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Ship response in short-crested irregular waves is calculated as the product of the frequency response function of ship response in regular waves and the directional spectrum of waves. However, the commonly used IACS and JONSWAP spectra may not accurately reproduce detailed spectra by wave hindcasting data and wave radar measurements, leading to over- or underestimation of ship responses. This study focuses on the reproducibility of a detailed directional spectrum by standard directional spectrum based on physical considerations concerning the mean spreading angle. This approach facilitates discussion on the limitations of reproducing a detailed directional spectrum with a standard directional spectrum. Furthermore, a procedure is proposed for the use of a standard directional spectrum based on the mean spreading angle as an indicator. Analysis using 6 example ships demonstrates that employing the procedure enables the extraction of highly reproducible and valuable data for short-term prediction of the added resistance in short-crested irregular waves. [ABSTRACT FROM AUTHOR]

This paper examines the acquisition of the measurement data of the spatial distribution of unsteady pressure on a ship advancing in waves. The purpose of the study is to investigate the reliability of the pressure data obtained by the unprecedented experiment and to provide experimental data of unsteady pressure which can be used for validation of arbitrary computation methods. The optical fiber sensing technology, so-called FBG (fiber Bragg gratings) sensing, is employed as the pressure sensors. In the experiment, 379 FBG pressure sensors (version 7; the latest version) in total are attached to the port side surface of ship model and also ordinary strain-type pressure sensors are embedded in the starboard side for validating reliability of FBG pressure sensors by comparing both results. In addition to the pressure distribution, measurement is made for unsteady hydrodynamic forces such as added mass, damping coefficients, and wave exciting forces, and also for ship motions and added resistance. Most of the measurement is repeated at least five times for each condition, and results of measured pressures are evaluated with mean value and standard deviation. Regarding the added resistance, the distribution for estimating added resistance is also extracted from obtained pressure distribution and its pressure contour is illustrated to show visually which hull region affects the added resistance significantly. Validation of the measured pressure with FBG pressure sensors is carried out also by integrating measured pressures over the ship model surface and comparing it with forces directly measured with load cells. The measured pressure distribution is compared with typical calculation results with the Rankine panel method in frequency domain to demonstrate usefulness of the spatial pressure data for validating the calculation method. Through these studies, it is confirmed that the measured unsteady pressures with FBG pressure sensors are accurate enough and valuable as the validation data for any calculation method. [ABSTRACT FROM AUTHOR]

The prediction of fuel consumption and resulting transportation costs is a crucial stage in ship design, particularly for conditions involving motion in waves. This study investigates the real-time fuel consumption of a container ship when sailing in waves. The overall ship performance is evaluated using a novel non-linear coupled hull-engine-propeller interaction model. A series of towing tank experiments for hull resistance in waves and propeller performance are conducted. The ship engine is mathematically modelled by a quasi-steady-state model equipped with a linear Proportional-Integrator (PI) governor. Various scenarios of shipping transportation are studied, and the resulting instantaneous fuel consumptions and their correlation to other dynamic particulars are demonstrated. Additionally, daily fuel consumption and fuel cost per voyage distance are presented. It is also shown that the controller can effectively adjust the fuel rate, resulting in minimum fuel consumption. The study concludes that there is no correlation between fuel consumption and the frequency of fuel rates. The present framework and mathematical model can also be employed for ship design and existing ships to predict the total required energy per voyage.

The impulse response method is a frequently used method to calculate ship seakeeping behavior. In this paper, the restoring and Froude-Krylov calculation is conducted with constant evaluation of panel pressures as well as Gauss quadrature and an analytical integration. The applied panel grid is coarsened by an adaptive algorithm which is based on a normal vector condition. The comparison of methods is based on grid convergence studies which are followed by a verification of forces with computational fluid dynamics (CFD) results on the fixed duisburg test case in waves. Validations with experimental results in head, oblique and following waves show that all integration methods are accurate. The exact integration is numerically sensitive in some cases. Gauss quadrature is highly accurate; however, the additional effort is not beneficial since the geometrical accuracy has-stronger influence on the force amplitudes than the integration method. Adaptive grid coarsening reduces the simulation time and is accurate up to a level, where the panel length comes close the wavelength. The added resistance at the investigated Froude number of 0.05 shows higher uncertainty levels, this applies to the results of both the numerical methods and model tests. [ABSTRACT FROM AUTHOR]

• Prediction method of steady wave forces acting on an obliquely moving ship in short waves is proposed. • The existing asymptotic formula is enhanced in terms of the wave amplitude and flow velocity near the ship. • Proposed method efficiently predicts course-keeping manoeuvres of a ship model in regular short waves. • Proposed method approximately predicts course-keeping manoeuvres even under rudder effectiveness for a full-scale ship. In this study, we propose a prediction method for steady wave forces acting on an obliquely moving ship in short waves. Particularly, we enhance an existing method that focuses on refraction of flow and waves in the vicinity of ship's waterline, in terms of the wave amplitude in the near region of the ship and the flow velocity. The former is theoretically modified by deriving an advection equation for wave energy on a ship-fixed frame, and the latter is improved by reflecting the results of computational fluid dynamics that automatically includes viscous effects. A comparison between the prediction and published captive model test results shows that the present method can more adequately capture the variation of the steady wave forces owing to the ship advancing speed and lateral drift than the original method, although the prediction accuracy is not necessarily improved under all conditions. To confirm the applicability of the present method for steady wave forces to ship manoeuvring problems, we predict course-keeping manoeuvres of a ship in regular short waves through a numerical simulation that considers only the steady wave forces in the equation of motion in calm water. The manoeuvring simulation results are validated using previously published free-running model test results, involving various rudder effectiveness conditions for the ship model and full-scale ships, both with and without engine limits. The comparison shows that the present method for steady wave forces is effective in predicting the course-keeping manoeuvres under rudder effectiveness conditions for a ship model in regular short waves. Nonetheless, the present method is insufficiently practical in terms of the manoeuvring simulation under rudder effectiveness conditions for a full-scale ship that is relatively more susceptible to waves. We confirm that an empirical correction for the computed steady wave surge forces based on the discrepancy between the measured and computed values under the ship resting enables the approximate prediction of the course-keeping manoeuvres even under the rudder effectiveness conditions for the full-scale ship. [ABSTRACT FROM AUTHOR]

