Marine hyperbolic efficient rudder and modeling design method thereof

Abstract

The invention relates to the technical field of ships, and discloses a marine hyperbolic efficient rudder which comprises a propeller hub and a hyperbolic rudder body, the hyperbolic rudder body is installed on the propeller hub, the center of the propeller hub is located on the vertical center line of the hyperbolic rudder body, and the hyperbolic rudder body comprises a rudder blade upper end face and a rudder blade lower end face. The rudder blade upper end face and the rudder blade lower end face are the top and the bottom of the hyperbolic rudder respectively, and the edge of the hyperbolic rudder between the rudder blade upper end face and the rudder blade lower end face is an arc which is a part of a hyperbolic curve. According to the hyperbolic efficient rudder for the ship, on the basis that the chord length of the rudder blade is not changed everywhere in the extension direction and the thicknesses of the upper end face and the lower end face of the rudder blade are not changed, the chord length ratio of the thickness of the rudder blade is changed along the extension, the thickness of a rudder middle body close to the center height of a propeller hub is reduced, the weight of the rudder is reduced, and steel is saved; propulsion efficiency under the same navigational speed is improved, appendage resistance of the rudder is reduced, and the requirement for main engine power is lowered.

Description

Technical Field

[0001] The present invention relates to the technical field of ships, and particularly relates to a marine hyperbolic efficient rudder and a modeling design method thereof. Background Art

[0002] A rudder is a marine steering device. The design of a rudder usually gives priority to its impact on the maneuverability of a ship, that is, how to increase the lift-drag ratio to improve the rudder efficiency. In the technical field of marine skills, with the extension of the concept of "high-performance rudder", the design of a rudder not only focuses on the maneuverability of a ship, but also gradually expands to the impact of the rudder on the rapidity of a ship (including ship resistance and ship propulsion efficiency). As a ship appendage, the rudder works in the wake of a propeller and will generate a certain appendage resistance. The interaction results of the rudder, the hull and the propeller determine the rapid performance of the ship during straight navigation. The spatial distribution of the wake field behind the ship's propeller is uneven and has typical three-dimensional flow characteristics. Conventional rudders usually have a certain airfoil profile in the section, and the thickness-chord ratio is fixed along the span. For a single-screw single-rudder ship, its chord line is located in the mid-longitudinal section of the ship. From the perspective of the wake field behind the ship's propeller, this conventional rudder is not the best rapidity design scheme. With the improvement of the design level, in order to maximize the energy-saving potential of ships, many high-performance rudders that are beneficial to improving the rapid performance of ships have been gradually developed. Classified from the design ideas, it includes two aspects: increasing the lift-drag ratio to improve the resistance performance and changing the local flow angle of attack to improve the propulsion efficiency.

[0003] In the prior art, taking the improvement of propulsion efficiency by changing the local flow angle of attack as the main starting point, such as the leading-edge twisted rudder, which twists the leading edge to adapt to the oncoming flow direction, rectifies the wake, suppresses the rotation of the wake, increases the axial induced velocity of the propeller, generates additional thrust, which is equivalent to recovering the rotational kinetic energy of the wake, thereby improving the propulsion efficiency and gradually becoming practical on medium and large ships. Especially large container ships with high speeds and high fuel consumption have generally taken the leading-edge twisted rudder as the main energy-saving measure. Existing patented technologies are based on this. For example, "A Design Method of a Ship Rudder and a Ship Rudder" disclosed in the application number "CN115959256A" proposes to divide the rudder blade into multiple sections along the span direction of the rudder blade, at least one section is an asymmetric section, and the angle of attack of the rudder blade at the position of each section is adjusted according to the oncoming flow angle of attack at the position where each section is located, so that the ship rudder can generate thrust in the forward direction when the hull is moving forward, improving the propulsion efficiency of the ship; "An Upper and Lower Twisted Different Direction Angle of Attack Rudder" disclosed in the application number "KR1020220111365A" proposes to twist the upper body and the lower body of the rudder in different directions to form an angle of attack to improve the propulsion efficiency.

