Method for hitting a submerged object based on a kinematic differential equation

Abstract

The application discloses a method for hitting a submerged object based on a motion differential equation, uses Newton's second law of motion to establish the relationship between velocity and force, and obtains a differential model of a projectile falling. According to the navigation speed of a ship, the flight speed, flight height and flight direction of an airplane, the wind direction and wind speed on the sea, the size and weight of the projectile and other related factors, an optimized differential model is further obtained, and the best bomb-throwing time of the airplane in the air is calculated by solving the differential model. The application combines a physical analysis method and a mathematical modeling method, and obtains the best bomb-throwing time when the airplane attacks various targets. The optimal model method is used for solving, the algorithm is accurate and has high precision, and is more in line with the actual situation.

Description

Technical Field

[0001] This invention belongs to the field of anti-submarine technology, and particularly relates to a method for hitting submerged objects based on the equation of motion. Background Technology

[0002] Military tactics have shifted from traditional tactics to integrated joint operations. Joint operations are the overall or basic external form of combat practice after the formation of a multi-service force structure.

[0003] In modern joint air and sea operations, aircraft play a crucial role, enabling them to promptly detect and strike moving targets on the surface and underwater while in flight. To maximize the effectiveness of aircraft on the battlefield and improve target destruction rates, it is essential to comprehensively consider various factors affecting bombing accuracy, such as the accuracy of bombing and the aircraft's flight speed, altitude, and direction; the target's location, size, speed, and direction; the size and weight of the bomb; wind speed and direction at sea; and the density and depth of the seawater. Providing an appropriate time for bombing is crucial to achieving the desired target destruction effect. Summary of the Invention

[0004] In view of this, the present invention proposes a method for hitting a submerged object based on the equation of motion, comprising the following steps:

[0005] During flight, the missile body is affected by the drag coefficient C. w Due to the influence of air resistance and wind force, given a fixed vertical distance between the missile and the ship, its velocity is affected by air resistance and wind force. This can be derived from Newton's second law of motion:

[0006]

[0007] Where ρ 空 Let V be the air density, a be the projectile acceleration, and V be the velocity. 风 Where is the wind speed, S is the cross-sectional area of ​​the projectile, V is the velocity of the projectile, and α is the angle between the direction of the aircraft's motion and the direction of the ship's motion.

[0008] The relationship between the missile body and the ship in terms of vertical distance in space is as follows:

[0009]

[0010] H is the altitude of the aircraft above sea level, which is known.

[0011] The distance between the missile and the ship's horizontal movement is affected by the wind.

[0012]

[0013]

[0014] Solving for the given information, we get:

[0015]

[0016] and

[0017] Among them, the time t1 and V of the ship collision in space. 垂 The velocity of the projectile in the vertical direction;

[0018] Analyzing the horizontal forces, according to Newton's second law, we get:

[0019]

[0020] V 水 The velocity of the projectile in the horizontal direction;

[0021] The horizontal velocity and horizontal displacement are obtained as follows:

[0022]

[0023]

[0024] Where F is the wind resistance, S 水平 This represents the horizontal displacement of the projectile.

[0025] By analyzing the forces acting in the horizontal direction, according to Newton's second law, we get:

[0026]

[0027] Furthermore, the horizontal displacement of the target during time t1 is: S0 = V 舰 t1, V 舰 For target speed;

[0028] During flight, the projectile is affected by wind speed, causing the actual impact point to deviate by S1, which makes a certain angle with the ship's sailing direction, and the angle is β, tanβ=S0 / S1, β∈(0-360°).

[0029] Furthermore, when the angle between the aircraft's direction of motion and the ship's direction is 45 degrees:

[0030]

[0031]

[0032]

[0033]

[0034]

[0035]

[0036]

[0037] Drop bombs at a distance of S0 from the enemy ship, bearing β to the right rear of the enemy ship.

