A method for calculating atmospheric drag of a LEO spacecraft based on attitude rotation mode

Abstract

The application discloses a method for calculating atmospheric resistance of LEO spacecraft based on posture rotation mode, and relates to the field of wind tunnel test, and comprises the following steps: S1, selecting a corresponding posture rotation mode of the spacecraft according to a scene; S2, calculating the windward area and atmospheric resistance of the posture rotation mode of the spacecraft selected in S1 in a period; and S3, based on the calculation result of S2, calculating the period average atmospheric resistance of the spacecraft in the corresponding posture rotation mode; the method for calculating atmospheric resistance of LEO spacecraft based on posture rotation mode is a fast and efficient algorithm for atmospheric resistance under the operation condition of dynamic change of the in-orbit spacecraft posture, the period average atmospheric resistance is obtained by precisely calculating the atmospheric resistance in the rotation period, and thus an important basic prerequisite is provided for the medium and long term analysis and prediction of the orbit parameters of the LEO spacecraft.

Description

Technical Field

[0001] This invention relates to the technical field of applying aerodynamics, computer-aided design, and analytical geometry of numerical model meshes to wind tunnel testing. More specifically, this invention relates to a method for calculating atmospheric drag of LEO spacecraft based on attitude rotation modes. Background Technology

[0002] Spacecraft operating in Low Earth Orbit (LEO) typically orbit at altitudes less than 2000 km above the Earth's surface. After completing their mission or losing power, these spacecraft gradually decrease in altitude and eventually re-enter Earth's dense atmosphere. Tracking, monitoring, and analyzing their operational parameters is a routine and ongoing process. While the effect of the thin atmosphere on spacecraft within the LEO altitude range is weak, its impact is substantial. The primary reason for the altitude decay of freely flying LEO spacecraft is the continuous dissipation of drag from the thin atmosphere.

[0003] Based on several examples of spacecraft orbital decay in engineering practice, freely flying LEO spacecraft are often in various attitude changes, with tumbling being the norm and not tumbling being rare. There are three main reasons for tumbling: first, interference from various uncertainties in the flight environment, including lunar and solar perturbations, Earth's non-spherical perturbations, gravitational gradient moments, solar radiation particles, electromagnetic interactions, atmospheric density drift, etc.; second, the synchronous rotation of the inertial aerodynamic attitude of spacecraft orbiting the Earth with the same period, resulting in backward tumbling; and third, active spin initiation by the design scheme. Orbital decay analysis and prediction require understanding the magnitude of drag, which is closely related to the spacecraft's attitude.

[0004] In orbital dynamics, the fundamental parameter of atmospheric influence is the aerodynamic drag experienced by the spacecraft. Above 120 km, aerodynamics considers the spacecraft to be in a state of free molecular flow. Therefore, determining the atmospheric drag of free molecular flow for LEO spacecraft is a crucial technical issue. For ultra-low Earth orbit (LEO) spacecraft with altitudes ranging from 200 km to 500 km, without energy replenishment, they will generally re-enter the dense atmosphere and re-enter the reef within a limited time due to orbital decay. For spacecraft such as the space station operating at an altitude of around 400 km, the time from orbital decay to re-entry is generally within a few years.

[0005] In academia, various methods for calculating atmospheric drag on spacecraft are collectively referred to as atmospheric drag models, which are one of the main factors affecting the accuracy of orbit determination and prediction. For LEO spacecraft, the accuracy of atmospheric drag models primarily depends on the accuracy of atmospheric density, drag coefficient, and effective frontal area. Existing atmospheric density models are relatively accurate and widely used, such as the CIRA series, DTM series, Jacchia series, and MSIS series. Furthermore, since the assumption of free molecular flow in the orbital environment holds, the drag coefficient of the spacecraft in orbit can be considered constant. Therefore, analyzing the attitude rotation patterns of LEO spacecraft to evaluate the effective frontal area becomes a key factor in determining the accuracy of atmospheric drag models.

[0006] Currently, the windward area is obtained in two ways when modeling atmospheric drag: one approach assumes it to be a constant value; the other estimates it as a parameter along with orbital parameters. For spacecraft with complex shapes and diverse attitude and orbital motion patterns, the former method is too inaccurate, while the latter is difficult to solve. Spacecraft often have complex shapes and large attitude variations, making it difficult to accurately calculate their effective windward area during operation, which affects the accuracy of atmospheric drag modeling. Summary of the Invention

[0007] One object of the present invention is to solve at least the above-mentioned problems and / or defects, and to provide at least the advantages described below.

