CN117406767A - Aircraft flight trajectory rapid generation method based on flight plan - Google Patents

Abstract

The invention discloses a flight plan-based rapid generation method of an aircraft flight track, which aims at acquiring track data of different models; performing flight phase division according to the track data; determining key performance parameters; extracting key performance parameter values of each flight stage from the track data; establishing a flight performance database; according to the change rule of the aircraft track parameters, a kinematic model comprising a track data model and a track point coordinate model is established; obtaining data such as track point speed, track point height, aircraft flying course and the like by using a track data model, and importing the data into a track point coordinate model to generate airport coordinate system coordinates and longitude and latitude coordinates of the track points; and according to the formulated flight plan, importing flight information such as coordinates of a flying route point, cruising height, cruising speed and the like of the aircraft in a kinematic model, calling a flight performance database, and generating track data. The invention accords with the flight standard of China; and the track generation time can be greatly reduced.

Description

Aircraft flight trajectory rapid generation method based on flight plan

Technical Field

The invention belongs to the technical field of automation and intellectualization of civil aviation air traffic control, and particularly relates to a rapid generation method of an aircraft flight track based on a flight plan.

Background

In the period of high-speed development of civil aviation industry in China, the air traffic environment becomes more and more complex while the air transportation market is rapidly expanded. The rapid increase of the passenger and cargo traffic and the lack of space capacity planning cause the conditions of air traffic congestion and blockage, flight delay, flight conflict and the like, which are unfavorable for civil aviation safe operation and air traffic management. Therefore, the airspace capacity evaluation, airspace operation efficiency evaluation and traffic flow conflict safety evaluation are accurately, reasonably and effectively performed, and are important methods for improving airspace utilization rate, airport service capability and civil aviation operation safety. The use of computer simulation techniques to simulate airspace operation has become one of the most commonly used evaluation methods.

The computer simulation technology is to simulate the actual situation through a scene model and operation data. Aircraft flight trajectory data based on flight plans is essential when simulating airspace operation using computer simulation techniques. Since the number of flight in the time-space domain is huge and the flight plan needs to be adjusted according to the simulation situation, a large amount of flight trajectory data is required to be generated according to the flight plan in a short time. The flight performance database is a performance parameter value of an important node in the flight process of the aircraft, and is a database necessary for track generation. The commonly used flight performance database is built from performance reports published by aircraft manufacturers and proprietary flight data. But these sources are costly and have some licensing limitations. In addition, the model is developed according to foreign flight rules, which means that the model does not accord with the actual running situation of China, so that the track generation research becomes difficult. Most commercial aircraft today are equipped with radar devices and aircraft flight data becomes more readily available, and aircraft performance monitoring data such as position, altitude, speed, etc. is available.

Trajectory generation models have different classifications, the most complex six-degree-of-freedom models are commonly used for aircraft flight control studies, and particle models are commonly used for aircraft flight trajectory studies. In the particle model, the roll, pitch and yaw movements of the aircraft are ignored, leaving only horizontal and vertical movements. There are two different types of particle models, kinetic models and kinematic models. The main difference is that the kinetic model concentrates on force and energy, whereas the kinematic model only deals with the motion of the aircraft. The kinetic and kinematic models are each of advantage, and overall, the kinematic method is simpler by removing the forces in the model.

Disclosure of Invention

The invention aims to: the invention provides a rapid generation method of an aircraft flight track based on a flight plan, which establishes a flight performance database through domestic track data and a performance parameter statistical model, and accords with the flight standard of China; and a particle kinematics model is built according to the flight rule of the aircraft, so that the track generation time is greatly reduced.

The technical scheme is as follows: the invention relates to a rapid generation method of an aircraft flight track based on a flight plan, which specifically comprises the following steps:

(1) Track data are acquired for different models; performing flight phase division according to the track data;

(2) Determining key performance parameters according to the flight phases divided in the step (1);

(3) Extracting key performance parameter values of each flight stage from the track data;

(4) Establishing a flight performance database;

(5) Establishing a track data model according to the change rule of the aircraft track parameters; the track data model comprises an off-site flight track data model, a cruise flight track data model and an on-site flight track data model;

(6) Establishing a track point coordinate model;

(7) Establishing a kinematic model: the kinematic model consists of a track data model and a track point coordinate model; obtaining track attributes by using a track data model, and importing the track attributes into a track point coordinate model to generate airport coordinate system coordinates and longitude and latitude coordinates of the track points;

(8) And according to the formulated flight plan, importing flight information such as coordinates of a flying route point, cruising height, cruising speed and the like of the aircraft in a kinematic model, calling a flight performance database, and generating track data.

Further, the flight phase of step (1) is divided into:

increasing from zero speed to altitude to 35 feet is a takeoff phase; the elevation from 35 feet to 1000 feet is an initial climbing stage; the elevation is raised from 1000 feet to cruising elevation as a climbing stage; the descending stage is that the height is reduced to 1000 feet from the cruising height; the height is reduced from 1000 feet to 35 feet as the final approach stage; the landing phase from 35 feet altitude to zero speed drop.

Further, the implementation process of the step (2) is as follows:

each performance parameter is of different importance for different flight phases, and the key performance parameters are selected as follows:

a takeoff stage: including the ground clearance V _tof Acceleration of take-off a _tof ；

An initial climbing stage: including initial climb vertical velocity κ _ic Initial climbing height h _ic Initial climbing acceleration a _ic ；

Climbing stage: including equal correction of vertical velocity kappa before airspeed climb _precas,cl Altitude h when waiting for correcting airspeed to climb _cas,cl Equal correction of airspeed climb speed V _cas,cl Vertical velocity kappa at equal corrected airspeed climb _cas,cl Height h at equal Mach number climb _mach,cl Equal Mach number climb speed M _cl Vertical velocity kappa at equal Mach number climb _mach,cl ；

Cruising phase: cruising altitude h _cr Cruise speed V _cr Initial cruise acceleration a _cr ；

The descending stage: including the speed M at which the mach number drops _de High when the mach number is reducedDegree h _mach,de Vertical velocity kappa at equal Mach number drop _mach,de Equal corrected airspeed drop velocity V _cas,de Altitude h at equal corrected airspeed drop _cas,de Vertical velocity κ when equi-corrected airspeed falls _cas,de Vertical velocity κ after equal corrected airspeed decrease _postcas,de ；

And finally, a approaching stage: including last approach vertical velocity κ _fa Last approach height h _fa Last approach speed V _app ；

Landing stage: including the ground speed V _tcd Landing acceleration a _lnd 。

Further, the implementation process of the step (3) is as follows:

a takeoff stage: obtaining a distance value d according to coordinates of a starting point and an ending point of a ground running section, and obtaining a take-off acceleration a through second-order polynomial fitting according to time and airspeed _tof The method comprises the steps of carrying out a first treatment on the surface of the The ground leaving speed is as follows:

