WO2022174757A1

WO2022174757A1 - Air-cooled battery cooling system and cooling flow channel design method

Info

Publication number: WO2022174757A1
Application number: PCT/CN2022/076149
Authority: WO
Inventors: 孙士杰; 耿宇明; 刘涛; 刘鹏; 卢军; 陈雷
Original assignee: 中国第一汽车股份有限公司
Priority date: 2021-02-18
Filing date: 2022-02-14
Publication date: 2022-08-25
Also published as: CN113013529B; CN113013529A

Abstract

Provided in the present application are an air-cooled battery cooling system and a cooling flow channel design method. The air-cooled battery cooling system comprises a cooling flow channel and a plurality of cells, wherein the cooling flow channel comprises a main flow channel and a plurality of branch flow channels; one end of the main flow channel is provided with an air inlet, and the other end thereof is provided with a flow guide portion; the flow guide portion is wedge-shaped, and comprises a first inclined plane and a second inclined plane that extend in the lengthwise direction of the main flow channel, and have an included angle therebetween; the plurality of branch flow channels are uniformly arranged in parallel at two sides of the main flow channel in a spaced manner; each branch flow channel comprises a branch air inlet and a branch air outlet; a plurality of branch air inlets are all in communication with the main flow channel; and the cells are arranged at the two sides of the main flow channel and are attached to the branch flow channels.

Description

Air-cooled battery cooling system and cooling channel design method

This application claims the priority of the Chinese patent application with application number 202110202571.3 filed with the China Patent Office on February 18, 2021, the entire contents of which are incorporated herein by reference.

technical field

The present application relates to the technical field of power batteries, for example, to an air-cooled battery cooling system and a cooling channel design method.

Background technique

With the increase in the number of electric vehicles in the market, the life of the power battery has received more and more attention. The life of the power battery is greatly affected by the battery temperature. In the battery system, when the temperature difference between the cells and the cells increases, the life of the cells will be greatly reduced. The battery cooling system is divided into series air-cooled cooling and parallel air-cooled cooling. The uneven distribution of cooling medium flow between multiple branch channels in the parallel cooling system is an important reason for the temperature difference between cells. Therefore, in the design of cooling channels for air-cooled batteries, it is an important criterion to ensure that the flow between multiple branch channels is uniform, while the structural design and size optimization of cooling channels rely on the experience of engineers, the optimization efficiency is low, and the optimization results are difficult to guarantee .

SUMMARY OF THE INVENTION

The present application provides an air-cooled battery cooling system and a cooling channel design method. The air-cooled battery cooling system solves the problem of uneven distribution of cooling medium flow in a parallel battery cooling system, reduces the temperature difference between cells, and prolongs the power battery. The cooling flow channel design method realizes the automation of the cooling flow channel structure size design and optimization process, improves the optimization efficiency, and ensures the reliability of the optimization results.

An air-cooled battery cooling system is provided, including:

A cooling flow channel, the cooling flow channel includes:

The main flow channel, one end of the main flow channel has an air inlet, and the other end of the main channel away from the air inlet is provided with a flow guide portion, the flow guide portion is wedge-shaped, and the flow guide portion includes a first slope and a second Two inclined surfaces, the first inclined surface and the second inclined surface extend along the length direction of the main channel and have an included angle;

A plurality of branch flow channels, the plurality of branch flow channels are arranged in parallel on both sides of the main flow channel at uniform intervals, the branch flow channels include a branch air inlet and a branch air outlet, and the plurality of branch air inlets are all connected to the main flow. road;

A plurality of battery cells, the plurality of battery cells are respectively arranged on both sides of the main channel, and the battery cores are attached to the branch channel.

As an exemplary structure of the present application, the included angle is not greater than 30°.

As an exemplary structure of the present application, the length of the flow guide portion is not greater than 70% of the length of the main channel.

As an exemplary structure of the present application, it further includes two air outlet channels, the two air outlet channels are respectively disposed on both sides of the main channel, and the plurality of branch air outlets are all connected to the air outlet channels , and one end of the air outlet channel has an air outlet.

As an exemplary structure of the present application, it further includes a cooling fan and an air inlet channel, one end of the air inlet channel is connected to the cooling fan, and the other end of the air inlet channel away from the cooling fan is connected to the air inlet .

