Apparatus and method for estimating maximum allowable compensation angle considering asymmetric rudder torque of twin-screw ships

Abstract

An apparatus and method for estimating the maximum allowable compensation angle considering the asymmetric rudder torque of a twin-shaft vessel are disclosed. The method for estimating the maximum allowable compensation angle considering the asymmetric rudder torque of a twin-shaft vessel includes the steps of: calculating the forward distance and turning diameter according to the initial speed of the target vessel and the synchronized port and starboard rudder angles through a turning simulation of the target vessel; calculating the convergence speed of the target vessel when the target vessel reaches the turning diameter; calculating the time series of rudder torque according to the fixed rudder angle and the compensation rudder angle pre-set on the port and starboard rudder of the target vessel using a pre-set mathematical model; and calculating the maximum allowable compensation angle according to the speed and rudder angle of the target vessel using a mathematical model.

Description

Technology Field

[0001] The present invention relates to an apparatus and method for estimating the maximum allowable compensation angle considering the asymmetric rudder torque of a twin-axis line. Background Technology

[0002] As ships become larger, twin-shaft vessels equipped with two propellers and two rudders are being designed and constructed to enhance operational safety and efficiency. Research has primarily focused on twin-shaft merchant vessels such as 174K-class natural gas carriers (LNGCs) and ultra-large container ships; however, in merchant vessels, it is common practice to control the steering gear and rudder with the same value due to the convenience of design and control. Nevertheless, the port and starboard rudders are sometimes controlled individually in limited cases, such as when it is necessary to evaluate maneuverability or operational safety in the event of a failure of the propellers and rudders of a twin-shaft vessel, when port and starboard rudders are used for roll damping, or when port and starboard propellers and rudders are used for berthing.

[0003] However, during actual ship maneuvering, the hydrodynamic forces acting on the port and starboard rudders are not uniform, as they are influenced by the ship's drift angle, (angular) velocity, and propeller flow. Computational Fluid Dynamics (CFD) has been used to analyze the asymmetry of propeller and rudder behavior in twin-shaft vessels, and the estimated maneuverability performance of twin-shaft vessels considering this asymmetry has been verified by comparing it with model test results. A synchronized control technique for the port and starboard rudders has been proposed to compensate for the asymmetry of rudder forces acting on twin-shaft vessels.

[0004] Recently, while conducting a technical review with a large shipyard regarding the improvement of operational safety and efficiency of twin-shaft vessels, we recognized the possibility of developing an intelligent navigation system that takes into account the asymmetry of hydrodynamic forces acting on the port and starboard rudders. During the sea trials of a 174K-class twin-shaft natural gas carrier, asymmetry of port and starboard rudder torque was observed.

[0005] Figure 1 is a diagram showing an example of asymmetric pressure acting on the port and starboard rudders calculated through computational fluid dynamics analysis.

[0006] As shown in Figure 1, the asymmetry of pressure acting on the rudder was also verified using computational fluid dynamics. When observing the rudder torque indicator during sea trials, a tendency was observed where, during a 35° turn to the port and starboard sides, less rudder torque was measured on the rudder located on the outer side of the turning radius, while more torque was measured on the rudder located on the inner side. It was determined that if the rudder with the lower torque acting according to the direction of the maneuvering motion were additionally controlled, the turning force acting on the vessel could be improved or multilayered. This is similar to how, in vessels equipped with flap rudders, turning force is enhanced or steering is facilitated through combinations of turning forces of various magnitudes by generating additional force through flap control in addition to the force generated through rudder control. Separately from this initial review, a request was received from an overseas shipowner for the advancement of an intelligent navigation system through the non-coupled control of port and starboard rudders on twin-shaft vessels, reaffirming the necessity of related research. Prior art literature

[0007] Korean Patent Publication No. 10-1623097 (May 16, 2016) The problem to be solved

[0008] The present invention aims to provide an apparatus and method for estimating the maximum allowable compensation angle considering the asymmetric rudder torque of a twin-axis line, which estimates the maximum allowable compensation angle considering the asymmetric rudder torque of a twin-axis line using a mathematical model of a twin-axis line considering the asymmetric rudder torque. means of solving the problem

[0009] According to one aspect of the present invention, a method for estimating a maximum allowable compensation angle considering an asymmetric tether torque of a twin-axis line is disclosed, performed by a maximum allowable compensation angle estimation device.

