Method and device for automatically measuring and calculating buoyancy and buoyancy center axial coordinates of underwater vehicle

Abstract

The invention relates to a method and device for automatically measuring and calculating buoyancy and buoyancy center axial coordinates of an underwater vehicle, and aims at solving the problems that traditional manual measurement is tedious in operation and low in precision. The method comprises the following steps: injecting water into the water tank to overflow the mounting rack; hoisting the empty frame, inputting the weight and center-of-mass coordinates of the aircraft in the air, collecting the measurement values of the weighing sensors at four corners, and calculating the distance from the frame weight and the center-of-mass to the rear sensor; the sensor value is collected for the second time after the aircraft is installed, and the distance value is obtained through the laser range finder; and finally calculating buoyancy and buoyancy center axial coordinates based on a moment balance formula. The sensor automatically collects data, the controller intelligently calculates, full-process automatic measurement and calculation are achieved, and operation is easy, convenient and rapid; manual observation and recording errors are eliminated, and the measurement repeatability is high; by combining a high-precision sensor and a moment balance principle, the result is accurate and reliable, and the method is suitable for multiple scenes of research, development, production and maintenance.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of underwater vehicle testing, in particular to a method and device for automatically measuring buoyancy and axial coordinates of a floating center of an underwater vehicle. BACKGROUND

[0002] The buoyancy and the position of the floating center are core performance parameters of the underwater vehicle, which directly affect the state regulation, motion stability and control characteristics of the underwater vehicle. The relative position relationship between the floating center and the center of mass is a key factor for determining the static pitch attitude and dynamic flight attitude control of the underwater vehicle. For a left-right symmetrical underwater vehicle, the lateral and vertical positions of the floating center have relative fixity, and have limited influence on the overall performance of the underwater vehicle. The axial relative position of the floating center and the center of mass plays a decisive role in the performance of the underwater vehicle, and the axial coordinates of the floating center as a key parameter for representing the vertical distance of the floating center relative to the reference plane (usually the tail plane) are important for the design and performance verification of the underwater vehicle.

[0003] Currently, the measurement method of the axial coordinates of the floating center of the underwater vehicle mainly refers to the national standard GJB2852-97 "Torpedo Weight Test Method". The core process of the method is to place the underwater vehicle to be measured in a water tank, manually load standard weights at both ends of the underwater vehicle, and calculate the buoyancy and the position of the floating center based on the weight and the scale information of the loading position. However, since the whole process relies on manual handling of weights, visual reading of scales and manual recording, the measurement method has significant limitations: first, the operation chain is long, and the data collection needs to be completed by repeatedly adding and removing weights and adjusting the position of the weights, which is time-consuming and tedious, and requires the use of dock and lifting resources; second, the human error is large, and the measurement process relies on manual observation of the scale and recording of the data, which may lead to inconsistency of repeated measurement results due to observation deviation of different operators and human recording errors, thereby affecting the measurement accuracy and reliability.

[0004] In summary, with the development of underwater vehicles towards long-range, low-noise and high-maneuvering, higher requirements are put forward for the measurement accuracy and efficiency of the axial coordinates of the floating center, and the traditional manual weight method cannot meet the development and production requirements, and a new method for automatically measuring the buoyancy and the axial coordinates of the floating center is needed. SUMMARY

[0005] In view of the above technical bottlenecks in the prior art, the present application proposes a new method for automatically measuring the buoyancy and the position of the floating center (axial coordinates of the floating center) of an underwater vehicle using sensors and a corresponding measuring device, which aims to reduce manual intervention to solve the problems of inconvenient measurement, tedious process, heavy workload and low repeatability of manual measurement of the buoyancy and the position of the floating center.

[0006] This invention utilizes modern high-precision sensor measurement technology and computer technology to automatically measure the static forces and lever arms of an underwater vehicle in water. Based on the principle of torque balance, a torque balance formula is established, and the computer calculates the buoyancy and center of buoyancy of the tested vehicle.

[0007] The external data required for this invention includes the calculated weight of the aircraft and the axial coordinates of its center of gravity. This work is done by a land-based weighing device, meaning that the weight of the aircraft and the axial coordinates of its center of gravity are known.