As an exemplary structure of the present application, the first inclined plane and the second inclined plane are symmetrical to the central axis of the main flow channel.

As an exemplary structure of the present application, the first inclined surface and the second inclined surface are both flat surfaces.

A cooling channel design method is also provided, which is applied to design the above air-cooled battery cooling system, including:

Step S1, setting the target value of the parameter to be optimized of the cooling flow channel, the parameter to be optimized includes the flow mean square error and the flow resistance of a plurality of branch flow channels, the target value of the flow mean square error is χ, the flow resistance The target value is P;

Step S2, designing the air guide portion, and selecting the design dimensions X1, X2, X3... of the air guide portion, X1, X2, X3... as the designated initial values;

Step S3, generating the digital-analog S0 of the cooling channel according to X1, X2, X3...;

Step S4, using the digital model S0 to perform computational fluid dynamics simulation, and the calculation program is Y0;

Step S5, according to the calculation result of the computational fluid dynamics simulation, extract the flow M1, M2, ... and flow resistance P0 of the plurality of branch flow channels, and use M1, M2, ... to calculate the flow mean square error χ0 of the cooling flow channel ;

Step S6, judge whether χ0, P0 are equal to χ, P, if χ0, P0 are equal to χ, P, end the calculation, at this time X1, X2, X3... are the design dimensions of the guide portion; if χ0, P0 are not equal to χ, P, pass χ0 and P0 to the optimization algorithm;

Step S7, calculate X1', X2', X3'... based on χ0, P0 and X1, X2, X3... through an optimization algorithm;

Step S8, using X1', X2', X3'... and repeating steps S3-S7 until χn, Pn are equal to the target values χ, P, at this time, X1 ⁿ , X2 ⁿ , X3 ⁿ . design size.

As an exemplary technical solution of the present application, in the step S2, it includes: X1, X2, X3 and X4, wherein X1 is the length of the air guide portion, and X2 is the width of the end of the air guide portion .

As an exemplary technical solution of the present application, the step S2 further includes: selecting a control point on the first inclined plane or the second inclined plane, and the length between the control point and the end of the diversion portion is X3 , the width of the guide portion at the control point is X4.

Description of drawings

1 is a schematic structural diagram of an air-cooled battery cooling system provided in Embodiment 1 of the present application;

2 is a top view of the structure of the air-cooled battery cooling system provided in Embodiment 1 of the present application;

3 is a flowchart of a cooling flow channel design method provided in Embodiment 2 of the present application;

4 is a schematic structural diagram of a cooling flow channel provided in Embodiment 2 of the present application;

5 is a schematic structural diagram of a flow guide provided in Embodiment 2 of the present application;

6 is a schematic structural diagram of a cooling flow channel design device provided by an embodiment of the present application;

FIG. 7 is a schematic structural diagram of a device provided by an embodiment of the present application.

In the picture:

1. Cooling channel; 11. Main channel; 111. Air inlet; 12. Air guide; 121. First slope; 122. Second slope; 123. Included angle;

2. Cells;

3. Air outlet channel; 31. Air outlet;

4. Cooling fan;

5. Air inlet channel.

Detailed ways

The present application will be described below with reference to the accompanying drawings and embodiments. The embodiments described here are only used to explain the present application, but not to limit the present application. For convenience of description, the drawings only show some but not all structures related to the present application.

In the description of this application, unless otherwise specified and limited, the terms "connected", "connected" and "fixed" should be understood in a broad sense, for example, it may be a fixed connection, a detachable connection, or an integral body; It can be a mechanical connection or an electrical connection; it can be a direct connection or an indirect connection through an intermediate medium, and it can be the internal connection of two elements or the interaction relationship between the two elements. The meanings of the above terms in this application can be understood according to actual situations.

In this application, unless otherwise specified and limited, a first feature "on" or "under" a second feature may include direct contact between the first feature and the second feature, or may include the first feature and the second feature Not directly but through additional features between them. Also, the first feature being "above", "over" and "above" the second feature includes the first feature being directly above and obliquely above the second feature, or simply means that the first feature is level higher than the second feature. The first feature is "below", "below" and "below" the second feature includes the first feature being directly below and diagonally below the second feature, or simply means that the first feature has a lower level than the second feature.

