A method for characterizing the range capability of civil aircraft under natural wind field conditions based on vector integral.

Abstract

This invention discloses a method for characterizing the range capability of civil aircraft under natural wind field conditions based on vector integrals, relating to the fields of aircraft conceptual design and air traffic management. The method involves: dividing the geographical area into grids; acquiring upper-altitude wind field data at the grid centers; generating wind direction and wind speed vector models based on wind direction and wind speed data from each grid center; setting a center for drawing a range circle map and determining the endpoints of radial straight line segments radiating from this center; generating a straight line function between the range circle map center and each endpoint; using the wind direction and wind speed vector models, calculating the vector product of the wind direction and wind speed vectors within each grid with respect to the radial straight line segments, comparing this product with the length of the straight line function segment, and stopping when the difference is less than a precision threshold; finally, connecting the endpoints to form a smooth, irregular closed curve, i.e., the range capability characterization map.

Description

Technical Field

[0001] This invention relates to four-dimensional trajectory prediction of aircraft in aircraft conceptual design and air traffic management systems, specifically to a method for characterizing the range capability of civil aircraft and planning routes under natural wind field conditions based on vector integral. Background Technology

[0002] With the rapid development of the civil aviation industry, air traffic volume is constantly increasing, and problems such as flight delays and airspace congestion occur frequently. To solve these problems, a systematic solution based on four-dimensional trajectory operation is proposed. Existing trajectory planning studies have many input parameters, many calculation steps, and excessively high solution accuracy, making it difficult to perform batch calculations and unable to represent trajectory patterns over a wide range.

[0003] Civil aircraft manufacturers face significant challenges in characterizing range capabilities. The impact of upper-altitude wind fields on range is both complex and cumulative. Because aircraft have long maximum ranges, the magnitude and direction of winds along flight paths are discontinuous variables, requiring segmented consideration of their impact on range, with earlier segments influencing later ones, necessitating cumulative calculations and considerations. However, currently, there is a lack of an effective method for continuously, systematically, and in batches calculating the impact of winds along flight paths on range, resulting in an inability to accurately assess the influence of upper-altitude wind fields on the range of civil aircraft. Summary of the Invention

[0004] Existing technologies lack an effective method for continuously, systematically, and in batches calculating the impact of en-route winds on flight range, resulting in the inability to accurately assess the impact of high-altitude wind fields on the range of civil aircraft. To address this problem, this invention provides a method for characterizing the range capability of civil aircraft under natural wind field conditions based on vector integrals.

[0005] A method for characterizing the range capability of civil aircraft under natural wind field conditions based on vector integral includes the following steps:

[0006] Step 1: Set the geographic scope and then divide the set geographic scope into grids;

[0007] Step 2: Obtain the upper-level wind field data at the grid center. The upper-level wind field data shall include at least wind speed data and wind direction data.

[0008] Step 3: Generate wind direction vector model and wind speed vector model based on the wind direction and wind speed data of each grid center;

[0009] Step 4: Set the center of the route circle map and determine the endpoints of the radial straight line segments from the center of the route circle map.

[0010] Step 5: Generate a linear function between the center and each endpoint of the flight path circle map;

[0011] Step 6: Using the wind direction vector model and wind speed vector model, calculate the vector product of the wind direction vector and wind speed vector with respect to the radial line segment in each grid, and use it as the vector integral;

[0012] Step 7: Compare the lengths of the vector integral line segment and the linear function line segment to determine whether the iteration accuracy has reached the preset threshold. If yes, proceed to step 8; otherwise, return to step 6.

[0013] Step 8: Connect the far endpoints of each vector integral line segment with a smooth curve to form a closed figure;

[0014] Step 9: Output the range capability characterization results.

[0015] Preferably, step 1 consists of the following steps:

[0016] Step 101: Select the geographical range based on the aircraft's theoretical design range and the main target market of interest;

[0017] Step 102: Divide the region into grids based on the geometric dimensions of the geographical extent;

[0018] Step 103: Calculate the longitude and latitude coordinates of a single grid center one by one and store them in pairs.

[0019] Preferably, step 2 consists of the following steps:

[0020] Step 201: Query wind speed and wind direction data at different heights of a single grid center using meteorological data;

[0021] Step 202: Store the wind speed data and wind direction data as vector pairs in the form of two-directional velocity components, including meridional and zonal vector values;

[0022] Step 203: Obtain temperature and standard atmospheric parameters, including standard sea-level pressure and standard temperature.

[0023] Preferably, step 4 specifically involves the following steps:

[0024] Step 401: Select and set the center of the flight path map drawing according to the requirements;

[0025] Step 402: According to actual needs, starting from the center of the route circle map, radially divide the route according to each navigation direction angle to form radial straight line segments;

[0026] Step 403: Obtain the longitude and latitude coordinates of the endpoint after algebraic calculation of the designed flight path along the radial straight line segments from the center of the flight path map drawing center through code calculation.

[0027] Preferably, step 5 consists of the following steps:

[0028] Using linear functions and grid center data, a linear programming model is constructed, with the length of the straight line segment as the independent variable and flight time as the dependent variable, to establish a flight time prediction model. For a typical jet passenger aircraft, the impact of route winds on flight distance is a continuous linear change, which can be simply characterized as:

[0029] ;

[0030] in This is the actual voyage distance affected by the wind along the route. It's the wind of the shipping route. It is the theoretical design range under windless conditions. It is a coefficient characterizing the impact of wind along the flight path on the flight distance. Obtained from the meteorological database via step 202. Obtained from aircraft design manuals or instruction manuals. It was calculated using a simple flight plan of the aircraft.

