A method for calculating a track of a turn through a point
By calculating the over-the-point turn trajectory, the problem of poor trajectory determinism and repeatability is solved, the flight quality of the carrier aircraft during over-the-point turns is improved, and the accuracy and safety of the trajectory are achieved.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Patents(China)
- Current Assignee / Owner
- XIAN FLIGHT SELF CONTROL INST OF AVIC
- Filing Date
- 2022-11-11
- Publication Date
- 2026-06-09
AI Technical Summary
In existing technologies, the determinability and repeatability of flight paths are poor, resulting in low flight quality when the aircraft makes point turns. In particular, when point turns are required at waypoints, the flight path deviation is large, leading to lower flight quality.
By calculating the turning trajectory through the waypoint, including obtaining the azimuth difference of the waypoint, determining the turning direction, calculating the parameters of the transition arc and the straight transition segment, and accurately solving the turning arc, the pilot's perception ability and flight quality are improved.
It increases the determinability and repeatability of flight paths, improves the flight quality of the aircraft during turn segments when making point turns, and ensures the accuracy and safety of flight.
Smart Images
Figure CN115755962B_ABST
Abstract
Description
Technical Field
[0001] This invention relates to the technical field of flight management systems, and specifically to a method for calculating a turn trajectory. Background Technology
[0002] Turning over points is a crucial transition method in civil aviation flight procedures. It increases the predictability and repeatability of flight paths and improves the flight quality of aircraft during turn segments. Therefore, transitions are an indispensable part of aircraft flight management systems. Currently, manned aircraft in China primarily operate on straight segments. When waypoints require turning over points, transition routes are not constructed. This increases the uncertainty of the flight path; aircraft with different performance characteristics exhibit significant path deviations and lower flight quality. Summary of the Invention
[0003] The purpose of this invention is to provide a method for calculating the trajectory of a point-through turn, which increases the determinability and repeatability of the trajectory, and at the same time improves the flight quality of the aircraft during the turning segment when making a point-through turn.
[0004] The technical solution of this invention: In order to achieve the above-mentioned objective, a method for calculating the turning trajectory at a passing point is proposed, which specifically includes the following steps:
[0005] Step 1: According to the flight plan data, the flight path passes through the first waypoint, the second waypoint, and the third waypoint in sequence. The flight path between the first waypoint and the second waypoint is recorded as the first segment, and the flight path between the second waypoint and the third waypoint is recorded as the second segment. The azimuth angles from the first waypoint to the second waypoint and from the second waypoint to the third waypoint are obtained respectively. The absolute value range of the difference between the azimuth angles from the first waypoint to the second waypoint and from the second waypoint to the third waypoint is 60-180 degrees. From the second waypoint to the third waypoint, the second segment includes, in sequence, transition arc 1, a straight transition segment, transition arc 2, and an exit straight segment.
[0006] Step 2: Determine the turning direction from the first waypoint to the second waypoint based on the azimuth angle between the first waypoint and the second waypoint;
[0007] Step 3: Calculate the azimuth angle of the straight transition section in the second segment based on the turning direction from the first segment to the second segment;
[0008] Step 4: Based on the azimuth angle of the straight transition segment calculated in Step 3, calculate the central angle corresponding to the transition arc 1 in the second flight segment;
[0009] Step 5: Calculate the starting coordinates of the straight transition segment based on the central angle corresponding to the transition arc 1 obtained in Step 4;
[0010] Step 6: Calculate the end coordinates of the straight transition segment based on the starting coordinates of the straight transition segment;
[0011] Step 7: Calculate the coordinates of the turning center corresponding to the transition arc 1;
[0012] Step 8: Calculate the coordinates of the turning center corresponding to the transition arc 2;
[0013] Step 9: Calculate the coordinates of the turning end point corresponding to the transition arc 2;
[0014] Step 10: Based on the turning direction, the azimuth angle of the straight transition segment, the coordinates of the starting point of the straight transition segment, the coordinates of the ending point of the straight transition segment, the coordinates of the turning center corresponding to transition arc 1, the coordinates of the turning center corresponding to transition arc 2, and the coordinates of the turning end point corresponding to transition arc 2, combined with the first waypoint, the second waypoint, and the third waypoint in the flight plan, the complete trajectory of the over-point turn is finally calculated.
