Method for calculating optimal time of aircraft dropping object based on cyclic evolution algorithm

Abstract

The application discloses a method for calculating the best time for an airplane to drop an object based on a cyclic evolution algorithm, establishes a body coordinate system with a bomb drop point as the origin, analyzes the force condition of a bomb in the air according to Newton's mechanics theory, constructs a model for the best time for the airplane to drop the bomb based on the cyclic evolution algorithm, and determines the best time for the airplane to drop the bomb under four conditions that the airplane and the underwater submarine move in the same direction, in the opposite direction, perpendicularly or at a 45-degree angle, i.e. calculates the horizontal distance between the airplane and the target and the angle of view when the bomb is dropped. The application can calculate the best time for the airplane to attack the target when the airplane and the target form an arbitrary angle, and the model is simple in basic principle, easy to understand and simple to solve.

Description

Technical Field

[0001] This invention belongs to the field of anti-submarine warfare technology, and in particular relates to a method for calculating the optimal timing for aircraft to drop objects based on a cyclic evolution algorithm. Background Technology

[0002] In modern joint air and sea operations, it is frequently necessary to use aircraft to bombard moving targets on the surface and underwater. Therefore, analyzing the timing of aerial bombing is an important topic. Existing models are built under certain ideal conditions and have their own limitations. In addition, the model building process involves a certain degree of subjectivity, which may lead to discrepancies and requires further improvement. Summary of the Invention

[0003] In view of this, this invention studies the optimal timing for aircraft bombing and proposes a method for calculating the optimal timing for aircraft to drop objects based on a cyclic evolution algorithm. This method simplifies such problems into the problem of bombs encountering targets. Based on the given data, combined with the target's length and motion state, a modeling analysis was performed to determine the optimal timing for bombing and also to predict the range of effective timing for bombing.

[0004] To achieve the above objectives, the present invention discloses a method for calculating the optimal timing for aircraft object delivery based on a cyclic evolution algorithm, comprising the following steps:

[0005] Decompose the trajectory of the bomb falling in the water into n positions, with the time interval between two adjacent positions being Δt. Relate the velocity of the bomb at the (i+≤i≤n)th position to the velocity at the i-th position:

[0006]

[0007] The relationship between the position of the (i+1)th bomb (1≤i≤n) and the displacement of the position of the ith bomb:

[0008]

[0009] Among them, S BP1 h1 is the horizontal distance from the bomb's drop to its impact point, and h1 is the aircraft's altitude above the sea level; the above two formulas are the established iterative evolution algorithm;

[0010] The optimal timing for bombing is determined based on the cyclic evolution algorithm under four scenarios: the aircraft and the underwater submarine are moving in the same direction, opposite direction, perpendicularly, and at a 45-degree angle. This involves calculating the horizontal distance S between the aircraft and the target at the time of bombing. Mo And the downward angle β.

[0011] Preferably, when the target and the aircraft are aligned, M is the target position at the time of bombing, B is the point of impact, P1 and P2 are the projections of the aircraft onto the sea surface and the underwater depth of the target at the time of bombing, respectively, β is the downward angle from which the aircraft observes the target, and S... MP2 S is the horizontal distance from the target to the z-axis at the time of bombing. Mo S is the distance from the bomb to the target when the bomb is dropped. BP2 t1 represents the horizontal distance the bomb travels when it hits the target, and t1 represents the time the bomb spends in the air when it hits the target.

[0012] Based on the relationship between the bomb and the target's position, the equations for the optimal distance and downward angle are derived:

[0013]

[0014] h2 is the height of the target below the horizontal plane, L 目 Let the target length be t2; calculate the underwater travel time t2 when the bomb hits the target, substitute the parameters to solve the equation, and determine the distance S between the aircraft and the target at the time of bombing. Mo And the downward angle β.

[0015] Preferably, when the target is opposite to the aircraft, the optimal distance and downward angle equations are:

[0016]

[0017] Calculate the underwater travel time t2 when the bomb hits the target, substitute the parameters to solve the equation, and determine the distance S between the aircraft and the target at the time of bombing. Mo And the downward angle β.