[0010] A method for estimating the maximum allowable compensation angle considering the asymmetric rudder torque of a twin-shaft vessel according to an embodiment of the present invention comprises: a step of calculating a forward distance and a turning diameter according to the initial speed and synchronized port and starboard rudder angles of the target vessel through a turning simulation of the target vessel; a step of calculating the convergence speed of the target vessel when the target vessel reaches the turning diameter; a step of calculating a time series of rudder torque according to a fixed rudder angle and a compensation rudder angle pre-set on the port and starboard rudder of the target vessel using a pre-set mathematical model; and a step of calculating the maximum allowable compensation angle according to the speed and rudder angle of the target vessel using the mathematical model.

[0011] According to another aspect of the present invention, a device for estimating a maximum allowable compensation angle considering asymmetric tether torque of a twin-axis line is disclosed.

[0012] A device for estimating a maximum allowable compensation angle considering asymmetric rudder torque of a twin-shaft vessel according to an embodiment of the present invention comprises a memory for storing instructions and a processor for executing instructions, wherein the instructions perform a method for estimating a maximum allowable compensation angle, comprising the steps of: calculating a forward distance and a turning diameter according to the initial speed and synchronized port and starboard rudder angles of the target vessel through a turning simulation of the target vessel; calculating a convergence speed of the target vessel when the target vessel reaches the turning diameter; calculating a time series of rudder torque according to a fixed rudder angle and a compensation rudder angle pre-set on the port and starboard rudder of the target vessel using a pre-set mathematical model; and calculating a maximum allowable compensation angle according to the speed and rudder angle of the target vessel using the mathematical model. Effects of the invention

[0013] The apparatus and method for estimating the maximum allowable compensation angle considering the asymmetric rudder torque of a twin-axis line according to an embodiment of the present invention can estimate the maximum allowable compensation angle considering the asymmetric rudder torque of a twin-axis line by using a mathematical model of a twin-axis line considering the asymmetric rudder torque. Brief explanation of the drawing

[0014] Figure 1 is a diagram showing an example of asymmetric pressure acting on port and starboard rudders calculated through computational fluid dynamics analysis. FIG. 2 is a diagram showing the definition of an axis system of a mathematical model according to an embodiment of the present invention. FIGS. 3 to 6 are drawings for explaining a mathematical model according to an embodiment of the present invention. FIG. 7 is a flowchart schematically illustrating a method for estimating the maximum allowable compensation angle considering the asymmetric rudder torque of a twin axis, performed by a device for estimating the maximum allowable compensation angle according to an embodiment of the present invention. FIGS. 8 to 12 are drawings for explaining a method for estimating the maximum allowable compensation angle considering the asymmetric tachometer torque of a twin axis according to an embodiment of the present invention of FIG. 7. FIG. 13 is a diagram schematically illustrating the configuration of a maximum allowable compensation angle estimation device considering asymmetric tether torque of a twin-axis line according to an embodiment of the present invention. Specific details for implementing the invention

[0015] As used in this specification, singular expressions include plural expressions unless the context clearly indicates otherwise. In this specification, terms such as "composed" or "comprising" should not be interpreted as necessarily including all of the various components or steps described in the specification, and should be interpreted as meaning that some of the components or steps may be excluded, or that additional components or steps may be included. Furthermore, terms such as "...part," "module," etc., as used in the specification refer to a unit that processes at least one function or operation, which may be implemented in hardware or software, or a combination of hardware and software.

