CN110082033B - Device and method for measuring gravity center of water carrier in motion state - Google Patents

Device and method for measuring gravity center of water carrier in motion state Download PDF

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CN110082033B
CN110082033B CN201811508951.4A CN201811508951A CN110082033B CN 110082033 B CN110082033 B CN 110082033B CN 201811508951 A CN201811508951 A CN 201811508951A CN 110082033 B CN110082033 B CN 110082033B
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water carrier
gnss
water
coordinate system
gravity center
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CN110082033A (en
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李治远
胡俊
吴永亭
张海泉
张彬彬
豆虎林
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First Institute of Oceanography MNR
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    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B63—SHIPS OR OTHER WATERBORNE VESSELS; RELATED EQUIPMENT
    • B63B—SHIPS OR OTHER WATERBORNE VESSELS; EQUIPMENT FOR SHIPPING 
    • B63B39/00—Equipment to decrease pitch, roll, or like unwanted vessel movements; Apparatus for indicating vessel attitude
    • B63B39/12—Equipment to decrease pitch, roll, or like unwanted vessel movements; Apparatus for indicating vessel attitude for indicating draught or load
    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B63—SHIPS OR OTHER WATERBORNE VESSELS; RELATED EQUIPMENT
    • B63B—SHIPS OR OTHER WATERBORNE VESSELS; EQUIPMENT FOR SHIPPING 
    • B63B39/00—Equipment to decrease pitch, roll, or like unwanted vessel movements; Apparatus for indicating vessel attitude
    • B63B39/14—Equipment to decrease pitch, roll, or like unwanted vessel movements; Apparatus for indicating vessel attitude for indicating inclination or duration of roll
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01M—TESTING STATIC OR DYNAMIC BALANCE OF MACHINES OR STRUCTURES; TESTING OF STRUCTURES OR APPARATUS, NOT OTHERWISE PROVIDED FOR
    • G01M1/00—Testing static or dynamic balance of machines or structures
    • G01M1/12—Static balancing; Determining position of centre of gravity
    • G01M1/122—Determining position of centre of gravity

Abstract

The invention provides a device for measuring the gravity center of a water carrier in a motion state, which is characterized by comprising the following components: the GNSS signal receiving device is used for receiving GNSS satellite signals in real time and calculating the geographical coordinates of observation points, and the number of the GNSS signal receiving device is 4 or more, wherein the two GNSS signal receiving devices are arranged in the heading direction of the water carrier; the attitude sensor device is used for acquiring the attitude values of the rolling, pitching and heaving of the water carrier in real time; and the CPU recording and processing device is connected with each GNSS signal receiving device and the attitude sensor, records the observed values of each device in real time and processes the observed values to obtain the coordinates of the gravity center of the water carrier under the water carrier coordinate system. The invention provides a device and a method for measuring the gravity center of a water carrier, which aim at solving the problems of irrational, inaccurate and the like of the existing method for determining the gravity center of the water carrier and can accurately acquire the gravity center position of the water carrier in real time.

Description

Device and method for measuring gravity center of water carrier in motion state
Technical Field
The invention relates to the field of gravity center measurement, in particular to a gravity center measuring device and method for a water large-scale water carrier in a motion state.
Background
The measuring technology of the center of gravity of the water carrier is crucial to the load and the navigation safety of the water carrier. Because the water carrier has huge structure and weight, the water carrier is in a state of continuous swinging, shaking and moving in water, the gravity center of the water carrier cannot be determined by a supporting method, a hanging method and the like, and the gravity center position of the water carrier also changes along with the configuration change of goods and the supplement and consumption of fuel oil and fresh water.
The center of gravity of the water large-scale water carrier is obtained by estimating a model according to a design model and construction materials during construction. The estimation is only suitable for the gravity center position of the large water carrier in the factory period, and the error of the model can cause that the deviation of the estimated gravity center position and the actual position is too large. And once the weight of the water carrier and the goods of the water carrier, the consumption of fuel oil and fresh water and the like are changed too much, the position of the center of gravity of the water carrier and the goods of the water carrier can be changed greatly. Meanwhile, with the popularization of the DP system in modern water carriers, the excellent function of the DP system greatly depends on the accurate gravity center position of the water carrier. The existing measurement technical method can not realize the real-time and accurate acquisition of the gravity center position of the water carrier.
