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Article

Impact of Wind-Assisted Propulsion on Fuel Savings and Propeller Efficiency: A Case Study

Faculty of Maritime Studies, University of Split, 21000 Split, Croatia
*
Author to whom correspondence should be addressed.
J. Mar. Sci. Eng. 2024, 12(11), 2100; https://doi.org/10.3390/jmse12112100
Submission received: 21 October 2024 / Revised: 7 November 2024 / Accepted: 16 November 2024 / Published: 19 November 2024
(This article belongs to the Special Issue Green Shipping Corridors and GHG Emissions)

Abstract

:
In order to meet current and future efforts to reduce fuel consumption and gas emissions, an increasing number of ships are being retrofitted with one of the wind-assisted propulsion solutions. In this paper, the effects of retrofitted wind-assisted propulsion on the efficiency of the propeller are investigated. The installed ship propeller is usually designed to operate under specific conditions; once the thrust force from the sails is added, the operating point of the propeller changes. Taking into consideration the reduced efficiency of the propeller, which is no longer operating in its optimal regime, the actual wind-assisted propulsion contribution can be calculated. The wind-assisted contribution is calculated with a velocity prediction program as a reduction in conventional propulsion power output by maintaining the vessel’s designed speed. From the calculated variations in sail thrust force, dependent on the wind speed, the propeller efficiency is analyzed for different operating states. The propulsion efficiency of the propeller was analyzed with a performance characteristics calculation tool that has been developed and presented in this paper. From the meteorological data obtained from Copernicus Marine Services and available ship documentation, a case study was conducted for a selected route.