[0008] To achieve the above objectives, this application provides the following technical solution: The first aspect of this application provides a method for automatically calculating the buoyancy and axial coordinates of the center of buoyancy of an underwater vehicle, such as... Figure 3 As shown, this method includes the following steps: S1: Fill the water tank with water so that the water level covers the underwater vehicle mounting frame; S2: Lift the rectangular frame used to support the underwater vehicle off the water surface, power on the controller and input the weight G of the underwater vehicle in the air and the axial coordinate K of its center of mass, and at the same time power on the four weighing sensors installed at the four corners of the rectangular frame. S3: Hang the rectangular frame onto the water tank. The controller collects the measurement values ​​from the four weighing sensors: the value G from the right front weighing sensor. 11 Left front weighing sensor value G 12 Left rear weighing sensor value G 13 Right rear weighing sensor value G 14 ; S4: The controller follows formula G 10 =G 11 +G 12 +G 13 +G 14 Calculate the weight G of the rectangular frame in the water tank. 10 ; S5: The controller follows formula X 10 =(G 11+ G 12 )×X 11 / G 10 Calculate the distance X from the center of mass of the rectangular frame in the water tank to the rear weighing sensor. 10 , where X 11 This is the distance between the front and rear weighing sensors; S6: Lift the rectangular frame and fix the underwater vehicle in the underwater vehicle mounting bracket located directly below the rectangular frame; S7: Lower the rectangular frame containing the underwater vehicle back onto the water tank. The controller collects new measurements from the four load cells: G value from the right front load cell. 21 Left front weighing sensor value G22 , left rear load cell value G 23 , right rear load cell value G 24 ; S8: the tape is attached to the tail end of the underwater vehicle, and the controller controls the laser range finder to be powered on and collects the measurement value L; S9: the controller calculates the buoyancy F of the underwater vehicle according to the formula F=G 10+ G-G 21- G 22- G 23- G 24 S10: the controller calculates the axial coordinate X of the underwater vehicle's center of buoyancy according to the formula Gx(K-L)+G 10 x X 10 =(G 21 +G 22 ) x X 11 +F x X.

[0009] Further, in the method of the present application, the four load cells are arranged at the four corners of the rectangular frame, specifically: right front load cell A10, left front load cell B2, left rear load cell C6, and right rear load cell D11, wherein the left rear load cell C6 and the right rear load cell D11 are arranged in the front-rear direction.

[0010] Further, in the method of the present application, the laser range finder is installed on the rectangular frame, with the measurement starting point located on the line connecting the left rear load cell C6 and the right rear load cell D11, and the measurement direction being perpendicular to the tape attached to the tail end of the underwater vehicle.

[0011] The second aspect of the present application provides an automatic buoyancy and center of buoyancy axial coordinate measuring device for underwater vehicles, which is used to implement the automatic buoyancy and center of buoyancy axial coordinate measuring method for underwater vehicles described above, and the device comprises: a rectangular frame 4 for carrying an underwater vehicle mounting frame; an underwater vehicle mounting frame 9 arranged directly below the rectangular frame 4 for positioning and restraining the underwater vehicle; four load cells, namely right front load cell A10, left front load cell B2, left rear load cell C6, and right rear load cell D11, respectively, which are installed at the four corners of the rectangular frame 4 for measuring the reaction force of the frame-underwater vehicle system in water; a laser range finder 5 installed on the rectangular frame 4 for non-contact measurement of the horizontal distance from the underwater vehicle tail end reference to the line connecting the left rear load cell C6 and the right rear load cell D11; a tape 8 attached to the tail end of the underwater vehicle for measurement positioning of the laser range finder 5.​ The water tank 1 provides a support base for the rectangular frame 4 and ensures that the underwater vehicle is completely submerged. The controller 3 is electrically connected to the four load sensors and the laser range finder 5, and is used to collect the measurement values of the load sensors and the laser range finder 5, and calculate the buoyancy and axial coordinate of the center of buoyancy of the underwater vehicle according to the principle of moment balance.

[0012] Further, in the device of the present application, the measurement starting point of the laser range finder 5 is located on the line connecting the left rear load sensor C6 and the right rear load sensor D11, and the measurement direction is perpendicular to the staff 8 abutting against the tail end of the underwater vehicle.

[0013] Further, in the device of the present application, the rectangular frame 4 is supported on the upper part of the water tank 1 by the four load sensors A10, B2, C6, and D11.