Disclosure of Invention
The invention provides a device and a method for measuring the gravity center of a water carrier, which aim at solving the problems of irrational, inaccurate and the like of the existing method for determining the gravity center of the water carrier and can accurately acquire the gravity center position of the water carrier in real time.
Aiming at the problems, the following technical scheme is provided: a device for measuring the center of gravity of a water craft in a sport state, comprising:
the GNSS signal receiving device is used for receiving GNSS satellite signals in real time and calculating the geographical coordinates of observation points, and the number of the GNSS signal receiving device is 4 or more, wherein the two GNSS signal receiving devices are arranged in the heading direction of the water carrier;
the attitude sensor device is used for acquiring the attitude values of the rolling, pitching and heaving of the water carrier in real time;
and the CPU recording and processing device is connected with each GNSS signal receiving device and the attitude sensor, records the observed values of each device in real time and processes the observed values to obtain the coordinates of the gravity center of the water carrier under the water carrier coordinate system.
The invention is further configured to: the GNSS signal receiving device comprises a GNSS receiving antenna, the GNSS receiving antenna receives the GNSS ranging code and the carrier signal and receives the GNSS differential signal or the CORS station signal in real time.
The invention is further configured to: the attitude sensor device is provided with a spatial rectangular reference coordinate system of the attitude sensor device, and comprises an attitude sensor and a measuring device for measuring the rolling, the pitching, the heaving and the heading of the water carrier in real time.
The invention is further configured to: the CPU recording and processing device is connected with the GNSS receiving antennas through equal-length feeder lines, analyzes and processes signals received by the GNSS receiving antennas, obtains GNSS time information and accurate geographic coordinates of each observation point, and accurately aligns system time of the CPU recording and processing device with the GNSS time.
The invention is further configured to: the CPU recording and processing device is connected with the attitude sensor through a communication cable, coordinates of each observation point in a water carrier coordinate system are input into the CPU recording and processing device through the communication cable, and the CPU recording and processing device is combined with the observation values of each device to calculate the barycentric coordinates of the water carrier.
The invention is further configured to: the GNSS receiving antenna comprises a fixed workpiece which enables the GNSS receiving antenna and the observation point to be fixedly connected together.
The invention is further configured to: the attitude sensor comprises a fixed base and a fixed workpiece, wherein the fixed base and the fixed workpiece are used for fixedly connecting the attitude sensor and the water carrier together.
The invention is further configured to: the CPU recording and processing device comprises:
the memory is used for storing the observed values of all the devices and the processed data and results;
fixing the workpiece to prevent the CPU recording and processing device from shaking on the water carrier;
a physical interface for connecting and communicating with other devices;
and the manual interaction equipment is used for inputting necessary parameters and sending instructions to the CPU recording and processing device and outputting and displaying processing results.
A method for measuring the gravity center of a water carrier in a motion state is characterized in that the method for measuring the gravity center position of the water carrier under a dynamic condition comprises the following steps:
(1) establishing a coordinate system of the water carrier: selecting a reference point of a coordinate system of the water carrier, and establishing a space rectangular coordinate system by taking the ship bow direction as one axis to determine the three-dimensional coordinates of the observation point under the coordinate system;
(2) selecting and acquiring three-dimensional coordinates of an observation point: selecting at least 4 non-collinear observation points on the water carrier, wherein the observation points need to have a wide air view, and the two observation points are arranged in the heading direction of the water carrier, and acquiring the coordinates of each observation point on the water carrier coordinate system by using a measurement method;
(3) erecting a GNSS receiving antenna: erecting a GNSS receiving antenna at the observation point selected in the step (2) to acquire a GNSS signal in real time;
(4) installing an attitude sensor: installing an attitude sensor at a known position near the estimated center of gravity of the water carrier, and enabling three axes of a reference system of the sensor and a coordinate system of the water carrier to be parallel to each other respectively;
(5) connection and setting of the CPU recording and processing means: connecting each GNSS receiving antenna with a CPU recording and processing device by using an equal-length feeder line, connecting an attitude sensor with the CPU recording and processing device by using a signal cable, inputting a three-dimensional coordinate of each observation point in a water carrier coordinate system into the CPU recording and processing device, and extracting GNSS time from signals received by the GNSS receiving antennas by the CPU recording and processing device and accurately timing with a self system;
(6) the CPU recording and processing means calculate and process the incoming data: the method comprises the steps of processing signals received by GNSS receiving antennas to obtain accurate three-dimensional geographic coordinates of each observation point at different moments, calculating a heading value of the water carrier by using two GNSS receiving antennas in the heading direction, calculating coordinates of the gravity center of the water carrier in a water carrier coordinate system by using three-dimensional coordinates of each observation point in the water carrier coordinate system, three-dimensional coordinates and coordinate changes in the geographic coordinate system, and the relationship between attitude sensor data and the heading value of the water carrier.
