Dynamic modeling and analysis method for gull-wing morphing aircraft

Abstract

The invention discloses a dynamic modeling and analysis method for a gull-wing morphing aircraft in the technical field of flight system control. The dynamic modeling and analysis method comprises the following steps: S1, calculating aerodynamic force and torque borne by the aircraft according to a three-dimensional lift line theory; s2, establishing a multi-body dynamic model through a quasi-Lagrange equation; s3, analyzing the aerodynamic characteristics of the aircraft according to the calculation result of the experiment; s4, analyzing the kinematics characteristics of the aircraft according to the calculation result of the experiment; and S5, adjusting the wing configuration according to the analysis result, so that the aircraft keeps stable flight. The method solves the problem that a traditional variant aircraft is not matched in performance at different flight stages, especially is large in lift force loss under the low-speed condition.

Description

Technical Field

[0001] The invention relates to the technical field of flight system control, and in particular to a dynamics modeling and motion characteristics research scheme for a gull-wing variant aircraft. Background Art

[0002] Traditional transformable aircraft have performance mismatches in different flight phases, especially large lift losses at low speeds; the gull-wing transformable aircraft, with its unique large aspect ratio wing design, can adapt to different environments and mission requirements by adjusting the wing shape or structure during flight, thereby improving the aircraft's lift-to-drag ratio and fuel efficiency and extending its flight time; at the same time, the aircraft can adjust the folding angle of the wings in sections according to different flight phases (such as takeoff, cruising, and landing) to improve aerodynamic efficiency and flight stability; in addition, its versatile flight modes enable the aircraft to flexibly switch when performing reconnaissance or strike missions, greatly improving its ability to complete flight missions.

[0003] The present invention proposes a scheme for dynamic modeling and motion characteristics research of a gull-wing variant aircraft; the structure adopts quasi-Lagrangian equations to establish a nonlinear multi-body dynamic model that fully describes the motion characteristics of the folding wing as a whole and each unit wing, and uses three-dimensional lift line theory to respectively calculate the relevant aerodynamic forces and moments of the aircraft; the results show that when flying at a low angle of attack, the lift-to-drag ratio of the aircraft is relatively large, the longitudinal stability is good, and the flight performance is good at this time; while at a high angle of attack, the lift-to-drag ratio of the aircraft becomes smaller, the longitudinal stability becomes worse, and the aircraft is at risk of stalling. Summary of the invention

[0004] In view of the deficiencies in the prior art, the present invention provides a dynamic modeling and analysis method for a gull-wing variant aircraft to solve the problem of performance mismatch of traditional variant aircraft in different flight stages, especially large lift loss at low speeds. Compared with traditional variant aircraft such as variable-sweep aircraft, which perform well at high-speed cruising but cannot effectively reduce induced drag at low-speed flight, the gull-wing variant aircraft reduces the lift loss of the aircraft due to its unique airfoil design; at the same time, when facing a more complex and changeable flight environment, the variable-sweep wing aircraft is prone to greater aerodynamic interference due to the large changes in the wing surface, while the gull-wing shape can better disperse pressure changes and reduce the impact of flow field disturbances on lift.

[0005] The object of the present invention is achieved by: a dynamic modeling and analysis method of a gull-wing morphing aircraft, comprising the following steps:

[0006] S1. Calculate the aerodynamic force and moment of the aircraft according to the three-dimensional lift line theory;

[0007] S2. Establish a multi-body dynamics model through the quasi-Lagrangian equation;

[0008] S3. Analyze the aerodynamic characteristics of the aircraft based on the experimental calculation results;

[0009] S4. Analyze the kinematic characteristics of the aircraft based on the experimental calculation results;

[0010] S5. Adjust the wing configuration based on the analysis results to ensure that the aircraft maintains stable flight.

