Dynamic model of fixed-wing aircraft

Abstract

The invention discloses a dynamic model of a fixed-wing aircraft, and relates to the technical field of flight training. Comprising an aircraft mass center kinetic equation of the fixed wing aircraft, a mass center rotation kinetic equation, an aircraft aerodynamic characteristic calculation model, an aircraft kinetic equation resolving model, an abnormal flight state trajectory and attitude inverse solution calculation model and a ski-jump take-off and carrier landing model. Wherein the aircraft aerodynamic characteristic calculation model is used for calculating aerodynamic force and aerodynamic moment of the fixed-wing aircraft; the aircraft kinetic equation resolving model is used for resolving the aircraft mass center kinetic equation and the mass center rotation kinetic equation; the abnormal flight state trajectory and attitude inverse solution calculation model is used for inverse solution calculation of stress and torque of the fixed wing aircraft in an abnormal flight state; and the ski-jump takeoff and carrier landing model is used for solving the carrier landing arresting longitudinal load problem of the fixed-wing aircraft. The technical problems that in the prior art, the flight training process is abstract in theory and large in difficulty are solved.

Description

Technical Field

[0001] This invention relates to the field of flight training technology, specifically to a dynamic model of a fixed-wing aircraft. Background Technology

[0002] Flight Principles is a crucial professional course in the aviation theory education of flight cadets. Based on the fundamental concepts, knowledge, and theories of aerodynamics and flight dynamics, and with the principles of aircraft piloting as its core content, Flight Principles is a specialized course that studies the aerodynamic performance characteristics, flight performance characteristics, and flight control principles of aircraft. The effectiveness of Flight Principles is closely related to the future flying ability of trainees, the quality of flight training, and flight safety.

[0003] The course on the principles of fixed-wing flight covers the aerodynamic characteristics, handling and stability characteristics, flight performance, and the control principles of various flight maneuvers. The course content is systematic, theoretically abstract, and quite challenging, posing a considerable difficulty for beginners without flight experience. However, flight students urgently need to apply this knowledge of flight principles to their practical flight training after arriving at the field. Summary of the Invention

[0004] The purpose of this invention is to provide a dynamic model for a fixed-wing aircraft in order to solve at least one of the above-mentioned technical problems.

[0005] This invention provides a dynamic model of a fixed-wing aircraft, including: the aircraft's center-of-mass dynamic equation, the rotational dynamic equation around the center of mass, a calculation model for the aircraft's aerodynamic characteristics, a model for solving the aircraft's dynamic equations, a calculation model for the trajectory and attitude inverse kinematics of abnormal flight states, and models for ski-jump takeoff and carrier landing; wherein, the aircraft's center-of-mass dynamic equation is the center-of-mass dynamic equation of the body axis system obtained by decomposing Newton's dynamics formulas in the body coordinate system; the rotational dynamic equation around the center of mass includes the rotational dynamics equation of the body axis system obtained by decomposing rotational dynamics formulas in the body coordinate system; the aircraft's aerodynamic characteristics calculation model, a model for solving the aircraft's dynamic equations, a model for calculating the trajectory and attitude in abnormal flight states, and models for ski-jump takeoff and carrier landing; wherein, the aircraft's center-of-mass dynamic equation is the center-of-mass dynamic equation of the body axis system obtained by decomposing rotational dynamics formulas in the body coordinate system; the aircraft's rotational dynamic equation around the center of mass includes the rotational dynamic equation of the body axis system obtained by decomposing rotational dynamics formulas in the body coordinate system; the aircraft's rotational dynamic equation around the center of mass... The aerodynamic characteristic calculation model is used to calculate the aerodynamic forces and aerodynamic moments of the fixed-wing aircraft based on the basic principles of aircraft aerodynamics; the aircraft dynamic equation solving model is used to solve the aircraft's center-of-mass dynamic equation and the rotational dynamic equation around the center-of-mass to obtain the position and attitude parameters of the fixed-wing aircraft; the inverse equation calculation model for abnormal flight trajectory and attitude is used to calculate the forces and moments of the fixed-wing aircraft under abnormal flight conditions by performing inverse equation calculations on trajectory and attitude data; and the ski-jump takeoff and carrier landing model is used to solve the longitudinal load problem of the fixed-wing aircraft during arrested carrier landing.

[0006] Optionally, the aircraft's center-of-gravity dynamic equations include: In the formula, These are the components of flight speed along the three body axes; These represent the components of the aircraft's rotational angular velocity along the three fuselage axes; m is the mass of the fixed-wing aircraft; and Y, Q, Z, and P are the aerodynamic lift, drag, side force, and engine thrust of the fixed-wing aircraft, respectively. These are the angle of attack and sideslip angle of the fixed-wing aircraft, respectively. These are the bank angle, pitch angle, and yaw angle of the fixed-wing aircraft, respectively.