Accurate resistance performance evaluation is essential to predict the minimum propulsion horsepower required for ships in real sea. Therefore, in this paper, the added resistance performance of K-Supramax in various wave conditions was calculated using CFD (Computational Fluid Dynamics). First, to compare the resistance performance according to the DOF (Degree of Freedom), the added resistance performance in the head regular wave was investigated and compared with the experiment. The 2DOF and 6DOF results in the head regular wave had no significant differences. Second, to compare the resistance performance among various wave conditions, the effect of the heading angle was analyzed by comparing resistance and motion RAOs (Response Amplitude Operators) in bow quartering sea conditions using 6DOF. The added resistance showed the highest value near the resonance frequency of 170°. As the heading angle increased, the added resistance tended to decrease, regardless of the wavelength ratio. Also, the added resistance performance in irregular waves was investigated with reference to the adverse conditions. The spectral method, which linearly superimposes regular wave results, and the added resistance generated during irregular waves directly through CFD were compared. The resistance in irregular waves increased by approximately 92% for the spectral method and by approximately 72% for the direct irregular wave calculation compared to the resistance in calm water. In addition, the PSD (Power Spectral Density) of resistance and the distribution of motion RAOs obtained from direct irregular wave calculations were investigated. [ABSTRACT FROM AUTHOR]

Crew boat is a type of vessels used for the mobility of offshore workers and logistical supply needed for the offshore platform. Crew boat KCT-1901 is categorized as a planning boat with hard chine body. KCT-1901 requires an added power when it is sailing through a seaway. The reason behind this is because when a ship sails through a seaway, the ships experienced a heave and pitch motion resulted in added resistance and hence added power. The goal of the investigation is to estimate added resistance and added power of the crew boat using computational fluid dynamic (CFD) method and tested in calm water and in waves with several Froude numbers (Fr) and wave periods. A method developed by Savitsky is used for verification at high-speed mode. The largest total resistance using CFD in calm water is 38.98 kN and using Savitsky method is 39.00 kN obtained at Fr 0.72. Both are in good agreement and the discrepancy is less than 0.1%. Comparative study was carried out against experimental test in a towing tank. The drag forces tested at Fr 0.12 and 0.24, between the two approaches, showed a discrepancy of about 4%. Further CFD test was conducted on wave pattern analysis, which demonstrated that as the Fr increases the becomes clearer and stronger and tests in waves condition at lower wave period showed that the transverse wave becomes more apparent. Therefore, overall can be said that the CFD simulation showed such a good agreement with empirical Savitsky method and experimental tank test.

The need for maritime freight transport of various goods has never been greater. Consequently, ships are designed with ever-increasing dimensions, with the emphasis, of course, on length. One of the many challenges in the design of large ships is the prediction of their behavior in waves, i.e., motions, and consequently, added resistance. In this paper, a comparative study of two numerical tools for estimating ship motions and added resistance is presented. The first tool is the well-established DNV's commercial seakeeping code Wasim, a weakly nonlinear potential flow (PF) solver based on a Rankine panel method. The other is the increasingly recognized open-source Computational Fluid Dynamic (CFD) toolkit OpenFOAM®, a viscous flow solver with a turbulence model; it is based on the finite volume method (FVM) combined with a volume-of-fluid (VOF) technique for sea-surface evolution. The study is carried out for two ship seakeeping cases in head-sea regular waves, respectively, without and with ship forward speed. The first case refers to a 6750 TEU containership scale model developed at the LHEEA laboratory in Nantes for a benchmark study, providing experimental data for all test cases. Pitch and heave response is calculated and compared with the experimental values. The second case refers to a KRISO container ship, an extensively researched hull model in ship hydrodynamics. In addition to the pitch and heave, added resistance is also calculated and compared with the experimental values. Hence, it provides a comprehensive basis for a comparative analysis between the selected solvers. The results are systematically analyzed and discussed in detail. For both cases, deterioration of the PF solution with increasing wave steepness is observed, thus suggesting limitations in the modeled nonlinear effects as a possible reason. The accuracy of the CFD solver greatly depends on the spatial discretization characteristics, thus suggesting the need for grid independence studies, as such tools are crucial for accurate results of the examined wave–body interaction scenarios. [ABSTRACT FROM AUTHOR]

Biofouling attaches to immersed surfaces in between hull cleanings. Due to high speeds and relatively short port times, biofilm often attaches to the immersed surfaces of containerships. In most cases, this type of fouling is not given much importance since it is assumed that it will not cause any fouling penalties. In this paper, the fouling penalties related to fouling with biofilm on the example of the Post Panamax and Post Panamax Plus containership fleets sailing in the Adriatic Sea are assessed. In addition, the investigation is performed for real environmental conditions that a containership can encounter on a sailing route passing through the Adriatic Sea. Thus, the impact of waves and wind is taken into account based on mean values of significant wave height and wind speed for containerships sailing at the design speed along the analyzed route. The procedure for the determination of the detrimental effects of biofilm on the increase in fuel consumption and carbon dioxide emissions is given. Further, the proposed procedure includes the determination of calm water resistance by the Holtrop and Mennen method, the added resistance in waves by Liu and Papanikolaou's method, spectral analysis using the Tabain's spectrum for the Adriatic Sea, the wind resistance by the Blendermann method, and added resistance due to biofouling using the Granville method. Thereafter, a time-dependent biofouling growth model proposed by Uzun et al. is incorporated, and the adequate timing for underwater hull cleaning is determined for several hull cleaning costs. The obtained results demonstrate that, from an environmental point of view, proactive hull cleaning should be applied, while, from an economic perspective, optimal timing for underwater hull cleaning is recommended. [ABSTRACT FROM AUTHOR]

Amid a global effort in reducing the shipping ecologic impact, the study of the particular case of added resistance of high speed vessels cruising in a seaway has been approached by a very limited number of authors. In this study, we provide a comprehensive and systematic assessment of the added resistance of a planing hull in regular waves. The data are analyzed in both the time and frequency domains in order to fully characterize the added resistance and highlight its correlation with hull motions. It is found that peak added resistance modulation occurs for shorter waves with respect to the peak average added resistance, and slenderness is beneficial only in terms of modulation. Nonlinearity of both the average and first harmonic amplitude is also shown. In addition, results of the phase analysis show a correlation between the added resistance phase and average added resistance. [ABSTRACT FROM AUTHOR]