[0031] Preferably, step 6 specifically involves the following steps:

[0032] Step 601: Obtain several sets of straight line functions connecting the center and endpoint of the flight path map by solving the code;

[0033] Step 602: Represent the linear function within the geographical area selected in step 1;

[0034] Step 603: Construct vector integrals based on the vectors generated from the data at each grid center.

[0035] Preferably, step 603 specifically involves the following steps:

[0036] Step 6031: Calculate the wind-induced drag along the flight path using the wind direction vector model and the wind speed vector model. Calculate the vector product of the wind vector in each grid with respect to the radial straight line segment. Continuously calculate the calculation results of all grids traversed by each radial straight line segment to obtain the vector integral calculation results.

[0037] Preferably, in step 6031, a vector model of wind direction and speed is constructed based on the wind direction and speed information of each grid center. The wind direction and speed are also stored in pairs, where the meridional vector component is... The latitudinal vector component is ;

[0038]

[0039]

[0040] This refers to the actual wind speed at high altitudes. The angle between the wind direction and due north;

[0041] The wind direction and speed vectors at the center of each grid are represented by several pairs. Formal storage;

[0042] The lower limit of integration is defined by the starting point of each radial line segment, and the upper limit of integration is defined by the ending point. The variable of integration is the position coordinates on the line segment. That is, the integration interval is ,in For the first The length of a radial straight line segment;

[0043] The integrand is the product of the projection of the wind vector onto the flight direction on the straight segment and the aircraft's flight-related parameters, specifically in the form of:

[0044] ;

[0045] For position The projection of the wind vector onto the flight direction. The air density at that altitude. For the reference area of ​​the aircraft, This is the aircraft's drag coefficient;

[0046] By combining the aircraft's fuel consumption model and correcting the theoretical range through the total effect of wind-induced drag, the actual range after considering the influence of natural wind fields is obtained.

[0047] Based on the corrected actual flight distance, the final endpoint position of each straight segment is determined.

[0048] Preferably, step 7 specifically involves the following steps:

[0049] Step 701: Compare the lengths of the vector integral line segment and the linear function line segment;

[0050] Step 702: If the difference between the length of the vector integral line segment and the length of the linear function line segment is greater than the preset iteration accuracy difference, repeat steps 5-6 and compare the newly obtained length of the vector integral line segment with the previous calculation result.

[0051] Step 703: Stop iterating when the difference in length between the vector integral line segment and the linear function line segment is less than the difference in iteration accuracy.

[0052] Preferably, step 8 specifically involves the following steps:

[0053] Step 801: Set the starting point of the length of the vector integral line segment at the end of the iteration as the center of the flight path map selected in step 3;

[0054] Step 802: Characterize the longitude and latitude coordinates of the endpoint of the line segment in terms of geographical scope;

[0055] Step 803: Connect the endpoints across the geographic area using code to form a smooth curve;

[0056] Step 804: Form an irregular closed curve shape.

[0057] Preferably, in step 103, the Gauss-Kruger projection transformation formula is used to convert latitude and longitude to plane coordinates, as follows:

[0058] Gauss-Kruger projection forward calculation formula:

[0059] ;

[0060]

[0061] , Using Cartesian coordinates, Latitude Longitude It represents the longitude of the central meridian.

[0062] Gauss-Kruger projection inverse calculation formula:

[0063]

[0064]

[0065] This is an approximate latitude.

[0066] Preferably, in step 803, the third-order Bézier curve method is used to connect the various endpoints with a smooth curve. The specific principle is as follows:

[0067] Curve equation: The parametric equation of a third-order Bézier curve is:

[0068] ;

[0069] and These are two adjacent endpoints, i.e., the start and end points of the curve. and These are control points; by adjusting their positions, a smooth transition of the curve can be achieved.

[0070] Control point determination method:

[0071] With three adjacent endpoints , , For example, the rules for determining control points are as follows:

[0072] arrive End point of the curve :

[0073] ;

[0074] arrive Control points of the curve :

[0075] .

[0076] Preferably, in step 201, the meteorological data is meteorological forecast data in GRIB format, which comes from a meteorological bureau or meteorological forecasting center;

[0077] In step 202, the two-directional velocity components include the meridional velocity. and latitudinal velocity ;

[0078] In step 203, the standard sea-level air pressure is The standard temperature is .

[0079] Preferably, in step 102, the size of the mesh split can be set to... or The specific dimensions and accuracy requirements of the geographical area are determined accordingly.

[0080] Preferably, in step 302, the longitude and latitude coordinates of the endpoint in each angular direction are obtained by calculating the length of the straight segment of the theoretical design voyage and the voyage direction angle.

[0081] Preferably, in step 601, the straight line function parameters connecting the center of the flight path map and each endpoint are calculated using the longitude and latitude coordinate conversion formula.

[0082] Preferably, in step 5, with minimizing the flight time deviation as the core objective, the objective function is constructed as follows:

[0083] ;

[0084] This is the sum of squares of the flight time deviation. The number of radial straight line segments in this method ≥360, For the first The actual flight time corresponding to each straight segment. For the first predicted by the model Flight time for a straight segment;

[0085] The constraints in this step are as follows:

[0086] Maximum thrust constraint for aircraft: During flight, the engine thrust cannot exceed the design maximum continuous cruise thrust, i.e.:

[0087] ;

[0088] For the first The actual thrust of the engine during a straight segment of flight. The maximum continuous cruise thrust designed for aircraft engines;

[0089] Fuel consumption rate constraint: The fuel consumption rate must be controlled within the reasonable range of the aircraft design, that is:

[0090] ;

[0091] For the first Fuel consumption rate during a straight-line flight segment. The maximum permissible fuel consumption rate designed for an aircraft;

[0092] Speed ​​constraints: The aircraft's flight speed must be within the safe flight speed range, neither lower than the stall speed nor exceeding the maximum design speed, i.e.:

[0093] ;

[0094] For the first The speed of flight on a straight segment, This is the aircraft's stall speed. This is the aircraft's maximum design speed.