[0011] Furthermore, in S1, the aerodynamic force and moment acting on the aircraft are calculated according to the three-dimensional lift line theory, including the following steps:

[0012] Consider a variant of a general classical two-dimensional airfoil:

[0013]

[0014] in, is the atmospheric density, is the flight speed, is the relative area of ​​the wing, is the drag on the aircraft. is the lift generated by the entire airfoil. is the pitch moment of the aircraft, is the mean geometric chord length, is the wing span, It represents the chord length along the span of the wing; is the drag coefficient, is the lift coefficient, is the pitching moment coefficient;

[0015] S1.1 Calculate the induced velocity at any point on the wing; assume that the three-dimensional effect and edge effect are not considered, apply the two-dimensional Kutarzhukovsky vortex lift theory to the three-dimensional wing, and then extend the lift line theory to the case of non-planar three-dimensional curved wings; and consider the influence of the attached vortex, combine the finite span wing with horseshoe vortices, and distribute the attached vortices at the 1 / 4 chord line, and be consistent with the deformation of the sweep and the upward inversion. Apply the Biot-Savart theorem to each group of horseshoe vortices, and derive a complete horseshoe vortex consisting of a finite attached vortex and two semi-infinite vortex lines. For any point in space The induced velocity calculation formula is:

[0016]

[0017] in, is the unit vortex strength, is the distance to the vortex center; is the velocity at the vortex point, is the far-field velocity;

[0018] S1.2 Calculate the lift acting on the aircraft;

[0019] S1.2.1 Calculate the local lift of the aircraft:

[0020]

[0021] in, is the lift at a certain position on the wing, is the free flow speed, is the circulation at a certain position on the wing, is the spanwise coordinate of the wing;

[0022] Step 1.2.2 Obtain the total lift and moment of the aircraft based on the local lift; integrate the local lift along the span to obtain the total lift:

[0023]

[0024] The total moment is calculated by integrating the distance between the lift application point and the wing reference point, i.e.

[0025]

[0026] in, is the position of the reference point, which is the chord length of the wing ;

[0027] S1.3 Calculate the drag on the aircraft:

[0028]

[0029] in, is the total lift, is the lift efficiency factor, and its value is between 0.85 and 0.95. is the wingspan, is the atmospheric density.

[0030] Furthermore, in S2, a multi-body dynamics model is established and a dynamics equation is constructed by using a quasi-Lagrangian equation, which specifically includes the following steps:

[0031] S2.1 Establish a coordinate system;

[0032] A global coordinate system fixed to the fuselage and a local coordinate system of each unit wing are introduced. The fuselage is named , connecting the main wing and aileron from the fuselage to the right and defined as , The connection point between the main wing and the aileron is named , is the main wing folding angle, is the aileron folding angle. The left and right wings always remain symmetrical. The global coordinate system The origin of the coordinates is located at the center , the coordinate system of the local unit wing The origin of the coordinates is located at the centroid of each unit wing, where the subscript It is a unit wing, namely the main wing and aileron , the inertial coordinate system is ;

[0033] Select the generalized coordinates and calculate the pseudo-velocity; the generalized coordinates of the aircraft are selected as:

[0034]

[0035] The speed is to be selected as:

[0036]

[0037] in, Indicates the fuselage The position vector of the center of mass in the inertial coordinate system, It represents the Euler attitude angle of the fuselage relative to the ground inertial coordinate system. Respectively represent the relative roll angle between each unit wing; is the translation speed of the fuselage in its coordinate system, is the rotation angle of the fuselage in the central coordinate system, is the angular velocity of the angle between the unit wings;

[0038] According to the relationship between the pseudo-velocity and the generalized velocity, the pseudo-velocity of the aircraft is obtained as:

[0039]

[0040] in, is the transformation matrix from the inertial coordinate system to the central coordinate system, is the conversion matrix between Euler angular velocity and body axis angular velocity;

[0041] S2.2 Solve the aerodynamic forces and moments of each unit wing in the local coordinate system; main wing In its local body coordinate system The velocity and angular velocity can be expressed as:

[0042]

[0043] in, is the local body coordinate system From the fuselage Center of mass pointing unit wing The vector of the center of mass, For modules To module The transformation matrix is:

[0044]

[0045] in, is the fold angle of the wing;