Ship resistance is an important characteristic to predict in the preliminary design stage. Proper prediction of ship resistance implies the fulfillment of the required speed and power of a ship. The assumed body characteristics of a ship model should also be properly considered when investigating ship resistance. In the present study, the assumption of a hydroelastic body for a ship model was used in an experiment on total ship resistance and added resistance in calm water and waves. Two hydroelastic models were used: a hydroelastic body with a bulbous bow (HB) and a hydroelastic body without a bulbous bow (HWB). The wavelength considered ranged from 0.5 L to 1.3 L, and the Froude number (Fn) considered ranged from 0.058 to 0.232. In the presented results, the total resistance coefficient of the HWB was higher than that of a rigid body without a bulbous bow (RWB). The average difference of magnitude between the HWB and RWB was 30.49% for calm water conditions and 30.37% for overall wave conditions. The total resistance of the HB was higher than that of the rigid body with a bulbous bow (RB), and the difference of magnitude was approximately 31.47% for calm water conditions and 31.68% for overall wave conditions. The added resistance coefficient of the HWB tended to increase with an increase in the wavelength, from 0.5 L to 1.1 L, and then decrease until 1.5 L. The overall tendency of the added resistance coefficient of the HB was significantly different from the other numerical results. Although the tendencies were different, most of the presented results were in the same range as the other numerical results.

In this study, we investigate the influence of wave steepness on both ship motions and added resistance in regular head waves by conducting simulations at three distinct wave steepness levels using unsteady RANS method. Numerical results show that, when wavelength comparable to the ship length, the interaction of body nonlinearity and wave nonlinearity results in highly nonlinear behavior in the time history of added resistance. The study illustrates, step-by-step, the hydrodynamic pressure distribution on the hull during an encounter period, highlighting the time-varying nature of the added resistance. Examining the visualised results, it is observed that in certain instances, high pressure may be exerted on the flat bottom of the trimmed ship and contribute significantly to the added resistance. It is observed that, when wavelength is comparable to ship length, the added resistance coefficient decreases with increasing wave steepness. Specifically, at λ/L PP = 1.15, | C A W , H / λ = 1 / 30 − C A W , H / λ = 1 / 60 | C A W , H / λ = 1 / 60 = 27.1%. In relatively short waves the diffraction phenomena dominate and the resulting added resistance exhibits limited nonlinearity. However, obtaining stable results in such cases proves challenging. Finally, the influence of wave steepness on added resistance is quantified. The results are useful for improving the transparent methods for predicting the added resistance in wave. • Extensive validation of the CFD simulation results of time history of heave, pitch, and added resistance against experimental data. • Visualised ship motions and spatial pressure distribution to illustrate the generation of added resistance. • In relatively long waves, the added resistance coefficient decreases as wave steepness increases and its time history shows strong nonlinear behavior. • In relatively short waves, the motion-constrainedadded resistance coefficient is different from that in motion-free mode. [ABSTRACT FROM AUTHOR]

Experimental and numerical methods were employed to investigate the added resistance and seakeeping performance of an innovative unmanned catamaran for offshore surveying. Model experiments validated numerical results from viscous flow computational fluid dynamics (CFD) modeling using the unsteady Reynolds-averaged Navier–Stokes (URANS) equations and the potential flow method. URANS modeling precisely predicted the catamaran's performance in regular waves, and the potential flow method offered effective short-term predictions in irregular waves. Simulations were performed at three velocities (4, 6, and 8 knots). The results highlight the fundamental relationships between added resistance and motion responses with changing wave conditions. The extreme motion responses generated by typical actual sea conditions are summarized. The added resistance and motion responses are greatest when the wavelength is slightly longer than the length of the catamaran and the encounter frequency, f e , is ∼1.2. The optimal velocity of the catamaran is 6 knots. The seakeeping performance of the catamaran was assessed using existing indicators for manned vessels. Compared with manned vessels, unmanned survey vessels are more tolerant of first-order motion response but require stricter limitations on second-order accelerations in each degree of freedom. • URANS method with potential flow method enable comprehensive and efficient performance prediction of the case catamaran. • The motion prediction of full-scale catamaran under irregular waves in actual sea states were carried out. • As the speed increases, the status of the newly designed catamaran translates from a displacement vessel to a planing craft. • Future enhancements for the formulation of seakeeping criteria for unmanned ships were proposed. [ABSTRACT FROM AUTHOR]

Accurate resistance performance evaluation is essential to predict the minimum propulsion horsepower required for ships in real sea. Therefore, in this paper, the added resistance performance of K-Supramax in various wave conditions was calculated using CFD (Computational Fluid Dynamics). First, to compare the resistance performance according to the DOF (Degree of Freedom), the added resistance performance in the head regular wave was investigated and compared with the experiment. The 2DOF and 6DOF results in the head regular wave had no significant differences. Second, to compare the resistance performance among various wave conditions, the effect of the heading angle was analyzed by comparing resistance and motion RAOs (Response Amplitude Operators) in bow quartering sea conditions using 6DOF. The added resistance showed the highest value near the resonance frequency of 170°. As the heading angle increased, the added resistance tended to decrease, regardless of the wavelength ratio. Also, the added resistance performance in irregular waves was investigated with reference to the adverse conditions. The spectral method, which linearly superimposes regular wave results, and the added resistance generated during irregular waves directly through CFD were compared. The resistance in irregular waves increased by approximately 92% for the spectral method and by approximately 72% for the direct irregular wave calculation compared to the resistance in calm water. In addition, the PSD (Power Spectral Density) of resistance and the distribution of motion RAOs obtained from direct irregular wave calculations were investigated.

ObjectiveTo address the problem of wave amplitude attenuation and phase shift with respect to propagation time and distance in numerical simulation, a set of parametric design methods that can stabilize wave generation in multiple periods is given. MethodsBased on Navier-Stokes equations and volume of fluid (VOF) method, a numerical simulation of fifth-order Stokes wave is carried out. Through the analysis of the discrete scheme of the one-dimensional wave equation, the influence of several important parameters on wave-generation effect is studied. Finally, the proposed parametric design method is used to carry out the three-dimensional numerical calculation of the resistance and motion response of the KRISO container ship (KCS) in head seas. ResultsThe results show that parameters such as inner iteration times, grid resolution, and Courant number can be accurately set according to certain rules to ensure that the error of wave amplitude is about 5% within 20 wave periods and about 10% within 40 wave periods. Through the three-dimensional numerical calculation of a KCS ship, the results obtained show an error of about 10% compared with the experimental results of model, Conclusionwhich verifies the feasibility of this method.