1. Introduction

Wind-assisted propulsion systems have demonstrated significant potential in reducing CO2 emissions and fuel consumption, making them an effective method for enhancing the environmental sustainability of maritime operations. Researchers’ interest in wind-assisted propulsion systems (WAPS) technology has also increased, resulting in numerous studies and innovations aimed at optimizing ships’ efficiency and performance, making them more viable and beneficial for the maritime industry. Concurrently, a growing number of ship owners are adopting these systems, recognizing the dual benefits of cost savings and reduced environmental impact. As a result, wind-assisted propulsion is becoming an increasingly popular solution in the maritime industry [1,2,3,4].
There are six different categories of wind-assisted propulsion technologies. These include rotor sails, hard sails, suction wings, kites and soft sails (traditional fabric sails that have been adapted for modern ships) [2,4,5]. According to [2], as of mid-2023, WAPS have been installed on 30 vessels, with an additional 26 ships either in the process of installation or scheduled for future installation. The trend is shown in Figure 1. Of these, 16 are newbuilds, while 38 existing ships are undergoing retrofitting (no data are available for two installations). In the WAPS review in [6], from 2021, it was concluded that, although the current adoptions present only a small percentage of the total fleet, research consistently shows that WAPS have the potential to make ships more energy efficient (rotors: 0.4–50%; kites: 1–50%; rigid sails: 5–60%; soft sails: 4.2–35%; wind turbines: 1–4%). Similar values have been confirmed in more recent (2022–2024) studies in [2,7,8,9,10].
The focus of this research is propulsion power prediction, with particular emphasis on the effects of a retrofitted wind-assisted propulsion system on the efficiency of the propeller and, thus, on the overall efficiency of WAPS.
The potential of WAPS to reduce fuel consumption can be evaluated by numerical simulations and measurements. Numerical simulations involve calculating the reduction in propulsion power for a predetermined route by incorporating several input variables, such as weather conditions, hydrodynamic and aerodynamic characteristics of both the ship and the WAPS, ship dimensions, engine and propeller data and ship speed [2,11,12,13,14]. In [15], the modeling of the hydrodynamic properties of a wind-powered cargo is evaluated. Errors and uncertainties in the simulations have been quantified with convergence studies and a comparison with towing tank experiments. Procedures and guidelines for ship-related computer fluid dynamics (CFD) applications according to the International Towing Tank Conference (ITTC) are presented in [16,17]. In [18], numerical performance models of two wind power technologies, Flettner rotors and kites, were created and investigated for five different routes, taking into consideration weather data. The results show that a general cargo carrier in the model was able to achieve a power reduction in the main engine by up to 50%. In [15], another case study was conducted using CFD, where large rigid sails on the upper deck act as the main propulsion. The sails are made of an advanced lightweight material, such as carbon fiber reinforced plastic (CFRP). According to the energy-saving simulation in the actual voyage (Yokohama to Seattle), it was found that fuel oil savings of 20 to 30% are very possible. A numerical method for modelling wind-assisted ships was carried out in [19], where the ratio between the propeller thrust of a ship with and without wings is used as a measure of the energy efficiency. The velocity prediction program (VPP) presented in the paper suggests a propeller power reduction of approximately 10% when slow steaming in winds of 13 knots. Different combinations of the number of wings and wing chords were compared. In [20], a performance prediction model was created using empirical analytical methods, with the focus of simplifying input data, where only ship type, design speed and propeller revolution (RPM) are required. The remaining dimensions are estimated by the model using empirical formulas. Another good example of a performance prediction program (PPP) is presented in [21]. A six degrees of freedom (DoF) model was created and validated on a wind-assisted product tanker vessel. A comparison of three different concepts (rotor sails, rigid wing sails and DynaRigs) was made, and general savings were evaluated. Based on the presented model, the findings indicate that rotor sails outperform other WAPS in downwind and broad, the DynaRig excels in upwind situations, while the rigid wing sail with a trailing edge slotted flap demonstrates superior performance across a broad spectrum of reaching wind angles. From these publications, it can be concluded that the WAPS technology has still not reached its peak, and further advancements are discovered daily. Researchers and engineers are continuously working to improve the efficiency and performance of various WAPS [22]. With ongoing progress in materials, aerodynamics and system control, we can expect significant innovations that will further enhance the effectiveness and applicability of these technologies in the near future.