[0095] Straight line segment length constraint: The length of each radial straight line segment must be related to the aircraft's designed flight range and meet the geographical coverage requirements, that is:

[0096] ;

[0097] For the first The length of the straight line segment, The theoretical flight range of the aircraft under windless conditions.

[0098] Preferably, in step 6, if the difference between the length of the vector integral line segment after iterative calculation and the length of the vector integral line segment or the line function line segment after the previous iteration exceeds 1%, the iteration continues if it exceeds 1%; otherwise, the iteration stops.

[0099] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0100] 1. This invention achieves continuous, systematic, and batch calculation of route winds by setting the geographical scope, performing grid splitting, acquiring upper-altitude wind data, setting the center of the flight path map, calculating the latitude and longitude coordinates of the endpoint, generating a linear function, and solving vector integrals. This overcomes the problem of the lack of effective methods for assessing the impact of route winds in the existing technology.

[0101] 2. This invention uses a combination of grid splitting and vector integration to accurately reflect the complex and progressive impact of high-altitude wind fields on the range of civil aircraft, effectively solving the problem that traditional range capability characterization methods cannot fully consider the impact of high-altitude winds on flight path distance and direction;

[0102] 3. This invention achieves automated calculation of range capability representation through code computation, avoiding the limitations of manual operation, improving calculation efficiency and accuracy, and meeting the ever-increasing demand of air traffic flow.

[0103] 4. The range capability representation map generated by this invention connects each endpoint with a smooth curve, forming an irregular closed curve graphic, which provides designers, manufacturers and users with an intuitive and three-dimensional range capability display tool, effectively improving the quality of route network planning;

[0104] 5. By setting the center of the flight path map and 360 endpoints, this invention achieves a comprehensive characterization of flight capability, overcoming the limitations of existing technologies that only consider conflict detection and resolution under deterministic conditions.

[0105] 6. This invention adopts an iterative calculation method, which controls the calculation accuracy by comparing the calculation result with the preset accuracy difference, thus ensuring the accuracy and reliability of the range capability characterization and effectively solving the problems of large errors and poor usability caused by local non-closure in traditional characterization methods. Attached Figure Description

[0106] Figure 1 This is an overall flowchart of the present invention;

[0107] Figure 2 This is a detailed flowchart of step 1 of the present invention;

[0108] Figure 3 This is a detailed flowchart of step 2 of the present invention;

[0109] Figure 4 This is a detailed flowchart of step 8 of the present invention; Detailed Implementation

[0110] Please refer to Figures 1 to 4 This invention provides a method for characterizing the range capability of civil aircraft under natural wind field conditions based on vector integral. The specific implementation steps are as follows:

[0111] Step 1: Set the geographic scope and then divide the set geographic scope into grids;

[0112] Step 101: Based on the selected aircraft model, the designed range is 6900km. The primary target market is the Chinese market. The selected geographical area is 73.5°E (western boundary) ~ 135.1°E (eastern boundary) and 4.1°N (southern boundary) ~ 53.5°N (northern boundary), forming... A rectangular area;

[0113] Step 102: Divide the above area into The grid consists of 600×550 grids to ensure that the grid evenly covers the entire area;

[0114] Step 103: Using the longitude and latitude coordinate conversion formula, calculate the longitude and latitude coordinates of each grid center.

[0115] The Gauss-Kruger projection transformation formula is used to convert geodetic coordinates (latitude and longitude) to plane coordinates. The specific formula is as follows:

[0116] Gauss-Kruger projection forward calculation formula:

[0117] ;

[0118]

[0119] , Using Cartesian coordinates, Latitude Longitude It represents the longitude of the central meridian.

[0120] Gauss-Kruger projection inverse calculation formula:

[0121]

[0122]

[0123] Approximate latitude (which can be obtained through plane coordinates) (Preliminary estimate).

[0124] Step 2: Obtain the upper-level wind field data at the grid center. The upper-level wind field data shall include at least wind speed data and wind direction data.

[0125] Step 201: Query the wind speed and wind direction data at different heights of a single grid center using meteorological data (GRIB format meteorological forecast data provided by the China Meteorological Administration);

[0126] Step 202: Store the acquired wind speed and wind direction data as two-directional velocity components, with the meridional velocity being... The latitudinal velocity is ;

[0127] Step 203: Obtain standard atmospheric parameters: Standard sea level pressure is... The standard temperature is .

[0128] Step 3: Generate wind direction vector model and wind speed vector model based on the wind direction and wind speed data of each grid center;

[0129] Step 4: Set the center of the route circle map and determine the endpoints of the radial straight line segments from the center of the route circle map.

[0130] Step 401: Select point A near Beijing as the center for drawing the flight path map, with longitude: 116.324 and latitude: 40.003.

[0131] Step 402: Using theoretical design of the voyage and navigation direction angle, calculate the longitude and latitude coordinates of the destination in each direction, for a total of 360 destinations.