[0016] Hereinafter, various embodiments of the present invention will be described in detail with reference to the attached drawings.

[0017] FIG. 2 is a diagram showing the definition of an axis system of a mathematical model according to an embodiment of the present invention, and FIGS. 3 to 6 are diagrams for explaining a mathematical model according to an embodiment of the present invention. Hereinafter, a mathematical model according to an embodiment of the present invention will be described with reference to FIGS. 2 to 6.

[0018] In the present invention, a 174K-class natural gas carrier is used as the target vessel. The table below shows the main specifications of the hull, propeller, and rudder of the target vessel.

[0019]

[0020] A mathematical model is constructed based on the 3-degrees-of-freedom maneuvering equation to estimate the rudder torque during the maneuvering motion of a 174K-class natural gas carrier. In Fig. 2, x g and y grepresents the vertical and horizontal axes of the Earth-fixed coordinate system, and x and y represent the longitudinal and transverse axes of the hull in the NED-based hull-fixed coordinate system. u, v, and r represent the (angular) velocities of surge, sway, and yaw, respectively, and X, Y, and N represent the forces and moments. δ PORT and δ STBD represents the port and starboard rudder control angles, β represents the drift angle, and ψ represents the heading angle.

[0021] Since the mathematical model derived the equations of maneuvering motion based on the center of gravity, it can be expressed by the following mathematical formula.

[0022]

[0023] Here, represents the (angular) acceleration of fore-and-aft, sway, and bow, m represents the mass of the ship, and I zz represents the mass moment of inertia. Also, the subscripts H, P, and R represent the fluid forces acting on the hull, propeller, and rudder, respectively.

[0024] The mathematical model regarding the fluid forces acting on the hull can be expressed by the following mathematical formula.

[0025]

[0026] Here, the coefficients X, Y, and N, which have the (angular) velocity components as subscripts, represent the fluid force coefficients, and the dimensionless value m x , m y , J zz represents the added mass and added mass moment of inertia, respectively.

[0027] The mathematical model regarding the fluid force acting on the thruster can be expressed by the following equation, and the calculation is performed considering the installation positions of the thrusters on the port and starboard sides.

[0028]

[0029] Here, td is the thrust reduction factor, K T is the thrust coefficient obtained from the thruster standalone test, J is the advance ratio, ρ is the seawater density, n is the revolutions per second, D P is the thruster diameter, y p represents the distance of the propeller shaft system from the hull centerline, respectively. Also, the subscripts PORT and STBD represent port and starboard, respectively.

[0030] The mathematical model regarding the fluid force acting on the rudder can be expressed by the following mathematical formula, and the calculation is performed considering the installation positions of the port and starboard rudders.

[0031]

[0032] The vertical component of the rudder force (F') required to calculate the force and moment acting on the rudder N ), effective angle of incidence of other inflow velocities (α R ), combined velocity of other inflows (U R ) can be expressed by the following mathematical formula.

[0033]

[0034] Here, f α is the slope of the other direct pressure coefficient.

[0035]

[0036] The empirical formula developed by the International Classification Society, widely used for designing the rudder area and steering gear capacity of ships, can be expressed by the following mathematical formula.

[0037]

[0038] Here, T R Eun Ta Took, F R ε represents the rudder force, and r represents the distance from the center of pressure acting on the rudder to the rudder axis. K1, K2, and K3 are values ​​calculated using a formula considering the ship and rudder design information, A represents the rudder area, and V represents the ship's operating speed.

[0039] Regarding the possibility of estimating asymmetric rudder torque acting on the port and starboard rudders, the empirical formulas for rudder torque developed by the International Classification Societies were designed to design rudder area and steering gear capacity; therefore, they cannot account for the asymmetry of rudder torque resulting from port and starboard rudder flow characteristics under any maneuvering conditions.