[0015] In one possible embodiment, step 1, based on flight plan data, designates the first waypoint as P0; the second waypoint as P1; the third waypoint as P2; the first segment as P0P1; the second segment as P1P2; and the azimuth angle from the first waypoint to the second waypoint as χ. i The azimuth angle from the second waypoint to the third waypoint is denoted as χ. f ;
[0016] Determining the turning direction from the first segment to the second segment in step 2 specifically includes the following steps:
[0017] ①When When 0 < χ f -χ i If π, the plane turns right; if or π < χ f -χ i If the value is less than 2π, the plane will turn left.
[0018] ②When When 0 < χ f -χ i <π or The plane turns right; if -π < χ f -χ i <0, the plane turns left;
[0019] ③When When -π < χ f -χi <0 or The plane turns left; if 0 < χ f -χ i <π, the plane turns right;
[0020] ④ When When -π < χ f -χ i <0, the plane turns left, if or -2π<χ f -χ i <-π, the plane turns right.
[0021] In one possible embodiment, the azimuth angle of the straight transition segment in step 3 is denoted as χ. m The specific calculation process includes:
[0022] when hour,
[0023] when hour,
[0024] when hour,
[0025] In one possible embodiment, step 4 calculates the central angle corresponding to the transition arc 1, denoted as Δχ, based on the azimuth angle of the straight transition segment. Specifically, this includes the following steps:
[0026]
[0027] In one possible embodiment, the starting point coordinates of the straight transition segment in step 5 are designated as P3, and the specific calculation process includes:
[0028] The angle ∠P1P3 formed by the tangent to transition arc 1 at point P1 and the line P1P3 is equal to... Find the azimuth angle of the line from point P1 to point P3 using the following steps.
[0029] when hour,
[0030] when hour,
[0031] when hour,
[0032] The distance from point P1 to point P3 is Where R1 is the turning radius of the aircraft at point P1;
[0033]
[0034] Where V1 is the aircraft speed in the first segment, g is the gravitational acceleration, and φ is the maximum roll angle of the aircraft.
[0035] Given that the latitude and longitude of P1 are P3 latitude and longitude are R e Let be the Earth's radius, then:
[0036]
[0037]
[0038] In one possible embodiment, the coordinates of the end point of the straight transition segment in step 6 are marked as P4, and the specific calculation process of the coordinates of the start point P4 of the straight transition segment includes:
[0039] The distance D2 from point P4 to the straight line P1P2 containing the second flight segment is Where R2 is the turning radius of the aircraft at point P2;
[0040]
[0041] Where V2 is the aircraft speed in the second segment, g is the gravitational acceleration, and φ is the maximum roll angle of the aircraft;
[0042] Assume the distance from point P3 to line P1P2 is D1, and the distance from point P3 to point P4 is... Set P4 latitude and longitude as have:
[0043]
[0044]
[0045] In one possible embodiment, step 7, calculating the coordinates of the turning center O1 corresponding to the transition arc 1, specifically includes:
[0046] Let the azimuth angle between the starting point P1 of transition arc 1 and the center O1 of transition arc 1 be . The specific calculation process includes:
[0047] when hour,
[0048] when hour,
[0049] when hour,
[0050] when hour,
[0051] Let O1 be the latitude and longitude. have:
[0052]
[0053]
[0054] Where R1 is the turning radius of the aircraft at point P1;
[0055]
[0056] Where V1 is the aircraft speed in the first segment, g is the gravitational acceleration, and φ is the maximum roll angle of the aircraft.
