A method for measuring the attitude angle of a freely dropped object in a wind tunnel test using a binocular system

Abstract

This invention discloses a method for measuring the attitude angle of a freely placed object in a wind tunnel experiment using a binocular system, belonging to the field of aerodynamic testing based on photogrammetry. The method includes: setting up a binocular system inside the wind tunnel and calibrating its internal and external parameters using a crosshair; reconstructing the surface markers of a calibration plate outside the wind tunnel using photogrammetry and establishing a local coordinate system; placing the calibration plate inside the wind tunnel so that each vector of the local coordinate system is parallel or perpendicular to the incoming flow vector, and calibrating the wind tunnel coordinate system using the resection method; photogrammetric measurement and initial pose installation of the surface markers of the placed object; acquiring images of the placed object in various states and reconstructing the three-dimensional coordinates of the surface markers; using a reference state where all attitude angles of the placed object are 0°, comparing the rigid body transformation relationship between the point cloud of the blowing state and the reference state point cloud to obtain the attitude angle data. This invention can achieve alignment between the wind tunnel coordinate system and the binocular system coordinate system, is not limited by the shape of the placed object, and provides non-contact, high-precision calculation of the placed object's attitude angle data.

Description

Technical Field

[0001] This invention relates to a method for measuring the attitude angle of a freely placed object in a wind tunnel test using a binocular system, belonging to the field of aerodynamic testing. Background Technology

[0002] In wind tunnel testing, the attitude measurement of objects is a key basis for aircraft design, and visual measurement methods, as non-contact, high-precision, and high-efficiency measurement means, have been gradually applied to wind tunnel testing.

[0003] Wind tunnel attitude measurement tests for objects launched face various challenges, such as: these tests are often conducted in large-scale wind tunnels, resulting in a large field of view for the camera; the mainstream Zhang Zhengyou calibration method requires a high-precision large-format checkerboard grid for this purpose, but the difficulty in manufacturing and maintaining such a grid leads to low calibration accuracy; attitude measurement tests must be conducted in the wind tunnel coordinate system, which theoretically requires that all axial vectors of the wind tunnel coordinate system be absolutely parallel or perpendicular to the incoming flow vector; however, the visual measurement camera coordinate system is a virtual coordinate system, highlighting the difficulty in aligning the camera measurement coordinate system with the wind tunnel coordinate system; furthermore, current research on visual attitude measurement in wind tunnels mainly focuses on angle-of-attack attitude measurement in stepped or continuously variable angle-of-attack tests, resulting in relatively small attitude changes. Measuring the complex motion attitude of free-flying objects launched from aircraft is particularly challenging, especially eliminating the coupling effects between different angles when the object's attitude undergoes large-angle changes. Summary of the Invention

[0004] To address the aforementioned problems, this invention proposes a method for measuring the attitude angle of freely placed objects in wind tunnel tests using a binocular system. This invention can complete high-precision camera calibration and wind tunnel coordinate system calibration without the need to manufacture high-precision, large-format targets; it is not limited by the shape of the placed object and can achieve attitude calculation including pitch angle, sideslip angle, and roll angle.

[0005] To achieve the above objectives, the present invention adopts the following technical solution:

[0006] This invention discloses a method for measuring the attitude angle of a freely placed object in a wind tunnel test using a binocular system, comprising the following steps:

[0007] S1: A binocular system is installed in the wind tunnel, and the internal and external parameters of the binocular system are calibrated using a crosshair; the binocular system includes two industrial cameras.

[0008] S2: Photogrammetry is used to reconstruct the surface markers of the calibration plate outside the wind tunnel and establish a local coordinate system. To obtain the coordinates in the local coordinate system ;

[0009] S3: Place a calibration plate inside the wind tunnel. The vectors in the local coordinate system should be parallel or perpendicular to the incoming flow vector. Use the resection method to calibrate the wind tunnel coordinate system. ;

[0010] S4: Photogrammetry of the surface markers of the object to obtain the three-dimensional coordinates of all points on the surface of the object. And perform initial pose installation;

[0011] S5: Acquire images of the deployed object at various states and reconstruct the three-dimensional coordinates of surface marker points. ;

[0012] S6: Using the condition where the attitude angle of the deployed object is 0° as the baseline, compare the point cloud under the blowing wind condition. and baseline state point cloud The rigid body transformation relationship is used to obtain attitude angle data.

