A SAILING SPEED ADVISORY FOR THE BEREZINA

Transcription

1 BSc Research Project A SAILING SPEED ADVISORY FOR THE BEREZINA Authors: R. van der Bles, J. Termorshuizen, S.M.A. Tjin-A-Djie, E.G. de Waal 1st Supervisor: M. Godjevac, PhD. 2nd Supervisor: Prof.dr.ir. T.J.C. van Terswisga Submitted to the Department of Maritime Engineering on December 19, 2014 in partial fulfillment of the requirements for the degree of Bachelor of Science in Maritime Engineering

2 Abstract A ship sailing in shallow inland waters experiences shallow water effects. These effects cause an increase in ship resistance, a decrease in sailing speed and an increase in fuel consumption. This report focuses on the shallow water effects that are experienced by the Berezina, an old tug boat functioning as a platform to test maritime innovations and techniques in the field of sustainability. By adapting the sailing speed to the water depth the increase in resistance is repulsed and therefore a reduction in fuel consumption is achieved. Various methods have been proposed to quantify the resistance increase by scientists such as Schlichting, Lackenby, Millward, Kamar and Jiang. All methods focus on wave resistance or viscous resistance and neither one of them combine these components. It is chosen to carry out a literature study into the shallow water correction methods of abovementioned scientists and match these methods with speed trials conducted on board the Berezina. The Holtrop & Mennen resistance prediction method is used as a baseline for the matching. The matching shows that the best fitting shallow water correction method is that of Jiang. Based upon this method a scenario simulator was programmed in which different scenarios were tested. Chapter 5 covers the literature study and chapter 6 discusses the procedure of conducting speed trials and the processing of the results obtained by them. Chapter 7 contains the matching of the correction methods found during the literature study with the results obtained by the speed trials and Holtrop & Mennen. Chapter 8 shows the design and working of the scenario simulator and the results that were obtained from it. Conclusions emerging from the research project are given in chapter 9 and finally, in chapter 10 recommendations for further research are included. Thanks go out to Milinko Godjevac and Tom van Terwisga who supervised us during this research project. Also, we would like to thank Erik Rotteveel for contributing a clear vision on the correction methods. Finally, we would like to thank Robert Hekkenberg and Ido Akkerman for providing useful feedback on the study, the research and the report itself.

3 Nomenclature Roman Variables A m Midship area [m 2 ] A OD Lateral projected area of superstructures etc. on deck [m 2 ] A w Waterline area [m 2 ] A XV Area of maximum transverse section exposed to the wind [m 2 ] A Y V Projected lateral area above the water line [m 2 ] B C AA C ALF c b C F C LF c m C MC c p c wp C XLI D Beam [m] Wind resistance coefficient Additional coefficient caused by three-dimensional flow effects Block coefficient Frictional resistance coefficient Additional coefficient caused by longitudinal flow Midship coefficient Horizontal distance from midship section to centre of lateral projected area A Y V [m] Prismatic coefficient Waterplane coefficient Additional coefficient caused by the linear potential theory Depth [m] 1

4 2 F n h Froude depth number g Gravitational acceleration [9.81 m/s 2 ] h H BR k k e k p L L CB L OA L P P L W L M B ṁ f M P M S n e n p P B P E P O P P P S P T Q R A R AA Water depth [m] Height of top of superstructure [m] Form factor Number of engines Number of propellers see L OA Longitudinal center of buoyancy [m] Length overall [m] Length between perpendiculars [m] Length of the water line [m] Engine brake torque [Nm] Mass flow of fuel [kg/s] Propeller torque [Nm] Shaft torque [Nm] Engine speed [rev/s] Propeller speed [rev/s] Brake power [W] Effective towing power [W] Open water propeller power [W] Delivered propeller power [W] Shaft power [W] Thrust power [W] Torque [Nm] Resistance increase due to the correlation between model and ship [N] Resistance increase due to relative wind [N]

5 3 R AP P R B R F R T R T R R w S bm sf c t T T a T f V V E V S V W R V w W eff z v Resistance increase due to appendages [N] Resistance increase due to bulbous bow [N] Resistance increase due to friction [N] Total ship resitance [N] Resistance increase due to stern [N] Resistance increase due to wave-making and wave-breaking [N] Maximum bow squat [m] Specific fuel consumption [kg/ws] Thrust deduction factor Draught [m] Draught at aft perpendicular [m] Draught at forward perpendicular [m] Sailing speed [m/s] Effective sailing speed [m/s] See V Relative wind speed [m/s] Sailing speed in deep water [m/s] Wake factor Effective widt of the waterway [m] Dynamic sinkage [m]

6 4 Greek Variables α Half angle of entrance [ ] η GB η H η O η R η S Gearbox efficiency Hull efficency Open water propeller efficiency Relative rotative efficiency Shaft efficiency ψ W R Relative wind direction [ ] θ Leading wave angle [ ] ρ Density [kg/m 3 ]

7 Contents 1 Introduction 12 2 Problem Definition The Assignment and Main Challenges The Berezina Assignment Background Main Goal, Main Question and Sub Questions Hypothesis Objectives and Scope Objectives Scope Work Plan Literature Speed Trials Scenario Simulation Literature Definition of Shallow Water Division between Deep and Shallow Water Distinction within Shallow Water Shallow Water Effects Viscous Flow and Form Factor Wave Resistance Sinkage and Trim Hull Efficiency and Open Water Efficiency Squat Effect Shallow Water Correction Methods Schlichting (1934) Lackenby (1963) Millward (1989) Kamar (1996) Jiang (2001)

8 CONTENTS 6 6 Speed Trial Tests Procedure of Conducting Speed Trials Processing of the Speed Trial Results Background Information Speed Trial Results Matching of Literature and Speed Trial Tests Theoretical Deep Water Resistance Holtrop & Mennen Method Van Oortmerssen Method Resistance Prediction The Berezina s Resistance Power Estimation Correction of the Speed Trial Results Speed Trial Results Compared to Holtrop & Mennen Results Applying Shallow Water Correction Methods Schlichting (1934) Lackenby (1963) Millward (1989) Kamar (1996) Jiang (2001) Results Scenario Simulation Simulator Simplifications Inner Workings of the Scenario Simulator Speed Advisory Expectations Results of the Scenario Simulation Route Route Route Route Conclusions Recommendations Validating the Speed Trial Results Shallow Water Correction Methods Validating the Scenario Simulator Speed Optimization Algorithm A Berezina Engine Specifications 76 B Main Specifications, Form Coefficients and Stern 77 B.1 Main Specifications B.2 Form Coefficients B.3 Stern

9 CONTENTS 7 C Numerical Results of the Resistance Methods 81 D PropCalc 83 D.1 Fixed Parameters D.2 Method D.3 Input D.4 Matching E Output of the Power Estimation 87 F MatLab Code of the Simulator 89

10 List of Figures 5.1 Leading wave decay (n) as a function of depth-length ratio (h/l). [21] Bow wave angle as a function of Froude depth number. [21] Map of the Mooie Nel and Noorder Buiten Spaarne, near Haarlem Relative wind of runs 1 and Relative wind of runs 3 and Relative wind of runs 5 and Relative wind of runs 7 and Relative wind of runs 9 and Relative wind of runs 11 and Input for the Holtrop & Mennen resistance method Results from the Holtrop & Mennen resistance method Input for the Van Oortmerssen resistance method Results from the Van Oortmerssen resistance method Results from the Holtrop & Mennen- and the Van Oortmerssen resistance methods Corrected power and resistance for the Berezina s speed trial results Speed trials and Holtrop & Mennen resistance values Speed trial resistances compared with Holtrop & Mennen resistance curves, corrected for different values of C F Different channel types, according to Briggs. [1] Berezina s resistance-speed curves at h = 2.3m The Graphical User Interface of the simulator The Graphical User Interface of the simulator after running calculations Route 1: Constant depth profile Route 2: A single depth change of 2m Route 2: Fuel savings at different mean Froude depth numbers Route 2: At mean Froude depth number Route 3: Varying water depth profile Route 3: Fuel savings at different mean Froude depth numbers Route 4: A single depth change of 10m A.1 Torque curve of the VW TDI [26] B.1 Main dimensions of a vessel B.2 Definition of the half angle of entrance B.3 Standard shapes for cross sectional areas