[0046] Similarly, we get aileron In the local body coordinate system The velocity and angular velocity can be expressed as:

[0047]

[0048] The local angle of attack and sideslip angle of each unit wing can be expressed as:

[0049]

[0050] The aerodynamic force and moment of each unit wing in the local airflow coordinate system can be expressed as:

[0051]

[0052] Among them, the subscript Indicates each unit wing, namely the main wing and aileron , , , Unit Wing lift, drag, and pitching moment coefficients;

[0053] S2.3 construct the dynamic equations of the multi-body dynamics of the aircraft;

[0054] S2.3.1 Calculate the external forces acting on the aircraft; first calculate the resultant external forces of each unit wing and fuselage in the central coordinate system, which can be expressed as:

[0055]

[0056] in, is the weight of each cabin or unit wing in the inertial system; Indicates unit wing aerodynamic forces in its local body coordinate system; Represented by the coordinate system arrive The coordinate transformation matrix of the central coordinate system is represented by a vector. ;

[0057] S2.3.2 Calculate the total external force and moment acting on the aircraft; total external moment It includes the aerodynamic force, aerodynamic moment and gravity of each unit wing, and its expression is:

[0058]

[0059] In the formula, represents the elevator moment;

[0060] S2.3.3 Calculate the generalized moments of the aircraft; According to the arbitrariness of generalized virtual displacement, it is assumed that the virtual displacement of a certain folding angle is is not zero, while the virtual displacements of other folding angles are all zero. The generalized force is calculated using the principle of virtual work. The center of mass of each unit wing and cabin is expressed in the central coordinate system as , given the folding angle Virtual displacement , and keep the other folding angles unchanged, and define the folding torque on the joint as , then the virtual work The calculation can be expressed as:

[0061]

[0062] Step S2.4: Derive the dynamic equation; Assuming that the system has no potential energy, the Lagrangian only contains kinetic energy, and gravity is treated as an external force, the overall dynamic equation of the folding-wing aircraft can be expressed as follows according to the quasi-Lagrangian equation:

[0063]

[0064] In the formula, Representation vector The antisymmetric matrix of Its physical meaning is: represents the component of the resultant external force in the central coordinate system, Represents the component of the total external moment in the central coordinate system.

[0065] Furthermore, S3 is specifically as follows: under the condition of symmetrical deformation without sideslip, the lateral forces and moments of the left and right unit wings on the center cancel each other out, and the local angle of attack of the unit wing is smaller than the global angle of attack under the deformation condition, so even when the global angle of attack is the stall angle of attack, the aircraft can maintain a good flight state; within the low angle of attack range, the drag is small, the lift is increased, the lift-to-drag ratio increases steadily, and the aircraft is suitable for cruising and stable flight; within the medium angle of attack range, A significant descent occurs, at which time the lift increases significantly, and the negative deflection of the rudder makes it suitable for maneuvering flight; within the high angle of attack range, the drag value is large and the lift-to-drag ratio decreases significantly. At this time, careful operation is required to avoid stalling the aircraft.

[0066] Furthermore, S4 is specifically as follows: in the state matrix obtained by linearization, its eigenvalue reflects the dynamic stability of the system; and under the condition of fixed straight and level flight, the stable configurations at different folding angles are taken as analysis objects.

[0067] Furthermore, based on the final result, it is determined how to adjust the wing configuration of the aircraft in the current flight state so that the aircraft maintains a steady flight state.

[0068] Compared with the prior art, the beneficial effects of the present invention are as follows: the present invention proposes a novel scheme for dynamic modeling and aerodynamic characteristics research of a gull-wing variant aircraft, adopts quasi-Lagrangian equations for multi-body dynamics modeling, combines three-dimensional lift line theory to calculate the aerodynamic force and torque of the aircraft, further optimizes the performance analysis method of the aircraft, and provides new ideas for solving the performance contradictions of variant aircraft in different flight stages, such as insufficient lift during low-speed takeoff and short-distance takeoff and landing. BRIEF DESCRIPTION OF THE DRAWINGS

[0069] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings required for use in the embodiments or the description of the prior art will be briefly introduced below. Obviously, the drawings described below are only embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on the provided drawings without paying creative work.