[0132] Step 5: Generate a linear function between the center and each endpoint of the flight path circle map;

[0133] Using linear functions and grid center data, a linear programming model is constructed, with the length of the straight line segment as the independent variable and flight time as the dependent variable, to establish a flight time prediction model. For a typical jet passenger aircraft, the impact of route winds on flight distance is a continuous linear change, which can be simply characterized as:

[0134] ;

[0135] in This is the actual voyage distance affected by the wind along the route. It's the wind of the shipping route. It is the theoretical design range under windless conditions. It is a coefficient characterizing the impact of wind along the flight path on the flight distance. Obtained from the meteorological database via step 202. Obtained from aircraft design manuals or instruction manuals. It was calculated using a simple flight plan of the aircraft.

[0136] In step 5, with minimizing the flight time deviation as the core objective, the objective function is constructed as follows:

[0137] ;

[0138] This is the sum of squares of the flight time deviation. The number of radial straight line segments in this method ≥360, For the first The actual flight time corresponding to each straight segment. For the first predicted by the model Flight time for a straight segment;

[0139] The objective function is designed to make the predicted flight time as close as possible to the actual flight time, ensuring the accuracy of the model's estimation of flight time and providing a reliable time dimension basis for subsequent flight capability characterization.

[0140] The constraints in this step are as follows:

[0141] Maximum thrust constraint for aircraft: During flight, the engine thrust cannot exceed the design maximum continuous cruise thrust, i.e.:

[0142] ;

[0143] For the first The actual thrust of the engine during a straight segment of flight. The maximum continuous cruise thrust designed for aircraft engines;

[0144] Fuel consumption rate constraint: Fuel consumption rate must be controlled within the reasonable range of the aircraft design to ensure the feasibility of the flight range, that is:

[0145] ;

[0146] For the first Fuel consumption rate during a straight-line flight segment. The maximum permissible fuel consumption rate designed for an aircraft;

[0147] Speed ​​constraints: The aircraft's flight speed must be within the safe flight speed range, neither lower than the stall speed nor exceeding the maximum design speed, i.e.:

[0148] ;

[0149] For the first The speed of flight on a straight segment, This is the aircraft's stall speed. This is the aircraft's maximum design speed.

[0150] Straight line segment length constraint: The length of each radial straight line segment must be related to the aircraft's designed flight range and meet the geographical coverage requirements, that is:

[0151] ;

[0152] For the first The length of the straight line segment, The theoretical flight range of the aircraft under windless conditions.

[0153] Step 6: Using the wind direction vector model and wind speed vector model, calculate the vector product of the wind direction vector and wind speed vector with respect to the radial line segment in each grid, and use it as the vector integral;

[0154] Preferably, step 6 specifically involves the following steps:

[0155] Step 601: Obtain several sets of straight line functions connecting the center and endpoint of the flight path map by solving the code;

[0156] Step 602: Represent the linear function within the geographical area selected in step 1;

[0157] Step 603: Construct vector integrals based on the vectors generated from the data at each grid center.

[0158] Preferably, step 603 specifically involves the following steps:

[0159] Step 6031: Using the vector model of wind direction and wind speed, calculate the wind-induced drag along the route, calculate the vector product of the wind vector in each grid with the radial straight line segment, continuously calculate the calculation results of all grids through which each radial straight line segment passes, and obtain the vector integral calculation results.

[0160] Preferably, step 6031 specifically involves the following steps:

[0161] Based on the wind direction and speed information at each grid center, a vector model of wind direction and speed is constructed. Wind direction and speed are also stored in pairs, where the meridional vector component is... The latitudinal vector component is .

[0162]

[0163]

[0164] This refers to the actual wind speed at high altitudes. It is the angle between the wind direction and due north.

[0165] The wind direction and speed vectors at the center of each grid are represented by several pairs. It is stored in a formal format, which facilitates subsequent vector integral calculations.

[0166] The lower limit of integration is defined by the starting point (center of the flight path map) of each radial straight line segment, and the upper limit of integration is defined by the ending point. The integration variable is the position coordinates on the straight line segment. That is, the integration interval is ,in For the first The length of a radial straight line segment.

[0167] The integrand is the product of the projection of the wind vector onto the flight direction on the straight segment and the aircraft's flight-related parameters, specifically in the form of:

[0168] ;

[0169] For position The projection of the wind vector onto the flight direction. This is the air density at that altitude (which can be calculated based on standard atmospheric parameters). For the reference area of ​​the aircraft, This is the aircraft's drag coefficient (determined by the aircraft's aerodynamic design parameters).

[0170] By combining the aircraft's fuel consumption model and correcting the theoretical range through the total effect of wind-induced drag, the actual range after considering the influence of natural wind fields is obtained.

[0171] Based on the corrected actual flight distance, the final endpoint of each straight line segment is determined, providing accurate data support for the subsequent drawing of the flight capability characterization map.

[0172] Step 7: Compare the lengths of the vector integral line segment and the linear function line segment to determine whether the iteration accuracy has reached the preset threshold. If yes, proceed to step 8; otherwise, return to step 6.

[0173] Preferably, step 7 specifically involves the following steps:

[0174] Step 701: Compare the lengths of the vector integral line segment and the linear function line segment.

[0175] Step 702: If the difference in length between the vector integral line segment and the linear function line segment exceeds 1%, repeat steps 5 and 6 until the difference is less than 1%.

[0176] Step 703: When the length difference is less than 1%, output the final straight segment of the flight path.

