Rain enhancement and hail suppression rocket projectile trajectory prediction method and system fused with three-dimensional meteorological field
By constructing a three-dimensional meteorological field and thrust-temperature adaptive modeling, combined with six-degree-of-freedom dynamic modeling, the problems of accuracy and temperature adaptability in rocket trajectory prediction were solved, achieving high-precision trajectory simulation and providing a scientific basis and safety assessment for artificial weather modification operations.
Patent Information
- Application Number
- CN202610091480.X
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2026-01-23
- Publication Date
- 2026-05-08
AI Technical Summary
Existing rocket trajectory prediction methods fail to accurately reflect the space motion state under real atmospheric conditions, and the thrust model lacks temperature adaptability, resulting in low prediction accuracy and making it impossible to achieve full-process simulation and field verification.
By constructing a three-dimensional meteorological field, employing thrust-temperature adaptive modeling and six-degree-of-freedom dynamic modeling, and combining the equations of translation and rotation around the center of mass, numerical integration is performed to generate high-precision rocket trajectory predictions.
It significantly improves the accuracy and reliability of trajectory prediction. The simulation results are in high agreement with the measured data. The total flight time error is less than 1%, and the landing error is less than 2 kilometers, which enhances the scientific nature and safety of the operation.
Smart Images
Figure CN121997588A_ABST
Abstract
Description
Technical Field
[0001] This invention relates to the field of weather modification technology, specifically to a method for predicting the trajectory of rain-enhancing and hail-suppressing rockets by integrating a three-dimensional meteorological field. Background Technology
[0002] Artificial weather modification is a comprehensive engineering project that alters local meteorological conditions to increase precipitation and mitigate hail damage. Rain enhancement and hail suppression rockets are commonly used equipment, and their flight trajectory directly affects the spatial location of the seeding area and the safe operational range. In artificial rain enhancement or hail suppression operations, operators typically select the launch elevation and azimuth based on ground and upper-air meteorological conditions to seed the catalyst within the target cloud. However, due to complex wind fields, temperature distribution, and the aerodynamic characteristics of the rocket, the actual flight trajectory often deviates significantly from the ideal trajectory, causing the catalyst to fail to be released in the intended cloud area, affecting operational effectiveness, and potentially posing safety risks.
[0003] Existing rocket trajectory prediction methods are mostly based on simplified two-dimensional or three-degree-of-freedom external ballistic models, considering only the effects of air drag and gravity in the vertical direction, while ignoring factors such as complex wind fields, atmospheric density, and crosswind interference. While these models are computationally fast, their prediction accuracy is low, failing to accurately reflect the rocket's spatial motion in a real atmospheric environment. Furthermore, meteorological data often consists mainly of discrete altitude data output from radiosondes or numerical weather prediction models; directly using discrete data leads to discontinuities and numerical instability in trajectory simulations. In addition, the thrust curves of rocket engines differ significantly under different launch temperatures. Traditional methods generally approximate these curves using experimental curves or empirical correction coefficients at a single temperature, which struggles to accurately describe the thrust variation under different ambient temperatures, further reducing the accuracy of trajectory simulations.
[0004] Therefore, there is an urgent need for a high-precision trajectory prediction method that can be based on actual meteorological data, integrate engine thrust and temperature characteristics, and consider the coupling effect of full three-dimensional wind field and aerodynamics, so as to realize the dynamic simulation of the entire process of rain enhancement / hail suppression rockets from launch and seeding to parachute opening and landing, and provide scientific decision-making basis and safety assessment means for artificial weather modification operations. Summary of the Invention
[0005] The technical problem to be solved by this invention is: how to solve the problems existing in the trajectory prediction of artificial rain enhancement and hail suppression rockets, such as discrete meteorological data, lack of temperature adaptability of thrust models, oversimplification of aerodynamic modeling, and lack of full-process simulation and experimental verification. This invention provides a method for predicting the trajectory of rain enhancement and hail suppression rockets by integrating a three-dimensional meteorological field.
[0006] The present invention solves the above-mentioned technical problems through the following technical solution, and the present invention includes the following steps:
[0007] S1: Construction of a 3D Meteorological Field
[0008] Based on discrete meteorological data obtained by radiosonde equipment, a three-dimensional meteorological field that continuously varies with altitude is constructed through interpolation and smoothing.
[0009] S2: Thrust-Temperature Adaptive Modeling
[0010] Using launch temperature as input, and based on engine thrust-time curves at multiple reference temperatures, a thrust-temperature adaptive modeling method is employed to generate thrust-time curves at launch temperature.