[0013] Preferably, step S1 specifically includes:

[0014] The intrinsic and extrinsic parameters of the binocular camera are calibrated using a crosshair scale. Ten intrinsic parameters are included: focal length, two principal point offset parameters, three radial distortion parameters, two eccentric distortion parameters, and two image plane distortion parameters. Extrinsic parameters include the rotation and translation matrices of each industrial camera relative to the world coordinate system.

[0015] Preferably, step S2 specifically includes:

[0016] S21: A calibration plate is formed by spraying circular feature marks onto its surface; the adjacent boundaries of the calibration plate are perpendicular to each other, and its shape is a cuboid.

[0017] S22: Industrial close-range photogrammetry is used to reconstruct the global point coordinates of circular feature points on the calibration plate surface in three dimensions. .

[0018] S23: Global point coordinates Establish a local coordinate system such that all vectors in the local coordinate system are perpendicular or parallel to the boundary of the calibration plate, and obtain the three-dimensional coordinates of the global point in the local coordinate system. .

[0019] Preferably, step S22 specifically includes:

[0020] Before the experiment, images of the calibration plate were taken from various angles outside the wind tunnel using a DSLR camera. Using industrial close-range photogrammetry, 3D reconstruction of the circular feature points on the calibration plate surface was performed to obtain the global point coordinates of each marker point on the calibration plate surface in the photogrammetric coordinate system. .

[0021] Preferably, step S3 specifically includes:

[0022] In wind tunnel testing, the attitude angle of the object is calculated in the wind tunnel coordinate system. The establishment of the wind tunnel coordinate system only cares about the direction vector and not the position of the origin. After the camera is calibrated, the measurement coordinate system of the binocular system is under a certain reference camera coordinate system. Therefore, the measurement coordinate system of the binocular system should be aligned with the wind tunnel coordinate system.

[0023] Inside the wind tunnel, a calibration plate is placed. The vectors in the local coordinate system are parallel or perpendicular to the incoming flow vector. The coordinates of three-dimensional points on the surface of the calibration plate are determined using this local coordinate system. and corresponding points in the left and right images , Construct least-squares equations and use the resection method to calibrate the wind tunnel coordinate system for the binocular system. .

[0024] Preferably, step S5 specifically includes:

[0025] S51: Calculate the three-dimensional coordinates of each state marker point on the surface of the object using the least squares method. :

[0026]

[0027] In the formula:

[0028]

[0029]

[0030] in, The coordinates of the three-dimensional point to be reconstructed; , These are the pixel coordinates on the left and right images after distortion correction; , These are the elements of the extrinsic parameter matrices of the left and right cameras in the stereo system, respectively. This is the transformation matrix that projects points from the wind tunnel coordinate system to the camera coordinate system, where i and j are the subscripts of the matrix elements. .

[0031] S52: Three-dimensional coordinates of all points on the surface of the project in the world coordinate system Three-dimensional coordinates of points on the surface of the object under various states in the wind tunnel coordinate system Alignment yields the three-dimensional coordinates of all points on the surface of the object under each state. .

[0032] Preferably, step S6 specifically includes:

[0033] S61: Using the condition that all the attitude angles of the deployed objects are 0° as the baseline state, calculate the point cloud reflecting the baseline state. Point clouds in the state of blowing wind Rotation matrix for attitude changes and translation matrix

[0034] S62: by rotation matrix Calculate the angle of attack attitude of the launched object , in This represents the X-axis vector of the model's body coordinate system when the model is in its baseline state. Indicates the first State body coordinate axis vector On the airflow coordinate axis Projection vector of the plane:

[0035]

[0036] S63: by rotation matrix Calculate the sideslip angle attitude of the deployed object , in This represents the Y-axis vector of the model's body coordinate system when the model is in its baseline state. Indicates the first State body coordinate axis vector On the airflow coordinate axis Projection vector of the plane:

[0037]

[0038] S64: by rotation matrix Calculate the roll angle and attitude of the deployed object :

[0039]

[0040] in, , They represent the first State rotation matrix Quantity.