[0038] Furthermore, when the aircraft's direction of motion is perpendicular to the ship's direction:

[0039]

[0040]

[0041]

[0042]

[0043] S0 = V 舰 t1

[0044]

[0045] Drop bombs at a distance of S from the enemy ship, in the bearing arctan S / S0 to the right rear of the enemy ship.

[0046] Furthermore, when the aircraft's direction of motion is at a 135-degree angle to the ship's direction:

[0047]

[0048]

[0049] S0 = V 舰 t1

[0050]

[0051] Drop bombs at a distance of S from the enemy ship, in the arctan S / S0 bearing to the right rear of the ship.

[0052] Furthermore, when the target is underwater, and the underwater trajectory of the projectile forms a 45-degree angle with the ship's direction:

[0053]

[0054] V2 is the projectile's velocity upon entering the water, β is the projectile's angle of entry into the water, C is the water drag coefficient, and t2 is the time from entering the water to hitting the target.

[0055]

[0056]

[0057]

[0058]

[0059] ρ 液 The density of seawater;

[0060] Drop bombs at an arctanh / S0 bearing to the right rear of the target, at a distance of S0 meters from the enemy ship, where h is the submarine's diving depth.

[0061] The beneficial effects of this invention are as follows:

[0062] (1) The physical analysis method and the mathematical modeling method were combined and the corresponding analysis was carried out. Finally, the optimal launch time for the aircraft to strike each target was obtained.

[0063] (2) When the projectile moves in the air and underwater, the resultant force of wind resistance, air resistance and water resistance on the projectile is calculated.

[0064] (3) A comprehensive analysis of the movement direction of targets such as submarines and ships was conducted.

[0065] (4) The model considers many factors and can accurately calculate the final result.

[0066] (5) The model is solved using the optimization model method. The algorithm is meticulous, the accuracy is high, and it is more in line with the actual situation. Attached Figure Description

[0067] Figure 1 Schematic diagram of a projectile at a 45° angle to a ship in the air;

[0068] Figure 2 Schematic diagram of a projectile moving in the same or opposite direction to a ship in the air;

[0069] Figure 3 Schematic diagram of a projectile at a 90° angle to a ship in the air;

[0070] Figure 4 Schematic diagram of a projectile at a 135° angle to a ship in the air;

[0071] Figure 5 A schematic diagram of a projectile sinking an underwater ship in space;

[0072] Figure 6 A schematic diagram of the underwater trajectory of the missile body when it forms a 45° angle with the ship. Detailed Implementation

[0073] 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.

[0074] For surface targets, this invention uses Newton's second law of motion to establish the relationship between velocity and force, deriving a differential model for the missile's descent. By comprehensively considering factors such as ship speed, aircraft speed, altitude, and direction, wind direction and speed at sea, and the size and weight of the missile, an optimized differential model is further derived. By solving this model, the optimal timing for bombing by the aircraft in the air can be calculated.

[0075] For a target at a fixed depth underwater, a bomber flying in the air must take into account the buoyancy of the seawater on the missile body as it travels in the water. Based on Archimedes' principle, the buoyancy change relationship between the missile body and the point of impact is analyzed, thereby deduce the optimal angle of entry into the water and the optimal launch time for the bomber.

[0076] To simplify the problem, the present invention makes the following assumptions:

[0077] (1) For a target that is an approximately rectangular surface ship measuring 100 x 30 meters, traveling at a speed of 25 knots, the aircraft is provided with a precise bombing opportunity by comprehensively considering factors such as the size and weight of the bomb, the wind speed and direction at sea, the target's location, speed, and direction of motion. (1 knot = 1852 meters / hour)

[0078] (2) For a target approximately cylindrical submarine 100 meters long and 9 meters wide at a maximum width, with a diving depth of 30 meters and a speed of 15 knots, the aircraft can provide precise bombing opportunities based on factors such as the missile's flight speed, wind direction and speed at sea, seawater density, and the target submarine's diving depth, thus achieving the expected strike on the underwater submarine target. (1 knot = 1852 meters / hour)

[0079] This invention makes the following assumptions:

[0080] (1) There is a certain temperature difference between the aircraft and the target (because the temperature drops by about 6°C for every 1000 meters increase in distance), but its impact on the flight of the missile is small and can be ignored.