[0011] S3: Six-degree-of-freedom dynamic modeling
[0012] Based on the theory of rocket external ballistics, a six-degree-of-freedom external ballistic dynamics model was established that couples the equations of translation of the center of mass and the equations of rotation about the center of mass.
[0013] S4: Numerical integration of ballistics
[0014] The three-dimensional meteorological field generated in step S1 and the thrust-time curve generated in step S2 are used as external inputs and substituted into the dynamic model established in step S3. The dynamic equations are numerically integrated in the time dimension to obtain the complete ballistic trajectory.
[0015] S5: Results Output and Application
[0016] Output ballistic trajectory simulation results for operation planning, effect evaluation and safety management.
[0017] Furthermore, in step S1, the specific processing procedure is as follows:
[0018] S11: Obtain the original wind speed and wind direction data at each altitude level, decompose the wind direction angle into an east-west component U and a north-south component V, and perform linear interpolation on the U and V components, as well as temperature and air pressure, at the vertical height to obtain the data sequence of the intermediate altitude level.
[0019] S12: The interpolated intermediate height layer U and V components are restored to wind speed and wind direction through vector synthesis; then, all interpolation sequences, including wind speed, wind direction, temperature, and air pressure, are subjected to polynomial smoothing.
[0020] S13: Finally, a three-dimensional meteorological field with physical continuity and smoothness is generated.
[0021] Furthermore, in step S2, the specific processing procedure of the thrust-temperature adaptive modeling method is as follows:
[0022] S21: Time axis normalization
[0023] Multiple thrust-time curves measured at the reference temperature were selected, and their time axes were uniformly scaled and resampled onto a standardized time axis.
[0024] S22: Temperature dimension interpolation
[0025] At each point in time on the standardized time axis, the thrust values of multiple reference curves are piecewise linearly interpolated with temperature as the variable to obtain the thrust value at the corresponding standard time point at the launch temperature.
[0026] S23: Reverse scaling of the time axis
[0027] Based on the estimated combustion duration of the engine at launch temperature, the standardized time axis is inversely scaled to restore the actual physical time, ultimately generating the thrust-time curve at launch temperature.
[0028] Furthermore, in step S3, the specific processing procedure is as follows:
[0029] S31: Before the parachute deploys, the rocket is considered a rigid body of variable mass. Its motion is described by the equations of translation around the center of mass and the equations of rotation around the center of mass. The corresponding equations of motion of the center of mass are expressed in the ballistic coordinate system as follows:
[0030] ;
[0031] ;
[0032] ;
[0033] in, This represents the magnitude of the rocket's center of mass velocity. and These are the ballistic yaw angle and the ballistic tilt angle, respectively, which describe the direction of the velocity vector in the horizontal plane and the angle between it and the horizontal plane; The coordinates of the rocket's center of mass in the geodetic coordinate system; For including thrust and drag And the projection of the resultant external force of the gravitational component onto the three axes of the ballistic coordinate system; The instantaneous mass of the rocket; Atmospheric density, This is a reference area, which varies depending on the umbrella's opening position. The drag coefficient, This is the wind speed vector;
[0034] S32: Equation of rotation about the center of mass in the spring axis coordinate system ( The Euler equations of motion and attitude kinematics describing the projectile's angular motion are as follows:
[0035] ;
[0036] in, The components of the projectile's angular velocity along the three axes of the projectile's coordinate system; and These are the polar moment of inertia and the equatorial moment of inertia of the projectile, respectively. This represents the component of the external torque on the corresponding axis. , , These are the missile's yaw, pitch, and roll attitude angles, respectively.
[0037] S33: To address the systematic deviations caused by low-level wind fields on the trajectory of uncontrolled rockets, a pre-launch angle correction based on measured wind fields is introduced at the beginning of the simulation, according to the target azimuth angle. Calculate the relative angle between the wind vector and the direction of the wind. The wind vector is decomposed into longitudinal wind components along the firing plane. Crosswind component perpendicular to the firing plane And based on the longitudinal wind coefficient With crosswind coefficient Calculate the corrections for pitch and yaw angles. and The calculation formula is as follows:
[0038] ;
[0039] ;
[0040] The final mounting and launch angle is This enables the pre-suppression of wind-induced deviations;
[0041] S34: After the rocket's parachute deploys, its dynamic characteristics undergo a sudden change; the model switches to a high-damped mass model, where air resistance becomes the dominant factor; to simulate the dynamic process of the parachute's inflation and deployment, a time-varying first-order inertial element is introduced to describe the effective drag area. The pattern of change:
[0042] ;
[0043] in, The projected area of the umbrella canopy after it is fully inflated. This is the inflation time constant.
