Method for rapidly designing air suction mode climbing section track of combined power aircraft in consideration of multiple constraints
By using thrust characteristic analysis and Newton's iteration method to design the air-breathing mode climb trajectory of a combined-power aircraft that satisfies multiple constraints, the problem of traditional methods being unable to take multiple constraints into account is solved, and rapid design and performance improvement are achieved.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- HARBIN INST OF TECH
- Filing Date
- 2025-12-10
- Publication Date
- 2026-04-24
AI Technical Summary
Traditional methods struggle to rapidly design the trajectory of the air-breathing mode climb phase of a combined-powered aircraft under multiple constraints, especially under flight process constraints such as dynamic pressure, normal overload, and rate of change of angle of attack. Furthermore, existing trajectory optimization methods are slow to solve, which affects flight performance.
By analyzing thrust characteristics, generating a height-velocity profile with maximum specific impulse, designing a track angle profile, and using Newton's iterative angle-of-attack command, the trajectory design for the air-breathing mode climb phase of a combined-powered aircraft that satisfies constraints on dynamic pressure, normal overload, and rate of change of angle of attack is achieved.
It enhances the carrying capacity of combined-powered aircraft, improves their adaptability to complex environments and missions, and supports the rapid iteration of overall aircraft design.
Smart Images
Figure CN121920003A_ABST
Abstract
Description
Technical Field
[0001] This invention belongs to the field of aircraft trajectory design and relates to a trajectory design method for combined-powered aircraft, specifically a rapid trajectory design method for the air-breathing mode climb phase of a combined-powered aircraft that considers multiple constraints. Background Technology
[0002] With the development of flight missions, traditional launch vehicle platforms are prohibitively expensive, failing to meet the economic demands of a massive number of missions. Combined-fuel aircraft, due to their low cost, fast response speed, high reliability, and strong maneuverability, are becoming increasingly important. However, the aerodynamic performance and engine performance of combined-fuel aircraft are highly coupled, and the flight process involves dramatic changes in state and complex flight environments, making it difficult for traditional methods to simultaneously address multiple flight constraints. Therefore, how to achieve rapid design of the air-breathing mode climb trajectory through thrust performance analysis under multiple constraints such as dynamic pressure, normal overload, and rate of change of angle of attack, thereby improving the carrying capacity of combined-fuel aircraft and supporting rapid iteration of the overall aircraft design, is a key technical problem that urgently needs to be overcome.
[0003] The impact of multiple constraints and air-breathing modes on the climb trajectory design of combined-fuel aircraft is mainly reflected in:
[0004] 1. Air-breathing engines are constrained by their operating envelope. Because air-breathing engines are greatly affected by atmospheric parameters, engine parameters such as thrust and specific impulse change drastically with altitude and speed, making it difficult to achieve a smooth climb during the air-breathing mode climb phase.
[0005] 2. Combined-fuel aircraft exhibit severe aero-thrust coupling in the air-breathing mode, and their flight states change drastically and the flight environment is complex. Traditional trajectory design methods struggle to account for constraints such as full-profile dynamic pressure, normal overload, and rate of change of angle of attack, while trajectory optimization-based methods are slow to solve, severely impacting the flight performance of combined-fuel aircraft.
[0006] Therefore, there is an urgent need to develop a rapid design method for the trajectory of the air-breathing mode climb phase of a combined-powered aircraft that considers multiple constraints, so as to improve the carrying capacity of the combined-powered aircraft and support the rapid iteration of the overall aircraft design. Summary of the Invention
[0007] To overcome the problems of severe dynamic coupling of air pressure during the climb phase of air-breathing mode in existing combined-propellant aircraft, and the difficulty in meeting flight process constraints such as dynamic pressure, normal overload, and rate of change of angle of attack under drastically changing flight environments, as well as the slow solution speed of trajectory optimization-based methods, this invention provides a rapid trajectory design method for the climb phase of air-breathing mode in combined-propellant aircraft that considers multiple constraints. This method can improve the carrying capacity of combined-propellant aircraft and enhance their adaptability to complex environments and missions.
