Whole-course trajectory firing table compilation method for air-water cross-medium cannonball and firing table

Abstract

The invention discloses an air-water cross-medium shell whole-course trajectory firing table compiling method, and belongs to the technical field of outer ballistic cross-medium trajectory correction theories, cross-medium fluid dynamics and artillery firing table compiling. The method comprises numerical simulation of an air trajectory, a water entry trajectory and a water trajectory and a whole-course trajectory shot table fast interpolation algorithm. Wherein the air trajectory is solved based on a six-degree-of-freedom trajectory model; the water entry trajectory and the underwater trajectory are obtained by solving a fluid control equation by adopting a fluid volume (VOF) multiphase flow model, a turbulence model, a cavitation model and a dynamic grid technology; the full-ballistic shot table fast interpolation algorithm is realized based on a least square method and a linear interpolation algorithm. The method is suitable for the cannonball trajectory air-water cross-medium condition, the rapid and accurate calculation problem of firing elements of an artillery fire control system in the air-water cross-medium environment of the firing table is solved, the continuity of the cross-medium full-trajectory firing table is achieved, the blank of the cross-medium firing table is filled up, and the cross-domain combat ability of an artillery weapon system is effectively improved.

Description

Technical Field

[0001] This application belongs to the technical fields of external ballistics cross-medium ballistic correction theory, cross-medium fluid dynamics and artillery firing table compilation, specifically involving a method for compiling a full-range ballistic firing table for air-water cross-medium projectiles and the firing table itself. Background Technology

[0002] Firing tables are the core data foundation of a weapon system, systematically recording the full-course ballistic parameters of a projectile under different firing parameters, and are a prerequisite for maximizing combat effectiveness. For traditional artillery shells whose internal and external trajectories both move in a single air medium, the technology for compiling firing tables is relatively mature. The core of this mature method lies in: establishing an accurate ballistic model for theoretical calculations, and supplementing it with numerous live-fire tests to verify and correct the model.

[0003] With the development of military needs, air-to-water cross-medium projectiles can travel from air to water and continue their journey to complete combat missions. This has become one of the important development directions of modern naval weapon systems and has high military value in anti-submarine warfare, mine countermeasures, and attacking underwater facilities.

[0004] However, the ballistic motion of air-water cross-medium projectiles involves a complex process of crossing both air and water media, and its physical characteristics differ fundamentally from those of single-medium projectiles. This poses a significant challenge to traditional firing table compilation methods, primarily due to the extreme complexity of the dynamic model: cross-medium ballistics is a highly nonlinear, multi-field coupled transient process. Upon entering the water, the projectile experiences a massive impact load, generating complex hydrodynamic effects such as supercavitation. These effects cause drastic and discontinuous changes in the projectile's stress state during the extremely short time it traverses the water surface. Therefore, traditional single-medium ballistic models cannot accurately describe this complex physical process. Compiling a full-course cross-medium ballistic firing table requires establishing a coupled dynamic model that encompasses the three stages of air flight, water entry transition, and underwater navigation. Currently, there is a lack of efficient and high-precision integrated simulation calculation methods for the entire cross-medium process. Relying entirely on traditional test-centered firing table compilation methods, i.e., acquiring data through numerous live-fire exercises under various conditions, faces numerous problems such as extremely high costs, long cycles, lack of underwater testing methods, and limitations imposed by test site conditions and safety factors.

[0005] In summary, existing technologies lack a method for compiling firing tables that can effectively address the complexity of the entire trajectory of air-to-water cross-medium projectiles while balancing computational accuracy and engineering efficiency. This technological bottleneck severely restricts the practical application and effectiveness of cross-medium munitions. Therefore, there is an urgent need to research a new and scientific method for compiling firing tables for the entire trajectory of air-to-water cross-medium projectiles to solve the aforementioned technical challenges.

[0006] Application content

[0007] To address the shortcomings of existing technologies, the purpose of this application is to provide a method for compiling a full-course ballistic firing table for air-water cross-medium projectiles and the firing table itself.