On the other hand, calculation methods for propeller characteristics have been well-established, primarily through empirical methods [23,24]. Propellers are divided into series based on their design characteristics and performance parameters. One of the most extensive and widely used propeller series is the Wageningen B. The Wageningen B-screw propeller series was first presented in [24] in 1938, with following papers detailing further developments in the 1940s. In 1975, further significant contributions were made by [25]. Troost’s data were expanded, providing additional computer-analyzed data and refining the empirical models by developing polynomial equations and a set of coefficients allowing for accurate predictions of thrust and torque still used in ship design and performance analysis. A comprehensive reference on this subject is [23], which details various empirical approaches and methodologies for understanding and predicting propeller performance. In [26], the optimization of fuel efficiency with propeller design was analyzed on a case study bulk carrier model considering the hull–propulsor interaction, which includes factors such as the wake fraction (w), thrust deduction fraction (t) and relative rotative efficiency (ηR). This model was later developed further by the same author in [27], with detailed expressions for ship resistance, w, t and ηR elaborated in [28]. In [29], a procedure for matching propulsor and engine, including propeller–hull interactions, is described using the same calculations as in [26], with regards to the change in the propeller operating point in off-design situations. However, there are very few studies that focus on the optimization of propellers for ships with WAPS.
In 1985, paper [30] was published investigating propeller performance of two vessels with WAPS in operating scenarios with constant speed and constant power. It was concluded that, if the ship is operating in fixed-speed mode, the engine will operate in a low efficiency area, resulting in an additional increase in specific fuel oil consumption (SFOC) and potential maintenance issues due to the engine operating in a non-optimal regime. On the other hand, if an engine with lower power margins is chosen, it reaches revolution limits when demand is higher, such as in conditions without wind assistance.
The chosen engine must have more operating points taken into consideration when matching with a propeller in order to meet the power requirements for all operating conditions, which vary more for WAPS ships compared to conventional ships. Specifically, lightly loaded propellers and off-design scenarios occur more frequently and need to be addressed early in the design phase for WAPS vessels. Moreover, it is worth mentioning that lightly loaded propellers can be associated with pressure side cavitation [31]. In [32], a tool has been developed to assist in Flettner rotor–engine–propeller matching in the design phase and in operation to set optimal parameters in terms of rotor and engine RPM values and controllable pitch propeller (CPP) parameters.
The expected variations in propeller efficiency (η0) and change in the operating point along the propeller efficiency curve dependent on sail added thrust are presented in [30,33]. In the research in [31,34], and later gathered in [33], it was concluded that the manual process of propeller optimization is a very laborious process, and a user interface was created to accelerate the evaluation procedure. Optimization was carried out with the use of genetic algorithms, machine learning and support-vector machines on an open-source oil tanker model “KVLCC2“. Another tool for propeller–WAPS optimization was developed and presented on the data based on “KVLCC2” in [35]. The tool is comprised of a mathematical model able to predict the theoretical propeller and engine performance and assess the cost benefit of a fixed pitch propeller (FPP) and a controllable pitch propeller for wind-assisted and wind-powered ships. In [36], a numerical tool was developed to estimate WAPS fuel-reduction efficiency with a four DoF digital twin model, where the influence of WAPS was examined for a CPP. As shown in [35], the thrust requirement from a conventional marine propulsion system varies based on the net thrust provided by the WAPS and the efficiency of the propeller at that operation point. As the force from the WAPS increases, the propeller and engine are offloaded to meet the new thrust requirements; this unloading results in a reduction in the propeller rotational speed, leading to an increase in the advance ratio (J), and consequently, the open water efficiency (η0) changes along the η0 curve. For the studied vessel in [35], propeller and engine performance optimization results in up to 12% fuel savings. Ignoring these performance variations can significantly affect the actual savings from WPS installations, thus impacting their overall economic viability.
Through the process of literature review, it was established that, although there is an abundance of recent studies on WAPS and propeller performance, there is a scarcity of research addressing the direct impact of WAPS on propeller efficiency. This gap in the literature pointed out the necessity of conducting this research in order to present a straightforward analytical method to assess the influence of WAPS on propeller performance.
In this paper, a model based on analytical and empirical methods is presented. The model was created to accurately predict the thrust delivered from the sail and its impact on the propeller performance. This paper is divided into five sections: Introduction, Methodology, Case Study Ship Model, Analysis/Results and Conclusions. In the Introduction part of this paper, an overview of significant literature regarding the subject has been presented. In the Methodology section, this paper details the application of the WAPS model, which is used to calculate the forces generated by the sails. Additionally, the integration of a propeller model to evaluate the performance characteristics of the propeller when the ship operates under sail power is explained. The Weather/Route section describes the weather data properties and the route selected for the case study. In the section titled Case Study Ship Model, the ship’s particulars along with the size of the sails and the potential for aerodynamic force are provided. The Analysis/Results and Conclusion sections show the results, presented in tables and diagrams, and closing remarks of the research conducted.