In the description of this embodiment, the terms "up", "down", "left", "right" and other azimuth or positional relationships are based on the azimuth or positional relationship shown in the accompanying drawings, which are only for the convenience of description and simplifying operations. Rather than indicating or implying that the referred device or element must have a particular orientation, be constructed and operate in a particular orientation, it should not be construed as a limitation on the application. In addition, the terms "first" and "second" are only used for distinction in description, and have no special meaning.

Example 1

As shown in FIG. 1 and FIG. 2 , an embodiment of the present application provides an air-cooled battery cooling system, including a cooling channel 1 and a plurality of battery cells 2 . The cooling channel 1 includes a main channel 11 and a plurality of branch channels 13; one end of the main channel 11 has an air inlet 111, and the other end of the main channel 11 away from the air inlet 111 is provided with a flow guide 12, and the flow guide 12 is wedge-shaped, The diversion portion 12 includes a first inclined surface 121 and a second inclined surface 122. The first inclined surface 121 and the second inclined surface 122 extend along the length direction of the main channel 11 and have an included angle 123; the plurality of branch channels 13 are arranged side by side at an even interval. On both sides of the main flow channel 11 , the branch flow channels 13 include branch air inlets and branch air outlets, and the plurality of branch air inlets are all connected to the main flow channel 11 . The plurality of cells 2 are respectively disposed on both sides of the main flow channel 11 , and the cells 2 are attached to the branch flow channels 13 . The cooling air enters the main flow channel 11 from the air inlet 111. Since the main flow channel 11 is provided with a diversion portion 12, under the diversion of the first inclined surface 121 and the second inclined surface 122, the air flow of the end of the main flow channel 11 away from the air inlet 111 is increased. The flow rate of the cooling medium is increased, the flow rate drop at both ends of the partial branch flow channels 13 located at this end is increased, and the pressure difference between the branch air inlets and the branch air outlets of the multiple branch flow channels 13 is adjusted, so that the multiple branch flow channels in the main flow channel 11 The flow rate of the channel 13 is uniform, reducing the temperature difference between the battery cells 2 and prolonging the life of the battery.

The included angle 123 is not greater than 30°. The length of the guide portion 12 is not greater than 70% of the length of the main channel 11 . The size of the included angle 123 and the length of the guide portion 12 affect the flow guide effect of the air-cooled battery cooling system. After optimization calculation and analysis, when the included angle 123 is not greater than 30°, the length of the guide portion 12 is not greater than the length of the main channel 11 When it is 70%, a better diversion effect can be achieved, so that the flow distribution of the plurality of branch flow channels 13 is uniform, and the flow resistance is smaller.

The air-cooled battery cooling system also includes two air outlet channels 3, a cooling fan 4 and an air inlet channel 5. The two air outlet channels 3 are respectively arranged on both sides of the main channel 11, and the branch air outlets of the plurality of branch channels 13 are all The air outlet channel 3 is communicated with, and one end of the air outlet channel 3 has an air outlet 31 . As shown in FIG. 2 , the arrow in the figure indicates the flow direction of the cooling medium. One end of the air inlet channel 5 is connected to the cooling fan 4 , and the other end of the air inlet channel 5 away from the cooling fan 4 is connected to the air inlet 111 . The cooling fan 4 is used to provide a cooling medium, and the cold air enters the main channel 11 from the air inlet channel 5 through the air inlet 111, and is guided by the diversion part 12 to distribute the flow evenly among the plurality of branch channels 13, reducing the number of The temperature difference between the cells 2 takes away the heat generated by the cells 2.

The first inclined surface 121 and the second inclined surface 122 are symmetrical to the central axis of the main channel 11 , so that the cooling medium flow rates of the plurality of branch channels 13 on both sides of the main channel 11 can be uniform.

The first inclined surface 121 and the second inclined surface 122 are both flat surfaces. After optimization calculation and analysis, compared with the curved surface, the first inclined surface 121 and the second inclined surface 122 of the plane can achieve better flow guiding effect.

Embodiment 2

As shown in FIGS. 3-5 , an embodiment of the present application provides a cooling channel design method, which is applied to design the air-cooled battery cooling system in Embodiment 1, and includes the following steps.

Step S1, set the target value of the parameter to be optimized of the cooling channel 1, the parameter to be optimized includes the flow mean square error and the flow resistance of the plurality of branch flow channels 13, the target value of the flow mean square error is χ, and the target value of the flow resistance is χ. P. Wherein, the value of χ represents the flow uniformity of the plurality of branch flow channels 13 of the cooling flow channel 1 .