11 LIST OF FIGURES 9 C.1 Numerical overview of the results of the Holtrop & Mennen method C.2 Numerical overview of the results of the Van Oortmerssen method D.1 Optimization methods PropCalc D.2 Input for PropCalc D.3 Open water diagram for propeller B E.1 Output of the power estimation

12 List of Tables 2.1 Main dimensions of the Berezina Work plan for the research project, per category Work plan for the research project, per document Shallow water characterization summary. [20] Power and torque according to Volkswagen Marine. [26] Average values of the measured parameters during speed trials Non-dimensional parameters for components of the wind resistance coefficient. [3] Calculated components of C AA Calculation of C AA and R AA Limitations to the Holtrop & Mennen method and variety in vessel types. [17] Limitations to the Van Oortmerssen method compared with the Berezina s parameters. [25] Main specifications of the Berezina Efficiencies and constant assumed for the Berezina s engine Numerical values and ratio of the Van Ootmerssen and the Holtrop & Mennen method Results after correction by Schlichting s method Results after correction by Lackenby s method Results after correction by Millward s method Results after correction by Millward s method. (2) Results after correction by Kamar s method Results after correction by Kamar s method. (2) Water depth draught coefficients Various methods and their applicability to calculate the dynamic sinkage. [1] Length - water depth coefficients Results for the maximum bow squat calculation, using Millward s equation Results after correction by Jiang s method Results after correction by Jiang s method. (2) A.1 Specifications of the VW TDI [26] D.1 Fixed parameters of the current propeller design D.2 Range of possible propeller designs D.3 Diameter and P/D ratios for various propellers

13 LIST OF TABLES 11 D.4 Estimated design parameters for propeller B

14 Chapter 1 Introduction A reduction in fuel consumption of 10% could be achieved when adjusting the Berezina s sailing speed to the water depth on inland waterways. This statement is the hypothesis of this report, which is specified for the Berezina. The Berezina is an old tug boat, which is nowadays used as an Energy ship for the Fair Nature foundation. The vessel functions as a platform to test maritime innovations in the field of sustainability. It has been proven that sailing in shallow or confined waters has a negative influence on the performance of a vessel. As can be noticed in practice and has been shown in earlier research projects, the resistance of a vessel increases when it sails in shallow or confined waters. Therefore, a correlation between the increase in resistance and the change in water depth has to be found. If there is such a correlation it could be used to adjust the sailing speed in order to decrease the resistance at a constant water depth. So far, a number of researches have been performed to determine the effects of sailing in shallow water on the resistance of a vessel. This research project is based on the papers written by Schlichting (1934), Lackenby (1963), Millward (1989), Kamar (1996) and Jiang (2001), who all developed correction methods to compensate for the added resistance effects of sailing in shallow waters. The methods of Schlichting and Lackenby focus on the added wave resistance due to sailing in shallow waters, where Millward and Kamar correct for the effects on the viscous resistance. The focus of Jiang s research is on the influence of the dynamic sinkage on the resistance of a vessel. The main goal of this research project is to reduce the Berezina s fuel consumption over a predefined route, compared to the fuel consumption of the Berezina when sailing the same route at a constant speed. This goal has to be accomplished by adapting the sailing speed to the water depth. In order to adjust the sailing speed in such a way that fuel reduction can be achieved an educated advisory speed must be given. Therefore an applicable correction method for the shallow water effects, experienced by the Berezina, has to be found. Research should turn out if one of the existing methods could be used or a new correction method has to be developed. Eventually, the correction method is implemented into a scenario simulation model, which simulates routes with routes with various depth profiles. 12

15 CHAPTER 1. INTRODUCTION 13 The report consists of three parts. The first part consists of a literature study on the definition of shallow water and the effects of shallow water on the resistance of a vessel. The second part includes a determination of the resistance obtained by the speed trial measurements. The speed trial results are to be validated by the results of the Holtrop & Mennen resistance prediction method. The influence of each correction method on the total resistance is calculated for and compared to the shallow water condition. Finally a suitable correction method is chosen. In the third part various simulations are performed to give an indication of the amount of fuel which can be saved by adapting the sailing speed to the changing water depth. The results of the scenario simulation are based on the chosen correction method. Following this study, the results of adjusting the sailing speed in relation to the changing water depth on the amount of consumed fuel will be clarified.

16 Chapter 2 Problem Definition In this chapter the main goal and the background of the assignment are clarified. The assignment can be found in section 2.1. Section 2.2 covers details of the Berezina, the tugboat that is used as the reference ship for this research project. In section 2.3 the background of the assignment for the project is explained. The main goal and the raised main- and sub questions are specified in section 2.4. This chapter ends with a hypothesis, given in section The Assignment and Main Challenges As can be noticed in practice and has been shown in earlier research projects, the resistance of a ship increases when it sails in shallow or confined waters. An increase in resistance will lead to higher fuel consumption. Therefore, the assigment is to find a correlation between a vessel s resistance increase and the water depth. This research project will focus on defining a vessel s resistance as a function of the speed with respect to the water depth. The goal is to provide a sailing speed advisory in which the speed is adapted to the water depth which will lead to a decrease in resistance and therefore a decrease in fuel consumption. The reference ship is the Berezina, more information on the Berezina can be found in the next section. The sailing speed advisory will be customized for the Berezina. The main challenges in this assignment are: 1. finding a correlation between water depth and speed; This correlation can be found when a correlation between the water depth and resistance increase and a correlation between the resistance increase and the sailing speed is found. It is important to find such a correlation because it will give an indication on how much influence the water depth has on the resistance land sailing speed of the vessel and thus on the toal fuel consumption of the vessel on a given route with set time limit. 2. determining the accuracy of the speed trial measurements; The speed trial results will form a reference for the programming of the sailing speed advisory. The results need to be as accurate as possible to provide a realistic reference. 3. validating the sailing speed advisory. The sailing speed advisory can be validated by means of test runs with the Berezina to see if the output provided by the advisory are corresponding to the real-time output. 14

17 CHAPTER 2. PROBLEM DEFINITION 15 The societal problem that is to be solved is the exhaust of polluting gasses into the air due to inland shipping. The underlying thought of this research is to eventually reduce this amount of exhaust gasses. A reduction of the fuel consumption on a predefined route leads to a reduction of harmful exhaust gasses as fuels content harmful components. This reduction in fuel consumption is to be achieved by reducing the resistance increase of the ship due to shallow water effects. 2.2 The Berezina The Berezina will be the reference ship for this research project. The Berezina is an old tugboat that is nowadays used as an Energy Ship for the Fair Nature Foundation 1, a foundation that focuses on issues like climate change, consumer behavior and sustainable energies. The foundation is engaged in the enlightenment of people on these subjects and it stimulates people to start projects that deal with energy problems. The Berezina functions as a platform to test maritime innovations and techniques in the field of sustainability. The dimensions of the Berezina are given in table 2.1. Specifications of the engine of the Berezina can be found in Appendix A. L OA [m] 20.6 L P P [m] 18.6 B [m] 4.59 T [m] 1.30 D [m] 2.14 Table 2.1: Main dimensions of the Berezina. 2.3 Assignment Background The assignment is a response to the work produced by M. Godjevac and K.H. van der Meij [4] for the EU project MoveIT wherein measurements have been done on the performance of European inland ships. It was concluded that the variation in operational conditions is mainly caused by fluctuation of water level. The main focus in this research is therefore the effect of shallow water on ships, with respect to the water depth. Because the Berezina is the reference ship all conclusions will be drawn with regard to this ship. A number of papers have been written about the effects of shallow water on the resistance of vessels. During this research project, the theories and correction methods of Schlichting (1934) [23], Lackenby (1963) [13], Millward (1989) [16], Kamar (1996) [10] and Jiang (2001) [9] are taken into consideration. An oversight of these different theories and publications can be found in section 5.3. There are several methods to determine the effect of shallow water on the speed of a vessel, however none of these methods deal with all aspects of the effect of shallow water. That is not to say that the methods are unuseful, but there is no correction method that is generally stated to be correct for all ships. The objective of this research project is to find a correction method that is applicable to the Berezina by matching the abovementioned methods and the speed trial results. This should result in a reduction in fuel consumption. The objectives and scope are furthermore explained in chapter