[0044] Furthermore, in step S3, the six-degree-of-freedom external ballistic dynamics model divides the rocket's flight process into at least four stages: Stage 1 is the active phase, assuming that the mass is consumed due to the continuous and uniform combustion of the propellant, following the formula... , Stage 1 is the propellant loss rate; Stage 2 is the free-glide stage, where fuel is exhausted and thrust is 0; Stage 3 is the catalyst dispersal stage, where the catalyst is uniformly dispersed, satisfying the requirements. , Phase 4 is the catalyst loss rate; Phase 5 is the parachute landing phase, where the rocket's safe landing system is activated, and the rocket drifts to the ground with the wind.
[0045] Furthermore, in step S4, the RK4 method is used to perform numerical integration of the dynamic equations with a set time step, and the formula is as follows:
[0046] ;
[0047] ;
[0048] in, The time step for numerical integration. For the current moment The state vector; to This represents the rate of change of state at different prediction points within the current time step.
[0049] Furthermore, in step S5, the ballistic trajectory simulation results include time, three-dimensional position, velocity vector, attitude angle, engine thrust, aerodynamic force, gravity, air density, and trajectory plot data for visualization.
[0050] Furthermore, the method also includes the following steps:
[0051] S6: Model Validation and Parameter Calibration
[0052] The ballistic trajectory output in step S4 is compared with the measured trajectory. Based on the error between the simulation and the measurement, the pitch coefficient is adjusted accordingly. Crosswind coefficient drag coefficient To optimize model performance.
[0053] This invention also provides a rain enhancement and hail suppression rocket trajectory prediction system that integrates a three-dimensional meteorological field, applied to the above-mentioned method, including:
[0054] The meteorological field construction module is used to construct a three-dimensional meteorological field that continuously varies with altitude based on discrete meteorological data obtained by radiosonde equipment through interpolation and smoothing.
[0055] The thrust-temperature modeling module is used to take the launch temperature as input and generate the thrust-time curve at the launch temperature based on the engine thrust-time curves at multiple reference temperatures using a thrust-temperature adaptive modeling method.
[0056] The dynamics modeling module is used to establish a six-degree-of-freedom external ballistic dynamics model based on rocket external ballistics theory, which couples the translational equations of the center of mass and the rotational equations around the center of mass.
[0057] The ballistic trajectory solving module is used to take the three-dimensional meteorological field generated in step S1 and the thrust-time curve generated in step S2 as external inputs, substitute them into the dynamic model established in step S3, and perform numerical integration of the dynamic equations in the time dimension to obtain the complete ballistic trajectory.
[0058] The output and application module is used to output the ballistic trajectory simulation results for operation planning, effect evaluation and safety management.
[0059] The present invention has the following advantages over the prior art:
[0060] 1. Significantly improved the accuracy and reliability of trajectory prediction.
[0061] This invention overcomes the problem of large prediction bias caused by neglecting complex meteorological conditions in existing simplified models by constructing a continuous three-dimensional dynamic meteorological field and employing a refined six-degree-of-freedom (6-DoF) physical model. Experimental results show that the predicted trajectory of this invention is in high agreement with measured GPS data, the prediction error of the total flight time is less than 1%, and the landing error is less than 2 kilometers even when there are spatiotemporal differences in meteorological data. This provides a reliable numerical simulation tool for achieving precise operations.
[0062] 2. Enhanced the physical realism and environmental adaptability of the model.
[0063] This invention establishes a thrust-temperature adaptive model that can accurately generate engine thrust curves based on actual launch temperatures, overcoming the technical deficiency of traditional methods that ignore the dependence of engine thrust on temperature. Simultaneously, the model specifically introduces a yaw angle correction algorithm for the "head-heavy, tail-light" structure of rockets, accurately simulating their unique "head-to-head" aerodynamic effect, making the simulation process closer to the real physical world.
[0064] 3. Improved the scientific level and safety of weather modification operations.
[0065] This invention enables full-process trajectory simulation from launch to landing, providing a strong scientific basis for refined operational planning and pre-assessment of catalyst dispersal effects. Furthermore, this invention allows for quantitative analysis of the impact of weather time-varying phenomena on debris landing points, which has extremely important practical application value for scientifically assessing debris landing area ranges and strengthening operational safety management.