Step S2 , designing the air guide portion 12 , and selecting the design dimensions X1 , X2 , X3 . . . of the air guide portion 12 , and X1 , X2 , X3 . In this step, the initial values of X1, X2, X3 . . . are designated by the designer according to experience.

In step S3, the cooling channel 1 is designed according to X1, X2, X3 . . . to generate a digital model S0 (Three-dimensional (3D) structural design).

Step S4, using the digital model S0 to perform computational fluid dynamics simulation (Computational Fluid Dynamics (CFD) calculation).

Step S5, according to the computational fluid dynamics simulation results, extract the flow rates M1, M2, .

Step S6, judge whether χ0, P0 are equal to χ, P, if χ0, P0 are equal to χ, P, end the calculation, at this time X1, X2, X3... are the design dimensions of the diversion part 12; if χ0, P0 are not equal to χ , P, pass χ0 and P0 to the optimization algorithm. In this step, the optimization algorithm includes but is not limited to a genetic algorithm.

Step S7, the optimization algorithm calculates X1', X2', X3'... based on χ0, P0 and X1, X2, X3....

Step S8, using X1', X2', X3'... and repeating steps S3-S7 until χn, Pn are equal to the target values χ, P, at this time, X1 ⁿ , X2 ⁿ , X3 ⁿ . . . are the guide portion 12 design size.

The cooling flow channel design method of this embodiment combines optimization algorithm, CFD simulation analysis and 3D structure design, realizes the structural dimension design of cooling flow channel 1 and the automation of the optimization process, improves optimization efficiency, and ensures the reliability of optimization results.

In the embodiment of the present application, in step S2 , the selected design dimensions of the air guide portion 12 include X1 , X2 , X3 and X4 , where X1 is the length of the air guide portion 12 , and X2 is the width of the end of the air guide portion 12 . Through X1 and X2, the included angle 123 of the air guide portion 12 can be determined.

In step S2, the embodiment of the present application further includes: selecting a control point 1211 on the first inclined plane 121 or the second inclined plane 122, the length between the control point 1211 and the end of the guide portion 12 is X3, and the guide portion 12 is in the control The width at point 1211 is X4. As shown in FIG. 5 , by selecting the control point 1211 , the shapes of the first inclined surface 121 and the second inclined surface 122 of the flow guide portion 12 can be calculated and analyzed. In the embodiment of the present application, after calculation, when the first inclined surface 121 and the second inclined surface 122 are planes, the flow guiding effect of the flow guiding portion 12 is better.

In the air-cooled battery cooling system and the cooling channel design method provided by the present application, the air-cooled battery cooling system is provided with a wedge-shaped guide portion 12 at one end of the main channel 11 away from the air inlet 111 , and the guide portion 12 has a first slope. 121 and the second inclined surface 122, improve the cooling medium flow rate at one end of the main channel 11 away from the air inlet 111, increase the flow rate drop of some branch flow channels 13 located at this end, and adjust the branch air inlets and branch outlets of the plurality of branch flow channels 13. The pressure difference between the tuyere makes the flow of the multiple branch channels 13 in the main channel 11 uniform, reducing the temperature difference between the cells 2 and prolonging the life of the battery; the cooling channel design method will be optimized algorithm, CFD simulation analysis Combined with 3D structural design, the structural size design of the cooling flow channel and the automation of the optimization process are realized, the optimization efficiency is improved, and the reliability of the optimization results is guaranteed.

FIG. 6 shows a schematic structural diagram of a cooling channel design device provided by an embodiment of the present application. The embodiment of the present application can be applied to the design of a cooling channel, and the above-mentioned implementation can be realized by the cooling channel design device provided by the present application. The cooling runner design method provided by the example.

As shown in FIG. 6 , the cooling channel design device in the embodiment of the present application includes the following modules.