[0004] Generally speaking, the vast majority of the prior art improves the propulsion efficiency of ships from the perspective of changing the local angle of attack of the rudder blade section, but makes relatively large changes to the overall shape and structural form of the rudder, making the rudder shape very complex and unconventional. Summary of the Invention

[0005] The technical problem to be solved by the present invention is that the prior art improves the ship propulsion efficiency by changing the local angle of attack of the rudder blade section, which results in a large change in the overall rudder shape and structure, making the rudder shape very complex and unconventional.

[0006] To solve the above technical problem, the technical solution of the present invention is to provide a marine hyperbolic high-efficiency rudder, including a hub and a hyperbolic rudder. The hyperbolic rudder is installed on the hub, and the center of the hub is located on the vertical center line of the hyperbolic rudder. The hyperbolic rudder includes an upper rudder blade surface and a lower rudder blade surface. The upper rudder blade surface and the lower rudder blade surface are respectively the top and bottom of the hyperbolic rudder. The edge of the hyperbolic rudder between the two is an arc that is a part of a hyperbola. Above the minimum thickness of the two side edges of the hyperbolic rudder are the upper half branches of the port side and starboard side of the hyperbolic rudder, and below the minimum thickness are the lower half branches of the port side and starboard side of the hyperbolic rudder.

[0007] Optionally, the minimum thickness of the two side edges of the hyperbolic rudder is located above the center of the hub.

[0008] Optionally, a false rudder is connected to the upper rudder blade surface.

[0009] Optionally, both the upper rudder blade surface and the lower rudder blade surface are symmetric about the vertical center line of the hyperbolic rudder.

[0010] A modeling design method for a marine hyperbolic high-efficiency rudder includes the following steps:

[0011] S1. Define the height of the upper and lower rudder blade surfaces and the rudder blade thickness;

[0012] S2. Define the minimum value of the maximum thickness of the hyperbolic rudder along the span direction and the position where the minimum value appears;

[0013] S3. Calculate the thickness distribution of the rudder blade of the port and starboard parts of the hyperbolic rudder along the span direction;

[0014] S4. Calculate the thickness distribution of a conventional rudder with an equal thickness chord ratio along the span direction;

[0015] S5. According to the thickness ratio at the same height of the hyperbolic rudder and the conventional rudder, perform one-way scaling modeling on the conventional rudder in the lateral direction;

[0016] S6. Obtain the geometric model of the hyperbolic rudder.

[0017] Optionally, in step S1, define endpoints A, B on the upper rudder blade surface and endpoints D, C on the lower rudder blade surface of the hyperbolic rudder, and set the thickness of the upper rudder blade surface, i.e., the length of line segment AB, as the rudder blade thickness t U; The height from the upper end face of the rudder blade to the center of the propeller hub is H U ; The thickness of the lower end face of the rudder blade, i.e., the length of line segment CD, is the thickness t of the rudder blade L ; The height from the lower end face of the rudder blade to the center of the propeller hub is H L .

[0018] Optionally, what is enclosed by line segment AB, line segment BC, line segment CD, and line segment DA is a conventional rudder

[0019] Optionally, in step S2, the endpoints E and F are defined as the vertices of the hyperbolas on both sides of the hyperbolic rudder, and the length of line segment EF is the minimum value of the maximum thickness of the hyperbolic rudder in the spanwise direction

[0020] Optionally, in step S3, the calculation method for the thickness distribution of the rudder blade of the left and right sides of the hyperbolic rudder along the spanwise direction is as follows

[0021] S31. Set the vertical height from the hyperbola vertices E and F to the center of the propeller hub as H 0 (-H L / 3 < H 0 < H U / 3), and the thickness of the rudder blade of the conventional rudder at the heights of the hyperbola vertices E and F is t M ;