[0066] 4. Provides a complete closed-loop technology system of "modeling-simulation-verification".
[0067] This invention not only proposes a high-precision modeling and simulation method, but also clarifies the technical path for verifying the model and calibrating parameters using onboard GPS test data. This approach, which combines theoretical models with field test data, forms a scientific and rigorous technical closed loop, ensuring the effectiveness of the model and providing an iterative basis for its continuous optimization, thus filling the gap in existing research where theory and practice are disconnected. Attached Figure Description
[0068] Figure 1 This is a flowchart illustrating the analysis of the trajectory prediction method for rain enhancement and hail suppression rockets that integrates a three-dimensional meteorological field in this embodiment of the invention.
[0069] Figure 2(a) is a diagram showing the vertical distribution of atmospheric pressure in an embodiment of the present invention;
[0070] Figure 2(b) is a vertical distribution diagram of ambient temperature in an embodiment of the present invention;
[0071] Figure 2(c) is a diagram showing the variation of high-altitude wind speed in an embodiment of the present invention;
[0072] Figure 2(d) is an upper-level wind rose diagram in an embodiment of the present invention;
[0073] Figure 3 This is a reference image of the time-thrust curve generated at 20°C in an embodiment of the present invention.
[0074] Figure 4 This is a height-time curve diagram in an embodiment of the present invention;
[0075] Figure 5(a) is a comparison diagram of the model simulation and the actual horizontal projection trajectory in the embodiment of the present invention;
[0076] Figure 5(b) is a comparison diagram of the model simulation and the actual trajectory lateral height projection trajectory in the embodiment of the present invention;
[0077] Figure 5(c) is a comparison diagram of the longitudinal height projection trajectory of the model simulation and the actual trajectory in the embodiment of the present invention. Detailed Implementation
[0078] The embodiments of the present invention are described in detail below. These embodiments are implemented based on the technical solution of the present invention, and provide detailed implementation methods and specific operation processes. However, the scope of protection of the present invention is not limited to the following embodiments.
[0079] Example 1
[0080] like Figure 1 As shown, this embodiment provides a technical solution: a method for predicting the trajectory of rain-enhancing and hail-suppressing rockets by integrating a three-dimensional meteorological field, comprising the following steps:
[0081] S1: Construction of a 3D Meteorological Field
[0082] Based on discrete meteorological data (including temperature, air pressure, wind speed and wind direction) obtained by radiosonde equipment, a three-dimensional meteorological field that continuously varies with altitude is constructed through interpolation and smoothing.
[0083] S2: Thrust-Temperature Adaptive Modeling
[0084] It is used to take the launch temperature as input and generate a thrust-time curve that is precisely matched to the launch temperature based on the engine thrust-time curves at multiple reference temperatures;
[0085] S3: Six-DOF (6-DoF) Dynamic Modeling
[0086] A six-degree-of-freedom external ballistic dynamics model was established, which coupled the equations of translational motion of the center of mass and the equations of rotation about the center of mass.
[0087] S4: Numerical integration of ballistics
[0088] The three-dimensional meteorological field generated in step S1 and the thrust-time curve generated in step S2 are used as external inputs and substituted into the dynamic model established in step S3. The dynamic equations are numerically integrated in the time dimension to obtain the complete ballistic trajectory.
[0089] S5: Results Output and Application
[0090] Output trajectory simulation results, including but not limited to time series data such as position, velocity, attitude angle, and environmental factors, for use in job planning, effect evaluation, and safety management.
[0091] In this embodiment, the specific process of constructing the three-dimensional meteorological field in step S1 is as follows:
[0092] To avoid abrupt changes in wind direction angle during interpolation around 0° to 360°, the wind direction angle is first decomposed into east-west (U) and north-south (V) velocity components. Then, linear interpolation is performed on the U, V, temperature, and air pressure components at vertical heights. Finally, the interpolated U and V components at each height level are recombined to obtain wind speed and direction, and all interpolation sequences are smoothed using polynomials to eliminate potential observational noise or local anomalies, ensuring the physical continuity and smoothness of the final generated three-dimensional meteorological field.
[0093] In this embodiment, the specific process of thrust-temperature adaptive modeling in step S2 is as follows:
[0094] Time axis normalization: Select several thrust-time curves measured at reference temperatures (such as -20℃, 15℃, 50℃), scale their time axes uniformly, and resample them onto a standardized time axis.
[0095] Temperature-dimensional interpolation: At each time point on the standardized time axis, the thrust values of multiple reference curves are piecewise linearly interpolated with temperature as the variable to obtain the thrust value at that time point at the launch temperature.
