A calculation method for energy-saving effect of wind-assisted propulsion ships

Abstract

The present invention relates to the field of ship energy conservation technology, and in particular to a method for calculating the energy conservation effect of a wind-assisted propulsion ship, comprising: setting ideal conditions based on empirical values ​​to obtain iterative initial values; constructing a linear equation system of the generalized secant method based on a four-degree-of-freedom mechanical equilibrium equation system and calculating a weight matrix; weighting the iterative initial values ​​to obtain iterative results; calculating iterative condition parameters and iterating forward; determining the iterative conditions, and continuing the iterative process when the iterative conditions are met, and outputting the first iterative initial value when the iterative conditions are not met. The present invention adapts to the complexity of the equation system expression in the wind-assisted propulsion ship energy conservation effect evaluation model, is easy to use, can avoid the occurrence of ill-conditioned matrices in the iterative process, has fast convergence, and produces accurate results.

Description

Technical Field

[0001] The present invention relates to the technical field of ship energy conservation, and in particular to a method for calculating the energy conservation effect of a wind-assisted propulsion ship. Background Art

[0002] The energy-saving evaluation model for wind-assisted propulsion ships includes a four-degree-of-freedom mechanical equilibrium equation system, as well as the relationship between the hydrodynamic and aerodynamic forces acting on the ship, its navigation attitude (rudder angle, drift angle, and heel angle), and effective thrust. The model is detailed below.

[0003] The coordinate system of the wind-assisted propulsion ship is as follows Figure 1 As shown, the coordinate origin is at the bow, the height is the keel, the X axis points to the stern, the Y axis points to the starboard, and the Z axis is vertically upward.

[0004] The positive and negative definitions of ship (including appendages) motion and wind direction angle are as follows:

[0005] (1) Drift angle - the angle between the heading and the heading, with counterclockwise being positive;

[0006] (2) Rudder angle - right rudder is positive;

[0007] (3) Heel angle - positive for left heel;

[0008] (4) Wind direction angle - the angle between the positive direction of the X-axis and the wind direction, with counterclockwise being positive.

[0009] According to this coordinate system and the definition of positive and negative, in a specific sea condition (wind: true wind direction TWA, true wind speed TWS; wave: three-in-one average wave height H 1 / 3 , peak period T p ) and specific speed V S Under this condition, the ship's four-degree-of-freedom mechanical equilibrium equations are as follows:

[0010]

[0011]

[0012] Where,

[0013] β-drift angle;

[0014] δ-rudder angle;

[0015] - heel angle;

[0016] GM-high static stability;

[0017] △-displacement;

[0018] g-gravitational acceleration;

[0019] XCw - hydrostatic resistance;

[0020] X AW - Wave resistance increase;

[0021] X H and Y H - Additional resistance and lateral force due to drift angle;

[0022] CLR - the distance from the point of action of the drift angle additional resistance and lateral force to the bow;

[0023] z H - Z coordinate of the point of action of the drift angle additional resistance and lateral force;

[0024] X w and Y w - windward forces acting on the hull and superstructure above the waterline;

[0025] X W 、y W and z W - Coordinates of the points above the waterline where the windward forces act on the hull and superstructure;

[0026] X S and Y S -Thrust and lateral force generated by wind-assisted propulsion devices;

[0027] x S 、y S and z S - Coordinates of the points of application of thrust and lateral forces generated by the wind-assisted propulsion device;

[0028] X R and Y R - Rudder force;

[0029] z R -Z coordinate of the point of action of the rudder force;

[0030] T E - effective thrust of the main propulsion system;

[0031] L PP - Length between perpendiculars of the ship.

[0032] In this set of mechanical equilibrium equations, the relationship between hydrodynamics and aerodynamics and navigation attitude and effective thrust can be obtained by adopting low / mid fidelity methods, such as empirical / semi-empirical formulas, or by high fidelity methods, such as three-dimensional CFD calculations or model tests.