V _tof ＝V _e +a _tof (t _tof -t _e ) (2)

wherein t is _tof The lift-off time is determined by the vertical speed and the height during the first air observation; t is t ₁ For the first air observation time, h ₁ For the first air observation height, κ ₁ For vertical velocity, V, in the first air observation _tof To get off the ground, V _e For the last ground observation speed, a _tof To take-off acceleration, t _e The time of the last ground observation is the time;

an initial climbing stage: the initial climbing vertical speed is directly calculated by using track data;

the climbing stage starts from the state that the aircraft reaches the smooth finish, and continues until the aircraft reaches the cruising altitude; comprises three stages of equal correction airspeed climbing, equal correction airspeed climbing and equal Mach number climbing; the aircraft first accelerates to a target corrected airspeed and then flies according to the corrected airspeed; the Mach number of the aircraft increases with the effects of increasing vacuum velocity and decreasing speed of sound during flight; when a certain Mach number is reached, the aircraft flies according to the Mach number until reaching the cruising altitude; as shown in the formula:

Wherein f _cas (t) is a corrected airspeed expression, G ₂ To correct airspeed factor, t _cas To equal correct the airspeed climb time, y _cas To equal correct the airspeed climb speed, t _mach The method comprises the steps of correcting the airspeed climbing ending time for equal speed and simultaneously starting the climbing of equal Mach number; f (f) _mach (t) is Mach number expression, G ₁ Is Mach number factor, y _mach Is equal Mach number climbing speed;

for Mach number, at t _mach The mach number is an increasing segment before and a constant segment after; extracting the equal Mach number climb start time t using least squares fitting _mach And equal Mach number y _mach The method comprises the steps of carrying out a first treatment on the surface of the For the corrected airspeed profile, the entire climb phase is equally divided into a corrected airspeed increase portion and an equal corrected airspeed portion, using t _mac h is taken as the cut-off time, and the fitting time sequence is from the beginning to t _mac h, performing H; equal correction airspeed climb speed y is also obtained by a least square method _cas Equal correction airspeed climb time t _cas And by extracting the aircraft at time t _mach Identifying a cross height; at determination t _cas And t _mach Thereafter, an equal corrected airspeed and an equal Mach number climb start crossover height h is obtained _cas,cl ，h _mach,cl The method comprises the steps of carrying out a first treatment on the surface of the And calculating vertical velocities corresponding to the three zones, including the vertical velocity kappa before equal corrected airspeed climb _precas,cl EtcCorrecting vertical velocity kappa during airspeed climb _cas,cl Vertical velocity kappa at equal Mach number climb _mach,cl ；

Cruise altitude and cruise speed during cruise phase are the altitude and speed specified in the flight plan, initial cruise acceleration a _cr Is the equal Mach number climbing speed M _cl Accelerating to cruising speed V _cr The average acceleration of (2) is directly calculated by using the track data;

the descending stage is similar to the climbing stage, from the cruising altitude, the aircraft goes through the three stages of equal Mach number descending, equal correction airspeed descending and equal correction airspeed descending before reaching the final approach altitude, and the calculation method of the performance parameters is the same as that of the climbing stage;

the final approach stage provides that the final approach height is 1000 feet, and the other two performance parameters are directly calculated by using track data;

the landing phase and the takeoff phase are calculated by the same method.

Further, the implementation process of the step (4) is as follows:

describing each performance parameter by using three parts, obtaining an optimal value omega from the performance parameter values based on a normal distribution method, and obtaining a minimum value omega from different confidence intervals _min And a maximum value omega _max The method comprises the steps of carrying out a first treatment on the surface of the Setting different confidence intervals according to the types of the parameters; the minimum value and the maximum value define flight envelope limits observed when the aircraft flies, and a probability value method is used for generating a large amount of track data in the flight envelope; and integrating the performance parameters of each flight stage of the common machine type to obtain a flight performance database.

Further, the construction process of the off-site flight trajectory data model is as follows:

when the corrected airspeed is less than the ground speed V _tof When the current track point has the following speed:

v _i ＝v _i-1 +a _tof ×△t (8)

wherein v is _i For the current track point velocity, v _i-1 A is the speed of the last track point _tof For the acceleration of the take-off,Δt represents the time step; at this time, the vertical speed is 0, and this stage is the take-off stage;

when the corrected airspeed is greater than the ground speed V _tof But at altitudes less than 1000ft, the current track point velocity and altitude are respectively:

v _i ＝v _i-1 +a _c ×△t (9)

h _i ＝h _i-1 +κ _ic ×△t (10)

wherein a is _c Represents the initial climbing acceleration, and the vertical speed is equal to the initial climbing vertical speed kappa _ic This phase is the initial climb phase;

altitude h when altitude is greater than 1000ft but less than equal corrected airspeed climb _cas,cl When the current track point is at the height:

h _i ＝h _i-1 +κ _precas,cl ×△t (11)

if the velocity is less than the constant corrected airspeed, the velocity is calculated as shown in equation (9); if the speed is greater than the constant corrected airspeed, the speed is obtained by the altitude h of the current track point and the speed of the last track point, as shown in formula (15); vertical velocity is equal to vertical velocity kappa before equal correction airspeed climb _precas,cl This stage is the pre-climb equal corrected airspeed stage:

wherein: p (P) ₀ At standard atmospheric pressure ρ ₀ The standard atmospheric pressure density is represented by ρ, the current atmospheric pressure is represented by P;

Altitude h when altitude is greater than equal corrected airspeed climb _cas,cl But is smaller than the height h when climbing with equal Mach number _mach,cl Speed V at ascent from equi-corrected airspeed _cas,cl Obtaining the height of the current track point; vertical velocity equal to equal corrected airspeed climb vertical velocity κ _cas,cl This phase is the equal correction airspeed climb phase; the current track point speed and altitude are calculated as follows:

h _i ＝h _i-1 +κ _cas,cl ×△t (17)

height h when the height is greater than the Mach number _mach,cl But less than cruising height h _cr At the same time, the speed of the current track point is increased from the speed M when the Mach number is increased _cl And obtaining the sound velocity of the current altitude:

v _i ＝M _cl ×A _i (18)

wherein A is _i The sound speed of the height of the current track point is represented; t (T) _i A temperature representing the altitude at which the current track point is located; vertical velocity is equal to vertical velocity kappa at equal Mach climb _mach,cl The stage is a Mach number climbing stage, and the height of the current track point is as follows:

h _i ＝h _i-1 +κ _mach,cl ×△t (20)。

further, the cruising flight trajectory data model construction process is as follows:

the cruise altitude h given in the flight plan needs to be maintained during cruise flight _cr And cruising speed V _cr The method comprises the steps of carrying out a first treatment on the surface of the When the altitude is equal to the cruising altitude, the current track point speed is calculated as follows:

v _i ＝v _i-1 +a _cr ×△t (21)

wherein a is _cr Is an initial cruise acceleration; when the speed reaches the specified cruising speed, the cruising speed is kept to fly continuously, and the stage is a cruising stage; and when the flying distance is larger than the given flying distance in the flying plan, ending the flying period.