18 CHAPTER 2. PROBLEM DEFINITION Main Goal, Main Question and Sub Questions The main goal of this research project is to achieve a reduction in fuel consumption for the Berezina. This reduction should be accomplished by adapting the sailing speed to the water depth. By adapting the sailing speed to the water depth, the resistance will decrease and the fuel consumption will be reduced. One of the goals is creating a scenario simulator which provides a sailing speed advice to the ship owner of the Berezina while not compromising on the intended arrival time. More information about the design of the scenario simulator can be found in section 3.2. To achieve satisfying results, real time measurements have to be done to acquire the ship s resistance curves by means of on-board speed trial tests. The research project is successful when a mathematical model is produced which gives reliable results and can be used to reduce the fuel consumption of the Berezina. Good research always starts with the construction of a main question and sub questions. The resistance of a vessel sailing in shallow and confined waterways, with respect to the water depth is the unknown parameter in this research. Adapting the sailing speed to varying water depth and resistance should lead to a reduction of the fuel consumption. To investigate the interaction between the water depth and the sailing speed, the following main research question is raised: To which extent can the fuel consumption of the Berezina be reduced, when the vessel s sailing speed is varied in shallow waters on inland waterways, with respect to the water depth? To achieve an answer to this main question the following sub questions have been raised: 1. When is water shallow? 2. How does the water depth influence the resistance of the vessel? 3. How can a correction, due to the variation in water depth, in the vessels resistance be calculated? 4. What is the influence of the change in water depth on the fuel consumption? 5. How can all these relations be combined to achieve reduction of fuel consumption? Answering these questions one by one should provide enough information to construct a scenario simulator by which different scenarios of a ship sailing in shallow and confined waters can be simulated. Adapting the sailing speed to the varying water depth should lead to a reduction in fuel consumption and an answer to the main question will be given by means of the scenario simulation. 2.5 Hypothesis The main goal of this research is to reduce the Berezina s fuel consumption by adjusting the sailing speed in relation to the water depth when sailing in shallow waters. To give an indication of the expected results, the hypothesis has been raised: If the sailing speed is adjusted to the effects of sailing in shallow water, then a 10 % reduction of fuel consumption will be achieved.

19 Chapter 3 Objectives and Scope In this chapter the objectives and the scope of the research project are stated. Section 3.1 contains the objectives of the research project. This section provides the goals which are to be achieved with this project. Section 3.2 provides the parameters to which the research project will be confined in its entirety. 3.1 Objectives The research project contains four objectives. These are as follows: 1. Learning about the possible effects of sailing in shallow waers on the resistance of a vessel. 2. Obtaining the resistance of the Berezina by means of speed trial tests on board the Berezina following the procedures and guidelines provided by the ITTC [7]. 3. Comparing existing shallow water effect correction methods with results of the speed trial tests and match the methods and the speed trial test results so that the programming of a scenario simulator can be constructed. 4. Creating a scenario simulator which provides an advice on the sailing speed when adapted to the water depth in shallow water so that a reduction in fuel consumption will be achieved. 3.2 Scope The research project is subjected to a set of parameters that confine it so that it is possible to do this project within the given time. The boundaries are drawn up as follows: 1. The research is done solely on the Berezina. The mathematical model will be specified for the properties of the Berezina. 2. The width of the waterway is not taken into account, neither are the consequential effects. 3. The effects of current and waves are considered non-existent because they are expected to be negligible in the waterway during the conduction of on-board speed trial tests. 4. A scenario simulator will be used because the programming involved to use actual maps of waterways is too complex to do in the time given for the research project. 17

20 CHAPTER 3. OBJECTIVES AND SCOPE 18 The scenario simulator mentioned in the fourth boundary as listed above is also subjected to a set of boundaries. The boundaries concerning the scenario simulator are as follows: 1. It is assumed that the vessel s heading is constant, the ship sails straight forward and no turns are to be taken. 2. The arrival time for the Berezina s destination is fixed and therefore the arrival time is not to be changed when the sailing speed is adapted. 3. The water depth does not vary gradually. Instead, the water depth varies instantaneously. 4. In the scenario simulator the effects of wind are not taken into account for the speed trials will already be corrected for the influence of the wind. 5. It is assumed that the vessel s sailing speed is varied instantaneously. 6. The Berezina has a speed limit of 9,2 knots. Section contains more boundaries and simplifications regarding the scenario simulation.

21 Chapter 4 Work Plan In this chapter the overall project approach is clarified. The different aspects of the research project are divided up into three categories: a literature study, speed trials and a scenario simulation. The approach of the first aspect which is the literature study can be found in section 4.1. The second aspect is the experimental part of the research: the conduction of speed trials on board the Berezina. Section 4.2 contains an explanation and a justification of these speed trials. The third and last section, section 4.3 encloses the final part of the project which is a scenario simulation. Table 4.1 and table 4.2 contain extensive plans of all the tasks that need to be done, including the distribution of the tasks between the group members concerning chapters 1 to 9 and a time planning for the chapters 5 to 9 that contain information leading to a satisfying answer to the main question and sub questions. 4.1 Literature After collecting literature, five theories have been selected which will be further elaborated on in section 5.3. These theories were published by Schlichting [23], Lackenby [13], Millward [16], Kamar [10] and Jiang [9]. The collected literature is used to find a definition of the sailing speed correction appropriate for the Berezina when experiencing shallow water effects. The results of the literature study are compared and matched to the results of the speed trials to verify that the defined corrections are valid for and in accordance with the effects that the Berezina experiences. The matching process can be found in chapter Speed Trials In order to apply sailing speed corrections to the Berezina, the ship s resistance needs to be defined for it is the resistance of the vessel that is affected by shallow water effects. An estimation of the ship s resistance can be achieved by conducting speed trials. For conducting on board speed trials the vessel s dimensions and the specifications of the vessel s engine have to be known. The speed trials are conducted according to the guidelines of the International Towing Tank Conference, or shortly ITTC [7]. Parameters that are variable and determined during the speed trials are water depth, sailing speed and heading of the ship, but also wind direction and wind speed. An extended overview of the conduction of speed trials and the results of the speed trials can be found in chapter 6. 19