[0177] Step 8: Connect the far endpoints of each vector integral line segment with a smooth curve to form a closed figure;

[0178] Step 801: Take the center of the final flight path map as the starting point and connect each endpoint with a smooth curve;

[0179] Step 802: Characterize the longitude and latitude coordinates of each endpoint within the geographical area;

[0180] Step 803: Connect all endpoints with a smooth curve using the third-order Bézier curve method. The specific principle is as follows:

[0181] Curve equation: The parametric equation of a third-order Bézier curve is:

[0182] ;

[0183] and These are two adjacent endpoints (the start and end points of the curve). and These are control points; by adjusting their positions, a smooth transition of the curve can be achieved.

[0184] Control point determination method:

[0185] With three adjacent endpoints , , For example, the rules for determining control points are as follows:

[0186] ( arrive (End point of the curve, control point)

[0187] ;

[0188] ( arrive (Start point control point of the curve)

[0189] .

[0190] The control points determined by this method can ensure the continuity of tangents between adjacent curve segments, thus achieving a smooth closure of the overall curve.

[0191] Step 804: Obtain the irregular closed curve graph, which is the characterization graph of the range capability of civil aircraft under the required natural wind field conditions.

[0192] Step 9: Output the range capability characterization results.

[0193] This invention also provides a method for characterizing the range capability of civil aircraft under natural wind field conditions based on vector integral, the specific implementation steps of which are as follows:

[0194] Step 1: Set the geographic scope and then divide the set geographic scope into grids;

[0195] Step 101: Based on the selected aircraft model, the designed range is 1500km. The primary target market is the European market. The selected geographical area is 7.00°W (western boundary) ~ 12.00°E (eastern boundary) and 43.00°N (southern boundary) ~ 50.00°N (northern boundary), forming... A rectangular area;

[0196] Step 102: Divide the above area into The grid consists of 100×70 grids to ensure that the grid evenly covers the entire area;

[0197] Step 103: Since the target calculation area is rectangular, each segmented grid is still rectangular. Calculate the longitude and latitude coordinates of the center of each grid rectangle.

[0198] The Gauss-Kruger projection transformation formula is used to convert geodetic coordinates (latitude and longitude) to plane coordinates. The specific formula is as follows:

[0199] Gauss-Kruger projection forward calculation formula:

[0200] ;

[0201]

[0202] , Using Cartesian coordinates, Latitude Longitude It represents the longitude of the central meridian.

[0203] Gauss-Kruger projection inverse calculation formula:

[0204]

[0205]

[0206] Approximate latitude (which can be obtained through plane coordinates) (Preliminary estimate).

[0207] Taking a specific grid from the European market case as an example, the detailed calculation process is as follows:

[0208] Given conditions: The target geographical area is 7.00°W (western boundary) ~ 12.00°E (eastern boundary), 43.00°N (southern boundary) ~ 50.00°N (northern boundary), with a grid size of [not specified]. Select the central meridian (prime meridian).

[0209] Grid position determined:

[0210] Suppose a grid cell is located in the 20th row (counted from north to south) and 30th column (counted from west to east) of a geographic area.

[0211] Plane coordinate calculation:

[0212] Planar coordinates of grid center point : ;

[0213] Planar coordinates of grid center point : .

[0214] Latitude and longitude conversion calculation:

[0215] plane coordinates Substituting into the Gauss-Kruger inverse formula, we obtain: latitude ;longitude .

[0216] That is, the latitude and longitude coordinates of the center of the grid are (13.5°W, 47.37°N).

[0217] Step 2: Obtain upper-level wind field data;

[0218] Step 201: Obtain parameters such as wind speed, wind direction, temperature, and humidity at the grid center point using the GRIB format weather forecast data provided by the European Centre for Medium-Range Weather Forecasts (ECMWF).

[0219] Step 202: Store the acquired data in the form of two-directional velocity components, with the eastward velocity being... The northbound speed is ;

[0220] Step 203: Obtain standard atmospheric parameters: Standard sea level pressure is... The standard temperature is .

[0221] Step 3: Generate wind direction vector model and wind speed vector model based on the wind direction and wind speed data of each grid center;

[0222] Step 4: Set the center of the route circle map and determine the endpoints of the radial straight line segments from the center of the route circle map.

[0223] Step 401: Select point B in Paris, France as the center for drawing the route circle map, with longitude: 2.34 and latitude: 48.86.

[0224] Step 402: Using theoretical design of the voyage and navigation direction angle, calculate the longitude and latitude coordinates of the destination in each direction, for a total of 360 destinations.

[0225] Step 5: Generate a linear function between the center and each endpoint of the flight path circle map;

[0226] Using linear functions and grid center data, a linear programming model is constructed, with the length of the straight line segment as the independent variable and flight time as the dependent variable, to establish a flight time prediction model. For a typical jet passenger aircraft, the impact of route winds on flight distance is a continuous linear change, which can be simply characterized as:

[0227] ;

[0228] in This is the actual voyage distance affected by the wind along the route. It's the wind of the shipping route. It is the theoretical design range under windless conditions. It is a coefficient characterizing the impact of wind along the flight path on the flight distance. Obtained from the meteorological database via step 202. Obtained from aircraft design manuals or instruction manuals. It was calculated using a simple flight plan of the aircraft.

[0229] In step 5, with minimizing the flight time deviation as the core objective, the objective function is constructed as follows:

[0230] ;

[0231] This is the sum of squares of the flight time deviation. The number of radial straight line segments in this method ≥360, For the first The actual flight time corresponding to each straight segment. For the first predicted by the model Flight time for a straight segment;

[0232] The objective function is designed to make the predicted flight time as close as possible to the actual flight time, ensuring the accuracy of the model's estimation of flight time and providing a reliable time dimension basis for subsequent flight capability characterization.