Further, the construction process of the approach flight trajectory data model is as follows:

flight when cruisingThe distance is greater than the cruising distance given in the flight plan, and the altitude is less than cruising altitude h _cr But is greater than the mach number falling height h _mach,de At the same time, the speed is reduced from the Mach number to the speed M _de And obtaining the altitude, wherein the current track point speed and the altitude are as follows:

v _i ＝M _de ·A _i (22)

h _i ＝h _i-1 +κ _mach,de ×△t (23)

wherein, kappa _mach,de The vertical speed is equal Mach number falling, and the period is equal Mach number falling period;

when the altitude is smaller than the Mach number, the altitude h is reduced _mach,de But is greater than the altitude h at equal corrected airspeed climb _cas,de The speed and altitude of the current track point are:

h _i ＝h _i-1 +κ _cas,de ×△t (25)

wherein V is _cas,de To equally correct the speed at which airspeed falls, VS _cas,de For the vertical velocity at which the equal corrected airspeed falls, this stage is the equal corrected airspeed fall stage;

when the altitude is smaller than the altitude when the equal correction airspeed climbs but larger than 1000ft, the altitude of the current track point is shown in a formula (26), and when the speed is larger than the last approach speed, the speed of the current track point is calculated as shown in a formula (27); otherwise the velocity is calculated as shown in equation (28),

h _i ＝h _i-1 +κ _postcas,de ×△t (26)

v _i ＝v _i-1 +a _d ×△t (28)

wherein a is _d Correcting acceleration after airspeed drops for equal; kappa (kappa) _postcas,de For the vertical velocity after the equal corrected airspeed drops, this stage is the equal corrected airspeed drop stage;

When the height is less than 1000ft but greater than zero, the speed and height are:

v _i ＝V _app (29)

h _i ＝h _i-1 +κ _fa ×△t (30)

wherein, kappa _fa For the last approach vertical velocity, this stage is the last approach stage;

when the altitude is equal to zero but the velocity is greater than zero, the landing acceleration is a _lnd The speed is as follows:

v _i ＝v _i-1 +a _lnd ×△t (31)

wherein the vertical velocity is zero, this stage is the landing stage; when the speed is zero, the landing phase ends.

Further, the implementation process of the step (6) is as follows:

establishing an airport coordinate system taking an airport datum point as an origin: pointing the magnetic north through the origin as a Y axis, pointing the magnetic north right through the origin as an X axis, and pointing the magnetic north through the origin as a Z axis;

establishing a straight line flight model: firstly, determining airport coordinate system coordinates of a starting point and an ending point of a straight line flight section by using a longitude and latitude conversion formula, and calculating a straight line flight range by using a distance formula between the two points; secondly, according to the heading and airspeed of the aircraft, calculating the flying distance in unit time, as shown in a formula (32); finally, performing superposition calculation by using the airport coordinate system coordinates of the starting point to obtain the airport coordinate system coordinates of the track point, as shown in formulas (33) and (34), obtaining the longitude and latitude coordinates of the track point through a longitude and latitude conversion formula, and ending the straight line flight when the flying distance of the aircraft exceeds the straight line flight range;

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

x _i ＝x _i-1 +l×sin(head _i ) (33)

y _i ＝y _i-1 +l×cos(head _i ) (34)

Wherein v is _i Is the current aircraft speed; Δt is the time interval; kappa (kappa) _i For the current vertical speed of the aircraft, l is the horizontal distance flown per unit time, x _i ,y _i The coordinates of the current track point; x is x _i-1 ,y _i-1 The coordinates of the previous track point; head part _i The method comprises the steps that the heading of an aircraft at a current track point is the heading to be flown, which is marked on a chart in a straight-line flight section, and the heading is unchanged in the whole straight-line flight section;

building a turning flight model: when the continuous three navigation points are not on the same straight line, the course changes between the two navigation sections, and the aircraft needs to perform turning operation to change the course, so that a section of turning track is connected between the two straight line navigation sections; firstly, determining airport coordinate system coordinates of a turning flight starting point and an ending point and turning rate of an aircraft, when a specific turning rate is marked on a chart, using a specified turning rate, otherwise, using a standard turning rate of 3 degrees per second; determining turning time according to the course difference and turning rate of two adjacent sections of tracks, and obtaining a turning course through the turning time and the airspeed; secondly, approximating the turning track flown in unit time to a straight track, determining the flying course of the straight track, and calculating the distance flown in unit time; finally, the airport coordinate system coordinates of the track points are obtained by carrying out superposition calculation by starting with the airport coordinate system coordinates of the starting point, as shown in formulas (35) to (37), the longitude and latitude coordinates of the track points are obtained through a longitude and latitude conversion formula, and when the flying distance of the aircraft exceeds the turning flight course, turning flight is finished:

head _i ＝head _i-1 ±γ×△t (35)

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

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

Wherein head _i Pointing for current trackHeading, head of air vehicle _i-1 The course is flown by the aircraft at the previous track point, gamma is the turning rate, and when the aircraft changes the course, the left turn is reduced, and the right turn is added; kappa (kappa) _i-1 V is the vertical velocity of the aircraft at the last track point _i-1 The average speed of the aircraft turn for the last track point.

Further, the track attribute in step (7) includes track point speed, track point altitude, flight distance of the aircraft and flight direction data of the aircraft.

The beneficial effects are that: compared with the prior art, the invention has the beneficial effects that: the invention utilizes domestic track data to construct the flight performance database, which accords with the flight condition of China; the kinematic particle model used in the invention regards the aircraft as particles, only horizontal and vertical motions are left, so that the complexity of the model is reduced, and the flight track can be quickly generated by only introducing route point coordinates, altitude, speed limit and the like in batches; according to the method, the optimal value, the maximum value and the minimum value of the key performance parameters of each flight stage are calculated respectively, probability sampling can be carried out in the performance envelope to randomly generate a large number of flight tracks, and the flight tracks can be adjusted according to the historical tracks of the target airport, so that the method has good adaptability.

Drawings

FIG. 1 is a flow chart of the present invention;

FIG. 2 is a graph of speed and altitude change during the climb phase;

FIG. 3 is a Cartesian coordinate system diagram of an airport;

fig. 4 is a schematic diagram of a turning model.

Detailed Description

The invention is described in further detail below with reference to the accompanying drawings.

As shown in fig. 1, the invention provides a method for rapidly generating an aircraft flight track based on a flight plan, which specifically comprises the following steps:

step 1: and (5) flight phase division.

Firstly, track data of common machine types in China are collected, and at least 5000 track data are collected for each machine type. Secondly, carrying out flight phase division on the track data, wherein the increase from zero speed to height to 35 feet is a take-off phase; the elevation from 35 feet to 1000 feet is an initial climbing stage; the ascent from 1000 feet to cruising altitude is the climb phase. The descending stage is that the height is reduced to 1000 feet from the cruising height; the height is reduced from 1000 feet to 35 feet as the final approach stage; the landing phase from 35 feet altitude to zero speed drop. Finally, the height at the beginning and end of each flight phase, and the number of track points that occur, are checked using an evaluation program. To ensure that each piece of track data has certain integrity and reliability.

Step 2: key performance parameters are determined.