[0008] The first aspect of this application provides a method for compiling a full-range ballistic firing table for an air-water cross-medium projectile, comprising: Step 1: Calculate aerodynamic parameters: Based on the Computational Fluid Dynamics (CFD) method, the aerodynamic coefficients of the projectile under different combinations of flight Mach number and angle of attack in the air phase are obtained through numerical simulation; Step 2: Establish and solve the airborne ballistic model: Based on the theory of flight mechanics, establish a six-degree-of-freedom rigid body ballistic model of the projectile; combined with the aerodynamic coefficients obtained in Step 1, write an airborne ballistic program to solve the ballistic differential equations and obtain the airborne ballistic trajectory under the corresponding initial conditions. Step 3: Verify and correct the ballistic model: Collect the initial conditions and impact data of the live-fire flight test, compare them with the simulation results, and iteratively correct the aerodynamic parameters to make the simulated impact point coincide with the test impact point within the preset tolerance range, thus completing the verification of the air ballistic program. Step 4: Calculate the air trajectory corresponding to the specified range: Based on the verified trajectory program, for the surface target, the numerical calculation method is used to solve the launch angle corresponding to each specified range, and N air trajectories and their trajectory parameters are calculated. Step 5: Calculate the hydrodynamic parameters of the entry section and the water section: Based on the computational fluid dynamics (CFD) method, construct a numerical simulation system that includes a multiphase flow model, a turbulence model and a cavitation model, and calculate the hydrodynamic coefficients of the projectile under different entry velocities and entry angles. Step 6: Establish and solve the water entry / underwater ballistic model: Use the finite volume method to discretize the fluid control equations in time and space, and combine dynamic mesh technology to establish a mathematical simulation model of water entry impact and underwater navigation, so as to realize the coupled solution of water entry cavitation evolution and underwater ballistics. Step 7: Cross-medium full-range ballistic connection and synthesis: Take the state parameters of the N air ballistic ends obtained in Step 4 as the initial conditions, substitute them into the model in Step 6, take the maximum target depth specified in the firing table as the termination condition, use the hydrodynamic coefficient in Step 5 to calculate the ballistic continuation, and synthesize N complete and seamless cross-medium full-range ballistics. Step 8: Based on all the cross-medium full-range ballistics generated in Step 7, perform firing table data filtering and compilation.

[0009] Optionally, the aerodynamic coefficients include lift coefficient, drag coefficient, and lateral force coefficient.

[0010] Optionally, the six-degree-of-freedom rigid body ballistic model includes: The specific form of the six-degree-of-freedom rigid body ballistic model is as follows: (1) In the formula: For speed; The trajectory inclination angle; The ballistic deflection angle; , , These are roll rate, yaw rate, and pitch rate, respectively. The pitch angle; Yaw angle; This refers to the roll angle; , , For range, altitude, and lateral deviation; For missile mass; , , These are the moments of inertia of the projectile about the corresponding coordinate axes; , , These are respectively roll, yaw, and pitch moments; It is the acceleration due to gravity; , , These are drag, lift, and lateral force, respectively.

[0011] The aerodynamics , , Determined by the following expression: (2) In the formula: air density; The characteristic area; This is the drag coefficient; The lift coefficient; This is the lateral force coefficient.

[0012] Furthermore, the geometric relationships between the angles are described by the following equation: (3) In the formula: , For angle of attack and sideslip angle, The velocity tilt angle.

[0013] Optionally, the ballistic differential equations can be solved numerically by using the fixed-step fourth-order Runge-Kutta method.

[0014] Optionally, the numerical calculation method is the binary search method.

[0015] Optionally, in step 5, the multiphase flow model is a fluid volume (VOF) model, the turbulence model is a Reynolds-averaged Navier-Stokes (RANS) model, and the cavitation model is a Schnerr and Sauer cavitation model.

[0016] Optionally, the data screening and compilation of the firing table in step 8 includes: (a) Basic table compilation: Based on the target depth range and interval, corresponding data are screened from the entire trajectory to establish a basic table structure. Using the defined horizontal distance as the benchmark, other trajectory parameters are interpolated using a one-dimensional linear interpolation method to generate a basic table in a standard format; (b) Correction table compilation: A correction table structure is established. Based on the basic trajectory data, the trajectory correction amount corresponding to the disturbance factors is calculated using a one-dimensional linear interpolation method to complete the correction table compilation.