[0041] This invention addresses the problem of significantly reduced attitude angle measurement accuracy due to camera vibration in actual wind tunnel environments. It proposes an improvement by using a baseline state where all object attitude angles are 0°, and obtaining attitude angle data by comparing the rigid body transformation relationships between the point cloud of the wind-blown state and the baseline state point cloud. Experimental verification shows that, in a laboratory environment, using the readings of a high-precision dual-axis turntable as the standard value, the average error of calculating the angle of attack, sideslip angle, and roll angle of the composite motion using the algorithm of this invention is within 0.01°, demonstrating high measurement accuracy. In actual wind tunnel dynamic vibration environments, compared to direct attitude angle calculation, the method of this invention significantly improves the accuracy of attitude angle calculation, achieving an accuracy better than 0.1°. This effectively meets the measurement requirements for the attitude angles of aircraft and their objects in wind tunnel tests, and is particularly suitable for attitude angle measurement in wind tunnel tests under vibration environments. Attached Figure Description

[0042] Figure 1 This is a flowchart of the present invention;

[0043] Figure 2 This is a diagram of the test scenario for this invention;

[0044] Figure 3 This is a schematic diagram of photogrammetry of the marking points on the calibration plate surface of the present invention;

[0045] Figure 4 This is a schematic diagram of a local coordinate system on the surface of the calibration plate of the present invention;

[0046] Figure 5 This is a schematic diagram of the wind tunnel coordinate system calibration of the present invention;

[0047] Figure 6 This invention relates to a crosshair scale used for camera calibration;

[0048] Figure 7 This is a real-time status diagram disclosed in an embodiment of the present invention;

[0049] The labels in the attached diagram are as follows: a1, incoming flow; a2, projected object; a3, two cameras of the binocular system; c1, coded marker point; c2, non-coded marker point; c3, local coordinate system of the calibration board; d1, calibration board; d2, local coordinate system; d3, wind tunnel coordinate system; d4, two cameras of the binocular system. Detailed Implementation

[0050] The embodiments of the present invention will be described in detail below. It should be emphasized that the following description is merely exemplary and not intended to limit the scope and application of the present invention.

[0051] It should be noted that when a component is referred to as "fixed to" or "set on" another component, it can be directly on or indirectly on that other component. When a component is referred to as "connected to" another component, it can be directly connected to or indirectly connected to that other component. Furthermore, a connection can be used for both fixing and circuit / signal connectivity.

[0052] It should be understood that the terms "length", "width", "up", "down", "front", "back", "left", "right", "vertical", "horizontal", "top", "bottom", "inner", and "outer" indicate the orientation or positional relationship based on the orientation or positional relationship shown in the accompanying drawings. They are only for the convenience of describing the embodiments of the present invention and simplifying the description, and do not indicate or imply that the device or element referred to must have a specific orientation, or be constructed and operated in a specific orientation. Therefore, they should not be construed as limitations on the present invention.

[0053] Furthermore, the terms "first" and "second" are used for descriptive purposes only and should not be construed as indicating or implying relative importance or implicitly specifying the number of technical features indicated. Thus, a feature defined as "first" or "second" may explicitly or implicitly include one or more of that feature. In the description of embodiments of the present invention, "a plurality of" means two or more, unless otherwise explicitly specified.

[0054] like Figure 1 As shown, one embodiment of the present invention discloses a method for measuring the attitude angle of a freely placed object in a wind tunnel test using a binocular system, comprising the following six parts: S1: A binocular system is arranged inside the wind tunnel, and the internal and external parameters of the binocular system are calibrated using a crosshair; S2: Outside the wind tunnel, photogrammetry is used to reconstruct the marked points on the calibration plate surface and establish a local coordinate system. To obtain the three-dimensional coordinates of the global point in the local coordinate system. S3: Place a calibration plate inside the wind tunnel. The vectors in the local coordinate system are parallel or perpendicular to the incoming flow vector. Use the resection method to calibrate the wind tunnel coordinate system. S4: Photogrammetry of the surface markers of the object to obtain the three-dimensional coordinates of all points on the surface of the object. S5: Acquire images of the deployed object in various states and reconstruct the three-dimensional coordinates of the surface marker points. S6: Using the condition where the attitude angle of the deployed object is 0° as the baseline, compare the point cloud under the blowing wind condition. and baseline state point cloud The rigid body transformation relationship is used to obtain attitude angle data.

[0055] The specific implementation process is as follows:

[0056] Step 1: Deploy the binocular system in the wind tunnel and calibrate its internal and external parameters:

[0057] like Figure 2 As shown, before the experiment, based on the wind tunnel test measurement requirements and the on-site installation conditions, appropriate camera models and lenses were selected, and their installation positions were rationally arranged so that the optical axis angle between the two cameras a3 of the binocular system was approximately 30°, and the common field of view should encompass the model's motion space. Specifically, because the object a2, under the influence of the incoming flow a1, moves at extremely high speeds in the wind tunnel experiment, with its fall time typically ranging from several hundred milliseconds, two cameras a3 of a high frame rate and high resolution binocular system should be selected.