The target value setting module 610 is set to set the target value of the parameter to be optimized of the cooling channel, the parameter to be optimized includes the flow mean square error and the flow resistance of the plurality of branch flow channels, and the target value of the flow mean square error is χ, the target value of the flow resistance is P;

The air guide portion design module 620 is set to design the air guide portion, and selects the design dimensions X1, X2, X3, . . . of the air guide portion as the designated initial values;

The digital-analog generating module 630 is configured to generate the digital-analog S0 of the cooling flow channel according to X1, X2, X3...;

The simulation module 640 is configured to use the digital model S0 to perform computational fluid dynamics simulation, and the calculation program is Y0;

The flow mean square error calculation module 650 is configured to extract the flow rates M1, M2, . The mean square error of the flow of the channel χ0;

The judgment module 660 is set to judge whether χ0, P0 are equal to χ, P, if χ0, P0 are equal to χ, P, end the calculation, at this time X1, X2, X3... are the design dimensions of the diversion portion; if χ0, P0 is not equal to χ, P, pass χ0 and P0 to the optimization algorithm;

The calculation module 670 is configured to calculate X1', X2', X3'... based on χ0, P0 and X1, X2, X3... through an optimization algorithm;

The determination module 680 is set to use X1', X2', X3'... to repeatedly execute the digital-analog generation module to the calculation module until χn, Pn are equal to the target values χ, P, at this time, X1 ⁿ , X2 ⁿ , X3 ⁿ . . . That is, the design size of the guide portion.

The design module of the air guide includes X1, X2, X3 and X4, wherein X1 is the length of the air guide, and X2 is the width of the end of the air guide.

The design module of the air guide portion further includes: selecting a control point on the first inclined plane or the second inclined plane, the length between the control point and the end of the air guide portion is X3, and the air guide portion is located on the The width at the control point is X4.

The cooling channel design device provided by the embodiment of the present application belongs to the same concept as the cooling channel design method provided by the above-mentioned embodiment. It has the same effect as the above-mentioned embodiment.

FIG. 7 is a schematic structural diagram of a device provided by the application. As shown in FIG. 7 , the device includes a processor 70, a memory 71, an input device 72 and an output device 73; the number of processors 70 in the device may be one or more 7, a processor 70 is used as an example; the processor 70, memory 71, input device 72, and output device 73 in the device can be connected by a bus or other means, and the connection by a bus is taken as an example in FIG. 7.

As a computer-readable storage medium, the memory 71 can be used to store software programs, computer-executable programs, and modules, such as program instructions/modules corresponding to the cooling flow channel design method in the embodiments of the present application. The processor 70 executes various functional applications and data processing of the device by running the software programs, instructions and modules stored in the memory 71 , that is, to implement the above-mentioned method.

The memory 71 may include a storage program area and a storage data area, wherein the storage program area may store an operating system, an application program required for at least one function; the storage data area may store data created according to use of the terminal, and the like. In addition, the memory 71 may include high-speed random access memory, and may also include non-volatile memory, such as at least one magnetic disk storage device, flash memory device, or other non-volatile solid-state storage device. In some instances, memory 71 may include memory located remotely from processor 70, which may be connected to the device through a network. Examples of such networks include, but are not limited to, the Internet, an intranet, a local area network, a mobile communication network, and combinations thereof.

The input device 72 may be configured to receive input information, etc., and to generate signal input related to user settings and functional control of the device. The output device 73 may include a display device such as a display screen.

Embodiments of the present application further provide a storage medium containing computer-executable instructions, when the computer-executable instructions are executed by a computer processor for executing a cooling flow channel design method, including:

A storage medium containing computer-executable instructions provided by the embodiments of the present application, the computer-executable instructions are not limited to the above-mentioned method operations, and can also execute the related cooling flow channel design methods provided by any embodiment of the present application. operate. The storage medium may be a non-transitory storage medium.

Through the above description of the embodiments, the present application can be implemented by software and necessary general-purpose hardware, and can also be implemented by hardware. The present application can be embodied in the form of a software product, and the computer software product can be stored in a computer-readable storage medium, such as a floppy disk of a computer, a read-only memory (Read-Only Memory, ROM), a random access memory (Random Access Memory) , RAM), flash memory (FLASH), hard disk or optical disk, etc., including multiple instructions to make a computer device (which may be a personal computer, a server, or a network device, etc.) execute the methods described in the various embodiments of the present application.

In the embodiment of the above device, the multiple units and modules included are only divided according to the functional logic, but are not limited to the above-mentioned division, as long as the corresponding functions can be realized; in addition, the names of the multiple functional units are also It is only for the convenience of distinguishing from each other, and is not intended to limit the protection scope of the present application.