The invention is further configured to: and (2) determining the three-dimensional coordinates of the observation points in the coordinate system of the water carrier by using the way of the arrangement drawing of the water carrier in the step (1).
The invention has the beneficial effects that: the technical scheme provided by the invention can realize the real-time accurate acquisition of the gravity center position of the water carrier, and has great help for the power distribution, the cargo counterweight distribution, the navigation safety, the accurate dynamic positioning and the like of the water carrier; meanwhile, with the continuous development of the GNSS positioning technology, the centimeter-level or even millimeter-level GNSS positioning technology has been widely applied; attitude sensors such as vertical reference cells have also achieved second-order measurement accuracy.
The method for measuring the position of the center of gravity of the water carrier has the advantages of being easy to operate and capable of rapidly obtaining results in real time, and the device for measuring the position of the center of gravity of the water carrier has the advantages of being low in cost and capable of automatically calculating and processing, and can be widely applied to the measurement of the center of gravity of the water carrier.
For example, the gravity center position of the ship can be accurately measured on a large cargo ship, so that the ship staff can reasonably arrange the storage position of the cargo, the balance weight of the waterborne carrier can be prevented from being unbalanced, and the waterborne carrier can be ensured to sail safely.
For example, the gravity center position of an aquatic carrier is accurately measured in a scientific investigation ship, so that investigation equipment such as a multi-beam ultra-short baseline underwater positioning system and a shallow stratum profiler can obtain more accurate measurement results.
For example, the gravity center position of the platform is accurately measured in the water drilling platform provided with the DP system, so that the reasonable power distribution of each propeller is facilitated, the positioning precision of the platform is improved, and the safe production of the platform is guaranteed.
Drawings
FIG. 1 is a schematic flow chart of a method for measuring the center of gravity of a water carrier according to an embodiment of the present invention;
FIG. 2 is a schematic diagram of an on-water vehicle coordinate system and a geographic coordinate system in an embodiment of the invention;
FIG. 3 is a schematic view of functional modules in the water vehicle in an embodiment of the present invention;
FIG. 4 is a schematic view of a processing scheme of a CPU recording and processing device in an embodiment of the present invention;
the figure shows schematically: 1-GNSS receiving antenna; a 2-GNSS receive antenna; a 3-GNSS receive antenna; a 4-GNSS receive antenna; 5-attitude sensor; 6-a CPU recording and processing device; o-xyz is a geospatial rectangular coordinate system; O-XVYVZVIs the rectangular coordinate of the water carrier.
Detailed Description
The following detailed description of embodiments of the present invention is provided in connection with the accompanying drawings and examples. The following examples are intended to illustrate the invention but are not intended to limit the scope of the invention.
A device for measuring the center of gravity of a water craft in a sport state, comprising: GNSS signal receiving device, attitude sensor device, CPU recording and processing device;
the GNSS signal receiving device is used for receiving GNSS satellite signals in real time and calculating the geographical coordinates of observation points, and the number of the GNSS signal receiving device is 4 or more, wherein the two GNSS signal receiving devices are arranged in the heading direction of the water carrier; the GNSS signal receiving device comprises a GNSS receiving antenna, the GNSS receiving antenna receives the GNSS ranging code and the carrier signal and receives the GNSS differential signal or the CORS station signal in real time. The GNSS receiving antenna comprises a fixed workpiece which enables the GNSS receiving antenna and the observation point to be fixedly connected together.