[0018] Preferably, when the target is perpendicular to the aircraft, the aircraft's position O at the time of bombing, the target's initial position M, and the projection of the aircraft's underwater depth P2 onto the target form a right triangle P2OM. S is then obtained by solving triangle P2MB. MP2 Then, within the right triangle P2OM formed by the initial positions of the aircraft and the target at the time of bombing and the projection of the aircraft onto the sea level, calculate S. MO And β, to obtain the bombing timing of the aircraft under vertical conditions;

[0019] Establish the equations for optimal distance and top angle.

[0020]

[0021] Calculate the underwater travel time t2 when the bomb hits the target, substitute the parameters to solve the equation, and determine the distance S between the aircraft and the target at the time of bombing. Mo And the downward angle β.

[0022] Preferably, when the target is at a 45-degree angle to the aircraft, the optimal distance and downward angle equations are derived:

[0023]

[0024] Calculate the underwater travel time t2 when the bomb hits the target, substitute the parameters to solve the equation, and determine the distance S between the aircraft and the target at the time of bombing. Mo And the downward angle β.

[0025] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0026] 1) It can explore the optimal bombing time when the aircraft attacks the target at any angle.

[0027] 2) The model uses simple and easy-to-understand basic principles, and the solution is simple and easy to implement.

[0028] 3) The model is relatively realistic and has strong guiding significance for actual situations. The model and algorithm established by this invention are not only applicable to determining the timing of bombing by bombers against surface and underwater targets, but also help to solve many practical problems in the military field, such as airdropping supplies and equipment, and searching for and locating crashed aircraft, and have broad reference value. Attached Figure Description

[0029] Figure 1 A schematic diagram of the bomb hitting an underwater target according to the present invention;

[0030] Figure 2 Diagram of the forces acting on a bomb underwater;

[0031] Figure 3 A schematic diagram showing the aircraft's trajectory aligned with that of the target.

[0032] Figure 4 A diagram illustrating the opposite trajectories of the aircraft and the target.

[0033] Figure 5 A schematic diagram showing the perpendicularity of the aircraft's trajectory to the target's trajectory;

[0034] Figure 6 A schematic diagram showing the aircraft's trajectory at a 45-degree angle to the target's movement.

[0035] Figure 7 Diagram of the underwater trajectory of the bomb. Detailed Implementation

[0036] The present invention will be further described below with reference to the accompanying drawings, but this is not intended to limit the present invention in any way. Any modifications or substitutions made based on the teachings of the present invention shall fall within the protection scope of the present invention.

[0037] The optimal timing for an aircraft to drop bombs in the air can be simplified to the problem of the bomb encountering the target. The optimal timing for dropping bombs is determined by the distance between the aircraft and the target and the angle at which the aircraft views the target from above.

[0038] The optimal timing for bombing was determined under four scenarios: the aircraft and the submarine moving in the same direction, opposite direction, perpendicularly, and at a 45-degree angle. The bomb's motion is divided into two phases: airborne and underwater. The analysis of airborne motion involves constructing a coordinate system centered on the bombing point and, based on Newtonian mechanics, building a model for the optimal bombing timing using a cyclic evolution algorithm. Matlab software was used to calculate the bomb's flight time, horizontal distance, and velocity upon impact with the target ship. By considering and neglecting the target ship's length, the distance between the aircraft and the target ship and the angle of attack were determined under the four scenarios. The analysis of the physical laws governing underwater bomb motion is as follows: the bomb decelerates under the influence of gravity, buoyancy, and drag. Newton's second law and related physical theories such as velocity, acceleration, and displacement were applied to establish a mathematical model. Matlab software was used to calculate the bomb's flight time and underwater distance, and the optimal bombing timing was determined by solving triangles.

[0039] The assumptions of the model in this invention are as follows:

[0040] Assumption 1: The bomb is considered as a point mass.

[0041] Assumption 2: Assume the sea surface is horizontal.

[0042] Assumption 3: Ignore the width of the target.