Claims

An air-cooled battery cooling system includes:

a cooling flow channel (1), the cooling flow channel (1) includes: a main flow channel (11) and a plurality of branch flow channels (13);

One end of the main channel (11) is provided with an air inlet (111), and the other end of the main channel (11) away from the air inlet (111) is provided with a flow guide (12), and the flow guide (12) ) is wedge-shaped, and the guide portion (12) includes a first inclined surface (121) and a second inclined surface (122), the first inclined surface (121) and the second inclined surface (122) along the main channel ( 11) extending in the length direction, and there is an included angle (123) between the first inclined surface (121) and the second inclined surface (122);

The plurality of branch flow channels (13) are arranged side by side at an even interval on both sides of the main flow channel (11), the branch flow channels (13) include branch air inlets and branch air outlets, and the plurality of branch air inlets are all connected to each other. the main channel (11);

A plurality of electric cells (2), the plurality of electric cells (2) are respectively disposed on both sides of the main flow channel (11), and the electric cells (2) are attached to the branch flow channel (13).
The air-cooled battery cooling system according to claim 1, wherein the included angle (123) is not greater than 30°.
The air-cooled battery cooling system according to claim 1, wherein the length of the guide portion (12) is not greater than 70% of the length of the main channel (11).
The air-cooled battery cooling system according to claim 1, further comprising two air outlet channels (3), the two air outlet channels (3) are respectively disposed on both sides of the main channel (11), the The plurality of branch air outlets are all connected to the air outlet channel (3), and one end of the air outlet channel (3) is provided with an air outlet (31).
The air-cooled battery cooling system according to claim 1, further comprising a cooling fan (4) and an air inlet channel (5), one end of the air inlet channel (5) is connected to the cooling fan (4), and the air inlet channel (5) is connected to the cooling fan (4). The other end of the air flow channel (5) away from the cooling fan (4) communicates with the air inlet (111).
The air-cooled battery cooling system according to claim 1, wherein the first inclined plane (121) and the second inclined plane (122) are symmetrical to the central axis of the main flow channel (11).
The air-cooled battery cooling system according to claim 1, wherein the first inclined surface (121) and the second inclined surface (122) are both flat surfaces.
A cooling channel design method, applied to the design of the air-cooled battery cooling system according to any one of claims 1-7, comprising:

Step S1, setting the target value of the parameter to be optimized of the cooling channel (1), wherein the parameter to be optimized includes the flow mean square error and the flow resistance of the plurality of branch flow channels (13), the target value of the flow mean square error The value is χ, and the target value of the flow resistance is P;

Step S2, designing the air guide portion (12), and selecting the design dimensions X1, X2, X3... of the air guide portion (12), wherein X1, X2, X3... are designated initial values;

Step S3, generating the digital analog S0 of the cooling flow channel (1) according to X1, X2, X3...;

Step S4, using the numerical model S0 to perform computational fluid dynamics simulation, wherein the calculation program is Y0;

Step S5, according to the calculation result of the computational fluid dynamics simulation, extract the flow rates M1, M2, . The flow mean square error χ0 of the flow channel (1);

Step S6, judge whether χ0, and P0 are respectively equal to χ, and P, in the case that χ0, and P0 are respectively equal to χ, and P, end the calculation, and use X1, X2, X3... as described diversion part (12) The design size of χ0, P0 are not equal to χ, P, pass χ0 and P0 to the optimization algorithm;

Step S7, calculate X1', X2', X3'... based on χ0, P0 and X1, X2, X3... through the optimization algorithm;

Step S8, using X1', X2', X3'..., repeating steps S3-S7 until χn, and Pn are equal to the target values χ, and P, respectively, using X1 n , X2 n , X3 n . . . as the diversion Design dimensions of the part (12).
The method according to claim 8, wherein, in the step S2, the design dimensions X1, X2, X3 . . . of the air guide (12) include X1, X2, X3 and X4, wherein The length of the guide portion (12), X2 is the width of the end of the guide portion (12).
The method according to claim 8, wherein in the step S2, it further comprises: selecting a control point (1211) on the first inclined plane (121) or the second inclined plane (122), the control point (1211) The length between it and the end of the guide portion (12) is X3, and the width of the guide portion (12) at the control point (1211) is X4.