[0040] To correct this, the inertia force (F) estimated from the steering motion equations N ) this F of mathematical formula 7 R By assuming that it is equal to, the hydrodynamic force and rudder torque acting on the port and starboard rudders are estimated, respectively, in any steering motion state. At this time, the reason for the difference reflected in the port and starboard rudder torques is due to the γ1 and γ2 components acting on the port and starboard rudders.

[0041] Before estimating the asymmetric rudder torque by applying the aforementioned mathematical model, verification of the applied mathematical model and code was performed. Figures 3 to 5 show the simulation results of the target vessel's 35° turn, 10° / 10° zigzag, and 20° / 20° zigzag, respectively. The table below shows the internal simulation results provided by HD Hyundai Heavy Industries and the results calculated from the code written for the present invention as error rates.

[0042]

[0043] The revolutions per minute required to maintain the initial speed during maneuvering were calculated, and the results showed a negligible difference of within 1% from the revolutions per minute on the designed speed-revolutions per minute curve. In the case of a 35° turn, it was confirmed that there were minor differences in terms of forward distance, turning diameter, and arrival time, thereby confirming the validity of the mathematical model. However, in the case of the zigzag test, it was observed that the error rate was somewhat large. This is because the magnitude of the reference value for the overshoot angle is small, and the actual error is not significant. Although design and model test information provided by HD Hyundai Heavy Industries was used, the occurrence of errors is due to differences such as deriving some unprovided values ​​from empirical formulas, differences in numerical analysis techniques, and the use of regression analysis to consider resistance and propeller characteristics.

[0044] Figure 6 shows the time series of rudder torque applied to the port and starboard rudders during a 35° turn (port). In the International Classification Society's empirical formula, since the rudder torque varies according to design information including the ship's speed, it is observed that it has the largest value at the initial point where the turn begins. On the other hand, when the modified method was applied, it showed a tendency to increase rapidly after the turn began, reach a peak, and then decrease and converge. This is similar to the characteristics of the time series of the ship's (angular) speed calculated during the turning process.

[0045] However, as explained in Equation 7, when using the modified rudder torque empirical formula, the flow characteristics entering the port and starboard rudders can be taken into account, so as shown in Fig. 6, it can be confirmed that port and starboard rudder torque asymmetry appears.

[0046] FIG. 7 is a flowchart schematically illustrating a method for estimating a maximum allowable compensation angle considering an asymmetric rudder torque of a twin-axis line performed by a device for estimating a maximum allowable compensation angle according to an embodiment of the present invention, and FIGS. 8 to 12 are drawings for explaining the method for estimating a maximum allowable compensation angle considering an asymmetric rudder torque of a twin-axis line according to an embodiment of the present invention of FIG. 7. Hereinafter, with reference to FIG. 7, a method for estimating a maximum allowable compensation angle considering an asymmetric rudder torque of a twin-axis line according to an embodiment of the present invention will be described, with reference to FIGS. 8 to 12.

[0047] The definition of the compensation angle proposed from the perspective of the advancement of intelligent navigation systems is as follows. Generally, in a turning vessel, a greater rudder torque acts on the inner rudder than on the outer rudder of the turning diameter.

[0048] First, when the inside rudder maintains the existing rudder angle and the outside rudder is used more significantly, the difference between the port and starboard rudder angles is defined as the compensation angle.

[0049] Second, when a steady state is reached during turning, based on the converged rudder torque, the outer rudder torque can be controlled to be greater up to a range that does not exceed the inner rudder torque. In this case, the maximum value of the compensation angle is defined as the maximum allowable compensation angle.

[0050] Third, the maximum angle of descent cannot exceed 35°, and the difference between the maximum angle of descent (35°) and the fixed inner angle of descent is assumed to be the limit value of the maximum allowable compensation angle under the corresponding conditions.

[0051] Using a validated mathematical model, the ship's dynamic characteristics related to asymmetric rudder torque are examined, and the maximum allowable compensation angle is determined. To this end, the calculation conditions are summarized as shown in the table below.

