Modeling method of three-channel axisymmetric layout aerodynamic force mathematical model of duck tail rudder

Abstract

The application provides a kind of duck tail rudder three channel axisymmetric layout aerodynamic force mathematical model modeling method and system, comprising: according to the symmetry of missile shape, obtain the static aerodynamic force mathematical model of missile;Using wind tunnel test to obtain the input of static aerodynamic force mathematical model of missile, that is, obtain sample data;Through sample data, solve each coefficient of static aerodynamic force mathematical model of missile, and then obtain the static aerodynamic force mathematical model of missile, that is, generate aerodynamic database;Integrate aerodynamic database into missile dynamics simulation model, for six degree of freedom motion equation solution.The application improves the interpolation accuracy of duck tail rudder layout missile aerodynamic force data by the coefficient of angle of attack and mach number bilinear interpolation, solves the problem of high-precision aerodynamic force data required by the trajectory and control professional full airspace numerical simulation of axisymmetric missile with duck tail rudder three channel full control (XX type).At the same time, the number of wind tunnel tests is reduced, the cost is reduced, the efficiency is improved, and it is environmentally friendly.

Description

Technical Field

[0001] This invention relates to the modeling of aerodynamic mathematical models, specifically to a modeling method and system for aerodynamic mathematical models of a three-channel axisymmetric layout canard rudder. Background Technology

[0002] To evaluate the characteristics of guidance, control, and autopilot, the most suitable aerodynamic characteristics are described in terms of M, H, Φ, Φ. F α Φ δ Pc δ Yc , δ Rc δ Pt δ Yt , and δ Rt The static aerodynamic forces and moments C experienced by the missile throughout its flight range N C A C Z m X m Y and m Z This is a three-dimensional representation of the aforementioned variable functions. These data can be used as part of a full six-degree-of-freedom missile system trajectory simulation. Because sufficient aerodynamic data needs to be accumulated to provide a three-dimensional representation, a large-scale wind tunnel testing or numerical computation plan is required. The method of three-dimensional representation should be carefully considered and used to guide the testing or computation plan. To provide a representation consistent with the data (especially in the most likely flight range) and to minimize computer storage requirements, it is necessary to perform substantive analysis of the data and establish a corresponding format.

[0003] Currently, traditional mathematical model interpolation methods in China all employ linear interpolation. This method requires a large amount of wind tunnel test data to ensure a certain level of accuracy, resulting in long testing cycles, high costs, and poor environmental impact. Furthermore, it faces challenges such as the difficulty of mapping complex control surface efficiency data across different quadrants.

[0004] Patent document CN113505434A discloses a method for manufacturing an axisymmetric aircraft based on an aerodynamic mathematical model, characterized by the following steps: Step 1: Establishing an aerodynamic mathematical model; Step 2: Constructing and simulating the aircraft's flight mechanics, control system, structural system, and electrical system based on the aerodynamic mathematical model, and manufacturing the aircraft based on the simulation results.

[0005] Regarding the aforementioned prior art, the inventors believe that there is still room for improvement in the efficiency, cost, and accuracy of the aerodynamic mathematical model of the above method. Summary of the Invention

[0006] To address the shortcomings of existing technologies, the purpose of this invention is to provide a modeling method and system for aerodynamic mathematical models of a three-channel axisymmetric layout of a canard rudder.

[0007] A modeling method for aerodynamic mathematical model of a three-channel axisymmetric layout of a canard rudder provided by the present invention includes:

[0008] Step S1: Based on the symmetry of the missile's shape, obtain the static aerodynamic mathematical model of the missile;

[0009] Step S2: Obtain the input of the static aerodynamic mathematical model of the missile using wind tunnel testing, i.e., obtain sample data;

[0010] Step S3: Solve the coefficients of the static aerodynamic mathematical model of the missile using the sample data, and then obtain the static aerodynamic mathematical model of the missile, that is, generate the aerodynamic database;

[0011] Step S4: Integrate the aerodynamic database into the missile dynamics simulation model for solving the six-degree-of-freedom motion equations.

[0012] Preferably, step S1 includes: deriving a static aerodynamic mathematical model of the missile based on the mathematical principles of trigonometric function series expansion and the symmetry of the missile's shape.

