Rapid calculation method for flight envelope of high-subsonic-speed fixed-wing aircraft

Abstract

The invention discloses a rapid calculation method for a flight envelope of a high-subsonic-speed fixed-wing aircraft. The rapid calculation method comprises the following steps: acquiring basic input parameters of a dynamic model of the high-subsonic-speed fixed-wing aircraft; based on the basic input parameters of the kinetic model, performing iterative approximation calculation on the flight attack angle by taking the condition that the available thrust of an engine is not less than the flight resistance as an iteration constraint condition, and determining a boundary parameter set for defining a flight envelope boundary; and based on the boundary parameter set, obtaining a flight envelope of the high-subsonic-speed fixed-wing aircraft. Traversal iterative approximation is implemented by using the high-speed calculation capability of a computer, and the balance relationship between thrust and resistance is verified in real time in each iteration, so that the calculation efficiency of the flight envelope boundary of the high-subsonic-speed fixed-wing aircraft and the adaptability to a complex nonlinear pneumatic system are remarkably improved; the problems that a traditional method depending on an analytic formula and experience is insufficient in calculation precision under the working conditions of strong nonlinearity and full coupling, and seriously depends on step iteration and a large number of experimental verification are solved.

Description

Technical Field

[0001] This invention relates to the field of aircraft design technology, and in particular to a rapid calculation method for the flight envelope of a high subsonic fixed-wing aircraft. Background Technology

[0002] High-subsonic fixed-wing aircraft are core aircraft in modern air transport systems and primary carriers of key military capabilities such as strategic airlift and early warning command. Their cruising speeds typically range from Mach 0.7 to Mach 0.95. This speed range falls precisely at the physical abrupt change stage of transonic flow, resulting in strong nonlinear, discontinuous, and abruptly changing aerodynamic forces and moments. For example, the occurrence and movement of shock waves are extremely sensitive to flight conditions. These characteristics pose severe challenges to the design, analysis, and control of high-subsonic fixed-wing aircraft, making their development a complex systems engineering project involving deep coupling of multiple disciplines such as aerodynamics, flight control, structure, and propulsion.

[0003] In the development of such aircraft, the flight envelope is the primary criterion for assessing whether it meets design requirements, as it clarifies the safe and feasible boundaries of the aircraft in terms of speed, altitude, and maneuverability. Traditional methods for determining the flight envelope mainly rely on analytical or semi-analytical formulas based on physical principles, combined with engineering empirical formulas obtained from numerous wind tunnel and flight tests. This method typically determines each boundary iteratively in a step-by-step, discipline-specific manner under limited computational resources. For example, it determines the maximum speed through drag-thrust balance, the stall speed through the maximum lift coefficient, and the dynamic pressure and overload boundaries through structural strength constraints. Although this classic method has played an important role in the history of aviation development, it is inherently dependent on empirical formulas and linear assumptions, making it difficult to accurately handle the intense nonlinear and fully coupled aerodynamic phenomena under high subsonic conditions. Furthermore, traditional methods usually select discrete "design points" within the envelope for calculation, making it difficult to achieve a continuous and comprehensive revelation of performance across the entire envelope.

[0004] With the rapid development of computer technology, computing power has been greatly enhanced, making it possible to achieve high-precision, dynamic, rapid derivation and iterative calculation of flight envelopes. In the early stages of aircraft design, there is an urgent need for a flight envelope estimation method that can quickly assess the feasibility of design schemes and identify problems before manufacturing physical prototypes. This method can significantly shorten the demonstration cycle, save substantial R&D costs and time, and provide crucial data support for subsequent detailed design, flight control law formulation, and mission planning. Therefore, developing a method suitable for high subsonic fixed-wing aircraft, capable of effectively handling their complex aerodynamic characteristics and achieving rapid calculation of flight envelopes, has significant engineering value and practical implications. Summary of the Invention

[0005] The purpose of this invention is to provide a rapid calculation method for the flight envelope of a high subsonic fixed-wing aircraft. By utilizing the high-speed computing power of computers to perform traversal iterative approximation and verifying the balance between thrust and drag in real time during each iteration, the calculation efficiency of the flight envelope boundary of the high subsonic fixed-wing aircraft and its adaptability to complex nonlinear aerodynamic systems are significantly improved. This solves the problems of insufficient calculation accuracy of traditional methods that rely on analytical formulas and experience under strongly nonlinear and fully coupled conditions, and the heavy reliance on step-by-step iteration and extensive experimental verification.

[0006] To address the aforementioned technical problems, this invention provides a method for rapidly calculating the flight envelope of a high subsonic fixed-wing aircraft, thereby obtaining the basic input parameters of the dynamic model of the high subsonic fixed-wing aircraft. Based on the basic input parameters of the dynamic model, the angle of attack is iteratively approximated by using the condition that the available thrust of the engine is not less than the flight drag as the iterative constraint, and the set of boundary parameters used to define the boundary of the flight envelope is determined. Based on the set of boundary parameters, the flight envelope of the high subsonic fixed-wing aircraft is obtained.

[0007] Furthermore, the basic input parameters of the dynamic model include at least: preset overall parameters, engine thrust characteristic data, and aerodynamic characteristic parameters.

[0008] Furthermore, the set of boundary parameters includes: the minimum and maximum flight speeds at each altitude within the preset flight altitude range, and the maximum available positive angle of attack and the maximum available negative angle of attack at each state point within the preset flight speed-altitude range; Based on the fundamental input parameters of the aforementioned dynamic model, the set of boundary parameters used to define the flight envelope boundary is determined by iteratively approximating the flight angle of attack with the engine's available thrust not being less than the flight drag as the iterative constraint. This includes: Traverse the preset flight altitude range. For each flight altitude, iteratively adjust the flight angle of attack and verify whether the available thrust of the engine is not less than the flight drag of the corresponding state. Sequentially solve to determine the minimum and maximum flight speeds at the flight altitudes and obtain the parameters defining the velocity-altitude boundary in the flight envelope. The system iterates through the state combinations formed by the preset flight speed range and the flight altitude range. For each state combination, it iterates and adjusts the flight angle of attack and checks whether the available engine thrust is not less than the flight drag of the corresponding state. It then solves and determines the maximum available positive angle of attack and the maximum available negative angle of attack under the state combination, thereby obtaining the parameters that define the overload boundary in the flight envelope.

[0009] Further, determining the minimum flight speed at the stated flight altitude includes: The maximum available positive angle of attack at the flight altitude is set as the initial angle of attack, and the initial flight speed that satisfies the balance between torque and lift is calculated at the initial angle of attack. Calculate the flight drag and available engine thrust of the aircraft at the initial angle of attack and initial flight speed. When the available thrust of the engine is not less than the flight drag, the initial flight speed is determined as the minimum flight speed; When the available thrust of the engine is less than the flight drag, the initial angle of attack is iteratively reduced and the corresponding flight speed, flight drag and available thrust of the engine are recalculated until the condition that the available thrust of the engine is not less than the flight drag is met, and the flight speed at this time is determined as the minimum flight speed.