[0033] This mechanical equilibrium equation group consists of four nonlinear equations, solving β, δ, and TE Four unknowns form a mathematically closed system. Since the unknowns in this model are highly coupled and have implicit relationships with each other, a numerical algorithm is required to solve them. The calculation method requires:

[0034] (1) Adapting to the complexity of the equations used in the energy-saving effect evaluation model for wind-assisted propulsion ships;

[0035] (2) The iterative process avoids the occurrence of ill-conditioned matrices;

[0036] (3) rapid convergence;

[0037] (4) The results are accurate (the right side of the equal sign of the mechanical equilibrium equations returns to zero and the numerical value should be a minimum).

[0038] Existing methods for calculating the energy-saving effect of wind-assisted propulsion ships, that is, solving the energy-saving effect evaluation model, include direct solution using a nonlinear equation root-finding algorithm, and first converting the equation root-finding problem into a function extreme value problem and then solving it.

[0039] Direct solutions are achieved using root-finding algorithms for nonlinear equations, including the Newton-Raphson method, the fixed-point iteration method, and the secant method. The Newton-Raphson method requires derivatives and cannot cope with the complexity of the equations used in energy-saving effect evaluation models. The fixed-point iteration method converges slowly and requires an initial iteration range spanning positive and negative values. When solving energy-saving effect evaluation models, it is difficult to devise a calculation method for the initial iteration range to ensure that the iteration process does not produce ill-conditioned matrices and ultimately converges to the correct value. The secant method does not require derivatives and converges quickly, but whether the iteration process produces ill-conditioned matrices and whether it converges to the correct value depends on the selection of the initial iteration value. Currently, the initial iteration value is mainly based on enumeration attempts, and there is no fixed method for calculating the initial iteration value.

[0040] The current approach is to first transform the root-finding problem of a system of equations into the problem of finding the extreme value of a function, and then solve it. The main approach is the Nelder-Mead Simplex algorithm. The details are as follows.

[0041] Formulas (1)-(4) can be simplified to formulas (5)-(8):

[0042]

[0043] Formulas (5)-(8) are equivalent to formula (9):

[0044]

[0045] This is equivalent to the function Reach the minimum value. Therefore, the problem of finding the root of the system of equations is transformed into finding the function The minimum value problem is solved by applying the Nelder-Mead Simplex algorithm. After research, it is found that when this method is applied to solve the energy-saving effect evaluation model, the convergence is poor and it is difficult to converge to the correct value. That is, the rudder angle δ, drift angle β, and heel angle obtained by the final solution are Substitute the effective thrust TE into equations (1)-(4), and the right side of the equal sign will not return to zero. Summary of the Invention

[0046] In order to solve the technical problem in the prior art that the Nelder-Mead Simp1ex algorithm has poor convergence and is difficult to converge to the correct value when solving the energy-saving effect evaluation model, the present invention proposes a method for calculating the energy-saving effect of wind-assisted propulsion ships, which combines the secant method to perform initial value iteration, thereby solving the energy-saving effect evaluation model of wind-assisted propulsion ships to obtain the energy-saving effect.

[0047] The present invention is achieved through the following technical solutions:

[0048] A method for calculating the energy-saving effect of a wind-assisted propulsion ship comprises the following steps:

[0049] Step 1: Initialize the iterative program, set iter = 1, and give the independent variables rudder angle δ, drift angle β, and heel angle Effective thrust T E The independent variable residual_x, the dependent variable resultant force ∑F X ,∑F Y and resultant moment ΣM Z ,∑M X The dependent variable residual_f is assigned a residual initial value, and the residual initial value is any value greater than the convergence standard.

[0050] Step 2: Set ideal conditions based on experience to obtain the rudder angle δ, drift angle β, and heel angle under ideal conditions. Effective thrust T E The initial value of the iteration

[0051] Iteration initial value The construction method is:

[0052] The first step is to set an ideal condition based on experience, including:

[0053] Consider the initial hydrostatic resistance X CW0 and wave resistance X AW0 is a constant;

[0054] It is considered that the headwind force on the hull and superstructure above the waterline is X w 、Y w It has nothing to do with the drift angle. Let β = 0 and calculate X W0 , Y W0 The coordinates of the points where the windward force acts on the hull and superstructure above the waterline are x W0 ,y W0 , Z W0