2. Methodology

A model was created using the Python program language in order to analytically capture the aerodynamic impact of the WAPS and hydrodynamic effects on the propeller caused by the interaction with WAPS. The aerodynamic impact of the sail in this model is interpreted in the form of a VPP considering only the forward component of the total aerodynamic force. VPP is a tool commonly used in sailing regattas to determine handicaps, but it is also utilized in the maritime industry to predict a ship’s performance under various conditions by simulating the ship’s interaction with wind, waves and currents. The key output variable from the aerodynamic model is the total force from the sails, which then becomes an input variable in the propeller performance characteristics calculation program. In the propeller module, thrust force and propeller efficiency are calculated based on the Wageningen B-screw standard series, where the propeller is described by a set of polynomials. These polynomials were generated from the original propeller model’s open-water test using multiple regression analysis [25]. The open-water test is a well-established procedure for estimating propeller efficiency through the open-water diagram, guidelines and procedures described in [37].
For the case study vessel, a propeller performance diagram was created based on the ship’s characteristics, propeller geometry and sea trial data. From there, for each value of the sail force, the required force from the propeller was reduced, and accordingly, a new operational point was calculated.

2.1. Aerodynamic Forces

The contribution of added wind propulsion is analyzed by a VPP created for this purpose. The VPP presented in this paper is composed of two parts: the mathematical model of the ship and an algorithm for solving the equations of motion. In the sail model, sway forces are neglected, and the total aerodynamic force (Fm) is calculated as the difference between lift and drag dependent on the attack angle (the angle between the ship course and the apparent wind direction) (βa) [38]. The apparent wind speed and direction refer to the wind experienced on a moving vessel. The apparent wind results from the vector sum of the true wind (wind observed when stationary) and the wind generated by the vessel’s forward motion. Therefore, the aerodynamic force generated by the sails is as follows:
F m = P a sin   β a R a cos   β a
where the drag force (Ra) and lift force (Pa) developed by the sails are calculated with the following expressions, in which SA is the total sail area in m2, Va is the apparent wind speed, and ρ is the air density (1.29 kg/m3) [12]:
R a = 0.5 ρ C r β a S A V a 2
P a = 0.5 ρ C p β a S A V a 2
The coefficients Cr and Cp are defined as a function of the sail shape and the angle of attack. Figure 2 shows the aerodynamic coefficients used in this case study, obtained from [39]. The curves were fitted into the code using the piecewise cubic hermite interpolating polynomial (PCHIP) method. For each change in ship or wind speed and direction, the apparent wind direction changes, and the VPP determines new Cr and Cp values. In Figure 2, the PCHIB interpolation is shown for the Cr and Cp values in relation to the apparent wind angle.

2.2. Propeller

When designing vessels for conventional propulsion, propeller design is generally focused on a specific design condition. However, with wind propulsion, the vessel operates under a much broader range of conditions, leading to a wide load spectrum for both the propeller and the engine. In wind-powered vessels, this load range can vary dramatically, presenting a unique set of challenges [33,40].
A performance characteristics calculation tool has been developed and presented in this paper. The calculation tool is based on Wageningen B-screw series propellers and consists of different modules that allow for investigating the change in characteristics in respect to different scenarios that may occur when WAPS is introduced.
The thrust calculator module calculates thrust (T) and η0 based on empirical formulas for the design of Wageningen B-screw series propellers. The open-water propeller characteristics of the Wageningen B series for the Reynolds number 2 × 106 are presented as polynomial functions shown in Equations (10) and (11) [23]. The required input data and constants are presented in Table 1.
The forces and moments produced by the propeller are expressed in the most fundamental form in terms of a series of non-dimensional characteristics that are completely general for a specific geometric configuration [23]. The open-water test results for B-series propellers are conventionally presented in the form of thrust and torque coefficients (KT) and (KQ), expressed as functions of the advance coefficient. Expressions for the coefficients and efficiency are shown in Equations (4)–(7):
K T = T ρ n 2 D 4
K Q = Q ρ n 2 D 5
J = V a n D
η o = K T K Q J 2 π
The cavitation criteria for the necessary blade surface area required to minimize the risk of cavitation can be determined with the expressions in [23]. Cavitation calculations have been neglected in this research.
The wake fraction coefficient represents the reduction in effective water velocity that the propeller experiences due to the flow disturbance created by the hull moving through the water. The wake fraction coefficient quantifies this reduction, with higher values indicating a more significant decrease in the inflow velocity to the propeller. For this case study, since w was unknown, it was “reversed engineered” from sea trial data by identifying its correct value w until KT and KQ matched. The error, in terms of engine power, is 0.08% for the power calculated with Equation (16). For the remaining calculations under varying conditions, a constant wake factor was assumed. Given that the input value is ship speed, J and the Reynolds number (Rn) are expressed with the following equations:
J = V b 0.5144 1 w n D
R n = n D 2 ν
The open-water characteristics of the series are presented as polynomial functions for a Reynolds number 2 × 106 by Equations (10) and (11). The coefficients s, t, u and v and the ΔKT and ΔKQ polynomials for Reynolds number effect (above Rn = 2 × 106), from Equations (12) and (13), are reproduced in tables in [23,25].
K Q = n = 1 47 C n ( J ) S n ( P D ) t n ¸ ( A e A o ) u n ( Z ) v n
K T = n = 1 39 C n ( J ) S n ( P D ) t n ¸ ( A e A o ) u n ( Z ) v n
To extend this calculation further so that the propeller characteristics can be predicted for other Reynolds numbers within the range 2 × 106 to 2 × 109, a set of corrections of the following form was derived:
K T R n = K T R n = 2 10 6 + Δ   K T R n
K Q R n = K Q R n = 2 10 6 + Δ   K Q R n
Using this methodology and by plotting a range of RPM values, propeller characteristic curves can be obtained, and the initial operating point of the propeller can be determined. Figure 3 shows the propeller characteristics diagram for the case study vessel showing KT, KQ and η0 plotted against J. This diagram provides a perspective on how propeller performance parameters may vary with changes in operating conditions.
Once the initial T and Q are calculated, as shown in Equations (14) and (15), for all further (wind-assisted) operating points, the RPM calculator module iterates to find the RPM value corresponding to the desired thrust. When the thrust required from the propeller is known and the new RPM value is found, other propeller parameters are calculated including η0.
T = K T R n = 2 10 6 + Δ   K T R n ( ρ n 2 D 4 )
Q = K Q R n = 2 10 6 + Δ   K Q R n ( ρ n 2 D 5 )
The net T value, i.e., the thrust deducted by the thrust deduction factor, is also presented in the results. In general, the value of t increases when w increases. As the wake coefficient remained constant in this research, the calculations were performed with a constant t value, fixed at 0.1. To calculate the exact value of t, research should be carried out on different models with special attention to the hull, as the shape of the hull may have the most significant influence on the thrust deduction coefficient [41,42].
To calculate fuel consumption, engine power is derived from Equation (16) and the SFOC map for all engine loads (data taken from engine shop test results). Figure 4 shows a diagram depicting the relations between T and η0 at different RPMs.
P = 2 π R P M 60 Q