[0007] Optionally, the equations of motion about the center of mass include: In the formula, These are the moments of inertia of the fixed-wing aircraft relative to the three fuselage axes; Let be the product of inertia of the fixed-wing aircraft relative to the x and y axes; These are the components of the aircraft's rotational angular velocity along the three fuselage axes; These are the components of the torque vector acting on the aircraft along the three body axes.

[0008] Optionally, the aerodynamic forces include the aerodynamic lift, drag, and engine thrust of the fixed-wing aircraft; the aerodynamic torques include the control torques and stabilizing torques decomposed to each airframe axis.

[0009] Optionally, the aircraft dynamics equation solution model includes: integrating the aircraft center-of-mass dynamics equation to obtain the components of the aircraft velocity in the body coordinate system, and then integrating again to obtain the position parameters of the fixed-wing aircraft; and solving the rotational dynamics equation around the center of mass based on the quaternion method to obtain the attitude parameters of the fixed-wing aircraft.

[0010] Optionally, the inverse kinematics calculation model for the abnormal flight trajectory and attitude includes: calculating the trajectory angle of the fixed-wing aircraft based on its speed, attitude angle, and aerodynamic angle in the abnormal flight state; the trajectory angle includes pitch angle, yaw angle, and roll angle; constructing a first transformation matrix from the trajectory coordinate system to the ground coordinate system based on the trajectory angle, and constructing a second transformation matrix from the ground coordinate system to the body coordinate system based on the attitude angle; obtaining the velocity components of the fixed-wing aircraft in the body coordinate system based on the aircraft speed, the first transformation matrix, and the second transformation matrix; substituting the velocity components of the body coordinate system into the aircraft's center of mass dynamic equation, and calculating the forces acting on the fixed-wing aircraft in the abnormal flight state through inverse kinematics; substituting the rotational angular velocity of the fixed-wing aircraft in the abnormal flight state into the rotational dynamic equation around the center of mass, and calculating the torque of the fixed-wing aircraft in the abnormal flight state through inverse kinematics.

[0011] Optionally, the ski-jump takeoff and landing model includes: constructing the center-of-mass dynamic equations of the fixed-wing aircraft in the target inertial frame and the center-of-mass rotational dynamic equations in the body coordinate system; constructing the multi-body dynamic equations of the fixed-wing aircraft based on the center-of-mass dynamic equations and the center-of-mass rotational dynamic equations; the multi-body dynamic equations include: the equation of the angular acceleration of the fixed-wing aircraft about the center of mass relative to the target inertial frame in the body coordinate system, and the center-of-mass dynamic equation of the landing gear of the fixed-wing aircraft in the body coordinate system; constructing the longitudinal dynamic equations of the fixed-wing aircraft when it is attached to the landing gear; and substituting the longitudinal dynamic equations into the multi-body dynamic equations to obtain the landing gear motion model of the fixed-wing aircraft.

[0012] Optionally, the equation for the angular acceleration of the fixed-wing aircraft about its center of mass relative to the target inertial frame in the body coordinate system includes: The landing gear dynamic equations of the fixed-wing aircraft in the body coordinate system include: In the formula, This is the aerodynamic torque matrix; Let D be the contact point between the i-th tire and the ramp. i The skew-symmetric matrix form of coordinates in the aircraft body coordinate system. Let i be the mass of the moving part of the landing gear. It is the force matrix of the deck on the landing gear. It is the transformation matrix of the forces exerted by the deck on the landing gear to the fuselage axis system. It is a matrix of rotational angular velocities. These are the forces exerted on the landing gear by the swashplate, the damper force, and the limiting force caused by the piston displacement, respectively. BI It is the skew-symmetric matrix of the aircraft's rotational angular velocity in the inertial frame in the body coordinate system. Here is the rotational angular acceleration matrix of the body coordinate system. Here is the rotational inertia matrix. Let be the acceleration of the aircraft in the body coordinate system, derived from the angular acceleration of rotation in the inertial frame. It is the skew-symmetric matrix of the aircraft in the body coordinate system after its rotational angular acceleration in the inertial frame. Let be the transformation matrix from the swashplate force acting on the landing gear to the fuselage axis coordinate system. This is the skew-symmetric matrix representation of the forces acting on the landing gear from the ramp plate to the coordinates in the body coordinate system. Let be the matrix of gravitational acceleration in the body axis system. It is the body axis coordinate system matrix of the first tire contact point with mass G1. Let be the skew-symmetric matrix of the tire contact point coordinates in the inertial frame within the body coordinate system. This is the transformation matrix from the inertial frame to the body axis.

[0013] Optionally, the longitudinal dynamic equations of the fixed-wing aircraft during carrier landing include: In the formula, m is the mass of the fixed-wing aircraft, s is the forward distance of the aircraft after it is hooked up to the arresting cable, k is the damping coefficient of the arresting cable, l is the deck speed of the arresting cable, and t is time.