[0057] In one possible embodiment, step 8 involves calculating the coordinates of the turning center O2 corresponding to the transition arc 2;
[0058] Assume the heading angle from point P4 to the center point O2 of arc 2. Then we have:
[0059]
[0060] The distance from point P4 to the center point O2 of arc 2 is R2. Let the latitude and longitude of O2 be... have:
[0061]
[0062]
[0063] In one possible embodiment, the specific calculation process for the coordinates of the turning end point P5 corresponding to the transition arc 2 in step 9 includes:
[0064] Let the distance from point P1 to point P5 be |P1P5|, and calculate it using the following formula:
[0065]
[0066] The azimuth angle from point P1 to point P5 is χ. f Let the latitude and longitude of P5 be... have:
[0067]
[0068]
[0069] The advantages and effects of this invention can be:
[0070] (1) Increase the determinability and repeatability of flight paths;
[0071] (2) Accurately calculate the turning arc during over-point flight to improve the pilot's perception ability.
[0072] (3) Improved the flight quality of the aircraft during the turning segment when it makes a point turn. Attached Figure Description
[0073] Figure 1 A schematic diagram illustrating the transition path. Detailed Implementation
[0074] The invention will now be further described with reference to the accompanying drawings.
[0075] A method for calculating the trajectory of a turn with a passing point, the specific operation steps are as follows:
[0076] Step 1: Based on the flight plan data, obtain the heading angle parameters for the two preceding and following flight segments.
[0077] See Figure 1 As shown, according to the flight plan data, the first waypoint is denoted as P0; the second waypoint as P1; the third waypoint as P2; the first segment as P0P1; the second segment as P1P2; and the azimuth angle from the first waypoint to the second waypoint as χ. i The azimuth angle from the second waypoint to the third waypoint is denoted as χ. f ;
[0078] Step 2: Calculate the turning direction based on the azimuth from the first waypoint to the second waypoint, and the azimuth from the second waypoint to the third waypoint.
[0079] ①When When 0 < χ f -χ i If π, the plane turns right; if or π < χ f -χ i If the value is less than 2π, the plane will turn left.
[0080] ②When When 0 < χ f -χ i <π or The plane turns right; if -π < χ f -χ i <0, the plane turns left;
[0081] ③When When -π < χ f -χ i <0 or The plane turns left; if 0 < χ f -χ i <π, the plane turns right.
[0082] ④ When When -π < χ f -χ i <0, the plane turns left, if or -2π<χ f -χ i <-π, the plane turns right.
[0083] Step 3: Calculate the azimuth angle χ of the straight transition segment. m :
[0084] when hour,
[0085] when hour,
[0086] when hour,
[0087] Step 4: Calculate the central angle Δχ corresponding to transition arc 1:
[0088]
[0089] Step 5: Calculate the coordinates of the starting point of the straight transition segment.
[0090] Assuming the starting point coordinates of the straight transition segment are P3, the angle ∠P1P3 formed by the tangent line to the transition arc 1 at point P1 and the straight line P1P3 is equal to... Therefore, the azimuth angle of the line from point P1 to point P3 can be calculated using the following method.
[0091] when hour,
[0092] when hour,
[0093] when hour,
[0094] The distance from point P1 to point P3 is Where R1 is the turning radius of the aircraft at point P1;
[0095]
[0096] Where V1 is the aircraft speed in the first segment, g is the gravitational acceleration, and φ is the maximum roll angle of the aircraft.
[0097] Set the latitude and longitude of P1 as P3 latitude and longitude are R e Let be the Earth's radius, then:
[0098]
[0099]
[0100] Step 6: Calculate the coordinates P4 of the end point of the straight transition segment.
[0101] The distance D2 from point P4 to the straight line P1P2 containing the second flight segment is Where R2 is the turning radius of the aircraft at point P2;
[0102]
[0103] Where V2 is the aircraft speed in the second segment, g is the gravitational acceleration, and φ is the maximum roll angle of the aircraft;
[0104] Assume the distance from point P3 to line P1P2 is D1, and the distance from point P3 to point P4 is... Set P4 latitude and longitude as have:
[0105]
[0106]
[0107] Step 7: Calculate the coordinates O1 of the turning center corresponding to transition arc 1.
