Modelica-based FPSO navigation sea condition modeling method

Abstract

The invention belongs to the field of electric digital data processing, and discloses an FPSO navigation sea condition modeling method based on modelia, and the modeling method comprises the steps: employing a modelia language to carry out the modeling of a self-propulsion resistance model and a sea condition environment model; the ship body resistance is obtained after the self-propelled resistance model is modeled; the total additional resistance is obtained after the sea condition environment model is modeled; and the ship body resistance and the total additional resistance are added to obtain the total navigation resistance of the FPSO ship. By means of the method, the complex marine environment can be effectively dealt with, and a dynamics simulation tool of the modelica language is applied to FPSO design. The resistance change of the self-propelled FPSO under various sea conditions can be accurately modeled and analyzed, various variables such as the wind speed, the wave height, the temperature and the salinity are considered, and the dynamic behaviors of the self-propelled FPSO in the navigation and operation process are simulated.

Description

Technical Field

[0001] The invention belongs to the field of electric digital data processing, and in particular relates to a FPSO navigation sea condition modeling method based on Modelica. Background Art

[0002] FPSO (Floating Production Storage and Offloading) is a key equipment widely used in offshore oil and gas production. As a floating platform integrating oil and gas processing, storage and transportation, FPSO operates in harsh marine environment and is significantly affected by external environment such as wind and waves. Therefore, accurate analysis of the resistance FPSO bears during navigation and operation is of great guiding significance for its design, operation and maintenance.

[0003] The Modelica language unifies various multi-domain unified modeling mechanisms in principle, directly supports block diagram-based modeling, object-oriented and component-oriented modeling, and enables it to simultaneously describe mechanical, hydraulic and control systems through a generalized Kirchhoff network mechanism based on ports and connections, providing an ideal platform for multi-domain coupled modeling of resistance and sea environment systems. Summary of the invention

[0004] The present invention provides a FPSO navigation sea condition modeling method based on Modelica, which can effectively cope with complex marine environments and apply the dynamic simulation tool of Modelica language in FPSO design. It can accurately model and analyze the resistance changes of self-propelled FPSO under various sea conditions, consider multiple variables such as wind speed, wave height, temperature, salinity, etc., and simulate its dynamic behavior during navigation and operation.

[0005] To achieve the above object, the present invention provides the following technical solution: a modeling method for FPSO navigation sea conditions based on Modelica, characterized in that: the modeling method comprises using Modelica language to model a self-propulsion resistance model and a sea condition environment model respectively; after the self-propulsion resistance model is modeled, the hull resistance is obtained; after the sea condition environment model is modeled, the total additional resistance is obtained; the hull resistance is added to the total additional resistance to obtain the total navigation resistance of the FPSO ship; the modeling method comprises the following steps: S1: Build a ship self-propulsion resistance model to obtain the hull resistance, the calculation formula is: (1) Among them, R t is the hull resistance, R f is the friction resistance, k 1 is the ship type coefficient, R app is the accessory resistance, R w is the wave resistance, R bis the attachment resistance, R tr is the fluid resistance, R a is additional resistance; S2: Build a sea condition model to obtain the total additional resistance, which is calculated as follows: (2) in, is the total additional resistance, is wind resistance, Adding resistance to waves, For additional sea state resistance; S3: Add the hull resistance obtained in step S1 and the total additional resistance obtained in step S2 to obtain the total navigation resistance of the FPSO vessel.

[0006] Preferably, the friction resistance R in step S1 f The calculation formula is: (3) Where V is the ship speed, ρ is the seawater density, C f is the friction coefficient, S wt is the wet surface area of ​​the hull.

[0007] Preferably, the accessory resistance R in step S1 app The calculation formula is: (4) Where V is the ship speed, ρ is the seawater density, S k2 is the wetted surface area of ​​the external attachment, C f is the friction coefficient, n Bt is the number of bow thrusters, d is the thruster diameter, C Bot is the thruster drag coefficient.

[0008] Preferably, the wave resistance R in step S1 w The calculation formula is: (5) Among them, c 1 、c 2 、c 5 is the correction factor related to the hull characteristics, c 1 is the wave resistance coefficient, c 2 is the wave direction coefficient, c 5 is the ship speed coefficient, Vol is the displacement volume, ρ is the seawater density, m 1 is the exponential decay part of the wave resistance, m 2 To adjust the fluctuation term in wave resistance, F nis the Froude number of the ship, g is the acceleration due to gravity, and λ is the wavelength.