22 CHAPTER 4. WORK PLAN Scenario Simulation A satisfying answer to the main question To which extent can the fuel consumption of the Berezina be reduced, when the vessel s sailing speed is varied in shallow waters on inland waterways, with respect to the water depth? can be achieved by comparing the fuel consumption in the situation without adapting the sailing speed, to the fuel consumption of the vessel when on the same route, within the same length of time, the sailing speed is adapted with respect to the water depth. Due to limited duration of the research project, the decision has been made to create a number of 4 datasets which represent possible routes on which the Berezina sails, with varying water depth and varying lenght. These possible routes represent different scenarios that could be faced by the Berezina and will be tested and compared by means of scenario simulation. The boundaries that are set for the scenario simulation can be found in section 3.2. A further elaboration of the simulator can be found in chapter 8 in which also the outcomes of the simulation and a clarification of the outcome of the different scenarios can be found. Task Responsible Person(s) Deadline Literature study Collect Literature All September 22, 2014 Determine what Information is Useful All September 24, 2014 Document Correction Methods Roel van der Bles, December 5, 2014 Lisa de Waal Document Power Estimation Jelmar Termorshuizen December 12, 2014 Document Matching of Methods and Speed Trials Stephanie Tjin-A-Djie December 12, 2014 Speed Trials Prepare Speed Trials Stephanie Tjin-A-Djie October 14, 2014 Conduct Speed Trials All October 14, 2014 Document Speed Trials - Procedures Stephanie Tjin-A-Djie December 12, 2014 Document Speed Trials - Results Stephanie Tjin-A-Djie December 12, 2014 Scenario Simulation Design Simulator Roel van der Bles December 3, 2014 Document Goal of the Simulation Jelmar Termorshuizen December 15, 2014 Create Various Scenarios Roel van der Bles December 12, 2014 Run Scenarios and Draw Conclusions Roel van der bles, December 15, 2014 Jelmar Termorshuizen Table 4.1: Work plan for the research project, per category.

23 CHAPTER 4. WORK PLAN 21 Document Responsible Person(s) Deadline Plan of Approach Document Summary Jelmar Termorshuizen September 25, 2014 Document Introduction Roel van der Bles September 25, 2014 Document Problem Definition Jelmar Termorshuizen September 23, 2014 Document Literature Lisa de Waal September 23, 2014 Document Overall Project Approach Lisa de Waal September 23, 2014 Document Plan of Approach Primary Research Stephanie Tjin-A-Djie September 23, 2014 Document Conclusions Roel van der Bles September 25, 2014 Compose and Finalize Plan of Approach Lisa de Waal October 1, 2014 Final Report Document Abstract Lisa de Waal December 16, 2014 Document Introduction Jelmar Termorshuizen December 16, 2014 Document Problem Definition Stephanie Tjin-A-Djie, November 28, 2014 Lisa de Waal Document Objectives & Scope Stephanie Tjin-A-Djie November 28, 2014 Lisa de Waal Document Work Plan Lisa de Waal November 2014 Document Literature Study Roel van der Bles, December 5, 2014 Lisa de Waal Document Speed Trials Stephanie Tjin-A-Djie December 5, 2014 Document Matching Literature & Speed Trials Jelmar Termorshuizen, December 14, 2014 Stephanie Tjin-A-Djie Document Scenario Simulation Roel van der Bles, December 15, 2014 Jelmar Termorshuizen Document Conclusions Stephanie Tjin-A-Djie December 16, 2014 Document Recommendations Roel van der Bles December 16, 2014 Compose and Finalize Final Report Lisa de Waal December 16, 2014 Paper Compose Paper Stephanie Tjin-A-Djie December 12, 2014 Finalize Paper Lisa de Waal December 17, 2014 Table 4.2: Work plan for the research project, per document.

24 Chapter 5 Literature This chapter covers the literature study part of the research project. The first section, section 5.1 contains a definition of the division between deep and shallow water. The first sub question, When is water shallow?, is answered after this section. In section 5.2 the different effects vessels experience when sailing in shallow water are given. The correction methods mentioned in section4.1, the theories defined by Schlichting [23], Lackenby [13], Millward [16], Kamar [10] and Jiang [9] are explained and worked out in section Definition of Shallow Water In order to investigate the impact of shallow water on the resistance and therefore the sailing speed, a definition of shallow water is required. This section provides such a division between deep water and shallow water in the first subsection: subsection Subsection contains a further distinction within the domain of shallow water Division between Deep and Shallow Water A clear-cut definition of when a vessel is sailing in shallow water and thus experiencing shallow water effects does not exist, for this complex problem is caused by multiple physical variables. Yet, a group of researchers at the Australian Maritime College of the University of Tasmania [20] has introduced guidelines for establishing whether ships are sailing in deep water or in shallow water. The researchers have stated that water is deep if the Froude depth number is below 0.5. The Froude depth number can be found with equation 5.1 : F n h = V gh (5.1) This definition implies that a vessel is sailing in shallow water whenever the Froude depth number is higher than 0.5. A Froude depth number below 0.5 implicates that the ship is sailing in deep water. This definition will be persevered during the research project. 22

25 CHAPTER 5. LITERATURE Distinction within Shallow Water Next to the difference between deep and shallow water a distinction can be made within the domain of shallow water. Shallow water then can be labeled sub-critical, critical and super-critical. The distinction between deep water and shallow water and a summary of the categories within the domain of shallow water can be found in table 5.1. The researchers in Australia stated by definition that if one of the conditions belonging to the deep water operational zone is not met, the operational zone can be considered shallow water. The distinction between sub-critical, critical en super-critical shallow water also depends on the Froude depth number but the categorization is mostly based on wash characterizations: the waves caused by a moving vessel. Table 5.1 shows that the wave system is divergent for any water depth. Those waves are observed as the wake of the vessel. Transverse waves are perpendicular to the direction of wave propagation. As the water depth decreases for a given speed, which leads to an increase in Froude depth number, the divergent wave system increases to about 90. The transverse waves completely vanish in this situation and only the divergent wave system remains. Operational zone Characterization Deep Water Shallow Water Shallow Water Shallow Water Sub-critical Critical Super-critical Froude Depth Number F n h < < F n h < 1.0 F n h 1.0 F n h > 1.0 Divergent Wave System Yes Yes Yes Yes Transverse Wave System Yes Diminishing None None Leading Wave Angle Constant at θ 90 θ θ Leading Wave Decay Constant at 1 3 Variable f (F n h ) Variable f (F n h ) Variable f (F n h ) Wave System Dispersive Yes Diminishing No Increasing Solitons No No Yes No Spectral Wavelet Analysis Constant Variable with time Variable for fixed Fn Variable with time Variable with time Performance Constant with time Increasing Variable with time Reducing (oscillating) Table 5.1: Shallow water characterization summary. [20] The next characterization is the angle of the leading wave. The change in leading wave angle goes along with the change in transverse wave system. Figure 5.2 shows the outcome of the authors previous research inter alia regarding divergent wave angle and decay [21]. The leading wave angle is called the bow wave angle in this case. An extrema in leading wave angle occurs at around F n h = 0.9. During the same research the leading wave decay coefficient was investigated. As figure 5.1 shows, the decay coefficient n turns out to be depending on the Froude depth number and varies between -1.0 to -0.2 and is constant only in deep water, where F n h < 0.5. As shown in table 5.1, the only non-dispersive wave system is found in critical shallow water. This is where solitons appear. The researchers at the Australian Maritime College give the following definition: A soliton is a single non-dispersive wave with no preceding or following trough. Solitons are cyclical and time dependent in nature. [20] Consequently, the only domain possibly showing solitons is that of critical shallow water.

26 CHAPTER 5. LITERATURE 24 The penultimate characterization is the spectral wavelet analysis. This is similar to Fourier analysis as both techniques break down signals within a time domain into individual components. The next step is to plot the components in the frequency domain. The only difference is that in wavelet analysis it is also possible to determine at which instant an event occurred within the signal. The wavelet analyses are to be reviewed with regard to the value, location and frequency of the peak spectral energy and the form and frequency range of the global spectral energy. Finally, table 5.1 mentions performance as one of the characterizations. This performance is not a wash characterization as such but also contributes to the distinction between the operational zones. The performance depends among others upon resistance, sinkage and trim. The resistance of a vessel changes as the water depth varies. The most noticeable change will be found in sailing speed. Section 5.2 takes a closer look on this aspect. A different aspect is the sinkage. A vessel can be regarded as a free-floating body. It will sink and trim as the body is subjected to forces. The constrained flow around the body causes a change in pressure which leads to a suction effect towards the boundary. A similar effect occurs when a vessel moves towards a bank or to other vessels. The vessel sinks and trims, and the phenomenon called squat will occur. A further elaboration on sinkage, trim and squat can be found in subsections and The magnitude of squat depends directly upon the sailing speed, the hull form and the ratio between water depth and ship draught. The corrections found in the collected literature only consider the division between deep water and shallow water. Therefore the different operational zones within the domain of shallow water will not be addressed.