The outrigger symmetry of a trimaran is believed to significantly affect its hydrodynamic functioning. The present study was conducted to investigate the added resistance responses and experimental vertical motion of a wave-piercing trimaran in regular head waves. A series of experiments have been carried out in the National Iranian Marine Laboratory (NIMALA) towing tank to determine the effect of side hulls symmetry on the heave and pitch motions and added resistance. The models were tested over a range of wave frequencies and Froude numbers using both symmetric and asymmetric outriggers. According to the results, the symmetric side hull form based on heave motion, the outboard form in terms of pitch motion and added resistance have better performances among these three kinds of side hull forms. Furthermore, there are local maximum and minimum points on the ship motion response curves due to heave and pitch coupling in their respective frequencies.

In the present study, the hull form of an 1,800 TEU containership was developed to reduce fuel consumption under real operation conditions. Contrary to the conventional hull form design practice in terms of the calm-sea performance, the hull form design in this study was aimed at improving the performance of a ship under in-service condition, which is closely associated with the added resistance due to waves. In order to reduce the added resistance due to waves, the bow hull form was modified to have sharper entrance with increased length between perpendicular. This enabled the waves to follow the bow part more smoothly. The added resistance of the developed hull was predicted by means of a series of CFD simulations in regular waves with wavelengths λ/Lpp=0.5∼2.0. The added resistance at irregular waves was calculated by frequency integration. The Daily Fuel Oil Consumption (DFOC) was subsequently calculated based on the wave statistics on the operating route. The significance of the present study lies in the point that the performance evaluation was carried out by means of the free-surface CFD simulation in the presence of regular waves. Final performance verification was made through a series of model tests. The resulting DFOC and daily CO2 emission for the optimal hull form under the in-service conditions was found to be reduced by 7.65%. Furthermore, the calm-sea DFOC and CO2 emission were also improved by 3.43%.

Bow shape has been recognized as an important factor influencing the seakeeping performance and added resistance of ships. This paper presents a numerical comparative study on added resistance and seakeeping of model ships with 'X-bow' and a wave-piercing monohull in regular head waves using a computational fluid dynamics (CFD) software. Different wave heights, wavelengths and forward speeds are considered in the systematic investigation in order to characterize the added resistance and wave-induced motions, and to explore the local wave patterns. The results show a considerably different hydrodynamic characteristic by different bow shapes. [ABSTRACT FROM AUTHOR]

The need for maritime freight transport of various goods has never been greater. Consequently, ships are designed with ever-increasing dimensions, with the emphasis, of course, on length. One of the many challenges in the design of large ships is the prediction of their behavior in waves, i.e., motions, and consequently, added resistance. In this paper, a comparative study of two numerical tools for estimating ship motions and added resistance is presented. The first tool is the well-established DNV’s commercial seakeeping code Wasim, a weakly nonlinear potential flow (PF) solver based on a Rankine panel method. The other is the increasingly recognized open-source Computational Fluid Dynamic (CFD) toolkit OpenFOAM®, a viscous flow solver with a turbulence model; it is based on the finite volume method (FVM) combined with a volume-of-fluid (VOF) technique for sea-surface evolution. The study is carried out for two ship seakeeping cases in head-sea regular waves, respectively, without and with ship forward speed. The first case refers to a 6750 TEU containership scale model developed at the LHEEA laboratory in Nantes for a benchmark study, providing experimental data for all test cases. Pitch and heave response is calculated and compared with the experimental values. The second case refers to a KRISO container ship, an extensively researched hull model in ship hydrodynamics. In addition to the pitch and heave, added resistance is also calculated and compared with the experimental values. Hence, it provides a comprehensive basis for a comparative analysis between the selected solvers. The results are systematically analyzed and discussed in detail. For both cases, deterioration of the PF solution with increasing wave steepness is observed, thus suggesting limitations in the modeled nonlinear effects as a possible reason. The accuracy of the CFD solver greatly depends on the spatial discretization characteristics, thus suggesting the need for grid independence studies, as such tools are crucial for accurate results of the examined wave–body interaction scenarios.

Ship resistance is an important characteristic to predict in the preliminary design stage. Proper prediction of ship resistance implies the fulfillment of the required speed and power of a ship. The assumed body characteristics of a ship model should also be properly considered when investigating ship resistance. In the present study, the assumption of a hydroelastic body for a ship model was used in an experiment on total ship resistance and added resistance in calm water and waves. Two hydroelastic models were used: a hydroelastic body with a bulbous bow (HB) and a hydroelastic body without a bulbous bow (HWB). The wavelength considered ranged from 0.5 L to 1.3 L, and the Froude number (Fn) considered ranged from 0.058 to 0.232. In the presented results, the total resistance coefficient of the HWB was higher than that of a rigid body without a bulbous bow (RWB). The average difference of magnitude between the HWB and RWB was 30.49% for calm water conditions and 30.37% for overall wave conditions. The total resistance of the HB was higher than that of the rigid body with a bulbous bow (RB), and the difference of magnitude was approximately 31.47% for calm water conditions and 31.68% for overall wave conditions. The added resistance coefficient of the HWB tended to increase with an increase in the wavelength, from 0.5 L to 1.1 L, and then decrease until 1.5 L. The overall tendency of the added resistance coefficient of the HB was significantly different from the other numerical results. Although the tendencies were different, most of the presented results were in the same range as the other numerical results. [ABSTRACT FROM AUTHOR]

The enhanced unified theory (EUT) has been used as a core theory in the integrated system developed at the Research Initiative on Oceangoing Ships (RIOS) of Osaka University for predicting the propulsion and seakeeping performance of a ship in actual seas. In this study, the EUT is modified by adopting partially the solution method in the rational strip theory of Ogilvie and Tuck as a particular solution in the inner problem, thereby a forward-speed effect in the convection term of the free-surface condition is incorporated in the inner solution. This forward-speed effect is analytically shown to contribute only to the cross-coupling radiation forces. Some other forward-speed and 3D effects important in a low-frequency range are also included in the homogeneous component of the inner solution through matching with the outer solution in a similar manner to the unified theory of Newman. Numerical computations are implemented for a slender modifiedWigley model and the RIOS bulk carrier model. Good agreement is confirmed in a comparison with experimental data for the cross-coupling added mass and damping coefficients between heave and pitch and also for the resulting ship motions, particularly in heave near the resonant frequency. The added resistance around the motion-resonant wavelength is found to be improved but sensitive to a slight change in heave and pitch motions. Thus, it is stressed that accurate prediction of the ship motions and resultant Kochin function is critical for more accurate prediction of the added resistance in waves. [ABSTRACT FROM AUTHOR]