[0008] The objective of this invention is achieved through the following technical solution:
[0009] A rapid design method for the climb trajectory of an air-breathing mode of a combined-powered aircraft considering multiple constraints includes the following steps:
[0010] Step 1: Thrust and drag characteristics analysis of air-breathing mode of combined-powered aircraft:
[0011] Based on the parameters and aerodynamic parameters of the air-breathing engine in the combined-propellant aircraft, thrust-drag characteristic analysis is performed. The operating range of the air-breathing engine is narrowed down to the point where the thrust-drag ratio meets the requirements of the climb phase, thus obtaining the operating range that satisfies the thrust-drag characteristics.
[0012] Engine parameters include engine thrust and specific impulse, expressed as follows:
[0013]
[0014] In the formula: For thrust, For the purpose of comparison, For height, For speed, It is a function of thrust with respect to altitude and velocity. It is a function of specific impulse with respect to height and velocity;
[0015] Aerodynamic parameters, including drag, are calculated using the following formula:
[0016]
[0017] In the formula: As resistance, For dynamic pressure, The drag coefficient, For reference area;
[0018] Step 2: Generating the height-velocity profile with maximum specific impulse:
[0019] Based on the results of thrust characteristic analysis and dynamic pressure constraints, a height-velocity profile is generated that satisfies the dynamic pressure constraints and maximizes the specific impulse of the air-breathing engine, wherein:
[0020] The formula for calculating dynamic pressure is:
[0021]
[0022] In the formula: For dynamic pressure, Atmospheric density, For speed;
[0023] Step 3: Generate track angle profile:
[0024] The desired track angle is designed based on the altitude-velocity profile with the maximum specific impulse, and the track angle profile is generated. The specific steps are as follows:
[0025] Step 3-1, the aircraft dynamics equations are expressed as:
[0026]
[0027] In the formula: For a high rate of change, For the rate of change of velocity, For speed, For the track angle, For acceleration;
[0028] Step 3-2, taking the differential of height with respect to velocity, we have:
[0029]
[0030] Step 3-3: Integrate over the height to obtain:
[0031]
[0032] In the formula: This is the initial height. For terminal height, The initial velocity, For the terminal speed, the transformation yields:
[0033]
[0034] Steps 3-4: Initial height within one integration step Initial velocity and terminal height Terminal speed At a given time, the acceleration of the aircraft Determine the desired track angle Thus, the track angle profile is obtained;
[0035] Step 4: Obtain the aircraft's angle-of-attack command constraints based on normal overload and rate of change of angle of attack:
[0036] Based on satisfying the dynamic pressure constraint, the trajectory of the combined-powered aircraft in the air-breathing mode climb phase is further made to satisfy the normal overload and angle of attack rate of change constraints, resulting in a trajectory that satisfies multiple constraints. The specific steps are as follows:
[0037] Step 4-1, Normal Overload Represented as:
[0038]
[0039] In the formula: For lift, As resistance, For the mass of the aircraft, For the angle of attack, It is the acceleration due to gravity;
[0040] Step 4-2: Obtain the angle-of-attack command constraint range using Newton's iteration method based on the normal overload constraint range:
[0041]
[0042] In the formula: This is the minimum angle of attack allowed for normal overload. This is the maximum angle of attack allowed for normal overload;
[0043] Step 4-3: Based on the angle-of-attack rate of change constraint and the aircraft's current angle of attack, obtain the angle-of-attack command constraint range for the aircraft after one integral step.
[0044]
[0045] In the formula: The current angle of attack of the aircraft. The integration step size is... For the maximum angle of attack change rate, The minimum angle of attack allowed by the rate of change of angle of attack. The maximum angle of attack allowed by the rate of change of angle of attack;
[0046] Step 4-4: Obtain a set of angle-of-attack command constraints from the combined-powered aircraft structure:
[0047]
[0048] In the formula: The minimum angle of attack allowed by the aircraft structure. The maximum angle of attack allowed by the aircraft structure;
[0049] Step 4-5: Obtain the final angle-of-attack command constraint range by taking the intersection of all constraints from Steps 4-2, 4-3, and 4-4.
[0050]
[0051] In the formula: This is the minimum value of the angle of attack command. This represents the maximum value of the angle of attack command.