27 CHAPTER 5. LITERATURE 25 Figure 5.1: Leading wave decay (n) as a function of depth-length ratio (h/l). [21] Figure 5.2: Bow wave angle as a function of Froude depth number. [21]

28 CHAPTER 5. LITERATURE Shallow Water Effects The next step is to determine the effects shallow waters have on vessels. Sailing in shallow water affects the resistance of the vessel, which can be divided into wave resistance and viscous resistance. It also has an effect on the trim and sinkage of the vessel and on the propulsive efficiency of the vessel. In subsection the effect on viscous flow and form factor are given. In subsection the effects on wave resistance are considered and subsection contains the effects of increased sinkage and trim. Subsection contains the effects on hull efficiency and open-water efficiency and lastly subsection explains the squat effect. Information in this section is generally based on Raven s A Computational Study [19] Viscous Flow and Form Factor The viscous resistance of a vessel is affected by shallow water effects. This effect can be linked to the change in the viscous flow and the form factor. Because the keel of the ship and the bottom of the waterway are considerably closer to each other in shallow waters the flow passes along the hull in a more horizontal direction. This change in flow changes the character of the pressure distribution over the hull which leads to a change in form factor. These effects are visible from low sailing speeds and are even more influential at higher sailing speeds Wave Resistance In this instance it is assumed that the dynamic trim and sinkage are not very different in shallow water than in deep water. When the vessel s sailing speed is relatively low the waves it makes are much the same in shallow water as they are in deep water. Although when the vessel picks up its speed the waves it makes are longer and react to the change in pressure distribution. The change in pressure distribution results in an increase in wave amplitude with consequently a small increase in wave resistance. However, wave length and direction are not yet affected in this case. From a speed that corresponds with F n h > 0.65 the wave length and shape of the wave pattern are influenced directly by the water depth. When the speed nears its critical point at F n h = 1.0, the wave resistance increases rapidly Sinkage and Trim The dynamic sinkage and trim change with the change in hull pressure distribution due to the variation in distance between the keel and the bottom of the waterway. When the vessel sails at a relatively low speed the sinkage varies along the lines of a V 2 scale. The change in resistance is variable per case, generally the viscous resistance and wave resistance will increase because the vessel will have a bigger draught. However, this does not lead to a change in form factor but substitutes an extra input along the lines of V 2 to the viscous resistance Hull Efficiency and Open Water Efficiency The net effect on the hull efficiency is not yet expressed clearly, however. The changed viscous flow affects the wake field and leads to an increase in wake fraction. A bigger thrust deduction factor is expected in very shallow water. The open water efficiency lowers in shallow waters due to a smaller inflow speed to the propeller and a bigger thrust to keep the speed constant. Because of these changes a range of effects occur and make it a complicated task to predict the resulting speed loss or power increase for a vessel in shallow water.

29 CHAPTER 5. LITERATURE Squat Effect Marine Insight [15] provides the following definition of squat: When a ship moves through the shallow water, some of the water displaced rushes under the vessel to rise again at the stern. This decreases the upward pressure on the hull, making the ship sink deeper in the water than normal and slowing the vessel. This is known as squat effect, which increases with the speed of the vessel. The phenomenon is caused by the flow of water that under normal circumstances flows under the hull but encounters resistance due to the closeness of the ship to the bottom of the waterway. This effect was elaborated in subsection The squat effect is also a result of the combination of sinkage and trim which is discussed already in section Shallow Water Correction Methods Different methods have been proposed in order to give a correction for shallow water effects. These shallow water correction methods either give a speed correction or a resistance correction. When a speed correction is given, the deep water and shallow water speed at which the Berezina has the same resistance can be found. A deep water resistance prediction method such as that of Holtrop & Mennen [5] can then be used to find the resistance of the vessel. Subsections 1 to 5 contain the correction methods as formulated by respectively Schlichting [23], Lackenby [13], Millward [16], Kamar [10] and Jiang [9]. Within the subsections it is also stated why the correction methods are to be considered in chapter 7 where the correction methods and results of the on-board speed trials are matched in order to find an accurate method which can be applied to the Berezina Schlichting (1934) Probably the oldest commonly applied correction method is formulated by Otto Schlichting in 1934 [23]. This method provides a speed correction. Schlichting assumes that the wave resistance of a vessel in shallow water is equal to the wave resistance of a vessel in deep water at a higher sailing speed with transverse waves of the same length. Schlichting derived the following shallow water correction for the sailing speed: V V = tanhf n h 2 In order to determine the shallow water resistance prediction method this equation can be rewritten into the equation 5.3. The resulting deep water speed can then be used in a deep water resistance program to determine the resistance. 2 V = V tanhf n h (5.3) While this method is one of the most well-known shallow water correction methods, it has some significant flaws. It is based on the data from only 3 vessels, all naval cruisers of which the dimensions are not comparable to the Berezina s. After deriving the speed correction Schlichting verified his method by applying it to 6 other vessels, all of which were fast vessels, so the wave resistance correction was very dominant. (5.2)

30 CHAPTER 5. LITERATURE 28 Schlichting also applies a correction for the change of the frictional resistance. However, as Raven [19] points out, this correction for frictional resistance has been derived empirically from measured shallow water resistance curves, and therefore also contains neglected effects on wave resistance, e.g. the increase of wave amplitude in shallow water. This is expressed as a speed correction to be applied to the resistance curve, given in a diagram as a function of A m /h Lackenby (1963) The method Lackenby published [13] in 1963 may very well be the most commonly correction method for shallow water effects nowadays. Lackenby expanded the method that was formulated by Schlichting and derived a new correction method for the sailing speed. This equation estimates the speed loss of a vessel sailing in shallow water compared to the speed of that same vessel sailing in deep water. Just like Schlichting s method, this correction method is based upon the parameter Am /h: ( ) V Am = V h tanhf n h (5.4) Rotteveel [22] rewrites this equation into the equation given in equation 5.5: ( ( ) ) Am V = V h tanhf n h V (5.5) This equation can be solved for V which can then be used to find the resistance using a deep water resistance estimation method such as Holtrop-Mennen [5]. Since Lackenby based his method on Schlichtings work, he builds upon his flaws as well, without incorporating new experimental data to construct this model. This makes the method of Lackenby as, if not more, unreliable as the method derived by Schlichting. Although because these correction methods are commonly used in the maritime industry they will be taken into account when the different correction methods and the results of the on-board speed trials are matched in chapter Millward (1989) Millward formulated a resistance correction method which was published in 1989 [16]. This correction method provides an estimate of the increase in form factor due to shallow water as follows: ( ) 1.72 T k = (5.6) h This resistance correction solely focuses on the viscous resistance, unlike the previous methods. Therefore it provides an increase in resistance for a single component of the resistance, unlike the methods of Schlichting and Lackenby which give a correction for the overall speed and where both wave resistance and viscous resistance are affected. Yet, related to this difference in resistance components, another difference between the method of Millward and the previous methods can be found. Millward has based his approach upon the parameter T/h instead of the parameter Am /h. Raven [19] comments that whereas Millwards approach seems sound and his work is based upon large model testing effort, some deep-water form factors seem slightly off and the models might have been affected by laminar flow. Also, no corrections for tank wall effects seem to have been made. It does however tell more about the viscous resistance in shallow water and therefore the correction method of Millward will be considered while matching the different methods in chapter 7.