[0014] This invention provides a dynamic model for fixed-wing aircraft, establishing and solving a multibody dynamic model system for ski-jump takeoff and carrier landing. In the absence of relevant parameters, it proposes a simple calculation method for the longitudinal load problem of aircraft arresting during carrier landing, and applies this method to determine the damping parameters of the arresting gear. This invention significantly enhances flight trainees' understanding and mastery of aircraft balance, stability, and controllability, takeoff and landing routes, various aerobatic maneuvers, and special situation flight characteristics, effectively ensuring learning outcomes, improving the learning environment, and enhancing teaching quality, thus organically combining theoretical teaching with field flight training. Attached Figure Description

[0015] To more clearly illustrate the technical solutions in the embodiments of this application or the prior art, the drawings used in the description of the specific embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are some embodiments of this application. For those skilled in the art, other drawings can be obtained from these drawings without creative effort.

[0016] Figure 1 A schematic diagram of a fixed-wing aircraft dynamics model provided in an embodiment of the present invention; Figure 2 A schematic diagram of another fixed-wing aircraft dynamics model provided in an embodiment of the present invention; Figure 3 A schematic diagram of a multibody dynamics system provided in this embodiment of the invention; Figure 4 This invention provides a schematic diagram of the force exerted by an arresting cable on an aircraft. Detailed Implementation

[0017] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without creative effort are within the scope of protection of the present invention.

[0018] Figure 1 This is a schematic diagram of a fixed-wing aircraft dynamics model provided by an embodiment of the present invention. Figure 2 This is a schematic diagram of another fixed-wing aircraft dynamics model provided according to an embodiment of the present invention. Figure 1 and Figure 2 As shown, the model includes: the aircraft's center-of-mass dynamics equations, the rotational dynamics equations around the center of mass, the aircraft's aerodynamic characteristics calculation model, the aircraft's dynamics equations solution model, the inverse kinematics calculation model for abnormal flight trajectories and attitudes, and ski-jump takeoff and carrier landing models; among which, The equation of motion of the aircraft's center of mass is the equation of motion of the center of mass of the body axis system obtained by decomposing Newton's dynamic formula in the body coordinate system. The dynamic equations of rotation about the center of mass include the dynamic equations of rotation about the center of mass of the body axis system obtained by decomposing the rotational dynamics formula in the body coordinate system; Aircraft aerodynamic characteristic calculation model, used to calculate the aerodynamic forces and aerodynamic moments of fixed-wing aircraft based on the basic principles of aircraft aerodynamics; Aerodynamic forces include the aerodynamic lift, drag, and engine thrust of a fixed-wing aircraft; aerodynamic moments include the control moments and stabilizing moments distributed to each airframe axis.

[0019] The aircraft dynamics equation solving model is used to solve the aircraft's center-of-mass dynamics equation and rotational dynamics equation around the center of mass, and obtain the position and attitude parameters of the fixed-wing aircraft. An inverse kinematics calculation model for abnormal flight states is used to obtain the forces and moments of a fixed-wing aircraft in abnormal flight states by performing inverse kinematics calculations on trajectory and attitude data. Ski-jump takeoff and landing models are used to solve the longitudinal load problem of arrested landing of fixed-wing aircraft.

[0020] Specifically, the fixed-wing aircraft dynamics model provided in this embodiment of the invention derives the aircraft's center-of-mass dynamics equation by decomposing Newton's most basic dynamics formulas in the body coordinate system, and derives the rotational dynamics equations in the body coordinate system, thus obtaining the rotational dynamics equations of the center-of-mass of the body coordinate system. The aircraft's attitude angles are then calculated using the quaternion method. Establishing and solving the aircraft's motion equations requires determining the aerodynamic forces and moments acting on the aircraft. Aerodynamic forces include lift, drag, and engine thrust, while aerodynamic moments include control moments and stabilizing moments decomposed to each body axis. According to the basic principles of aircraft aerodynamics, the aerodynamic forces and moments on the aircraft are related to the aircraft's airflow angle and velocity. After obtaining the aircraft's angle of attack, sideslip angle, and velocity, the aerodynamic characteristics of the aircraft are calculated using numerical methods to solve the dynamics equations. Real-time numerical calculations of the fixed-wing aircraft's dynamic characteristics are performed, and parameters such as the aircraft's position and attitude are determined through motion relationship calculations and coordinate transformations, providing core data for the entire flight process. For abnormal flight conditions such as stall spins, the forces and moments acting on the aircraft are obtained by inverse kinematics calculations using trajectory and attitude data. For the longitudinal load problem of aircraft arrested landing, corresponding multibody dynamic models for ski-jump takeoff and landing are established and solved.