And (3) respectively establishing key performance parameters according to the flight phases divided in the step (1), wherein the importance of each performance parameter for different flight phases is different. The flight performance parameters selected in this embodiment are listed as follows by flight phase:

a takeoff stage: including the ground clearance V _tof Acceleration of take-off a _tof 。

An initial climbing stage: including initial climb vertical velocity κ _ic Initial climbing height h _ic Initial climbing acceleration a _ic 。

Climbing stage: including equal correction of vertical velocity kappa before airspeed climb _precas,cl Altitude h when waiting for correcting airspeed to climb _cas,cl Equal correction of airspeed climb speed V _cas,cl Vertical velocity kappa at equal corrected airspeed climb _cas,cl Height h at equal Mach number climb _mach,cl Equal Mach number climb speed M _cl Vertical velocity kappa at equal Mach number climb _mach,cl 。

Cruising phase: cruising altitude h _cr Cruise speed V _cr Initial cruise acceleration a _cr 。

The descending stage: including the speed M at which the mach number drops _de Height h at equal Mach number drop _mach,de Vertical velocity kappa at equal Mach number drop _mach,de Equal corrected airspeed drop velocity V _cas,de Altitude h at equal corrected airspeed drop _cas,de Vertical velocity when equal corrected airspeed fallsDegree kappa _cas,de Vertical velocity κ after equal corrected airspeed decrease _postcas,de 。

And finally, a approaching stage: including last approach vertical velocity κ _fa Last approach height h _fa Last approach speed V _app 。

Landing stage: including the ground speed V _tcd Landing acceleration a _lnd 。

Providing an initial climbing height of 1000 feet and an initial climbing acceleration of 0.5m/s; the acceleration after the equal corrected airspeed drops is-0.2 m/s and the final approach altitude is 1000 feet. And the accelerations of all the flight phases are the average acceleration of this phase and the vertical velocities of all the flight phases are the average vertical velocities of this phase.

Step 3: the performance parameter values are calculated.

Key performance parameter values for each flight phase are extracted from the trajectory data. Wherein the units of distance and height are m, the units of velocity and vertical velocity are m/s, and the units of acceleration are m/s ² 。

During the take-off phase, the most important parameter is the take-off acceleration a _tof And a ground clearance V _tof . Obtaining a distance value d according to the longitude and latitude of a starting point and an ending point of the ground running section, and obtaining a take-off acceleration a through second-order polynomial fitting according to time and airspeed _tof . For the ground clearance speed, the estimation of the ground clearance speed is more complicated because the data update rate is lower. There is typically a few seconds between the last ground data sample and the first airborne observation. To estimate the exact moment of lift-off, the vertical rate and moment at the first air observation are used to estimate the lift-off time t _tof . The result is compared with the previously calculated a _tof Combining, a ground clearance is obtained as follows:

V _tof ＝V _e +a _tof (t _tof -t _e ) (2)

wherein t is _tof The lift-off time is determined by the vertical speed and the height during the first air observation; t is t ₁ For the first air observation time, h ₁ For the first air observation height, κ ₁ For vertical velocity, V, in the first air observation _tof To get off the ground, V _e For the last ground observation speed, a _tof To take-off acceleration, t _e The time of the last ground observation.

The initial climb phase is defined as the aircraft climbing from 35 feet to 1000 feet in altitude. During this stage, the retraction of the landing gear and flaps is mainly completed. However, since the initial climb segment lasts only a short time, its trajectory points are relatively few. The parameter to be studied is the initial climbing height h _ic Initial climbing acceleration a _ic And initial climb vertical speed κ _ic . The initial climbing elevation is defined to be 1000 feet, and the initial climbing acceleration is 0.5m/s ² The initial climb vertical velocity is calculated directly using trajectory data.

The climbing stage starts from the state that the aircraft reaches the smooth finish, and continues until the aircraft reaches the cruising altitude. Comprises three stages of equal corrected airspeed front climbing, equal corrected airspeed climbing and equal Mach number climbing. The aircraft first accelerates to a target corrected airspeed and then flies according to the corrected airspeed. The Mach number of the aircraft increases with increasing vacuum velocity during flight, and is also affected by the decreasing speed of sound. When a certain Mach number is reached, the aircraft flies according to the Mach number until reaching the cruising altitude. As shown in the formula:

Wherein f _cas (t) is a corrected airspeed expression, G ₂ To correct airspeed factor, t _cas Climbing to equal correct airspeedRise time, y _cas To equal correct the airspeed climb speed, t _mach The airspeed climb end time is corrected for equal, while the mach number climb start time is corrected for equal. f (f) _mach (t) is Mach number expression, G ₁ Is Mach number factor, y _mach Is equal Mach number climb speed.

The climbing stage speed and altitude change is shown in figure 2, t _cl,start And t _cl,end The moment of beginning and ending climbing, the broken line is a corrected airspeed change curve, at t _cas The increasing section is followed by the constant section. The dotted line is Mach number variation curve at t _mach The increasing section is preceded by a constant section. The solid line is a height variation curve, and the height is increased throughout the process.

For Mach number, at t _mach The mach number is increased in the front, followed by a constant segment. Extracting the equal Mach number climb start time t using least squares fitting _mach And equal Mach number y _mach The method comprises the steps of carrying out a first treatment on the surface of the For the corrected airspeed profile, the entire climb phase is equally divided into a corrected airspeed increase portion and an equal corrected airspeed portion, using t _mach As a deadline, the time series is fitted from the beginning until t _mach . Equal correction airspeed climb speed y is also obtained by a least square method _cas Equal correction airspeed climb time t _cas And by extracting the aircraft at time t _mach To identify the intersection height. At determination t _cas And t _mach Thereafter, the equal corrected airspeed and the intersection height h at the beginning of the equal Mach number climb can be obtained _cas,cl ，h _mach,cl The method comprises the steps of carrying out a first treatment on the surface of the And calculating vertical velocities corresponding to the three zones, including the vertical velocity kappa before equal corrected airspeed climb _precas,cl Vertical velocity kappa at equal corrected airspeed climb _cas,cl Vertical velocity kappa at equal Mach number climb _mach,cl 。

Cruise altitude h of cruise phase _cr And cruising speed V _cr Is the altitude and speed specified in the flight plan, the initial cruising acceleration a _cr Is the equal Mach number climbing speed M _cl Accelerating to cruising speedV _cr Is calculated directly using the trajectory data.

The descending stage of the aircraft is similar to the climbing stage, from the cruising altitude, the aircraft undergoes equal Mach number descending before reaching the final approach altitude, equal corrected airspeed descending, and equal corrected airspeed descending in three stages, and the calculation method of the performance parameters is the same as that of the climbing stage.

The final approach phase is similar to the initial climb phase, representing the end of descent, and describes an approach trajectory profile from 1,000 feet down to 35 feet by building a generic model. The flight parameter required in the final approach stage is the final approach vertical velocity κ _fa Last approach height h _fa Last approach speed V _app Wherein the final approach height is specified to be 1000 feet, and the remaining two performance parameters are directly calculated using the trajectory data.

The landing phase is similar to the takeoff phase, and the ground speed V of the aircraft needs to be calculated _tcd And landing acceleration a _lnd . The calculation method of the two performance parameters is the same as the calculation method of the take-off stage.