[0009] Preferably, the attached resistance R in step S1 b The calculation formula is: (6) Among them, P b is the resistance coefficient related to the appendage, F n is the Froude number of the ship, g is the acceleration due to gravity, ρ is the density of seawater, A b is the wet surface area of ​​the appendage.

[0010] Preferably, the fluid resistance R in step S1 tr The calculation formula is: (7) Where ρ is the seawater density, V is the ship speed, and A tr is the surface area of ​​the towed object, c 6 is the drag coefficient.

[0011] Preferably, the additional resistance R in step S1 a The calculation formula is: (8) Where ρ is the seawater density, V is the ship speed, S w is the windward area, is the air resistance coefficient.

[0012] Preferably, the stroke resistance in step S2 The calculation formula is: (9) (10) (11) (12) (13) (14) Where V is the ship speed, is the wind speed, β is the relative angle of the wind, is the relative wind speed, is the relative wind direction angle, CDL is the drag coefficient, S w is the windward area, is relative to the frontal area S w The headwind drag coefficient, is the windward area of ​​the ship's side, is the air density, is the hull shape coefficient, is the crossbeam drag coefficient.

[0013] Preferably, the wave additional resistance in step S2 The calculation formula is: (15) Among them, ρ is the seawater density, g is the gravitational acceleration, H is the effective wave height, b is the hull width, is the waterline length of the hull.

[0014] Preferably, the additional sea resistance in step S2 is The calculation formula is: (16) (17) (18) (19) (20) (twenty one) (twenty two) in, is the total resistance based on standard seawater density and viscosity, ρ is the seawater density, is the standard seawater density, is the friction resistance term, is the standard friction coefficient, is the friction coefficient under the current sea conditions, S wt is the wet surface area of ​​the hull, V is the ship speed, is the Reynolds number under current conditions, is the Reynolds number under standard conditions, v is the kinematic viscosity of seawater, is the kinematic viscosity under standard conditions, is the waterline length of the hull.

[0015] Compared with the prior art, the present invention has the following beneficial effects: 1. Modeling with the Modelica language can achieve unified modeling and simulation of the marine environment and navigation resistance of the FPSO system in different fields. The non-causal characteristics of the Modelica language make the coupling between models more flexible, improving the reusability and reconfigurability of the model; 2. Through FPSO model simulation, engineers can optimize the hull shape and structural configuration of the FPSO during the design phase, reduce resistance and improve energy efficiency. In addition, the simulation model can also be used for FPSO operation management, helping to predict and analyze operating performance under extreme sea conditions, thereby ensuring the long-term safety and economy of the system; 3. The present invention introduces the navigation resistance model and the sea environment model to describe in detail the changes in the navigation resistance of ships under complex sea conditions. The model inputs the geometric parameters of the hull (such as ship length, draft, ship width, etc.) and sea environment parameters (such as wind speed, wave height, wave period, etc.), and outputs the total resistance, speed, acceleration and other performance parameters of the hull in real time, thereby helping to optimize the operation efficiency of the ship; DETAILED DESCRIPTION

[0016] The following will be combined with the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, rather than all the embodiments. The following description of at least one exemplary embodiment is actually only illustrative and is by no means intended to limit the present invention and its application or use. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0017] The present invention provides a technical solution: a modeling method for FPSO navigation sea conditions based on Modelica, the modeling method comprises using Modelica language to respectively model a self-propulsion resistance model and a sea condition environment model; after the self-propulsion resistance model is modeled, a hull resistance is obtained; after the sea condition environment model is modeled, a total additional resistance is obtained; the hull resistance is added to the total additional resistance to obtain the total navigation resistance of the FPSO ship navigation; the modeling method comprises the following steps: S1: Build a ship self-propulsion resistance model to obtain the hull resistance, the calculation formula is: (1) Among them, R t is the hull resistance, R f is the friction resistance, k 1 is the ship type coefficient, which is related to the FPSO hull characteristics and operating sea conditions. app is the accessory resistance, R w is the wave resistance, R b is the attachment resistance, R tr is the fluid resistance, R a is additional resistance; The ship self-propelled resistance optimization model is the core model for the analysis of the navigation resistance of the self-propelled FPSO hull. Its function is to provide resistance analysis of the hull in complex sea conditions and provide optimization suggestions for the hull design and operation. By calculating the friction resistance, appendage resistance, wave resistance, etc., combined with the sea condition parameters, the resistance of the FPSO under different operating conditions is optimized, and ultimately the navigation efficiency of the FPSO at sea is improved and energy consumption is reduced.