[0055] Consider the wind-assisted propulsion device rotor sail thrust X S and lateral force Y S It is independent of the drift angle and the heel angle, let β = 0 and Calculate X S0 , Y S0 The coordinates of the points of action of the thrust and lateral force generated by the wind-assisted propulsion device are x S0 ,y S0 , Z S0 ;

[0056] It is considered that the steering force adds resistance X R and lateral force Y R Regardless of the effective thrust, let T E0 =0, we get:

[0057] (1)X R0 (δ, β, T E )=X R0 (δ, β);

[0058] (2)Y R0 (δ, β, T E )=Y R0 (δ, β);

[0059] It is assumed that the distance CLR0 from the point of action of the drift angle additional force to the bow is almost 0, and the distance Z from the rudder additional force and the drift angle additional force to the keel is R0 and Z H0 All are 1 / 2 draft, which is a constant;

[0060] In the second step, based on the parameters under ideal conditions obtained in the first step, the initial four-degree-of-freedom mechanical equilibrium equations are constructed as shown in Equations (10)-(13):

[0061] ∑F X0 =X CW0 +X AW0 +X H0 (β0)+X W0 +X S0 +X R0 (δ0,β0) (10)

[0062] +T E0=0

[0063] ∑F Y0 =Y H0 (β0)+Y R0 (δ0,β0)+Y S0 +Y w0 =0 (11)

[0064]

[0065] Equations (11)-(13) form a linear system, as shown in Equation (14):

[0066]

[0067] The third step is to solve the linear system obtained in the second step and get

[0068] The fourth step is based on Obtain

[0069] Step 5: According to Find X H0 (β0) and X R0 (δ0, β0);

[0070] Step 6: X H0 (β0) and X R0 Substitute (δ0, β0) into formula (10) to obtain T E0 .

[0071] At this point, the first iteration initial value is obtained

[0072] Step 3: Iteration initial value based on step 2 Change any one of the parameters, keep the other parameters unchanged, and get the other 4 iterative initial values k=1, 2, 3, 4.

[0073] Specifically, the other four iteration initial values The construction method for k=1, 2, 3, 4 is:

[0074] (1)

[0075] (2)

[0076] (3)

[0077] (3)

[0078] According to experience, q is taken as 10%.

[0079] At this point, all five sets of iterative initial values ​​are obtained.

[0080] According to the calculation experience under actual working conditions, the iterative initial values ​​constructed based on steps 2 and 3 will not produce ill-conditioned matrices during the iteration process and can converge to the correct results.

[0081] Step 4: Based on the 5 initial values ​​of iteration, form an iteration set k=0,1,2,3,4,determine whether the set meets the iteration conditions. If the iteration conditions are met, perform weighted iteration based on the generalized secant method. If the iteration conditions are not met, output the result of the first iteration initial value.

[0082] The iteration conditions are: iter < maximum number of iteration steps, independent variable residual_x > convergence criterion, and dependent variable residual_f > convergence criterion are satisfied at the same time.

[0083] Step 5: Construct the linear equation system Ap=b of the generalized secant method and solve for p;

[0084] Where A is the parameter matrix constructed based on the iterative set according to the ship's four-degree-of-freedom mechanical equilibrium equations, b is the constant term matrix, and the weight matrix p = {p0, p1, p2, p3, p4} T .

[0085] Specifically, the method for constructing the expressions of A and b in the linear equation system Ap=b is:

[0086]

[0087] The generalized secant method equation constructed based on step 5 does not require derivative calculation, is easy to use, and adapts to the complexity of the equation group expression in the wind-assisted propulsion ship energy-saving effect evaluation model. And the secant method is used for calculation, and the convergence speed is fast. In the present invention, if the convergence condition is set to 10 -8 , it can basically converge within 20 steps.

[0088] Step 6: Based on the weight matrix p obtained in step 5, weight the 5 sets of iterations to obtain the iteration result

[0089] Specifically, the The calculation method is as shown in formula (19):

[0090]

[0091] Step 7: The iterative result obtained in step 6 Substitute into the ship's four-degree-of-freedom mechanical equilibrium equations, such as Equations (1)-(4), and calculate ∑Fx, ∑Fy, ∑Mz, and ∑Mx.