[0052]

[0053] The vessel speed is examined for 5.0 knots, 13.0 knots, and 21.0 knots, respectively, based on the maneuvering sea trial speed of 18.5 knots. For the turning simulation to examine dynamic characteristics, the reference rudder angles are 5°, 15°, 25°, and 35°. However, the figure explaining the process of deriving the maximum allowable compensation angle was created based on a port rudder angle of 20°. In particular, under the condition that the port rudder is fixed, angles from 1° to 35° were examined to find the maximum allowable compensation angle of the starboard rudder. However, since the limit value of the maximum allowable rudder angle could not be exceeded, the search was conducted from 1° to the limit value n°.

[0054] In step S110, the maximum allowable compensation angle estimation device calculates turning performance by steering angle.

[0055] The forward distance and turning diameter were calculated according to the ship's initial speed and rudder angle as shown in the table below.

[0056]

[0057]

[0058] For review, simulations were performed under the synchronized conditions shown in Table 3. Since the maneuverability index cannot be explicitly stated due to internal regulations at large shipyards, it was expressed as a relative ratio based on the simulation values ​​at maneuvering sea trial speeds. It can be observed that if the commanded rudder angle is the same, the difference in forward distance and turning diameter is negligible. This is because, generally, the estimation of a ship's maneuverability performance is based on the assumption that the hydrodynamic coefficient does not change with speed. On the other hand, it can be seen that the forward distance and turning diameter increase significantly as the magnitude of the commanded rudder angle decreases. This is because the magnitude of the turning moment caused by the hydrodynamic force acting on the rudder is relative to the rudder angle (δ PORT , δ STBD This is because it changes depending on ).

[0059] In step S120, the maximum allowable compensation angle estimation device calculates the convergence rate for each angle.

[0060] The table below shows the convergence speed of the vessel when the turning diameter is reached.

[0061]

[0062] It can be observed that when the ship's initial speed is low, the converged speed tends to be lower, while the converged speed increases as the commanded rudder angle decreases. This is because if the magnitude of the turning moment resulting from the ship's rudder control is small, the angle of drift during turning decreases, the magnitude of the fluid force acting on the hull decreases, and the resulting speed reduction is minimal.

[0063] In step S130, the maximum allowable compensation angle estimation device calculates the conditional ta-torque.

[0064] From the perspective of ship maneuvering motion, the tendency of turning motion with the port and starboard rudders synchronized has been confirmed. Based on the verified mathematical model, iterative calculations were performed for the fixed rudder angle and compensated rudder angle specified in Table 3 to estimate the maximum allowable compensation angle.

[0065] In Figures 8 to 10, results obtained at 21.0 knots are presented. First, the time series of rudder torque shows a trend similar to that examined in Figure 6. However, there is a section in Figure 8 where the starboard rudder torque has a negative sign; since port turning is performed under conditions where the sum of the turning moments acting on the hull, propeller, and rudder is positive, port turning is possible even if the rudder torque has a negative sign in some sections. Additionally, it can be seen that the port rudder torque is greater than the starboard rudder torque during a 20° turn. Therefore, turning force can be improved by adding a compensation value to the starboard rudder.

[0066] In Fig. 9, a compensation angle of 4° was considered, and in Fig. 10, a compensation angle of 5° was considered. At 4°, the starboard rudder torque is smaller than the port rudder torque, so the compensation limit value was not exceeded, but at 5°, it can be considered that the compensation limit value was exceeded.

[0067] In step S140, the maximum allowable compensation angle estimation device derives the maximum allowable compensation angle.

[0068] Based on the conditions listed in Table 3, the maximum allowable compensation angle was calculated iteratively according to the ship's speed and rudder angle. As a result of the calculation, the effect of the ship's initial speed on the maximum allowable compensation angle was minimal, so the maximum allowable compensation angle was estimated and analyzed only at an initial speed of 18.5 knots.