[0052] Step 5: Calculation of angle of attack command based on Newton's iterative method:
[0053] The angle-of-attack command satisfying the normal overload constraint and the rate of change of angle of attack constraint is obtained from the track angle profile using the Newton-Raphson iteration method. Based on the angle-of-attack command, the trajectory of the air-breathing mode climb segment of the combined-powered aircraft satisfying the constraints of dynamic pressure, normal overload, and rate of change of angle of attack is finally obtained. The specific steps are as follows:
[0054] Step 5-1: Utilize the desired track angle The difference between the current track angle and the expected track angle change is obtained. ;
[0055] Step 5-2: Based on the integration step size Change in desired track angle The desired rate of change of the trajectory angle is obtained, and the angle of attack is iterated based on Newton's iteration method. This makes the following equation true:
[0056]
[0057] In the formula: To allow for error, the angle of attack is obtained. ;
[0058] Step 5-3: Limit the amplitude according to the angle of attack command constraint range:
[0059]
[0060] In the formula: This is the minimum value of the angle of attack command. This represents the maximum value of the angle of attack command. The angle of attack is obtained from Newton's iteration. To obtain the angle-of-attack command that satisfies the constraints of normal overload and rate of change of angle of attack;
[0061] Step 5-4: Integrate the angle of attack command to achieve rapid design of the air-breathing mode climb trajectory of a combined-powered aircraft that considers dynamic pressure, normal overload, and angle of attack rate of change constraints.
[0062] Compared with the prior art, the present invention has the following advantages:
[0063] This invention analyzes the thrust-drag characteristics of an air-breathing engine in a combined-propellant aircraft based on its parameters and aerodynamic parameters, obtaining a height-velocity profile that maximizes the specific impulse of the air-breathing engine while satisfying dynamic pressure constraints. This provides a solid foundation for trajectory design during the climb phase of the air-breathing mode in a combined-propellant aircraft. Based on the height-velocity profile, a desired track angle is designed to obtain a track angle profile, resulting in smoother trajectory parameter changes. By integrating the angle-of-attack command obtained through Newton's iteration method, which satisfies constraints on normal overload and rate of change of angle of attack, rapid trajectory design for the climb phase of the air-breathing mode in a combined-propellant aircraft, considering constraints such as dynamic pressure, normal overload, and rate of change of angle of attack, is achieved. This enhances the carrying capacity of the combined-propellant aircraft and supports rapid iteration of the overall aircraft design. Attached Figure Description
[0064] Figure 1 A flowchart of a rapid design method for the climb trajectory of an air-breathing mode of a combined-powered aircraft considering multiple constraints;
[0065] Figure 2 A simulation diagram of the maximum specific impulse altitude-velocity profile for the climb phase of an air-breathing mode of a combined-powered aircraft, satisfying dynamic pressure constraints.
[0066] Figure 3 A schematic diagram of the angle of attack command for the climb phase of an air-breathing mode of a combined-powered aircraft;
[0067] Figure 4 A schematic diagram of the velocity during the climb phase of an air-breathing mode for a combined-propellant aircraft.
[0068] Figure 5 This is a schematic diagram showing the altitude of the air-breathing mode climb phase of a combined-powered aircraft. Detailed Implementation
[0069] The technical solution of the present invention will be further described below with reference to the accompanying drawings, but it is not limited thereto. Any modifications or equivalent substitutions to the technical solution of the present invention that do not depart from the spirit and scope of the technical solution of the present invention should be covered within the protection scope of the present invention.
[0070] This invention provides a rapid design method for the climb trajectory of a combined-powered aircraft in the air-breathing mode, considering multiple constraints, such as... Figure 1 As shown, the method includes the following steps:
[0071] Step 1: Thrust and drag characteristics analysis of air-breathing mode of combined-powered aircraft:
[0072] To address the issues of severe aerodynamic coupling and drastic changes in the flight environment during the climb phase of the air-breathing mode of combined-propellant aircraft, thrust-drag characteristics are analyzed based on the engine parameters and aerodynamic parameters of the air-breathing mode of the combined-propellant aircraft.
[0073] The air-breathing engine of a combined-propellant aircraft has an operating envelope constraint in the form of altitude-velocity; the engine cannot operate outside its operating range. The expressions for engine thrust and specific impulse are as follows:
[0074]
[0075] In the formula: For thrust, For the purpose of comparison, For height, For speed, It is a function of thrust with respect to altitude and velocity. It is a function of specific impulse with respect to height and velocity.
[0076] The formula for calculating resistance is:
[0077]
[0078] In the formula: As resistance, For dynamic pressure, The drag coefficient, For reference area.