[0010] Further, determining the maximum flight speed at the stated flight altitude includes: Starting from the minimum flight speed at the specified flight altitude, calculate the trim angle of attack, trim rudder deflection, and level flight drag that satisfy the level flight balance conditions at the current flight speed, and obtain the corresponding available engine thrust. When the available thrust of the engine is greater than the level flight drag, increase the current flight speed and repeat the calculation and acquisition steps; When the available thrust of the engine is less than or equal to the level flight drag, the current flight speed before the increase is determined as the maximum flight speed.

[0011] Further, determining the maximum usable positive angle of attack under the aforementioned state combination includes: Set the maximum available aerodynamic angle of attack at the flight altitude as the current angle of attack; Calculate the flight drag and available engine thrust of the aircraft at the current positive angle of attack, flight altitude, and flight speed. When the available thrust of the engine is not less than the flight drag, the current positive angle of attack is determined as the maximum available positive angle of attack under the state combination; When the available thrust of the engine is less than the flight drag, the current positive angle of attack is iteratively reduced and the corresponding flight drag and available thrust of the engine are recalculated until the condition that the available thrust of the engine is not less than the flight drag is met, and the angle of attack corresponding to this time is determined as the maximum available positive angle of attack under the state combination.

[0012] Further, determining the maximum usable negative angle of attack under the aforementioned state combination includes: Set the maximum available negative angle of attack at the flight altitude as the current negative angle of attack; Calculate the flight drag and available engine thrust of the aircraft under the current negative angle of attack, flight altitude, and flight speed conditions; When the available thrust of the engine is not less than the flight drag, the current negative angle of attack is determined as the maximum available negative angle of attack under the state combination; When the available thrust of the engine is less than the flight drag, the current negative angle of attack is iteratively increased and the corresponding flight drag and available thrust of the engine are recalculated until the condition that the available thrust of the engine is not less than the flight drag is met, and the angle of attack corresponding to this time is determined as the maximum available negative angle of attack under the state combination.

[0013] Further, obtaining the flight envelope of the high subsonic fixed-wing aircraft based on the set of boundary parameters includes: Based on the minimum and maximum flight speeds at different flight altitudes in the set of boundary parameters, a velocity-altitude envelope boundary characterizing the range of permissible flight speeds of the aircraft is formed in the velocity-altitude coordinate system. Based on the maximum available positive angle of attack and the maximum available negative angle of attack under different state combinations in the boundary parameter set, and combined with the flight kinematics under the corresponding state combinations and the aerodynamic characteristic parameters in the basic input parameters of the dynamic model, the maximum positive overload value and the maximum negative overload value, which characterize the performance limit of the aircraft in the aerodynamic and dynamic dimensions under the corresponding state combinations, are calculated respectively, and an overload envelope boundary characterizing the allowable maneuver overload range of the aircraft is formed in the velocity-overload coordinate system. The output is the flight envelope of the high subsonic fixed-wing aircraft, which is formed by the velocity-altitude envelope boundary and the overload envelope boundary.

[0014] Furthermore, the overload envelope boundary is the overload capacity limit that the aerodynamic and propulsion system of the aircraft can provide, independent of the structural strength limitations of the aircraft.

[0015] Furthermore, the engine's usable thrust can be obtained in the following ways: Based on the flight altitude, flight speed, and angle of attack corresponding to the current iteration step, query the engine thrust characteristic data table established based on the engine thrust characteristic data; Based on the flight altitude, flight speed, and flight angle of attack, the corresponding available engine thrust is determined from the engine thrust characteristic data table through interpolation calculation.

[0016] The above-described technical solutions of the embodiments of the present invention have the following beneficial technical effects: 1. By constructing an iterative approximation calculation process with the combination of flight altitude and speed states as the traversal framework and thrust not less than drag as the real-time verification condition, the high-speed processing power of computers is fully utilized to achieve efficient and automatic solution of the flight envelope boundary. This significantly improves the efficiency of envelope calculation, enables rapid results in the design and demonstration stage, and effectively overcomes the inherent limitations of traditional analytical methods in accurately handling high subsonic strongly nonlinear aerodynamic coupling problems, providing key support for scheme iteration and early verification. 2. The basic input parameters of the dynamic model allow the engine and aerodynamic models to be constructed using mathematical models of varying precision, ranging from simple linear to complex nonlinear and strongly coupled. This endows the method with strong adaptability and scalability, enabling it to be compatible with the data foundation of different design stages and the characteristics of different aircraft models. It can perform both rapid estimation and high-fidelity analysis, thus solving the problem that traditional methods rely on fixed empirical formulas and are difficult to flexibly adapt to different model precision and complex system characteristics. 3. The calculated overload envelope boundary is defined as the capability boundary determined by the ultimate performance of the aircraft's aerodynamic and propulsion systems, and it is decoupled from the structural strength constraints of the aircraft. This allows the obtained envelope data to more purely reflect the aerodynamic potential of the aircraft, providing key performance benchmarks beyond the traditional structural constraint envelope for flight control law design, envelope protection system development, and extreme mission planning. This solves the problem of insufficient boundary information in traditional envelopes when guiding controller design and exploring flight performance. Attached Figure Description

[0017] Figure 1 This is a flowchart of a method for rapidly calculating the flight envelope of a high subsonic fixed-wing aircraft provided in an embodiment of the present invention; Figure 2 This is a schematic diagram of the high-speed target drone flight envelope calculation process provided in an embodiment of the present invention. Detailed Implementation

[0018] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to specific embodiments and the accompanying drawings. It should be understood that these descriptions are merely exemplary and not intended to limit the scope of the invention. Furthermore, descriptions of well-known structures and techniques are omitted in the following description to avoid unnecessarily obscuring the concept of the invention.

[0019] Please refer to Figure 1 and Figure 2 This invention provides a method for rapidly calculating the flight envelope of a high subsonic fixed-wing aircraft, comprising the following steps: Step S100: Obtain the basic input parameters of the dynamic model of the high subsonic fixed-wing aircraft.

[0020] Obtaining the basic input parameters for the dynamic model of a high subsonic fixed-wing aircraft is the data preparation stage for initiating the entire rapid calculation process, building a complete and computable physical model foundation for subsequent numerical simulations. Specifically, the basic input parameters for the dynamic model must explicitly include at least three parts in the embodiments: First, the aircraft's preset overall parameters, such as takeoff weight and center of gravity position estimated based on component mass distribution, which define the aircraft's inertial characteristics; second, engine thrust characteristic data, which is usually provided in the form of data tables or mathematical models, describing the engine's available thrust at different flight altitudes, speeds, and possible throttle states; and third, aerodynamic characteristic parameters, which cover a series of relationships between lift coefficient, drag coefficient, pitching moment coefficient, etc., as a function of Mach number and angle of attack, especially defining the limiting characteristics such as the maximum available positive angle of attack and negative angle of attack. These parameters can be obtained from preliminary design estimates, component databases, low-precision computational fluid dynamics (CFD) results, or scaled data from existing similar aircraft models. They can be obtained quickly in the early stages of design, and their model complexity can be flexibly selected as needed, ranging from simple linear estimation models to complex nonlinear high-fidelity models.

