Solid bundle rocket booster impact point calculation method

Abstract

The application discloses a solid binding rocket booster landing point calculation method, which comprises the following steps: establishing a six-degree-of-freedom dynamics model of a solid booster; the six-degree-of-freedom dynamics model is a function of passive section state variables about the total moment on the rocket system; establishing an angle of attack model and an angle of incidence model; obtaining the total moment on the rocket system in the falling process of the booster according to the angle of attack model and the angle of incidence model; taking the data of the booster separation point as the simulation initial value, substituting the total moment on the rocket system into the six-degree-of-freedom dynamics model for simulation, and obtaining the booster landing point information. The application can quickly analyze the trajectory characteristic parameters of the solid booster in the falling section, find the passive section motion law, and make the solid booster landing point calculation result more accurate.

Description

Technical Field

[0001] This invention relates to a method for calculating the impact point of a solid-propellant rocket booster, applicable to the calculation of the impact point of solid-propellant boosters in solid-propellant launch vehicles, and belongs to the field of launch vehicle trajectory design. Background Technology

[0002] Solid-propellant launch vehicles utilize the high thrust-to-weight ratio of solid boosters to effectively increase the rocket's payload capacity. However, because solid boosters will return to Earth uncontrolled after separation, landing safety is paramount. Solid boosters exhibit different characteristics during the passive descent phase compared to liquid boosters. The separation point mass of a solid booster is significantly greater than that of a liquid booster. While the center of mass of a liquid booster is concentrated at the tail engine, the center of mass of a solid booster is generally located slightly below the booster's center. During uncontrolled descent, the liquid booster, under the influence of aerodynamic torque, will... The solid rocket booster eventually stabilizes with its tail engine pointing downwards. However, due to the repeated changes in the pressure center, the solid rocket booster's attitude remains in a state of rotation during its descent. Therefore, it is necessary to establish a refined aerodynamic and aerodynamic torque model to analyze the ballistic characteristics of the solid rocket booster during its descent. At the same time, because the solid rocket booster has a large mass and a high impact velocity, higher requirements are placed on the accuracy of the solid rocket booster's impact point calculation. Existing three-degree-of-freedom impact point calculation methods only consider the motion of the center of mass of the falling body and are not suitable for the motion state of the solid rocket booster, thus failing to meet the high-precision requirements. Summary of the Invention

[0003] The purpose of this invention is to overcome the above-mentioned defects and provide a method for calculating the landing point of a solid rocket booster. This method solves the technical problem that the traditional three-degree-of-freedom landing point calculation method cannot meet the high-precision requirements. This invention can quickly analyze the trajectory characteristic parameters of the solid rocket booster during the descent phase and discover its passive phase motion law, making the landing point calculation results of the solid rocket booster more accurate.

[0004] To achieve the above-mentioned objectives, the present invention provides the following technical solution:

[0005] This invention relates to a method for calculating the landing point of a solid rocket booster, belonging to the field of launch vehicle trajectory design. The method includes the following steps: First, a 6-DOF dynamic model of the solid rocket booster is established, defining the incoming flow angle of attack. Aerodynamic simulation modeling is used to generate aerodynamic data for the passive phase of the booster under different incoming flow angles of attack and Mach numbers. Then, formulas for aerodynamic forces and moments during the booster's descent are established. Based on the position, velocity, altitude, attitude, and mass of the booster separation point, dynamic simulation is performed to calculate the passive phase landing point of the solid rocket booster in an uncontrolled state. The aerodynamic force change curves and attitude motion curves of the solid rocket booster during descent are analyzed, providing theoretical support for better prediction of the booster's landing point. This design method provides a refined modeling of the aerodynamic forces and moments experienced by the solid rocket booster during descent, enabling rapid analysis of various trajectory characteristic parameters during the descent phase and revealing the motion law of its passive phase, thus making the calculated landing point more accurate.