[0018] In the process of resistance calculation, the Holtrop method better describes the resistance composition of the hull, which includes linearized resistance components such as friction resistance and appendage resistance. Wave resistance is introduced into the resistance model to obtain the resistance model of the self-propelled FPSO.

[0019] S2: Build a sea condition model to obtain the total additional resistance, which is calculated as follows: (2) in, is the total additional resistance, is wind resistance, Adding resistance to waves, For additional sea state resistance; Through accurate modeling of factors such as wind, waves and sea conditions, the total additional resistance of the hull under different sea conditions is dynamically calculated. Combined with the geometric structure of the FPSO hull and sea condition parameters, the resistance of the ship under different operating conditions is optimized and controlled, ensuring that the FPSO has the best navigation efficiency and stability in the changing marine environment.

[0020] The sea condition environment model takes speed, wind speed, wave height, wave period and other parameters as input, and estimates the stress of FPSO in different sea conditions in real time by selecting a suitable calculation model. The input data of the model not only takes into account the physical characteristics of the hull (such as ship width, draft, wet surface area, etc.), but also includes external environmental factors such as air density, seawater density, wind speed direction and wave characteristics. Based on these inputs, the model can simulate the resistance change trend of FPSO in various sea conditions, providing a key reference for the self-propelled system.

[0021] S3: Add the hull resistance obtained in step S1 and the total additional resistance obtained in step S2 to obtain the total navigation resistance of the FPSO vessel.

[0022] In step S1, the friction resistance R f The calculation formula is: (3) Where V is the ship speed, ρ is the seawater density, C f is the friction coefficient, S wtis the wet surface area of ​​the hull. Frictional resistance is the main resistance component caused by the relative motion between the hull surface and the seawater.

[0023] The accessory resistance R in step S1 app The calculation formula is: (4) Where V is the ship speed, ρ is the seawater density, S k2 is the wetted surface area of ​​the external attachment, C f is the friction coefficient, n Bt is the number of bow thrusters, d is the thruster diameter, C Bot is the thruster drag coefficient. The accessory resistance takes into account the influence of various exposed structures on the ship, such as thrusters, propeller shaft brackets, etc.

[0024] The wave resistance R in step S1 w The calculation formula is: (5) Among them, c 1 、c 2 、c 5 is the correction factor related to the hull characteristics, c 1 is the wave resistance coefficient, c 2 is the wave direction coefficient, c 5 is the ship speed coefficient, Vol is the displacement volume, ρ is the seawater density, m 1 is the exponential decay part of the wave resistance, m 2 To adjust the fluctuation term in wave resistance, F n is the Froude number of the hull, g is the acceleration due to gravity, and λ is the wavelength. Wave drag is the hydrodynamic reaction force caused by the motion of the ship in the waves.

[0025] The attached resistance R in step S1 b The calculation formula is: (6) Among them, P b is the resistance coefficient related to the appendage, F n is the Froude number of the ship, g is the acceleration due to gravity, ρ is the density of seawater, A b is the wet surface area of ​​the appendage. The appendage resistance is mainly caused by the non-smooth parts of the hull (such as ballast tanks, keels, rudders and other appendage structures). This part of the resistance is usually estimated by the above empirical formula.

[0026] The fluid resistance R in step S1 tr The calculation formula is: (7) Where ρ is the seawater density, V is the ship speed, and A tr is the surface area of ​​the towed object, c 6 is the drag coefficient. Fluid resistance refers to the resistance between the hull and the water due to the fluid dynamics effect, especially the effects of the hull's geometry, fluid viscosity, flow separation and other factors on the resistance.

[0027] Additional resistance R in step S1 a The calculation formula is: (8) Where ρ is the seawater density, V is the ship speed, S w is the windward area, is the air resistance coefficient. Additional resistance is the additional resistance caused by special fluid conditions (such as changes in seawater temperature and salinity), which is particularly significant in extreme sea conditions. In some embodiments, the additional resistance also includes corrections for changes in temperature, salinity and density.