[0079] Since the dynamic pressure is large when the specific impulse of an air-breathing engine is large, and as can be seen from the above formula, the resistance is also large when the dynamic pressure is large. Therefore, the thrust-resistance characteristic analysis is performed to narrow the working range of the air-breathing engine to the point where the thrust-resistance ratio meets the requirements of the climbing section, thus obtaining the working range that meets the thrust-resistance characteristics.
[0080] Step 2: Generating the height-velocity profile with maximum specific impulse:
[0081] Based on the results of thrust characteristic analysis and dynamic pressure constraints, a height-velocity profile is generated that satisfies the dynamic pressure constraints and maximizes the specific impulse of the air-breathing engine. The combined-powered aircraft has the maximum specific impulse and the maximum carrying capacity when flying on this profile.
[0082] The formula for calculating dynamic pressure is:
[0083]
[0084] In the formula: For dynamic pressure, Atmospheric density, Let velocity be the velocity. Since atmospheric density is a function of altitude, the dynamic pressure constraint curve is plotted on the altitude-velocity diagram based on the dynamic pressure constraint to obtain the working range that satisfies the dynamic pressure constraint. Within this working range, the altitude-velocity profile with the maximum specific impulse satisfying the dynamic pressure constraint for the aircraft is obtained, as shown below. Figure 2 As shown.
[0085] Step 3: Generate track angle profile:
[0086] To address the issues of severe aerodynamic coupling and drastic changes in the flight environment during the climb phase of the air-breathing mode in combined-fuel aircraft, the desired track angle is designed based on the altitude-velocity profile with the highest specific impulse. This generates a track angle profile, which makes the trajectory parameters change slowly and smoothly, thereby obtaining a smoother trajectory for directly designing the angle of attack command.
[0087] From the equations of motion of the aircraft, we have:
[0088]
[0089] In the formula: For a high rate of change, For the rate of change of velocity, For speed, For the track angle, Let the velocity be the acceleration. Taking the differential of height with respect to velocity, we have:
[0090]
[0091] During the analysis, it is approximately assumed that the track angle within each integration step is... and acceleration All remain constant, so integrating over the height yields:
[0092]
[0093] In the formula: The initial height, For terminal height, The initial velocity, The terminal speed is given by the transformation:
[0094]
[0095] The above formula shows that when the initial height is within an integration step... Initial velocity and terminal height Terminal speed Given a time, the acceleration of the aircraft can be used. Determine the desired track angle Within one integration step, the initial height Initial velocity acceleration It is determined by the current state of the aircraft, while the terminal altitude Terminal speed Based on the altitude-velocity profile described above, the desired track angle is determined, thus obtaining the track angle profile.
[0096] Step 4: Obtain the aircraft's angle-of-attack command constraints based on normal overload and rate of change of angle of attack:
[0097] Based on satisfying the dynamic pressure constraint, the trajectory of the combined propulsion aircraft in the air-breathing mode climb segment is further made to satisfy the normal overload and angle of attack rate of change constraints, resulting in a trajectory that satisfies multiple constraints.
[0098] First, normal overload It can be represented as:
[0099]
[0100] In the formula: For lift, As resistance, For the mass of the aircraft, For the angle of attack, This is the acceleration due to gravity.
[0101] Given a fixed aircraft parameter such as mass, lift and resistance All are angles of attack The function, obtained using Newton's iteration method, yields the angle-of-attack command constraint range based on the normal overload constraint range, as follows:
[0102]
[0103] In the formula: This is the minimum angle of attack allowed for normal overload. This is the maximum angle of attack allowed for normal overload.
[0104] During flight of a combined-powered aircraft, the angle of attack cannot change too drastically due to limitations in the actuators. Therefore, it is necessary to constrain the rate of change of angle of attack. Based on the constraint of the rate of change of angle of attack and the current angle of attack of the aircraft, the constraint range of the angle of attack command after one integral step can be obtained as follows:
[0105]
[0106] In the formula: The current angle of attack of the aircraft. For the integration step size, For the maximum angle of attack change rate, The minimum angle of attack allowed by the rate of change of angle of attack. This represents the maximum angle of attack allowed by the rate of change of angle of attack.
[0107] Finally, based on the structure of the combined-powered aircraft, a set of angle-of-attack command constraints can be obtained as follows:
[0108]
[0109] In the formula: The minimum angle of attack allowed by the aircraft structure. This is the maximum angle of attack allowed by the aircraft structure.
[0110] The final angle-of-attack command constraint range is obtained by intersecting all the above constraints.