[0017] Optionally, the ballistic parameters include launch angle, horizontal distance into the water, angle into the water, velocity into the water, flight time in the air, underwater travel time, landing velocity at the moment of encounter, angle of impact at the moment of encounter, and intermediate error of the landing point.

[0018] Optionally, the disturbance factors include at least one of crosswind, longitudinal wind, air pressure, air temperature, propellant temperature, initial velocity deviation, firing line height deviation, firing angle deviation, target speed, and heading.

[0019] The second aspect of this application provides a full-course ballistic firing table for an air-to-water cross-medium projectile, compiled by the method described above. It includes the launch angle, flight time, impact velocity, water entry attitude, and time and location information of reaching a specified depth underwater for each range under standard firing conditions. It also provides a correction dataset for initial velocity deviation, meteorological and marine environmental disturbances.

[0020] The beneficial effects and significant advantages of this application are: (1) Integrated modeling and data generation of cross-medium ballistics have been achieved. This application creates a unified mathematical model that can accurately describe the entire process from air flight, water impact to underwater navigation by coupling airborne CFD calculation, water entry / underwater multiphase flow simulation and rigid body ballistics. This solves the problem of fragmented ballistic modeling caused by abrupt changes in the physical properties of the medium, realizes the seamless link between airborne and underwater ballistics, and provides a continuous and complete data source of firing tables for cross-medium munitions.

[0021] (2) Improved the strike effectiveness and decision-making speed of cross-medium firepower. The high-precision firing table generated by this application provides a reliable data kernel for the fire control system, enabling rapid and accurate ballistic calculation and firing data setting in complex cross-medium combat environments, significantly shortening the decision-making cycle from target detection to fire strike, and increasing the hit probability of the first shot.

[0022] (3) The technical solution is guaranteed to be practical and robust in engineering applications. The technical approach of this application deeply integrates well-proven mature numerical methods (such as the Runge-Kutta method, VOF model, and FVM method) and modular verification process, ensuring the stability of the calculation results and the reliability of the method. This solution has high computational efficiency, low hardware dependence, and the potential to quickly and accurately compile and support shooting tables under actual combat conditions, with significant application value.

[0023] Other technical effects resulting from the additional features will be further illustrated in the corresponding embodiments. Attached Figure Description

[0024] Other features, objects, and advantages of this application will become more apparent from the following detailed description of non-limiting embodiments with reference to the accompanying drawings: Figure 1 A flowchart for the bisection method calculation of the firing angle corresponding to the air trajectory firing range in the firing table; Figure 2 A flowchart for compiling the full trajectory of an air-water cross-medium projectile. Detailed Implementation

[0025] The present application will now be described in detail with reference to specific embodiments. These embodiments will help those skilled in the art to further understand the present application, but do not limit the present application in any way. It should be noted that those skilled in the art can make several modifications and improvements without departing from the concept of the present application, and these all fall within the protection scope of the present application. Parts not described in detail in the following embodiments can be implemented using existing technology.

[0026] The present invention will now be described in detail with reference to the accompanying drawings and specific embodiments. It should be understood that the embodiments described herein are intended to help understand the technical solutions and core principles of the present invention, and are not intended to limit the scope of protection of the present invention. Any simple modifications or equivalent transformations based on the spirit and essence of the present invention should be included within the scope of protection defined by the claims of the present invention.

[0027] like Figure 1 As shown, this invention provides a method for compiling a complete trajectory firing table for an air-to-water cross-medium projectile. The core of this method lies in establishing and solving air, water-entry, and underwater trajectory models sequentially through a combination of numerical simulation and experimentation. Finally, through data integration and interpolation, a complete firing table is generated. The specific implementation steps are as follows:

[0028] Step 1: Calculate aerodynamic parameters

[0029] This step aims to obtain the aerodynamic parameters necessary for constructing an airborne ballistic model through CFD simulation. Specifically, a mature CFD program is used to establish a computational model based on the projectile's geometry. Subsequently, calculation conditions are set according to various combinations of flight speed and angle of attack listed in Table 1, and numerical simulations are performed. Finally, through computational simulation, the lift coefficient corresponding to each set of conditions in Table 1 is directly output. drag coefficient With lateral force coefficient These coefficient matrices will serve as input data for subsequent air ballistic procedures, ensuring the aerodynamic accuracy of the model.