[0021] One of the core advantages of the aforementioned rapid calculation method lies in its broad tolerance for the complexity of the input mathematical model. Whether it's the engine thrust characteristic data or aerodynamic characteristic parameters obtained in step S100, the underlying generative model is unrestricted. Specifically, the engine thrust model can range from simple, altitude- and velocity-based binary linear fitting formulas to complex, highly nonlinear, high-fidelity numerical models that consider numerous factors such as intake distortion, Reynolds number effects, and throttle transients. Similarly, aerodynamic characteristic parameters can originate from linear estimations based on empirical formulas, or from precise computational fluid dynamics (CFD) simulations or wind tunnel test data that fully capture nonlinear phenomena such as transonic shock waves, flow separation, and aeroelastic coupling. The iterative approximation calculation process of this invention does not rely on the inherent linear assumptions of the model. As long as the required thrust and aerodynamic coefficients can be provided for each traversed state point, this method is applicable regardless of the complexity of the model from which these data originate. This characteristic ensures that the method can be used throughout the entire lifecycle of aircraft design: in the conceptual design phase, a fast and conservative linear model is used for large-scale scheme screening; in the preliminary and detailed design phases, a higher fidelity nonlinear model can be seamlessly integrated for accurate performance verification.

[0022] Step S200: Based on the basic input parameters of the dynamic model, the flight angle of attack is iteratively approximated by using the condition that the available thrust of the engine is not less than the flight drag as an iterative constraint, and the set of boundary parameters used to define the boundary of the flight envelope is determined.

[0023] The above implementation relies on a computer program to systematically traverse and iteratively search a preset flight state space, transforming the solution of the flight envelope boundaries (such as minimum speed, maximum speed, and maximum available angle of attack) into a numerical optimization problem at discrete state points, constrained by the basic physical feasibility of thrust ≥ drag. In specific implementation, all flight altitudes of interest are first traversed. For each altitude, starting from a theoretical aerodynamic limit angle of attack (such as the maximum positive angle of attack), the angle of attack is iteratively adjusted while simultaneously calculating the corresponding equilibrium speed, drag, and available thrust until the minimum speed point that precisely satisfies the requirement that thrust can overcome drag is found; this is the stall speed boundary at that altitude. Subsequently, starting from this minimum speed, the speed is gradually increased. At each calculated speed, the trim angle of attack and corresponding drag required to maintain level flight are calculated and compared with the maximum available thrust of the engine in that state, thereby iteratively searching for the maximum speed point where thrust and drag are balanced. For the maneuver overload boundary, a similar iterative approach is then used on each grid point (state combination) within a two-dimensional grid composed of height and velocity. Starting from the maximum positive and negative angles of attack, a search is performed inward to find the maximum positive and negative usable angles of attack that satisfy the thrust ≥ drag constraint at that point. These angles of attack values ​​are directly related to the ultimate lift of that state, and thus the overload capacity can be derived. The entire S200 step automatically outputs a set of discrete boundary point data, i.e., a set of boundary parameters, through this systematic cycle of traversal-hypothesis-verification-adjustment.

[0024] Step S300: Based on the set of boundary parameters, obtain the flight envelope of the high subsonic fixed-wing aircraft.

[0025] The discrete boundary parameter points calculated in step S200 are transformed and integrated into a standard, intuitive envelope chart for engineering applications. By connecting or fitting the minimum and maximum velocity data points at each altitude, a velocity range boundary characterizing the aircraft's sustainable level flight can be formed on the velocity-altitude (VH) chart. Simultaneously, using the maximum usable positive and negative angles of attack calculated at each state point (altitude-velocity combination), combined with the dynamic pressure calculated from the atmospheric density and velocity at that state, and the lift coefficient curve in the aerodynamic model, the maximum positive and negative normal overloads that the aircraft can generate at that state point due to aerodynamics and propulsion can be calculated. The upper and lower boundaries formed by all these overload values ​​on the velocity-overload (Vn) chart constitute the aircraft's maneuvering overload capacity envelope. The overload envelope calculated above reflects the performance potential limit of the combined action of the aerodynamic and propulsion systems; it is a capacity boundary, which may differ in physical meaning and numerical value from the allowable boundary traditionally given by structural strength limitations. Finally, the output flight envelope is defined jointly by the aforementioned velocity-altitude boundary and maneuvering overload boundary.

[0026] Through the above method, this invention enables the efficient and automated calculation of the theoretical flight envelope of a high subsonic fixed-wing aircraft in the early stages of design, based solely on preliminary and rapidly obtainable model parameters. This method significantly shortens the cycle of traditional envelope determination, which relies heavily on manual calculations, specialized iterations, and costly experiments. It can quickly identify design shortcomings (such as insufficient thrust or excessive drag) during the feasibility study phase, guiding the adjustment of design parameters and providing clear, physical model-based performance boundary references for flight control system design. Therefore, it demonstrates substantial technical effectiveness in improving design efficiency and reducing R&D risks and costs.

[0027] Specifically, the set of boundary parameters includes: the minimum and maximum flight speeds at each altitude within the preset flight altitude range, and the maximum available positive angle of attack and the maximum available negative angle of attack at each state point within the preset flight speed-altitude range.

[0028] The boundary parameter set is the core dataset output by the systematic iterative calculation in step S200, used to digitally define the geometry of the flight envelope. This set is not a single numerical value, but a structured data group, which includes two logical levels: The first level consists of extreme values ​​distributed along the flight altitude dimension, representing the boundaries of the sustainable level flight speed range of the aircraft. That is, at each preset flight altitude, the minimum and maximum flight speeds are determined through iterative solutions. The minimum flight speed represents the lowest speed at which the aircraft can generate sufficient lift aerodynamically to balance gravity and whose engine thrust is sufficient to overcome the corresponding state drag at that altitude. It is usually constrained by both stall characteristics and available thrust. The maximum flight speed represents the highest speed at which the aircraft, under the condition of moment trim, can achieve the maximum available thrust of its engine just enough to balance the flight drag (especially wave drag) that increases sharply due to the increase in speed. This is the result of balancing the performance of the power plant and aerodynamic drag. The second level involves iteratively searching for the maximum available positive angle of attack and the maximum available negative angle of attack at each discrete flight speed-altitude state combination point within a two-dimensional state space spanned by preset flight altitude and flight speed ranges. These two parameters define the limits of pitch control angles that the aircraft can actually safely use under each specific altitude-speed condition, provided that the available engine thrust is not less than the flight drag generated at that angle of attack. They are directly related to the maximum positive normal lift and maximum negative normal lift that the aircraft can generate through aerodynamic control at that state point, and are direct inputs to the computer's dynamic overload boundary. Therefore, this set of boundary parameters essentially discretizes the continuous flight envelope boundary into a series of key feature points, completely encoding the generation information of the velocity boundary (VH diagram) and the potential overload capacity boundary (Vn diagram), providing all the necessary and sufficient input conditions for the final graphical or data-based synthesis of the flight envelope in step S300.