[0006] This invention provides a method for calculating the landing point of a solid-propellant rocket booster, comprising:

[0007] A six-degree-of-freedom dynamic model of the solid rocket booster is established; the six-degree-of-freedom dynamic model is a function of the state variables of the passive segment with respect to the resultant torque on the rocket system;

[0008] Establish the incoming flow angle of attack model and the incoming flow azimuth model; based on the incoming flow angle of attack model and the incoming flow azimuth model, obtain the resultant torque on the rocket system during the booster's descent;

[0009] Obtain data on the booster separation point;

[0010] Using the data from the booster separation point as the initial value for simulation, the resultant torque on the rocket system is substituted into the six-degree-of-freedom dynamic model for simulation to obtain the booster landing point information.

[0011] Furthermore, the six-degree-of-freedom dynamic model includes:

[0012]

[0013] Among them, X t For the passive segment state variable, The position of the launch inertial system for solid-propellant rocket boosters. Let [q0 q1 q2 q3] be the inertial velocity of the solid rocket booster. T For the attitude quaternion of a solid-propellant rocket booster, [ω bx ω by ω bz ] T Let G be the angular velocity of the rocket and G be the mass of the solid rocket booster.

[0014] [ω bx ωby ω bz ] T The resultant torque [M] on the arrow system bx M by M bz ] T The function.

[0015] Furthermore, the six-degree-of-freedom dynamic model also includes:

[0016]

[0017] in, [q0 q1 q2 q3] T The derivative, For [ω bx ω by ω bz ] T The derivative, Let the apparent acceleration be the coordinate component in the arrow system. The acceleration due to Earth's gravity in the Earth-centered inertial frame of reference. [MI] represents the total time per second consumed by the passive segment, and [MI] represents the inertia matrix. -1 It is the inverse of the inertia matrix. The transformation matrix from the arrow system to the launch inertial system.

[0018] Furthermore, the incoming flow angle of attack model is as follows:

[0019]

[0020] Where, α Q The angle of attack of the incoming flow is specifically the angle between the rocket's velocity vector relative to the incoming flow and the X1 axis of the rocket's coordinate system, α. Q ∈[0, π];|V Q | is the velocity vector V of the rocket relative to the incoming flow. Q The model; V is the velocity vector of the rocket relative to the incoming flow. Q The components of the X1 axis in the arrow body coordinate system.

[0021] Furthermore, the azimuth model is as follows:

[0022]

[0023] Where, Φ Q The azimuth angle of the incoming flow is specifically determined by rotating the rocket body coordinate system according to the right-hand rule in the positive direction of the X1 axis, with the rocket body reference I to... The included angle, Φ Q ∈[0, 2π); For V Q Components along the Y1 axis in the arrow body coordinate system; For V Q The components of the Z1 axis in the rocket body coordinate system, For V Q Components in the Y1Z1 plane of the rocket body coordinate system.

[0024] Furthermore, methods for establishing the resultant torque on the rocket system during the booster's descent based on the incoming angle of attack model and azimuth model include:

[0025] Under different incoming flow angles of attack and different Mach numbers, the aerodynamic drag coefficient C is obtained through aerodynamic simulation modeling. x and normal force coefficient C n A table of two-dimensional passive section aerodynamic interpolation numbers for incoming flow angle of attack and Mach number;

[0026] Based on the current booster status X t Get V Q ;

[0027] According to V Q The current incoming flow angle of attack α is obtained from the incoming flow angle of attack model. Q And Mach number; based on the two-dimensional passive section aerodynamic interpolation table, the current incoming flow angle of attack α is... Q The current aerodynamic drag coefficient C is obtained by two-dimensional interpolation with the Mach number. x and normal force coefficient C n ;

[0028] According to V Q The current incoming flow azimuth Φ is obtained from the azimuth model. Q ;

[0029] Based on the current aerodynamic drag coefficient C x Normal force coefficient C n and the azimuth angle of the incoming flow Φ Q Obtain the components of the current aerodynamic force in the rocket body coordinate system;

[0030] The resultant torque on the current rocket system during the booster's descent is obtained based on the components of the current aerodynamic force in the rocket body coordinate system.