[0030] Table 1. Pneumatic Simulation Operating Conditions

[0031] Step 2: Establish and solve the air ballistic model

[0032] This step aims to establish an airborne ballistic model based on rigid body ballistics theory. Specifically, a six-degree-of-freedom ballistic equation set is established to describe the motion of a projectile in the air medium: (1) In the formula: For speed; The trajectory inclination angle; The ballistic deflection angle; , , These are roll rate, yaw rate, and pitch rate, respectively. The pitch angle; Yaw angle; This refers to the roll angle; , , For range, altitude, and lateral deviation; For missile mass; , , These are the moments of inertia of the projectile about the corresponding coordinate axes; , , These are respectively roll, yaw, and pitch moments; It is the acceleration due to gravity; , , These are drag, lift, and lateral force, respectively.

[0033] The aerodynamics , , Determined by the following expression: (2) In the formula: air density; The characteristic area is denoted as .

[0034] Furthermore, the geometric relationships between the angles are described by the following equation: (3) In the formula: , For angle of attack and sideslip angle, The velocity tilt angle.

[0035] To solve the ballistic differential equations established in the above steps, this invention employs the computationally stable and accurate fixed-step fourth-order Runge-Kutta method. This method is a self-starting, single-step numerical integration method, easy to program and convenient to adjust the step size. For the first-order differential equation of the following form... (4) If known Time parameters Then, the fourth-order Runge-Kutta method can be used to obtain the result. time Approximate value: (5)

[0036] The advantage of this method is that it only requires calculating the right-hand side function value four times for each integration step, and then linearly combining them to obtain a high-precision increment. Given initial conditions, this method can be used to calculate the complete air trajectory and the evolution of all its parameters.

[0037] Step 3: Verify and correct the aerial ballistic model

[0038] This step verifies and corrects the airborne ballistic program using live-fire test data, aiming to establish a high-confidence simulation model. Specifically, first, a complete dataset from multiple live-fire flight tests is collected, including but not limited to initial conditions such as initial velocity, firing angle, and fire line altitude, as well as terminal data such as ballistic impact coordinates obtained through measuring equipment. Then, the initial conditions of the above tests are rigorously reproduced in the established ballistic simulation program, and the model is run to obtain simulated terminal data (mainly impact coordinates). Next, the deviation between the simulated impact point and the experimentally measured impact point is calculated. Based on this deviation, a parameter identification and optimization algorithm (such as the least squares method) is used, with the drag coefficient as the main correction target, to iteratively adjust the aerodynamic parameters in the ballistic model until the deviation meets the preset accuracy criteria, completing the closed-loop correction of the ballistic model.

[0039] Step 4: Calculate the air trajectory corresponding to the fixed range.

[0040] This step aims to use the validated high-fidelity ballistic model to calculate the launch angle and complete ballistic data corresponding to each standard range specified in the firing table. Specifically, the target is set as a surface target (i.e., the target height is zero). For each specified range in the firing table, the following method is used... Figure 2 The bisection iterative process shown is used to inversely solve for the corresponding emission angle: (1) Pre-set a reasonable search range for the firing angle. And set the desired distance difference from the target range. ; (2) Take the midpoint of the interval The launch angle is substituted into the ballistic program for calculation; (3) Calculate the distance difference between the range corresponding to the average firing angle and the target range. ; (4) Distance difference Compared with 0, if Update the search range Otherwise, update the search range. ; (5) If ,but That is, the desired angle of incidence, output as: Otherwise, go to (2) and repeat until convergence.

[0041] This process allows for the calculation of the precise launch angle for each specified range, and simultaneously calculates and stores the complete N air trajectory parameters at that launch angle, especially the pitch angle and velocity at the end of the trajectory, providing accurate initial conditions for subsequent water-entry trajectory calculations.

[0042] Step 5: Calculate the hydrodynamic parameters of the inlet section and the water section.