[0029] Accordingly, the basic input parameters based on the dynamic model in step S200 are used to iteratively approximate the flight angle of attack by using the engine's available thrust not being less than the flight drag as an iterative constraint, to determine the set of boundary parameters used to define the flight envelope boundary, including: Step S210: Traverse the preset flight altitude range. For each flight altitude, iteratively adjust the flight angle of attack and verify whether the available thrust of the engine is not less than the flight drag of the corresponding state. Solve in sequence to determine the minimum and maximum flight speeds at the flight altitudes and obtain the parameters of the speed-altitude boundary in the defined flight envelope.

[0030] At a fixed altitude, atmospheric density and engine performance are relatively fixed, and the velocity boundary of the aircraft is jointly determined by aerodynamic lift characteristics and engine thrust-drag balance. To solve for the minimum flight speed, the maximum usable positive angle of attack allowed by the aerodynamic model at that altitude is used as the starting point. A theoretical speed is calculated based on the principles of lift-weight balance and moment balance. Subsequently, the flight drag under this combination of angle of attack and speed is calculated and compared with the engine's usable thrust at that state. If the thrust is insufficient to overcome the drag, the angle of attack is slightly reduced by a preset step size, and a new equilibrium speed and corresponding drag and thrust are recalculated. This process is repeated until the condition of thrust ≥ drag is first met. The speed at this point is the actual minimum flight speed at that altitude under both aerodynamic and dynamic constraints. To solve for the maximum flight speed, the newly obtained minimum speed is used as the current trial speed. The trim angle of attack and corresponding trim drag required to maintain level flight (satisfying lift-weight balance and moment balance) at this speed are calculated and compared with the engine's maximum usable thrust at the current speed. If there is a thrust surplus, the speed is increased step by step, and the above trim and comparison process is repeated; when the speed is increased to a point where the engine's maximum available thrust is exactly less than or equal to the trim drag, the previous speed is the maximum flight speed at that altitude. By traversing all preset altitudes and performing the above double iteration, a speed-altitude envelope boundary is finally obtained, consisting of discrete (altitude, minimum speed) points and (altitude, maximum speed) points.

[0031] Step S220: Iterate through the state combinations formed by the preset flight speed range and flight altitude range. For each state combination, iterate and adjust the flight angle of attack and check whether the available engine thrust is not less than the flight drag of the corresponding state. Solve and determine the maximum available positive angle of attack and the maximum available negative angle of attack under the state combination in turn to obtain the parameters of the overload boundary in the defined flight envelope.

[0032] At any given altitude-velocity state, the maximum normal overload achievable by an aircraft is directly limited by the maximum angle of attack usable at that state. This angle-of-attack limit is fundamentally constrained by the requirement that the engine's available thrust must overcome the drag generated by that angle of attack. For each state point in the mesh, the theoretical maximum positive angle of attack at that altitude is first obtained from the aerodynamic model as the starting point for the search. The drag of the aircraft at this angle of attack is calculated and compared with the engine's available thrust at the current altitude and velocity. If the thrust meets the requirement, then this angle of attack is the maximum usable positive angle of attack for that state point; if not, the angle of attack value is iteratively decreased until a maximum positive angle of attack that satisfies the thrust constraint is found. Similarly, starting with the maximum negative angle of attack, the maximum usable negative angle of attack that satisfies the constraint is searched by iteratively increasing the angle of attack (adjusting towards zero). These two angle-of-attack parameters determine the positive and negative normal lift limits achievable by the aircraft at that state point, purely from the perspective of aerodynamic forces and engine capabilities, without considering structural strength limitations. After all state points have been calculated, a data field covering the entire domain of interest and relating to the maximum available positive / negative angle of attack is obtained. This data field is the basis for subsequent calculations of the overload boundary.

[0033] Furthermore, the solution in step S210 to determine the minimum flight speed at the flight altitude includes: Step S211a: Set the maximum available positive angle of attack at the flight altitude as the initial angle of attack, and calculate the initial flight speed that satisfies the balance between torque and lift at the initial angle of attack.

[0034] The search begins by setting the maximum available positive angle of attack (POA) at the current calculated altitude, as given by the aerodynamic characteristic model. This OPA represents the theoretically maximum positive angle of attack achievable by the airfoil or overall configuration of the aircraft at this altitude without stall or other critical aerodynamic separation conditions; it is a limit value defined purely by aerodynamic data. Based on this initial OPA, the known weight of the aircraft, the atmospheric density at the current altitude, and the lift coefficient corresponding to the OPA in the aerodynamic model, the equilibrium equations for equal lift and gravity are solved to calculate the theoretical initial flight speed required to keep the aircraft suspended in the air. Simultaneously, to ensure that this state is mechanically achievable, the given center of mass position and pitch moment coefficient are used to verify or adjust the combination of OPA and speed to satisfy the basic pitch moment balance condition. This step assumes that the aircraft flies at optimal aerodynamic efficiency (near the maximum lift coefficient), thus theoretically obtaining the minimum possible speed value.

[0035] Step S211b: Calculate the flight drag and available engine thrust of the aircraft at the initial angle of attack and initial flight speed.

[0036] After obtaining the initial flight speed, it is necessary to assess whether the aircraft has sufficient propulsion capability in this state. First, the aerodynamic model is invoked, and the total drag experienced by the aircraft is calculated based on the current Mach number (obtained from the speed and local speed of sound), the initial angle of attack, and other relevant parameters. This drag includes zero-lift drag independent of lift, induced drag generated by lift, and trim drag generated by the control surface deflection required to balance the pitch moment. Simultaneously with the calculation of flight drag, based on the current flight altitude, initial flight speed, and preset engine operating conditions (usually maximum continuous thrust or takeoff thrust, etc.), the engine mathematical model (such as a thrust characteristic data table) is consulted or invoked, and the available thrust that the engine can provide in this flight state is determined through numerical methods such as interpolation.

[0037] Step S211c: When the available thrust of the engine is not less than the flight drag, the initial flight speed is determined as the minimum flight speed.

[0038] If the engine's available thrust calculated in step S211b is greater than or equal to the flight drag, it proves that even when flying at the aerodynamic limit angle of attack, the aircraft's power reserve is sufficient to overcome all drag. In this case, the aerodynamic limit directly determines the minimum speed, and the initial flight speed is confirmed as the truly feasible minimum flight speed at that altitude.

[0039] In step S211d, when the available thrust of the engine is less than the flight drag, the initial angle of attack is iteratively reduced and the corresponding flight speed, flight drag and available thrust of the engine are recalculated until the condition that the available thrust of the engine is not less than the flight drag is met, and the flight speed corresponding to this time is determined as the minimum flight speed.

[0040] When the available engine thrust is less than the flight drag, it indicates that the thrust required for optimal aerodynamic performance exceeds the engine's actual capacity. At this point, the constraint shifts from aerodynamic limits to a power bottleneck. An iterative loop then begins, reducing the current angle of attack value by a preset, sufficiently fine step size (e.g., 0.01 degrees). Based on the new, smaller angle of attack, the (lower) flight speed that satisfies lift-weight balance is recalculated, and step S211b is executed again to recalculate drag and thrust under the new conditions. This cycle of reducing angle of attack, updating speed, recalculating thrust, and comparing continues, simulating a pilot's attempt to reduce drag by decreasing the angle of attack to maintain flight under insufficient power. The iterative process continues until a certain angle of attack and its corresponding speed are found, at which point the available engine thrust first reaches or slightly exceeds the flight drag. The corresponding flight speed at this point is the minimum practically flyable speed at that altitude, simultaneously satisfying aerodynamic lift requirements and engine thrust limitations.