[0092]

[0093] Step 8: Based on the result from step 6 And ∑Fx, ∑Fy, ∑Mz, ∑Mx obtained in step 7, calculate the independent variable residual_x and the dependent variable residual_f.

[0094] Specifically, the calculation method of the independent variable residual_x is as shown in formula (17):

[0095]

[0096] The calculation method of the dependent variable residual_f is as shown in formula (18):

[0097]

[0098] Step nine, and k=1, 2, 3, 4; form a new iterative set k=1,2,3,4,5;re-assign the iterative set forward to obtain k=1, 2, 3, 4, 5; the assignment method is: k=1, 2, 3, 4, 5, and iter++, return to step 4 and re-judge the iterative condition.

[0099] Furthermore, after the step 4 determines that the iteration condition is not satisfied and outputs the result, based on the output of the first iteration initial value The following methods are used to calculate fuel savings for a specific trip:

[0100] The first step is to obtain the effective thrust T based on step 4 E , and then calculate the effective power P E and the required host power P S ;

[0101] The second step is to calculate the required main engine power with and without the wind-assisted propulsion device to obtain the energy-saving effect of the wind-assisted propulsion device;

[0102] The third step is to calculate the power saving and energy saving effect under different wind speeds and wind directions;

[0103] The fourth step is to calculate the power savings for a specific voyage by applying the Global Wind Probability Matrix (GWP) recommended by the IMO.

[0104] The fifth step is to calculate the fuel savings for a specific voyage using the ship's fuel consumption rate SFOC.

[0105] The beneficial effects of the present invention are:

[0106] (1) Adapting to the complexity of the equation expressions in the wind-assisted propulsion ship energy-saving effect evaluation model; using this solution, there is no need for derivatives, and there is no need to convert the root-finding problem of the nonlinear equation group into the problem of finding the minimum value of the function. The mathematical principles are easy to understand and easy to apply.

[0107] (2) The iterative process avoids the occurrence of ill-conditioned matrices.

[0108] (3) Faster convergence; if the convergence condition is set to 10 -8 , then it can basically converge within 20 steps. It can converge to the correct value, that is, the final solution of the rudder angle δ, drift angle β, heel angle Substituting the effective thrust TE into equations (1)-(4), the right side of the equal sign can return to zero, and the numerical value is a minimum.

[0109] (4) The results are accurate (the right side of the equal sign of the mechanical equilibrium equations returns to zero and the numerical value should be a minimum). BRIEF DESCRIPTION OF THE DRAWINGS

[0110] Figure 1 Coordinate system for wind-assisted propulsion ships.

[0111] Figure 2 Flowchart of the algorithm for solving the energy-saving effect evaluation model of wind-assisted propulsion ships using the secant method. DETAILED DESCRIPTION

[0112] The present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments.

[0113] The present invention discloses a method for calculating the energy-saving effect of wind-assisted propulsion ships, which combines the secant method to perform initial value iteration to solve the wind-assisted propulsion ship energy-saving effect evaluation model, so as to achieve the effects of adapting to the complexity of the equation group expression in the wind-assisted propulsion ship energy-saving effect evaluation model, being easy to use, avoiding the occurrence of ill-conditioned matrices in the iterative process, fast convergence, and accurate results. The algorithm flow of the present invention is as follows Figure 2 As shown, the following steps are included:

[0114] Step 1: Initialize the iterative program, set iter = 1, and give the independent variables rudder angle δ, drift angle β, and heel angle Effective thrust T E The independent variable residual_x, the dependent variable resultant force ∑F X ,∑F Y and resultant moment ΣM Z ,∑M x The dependent variable residual_f is assigned a residual initial value, and the residual initial value is any value greater than the convergence standard;

[0115] Step 2: Set ideal conditions based on experience to obtain the rudder angle δ, drift angle β, and heel angle under ideal conditions. Effective thrust T E The initial value of the iteration

[0116] Specifically, the iteration initial value The construction method is:

[0117] The first step is to set an ideal condition based on experience, including:

[0118] Consider the initial hydrostatic resistance X CW0 and wave resistance X AW0 is a constant;