[0108] Assume the azimuth angle between the starting point P1 of transition arc 1 and the center O1 of transition arc 1 is... The specific calculation process includes:
[0109] when hour,
[0110] when hour,
[0111] when hour,
[0112] when hour,
[0113] Set O1 latitude and longitude as have:
[0114]
[0115]
[0116] Where R1 is the turning radius of the aircraft at point P1;
[0117]
[0118] Where V1 is the aircraft speed in the first segment, g is the gravitational acceleration, and φ is the maximum roll angle of the aircraft.
[0119] Step 8: Calculate the coordinates of the turning center corresponding to transition arc 2.
[0120] Assume the heading angle from point P4 to the center point O2 of arc 2. Then we have:
[0121]
[0122] The distance from point P4 to the center point O2 of arc 2 is R2. Let the latitude and longitude of O2 be... have:
[0123]
[0124]
[0125] Step 9: Calculate the coordinates of the turning end point corresponding to transition arc 2.
[0126] The distance from point P1 to point P5 is |P1P5|, and its calculation formula is:
[0127]
[0128] The azimuth angle from point P1 to point P5 is χ. f Set P5 latitude and longitude as have:
[0129]
[0130]
[0131] Step 10: Based on the turning direction, the azimuth angle of the straight transition segment, the coordinates of the starting point of the straight transition segment, the coordinates of the ending point of the straight transition segment, the coordinates of the turning center corresponding to transition arc 1, the coordinates of the turning center corresponding to transition arc 2, and the coordinates of the turning end point corresponding to transition arc 2, combined with the first waypoint, the second waypoint, and the third waypoint in the flight plan, the complete trajectory of the over-point turn is finally calculated.
[0132] The parameters of transition arc 1 are: turning radius R1, turning center coordinates O1. Coordinates of the starting point of the turn P1 End point of the turn P3
[0133] The parameters for the straight transition segment are: the coordinates of the endpoint of the straight transition segment, P4. The coordinates of the starting point P3 of the straight transition segment are latitude and longitude.
[0134] The parameters of transition arc 2 are: turning radius R2, turning center coordinates O2. Coordinates of the starting point of the turn P4 End of turn P5
Claims
1. A method for calculating the trajectory of a turning point, characterized in that: Specifically, the steps include the following: Step 1: According to the flight plan data, the flight path passes through the first waypoint, the second waypoint, and the third waypoint in sequence. The flight path between the first waypoint and the second waypoint is recorded as the first segment, and the flight path between the second waypoint and the third waypoint is recorded as the second segment. Obtain the azimuth from the first waypoint to the second waypoint and the azimuth from the second waypoint to the third waypoint. The absolute value of the difference between the azimuth angle from the first waypoint to the second waypoint and the azimuth angle from the second waypoint to the third waypoint is 60-180 degrees; from the second waypoint to the third waypoint, the second segment sequentially includes transition arc 1, straight transition segment, transition arc 2, and exit straight segment. In step 1, based on flight plan data, the first waypoint is denoted as P0; the second waypoint as P1; the third waypoint as P2; and the first segment as... The second segment is denoted as The azimuth angle from the first waypoint to the second waypoint is denoted as... The azimuth angle from the second waypoint to the third waypoint is denoted as ; Step 2: Determine the turning direction from the first waypoint to the second waypoint based on the azimuth angle from the first waypoint to the second waypoint and the azimuth angle from the second waypoint to the third waypoint; Determining the turning direction from the first segment to the second segment in step 2 specifically includes the following steps: when At that time, if The plane turns right; if or The plane turned left; when At that time, if or The plane turns right; if The plane turned left; when At that time, if or The plane turns left; if The plane turned right; when At that time, if The plane turns left, if or The plane turned right; Step 3: Based on the turning direction from the first segment to the second segment, calculate the azimuth angle of the straight transition section in the second segment; the azimuth angle of the straight transition section in Step 3 is denoted as... The specific calculation process includes: when hour, when hour, when