[0070] Figure 1 The horseshoe vortex of the present invention is distributed in Schematic diagram of the string line.

[0071] Figure 2 It is a schematic diagram of determining the position and direction of the horseshoe vortex and the direction induction of the present invention.

[0072] Figure 3 It is a schematic diagram of the coordinate system of the present invention.

[0073] Figure 4 It is a schematic diagram of the local angle of attack of the present invention under static folding.

[0074] Figure 5 It is a schematic diagram of aerodynamic force and moment under dynamic folding of the present invention.

[0075] Figure 6 Schematic diagram of the drag coefficient of the present invention.

[0076] Figure 7 It is a schematic diagram of the lift coefficient of the present invention.

[0077] Figure 8 It is a schematic diagram of the pitch moment coefficient of the present invention.

[0078] Fig. 9It is a schematic diagram of the modal distribution of the present invention as the folding angle changes. DETAILED DESCRIPTION

[0079] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0080] A research program for dynamic modeling and analysis of a novel gull-wing morphing aircraft includes the following steps:

[0081] Step S1, calculating the aerodynamic force and moment exerted on the aircraft according to the three-dimensional lift line theory; specifically comprising the following steps:

[0082] Consider a general classical two-dimensional wing-shaped variant aircraft

[0083]

[0084] in, is the atmospheric density, is the flight speed, is the relative area of ​​the wing, is the drag on the aircraft. is the lift generated by the entire airfoil. is the pitch moment of the aircraft, is the mean geometric chord length, is the wing span, It represents the chord length along the span of the wing; is the drag coefficient, is the lift coefficient, is the pitching moment coefficient;

[0085] Step S1.1 Calculate the induced velocity at any point on the wing; Assuming that the three-dimensional effect and edge effect are not considered, we apply the two-dimensional Kutarzhukovsky vortex lift theory to the three-dimensional wing, and further extend the lift line theory to the case of non-planar three-dimensional curved wings; and consider the influence of the attached vortex, combine the finite span wing with horseshoe vortices, such as Figure 1 As shown in the figure, the attached vortex is distributed at the 1 / 4 chord line and is consistent with the deformation of the sweep and upward inversion. The position and direction of the horseshoe vortex at this point and the direction induction are determined as follows: Figure 2 As shown, applying Biot-Savart's theorem to each group of horseshoe vortices, the induced velocity at any point is derived as:

[0086]

[0087] in, is the unit vortex strength, is the distance to the vortex center; using the trigonometric relationship:

[0088]

[0089] Equation 2 is converted to:

[0090]

[0091] And because the eddy current velocity is:

[0092]

[0093] in, is the velocity at the vortex point, is the far-field velocity;

[0094] Based on equations (4) and (5), the complete horseshoe vortex consisting of a finite attachment vortex and two semi-infinite vortex lines is derived: For any point in space The induction speed is:

[0095]

[0096] Step 1.2 Calculate the lift on the aircraft;

[0097] Step 1.2.1 Calculate the local lift of the aircraft; based on equation (6) and combined with the Kuttarukovsky theorem:

[0098]

[0099] in, is the lift per unit length, is the fluid density, is the incoming velocity of the fluid;

[0100] Combining equations (1) to (7), the local airflow circulation at each position of the wing is obtained as:

[0101]

[0102] in, is the fluid density, is the fluid velocity, is the spanwise coordinate of the wing, is the lift coefficient of the wing at this angle of attack, is a diagonal array consisting of the chord lengths of the wing segments, is the column vector composed of the geometric angles of attack of the segment; is the aerodynamic influence coefficient matrix, which is used to calculate the induced velocity of each segment;

[0103] Based on formula (8), the local lift at each position of the wing is further obtained as:

[0104]

[0105] in, is the lift at a certain position on the wing, is the free flow speed, is the circulation at a certain position on the wing, is the spanwise coordinate of the wing;

[0106] Step 1.2.2 Obtain the total lift and moment of the aircraft based on the local lift; Based on equation (9), integrate the local lift along the span to obtain the total lift:

[0107]

[0108] The total moment can be calculated by integrating the distance between the lift action point and the wing reference point, i.e.