[0043] Assumption 4: Assume that wind speed has no effect on the movement of the bomb.

[0044] Assumption 5: Assume that the density of air and seawater is constant.

[0045] Assumption 6: Assume that the drag coefficient remains constant in air and seawater.

[0046] Assumption 7: Assume that the bomb is completely submerged in water the moment it hits the water.

[0047] The symbols are explained as follows:

[0048] The resistance encountered by the F-bomb

[0049] F f - The buoyancy of the seawater acting on the bomb

[0050] v-Speed ​​of the bomb

[0051] ρ - density of the bomb

[0052] ρ0 - density of seawater

[0053] β - The aircraft's downward view (the target ship's upward view).

[0054] t1 - Time it takes for the bomb to travel through the air

[0055] t2 - Time it takes for the bomb to travel in the seawater

[0056] S-distance

[0057] S-Bomb Cross-sectional Area

[0058] C - Drag coefficient

[0059] m - bomb mass

[0060] g - acceleration due to gravity

[0061] V d -Bomb volume

[0062] Model building

[0063] In modern joint air and sea operations, it is frequently necessary to use aircraft to bomb and attack moving targets on the surface and underwater. Therefore, analyzing the timing of aerial bombing is an important topic. The optimal timing for aerial bombing can be simplified to a bomb-target encounter problem, where the optimal timing is determined by the distance between the aircraft and the target and the aircraft's angle of view of the target at the time of bombing. This invention studies the optimal timing for aerial bombing, which can be simplified to a bomb-target encounter problem. Based on given data, combined with the target's length and motion state, a modeling analysis was performed to determine the optimal bombing timing, and the range of effective bombing opportunities was also predicted.

[0064] To simplify the problem, this invention assumes that a bomber has a flight speed of 200 m / s and a flight altitude of 1000 m; the bomb has a radius of 0.25 m and a density of 0.8 × 10 kg / m³; the wind speed at sea is 10 m / s; the target is an approximately cylindrical submarine that is 100 m long and 9 m wide at its maximum width, with a diving depth of 30 m and a speed of 15 knots.

[0065] The model is used to analyze the accuracy of aircraft bombing and the relationship between various factors. For the three targets to be attacked, the optimal time for aircraft to drop bombs is determined for cases where the aircraft and the target move in the same direction, opposite direction, perpendicular, and at a 45-degree angle. The model results are then simulated and verified.

[0066] Example 1

[0067] A coordinate system is established with the aircraft's center of gravity at the moment of bomb release as the origin o. The ox axis lies in the aircraft's reference plane, parallel to the fuselage axis and pointing forward. The oy axis is perpendicular to the aircraft's reference plane and points to the right of the aircraft. The oz axis lies in the reference plane, perpendicular to the xoy plane and pointing downwards from the aircraft. The aircraft's target is an underwater submarine. The bomb's flight process consists of two phases: flight on the water and underwater flight. The entire process is described in [the original text]. Figure 1 .

[0068] The physical laws governing the movement of a bomb underwater. Since the bomb's entry into the water is extremely brief, we can assume that the bomb experiences a buoyant force F from the water. f =ρ0gV d (ρ0 is the density of seawater) is constant, therefore the bomb is subjected to gravity, buoyancy, and drag force in the opposite direction of its velocity underwater. Its force analysis is as follows: Figure 2 As shown.

[0069] Applying Newton's second law and the relationship between velocity, acceleration, and displacement, we can decompose the force along the x-axis and z-axis to obtain:

[0070]

[0071] The trajectory of the bomb falling in the water is decomposed into n positions, with the time interval between two adjacent positions being Δt. Combining with equation (1), the relationship between the velocity of the i+≤i≤n)th bomb position and the velocity of the i-th bomb position is as follows:

[0072]

[0073] The relationship between the position of the (i+1)th bomb (1≤i≤n) and the displacement of the position of the ith bomb:

[0074] S BP1 h1 is the horizontal distance from the bomb's drop to its impact point on the target, and h1 is the altitude of the aircraft above the sea level. Equations (2) and (3) constitute the established iterative evolution algorithm.