Recently, several changes have been observed in the Earth’s environment. This is also applicable to the ocean environment. The concept of weather routing has been applied for ship navigation for a long time. Many service providers offer weather routing service with the availability of high-quality satellite data. Unfortunately, not much information is available in the public domain as to how much the recent change in the weather pattern has affected ship navigation. The purpose of this paper is to fill this information gap. We investigate the influence of recent changes in the ocean environment on ship navigation. Weather data from ECMWF, namely ERA-Interim, is used for this purpose. The ECMWF data for the last 27 years is analysed. We compute the statistical characteristics of this data for the first 10 years, last 10 years, and 27 years. The statistical characteristics of the data are determined based on “summer” and “winter” zones as defined by international maritime regulations. Six different worldwide commercial ship routes are selected covering all the ocean regions. Navigation on great ellipse with waypoint is considered. MMG type ship manoeuvring model for 3 different ship types (DTMB 5415, PCC, VLCC) is used. The added resistance due to wave, wind and the effort of keeping the ship on the desired course using autopilot in the rough ocean environment is included in the MMG model. The fuel consumption and the duration of each one of the voyage are computed. Based on the analysis and simulation results it is shown that: (i) The mean wave height, wave period, and wind speed has increased in some ocean zones and decreased in other ocean zones. If any change has occurred, it is uniform for both seasons (summer and winter). (ii) In which ocean regions there is a perceptible change in fuel consumption, average ship speed and voyage time due to the changes in the weather pattern. (iii) The changing weather pattern in different ocean zones affects each ship type differently.

The increase of seakeeping performance is of particular importance for car and passenger ferries, service ships in the gas and oil extraction industry and offshore wind power farm industry, as well as for special purpose ships (including military applications). In the water areas of the Baltic Sea, North Sea, and Mediterranean Sea, which are characterised by a short and steep wave, the hull shape has a substantial impact on the operational capacity and propulsion efficiency of the ship, as well as on comfort and safety of navigation. The article analyses selected aspects of seakeeping for four variants of a selected case study vessel, indicating practical limitations of the strip method. The analysed aspects included hull heaving and pitching, added resistance, Motion Thickness Indicator (MSI), and Subjective Magnitude (SM). Experimental tests were also performed in the towing tank. Their comparison with the numerical results has indicated high inaccuracy of the strip method. What is more, the simplified representation of hull shape used in the strip method makes it impossible to analyse the effect of hull shape changes on the predicted seakeeping characteristics. Especially for the case of head wave, neglecting highly non-linear phenomena, such as slamming or head wave breaking, in strip method-based computer simulations will significantly decrease the reliability of the obtained results. When using the strip method, the seakeeping analysis should be complemented with model tests in a towing tank, or by another more complex numerical analysis, such as CFD for instance.

The outrigger symmetry of a trimaran is believed to significantly affect its hydrodynamic functioning. The present study was conducted to investigate the added resistance responses and experimental vertical motion of a wave-piercing trimaran in regular head waves. A series of experiments have been carried out in the National Iranian Marine Laboratory (NIMALA) towing tank to determine the effect of side hulls symmetry on the heave and pitch motions and added resistance. The models were tested over a range of wave frequencies and Froude numbers using both symmetric and asymmetric outriggers. According to the results, the symmetric side hull form based on heave motion, the outboard form in terms of pitch motion and added resistance have better performances among these three kinds of side hull forms. Furthermore, there are local maximum and minimum points on the ship motion response curves due to heave and pitch coupling in their respective frequencies. [ABSTRACT FROM AUTHOR]

The added resistance is a resistance component that is not yet satisfactorily predicted, although its accurate estimation is crucial – both from an environmental and economic point of view – from the design stage of a ship until its operation. One of the possible sources of overprediction is the occurrence of bow wave breaking. The first aim of this paper is to study the effect of bow wave breaking on added resistance by combining visual observations with resistance tests. On the other hand, as the bow region of a ship appears to be the most dominant contributor to added resistance, this paper introduces a dynamic waterline detection method involving stereo vision. This experimental method is applied to reach the second aim of this paper, which is to stress the importance of the relative wave elevation in the bow region of the ship. By placing stereo rigs inside the hull of a semi-transparent ship, the waterline at each momnent in time can be tracked using an edge detection algorithm. By performing resistance tests on the Delft Systematic Deadrise Series ship model no. 523, the added resistance is observed to be proportional to the relative wave height squared. The data of the experiment and the information necessary to reproduce the experiment are shared through . [ABSTRACT FROM AUTHOR]

In this study, the added resistance and seakeeping performance of the KVLCC2 ship is investigated by using the spectral wave explicit Navier-Stokes equations (SWENSE) method. The SWENSE method is based on the decomposition of the total field into an incident part explicitly obtained by the wave potential flow theory and a complementary part solved with a modified Reynolds-averaged Navier-Stokes solver. Therefore, the computational efficiency can be achieved by using a relatively coarse mesh in the far field, retaining the accuracy of the incident waves. A parametric study is performed under regular wave conditions with 3Degree of Freedom (DOF) motions of the hull. The results are compared with the large literature available. An additional case is simulated to demonstrate the capability of the present method in simulating seakeeping problems in irregular sea states. Good agreement between the computed results with the reference data can be observed for the hull model, which indicates that the added resistance and seakeeping performances can be well predicted by the present method. [ABSTRACT FROM AUTHOR]