[0031] Furthermore, the components of the current aerodynamic forces in the rocket body coordinate system [XYZ] T for:

[0032]

[0033] Where q is the rocket's flight kinetic pressure; S m This is the aerodynamic reference area for the booster. For the lateral aerodynamic force of the arrow body, C n This is the normal force coefficient.

[0034] Furthermore, during the booster's descent, the resultant torque on the rocket system is equal to the aerodynamic torque, which includes the torque [M] caused by aerodynamic forces. ax M ay M az ] T Damping torque [M] caused by booster rotation ωax M ωay M ωaz ] T ;

[0035]

[0036]

[0037] Among them, X p X is the theoretical apex distance from the center of pressure; z This is the distance from the center of mass to the theoretical cusp. The damping moment coefficient; l k V is the reference length of the booster; V is the current velocity of the booster.

[0038] Furthermore, the booster separation point data includes the booster's position at the separation point. [q0q1 q2 q3] T 、[ω bx ω by ω bz ] T And G.

[0039] Furthermore, the information regarding the booster's landing point includes the latitude and longitude of the landmass at the time of the booster's landing.

[0040] Compared with the prior art, the present invention has at least one of the following advantages:

[0041] (1) The present invention proposes a method for calculating the landing point of a solid rocket booster, which can realistically analyze the changes in the center of mass and attitude of the solid booster during uncontrolled descent. This method can more realistically reflect the descent process of the booster and improve the accuracy of the landing point calculation of the solid booster.

[0042] (2) This invention takes into account the torque caused by the aerodynamic force of the booster and the damping torque caused by the booster rotation, and proposes a six-degree-of-freedom dynamic model that conforms to the falling process of the solid booster, which is beneficial to reflecting the motion state of the solid booster.

[0043] (3) The present invention establishes the incoming flow angle of attack model and the incoming flow azimuth model, which effectively improves the calculation model of aerodynamic force and aerodynamic torque, and improves the accuracy of booster landing point calculation. Attached Figure Description

[0044] Figure 1 This is a flowchart of the solid-fuel rocket booster landing point calculation method of the present invention;

[0045] Figure 2 The pitch attitude angle curve of the first-stage passive segment obtained by this invention;

[0046] Figure 3 This is the attitude angle curve of the passive segment of the booster in this invention. Detailed Implementation

[0047] The features and advantages of the present invention will become clearer and more apparent from the following detailed description.

[0048] The term “exemplary” as used herein means “serving as an example, embodiment, or illustration.” Any embodiment illustrated herein as “exemplary” is not necessarily to be construed as superior to or better than other embodiments. Although various aspects of embodiments are shown in the accompanying drawings, the drawings are not necessarily drawn to scale unless specifically indicated otherwise.

[0049] This invention establishes a 6-DOF dynamic model of a solid rocket booster, defines the incoming flow angle of attack, and generates aerodynamic data of the passive section of the booster under different incoming flow angles of attack and different Mach numbers through aerodynamic simulation modeling, so as to perform refined modeling of the aerodynamic forces and torques experienced by the solid rocket booster during its descent.

[0050] like Figure 1 The specific implementation process of this invention is as follows:

[0051] Step 1: Establish a 6-DOF dynamic model of the solid rocket booster;

[0052]

[0053]

[0054] In the above formula, X t For the passive segment state variable, The position of the solid-propellant inertial system. For the inertial frame velocity of the solid-propellant booster, a four-element system [q0 q1 q2 q3] is used. T The attitude angle equations are solved, where G is the mass of the solid rocket booster. The transformation matrix from the arrow system to the launch inertial system. Let the apparent acceleration be the coordinate component in the arrow system. This represents the Earth's gravitational acceleration in the Earth-centric inertial frame of reference. The total time per second consumed by the passive segment, [M bx M by M bz ] TThe resultant torque of the arrow system is [MI], while the torque in the passive segment is mainly caused by aerodynamic forces. [MI] is the inertia matrix. -1 It is the inverse of the inertia matrix.