[0041] Furthermore, the solution in step S210, which determines the maximum flight speed at the flight altitude, includes: Step S212a: Starting from the minimum flight speed at the flight altitude, calculate the trim angle of attack, trim rudder deflection, and level flight drag that meet the level flight balance conditions at the current flight speed, and obtain the corresponding available engine thrust.

[0042] Using the minimum flight speed obtained at the same flight altitude as the initial trial value, and assuming the aircraft maintains strictly horizontal straight flight (level flight) at this speed, the aerodynamic characteristic model is invoked to solve for a specific angle of attack (trimmed angle of attack) that simultaneously satisfies lift and gravity balance (providing sufficient normal force) and pitch moment balance (ensuring longitudinal attitude stability). Simultaneously, the rudder or elevator deflection required to achieve this moment balance is calculated, i.e., trim deflection. The total drag of the aircraft under this trim state is the level flight drag, accurately reflecting the drag that must be overcome to maintain baseline flight at this speed. Meanwhile, based on the current flight altitude, current flight speed, and engine certification operating status, the corresponding available engine thrust is obtained from the engine thrust characteristic model.

[0043] Step S212b: When the available thrust of the engine is greater than the drag during level flight, increase the current flight speed and repeat the calculation and acquisition steps.

[0044] If, at the current speed, the calculated available engine thrust is greater than the level flight drag, it indicates that the aircraft possesses remaining thrust potential in this state; this remaining thrust can theoretically be used for acceleration or climb. Therefore, the current flight speed is increased by a preset speed step (e.g., 0.5 m / s) to explore a higher speed state point in the speed-altitude space. Subsequently, for this new, higher speed, step S212a is completely repeated: the new trim angle of attack, new trim rudder deflection, and the corresponding level flight drag that satisfy the level flight conditions at the new speed are recalculated, and the available engine thrust corresponding to the new speed is obtained again. This cycle of increasing speed, recalculating trim, and obtaining thrust simulates the process of the aircraft gradually accelerating from a low speed and verifies the thrust-drag balance relationship in level flight at each discrete speed point.

[0045] Step S212c: When the available thrust of the engine is less than or equal to the drag during level flight, the current flight speed before the increase is determined as the maximum flight speed.

[0046] As the speed gradually increases during the iteration process, level flight drag (especially wave drag, which increases sharply with Mach number) typically grows rapidly, while the available engine thrust exhibits specific characteristic curves with speed and altitude. When the iteration reaches a certain speed point, if the calculation shows that the available engine thrust in that state is less than or equal to the level flight drag, it indicates that even if the aircraft uses all available thrust to overcome drag, it cannot maintain level, uniform flight at that speed; to maintain this speed, altitude (descent) must be sacrificed to replenish kinetic energy. Therefore, this speed point has exceeded the aircraft's level flight capability boundary. According to the rules of numerical iteration, the maximum speed that satisfies the level flight condition should be located between the last speed point where engine thrust is greater than drag and the first speed point where engine thrust is less than or equal to drag. Based on this, the current flight speed before the increase, i.e., the speed value that last satisfied the thrust > drag condition, is determined as the maximum flight speed at that flight altitude.

[0047] Further, the step S220 of determining the maximum available positive angle of attack under the combined states includes: Step S221a: Set the maximum available aerodynamic positive angle of attack at the flight altitude as the current positive angle of attack.

[0048] The maximum available positive angle of attack defined by the aerodynamic characteristic database or model at the current flight altitude is assigned to the iterative variable current positive angle of attack. This maximum available positive angle of attack is a theoretical value related to the flight altitude, which is usually determined by the airfoil stall characteristics, wing sweep angle, Mach number and possible high lift device configuration. It represents the maximum lift coefficient that the aerodynamic surface can provide or the positive angle of attack limit corresponding to a specific separation boundary at this altitude without considering power limitations.

[0049] Step S221b: Calculate the flight drag and available engine thrust of the aircraft under the current positive angle of attack, flight altitude and flight speed.

[0050] Based on the fixed flight altitude, flight speed, and the set current positive angle of attack, two parallel calculations are performed. First, the aerodynamic model is invoked to calculate the flight drag generated by the aircraft in this configuration, based on the current Mach number, angle of attack, and other relevant parameters. This drag includes the induced drag component corresponding to the current lift. Simultaneously, based on the same flight altitude, flight speed, and engine operating settings, the available engine thrust in this state is obtained or calculated from the engine thrust characteristic data.

[0051] Step S221c: When the available thrust of the engine is not less than the flight drag, the current positive angle of attack is determined as the maximum available positive angle of attack under the state combination.

[0052] If the engine's available thrust calculated in step S221b is greater than or equal to the flight drag, it indicates that at the current altitude and speed, even if the aircraft flies at the theoretical aerodynamic limit positive angle of attack, its engine can provide sufficient thrust to balance the drag generated by that angle of attack. Therefore, this current positive angle of attack (i.e., the maximum aerodynamic available positive angle of attack) is also feasible at the power level, and can therefore be directly determined as the actual maximum available positive angle of attack under this state combination.

[0053] In step S221d, when the available thrust of the engine is less than the flight drag, the current positive angle of attack is iteratively reduced and the corresponding flight drag and available thrust of the engine are recalculated until the condition that the available thrust of the engine is not less than the flight drag is met, and the angle of attack corresponding to this time is determined as the maximum available positive angle of attack under the state combination.

[0054] If the available engine thrust is less than the flight drag, it indicates that the drag exceeds the propulsion system's capacity at the aerodynamic limit attitude. At this point, an iterative process is initiated, decreasing the current positive angle of attack in preset small steps. After each decrease in angle of attack, step S221b is re-executed to calculate the flight drag and available engine thrust at the new angle of attack (with constant altitude and speed). Since drag typically decreases with decreasing angle of attack, while available thrust only changes with altitude and speed (a constant value under the current fixed state combination), this iterative process essentially seeks a smaller angle of attack that allows thrust to overcome drag. The iteration continues until an angle of attack value is found such that its corresponding drag is for the first time not greater than the available thrust. The loop terminates at this point, and this maximum positive angle of attack value satisfying the thrust ≥ drag constraint is determined as the actual maximum available positive angle of attack under this specific altitude-speed state combination.

[0055] Furthermore, the solution for the maximum available negative angle of attack under the combined states in step S220 includes: Step S222a: Set the maximum available negative angle of attack at the flight altitude as the current negative angle of attack.

[0056] Assign the maximum available negative angle of attack provided by the aerodynamic characteristic model at the current flight altitude to the iterative variable (i.e., the current negative angle of attack). This maximum available negative angle of attack is a theoretical negative limit value, which is usually determined by the aerodynamic characteristics of the aircraft airfoil or overall aircraft layout in the negative angle of attack direction, such as the boundary of flow separation on the lower surface or the sharp decrease in control surface efficiency. It represents the extreme value of the negative attitude angle allowed by pure aerodynamic angle without considering the limitations of the power system.