This paper discusses mathematical modeling of a ship equipped with energy-saving wing devices. Therewith, the ship is mathematically represented by an elongated hull with high-aspect-ratio wings mounted near its bow and stern. Equations, describing ship motions in regular oncoming waves, are written in the spirit of strip theory with account of inertial and damping influence of energy-saving wing elements with the use of linear expansion of wing-related forces with respect to heave and pitch perturbations. This approach readily yields fast numerical solutions for the propulsion of a ship with wings in waves. The latter solutions are then used as an input for calculation of thrust on wing elements on the basis of classical unsteady foil theories corrected for finite aspect ratio. To evaluate speed of the ship in the modes which allow cruising exclusively by wave power, it is hypothetically assumed that in this case, the wave-generated thrust on the wings equals total drag of the ship-plus-wings system, the latter being defined as a sum of its viscous, wave-making, induced (for wing elements) and added-wave components. Excepting the added-wave term and wings' contributions, the total drag is calculated herein by Holtrop method whereas added-wave resistance is evaluated with Beukelman-Gerritsma formula involving kinematic parameters of heaving and pitching motions of the ship calculated both without and with account of the wings. Also discussed in the paper is a decrease of added wave resistance for a ship with wings as compared to that of ship without wings. Finally, the energy efficiency design index (EEDI) introduced by the International Maritime Organization (IMO) is discussed for representative sea conditions as a measure of ship environmental friendliness. [ABSTRACT FROM AUTHOR]

Nowadays, the optimal use of energy, speed increase, fuel consumption reduction and environmental pollution prevention are essential in the ship design and manufacturing discussion. So it is critical to be able to estimate ship's response to waves, since the resulting added resistance and increasing fuel consumption also increasing environmental pollution. In this study, the numerical solution of the Iran-Bushehr container ship model was determined to simulate the free surface flow around the hull and estimate the total resistance and investigate ship motions in 2 degree-of-freedom (heave and pitch) in regular head waves. Finally, the results of simulation in different conditions are presented and compared. KCS container ship used for validation. CFD codes in Star-CCM+ used to calculate three dimensional, incompressible, unsteady RANS equations.

Amid a global effort in reducing the shipping ecologic impact, the study of the particular case of added resistance of high speed vessels cruising in a seaway has been approached by a very limited number of authors. In this study, we provide a comprehensive and systematic assessment of the added resistance of a planing hull in regular waves. The data are analyzed in both the time and frequency domains in order to fully characterize the added resistance and highlight its correlation with hull motions. It is found that peak added resistance modulation occurs for shorter waves with respect to the peak average added resistance, and slenderness is beneficial only in terms of modulation. Nonlinearity of both the average and first harmonic amplitude is also shown. In addition, results of the phase analysis show a correlation between the added resistance phase and average added resistance.

Biofouling attaches to immersed surfaces in between hull cleanings. Due to high speeds and relatively short port times, biofilm often attaches to the immersed surfaces of containerships. In most cases, this type of fouling is not given much importance since it is assumed that it will not cause any fouling penalties. In this paper, the fouling penalties related to fouling with biofilm on the example of the Post Panamax and Post Panamax Plus containership fleets sailing in the Adriatic Sea are assessed. In addition, the investigation is performed for real environmental conditions that a containership can encounter on a sailing route passing through the Adriatic Sea. Thus, the impact of waves and wind is taken into account based on mean values of significant wave height and wind speed for containerships sailing at the design speed along the analyzed route. The procedure for the determination of the detrimental effects of biofilm on the increase in fuel consumption and carbon dioxide emissions is given. Further, the proposed procedure includes the determination of calm water resistance by the Holtrop and Mennen method, the added resistance in waves by Liu and Papanikolaou’s method, spectral analysis using the Tabain’s spectrum for the Adriatic Sea, the wind resistance by the Blendermann method, and added resistance due to biofouling using the Granville method. Thereafter, a time-dependent biofouling growth model proposed by Uzun et al. is incorporated, and the adequate timing for underwater hull cleaning is determined for several hull cleaning costs. The obtained results demonstrate that, from an environmental point of view, proactive hull cleaning should be applied, while, from an economic perspective, optimal timing for underwater hull cleaning is recommended.

The total resistance of ship in waves is composed of calm water resistance and added resistance in waves. The added resistance in waves is one of the main causes of an involuntary speed reduction of a ship. It may cause a significant increase in ship resistance and consequently increased fuel consumption and carbon dioxide emission, especially at heavier sea states. Thus, the added resistance is very important from both an economic and environmental point of view. In this paper, an increase in fuel consumption is calculated for container ship on a typical North Atlantic route. The calm water resistance is calculated utilizing Computational Fluid Dynamics based on the viscous flow theory at model scale and the obtained results are extrapolated to full scale. The added resistance in waves is calculated using three-dimensional panel code based on the free surface Green function, for the sake of simplicity. It is calculated at regular waves and the mean value of the added resistance at certain sea states is obtained by means of spectral analysis. Two-parameter Bretschneider wave spectrum recommended for the North Atlantic, defined by significant wave height and zero crossing period, is used in the spectral analysis. The obtained results may provide valuable insight into the important environmental issue of pollution reduction.

Almost 4 years after the appearance of Salvesen-Tuck-Faltinsen (STF) strip theory (Salvesen et al., 1970, "Ship Motions and Sea Loads," Annual Meeting of the Society of Naval Architecture and Marine Engineers (SNAME), New York, Nov. 12-13), Salvesen in 1974 published his popular method for calculation of added resistance (Salvesen, 1974, "Second-Order Steady State Forces and Moments on Surface Ships in Oblique Regular Waves," Vol. 22; Salvesen, 1978, "Added Resistance of Ships in Waves," J. Hydronautics, 12(1), pp. 24-34). His method is based on an exact near-field formulation; however, he applied the long-wave and the weak-scatterer assumptions to present his approximate method using the integrated quantities (hydrodynamic and geometrical coefficients). Considering the available computational powers in the 1970s, both of these assumptions were absolutely justifiable. The intention of this paper is to disseminate the results of a recent study at the Technical University of Denmark, whereby the Salvesen's formulation has been revisited and the added resistance is computed from the original exact equation without invoking the weak-scatterer or the long-wave assumptions. This is performed using the solutions of the radiation and the scattering problems, obtained by a low-order boundary element method and the two-dimensional free-surface Green function inside our in-house STF theory implementation (Bingham and Amini-Afshar, 2020, DTU_Strip Theory Solver). The weak-scatterer assumption is then removed through a direct calculation of the x-derivatives of the velocity potentials and the normal vectors along the body. Knowing the velocity potentials over each panel, the long-wave assumption is also avoided by a piece-wise analytical integration of sectional Kochin Function (Kochin, 1936, "On the Wave Resistance and Lift of Bodies Submerged in Fluid," Transactions of the Conference on the Theory of Wave Resistance, Moscow.). The presented results for five ship geometries testify that the correct treatment of the original equation is achieved only after both of the above-mentioned assumptions are removed. Implemented in this manner, Salvesen's method proves to be relatively more accurate and robust than has been generally perceived during all these years. [ABSTRACT FROM AUTHOR]