[0119] Assuming that the windward forces Xw and Yw on the hull and superstructure above the waterline have nothing to do with the drift angle, let β = 0 and calculate X W0 , Y W0 The coordinates of the points where the windward force acts on the hull and superstructure above the waterline are x W0 ,y W0 , Z W0 ;

[0120] Consider the wind-assisted propulsion device rotor sail thrust X S and lateral force Y S It is independent of the drift angle and the heel angle, let β = 0 and Calculate X S0 , Y S0 The coordinates of the points of action of the thrust and lateral force generated by the wind-assisted propulsion device are x S0 ,y S0 , Z S0

[0121] It is considered that the steering force adds resistance X R and lateral force Y R Regardless of the effective thrust, let T E0 =0, we get:

[0122] (1)X R0 (δ, β, T E)=X R0 (δ, β);

[0123] (2)Y R0 (δ, β, T E )=Y R0 (δ, β);

[0124] It is assumed that the distance CLR0 from the point of action of the drift angle additional force to the bow is almost 0, and the distance z from the rudder additional force and the drift angle additional force to the keel is R0 and z H0 All are 1 / 2 draft, which is a constant;

[0125] In the second step, based on the parameters under ideal conditions obtained in the first step, the initial four-degree-of-freedom mechanical equilibrium equations are constructed as shown in Equations (10)-(13):

[0126] ∑F x0 =X CW0 +X AW0 +X H0 (β0)+X W0 +X S0 +X R0 (δ0,β0) (10)+T E0 =0

[0127] ∑F Y0 =Y H0 (β0)+Y R0 (δ0,β0)+Y S0 +Y W0 =0 (11)

[0128]

[0129] It can be seen that equations (11)-(13) form a linear system Ax=b, as shown in equation (14):

[0130]

[0131] Among them, X H and Y H is the additional resistance and lateral force of the drift angle, GM is the static stability, △ is the displacement, g is the acceleration of gravity, L PP The length between perpendiculars of the ship.

[0132] The third step is to solve this linear system and obtain:

[0133] The fourth step is based on Obtain

[0134] Step 5: According to Find X H0(β0) and X R0 (δ0, β0).

[0135] Step 6: X H0 (β0) and X R0 Substitute (δ0, β0) into formula (10) to obtain T E0 .

[0136] At this point, the initial value of the iteration Sure.

[0137] Step 3: Iteration initial value based on step 2 Change any one of the parameters, keep the other parameters unchanged, and get the other 4 iterative initial values k = 1, 2, 3, 4;

[0138] Specifically, the other four iteration initial values The construction method for k=1, 2, 3, 4 is:

[0139] (1)

[0140] (2)

[0141] (3)

[0142] (3)

[0143] Here, q is a percentage, and experience shows that 10% is appropriate.

[0144] At this point, all five sets of iterative initial values ​​have been determined.

[0145] According to the calculation experience under actual working conditions, the iterative initial values ​​constructed based on steps 2 and 3 will not produce ill-conditioned matrices during the iteration process and can converge to the correct results.

[0146] Step 4: Based on the 5 initial values ​​of iteration, form an iteration set k==0, 1, 2, 3, 4, determine whether the set meets the following iteration conditions:

[0147] At the same time, iter<maximum number of iterations, independent variable residualx> convergence criteria, and dependent variable residual_f> convergence criteria are met.

[0148] If the iteration conditions are met, weighted iteration is performed based on the generalized secant method. If the iteration conditions are not met, the first iteration initial value of the result is output.

[0149] Step 5: Construct the linear equation system Ap=b of the generalized secant method and solve for p.

[0150] Where A is the parameter matrix constructed based on the iterative set according to the ship's four-degree-of-freedom mechanical equilibrium equations, b is the constant term matrix, and the weight matrix p = {p0, p1, p2, p3, p4} T .

[0151] Specifically, the expressions of A and b in the linear equation system Ap=b are as follows:

[0152]

[0153] The generalized secant method equation constructed based on step 5 does not require derivative calculation, is easy to use, and adapts to the complexity of the equation group expression in the wind-assisted propulsion ship energy-saving effect evaluation model. And the secant method is used for calculation, and the convergence speed is fast. In the present invention, if the convergence condition is set to 10 -8 , it can basically converge within 20 steps.