31 CHAPTER 5. LITERATURE Kamar (1996) Like Millward, Kamar also focuses on the increase in form factor due to shallow water effects. The correction method Kamar defined was published in 1996 [10]. Kamar derived the following equation: k = ( c b B BT L 2 OA ) ( ) T (5.7) h It can be found that the main dimensions of the vessel play a big role in Kamar s method. The method is based on empirical derived expressions for form factors in deep water. These expressions are translated to expressions in shallow water considering model tests of 7 other ship models. This correction method of the form factor will nonetheless be considered in chapter 7 for it can show whether it specifies the method of Millward regarding the form factor and it can lead to a more clear vision on how a correction method for the Berezina is defined Jiang (2001) Jiang proposes a speed correction which results in an effective speed based on the dynamic sinkage of the vessel. This dynamic sinkage is also known as squat. This resulting effective speed combines the blockage effect near the vessel, which is important for the viscous resistance, and the effective depth-effect under the vessel, which is important for the wave effect. The equation that Jiang has derived for this effective speed is shown in equation 5.8: V E = V 1+2gzv V 2 1 z v h (5.8) In this equation, z v is the dynamic sinkage of the vessel and can be calculated by using a squat prediction method, of which there are several available. More information on squat effects can be found in subsection The effective speed can be used in a deep water resistance estimation method. This method is the most currently proposed method and gives a different approach than the previous explained methods. Jiang states that his method remains valid when stronger shallow water effects occur. Because of Jiang s statement and the fact that this method approaches shallow water effects in a different way this method is taken into account when matching correction methods to the results of the speed trials obtained on board the Berezina.

32 Chapter 6 Speed Trial Tests In this chapter the speed trials are being discussed in detail. Section 6.1 contains a description of the speed trials that have to be conducted. In section 6.2 the speed trial results are processed further along the guidelines of the document of the ITTC [7]. 6.1 Procedure of Conducting Speed Trials The speed trials with the Berezina will be conducted following the rules and guidelines of the ITTC. Part one of the ITTC document Recommended Procedures and Guidelines, Speed and Power Trials [7] deals with the preparation and implementation of the speed trials. In preparation the responsibilities are divided among the group members. Jelmar Termorshuizen is responsible for the measurement of the wind speed and direction. Roel van der Bles responsibility is the tracking of time and GPS coordinates. Writing down all of the data from the Berezina s dashboard i.e. the fuel consumption, heading, waterdepth etc. is the responsibility of Lisa de Waal and lastly the responsibility of overlooking the whole procedure, preparing for the trials and processing the results lies with Stephanie Tjin-A-Djie. The idea of the speed trial is to do test runs on different constant sailing speeds and certain depths and finding the corresponding fuel consumption and engine power. In the previous chapter, in section 5.1, the definition of shallow water is given, this is used to determine the depths on which will be tested. This leads to a depth of approximately 2 metres for the shallow water runs and 6 metres for the deep water runs. During the preparation it was decided that the runs would be done on 3 different speeds going upstream and downstream for both shallow water and deep water, this gives a total of 12 runs. In every run all of the aforementioned data needs to be catalogued. The speed trials were conducted on October 14. The deep water runs were conducted on the Mooie Nel, a small lake near Haarlem, the Netherlands, of which a map can be found in figure 6.1. The shallow water runs were conducted on the Noorder Buiten Spaarne, adjacent to the Mooie Nel. On the day the speed trials were conducted some unforeseen factors forced a revision on the original plan. The Berezina does not have a speedometer and on the waterway which will be used for the speed trials there is no current present. Also, it was not possible to sail the exact same route up and down and the depth kept varying on each run. The solution for these problems was to not use the current but the wind direction as a reference, not use a constant sailing speed but to keep the rpms of the engine constant and to calculate an average of the 30

33 CHAPTER 6. SPEED TRIAL TESTS 31 waterdepth over the duration of the run. All of this led to 6 runs in shallow water and 6 runs in deep water. In both cases 2 runs were done on 2000 rpm, 2 were done on 1500 rpm and 2 were done on 1000 rpm. Of the 2 runs per fixed rpm one was done with the wind on the port side and one with the wind on the starboard side in shallow water. In deep water one of the 2 runs corresponding to a fixed rpm was done with the Berezina going downwind and the other run with the Berezina experiencing headwind. In the next section the values of all of the data is catalogued. Figure 6.1: Map of the Mooie Nel and Noorder Buiten Spaarne, near Haarlem. 6.2 Processing of the Speed Trial Results In this section the results of the speed trials are processed. In order to process the results in a clear way, the first subsection, subsection contains some background information and a quick oversight of the steps that need to be followed during the process. In subsection the steps given in the first subsection are worked out Background Information According to the ITTC document Recommended Procedures and Guidelines, Speed and Power Trials Part 1 [7] and Part 2 [8] fourteen steps need to be taken to process the results provided by the conducted speed trials on board the Berezina. All appendixes mentioned in this and the following subsection can be found in this same document publicized by the ITTC. However, not all steps will be gone through because not all steps given are relevant to the conducted test as this document is used for sea trials and the speed trials on board the Berezina are done on inland waters. Another argument for not following all of the steps is that some conditions will not be applicable for the Berezina as she is a much smaller vessel then the vessels for which these trials are used. This will be further elaborated in subsection The fourteen given steps contain the following instructions: 1. Derive the average values of each measured parameter for each speed run. The average speed is found from the GPS recorded start and end positions of each Speed Run and the elapsed time. 2. Derive the true wind speed and direction for each Double Run by the method described in Appendix B [8].

34 CHAPTER 6. SPEED TRIAL TESTS Correction of power due to resistance increase due to wind. 4. Correction of power due to resistance increase due to waves. 5. Correction of power due to resistance increase due to effect of water temperature and salinity. 6. Correction of speed due to the effect of shallow water. 7. Correction of power for the difference of displacement and trim from the specific contractual and EEDI (Energy Efficiency Design Index conditions). 8. Correction of the rpm and propulsive efficiency from the load variation model test results. 9. Average the speed, rpm and power over the two runs of each Double Run and over the Double Runs for the same power setting according to the mean of means method [18] to eliminate the effect of current. 10. Check the current speed for each individual speed run by comparing the mean of means result at one power setting (step 9) with the results of step Use the speed/power curve from the model test for the specific ship design at the trial draught. Shift this curve along the power axis to find the best fit with all averaged corrected speed/power points (from step 9) according to the least squares method [14]. 12. Intersect the curve at the specified power to derive the ship s speed at trial draught in ideal conditions. 13. Apply the conversion to other stipulated load conditions according to Appendix A [8]. 14. Apply corrections for the contractual weather conditions if these deviate from Ideal Conditions Speed Trial Results It can be found that only steps 1 to 3 of the document obtained by the ITTC are applied during the process. A justification for this choice is given in this subsection. All steps are discussed one by one. Table 6.1 gives an oversight of the power and torque for the rpms used during the speed trials, according to the curve shown in figure A.1 in Appendix A : Rpm Power Torque [kw] [Nm] Table 6.1: Power and torque according to Volkswagen Marine. [26] According to the first step, the average values of each measured parameter have to be derived, for each speed run. The results are shown in table 6.2. Run 1 to run 6 are done in shallow water, run 7 to run 12 are done in deep water. Written in brackets is the wind direction. SB represents wind coming from starboard, likewise PS stands for portside. DW means that the Berezina was sailing downwind, HW represents sailing headwind.