2.3. Weather and Route

Weather data were obtained from Copernicus Marine Services for the year 2023. The historical data show hourly values for wind speed and direction 10 m above sea level. In Figure 5, a map of the Adriatic Sea is shown with the data points depicted; highlighted are the points of the route used in this study between two Croatian cargo ports, Rijeka and Ploče. In this stage of the research, the Adriatic Sea was set as the boundary in order to have a more efficient volume of data; the route itself was chosen as it covers a significant part of the Adriatic Sea. The waypoints were obtained by a chart-plotting software and then cross-referenced with the weather data points to find the closest match. The closest points are highlighted in red in Figure 5.
Figure 6 shows a heat map that was created with the data provided to give a deeper insight into the weather of the area in question.

3. Case Study Ship Model

Given the available data, specifically propeller dimension details, a ship was chosen for this case study. The case study ship has a travel speed of 26.8 knots, achieved with a Hyundai B&W 12K98ME-C engine; the ship particulars are shown in Table 2. The propeller dimensions for the case study vessel are presented as the input data in Table 1.
Since the scenario where sails are retrofitted is being simulated, the sail size needed to be defined. According to [3], the size of the sails to be installed can be approximated by the following restrictions:
n u m b e r   o f   s a i l s s a i l   a r e a d e a d w e i g h t 2 3 < 2.25
n u m b e r   o f   s a i l s 1 B L < 0.3
In regards to the previously mentioned restrictions, the sail size was approximated as three 1900 m2 sails. A better-optimized sail would provide better thrust and overall performance, but that is not the focus of this paper.
Figure 7 shows two polar diagrams for different ship speeds; the sail force generated from the sails is illustrated under different wind conditions. The radial axis (extending outward from the center) represents the magnitude of the sail force in kN, the angular axis represents the true wind direction (βt), and the curved lines correspond to different wind speeds as indicated on the legend. From the shape of the curves and scale of the values, the influence of the wind speed, ship speed and wind direction can be observed.
Figure 8 shows a polar plot that was created for visualizing how different wind conditions contribute to the propulsion of the vessel. The plots show the combinations of βt and Vt required to achieve 20% and 40% of the vessel’s total thrust demand (at constant speed). The radial axis represents the true wind speed, and the angular axis represents the true wind direction relative to the vessel. Aerodynamic force in kN is plotted with a 10% margin of the target value.
From the data calculated by the VPP and depicted in Figure 8, with a favorable wind direction, 20% thrust demand can be obtained with a minimum wind speed of 9 m/s, which can still be considered a moderate wind. For 40% demand, a minimum wind speed of 15 m/s is necessary; this is achievable with a true wind direction between 45 and 90°. At such high wind speed, an increase in wave resistance is expected, resulting in a higher output from the engine. A good overview of sail- and wave-induced resistance can be found in [42].