[0013] Preferably, step S3 includes using a static aerodynamic mathematical model to formulate a corresponding numerical calculation project or a wind tunnel test project, and then obtaining the input of the static aerodynamic mathematical model based on the numerical calculation project or the wind tunnel test project, i.e., obtaining sample data.

[0014] Preferably, the static aerodynamic mathematical model of the missile includes:

[0015] Bilinear interpolation of coefficients between angle of attack and Mach number, for a given M, α Φ have

[0016]

[0017]

[0018] [C A1 C A2 ] T =[1,1] T (C A +Fri(H))

[0019] In the formula, [a ij ],[b ij [ ] is the coefficient matrix, Fri(H) is the frictional resistance obtained through engineering calculation methods, H represents altitude, M represents Mach number, α Φ Indicates the composite angle of attack, CN C Z and C A These represent the static normal force coefficient, static lateral force coefficient, and static axial force coefficient of the projectile's forebody, respectively, m X m Y and m Z X represents the static roll moment coefficient, static yaw moment coefficient, and static pitch moment coefficient of the entire missile, respectively. CM X represents the missile's center of mass. R Representing torque data m Y m Z Reference point, Lr represents the reference length, x j and y j These are defined as a 268-dimensional column vector and a 234-dimensional column vector, respectively, where O, X, Y, and Z represent the axis of revolution.

[0020] Preferably, the defined 268-dimensional column vector and 234-dimensional column vector include:

[0021] Define a 268-dimensional column vector x = [x1, x2, ..., xn] 268 ] T And a 234-dimensional column vector y = [y1, y2, ... y 234 ] T

[0022] Each column vector is defined based on the airflow roll angle, tail rudder pitch angle, tail rudder yaw angle, tail rudder aileron angle, canard pitch angle, canard yaw angle, and canard aileron angle.

[0023] A modeling system for aerodynamic mathematical modeling of a three-channel axisymmetric layout of a canard rudder, provided by the present invention, includes:

[0024] Module M1: Based on the symmetry of the missile's shape, obtain the static aerodynamic mathematical model of the missile;

[0025] Module M2: Obtains the input of the static aerodynamic mathematical model of the missile using wind tunnel testing, i.e., obtains sample data;

[0026] Module M3: Solve the coefficients of the static aerodynamic mathematical model of the missile using the sample data, and then obtain the static aerodynamic mathematical model of the missile, that is, generate the aerodynamic database;

[0027] Module M4: Integrates the aerodynamic database into the missile dynamics simulation model for solving the six-degree-of-freedom motion equations.

[0028] Preferably, module M1 includes: a static aerodynamic mathematical model of the missile derived based on the mathematical principles of trigonometric function series expansion and the symmetry of the missile's shape.

[0029] Preferably, module M3 includes developing corresponding numerical calculation projects or wind tunnel test projects using a static aerodynamic mathematical model, and then obtaining the input of the static aerodynamic mathematical model based on the numerical calculation projects or the wind tunnel test projects, i.e., obtaining sample data.

[0030] Preferably, the static aerodynamic mathematical model of the missile includes:

[0031] Bilinear interpolation of coefficients between angle of attack and Mach number, for a given M, α Φ have

[0032]

[0033]

[0034] [C A1 C A2 ] T =[1,1] T (C A +Fri(H))

[0035] In the formula, [a ij ],[b ij [ ] is the coefficient matrix, Fri(H) is the frictional resistance obtained through an engineering calculation system, H represents altitude, M represents Mach number, α Φ Indicates the composite angle of attack, C N C Z and C A These represent the static normal force coefficient, static lateral force coefficient, and static axial force coefficient of the projectile's forebody, respectively, m X m Y and m Z X represents the static roll moment coefficient, static yaw moment coefficient, and static pitch moment coefficient of the entire missile, respectively. CM X represents the missile's center of mass. R Representing torque data m Y m Z Reference point, Lr represents the reference length, x j and y j These are defined as a 268-dimensional column vector and a 234-dimensional column vector, respectively, where O, X, Y, and Z represent the axis of revolution.

[0036] Preferably, the defined 268-dimensional column vector and 234-dimensional column vector include:

[0037] Define a 268-dimensional column vector x = [x1, x2, ..., x268]T and a 234-dimensional column vector y = [y1, y2, ..., y234]T.