[0008] To achieve these objectives and other advantages of the present invention, a method for calculating atmospheric drag of a LEO spacecraft based on attitude rotation modes is provided, comprising:

[0009] S1. Select the corresponding attitude rotation mode of the spacecraft according to the scenario;

[0010] S2. Calculate the windward area and atmospheric drag of the spacecraft attitude rotation mode selected in S1 during the period;

[0011] S3. Based on the calculation results of S2, the periodic average atmospheric drag under the corresponding attitude rotation mode of the spacecraft is calculated.

[0012] In S1, the types of attitude rotation modes include: longitudinal roll mode (TARM), limited lateral coupling longitudinal roll mode (LARM), and free rotation mode (FRRM).

[0013] In the corresponding scenario, the selection of the attitude rotation mode is based on the actual engineering situation, which includes the flight scheme design based on the actual engineering situation and the calculation of internal and external test results.

[0014] Preferably, in TARM mode, the frontal area and atmospheric drag are continuously calculated at preset intervals within the angle of attack range of -180° to 180°.

[0015] In LARM mode, within the angle of attack range of -180° to 180°, between 0° and β... T Within the sideslip angle range, the windward area and atmospheric drag are continuously calculated at preset intervals.

[0016] In FRRM mode, the frontal area and atmospheric drag are continuously calculated at preset intervals within the angle of attack range of -180° to 180° and the sideslip angle range of 0° to 180°.

[0017] Preferably, the windward area S W The calculation formula is:

[0018]

[0019] In the above formula, N XY This represents the count of all non-zero cells within the projected grid within the coordinate range of the projected section. The area of ​​each cell.

[0020] Preferably, the atmospheric drag F k The calculation formula is:

[0021]

[0022] Where ρ is the atmospheric density at the spacecraft's flight environment, calculated or obtained from different atmospheric models, V is the incoming flow velocity, i.e., the spacecraft's flight velocity, and C... D0 S is the drag coefficient of free molecular flow per unit sphere. W This refers to the windward area of ​​the spacecraft.

[0023] Preferably, in S3, the periodic average atmospheric drag F in TARM mode is... D The calculation formula is as follows:

[0024]

[0025] Where, N A F is the number of angle-of-attack states used to calculate atmospheric drag during the longitudinal roll period. D,i F represents the atmospheric drag at angle of attack i. D,i Through atmospheric drag F k The formula is used to calculate it.

[0026] Preferably, in S3, the periodic average atmospheric drag F in LARM mode and FRM mode is...D The calculation formula is as follows:

[0027]

[0028] Where, N A N represents the number of angle-of-attack states used to calculate atmospheric drag during the longitudinal roll cycle. T F is the number of sideslip angle states used to calculate atmospheric drag during the lateral roll cycle. D,ij F represents the atmospheric drag under the combined angle of attack (i) and sideslip angle (j). D,ij Through atmospheric drag F k The formula is used to calculate it.

[0029] The present invention has at least the following beneficial effects:

[0030] Firstly, it pioneered the summarization of three rotation modes for LEO spacecraft attitude changes, which can basically cover the normal state of spacecraft free flight in orbit.

[0031] Secondly, by utilizing the digital model of spacecraft configuration in modern aerospace engineering, a fully digital method can be used to quickly, efficiently, and accurately obtain the windward area and atmospheric drag parameters of the spacecraft during flight.

[0032] Third, the periodic average atmospheric drag is obtained by calculating the atmospheric drag during the rotation period, thus providing an important basic premise for the medium- and long-term analysis and prediction of the LEO spacecraft's orbital parameters.

[0033] Other advantages, objectives and features of the present invention will become apparent in part from the following description, and in part from those skilled in the art through study and practice of the invention. Attached Figure Description

[0034] Figure 1 The flowchart shows the atmospheric drag algorithm for LEO spacecraft based on attitude rotation mode.

[0035] Figure 2 This is a schematic diagram of the shape and reference coordinate system of an example spacecraft;

[0036] Figure 3 This is a schematic diagram of the surface mesh of an example spacecraft digital model;

[0037] Figure 4 The frontal area of ​​the longitudinal roll mode TARM varies with the angle of attack, and the atmospheric drag varies with the angle of attack at altitudes of 400 km, 300 km, 200 km, 150 km, 120 km and 100 km.