[0081] (2) The sea wind speed between the aircraft and the target is a constant.

[0082] (3) Since the atmospheric pressure and air density do not change much within an altitude of 1000 meters, a fixed value of 1.29 kg / m³ is taken. 3

[0083] (4) Assuming that the changes in ocean currents have little effect on the movement of the projectile in the water, and that the impact point will not be significantly deflected, the effect can be ignored.

[0084] The parameters have the following meanings:

[0085] m - mass of the projectile;

[0086] S - Cross-sectional area of ​​the projectile;

[0087] V 垂 -Vertical velocity;

[0088] C - Water resistance coefficient;

[0089] V 水 - Horizontal velocity;

[0090] V 排 - The volume of water displaced by the projectile;

[0091] F - Wind resistance;

[0092] ρ 液 -Seawater density;

[0093] ρ 空 -Air density;

[0094] Model building and solution

[0095] A differential equation of the form y' + P(x)y = Q(x) is called a first-order linear differential equation, and Q(x) is called a free term. First-order means that the derivative of the equation with respect to y is the first derivative. Linear means that each term in the simplified equation has a degree of 0 or 1 with respect to y and y'.

[0096] (1) When Q(x)≡0, the equation is y'+P(x)y=0, which is called a first-order homogeneous linear differential equation. (Because y' is a first-order term in terms of y and its derivatives, and P(x)y is a first-order term, they are also zero-order terms in terms of x and its derivatives, so they are homogeneous.)

[0097] (2) When Q(x)≠0, the equation y'+P(x)y=Q(x) is called a first-order non-homogeneous linear differential equation.

[0098] (Depend on

[0099] Since Q(x) does not contain y or its derivative, it is a zero-order term in terms of y and its derivatives. Because the equation contains both first-order and zero-order terms, it is non-homogeneous.

[0100] The method of variation of constants is generally used to solve first-order linear differential equations. The general solution of a first-order linear differential equation can be obtained through the method of variation of constants.

[0101] For a first-order homogeneous linear differential equation:

[0102]

[0103] Its general solution is in the form of:

[0104] y = Ce - ∫P(x)dx

[0105] Momentum is A point mass, under external force Under the influence of the external force, the rate of change of its momentum with time is proportional to the external force acting on the particle and is in the same direction as the external force; expressed by the formula:

[0106] Projectile dispersion refers to the dispersion of the impact point or detonation point of projectiles within a certain area (or space) when the same weapon system fires continuously under the same conditions. Projectile dispersion is caused by random factors, including errors in target determination, firing data setting, weapon and ammunition performance, mutual interference, and meteorological conditions. Examples include: random variations in propellant charge, charge density, propellant temperature, chamber volume, and ignition system; random variations in projectile mass and its distribution, and projectile shape; random variations in the gap between the projectile and the gun, and weapon vibration; random variations in atmospheric parameters; random variations in the firing, operation, aiming, transportation, and storage of the weapon system; thrust eccentricity of rockets; interference from the missile mechanism at the moment of bomb release; interference from the sabot during the discarding process of armor-piercing discarding sabot projectiles; random variations in the action time of the airburst fuse; random interference from the vibration of the transport vehicle when the weapon is fired from a vehicle; and mutual interference between individual rounds or between multiple weapon barrels during continuous fire.