[0109]

[0110] in, is the location of the reference point, usually the chord length of the wing ;

[0111] Assuming that the aircraft is only affected by induced drag, when the wing generates lift, the pressure difference on both sides of the wing will form wingtip vortices at the trailing edge of the wing. These vortices cause downwash behind the wing. The change in angle of attack caused by this downwash is called the induced angle of attack, recorded as , then the relationship between the induced angle of attack is:

[0112]

[0113] in, is the induced velocity, is the free-flow speed;

[0114] Based on the above analysis, the induced resistance is:

[0115]

[0116] in, is the total lift, is the lift efficiency factor, and its value is usually between 0.85 and 0.95. is the wing span;

[0117] After obtaining the aerodynamic force (including lift and drag) and moment, the drag coefficient is calculated according to formula (1): , lift coefficient and the pitching moment coefficient .

[0118] Step S2, establishing a multi-body dynamics model and constructing a dynamics equation through a quasi-Lagrangian equation; specifically comprising the following steps:

[0119] Step S2.1 Establish a coordinate system, such as Figure 3 As shown in the figure, a global coordinate system fixed to the fuselage and a local coordinate system of each unit wing are introduced. The fuselage is named , connecting the main wing and aileron from the fuselage to the right and defined as , The connection point between the main wing and the aileron is named , is the main wing folding angle, is the aileron folding angle. The left and right wings always remain symmetrical. The global coordinate system The origin of the coordinates is located at the center , the coordinate system of the local unit wing The origin of the coordinates is located at the centroid of each unit wing, where the subscript It is a unit wing, namely the main wing and aileron , the inertial coordinate system is ;

[0120] Select the generalized coordinates and calculate the pseudo-velocity; the generalized coordinates of the aircraft are selected as:

[0121]

[0122] The speed is to be selected as:

[0123]

[0124] in, Indicates the fuselage The position vector of the center of mass in the inertial coordinate system, It represents the Euler attitude angle of the fuselage relative to the ground inertial coordinate system. Respectively represent the relative roll angle between each unit wing;

[0125] is the translation speed of the fuselage in its coordinate system, is the rotation angle of the fuselage in the central coordinate system, is the angular velocity of the angle between the unit wings;

[0126] According to the relationship between the pseudo-velocity and the generalized velocity, the pseudo-velocity of the aircraft is obtained as:

[0127]

[0128] in, is the transformation matrix from the inertial coordinate system to the central coordinate system, is the conversion matrix between Euler angular velocity and body axis angular velocity;

[0129] Step S2.2: Solve the aerodynamic forces and moments of each unit wing in the local coordinate system; main wing In its local body coordinate system The velocity and angular velocity can be expressed as:

[0130]

[0131] in, is the local body coordinate system From the fuselage Center of mass pointing unit wing The vector of the center of mass, For modules To module The transformation matrix:

[0132]

[0133] in, is the fold angle of the wing;

[0134] Similarly, we get aileron In the local body coordinate system The velocity and angular velocity can be expressed as:

[0135]

[0136] The local angle of attack and sideslip angle of each unit wing can be expressed as:

[0137]

[0138] Therefore, the aerodynamic force and moment of each unit wing in the local airflow coordinate system can be expressed as:

[0139]

[0140] Among them, the subscript Indicates each unit wing, namely the main wing and aileron , , , Unit Wing lift, drag, and pitching moment coefficients;

[0141] Step S2.3: Calculate the dynamic equations of the multi-body dynamics of the aircraft;

[0142] Step S2.3.1 Calculate the external forces acting on the aircraft. In addition to gravity, the main forces acting on the gull-wing variant aircraft also include the aerodynamic forces and aerodynamic moments of each unit wing, as well as the folding and unfolding moments on the folding and unfolding mechanism. In order to facilitate the calculation of generalized forces and generalized moments, we first calculate the resultant external forces of each unit wing and the fuselage in the central coordinate system, which can be expressed as:

[0143]

[0144] in, is the weight of each cabin or unit wing in the inertial system; Indicates unit wing aerodynamic forces in its local body coordinate system; Represented by the coordinate system arrive The coordinate transformation matrix of the central coordinate system is represented by a vector.