[0021] Analyzing the motion of an object is inseparable from coordinate systems. First, we define two coordinate systems and corresponding motion variables relevant to this invention: The absolute coordinate system uses the most commonly used ground coordinate system. replace, It is fixedly connected to the ground. The origin is chosen at a certain point on the ground, usually at the initial position of the object's motion; the axis... It is vertically upward; axis Within the horizontal plane, its direction can be arbitrarily chosen, usually based on what is convenient for describing the motion of an object; axis Pointing according to the right-hand rule The right side of the axis direction. The main function of the ground coordinate system is to serve as a reference for measuring the position and orientation of objects. For an object to be displayed correctly in a visual simulation, its position and orientation relative to the visual simulation coordinate system must be determined. The definition of the coordinate system in the visual simulation is similar to that of the ground coordinate system; the ground coordinate system can be transformed into the visual simulation coordinate system through simple coordinate transformations. Body coordinate system It is fixedly connected to the object itself. The origin is at the center of mass of the aircraft; the longitudinal axis is along the structural longitudinal axis of the object and points forward; the vertical axis is generally within the plane of symmetry of the object, perpendicular to the longitudinal axis and points downward; the transverse axis is perpendicular to the plane of symmetry and points to the right.

[0022] Body coordinate system Ground coordinate system The relationship is expressed using three Euler angles or attitude angles. To determine. These are respectively called roll angle, pitch angle, and yaw angle, and their range is as follows: .

[0023] Preferably, a dynamic model for a fixed-wing aircraft is characterized by using the center-of-mass dynamic equation and the center-of-mass rotation dynamic equation as a complete dynamic model and solving them simultaneously. The center-of-mass dynamic equation is derived from Newton's most fundamental formulas for the dynamics of objects. To bring out, to By decomposing the equations in the body coordinate system and deriving and simplifying them, we obtain the dynamic equations of the center of mass of the body axis system: In the above formula, These are the components of flight speed along the three body axes; These are the components of the aircraft's rotational angular velocity along the three fuselage axes; These are the components of the forces acting on the aircraft along the three body axes. The forces acting on the aircraft include aerodynamic lift Y, drag Q, and side force Z, as well as engine thrust P. These forces are decomposed along the three body axes, resulting in the following equations of motion for the aircraft's center of mass: In the above formula, m is the mass of the fixed-wing aircraft. For the aircraft's angle of attack and sideslip angle; These are the aircraft's three attitude angles: bank angle, pitch angle, and yaw angle.

[0024] Specifically, the solution model for aircraft dynamics equations includes: Integrating the aircraft's center of mass dynamics equations yields the components of the aircraft's velocity in the body coordinate system; further integration yields the position parameters of the fixed-wing aircraft. The attitude parameters of a fixed-wing aircraft are obtained by solving the dynamic equations of rotation about the center of mass using the quaternion method.

[0025] Specifically, the body velocity component is converted to the ground velocity component using the following formula.

[0026] Integrating the results gives the aircraft's position relative to the ground coordinate system. ), which is the position parameter.

[0027] The equation of motion for a fixed-wing aircraft about its center of mass is derived from the formula for the dynamics of rotation of an object. Leading out, among which For the angular momentum of the aircraft, This is the total torque vector of external forces on the aircraft. By decomposing the equations in the body coordinate system and deriving and simplifying them, we obtain the dynamic equations for the rotation of the center of mass of the body axis system: In the formula, These are the moments of inertia of a fixed-wing aircraft relative to its three fuselage axes; The product of inertia of a fixed-wing aircraft relative to the x and y axes; These are the components of the aircraft's rotational angular velocity along the three fuselage axes; These are the components of the torque vector acting on the aircraft along the three body axes. Integrating the above equation yields the components of the aircraft's rotational angular velocity in the body coordinate system.

[0028] After obtaining the components of the aircraft's rotational angular velocity in the body coordinate system, the quaternion method is applied to determine the aircraft's attitude angles. However, when using the Euler method to determine the Euler equations for aircraft attitude, singularities appear in the equations at a pitch angle of 90 degrees. An effective way to avoid these singularities is to use the quaternion method in the aircraft's motion equations.

[0029] A system of equations of motion is established within the aircraft's axis system. The solution order using the Euler method is: aircraft velocity → Euler velocity → Euler angles. The solution order using the quaternion method is: aircraft velocity → quaternion velocity → quaternion → direction cosine → Euler angles. The four elements q0, q1, q2, and q3 of the quaternion method are related to the aircraft's bank angle. Pitch angle and yaw angle The relationship is: Solving the torque equation yields the aircraft's speed. The relationship between the speed of the aircraft and the quaternion speed is: In the above formula , , Let be the angular velocity of the aircraft about its body axis. After solving for the quaternion velocity of the aircraft using the above formula, integrate to obtain the quaternion, and then use the following formula to solve for the Euler angles of the aircraft: In the above formula, sgn[] represents the sign of the expression. The initial value of the quaternion is determined after the initial state of the aircraft is set, using the initial values ​​of the Euler angles and the four elements q0, q1, q2, q3, and the aircraft's bank angle. Pitch angle and yaw angle The relationship formula is used to determine this.

[0030] To solve the equations of motion for an aircraft, it is necessary to determine the aerodynamic forces and moments acting on the aircraft. Aerodynamic forces include lift, drag, and engine thrust; aerodynamic moments include control moments and stabilizing moments distributed to the various axes of the aircraft. According to the basic principles of aircraft aerodynamics, the aerodynamic forces and moments on an aircraft are related to the aircraft's airflow angle and velocity.