[0057] Step S222b: Calculate the flight drag and available engine thrust of the aircraft under the current negative angle of attack, flight altitude and flight speed.

[0058] Based on the determined flight altitude, flight speed, and the set current negative angle of attack, two calculations are performed in parallel. First, the aerodynamic model is invoked, and based on the current Mach number, negative angle of attack, and other necessary parameters, the flight drag generated by the aircraft in this negative attitude is calculated. This drag includes the induced drag component corresponding to the negative lift. Simultaneously, based on the same flight altitude and speed conditions, and combined with the engine's operating mode, the available engine thrust in this state is obtained from the engine thrust characteristic model.

[0059] Step S222c: When the available thrust of the engine is not less than the flight drag, the current negative angle of attack is determined as the maximum available negative angle of attack under the state combination.

[0060] If the calculated available engine thrust is greater than or equal to the flight drag at the current negative angle of attack, it indicates that even if the aircraft is at the theoretical aerodynamic negative angle of attack limit under this flight condition, its engine thrust is sufficient to balance the resulting drag. Therefore, this current negative angle of attack (i.e., the maximum aerodynamic available negative angle of attack) can be determined as the actual maximum available negative angle of attack under this combination of conditions.

[0061] In step S222d, when the available engine thrust is less than the flight drag, the current negative angle of attack is iteratively increased and the corresponding flight drag and available engine thrust are recalculated until the condition that the available engine thrust is not less than the flight drag is met, and the angle of attack corresponding to this time is determined as the maximum available negative angle of attack under the state combination.

[0062] When the engine's available thrust is less than the flight drag, it indicates that the drag generated under the aerodynamic negative limit attitude exceeds the engine's ability to overcome it. At this point, an iterative process is initiated, increasing the current negative angle of attack by a preset step size. It's important to note that since the negative angle of attack is negative, increasing its value means adjusting it towards zero (i.e., increasing the algebraic value), for example, from -10 degrees to -9.99 degrees, which typically leads to a decrease in drag. After each adjustment, step S222b is re-executed to calculate the drag and thrust at the new angle of attack. The iterative process continues until a negative angle of attack value is found such that, for the first time, the engine's available thrust is not less than its flight drag in this state. At this point, the iteration cycle terminates, and this negative angle of attack with the largest algebraic value that satisfies the thrust ≥ drag constraint (i.e., the negative angle of attack closest to zero) is determined as the maximum available negative angle of attack for that specific altitude-velocity state combination.

[0063] Further, in step S300, the flight envelope of the high subsonic fixed-wing aircraft is obtained based on the set of boundary parameters, including: Step S310: Based on the minimum and maximum flight speeds at different flight altitudes in the boundary parameter set, form a velocity-altitude envelope boundary in the velocity-altitude coordinate system that characterizes the range of allowable flight speeds of the aircraft.

[0064] The input is a subset of the boundary parameter set output after step S210 iterates through all preset altitudes, consisting of a series of pairs of (altitude, minimum flight speed) and (altitude, maximum flight speed) data points. In engineering implementation, these discrete data points are plotted or mapped onto a coordinate system with flight speed as the horizontal axis and flight altitude as the vertical axis. Subsequently, through linear interpolation, spline curve fitting, or other data smoothing methods, these groups of data points representing the low-speed and high-speed sides are connected to form two continuous (or piecewise continuous) curves. The lower boundary curve represents the minimum speed limit at which the aircraft can maintain continuous flight at different altitudes, usually determined by stall characteristics and power. The upper boundary curve represents the maximum speed limit at which the engine's maximum thrust can overcome aerodynamic drag at different altitudes. The region enclosed by these two curves is the safe and sustainable level flight range of the aircraft in the speed and altitude dimensions, and is the core component of the classic flight envelope.

[0065] Step S320: Based on the maximum available positive angle of attack and the maximum available negative angle of attack under different state combinations in the boundary parameter set, and combined with the aerodynamic characteristic parameters in the basic input parameters of the flight pressure and dynamics model under the corresponding state combinations, calculate the maximum positive overload value and the maximum negative overload value that characterize the performance limit of the aircraft in the aerodynamic and dynamic dimensions under the corresponding state combinations, and form the overload envelope boundary characterizing the allowable maneuver overload range of the aircraft in the velocity-overload coordinate system.

[0066] The input is another key subset of the boundary parameter set, which is the maximum available positive angle of attack and the maximum available negative angle of attack solved for each traversed (altitude, velocity) state combination. Based on the aerodynamic lift formula, the angle of attack information is converted into overload information. For each state point, the flight dynamic pressure of that state is first calculated based on its flight velocity and atmospheric density at its altitude. Then, the aerodynamic characteristic parameters in the basic input parameters of the dynamic model are called, especially the functional relationship between the lift coefficient and the angle of attack. Substituting the previously solved maximum available positive angle of attack into this function yields the maximum positive lift coefficient for that state; similarly, the maximum available negative angle of attack yields the maximum negative lift coefficient. Subsequently, according to the lift formula (lift = lift coefficient × dynamic pressure × reference area), the maximum positive lift and maximum negative lift that the aircraft can generate at that state point by aerodynamic forces are calculated. Finally, dividing these two lift values ​​by the weight of the aircraft respectively yields the maximum positive overload and maximum negative overload values ​​corresponding to that state point. This process is repeated for all state points to obtain a discrete (velocity, positive / negative overload) data field covering the airspace of interest. In the velocity-overload (Vn) coordinate system, the discrete sets of maximum positive and negative overload values ​​corresponding to all state points, varying with velocity, are used to form two boundary curves through curve fitting or envelope extraction. These two curves define the normal overload limit that the aircraft can achieve at different velocities at a given altitude (or the most conservative combined boundary projected at all altitudes). This limit is entirely determined by the aerodynamic lift generation capability and the engine's ability to overcome corresponding drag, constituting the aircraft's maneuverability envelope.

[0067] Step S330: Output the flight envelope of the high subsonic fixed-wing aircraft, which is composed of the velocity-altitude envelope boundary and the overload envelope boundary.

[0068] The velocity-altitude envelope boundary (VH diagram) generated in step S310 and the overload envelope boundary (Vn diagram) generated in step S320 are logically correlated and encapsulated, and jointly defined as the flight envelope of the high subsonic fixed-wing aircraft. At the implementation level, the output can be a coordinate sequence of two sets of boundary curves saved as a data file, or it can be a directly generated two-dimensional composite chart conforming to engineering standards. The output envelope data clearly distinguishes the permissible flight state (within the envelope) and the prohibited or dangerous state (outside the envelope) of the aircraft, providing designers with a direct basis for evaluating the performance of the design.

[0069] Specifically, the overload envelope boundary is the limit value of the overload capacity that the aerodynamic and propulsion system of the aircraft can provide, independent of the structural strength limitations of the aircraft.