[0107] Projectile dispersion is one of the important performance indicators of a weapon system. The smaller the deviation of the point of impact (detonation) from the average point of impact or the center of dispersion, the smaller the projectile dispersion, i.e., the higher the firing density. The probability deviation (also known as probability error) or root mean square error relative to the center of dispersion is usually used to characterize the firing density. The dispersion of the point of impact or detonation follows a pattern. The distance dispersion of the point of impact follows a normal distribution, characterized by a symmetrical distribution with denser distribution in the center and sparser distribution at the edges, and has a limit range. Projectile dispersion is an important parameter for measuring the hit probability of shooting and bombing. It has a significant impact on pre-battle ammunition preparation, firing methods, service usage, and firepower application. Reasonable design schemes and technical measures, precise manufacturing processes, proper storage, thorough firing preparation, and improving the operational skills of firing personnel, as well as adopting appropriate aiming methods, all contribute to reducing projectile dispersion and improving the hit probability.

[0108] During flight, the projectile is affected by gravity and air resistance in the vertical direction, resulting in a downward net acceleration. According to Newton's second law of motion, the relationship between the net external force and the acceleration can be derived. Furthermore, by differentiating the acceleration with time, the relationship between the vertical velocity and time, as well as the relationship between the vertical distance and time, can be obtained.

[0109] Wind tunnel tests can be used to measure the speed of a projectile during flight. When the projectile is tested in a wind tunnel, the wind speed is used to simulate its flight speed. Testing instruments then determine how much force the projectile needs to withstand this wind speed to ensure its flight speed is not significantly affected by the wind. After measuring the required force, wind resistance is determined, and the drag coefficient can then be calculated using aerodynamic formulas.

[0110] drag coefficient C w = Frontal wind resistance F × 2 ÷ (air density ρ) 空 × Projected area of ​​the projectile's front A × Projectile velocity V squared. The drag coefficient of a projectile is fixed, and the drag force experienced by the projectile at various velocities can be calculated based on the drag coefficient.

[0111] When a projectile is in flight, it must overcome resistance from both mechanical wear and air resistance. As the projectile's speed increases, air resistance gradually becomes the most significant drag factor. Generally, the wind resistance experienced by a projectile in flight primarily comes from the front, unless the lateral wind speed is exceptionally high. Otherwise, it does not significantly affect the projectile's flight. Wind resistance has a substantial impact on projectile performance; a lower drag coefficient indicates less susceptibility to air resistance, and vice versa. Therefore, a lower drag coefficient is better. Generally speaking, the more streamlined a projectile is, the lower its drag coefficient will be; a drag coefficient is typically taken as 0.5.

[0112] During flight, the projectile's actual trajectory differs from its trajectory without wind, due to the influence of wind. This difference is influenced by the drag coefficient C. w Due to the influence of air resistance and wind, and given that the vertical distance between the missile and the ship is constant, its speed is affected by air resistance and wind force. This can be derived from Newton's second law of motion.

[0113]

[0114] By processing the data, the relationship between the missile and the ship in terms of vertical distance in space can be obtained.

[0115]

[0116] We can deduce that time t1, the spatial distance of the projectile and the horizontal movement distance of the ship are affected by the wind, and we can deduce... Considering the relative distance traveled by the ship during the collision time t1 in space, the aircraft moves in the same direction as the target, opposite to it, perpendicular to it, and at a 45° angle to ensure that the missile hits the water surface target.

[0117] Its drag coefficient is a dimensionless value that describes the shape of the projectile. The drag coefficient (Cw) varies depending on the projectile shape, generally ranging from 0.3 to 0.6. A streamlined projectile cross-section results in a very small change in projectile velocity and does not form vortices.

[0118]

[0119] By solving, we obtain:

[0120]

[0121] and Analyzing the horizontal forces, according to Newton's second law, we get:

[0122]

[0123] The horizontal velocity and horizontal displacement are obtained as follows:

[0124]

[0125]

[0126] By analyzing the forces acting in the horizontal direction, according to Newton's second law, we get:

[0127]

[0128] Solving the differential equation, we get

[0129]

[0130]

[0131] S0 = V 舰 t1

[0132] During flight, the projectile's impact point is affected by wind speed, causing a deviation ΔX = S1 from the ship's direction of travel, with an angle β between the projectile and the ship's course. (tanβ = S0 / S1, β ∈ (0-360°))

[0133] During flight, the missile is affected by wind resistance and air resistance in the horizontal direction. Under the influence of these two forces, a resultant acceleration is generated. According to Newton's second law of motion, the relationship between the resultant external force and the acceleration can be obtained. Furthermore, by differentiating the acceleration with time, the relationship between the vertical velocity and time, as well as the relationship between the vertical distance and time, can be obtained.