[0154] Step 6: Based on the weight matrix p obtained in step 5, weight the 5 sets of iterations to obtain the iteration result

[0155] Specifically, the calculation method is as shown in formula (19):

[0156]

[0157] Step 7: Substitute into formulas (1)-(4) to calculate ∑Fx, ∑Fy, ∑Mz, and ∑Mx.

[0158] Step 8. Calculate the independent variable residual x and the dependent variable residual f.

[0159] Specifically, the calculation method of the independent variable residual_x is as follows:

[0160]

[0161] The calculation method of the dependent variable residual_f is as follows:

[0162]

[0163] Step nine, and k=1, 2, 3, 4; form a new iterative set k=1,2,3,4,5;re-assign the iterative set forward to obtain k=1, 2, 3, 4, 5; the assignment method is: k=1, 2, 3, 4, 5, and iter++, return to step 4 and re-judge the iterative condition.

[0164] Furthermore, after the step 4 determines that the iteration condition is not satisfied and outputs the result, the output result can be used to The fuel savings for a specific voyage can be obtained by:

[0165] According to the effective thrust T E , and then obtain the effective power P E and the required host power P S . The required main engine power is calculated with and without wind-assisted propulsion devices, so as to obtain the energy-saving effect of wind-assisted propulsion devices, and the coupling effect between the hull, main propeller and wind-assisted propulsion devices is analyzed under typical meteorological conditions and typical wind-assisted propulsion device layouts. The power savings and energy-saving effects under different wind speeds and wind directions are calculated, and the power savings for a specific voyage can be obtained by applying the Global Wind Probability Matrix (Global Wind Probability Matrix) recommended by IMO. Finally, the fuel savings for a specific voyage can be obtained by using the ship fuel consumption rate SFOC.

[0166] It should be noted that the specific embodiments described above can enable those skilled in the art to more fully understand the present invention, but do not limit the present invention in any way. Therefore, although this specification has described the present invention in detail with reference to the drawings and embodiments, those skilled in the art should understand that the present invention can still be modified or replaced with equivalents. In short, all technical solutions and improvements that do not depart from the spirit and scope of the present invention should be included in the scope of protection of the patent for the present invention.

Claims

1. A method for calculating the energy-saving effect of a wind-assisted propulsion ship, characterized in that: Step 1: Initialize the iterative program, set iter = 1, and give the independent variables rudder angle δ, drift angle β, and heel angle Effective thrust T E The independent variable residual_x, the dependent variable resultant force ∑F X ,∑F Y and resultant moment ΣM Z ,∑M X The dependent variable residual_f is assigned a residual initial value, and the residual initial value is any value greater than the convergence standard; Step 2: Set ideal conditions based on experience to obtain the rudder angle δ, drift angle β, and heel angle under ideal conditions. Effective thrust T E The initial value of the iteration Step 3: Iteration initial value based on step 2 Change any one of the parameters, keep the other parameters unchanged, and get the other 4 iterative initial values Step 4: Based on the 5 initial values ​​of iteration, form an iteration set Determine whether the set meets the iteration conditions. If so, perform weighted iteration based on the generalized secant method. If not, output the result of the first iteration initial value. The iteration conditions are: simultaneously satisfying iter<maximum number of iteration steps, independent variable residual_x> convergence criteria, and dependent variable residual_f> convergence criteria; Step 5: Construct the linear equation system Ap=b of the generalized secant method and solve for p; Where A is the parameter matrix constructed based on the iterative set according to the ship's four-degree-of-freedom mechanical equilibrium equations, b is the constant term matrix, and the weight matrix p = {p0, p1, p2, p3, p4} T ; Step 6: Based on the weight matrix p obtained in step 5, weight the 5 sets of iterations to obtain the iteration result Step 7: The iterative result obtained in step 6 Substitute into the ship's four-degree-of-freedom mechanical equilibrium equations to calculate ∑Fx, ∑Fy, ∑Mz, and ∑Mx; Step 8: Based on the result from step 6 Calculate the independent variable residual_x and the dependent variable residual_f using ∑Fx, ∑Fy, ∑Mz, and ∑Mx obtained in step 7; Step nine, and Form a new iterable set Reassign the iterable set forward to get The assignment method is: And iter++, return to step 4 to re-judge the iteration condition.