[0038] Each column vector is defined based on the airflow roll angle, tail rudder pitch angle, tail rudder yaw angle, tail rudder aileron angle, canard pitch angle, canard yaw angle, and canard aileron angle.

[0039] Compared with the prior art, the present invention has the following beneficial effects:

[0040] 1. This invention improves the interpolation accuracy of aerodynamic data for canard-fin missiles and solves the problem of high-precision aerodynamic data required for full-space numerical simulation of the trajectory and control of axisymmetric missiles with three-channel full control (XX type).

[0041] 2. Compared with other interpolation methods, this invention reduces the number of wind tunnel tests while ensuring accuracy, lowering costs and increasing efficiency, and is environmentally friendly. Furthermore, it solves the problems of static aerodynamic simulation of a canard-finned three-channel fully controlled (XX-type) axisymmetric missile and mapping complex control surface efficiency data across different quadrants.

[0042] 3. Based on experimental data, this invention programs and establishes a dynamic library of three-dimensional static aerodynamic interpolation for canard rudder three-channel fully controlled (XX type) axisymmetric missiles for use by relevant professionals. Some items are omitted to construct new aerodynamic models to meet the needs of different design stages. Attached Figure Description

[0043] Other features, objects, and advantages of the present invention will become more apparent from the following detailed description of non-limiting embodiments with reference to the accompanying drawings:

[0044] Figure 1 A schematic diagram illustrating the modeling method for the aerodynamic mathematical model of a three-channel axisymmetric layout of a ducktail rudder.

[0045] Figure 2 This is a schematic diagram illustrating the definition of the coordinate system and the canard deflection angle in this invention.

[0046] Figure 3 This is a schematic diagram illustrating the definition of the coordinate system and the tail rudder deflection angle in this invention. Detailed Implementation

[0047] The present invention 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 invention, but do not limit the invention in any way. It should be noted that those skilled in the art can make several changes and improvements without departing from the concept of the present invention. These all fall within the protection scope of the present invention.

[0048] Starting from the fundamental theory of aerodynamics, this invention uses Taylor and Fourier multiple hybrid series expansion techniques to derive a three-dimensional static aerodynamic mathematical model of the canard rudder three-channel fully controlled (XX type) axisymmetric missile layout that meets accuracy requirements, saves wind tunnel testing costs, and shortens the cycle.

[0049] The mathematical model established in this invention can analyze missile performance across the entire flight range, not just near the trim point. Six-degree-of-freedom ballistic simulations using this mathematical model can be used to calculate missile performance against maneuvering targets, recalculate the flight trajectory based on missile parameters measured from the launch platform, check flight conditions, and troubleshoot malfunctions.

[0050] Example 1

[0051] The present invention provides a modeling method for aerodynamic mathematical models of a three-channel axisymmetric layout of a canard rudder, such as... Figure 1 As shown, it includes:

[0052] Step S1: Based on the symmetry of the missile's shape, obtain the static aerodynamic mathematical model of the missile. Specifically, this includes deriving the static aerodynamic mathematical model of the missile based on the mathematical principles of trigonometric function series expansion and the symmetry of the missile's shape.

[0053] Step S2: Obtain the input to the static aerodynamic mathematical model of the missile using wind tunnel testing, i.e., obtain sample data. Specifically, this includes using the static aerodynamic mathematical model to formulate corresponding numerical calculation projects or wind tunnel test projects, and then obtaining the input to the static aerodynamic mathematical model based on the numerical calculation projects or the wind tunnel test projects, i.e., obtaining sample data.

[0054] The tests include full-body shape force measurement items and axisymmetric shape full-body force measurement items. Table 1 shows the full-body shape force measurement items, and Table 2 shows the axisymmetric shape full-body force measurement items. The subscript `max` indicates the maximum value, `Φ` represents the airflow roll angle, and `δ`... Pt δ Yt and δ Rt These represent the tail rudder pitch deflection, tail rudder yaw deflection, and tail rudder aileron deflection, respectively. δ Pc δ Yc and δ Rc These represent the canard pitch angle, canard yaw angle, and canard aileron angle, respectively.