[0022] S32. Set the thickness reduction ratio of the left side of the hyperbolic rudder at vertex E compared to the conventional rudder as R 1 (0 < R 1 ≤ 2 / 3); the thickness reduction ratio of the right side of the hyperbolic rudder at vertex F compared to the conventional rudder is R 2 (0 < R 2 ≤ 2 / 3);

[0023] S33. Calibrate the coordinates of each endpoint and vertex. Endpoint A: (-t U / 2, H U ); Endpoint B: (t U / 2, H U ); Endpoint C: (t L / 2, -H L ); Endpoint D: (-t L / 2, -H L ); Vertex E: (-(1 - R 1 )t M / 2, H 0 ); Vertex F: ((1 - R 2 )t M / 2, H 0 );

[0024] S34. Obtain the function equations of the upper half branch of the starboard side of the hyperbolic rudder, the upper half branch of the port side of the hyperbolic rudder, the lower half branch of the port side of the hyperbolic rudder, and the lower half branch of the starboard side of the hyperbolic rudder based on the coordinates of each endpoint and vertex:

[0025] Upper half branch of the port side of the hyperbolic rudder:

[0026]

[0027] Where,

[0028]

[0029] c 21 = H 0

[0030] Upper half branch of the starboard side of the hyperbolic rudder:

[0031]

[0032] Where,

[0033]

[0034]

[0035] Lower half branch of the port side of the hyperbolic rudder:

[0036]

[0037] Where,

[0038]

[0039] c 23 = H 0

[0040] Lower half branch of the starboard side of the hyperbolic rudder:

[0041]

[0042] Where,

[0043]

[0044] c 24 = H 0 ;

[0045] S35. Calculate the thickness distribution along the span direction of the port and starboard parts of the rudder blade according to the above function equations:

[0046] Arc BC:

[0047]

[0048] Arc DA:

[0049]

[0050] Optionally, in step S5, according to the thicknesses of the hyperbolic rudder and the conventional rudder at the same height along the span direction, the ratio of the thickness of the hyperbolic rudder to the thickness of the conventional rudder at the same height along the span direction is calculated. Then, while keeping the chord length of the rudder blade at each height of the conventional rudder unchanged, the conventional rudder is scaled unidirectionally in the y direction according to the thickness ratio, so as to complete the modeling of the entire hyperbolic rudder.

[0051] In summary, the marine hyperbolic high-efficiency rudder designed by the present invention has the same side shape as the conventional rudder, and is obtained by changing the thicknesses at different heights along the span direction of the conventional rudder. On the basis of ensuring that the chord length of the rudder blade remains unchanged along the span direction and the thicknesses of the upper and lower end faces of the rudder blade remain unchanged, the thickness-chord ratio of the rudder blade changes along the span, and the thickness-chord ratio and the section height satisfy a hyperbolic function relationship, so that the thickness of the middle body of the rudder near the hub center height is reduced, the weight of the rudder is reduced, steel is saved, the propulsion efficiency at the same ship speed is improved, the appendage resistance of the rudder is reduced, and the demand for the main engine power is reduced. Description of the Drawings

[0052] Figure 1 It is a schematic diagram of the overall layout of the hyperbolic rudder of the present invention;

[0053] Figure 2 It is a schematic diagram of the modeling process of the hyperbolic rudder of the present invention;

[0054] Figure 3 It is a schematic diagram of the geometric model of the ship-borne conventional rudder;

[0055] Figure 4 It is a schematic diagram of the geometric model of the ship-borne hyperbolic rudder of the present invention;

[0056] In the figure: 11, false rudder; 14, upper end face of the rudder blade; 15, lower end face of the rudder blade; 21, upper half branch of the left side of the hyperbolic rudder; 22, upper half branch of the right side of the hyperbolic rudder; 23, lower half branch of the left side of the hyperbolic rudder; 24, lower half branch of the right side of the hyperbolic rudder; 3, propeller hub. Detailed Embodiment

[0057] The following is a further detailed description of the present invention in conjunction with Figures 1-4 to the present invention.

