A flight plan-based aircraft flight trajectory rapid generation method

Abstract

The application discloses a kind of aircraft flight trajectory quick generation method based on flight plan, trajectory data is acquired to different models;Flight phase is divided according to trajectory data;Determine key performance parameters;From trajectory data, the key performance parameter value of each flight phase is extracted;Establish flight performance database;According to the change rule of aircraft trajectory parameter, the kinematic model including trajectory data model and trajectory point coordinate model is established;Using trajectory data model obtains trajectory point speed, trajectory point height, aircraft flies the range, aircraft flies the heading data such as, imports trajectory point coordinate model and generates the airport coordinate system coordinate and latitude and longitude coordinate of trajectory point;According to the formulated flight plan, in kinematic model, aircraft flies the waypoint coordinate and cruising altitude, cruising speed such as flight information are imported, call flight performance database, generate trajectory data.The application conforms to the flight standard of our country;And can greatly reduce trajectory generation time.

Description

Technical Field

[0001] This invention belongs to the field of civil air traffic control automation and intelligence technology, specifically relating to a method for rapidly generating aircraft flight trajectories based on flight plans. Background Technology

[0002] my country's civil aviation industry is currently experiencing rapid development. While the air transport market is expanding rapidly, the air traffic environment is becoming increasingly complex. The surge in passenger and cargo traffic, coupled with a lack of airspace capacity planning, has led to air traffic congestion and delays, flight conflicts, and other issues, which are detrimental to civil aviation safety and air traffic management. Therefore, accurate, reasonable, and effective airspace capacity assessment, airspace operational efficiency assessment, and traffic flow conflict safety assessment are crucial methods for improving airspace utilization, enhancing airport service capabilities, and ensuring civil aviation operational safety. Currently, using computer simulation technology to simulate airspace operations has become one of the most commonly used assessment methods.

[0003] Computer simulation technology simulates actual conditions using scenario models and operational data. When using computer simulation technology to simulate airspace operations, aircraft flight trajectory data based on flight plans is essential. Due to the massive number of flights in the airspace during simulations and the need to adjust flight plans according to the simulation results, a large amount of flight trajectory data must be generated within a short period of time according to the flight plans. Flight performance databases contain performance parameter values ​​for important nodes during aircraft flight and are necessary for trajectory generation. Commonly used flight performance databases are built based on performance reports published by aircraft manufacturers and proprietary flight data. However, these data sources are costly and subject to certain licensing restrictions. Furthermore, the models themselves are developed according to foreign flight regulations, meaning they do not conform to actual operational conditions in my country, making trajectory generation research difficult. Nowadays, most commercial aircraft are equipped with radar equipment, making aircraft flight data more readily available, providing aircraft performance monitoring data such as position, altitude, and speed.

[0004] Trajectory generation models are classified in different ways. The most complex six-degree-of-freedom model is often used in aircraft flight control studies, while the point mass model is commonly used for aircraft flight trajectory studies. In the point mass model, the aircraft's roll, pitch, and yaw motions are ignored, leaving only horizontal and vertical motions. There are two different types of point mass models: dynamic models and kinematic models. The main difference is that dynamic models focus on forces and energy, while kinematic models only deal with the aircraft's motion. Dynamic and kinematic models each have their advantages and disadvantages; generally speaking, the kinematic method is simpler by removing forces from the model. Summary of the Invention

[0005] Purpose of the invention: This invention proposes a method for rapid generation of aircraft flight trajectories based on flight plans. It establishes a flight performance database by using domestic trajectory data and performance parameter statistical models, which conforms to my country's flight standards. It also establishes a point mass kinematic model based on the flight laws of aircraft, which greatly reduces the trajectory generation time.

[0006] Technical solution: The present invention provides a method for rapidly generating aircraft flight trajectories based on flight plans, which specifically includes the following steps:

[0007] (1) Acquire trajectory data for different aircraft types; divide flight phases based on trajectory data;

[0008] (2) Determine the key performance parameters based on the flight phases divided in step (1);

[0009] (3) Extract key performance parameter values ​​for each flight phase from the trajectory data;

[0010] (4) Establish a flight performance database;

[0011] (5) Establish a trajectory data model based on the variation law of aircraft trajectory parameters; the trajectory data model includes a departure flight trajectory data model, a cruise flight trajectory data model, and an arrival flight trajectory data model;

[0012] (6) Establish the trajectory point coordinate model;

[0013] (7) Establish a kinematic model: The kinematic model consists of a trajectory data model and a trajectory point coordinate model; use the trajectory data model to obtain trajectory attributes, and import them into the trajectory point coordinate model to generate the airport coordinate system coordinates and latitude and longitude coordinates of the trajectory points;

[0014] (8) Based on the established flight plan, import the flight information such as the waypoint coordinates, cruising altitude, and cruising speed of the aircraft into the kinematic model, call the flight performance database, and generate trajectory data.

[0015] Furthermore, the flight phase described in step (1) is divided into:

[0016] The takeoff phase is from zero speed to an altitude of 35 feet; the initial climb phase is from 35 feet to 1000 feet; the climb phase is from 1000 feet to cruising altitude; the descent phase is from cruising altitude to 1000 feet; the final approach phase is from 1000 feet to 35 feet; and the landing phase is from 35 feet to zero speed.

[0017] Furthermore, the implementation process of step (2) is as follows:

[0018] The importance of each performance parameter varies for different flight phases. The key performance parameters are selected for different flight phases as follows:

[0019] Takeoff phase: including takeoff speed V tof Takeoff acceleration a tof ;

[0020] Initial climb phase: including initial vertical climb velocity κ ic Initial climb height h ic Initial climb acceleration a ic ;

[0021] Climb phase: including vertical velocity κ before climb at constant corrected airspeed. precas,cl Altitude h during corrected airspeed climb cas,cl Corrected airspeed climb rate V cas,cl Vertical velocity κ during corrected airspeed climb cas,cl Height h during Mach number increase mach,cl Mach number climb rate M cl Vertical velocity κ during Mach number increase mach,cl ;

[0022] Cruise phase: Cruise altitude h cr Cruise speed V cr Initial cruise acceleration a cr ;

[0023] The descent phase includes the velocity M during the descent at a constant Mach number. de When the Mach number decreases, the height h mach,de Vertical velocity κ when Mach number decreases mach,de Corrected airspeed descent velocity V cas,de Altitude h during descent at corrected airspeed cas,de Vertical velocity κ during descent at the corrected airspeed cas,de Vertical velocity κ after corrected airspeed decrease postcas,de ;

[0024] Final approach phase: including final approach vertical velocity κ fa Final approach altitude h fa Final approach velocity V app ;

[0025] Landing phase: including touchdown velocity V tcd Landing acceleration a lnd .