[0031] According to the definitions of aircraft angle of attack and sideslip angle, the angle of attack and sideslip angle can be obtained from the following formulas: The flight speed is obtained from the following formula: Once the aircraft's angle of attack, sideslip angle, and speed are obtained, its aerodynamic forces and moments can be determined based on the aircraft's aerodynamic characteristics.

[0032] In the above equation, the deflection angle of the control surface is σ. x (Aileron), σ y (Rudder), σ z (Elevator), Throttle opening σ p The flaps, ailerons, landing gear, and speed brakes are known pilot input parameters. These equations, when combined, form a closed system and can be solved. To obtain the aircraft's motion, these differential equations are solved numerically. The aircraft's equations of motion can generally be summarized into the following system of first-order ordinary differential equations: The numerical solution of the differential equation adopts a one-step method, based on... The differential value at this point To determine the value of the next point. .

[0033] To maintain synchronization with the virtual visual scene, the calculation step size is... The time interval between two frames of a view.

[0034] Specifically, the inverse kinematics calculation model for abnormal flight trajectory and attitude includes: Based on the aircraft speed, attitude angles, and aerodynamic angles of a fixed-wing aircraft in abnormal flight conditions, calculate the trajectory angle of the fixed-wing aircraft; the trajectory angle includes pitch angle, yaw angle, and roll angle. A first transformation matrix from the track coordinate system to the ground coordinate system is constructed based on the track angle, and a second transformation matrix from the ground coordinate system to the body coordinate system is constructed based on the attitude angle. Based on the aircraft velocity, the first transformation matrix, and the second transformation matrix, the velocity components of the fixed-wing aircraft's body coordinate system are obtained. Substituting the velocity components of the body coordinate system into the aircraft's center of mass dynamics equation, the forces acting on the fixed-wing aircraft under abnormal flight conditions are obtained through inverse kinematics calculation. Substituting the rotational angular velocity of the fixed-wing aircraft under abnormal flight conditions into the dynamic equation of rotation about the center of mass, the torque of the fixed-wing aircraft under abnormal flight conditions is obtained by inverse calculation.

[0035] In an optional embodiment of this invention, abnormal flight states include stall spin states. In abnormal flight states such as stall spins, the aerodynamic forces acting on the aircraft are extremely complex and highly irregular, changing with the aircraft's aerodynamic state. Determining the forces and moments acting on the aircraft under these conditions is a current challenge in the field of aerodynamics. Based on multiple stall spin test flights of relevant aircraft, this invention obtains dynamic data on the conditions under which an aircraft enters a stall spin under different circumstances, including the transition phase, the stall spin itself, and the recovery phase. Data fitting is performed on these discrete data, and the inverse kinematics model is applied to calculate the forces and moments acting on the aircraft. This process is essentially the reverse of the kinematics model's solution, as detailed below: Given the aircraft's speed V and attitude angle , , aerodynamic angle , Then, the following formula is used to obtain the aircraft's flight path angle and pitch angle. Deflection angle Inclination angle : Obtain the transformation matrix from the track coordinate system to the ground coordinate system. Thus, the velocity component V of the aircraft relative to the ground is obtained. xd V yd V zd : The velocity component V of the aircraft relative to the body coordinates is obtained through the transformation matrix from ground coordinates to body coordinates. xt V yt V zt : From the following formula: get: This gives us the expressions for the lift, drag, and lateral forces.

[0036] The inverse calculation process for torque is as follows: Given the aircraft's rotational angular velocity , , From now on, by the following formula: get: The torques acting on an aircraft include aerodynamic torque and control torque. When an aircraft enters a deep stall or spin, the external torques are considered to be primarily aerodynamic torques. This gives us the force and torque situation of an aircraft in a stall or spin condition.

[0037] Specifically, the ski-jump takeoff and landing models include: The dynamic equations of the center of mass of the fixed-wing aircraft in the target inertial frame and the dynamic equations of the rotation of the center of mass in the body coordinate system are constructed respectively. Based on the center of mass dynamics equation and the center of mass rotation dynamics equation, a multibody dynamics equation for a fixed-wing aircraft is constructed. The multibody dynamics equation includes: the equation of the angular acceleration of the fixed-wing aircraft about the center of mass relative to the target inertial frame in the body coordinate system, and the center of mass dynamics equation of the landing gear of the fixed-wing aircraft in the body coordinate system. Construct the longitudinal dynamic equations of a fixed-wing aircraft during carrier landing with its hooks attached. Substituting the longitudinal dynamics equations into the multibody dynamics equations yields the landing cable motion model for a fixed-wing aircraft.