35 CHAPTER 6. SPEED TRIAL TESTS 33 Depth Speed Wind Revs Heading PWG Fuel [m] [kn] speed [rpm] [deg] [%] consumption [m/s] [l/h] Run 1 (PS) Run 2 (SB) Run 3 (PS) Run 4 (SB) Run 5 (PS) Run 6 (SB) Run 7 (DW) Run 8 (HW) Run 9 (DW) Run 10 (HW) Run 11 (DW) Run 12 (HW) Table 6.2: Average values of the measured parameters during speed trials. Step 2 contains a derivation of true wind speed and direction. In figures 6.2 to 6.7 the Averaging process for the true wind vectors according to Appendix B1 [8] are given. These figures show the following vectors as the average of 2 runs: ˆ V n : Ship movement vector at run n. ˆ V W Rn : Measured relative wind vector at run n. ˆ UZ A : Averaged true wind vector. Appendix B2 Correction for the height of the anemometer [8] will not be used because one of the variables must come from wind tunnel tests and these were not conducted for the Berezina. In step 3 the increase of resistance due to wind is calculated according to Appendix C and paragraph of ITTC- Recommended Procedures and Guidelines Part 2. In this appendix a regression equation based on model tests is given, this equation was created by Fujiwara et al [3] and is defined as follows: C AA = C LF cosψ W R +C XLI ( sinψ W R 1 2 sinψ W Rcos 2 ψ W R ) sinψ W R cosψ W R +C ALF sinψ W R cos 3 ψ W R (6.1) C AA is the wind resistance coefficient and the calculated element in this equation. The values of C LF, C XLI and C ALF can be calculated for 0 ψ W R 90 with the following euations: A Y V C LF = β 10 + β 11 L OA B + β C MC 12 (6.2) L OA A Y V A XV C XLI = δ 10 + δ 11 + δ 12 (6.3) L OA H BR BH BR The non-dimensional parameters are provided by table 6.3. C ALF = ε 10 + ε 11 A OD A Y V + ε 12 B L OA (6.4)

36 CHAPTER 6. SPEED TRIAL TESTS 34 j i β ij δ ij ε ij Table 6.3: Non-dimensional parameters for components of the wind resistance coefficient. [3] C AA is now used to calculate the resistance change due to the wind, R AA. The equation for R AA is: R AA = 1 2 ρ air V 2 W R ψ W R A XV C AA (6.5) In this equation A XV represents the area of maximum transverse section that is exposed to the wind, which has a value of m 2. V W R is the relative wind speed and ψ W R is the relative wind direction. The density of air, ρ air is set at kg/m 3. An approximation of ψ W R is measured during the speed trial tests and corrected according to step 2 of this process. C AA and R AA are calculated for various runs and given in table 6.5. Again, in this table SB represents wind coming from starboard, PS stands for portside. DW downwind, HW represents the Berezina sailing headwind. The particular components needed for calculating C AA and R AA are given in table 6.4. The wind for a set of two runs comes from the same direction. This means that the values for the both runs are identical. For run 12 this is a little different for the value is the same but in another directino. This is because a ship has the opposite effect when sailing downwind than the effect it experiences when sailing headwind. L OA [m] 20.6 β C LF B [m] 4.59 β C MC [m] β C XLI A Y V [m 2 ] δ A XV [m 2 ] δ C ALF H BR [m] 2.36 δ A OD [m 2 ] ε ε ε Table 6.4: Calculated components of C AA. Step 4 contains a correction for the waves that are present during the speed runs. However, at the day of conducting the speed trials hardly any waves were present so this step will not be needed. The fifth step stipulates a correction of the ship due to the salinity of the water and the temperature of the water. There was no way to determine the temperature of the water and the salinity of the water so this correction was declared irrelevant. Also, it may be irrelevant because the trials were obtained on inland waters where the water is fresh instead of salt and the guidelines are assuming the water to be fresh.

37 CHAPTER 6. SPEED TRIAL TESTS 35 Run ψ W R [ ] cos ψ W R sin ψ W R C AA V W R [m/s] R AA [N] Run 1 (PS) Run 2 (SB) 8 0 Run 3 (PS) Run 4 (SB) Run 5 (PS) Run 6 (SB) Run 7 (DW) Run 8 (HW) Run 9 (DW) Run 10 (HW) Run 11 (DW) Run 12 (HW) Table 6.5: Calculation of C AA and R AA. The ITTC- Recommended Procedures and Guidelines, Part 2 uses the method by Lackenby for the effects of shallow water which should be applied according to step 6. Because this method will be used separately in this research project to provide the effects of shallow water this will not be used during the processing of the conducted speed trials. Here, no effects for shallow water will be used because the speed trials will be placed next to the effects as formulated by Lackenby, Schlichting, Jiang et cetera so if the method by Lackenby is used here, comparing with other effects will give invalid values. Step 7 depicts a correction of power for the difference of displacement and trim from the stipulated contractual and EEDI conditions. There are no contractual and EEDI conditions for the Berezina so this step is regarded as irrelevant. Step 8 encloses correction of the rpm and propulsive efficiency from the load variation model test results. No load variation model tests were done for the Berezina so this step will not be taken into account. According to step 9 the speed, rpm and power over two runs should be averaged. The speed trial is corrected for the current but on the Mooie Nel, the waterway where the trials were conducted, no current was present. This step will not be followed. Likewise, the steps 10 to 12 will not be followed as they are connected to step 9. The second-to-last step, step 13, corresponds with Appendix A [8]. In this appendix ballast speed/power test results and load conditions are applied. The Berezina is not a cargo ship, therefore step 13 is not relevant to the results of the Berezina. Finally, step 14 corresponds with a deviation in weather conditions from the contractual conditions to Ideal Conditions. In this case no contractual conditions were given so this step is skipped as well.

38 CHAPTER 6. SPEED TRIAL TESTS 36 Figure 6.2: Relative wind of runs 1 and 2. Figure 6.3: Relative wind of runs 3 and 4.

39 CHAPTER 6. SPEED TRIAL TESTS 37 Figure 6.4: Relative wind of runs 5 and 6. Figure 6.5: Relative wind of runs 7 and 8.

40 CHAPTER 6. SPEED TRIAL TESTS 38 Figure 6.6: Relative wind of runs 9 and 10. Figure 6.7: Relative wind of runs 11 and 12.

41 Chapter 7 Matching of Literature and Speed Trial Tests In this chapter the literature will be compared with the speed trial results to find the best shallow water correction method for the Berezina. In order to do this firstly the theoretical deep water resistance of the Berezina is calculated in section 7.1. After this the method for power estimation and the determination of the needed effeciences are discussed in section 7.2, after which in section 7.3 the wind correction for the speed trials can be applied. In section 7.4 the deep water speed trial results are compared to the theoretical deep water resistance, and in section 7.5 the shallow water speed trials are compared with the different shallow water correction methods. Finally in section 7.6 a conclusion is drawn for the most appropriate shallow water correction method for the Berezina. 7.1 Theoretical Deep Water Resistance In this section the decomposition of the Berezina s total resistance in deep water is described. The results from this calculation are used to verify the results from the deep water speed trial measurements on board the Berezina. The most common methods to determine a vessels resistance are model testing and statistical analysis. Since no scale model of the Berezina is available and the construction of such a model does not fit in the scope of this research project, the choice has been made to use statistical analysis methods to predict the Berezina s deep water resistance. There are numerous statistical methods to predict a vessel s resistance, but not every prediction method is applicable for the Berezina. There are methods specified for seagoing vessels, large displacement vessels, small displacement vessels, naval vessels, high speed planing vessels, multihull vessels, et cetera. Since the Berezina is a relatively small tug boat, the focus of this section is on the resistance prediction methods for small displacement vessels. The discussed methods are the Holtrop & Mennen method [5] [17] in subsection 7.1.1, because of its large variety of vessels and the Van Oortmerssen method in subsection 7.1.2, because this method is specially focused on small displacement vessels. Subsection contains a resistance prediction according to both prediction methods. Finally the conclusions will be drawn about what method is best applicable to determine the Berezina s resistance in subsection