[0026] Furthermore, the implementation process of step (3) is as follows:

[0027] Takeoff Phase: The distance d is calculated based on the coordinates of the starting and ending points of the ground taxiing section. Then, the takeoff acceleration a is obtained by fitting a second-order polynomial based on the time and airspeed. tof The takeoff speed is:

[0028]

[0029] V tof =V e +a tof (t tof -t e (2)

[0030] Among them, t tof The launch time is determined by the vertical velocity and altitude at the time of the first aerial observation; t1 is the time of the first aerial observation, h1 is the altitude at the time of the first aerial observation, κ1 is the vertical velocity at the time of the first aerial observation, and V... tof V is the velocity at which the object leaves the ground. e For the velocity of the last ground observation, a tof For takeoff acceleration, t e This refers to the moment of the last ground observation;

[0031] Initial climb phase: The initial vertical speed is calculated directly from the trajectory data;

[0032] The climb phase begins when the aircraft reaches its clean configuration and continues until it reaches its cruising altitude. It includes three phases: climb before corrected airspeed, climb at corrected airspeed, and climb at constant Mach number. The aircraft first accelerates to the target corrected airspeed and then flies at that corrected airspeed. During flight, the aircraft's Mach number increases due to the increase in airspeed and the decrease in the speed of sound. When a certain Mach number is reached, the aircraft will fly at constant Mach number until it reaches its cruising altitude, as shown in the formula:

[0033]

[0034]

[0035] Among them, f cas (t) is the corrected airspeed expression, G2 is the corrected airspeed factor, and t cas To equalize the airspeed climb time, y cas To equalize the airspeed climb rate, t mach This is the end time of the equal-correction airspeed climb, and also the start time of the equal-Mach number climb; f mach (t) is the Mach number expression, G1 is the Mach number factor, and y mach The rate of ascent at constant Mach number;

[0036] For Mach number, at tmach The Mach number initially represents an increasing segment, followed by a constant segment; least squares fitting is used to extract the start time t of the constant Mach number climb. mach And equal Mach climb rate y mach For the corrected airspeed change curve, the entire climb phase is also divided into a corrected airspeed increase portion and a constant corrected airspeed portion, using t mac h is used as the cutoff time, and the fitted time series starts from the beginning until t. mac h; Similarly, the equal-corrected airspeed climb rate y is obtained using the least squares method. cas and the time t for corrected airspeed climb cas And by extracting the spacecraft at time t mach Use height data to identify intersection height; in determining t cas and t mach Then, obtain the crossover altitude h at the start of the constant-corrected airspeed and constant-Mach-number climb. cas,cl h mach,cl And calculate the vertical velocity corresponding to these three sections, including the vertical velocity κ before climbing at constant airspeed. precas,cl Vertical velocity κ during corrected airspeed climb cas,cl Vertical velocity κ during Mach number increase mach,cl ;

[0037] The cruise altitude and speed during the cruise phase are those specified in the flight plan, and the initial cruise acceleration a cr It is the rate of ascent M at Mach number. cl Accelerate to cruising speed V cr The average acceleration is calculated directly from the trajectory data;

[0038] The descent phase is similar to the climb phase. Starting from the cruise altitude, the aircraft goes through three phases before reaching the final approach altitude: constant Mach number descent, constant airspeed descent, and descent after constant airspeed descent. The calculation method for performance parameters is the same as that for the climb phase.

[0039] The final approach phase specifies a final approach altitude of 1,000 feet, while the other two performance parameters are calculated directly from the trajectory data.

[0040] The calculation method for the landing phase is the same as that for the takeoff phase.

[0041] Furthermore, the implementation process of step (4) is as follows:

[0042] Each performance parameter is described using three parts: the optimal value ω is obtained from the performance parameter values ​​based on the normal distribution method, and the minimum value ω is obtained from different confidence intervals. min and maximum value ω maxDifferent confidence intervals are set according to the type of parameters; the minimum and maximum values ​​define the flight envelope limits that the aircraft follows during flight, and a large amount of trajectory data is generated within the flight envelope using a probabilistic value-taking method; the performance parameters of common aircraft models for each flight phase are integrated to obtain a flight performance database.

[0043] Furthermore, the process of constructing the departure flight trajectory data model is as follows:

[0044] When the corrected airspeed is less than the takeoff speed V tof At that time, the speed of the current waypoint is:

[0045] v i =v i-1 +a tof ×△t (8)

[0046] Among them, v i v is the current speed at the waypoint. i-1 a is the velocity at the previous waypoint. tof This is the takeoff acceleration, and Δt represents the time step; at this point, the vertical velocity is 0, and this stage is the takeoff stage.

[0047] When the corrected airspeed is greater than the takeoff speed V tof However, when the altitude is less than 1000 ft, the speed and altitude of the current waypoint are as follows:

[0048] v i =v i-1 +a c ×△t (9)

[0049] h i =h i-1 +κ ic ×△t (10)

[0050] Among them, a c This represents the initial climb acceleration, and the vertical velocity is equal to the initial climb vertical velocity κ. ic This stage is the initial climb stage;

[0051] When the altitude is greater than 1000 ft but less than the altitude h when climbing at the corrected airspeed cas,cl At that time, the altitude of the current waypoint is:

[0052] h i =h i-1 +κ precas,cl ×△t (11)

[0053] If the speed is less than the constant corrected airspeed, the speed is calculated as shown in formula (9); if the speed is greater than the constant corrected airspeed, the speed is obtained from the altitude h of the current waypoint and the speed of the previous waypoint, as shown in formula (15); the vertical speed is equal to the vertical speed κ before climbing at constant corrected airspeed. precas,cl This stage is the pre-climb stage at constant airspeed correction:

[0054]

[0055] Where: P0 is standard atmospheric pressure, ρ0 is standard atmospheric pressure density, ρ is current atmospheric density, and P is current atmospheric pressure;

[0056] When the altitude is greater than the altitude h during constant-corrected airspeed climb. cas,cl But the height h is less than the height when climbing at a constant Mach number. mach,cl The speed V during constant-corrected airspeed climb cas,cl The vertical speed is obtained from the altitude of the current waypoint; the vertical speed is equal to the vertical speed κ obtained from the constant-correction airspeed climb. cas,cl This phase is the constant-correction airspeed climb phase; the current waypoint speed and altitude are calculated as follows:

[0057]

[0058] h i =h i-1 +κ cas,cl ×△t (17)

[0059] When climbing at a height greater than the constant Mach number, the height h mach,cl But less than the cruising altitude h cr At that time, the speed of the current waypoint increases from the speed M during the climb from the constant Mach number. cl Calculate the speed of sound at the current altitude:

[0060] v i =M cl ×A i (18)

[0061]

[0062] Among them, A i The speed of sound at the current waypoint's altitude; T i The temperature at the current trackpoint's altitude; the vertical velocity is equal to the vertical velocity κ during constant Mach climb. mach,cl This stage is the constant Mach number climb stage, and the current trackpoint altitude is:

[0063] h i =h i-1 +κ mach,cl ×△t (20).