[0145]

[0146] Step S2.3.2 Calculate the total external force and torque on the aircraft; Total external torque It includes the aerodynamic force, aerodynamic moment and gravity of each unit wing, and its expression is:

[0147]

[0148] In the formula, represents the elevator moment;

[0149] Step S2.3.3: Calculate the generalized moment of the aircraft; According to the arbitrariness of generalized virtual displacement, it is assumed that the virtual displacement of a certain folding angle is is not zero, while the virtual displacements of other folding angles are all zero. The generalized force is calculated using the principle of virtual work. The center of mass of each unit wing and cabin is expressed in the central coordinate system as , given the folding angle Virtual displacement , and keep the other folding angles unchanged, and define the folding torque on the joint as , then the virtual work The calculation can be expressed as:

[0150]

[0151] Step S2.5: Derive the dynamic equation; Assuming that the system has no potential energy, the Lagrangian only contains kinetic energy, and gravity is treated as an external force, the overall dynamic equation of the folding-wing aircraft can be expressed as follows according to the quasi-Lagrangian equation:

[0152]

[0153] In the formula, Representation vector The antisymmetric matrix of Its physical meaning is: represents the component of the resultant external force in the central coordinate system, represents the component of the total external moment in the central coordinate system;

[0154] Step S3, analyze the aerodynamic characteristics of the aircraft according to the experimental calculation results; in the case of symmetrical deformation without sideslip, the lateral forces and moments of the left and right unit wings on the center cancel each other out, and the local angle of attack of the unit wing is Changes such as Figure 4 As shown in the figure, the local angle of attack of the unit wing is smaller than the global angle of attack under the deformation condition, so the aircraft can maintain a good flight state even when the global angle of attack is the stall angle of attack;

[0155] Given Mach number , angle of attack for and , Take both To simulate the flight state, take the deflection angle of the rudder surface as ; And the aircraft control surface has no deflection At this time, the aerodynamic force and torque of the gull-wing variant aircraft are as follows: Figure 5 As shown;

[0156] In order to analyze the aerodynamic characteristics of the gull-wing variant aircraft in more detail, Figures 6 to 8 The drag coefficient is plotted , lift coefficient and the pitching moment coefficient relationship diagram; in the figure The main wing folding angle is , the aileron folding angle is ; Among them, low angle of attack means the angle of attack range is to , the mid-attack angle range is to , the high angle of attack range is above;

[0157] according to Figure 5-Figure 8 The numerical simulation results show that in the low angle of attack range, the drag is small, the lift is increased, the lift-to-drag ratio increases steadily, and the aircraft is suitable for cruising and stable flight; in the medium angle of attack range, A significant descent occurs, at which time the lift increases significantly and the rudder surface deflects negatively. It is suitable for maneuvering flight; in the high angle of attack range, the drag value is large and the lift-to-drag ratio is significantly reduced. At this time, careful operation is required to avoid stalling the aircraft.

[0158] Step S4, analyzing the kinematic characteristics of the aircraft according to the experimental calculation results; comprising the following steps:

[0159] In the linearized state matrix, its eigenvalue reflects the dynamic stability of the system; The stable configurations under different folding angles are taken as the analysis objects under the condition of fixed straight and level flight. The eigenvalue distribution of the state matrix Fig. 9 The specific value distribution is shown in Table 1

[0160]

[0161] Step S5, end the algorithm, and determine based on the final result how to adjust the wing configuration of the aircraft in the current flight state so that the aircraft maintains a steady state of flight.

[0162] The above embodiments are only used to help understand the method and core idea of ​​the present invention. It should be noted that, for those skilled in the art, several improvements and modifications can be made to the present invention without departing from the principles of the present invention, and these improvements and modifications also fall within the scope of protection of the claims of the present invention.