4. Results and Discussion

The aim of this analysis was propulsion power prediction at constant speed with regard to WAPS impact on the efficiency of the propeller and overall efficiency of WAPS. The results presented indeed confirm the shift in the operating point position along the propeller curve as the literature review indicated. However, in this case study, both the SFOC and propeller efficiency were improved when 20% and 40% thrusts were simulated from WAPS. In Figure 9, the SFOC map is presented based on the ME shop test results, showing the initial working point (WP) with an engine power of 65,041 kW at 109.5 RPM and a SFOC value of 172.11 g/kWh. Both wind-assisted points are below the initial operating point SFOC value, representing an increase in fuel efficiency. Still, other factors must be considered when discussing prolonged engine operation at reduced RPMs. These factors may include material wear, oil consumption, higher emissions, carbon build-up and vibrations resulting in possible maintenance costs. Engine performance while slow steaming should be considered, but it is a research task for itself. This paper will not cover the analysis of these aspects; the impact of reduced RPM operation on an engine is covered in [43,44,45].
In Figure 10, the KT, KQ and η0 curves are shown for the presented case study. The reduction in thrust demand from the main engine in three operating points is visible from the diagram, where the RPM lines are drawn for the corresponding engine load. From the diagram, it is obvious that, for the geometry of the installed propeller, the efficiency is increasing within the selected range of RPMs. It should be noted that this is not always the case; more often than not, the operating points with significant thrust reduction fall after the η0 peak value, thus resulting in a propeller efficiency drop.
With the positive trend of both the propeller efficiency and SFOC, the engine demands less power and has a better fuel consumption rate, resulting in a 24.8% fuel reduction for 20% of the initial power demand provided by the wind (45.3% for 40%, respectively). The data calculated for the three scenarios are summarized in Table 3.
Using meteorological data from the Adriatic Sea, fuel oil savings were calculated for the case study vessel navigating eastbound on the presented route. Figure 11 illustrates a 3D map of fuel consumption, displaying the seasonal averages for summer and winter across all points within the study area (Figure 5). The diagram reveals that, from the initial average fuel consumption of approximately 11.2 t/h (without sails), significant reductions are achievable. In winter, an average savings of 1.4 t/h, or 12.5%, can be realized across the Adriatic Sea; this is calculated for the ship sailing eastbound with a course of 120°, with mean winter wind values for all points in the area. These data relate specifically to this ship, on this route, with this particular sail. Changing any of these parameters will alter the data. The analysis was conducted for conditions that might be referred to as the most common metocean conditions in the Adriatic in order to obtain a broader understanding of whether it is even possible to achieve the expected savings with this ship in the Adriatic. The data were obtained for a specific wind direction and speed (for each data point) averaged from all available values. These values actually represent what is the highest probability of occurrence for the Adriatic Sea. Naturally, the actual savings depend on the specific ship, location, WAPS technology and metocean conditions. The savings presented provide an order of magnitude estimate of the potential savings under specific conditions that represent typical seasonal conditions in the Adriatic.
Figure 12 illustrates the average daily fuel consumption and potential fuel savings (in t/day) at waypoints along the case study route for 2023. The figure highlights fuel savings opportunities across the route throughout the year.
To estimate the economic impact of WAPS, average values are presented in Figure 13 based on the case study scenario. Different color lines (with reduced transparency) represent monthly mean fuel consumption values at various waypoints, while the blue line represents the monthly means with all waypoints merged. From the diagram, it can be observed that (as expected) fuel consumption is reduced less during the summer months when the wind intensity is the least. Given the Adriatic’s typically mild wind conditions and the speed of the vessel in this scenario, it is worth noting that a slower ship in windier regions would likely experience even greater benefits from WAPS. Also, in Figure 13, the scatter of the data in relation to true wind can be observed. A real range of wind speeds and angles, indirectly inputted into the model through various waypoints and ship courses, influences the apparent wind, which then determines power reduction and fuel consumption. From the figure, a fuel consumption scatter of up to 15% is observed in January due to higher variations, and a fuel consumption scatter of only 2.2% is observed in July when the weather is more consistent.
In Figure 14, the influence of a change in wind speed and wind direction on fuel consumption can be observed. The base line set points for the parameters are 18 m/s for Vt, 50° for βt and 26.8 knots for operational ship speed. The influence of the wind speed on fuel consumption, shown in Figure 14, is calculated with the wind angle fixed on the base line value, and vice versa.
In Table 4, each variable is independently varied by a fixed percentage (±10%) from the base line values, and the corresponding change in fuel consumption is measured. The results are presented as sensitivity factors, which indicate the relative influence of each variable on fuel consumption. A higher sensitivity factor implies that the variable has a greater impact on fuel consumption.