[0064] Furthermore, the process of constructing the cruise flight trajectory data model is as follows:

[0065] During cruise flight, the cruise altitude h specified in the flight plan must be maintained. cr and cruising speed V cr When the altitude equals the cruising altitude, the current waypoint speed is calculated using the following formula:

[0066] v i =v i-1 +a cr ×△t (21)

[0067] Among them, a cr The initial cruise acceleration is used; once the speed reaches the specified cruise speed, the cruise speed is maintained and flight continues; this phase is called the cruise phase; the cruise phase ends when the flight distance during cruise flight exceeds the cruise distance given in the flight plan.

[0068] Furthermore, the process of constructing the approach flight trajectory data model is as follows:

[0069] When the flight distance during cruise is greater than the cruise distance given in the flight plan, and the altitude is less than the cruise altitude h. cr But greater than the drop height h at constant Mach numbers mach,de When the velocity decreases from the constant Mach number, the velocity M de The current waypoint's speed and altitude are calculated from the given information:

[0070] v i =M de ·A i (twenty two)

[0071] h i =h i-1 +κ mach,de ×△t (23)

[0072] Among them, κ mach,de This is the vertical velocity during the constant Mach number decrease phase;

[0073] When the height is less than the descent height h at the constant Mach number mach,de But greater than the altitude h when climbing at constant corrected airspeed. cas,de The current speed and altitude of the waypoint are:

[0074]

[0075] h i =h i-1 +κ cas,de ×△t (25)

[0076] Among them, Vcas,de To compensate for the airspeed decrease during equalization, VS cas,de This is the vertical velocity during the constant-corrected airspeed descent phase;

[0077] When the altitude is less than the altitude during constant-corrected airspeed climb but greater than 1000 ft, the altitude of the current waypoint is as shown in formula (26). If the speed is greater than the last approach speed, the speed of the current waypoint is calculated as shown in formula (27); otherwise, the speed is calculated as shown in formula (28).

[0078] h i =h i-1 +κ postcas,de ×△t (26)

[0079]

[0080] v i =v i-1 +a d ×△t (28)

[0081] Among them, a d To compensate for the acceleration after the airspeed decreases; κ postcas,de This is the vertical velocity after the constant-corrected airspeed descent; this stage is the descent stage after the constant-corrected airspeed descent.

[0082] When the altitude is less than 1000ft but greater than zero, the speed and altitude are:

[0083] v i =V app (29)

[0084] h i =h i-1 +κ fa ×△t (30)

[0085] Among them, κ fa This is the final approach vertical velocity; this phase is the final approach phase.

[0086] When the altitude is zero but the velocity is greater than zero, the landing acceleration is a. lnd The speed is:

[0087] v i =v i-1 +a lnd ×△t (31)

[0088] The landing phase occurs when the vertical velocity is zero; the landing phase ends when the velocity reaches zero.

[0089] Furthermore, the implementation process of step (6) is as follows:

[0090] Establish an airport coordinate system with the airport reference point as the origin: the Y-axis is the line from the origin to magnetic north, the X-axis is the line from the origin perpendicular to magnetic north to the right, and the Z-axis is the line from the origin perpendicular to the XOY plane.

[0091] Establish a straight flight model: First, use the latitude and longitude conversion formula to determine the airport coordinate system coordinates of the starting and ending points of the straight flight segment, and use the distance formula between the two points to calculate the straight flight distance; second, calculate the distance flown by the aircraft per unit time based on the aircraft's heading and airspeed, as shown in formula (32); finally, start with the airport coordinate system coordinates of the starting point and perform superposition calculation to obtain the airport coordinate system coordinates of the trajectory points, as shown in formulas (33) and (34), and obtain the latitude and longitude coordinates of the trajectory points through the latitude and longitude conversion formula. The straight flight ends when the distance flown by the aircraft exceeds the straight flight distance.

[0092] l = v i ×sin[arccos(κ i / v i )]×△t (32)

[0093] x i =x i-1 +l×sin(head i (33)

[0094] y i =y i-1 +l×cos(head i (34)

[0095] Among them, v i κ represents the current aircraft speed; Δt represents the time interval; i Let x be the current vertical velocity of the aircraft, l be the horizontal distance traveled per unit time, and x be the horizontal distance traveled per unit time. i ,y i x represents the coordinates of the current trajectory point; i-1 ,y i-1 The coordinates of the previous trajectory point; head i The heading of the aircraft at the current waypoint. During the straight flight segment, the heading is the heading marked on the chart and remains unchanged throughout the entire straight flight segment.

[0096] Establish a turning flight model: When three consecutive waypoints are not on the same straight line, it indicates that the heading has changed between two segments, and the aircraft needs to make a turning maneuver to change the heading. This results in a turning trajectory connecting the two straight segments. First, determine the airport coordinate system coordinates of the starting and ending points of the turning flight and the turning rate of the aircraft. When the turning rate is clearly marked on the chart, use the specified turning rate; otherwise, use the standard turning rate of 3 degrees per second. Determine the turning time based on the difference in heading between two adjacent segments and the turning rate. The turning distance can be obtained through the turning time and airspeed. Second, approximate the turning trajectory flown per unit time as a straight trajectory, determine its flight heading, and calculate the distance flown per unit time. Finally, start by superimposing the airport coordinate system coordinates of the starting point to obtain the airport coordinate system coordinates of the trajectory points, as shown in formulas (35) to (37). Obtain the latitude and longitude coordinates of the trajectory points through the latitude and longitude conversion formula. The turning flight ends when the distance flown by the aircraft exceeds the turning flight distance.

[0097] head i =head i-1 ±γ×△t (35)

[0098] x i =x i-1 +v i-1 ×sin[arccos(κ i-1 / v i-1 )]×△t×sin(head i (36)

[0099] y i =y i-1 +v i-1 ×sin[arccos(κ i-1 / v i-1 )]×△t×cos(head i (37)

[0100] Among them, head i The heading of the aircraft at the current waypoint, head i-1 γ represents the heading of the aircraft at the previous waypoint, and γ is the turning rate. When the aircraft changes course, a left turn decreases the turning rate, and a right turn increases it. i-1 v is the vertical velocity of the aircraft at the previous waypoint. i-1 This represents the aircraft's average turning speed at the previous waypoint.

[0101] Furthermore, the trajectory attributes described in step (7) include trajectory point speed, trajectory point altitude, aircraft flight distance, and aircraft flight heading data.

[0102] Beneficial Effects: Compared with existing technologies, the beneficial effects of this invention are as follows: This invention utilizes domestic trajectory data to construct a flight performance database, which is consistent with my country's flight conditions; the kinematic mass model used in this invention treats the aircraft as a point mass, leaving only horizontal and vertical motion, thus reducing the complexity of the model. Flight trajectories can be quickly generated simply by batch importing waypoint coordinates, altitude, speed limits, etc.; this invention calculates the optimal, maximum, and minimum values ​​of key performance parameters for each flight phase, and can randomly generate a large number of flight trajectories through probability sampling within the performance envelope. It can also be adjusted based on historical trajectories of the target airport, demonstrating good adaptability. Attached Figure Description

[0103] Figure 1 This is a flowchart of the present invention;

[0104] Figure 2 This is a graph showing the changes in speed and altitude during the ascent phase;

[0105] Figure 3 Airport Cartesian coordinate system diagram;

[0106] Figure 4 This is a schematic diagram of a turning model. Detailed Implementation

[0107] The present invention will now be described in further detail with reference to the accompanying drawings.