[0134] Air resistance refers to the force exerted by air on a moving object, generated by the elastic force of air on the projectile. When a projectile flies through air, the component of the air force acting on it relative to the air in the direction of flight is proportional to the square of its velocity; the faster the projectile's velocity, the greater the resistance. During flight, resistance is caused by factors such as the compression of air in front of the projectile, friction between the projectile's sides and the air, and the partial vacuum behind the projectile's tail. When flying against a wind, the wind force is also considered. In real life, free fall is also affected by air resistance; its speed, contact area, and air density all influence its magnitude. If air resistance accounts for a large proportion of the projectile's overall drag, it will affect the projectile's speed and accuracy.

[0135] Example 1

[0136] Assuming the target is an approximately rectangular surface ship measuring 100 x 30 meters, sailing at 25 knots, and a bomber is flying 1000 meters above the target ship at a speed of 200 m / s, with a wind speed of 10 m / s at sea, the aircraft must seize the optimal time to drop its bombs in order to accurately strike the target.

[0137] According to the principles of kinematics, when an aircraft releases a bomb, it undergoes a projectile-like motion. The forces acting on the bomb can be analyzed accordingly. The thrust or drag caused by the wind speed during flight, as well as the thrust or drag caused by the air, can be considered. The net force acting on the bomb during flight can be calculated. Then, the optimal timing for the aircraft to release the bomb can be determined from the cases given in the question: opposite direction, perpendicular, and at a 45° angle.

[0138] (a) At a 45-degree angle

[0139]

[0140]

[0141]

[0142]

[0143] S0 = V 舰 t1

[0144]

[0145]

[0146]

[0147]

[0148] Analysis revealed that the bomb was dropped from a bearing β to the right rear of the enemy ship, at a distance S0 from the enemy ship.

[0149] (II) Vertical Case

[0150]

[0151]

[0152]

[0153]

[0154] S0 = V 舰 t1

[0155]

[0156] Analysis revealed that the bomb was dropped from a distance of S, at an arctan S / S0 bearing to the right rear of the enemy ship.

[0157] (III) Cases at a 135-degree angle:

[0158]

[0159]

[0160] S0 = V 舰 t1

[0161]

[0162] Analysis revealed that the bomb was dropped from a distance of S, at an arctan S / S0 bearing to the right rear of the enemy ship.

[0163] Example 2

[0164] Based on Example 1, the force analysis is performed on the missile body during its flight. The bomber strikes a submarine 30 meters underwater. When the missile body enters the water to strike the target submarine, it will form a certain angle of incidence with the sea surface. At this time, the missile body will be subject to resistance in the water. According to Archimedes' principle, the missile body will be subject to buoyancy from the seawater. The forces acting on the missile body after entering the water can be analyzed. The resultant force acting on the missile body after entering the water can be calculated, and the corresponding differential equation can be established.

[0165] An object immersed in a still fluid (gas or liquid) experiences a buoyant force equal to the weight of the fluid displaced by the object, directed perpendicularly upwards through the centroid of the displaced fluid. Archimedes' principle: F 浮 =G 排 =m 排 g = ρ 液gV 排 .

[0166] (1) If the lower surface of an object is not in complete contact with the fluid, such as a bridge pier submerged in water, a sunken ship driven into the seabed, or a pile driven into the lakebed, the force exerted by the water is not equal to the force specified in the principle.