[0058] The present invention discloses a marine hyperbolic high-efficiency rudder. Starting from the perspective of changing the thickness-chord ratio of the rudder, without changing the angle of attack of each section of the rudder blade, but changing the thickness distribution of the rudder along the span direction, the propulsion efficiency is improved by minimizing the modification of the rudder shape, while ensuring that the rudder area remains unchanged, reducing the impact on the maneuvering performance, and reducing the overall weight of the rudder. Refer to Figure 1, including a hub 3 and a hyperbolic rudder. The hyperbolic rudder is installed on the hub 3, and the center of the hub 3 is located on the vertical center line of the hyperbolic rudder. The hyperbolic rudder includes an upper rudder face 14 and a lower rudder face 15. The upper rudder face 14 and the lower rudder face 15 are respectively the top and bottom of the hyperbolic rudder. The edge of the hyperbolic rudder between the two is an arc that is a part of a hyperbola. Above the minimum thickness of both sides of the hyperbolic rudder are the upper half branches 21 of the port side and 22 of the starboard side of the hyperbolic rudder, and below the minimum thickness are the lower half branches 23 of the port side and 24 of the starboard side of the hyperbolic rudder; the minimum thickness of both sides of the hyperbolic rudder is located above the center of the hub 3; a false rudder 11 is connected to the upper rudder face 14; both the upper rudder face 14 and the lower rudder face 15 are symmetric about the vertical center line of the hyperbolic rudder.

[0059] The present invention also discloses a modeling design method for a marine hyperbolic high-efficiency rudder, referring to Figure 2 , including the following steps:

[0060] S1. Define the height of the upper and lower rudder faces of the rudder blade and the thickness of the rudder blade;

[0061] Specifically, define endpoints A, B on the upper rudder face 14 of the hyperbolic rudder and endpoints D, C on the lower rudder face 15, and set the thickness of the upper rudder face 14, that is, the length of line segment AB, as the rudder blade thickness t U ; the height from the upper rudder face 14 to the center of the hub 3 is H U ; the thickness of the lower rudder face 15, that is, the length of line segment CD, is the rudder blade thickness t L ; the height from the lower rudder face 15 to the center of the hub 3 is H L , and the figure enclosed by line segment AB, line segment BC, line segment CD, and line segment DA is a conventional rudder;

[0062] S2. Define the minimum value of the maximum thickness of the hyperbolic rudder along the span direction and the position where the minimum value appears;

[0063] Specifically, define endpoints E and F as the vertices of the hyperbola on both sides of the hyperbolic rudder, and the length of line segment EF is the minimum value of the maximum thickness of the hyperbolic rudder along the span direction;

[0064] S3. Calculate the thickness distribution of the rudder blade parts on the port and starboard sides of the hyperbolic rudder along the span direction;

[0065] S31. Set the vertical height from the hyperbola vertices E, F to the center of the hub 3 as (H 0 -H L / 3 < H 0 < H U / 3), and the thickness of the conventional rudder blade at the height of the hyperbola vertices E, F is t M ;

[0066] S32. Set the thickness reduction ratio of the left - hand side part of the hyperbolic rudder at the vertex E compared to the conventional rudder as R 1 (0 < R 1 ≤ 2 / 3); Set the thickness reduction ratio of the right - hand side part of the hyperbolic rudder at the vertex F compared to the conventional rudder as R 2 (0 < R 2 ≤ 2 / 3);