2. A method for calculating energy-saving effects of wind-assisted propulsion ships according to claim 1, characterized in that: In the step 2, the initial value of the iteration The construction method is: The first step is to set an ideal condition based on experience, including: Consider the initial hydrostatic resistance X CW0 and wave resistance X AW0 is a constant; It is considered that the headwind force on the hull and superstructure above the waterline is X W 、Y W It has nothing to do with the drift angle. Let β = 0 and calculate X W0 , Y W0 The coordinates of the points where the windward force acts on the hull and superstructure above the waterline are x W0 ,y W0 , z W0 ; Consider the wind-assisted propulsion device rotor sail thrust X S and lateral force Y S It is independent of the drift angle and the heel angle, let β = 0 and Calculate X S0 , Y S0 The coordinates of the points of action of the thrust and lateral force generated by the wind-assisted propulsion device are x S0 ,y S0 , z S0 ; It is considered that the steering force adds resistance X R and lateral force Y R Regardless of the effective thrust, let T E0 =0, we get: (1)X R0 (d,b,T E )=X R0 (d,b); (2)Y R0 (d,b,T E )=Y R0 (d,b); It is assumed that the distance CLR0 from the point of action of the drift angle additional force to the bow is almost 0, and the distance z from the rudder additional force and the drift angle additional force to the keel is R0 and z H0 All are 1 / 2 draft, which is a constant; In the second step, based on the parameters under ideal conditions obtained in the first step, the initial four-degree-of-freedom mechanical equilibrium equations are constructed as shown in Equations (10)-(13): Among them, X H and Y H is the additional resistance and lateral force of the drift angle, GM is the static stability, Δ is the displacement, g is the acceleration of gravity, L PP is the length between perpendiculars of the ship; Equations (11)-(13) form a linear system, as shown in Equation (14): The third step is to solve the linear system obtained in the second step and get The fourth step is based on Obtain Step 5: According to Find X H0 (β0) and X R0 (δ0,β0); Step 6: X H0 (β0) and X R0 Substitute (δ0,β0) into formula (10) to obtain T E0 .

3. A method for calculating energy-saving effects of wind-assisted propulsion ships according to claim 1, characterized in that: In step 3, the other 4 iteration initial values The construction method is: (1) (2) (3) (3) According to experience, q is taken as 10%.

4. A method for calculating energy-saving effects of wind-assisted propulsion ships according to claim 1, characterized in that: In step 5, the method for constructing the expressions of A and b of the linear equation system Ap=b is:

5. A method for calculating energy-saving effects of wind-assisted propulsion ships according to claim 1, characterized in that: In the step six, the The calculation method is as shown in formula (19):

6. A method for calculating energy-saving effects of wind-assisted propulsion ships according to claim 1, characterized in that: In step seven, the ship's four-degree-of-freedom mechanical equilibrium equations are as follows:

7. A method for calculating energy-saving effects of wind-assisted propulsion ships according to claim 1, characterized in that: In step eight, the calculation method of the independent variable residual_x is as shown in formula (17):

8. A method for calculating energy-saving effects of wind-assisted propulsion ships according to claim 1, characterized in that: In step eight, the dependent variable residual_f is calculated as follows:

9. A method for calculating fuel savings for a specific voyage based on the method of any one of claims 1 to 8, characterized in that: The first step is to obtain the effective thrust T based on step 4 E , and then calculate the effective power P E and the required host power P S ; The second step is to calculate the required main engine power with and without the wind-assisted propulsion device to obtain the energy-saving effect of the wind-assisted propulsion device; The third step is to calculate the power saving and energy saving effect under different wind speeds and wind directions; The fourth step is to calculate the power savings for a specific voyage by applying the Global Wind Probability Matrix (IMO recommended global average route wind speed and direction probability matrix). The fifth step is to calculate the fuel savings for a specific voyage using the ship's fuel consumption rate SFOC.

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