[0043] This step uses high-precision fluid dynamics simulation to obtain the complex fluid loads experienced by the projectile during water impact and underwater navigation, which forms the basis for establishing an underwater ballistic model. Specifically, the following numerical simulation system is constructed: (1) Multiphase flow model The Volume of Fluid (VOF) method is used to simulate the interaction between the gas and water phases. The VOF method traces the free interface by solving the volume fraction transport equation for the air phase: (6) By solving for the air phase volume fraction within each grid cell of the computational domain It can accurately distinguish phase distribution: 1) When At that time, the unit contained a pure aqueous phase; 2) When At that time, the unit contains a pure air phase; 3) When At that time, a gas-water interface exists within the unit.

[0044] (2) Turbulence model

[0045] The Reynolds Averaged Navier-Stokes (RANS) turbulence model is used to handle the strong turbulence effects during the water ingress process. The RANS method decomposes transient flow into time-averaged flow and fluctuating flow. By modeling the fluctuating term, it significantly reduces computational costs while maintaining computational accuracy, avoiding the huge resource consumption of direct numerical simulation.

[0046] (3) Schnerr and Sauer cavitation model

[0047] The Schnerr and Sauer cavitation model was used to predict the generation and development of cavitation bubbles. This model describes bubble dynamics based on the Rayleigh-Plesset equations and simulates the cavitation process by solving the mass transport equations for the water vapor phase. (7) In the formula: Where is the radius of the gas nucleus. This represents the volume fraction of non-condensable gases. and These are the empirical coefficients for condensation and evaporation, respectively.

[0048] Based on the above model combination, a numerical simulation environment for projectile entry into water was established, and a series of calculations were performed on various working conditions covering the terminal velocity and elevation angle range obtained in step 4. Finally, the drag coefficient, lift coefficient, and lateral force coefficient of the projectile under each working condition were extracted from the simulation results to construct a complete hydrodynamic coefficient database, providing accurate load input for subsequent dynamic calculations of water entry and underwater trajectory.

[0049] Step 6: Establish and solve the ballistic model for water entry / underwater travel.

[0050] This step, based on the hydrodynamic simulation system established in step 5 and the obtained hydrodynamic coefficients, constructs and solves the water entry / underwater ballistic coupling model. Specifically, the finite volume method (FEM) is used to spatially discretize and temporally advance the fluid control equations (including mass and momentum conservation equations and additional equations for the VOF and cavitation models). Preferably, dynamic meshing or overlapping meshing techniques are combined to dynamically update the computational domain changes caused by the projectile motion, accurately capturing the interaction between the projectile and the fluid interface.

[0051] Using the above method, a strongly coupled mathematical simulation model is established that can simultaneously solve for fluid field evolution (including cavitation generation and collapse) and rigid body trajectory motion. This model fully considers the interaction between the drastic hydrodynamic changes and the projectile motion during water entry, thereby achieving high-precision simulation of water entry impact load, trajectory stability, and underwater trajectory.

[0052] Step 7: Cross-medium full-range ballistic connection and synthesis

[0053] This step aims to complete the physical connection and data synthesis of air and underwater ballistics, generating a complete cross-medium ballistic dataset, which is the core of compiling the full-range firing table. Specifically, the terminal motion states (mainly including terminal velocity, spatial position, and projectile attitude angle) of the N standard air trajectories calculated in step 4 are used as the initial input conditions for the water entry / underwater ballistic model described in step 6. Underwater ballistic calculations are initiated using these initial conditions, and the maximum underwater travel depth of the target, a tactical indicator specified in the firing table, is used as the unified ballistic termination condition.

[0054] Finally, each independent air trajectory is seamlessly spliced ​​with its corresponding water entry and underwater trajectory to create N physically continuous cross-medium trajectories that start from the launch point, undergo air flight, water entry transition, and end underwater. These N complete trajectories form the complete data foundation for subsequent firing table compilation.

[0055] Step 8: Data filtering and table compilation in the injection table: After obtaining N complete cross-medium full-range ballistic data, this step aims to filter and linearly interpolate these data to ultimately generate a firing table document that can be directly used by the fire control system, including a basic table and a correction table.

[0056] (1) Basic table compilation

[0057] The basic table is the core of the firing table, providing ballistic parameters under standard conditions.