[0067] S33. Refer to Figure 1 , taking the center of the propeller hub 3 as the origin, establish a coordinate system, with the upward direction as the positive y - axis direction and the right - hand direction as the positive x - axis direction, and mark the coordinates of each endpoint and vertex. Endpoint A: (-t U / 2, H U ); Endpoint B: (t U / 2, H U ); Endpoint C: (t L / 2, -H L ); Endpoint D: (-t L / 2, -H L ); Vertex E: (-(1 - R 1 )t M / 2, H 0 ); Vertex F: ((1 - R 2 )t M / 2, H 0 ), where point A and point B are symmetric about the mid - longitudinal plane of the hull (i.e., symmetric about the y - axis), and point C and point D are symmetric about the mid - longitudinal plane of the hull (i.e., symmetric about the y - axis);

[0068] S34. Obtain the function equations of the upper - half branch 21 (arc AE) of the left - hand side of the hyperbolic rudder, the upper - half branch 22 (arc BF) of the right - hand side of the hyperbolic rudder, the lower - half branch 23 (arc DE) of the left - hand side of the hyperbolic rudder, and the lower - half branch 24 (arc CF) of the right - hand side of the hyperbolic rudder according to the coordinates of each endpoint and vertex:

[0069] The upper - half branch 21 of the left - hand side of the hyperbolic rudder:

[0070]

[0071] Among them,

[0072]

[0073] c 21 = H 0

[0074] The upper - half branch 22 of the right - hand side of the hyperbolic rudder:

[0075]

[0076] Among them,

[0077]

[0078] c 22 = H 0

[0079] Lower half branch 23 of the hyperbolic rudder on the port side:

[0080]

[0081] Wherein,

[0082]

[0083] c 23 = H 0

[0084] Lower half branch 24 of the hyperbolic rudder on the starboard side:

[0085]

[0086] Wherein,

[0087]

[0088] c 24 = H 0 ;

[0089] S35. Calculate the thickness distribution along the span direction of the rudder blades on the port and starboard sides according to the above function equation:

[0090] Arc BC:

[0091]

[0092] Arc DA:

[0093]

[0094] S4. Calculate the thickness distribution along the span direction of a conventional rudder with a constant thickness-chord ratio:

[0095] It is known that the chord length distribution of the rudder blade of a conventional rudder along the span direction is C = f(z), where z represents the span direction (from top to bottom). It is known that the thickness-chord ratio of a conventional rudder is a constant K = t / C = constant. Multiply the two formulas to obtain the thickness distribution along the span direction of a conventional rudder with a constant thickness-chord ratio: t = f(z) × k;

[0096] S5. Perform one-way scaling modeling in the lateral direction on the conventional rudder according to the thickness ratio at the same height of the hyperbolic rudder and the conventional rudder;

[0097] Specifically, based on the thickness distribution along the span direction of the port and starboard rudder blades obtained in steps S3 and S4 and the thickness distribution along the span direction of a conventional rudder with a constant thickness chord ratio, the thicknesses of the hyperbolic rudder and the conventional rudder at the same height along the span direction are calculated. The ratio of the thickness of the hyperbolic rudder to the thickness of the conventional rudder along the span direction at the same height is calculated. Then, while keeping the chord length of the rudder blade at each height of the conventional rudder unchanged, the conventional rudder is scaled unidirectionally in the y direction according to the thickness ratio, thereby completing the modeling of the entire hyperbolic rudder;

[0098] S6. Obtain the geometric model of the hyperbolic rudder.

[0099] Embodiment

[0100] Refer to Figure 3 and Figure 4 In this embodiment, the present invention will be specifically described. The hyperbolic high-efficiency rudder and the conventional rudder of the present invention are respectively installed on a certain type of gas ship. The dummy rudder 11 parts of the two rudders are exactly the same, and the upper end face 14 and the lower end face 15 of the rudder blade completely coincide. The thickness of the hyperbolic rudder is reduced at the height of the propeller axis.

[0101] The CFD viscous flow numerical calculation method is used to conduct a comparative calculation of the rapid performance of the ship at the designed draft and designed speed. The calculation adopts the model scale volume force self-propulsion calculation method recognized in the industry, and the actual ship rapid performance is obtained through reasonable conversion methods. When comparing the two rudders, it is ensured that the calculation grids, parameters, and settings are all the same; when predicting the actual ship performance of the two rudders, it is ensured that the conversion processes, methods, and coefficients are all the same.