[0055] Table 1. Force Measurement Items for the Overall Projectile Shape Test

[0056] Φ <![CDATA[δ P× ]]> <![CDATA[δ Y× ]]> <![CDATA[δ R× ]]> <![CDATA[δ P+ ]]> <![CDATA[δ Y+ ]]> <![CDATA[δ R+ ]]> 1 112.5 0 0 0 0 0 0 2 135 0 0 0 0 0 0 3 157.5 0 0 0 0 0 0 4 180 0 0 0 0 0 0 5 202.5 0 0 0 0 0 0 6 225 0 0 0 0 0 0 7 0 0 0 0 0 0 0 8 22.5 0 0 0 0 0 0 9 45 0 0 0 0 0 0

[0057] Table 2. Items for the All-Armor Force Measurement Test of Axisymmetric Shape

[0058]

[0059]

[0060]

[0061]

[0062]

[0063]

[0064]

[0065]

[0066] Step S3: Solve the coefficients of the static aerodynamic mathematical model of the missile using the sample data, and then obtain the static aerodynamic mathematical model of the missile, that is, generate the aerodynamic database.

[0067] Step S4: Integrate the aerodynamic database into the missile dynamics simulation model for solving the six-degree-of-freedom motion equations.

[0068] Specifically, such as Figure 2 and Figure 3 As shown, the obtained static aerodynamic mathematical model of the missile includes:

[0069] Bilinear interpolation of coefficients between angle of attack and Mach number, for a given M, α Φ have,

[0070]

[0071]

[0072] [C A1 C A2 ] T =[1,1] T (C A +Fri(H))

[0073] In the formula, [a ij ],[b ij [ ] is the coefficient matrix, Fri(H) is the frictional resistance obtained through engineering calculation methods, H represents altitude in kilometers, M represents Mach number, α Φ The angle of attack is the angle between the velocity vector and the OX axis. N C Z and C A These represent the static normal force coefficient, static lateral force coefficient, and static axial force coefficient of the projectile's forebody, respectively, mX m Y and m Z X represents the static roll moment coefficient, static yaw moment coefficient, and static pitch moment coefficient of the entire missile, respectively. CM X represents the missile's center of mass, in meters. R Representing torque data m Y m Z Reference point, in meters; Lr represents reference length, typically the missile length, in meters; x j and y j These are defined as a 268-dimensional column vector and a 234-dimensional column vector, respectively, where O, X, Y, and Z represent the axis of revolution.

[0074] Furthermore, the defined 268-dimensional column vector and 234-dimensional column vector include:

[0075] Define a 268-dimensional column vector x = [x1, x2, ..., xn] 268 ] T And a 234-dimensional column vector y = [y1, y2, ... y 234 ] T

[0076] in,

[0077] x1=1, x2=cos4Φ, x3=cos8Φ, x4=δ Yt cosΦ+δ Pt sinΦ, x7=δ Yt δ Pt sin2Φ, x 23 =δ Rt (δ Pt cosΦ-δ Yt sinΦ), x 36 =δ Yc cosΦ+δ Pc sinΦ, x 39 =δ Yc δ Pc sin2Φ, x55 =d Rc (d Pc cosΦ-δ Yc sinΦ), x 68 =(δ Yt cosΦ+δ Pt sinΦ)(δ Yc cosΦ+δ Pc sinΦ), x 73 =(δ Pt cosΦ-δ Yt sinΦ)(δ Pc cosΦ-δ Yc sinΦ), x 92 =d Rt d Rc ,x 93 =d Rt d Rc cos4Φ, x 105 =d Rt (d Pt cosΦ-δ Yt sinΦ)δ Rc (d Pc cosΦ-δ Yc sinΦ),

[0078]

[0079]

[0080]

[0081]

[0082]

[0083]

[0084]

[0085]

[0086]

[0087]

[0088]

[0089]

[0090]

[0091]

[0092]

[0093]

[0094]

[0095]

[0096]

[0097]

[0098]

[0099]

[0100]

[0101]

[0102]

[0103]

[0104]

[0105]

[0106]

[0107]

[0108]

[0109]

[0110]

[0111]

[0112]

[0113]

[0114]

[0115]