[0075] Determining the optimal timing for bombing in four scenarios—where the aircraft moves in the same direction as, opposite to, perpendicular to, and at a 45-degree angle to the submarine at a depth of 30 meters—involves analyzing the horizontal distance and downward angle between the aircraft and the target at the time of bombing.

[0076] Scenario 1: When the target and the aircraft are moving in the same direction, the trajectories of the aircraft and the target are as follows: Figure 3 As shown in the figure, M is the target position at the time of bombing, B is the point of impact, P1 and P2 are the projections of the bomb on the sea surface at a depth of 30m at the time of bombing, β is the downward angle of the aircraft observing the target, and S... MP2 S is the horizontal distance from the target to the z-axis at the time of bombing. Mo S is the distance from the bomb to the target when the bomb is dropped. BP2 This represents the horizontal distance the bomb travels when it hits the target.

[0077] Based on the relationship between the bomb and the target's position, the equations for the optimal distance and downward angle can be derived:

[0078]

[0079] h2 is the height of the target below the horizontal plane.

[0080] Based on the submarine's length, the equations for effective range and downward angle can be derived:

[0081]

[0082] Scenario 2: When the target and the aircraft are moving in opposite directions, the trajectories of the aircraft and the target are as follows: Figure 4 As shown:

[0083] Optimal distance and angle equations

[0084]

[0085] Effective distance and angle of view equations:

[0086]

[0087] Scenario 3: When the target is perpendicular to the aircraft, the trajectories of the aircraft and the target are as follows: Figure 5 As shown, through Figure 5 It can be observed that when the bomb is dropped, the initial position M of the aircraft O relative to the target and the projection P2 of the aircraft to a depth of 30m form a right triangle P2OM. S can be obtained by solving triangle P2MB. MP2 Then, within the right triangle P2OM formed by the initial positions of the aircraft and the target at the time of bombing and the projection of the aircraft onto the sea level, calculate S. MO And β, which is the timing of bombing by the aircraft under vertical conditions.

[0088] Similarly, the equations for the optimal distance and the downward angle are obtained.

[0089]

[0090] Effective distance and angle of view equations:

[0091]

[0092] Case 4: When the target is at a 45-degree angle to the aircraft, the difference from the perpendicular case is that triangle P2MB is a general triangle, and S can be calculated using the cosine law. MP2 Then, the timing of the bombing can be determined using the right triangle P2OM. The trajectories of the aircraft and the target ship are as follows: Figure 6 As shown.

[0093] Equations for optimal distance and downward angle:

[0094]

[0095] Effective distance and angle of view equations:

[0096]

[0097] Using Matlab software, with Δt = 0.001s, the underwater motion time t2 of the bomb when it hits the target is obtained, and the horizontal distance S of the bomb underwater is obtained. Solving equations (4) to (11) will determine the distance S between the aircraft and the target when the bomb is dropped. Mo and the downward angle β,

[0098] The model was tested when the aircraft's heading was perpendicular to the underwater submarine's direction of motion. Using β = 36.8°, the distance S from the submarine to the point of impact at the time of bomb release was calculated. MB =103.31m, then calculate the actual distance S traveled by the submarine within time t1+t2. M =138.12m, calculate S M -S MB =34.81m. Therefore, when the downward angle β = 36.8°, the bomb hit a point 34.81 meters behind the center of the submarine.

[0099] Example 2

[0100] This invention assumes the target submarine's possible diving depth is 20-60 meters, with other parameters remaining constant. If the bomb misses the target, it will surface after diving to a certain depth and eventually float on the surface. Therefore, in solving the problem, the first step is to use Matlab to simulate the bomb's underwater trajectory. It was found that the bomb's speed decreases to zero at around 80 meters and it begins to rise. Since the diving depth in this embodiment is 20-60 meters, the model-solving method in Example 1 is applied to determine the optimal timing for the aircraft to drop the bomb when the target is at different depths.