[0111]
[0112] In the formula: This is the minimum value of the angle of attack command. This represents the maximum value of the angle of attack command.
[0113] Step 5: Calculation of angle of attack command based on Newton's iterative method:
[0114] The angle of attack command that satisfies the normal overload constraint and the rate of change of angle of attack constraint is obtained by using the Newton iteration method based on the track angle profile. The trajectory of the combined propulsion aircraft in the air-breathing mode climb segment that satisfies the constraints of dynamic pressure, normal overload, and rate of change of angle of attack is finally obtained by integrating the angle of attack command.
[0115] The iterative formula is derived from the track angle profile. The desired track angle is then used. The difference between the current track angle and the current track angle can be used to obtain the expected change in track angle. The simplified dynamic equations are as follows:
[0116]
[0117] In the formula, The distance from the Earth's center. It is the acceleration due to gravity. For engine thrust, For lift, For the mass of the aircraft, For speed, For the angle of attack, For the track angle, Let be the rate of change of the track angle. In the above equation, once altitude, speed, current track angle, and mass are determined, the right side of the equation is only a function of the angle of attack. That is:
[0118]
[0119] In the formula: Angle of attack. Based on the integral step size. It can be determined by the expected change in track angle. The desired rate of change of the trajectory angle is obtained, and the angle of attack is iterated based on Newton's iteration method. This makes the following equation true:
[0120]
[0121] In the formula: To account for the tolerance, the angle of attack can then be obtained. And based on the angle-of-attack command constraint range in step 4, the amplitude is limited as follows:
[0122]
[0123] In the formula: This is the minimum value of the angle of attack command. This represents the maximum value of the angle of attack command. The angle of attack is obtained from Newton's iteration. To obtain the final angle-of-attack command that satisfies the constraints of normal overload and rate of change of angle of attack, the angle-of-attack command is integrated to achieve rapid design of the air-breathing mode climb trajectory of the combined-powered aircraft, taking into account constraints such as dynamic pressure, normal overload, and rate of change of angle of attack. This improves the carrying capacity of the combined-powered aircraft and supports rapid iteration of the overall aircraft design.
[0124] Simulation example:
[0125] Based on the thrust-drag characteristic analysis of the air-breathing mode engine parameters and aerodynamic parameters of the combined-propellant aircraft, the altitude-velocity profile that maximizes the specific impulse while satisfying the dynamic pressure constraint is obtained as follows: Figure 2 As shown. The angle-of-attack command that satisfies the constraints of dynamic pressure, normal overload, and rate of change of angle of attack, obtained using Newton's iteration method, is as follows: Figure 3 As shown, the velocity-time curve of the air-breathing mode climb trajectory of the combined-powered aircraft obtained by integrating the angle-of-attack command is as follows: Figure 4 As shown, the height-time curve is as follows: Figure 5 As shown.
Claims
1. A rapid design method for the trajectory of the air-breathing mode climb phase of a combined-powered aircraft considering multiple constraints, characterized in that... The method includes the following steps: Step 1: Thrust and drag characteristics analysis of air-breathing mode of combined-powered aircraft: Based on the parameters and aerodynamic parameters of the air-breathing engine of the combined propulsion aircraft, the thrust-drag characteristics are analyzed, and the working range of the air-breathing engine is narrowed down to the point where the thrust-drag ratio meets the requirements of the climb section, thus obtaining the working range that meets the thrust-drag characteristics. Step 2: Generating the height-velocity profile with maximum specific impulse: Based on the results of thrust characteristic analysis and dynamic pressure constraints, a height-velocity profile that satisfies the dynamic pressure constraints and maximizes the specific impulse of the air-breathing engine is generated. Step 3: Generate track angle profile: The desired track angle is designed based on the altitude-velocity profile with the maximum specific impulse, and the track angle profile is generated. Step 4: Obtain the aircraft's angle-of-attack command constraints based on normal overload and rate of change of angle of attack: Based on satisfying the dynamic pressure constraint, the trajectory of the air-breathing mode climb segment of the combined propulsion aircraft is further made to satisfy the normal overload and angle of attack rate of change constraints, resulting in a trajectory that satisfies multiple constraints; Step 5: Calculation of angle of attack command based on Newton's iterative method: The angle of attack command that satisfies the normal overload constraint and the angle of attack rate of change constraint is obtained by using the Newton iteration method based on the track angle profile. The trajectory of the combined propulsion aircraft in the air-breathing mode climb segment that satisfies the constraints of dynamic pressure, normal overload, and angle of attack rate of change is finally obtained by integrating the angle of attack command.