[0096] Reverse scaling of the time axis: Based on the estimated combustion duration of the engine at launch temperature, the standardized time axis is reverse scaled to restore the actual physical time, ultimately generating a complete and accurate thrust-time curve at launch temperature.
[0097] In this embodiment, before the parachute deploys, the rocket is considered a variable-mass rigid body, and its motion is described by the equations of translation and rotation around the center of mass. Based on rocket external ballistics theory, the following model is constructed: This model comprehensively considers the effects of external forces such as gravity, thrust, aerodynamic drag, lift, and the Magnus effect. The equations of motion of the center of mass in the ballistic coordinate system are expressed as follows:
[0098] ;
[0099] ;
[0100] ;
[0101] in, This represents the magnitude of the rocket's center of mass velocity. and These are the ballistic yaw angle and the ballistic tilt angle, respectively, which describe the direction of the velocity vector in the horizontal plane and the angle between it and the horizontal plane; The coordinates of the rocket's center of mass in the geodetic coordinate system; For including thrust and drag And the projection of the resultant external force of the gravitational component onto the three axes of the ballistic coordinate system; The instantaneous mass of the rocket; Atmospheric density, This is a reference area, which varies depending on the umbrella's opening position. The drag coefficient, This is the wind speed vector;
[0102] The equation of the rotation of the center of mass in the spring-axis coordinate system ( The Euler equations of motion and attitude kinematics describing the projectile's angular motion are as follows:
[0103] ;
[0104] in, The components of the projectile's angular velocity along the three axes of the projectile's coordinate system; and These are the polar moment of inertia and the equatorial moment of inertia of the projectile, respectively. This represents the component of the external torque on the corresponding axis. , , These are the projectile's yaw, pitch, and roll attitude angles, respectively.
[0105] To address the systematic deviations caused by low-level wind fields on the trajectory of uncontrolled rockets, a pre-launch angle correction based on measured wind fields is introduced at the beginning of the simulation. This is based on the target azimuth angle. Calculate the relative angle between the wind vector and the direction of the wind. The wind vector is decomposed into longitudinal wind components along the firing plane. Crosswind component perpendicular to the firing plane And based on the longitudinal wind coefficient With crosswind coefficient Calculate the corrections for pitch and yaw angles. and The calculation process is shown in the formula:
[0106] ;
[0107] ;
[0108] The final mounting and launch angle is This allows for the pre-suppression of wind-induced deviations.
[0109] After the rocket's parachute deploys, its dynamic characteristics undergo a sudden change. The model switches to a highly damped point mass model, where air resistance becomes the dominant factor. To simulate the dynamic process of the parachute inflating and deploying, a time-varying first-order inertial element is introduced to describe the effective drag area. The pattern of change:
[0110]
[0111] in, The projected area of the umbrella canopy after it is fully inflated. This is the inflation time constant.
[0112] The model divides the rocket's flight process into at least four stages: Stage 1 is the active phase, assuming its mass is consumed by the continuous and uniform combustion of the propellant, following the formula... Stage 2 is the free-glide phase, during which fuel is exhausted and thrust is zero. Stage 3 is the catalyst dispersal phase, where the catalyst is evenly distributed to meet the requirements. Phase 4 is the parachute deployment phase, during which the rocket's safe landing system is activated, and the rocket mainly drifts to the ground with the wind.
[0113] In this embodiment, in step S4, the numerical integration of the dynamic equations preferably employs the fourth-order Runge-Kutta (RK4) method, with a fixed time step of 0.01 seconds, to ensure both computational accuracy and efficiency. The specific formula is shown below:
[0114] ;
[0115] ;
[0116] in, The time step for numerical integration is 0.01 seconds in this embodiment. For the current moment The state vector; to This represents the rate of change of state at different prediction points within the current time step.
[0117] In this embodiment, the simulation results output in step S5 include, but are not limited to: time, three-dimensional position (or longitude, latitude, altitude), velocity vector, attitude angle (pitch, yaw, roll), engine thrust, aerodynamic force, gravity, air density, and trajectory data for visualization, so as to compare with the missile-borne GPS measured data and optimize parameters.
[0118] In this embodiment, the method further includes a model verification and parameter calibration step based on measured trajectory data:
[0119] The simulated trajectory was compared with the measured trajectory recorded by onboard GPS and other equipment (onboard GPS measured data), especially during the descent phase after parachute deployment. Based on the discrepancy between the simulation and the actual measurement, key parameters (such as the pitch wind coefficient) were modified accordingly. Crosswind coefficient drag coefficient (etc.) to continuously optimize the model's predictive performance.