[0101] After entering the water, the bomb decelerates under the influence of gravity, buoyancy, and a force opposite to its velocity. It will surface after descending to a certain depth, and if it fails to hit its target, it will eventually float on the surface. The problem specifies a diving depth of 20–60 m. First, we need to use Matlab simulation to consider the bomb's specific trajectory within this diving depth range and generate its underwater velocity curve. (See...) Figure 7 .

[0102] Depend on Figure 7 It can be seen that the movement pattern of the bomb within the range of 20-60m is similar to the theoretical analysis results in Example 1. Therefore, combined with the calculation of the optimal timing for bombing by the aircraft in Example 1, the current diving depth is h0 (within the range of 20-60m):

[0103] 1. When the target and the aircraft are aligned, the equations for optimal timing and effective timing are:

[0104]

[0105] and:

[0106]

[0107] 2. When the target and the aircraft are in opposite directions, the equations for optimal timing and effective timing are:

[0108]

[0109] and:

[0110]

[0111] 3. When the target is perpendicular to the aircraft, the equations for optimal timing and effective timing are:

[0112]

[0113] Effective distance and angle of view equations:

[0114]

[0115] 4. When the target is at a 45-degree angle to the aircraft's direction, the equations for optimal timing and effective timing are:

[0116]

[0117] and

[0118]

[0119] By substituting the parameters and solving equations (12) to (19), the distance S between the aircraft and the target ship at the time of bombing can be determined. Mo And the downward angle β.

[0120] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0121] 1) It can explore the optimal bombing time when the aircraft attacks the target at any angle.

[0122] 2) The model uses simple and easy-to-understand basic principles, and the solution is simple and easy to implement.

[0123] 3) The model is relatively realistic and has strong guiding significance for actual situations. The model and algorithm established by this invention are not only applicable to determining the timing of bombing by bombers against surface and underwater targets, but also help to solve many practical problems in the military field, such as airdropping supplies and equipment, and searching for and locating crashed aircraft, and have broad reference value.

[0124] As used herein, the term "preferred" is meant as an example, illustration, or illustration. Any aspect or design described herein as "preferred" need not be construed as being more advantageous than other aspects or designs. Rather, the use of the term "preferred" is intended to present the concept in a specific manner. As used in this application, the term "or" is intended to mean an inclusive "or" rather than an exclusionary "or." That is, unless otherwise specified or clear from the context, "X uses A or B" naturally includes either of the permutations. That is, if X uses A; X uses B; or X uses both A and B, then "X uses A or B" is satisfied in any of the foregoing examples.

[0125] Furthermore, although this disclosure has been shown and described with respect to one or more implementations, equivalent variations and modifications will occur to those skilled in the art based on a reading and understanding of this specification and the accompanying drawings. This disclosure includes all such modifications and variations and is limited only by the scope of the appended claims. In particular, with respect to the various functions performed by the aforementioned components (e.g., elements, etc.), the terminology used to describe such components is intended to correspond to any component (unless otherwise indicated) that performs the specified function of said component (e.g., is functionally equivalent to it), even if structurally not equivalent to the disclosed structure performing the functions in the exemplary implementations of this disclosure shown herein. Moreover, although specific features of this disclosure have been disclosed with respect to only one of several implementations, such features may be combined with one or more features of other implementations that may be desirable and advantageous for a given or particular application. Furthermore, with regard to the use of the terms “comprising,” “having,” “containing,” or variations thereof in the Detailed Description or claims, such terms are intended to be included in a manner similar to the term “including.”

[0126] The functional units in this invention embodiment can be integrated into a processing module, or each unit can exist physically separately, or multiple units can be integrated into a module. The integrated module can be implemented in hardware or as a software functional module. If the integrated module is implemented as a software functional module and sold or used as an independent product, it can also be stored in a computer-readable storage medium. The storage medium mentioned above can be a read-only memory, a disk, or an optical disk, etc. The aforementioned devices or systems can execute the storage methods in the corresponding method embodiments.