[0058] Specifically, firstly, based on the target depth range and depth intervals specified in the firing table tactical indicators, a subset of all ballistic data whose endpoints meet the corresponding depth conditions is automatically selected from the full-range ballistic dataset synthesized in step 7. Then, a standardized structure and fields for the basic firing table are established. This structure defines all the required ballistic parameters for output, including the specified horizontal range, launch angle, horizontal distance into the water, velocity into the water, flight time, underwater travel time, landing velocity at the moment of encounter, landing angle at the moment of encounter, and intermediate error of the landing point. Next, using the specified horizontal range as the benchmark interpolation variable, a one-dimensional linear interpolation algorithm is used to process the selected ballistic data subset. This algorithm calculates the precise interpolation results for all other ballistic parameters at each standard range point. Finally, the regularized and continuous data after interpolation is filled into the preset firing table framework, generating a standardized basic firing table as shown in Table 2. This table establishes a precise mapping relationship between the firing command (launch angle) and the ballistic endpoint state (range, depth).

[0059] Table 2 Basic Table of Shooting Tables

[0060] (2) Compilation of the revision table

[0061] The correction table is used to correct deviations in the standard parameters in the basic table to address the impact of various disturbances in the actual shooting environment and ensure shooting accuracy in all mission scenarios.

[0062] Specifically, firstly, a structural framework for the firing table correction table is established based on standard specifications. This framework clearly defines the types of disturbance factors requiring correction (such as crosswind, forewind, air pressure, air temperature, propellant temperature, speed and heading, initial velocity deviation, fire line height deviation, and angle of attack deviation) and the level of each factor. Then, based on the basic ballistic data generated in step 7, sensitivity analysis is performed using the parametric perturbation method. That is, based on the standard initial conditions, a specific deviation of a single disturbance factor is systematically introduced, and the ballistic calculation is re-executed or existing data is used to obtain the ballistic endpoint data under this deviation condition. Next, the perturbed ballistic data is compared with the standard basic table data to calculate the correction amount for each disturbance factor at different levels on key parameters (especially angle of attack, horizontal distance, underwater travel time, and direction). During this process, the one-dimensional linear interpolation method is used again to smooth the data and obtain the precise correction value corresponding to any deviation amount. Finally, all calculated correction amounts are systematically filled into the correction table structures shown in Tables 3 and 4 according to their corresponding disturbance factors and levels, generating a complete firing table correction table. This table, used in conjunction with the basic table, together constitutes a high-precision cross-medium projectile fire application system capable of adapting to complex and ever-changing combat environments.

[0063] Table 3. Correction Table for Firing Tables (excluding speed / heading)

[0064] Table 4 Speed / Heading Correction Table (Range: m; Angle of Firing: mrad; Direction: mrad; Distance: m)

[0065] The foregoing has described some specific embodiments of this application. It should be understood that this application is not limited to the specific embodiments described above, and those skilled in the art can make various modifications or variations within the scope of the claims, which do not affect the substantive content of this application. The above-described preferred features can be used in any combination without conflict.

Claims

1. A method for compiling a full-course ballistic firing table for an air-water cross-medium projectile, characterized in that, include: Step 1: Calculate aerodynamic parameters: Based on computational fluid dynamics, obtain the aerodynamic coefficients of the projectile under different combinations of flight Mach number and angle of attack during the air phase through numerical simulation; Step 2: Establish and solve the airborne ballistic model: Based on the theory of flight mechanics, establish a six-degree-of-freedom rigid body ballistic model of the projectile; combined with the aerodynamic coefficients obtained in Step 1, write an airborne ballistic program to solve the ballistic differential equations and obtain the airborne ballistic trajectory under the corresponding initial conditions. Step 3: Verify and correct the ballistic model: Collect the initial conditions and impact data of the live-fire flight test, compare them with the simulation results, and iteratively correct the aerodynamic parameters to make the simulated impact point coincide with the test impact point within the preset tolerance range, thus completing the verification of the air ballistic program. Step 4: Calculate the air trajectory corresponding to the specified range: Based on the verified trajectory program, for the surface target, the numerical calculation method is used to solve the launch angle corresponding to each specified range, and N air trajectories and their trajectory parameters are calculated. Step 5: Calculate the hydrodynamic parameters of the entry section and the middle section of the water: Based on the computational fluid dynamics method, construct a numerical simulation system that includes a multiphase flow model, a turbulence model and a cavitation model, and calculate the hydrodynamic coefficients of the projectile under different entry velocities and entry angles. Step 6: Establish and solve the water entry / underwater ballistic model: Use the finite volume method to discretize the fluid control equations in time and space, and combine dynamic mesh technology to establish a mathematical simulation model of water entry impact and underwater navigation, so as to realize the coupled solution of water entry cavitation evolution and underwater ballistics. Step 7: Cross-medium full-range ballistic connection and synthesis: Take the state parameters of the N air ballistic ends obtained in Step 4 as the initial conditions, substitute them into the model in Step 6, take the maximum target depth specified in the firing table as the termination condition, use the hydrodynamic coefficient in Step 5 to calculate the ballistic continuation, and synthesize N complete and seamless cross-medium full-range ballistics. Step 8: Based on all the cross-medium full-range ballistics generated in Step 7, perform firing table data filtering and compilation.