Step 4: and establishing a flight performance database.

Each performance parameter is described using the following three sections. First, the optimum value ω is obtained from the performance parameter values using a normal distribution method. It should be noted that the obtained optimum value is not necessarily the optimum performance parameter value when the aircraft is in flight, and it may be regarded as a standard airline program profile, which corresponds to the APF in the BADA model. Second omega _min And omega _max Is the minimum and maximum value obtained from the different confidence intervals. Different confidence intervals are set according to the type of the parameter. The minimum and maximum values define flight envelope limits to which the aircraft is subject during flight, and a large amount of trajectory data may be generated within the flight envelope using a probabilistic valuation method. And finally, integrating the performance parameters of each flight stage of the common machine type to obtain a flight performance database.

Step 5: and establishing a track data model.

And establishing a track data model according to the change rule of the aircraft track parameters. Including speed, altitude, range, etc. First some initial conditions need to be set as follows:

t＝0,△t＝4s,h＝0,s＝0,v＝0,κ＝0,a _c ＝0.5m/s ² (5)

t _i ＝t _i-1 +△t (6)

s _i ＝s _i-1 +v×△t (7)

wherein t represents time of flight; delta t represents a time step, namely a time interval for generating the waypoints, and the Delta t can be arbitrarily set according to simulation requirements; h represents the flying height; s represents a flight course; v represents the speed; kappa represents vertical velocity; a, a _c Represents initial climbing acceleration of 0.5m/s ² 。

And 5.1, establishing an off-site flight trajectory data model.

1) When the corrected airspeed is less than the ground speed V _tof The speed is calculated as follows:

v _i ＝v _i-1 +a _tof ×△t (8)

v _i v is the current speed _i+1 A for the next track point speed _tof Is the take-off acceleration. At this time, the vertical speed is 0, and this stage is the take-off stage. The take-off acceleration and the later-mentioned flight performance parameters should be determined in the established flight performance database in accordance with the aircraft model.

2) When the corrected airspeed is greater than the ground speed V _tof However, when the height is less than 1000ft, the speed is calculated as shown in formula (9), a _c Represents initial climbing acceleration of 0.5m/s ² The method comprises the steps of carrying out a first treatment on the surface of the The vertical speed is equal to the initial climbing vertical speed kappa _ic The calculation of the height is shown in formula (10), and this stage is the initial climbing stage:

v _i ＝v _i-1 +a _c ×△t (9)

h _i ＝h _i-1 +κ _ic ×△t (10)

3) Altitude h when altitude is greater than 1000ft but less than equal corrected airspeed climb _cas,cl In this case, the height is calculated as shown in the formula (11), and thenAnd calculating the current atmospheric properties including the atmospheric temperature T, the atmospheric density rho and the atmospheric pressure P according to the current height. As shown in equations (12) through (14). If the velocity is less than the constant corrected airspeed, the velocity is calculated as shown in equation (9); if the velocity is greater than the constant corrected airspeed, the velocity is determined from the altitude h of the current track point and the velocity of the last track point, as shown in equation (15). Vertical velocity is equal to vertical velocity kappa before equal correction airspeed climb _precas,cl This phase is the pre-climb phase of equal corrected airspeed.

h _i ＝h _i-1 +κ _precas,cl ×△t (11)

T _i ＝288.15-0.0065×h _i (12)

ρ _i ＝1.225×(T _i /288.15) ^4.26 (13)

P＝ρ×R×T R＝287.0528 (14)

Wherein: p (P) ₀ Is at standard atmospheric pressure, R is a gas constant, ρ ₀ Is the standard atmospheric pressure density.

4) Altitude h when altitude is greater than equal corrected airspeed climb _cas,cl But is smaller than the height h when climbing with equal Mach number _mach,cl Speed V at ascent from equi-corrected airspeed _cas,cl And the height of the current track point. Vertical velocity equal to equal corrected airspeed climb vertical velocity κ _cas,cl This phase is the equal corrected airspeed climb phase. The speed and altitude calculations are shown below.

h _i ＝h _i-1 +κ _cas,cl ×△t (17)

5) Height h when the height is greater than the Mach number _mach,cl But less than cruising height h _cr At the time, the speed is increased from the Mach number at the time of speed M _cl And the current heightThe degree is calculated as shown in equation (18). The speed of sound at which A represents the altitude at which the track point is located is shown in equation (19). Vertical velocity is equal to vertical velocity kappa at equal Mach climb _mach,cl This stage is the equal Mach number climb stage, and the altitude calculation is shown in equation (20).

v _i ＝M _cl ×A _i (18)

h _i ＝h _i-1 +κ _mach,cl ×△t (20)

And 5.2, establishing a cruise flight trajectory data model.

The cruise altitude h given in the flight plan needs to be maintained during cruise flight _cr And cruising speed V _cr . When the altitude is equal to the cruising altitude, the speed is calculated as shown in formula (21),

v _i ＝v _i-1 +a _cr ×△t (21)

wherein a is _cr Is the initial cruise acceleration. When the speed reaches the prescribed cruising speed, the cruising speed is kept to fly, and the stage is a cruising stage. And when the flying distance is larger than the given flying distance in the flying plan, ending the flying period.

And 5.3, establishing an approach flight trajectory data model.

1) The flight distance when cruising is greater than the cruising distance given in the flight plan, and the altitude is less than the cruising altitude h _cr But is greater than the mach number falling height h _mach,de At the same time, the speed is reduced from the Mach number to the speed M _de And the altitude is obtained, the speed is shown as a formula (22), and the vertical speed is equal to the vertical speed kappa when the Mach number is reduced _mach,de This stage is the mach number reduction stage. The height calculation is shown in formula (23).

v _i ＝M _de ·A _i (22)

h _i ＝h _i-1 +κ _mach,de ×△t (23)

2) When the altitude is smaller than the Mach number, the altitude h is reduced _mach,de But is greater than the altitude h at equal corrected airspeed climb _cas,de Speed V at which the speed is reduced by equal correction airspeed _cas,de And the height is calculated as shown in a formula (24); vertical velocity is equal to vertical velocity kappa at equal corrected airspeed decrease _cas,de The height is shown in formula (25); this phase is the equal corrected airspeed drop phase.

h _i ＝h _i-1 +κ _cas,de ×△t (25)

3) When the altitude is smaller than the altitude at which the equal corrected airspeed climbs but greater than 1000ft, the altitude calculation is as shown in equation (26), and the vertical velocity is equal to the vertical velocity κ after the equal corrected airspeed has fallen _postcas,de If the speed is greater than the last approach speed, the speed is calculated as shown in formula (27), otherwise the speed is calculated as shown in formula (28), a _d To equal correct acceleration after airspeed drop, the acceleration is set to-0.2 m/s ² . The method comprises the steps of carrying out a first treatment on the surface of the This stage is the descent stage after equi-corrected airspeed.

h _i ＝h _i-1 +κ _postcas,de ×△t (26)

v _i ＝v _i-1 +a _d ×△t (28)

4) When the altitude is less than 1000ft but greater than zero, the velocity remains at the last approach velocity, as shown in equation (29), the vertical velocity equals the last approach vertical velocity κ _fa The altitude calculation is shown in equation (30), this stage being the last approach stage.

v _i ＝V _app (29)

h _i ＝h _i-1 +κ _fa ×△t (30)

5) When the altitude is equal to zero but the velocity is greater than zero, the landing acceleration is a _lnd The velocity is calculated as shown in equation (31) with zero vertical velocity, this stage being the landing stage. When the speed is zero, the landing phase ends.

v _i ＝v _i-1 +a _lnd ×△t (31)

Step 6: and establishing a track point coordinate model.