[0116] x 199 =d Rc (d Pt cosΦ-δ Yt sinΦ), x 231 =d Rt (d Pc cosΦ-δ Yc sinΦ), x260 =cosΦ+sinΦ,x 261 =sin2Φ,x 262 =cos3Φ-sin3Φ,x 263 =cos5Φ+sin5Φ,x 264 =sin6Φ,x 265 =cos7Φ-sin7Φ,x 266 =1, x 267 =cos4Φ,x 268 =cos8Φ;y1=sin4Φ,y2=δ Pt cosΦ-δ Yt sinΦ, y6=δ Rt ,y7=δ Rt cos4Φ, y 10 =d Rt (d Yt cosΦ+δ Pt sinΦ), y 16 =d Rt d Yt d Pt sin2Φ, y 26 =d Pc cosΦ-δ Yc sinΦ, y 30 =d Rc ,y 31 =d Rc cos4Φ, y 34 =d Rc (d Yc cosΦ+δ Pc sinΦ), y 40 =d Rc d Yc d Pc sin2Φ,

[0117]

[0118]

[0119]

[0120]

[0121]

[0122]

[0123]

[0124]

[0125]

[0126]

[0127]

[0128]

[0129]

[0130]

[0131]

[0132]

[0133]

[0134]

[0135]

[0136] y 103 =d Rt (d Pt cosΦ-δ Yt sinΦ)(δ Pc cosΦ-δ Yc sinΦ), y 130 =(δ Yt cosΦ+δ Pt sinΦ)δ Rc (d Yc cosΦ+δ Pc sinΦ), y 135 =(δ Pt cosΦ-δ Yt sinΦ)δ Rc (d Pc cosΦ-δ Yc sinΦ),

[0137]

[0138]

[0139]

[0140]

[0141]

[0142]

[0143]

[0144]

[0145]

[0146]

[0147]

[0148] y 162=δ Rc (δ Yt cosΦ+δ Pt sinΦ),

[0149]

[0150]

[0151]

[0152]

[0153] y 194 =δ Rt (δ Yc cosΦ+δ Pc sinΦ), y 200 =δ Rt δ Yc δ Pc sin2Φ, y 226 =sinΦ - cosΦ, y 227 =cos2Φ, y 228 =sin3Φ + cos3Φ, y 229 =sin5Φ - cos5Φ, y 230 =cos6Φ,y 231 =sin7Φ + cos7Φ, y 232 =1, y 233 =cosΦ + sinΦ, y 234 =sin4Φ;

[0154] In the formula, Φ represents the airflow roll angle, and δ Pt δ Yt and δ Rt These represent the tail rudder pitch deflection, tail rudder yaw deflection, and tail rudder aileron deflection, respectively. δ Pc δ Yc and δ RcThese represent the canard pitch deflection, canard yaw deflection, and canard aileron deflection, respectively. Specifically, as... Figure 2 and Figure 3 As shown, the rotating body axis system is OXYZ, with the origin O being the theoretical apex of the head. The positive X-axis points along the body axis towards the incoming flow, the positive Y-axis points in the direction of the projection of the incoming flow velocity onto the cross-section of the projectile, and the positive Z-axis is determined according to the right-hand rule.

[0155] This invention performs necessary numerical calculations based on the characteristics of the model, and programs a dynamic library of three-dimensional static aerodynamic interpolation for canard-finned three-channel fully controlled (Type XX) axisymmetric missiles, available for use by relevant professionals, based on experimental data. Some items can be omitted to construct new aerodynamic models to meet the needs of different design stages. This invention can be applied to canard-finned three-channel fully controlled (Type XX) axisymmetric high-maneuverability missiles.

[0156] Example 2

[0157] This invention also provides a modeling system for aerodynamic mathematical models of a three-channel axisymmetric layout of a canard rudder. Those skilled in the art can implement the modeling system for aerodynamic mathematical models of a three-channel axisymmetric layout of a canard rudder by executing the steps of the modeling method for the aerodynamic mathematical models of a three-channel axisymmetric layout of a canard rudder. That is, the modeling method for the aerodynamic mathematical models of a three-channel axisymmetric layout of a canard rudder can be understood as a preferred embodiment of the modeling system for the aerodynamic mathematical models of a three-channel axisymmetric layout of a canard rudder.