[0038] Figure 3 This is a schematic diagram of a multibody dynamics system according to an embodiment of the present invention. Figure 4 This is a schematic diagram illustrating the force exerted by an arresting cable on an aircraft according to an embodiment of the present invention. Figure 3 and Figure 4 As shown, the movement of fixed-wing aircraft on a ship includes ski-jump takeoff, landing, arresting, and go-around. The operating environment is more complex than on land, and related issues include multibody dynamics between the airframe, landing gear, and ship, as well as the estimation of longitudinal loads on the arresting cables. This invention uses ski-jump takeoff as an example to illustrate the establishment of a multibody dynamics model.

[0039] Considering the interaction between the movable parts of the landing gear and the aircraft body, and that this interaction occurs in the aircraft body coordinate system x B Since the directional components are not easily determined, we first treat the aircraft and its front and rear landing gear as a whole, with the following mass: In the above formula, , These represent the masses of the aircraft body and the moving part of the landing gear, numbered i. The equation of motion for the center of mass in the target inertial frame (I) is: In the above formula, These are aerodynamic force, thrust, and the force exerted by the deck on the landing gear. These are the transformation matrices from the aforementioned forces to the inertial frame, respectively.

[0040] The equation of motion for the center of mass rotation in the body coordinate system (B) is: In the above formula, For aerodynamic torque; Let D be the contact point between the i-th tire and the ramp. i The skew-symmetric matrix form of coordinates in the aircraft body coordinate system. If ( ( ) is the contact point D i In the aircraft's coordinate system, The specific expression is: After simplification, the expression for the angular acceleration of the aircraft relative to its inertial frame about its center of mass in the body coordinate system is obtained as follows: The landing gear, as a part of the aircraft, moves with the aircraft and also has relative motion. Therefore, the system consisting of the front and rear landing gear and the takeoff ramp can be considered as an inline multi-rigid-body system with flexible ends. The components are connected by complete (landing gear shock absorbers are considered sliding hinges) and incomplete constraints (displacement constraints between the aircraft tires and the ramp), forming a multi-body system. This allows for a clearer consideration of the landing gear system's motion relative to the aircraft body. Furthermore, the dynamic characteristics of the landing gear system are closely related to the aircraft's attitude angles relative to the ramp, thus providing a complete description of the motion relationship between the aircraft and the landing gear system. Taking the front landing gear as an example, the dynamic equations established on the body coordinate system (B) with the center of mass at point G1 are: In the above formula, This is the aerodynamic torque matrix; Let D be the contact point between the i-th tire and the ramp. i The skew-symmetric matrix form of coordinates in the aircraft body coordinate system. Let i be the mass of the moving part of the landing gear. It is the force matrix of the deck on the landing gear. It is the transformation matrix of the forces exerted by the deck on the landing gear to the fuselage axis system. It is a matrix of rotational angular velocities. These are the forces exerted on the landing gear by the ramp force, the damper force, and the limiting force caused by the piston displacement. It is the skew-symmetric matrix of the aircraft's rotational angular velocity in the inertial frame in the body coordinate system. Here is the rotational angular acceleration matrix of the body coordinate system. Here is the rotational inertia matrix. Let be the acceleration of the aircraft in the body coordinate system, derived from the angular acceleration of rotation in the inertial frame. It is the skew-symmetric matrix of the aircraft in the body coordinate system after its rotational angular acceleration in the inertial frame. The last four terms in the equation, namely... , , and These are the tangential acceleration, Coriolis acceleration, centripetal acceleration, and inertial acceleration of the aircraft's center of mass, which are generated due to the non-inertial body coordinate system. Let be the transformation matrix from the swashplate force acting on the landing gear to the fuselage axis coordinate system. This is the skew-symmetric matrix representation of the forces acting on the landing gear from the ramp plate to the coordinates in the body coordinate system. Let be the matrix of gravitational acceleration in the body axis system. S is the body axis coordinate system matrix of the first tire contact point with mass G1. BI Let be the skew-symmetric matrix of the tire contact point coordinates in the inertial frame within the body coordinate system. This is the transformation matrix from the inertial frame to the body axis.

[0041] After the aircraft lands and engages the arresting cables, it is primarily subjected to the longitudinal tensile load of the arresting cables. This load is related to many factors, including the characteristics of the arresting cables, the arresting distance, the aircraft weight, the landing speed, and the carrier's speed. This invention assumes that the carrier is moving at a constant velocity and neglects the influence of the inertial forces caused by the carrier's motion. The longitudinal dynamic equations of the aircraft can be simplified to the following form: In the above formula, m is the mass of the aircraft, s is the distance the aircraft travels after attaching to the cable, and F t It is engine thrust, F d It is the deck friction, F a It is the aerodynamic force, and F is the force exerted by the arresting cable on the aircraft. For simplified analysis, the tensions F1 and F2 in the arresting cable can be considered directly proportional to the speed of the arresting cable. Therefore, the force exerted by the arresting cable on the aircraft can be expressed by the following formula: In the above equation, l is the deck span of the arresting cable, k is the arresting cable damping coefficient, and η is the arresting cable angle. Neglecting deck friction, thrust, and aerodynamic forces, we obtain the simplified form of the aircraft's longitudinal dynamics equation: In the above formula, the damping coefficient k of the arresting cable can be determined by the condition that aircraft of different weights stop on a certain deck length. This gives us a simplified expression for the longitudinal load of the arresting cable, which can then be substituted into the previous multibody dynamics model to calculate the motion model of the aircraft after landing and engaging the arresting cable.