[0069] FIG. 11 illustrates the maximum allowable compensation angle of the starboard rudder according to a fixed port rudder angle during port turning. The red dotted line indicates the limit value of the compensation angle; it is marked as 0° because, at a 35° turn, the maximum rudder angle is reached and the starboard rudder cannot be further controlled. Looking at the illustrated compensation angle, it appears to show a slight increase as the port rudder angle increases, but because the magnitude is small, it is displayed as increasing between 2° and 3° and between 17° and 18°. Therefore, from the perspective of the advancement of intelligent navigation systems, it is possible to provide as input the maximum allowable compensation angle required for additional control of the rudder in the direction where less rudder torque is applied depending on the direction of the maneuvering motion.

[0070] Figure 12 shows the heading angle time series during a zigzag test considering the maximum allowable compensation angle. As mentioned in Figure 11, the maximum allowable compensation angle at a 10° rudder angle is 3°. Looking at the port and starboard rudder angle time series in Figure 12, it can be seen that a 3° compensation angle was considered for the starboard rudder during port steering, and a 3° compensation angle was considered for the port rudder during starboard steering. When compared to the time series of the 10° / 10° zigzag test in Figure 4, it can be seen that the time to reach the first overshoot angle decreased by -8.48%, and the time to reach the second overshoot angle decreased by -8.58%. Therefore, faster course changes can be expected through improved turning ability during course changes.

[0071] FIG. 13 is a diagram schematically illustrating the configuration of a maximum allowable compensation angle estimation device considering the asymmetric tether torque of a twin-axis line according to an embodiment of the present invention.

[0072] Referring to FIG. 13, a maximum allowable compensation angle estimation device considering asymmetric tether torque of a twin-axis line according to an embodiment of the present invention includes a processor (10), a memory (20), a communication unit (30), and an interface unit (40).

[0073] The processor (10) may be a CPU or a semiconductor device that executes processing instructions stored in memory (20).

[0074] The memory (20) may include various types of volatile or non-volatile memory media. For example, the memory (20) may include ROM, RAM, etc.

[0075] For example, memory (20) can store instructions for performing a method to estimate the maximum allowable compensation angle considering the asymmetric tether torque of a twin axis according to an embodiment of the present invention.

[0076] The communication unit (30) is a means for transmitting and receiving data with other devices through a communication network.

[0077] The interface section (40) may include a network interface and a user interface for connecting to a network.

[0078] Meanwhile, the components of the aforementioned embodiments can be easily identified from a process perspective. That is, each component can be identified as a separate process. Furthermore, the processes of the aforementioned embodiments can be easily identified from the perspective of the device components.

[0079] In addition, the technical details described above may be implemented in the form of program instructions that can be executed through various computer means and recorded on a computer-readable medium. The computer-readable medium may include program instructions, data files, data structures, etc., either individually or in combination. The program instructions recorded on the medium may be those specifically designed and configured for the embodiments, or they may be those known and available to those skilled in the art of computer software. Examples of computer-readable recording media include magnetic media such as hard disks, floppy disks, and magnetic tapes; optical recording media such as CD-ROMs and DVDs; magneto-optical media such as floptical disks; and hardware devices specifically configured to store and execute program instructions, such as ROM, RAM, and flash memory. Examples of program instructions include machine code, such as that generated by a compiler, as well as high-level language code that can be executed by a computer using an interpreter, etc. Hardware devices may be configured to operate as one or more software modules to perform the operations of the embodiments, and vice versa.