[0055] Step 2: Define the incoming flow angle of attack and azimuth angle. Through aerodynamic simulation modeling, generate a two-dimensional aerodynamic interpolation table of the passive section of the booster for different incoming flow angles of attack and different Mach numbers, and establish the formulas for aerodynamic forces and aerodynamic torques during the booster's descent.

[0056]

[0057]

[0058] in:

[0059] α Q : Angle of attack of the incoming flow, the angle between the rocket's velocity vector relative to the incoming flow and the X1 axis of the rocket's coordinate system;

[0060] Φ Q : Incoming flow azimuth angle, rotated according to the right-hand rule of the positive direction of the X1 axis of the system, from the reference point I of the rocket body (rocket body-Y1 axis) to The included angle;

[0061] The rocket's velocity vector V relative to the incoming flow Q Components along the X1 axis in the arrow body coordinate system;

[0062] V Q Components along the Y1 axis in the arrow body coordinate system;

[0063] V Q Components along the Z1 axis in the rocket body coordinate system;

[0064] |V Q |: The rocket's velocity vector relative to the incoming flow, V Q The model;

[0065] α Q ∈[0, π], Φ Q ∈[0, 2π)

[0066] Aerodynamic components in the rocket body coordinate system:

[0067]

[0068] in:

[0069] X, Y, Z: Aerodynamic components of the solid rocket booster in the rocket system;

[0070] q: Rocket flight kinetic pressure;

[0071] Sm : Aerodynamic reference area of ​​the booster;

[0072] C x Aerodynamic drag coefficient;

[0073] C n : Normal force coefficient;

[0074] C x With C n Aerodynamic coefficients are obtained through the current incoming flow angle of attack α Q Substituting the current Mach number into the two-dimensional aerodynamic interpolation table of the passive section of the booster, we can perform two-dimensional interpolation to obtain the result.

[0075] The aerodynamic torque acting on a solid rocket booster includes the torque caused by aerodynamic forces and the damping torque caused by the rotation of the rigid body.

[0076]

[0077] Among them, M ax M ay M az The torque is caused by aerodynamic forces;

[0078] X p This is the theoretical apex distance from the pressure center;

[0079] X z This is the distance from the center of mass to the theoretical cusp.

[0080] M ωax M ωay M ωaz This is the aerodynamic damping torque;

[0081] This is the damping moment coefficient;

[0082] ω bx ω by ω bz The angular velocity of the rigid body;

[0083] l k This is the reference length for the solid rocket booster;

[0084] The external torque acting on the passive segment level is as follows:

[0085]

[0086] Step 3: Obtain the location of the booster separation point speed Attitude [q0 q1 q2q3], attitude angular velocity [ω] bx ω by ω bzMass G data is used as the initial values ​​for the integral of the dynamic model of the passive section of the solid rocket booster.

[0087] Step 4: 6-DOF simulation of the passive section of the booster; calculate the changes in the center of mass and attitude of the solid rocket booster under the action of aerodynamic forces and torques using a 6-DOF dynamic model, i.e. and [q0 q1 q2 q3] T ;

[0088] Step 5: Calculate the booster landing point; the height at which the booster lands is 0, calculated using a 6-DOF simulation. By obtaining the latitude and longitude of the booster when it lands, we can obtain the location information of the booster's landing point.

[0089] Example:

[0090] The application of the present invention will be described below with reference to specific embodiments.

[0091] The application of this invention will be explained using a solid-propellant launch vehicle as an example. First, the correctness of the method will be verified by taking the core stage as an example, and then the passive section of the solid booster will be simulated.

[0092] According to step 1 of the present invention, a 6-DOF dynamic model of the core level is established.

[0093] The rotational inertia data after core-level separation are shown in Table 1;

[0094] Table 1. Relevant parameters after core separation.

[0095]

[0096]

[0097] And I xy =I xz =I yx =I yz =I zx =I zy =0.