[0120] Example 2
[0121] This embodiment uses a real-world artificial weather modification field experiment as an example to fully demonstrate the technical process of the method of the present invention.
[0122] 1. Construction of a 3D meteorological field: This embodiment selects a rain enhancement operation conducted in a certain city as the verification object. First, the vertical radiosonde data released by Weining Meteorological Station (station number 56691), the closest meteorological station to the operation site, at 20:00 on the day of the operation was obtained. As shown in Figures 2(a)-2(d), the data shows that there is a complex vertical wind shear structure in the sky above the operation area: at an altitude of 2000 to 3500 meters, a stable southerly airflow prevails; above 3500 meters, the wind direction rotates clockwise, transitioning to pure westerly winds at 4000 meters, and at even higher levels, the airflow is southwesterly.
[0123] To construct a continuous three-dimensional meteorological field, this invention first decomposes the wind direction angle at each altitude level into east-west (U) and north-south (V) velocity components. Subsequently, the U and V components, along with meteorological parameters such as temperature and air pressure, are linearly interpolated along the vertical axis, and the interpolated sequence is then smoothed using polynomials. This method generates a physically realistic dynamic meteorological field that continuously varies with altitude from the ground to an altitude of 10,000 meters, providing accurate environmental input for subsequent dynamic calculations.
[0124] 2. Thrust-Temperature Adaptive Modeling: The ambient ground temperature at the work site is approximately 20°C. This invention uses this temperature as input and calls the thrust-temperature adaptive model. Based on three measured engine thrust baseline curves at standard temperatures (-20°C, 15°C, and 50°C), this model generates a thrust-time curve that perfectly matches the 20°C ambient temperature through three steps: time axis normalization, linear interpolation of the temperature dimension, and inverse scaling of the time axis. Figure 3 As shown, the generated curves exhibit reasonable physical characteristics in terms of peak thrust and burn duration, ensuring the accuracy of the initial dynamic conditions for ballistic simulation.
[0125] 3. Six-DoF Dynamics Modeling: The simulation object in this embodiment is the WR-98GPS rain-enhancing and hail-suppressing rocket. Based on its design parameters, the key physical characteristics of the model are set as follows: total mass is 8.3 kg, length is 1450 mm, center of mass distance from tail is 874 mm, catalyst seeding begins 7 seconds after launch at a rate of 21 g / s, and the parachute opens 33 ± 2 seconds after launch.
[0126] The established six-degree-of-freedom dynamic model divides the rocket flight process into three stages:
[0127] During the acceleration phase: thrust, gravity, and air resistance are taken into account.
[0128] Catalyst seeding stage: thrust is zero, and the mass of the projectile decreases at a rate of 21 g / s.
[0129] Parachute deceleration phase: Air resistance is calculated using the equivalent area and drag coefficient of the parachute.
[0130] 4. Numerical Integral Solution of Ballistic Trajectory: The initial launch conditions for the simulation are set as follows: launch site altitude 2065m, launch azimuth 167°, and elevation 55°. The three-dimensional meteorological field constructed in step S1 and the thrust curve generated in step S2 are used as external inputs and substituted into the six-degree-of-freedom dynamic model in step S3. The fourth-order Runge-Kutta (RK4) method with a time step of 0.01 seconds is used to numerically integrate the dynamic equations of the entire flight process, thereby solving for the complete ballistic trajectory from launch to landing.
[0131] 5. Results Output and Validation
[0132] The simulated trajectory was compared and verified with the actual trajectory recorded by the GPS on the rocket.
[0133] Altitude-time curve comparison: such as Figure 4 As shown, in this experiment, the actual flight time was approximately 412 seconds, while the model predicted a time of 412.91 seconds, with an error of less than 1%. The overall trend of the simulation curve is highly consistent with the measured data, proving that the model can reliably reproduce the entire flight dynamics of the rocket.
[0134] Three-dimensional spatial trajectory comparison: As shown in Figures 5(a) and 5(b), the simulated trajectory precisely matches the measured trajectory during the powered flight phase and near the apex. During the descent phase after parachute deployment, due to the time difference between the rocket launch time (20:35) and the sounding data acquisition time (20:00), the wind field becomes time-varying, causing a certain deviation between the simulated and measured trajectories in the horizontal drift direction. However, the overall amplitude and trend of the drift are similar. For example, the simulated impact point distance of the rocket is 714m, and the error is within the allowable range for actual operations, demonstrating practical effectiveness.