The attitude sensor device is used for acquiring the attitude values of the rolling, pitching and heaving of the water carrier in real time; the attitude sensor device is provided with a spatial rectangular reference coordinate system of the attitude sensor device, and comprises an attitude sensor and a measuring device for measuring the rolling, the pitching, the heaving and the heading of the water carrier in real time. The attitude sensor comprises a fixed base and a fixed workpiece, wherein the fixed base and the fixed workpiece are used for fixedly connecting the attitude sensor and the water carrier together.
And the CPU recording and processing device is connected with each GNSS signal receiving device and the attitude sensor, records the observed values of each device in real time and processes the observed values to obtain the coordinates of the gravity center of the water carrier under the water carrier coordinate system. The CPU recording and processing device is connected with the GNSS receiving antennas through equal-length feeder lines, analyzes and processes signals received by the GNSS receiving antennas, obtains GNSS time information and accurate geographic coordinates of each observation point, and accurately aligns system time of the CPU recording and processing device with the GNSS time.
The CPU recording and processing device is connected with the attitude sensor through a communication cable, coordinates of each observation point in a water carrier coordinate system are input into the CPU recording and processing device through the communication cable, and the CPU recording and processing device is combined with the observation values of each device to calculate the barycentric coordinates of the water carrier.
The CPU recording and processing device comprises: the memory is used for storing the observed values of all the devices and the processed data and results; fixing the workpiece to prevent the CPU recording and processing device from shaking on the water carrier; a physical interface for connecting and communicating with other devices; and the manual interaction equipment is used for inputting necessary parameters and sending instructions to the CPU recording and processing device and outputting and displaying processing results.
Fig. 1 shows a flow chart of a method for measuring the center of gravity of a water vehicle according to an embodiment of the invention. The method for determining the center of gravity of the water carrier comprises the following steps:
establishing a coordinate system of the water carrier: selecting a reference point O of a coordinate system of the water carrier, and taking the direction of the bow as an axis OXVEstablishing a spatial rectangular coordinate system O-XVYVZVFor determining observation point P in subsequent stepsiThree-dimensional coordinates P in said coordinate systemi(Xi,Yi,Zi)V；
Selecting and acquiring three-dimensional coordinates of an observation point: selecting at least 4 non-collinear observation points P on a water carrieriThe observation points need to have wide air vision, and two of the observation points are arranged in the heading direction OX of the water carrierVThe above. For convenience of illustration of the principle and the operation steps, suitable positions of the observation points are given in fig. 3: p1、P2、P3And P4. Obtaining individual observation points P using measuring devices, e.g. measuring tools such as total stations, theodolites, levels, rulers, threads, or the likeiOn-water carrier coordinate system O-XVYVZVCoordinate P of (1)i(Xi,Yi,Zi)VOr inquiring the coordinates of each observation point by using a system drawing during the construction of the water carrier;
erecting GNSS receiving antennas 1, 2, 3 and 4: observation point P selected in the previous stepiThe GNSS receiving antenna is erected to obtain GNSS signals in real time, the GNSS signals are rich in types and comprise GNSS time service information, C/A codes, L1 carrier waves, L2 carrier waves, satellite ephemeris files and GNSS signalsDifferential signals, CORS station differential signals, etc.; the information is comprehensively used, so that accurate time information and a high-precision positioning result can be obtained.
