean square error of the shooting error in terms of angle is determined by the following method:

[0070]

[0071] Shooting error The probability distribution function in polar coordinates takes the following form:

[0072]

[0073] in Let be a random variable in the probability density function of shooting error.

[0074] Furthermore, the equivalent area of ​​the target's attack surface of the ammunition described in step 3. Determined by the following method:

[0075] Based on the spatial relationship between the weapon and the target in a Cartesian coordinate system at the time of firing, and given the target's projected area, the equivalent area of ​​the target on the attack surface can be obtained. .

[0076] Furthermore, the error in the flight direction of the ammunition described in step 5. Determined by the following method:

[0077] Based on the ammunition's flight time error Ammunition opening distance and the muzzle velocity of the projectile provided by the corresponding weapon firing table. ,Sure The mean square error is:

[0078]

[0079] It follows a Gaussian distribution with a mean of 1 / 2. The root mean square error of the ammunition in its flight direction is The probability density distribution function is:

[0080] .

[0081] Furthermore, in step 7, the ammunition opening distance... Determined by the following method:

[0082]

[0083] in, The number of bullets that hit the target, i.e., the number of hits. The magazine opening distance corresponding to firing ammunition.

[0084] Furthermore, the probability of damage from the ammunition described in step 8. Determined by the following method:

[0085] Target hit The probability of damage from firing a bullet is

[0086]

[0087] The probability of damage from a single AHEAD round is:

[0088]

[0089] in, The number of bullets that hit the target, with a value of ; The maximum number of bullets that can hit the target corresponding to the probability of target destruction; Target hit The probability of damage from a bullet; and These represent the target hit. hair and The magazine opening distance corresponding to the launch site; Indicates target hit The corresponding magazine opening distance for firing projectiles; and Then the target is hit. Firing bullets and hitting targets The probability of damage corresponding to each bullet fired is calculated based on target vulnerability analysis and bullet-target rendezvous parameters, as shown in the table below:

[0090] Table 1. Probability of Damage to Target with Different Numbers of Bullets

[0091]

[0092] in, This indicates that when the number of bullets hitting the target exceeds a certain threshold, the probability of a bullet damaging the target reaches a fixed value, which is the maximum probability of a single AHEAD bullet damaging the target.

[0093] Furthermore, based on the damage probability calculation model, the optimal opening distance for the ammunition to achieve the maximum damage probability is determined by iterating through the opening distances, including:

[0094] The optimal breech-opening distance mentioned in step 9, and the programmability of AHEAD ammunition, are reflected in the configurable breech-opening distance. This involves iterating through the breech-opening distances, i.e., traversing the range of breech-opening distances. Based on the required calculation accuracy (e.g., with an interval of 0.01), the damage probability calculation model given in step 8 is used to calculate the damage probability corresponding to all opening distances. The maximum damage probability corresponds to the optimal opening distance.

[0095] Furthermore, if the shooting error And the error in the flight direction of the ammunition If a random distribution other than a Gaussian distribution is followed, it is set as the actual distribution.

[0096] The present application is further described below with reference to specific embodiments.

[0097] This embodiment is applied to the calculation of the probability of a weapon's burst fire hit, as detailed below:

[0098] Taking a certain type of anti-aircraft gun as an example, equipped with AHEAD ammunition, the projectile has an initial velocity of 1050 m / s, a cylindrical shape, a mass of 3.3g, and 152 ammunition in the magazine; flight conditions: flight speed 50 m / s, altitude 200 m, flight path 300 m, heading angle 30°, horizontal constant speed straight flight, slant distance 1000 m, single-shot firing; the set magazine opening distance is 6 meters. The time error (mean square deviation) of the ammunition in the flight direction is 0.003 seconds, and the velocity at the magazine opening is 1000 m / s; the firing error of the weapon system, converted to polar coordinates, has a radial error mean square deviation of 2.45 meters, a mean of 0.8, and an angular mean square deviation of 0.1 radians; the target is a certain type of UAV, and its projection on the attack surface is 0.5 m².

[0099] The root mean square error of the bullet opening is calculated as follows: The calculated ammunition magazine opening distance and the number of bullets hitting the target are shown in the table below:

[0100] Table 2: Relationship between the number of bullets hitting the target and the firing distance

[0101]

[0102] The probability of damage to the target from different numbers of bullets is shown in the table below:

[0103] Table 3: Target Damage Probability Corresponding to Different Numbers of Bullets Hit the Target

[0104]

[0105] The damage probability of a single AHEAD round under hit conditions is calculated and shown in the table below:

[0106] Table 4: Target Damage Probability Corresponding to Different Numbers of Bullets Hit the Target

[0107]

[0108] In this embodiment, the ammunition opening distance is set to 6 meters. Following the specific steps, an over-calculation is performed on the opening distance to obtain the relationship between the opening distance and the probability of damage. Figure 2 As shown.

[0109] from Figure 2 The calculation results show that the probability of damage from a single AHEAD round is highest at an opening distance of 11.2 meters, with a value of 0.3424. Compared with the probability of damage from a round at an opening distance of 6 meters given in the example, this represents an improvement of 39.53%.