[0102] Table 1 is a comparison of the predicted results of the actual ship rapid performance with the two rudders:

[0103] Table 1 Analysis of the energy-saving effect of the implementation case

[0104] Draft Speed Propulsion efficiency Effective power Received power Conventional rudder 9.5m 16.5 kn 0.747 8195.6 kW 10976.8 kW Hyperbolic rudder 9.5m 16.5 kn 0.760 8173.4 kW 10759.7 kW Relative comparison / / +1.7％ -0.3％ -2.0％

[0105] As can be seen from the table, compared with the conventional rudder, the hyperbolic rudder has a 1.7% increase in propulsion efficiency and a 2% reduction in received power, with a significant energy-saving effect.

[0106] It should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and not to limit them. Although the present invention has been described in detail with reference to the preferred embodiments, those of ordinary skill in the art should understand that the technical solutions of the present invention can be modified or equivalently replaced without departing from the spirit and scope of the technical solutions of the present invention, and they should all be covered within the scope of the claims of the present invention.

Claims

1. A hyperbolic high-efficiency rudder for a ship, characterized in that: It includes a hub (3) and a hyperbolic rudder. The hyperbolic rudder is installed on the hub (3). The center of the hub (3) is located on the vertical center line of the hyperbolic rudder. The hyperbolic rudder includes an upper end face (14) of the rudder blade and a lower end face (15) of the rudder blade. The upper end face (14) and the lower end face (15) of the rudder blade are respectively the top and bottom of the hyperbolic rudder. The edge of the hyperbolic rudder between the two is an arc that is a part of a hyperbola. Above the minimum thickness of both sides of the hyperbolic rudder is the upper half branch (21) of the port side of the hyperbolic rudder and the upper half branch (22) of the starboard side of the hyperbolic rudder. Below the minimum thickness is the lower half branch (23) of the port side of the hyperbolic rudder and the lower half branch (24) of the starboard side of the hyperbolic rudder.

2. The ship-use hyperbolic high-efficiency rudder according to claim 1, characterized in that: The minimum thickness of both sides of the hyperbolic rudder is located above the center of the hub (3).

3. The ship-use hyperbolic high-efficiency rudder according to claim 1, characterized in that: A false rudder (11) is connected to the upper end face (14) of the rudder blade.

4. The ship-use hyperbolic high-efficiency rudder according to claim 1, characterized in that: Both the upper end face (14) and the lower end face (15) of the rudder blade are symmetric about the vertical center line of the hyperbolic rudder.

5. A modeling and design method for a hyperbolic high-efficiency rudder for a ship, characterized in that: It includes the following steps: S1. Define the height of the upper end face and the lower end face of the rudder blade and the thickness of the rudder blade. S2. Define the minimum value of the maximum thickness of the hyperbolic rudder along the span direction and the position where the minimum value appears. S3. Calculate the thickness distribution of the rudder blade of the port side and the starboard side of the hyperbolic rudder along the span direction. S4. Calculate the thickness distribution of a conventional rudder with a constant thickness chord ratio along the span direction. S5. According to the thickness ratio at the same height of the hyperbolic rudder and the conventional rudder, perform one-way scaling modeling on the conventional rudder in the lateral direction. S6. Obtain the geometric model of the hyperbolic rudder.

6. The modeling and design method of the hyperbolic high-efficiency rudder for a ship according to claim 5, characterized in that: In step S1, end points A, B, D and C are defined on the upper end surface (14) and the lower end surface (15) of the hyperbolic rudder blade, respectively, and the thickness of the upper end surface (14) of the rudder blade, i.e., the length of the line segment AB, is set to be the rudder blade thickness t U The height from the upper end surface (14) of the rudder blade to the center of the hub (3) is H U The thickness of the lower end surface (15) of the rudder blade, i.e. the length of the line segment CD, is the thickness of the rudder blade t L The height from the lower end surface of the rudder blade (15) to the center of the hub (3) is H L .