[0098] According to step 2 of the present invention, aerodynamic data of the passive section of the booster under different incoming flow angles of attack and different Mach numbers (two-dimensional passive section aerodynamic interpolation table) is generated by aerodynamic simulation modeling, as shown in Table 2;

[0099] Table 2 Aerodynamic data for the first-stage passive section of the core.

[0100]

[0101] According to step 3 of the present invention, the position, velocity, attitude, attitude angular velocity, and mass data of the booster separation point are obtained, as shown in data table 3.

[0102] Table 3 Core Primary Separation Point Parameters

[0103]

[0104]

[0105] in The attitude angles of the launch vehicle from the inertial frame can be obtained using the following formula: [q0 q1 q2 q3] T :

[0106]

[0107]

[0108] in for The number in the i-th row and j-th column.

[0109] According to steps 1, 2, and 3 of the present invention, a simulation of the passive segment with 6 degrees of freedom is performed on the core stage. The simulation results are as follows: Figure 2 ,Depend on Figure 2 As can be seen, when the method of this invention is used to perform simulation calculations on the first stage, compared with the traditional 3-DOF rocket simulation results, the attitude of the booster gradually stabilizes under the action of aerodynamic torque after passing through the atmosphere during the descent process, which is basically consistent with the 3-DOF simulation results. This can indirectly verify the correctness of the method of this invention.

[0110] The following analysis uses the method of this invention to examine the characteristics of the passive section of a solid rocket booster:

[0111] According to step 1 of the present invention, a 6-DOF dynamic model of the solid rocket booster is established; the moment of inertia data after solid rocket booster separation is obtained, as shown in Table 4:

[0112] Table 4. Relevant parameters after booster separation

[0113]

[0114] And I xy =I xz =I yx =I yz =I zx =I zy =0.

[0115] According to step 2 of the present invention, aerodynamic data of the passive section of the booster under different incoming flow angles of attack and different Mach numbers (two-dimensional passive section aerodynamic interpolation table) is generated by aerodynamic simulation modeling, as shown in Table 5;

[0116] Table 5 Aerodynamic data of the passive section of the booster

[0117]

[0118]

[0119] According to step 3 of the present invention, the position, velocity, altitude, attitude, attitude angular velocity, and mass data of the booster separation point are obtained, as shown in data table 6.

[0120] Table 6 Parameters of the boost separation point

[0121]

[0122] According to steps 1, 2, and 3 of the present invention, a simulation of the passive segment (6 degrees of freedom) of the solid rocket booster is performed. The simulation results are as follows: Figure 3 ,Depend on Figure 3 It can be seen that after the solid rocket booster separates, its attitude tumbles significantly under the action of aerodynamic forces. In particular, the pitch angle of the solid rocket booster fluctuates violently when passing through the dense atmosphere. By the time of landing, the booster is in a flat position. This phenomenon is consistent with the video information of the booster before landing observed in the landing area during the actual launch of a solid rocket launch vehicle. As shown in Table 7, the range of the solid rocket booster landing point calculated using the 6-degree-of-freedom simulation model is about 5 km shorter than the range calculated using the traditional 3-degree-of-freedom simulation model.

[0123] Table 7 Calculation results of booster range

[0124]

[0125] The above embodiments illustrate that the method of the present invention is applicable to the landing point calculation of both the core stage and the passive stage of the solid rocket booster.

[0126] The present invention has been described in detail above with reference to specific embodiments and exemplary examples; however, these descriptions should not be construed as limiting the present invention. Those skilled in the art will understand that various equivalent substitutions, modifications, or improvements can be made to the technical solutions and embodiments of the present invention without departing from the spirit and scope of the invention, and all such modifications and improvements fall within the scope of the present invention. The scope of protection of the present invention is defined by the appended claims.

[0127] The contents not described in detail in this specification are common knowledge to those skilled in the art.