[0233] The constraints in this step are as follows:

[0234] Maximum thrust constraint for aircraft: During flight, the engine thrust cannot exceed the design maximum continuous cruise thrust, i.e.:

[0235] ;

[0236] For the first The actual thrust of the engine during a straight segment of flight. The maximum continuous cruise thrust designed for aircraft engines;

[0237] Fuel consumption rate constraint: Fuel consumption rate must be controlled within the reasonable range of the aircraft design to ensure the feasibility of the flight range, that is:

[0238] ;

[0239] For the first Fuel consumption rate during a straight-line flight segment. The maximum permissible fuel consumption rate designed for an aircraft;

[0240] Speed ​​constraints: The aircraft's flight speed must be within the safe flight speed range, neither lower than the stall speed nor exceeding the maximum design speed, i.e.:

[0241] ;

[0242] For the first The speed of flight on a straight segment, This is the aircraft's stall speed. This is the aircraft's maximum design speed.

[0243] Straight line segment length constraint: The length of each radial straight line segment must be related to the aircraft's designed flight range and meet the geographical coverage requirements, that is:

[0244] ;

[0245] For the first The length of the straight line segment, The theoretical flight range of the aircraft under windless conditions.

[0246] Step 6: Using the wind direction vector model and wind speed vector model, calculate the vector product of the wind direction vector and wind speed vector with respect to the radial line segment in each grid, and use it as the vector integral;

[0247] Preferably, step 6 specifically involves the following steps:

[0248] Step 601: Obtain several sets of straight line functions connecting the center and endpoint of the flight path map by solving the code;

[0249] Step 602: Represent the linear function within the geographical area selected in step 1;

[0250] Step 603: Construct vector integrals based on the vectors generated from the data at each grid center.

[0251] Preferably, step 603 specifically involves the following steps:

[0252] Step 6031: Using the vector model of wind direction and wind speed, calculate the wind-induced drag along the route, calculate the vector product of the wind vector in each grid with the radial straight line segment, continuously calculate the calculation results of all grids through which each radial straight line segment passes, and obtain the vector integral calculation results.

[0253] Preferably, step 6031 specifically involves the following steps:

[0254] Based on the wind direction and speed information at each grid center, a vector model of wind direction and speed is constructed. Wind direction and speed are also stored in pairs, where the meridional vector component is... The latitudinal vector component is .

[0255]

[0256]

[0257] This refers to the actual wind speed at high altitudes. It is the angle between the wind direction and due north.

[0258] The wind direction and speed vectors at the center of each grid are represented by several pairs. It is stored in a formal format, which facilitates subsequent vector integral calculations.

[0259] The lower limit of integration is defined by the starting point (center of the flight path map) of each radial straight line segment, and the upper limit of integration is defined by the ending point. The integration variable is the position coordinates on the straight line segment. That is, the integration interval is ,in For the first The length of a radial straight line segment.

[0260] The integrand is the product of the projection of the wind vector onto the flight direction on the straight segment and the aircraft's flight-related parameters, specifically in the form of:

[0261] ;

[0262] For position The projection of the wind vector onto the flight direction. This is the air density at that altitude (which can be calculated based on standard atmospheric parameters). For the reference area of ​​the aircraft, This is the aircraft's drag coefficient (determined by the aircraft's aerodynamic design parameters).

[0263] By combining the aircraft's fuel consumption model and correcting the theoretical range through the total effect of wind-induced drag, the actual range after considering the influence of natural wind fields is obtained.

[0264] Based on the corrected actual flight distance, the final endpoint of each straight line segment is determined, providing accurate data support for the subsequent drawing of the flight capability characterization map.

[0265] Step 7: Compare the lengths of the vector integral line segment and the linear function line segment to determine whether the iteration accuracy has reached the preset threshold. If yes, proceed to step 8; otherwise, return to step 6.

[0266] Preferably, step 7 specifically involves the following steps:

[0267] Step 701: Compare the lengths of the vector integral line segment and the linear function line segment.

[0268] Step 702: If the difference in length between the vector integral line segment and the linear function line segment exceeds 1%, repeat steps 5 and 6 until the difference is less than 1%.

[0269] Step 703: When the length difference is less than 1%, output the final straight segment of the flight path.

[0270] Step 8: Connect the far endpoints of each vector integral line segment with a smooth curve to form a closed figure;

[0271] Step 801: Take the center of the final flight path map as the starting point and connect each endpoint with a smooth curve;

[0272] Step 802: Characterize the longitude and latitude coordinates of each endpoint within the geographical area;

[0273] Step 803: Connect all endpoints with a smooth curve using the third-order Bézier curve method. The specific principle is as follows:

[0274] Curve equation: The parametric equation of a third-order Bézier curve is:

[0275] ;

[0276] and These are two adjacent endpoints (the start and end points of the curve). and These are control points; by adjusting their positions, a smooth transition of the curve can be achieved.

[0277] Control point determination method:

[0278] With three adjacent endpoints , , For example, the rules for determining control points are as follows:

[0279] ( arrive (End point of the curve, control point)

[0280] ;

[0281] ( arrive (Start point control point of the curve)

[0282] .

[0283] The control points determined by this method can ensure the continuity of tangents between adjacent curve segments, thus achieving a smooth closure of the overall curve.

[0284] Step 804: Obtain the irregular closed curve graph, which is the characterization graph of the range capability of civil aircraft under the required natural wind field conditions.