[0028] The above responsive ship resistances are embedded into the resistance optimization model through text modeling to simulate the resistance changes of FPSO under complex sea conditions. By simulating the self-propelled FPSO resistance optimization model, the requirements of FPSO for minimizing resistance under different operating conditions are met, and the optimal allocation and global control of energy efficiency are achieved.

[0029] Step S2 Stroke Resistance The calculation takes into account the influence of hull shape and wind direction on wind resistance. The calculation formula is: (9) (10) (11) (12) (13) (14) Where V is the ship speed, is the wind speed, β is the relative angle of the wind, is the relative wind speed, is the relative wind direction angle, CDL is the drag coefficient, S w is the windward area, is relative to the frontal area S w The headwind drag coefficient, is the windward area of ​​the ship's side, is the air density, is the hull shape coefficient, is the crossbeam wind resistance coefficient. Wind factors mainly affect wind resistance through relative angle and wind speed, and through the hull speed V and wind speed And the relative angle β of the wind, calculate the two relative velocity components V 1 and V 2。

[0030] Wave additional resistance in step S2 The calculation formula is: (15) Among them, ρ is the seawater density, g is the gravitational acceleration, H is the effective wave height, b is the hull width, is the waterline length of the hull. The modeling formula for wave additional resistance adopts the STAwave method. The term represents the effect of the shape ratio of the hull on the additional wave resistance. The square term of the effective wave height H shows that the wave height has a significant effect on the resistance. The higher the wave, the greater the resistance.

[0031] Additional sea resistance in step S2 The calculation formula is: (16) (17) (18) (19) (20) (twenty one) (twenty two) in, is the total resistance based on standard seawater density and viscosity, ρ is the seawater density, is the standard seawater density, is the friction resistance term, is the standard friction coefficient, is the friction coefficient under the current sea conditions, S wt is the wet surface area of ​​the hull, V is the ship speed, is the Reynolds number under current conditions, is the Reynolds number under standard conditions, v is the kinematic viscosity of seawater, is the kinematic viscosity under standard conditions, is the waterline length of the hull. The modeling method of the additional sea state resistance mainly considers the influence of the changes in density and friction coefficient caused by temperature and salinity on the hull resistance.

[0032] The above modeling of the sea condition environment further accurately estimates the additional sea condition resistance by calculating the effect of seawater density and viscosity on friction resistance. The changes in these parameters are usually affected by sea temperature and salinity. By inputting parameters such as wind speed, wave height and hull into the model, the output calculates the resistance of variable sea conditions.

[0033] The Holtrop method is used in the modeling of the ship's self-propulsion resistance model, which is more suitable for the ship design stage and is used to evaluate the resistance characteristics of different hull geometry design schemes. The Holtrop method takes into account more hull design factors and is suitable for use in design optimization and performance evaluation. The sea condition environment model modeling is suitable for navigation analysis under specific sea conditions, especially under conditions of large winds and waves, significant changes in temperature and salinity, to evaluate the impact of environmental factors on ship performance. It is suitable for dynamically adjusting the speed and route during the operation phase to ensure safety and economy. In practical applications, the sea condition model and the Holtrop method can be used complementary. The sea condition model provides a real-time assessment of the impact on the environment when the ship is running, while the Holtrop law helps optimize the hull shape and reduce the total resistance during the design phase, thereby improving the performance of the ship.

[0034] Example: The simulation simulates a ship sailing long distances in open waters and encountering strong winds and waves. The design goal is to analyze the sailing resistance of the ship through simulation, evaluate the sailing performance under different speeds and sea conditions, and optimize the performance based on the simulation results.

[0035] The specific parameter calculation and modeling process are as follows:

[0036] Hull waterline length = 100 meters, hull width b = 20 meters, draft d = 8 meters, hull wet surface area S wt =1500 square meters, displacement mass=50000 tons;

[0037] Wind speed =15 meters / second, wave height H=3 meters, wave period = 7 seconds, seawater density ρ = 1025 kg / m3, temperature T = 15 degrees Celsius, salinity S = 35 g / L;

[0038] Speed ​​V = 12 m / s; 1. The ship self-propulsion resistance model is built, and the Holtrop method is used to calculate the hull resistance of the ship at different speeds. The hull resistance includes friction resistance, attachment resistance, wave resistance, appendage resistance, fluid resistance and air resistance: (1) Friction resistance R f Calculation: ;