Mounting the attitude sensor 5: mounting attitude sensors at known positions P near the estimated center of gravity of the water vehicleVRS(XVRS,YVRS,ZVRS) And making the three axes O 'X', O 'y' and O 'z' of the reference system O '-X' y 'z' of said sensor and the on-water object coordinate system O-XVYVZVOf three axes OXV、OYVAnd OZVAre respectively parallel to each other; for example, after the equipment such as the PHINS, the POSMV, the MRU, etc. is installed on the water carrier and is subjected to installation deviation calibration (if three axes thereof are parallel to three axes of the hull coordinate system, the installation deviation calibration is not required), the attitude change value of the water carrier can be obtained, and further, since the water carrier is a rigid body, when the water carrier swings due to inertia, each point on the water carrier generates the same attitude change around the center of gravity;
connection and setting of the CPU recording and processing device 6: connecting each GNSS receiving antenna with the CPU device by using equal-length feeder lines, such as coaxial cables with better shielding performance, connecting the attitude sensor with the CPU device by using a signal cable, and connecting the three-dimensional coordinate P of each observation point in the water carrier coordinate systemi(Xi,Yi,Zi)VAnd three-dimensional coordinate P of attitude sensor in water carrier coordinate systemVRS(XVRS,YVRS,ZVRS) The required parameters can be input into the CPU device through interactive equipment such as a keyboard and a mouse. The CPU device firstly extracts GNSS time, such as GPS time, from signals received by a GNSS receiving antenna and precisely time-synchronizes with a system of the CPU device, so that all data transmitted into the CPU device have uniform and precise GPS time stamps, and observation values obtained by different observation equipment are ensured to have precise corresponding time information when an observation equation is established in the subsequent data processing process;
the CPU recording and processing means 6 calculate and process the incoming data: the signal received by the GNSS receiving antenna is obtained by processingAccurate three-dimensional geographic coordinate P of each observation point at different momentsi(xi,yi,zi)geo(ii) a Further, two GNSS receiving antennas P in the heading direction are utilized1And P2Calculating heading value heading of the waterborne carrier, wherein the calculation method comprises the following steps:
Figure GDA0002586807400000051
further, using the principles described in table 1, the header was obtained:
TABLE 1 coordinate Azimuth transformation
Figure GDA0002586807400000062
If a posture sensor such as a PHINS or a POS MV is used, the equipment automatically provides a heading value.
Next, three-dimensional coordinates P in the water carrier coordinate system of each observation point are usedi(Xi，Yi，Zi)VThree-dimensional coordinates P in a geographic coordinate systemi(xi，yi，zi)geoCalculating the gravity center P of the water carrier according to the relationship among the attitude data roll, pitch, heave and heading value heading obtained by the attitude sensorGCoordinate P in a coordinate system of a water borne bodyG(X，Y，Z)GThe calculation method is as follows:
Pi-geo＝R(heading，pitch，roll)＊Pi-v+Po
wherein, Pi-geoRepresenting the three-dimensional coordinates of the observation point in a geographic coordinate system,
Pi-geo＝[(xi，yi，zi)geo]T
(xi，yi，zi)georepresenting observation point PiCoordinates under a geographic reference system;
r (heading, pitch, roll) represents a rotation matrix consisting of heading, pitch, and roll values provided by heading measurement and attitude sensors, as follows:
Figure GDA0002586807400000061
in the formula, h, p and r respectively represent header, pitch and roll;
Pi-v＝[(Xi-XG，Yi-YG，Zi-ZG)]T
wherein, Xi、YiAnd ZiIs an observation point PiCoordinates in the coordinate system of the aquatic carrier, XG、YGAnd ZGThe coordinates of the gravity center of the waterborne carrier under a coordinate system of the waterborne carrier are obtained;
PO＝[(x0，y0，z0)geo]T
wherein x is0，y0，z0Representing the coordinates of the origin of the coordinate system of the water borne object under a geographic reference system;
in the formula (X)G，YG，ZG) And PO＝|(x0，y0，z0)geo|TAnd 6 of the parameters to be solved are simultaneously connected with a plurality of observation points, redundant observation quantities are considered so as to remove gross error observation values, so that 3 or more observation points are needed to form an observation equation, unknown parameters are solved by using a least square or other error distribution method, and the observation quantities at different observation moments can be used to form the observation equation so as to solve the optimal estimation value of the position of the gravity center of the water carrier in the water carrier coordinate system.
The above description is only a preferred embodiment of the present invention, and it should be noted that, for those skilled in the art, several modifications and variations can be made without departing from the technical principle of the present invention, and those modifications and variations assumed in the above are also considered to be within the protective scope of the present invention.

Claims (10)

1. A device for measuring the center of gravity of a water craft in a sport state, comprising:
the GNSS signal receiving device is used for receiving GNSS satellite signals in real time and calculating the geographical coordinates of observation points, and the number of the GNSS signal receiving device is 4 or more, wherein the two GNSS signal receiving devices are arranged in the heading direction of the water carrier;
the attitude sensor device is used for acquiring the attitude values of the rolling, pitching and heaving of the water carrier in real time;
and the CPU recording and processing device is connected with each GNSS signal receiving device and the attitude sensor, records the observed values of each device in real time and processes the observed values to obtain the coordinates of the gravity center of the water carrier under the water carrier coordinate system.