hour, ; Step 4: Based on the azimuth angle of the straight transition segment calculated in Step 3, calculate the central angle corresponding to the transition arc 1 in the second flight segment; Step 5: Calculate the starting coordinates of the straight transition segment based on the central angle corresponding to the transition arc 1 obtained in Step 4; Step 6: Calculate the end coordinates of the straight transition segment based on the starting coordinates of the straight transition segment; Step 7: Calculate the coordinates of the turning center corresponding to the transition arc 1; Step 8: Calculate the coordinates of the turning center corresponding to the transition arc 2; Step 9: Calculate the coordinates of the turning end point corresponding to the transition arc 2; Step 10: Based on the turning direction, the azimuth angle of the straight transition segment, the coordinates of the starting point of the straight transition segment, the coordinates of the ending point of the straight transition segment, the coordinates of the turning center corresponding to transition arc 1, the coordinates of the turning center corresponding to transition arc 2, and the coordinates of the turning end point corresponding to transition arc 2, combined with the first waypoint, the second waypoint, and the third waypoint in the flight plan, the complete trajectory of the over-point turn is finally calculated.
2. The method for calculating a turning trajectory at a point according to claim 1, characterized in that: Step 4 involves calculating the central angle corresponding to the transition arc 1 based on the azimuth angle of the straight transition segment, denoted as . Specifically, it includes the following steps: 。 3. The method for calculating a turning trajectory at a point according to claim 2, characterized in that: The coordinates of the starting point of the straight transition segment in step 5 are as follows: The specific calculation process includes: Transition arc 1 Tangent and line at a point The included angle equal Follow these steps to calculate from Click Azimuth of a line from a point ; when hour, when hour, when hour, ; Click The distance between the points is ,in For the aircraft The turning radius at the point; Where V1 is the aircraft speed in the first segment, and g is the acceleration due to gravity. This is the maximum roll angle of the aircraft; Known latitude and longitude , latitude and longitude , Let be the Earth's radius, then: 。 4. The method for calculating a turning trajectory at a point according to claim 3, characterized in that: In step 6, the coordinates of the endpoint of the straight transition segment are: The coordinates of the starting point of the straight transition segment The specific calculation process includes: Point to the straight line where the second flight segment is located The distance D2 is ,in For the aircraft The turning radius at the point; Where V2 is the aircraft speed in the second segment, and g is the acceleration due to gravity. This is the maximum roll angle of the aircraft; Assumption Point to line distance ,from Click The distance between the points is ,set up latitude and longitude ,have: 。 5. The method for calculating a turning trajectory at a point according to claim 4, characterized in that: Step 7 calculates the turning center corresponding to the transition arc 1. The specific process of coordinates includes: Let the starting point of the transition arc 1 be... Point to the center of transition arc 1 The azimuth of the point coordinates is The specific calculation process includes: when hour, when hour, when hour, when hour, set up latitude and longitude ,have: in For the aircraft The turning radius at the point; Where V1 is the aircraft speed in the first segment, and g is the acceleration due to gravity. This is the maximum roll angle of the aircraft.
6. The method for calculating a turning trajectory at a point according to claim 5, characterized in that: Step 8 describes calculating the turning center corresponding to transition arc 2. coordinate; Assumption Point to the center of arc 2 The heading angle of the point coordinates Then we have: Point to the center of arc 2 The distance between the point coordinates is ,set up latitude and longitude ,have: 。 7. The method for calculating a turning trajectory at a point according to claim 6, characterized in that: In step 9, the turning end point corresponding to transition arc 2. The specific calculation process for coordinates includes: Let from Click The distance between the points is Calculated according to the following formula: from Click The azimuth of the point is ,set up latitude and longitude ,have: 。