[0039] Use wet surface area Swt =1500, speed V=12, friction coefficient C f =0.002 for calculation, ;

[0040] (2) Attachment resistance R app Calculation: ;

[0041] Wetted surface area S of external accessories k2 =5 m², number of bow thrusters n Bt =4, thruster diameter d=0.3 m, thruster drag coefficient C Bto =0.8, ; ; ; ;

[0042] (3) Wave resistance R w Calculation: Wave resistance is calculated using the model described above, ;

[0043] (4) Attachment resistance R b Calculation: ;

[0044] The cross-sectional area of ​​the appendage A b =20 square meters, gravitational acceleration g=9.81m / s², the resistance coefficient related to the appendage P b =0.6, ; ; ; ; ; (5) Fluid resistance R tr Calculation: ; The surface area of ​​the towed object Atr = 40 square meters, the drag coefficient c 6 =0.8, ; (6) Additional resistance R a Calculation: ; Windward area S w =300, air resistance coefficient =0.8, ; Substitute all resistance terms into the hull resistance formula: ; ; 2. Model the sea condition environment to obtain the total additional resistance , by inputting sea condition parameters, calculate wind resistance , wave additional resistance , additional sea resistance : (1) Wind resistance Calculation: ; Relative wind speed =15m / s, relative wind direction angle =45°, drag coefficient CDL=0.8, frontal area S w =300m 2 , the windward area of ​​the ship's side =300m 2 , air density =1.225kg / m 3 , Hull shape coefficient =0.1, beam drag coefficient =1.0, drag coefficient CDL=0.8, ; (2) Additional wave resistance Calculation: ; ρ=1025, H=3, b=20, =100 ; (3) Additional sea resistance Calculation: ; =8000N, =5000N, depending on temperature and salinity, ; Substituting all resistance terms into the total additional resistance formula of the hull sea state environment model: ; ; ; In this embodiment, the resistances calculated based on the sea condition environment model and the Holtrop method are: Total additional resistance of sea condition model: 39166.87 N Holtrop hull resistance: 736693.85 N Therefore, the total sailing resistance of the FPSO ship is 39166.87N+736693.85N=775860.72N Analysis of the sources of resistance differences: The sea condition environment model focuses on the external effects of environmental factors on the hull (such as wind, waves, temperature and salinity), and focuses on calculating the resistance caused by wind speed, waves and temperature-salinity effects. The contribution of these external factors to the hull resistance is particularly important in severe sea conditions, but the internal geometric characteristics of the hull or specific design factors are not considered. Therefore, the total resistance value of the sea condition environment model is relatively small.

[0045] The Holtrop method is a more comprehensive resistance calculation method that not only takes into account external environmental resistance (such as air resistance), but also includes multiple items such as hull friction resistance, appendage resistance, wave resistance, and drag resistance. The Holtrop method takes into account factors such as the hull's geometric design, additional equipment, and appendages, making the resistance calculation more comprehensive. Therefore, the hull resistance calculated by the Holtrop method is significantly higher than the total additional resistance of the sea condition environment model.

[0046] The sea condition environment model provides the direct impact of the environment on the ship's navigation. It is suitable for real-time evaluation of the additional resistance brought by the external environment during navigation, which helps the navigation control and safety of the ship.

[0047] The Holtrop method is more suitable for use in the design phase. It helps optimize the hull structure and appendage arrangement through a comprehensive resistance assessment, provides a reliable hull resistance benchmark, and optimizes the overall performance of the ship.

[0048] Although embodiments of the present invention have been shown and described, it will be appreciated by those skilled in the art that various changes, modifications, substitutions and variations may be made to the embodiments without departing from the principles and spirit of the present invention, and that the scope of the present invention is defined by the appended claims and their equivalents.