[0135] This embodiment fully demonstrates that the present invention can perform high-precision simulation of the entire trajectory of rain-inducing and hail-suppressing rockets based on actual meteorological data and launch parameters. The results are in high agreement with the field test data, verifying the accuracy, reliability and practical value of the present invention.
[0136] Although embodiments of the present invention have been shown and described above, it is understood that the above embodiments are exemplary and should not be construed as limiting the present invention. Those skilled in the art can make changes, modifications, substitutions and variations to the above embodiments within the scope of the present invention.
Claims
1. A method for predicting the trajectory of rain-enhancing and hail-suppressing rockets by integrating a three-dimensional meteorological field, characterized in that, Includes the following steps: S1: Construction of a 3D Meteorological Field Based on discrete meteorological data obtained by radiosonde equipment, a three-dimensional meteorological field that continuously varies with altitude is constructed through interpolation and smoothing. S2: Thrust-Temperature Adaptive Modeling Using launch temperature as input, and based on engine thrust-time curves at multiple reference temperatures, a thrust-temperature adaptive modeling method is employed to generate thrust-time curves at launch temperature. S3: Six-degree-of-freedom dynamic modeling Based on the theory of rocket external ballistics, a six-degree-of-freedom external ballistic dynamics model was established that couples the equations of translation of the center of mass and the equations of rotation about the center of mass. S4: Numerical integration of ballistics The three-dimensional meteorological field generated in step S1 and the thrust-time curve generated in step S2 are used as external inputs and substituted into the dynamic model established in step S3. The dynamic equations are numerically integrated in the time dimension to obtain the complete ballistic trajectory. S5: Results Output and Application Output ballistic trajectory simulation results for operation planning, effect evaluation and safety management.
2. The method for predicting the trajectory of rain-enhancing and hail-suppressing rockets by integrating a three-dimensional meteorological field according to claim 1, characterized in that, In step S1, the specific processing procedure is as follows: S11: Obtain the original wind speed and wind direction data at each altitude level, decompose the wind direction angle into an east-west component U and a north-south component V, and perform linear interpolation on the U and V components, as well as temperature and air pressure, at the vertical height to obtain the data sequence of the intermediate altitude level. S12: The interpolated intermediate height layer U and V components are restored to wind speed and wind direction through vector synthesis; then, all interpolation sequences, including wind speed, wind direction, temperature, and air pressure, are subjected to polynomial smoothing. S13: Finally, a three-dimensional meteorological field with physical continuity and smoothness is generated.
3. The method for predicting the trajectory of rain-enhancing and hail-suppressing rockets by integrating a three-dimensional meteorological field according to claim 1, characterized in that, In step S2, the specific processing procedure of the thrust-temperature adaptive modeling method is as follows: S21: Time axis normalization Multiple thrust-time curves measured at the reference temperature were selected, and their time axes were uniformly scaled and resampled onto a standardized time axis. S22: Temperature dimension interpolation At each point in time on the standardized time axis, the thrust values of multiple reference curves are piecewise linearly interpolated with temperature as the variable to obtain the thrust value at the corresponding standard time point at the launch temperature. S23: Reverse scaling of the time axis Based on the estimated combustion duration of the engine at launch temperature, the standardized time axis is inversely scaled to restore the actual physical time, ultimately generating the thrust-time curve at launch temperature.