As the global warming, the Arctic Shipping Routes are gradually opened. The icebreakers are still in need to ensure the safe navigation of ships. During the voyage from East Asia to North-western Europe, the icebreaker will experience a long-distance voyage where over 60% of the distance is open water. As the bow of the icebreaker is full and the length-beam ratio is relatively high, it is quite important to study added resistance of the icebreaker. The results of added resistance, heave and pitch motion in regular waves are consistent with the variation trend using two methods. For computational efficiency, the nonlinear potential method was used to predict added resistance and vertical movement of the icebreaker at five wind directions. The added resistance in head waves is higher than in other wave directions. The maximum value was obtained at the wave length-ship length ratio of 1.2. The relationship between the phase of motion and resistance can be easily obtained. Meanwhile, the free surface around the hull can also be easily obtained. Moreover, compared to the CFD method, the nonlinear potential method can save more computing resources and time. It has important application value in the early design of the icebreaker. [ABSTRACT FROM AUTHOR]

Bow shape has been recognized as an important factor influencing the seakeeping performance and added resistance of ships. This paper presents a numerical comparative study on added resistance and seakeeping of model ships with ‘X-bow’ and a wave-piercing monohull in regular head waves using a computational fluid dynamics (CFD) software. Different wave heights, wavelengths and forward speeds are considered in the systematic investigation in order to characterize the added resistance and wave-induced motions, and to explore the local wave patterns. The results show a considerably different hydrodynamic characteristic by different bow shapes.

The study focuses on the analysis of the added resistance of a catamaran advancing both in regular waves and in a seaway. The numerical simulation has been carried out within the framework of potential flow theory by using a three dimensional, linear, Rankine source-based Boundary Element Method (BEM) and a Near-Field approach based on pressure integration for the first-order motions and the second-order longitudinal force prediction, respectively. A preliminary validation and verification study on both a mono-hull and a catamaran is proposed. A systematic analysis of the effect of some relevant operating and geometric parameters on the added resistance performance of a catamaran in waves is presented. Variations of the operating and geometric parameters include the advancing speed, the encounter angles from head to beam waves, the hull static trim and the demi-hulls separation. The trends of the added resistance pseudo-RAO are discussed in the light of the comparison against the reference design condition highlighting possible worse and optimal configurations. [ABSTRACT FROM AUTHOR]

Recently, several changes have been observed in the Earth's environment. This is also applicable to the ocean environment. The concept of weather routing has been applied for ship navigation for a long time. Many service providers offer weather routing service with the availability of high-quality satellite data. Unfortunately, not much information is available in the public domain as to how much the recent change in the weather pattern has affected ship navigation. The purpose of this paper is to fill this information gap. We investigate the influence of recent changes in the ocean environment on ship navigation. Weather data from ECMWF, namely ERA-Interim, is used for this purpose. The ECMWF data for the last 27 years is analysed. We compute the statistical characteristics of this data for the first 10 years, last 10 years, and 27 years. The statistical characteristics of the data are determined based on "summer" and "winter" zones as defined by international maritime regulations. Six different worldwide commercial ship routes are selected covering all the ocean regions. Navigation on great ellipse with waypoint is considered. MMG type ship manoeuvring model for 3 different ship types (DTMB 5415, PCC, VLCC) is used. The added resistance due to wave, wind and the effort of keeping the ship on the desired course using autopilot in the rough ocean environment is included in the MMG model. The fuel consumption and the duration of each one of the voyage are computed. Based on the analysis and simulation results it is shown that: (i) The mean wave height, wave period, and wind speed has increased in some ocean zones and decreased in other ocean zones. If any change has occurred, it is uniform for both seasons (summer and winter). (ii) In which ocean regions there is a perceptible change in fuel consumption, average ship speed and voyage time due to the changes in the weather pattern. (iii) The changing weather pattern in different ocean zones affects each ship type differently. [ABSTRACT FROM AUTHOR]

Prediction of the added resistance or corresponding speed loss in real sea conditions is essential to evaluate the performance of a ship. Assessment of the environmental impact on vessel performance is essential for route and cargo planning, optimization of fuel consumption and design, and configuration of engines and the main propulsion system. In the present study, added resistance and speed loss in real sea conditions are evaluated from1 year of onboard monitoring data of a platformsupply vessel (PSV) operating in the North Sea. The true sea margin is shown on an annual basis. Relative contributions from environmental conditions and vessel operation control are presented. Results are compared with model experiments and existing numerical methods for prediction of added resistance and speed loss in waves. The study shows that added resistance due to waves for this PSV is significantly larger than predicted by conventional frequency-domain calculations or model tests. No reason for the deviation is found, but it is anticipated that a combination of effects of longitudinal mass radius of gyration, differences in wavelength and steepness in model tests and reality, and nonlinear effects (not accounted for in the numerical calculations) is partly responsible for the deviations. For ships having similar main dimensions, the conventional ways of predicting added resistance or speed loss in waves is nonconservative, and improved methods should be sought. [ABSTRACT FROM AUTHOR]

In this study, the added resistance of a liquefied natural gas carrier (LNGC) in the presence of waves is studied experimentally and numerically.The ship model is an LNGC designed by Samsung Heavy Industries (SHI). Experiments on ship motion responses and added resistance under head sea conditions were conducted at the Seoul National University and SHI. The influences of the experimental methods (captive and self-propulsion methods), incident wave amplitude, and regular and irregular wave conditions on the added resistance are evaluated using the same model ship set at different scales. In the numerical studies, the motion responses and added resistance are obtained using three methods--the strip method by adopting momentum conservation; Rankine panel method using pressure integration; and computational fluid dynamics method, using the difference in the resistances in waves and calmwater. The experimental and numerical results under various conditions are compared, and the characteristics of the experimental and numerical results are discussed. [ABSTRACT FROM AUTHOR]