5. Conclusions

This study demonstrates the impact of WAPS on propeller performance. A model was developed using the Python programming language to analytically capture the aerodynamic effects of WAPS and the hydrodynamic response of the propeller. To quantify the influences of sail-generated thrust on the operating conditions of the propeller, a straightforward analytical method was developed and presented in this paper.
Propeller performance was evaluated with a performance calculation tool based on the Wageningen B-screw series. From the literature review, the shift of the propeller operating point was expected along the propeller performance curve. Using the established ship model, an aerodynamic analysis was carried out using a VPP to determine the sail force generated by WAPS. With the sail force quantified, the required thrust force from the propeller was recalculated and introduced as an input to the performance characteristic module. In the case study presented, the introduction of WAPS led to a notable improvement in propeller efficiency.
However, it is worth mentioning that this is often not the case. Depending on the propeller design, with the increase in the advance coefficient (due to reduced thrust demand), the operating point can move to a less-efficient region of the propeller curve, resulting in lower efficiency. In such scenarios, the benefits of wind-assisted propulsion would be partially reduced by the inefficiencies introduced by the propeller operating under suboptimal conditions.
For the case study vessel, a route was chosen across the Adriatic Sea, and with the wind data from Copernicus Marine Services, possible fuel savings were analyzed for the route. From the wind data of the route, it was concluded that an average of 12.5% in fuel reduction is possible if calculated by monthly mean wind values. Finally, the propeller influence on fuel consumption was obtained and presented for scenarios with 0.20 and 0.40 required power generated by the sail. With the propeller influence taken into account, a more precise evaluation of WAPS contribution is calculated.
Further development of the model will include a ship model with more DoF and a more comprehensive hull resistance evaluation. The improved version of the model will incorporate more detailed ship dynamics and, in that way, be a more realistic simulation of ship behavior. Effective methods for evaluating energy savings like this one can help in future implementation and further development of WAPS and, in that way, contribute to sustainable shipping practices.

Author Contributions

Conceptualization, A.Č. and M.K.; methodology, A.Č. and M.K.; software, A.Č. and Z.J.; formal analysis, A.Č. and M.K.; resources, M.K. and Z.J.; data curation, A.Č. and Z.J.; writing—original draft preparation, A.Č.; writing—review and editing, M.K.; visualization, A.Č. All authors have read and agreed to the published version of the manuscript.

Funding

This research received no external funding.

Institutional Review Board Statement

Not applicable.

Informed Consent Statement

Not applicable.

Data Availability Statement

Data are not available due to ongoing research.

Acknowledgments

The weather data used in this paper were obtained from Copernicus Marine Services and processed with support from the project “Remote sensing in a function of sustainable development of maritime sector” (HR-08 4000143488, ESARS).

Conflicts of Interest

The authors declare no conflicts of interest.