[0038] Figure 5 The distribution of the frontal area of ​​LARM30 in the limited lateral oscillation 30° coupled longitudinal roll mode as the attitude angle changes;

[0039] Figure 6 The distribution of the frontal area of ​​LARM45 in the limited lateral oscillation 45° coupled longitudinal roll mode as the attitude angle changes.

[0040] Figure 7 The distribution of the frontal area of ​​LARM60 in the limited lateral oscillation 60° coupled longitudinal roll mode as the attitude angle changes.

[0041] Figure 8 The distribution of the frontal area of ​​the FRRM in free rotation mode as a function of attitude angle;

[0042] Figure 9 The average frontal area during the TARM cycle calculated for different angle-of-attack intervals;

[0043] Figure 10 This shows the variation of TARM periodic average atmospheric drag with altitude.

[0044] Figure 11 The variation of the periodic average atmospheric drag in the LARM model at an altitude of 400 km with the oscillation range of different lateral attitude angles;

[0045] Figure 12 The variation of the periodic average atmospheric drag in the LARM model at an altitude of 200 km with the oscillation range of different lateral attitude angles;

[0046] Figure 13 The variation of the periodic average atmospheric drag in the LARM model at an altitude of 100 km with the oscillation range of different lateral attitude angles;

[0047] Figure 14 This shows the variation of flight altitude in the periodic mean atmospheric drag of the altitude FRRM model. Detailed Implementation

[0048] The present invention will now be described in further detail with reference to the accompanying drawings, so that those skilled in the art can implement it based on the description.

[0049] Based on the complex phenomena of spacecraft flight attitude changes in engineering practice, this invention summarizes three typical attitude rotation modes. Using the digital model, which is indispensable in modern spacecraft engineering, as a foundation, it employs object surface grid elements and windward section grid projection technology to accurately calculate the windward area and atmospheric drag of the spacecraft under various attitude modes. Based on this, an atmospheric drag algorithm for LEO spacecraft based on attitude rotation modes is constructed.

[0050] The invention provides an algorithm for atmospheric drag of free molecular flow in LEO spacecraft based on precise calculation of frontal area, such as... Figure 1 The flowchart shows the following three steps:

[0051] Step 1: Determine the spacecraft's attitude rotation mode based on the scenario. The three rotation modes are: longitudinal roll mode, limited lateral coupling longitudinal roll mode, and free rotation mode.

[0052] Uncontrolled autonomous spacecraft exhibit significant randomness in their attitude changes while orbiting the Earth. Based on engineering practice, these attitude changes can be categorized into three types: total axial rolling mode (TARM), limited lateral coupling axial rolling mode (LARM), and free rolling mode (FRRM). For ease of description, these three rotation modes are abbreviated as follows: total axial rolling mode (TARM); limited lateral coupling axial rolling mode (LARM); and free rolling mode (FRRM).

[0053] The specific rotation mode is selected based on the actual engineering situation, including flight scheme design and calculation of internal and external test results.

[0054] The Free Rotation Mode (FRRM mode) is the most generalized mode. The Longitudinal Tumble Mode (TARM mode) and the Limited Lateral Coupling Longitudinal Tumble Mode (LARM mode) can be considered as special degenerate or restricted modes of the FRRM mode. Lateral tumble in the TARM mode is not considered, and the lateral tumble angle in the LARM mode is limited to a certain range.

[0055] Regardless of the tumbling mode, it is subject to the limitation of tumbling angular velocity, that is, it is within the range of torque action limit and avoids being destroyed and disintegrated by rotational centrifugal force.

[0056] Step 2: Calculate the frontal area and atmospheric drag during the spacecraft's attitude rotation mode period.

[0057] The method for calculating the windward area of ​​an arbitrary attitude using the spacecraft digital model surface mesh element-windward section projection technique is as follows:

[0058] For generating surface meshes from 3D digital models of spacecraft, the mesh element information includes the center position, area, and unit outward normal vector of the mesh element. The spacecraft digital model is a 3D computer-aided design electronic file of the shape configuration commonly used in spacecraft design, manufacturing, or operation. Mesh generation software is used to generate surface meshes for spacecraft, which include two types: quadrilateral structured meshes and triangular unstructured meshes.