[0042] As described above, this invention provides a dynamic model for a fixed-wing aircraft. By establishing the aircraft's center-of-mass dynamic equations and rotational dynamic equations around the center of mass, the aerodynamic characteristics of the aircraft are calculated. Numerical solutions to the aircraft's dynamic equations are performed, and parameters such as the aircraft's position and attitude are determined through motion relationship calculations and coordinate transformations, providing core data for the entire flight process. For abnormal flight states such as stall spins, the forces and moments acting on the aircraft are obtained through inverse kinematics calculations of the trajectory and attitude data. By establishing and solving corresponding multibody dynamic models for ski-jump takeoff and carrier landing, the longitudinal load problem of aircraft arrested during carrier landings is solved. Compared with existing technologies, the beneficial effects of this invention are: 1. This invention establishes and solves a multibody dynamics model system for ski-jump takeoff and landing. In the absence of relevant parameters, a simple calculation method is proposed for the longitudinal load problem of aircraft arresting landing, and this method is applied to determine the damping parameters of the arresting gear.

[0043] 2. Precise aerodynamic calculations for aircraft in high angle-of-attack stall, spin, and other flight states remain an unsolved problem in aerodynamics. The aerodynamic characteristics of a specific aircraft can vary significantly under these conditions. These flight states are key topics taught in flight principles and are closely related to flight safety. This invention uses inverse kinematics to calculate the aerodynamics of an aircraft under these special flight states, based on its trajectory and attitude data from actual flight data, providing trainees with a relatively realistic visual display and experience of abnormal flight conditions.

[0044] It will be apparent to those skilled in the art that the present invention is not limited to the details of the exemplary embodiments described above, and that the invention can be implemented in other specific forms without departing from its spirit or essential characteristics. Therefore, the embodiments should be considered in all respects as exemplary and non-limiting, and the scope of the invention is defined by the appended claims rather than the foregoing description. Thus, all variations falling within the meaning and scope of equivalents of the claims are intended to be included within the present invention. No reference numerals in the claims should be construed as limiting the scope of the claims.

[0045] Furthermore, it should be understood that although this specification describes embodiments, not every embodiment contains only one independent technical solution. This narrative style is merely for clarity. Those skilled in the art should consider the specification as a whole, and the technical solutions in each embodiment can also be appropriately combined to form other embodiments that can be understood by those skilled in the art.

Claims

1. A fixed-wing aircraft dynamics model, characterized by, include: The dynamic equations of the center of mass of a fixed-wing aircraft, the dynamic equations of rotation about the center of mass, the calculation model of the aircraft's aerodynamic characteristics, the solution model of the aircraft's dynamic equations, the calculation model of the inverse solution of the trajectory and attitude in abnormal flight states, and the ski-jump takeoff and carrier landing models; among them; The aircraft's center of mass dynamics equation is the center of mass dynamics equation of the body axis system obtained by decomposing Newton's dynamics formula in the body coordinate system. The rotational dynamics equations about the center of mass include the rotational dynamics equations of the body axis system obtained by decomposing the rotational dynamics formulas in the body coordinate system. The aircraft aerodynamic characteristic calculation model is used to calculate the aerodynamic forces and aerodynamic moments of the fixed-wing aircraft based on the basic principles of aircraft aerodynamics. The aircraft dynamics equation solving model is used to solve the aircraft's center-of-mass dynamics equation and the rotational dynamics equation around the center of mass to obtain the position and attitude parameters of the fixed-wing aircraft. The inverse kinematics calculation model for abnormal flight trajectory and attitude is used to obtain the forces and moments of the fixed-wing aircraft in abnormal flight state by performing inverse kinematics calculation on trajectory and attitude data. The ski-jump takeoff and landing model is used to solve the longitudinal load problem of arrested landing of the fixed-wing aircraft.

2. The fixed-wing aircraft dynamics model of claim 1, wherein: The aircraft's center of mass dynamics equations include: wherein are respectively the components of the flight velocity on the three body axes; are respectively the components of the angular velocity of the aircraft on the three body axes; m is the mass of the fixed-wing aircraft, Y, Q, Z, P are respectively the aerodynamic lift, drag, side force and the thrust of the engines of the fixed-wing aircraft, are respectively the angle of attack and the sideslip angle of the fixed-wing aircraft; are respectively the bank, pitch and yaw angles of the fixed-wing aircraft.

3. The fixed-wing aircraft dynamics model of claim 1, wherein: The dynamic equations for rotation about the center of mass include: wherein Ixx, Iyy, Izz are the moments of inertia of the fixed-wing aircraft with respect to the three body axes; Ixy, Ixz, Iyz are the products of inertia of the fixed-wing aircraft with respect to the x, y axes; are the components of the angular velocity of the aircraft rotation in the three body axes, respectively; are the components of the moment vector acting on the aircraft in the three body axes, respectively.