Claims

1. A dynamic modeling and analysis method for a gull-wing morphing aircraft, characterized in that: The following steps are involved: S1. Calculate the aerodynamic force and moment of the aircraft according to the three-dimensional lift line theory; S2. Establish a multi-body dynamics model through the quasi-Lagrangian equation; S3. Analyze the aerodynamic characteristics of the aircraft based on the experimental calculation results; S4. Analyze the kinematic characteristics of the aircraft based on the experimental calculation results; S5. Adjust the wing configuration based on the analysis results to ensure that the aircraft maintains stable flight.

2. The method for dynamic modeling and analysis of a gull-wing morphing aircraft according to claim 1, characterized in that: In S1, the aerodynamic force and moment acting on the aircraft are calculated according to the three-dimensional lift line theory, including the following steps: Consider a variant of a general classical two-dimensional airfoil: in, is the atmospheric density, is the flight speed, is the relative area of ​​the wing, is the drag on the aircraft. is the lift generated by the entire airfoil. is the pitch moment of the aircraft, is the mean geometric chord length, is the wing span, It represents the chord length along the span of the wing; is the drag coefficient, is the lift coefficient, is the pitching moment coefficient; S1.1 Calculate the induced velocity at any point on the wing; assume that the three-dimensional effect and edge effect are not considered, apply the two-dimensional Kutarzhukovsky vortex lift theory to the three-dimensional wing, and then extend the lift line theory to the case of non-planar three-dimensional curved wings; and consider the influence of the attached vortex, combine the finite span wing with horseshoe vortices, and distribute the attached vortices at the 1 / 4 chord line, and be consistent with the deformation of the sweep and the upward inversion. Apply the Biot-Savart theorem to each group of horseshoe vortices, and derive a complete horseshoe vortex consisting of a finite attached vortex and two semi-infinite vortex lines. For any point in space The calculation formula of the induced velocity is: in, is the unit vortex strength, is the distance to the vortex center; is the velocity at the vortex point, is the far-field velocity; S1.2 Calculate the lift acting on the aircraft; S1.2.1 Calculate the local lift of the aircraft: in, is the lift at a certain position on the wing, is the free flow speed, is the circulation at a certain position on the wing, is the spanwise coordinate of the wing; Step 1.2.2 Obtain the total lift and moment of the aircraft based on the local lift; integrate the local lift along the span to obtain the total lift: The total moment is calculated by integrating the distance between the lift application point and the wing reference point, i.e. in, is the position of the reference point, which is the chord length of the wing ; S1.3 Calculate the drag on the aircraft: in, is the total lift, is the lift efficiency factor, and its value is between 0.85 and 0.

95. is the wingspan, is the atmospheric density.