7. The modeling and design method of the hyperbolic high-efficiency rudder for a ship according to claim 6, characterized in that: What is enclosed by line segment AB, line segment BC, line segment CD, and line segment DA is a conventional rudder.

8. The modeling and design method of the hyperbolic high-efficiency rudder for a ship according to claim 7, characterized in that: In step S2, the vertices of the hyperbola on both sides of the hyperbolic rudder define endpoints E and endpoint F. The length of line segment EF is the minimum value of the maximum thickness of the hyperbolic rudder along the span direction.

9. The modeling and design method of the hyperbolic high-efficiency rudder for a ship according to claim 8, characterized in that: In step S3, the calculation method for the thickness distribution of the rudder blade of the port side and the starboard side of the hyperbolic rudder along the span direction is as follows: S31, set the vertical height from the hyperbola vertices E and F to the center of the hub (3) to H0 (-H L / 3 <H0<H U / 3), the thickness of the conventional rudder blade at the height of the hyperbola apex E and F is t M ; S32. Set the thickness reduction ratio of the port side part of the hyperbolic rudder at vertex E compared to the conventional rudder as R1 (0 < R1 ≤ 2 / 3); the thickness reduction ratio of the starboard side part of the hyperbolic rudder at vertex F compared to the conventional rudder as R2 (0 < R2 ≤ 2 / 3). S33, calibrate the coordinates of each endpoint and vertex, endpoint A: (-t U / 2,H U ); endpoint B: (t U / 2,H U ); endpoint C: (t L / 2,-H L ); endpoint D: (-t L / 2,-H L ); Vertex E: (-(1-R1)t M / 2,H0); Vertex F: ((1-R2)t M / 2,H0); S34. According to the coordinates of each endpoint and vertex, obtain the function equations of the upper half branch (21) of the port side of the hyperbolic rudder, the upper half branch (22) of the starboard side of the hyperbolic rudder, the lower half branch (23) of the port side of the hyperbolic rudder, and the lower half branch (24) of the starboard side of the hyperbolic rudder: The upper half branch (21) of the port side of the hyperbolic rudder: Where, <h2 style=";text-align:left;direction:ltr">c<h2 style=";text-align:left;direction:ltr"> 21 <h2 style=";text-align:left;direction:ltr"> =H0 The upper half branch (22) of the starboard side of the hyperbolic rudder: Where, <h2 style=";text-align:left;direction:ltr">c<h2 style=";text-align:left;direction:ltr"> 22 <h2 style=";text-align:left;direction:ltr"> =H0 The lower half branch (23) of the port side of the hyperbolic rudder: Where, <h2 style=";text-align:left;direction:ltr">c<h2 style=";text-align:left;direction:ltr"> 23 <h2 style=";text-align:left;direction:ltr"> =H0 The lower half branch (24) of the starboard side of the hyperbolic rudder: Where, <h2 style=";text-align:left;direction:ltr">c<h2 style=";text-align:left;direction:ltr"> 24 <h2 style=";text-align:left;direction:ltr"> (H0) S35. According to the above function equations, calculate the thickness distribution of the rudder blade of the port side and the starboard side along the span direction: Arc BC: Arc DA:

10. The modeling and design method of the hyperbolic high-efficiency rudder for a ship according to claim 9, characterized in that: In step S5, the ratio of the thickness of the hyperbolic rudder and the conventional rudder at the same height in the direction of extension is calculated, and then the chord length of the rudder blade at each height of the conventional rudder is kept unchanged, and the conventional rudder is scaled unidirectionally in the y direction according to the thickness ratio, thereby completing the modeling of the entire hyperbolic rudder.

Images