[0108] like Figure 1 As shown, this invention proposes a method for rapidly generating aircraft flight trajectories based on flight plans, specifically including the following steps:

[0109] Step 1: Flight phase division.

[0110] First, trajectory data for commonly used aircraft models in my country were collected, with at least 5,000 trajectory data points collected for each model. Second, the trajectory data was divided into flight phases: takeoff from zero speed to 35 feet; initial climb from 35 feet to 1,000 feet; climb from 1,000 feet to cruising altitude; descent from cruising altitude to 1,000 feet; final approach from 1,000 feet to 35 feet; and landing from 35 feet to zero speed. Finally, an evaluation procedure was used to check the start and end altitudes of each flight phase, as well as the number of trajectory points, to ensure the completeness and reliability of each trajectory data point.

[0111] Step 2: Determine key performance parameters.

[0112] Key performance parameters are established for each flight phase as defined in step 1, with each parameter having varying importance for different flight phases. The flight performance parameters selected in this implementation are listed below by flight phase:

[0113] Takeoff phase: including takeoff speed V tof Takeoff acceleration a tof .

[0114] Initial climb phase: including initial vertical climb velocity κ ic Initial climb height h ic Initial climb acceleration a ic .

[0115] Climb phase: including vertical velocity κ before climb at constant corrected airspeed. precas,cl Altitude h during corrected airspeed climb cas,cl Corrected airspeed climb rate V cas,cl Vertical velocity κ during corrected airspeed climb cas,cl Height h during Mach number increase mach,cl Mach number climb rate M cl Vertical velocity κ during Mach number increase mach,cl .

[0116] Cruise phase: Cruise altitude h cr Cruise speed V cr Initial cruise acceleration a cr .

[0117] The descent phase includes the velocity M during the descent at a constant Mach number. de When the Mach number decreases, the height h mach,de Vertical velocity κ when Mach number decreases mach,de Corrected airspeed descent velocity V cas,de Altitude h during descent at corrected airspeed cas,de Vertical velocity κ during descent at the corrected airspeed cas,de Vertical velocity κ after corrected airspeed decrease postcas,de .

[0118] Final approach phase: including final approach vertical velocity κ fa Final approach altitude h fa Final approach velocity V app .

[0119] Landing phase: including touchdown velocity V tcd Landing acceleration a lnd .

[0120] The initial climb altitude is specified as 1000 feet, with an initial climb acceleration of 0.5 m / s²; after corrected airspeed descent, the acceleration is -0.2 m / s², and the final approach altitude is 1000 feet. Furthermore, the acceleration and vertical velocity for all flight phases are the average acceleration and vertical velocity for that phase.

[0121] Step 3: Calculate the performance parameter values.

[0122] Key performance parameters for each flight phase are extracted from the trajectory data. Distance and altitude are measured in meters (m), velocity and vertical velocity in meters per second (m / s), and acceleration in meters per second (m / s²). 2 .

[0123] During the takeoff phase, the most important parameter is the takeoff acceleration a. tof and ground speed V tof The distance d is calculated based on the latitude and longitude of the starting and ending points of the ground taxiing section. Then, the takeoff acceleration a is obtained by fitting a second-order polynomial based on the time and airspeed. tof For takeoff speed, estimation is more complex due to the lower data update rate. There is typically a several-second interval between the last ground data sample and the first aerial observation. To estimate the precise liftoff time, the liftoff time t is estimated using the vertical velocity and time of the first aerial observation. tof Compare this result with the previously calculated a. tof Combining these, we obtain the takeoff speed, as shown below:

[0124]

[0125] V tof =V e +a tof (t tof -t e (2)

[0126] Among them, t tof The launch time is determined by the vertical velocity and altitude at the time of the first aerial observation; t1 is the time of the first aerial observation, h1 is the altitude at the time of the first aerial observation, κ1 is the vertical velocity at the time of the first aerial observation, and V... tof V is the velocity at which the object leaves the ground. e For the velocity of the last ground observation, a tof For takeoff acceleration, t e This is the moment of the last ground-based observation.

[0127] The initial climb phase is defined as the aircraft ascending from 35 feet to 1000 feet. During this phase, the retraction of the landing gear and flaps is primarily completed. However, because the initial climb phase lasts only a short time, its trajectory points are relatively few. The parameter to be studied is the initial climb altitude h. ic Initial climb acceleration a ic and initial vertical climb velocity κ ic The initial climb altitude is specified as 1000 feet, and the initial climb acceleration is 0.5 m / s². 2 The initial vertical speed of ascent is calculated directly from the trajectory data.

[0128] The climb phase begins when the aircraft reaches its clean configuration and continues until it reaches its cruising altitude. It comprises three phases: climb before corrected airspeed, climb at corrected airspeed, and climb at constant Mach number. The aircraft first accelerates to the target corrected airspeed and then flies at that corrected airspeed. During flight, the aircraft's Mach number increases with increasing airspeed and is also affected by the decreasing speed of sound. When a certain Mach number is reached, the aircraft will fly at constant Mach number until it reaches its cruising altitude. As shown in the formula:

[0129]

[0130]

[0131] Among them, f cas (t) is the corrected airspeed expression, G2 is the corrected airspeed factor, and t cas To equalize the airspeed climb time, y cas To equalize the airspeed climb rate, t mach This is the end time of the constant-correction airspeed climb, and also the start time of the constant-Mach number climb. mach (t) is the Mach number expression, G1 is the Mach number factor, and y mach The rate of ascent at constant Mach number.

[0132] Changes in speed and altitude during the ascent phase, such as Figure 2 As shown, t cl,start and t cl,end The dashed lines represent the start and end points of the climb, and the décolleté is a correction curve for changes in airspeed. At t... cas The preceding segment represents the increasing segment, followed by the constant segment. The dotted line represents the Mach number variation curve, at t... mach The preceding section represents an increasing segment, followed by a constant segment. The solid line represents the height variation curve; throughout the entire process, the height continuously increases.

[0133] For Mach number, at t mach The preceding segment represents an increasing Mach number, followed by a constant Mach number segment. Least squares fitting is used to extract the start time t of the constant Mach number climb. machAnd equal Mach climb rate y mach For the corrected airspeed change curve, the entire climb phase is also divided into a corrected airspeed increase portion and a constant corrected airspeed portion, using t mach As the cutoff time, the fitted time series is from the beginning until t. mach Similarly, the equal-corrected airspeed climb rate y is obtained using the least squares method. cas and the time t for corrected airspeed climb cas And by extracting the spacecraft at time t mach The height data is used to identify the intersection height. In determining t... cas and t mach Afterwards, the crossover altitude h at the start of the constant-corrected airspeed and constant-Mach-number climb can be obtained. cas,cl h mach,cl And calculate the vertical velocity corresponding to these three sections, including the vertical velocity κ before climbing at constant airspeed. precas,cl Vertical velocity κ during corrected airspeed climb cas,cl Vertical velocity κ during Mach number increase mach,cl .