[0014] Further, in the device of the present application, the working process of the controller 3 includes: controlling the four load sensors to be powered on and collecting their measurement values when the rectangular frame 4 is empty (without placing the underwater vehicle), and calculating the weight G of the rectangular frame 4 in the water tank 10 and the weighted sum of the measurement values of the load sensors; controlling the four load sensors to collect their measurement values when the rectangular frame 4 carries the underwater vehicle, combining the distance L measured by the laser range finder 5, and calculating the buoyancy F and the axial coordinate X of the center of buoyancy of the underwater vehicle through the moment balance formula.

[0015] Further, in the device of the present application, the rectangular frame 4 is rigidly connected to the upper surface of the water tank 1 by the four load sensors; The underwater vehicle mounting rack 9 is installed below the rectangular frame 4 by mechanical fixation, and the space between the top of the underwater vehicle mounting rack 9 and the bottom of the rectangular frame 4 can accommodate the underwater vehicle.

[0016] Further, in the device of the present application, the rectangular frame 4 and the underwater vehicle mounting rack 9 are made of anodized aluminum alloy or 316L stainless steel.

[0017] The third aspect of the present application provides an electronic device, comprising a memory and a processor; The memory is used to store a computer program; The processor is used to execute the computer program to realize the calculation step in the automatic calculation method of the buoyancy and axial coordinate of the center of buoyancy of the underwater vehicle.

[0018] In summary, the present application aims at the deficiencies of the existing underwater vehicle buoyancy and float center axial coordinate measurement method of the existing rotary body, realizes the automation, standardization and high precision of the measurement process by integrating sensor technology and automatic control technology, and forms significant technical advantages in operation convenience, anti-interference ability and result reliability, etc. as follows: 1. Full-process automatic measurement, simple and fast operation The traditional method needs to manually mount the weight, adjust the position and manually record the data, which is tedious and time-consuming. The present application automatically collects weight and position data through weighing sensor and laser range finder, and the controller directly calculates the buoyancy and float center coordinates based on the preset algorithm. Only the basic steps such as "water injection → empty frame measurement → installation of vehicle → second measurement" need to be completed, without manual intervention adjustment or reading record throughout the process, significantly shortening the measurement time and improving the operation efficiency.

[0019] 2. Eliminate human interference, greatly improve repeatability The traditional method relies on manual observation and data recording, which is prone to result fluctuations due to differences in operator skills, visual deviations or recording delays. The present application realizes automatic data collection through high-precision sensors (output standardized electrical signals) and laser range finders (output digital distance values), and the controller calculates based on digital signals, completely avoiding human subjective errors. The repeatability deviation of multiple measurement results is reduced from 5%~10% to within 1%, and the consistency is significantly enhanced.

[0020] 3. High-precision sensing and scientific algorithm, accurate and reliable results High-precision data is obtained in real time by using weighing sensors (accuracy ≥0.1%FS) and laser range finders (accuracy ±0.1mm), and all parameters are obtained from sensor measurement or known input of land weighing device (such as vehicle centroid coordinates), avoiding the approximate error of "weight back calculation" in traditional methods, and the result is more reliable.

[0021] 4. Standardized process, suitable for multiple scene requirements The technical scheme does not rely on manual experience, and the measurement can be completed through the standardized interface and preset program of the controller, with low operation threshold; at the same time, it supports quick adaptation to different size vehicles (only needs to adjust the sensor spacing parameter), and is suitable for multiple scenes such as research and development verification, production detection and maintenance evaluation, providing stable and efficient technical support for underwater vehicle performance and quality control.

[0022] Other features and advantages of the present application will be described in detail in the subsequent specification, or can be understood by implementing the related technical solutions of the present application. The purpose and other advantages of the present application can be achieved by the technical features and technical means explicitly indicated in the specification, claims and drawings, and obtained by the implementation process of these technical contents. BRIEF DESCRIPTION OF DRAWINGS

[0023] In order to make the technical solutions of the present application clearer, the drawings involved in the embodiments will be briefly introduced as follows. It should be noted that the drawings only show some embodiments of the present application. Those skilled in the art can derive other related drawings from these drawings without any creative effort.

[0024] Figure 1 The overall structure side view of the underwater vehicle buoyancy and buoyancy center axial coordinate automatic measuring device provided by the embodiments of the present application.