[0167] (2) This principle does not apply if there is significant water flow relative to the object (see Bernoulli's equation). When a fish swims in water, the force calculated using Archimedes' principle is only a partial value due to the disturbance of the surrounding water. These situations require consideration of fluid dynamics effects. The lift force experienced by a hydrofoil, which is much greater than buoyancy, is a dynamic effect, and its laws differ from those of statics.

[0168] Water flow resistance is related to the shape and size of the channel cross-section, the length of the channel, the roughness of the channel surface, as well as the flow regime and velocity. For open channel flow, water flow resistance is related to the water depth.

[0169] For pressurized pipe flow, the flow resistance does not change with pressure, but is related to the pressure drop. When the flow is in the square of the resistance region, the flow resistance is proportional to the square of the average flow velocity. The flow resistance is not proportional to the water depth or pressure. When the flow velocity is very low, the flow resistance is very small regardless of the water depth or pressure. In the extreme case, when the velocity is zero, the resistance is also zero regardless of the water depth or pressure.

[0170] During flight, the missile's actual trajectory differs from its trajectory without wind. Due to the drag coefficient Cw, the vertical distance between the missile and the ship remains constant. Its velocity, influenced by air resistance and wind force, can be calculated using Newton's second law of motion.

[0171] By processing, the relationship between the projectile and the ship in terms of vertical distance in space can be obtained.

[0172]

[0173] We can deduce that time t, the spatial distance of the projectile and the horizontal distance of the ship are affected by the wind, and we can deduce...

[0174]

[0175] When a projectile enters water from the air, it changes the external forces acting on it as it moves from one medium to another. In the water, the projectile is affected by gravity, buoyancy, and water resistance in the numerical direction, resulting in a resultant acceleration, the resultant velocity of which is variable.

[0176]

[0177] By processing the data, the relationship between the projectile's vertical velocity and time can be derived, and consequently, the relationship between the vertical distance between the projectile and the underwater vessel and time. Similarly, the relationship between the horizontal distance between the projectile and the underwater vessel and time can also be derived. To ensure the aircraft hits the underwater vessel and causes damage, the closer the impact point is to the target's center, the greater the damage. The spatial distance between the aircraft and the underwater vessel varies.

[0178]

[0179]

[0180] (V is the projectile's entry velocity into the water, β is the projectile's entry angle into the water)

[0181] At a 45° angle

[0182]

[0183] (V is the projectile's entry velocity into the water, β is the projectile's entry angle into the water)

[0184] F 浮 =ρ 液 V 排 g

[0185] C is the water resistance coefficient;

[0186] h = 30m (the diving depth of the submarine)

[0187]

[0188]

[0189]

[0190]

[0191] Analysis revealed that the bomb was dropped 1689 meters to the right rear of the enemy ship at bearing arctan30 / 1689.

[0192] In Example 1, Newton's second law of motion was applied, and a solution method was established using calculus equations. Relationships were established between vertical velocity and time, vertical distance and time, horizontal velocity and time, and horizontal distance and time in relation to the ship. During flight, the bomb is affected by various factors, including its size, mass, sea wind speed and direction, and seawater density and depth. In Problem 1, the bomber's flight speed is 200 m / s, its altitude is 1000 m, the bomb radius is 0.25 m, and its density is 0.8 × 10³ kg / m³. The wind speed is 10 m / s. Its drag coefficient C... w It is a unitless numerical value, C w The value is generally between 0.3 and 0.6. In this model, Cw = 0.5, and the calculated time t1 = 16.8s. The actual horizontal movement distance of the projectile is consistent with, opposite to, perpendicular to, and at a 45° angle to the ship's direction. The actual horizontal movement distance of the projectile remains unchanged at 2348m.

[0193] In Example 2, Archimedes' theorem and Newton's second law of motion, along with calculus, were used to establish a model for solving the problem. The model calculated the relationship between the projectile's trajectory in the water and the underwater submarine's velocity and time in the vertical direction, the vertical distance and time, and the velocity and time in the horizontal direction. The relationship between distance and time is influenced by various factors, including the size and weight of the projectile, wind speed at sea, seawater density and depth, and the drag coefficient C. For an approximately cylindrical submarine 100m long, 9m wide, with a diving depth of 30m and a speed of 15 knots, the calculation yielded t1 = 23s.