[0134] Cruise altitude h during the cruise phase cr and cruising speed V cr The altitude and speed specified in the flight plan, and the initial cruise acceleration a cr It is the rate of ascent M at Mach number. cl Accelerate to cruising speed V cr The average acceleration is calculated directly using trajectory data.

[0135] The descent phase of an aircraft is similar to the climb phase. Starting from the cruise altitude, the aircraft goes through three phases before reaching the final approach altitude: a constant Mach number descent, a constant corrected airspeed descent, and a descent after the constant corrected airspeed. The calculation method for performance parameters is the same as that for the climb phase.

[0136] The final approach phase, similar to the initial climb phase, represents the end of the descent. A general model is established to describe the approach trajectory profile from 1,000 feet to a descent of 35 feet. The flight parameter required for the final approach phase is the final approach vertical velocity κ. fa Final approach altitude h fa Final approach velocity V app The final approach altitude is specified as 1,000 feet, and the other two performance parameters are calculated directly from the trajectory data.

[0137] The landing phase is similar to the takeoff phase, requiring the calculation of the aircraft's touchdown speed V. tcd and landing acceleration a lnd The calculation methods for the two performance parameters are the same as those for the takeoff phase.

[0138] Step 4: Establish a flight performance database.

[0139] Each performance parameter is described using the following three parts. First, the optimal value ω, obtained from the performance parameter values ​​using a normal distribution method. It should be noted that the obtained optimal value is not necessarily the best performance parameter value during aircraft flight; it can be viewed as a standard airline procedure profile, equivalent to the APF in the BADA model. Second, ω... min and ω max These are the minimum and maximum values ​​obtained from different confidence intervals. Different confidence intervals are set according to the type of parameter. The minimum and maximum values ​​define the flight envelope limits that the aircraft follows during flight, and a large amount of trajectory data can be generated within the flight envelope using probabilistic methods. Finally, the performance parameters of common aircraft models for each flight phase are integrated to obtain a flight performance database.

[0140] Step 5: Establish a trajectory data model.

[0141] Based on the variation patterns of aircraft trajectory parameters, a trajectory data model is established. This includes speed, altitude, and range. Initial conditions need to be set first, as shown below:

[0142] t=0, △t=4s, h=0, s=0, v=0, κ=0, a c =0.5m / s 2 (5)

[0143] t i =t i-1 +△t (6)

[0144] s i =s i-1 +v×△t (7)

[0145] Where t represents flight time; Δt represents time step, i.e., the time interval for generating waypoints, Δt can be arbitrarily set according to simulation needs; h represents flight altitude; s represents flight distance; v represents speed; κ represents vertical velocity; a c This represents the initial climb acceleration, which is 0.5 m / s². 2 .

[0146] Step 5.1 Establish a departure flight trajectory data model.

[0147] 1) When the corrected airspeed is less than the takeoff speed V tof The speed is calculated as follows:

[0148] v i =v i-1 +a tof ×△t (8)

[0149] v i v is the current speed. i+1 For the velocity at the next waypoint, a tof This is the takeoff acceleration. At this point, the vertical velocity is 0; this phase is the takeoff phase. The takeoff acceleration, and the flight performance parameters mentioned later, should be determined based on the aircraft model and from the established flight performance database.

[0150] 2) When the corrected airspeed is greater than the takeoff speed V tof However, when the height is less than 1000ft, the speed is calculated as shown in formula (9), a c This represents the initial climb acceleration, which is 0.5 m / s². 2 Vertical velocity equals initial climb vertical velocity κ ic The altitude is calculated as shown in formula (10). This stage is the initial climbing stage.

[0151] v i =v i-1 +a c ×△t (9)

[0152] h i =h i-1 +κ ic ×△t (10)

[0153] 3) When the altitude is greater than 1000ft but less than the altitude h during constant airspeed climb. cas,cl At this time, the altitude is calculated as shown in formula (11). The current atmospheric properties, including atmospheric temperature T, atmospheric density ρ, and atmospheric pressure P, are calculated from the current altitude. As shown in formulas (12) to (14). If the speed is less than the constant corrected airspeed, the speed is calculated as shown in formula (9); if the speed is greater than the constant corrected airspeed, the speed is obtained from the altitude h of the current track point and the speed of the previous track point, as shown in formula (15). The vertical speed is equal to the vertical speed κ before climbing at constant corrected airspeed. precas,cl This stage is the pre-climb stage before the equal-corrected airspeed.

[0154] h i =h i-1 +κ precas,cl ×△t (11)

[0155] T i =288.15 - 0.0065 × h i (12)

[0156] ρ i =1.225×(T) i / 288.15) 4.26 (13)

[0157] P = ρ × R × TR = 287.0528 (14)

[0158]

[0159] Where: P0 is standard atmospheric pressure, R is gas constant, and ρ0 is standard atmospheric pressure density.

[0160] 4) When the altitude is greater than the altitude h when climbing at the constant corrected airspeed cas,cl But the height h is less than the height when climbing at a constant Mach number. mach,cl The speed V during constant-corrected airspeed climb cas,cl The vertical speed is obtained from the altitude of the current waypoint. The vertical speed is equal to the vertical speed κ during constant-correction climb. cas,cl This stage is the constant-correction airspeed climb stage. The calculations for speed and altitude are shown below.

[0161]

[0162] h i =h i-1 +κ cas,cl ×△t (17)

[0163] 5) When climbing at a height greater than the constant Mach number, the height h mach,cl But less than the cruising altitude h cr When the speed increases from a constant Mach number, the speed M cl The velocity is calculated from the current altitude, as shown in formula (18). A represents the speed of sound at the altitude of the track point, as shown in formula (19). The vertical velocity is equal to the vertical velocity κ during constant Mach climb. mach,cl This stage is the constant Mach number ascent stage, and the height is calculated as shown in formula (20).

[0164] v i =M cl ×A i (18)

[0165]

[0166] h i =h i-1 +κ mach,cl ×△t (20)

[0167] Step 5.2 Establish a cruise flight trajectory data model.

[0168] During cruise flight, the cruise altitude h specified in the flight plan must be maintained. cr and cruising speed V cr When the altitude equals the cruising altitude, the speed is calculated as shown in formula (21).

[0169] v i =v i-1 +a cr ×△t (21)

[0170] Among them, a cr This is the initial cruise acceleration. Once the speed reaches the predetermined cruise speed, the flight continues at that speed; this phase is called the cruise phase. The cruise phase ends when the distance traveled during cruise exceeds the cruise distance specified in the flight plan.

[0171] Step 5.3 Establish the approach flight trajectory data model.