The total resistance of ship in waves is composed of calm water resistance and added resistance in waves. The added resistance in waves is one of the main causes of an involuntary speed reduction of a ship. It may cause a significant increase in ship resistance and consequently increased fuel consumption and carbon dioxide emission, especially at heavier sea states. Thus, the added resistance is very important from both an economic and environmental point of view. In this paper, an increase in fuel consumption is calculated for container ship on a typical North Atlantic route. The calm water resistance is calculated utilizing Computational Fluid Dynamics based on the viscous flow theory at model scale and the obtained results are extrapolated to full scale. The added resistance in waves is calculated using three-dimensional panel code based on the free surface Green function, for the sake of simplicity. It is calculated at regular waves and the mean value of the added resistance at certain sea states is obtained by means of spectral analysis. Two-parameter Bretschneider wave spectrum recommended for the North Atlantic, defined by significant wave height and zero crossing period, is used in the spectral analysis. The obtained results may provide valuable insight into the important environmental issue of pollution reduction. [ABSTRACT FROM AUTHOR]

This paper uses optimization techniques to obtain bow hull form of a 66,000 DWT bulk carrier in calm water and in waves. Parametric modification functions of SAC and section shape of DLWL are used for hull form variation. Multi-objective functions are applied to minimize the wave-making resistance in calm water and added resistance in regular head wave of λ/L = 0.5. WAVIS version 1.3 is used to obtain wave-making resistance. The modified Fujii and Takahashi's formula is applied to obtain the added resistance in short wave. The PSO algorithm is employed for the optimization technique. The resistance and motion characteristics in calm water and regular and irregular head waves of the three hull forms are compared. It has been shown that the optimal brings 13.2% reduction in the wave-making resistance and 13.8% reduction in the added resistance at λ/L = 0.5; and the mean added resistance reduces by 9.5% at sea state 5.

Added resistance in waves is the second-order steady force dependant on the ship motions. It significantly affects ship operability and cause speed loss. Therefore the required power and fuel consumption of a ship advancing in a seaway are increasing. In this paper, additional fuel consumption is approximated in relation to the increased resistance, i.e. the difference between the ship resistance in calm water and resistance while operating in waves. Ship advancing in regular head waves with different speeds is examined. Calm water resistance is calculated according to the potential flow theory and ITTC 1957 model-ship correlation line. The added resistance in waves is calculated using three-dimensional boundary element method based on the potential flow theory. Motion induced resistance due to heave and pitch motions as well as reflection induced resistance are taken into account. Therefore, overall assessment of added resistance in regular waves is achieved through evaluation of the ship drift forces and quadratic transfer function. The so-called near-field formulation is used to determine wave loads acting on the ship hull. Evaluation of increased fuel consumption is made on the basis of estimated added resistance for different speeds and wave frequencies. Correlation of fuel consumption with various wave frequencies that the ship may encounter in its voyage is obtained.

A ship navigating on the surface of the water may experience greater resistance, adversely affect-ing its speed and leading to energy loss. The added resistance of surface ships in both still water and waves are investigated, and the computation method of total speed loss is presented. An autopilot system is intro-duced to constrain the speed loss, and course keeping and rudder roll stabilization sliding mode control laws are proposed according to a compact control strategy. The two working conditions of "heading" and "heading plus anti-roll" are discussed, including roll stabilization, heading error, speed maintenance and rudder abrasion. The results show that the speed can be effectively maintained using this method, and from a commercial point of view, the fin-rudder roll stabilization control is not recommended for vessels equipped with both fins and rudders.

This study presents the full-scale resistance and seakeeping performance of an awarded Double-M craft designed as a 15 m next-generation Emergency Response and Rescue Vessel (ERRV). For this purpose, the Double-M craft is designed by comprising the benchmark Delft 372 catamaran with an additional center and two side hulls. First, the resistance and seakeeping analyses of Delft 372 catamaran are simulated on the model scale to verify and compare the numerical setup for Fr = 0.7. Second, the seakeeping performance of the full-scale Double-M craft is examined at Fr = 0.7 in regular head waves (λ/L = 1 to 2.5) for added resistance and 2-DOF motion responses. The turbulent flow is simulated by the unsteady RANS method with the Realizable Two-Layer k-ε scheme. The calm water is represented by the flat VOF (Volume of Fluid) wave, while the incident long waves are represented by the fifth-order Stokes wave. The residual resistance of the Double-M craft is improved by 2.45% compared to that of the Delft 372 catamaran. In the case of maximum improvement (at λ/L = 1.50), the relative added resistance of the Double-M craft is 10.34% lower than the Delft 372 catamaran; moreover, the heave and pitch motion responses were 72.5% and 35.5% less, respectively.

Resistance prediction of ships using computational fluid dynamics has gained popularity over the years because of its high accuracy and low cost. This paper conducts numerical estimations of the ship resistance and motion of a Japan bulk carrier model using SHIP_Motion, a Reynolds-averaged Navier–Stokes (RaNS)-based solver, and HydroSTAR, a commercial potential flow (PF)-based solver. The RaNS solver uses an overset-structured mesh and discretizes the flow field using the finite volume method, while the PF-based solver applies the three-dimensional panel method. In the calm water test, the total drag coefficient, sinkage, and trim were predicted using the RaNS solver following mesh dependency analysis, and the results were compared with the available experimental data. Next, calm water resistance was investigated for a range of Froude numbers. The added resistance in short-wave cases was simulated using both RaNS and PF solvers, and the results were compared. The PF solver showed better agreement with the RaNS solver for predicting motion responses than for predicting added resistance. While the added resistance results could not be directly validated because of the absence of experimental data, considering the previous accuracy of the RaNS solver in added resistance prediction and general added resistance profile of similar hull forms (bulk carriers), the prediction results could be concluded to be reliable. [ABSTRACT FROM AUTHOR]

This study focuses on the optimization of ship dimensions by considering hydrodynamic performance in waves. In actual seaways, a ship experiences speed loss due to environmental loads by waves and wind. Therefore, along with calm water resistance, speed loss in waves should be considered in the hull form design in order to improve operational efficiency in waves. However, a trade-off may be needed between total resistance on the ship and the speed loss in waves. To address this problem, Non-dominated Sorting Genetic Algorithm II, which is a multi-objective optimization method, is used to minimize the total resistance on a ship in seaways and the speed loss by additional resistance. In the optimization process, added resistance is predicted using a numerical method based on slender-body theory, Maruo's far-field formulation, and an empirical formula for added resistance in short waves. The speed loss in waves, which can be expressed by a weather factor (fw), is estimated using power–speed curves. This article introduces some examples of the sensitivity analysis of added resistance and speed loss in waves to the variations of ship dimensions. Finally, the optimization solutions on a Pareto front set are compared to a basis ship in terms of hull form, and the corresponding hydrodynamic performances are evaluated. [ABSTRACT FROM AUTHOR]