[0080] The embodiments of the present invention described above are disclosed for illustrative purposes only, and those skilled in the art with ordinary knowledge of the present invention may make various modifications, changes, and additions within the spirit and scope of the present invention, and such modifications, changes, and additions should be considered to fall within the scope of the following claims. Explanation of the symbols

[0081] 10: Processor 20: Memory 30: Communications Department 40: Interface section

Claims

Claim 1 A method for estimating a maximum allowable compensation angle considering asymmetric rudder torque of a twin-shaft vessel, performed by a device for estimating a maximum allowable compensation angle, comprising: a step of calculating a forward distance and a turning diameter according to the initial speed and synchronized port and starboard rudder angles of the target vessel through a turning simulation of the target vessel; a step of calculating the convergence speed of the target vessel when the target vessel reaches the turning diameter; a step of calculating a time series of rudder torque according to a fixed rudder angle and a compensated rudder angle pre-set for the port and starboard rudder of the target vessel using a pre-set mathematical model; and a step of calculating a maximum allowable compensation angle according to the speed and rudder angle of the target vessel using the mathematical model. Claim 2 A method for estimating the maximum allowable compensation angle considering the asymmetric rudder torque of a twin-axis line, characterized in that, in claim 1, the maximum allowable compensation angle is defined by the following conditions: Condition 1: When the inner rudder maintains the existing rudder angle and the outer rudder is used more significantly, the difference between the port and starboard rudder angles is defined as the compensation angle. Condition 2: When a steady state is reached during turning, based on the converged rudder torque, the outer rudder torque can be controlled to be larger up to a range that does not exceed the inner rudder torque, and the maximum value of the compensation angle is defined as the maximum allowable compensation angle. Condition 3: The maximum rudder angle cannot exceed 35°, and the difference between the maximum rudder angle (35°) and the fixed inner rudder angle is assumed as the limit value of the maximum allowable compensation angle under the said conditions. Claim 3 A method for estimating the maximum allowable compensation angle considering the asymmetric rudder torque of a twin axis, characterized in that, in claim 1, the mathematical model is represented by the following mathematical formula. Here, is the (angular) acceleration of fore-and-aft, sway, and bow, m is the mass of the ship, and I zz ε is the mass moment of inertia, the subscripts H, P, and R are the fluid forces acting on the hull, propeller, and rudder, respectively, X, Y, and N are the force and moment, and u, v, and r are the (angular) velocities of fore-and-aft, sway, and bow. Claim 4 A method for estimating the maximum allowable compensation angle considering the asymmetric rudder torque of a twin-shaft line, characterized in that, in paragraph 3, the mathematical model regarding the fluid force acting on the hull is represented by the following mathematical formula. Here, the coefficients X, Y, and N, which have (angular) velocity components as subscripts, are fluid force coefficients, and the dimensionless value m x , m y , J zz are the added mass and the added mass moment of inertia, respectively. Claim 5 A method for estimating the maximum allowable compensation angle considering the asymmetric rudder torque of a twin-axis line, characterized in that, in paragraph 3, the mathematical model regarding the fluid force acting on the propeller is represented by the following mathematical formula. Here, t d is the thrust reduction factor, and K T is the thrust coefficient obtained from a thruster-only test, J is the advance ratio, ρ is the seawater density, n is the revolutions per second, and D P is the thruster diameter, and y p is the distance of the propeller shaft system from the hull centerline, and the subscripts PORT and STBD represent port and starboard, respectively. Claim 6 A method for estimating the maximum allowable compensation angle considering the asymmetric rudder torque of a twin-axis line, characterized in that, in paragraph 3, the mathematical model regarding the fluid force acting on the rudder is represented by the following mathematical formula. Claim 7 A device for estimating a maximum allowable compensation angle considering asymmetric rudder torque of a twin-shaft vessel, comprising: a memory for storing instructions; and a processor for executing instructions, wherein the instructions include: a step of calculating a forward distance and a turning diameter according to the initial speed and synchronized port and starboard rudder angles of the target vessel through a turning simulation of the target vessel; a step of calculating the convergence speed of the target vessel when the target vessel reaches the turning diameter; a step of calculating a time series of rudder torque according to a fixed rudder angle and a compensation rudder angle pre-set for the port and starboard rudder of the target vessel using a pre-set mathematical model; and a step of calculating a maximum allowable compensation angle according to the speed and rudder angle of the target vessel using the mathematical model.

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