[0110] This application synthesizes firing error into random error by combining firing parameter error, follow-up error, stabilization platform error, and projectile dispersion error. Using the weapon's systematic difference as the mean, it constructs the firing error on the projectile-facing surface. The projectile flight time error and magazine opening time are combined to synthesize the magazine opening distance error in the ammunition's flight direction, thus calculating the probability of the ammunition damaging the target. Based on relevant firing error theories, this application accurately characterizes the firing error of AHEAD ammunition in three-dimensional space, enabling the calculation of the damage probability of each round of AHEAD weapon.

[0111] The embodiments described above do not constitute a limitation on the scope of protection of this application.

Claims

1. A method for calculating the damage probability and determining the optimal magazine opening distance of AHEAD ammunition, characterized in that, The method includes the following steps: Step 1: Measure the weapon's error parameters; these parameters include firing data errors. Follow-up error Stable platform error Systematic errors Projectile dispersion error Ammunition flight time error ; Step 2: Calculate the firing error of the ammunition on the attack surface. ; Step 3: Calculate the equivalent area of ​​the target on the incoming surface. ; Step 4: Determine the corresponding magazine opening distance based on the pre-set magazine opening time at the instant the ammunition leaves the muzzle. ; Step 5: Calculate the error of the ammunition in its flight direction. ; Step 6: Obtain the number of bullets contained in one AHEAD ammunition from the ammunition parameters. and the bullets scattered at a half-cone angle ; Step 7: Calculate the ammunition magazine opening distance under the given conditions of target area and number of bullet hits. ; Step 8: Based on the firing error of the ammunition on the attack surface Error in the flight direction of the ammunition The model for calculating the damage probability of ammunition is determined by considering the number of bullets hitting the target and the corresponding target damage probability, and the damage probability is calculated based on the specific parameters. Step 9: Based on the damage probability calculation model, determine the optimal opening distance for the ammunition to reach the maximum damage probability by iterating through the opening distances. The shooting parameters error mentioned in step 1 Follow-up error Stable platform error Systematic errors Projectile dispersion error and the error in the flight time of the ammunition The error parameters are in the following forms: ； in For shooting parameters error The mean square error in the radial direction and the mean square error in the angular direction These are the following errors The mean square error in the radial direction and the mean square error in the angular direction These are the stable platform errors. The mean square error in the radial direction and the mean square error in the angular direction These represent the root mean square error of the projectile dispersion in the radial direction and the root mean square error in the angular direction, respectively; systematic error. A constant value in the radial direction ; The mean square error of the launch time; Shooting error in step 2 Determined by the following method: Root mean square of shooting error in the radial direction It is determined by the following method: ； The root mean square error of the shooting error in terms of angle is determined by the following method: ； Shooting error The probability distribution function in polar coordinates takes the following form: ； in Let be a random variable in the probability density function of the shooting error; The probability of damage from the ammunition described in step 8 Determined by the following method: Target hit The probability of damage from firing a bullet is ； The probability of damage from a single AHEAD round is: ； in, The number of bullets that hit the target, with a value of ; The maximum number of bullets that can hit the target corresponding to the probability of target destruction; Target hit The probability of damage from a bullet; and These represent the target hit. hair and The magazine opening distance corresponding to the launch site; Indicates target hit The corresponding magazine opening distance for firing projectiles; and Then the target is hit. Firing bullets and hitting targets The probability of damage corresponding to each bullet is calculated based on target vulnerability analysis and bullet-target intersection parameters.

2. The method for calculating the damage probability and determining the optimal ammunition opening distance based on AHEAD ammunition according to claim 1, characterized in that, The equivalent area of ​​the target's attack surface of the ammunition mentioned in step 3 Determined by the following method: Based on the spatial relationship between the weapon and the target in a Cartesian coordinate system at the time of firing, and given the target's projected area, the equivalent area of ​​the target on the attack surface can be obtained. .

3. The method for calculating the damage probability and determining the optimal ammunition opening distance based on AHEAD ammunition according to claim 1, characterized in that, The error in the flight direction of the ammunition mentioned in step 5 Determined by the following method: Based on the ammunition's flight time error Ammunition opening distance and the muzzle velocity of the projectile provided by the corresponding weapon firing table. ,Sure The mean square error is: ； It follows a Gaussian distribution with a mean of 1 / 2. The root mean square error of the ammunition in its flight direction is The probability density distribution function is: 。 4. The method for calculating the damage probability and determining the optimal ammunition opening distance based on AHEAD ammunition according to claim 1, characterized in that, Ammunition opening distance in step 7 Determined by the following method: ； in, The number of bullets that hit the target, i.e., the number of hits. The magazine opening distance corresponding to firing ammunition.

5. The method for calculating the damage probability and determining the optimal ammunition opening distance based on AHEAD ammunition according to claim 4, characterized in that, Based on the damage probability calculation model, the optimal opening distance for the ammunition to achieve the maximum damage probability is determined by iterating through the opening distances, including: Iterate through the opening distances, i.e., the opening distances are within the range. Based on the required accuracy, the damage probability calculation model given in step 8 is used to calculate the damage probability corresponding to all opening distances. The maximum damage probability corresponds to the optimal opening distance.

6. The method for calculating the damage probability and determining the optimal ammunition opening distance based on AHEAD ammunition according to claim 1 or 2, characterized in that, If shooting error And the error in the flight direction of the ammunition If a random distribution other than a Gaussian distribution is followed, it is set as the actual distribution.

Images