[0158] A modeling system for aerodynamic mathematical modeling of a three-channel axisymmetric layout of a canard rudder, provided by the present invention, includes:

[0159] Module M1: Based on the symmetry of the missile's shape, derive the static aerodynamic mathematical model of the missile. This includes: deriving the static aerodynamic mathematical model of the missile based on the mathematical principles of trigonometric function series expansion and the symmetry of the missile's shape.

[0160] Module M2: Obtains input to the static aerodynamic mathematical model of the missile using wind tunnel testing, i.e., obtains sample data. This includes developing corresponding numerical calculation projects or wind tunnel test projects using the static aerodynamic mathematical model, and then obtaining the input to the static aerodynamic mathematical model based on the numerical calculation projects or the wind tunnel test projects, i.e., obtaining sample data.

[0161] Module M3: Solve for the coefficients of the missile's static aerodynamic mathematical model using the sample data, thereby obtaining the missile's static aerodynamic mathematical model, i.e., generating the aerodynamic database. The missile's static aerodynamic mathematical model includes:

[0162] Bilinear interpolation of coefficients between angle of attack and Mach number, for a given M, α Φhave

[0163]

[0164]

[0165] [C A1 C A2 ] T =[1,1] T (C A +Fri(H))

[0166] In the formula, [a ij ],[b ij [ ] is the coefficient matrix, Fri(H) is the frictional resistance obtained through an engineering calculation system, H represents altitude, M represents Mach number, α Φ Indicates the composite angle of attack, C N C Z and C A These represent the static normal force coefficient, static lateral force coefficient, and static axial force coefficient of the projectile's forebody, respectively, m X m Y and m Z X represents the static roll moment coefficient, static yaw moment coefficient, and static pitch moment coefficient of the entire missile, respectively. CM X represents the missile's center of mass. R Representing torque data m Y m Z Reference point, Lr represents the reference length, x j and y j These are defined as a 268-dimensional column vector and a 234-dimensional column vector, respectively, where O, X, Y, and Z represent the axis of revolution.

[0167] Specifically, a 268-dimensional column vector x = [x1, x2, ..., xx] is defined. 68 ] T And a 234-dimensional column vector y = [y1, y2, ... y 234 ] T Each column vector is defined based on the airflow roll angle, tail rudder pitch angle, tail rudder yaw angle, tail rudder aileron angle, canard pitch angle, canard yaw angle, and canard aileron angle.

[0168] Module M4: Integrates the aerodynamic database into the missile dynamics simulation model for solving the six-degree-of-freedom motion equations.

[0169] Those skilled in the art will understand that, in addition to implementing the system, apparatus, and their modules provided by this invention in purely computer-readable program code, the same program can be implemented in the form of logic gates, switches, application-specific integrated circuits, programmable logic controllers, and embedded microcontrollers by logically programming the method steps. Therefore, the system, apparatus, and their modules provided by this invention can be considered a hardware component, and the modules included therein for implementing various programs can also be considered structures within the hardware component; alternatively, modules for implementing various functions can be considered both software programs implementing the method and structures within the hardware component.

[0170] Specific embodiments of the present invention have been described above. It should be understood that the present invention is not limited to the specific embodiments described above, and those skilled in the art can make various changes or modifications within the scope of the claims, which do not affect the essence of the present invention. Unless otherwise specified, the embodiments and features described in this application can be arbitrarily combined with each other.

Claims

1. A modeling method for the aerodynamic mathematical model of a three-channel axisymmetric layout of a canard rudder, characterized in that, include: Step S1: Based on the symmetry of the missile's shape, obtain the static aerodynamic mathematical model of the missile; Step S2: Obtain the input of the static aerodynamic mathematical model of the missile using wind tunnel testing, i.e., obtain sample data; Step S3: Solve the coefficients of the static aerodynamic mathematical model of the missile using the sample data, and then obtain the static aerodynamic mathematical model of the missile, that is, generate the aerodynamic database; Step S4: Integrate the aerodynamic database into the missile dynamics simulation model for solving the six-degree-of-freedom motion equations; The static aerodynamic mathematical model of the missile includes: Bilinear interpolation of coefficients between angle of attack and Mach number, for a given , have In the formula, , The coefficient matrix, The frictional resistance is obtained through engineering calculations, where H represents altitude and M represents Mach number. Indicates the composite angle of attack. , and These represent the static normal force coefficient, static lateral force coefficient, and static axial force coefficient of the projectile's forebody, respectively. and These represent the static roll moment coefficient, static yaw moment coefficient, and static pitch moment coefficient of the entire missile, respectively. Indicates the missile's center of gravity. Representing torque data , Reference point Indicates the reference length. and These are defined as a 268-dimensional column vector and a 234-dimensional column vector, respectively, where O, X, Y, and Z represent the axis of revolution.