[0172] 1) When the flight distance during cruise is greater than the cruise distance given in the flight plan, and the altitude is less than the cruise altitude h. cr But greater than the drop height h at constant Mach numbers mach,de When the velocity decreases from the constant Mach number, the velocity M de The velocity is obtained from the height, as shown in formula (22). The vertical velocity is equal to the vertical velocity κ when descending at the same Mach number. mach,de This stage is the Mach number descent stage. The height is calculated as shown in formula (23).

[0173] v i =M de ·A i (twenty two)

[0174] h i =h i-1 +κ mach,de ×△t (23)

[0175] 2) When the height is less than the descent height h at constant Mach number mach,de But greater than the altitude h when climbing at constant corrected airspeed. cas,de The speed V decreases from the constant corrected airspeed. cas,de The vertical velocity is obtained from the altitude, as shown in formula (24); the vertical velocity is equal to the vertical velocity κ when descending at the constant corrected airspeed. cas,de The altitude is as shown in formula (25); this stage is the constant-corrected airspeed descent stage.

[0176]

[0177] h i =h i-1 +κ cas,de ×△t (25)

[0178] 3) When the altitude is less than the altitude during constant-corrected airspeed climb but greater than 1000 ft, the altitude is calculated as shown in formula (26), and the vertical velocity is equal to the vertical velocity κ after constant-corrected airspeed descent. postcas,deIf the speed is greater than the final approach speed, the speed is calculated as shown in formula (27); otherwise, the speed is calculated as shown in formula (28). d To compensate for the acceleration after the airspeed decreases, it is specified as -0.2 m / s². 2 This stage is the descent phase after the airspeed is corrected.

[0179] h i =h i-1 +κ postcas,de ×△t (26)

[0180]

[0181] v i =v i-1 +a d ×△t (28)

[0182] 4) When the altitude is less than 1000ft but greater than zero, the velocity remains the same as the final approach velocity, as shown in formula (29). The vertical velocity is equal to the final approach vertical velocity κ. fa The height calculation is shown in formula (30), and this stage is the final approach stage.

[0183] v i =V app (29)

[0184] h i =h i-1 +κ fa ×△t (30)

[0185] 5) When the altitude is zero but the velocity is greater than zero, the landing acceleration is a. lnd The velocity is calculated as shown in formula (31). The vertical velocity is zero, and this stage is the landing stage. When the velocity is zero, the landing stage ends.

[0186] v i =v i-1 +a lnd ×△t (31)

[0187] Step 6: Establish the trajectory point coordinate model.

[0188] Establish an airport coordinate system (hereinafter referred to as the coordinate system) with the airport reference point as the origin. The coordinate system is as follows: Figure 3 As shown: the Y-axis is the line from the origin to magnetic north; the X-axis is the line from the origin to the right perpendicular to magnetic north; and the Z-axis is the line from the origin perpendicular to the XOY plane.

[0189] 1) Establish a straight-line flight model.

[0190] First, the airport coordinates of the starting and ending points of the straight flight segment are determined using the latitude and longitude conversion formula, and the straight flight distance is calculated using the distance formula between the two points. Next, the distance traveled per unit time is calculated based on the aircraft's heading and airspeed, as shown in formula (32). Finally, the airport coordinates of the trajectory points are obtained by superimposing the coordinates of the starting point's airport coordinates, as shown in formulas (33) and (34), and the latitude and longitude coordinates of the trajectory points are obtained using the latitude and longitude conversion formula. The straight flight ends when the distance traveled by the aircraft exceeds the straight flight distance.

[0191] l = v i ×sin[arccos(κ i / v i )]×△t (32)

[0192] x i =x i-1 +l×sin(head i (33)

[0193] y i =y i-1 +l×cos(head i (34)

[0194] Among them, v i κ represents the current aircraft speed; Δt represents the time interval; i x represents the current vertical velocity of the aircraft, and l represents the horizontal distance traveled per unit time. i ,y i x represents the coordinates of the current trajectory point; i-1 ,y i-1 The coordinates of the previous trajectory point; head i The heading is the direction the aircraft is flying at the current waypoint. During the straight flight segment, the heading is the heading marked on the chart and remains unchanged throughout the entire straight flight segment.

[0195] 2) Establish a turning flight model.

[0196] like Figure 4 As shown, when three consecutive waypoints are not on the same straight line, it indicates that the course has changed between two segments, and the aircraft needs to make a turn to change course, which results in a turning trajectory connecting the two straight segments.

[0197] First, determine the airport coordinates of the starting and ending points of the turn, as well as the aircraft's turn rate. If a specific turn rate is marked on the aeronautical chart, use that rate; otherwise, use the standard turn rate of 3 degrees per second. Determine the turn time based on the difference in heading between two adjacent flight paths and the turn rate. The turn distance can then be calculated using the turn time and airspeed. For example... Figure 3 As shown, there is a turning track between navigation points P2 and P3. The heading before navigation point P2 is 62 degrees, and the heading after navigation point P3 is 242 degrees. If calculated using the standard turn rate, the turn lasts 60 seconds. If the time interval Δt is set to 4 seconds, 15 track points can be obtained.

[0198] Secondly, the turning trajectory flown within a unit time is approximated as a straight trajectory to determine its flight direction and calculate the distance flown within a unit time. Finally, the airport coordinate system coordinates of the trajectory points are obtained by superimposing the coordinates of the airport coordinate system of the starting point, as shown in formulas (35) to (37), and the latitude and longitude coordinates of the trajectory points are obtained through the latitude and longitude conversion formula. The turning flight ends when the distance flown by the aircraft exceeds the turning flight distance.

[0199] head i =head i-1 ±γ×△t (35)

[0200] x i =x i-1 +v i-1 ×sin[arccos(κ i-1 / v i-1 )]×△t×sin(head i (36)

[0201] y i =y i-1 +v i-1 ×sin[arccos(κ i-1 / v i-1 )]×△t×cos(head i (37)

[0202] In the formula, head i The heading of the aircraft at the current waypoint, head i-1 γ represents the heading of the aircraft at the previous waypoint, and γ is the turning rate. When the aircraft changes course, a left turn decreases the turning rate, and a right turn increases it. κ i-1 v is the vertical velocity of the aircraft at the previous waypoint. i-1 This represents the aircraft's average turning speed at the previous waypoint.

[0203] Step 7: Establish a kinematic model.

[0204] The kinematic model consists of a trajectory data model and a trajectory point coordinate model. The trajectory data model is used to obtain data such as trajectory point velocity, trajectory point altitude, aircraft flight distance, and aircraft heading. These data are then imported into the trajectory point coordinate model to generate the airport coordinate system coordinates and latitude / longitude coordinates of the trajectory points.

[0205] Step 8: Generate flight path.

[0206] Based on the established flight plan, the flight information, including the coordinates of waypoints, cruising altitude, and cruising speed, is imported into the kinematic model. The flight performance database is then accessed to generate trajectory data. When generating a large number of flight trajectories, flight plans can be categorized by airport and route, and imported in batches for rapid trajectory generation.