4. The method for predicting the trajectory of rain-enhancing and hail-suppressing rockets by integrating a three-dimensional meteorological field according to claim 1, characterized in that, In step S3, the specific processing procedure is as follows: S31: Before the parachute deploys, the rocket is considered a rigid body of variable mass. Its motion is described by the equations of translation around the center of mass and the equations of rotation around the center of mass. The corresponding equations of motion of the center of mass are expressed in the ballistic coordinate system as follows: ； ； ； in, This represents the magnitude of the rocket's center of mass velocity. and These are the ballistic yaw angle and the ballistic tilt angle, respectively, which describe the direction of the velocity vector in the horizontal plane and the angle between it and the horizontal plane; The coordinates of the rocket's center of mass in the geodetic coordinate system; For including thrust and drag And the projection of the resultant external force of the gravitational component onto the three axes of the ballistic coordinate system; The instantaneous mass of the rocket; Atmospheric density, This is a reference area, which varies depending on the umbrella's opening position. The drag coefficient, This is the wind speed vector; S32: Equation of rotation about the center of mass in the spring axis coordinate system ( The Euler equations of motion and attitude kinematics describing the projectile's angular motion are as follows: ； in, The components of the projectile's angular velocity along the three axes of the projectile's coordinate system; and These are the polar moment of inertia and the equatorial moment of inertia of the projectile, respectively. This represents the component of the external torque on the corresponding axis. , , These are the missile's yaw, pitch, and roll attitude angles, respectively. S33: To address the systematic deviations caused by low-level wind fields on the trajectory of uncontrolled rockets, a pre-launch angle correction based on measured wind fields is introduced at the beginning of the simulation, according to the target azimuth angle. Calculate the relative angle between the wind vector and the direction of the wind. The wind vector is decomposed into longitudinal wind components along the firing plane. Crosswind component perpendicular to the firing plane And based on the longitudinal wind coefficient With crosswind coefficient Calculate the corrections for pitch and yaw angles. and The calculation formula is as follows: ； ； The final mounting and launch angle is This enables the pre-suppression of wind-induced deviations; S34: After the rocket's parachute deploys, its dynamic characteristics undergo a sudden change; the model switches to a high-damped mass model, where air resistance becomes the dominant factor; to simulate the dynamic process of the parachute's inflation and deployment, a time-varying first-order inertial element is introduced to describe the effective drag area. The pattern of change: ； in, The projected area of the umbrella canopy after it is fully inflated. This is the inflation time constant.
5. The method for predicting the trajectory of rain-enhancing and hail-suppressing rockets by integrating a three-dimensional meteorological field according to claim 4, characterized in that, In step S3, the six-degree-of-freedom external ballistic dynamics model divides the rocket's flight process into at least four stages: Stage 1 is the active phase, assuming that the mass is consumed due to the continuous and uniform combustion of the propellant, following the formula... , Stage 1 is the propellant loss rate; Stage 2 is the free-glide stage, where fuel is exhausted and thrust is 0; Stage 3 is the catalyst dispersal stage, where the catalyst is uniformly dispersed, satisfying the requirements. , Phase 4 is the catalyst loss rate; Phase 5 is the parachute landing phase, where the rocket's safe landing system is activated, and the rocket drifts to the ground with the wind.
6. The method for predicting the trajectory of rain-enhancing and hail-suppressing rockets by integrating a three-dimensional meteorological field according to claim 1, characterized in that, In step S4, the RK4 method is used for numerical integration of the dynamic equations, and the time step is set for integration. The formula is as follows: ； ； in, The time step for numerical integration. For the current moment The state vector; to This represents the rate of change of state at different prediction points within the current time step.
7. The method for predicting the trajectory of rain-enhancing and hail-suppressing rockets by integrating a three-dimensional meteorological field according to claim 1, characterized in that, In step S5, the ballistic trajectory simulation results include time, three-dimensional position, velocity vector, attitude angle, engine thrust, aerodynamic force, gravity, air density, and trajectory plot data for visualization.
8. The method for predicting the trajectory of rain-enhancing and hail-suppressing rockets by integrating a three-dimensional meteorological field according to claim 1, characterized in that, The method further includes the following steps: S6: Model Validation and Parameter Calibration The ballistic trajectory output in step S4 is compared with the measured trajectory. Based on the error between the simulation and the measurement, the pitch coefficient is adjusted accordingly. Crosswind coefficient drag coefficient To optimize model performance.
9. A rain enhancement and hail suppression rocket trajectory prediction system integrating a three-dimensional meteorological field, applied to the method described in any one of claims 1 to 8, comprising: The meteorological field construction module is used to construct a three-dimensional meteorological field that continuously varies with altitude based on discrete meteorological data obtained by radiosonde equipment through interpolation and smoothing. The thrust-temperature modeling module is used to take the launch temperature as input and generate the thrust-time curve at the launch temperature based on the engine thrust-time curves at multiple reference temperatures using a thrust-temperature adaptive modeling method. The dynamics modeling module is used to establish a six-degree-of-freedom external ballistic dynamics model based on rocket external ballistics theory, which couples the translational equations of the center of mass and the rotational equations around the center of mass. The ballistic trajectory solving module is used to take the three-dimensional meteorological field generated in step S1 and the thrust-time curve generated in step S2 as external inputs, substitute them into the dynamic model established in step S3, and perform numerical integration of the dynamic equations in the time dimension to obtain the complete ballistic trajectory. The output and application module is used to output the ballistic trajectory simulation results for operation planning, effect evaluation and safety management.