2. The rapid trajectory design method for the air-breathing mode climb segment of a combined-powered aircraft considering multiple constraints, as described in claim 1, is characterized in that... In step 1, the engine parameters include engine thrust and specific impulse, expressed as follows: In the formula: For thrust, For the purpose of comparison, For height, For speed, It is a function of thrust with respect to altitude and velocity. It is a function of specific impulse with respect to height and velocity.
3. The rapid design method for the climb trajectory of a combined-powered aircraft considering multiple constraints in the air-breathing mode, as described in claim 1, is characterized in that... In step 1, the aerodynamic parameters include resistance, and the calculation formula is as follows: In the formula: As resistance, For dynamic pressure, The drag coefficient, For reference area.
4. The rapid design method for the climb trajectory of a combined-powered aircraft considering multiple constraints in the air-breathing mode, as described in claim 1, is characterized in that... In step 2, the formula for calculating dynamic pressure is: In the formula: For dynamic pressure, Atmospheric density, For speed.
5. The rapid design method for the climb trajectory of a combined-powered aircraft considering multiple constraints in the air-breathing mode, as described in claim 1, is characterized in that... The specific steps of step 3 are as follows: Step 3-1, the aircraft dynamics equations are expressed as: In the formula: For a high rate of change, For the rate of change of velocity, For speed, For the track angle, For acceleration; Step 3-2, taking the differential of height with respect to velocity, we have: Step 3-3: Integrate over the height to obtain: In the formula: This is the initial height. For terminal height, The initial velocity, For the terminal speed, the transformation yields: Steps 3-4: Initial height within one integration step Initial velocity and terminal height Terminal speed At a given time, the acceleration of the aircraft Determine the desired track angle The track angle profile is obtained.
6. The rapid design method for the climb trajectory of a combined-powered aircraft considering multiple constraints in the air-breathing mode, as described in claim 1, is characterized in that... The specific steps of step 4 are as follows: Step 4-1, Normal Overload Represented as: In the formula: For lift, As resistance, For the mass of the aircraft, For the angle of attack, It is the acceleration due to gravity; Step 4-2: Obtain the angle-of-attack command constraint range using Newton's iteration method based on the normal overload constraint range: In the formula: This is the minimum angle of attack allowed for normal overload. This is the maximum angle of attack allowed for normal overload; Step 4-3: Based on the angle-of-attack rate of change constraint and the aircraft's current angle of attack, obtain the angle-of-attack command constraint range for the aircraft after one integral step. In the formula: The current angle of attack of the aircraft. The integration step size is... For the maximum angle of attack change rate, The minimum angle of attack allowed by the rate of change of angle of attack. The maximum angle of attack allowed by the rate of change of angle of attack; Step 4-4: Obtain a set of angle-of-attack command constraints from the combined-powered aircraft structure: In the formula: The minimum angle of attack allowed by the aircraft structure. The maximum angle of attack allowed by the aircraft structure; Step 4-5: Obtain the final angle-of-attack command constraint range by taking the intersection of all constraints from Steps 4-2, 4-3, and 4-4. In the formula: This is the minimum value of the angle of attack command. This represents the maximum value of the angle of attack command.
7. The rapid design method for the climb trajectory of a combined-powered aircraft considering multiple constraints in the air-breathing mode, as described in claim 6, is characterized in that... The specific steps of step 5 are as follows: Step 5-1: Utilize the desired track angle The difference between the current track angle and the expected track angle change is obtained. ; Step 5-2: Based on the integration step size Change in desired track angle The desired rate of change of the trajectory angle is obtained, and the angle of attack is iterated based on Newton's iteration method. This makes the following equation true: In the formula: To allow for error, the angle of attack is obtained. ; Step 5-3: Limit the amplitude according to the angle of attack command constraint range: In the formula: This is the minimum value of the angle of attack command. This represents the maximum value of the angle of attack command. The angle of attack is obtained from Newton's iteration. To obtain the angle-of-attack command that satisfies the constraints of normal overload and rate of change of angle of attack; Step 5-4: Integrate the angle of attack command to achieve rapid design of the air-breathing mode climb trajectory of a combined-powered aircraft that considers dynamic pressure, normal overload, and angle of attack rate of change constraints.