[0059] A reference coordinate system is established, parallel to the longitudinal body axis of the spacecraft and the airflow direction. Coordinate rotation transformations are performed on the spacecraft's surface element information under different attitudes within this reference coordinate system. The origin of the reference coordinate system is located at the center of the spacecraft's attitude rotation (generally defined as the center of gravity), denoted as origin O, with coordinates (0,0,0). The X-axis is the longitudinal body axis of the spacecraft, with its positive direction opposite to the airflow direction, pointing from the center of rotation towards the head or front of the model. The Y-axis is the transverse axis of the spacecraft passing through the origin, with its positive direction pointing from the origin towards the right side of the spacecraft. The Z-axis is determined according to the right-hand rule of the X and Y axes, specifically pointing from the origin towards the bottom of the spacecraft. Once established, the reference coordinate system remains unchanged; all surface element coordinates and other information after attitude changes are described within this reference coordinate system.

[0060] A normalized grid is divided within the projected area of ​​the spacecraft's windward section, and surface elements are projected onto the windward section along the airflow direction. A grid scale L is used within the coordinate range of the projected section region. C The grid is divided into standardized grids, with the grid size typically being 2 to 5 times the side length of the square corresponding to the average area of ​​the face element.

[0061] The windward area of ​​the spacecraft in any attitude is obtained by counting the number of cells with projected surface elements and summing their areas. The projection information is recorded by traversing the cells and spacecraft grid cells within the windward section projection range. The so-called effective windward area cell is the cell with surface element projection. The criterion for surface element projection is that the YZ coordinate components of the surface element fall into the corresponding cell.

[0062] The area of ​​the projected grid on the windward section of the spacecraft is The calculation formula is as follows:

[0063]

[0064] Where c is the scale adjustment coefficient of the projected lattice on the windward section of the spacecraft, N is the total number of spacecraft elements, and ds i Let i be the area of ​​the element with index i.

[0065] The spacecraft's windward cross-section projects a lattice scale L. C The calculation formula is as follows:

[0066]

[0067] Define the normalized coordinates on the horizontal and vertical axes within the coordinate projection range as (I Y I Z ), then a group (I) Y I Z The coordinates correspond to a side of length L. C The square grid, the (I) Y I ZThe calculation formula for ) is as follows:

[0068]

[0069] Where INT() is the smallest integer, and a set of face coordinates (y, z) corresponds to a set of normalized integer coordinates (I). Y I Z ), and a group (I Y I Z () may correspond to multiple sets of (y, z);

[0070] Normalized coordinates (I) Y I Z The range of values ​​for I Y，min I Y，max I Z，min I Z，max Determined by the projection range boundary, its calculation method is as follows:

[0071] I Y，min =INT(Y min )

[0072] I Y，max =INT(Y max )

[0073] I Z，min =INT(Z) min )

[0074] I Z，max =INT(Z) max )

[0075] The number N normalized lattices within the projection range YZ The calculation formula is as follows:

[0076] N YZ =(I Y，max -I Y，min +1)·(I Z，max -OI Z，min +1).

[0077] The method for obtaining the windward area is as follows:

[0078] The projection information of each cell within the projection range is represented by the following data structure:

[0079]

[0080] Among them, I X I Y For lattice normalized coordinates, N jXY This represents the number of projected elements within a given cell.

[0081] IJ (j) and K J (j) represents the element number and unit outward normal vector state of the projection within the lattice, respectively; i XY For grid number;

[0082] Before recording the projection information, traverse all cells and initialize them so that all N cells are initialized. jXY =0, I J (j) and K J (j) is an empty array;

[0083] Iterate through all cells and face elements, and record the number N face elements projected into each cell. jXY Surface element number I J (j) Unit external normal vector state K J (j), then the windward area is S W The calculation formula is:

[0084]

[0085] Where, N XY N is within the projection range jXY The number of all non-zero cells. The area of ​​each cell.

[0086] The process of calculating the windward area and atmospheric drag during different rotation mode cycles based on the above specific attitude is as follows:

[0087] The frontal area and atmospheric drag in TARM mode are calculated within the angle of attack range of -180° to 180°, with uniform calculation intervals. The size of the calculation interval is selected according to the accuracy requirements.