An airport coordinate system (hereinafter referred to as a coordinate system) using an airport reference point as an origin is established, and the coordinate system is shown in fig. 3: the magnetic north is pointed by the over-origin as the Y axis, the over-origin is perpendicular to the magnetic north and right as the X axis, and the over-origin is perpendicular to the XOY plane as the Z axis.

1) And establishing a straight line flight model.

Firstly, determining airport coordinate system coordinates of a start point and an end point of a straight line flight section by using a longitude and latitude conversion formula, and calculating a straight line flight range by using a distance formula between the two points. And then the flying distance in unit time is calculated according to the heading and airspeed of the aircraft, as shown in a formula (32). And finally, performing superposition calculation by using the airport coordinate system coordinates of the starting point to obtain the airport coordinate system coordinates of the track point, wherein the airport coordinate system coordinates of the track point are obtained through longitude and latitude conversion formulas as shown in formulas (33) and (34), and when the flying distance of the aircraft exceeds the linear flight range, the linear flight is ended.

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

x _i ＝x _i-1 +l×sin(head _i ) (33)

y _i ＝y _i-1 +l×cos(head _i ) (34)

Wherein v is _i Is the current aircraft speed; Δt is the time interval; kappa (kappa) _i For the current vertical speed of the aircraft, l is the horizontal distance flown per unit time. X is x _i ,y _i The coordinates of the current track point; x is x _i-1 ,y _i-1 The coordinates of the previous track point; head part _i The heading of the aircraft at the current track point is the flight-required heading marked on the chart in the straight-line flight section, and the heading is unchanged in the whole straight-line flight section.

2) And establishing a turning flight model.

When three consecutive waypoints are not on the same straight line, as shown in fig. 4, indicating a change in heading between two legs, the aircraft is subjected to a turn maneuver to change heading, which results in a turn-around connection between the two straight legs.

First, the airport coordinate system coordinates of the starting point and the ending point of the turning flight and the turning rate of the aircraft are determined, when the explicit turning rate is marked on the chart, the specified turning rate is used, otherwise, the standard turning rate is used for 3 degrees per second. And determining turning time according to the course difference and turning rate of two adjacent sections of tracks, and obtaining the turning course through the turning time and the airspeed. As shown in fig. 3, at P ₂ And P ₃ A section of turning track is arranged between the two navigation points, P ₂ Heading before navigation point is 62 degrees, P ₃ The heading after the navigation point is 242 degrees. If calculated at the standard turning rate, the turning process lasts 60 seconds. If the time interval Δt is set to 4 seconds, 15 track points can be obtained.

And secondly, approximating the turning track flown in unit time to be a straight-line track, determining the flying course of the turning track, and calculating the distance flown in unit time. And finally, performing superposition calculation by using the airport coordinate system coordinates of the starting point to obtain the airport coordinate system coordinates of the track point, as shown in formulas (35) to (37), obtaining the longitude and latitude coordinates of the track point through a longitude and latitude conversion formula, and ending the turning flight when the flying distance of the aircraft exceeds the turning flight course.

head _i ＝head _i-1 ±γ×△t (35)

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

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

In head _i Heading, head, of the aircraft for the current track point _i-1 Flying for aircraft at last track pointAnd when the aircraft changes course, the left turn is reduced, and the right turn is increased. Kappa (kappa) _i-1 V is the vertical velocity of the aircraft at the last track point _i-1 The average speed of the aircraft turn for the last track point.

Step 7: and establishing a kinematic model.

The kinematic model consists of a track data model and a track point coordinate model. And obtaining data such as track point speed, track point height, aircraft flying course and the like by using a track data model, and importing the data into a track point coordinate model to generate airport coordinate system coordinates and longitude and latitude coordinates of the track points.

Step 8: a flight trajectory is generated.

And according to the formulated flight plan, importing flight information such as coordinates of a flying route point, cruising height, cruising speed and the like of the aircraft in a kinematic model, calling a flight performance database, and generating track data. When a large number of flight tracks are required to be generated, the flight plans can be classified according to airports and airlines, and the flight plans are imported in batches to quickly generate the flight tracks.

Furthermore, it should be understood that although the present disclosure describes embodiments, not every embodiment contains only one independent technical solution, and that such description is provided for clarity only, and that the technical solutions of the embodiments may be appropriately combined to form other embodiments that will be understood by those skilled in the art.

Claims (10)

1. The quick aircraft flight trajectory generation method based on the flight plan is characterized by comprising the following steps of:

(1) Track data are acquired for different models; performing flight phase division according to the track data;

(2) Determining key performance parameters according to the flight phases divided in the step (1);

(3) Extracting key performance parameter values of each flight stage from the track data;

(4) Establishing a flight performance database;

(5) Establishing a track data model according to the change rule of the aircraft track parameters; the track data model comprises an off-site flight track data model, a cruise flight track data model and an on-site flight track data model;

(6) Establishing a track point coordinate model;

(7) Establishing a kinematic model: the kinematic model consists of a track data model and a track point coordinate model; obtaining track attributes by using a track data model, and importing the track attributes into a track point coordinate model to generate airport coordinate system coordinates and longitude and latitude coordinates of the track points;

(8) And according to the formulated flight plan, importing flight information such as coordinates of a flying route point, cruising height, cruising speed and the like of the aircraft in a kinematic model, calling a flight performance database, and generating track data.

2. The method for rapidly generating a flight trajectory of an aircraft based on a flight plan of claim 1, wherein the flight phase division of step (1) is:

increasing from zero speed to altitude to 35 feet is a takeoff phase; the elevation from 35 feet to 1000 feet is an initial climbing stage; the elevation is raised from 1000 feet to cruising elevation as a climbing stage; the descending stage is that the height is reduced to 1000 feet from the cruising height; the height is reduced from 1000 feet to 35 feet as the final approach stage; the landing phase from 35 feet altitude to zero speed drop.