2. The method according to claim 1, characterized in that, The aerodynamic coefficients include lift coefficient, drag coefficient, and lateral force coefficient.

3. The method for compiling a full-course ballistic firing table for an air-water cross-medium projectile according to claim 1, characterized in that, The six-degree-of-freedom rigid body ballistic model includes: The specific form of the six-degree-of-freedom rigid body ballistic model is as follows: (1) In the formula: For speed; The trajectory inclination angle; This refers to the ballistic deflection angle; , , These are roll rate, yaw rate, and pitch rate, respectively. The pitch angle; Yaw angle; For roll angle; , , For range, altitude, and lateral deviation; For missile mass; , , These are the moments of inertia of the projectile about the corresponding coordinate axes; , , These are respectively roll, yaw, and pitch moments; It is the acceleration due to gravity; , , These are drag, lift, and lateral force, respectively. The aerodynamics , , Determined by the following expression: (2) In the formula: air density; The characteristic area; This is the drag coefficient; The lift coefficient; This is the lateral force coefficient; Furthermore, the geometric relationships between the angles are described by the following equation: (3) In the formula: , For angle of attack and sideslip angle, The velocity tilt angle.

4. The method according to claim 1, characterized in that, The ballistic differential equations are solved by numerical integration using the fixed-step fourth-order Runge-Kutta method.

5. The method according to claim 1, characterized in that, The numerical calculation method is the binary search method.

6. The method according to claim 1, characterized in that, In step 5, the multiphase flow model is a fluid volume (VOF) model, the turbulence model is a Reynolds-averaged Navier-Stokes (RANS) model, and the cavitation model is a Schnerrand-Sauer cavitation model.

7. The method according to claim 1, characterized in that, Step 8, which involves filtering and compiling ballistic data, includes: (a) compiling a basic table: based on the target depth range and interval, filtering corresponding data from the entire trajectory, establishing a basic table structure, using the defined horizontal distance as a benchmark, interpolating other ballistic parameters using a one-dimensional linear interpolation method, and generating a basic table in a standard format; (b) compiling a correction table: establishing a correction table structure, and based on the basic ballistic data, using a one-dimensional linear interpolation method, calculating the ballistic correction amount corresponding to the disturbance factors, and completing the compilation of the correction table.

8. The method according to claim 7, characterized in that, The ballistic parameters include launch angle, horizontal distance into the water, angle of entry into the water, speed into the water, flight time in the air, underwater travel time, landing speed at the moment of encounter, angle of entry at the moment of encounter, and intermediate error of the landing point.

9. The method according to claim 7, characterized in that, The disturbance factors include at least one of crosswind, longitudinal wind, air pressure, air temperature, propellant temperature, initial velocity deviation, firing line height deviation, firing angle deviation, target speed, and heading.

10. A ballistic trajectory firing table for an air-water cross-medium projectile, characterized in that, Compiled by the method described in any one of claims 1 to 9, it includes launch angle, flight time, impact velocity, water entry attitude, and time and position information of reaching a specified depth underwater for each range under standard launch conditions, and provides a correction dataset for initial velocity deviation, meteorological and marine environmental disturbances.

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