[0088] The frontal area and atmospheric drag of the LARM model are between 0° and β. T The angle of attack is calculated within the range of -180° to 180°, with uniform calculation intervals. The size of the calculation interval is selected according to the accuracy requirements.

[0089] The windward area and atmospheric drag of the FRRM model are calculated within the range of sideslip angle between 0° and 180° and angle of attack between -180° and 180°. The calculation intervals are uniform, and the size of the calculation interval is selected according to the accuracy requirements.

[0090] Let the atmospheric drag of the spacecraft at a certain attitude be F. k The calculation formula is as follows:

[0091]

[0092] Where ρ is the atmospheric density at the spacecraft's flight environment, calculated or obtained from different atmospheric models, V is the incoming flow velocity, i.e., the spacecraft's flight velocity, and C... D0 S is the drag coefficient for free molecular flow per unit sphere, calculated based on molecular collision theory, and is generally taken as around 2.2; W The frontal area of ​​the spacecraft.

[0093] Atmospheric drag F of the aforementioned spacecraft k In the calculation formula, assuming all other parameters are fixed, the spacecraft's frontal area S W The precise calculation of the windward area becomes the decisive factor; the flight attitude and rotation mode of the spacecraft can be determined by observation methods (including internal or external measurements), thus obtaining the prerequisite for accurate calculation of the windward area.

[0094] Step 3: Calculate the periodic average atmospheric drag under the spacecraft's attitude rotation mode.

[0095] In contrast to the long-term operation of spacecraft in orbit, the tumble angular velocity of a spacecraft is assumed to remain constant within a certain number of tumble cycles, meaning that the change in tumble angular velocity is adjusted at least by the number of tumble cycles.

[0096] The longitudinal roll rate and the lateral roll rate of a spacecraft can be different, that is, they can have different roll periods. In the long-term analysis and prediction of orbital parameters, the periodic average atmospheric drag is calculated according to the full combination of attitudes.

[0097] TARM mode periodic mean atmospheric drag F D The calculation formula is as follows:

[0098]

[0099] Where, N A F is the number of angle-of-attack states used to calculate atmospheric drag during the longitudinal roll period. D,i Let F be the atmospheric drag at angle of attack i. D,i Through atmospheric drag F k The formula is used to calculate it.

[0100] LARM and FFRM modes' periodic average atmospheric drag F D The calculation formula is as follows:

[0101]

[0102] Where, N A N represents the number of angle-of-attack states used to calculate atmospheric drag during the longitudinal roll cycle. T F is the number of sideslip angle states used to calculate atmospheric drag during the lateral roll cycle. D,ijF represents the atmospheric drag under the combined angle of attack (i) and sideslip angle (j). D,ij Through atmospheric drag F k The formula is used to calculate it.

[0103] This invention is a fast and efficient algorithm for atmospheric drag under dynamic attitude change conditions of on-orbit spacecraft. The three attitude rotation modes are applicable to common operating states of free flight of spacecraft in engineering practice. The calculation of atmospheric drag is based on the accurate calculation of the windward area of ​​the spacecraft under any attitude. The average atmospheric drag during the rotation period is an important basic premise for the medium and long-term analysis and prediction of spacecraft orbital fading parameters.

[0104] Example:

[0105] This invention presents an atmospheric drag algorithm for LEO spacecraft based on attitude rotation modes. To more clearly illustrate the technical solution of this invention, examples are provided. The examples use a simplified model constructed from a large fuel tank similar to the final stage of a large launch vehicle (hereinafter referred to as LSFT: Last Stage Fuel Tank) as an example. For three different rotation modes during in-orbit flight, the method described in this invention is applied to calculate the variation of atmospheric drag with attitude angle over the period and the periodic average atmospheric drag. The detailed algorithm process and results are as follows.

[0106] Step 1: Determine the spacecraft's attitude rotation mode based on the scenario. The three rotation modes are: longitudinal roll mode, limited lateral coupling longitudinal roll mode, and free rotation mode.

[0107] For the LSFT embodiment, in order to better illustrate the function and operation process of the present invention, it is set that three types of rotation modes will appear during operation, and subsequent steps will calculate the windward area and atmospheric drag for the three modes.