[0025] Figure 2 The overall structure top view of the underwater vehicle buoyancy and buoyancy center axial coordinate automatic measuring device provided by the embodiments of the present application.

[0026] Figure 3 The implementation flowchart of the underwater vehicle buoyancy and buoyancy center axial coordinate automatic measuring method provided by the embodiments of the present application.

[0027] Figure 4 The structure schematic diagram of the electronic device provided by the embodiments of the present application.

[0028] The marks in the figure: 1, water tank; 2, weighing sensor B; 3, controller; 4, rectangular frame; 5, laser range finder; 6, weighing sensor C; 7, underwater vehicle; 8, ruler; 9, underwater vehicle mounting rack; 10, weighing sensor A; 11, weighing sensor D. DETAILED DESCRIPTION

[0029] In order to make the technical solutions of the present application clearer, the drawings involved in the embodiments will be briefly introduced as follows. It should be noted that the drawings only show some embodiments of the present application. Those skilled in the art can derive other related drawings from these drawings without any creative effort.

[0030] In this document, the term "comprising" and any form of the term "comprise", such as "comprise", "comprises" and "comprised", are open-ended terms, and should be interpreted to mean "including, but not limited to", that is, the listed elements do not exhaust all possible elements, and other elements not explicitly mentioned can also be included. The term "based on" should be understood as "at least partially based on", that is, the basis or condition referred to can not be the only factor, and other related factors can also be involved. The term "one embodiment" should be understood as "at least one embodiment", that is, the described embodiment is not the only possible implementation, and other similar embodiments can also exist.

[0031] In the present application, the terms "one" and "multiple" used to modify the relevant elements or features are illustrative rather than restrictive. Unless otherwise explicitly stated in the context, "one" should be understood as "at least one" and "multiple" should be understood as "at least two". Those skilled in the art should reasonably interpret these terms according to the semantics and logical relationship of the context to ensure that they cover the possibility of "one or more".

[0032] Figure 1 and Figure 2 The figure shows the composition structure of the underwater vehicle buoyancy and buoyancy center axial coordinate automatic measuring device provided by the embodiment.

[0033] The device comprises a rectangular frame 4, an underwater vehicle mounting rack 9 arranged directly below the rectangular frame 4, four load sensors mounted at the four corners of the rectangular frame 4, a laser range finder 5 mounted on the rectangular frame 4, a ruler 8, a water tank 1 and a controller 3. The rectangular frame 4 is supported on the upper part of the water tank 1 by the four load sensors, and the four load sensors are respectively a load sensor A 10 located in the front right, a load sensor B 2 located in the front left, a load sensor C 6 located in the rear left, and a load sensor D 11 located in the rear right. The distance between the front and rear load sensors is X 11 , the ruler 8 is attached to the tail end of the underwater vehicle 7, the measurement starting point of the laser range finder 5 is located on the line connecting the load sensor C 6 and the load sensor D 11, and the measurement direction is perpendicular to the ruler 8, and the controller 3 collects the measurement values of the four load sensors and the laser range finder 5 and calculates the buoyancy and buoyancy center axial coordinate of the underwater vehicle 7.