3. The method for dynamic modeling and analysis of a gull-wing morphing aircraft according to claim 2, characterized in that: In S2, a multi-body dynamics model is established and a dynamics equation is constructed by using the quasi-Lagrangian equation, which specifically includes the following steps: S2.1 Establish a coordinate system; A global coordinate system fixed to the fuselage and a local coordinate system of each unit wing are introduced. The fuselage is named , connecting the main wing and aileron from the fuselage to the right and defined as , The connection point between the main wing and the aileron is named , is the main wing folding angle, is the aileron folding angle. The left and right wings always remain symmetrical. The global coordinate system The origin of the coordinates is located at the center , the coordinate system of the local unit wing The origin of the coordinates is located at the centroid of each unit wing, where the subscript It is a unit wing, namely the main wing and aileron , the inertial coordinate system is ; Select the generalized coordinates and calculate the pseudo-velocity; the generalized coordinates of the aircraft are selected as: The speed is to be selected as: in, Indicates the fuselage The position vector of the center of mass in the inertial coordinate system, It represents the Euler attitude angle of the fuselage relative to the ground inertial coordinate system. Respectively represent the relative roll angle between each unit wing; is the translation speed of the fuselage in its coordinate system, is the rotation angle of the fuselage in the central coordinate system, is the angular velocity of the angle between the unit wings; According to the relationship between the pseudo-velocity and the generalized velocity, the pseudo-velocity of the aircraft is obtained as: in, is the transformation matrix from the inertial coordinate system to the central coordinate system, is the conversion matrix between Euler angular velocity and body axis angular velocity; S2.2 Solve the aerodynamic forces and moments of each unit wing in the local coordinate system; main wing In its local body coordinate system The velocity and angular velocity can be expressed as: in, is the local body coordinate system From the fuselage Center of mass pointing unit wing The vector of the center of mass, For modules To module The transformation matrix is: in, is the fold angle of the wing; Similarly, we get aileron In the local body coordinate system The velocity and angular velocity can be expressed as: The local angle of attack and sideslip angle of each unit wing can be expressed as: The aerodynamic force and moment of each unit wing in the local airflow coordinate system can be expressed as: Among them, the subscript Indicates each unit wing, namely the main wing and aileron , , , Unit Wing lift, drag, and pitching moment coefficients; S2.3 construct the dynamic equations of the multi-body dynamics of the aircraft; S2.3.1 Calculate the external forces acting on the aircraft; first calculate the resultant external forces of each unit wing and fuselage in the central coordinate system, which can be expressed as: in, is the weight of each cabin or unit wing in the inertial system; Indicates unit wing aerodynamic forces in its local body coordinate system; Represented by the coordinate system arrive The coordinate transformation matrix of the central coordinate system is represented by a vector. ; S2.3.2 Calculate the total external force and moment acting on the aircraft; total external moment It includes the aerodynamic force, aerodynamic moment and gravity of each unit wing, and its expression is: In the formula, represents the elevator moment; S2.3.3 Calculate the generalized moments of the aircraft; According to the arbitrariness of generalized virtual displacement, it is assumed that the virtual displacement of a certain folding angle is is not zero, while the virtual displacements of other folding angles are all zero. The generalized force is calculated using the principle of virtual work. The center of mass of each unit wing and cabin is expressed in the central coordinate system as , given the folding angle Virtual displacement , and keep the other folding angles unchanged, and define the folding torque on the joint as , then the virtual work The calculation can be expressed as: Step S2.4: Derive the dynamic equation; Assuming that the system has no potential energy, the Lagrangian only contains kinetic energy, and gravity is treated as an external force, the overall dynamic equation of the folding-wing aircraft can be expressed as follows according to the quasi-Lagrangian equation: In the formula, Representation vector The antisymmetric matrix of Its physical meaning is: represents the component of the resultant external force in the central coordinate system, Represents the component of the total external moment in the central coordinate system.

4. The method for dynamic modeling and analysis of a gull-wing morphing aircraft according to claim 3, characterized in that: The S3 is specifically: in the case of symmetrical deformation without sideslip, the lateral forces and moments of the left and right unit wings on the center cancel each other out, and the local angle of attack of the unit wing is smaller than the global angle of attack under the deformation condition, so even when the global angle of attack is the stall angle of attack, the aircraft can maintain a good flight state; in the low angle of attack range, the drag is small, the lift is increased, the lift-to-drag ratio increases steadily, and the aircraft is suitable for cruising and stable flight; in the medium angle of attack range, A significant descent occurs, at which time the lift increases significantly, and the negative deflection of the rudder makes it suitable for maneuvering flight; within the high angle of attack range, the drag value is large and the lift-to-drag ratio decreases significantly. At this time, careful operation is required to avoid stalling the aircraft.

5. The method for dynamic modeling and analysis of a gull-wing morphing aircraft according to claim 4, characterized in that: The S4 is specifically: in the state matrix obtained by linearization, its eigenvalue reflects the dynamic stability of the system; under the condition of fixed straight and level flight, the stable configurations under different folding angles are taken as analysis objects.

6. The method for dynamic modeling and analysis of a gull-wing morphing aircraft according to claim 5, characterized in that: Based on the final result, it is determined how to adjust the wing configuration of the aircraft in the current flight state so that the aircraft maintains a steady state of flight.

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