[0207] Furthermore, it should be understood that although this specification describes embodiments, not every embodiment contains only one independent technical solution. This narrative style of the specification is merely for clarity. Those skilled in the art should regard the specification as a whole, and the technical solutions in each embodiment can also be appropriately combined to form other implementation methods that can be understood by those skilled in the art.

Claims

1. A method for rapidly generating aircraft flight trajectories based on flight plans, characterized in that, Includes the following steps: (1) Acquire trajectory data for different aircraft types; divide flight phases based on trajectory data; (2) Determine the key performance parameters based on the flight phases divided in step (1); (3) Extract key performance parameter values ​​for each flight phase from the trajectory data; (4) Establish a flight performance database; (5) Establish a trajectory data model based on the variation law of aircraft trajectory parameters; the trajectory data model includes a departure flight trajectory data model, a cruise flight trajectory data model, and an approach flight trajectory data model; (6) Establish the trajectory point coordinate model; (7) Establish a kinematic model: The kinematic model consists of a trajectory data model and a trajectory point coordinate model; use the trajectory data model to obtain trajectory attributes, and import them into the trajectory point coordinate model to generate the airport coordinate system coordinates and latitude and longitude coordinates of the trajectory points; (8) Based on the established flight plan, import flight information including the coordinates of the waypoints flown by the aircraft, the cruise altitude, and the cruise speed into the kinematic model, call the flight performance database, and generate trajectory data; The implementation process of step (3) is as follows: Takeoff Phase: The distance d is calculated based on the coordinates of the starting and ending points of the ground taxiing section. Then, the takeoff acceleration is obtained by fitting a second-order polynomial based on the time and airspeed. The takeoff speed is: （1） （2） in, The launch time is determined by the vertical velocity and altitude at the time of the first aerial observation; t1 is the time of the first aerial observation, and h1 is the altitude at the time of the first aerial observation. V is the vertical velocity during the first aerial observation. tof V is the velocity at which the object leaves the ground. e For the velocity of the last ground observation, a tof For takeoff acceleration, This refers to the moment of the last ground observation; Initial climb phase: The initial vertical speed is calculated directly from the trajectory data; The climb phase begins when the aircraft reaches its clean configuration and continues until it reaches its cruising altitude. It includes three phases: climb before corrected airspeed, climb at corrected airspeed, and climb at constant Mach number. The aircraft first accelerates to the target corrected airspeed and then flies at that corrected airspeed. During flight, the aircraft's Mach number increases due to the increase in airspeed and the decrease in the speed of sound. When a certain Mach number is reached, the aircraft will fly at constant Mach number until it reaches its cruising altitude, as shown in the formula: （3） （4） in, To correct the airspeed expression, To correct the airspeed factor, To equalize the airspeed climb time, To equalize the airspeed climb rate, This is the end time of the equal-correction airspeed climb, and also the start time of the equal-Mach number climb; The expression for Mach number is... Mach number factor The rate of ascent at constant Mach number; For Mach number, in The Mach number range before this point is an increasing segment, followed by a constant segment; least squares fitting is used to extract the start time of the constant Mach number climb. Mach number For the corrected airspeed change curve, the entire climb phase is also divided into a corrected airspeed increase portion and a constant corrected airspeed portion, using... As the cutoff time, the fitted time series is from the beginning until... Similarly, the equal-corrected airspeed climb rate is obtained using the least squares method. and equal correction airspeed climb time And by extracting the spacecraft at any time Use height data to identify intersection height; in determining and Then, obtain the cross altitude at the start of the constant-corrected airspeed and constant-Mach-number climb. , And calculate the vertical velocity corresponding to these three sections, including the vertical velocity before climbing at constant airspeed. Vertical velocity during corrected airspeed climb Vertical velocity during Mach number increase ; The cruise altitude and speed during the cruise phase are the altitude and speed specified in the flight plan, and the initial cruise acceleration... It is the rate of increase in Mach number. Accelerate to cruising speed The average acceleration is calculated directly from the trajectory data; The descent phase is similar to the climb phase. Starting from the cruise altitude, the aircraft goes through three phases before reaching the final approach altitude: constant Mach number descent, constant airspeed descent, and descent after constant airspeed descent. The calculation method for performance parameters is the same as that for the climb phase. The final approach phase specifies a final approach altitude of 1,000 feet, while the other two performance parameters are calculated directly from the trajectory data. The calculation methods for the landing phase and the takeoff phase are the same; The implementation process of step (4) is as follows: Each performance parameter is described using three parts, and the optimal value is obtained from the performance parameter values ​​based on the normal distribution method. Secondly, the minimum value obtained from different confidence intervals. and maximum value Different confidence intervals are set according to the type of parameters; the minimum and maximum values ​​define the flight envelope limits that the aircraft follows during flight, and a large amount of trajectory data is generated within the flight envelope using a probabilistic value-taking method; the performance parameters of common aircraft models for each flight phase are integrated to obtain a flight performance database.

2. The method for rapid generation of aircraft flight trajectories based on flight plans according to claim 1, characterized in that, The flight phase described in step (1) is divided into: The takeoff phase is from zero speed to an altitude of 35 feet; the initial climb phase is from 35 feet to 1000 feet; the climb phase is from 1000 feet to cruising altitude; the descent phase is from cruising altitude to 1000 feet; the final approach phase is from 1000 feet to 35 feet; and the landing phase is from 35 feet to zero speed.

3. The method for rapid generation of aircraft flight trajectories based on flight plans according to claim 1, characterized in that, The implementation process of step (2) is as follows: The importance of each performance parameter varies for different flight phases. The key performance parameters are selected for different flight phases as follows: Takeoff phase: including takeoff speed Takeoff acceleration ; Initial climb phase: including initial vertical climb speed Initial climb height Initial climb acceleration ; Climb phase: including vertical velocity before climb at constant corrected airspeed Altitude during corrected airspeed climb Corrected airspeed and climb rate Vertical velocity during corrected airspeed climb Height when Mach number increases Mach number climb rate Vertical velocity during Mach number increase ; Cruise Phase: Cruise Altitude cruising speed Initial cruise acceleration ; The descent phase includes the velocity during the Mach number decrease. Height when Mach number decreases Vertical velocity as Mach number decreases Corrected airspeed descent rate Altitude during corrected airspeed descent Vertical velocity during descent at the corrected airspeed Vertical velocity after corrected airspeed decrease ; Final approach phase: including final approach vertical velocity Final approach altitude Final approach speed ; Landing phase: including touchdown velocity Landing acceleration .