[0285] Step 9: Output the range capability characterization results.

[0286] It should be noted that, in this document, relational terms such as "first" and "second" are used only to distinguish one entity or operation from another, and do not necessarily require or imply any such actual relationship or order between these entities or operations. Furthermore, the terms "comprising," "including," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such process, method, article, or apparatus.

[0287] Although embodiments of the invention have been shown and described, it will be understood by those skilled in the art that various changes, modifications, substitutions and alterations can be made to these embodiments without departing from the principles and spirit of the invention, the scope of which is defined by the appended claims and their equivalents.

Claims

1. A method for characterizing the range capability of civil aircraft under natural wind field conditions based on vector integral, characterized in that, Includes the following steps: Step 1: Set the geographic scope and then divide the set geographic scope into grids; Step 2: Obtain the upper-level wind field data at the grid center. The upper-level wind field data shall include at least wind speed and wind direction data. Step 3: Generate wind direction vector model and wind speed vector model based on the wind direction and wind speed data of each grid center; Step 4: Set the center of the route circle map and determine the endpoints of the radial straight line segments from the center of the route circle map. Step 5: Generate a linear function between the center and each endpoint of the flight path circle map; Step 6: Using the wind direction vector model and wind speed vector model, calculate the vector product of the wind direction vector and wind speed vector with respect to the radial line segment in each grid, and use it as the vector integral; Step 7: Compare the lengths of the vector integral line segment and the linear function line segment to determine whether the iteration accuracy has reached the preset threshold. If yes, proceed to step 8; otherwise, return to step 6. Step 8: Connect the far endpoints of each vector integral line segment with a smooth curve to form a closed figure; Step 9: Output the range capability characterization results.

2. The method for characterizing the range capability of civil aircraft under natural wind field conditions based on vector integral as described in claim 1, characterized in that, Step 1 consists of the following steps: Step 101: Select the geographical range based on the aircraft's theoretical design range and the main target market of interest; Step 102: Divide the rectangular area formed by the geographical scope into grids; Step 103: Calculate the longitude and latitude coordinates of a single grid center one by one and store them in pairs.

3. The method for characterizing the range capability of civil aircraft under natural wind field conditions based on vector integral as described in claim 1, characterized in that, Step 2 consists of the following steps: Step 201: Query wind speed and wind direction data at different heights of a single grid center using meteorological data; Step 202: Store the wind speed data and wind direction data as vector pairs in the form of two-directional velocity components, including meridional and zonal vector values; Step 203: Obtain temperature and standard atmospheric parameters, including standard sea-level pressure and standard temperature.

4. The method for characterizing the range capability of civil aircraft under natural wind field conditions based on vector integral as described in claim 1, characterized in that, Step 4 consists of the following steps: Step 401: Select and set the center of the flight path map drawing according to the requirements; Step 402: According to actual needs, starting from the center of the route circle map, radially divide the route according to each navigation direction angle to form radial straight line segments; Step 403: Obtain the longitude and latitude coordinates of the endpoints of the radial straight line segments from the center of the flight path drawing, after algebraic calculation of the designed flight path, through code calculation.

5. The method for characterizing the range capability of civil aircraft under natural wind field conditions based on vector integral as described in claim 3, characterized in that, Step 5 involves the following steps: Using the linear function and grid center data, a linear programming model is constructed. With the length of the straight line segment as the independent variable and flight time as the dependent variable, a flight time prediction model is established. For a typical jet airliner, the impact of en-route winds on flight distance is a continuous linear change, which can be simply represented as: ； in This is the actual voyage distance affected by the wind along the route. It is the vector form of the high-altitude wind speed along the flight path. It is the theoretical design range under windless conditions. It is a coefficient characterizing the impact of wind along the flight path on the flight distance. Obtained from the meteorological database via step 202. Obtained from aircraft design manuals or instruction manuals. It was calculated using a simple flight plan of the aircraft.

6. The method for characterizing the range capability of civil aircraft under natural wind field conditions based on vector integral as described in claim 1, wherein step 6 specifically comprises: Step 601: Obtain several sets of straight line functions connecting the center and endpoint of the flight path map by solving the code; Step 602: Represent the linear function within the geographical area selected in step 1; Step 603: Construct vector integrals based on the vectors generated from the data at each grid center.

7. The method for characterizing the range capability of civil aircraft under natural wind field conditions based on vector integral as described in claim 6, characterized in that, Step 603 is as follows: Step 6031: Calculate the wind-induced drag along the flight path using the wind direction vector model and the wind speed vector model. Calculate the vector product of the wind vector in each grid with respect to the radial straight line segment. Continuously calculate the calculation results of all grids traversed by each radial straight line segment to obtain the vector integral calculation results.

8. The method for characterizing the range capability of civil aircraft under natural wind field conditions based on vector integral as described in claim 7, characterized in that, In step 6031, based on the wind direction and speed information of each grid center, a vector model of wind direction and speed is constructed. The wind direction and speed are also stored in pairs, where the meridional vector component is... The latitudinal vector component is ; The wind speed of the high-altitude flight path is in vector form. The angle between the wind direction and due north; The wind direction and speed vectors at the center of each grid are represented by several pairs. Formal storage; The lower limit of integration is defined by the starting point of each radial line segment, and the upper limit of integration is defined by the ending point. The variable of integration is the position coordinates on the line segment. That is, the integration interval is ,in For the first The length of a radial straight line segment; The integrand is the product of the projection of the wind vector onto the flight direction on the straight segment and the aircraft's flight-related parameters, specifically in the form of: ； For position The projection of the wind vector onto the flight direction. The air density at that altitude. For the reference area of ​​the aircraft, This is the aircraft's drag coefficient; By combining the aircraft's fuel consumption model and correcting the theoretical range through the total effect of wind-induced drag, the actual range after considering the influence of natural wind fields is obtained. Based on the corrected actual flight distance, the final endpoint position of each straight segment is determined.