[0194] The beneficial effects of this invention are as follows:

[0195] (1) The physical analysis method and the mathematical modeling method were combined and the corresponding analysis was carried out. Finally, the optimal launch time for the aircraft to strike each target was obtained.

[0196] (2) When the projectile moves in the air and underwater, we calculate the resultant force of wind resistance, air resistance and water resistance on the projectile.

[0197] (3) A comprehensive analysis of the movement direction of targets such as submarines and ships was conducted.

[0198] (4) The model considers many factors and can accurately calculate the final result.

[0199] (5) The model is solved using the optimization model method. The algorithm is meticulous, the accuracy is high, and it is more in line with the actual situation.

[0200] 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.

[0201] 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.”

[0202] 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.

[0203] 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 hitting a submerged object based on the equation of motion, characterized in that, Includes the following steps: During flight, the missile body is affected by the drag coefficient C. w Due to the influence of air resistance and wind force, given a fixed vertical distance between the missile and the ship, its velocity is affected by air resistance and wind force. This can be derived from Newton's second law of motion: ， in Let V be the air density, a be the projectile acceleration, and V be the velocity. 风 Where is the wind speed, S is the cross-sectional area of ​​the projectile, V is the velocity of the projectile, and α is the angle between the direction of the aircraft's motion and the direction of the ship's motion. The relationship between the missile body and the ship in terms of vertical distance in space is as follows: ， H is the altitude of the aircraft above sea level, which is known. The distance between the missile and the ship's horizontal movement is affected by the wind. , Solving for the given information, we get: and Among them, the time t1 of the collision between the ships in space, The velocity of the projectile in the vertical direction; Analyzing the horizontal forces, according to Newton's second law, we get: The velocity of the projectile in the horizontal direction; The horizontal velocity and horizontal displacement are obtained as follows: Where F is the wind resistance, S 水平 This represents the horizontal displacement of the projectile. By analyzing the forces acting in the horizontal direction, according to Newton's second law, we get: Furthermore, the horizontal displacement of the target during time t1 is: V 舰 For target speed; During flight, the projectile's impact point deviates by S1 due to wind speed, creating an angle with the ship's course. This angle is... , , Behind the right of its enemy ships The location is indicated by the bomb being dropped at a distance of S0 from the enemy ship.

2. The method for hitting a submerged object based on the equation of motion according to claim 1, characterized in that, When the angle between the aircraft's direction of motion and the ship's direction is 45 degrees: Behind the right of its enemy ships The location is indicated by the bomb being dropped at a distance of S0 from the enemy ship.

3. The method for hitting a submerged object based on the equation of motion according to claim 1, characterized in that, When the aircraft's direction of motion is perpendicular to the ship's direction: Drop bombs at a distance of S from the enemy ship, in the bearing arctan S / S0 to the right rear of the enemy ship.

4. The method for hitting a submerged object based on the equation of motion according to claim 1, characterized in that, When the aircraft's direction of motion is at a 135-degree angle to the ship's direction: Drop bombs at a distance of S from the enemy ship, in the arctan S / S0 bearing to the right rear of the ship.

5. The method for hitting a submerged object based on the equation of motion according to claim 1, characterized in that, When the target is underwater, and the underwater trajectory of the projectile forms a 45-degree angle with the direction of the ship: V2 is the velocity of the projectile upon entering the water. t2 is the angle of entry of the projectile into the water, C is the drag coefficient of the water, and t2 is the time from entry into the water to impact with the target. ρ 液 The density of seawater; Drop bombs at an arctanh / S0 bearing to the right rear of the target, at a distance of S0 meters from the enemy ship, where h is the submarine's diving depth.

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