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Figure 1. Number of ships equipped with WAPS [2].
Figure 1. Number of ships equipped with WAPS [2].
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Figure 2. Sail lift and drag coefficients from [39] fitted with PCHIP interpolation.
Figure 2. Sail lift and drag coefficients from [39] fitted with PCHIP interpolation.
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Figure 3. KT, KQ and η0 curves describing propeller characteristics for the case study vessel.
Figure 3. KT, KQ and η0 curves describing propeller characteristics for the case study vessel.
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Figure 4. T and η0 relations at different RPMs.
Figure 4. T and η0 relations at different RPMs.
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Figure 5. Selected area for wind data acquisition.
Figure 5. Selected area for wind data acquisition.
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Figure 6. Wind speed/direction occurrence probability map of the area of interest for the year 2023.
Figure 6. Wind speed/direction occurrence probability map of the area of interest for the year 2023.
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Figure 7. Polar plot for the case study vessel for two different vessel speeds.
Figure 7. Polar plot for the case study vessel for two different vessel speeds.
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Figure 8. Wind speed and true wind angle combinations in which 20% and 40% of required thrust is achievable.
Figure 8. Wind speed and true wind angle combinations in which 20% and 40% of required thrust is achievable.
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Figure 9. SFOC map from engine shop test results.
Figure 9. SFOC map from engine shop test results.
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Figure 10. Kt, Kq and η0 curves vs. J for case study vessel.
Figure 10. Kt, Kq and η0 curves vs. J for case study vessel.
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Figure 11. Potential fuel consumption with regards to wind in the Adriatic Sea.
Figure 11. Potential fuel consumption with regards to wind in the Adriatic Sea.
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Figure 12. Fuel consumption and savings on the sea route by waypoint monthly average.
Figure 12. Fuel consumption and savings on the sea route by waypoint monthly average.
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Figure 13. Monthly average fuel consumption (mean for all waypoints for Adriatic eastbound crossing).
Figure 13. Monthly average fuel consumption (mean for all waypoints for Adriatic eastbound crossing).
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Figure 14. Influence of wind speed and wind direction on fuel consumption.
Figure 14. Influence of wind speed and wind direction on fuel consumption.
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Table 1. Input data and constants for the case study vessel.
Table 1. Input data and constants for the case study vessel.
Input DataValueUnit
Ship speed, Vb26.8kn
Propeller revolutions, n109.5min−1
Propeller diameter, D8900mm
Propeller pitch (mean), P8320mm
Number of blades, z6-
Surface area ratio, Ae/Ao0.841-
Wake fraction coefficient, w0.312-
Thrust deduction coefficient, t0.1-
Fluid density, ρ1025kg/m3
Fluid kinematic viscosity, ν1.083 × 10−6m2/s
Table 2. Ship particulars.
Table 2. Ship particulars.
ParticularsInformation/ValueUnit
Vessel typeContainer carrier-
Vessel speed26.8kn
Engine typeHyundai B&W 12K98ME-C-
Engine power (N.C.R.), Pe72240 @ 104 RPMkW
Length overall, L363m
Breadth, B45.6m
Deadweight, DWT131863t
Table 3. Results for three different scenarios in case study vessel.
Table 3. Results for three different scenarios in case study vessel.
Initial Condition20% from WAPS40% from WAPSUnit
Vessel speed, Vb26.826.826.8kn
Engine power, Pe65,01649,87435,803kW
Engine speed, RPM 109.5100.193.0min−1
Thrust, T435134812611kN
Net thrust, Tnet391631332350kN
Torque, M583847603675kNm
Propeller efficiency, η00.630.660.69-
Thrust coefficient, Kt0.21475000.19462180.1688853-
Torque coefficient, Kq0.03237610.02990080.0267151-
Advance coefficient, J0.59972120.63831370.6866077-
Specific fuel oil consumption, SFOC172.1168.6170.8g/kWh
Daily fuel consumption268.55201.81146.8t
Savings relative to initial condition-24.8545.33%
Table 4. Sensitivity factors for key parameters.
Table 4. Sensitivity factors for key parameters.
ParameterSensitivity Factor
True Wind Speed, Vt9.04
True Wind Angle, βt3.56
Ship Speed, Vb4.8
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MDPI and ACS Style

Čalić, A.; Jurić, Z.; Katalinić, M. Impact of Wind-Assisted Propulsion on Fuel Savings and Propeller Efficiency: A Case Study. J. Mar. Sci. Eng. 2024, 12, 2100. https://doi.org/10.3390/jmse12112100

AMA Style

Čalić A, Jurić Z, Katalinić M. Impact of Wind-Assisted Propulsion on Fuel Savings and Propeller Efficiency: A Case Study. Journal of Marine Science and Engineering. 2024; 12(11):2100. https://doi.org/10.3390/jmse12112100

Chicago/Turabian Style

Čalić, Ante, Zdeslav Jurić, and Marko Katalinić. 2024. "Impact of Wind-Assisted Propulsion on Fuel Savings and Propeller Efficiency: A Case Study" Journal of Marine Science and Engineering 12, no. 11: 2100. https://doi.org/10.3390/jmse12112100

APA Style

Čalić, A., Jurić, Z., & Katalinić, M. (2024). Impact of Wind-Assisted Propulsion on Fuel Savings and Propeller Efficiency: A Case Study. Journal of Marine Science and Engineering, 12(11), 2100. https://doi.org/10.3390/jmse12112100

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