3. The method for rapidly generating the flight trajectory of the aircraft based on the flight plan according to claim 1, wherein the implementation process of the step (2) is as follows:

each performance parameter is of different importance for different flight phases, and the key performance parameters are selected as follows:

a takeoff stage: including the ground clearance V _tof Acceleration of take-off a _tof ；

An initial climbing stage: including initial climb vertical velocity κ _ic Initial climbing heighth _ic Initial climbing acceleration a _ic ；

Climbing stage: including equal correction of vertical velocity kappa before airspeed climb _precas,cl Altitude h when waiting for correcting airspeed to climb _cas,cl Equal correction of airspeed climb speed V _cas,cl Vertical velocity kappa at equal corrected airspeed climb _cas,cl Height h at equal Mach number climb _mach,cl Equal Mach number climb speed M _cl Vertical velocity kappa at equal Mach number climb _mach,cl ；

Cruising phase: cruising altitude h _cr Cruise speed V _cr Initial cruise acceleration a _cr ；

The descending stage: including the speed M at which the mach number drops _de Height h at equal Mach number drop _mach,de Vertical velocity kappa at equal Mach number drop _mach,de Equal corrected airspeed drop velocity V _cas,de Altitude h at equal corrected airspeed drop _cas,de Vertical velocity κ when equi-corrected airspeed falls _cas,de Vertical velocity κ after equal corrected airspeed decrease _postcas,de ；

And finally, a approaching stage: including last approach vertical velocity κ _fa Last approach height h _fa Last approach speed V _app ；

Landing stage: including the ground speed V _tcd Landing acceleration a _lnd 。

4. The method for rapidly generating the flight trajectory of the aircraft based on the flight plan according to claim 1, wherein the implementation process of the step (3) is as follows:

a takeoff stage: obtaining a distance value d according to coordinates of a starting point and an ending point of a ground running section, and obtaining a take-off acceleration a through second-order polynomial fitting according to time and airspeed _tof The method comprises the steps of carrying out a first treatment on the surface of the The ground leaving speed is as follows:

V _tof ＝V _e +a _tof (t _tof -t _e ) (2)

wherein t is _tof The lift-off time is determined by the vertical speed and the height during the first air observation; t is t ₁ For the first air observation time, h ₁ For the first air observation height, κ ₁ For vertical velocity, V, in the first air observation _tof To get off the ground, V _e For the last ground observation speed, a _tof To take-off acceleration, t _e The time of the last ground observation is the time;

an initial climbing stage: the initial climbing vertical speed is directly calculated by using track data;

the climbing stage starts from the state that the aircraft reaches the smooth finish, and continues until the aircraft reaches the cruising altitude; comprises three stages of equal correction airspeed climbing, equal correction airspeed climbing and equal Mach number climbing; the aircraft first accelerates to a target corrected airspeed and then flies according to the corrected airspeed; the Mach number of the aircraft increases with the effects of increasing vacuum velocity and decreasing speed of sound during flight; when a certain Mach number is reached, the aircraft flies according to the Mach number until reaching the cruising altitude; as shown in the formula:

Wherein f _cas (t) is a corrected airspeed expression, G ₂ To correct airspeed factor, t _cas To equal correct the airspeed climb time, y _cas To equal correct the airspeed climb speed, t _mach The method comprises the steps of correcting the airspeed climbing ending time for equal speed and simultaneously starting the climbing of equal Mach number; f (f) _mach (t) is Mach number expression, G ₁ Is Mach number factor, y _mach Is equal Mach number climbing speed;

for Mach number, at t _mach The mach number is an increasing segment before and a constant segment after; extracting the equal Mach number climb start time t using least squares fitting _mach And equal Mach number y _mach The method comprises the steps of carrying out a first treatment on the surface of the For the corrected airspeed profile, the entire climb phase is equally divided into a corrected airspeed increase portion and an equal corrected airspeed portion, using t _mach As a deadline, the time series is fitted from the beginning until t _mach The method comprises the steps of carrying out a first treatment on the surface of the Equal correction airspeed climb speed y is also obtained by a least square method _cas Equal correction airspeed climb time t _cas And by extracting the aircraft at time t _mach Identifying a cross height; at determination t _cas And t _mach Thereafter, an equal corrected airspeed and an equal Mach number climb start crossover height h is obtained _cas,cl ，h _mach,cl The method comprises the steps of carrying out a first treatment on the surface of the And calculating vertical velocities corresponding to the three zones, including the vertical velocity kappa before equal corrected airspeed climb _precas,cl Vertical velocity kappa at equal corrected airspeed climb _cas,cl Vertical velocity kappa at equal Mach number climb _mach,cl ；

Cruise altitude and cruise speed during cruise phase are the altitude and speed specified in the flight plan, initial cruise acceleration a _cr Is the equal Mach number climbing speed M _cl Accelerating to cruising speed V _cr The average acceleration of (2) is directly calculated by using the track data;

the descending stage is similar to the climbing stage, from the cruising altitude, the aircraft goes through the three stages of equal Mach number descending, equal correction airspeed descending and equal correction airspeed descending before reaching the final approach altitude, and the calculation method of the performance parameters is the same as that of the climbing stage;

the final approach stage provides that the final approach height is 1000 feet, and the other two performance parameters are directly calculated by using track data;

the landing phase and the takeoff phase are calculated by the same method.

5. The method for rapidly generating the flight trajectory of the aircraft based on the flight plan according to claim 1, wherein the implementation process of the step (4) is as follows:

describing each performance parameter by using three parts, obtaining an optimal value omega from the performance parameter values based on a normal distribution method, and obtaining a minimum value omega from different confidence intervals _min And a maximum value omega _max The method comprises the steps of carrying out a first treatment on the surface of the Setting different confidence intervals according to the types of the parameters; the minimum value and the maximum value define flight envelope limits observed when the aircraft flies, and a probability value method is used for generating a large amount of track data in the flight envelope; and integrating the performance parameters of each flight stage of the common machine type to obtain a flight performance database.

6. The method for rapidly generating the flight trajectory of the aircraft based on the flight plan according to claim 1, wherein the off-site flight trajectory data model construction process is as follows:

when the corrected airspeed is less than the ground speed V _tof When the current track point has the following speed:

v _i ＝v _i-1 +a _tof ×△t (8)

wherein v is _i For the current track point velocity, v _i-1 A is the speed of the last track point _tof For takeoff acceleration, Δt represents the time step; at this time, the vertical speed is 0, and this stage is the take-off stage;

when the corrected airspeed is greater than the ground speed V _tof But at altitudes less than 1000ft, the current track point velocity and altitude are respectively:

v _i ＝v _i-1 +a _c ×△t (9)

h _i ＝h _i-1 +κ _ic ×△t (10)

wherein a is _c Represents the initial climbing acceleration, and the vertical speed is equal to the initial climbing vertical speed kappa _ic This phase is the initial climb phase;

altitude h when altitude is greater than 1000ft but less than equal corrected airspeed climb _cas,cl When the current track point is at the height:

h _i ＝h _i-1 +κ _precas,cl ×△t (11)

if the velocity is less than the constant corrected airspeed, the velocity is calculated as shown in equation (9); if the speed is greater than the constant corrected airspeed, the speed is obtained by the altitude h of the current track point and the speed of the last track point, as shown in formula (15); vertical velocity is equal to vertical velocity kappa before equal correction airspeed climb _precas,cl This stage is the pre-climb equal corrected airspeed stage:

wherein: p (P) ₀ At standard atmospheric pressure ρ ₀ The standard atmospheric pressure density is represented by ρ, the current atmospheric pressure is represented by P;