[0058] In addition, if the wind tunnel test section has an optical window, the binocular system should be placed outside the optical window first.

[0059] After the two cameras a3 of the binocular system are installed, adjust the camera aperture and focus, and set an appropriate exposure time to ensure a clear image. Place the crosshairs at at least eight different locations within the wind tunnel and acquire calibration images. The placement locations should include the movement space of the object a2.

[0060] Based on the three-dimensional coordinates of the known marked points on the crosshair in the world coordinate system and the marker pixels obtained from left and right image detection in a binocular system The intrinsic and extrinsic parameters of the two cameras a3 in the binocular system were calibrated using the least squares method. The crosshair used for camera calibration is as follows: Figure 6 As shown, the scale is entirely black with coded dots sprayed on top.

[0061] Step 2: Three-dimensional point photogrammetry and establishment of local coordinate system on the calibration plate surface

[0062] like Figure 4 The diagram shows a schematic of the local coordinate system on the calibration plate surface. Several marker points are affixed to the calibration plate surface, including but not limited to coded marker point c1 or non-coded marker point c2. The distribution of these marker points should be as uniform and regular as possible, and each row or column of marker points should be parallel or perpendicular to the calibration plate boundary. Adjacent boundaries of the calibration plate should be perpendicular to each other and have a cuboid shape, so that subsequent constraints such as the shape of the calibration plate and the wind tunnel wall can ensure that the vectors of the local coordinate system c3 of the calibration plate are perpendicular or parallel to the vectors of the wind tunnel coordinate system.

[0063] Before the experiment, images of the calibration plate were taken from various angles outside the wind tunnel using a DSLR camera, such as... Figure 3 As shown. Using industrial close-range photogrammetry, the marking points c1 and c2 on the calibration plate surface are reconstructed in three dimensions, obtaining the global three-dimensional coordinates of each marking point p on the calibration plate surface in the photogrammetric coordinate system. .

[0064] The global three-dimensional coordinates of each marked point on the calibration plate surface were obtained through photogrammetry. Located in a photogrammetric coordinate system, which is typically situated in the camera coordinate system used to capture the first frame of the image, rather than on the calibration plate itself. Therefore, based on the constraint that the markers in each row or column on the calibration plate surface are parallel or perpendicular to the calibration plate boundary, a local coordinate system needs to be established for the global points on the calibration plate surface. This local coordinate system ensures that each vector is perpendicular or parallel to the calibration plate boundary, resulting in the local coordinate system c3 of the calibration plate shown in Figure 4.

[0065] Step 3: Wind tunnel coordinate system calibration

[0066] The global point in the local coordinate system d2 of the calibration plate d1 is obtained as described in step 2. Under the given coordinate conditions, by considering the geometric constraints between the calibration plate d1 and the wind tunnel, the calibration plate d1 is positioned so that each vector in its local coordinate system d2 is parallel or perpendicular to the incoming flow vector (e.g., ...). Figure 5 (As shown). If the calibration plate is rectangular, by attaching the calibration plate tightly to the side wall and bottom wall of the wind tunnel, the vectors in the local coordinate system of the calibration plate can be made parallel or perpendicular to the incoming flow vector.

[0067] Based on the three-dimensional point coordinates in the local coordinate system of the calibration plate surface And the corresponding points of images captured by the two cameras (d4) of the binocular system , By constructing the least squares equations, the wind tunnel coordinate system d3 can be calibrated using the resection method for the binocular system.

[0068] To calculate the attitude of a deployed object using visual measurement methods, at least three pairs of non-collinear corresponding points must be constructed from the reconstructed point cloud in each state and the point cloud reconstructed from the initial state frame. Due to the limited measurement range of binocular vision, only the three-dimensional coordinates of some marked points on the surface of the deployed object can be reconstructed during the reconstruction of each state frame. When the attitude of the deployed object changes significantly, there is often no overlap between the point cloud and the reference point cloud, making it impossible to calculate the attitude angle.