[0034] The underwater vehicle buoyancy and buoyancy center axial coordinate automatic measuring method provided by the embodiment is based on the above measuring device. The controller automatically collects the measurement values of each load sensor and the laser range finder. First, the weight of the rectangular frame in the water tank and the distance between the mass center of the rectangular frame and the rear load sensor are automatically measured. Then, the buoyancy and buoyancy center axial coordinate of the underwater vehicle are measured using the measurement values. The specific implementation process of the method includes the following steps: 1. Fill the water tank with water, and the water level should be higher than the underwater vehicle mounting rack; 2. Use a crane to lift the rectangular frame away from the water surface, power on the controller and input the weight G of the underwater vehicle in the air and the axial coordinate K of the mass center, and power on the four load sensors; 3. Use a crane to lift the rectangular frame onto the water tank, and the controller collects the measurement values of the four load sensors. The measurement value of the load sensor A located in the front right is represented by G11, the measurement value of the load sensor B located in the front left is represented by G12, the measurement value of the load sensor C located in the rear left is represented by G13, and the measurement value of the load sensor D located in the rear right is represented by G14. 4. The controller calculates the weight of the rectangular frame in the tank according to the formula G10=G11+G12+G13+G14; 5. The controller calculates the distance between the center of mass of the rectangular frame in the tank and the rear load sensor according to the formula X10=(G11+G12)×X11 / G10; 6. The rectangular frame is lifted and the underwater vehicle is fixed in the underwater vehicle mounting frame; 7. The rectangular frame with the underwater vehicle is lifted on the tank by the crane, and the controller collects the measurement values of the four load sensors, the measurement value of the load sensor A located at the right front is represented by G21, the measurement value of the load sensor B located at the left front is represented by G22, the measurement value of the load sensor C located at the left rear is represented by G23, and the measurement value of the load sensor D located at the right rear is represented by G24; 8. The ruler is attached to the tail end of the underwater vehicle, and the controller powers on the laser range finder and collects the measurement value L of the laser range finder; 9. The controller calculates the buoyancy of the underwater vehicle according to the formula F=G10+G-G21-G22-G23-G24; 10. The controller calculates the axial coordinate X of the center of buoyancy of the underwater vehicle according to the formula G(K-L)+G10•X10=(G21+G22)•X11+F•X.

[0035] As Figure 4 shown, the embodiment of the present application further discloses an electronic device, comprising: a processor 310, a communication interface 320, a memory 330 for storing a processor executable computer program, and a communication bus 340. Wherein the processor 310, the communication interface 320 and the memory 330 complete the communication among each other through the communication bus 340. The processor 310 realizes the calculation steps in the automatic calculation method of the buoyancy and the axial coordinate of the center of buoyancy of the underwater vehicle by running the executable computer program.

[0036] It can be understood that, in addition to including the memory and the processor, the electronic device can also include input devices (such as a keyboard), output devices (such as a display), and other communication modules. These input devices, output devices, and other communication modules all communicate with the processor through an I / O interface (i.e., an input / output interface).

[0037] While the foregoing discussion contains several specific implementation details, these details should not be construed as limiting the scope of this application. The above description is merely a preferred embodiment of this application and an explanation of the technical principles employed. Those skilled in the art should understand that the scope of this application is not limited to technical solutions formed by specific combinations of the above-described technical features. Furthermore, this application should also cover other technical solutions formed by any combination of the above-described technical features or their equivalents without departing from the foregoing disclosed concept.

[0038] Those skilled in the art should also understand that modifications can be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some of the technical features, without departing from the spirit and scope of the technical solutions of the embodiments of this application. These modifications or substitutions will not cause the essence of the corresponding technical solutions to deviate from the core spirit and scope of the technical solutions of the embodiments of this application.

Claims

1. A method for automatically calculating the buoyancy and axial coordinates of the center of buoyancy of an underwater vehicle, characterized in that, The method includes: S1: Fill the water tank with water so that the water level covers the underwater vehicle mounting frame; S2: Lift the rectangular frame used to support the underwater vehicle off the water surface, power on the controller and input the weight G of the underwater vehicle in the air and the axial coordinate K of its center of mass, and at the same time power on the four weighing sensors installed at the four corners of the rectangular frame. S3: Hang the rectangular frame onto the water tank. The controller collects the measurement values ​​from the four weighing sensors: the value G from the right front weighing sensor. 11 Left front weighing sensor value G 12 Left rear weighing sensor value G 13 Right rear weighing sensor value G 14 ; S4: The controller follows formula G 10 =G 11 +G 12 +G 13 +G 14 Calculate the weight G of the rectangular frame in the water tank. 10 ; S5: The controller follows formula X 10 =(G 11 +G 12 )×X 11 / G 10 Calculate the distance X from the center of mass of the rectangular frame in the water tank to the rear weighing sensor. 10 , where X 11 This is the distance between the front and rear weighing sensors; S6: Lift the rectangular frame and fix the underwater vehicle in the underwater vehicle mounting bracket located directly below the rectangular frame; S7: Lower the rectangular frame containing the underwater vehicle back onto the water tank. The controller collects new measurements from the four load cells: G value from the right front load cell. 21 Left front weighing sensor value G 22 Left rear weighing sensor value G 23 Right rear weighing sensor value G 24 ; S8: Place the ruler against the tail of the underwater vehicle, and the controller will power on the laser rangefinder and collect its measurement value L. S9: The controller is based on the formula F=G 10+ GG 21- G 22- G 23- G 24 Calculate the buoyancy F of the underwater vehicle; S10: The controller uses the formula G×(KL)+G 10 ×X 10 =(G 21 +G 22 )×X 11 +F×X calculates the axial coordinate X of the buoyancy center of the underwater vehicle.