altitude h when altitude is greater than equal corrected airspeed climb _cas,cl But is smaller than the height h when climbing with equal Mach number _mach,cl Speed V at ascent from equi-corrected airspeed _cas,cl Obtaining the height of the current track point; vertical velocity equal to equal corrected airspeed climb vertical velocity κ _cas,cl This phase is the equal correction airspeed climb phase; the current track point speed and altitude are calculated as follows:

h _i ＝h _i-1 +κ _cas,cl ×△t (17)

height h when the height is greater than the Mach number _mach,cl But less than cruising height h _cr At the same time, the speed of the current track point is increased from the speed M when the Mach number is increased _cl And obtaining the sound velocity of the current altitude:

v _i ＝M _cl ×A _i (18)

wherein A is _i The sound speed of the height of the current track point is represented; t (T) _i A temperature representing the altitude at which the current track point is located; vertical velocity is equal to vertical velocity kappa at equal Mach climb _mach,cl The stage is a Mach number climbing stage, and the height of the current track point is as follows:

h _i ＝h _i-1 +κ _mach,cl ×△t (20)。

7. the method for rapidly generating the flight trajectory of the aircraft based on the flight plan according to claim 1, wherein the cruising flight trajectory data model construction process is as follows:

the cruise altitude h given in the flight plan needs to be maintained during cruise flight _cr And cruising speed V _cr The method comprises the steps of carrying out a first treatment on the surface of the When the altitude is equal to the cruising altitude, the current track point speed is calculated as follows:

v _i ＝v _i-1 +a _cr ×△t (21)

wherein a is _cr Is an initial cruise acceleration; when the speed reaches the specified cruising speed, the cruising speed is kept to fly continuously, and the stage is a cruising stage; and when the flying distance is larger than the given flying distance in the flying plan, ending the flying period.

8. The method for rapidly generating the flight trajectory of the aircraft based on the flight plan according to claim 1, wherein the incoming flight trajectory data model construction process is as follows:

the flight distance when cruising is greater than the cruising distance given in the flight plan, and the altitude is less than the cruising altitude h _cr But is greater than the mach number falling height h _mach,de At the same time, the speed is reduced from the Mach number to the speed M _de And obtaining the altitude, wherein the current track point speed and the altitude are as follows:

v _i ＝M _de ·A _i (22)

h _i ＝h _i-1 +κ _mach,de ×△t (23)

Wherein, kappa _mach,de Is of equal MachThe vertical speed when the number is reduced, and the stage is equal Mach number reduction stage;

when the altitude is smaller than the Mach number, the altitude h is reduced _mach,de But is greater than the altitude h at equal corrected airspeed climb _cas,de The speed and altitude of the current track point are:

h _i ＝h _i-1 +κ _cas,de ×△t (25)

wherein V is _cas,de To equally correct the speed at which airspeed falls, VS _cas,de For the vertical velocity at which the equal corrected airspeed falls, this stage is the equal corrected airspeed fall stage;

when the altitude is smaller than the altitude when the equal correction airspeed climbs but larger than 1000ft, the altitude of the current track point is shown in a formula (26), and when the speed is larger than the last approach speed, the speed of the current track point is calculated as shown in a formula (27); otherwise the velocity is calculated as shown in equation (28),

h _i ＝h _i-1 +κ _postcas,de ×△t (26)

v _i ＝v _i-1 +a _d ×△t (28)

wherein a is _d Correcting acceleration after airspeed drops for equal; kappa (kappa) _postcas,de For the vertical velocity after the equal corrected airspeed drops, this stage is the equal corrected airspeed drop stage;

when the height is less than 1000ft but greater than zero, the speed and height are:

v _i ＝V _app (29)

h _i ＝h _i-1 +κ _fa ×△t (30)

wherein, kappa _fa For the last approach vertical velocity, this stage is the last approach stage;

when the altitude is equal to zero but the velocity is greater than zero, the landing acceleration is a _lnd The speed is as follows:

v _i ＝v _i-1 +a _lnd ×△t (31)

wherein the vertical velocity is zero, this stage is the landing stage; when the speed is zero, the landing phase ends.

9. The method for rapidly generating the flight trajectory of the aircraft based on the flight plan according to claim 1, wherein the implementation process of the step (6) is as follows:

establishing an airport coordinate system taking an airport datum point as an origin: pointing the magnetic north through the origin as a Y axis, pointing the magnetic north right through the origin as an X axis, and pointing the magnetic north through the origin as a Z axis;

establishing a straight line flight model: firstly, determining airport coordinate system coordinates of a starting point and an ending point of a straight line flight section by using a longitude and latitude conversion formula, and calculating a straight line flight range by using a distance formula between the two points; secondly, according to the heading and airspeed of the aircraft, calculating the flying distance in unit time, as shown in a formula (32); finally, performing superposition calculation by using the airport coordinate system coordinates of the starting point to obtain the airport coordinate system coordinates of the track point, as shown in formulas (33) and (34), obtaining the longitude and latitude coordinates of the track point through a longitude and latitude conversion formula, and ending the straight line flight when the flying distance of the aircraft exceeds the straight line flight range;

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

x _i ＝x _i-1 +l×sin(head _i ) (33)

y _i ＝y _i-1 +l×cos(head _i ) (34)

wherein v is _i Is the current aircraft speed; Δt is the time interval; kappa (kappa) _i For the current vertical speed of the aircraft, l is the horizontal distance flown per unit time, x _i ,y _i The coordinates of the current track point; x is x _i-1 ,y _i-1 The coordinates of the previous track point; head part _i For the heading of the aircraft at the current waypoint,in the straight line flight section, the course is the flight course marked on the chart and is unchanged in the whole straight line flight section;

building a turning flight model: when the continuous three navigation points are not on the same straight line, the course changes between the two navigation sections, and the aircraft needs to perform turning operation to change the course, so that a section of turning track is connected between the two straight line navigation sections; firstly, determining airport coordinate system coordinates of a turning flight starting point and an ending point and turning rate of an aircraft, when a specific turning rate is marked on a chart, using a specified turning rate, otherwise, using a standard turning rate of 3 degrees per second; determining turning time according to the course difference and turning rate of two adjacent sections of tracks, and obtaining a turning course through the turning time and the airspeed; secondly, approximating the turning track flown in unit time to a straight track, determining the flying course of the straight track, and calculating the distance flown in unit time; finally, the airport coordinate system coordinates of the track points are obtained by carrying out superposition calculation by starting with the airport coordinate system coordinates of the starting point, as shown in formulas (35) to (37), the longitude and latitude coordinates of the track points are obtained through a longitude and latitude conversion formula, and when the flying distance of the aircraft exceeds the turning flight course, turning flight is finished:

head _i ＝head _i-1 ±γ×△t (35)

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

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

Wherein head _i Heading, head, of the aircraft for the current track point _i-1 The course is flown by the aircraft at the previous track point, gamma is the turning rate, and when the aircraft changes the course, the left turn is reduced, and the right turn is added; kappa (kappa) _i-1 V is the vertical velocity of the aircraft at the last track point _i-1 The average speed of the aircraft turn for the last track point.

10. The method of claim 1, wherein the trajectory attributes in step (7) include trajectory point speed, trajectory point altitude, aircraft range, and aircraft direction data.