[0069] To ensure that the point cloud overlaps with the reference state for attitude angle calculation in real time, before the experiment, as described in step 2, industrial close-range photogrammetry technology was used to reconstruct the three-dimensional coordinates of all marked points on the surface of the object in the photogrammetric coordinate system. .

[0070] Step 5: Reconstruction of surface point clouds of the deployed object in various states

[0071] Images of each experimental state are acquired using a binocular system. Synchronous hard triggering must be used during the binocular camera acquisition process to ensure the synchronization of the binocular system.

[0072] First, a binocular system is used to reconstruct the three-dimensional coordinates of each state marker point on the surface of the object within the overlapping area. :

[0073]

[0074] In the formula:

[0075]

[0076]

[0077] in, The coordinates of the three-dimensional point to be reconstructed; , These are the pixel coordinates on the left and right images after distortion correction; , These are the elements of the extrinsic parameter matrices of the left and right cameras in the stereo system, respectively. This is the transformation matrix that projects points from the wind tunnel coordinate system to the camera coordinate system, where i and j are the subscripts of the matrix elements. .

[0078] However, as mentioned earlier, binocular systems have limited overlapping fields of view, and can only reconstruct the coordinates of some 3D points on the surface of the projected object. To obtain the coordinates of all 3D points on the surface of the projected object under various states, the coordinates of all points on the surface of the projected object in a photogrammetric coordinate system are used. Three-dimensional coordinates of points on the surface of the object under various states in the wind tunnel coordinate system Alignment yields the three-dimensional coordinates of all points on the surface of the object under each state. .

[0079] Step 6: Numerical calculation of attitude angles

[0080] Figure 7 This diagram illustrates the real-time state of the dropped object during its descent. During the experiment, the baseline state was set when all the object's attitude angles were 0°, and a point cloud reflecting this baseline state was calculated. Point clouds in the state of blowing wind Rotation matrix for attitude changes and translation matrix .

[0081] By rotation matrix Calculate the angle of attack attitude of the launched object , in This represents the X-axis vector of the model's body coordinate system when the model is in its baseline state. Indicates the first State body coordinate axis vector On the airflow coordinate axis Projection vector of the plane:

[0082]

[0083] By rotation matrix Calculate the sideslip angle attitude of the deployed object ,in This represents the Y-axis vector of the model's body coordinate system when the model is in its baseline state. Indicates the first State body coordinate axis vector On the airflow coordinate axis Projection vector of the plane:

[0084]

[0085] By rotation matrix Calculate the roll angle and attitude of the deployed object :

[0086]

[0087] in, , They represent the first State rotation matrix Quantity.

Claims

1. A method for measuring the attitude angle of a freely dropped object in a wind tunnel test using a binocular system, characterized in that... Includes the following steps: S1: A binocular system is installed in the wind tunnel, and its internal and external parameters are calibrated using a crosshair. The binocular system includes two industrial cameras. S2: Using photogrammetry, the marked points on the calibration plate surface are reconstructed outside the wind tunnel, and a local coordinate system is established. This allows us to obtain the coordinates of three-dimensional points on the calibration plate surface in the local coordinate system. ; S3: Place a calibration plate inside the wind tunnel, ensuring that the vectors in the local coordinate system of the calibration plate are parallel or perpendicular to the incoming flow vector; then, use the resection method to realize the wind tunnel coordinate system. Calibration; S4: Photogrammetry is performed on the marked points on the surface of the object to obtain the three-dimensional coordinates of all points on the surface of the object. And install the initial pose of the object to be placed; S5: Acquire images and reconstruct the 3D coordinates of the surface markers of the object under various states. ; S6: Using the condition where the attitude angle of the deployed object is 0° as the baseline, compare the point cloud under the blowing wind condition. and baseline state point cloud The rigid body transformation relationship is used to obtain attitude angle data.

2. The method for measuring the attitude angle of a freely placed object in a wind tunnel test using a binocular system according to claim 1, characterized in that, Step S1 specifically includes: The binocular camera's intrinsic and extrinsic parameters are calibrated using a crosshair scale. The intrinsic parameters include ten parameters: focal length, two principal point deviation parameters, three radial distortion parameters, two eccentric distortion parameters, and two image plane distortion parameters. The extrinsic parameters include the rotation and translation matrices of each industrial camera relative to the world coordinate system.