2. The modeling method for the aerodynamic mathematical model of the three-channel axisymmetric layout of the canard rudder according to claim 1, characterized in that, Step S1 includes: deriving the static aerodynamic mathematical model of the missile based on the mathematical principle of trigonometric function series expansion and the symmetry of the missile's shape.

3. The modeling method for the aerodynamic mathematical model of the three-channel axisymmetric layout of the canard rudder according to claim 1, characterized in that, Step S2 includes using a static aerodynamic mathematical model to formulate corresponding numerical calculation projects or wind tunnel test projects, and then obtaining the input of the static aerodynamic mathematical model based on the numerical calculation projects or the wind tunnel test projects, i.e., obtaining sample data.

4. The modeling method for the aerodynamic mathematical model of the three-channel axisymmetric layout of the canard rudder according to claim 1, characterized in that, The defined 268-dimensional column vector and 234-dimensional column vector include: Define a 268-dimensional column vector and a 234-dimensional column vector in, , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , ， ， ， ， ， ， ， ， ， ， ， ， ， ， ， ， ， ， ， ， ， ， ， ， ， , , , , , , ， , , , , , , , , , , , ， ， ， ， ， ， ， ， ， ， ， ， ， ， ， ， ， , , , ， , , , , , , , , , , , ， ， ， ， ， ， ， ， ， ， ， ， ， ， ， ， ， , , , ， , , , , , , , , , , , ， ， ， ， ， ， ， ， ， ， ， ， ， ， ， ， ， ， ， ， ， ， ， ， ， ， ， ， ， ， ， ， ， ， ， ， ， ， ， ， ， ， ， ， ， ， ， ， ， ， ， ， ， ， ， ， ， ， ， ， ， ， ， ， ， ， ， ， ， ， ， ， ， ， ， ， ， ， ， ， ， ， ， ， ， ， ， ， ， ； ， ， ， ， ， ， ， ， ， ， ， ， ， ， ， ， ， ， ， ， ， ， ， ， ， ， ， ， ， ， ， ， ， ， ， ， ， ， ， ， ， ， ， ， ， ， ， ， ， ， ， ， ， ， ， ， ， ， ， ， ， ， , , , , , , ， , , , , , , , , , , , ， ， ， ， ， ， ， ， ， ， ， ， ， ， ， ， ， , , , ， , , , , , , , , , , , ， ， ， ， ， ， ， ， ， ， ， ， ， ， ， ， ， , , , ， , , , , , , , , , , , ， ， ， ， ， ， ， ， ， ， ， ， ， ， ， ， ， ， ， ， ， ， ， ， ， ， ， ， ， ， ， ， ， ， ， ， ， ， ， ， ， ， ， ， ， ， ， ， ， ， ， ， ， ， ， ， ， ， ， ， ， ， ， ， ， ， ， ， ， ， ， ， ， ， ， ， ， ， ， ， ， , , , , , , , , ； In the formula, Indicates the airflow roll angle. , and These represent the tail rudder pitch deflection, tail rudder yaw deflection, and tail rudder aileron deflection, respectively. and These represent the canard pitch angle, canard yaw angle, and canard aileron angle, respectively.