[0108] For the ball-head spin configuration in this example, the range of 0° to 90° for the angle of attack and sideslip angle is equivalent to the original rotation mode having an angle of attack between -180° and 180° and a sideslip angle between 0° and 180°. Therefore, subsequent calculations all consider the angle of attack and sideslip angle to be between 0° and 90°. The specific parameters for the three attitude rotation modes in the embodiment are shown in Table 1. The codes in the table will be used to label the attitude rotation modes of the corresponding results in subsequent charts.

[0109] Table 1

[0110]

[0111]

[0112] Step 2: Calculate the frontal area and atmospheric drag of the spacecraft during the three attitude rotation modes.

[0113] The LSFT model and its reference coordinate system generated by the modeling software are as follows: Figure 2 As shown, the spacecraft configuration is simplified to a cylinder with spherical ends, with a longitudinal (i.e. axial) dimension of 32.5 meters, a diameter of 5 meters, and a total surface area of ​​approximately 510.5 square meters.

[0114] In this embodiment, the origin of the LSFT reference coordinate system is the geometric center, which is also the rotation center for spacecraft attitude changes. Once established, this reference coordinate system remains unchanged, and information such as spacecraft attitude changes and surface element coordinate outward normal vectors is described within this reference coordinate system.

[0115] LSFT spacecraft surface structure mesh generated using meshing software, such as Figure 3 As shown. According to statistics, the number of structured quadrilateral mesh elements in this example is 221,998.

[0116] In the longitudinal roll mode (TARM), the lateral change angle is zero, and it continuously rotates around a horizontal axis perpendicular to the airflow direction during flight. Figure 4 This describes the changes in the frontal area and atmospheric drag of the spacecraft LSFT in TARM mode as the angle of attack ranges from 0° to 90°. This corresponds to a quarter-cycle tumble process, and the changes in the other three quarter-cycles are symmetrical. Therefore, it is not necessary to calculate the results under other conditions in this embodiment. Figure 4 The figure also shows the windward area of ​​the TARM model spacecraft and the changes in atmospheric drag at six typical altitudes (400 km, 300 km, 200 km, 150 km, 120 km and 100 km).

[0117] Figures 5 to 7 Scatter plots of the spacecraft's frontal area under three typical cases of the finite lateral coupling longitudinal roll mode—LARM30, LARM45, and LARM60—are presented. The number "##" following the code "LARM##" indicates the range of lateral attitude oscillations. The lower limit of the frontal area at each angle of attack in the figures corresponds to the calculated result at a sideslip angle of 0°, while the upper limit corresponds to the calculated results at sideslip angles of 30°, 45°, and 60°, respectively.

[0118] Figure 8 This is a scatter plot of the spacecraft's frontal area under Free Rotation Mode (FRRM). The lower limit of the frontal area at each angle of attack corresponds to the calculated result at a sideslip angle of 0°, while the upper limit corresponds to the calculated result at a sideslip angle of 90°.

[0119] The calculation results of spacecraft atmospheric drag during the period under LARM and FRRM conditions are related not only to the aforementioned scatter point parameters, but also to the combined calculations with different flight altitudes and speeds, which will not be specifically given in this embodiment. In practical engineering application analysis, the periodic average results in the next step are of greater concern.

[0120] Step 3: Calculate the periodic average atmospheric drag under the three attitude rotation modes of the spacecraft.

[0121] Atmospheric drag calculations based on attitude rotation modes require consideration of specific attitude angle variations. In specific algorithms, the periodic average calculation results are somewhat correlated with the degree of attitude angle dispersion. Therefore, taking the TARM model as an example, we compared the calculations of the periodic average frontal area under different angle-of-attack intervals with varying granularities. The results are as follows: Figure 9 As shown in the figure, the angle-of-attack intervals (unit: degrees) are 10, 5, 2, 1, 0.5, 0.2, 0.1, and 0.01. From the trend of the average windward area in the figure, it can be seen that when the angle-of-attack interval is less than or equal to 1 degree, the average windward area no longer changes significantly. Therefore, in this embodiment, the attitude angle interval is set to 1 degree during discretization.

[0122] Figure 10 The atmospheric drag variation with altitude was calculated for the LSFT spacecraft in TARM attitude rotation mode with a periodic average windward area of ​​108.3829 square meters. The figure also shows the atmospheric drag variations under the minimum windward area (19.635 square meters) and maximum windward area (157.135 square meters) of the LSFT as a reference for comparison; the TARM periodic average atmospheric drag of the example is 68.97% of the maximum drag and 5.5199 times the minimum drag.