3. The method for measuring the attitude angle of a freely placed object in a wind tunnel test using a binocular system according to claim 1, characterized in that, Step S2 specifically includes: S21: A calibration plate with circular markings sprayed onto its surface; the adjacent boundaries of the calibration plate are perpendicular to each other, and the shape is a cuboid. S22: The global point coordinates are obtained by 3D reconstruction of the circular marker points on the calibration plate surface using industrial close-range photogrammetry technology. ; S23: Global point coordinates Establish a local coordinate system such that each vector in the local coordinate system is perpendicular or parallel to the boundary of the calibration plate, and obtain the three-dimensional coordinates of the calibration plate surface in the local coordinate system. .

4. The method for measuring the attitude angle of a freely placed object in a wind tunnel test using a binocular system according to claim 3, characterized in that, Step S22 specifically includes: Before the experiment, images of the calibration plate were taken from various angles outside the wind tunnel using a camera. Using industrial close-range photogrammetry, the circular markers on the calibration plate surface were reconstructed in 3D to obtain the global point coordinates of each marker on the calibration plate surface in the photogrammetric coordinate system. .

5. The method for measuring the attitude angle of a freely dropped object in a wind tunnel test using a binocular system according to claim 1, characterized in that, Step S3 specifically includes: A calibration plate placed inside the wind tunnel has its local coordinate system vectors parallel or perpendicular to the incoming flow vector; the three-dimensional point coordinates on the surface of the calibration plate under the local coordinate system are used. and the pixel coordinates of the same object point in the left and right camera images after distortion correction , The least squares equations were established to recalibrate the wind tunnel coordinate system, and the resection method was used to calibrate the wind tunnel coordinate system for the binocular system. .

6. The method for measuring the attitude angle of a freely placed object in a wind tunnel test using a binocular system according to claim 1, characterized in that, Step S4 specifically includes: First, mark points are reasonably arranged on the surface of the object to ensure that the number and distribution cover the entire surface of the object. Then, the mark points are photographed from multiple angles and shooting distances to obtain multiple sets of image data containing the mark point information. Since the object is three-dimensional, it is not a problem that some angles cannot capture all the mark points. Mark points with the same name will be found from multiple sets of photos later.

7. The method for measuring the attitude angle of a freely placed object in a wind tunnel test using a binocular system according to claim 1, characterized in that, Step S5 specifically includes: S51: Calculate the three-dimensional coordinates of each state marker point on the surface of the object using the least squares method. : In the formula: in, The coordinates of the three-dimensional point to be reconstructed; , These are the pixel coordinates of the same object point in the left and right camera images after distortion correction. , These are the elements of the extrinsic parameter matrices of the left and right cameras in the stereo system, respectively. This is the transformation matrix that projects points from the wind tunnel coordinate system to the camera coordinate system, where i and j are the subscripts of the matrix elements. , ; S52: Reconstruct the three-dimensional coordinates of the surface markers of the deployed object in the wind tunnel coordinate system. The SVD decomposition algorithm is used to align the point cloud. The three-dimensional coordinates of all surface markers of the deployed object in the wind tunnel coordinate system are obtained in the initial test frame.

8. The method for measuring the attitude angle of a freely placed object in a wind tunnel test using a binocular system according to claim 7, characterized in that, Step S52 specifically includes: Three-dimensional coordinates of all points on the surface of the project in the world coordinate system Three-dimensional coordinates of points on the surface of the object under various states in the wind tunnel coordinate system Alignment yields the three-dimensional coordinates of the surface markers of the deployed object under each state. .

9. The method for measuring the attitude angle of a freely placed object in a wind tunnel test using a binocular system according to claim 1, characterized in that, Step S6 specifically includes: S61: Using the condition that all the attitude angles of the deployed objects are 0° as the baseline state, calculate the point cloud reflecting the baseline state. Point clouds in the state of blowing wind Rotation matrix for attitude changes and translation matrix ; S62: by rotation matrix Calculate the angle of attack attitude of the launched object , in This represents the X-axis vector of the model's body coordinate system when the model is in its baseline state. Indicates the first State body coordinate axis vector On the airflow coordinate axis Projection vector of the plane: S63: by rotation matrix Calculate the sideslip angle attitude of the deployed object ,in This represents the Y-axis vector of the model's body coordinate system when the model is in its baseline state. Indicates the first State body coordinate axis vector On the airflow coordinate axis Projection vector of the plane: S64: by rotation matrix Calculate the roll angle and attitude of the deployed object : in, , They represent the first State rotation matrix Quantity.

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