Claims

1. A FPSO navigation sea condition modeling method based on Modelica, characterized by: The modeling method comprises using modelica language to model a self-propulsion resistance model and a sea environment model respectively; after the self-propulsion resistance model is modeled, the hull resistance is obtained; after the sea environment model is modeled, the total additional resistance is obtained; the hull resistance is added to the total additional resistance to obtain the total navigation resistance of the FPSO ship; the modeling method comprises the following steps: S1: Build a ship self-propulsion resistance model to obtain the hull resistance, the calculation formula is: （1） Among them, R t is the hull resistance, R f is the friction resistance, k1 is the ship type coefficient, R app is the accessory resistance, R w is the wave resistance, R b is the attachment resistance, R tr is the fluid resistance, R a is additional resistance; S2: Build a sea condition model to obtain the total additional resistance, which is calculated as follows: （2） in, is the total additional resistance, is wind resistance, Adding resistance to waves, For additional sea state resistance; S3: Add the hull resistance obtained in step S1 and the total additional resistance obtained in step S2 to obtain the total navigation resistance of the FPSO vessel.

2. The method for modeling FPSO navigation sea conditions based on Modelica according to claim 1, characterized in that: In step S1, the friction resistance R f The calculation formula is: （3） Where V is the ship speed, ρ is the seawater density, C f is the friction coefficient, S wt is the wet surface area of ​​the hull.

3. The method for modeling FPSO navigation sea conditions based on Modelica according to claim 1, characterized in that: In step S1, the accessory resistance R app The calculation formula is: （4） Where V is the ship speed, ρ is the seawater density, S k2 is the wetted surface area of ​​the external attachment, C f is the friction coefficient, n Bt is the number of bow thrusters, d is the thruster diameter, C Bot is the thruster drag coefficient.

4. The method for modeling FPSO navigation sea conditions based on Modelica according to claim 1, characterized in that: In step S1, the wave resistance R w The calculation formula is: （5） Among them, c1, c2, c5 are correction coefficients related to hull characteristics, c1 is the wave resistance coefficient, c2 is the wave direction coefficient, c5 is the ship speed coefficient, Vol is the displacement volume, ρ is the seawater density, m1 is the exponential decay part of the control wave resistance, m2 is the fluctuation term in the adjustment wave resistance, F n is the Froude number of the ship, g is the acceleration due to gravity, and λ is the wavelength.

5. The method for modeling FPSO navigation sea conditions based on Modelica according to claim 1, characterized in that: In step S1, the attached resistance R b The calculation formula is: （6） Among them, P b is the resistance coefficient related to the appendage, F n is the Froude number of the ship, g is the acceleration due to gravity, ρ is the density of seawater, A b is the wet surface area of ​​the appendage.

6. The method for modeling FPSO navigation sea conditions based on Modelica according to claim 1, characterized in that: In step S1, the fluid resistance R tr The calculation formula is: （7） Where ρ is the seawater density, V is the ship speed, and A tr is the surface area of ​​the towed object, and c6 is the drag coefficient.

7. The method for modeling FPSO navigation sea conditions based on Modelica according to claim 1, characterized in that: The additional resistance R in step S1 a The calculation formula is: （8） Where ρ is the seawater density, V is the ship speed, S w is the windward area, is the air resistance coefficient.

8. The method for modeling FPSO navigation sea conditions based on Modelica according to claim 1, characterized in that: Step S2: Stroke resistance The calculation formula is: （9） （10） （11） （12） （13） （14） Where V is the ship speed, is the wind speed, β is the relative angle of the wind, is the relative wind speed, is the relative wind direction angle, CDL is the drag coefficient, S w is the windward area, is relative to the frontal area S w The headwind drag coefficient, is the windward area of ​​the ship's side, is the air density, is the hull shape coefficient, is the crossbeam drag coefficient.

9. The method for modeling FPSO navigation sea conditions based on Modelica according to claim 1, characterized in that: The wave additional resistance in step S2 The calculation formula is: （15） Among them, ρ is the seawater density, g is the gravitational acceleration, H is the effective wave height, b is the hull width, is the waterline length of the hull.

10. The method for modeling FPSO navigation sea conditions based on Modelica according to claim 1, characterized in that: The additional sea resistance in step S2 The calculation formula is: （16） （17） （18） （19） （20） （21） （22） in, is the total resistance based on standard seawater density and viscosity, ρ is the seawater density, is the standard seawater density, is the friction resistance term, is the standard friction coefficient, is the friction coefficient under the current sea conditions, S wt is the wet surface area of ​​the hull, V is the ship speed, is the Reynolds number under current conditions, is the Reynolds number under standard conditions, v is the kinematic viscosity of seawater, is the kinematic viscosity under standard conditions, is the waterline length of the hull.

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