2. A water vehicle gravity center measuring device according to claim 1, wherein: the GNSS signal receiving device comprises a GNSS receiving antenna, the GNSS receiving antenna receives the GNSS ranging code and the carrier signal and receives the GNSS differential signal or the CORS station signal in real time.
3. A water vehicle gravity center measuring device according to claim 1, wherein: the attitude sensor device is provided with a spatial rectangular reference coordinate system of the attitude sensor device, and comprises an attitude sensor and a measuring device for measuring the rolling, the pitching, the heaving and the heading of the water carrier in real time.
4. A water vehicle gravity center measuring device according to claim 2, wherein: the CPU recording and processing device is connected with the GNSS receiving antennas through equal-length feeder lines, analyzes and processes signals received by the GNSS receiving antennas, obtains GNSS time information and accurate geographic coordinates of each observation point, and accurately aligns system time of the CPU recording and processing device with the GNSS time.
5. A water vehicle gravity center measuring device according to claim 3, wherein: the CPU recording and processing device is connected with the attitude sensor through a communication cable, coordinates of each observation point in a water carrier coordinate system are input into the CPU recording and processing device through the communication cable, and the CPU recording and processing device is combined with the observation values of each device to calculate the barycentric coordinates of the water carrier.
6. A water vehicle gravity center measuring device according to claim 2, wherein: the GNSS receiving antenna comprises a fixed workpiece which enables the GNSS receiving antenna and the observation point to be fixedly connected together.
7. A device for measuring the center of gravity of a water vehicle in a state of motion as claimed in claim 3, wherein said attitude sensor comprises a fixed base and a fixed workpiece for fixedly connecting the attitude sensor to the water vehicle.
8. The apparatus according to claim 1, wherein the CPU recording and processing means comprises:
the memory is used for storing the observed values of all the devices and the processed data and results;
fixing the workpiece to prevent the CPU recording and processing device from shaking on the water carrier;
a physical interface for connecting and communicating with other devices;
and the manual interaction equipment is used for inputting necessary parameters and sending instructions to the CPU recording and processing device and outputting and displaying processing results.
9. A method for measuring the gravity center of a water carrier in a motion state is characterized in that the method for measuring the gravity center position of the water carrier under a dynamic condition comprises the following steps:
(1) establishing a coordinate system of the water carrier: selecting a reference point of a coordinate system of the water carrier, and establishing a space rectangular coordinate system by taking the ship bow direction as one axis to determine the three-dimensional coordinates of the observation point under the coordinate system;
(2) selecting and acquiring three-dimensional coordinates of an observation point: selecting at least 4 non-collinear observation points on the water carrier, wherein the observation points need to have a wide air view, and the two observation points are arranged in the heading direction of the water carrier, and acquiring the coordinates of each observation point on the water carrier coordinate system by using a measurement method;
(3) erecting a GNSS receiving antenna: erecting a GNSS receiving antenna at the observation point selected in the step (2) to acquire a GNSS signal in real time;
(4) installing an attitude sensor: installing an attitude sensor at a known position near the estimated center of gravity of the water carrier, and enabling three axes of a reference system of the sensor and a coordinate system of the water carrier to be parallel to each other respectively;
(5) connection and setting of the CPU recording and processing means: connecting each GNSS receiving antenna with a CPU recording and processing device by using an equal-length feeder line, connecting an attitude sensor with the CPU recording and processing device by using a signal cable, inputting a three-dimensional coordinate of each observation point in a water carrier coordinate system into the CPU recording and processing device, and extracting GNSS time from signals received by the GNSS receiving antennas by the CPU recording and processing device and accurately timing with a self system;
(6) the CPU calculates and processes the incoming data: the method comprises the steps of processing signals received by GNSS receiving antennas to obtain accurate three-dimensional geographic coordinates of each observation point at different moments, calculating a heading value of the water carrier by using two GNSS receiving antennas in the heading direction, calculating coordinates of the gravity center of the water carrier in a water carrier coordinate system by using three-dimensional coordinates of each observation point in the water carrier coordinate system, three-dimensional coordinates and coordinate changes in the geographic coordinate system, and the relationship between attitude sensor data and the heading value of the water carrier.
10. The method of claim 9, wherein the method comprises the following steps: and (2) determining the three-dimensional coordinates of the observation points in the coordinate system of the water carrier by using the way of the arrangement drawing of the water carrier in the step (1).
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