2. The method according to claim 1, characterized in that, The four weighing sensors are respectively set at the four corners of the rectangular frame, specifically: right front weighing sensor A (10), left front weighing sensor B (2), left rear weighing sensor C (6), and right rear weighing sensor D (11), wherein the left rear weighing sensor C (6) and the right rear weighing sensor D (11) are set at intervals along the front-back direction.

3. The method according to claim 1, characterized in that, The laser rangefinder is mounted on a rectangular frame. Its measurement starting point is located on the line connecting the left rear weighing sensor C (6) and the right rear weighing sensor D (11). The measurement direction is perpendicular to the ruler attached to the tail of the underwater vehicle.

4. An automatic calculation device for buoyancy and axial coordinates of the center of buoyancy of an underwater vehicle, characterized in that, The device includes: A rectangular frame (4) is used to support the underwater vehicle mounting bracket; An underwater vehicle mounting bracket (9) is positioned directly below the rectangular frame (4) and is used to position and restrain the underwater vehicle. Four weighing sensors, namely right front weighing sensor A (10), left front weighing sensor B (2), left rear weighing sensor C (6), and right rear weighing sensor D (11), are installed at the four corners of the rectangular frame (4) to measure the support reaction force of the frame-underwater vehicle system in the water. A laser rangefinder (5) is mounted on a rectangular frame (4) for non-contact measurement of the horizontal distance from the tail reference of the underwater vehicle to the line connecting the left rear weighing sensor C (6) and the right rear weighing sensor D (11). The ruler (8) is attached to the tail end of the underwater vehicle and is used for measurement and positioning by the laser rangefinder (5); The water tank (1) is used to provide a still water environment to provide a supporting foundation for the rectangular frame (4) and to ensure that the underwater vehicle is completely submerged; The controller (3) is electrically connected to four weighing sensors and a laser rangefinder (5) to collect the measured values ​​of each weighing sensor and the laser rangefinder (5) and to calculate the buoyancy and axial coordinate of the buoyancy center of the underwater vehicle according to the torque balance principle.

5. The apparatus according to claim 4, characterized in that, The starting point of the laser rangefinder (5) is located on the line connecting the left rear weighing sensor C (6) and the right rear weighing sensor D (11), and the measurement direction is perpendicular to the ruler (8) attached to the tail of the underwater vehicle.

6. The apparatus according to claim 4, characterized in that, The rectangular frame (4) is supported on the upper part of the water tank (1) by four weighing sensors A (10), B (2), C (6), and D (11).

7. The apparatus according to claim 4, characterized in that, The workflow of the controller (3) includes: Power on the four weighing sensors and collect their measurements when the rectangular frame (4) is unloaded. Calculate the weight G of the rectangular frame (4) in the water tank. 10 and the weighted sum of the measurements from each weighing sensor; Four weighing sensors are controlled to collect their measurements when the underwater vehicle is supported by a rectangular frame (4). Combined with the distance L measured by the laser rangefinder (5), the buoyancy F and the axial coordinate X of the buoyancy center of the underwater vehicle are calculated by the torque balance formula.

8. The apparatus according to claim 4, characterized in that, The rectangular frame (4) is rigidly connected to the upper surface of the water tank (1) through four weighing sensors; The underwater vehicle mounting bracket (9) is mechanically fixed to the bottom of the rectangular frame (4), and a space is reserved between the top of the underwater vehicle mounting bracket (9) and the bottom of the rectangular frame (4) to accommodate the underwater vehicle.

9. The apparatus according to claim 4, characterized in that, The rectangular frame (4) and the underwater vehicle mounting bracket (9) are made of anodized aluminum alloy or 316L stainless steel.

10. An electronic device, characterized in that, include: Memory and processor; Memory: Used to store computer programs; Processor: Used to execute the computer program to implement the calculation steps in the automatic calculation method for buoyancy and axial coordinates of the buoyancy center of an underwater vehicle as described in any one of claims 1-3.

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