4. The fixed-wing aircraft dynamics model of claim 1, wherein: The aerodynamic forces include the aerodynamic lift, drag, and engine thrust of the fixed-wing aircraft; the aerodynamic torques include the control torques and stabilizing torques distributed to each airframe axis.

5. The fixed-wing aircraft dynamics model of claim 1, wherein: The aircraft dynamics equations solution model includes: Integrating the aircraft's center of mass dynamics equation yields the components of the aircraft's velocity in the body coordinate system, which are then integrated to obtain the position parameters of the fixed-wing aircraft. The attitude parameters of the fixed-wing aircraft are obtained by solving the dynamic equation of rotation about the center of mass using the quaternion method.

6. The fixed-wing aircraft dynamics model of claim 1, wherein: The abnormal flight trajectory and attitude inverse solution calculation model includes: Based on the aircraft speed, attitude angle, and aerodynamic angle of the fixed-wing aircraft in abnormal flight conditions, the flight path angle of the fixed-wing aircraft is calculated; the flight path angle includes pitch angle, yaw angle, and roll angle. A first transformation matrix from the trajectory coordinate system to the ground coordinate system is constructed based on the trajectory angle, and a second transformation matrix from the ground coordinate system to the body coordinate system is constructed based on the attitude angle. Based on the aircraft speed, the first transformation matrix, and the second transformation matrix, the velocity components of the fixed-wing aircraft in the body coordinate system are obtained. Substituting the velocity components of the body coordinate system into the aircraft's center of mass dynamics equation, the forces acting on the fixed-wing aircraft under abnormal flight conditions are obtained through inverse kinematics calculation. Substituting the rotational angular velocity of the fixed-wing aircraft under abnormal flight conditions into the dynamic equation of rotation about the center of mass, the torque of the fixed-wing aircraft under abnormal flight conditions is obtained by inverse calculation.

7. The fixed-wing aircraft dynamics model of claim 1, wherein: The ski-jump takeoff and landing model includes: The dynamic equations of the center of mass of the fixed-wing aircraft in the target inertial frame and the dynamic equations of the rotation of the center of mass in the body coordinate system are respectively constructed. Based on the center of mass dynamics equation and the center of mass rotation dynamics equation, the multibody dynamics equation of the fixed-wing aircraft is constructed; the multibody dynamics equation includes: the equation of the angular acceleration of the fixed-wing aircraft about the center of mass relative to the target inertial frame in the body coordinate system, and the center of mass dynamics equation of the landing gear of the fixed-wing aircraft in the body coordinate system. Construct the longitudinal dynamic equations of the fixed-wing aircraft during carrier landing with the cable attached. Substituting the longitudinal dynamics equation into the multibody dynamics equation yields the carrier-mounted cable motion model of the fixed-wing aircraft.

8. The fixed-wing aircraft dynamics model of claim 7, wherein: The equations for the angular acceleration of the fixed-wing aircraft about its center of mass relative to the target inertial frame in the body coordinate system include: The landing gear dynamic equations of the fixed-wing aircraft in the body coordinate system include: wherein is the aerodynamic force moment matrix; is the contact point D of the i-th tire with the ramp i is the skew-symmetric matrix form of the coordinates in the body coordinate system, is the mass of the i-th landing gear moving part, is the deck-to-landing gear force matrix, is the conversion matrix of the deck-to-landing gear force to the body axis system, is the matrix of the angular velocity of rotation, is the ramp force, the buffer force and the restriction force caused by the piston displacement respectively, is the skew-symmetric matrix of the angular velocity of rotation of the aircraft in the inertial system in the body coordinate system, is the matrix of the angular acceleration of rotation of the body coordinate system, is the moment of inertia matrix, is the acceleration of the angular acceleration of rotation of the aircraft in the inertial system converted into the body coordinate system, is the skew-symmetric matrix of the angular acceleration of rotation of the aircraft in the inertial system converted into the body coordinate system, is the conversion matrix of the ramp force received by the landing gear to the body axis coordinate system, is the skew-symmetric matrix form of the coordinates in the body coordinate system of the ramp force received by the landing gear, is the matrix of the gravitational acceleration in the body axis system, is the matrix of the body axis coordinate system of the first tire contact point of the mass point G1, BI is the skew-symmetric matrix of the tire contact point coordinates of the aircraft in the inertial system in the body coordinate system, is the conversion matrix of the inertial system to the body axis system.

9. The fixed-wing aircraft dynamics model according to claim 7, characterized in that: The longitudinal dynamic equations of the fixed-wing aircraft during carrier landing include: In the formula, m is the mass of the fixed-wing aircraft, s is the forward distance of the aircraft after it is hooked up to the arresting cable, k is the damping coefficient of the arresting cable, l is the deck speed of the arresting cable, and t is time.

Images