9. The method for characterizing the range capability of civil aircraft under natural wind field conditions based on vector integral as described in claim 1, characterized in that, Step 7 is as follows: Step 701: Compare the lengths of the vector integral line segment and the linear function line segment; Step 702: If the difference between the length of the vector integral line segment and the length of the linear function line segment is greater than the preset iteration accuracy difference, repeat steps 5-6 and compare the newly obtained length of the vector integral line segment with the previous calculation result. Step 703: Stop iterating when the difference in length between the vector integral line segment and the linear function line segment is less than the difference in iteration accuracy.

10. The method for characterizing the range capability of civil aircraft under natural wind field conditions based on vector integral as described in claim 1, characterized in that, Step 8 consists of the following steps: Step 801: Set the starting point of the length of the vector integral line segment at the end of the iteration as the center of the flight path map selected in step 4; Step 802: Characterize the longitude and latitude coordinates of the endpoint of the line segment in terms of geographical scope; Step 803: Connect the endpoints across the geographic area using code to form a smooth curve; Step 804: Form an irregular closed curve figure.

11. The method for characterizing the range capability of civil aircraft under natural wind field conditions based on vector integral as described in claim 2, characterized in that, In step 103, the Gauss-Kruger projection transformation formula is used to convert latitude and longitude to plane coordinates. The specific formula is as follows: Gauss-Kruger projection forward calculation formula: ； , Using Cartesian coordinates, Latitude Longitude Longitude of the central meridian; Gauss-Kruger projection inverse calculation formula: This is an approximate latitude.

12. The method for characterizing the range capability of civil aircraft under natural wind field conditions based on vector integral as described in claim 10, characterized in that, In step 803, the third-order Bézier curve method is used to connect the various endpoints with a smooth curve. The specific principle is as follows: Curve equation: The parametric equation of a third-order Bézier curve is: ； and These are two adjacent endpoints, i.e., the start and end points of the curve. and These are control points; by adjusting their positions, a smooth transition of the curve can be achieved. Control point determination method: With three adjacent endpoints , , For example, the rules for determining control points are as follows: arrive End point of the curve : ； arrive Control points of the curve : 。 13. The method for characterizing the range capability of civil aircraft under natural wind field conditions based on vector integral as described in claim 3, characterized in that, In step 201, the meteorological data is meteorological forecast data in GRIB format, which comes from the meteorological bureau or meteorological forecast center; In step 202, the two-directional velocity components include the meridional velocity. and latitudinal velocity ; In step 203, the standard sea-level air pressure is The standard temperature is .

14. The method for characterizing the range capability of civil aircraft under natural wind field conditions based on vector integral as described in claim 2, characterized in that, In step 102, the size of the mesh split can be set to... or The specific dimensions and accuracy requirements of the geographical area are determined accordingly.

15. The method for characterizing the range capability of civil aircraft under natural wind field conditions based on vector integral as described in claim 4, characterized in that, In step 402, the longitude and latitude coordinates of the endpoint in each angular direction are obtained by calculating the length of the straight segment of the theoretical design voyage and the voyage direction angle.

16. The method for characterizing the range capability of civil aircraft under natural wind field conditions based on vector integral as described in claim 6, characterized in that, In step 601, the straight line function parameters connecting the center of the flight path map and each endpoint are calculated using the longitude and latitude coordinate conversion formula.

17. The method for characterizing the range capability of civil aircraft under natural wind field conditions based on vector integral as described in claim 5, characterized in that, In step 5, with minimizing the flight time deviation as the core objective, the objective function is constructed as follows: ； This is the sum of squares of the flight time deviation. The number of radial straight line segments in this method ≥360, For the first The actual flight time corresponding to each straight segment. For the first predicted by the model Flight time for a straight segment; The constraints in this step are as follows: Maximum thrust constraint for aircraft: During flight, the engine thrust cannot exceed the design maximum continuous cruise thrust, i.e.: ； For the first The actual thrust of the engine during a straight segment of flight. The maximum continuous cruise thrust designed for aircraft engines; Fuel consumption rate constraint: The fuel consumption rate must be controlled within the reasonable range of the aircraft design, that is: ； For the first Fuel consumption rate during a straight-line flight segment. The maximum permissible fuel consumption rate designed for an aircraft; Speed ​​constraints: The aircraft's flight speed must be within the safe flight speed range, neither lower than the stall speed nor exceeding the maximum design speed, i.e.: ； For the first The speed of flight on a straight segment, This is the aircraft's stall speed. This is the aircraft's maximum design speed. Straight line segment length constraint: The length of each radial straight line segment must be related to the aircraft's designed flight range and meet the geographical coverage requirements, that is: ； For the first The length of the straight line segment, The theoretical flight range of the aircraft under windless conditions.

18. The method for characterizing the range capability of civil aircraft under natural wind field conditions based on vector integral as described in claim 7, characterized in that, In step 6, if the difference between the length of the vector integral line segment after iterative calculation and the length of the vector integral line segment or the line function line segment after the previous iteration exceeds 1%, the iteration continues; if it does not exceed 1%, the iteration stops.

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