[0127] In summary, the above embodiments are one implementation of the present invention, but the implementation of the present invention is not limited to the embodiments described above. Any changes, modifications, substitutions, combinations, or simplifications made that deviate from the spirit and principle of the present invention should be considered equivalent substitutions and are included within the protection scope of the present invention.

Claims

1. A method for calculating the optimal timing for aircraft object delivery based on a cyclic evolution algorithm, characterized in that, Includes the following steps: The trajectory of the bomb falling in the water is decomposed into n positions, and the time interval between any two adjacent positions is... , No. The relationship between the location of the i-th bomb and the velocity of the location of the i-th bomb: Among them, F f F is the buoyancy force of the seawater acting on the bomb. x and F z v represents the air resistance of the bomb along the x and z axes. x and v z Let x and z be the velocities of the bomb in the air. ; The relationship between the position of the (i+1)th bomb and the displacement of the position of the ith bomb: in, h is the horizontal distance from the bomb's drop to its impact point, and h1 is the aircraft's altitude above sea level. x and h z Let x be the distance of the bomb in the air along the x and z axes. The above two formulas represent the established iterative evolution algorithm. The optimal timing for bombing is determined based on the cyclic evolution algorithm under four scenarios: the aircraft and the underwater submarine are moving in the same direction, opposite direction, perpendicularly, and at a 45-degree angle. This involves calculating the horizontal distance S between the aircraft and the target at the time of bombing. Mo and overhead view .

2. The method for calculating the optimal timing for aircraft object delivery based on a cyclic evolution algorithm according to claim 1, characterized in that, When the target is aligned with the aircraft's direction, M represents the target's position at the time of bombing, and v M Let B be the bomb velocity, B be the point of impact, and P1 and P2 be the projections of the aircraft onto the sea surface and the underwater depth of the target, respectively, at the time of bombing. S is the downward angle from which the aircraft observes the target. MP2 S is the horizontal distance from the target to the z-axis at the time of bombing. Mo S is the distance from the bomb to the target when the bomb is dropped. BP2 t1 represents the horizontal distance the bomb travels when it hits the target, and t1 represents the time the bomb spends in the air when it hits the target. Based on the relationship between the bomb and the target's position, the equations for the optimal distance and downward angle are derived: h2 is the height of the target below the horizontal plane, L 目 Let the target length be t2; calculate the underwater travel time t2 when the bomb hits the target, substitute the parameters to solve the equation, and determine the distance S between the aircraft and the target at the time of bombing. Mo and overhead view .

3. The method for calculating the optimal timing for aircraft object delivery based on the iterative evolution algorithm according to claim 2, characterized in that, When the target is in the opposite direction from the aircraft, the optimal distance and downward angle equations are: Calculate the underwater travel time t2 when the bomb hits the target, substitute the parameters to solve the equation, and determine the distance S between the aircraft and the target at the time of bombing. Mo and overhead view .

4. The method for calculating the optimal timing for aircraft object delivery based on the iterative evolution algorithm according to claim 3, characterized in that, When the target is perpendicular to the aircraft, the aircraft's position O at the time of bombing, the target's initial position M, and the projection of the aircraft's underwater depth P2 onto the target form a right triangle P2OM. S is first obtained by solving triangle P2MB. MP2 Then, within the right triangle P2OM formed by the initial positions of the aircraft and the target at the time of bombing and the projection of the aircraft onto the sea level, calculate S. MO and This allows us to determine the timing of bombing by the aircraft under vertical conditions. Establish the equations for optimal distance and top angle. Calculate the underwater travel time t2 when the bomb hits the target, substitute the parameters to solve the equation, and determine the distance S between the aircraft and the target at the time of bombing. Mo and overhead view .

5. The method for calculating the optimal timing for aircraft object delivery based on the iterative evolution algorithm according to claim 4, characterized in that, When the target is at a 45-degree angle to the aircraft, the equations for the optimal distance and downward angle are as follows: Calculate the underwater travel time t2 when the bomb hits the target, substitute the parameters to solve the equation, and determine the distance S between the aircraft and the target at the time of bombing. Mo and overhead view .

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