[0070] The overload envelope boundary refers to the physically achievable maximum normal overload capacity limit, determined jointly by the aerodynamic characteristics of the aircraft and the thrust characteristics of the engine. This boundary value originates from the calculation process in step S320. Its core inputs are the maximum usable positive / negative angle of attack that satisfies the thrust ≥ drag constraint after iterative verification, along with the corresponding aerodynamic lift coefficient and flight pressure. It reflects the performance ceiling resulting from the combined effect of the aircraft's aerodynamic potential to generate lift and its ability to provide sufficient thrust in the propulsion system to maintain that lift state. This capability boundary is conceptually and numerically independent of the structural strength limitations determined by the airframe materials and structural design.

[0071] Traditional flight envelope overload boundaries typically use structural allowable values ​​as hard limits, while the method of this invention first calculates the aerodynamic potential boundary. In engineering practice, both define a complete flight safety boundary: actual flight maneuvers cannot exceed structural strength limits (to prevent airframe damage), and in most cases, will not reach the aerodynamic limit (usually the latter is higher than the former). Clearly distinguishing between these two allows the overload envelope provided by this invention to more clearly reveal the theoretical margin of aircraft performance. This provides crucial upper-level performance benchmark information that traditional structural constraint envelopes cannot provide for the design of flight control system envelope protection logic, control law optimization under extreme conditions, and exploration of the maximum maneuver potential of aircraft under special circumstances. This enables a more comprehensive and refined utilization of aircraft performance.

[0072] Furthermore, the available thrust of the engine involved in step S200 is obtained in the following manner: Step S201: Based on the flight altitude, flight speed, and flight angle of attack corresponding to the current iteration step, query the engine thrust characteristic data table established based on the engine thrust characteristic data.

[0073] The acquisition of engine thrust data relies on a pre-generated engine thrust characteristic data table, which is a discrete digital representation of engine performance built upon the engine thrust characteristic data. In the early design and validation phases, this data table typically originates from performance manuals provided by engine suppliers, models fitted using bench test data, or estimated data scaled based on similarity principles. The data table is usually multi-dimensional, indexed by key flight state parameters. For example, its core dimensions include at least flight altitude, flight Mach number, or flight speed, as well as engine state parameters that may affect thrust output (such as throttle position, angle of attack causing changes in intake conditions, etc.). When the iterative calculation reaches a specific state point (e.g., probing a specific angle of attack and speed combination when calculating minimum speed), step S201 first extracts the corresponding flight altitude, flight speed, and the currently calculated angle of attack (angle of attack may affect intake, thus indirectly affecting thrust) for that state point, using these parameters as query conditions to locate the engine thrust characteristic data table.

[0074] Step S202: Based on flight altitude, flight speed, and flight angle of attack, the corresponding available engine thrust is determined from the engine thrust characteristic data table through interpolation calculation.

[0075] Since the engine thrust characteristic data table stores thrust values ​​at a finite number of discrete state points, and the state point parameters (altitude, velocity, angle of attack) in the iterative calculation almost always fall between these discrete data points, interpolation calculations are necessary to obtain thrust estimates for the corresponding state. Step S202, based on the several reference data points (e.g., in a three-dimensional data table, possibly eight points forming a cubic grid) surrounding the current state point determined in step S201, executes the corresponding interpolation algorithm based on the relative positions of the current state parameters and these reference point parameters. Depending on the dimension and accuracy requirements of the data table, linear interpolation, bilinear interpolation, or more complex trilinear interpolation methods may be used. The output of this step is the engine's available thrust value precisely corresponding to the specific flight altitude, flight velocity, and flight angle of attack in the current iteration step. This process transforms the complex, potentially nonlinear, engine thrust characteristics into a definite value that can be quickly obtained through table lookup and calculation, providing efficient and reliable data support for thrust-drag comparisons during the iterative process.

[0076] Traditional flight envelope determination is essentially a divide-and-conquer, integrated sequential engineering process. Each discipline (aerodynamics, propulsion, structure, flight control) first independently calculates its responsible boundary portion based on simplified models or empirical formulas within its respective field (e.g., aerodynamics calculates stall speed, propulsion checks thrust-velocity boundaries, and structure specifies overload and dynamic pressure limits). Then, through multiple coordination meetings and iterations, these segmented, potentially conflicting boundaries are manually integrated and smoothed to create the final flight envelope. This process heavily relies on engineers' experience and struggles to continuously and precisely reveal the coupling relationships between parameters within the entire envelope. In stark contrast, the method described in this invention constructs a unified modeling-automatic solution digital process. The aircraft is viewed as a unified dynamic system composed of mass, engines, and aerodynamic forces. Through pre-defined program logic, the entire pre-defined flight state space is automatically and systematically traversed in the computer. At each state point, all relevant models (thrust and aerodynamic) are synchronously invoked for self-consistent equilibrium calculations, and decisions are made based on a unified physical criterion (thrust ≥ drag). This not only frees engineers from the burden of multidisciplinary coordination and manual drafting, but more importantly, through continuous and intensive state point calculations, it naturally generates a complete performance data field near the envelope boundary and even within the entire envelope, providing unprecedented data support for understanding the nonlinear characteristics of aircraft and identifying performance bottlenecks. This method transforms the traditional engineering analysis process, characterized by experience, segmentation, and discretization, into a digital simulation process characterized by models, unification, and continuity, representing a significant methodological advancement.

[0077] The embodiments of this invention aim to protect a rapid calculation method for the flight envelope of a high subsonic fixed-wing aircraft, which has the following effects: 1. By constructing an iterative approximation calculation process with the combination of flight altitude and speed states as the traversal framework and thrust not less than drag as the real-time verification condition, the high-speed processing power of computers is fully utilized to achieve efficient and automatic solution of the flight envelope boundary. This significantly improves the efficiency of envelope calculation, enables rapid results in the design and demonstration stage, and effectively overcomes the inherent limitations of traditional analytical methods in accurately handling high subsonic strongly nonlinear aerodynamic coupling problems, providing key support for scheme iteration and early verification. 2. The basic input parameters of the dynamic model allow the engine and aerodynamic models to be constructed using mathematical models of varying precision, ranging from simple linear to complex nonlinear and strongly coupled. This endows the method with strong adaptability and scalability, enabling it to be compatible with the data foundation of different design stages and the characteristics of different aircraft models. It can perform both rapid estimation and high-fidelity analysis, thus solving the problem that traditional methods rely on fixed empirical formulas and are difficult to flexibly adapt to different model precision and complex system characteristics. 3. The calculated overload envelope boundary is defined as the capability boundary determined by the ultimate performance of the aircraft's aerodynamic and propulsion systems, and it is decoupled from the structural strength constraints of the aircraft. This allows the obtained envelope data to more purely reflect the aerodynamic potential of the aircraft, providing key performance benchmarks beyond the traditional structural constraint envelope for flight control law design, envelope protection system development, and extreme mission planning. This solves the problem of insufficient boundary information in traditional envelopes when guiding controller design and exploring flight performance.

[0078] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and not to limit it. Although the present invention has been described in detail with reference to the above embodiments, those skilled in the art should understand that modifications or equivalent substitutions can still be made to the specific implementation of the present invention. Any modifications or equivalent substitutions that do not depart from the spirit and scope of the present invention should be covered within the scope of protection of the claims of the present invention.