4. The method for rapid generation of aircraft flight trajectories based on flight plans according to claim 1, characterized in that, The process of constructing the departure flight trajectory data model is as follows: When the corrected airspeed is less than the takeoff speed At that time, the speed of the current waypoint is: （8） in, The current speed at the waypoint. The speed at the previous waypoint, For takeoff acceleration, This indicates the time step; at this point, the vertical velocity is 0, and this stage is the takeoff stage. When the corrected airspeed is greater than the takeoff speed However, when the altitude is less than 1000 ft, the speed and altitude of the current waypoint are as follows: （9） （10） in, This represents the initial climb acceleration, and the vertical velocity is equal to the initial climb vertical velocity. This stage is the initial climb stage; When the altitude is greater than 1000 ft but less than the altitude when climbing at the corrected airspeed At that time, the altitude of the current waypoint is: （11） If the speed is less than the constant corrected airspeed, the speed is calculated as shown in formula (9); if the speed is greater than the constant corrected airspeed, the speed is determined by the altitude of the current waypoint. The vertical speed is obtained by combining the speed of the previous track point, as shown in formula (15); the vertical speed is equal to the vertical speed before climbing at the constant-corrected airspeed. This stage is the pre-climb stage at constant airspeed correction: （15） in: Standard atmospheric pressure Standard atmospheric pressure density, Given the current atmospheric density, Current atmospheric pressure; When the altitude is greater than the altitude during constant-corrected airspeed climb But less than the height when climbing at Mach number. The speed is the same as the speed during the constant-corrected airspeed climb. The vertical speed is obtained by calculating the altitude of the current waypoint; the vertical speed is equal to the vertical speed during climb with equal correction airspeed. This phase is the constant-correction airspeed climb phase; the current waypoint speed and altitude are calculated as follows: （16） （17） When climbing at a height greater than the constant Mach number, the height... But less than cruising altitude At that time, the speed at the current track point increases from the speed at the constant Mach number during the climb. Calculate the speed of sound at the current altitude: （18） （19） in, The speed of sound at the current trackpoint's altitude; The temperature at the current trackpoint altitude; vertical velocity is equal to the vertical velocity during constant Mach climb. This stage is the constant Mach number climb stage, and the current trackpoint altitude is: （20）。 5. The method for rapid generation of aircraft flight trajectories based on flight plans according to claim 1, characterized in that, The process of constructing the cruise flight trajectory data model is as follows: During cruise flight, the cruise altitude specified in the flight plan must be maintained. and cruising speed When the altitude equals the cruising altitude, the current waypoint speed is calculated using the following formula: （21） in, The initial cruise acceleration is used; once the speed reaches the specified cruise speed, the cruise speed is maintained and flight continues; this phase is called the cruise phase; the cruise phase ends when the flight distance during cruise flight exceeds the cruise distance given in the flight plan.

6. The method for rapid generation of aircraft flight trajectories based on flight plans according to claim 1, characterized in that, The process of constructing the approach flight trajectory data model is as follows: When the flight distance during cruise is greater than the cruise distance given in the flight plan, and the altitude is less than the cruise altitude. But greater than the drop height at Mach numbers. When the speed decreases from the constant Mach number, the speed The current waypoint's speed and altitude are calculated from the given information: （22） （23） in, This is the vertical velocity during the constant Mach number decrease phase; When the height is less than the descent height at constant Mach number But greater than the altitude achieved during climb at equal corrected airspeed. The current speed and altitude of the waypoint are: （24） （25） in, To compensate for the airspeed during descent, This is the vertical velocity during the constant-corrected airspeed descent phase; When the altitude is less than the altitude during constant-corrected airspeed climb but greater than 1000 ft, the altitude of the current waypoint is as shown in formula (26). If the speed is greater than the last approach speed, the speed of the current waypoint is calculated as shown in formula (27); otherwise, the speed is calculated as shown in formula (28). （26） （27） （28） in, To compensate for the acceleration after the airspeed decreases; This is the vertical velocity after the constant-corrected airspeed descent; this stage is the descent stage after the constant-corrected airspeed descent. When the altitude is less than 1000ft but greater than zero, the speed and altitude are: （29） （30） in, This is the final approach vertical velocity; this phase is the final approach phase. When the altitude is zero but the velocity is greater than zero, the landing acceleration is: The speed is: （31） The landing phase occurs when the vertical velocity is zero; the landing phase ends when the velocity reaches zero.

7. The method for rapid generation of aircraft flight trajectories based on flight plans according to claim 1, characterized in that, The implementation process of step (6) is as follows: Establish an airport coordinate system with the airport reference point as the origin: the Y-axis is the line from the origin to magnetic north, the X-axis is the line from the origin perpendicular to magnetic north to the right, and the Z-axis is the line from the origin perpendicular to the XOY plane. Establish a straight flight model: First, use the latitude and longitude conversion formula to determine the airport coordinate system coordinates of the starting and ending points of the straight flight segment, and use the distance formula between the two points to calculate the straight flight distance; second, calculate the distance flown by the aircraft per unit time based on the aircraft's heading and airspeed, as shown in formula (32); finally, start with the airport coordinate system coordinates of the starting point and perform superposition calculation to obtain the airport coordinate system coordinates of the trajectory points, as shown in formulas (33) and (34), and obtain the latitude and longitude coordinates of the trajectory points through the latitude and longitude conversion formula. The straight flight ends when the distance flown by the aircraft exceeds the straight flight distance. （32） （33） （34） in, The current speed of the aircraft; For time intervals; The current vertical speed of the aircraft. The horizontal distance traveled per unit time. , The coordinates of the current trajectory point; , These are the coordinates of the previous trajectory point; The heading of the aircraft at the current waypoint. During the straight flight segment, the heading is the heading marked on the chart and remains unchanged throughout the entire straight flight segment. Establish a turning flight model: When three consecutive waypoints are not on the same straight line, it indicates that the heading has changed between two segments, and the aircraft needs to make a turning maneuver to change the heading. This results in a turning trajectory connecting the two straight segments. First, determine the airport coordinate system coordinates of the starting and ending points of the turning flight and the turning rate of the aircraft. When the turning rate is clearly marked on the chart, use the specified turning rate; otherwise, use the standard turning rate of 3 degrees per second. Determine the turning time based on the heading difference and turning rate of the two adjacent segments. The turning distance can be obtained through the turning time and airspeed. Second, approximate the turning trajectory flown per unit time as a straight trajectory, determine its flight heading, and calculate the distance flown per unit time. Finally, start by superimposing the airport coordinate system coordinates of the starting point to obtain the airport coordinate system coordinates of the trajectory points, as shown in formulas (35) to (37). Obtain the latitude and longitude coordinates of the trajectory points through the latitude and longitude conversion formula. The turning flight ends when the distance flown by the aircraft exceeds the turning flight distance. （35） （36） （37） in, The current flight path of the aircraft at the waypoint. The heading of the aircraft at the previous waypoint. As the turning rate, when an aircraft changes course, turning left decreases the turning rate and turning right increases it. The vertical velocity of the aircraft at the previous waypoint. This represents the aircraft's average turning speed at the previous waypoint.

8. The method for rapid generation of aircraft flight trajectories based on flight plans according to claim 1, characterized in that, The trajectory attributes mentioned in step (7) include trajectory point speed, trajectory point altitude, aircraft flight distance, and aircraft flight heading data.

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