Claims

1. A method of calculating the impact point of a solid-bundled rocket booster, characterized by, include: Establish a six-degree-of-freedom dynamic model for a solid rocket booster; The six-degree-of-freedom dynamic model is a function of the state variables of the passive segment with respect to the resultant torque on the arrow system; Establish the incoming flow angle of attack model and the incoming flow azimuth model; based on the incoming flow angle of attack model and the incoming flow azimuth model, obtain the resultant torque on the rocket system during the booster's descent; Obtain data on the booster separation point; Using the data from the booster separation point as the initial value for simulation, the resultant torque on the rocket system is substituted into the six-degree-of-freedom dynamic model for simulation to obtain the booster landing point information. The incoming flow angle of attack model is: wherein, is the angle of attack of the incoming flow, specifically the angle between the velocity vector of the rocket relative to the incoming flow and the X1 axis of the rocket coordinate system, ; is the modulus of the velocity vector of the rocket relative to the incoming flow ; is the component of the velocity vector of the rocket relative to the incoming flow in the X1 axis of the rocket coordinate system. The azimuth model is as follows: in, The azimuth angle of the incoming flow is specifically determined by rotating the rocket body coordinate system according to the right-hand rule in the positive direction of the X1 axis, with the rocket body reference I to... The included angle, ; for Components along the Y1 axis in the arrow body coordinate system; for The components of the Z1 axis in the rocket body coordinate system, for Components in the Y1Z1 plane of the arrow body coordinate system; Methods for establishing the resultant moment of the rocket system during the booster's descent based on the incoming flow angle-of-attack model and azimuth model include: Under the conditions of different incoming flow attack angles and different Mach numbers, the aerodynamic drag coefficient and the normal force coefficient a two-dimensional passive phase aerodynamic interpolation table about the incoming flow attack angle and the Mach number; According to the current state of the booster Obtained ; According to and the current flow angle of attack and Mach number; based on the two-dimensional passive phase aerodynamic interpolation table, the current flow angle of attack and Mach number is two-dimensionally interpolated to obtain the current aerodynamic drag coefficient and normal force coefficient ; According to and the azimuth model to obtain the current inflow azimuth angle ; According to the current aerodynamic drag coefficient , the normal force coefficient , and the incoming flow azimuth angle , the current aerodynamic force components in the missile body coordinate system are obtained; The resultant torque on the current rocket system during the booster's descent is obtained based on the components of the current aerodynamic force in the rocket body coordinate system. the current aerodynamic force components in the body coordinate system are: wherein, is the rocket flight pressure; is the booster aerodynamic reference area; is the lateral aerodynamic force of the vehicle body, is the normal force coefficient; The resultant moment on the rocket system during the booster descent is equal to the aerodynamic moment, which comprises the moment caused by aerodynamic forces and the damping moment caused by the rotation of the booster ; wherein, is the distance from the center of pressure to the theoretical cusp point; is the distance from the center of mass to the theoretical cusp point; , , is the damping torque coefficient; is the reference length of the booster; is the current speed of the booster.

2. The method of claim 1, wherein, The six-degree-of-freedom dynamic model includes: in, For the passive segment state variable, The position of the launch inertial system for solid-propellant rocket boosters. The inertial velocity of the solid-propellant rocket booster. The attitude quaternion for solid-propellant rocket boosters. The angular velocity of the rocket is the resultant torque of the rocket system. The function, The mass of the solid-fuel rocket booster.

3. The method of claim 2, wherein: The six-degree-of-freedom dynamic model also includes: where is the derivative of , is the derivative of , is the coordinate component of the visual acceleration in the body frame, is the earth gravity acceleration in the earth-centered inertial frame, is the total elapsed time of the boost phase, is the inertia matrix, is the inverse of the inertia matrix, is the transformation matrix from the body frame to the inertial frame.

4. The method for calculating the landing point of a solid-propellant rocket booster according to claim 2, characterized in that, The data for the booster separation point includes the booster at the separation point. , , , and .

5. The method for calculating the landing point of a solid-fuel rocket booster according to claim 1, characterized in that, Information on the booster's landing point includes the latitude and longitude of the landmass at the time of the booster's landing.

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