5. A modeling system for aerodynamic mathematical models of a three-channel axisymmetric layout of a canard rudder, characterized in that, include: Module M1: Based on the symmetry of the missile's shape, obtain the static aerodynamic mathematical model of the missile; Module M2: Obtains the input of the static aerodynamic mathematical model of the missile using wind tunnel testing, i.e., obtains sample data; Module M3: Solve the coefficients of the static aerodynamic mathematical model of the missile using the sample data, and then obtain the static aerodynamic mathematical model of the missile, that is, generate the aerodynamic database; Module M4: Integrates the aerodynamic database into the missile dynamics simulation model for solving the six-degree-of-freedom equations of motion; The static aerodynamic mathematical model of the missile includes: Bilinear interpolation of coefficients between angle of attack and Mach number, for a given , have In the formula, , The coefficient matrix, The frictional resistance is obtained through an engineering calculation system, where H represents altitude and M represents Mach number. Indicates the composite angle of attack. , and These represent the static normal force coefficient, static lateral force coefficient, and static axial force coefficient of the projectile's forebody, respectively. and These represent the static roll moment coefficient, static yaw moment coefficient, and static pitch moment coefficient of the entire missile, respectively. Indicates the missile's center of gravity. Representing torque data , Reference point Indicates the reference length. and These are defined as a 268-dimensional column vector and a 234-dimensional column vector, respectively, where O, X, Y, and Z represent the axis of revolution.

6. The modeling system for the aerodynamic mathematical model of the three-channel axisymmetric layout of the canard rudder according to claim 5, characterized in that, Module M1 includes: a mathematical model of the static aerodynamics of the missile derived from the mathematical principles of trigonometric function series expansion and the symmetry of the missile's shape.

7. The modeling system for the aerodynamic mathematical model of the three-channel axisymmetric layout of the canard rudder according to claim 5, characterized in that, Module M2 includes developing corresponding numerical calculation projects or wind tunnel test projects using a static aerodynamic mathematical model, and then obtaining the input of the static aerodynamic mathematical model based on the numerical calculation project or the wind tunnel test project, i.e., obtaining sample data.

8. The modeling system for the aerodynamic mathematical model of the three-channel axisymmetric layout of the canard rudder according to claim 5, characterized in that, The defined 268-dimensional column vector and 234-dimensional column vector include: Define a 268-dimensional column vector and a 234-dimensional column vector in, , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , ， ， ， ， ， ， ， ， ， ， ， ， ， ， ， ， ， ， ， ， ， ， ， ， ， , , , , , , ， , , , , , , , , , , , ， ， ， ， ， ， ， ， ， ， ， ， ， ， ， ， ， , , , ， , , , , , , , , , , , ， ， ， ， ， ， ， ， ， ， ， ， ， ， ， ， ， , , , ， , , , , , , , , , , , ， ， ， ， ， ， ， ， ， ， ， ， ， ， ， ， ， ， ， ， ， ， ， ， ， ， ， ， ， ， ， ， ， ， ， ， ， ， ， ， ， ， ， ， ， ， ， ， ， ， ， ， ， ， ， ， ， ， ， ， ， ， ， ， ， ， ， ， ， ， ， ， ， ， ， ， ， ， ， ， ， ， ， ， ， ， ， ， ， ； ， ， ， ， ， ， ， ， ， ， ， ， ， ， ， ， ， ， ， ， ， ， ， ， ， ， ， ， ， ， ， ， ， ， ， ， ， ， ， ， ， ， ， ， ， ， ， ， ， ， ， ， ， ， ， ， ， ， ， ， ， ， , , , , , , ， , , , , , , , , , , , ， ， ， ， ， ， ， ， ， ， ， ， ， ， ， ， ， , , , ， , , , , , , , , , , , ， ， ， ， ， ， ， ， ， ， ， ， ， ， ， ， ， , , , ， , , , , , , , , , , , ， ， ， ， ， ， ， ， ， ， ， ， ， ， ， ， ， ， ， ， ， ， ， ， ， ， ， ， ， ， ， ， ， ， ， ， ， ， ， ， ， ， ， ， ， ， ， ， ， ， ， ， ， ， ， ， ， ， ， ， ， ， ， ， ， ， ， ， ， ， ， ， ， ， ， ， ， ， ， ， ， , , , , , , , , ； In the formula, Indicates the airflow roll angle. , and These represent the tail rudder pitch deflection, tail rudder yaw deflection, and tail rudder aileron deflection, respectively. and These represent the canard pitch angle, canard yaw angle, and canard aileron angle, respectively.

Images