Claims

1. A method for rapidly calculating the flight envelope of a high subsonic fixed-wing aircraft, characterized in that, Includes the following steps: Obtain the basic input parameters for the dynamic model of a high subsonic fixed-wing aircraft; Based on the basic input parameters of the dynamic model, the angle of attack is iteratively approximated by using the condition that the available thrust of the engine is not less than the flight drag as the iterative constraint, and the set of boundary parameters used to define the boundary of the flight envelope is determined. Based on the set of boundary parameters, the flight envelope of the high subsonic fixed-wing aircraft is obtained.

2. The method for rapidly calculating the flight envelope of a high subsonic fixed-wing aircraft according to claim 1, characterized in that, The basic input parameters of the dynamic model include at least: preset overall parameters, engine thrust characteristic data, and aerodynamic characteristic parameters.

3. The method for rapidly calculating the flight envelope of a high subsonic fixed-wing aircraft according to claim 2, characterized in that, The set of boundary parameters includes: the minimum and maximum flight speeds at each altitude within the preset flight altitude range, and the maximum available positive angle of attack and the maximum available negative angle of attack at each state point within the preset flight speed-altitude range; Based on the fundamental input parameters of the aforementioned dynamic model, the set of boundary parameters used to define the flight envelope boundary is determined by iteratively approximating the flight angle of attack with the engine's available thrust not being less than the flight drag as the iterative constraint. This includes: Traverse the preset flight altitude range. For each flight altitude, iteratively adjust the flight angle of attack and verify whether the available thrust of the engine is not less than the flight drag of the corresponding state. Sequentially solve to determine the minimum and maximum flight speeds at the flight altitudes and obtain the parameters defining the velocity-altitude boundary in the flight envelope. The system iterates through the state combinations formed by the preset flight speed range and the flight altitude range. For each state combination, it iterates and adjusts the flight angle of attack and checks whether the available engine thrust is not less than the flight drag of the corresponding state. It then solves and determines the maximum available positive angle of attack and the maximum available negative angle of attack under the state combination, thereby obtaining the parameters that define the overload boundary in the flight envelope.

4. The method for rapidly calculating the flight envelope of a high subsonic fixed-wing aircraft according to claim 3, characterized in that, Determining the minimum flight speed at the stated flight altitude includes: The maximum available positive angle of attack at the flight altitude is set as the initial angle of attack, and the initial flight speed that satisfies the balance between torque and lift is calculated at the initial angle of attack. Calculate the flight drag and available engine thrust of the aircraft at the initial angle of attack and initial flight speed. When the available thrust of the engine is not less than the flight drag, the initial flight speed is determined as the minimum flight speed; When the available thrust of the engine is less than the flight drag, the initial angle of attack is iteratively reduced and the corresponding flight speed, flight drag and available thrust of the engine are recalculated until the condition that the available thrust of the engine is not less than the flight drag is met, and the flight speed at this time is determined as the minimum flight speed.

5. The method for rapidly calculating the flight envelope of a high subsonic fixed-wing aircraft according to claim 3, characterized in that, Determining the maximum flight speed at the stated flight altitude includes: Starting from the minimum flight speed at the specified flight altitude, calculate the trim angle of attack, trim rudder deflection, and level flight drag that satisfy the level flight balance conditions at the current flight speed, and obtain the corresponding available engine thrust. When the available thrust of the engine is greater than the level flight drag, increase the current flight speed and repeat the calculation and acquisition steps; When the available thrust of the engine is less than or equal to the level flight drag, the current flight speed before the increase is determined as the maximum flight speed.

6. The method for rapidly calculating the flight envelope of a high subsonic fixed-wing aircraft according to claim 3, characterized in that, Determining the maximum usable positive angle of attack under the given state combination includes: Set the maximum available aerodynamic angle of attack at the flight altitude as the current angle of attack; Calculate the flight drag and available engine thrust of the aircraft at the current positive angle of attack, flight altitude, and flight speed. When the available thrust of the engine is not less than the flight drag, the current positive angle of attack is determined as the maximum available positive angle of attack under the state combination; When the available thrust of the engine is less than the flight drag, the current positive angle of attack is iteratively reduced and the corresponding flight drag and available thrust of the engine are recalculated until the condition that the available thrust of the engine is not less than the flight drag is met, and the angle of attack corresponding to this time is determined as the maximum available positive angle of attack under the state combination.

7. The method for rapidly calculating the flight envelope of a high subsonic fixed-wing aircraft according to claim 3, characterized in that, Determining the maximum usable negative angle of attack under the given state combination includes: Set the maximum available negative angle of attack at the flight altitude as the current negative angle of attack; Calculate the flight drag and available engine thrust of the aircraft under the current negative angle of attack, flight altitude, and flight speed conditions; When the available thrust of the engine is not less than the flight drag, the current negative angle of attack is determined as the maximum available negative angle of attack under the state combination; When the available thrust of the engine is less than the flight drag, the current negative angle of attack is iteratively increased and the corresponding flight drag and available thrust of the engine are recalculated until the condition that the available thrust of the engine is not less than the flight drag is met, and the angle of attack corresponding to this time is determined as the maximum available negative angle of attack under the state combination.

8. The method for rapidly calculating the flight envelope of a high subsonic fixed-wing aircraft according to any one of claims 3-7, characterized in that, The process of obtaining the flight envelope of the high subsonic fixed-wing aircraft based on the set of boundary parameters includes: Based on the minimum and maximum flight speeds at different flight altitudes in the set of boundary parameters, a velocity-altitude envelope boundary characterizing the range of permissible flight speeds of the aircraft is formed in the velocity-altitude coordinate system. Based on the maximum available positive angle of attack and the maximum available negative angle of attack under different state combinations in the boundary parameter set, and combined with the flight kinematics under the corresponding state combinations and the aerodynamic characteristic parameters in the basic input parameters of the dynamic model, the maximum positive overload value and the maximum negative overload value, which characterize the performance limit of the aircraft in the aerodynamic and dynamic dimensions under the corresponding state combinations, are calculated respectively, and an overload envelope boundary characterizing the allowable maneuver overload range of the aircraft is formed in the velocity-overload coordinate system. The output is the flight envelope of the high subsonic fixed-wing aircraft, which is formed by the velocity-altitude envelope boundary and the overload envelope boundary.

9. The method for rapidly calculating the flight envelope of a high subsonic fixed-wing aircraft according to claim 8, characterized in that, The overload envelope boundary is the limit value of the overload capacity that the aerodynamic and propulsion system of the aircraft can provide, independent of the structural strength limit of the aircraft.

10. The method for rapidly calculating the flight envelope of a high subsonic fixed-wing aircraft according to any one of claims 1-7, characterized in that, The engine's usable thrust is obtained through the following methods: Based on the flight altitude, flight speed, and angle of attack corresponding to the current iteration step, query the engine thrust characteristic data table established based on the engine thrust characteristic data; Based on the flight altitude, flight speed, and flight angle of attack, the corresponding available engine thrust is determined from the engine thrust characteristic data table through interpolation calculation.

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