[0123] Figures 11 to 13 The curves showing the variation of periodic average atmospheric drag of the LARM attitude rotation mode at three typical altitudes (400 km, 200 km, and 100 km) with different lateral oscillation ranges are presented. For the spacecraft in the example, the larger the lateral oscillation range, the greater the periodic average atmospheric drag.

[0124] Figure 14The atmospheric drag variation with altitude was calculated for the spacecraft LSFT with a periodic average windward area of ​​136.8384 square meters under FRRM attitude rotation mode. The figure also shows the atmospheric drag variations under the minimum windward area (19.635 square meters) and maximum windward area (157.135 square meters) of the LSFT as a reference for comparison; the FRRM periodic average atmospheric drag of the embodiment is 87.083% of the maximum drag and 6.969 times the minimum drag. The above scheme is only an illustration of a preferred example and is not limited thereto. Appropriate substitutions and / or modifications can be made according to user needs when implementing this invention.

[0125] The number of devices and processing scale described herein are for the purpose of simplifying the description of the invention. Applications, modifications, and variations of the invention will be readily apparent to those skilled in the art.

[0126] Although embodiments of the present invention have been disclosed above, they are not limited to the applications listed in the specification and embodiments. It can be applied to various fields suitable for the present invention. Other modifications can be readily made by those skilled in the art. Therefore, without departing from the general concept defined by the claims and their equivalents, the present invention is not limited to the specific details and examples shown and described herein.

Claims

1. A method for calculating atmospheric drag of a LEO spacecraft based on attitude rotation modes, characterized in that, include: S1. Select the corresponding attitude rotation mode of the spacecraft according to the scenario; S2. Calculate the windward area and atmospheric drag of the spacecraft attitude rotation mode selected in S1 during the period; S3. Based on the calculation results of S2, the periodic average atmospheric drag under the corresponding attitude rotation mode of the spacecraft is calculated. In S1, the types of attitude rotation modes include: longitudinal roll mode (TARM), limited lateral coupling longitudinal roll mode (LARM), and free rotation mode (FRRM). In the corresponding scenario, the selection of the attitude rotation mode is based on the actual engineering situation, which includes: flight scheme design and calculation of internal and external test results; In TARM mode, the frontal area and atmospheric drag are continuously calculated at preset intervals within the angle of attack range of -180º to 180º. In LARM mode, within the angle of attack range of -180º to 180º, and between 0º and... β T Within the sideslip angle range, the windward area and atmospheric drag are continuously calculated at preset intervals; In FRRM mode, the frontal area and atmospheric drag are continuously calculated at preset intervals within the angle of attack range of -180º to 180º and the sideslip angle range of 0º to 180º. The windward area S W The calculation formula is: In the above formula, N XY This represents the count of all non-zero cells within the projected grid within the coordinate range of the projected section. The area of ​​each cell; atmospheric drag F k The calculation formula is: in, ρ This refers to the atmospheric density at the spacecraft's flight environment, calculated or obtained from different atmospheric models. V The incoming flow velocity is also the spacecraft's flight velocity. C D0 The drag coefficient for free molecular flow per unit sphere. S W This refers to the windward area of ​​the spacecraft.

2. The method for calculating atmospheric drag of a LEO spacecraft based on attitude rotation mode as described in claim 1, characterized in that, In S3, the periodic average atmospheric drag in TARM mode F D The calculation formula is as follows: in, N A This represents the number of angle-of-attack states used to calculate atmospheric drag during the longitudinal roll cycle. F D,i For serial number i Atmospheric drag at the angle of attack, F D,i By atmospheric drag F k The formula is used to calculate it.

3. The method for calculating atmospheric drag of a LEO spacecraft based on attitude rotation mode as described in claim 1, characterized in that, In S3, the periodic average atmospheric drag in LARM and FFRM modes F D The calculation formula is as follows: in, N A This represents the number of angle-of-attack states used to calculate atmospheric drag during the longitudinal roll cycle. N T This represents the number of sideslip angle states used to calculate atmospheric drag during the lateral roll cycle. F D,ij For serial number i Angle of attack, serial number j Atmospheric drag under the combined sideslip angle conditions, F D,ij By atmospheric drag F k The formula is used to calculate.

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