42 CHAPTER 7. MATCHING OF LITERATURE AND SPEED TRIAL TESTS Holtrop & Mennen Method The Holtrop & Mennen method is based on the results of numerous model tests and real time resistance measurements. Although this method is based on seagoing vessels, due to the large variety of vessels (see table 7.1), it should be possible to make an accurate resistance prediction for the Berezina. This method provides a calculation of the total resistance of a vessel sailing in deep water, the effects of sailing in shallow water on the vessel s resistance not taking into account. To achieve reliable results a lot of vessel-particular input is required as discussed in subsection Before this method can be used to predict the Berezina s resistance, it should be checked if this method is applicable for the Berezina. From the model testing results some limitations can be raised, see table 7.1. The hull form parameters found for the Berezina are listed in table 7.2. It shows that the Berezina, mostly, fits in the Fishing Vessels, Tugs category. However, the B/T ratio of the Berezina does not fit in. Therefore the method s reliability is questionable for the Berezina. Ship Type L/B B/T c p F n max Tankers, Bulk Carriers 5.1 < L/B < < B/T < < c p < General Cargo 5.3 < L/B < < B/T < < c p < Fising Vessels, tugs 3.9 < L/B < < B/T < < c p < Container Ships, Frigates 6.0 < L/B < < B/T < < c p < Various 6.0 < L/B < < B/T < < c p < Table 7.1: Limitations to the Holtrop & Mennen method and variety in vessel types. [17] Van Oortmerssen Method The Van Oortmerssen method focuses on small displacement vessels such as tug boats, fishing vessels et cetera. The method is based on results from various model tests. Due to the scope of the model tests this method is only applicable [25] for vessels with limited dimensions as shown in table 7.2. As can be found in the table, the Berezina s specifications match the limitations for this method so the method should provide a reliable resistance prediction for the Berezina. Parameter Limitations Berezina min max L W L [m] [m 3 ] L/B B/T c p c m α Fn Table 7.2: Limitations to the Van Oortmerssen method compared with the Berezina s parameters. [25]

43 CHAPTER 7. MATCHING OF LITERATURE AND SPEED TRIAL TESTS Resistance Prediction First, the Berezina s resistance is predicted using the Holtrop & Mennen method, afterwards a prediction is made using the Van Oortmerssen method. The Holtrop & Mennen method uses various subcomponents to calculate the total resistance given in equation 6.6. The component R F represents the frictional component of the resistance. R AP P is the resistance component due to the appendages. In the case of the Berezina the appendages are already included in the form coefficients, so R AP P equals zero. The wave making and wave breaking resistances are merged into R w, where R B is the resistance component due to the pressure of the bulbous bow. Since the Berezina has no bulbous bow this component is negligible. The component R T R describes the influence of the immersed part of the stern on the total resistance and R A is the resistance component due to the correlation between model and ship. R T = R F (1 + k 1 ) + R AP P + R w + R B + R T R + R A (7.1) To calculate these resistance components, the Holtrop & Mennen method requires the main specifications of the vessel in order to achieve reliable results. These specifications are taken from the vessel s stability plan [2]. A brief overview of the required specifications is shown in table 7.3. Physical definitions of these specifications can be found in Appendix B. In order to distinguish the volume of the vessel from a rectangular block, form coefficients are used. The input for the Holtrop & Mennen program is shown in figure 7.1, a more detailed description can be found in Appendix B. As can be seen in figure 7.1 the areas of the appendages are zero. This does not mean that the Berezina has no appendages, however the influence of the appendages is already included in the form factors. L P P [m] L W L [m] B [m] 4.59 T a, T f [m] 1,30 [m 3 ] L CB, %ofl W L c m 0.77 c b c p c wp Table 7.3: Main specifications of the Berezina. The results from the Holtrop & Mennen prediction method can be seen in figure 7.2. The maximum sailing speed for the Berezina is approximately 9.2 knots, at this speed the total resistance is kn. See Appendix C for a numerical overview of the resistance components at the different speeds. The Van Oortmerssen method combines the wave making resistance and the frictional resistance into a total resistance component. The input parameters for this method are more or less similar to the input parameters for the Holtrop & Mennen method. However, the results are expected to be less accurate because the program requires a linesplan to define the form of the cross sectional area of the vessel and this linesplan is unavailable in case of the Berezina. An overview of the input for the Van Oortmerssen method can be found in figure 7.3. The calculated

44 CHAPTER 7. MATCHING OF LITERATURE AND SPEED TRIAL TESTS 42 values for the total resistance for this method are shown in figure 7.4. The graph shows that the total resistance at a speed of 9.2 knots is equal to kn. A numerical overview of the resistance components according to the Van Oortmerssen method is also given in Appendix C. Figure 7.1: Input for the Holtrop & Mennen resistance method. Figure 7.2: Results from the Holtrop & Mennen resistance method.

45 CHAPTER 7. MATCHING OF LITERATURE AND SPEED TRIAL TESTS 43 Figure 7.3: Input for the Van Oortmerssen resistance method. Figure 7.4: Results from the Van Oortmerssen resistance method.

46 CHAPTER 7. MATCHING OF LITERATURE AND SPEED TRIAL TESTS The Berezina s Resistance When the results of both methods are compared to each other as shown in figure 7.5 it can be seen that the total resistance curves have a similar slope up to a sailing speed of 7 knots, therefore the methods seem reliable to determine the Berezina s resistance up to 7 knots. When the speed increases further, the results of both methods start to deviate from each other. The Van Oortmerssen total resistance curve starts to approach a linear function, where the Holtrop & Mennen total resistance curve continues to follow a polynomial function. When the speed increases, the effect of the wave making and wave breaking resistance on the total resistance becomes more relevant. The increase in wave making and wave breaking resistance exceeds the increase in frictional resistance at higher speeds, so the expected total resistance curve for higher speeds is a polynomial function. Since the Holtrop & Mennen curve starts to follow a polynomial function, where the Van Oortmerssen curve starts to approach a linear function, the Holtrop & Mennen method seems to be the best approach of reality for the two methods. Therefore, the choice is made to use the Holtrop & Mennen results (see Appendix C) from this point on. Figure 7.5: Results from the Holtrop & Mennen- and the Van Oortmerssen resistance methods.

47 CHAPTER 7. MATCHING OF LITERATURE AND SPEED TRIAL TESTS Power Estimation To compare the amount of consumed fuel for the normal sailing condition and the adapted sailing speed condition, a correlation between the measured resistance and the fuel consumption has to be found. The method used to correlate the measured resistance of the vessel to the fuel consumption of the engine can be found in literature [11]. A brief overview of the calculations that have to be performed is given in this section. The first step in the process is to calculate the effective towing power. The effective towing power is the power that is required to move the vessel with a constant speed, see equation 7.2. P E = R T V S (7.2) In order to calculate the thrust power, the influences of the thrust deduction and the vessels wake on the power needed to move the ship have to be determined. These influences of the thrust deduction and the wake factor on the power are combined in the hull efficiency. Due to these influences in the water flow behind the ship the effective towing power is not equal to the thrust power. The next equation is valid for the hull efficiency. P E η H = k p P T = 1 t 1 w (7.3) Both the thrust deduction factor and the wake factor are known from the Holtrop & Mennen resistance prediction results. The Berezina s hull efficiency exceeds one and the vessel has only one propeller (k p =1), so the effective towing power is larger than the thrust power. When the open water conditions for the propeller are known, the power delivered to the propeller as torque can be calculated. The open water efficiency describes the ratio between the power needed to move the ship and the power the propeller delivers without interference of the vessel. The open water efficiency is a propeller specific parameter. Since there is not much information available about the Berezina s propeller, the open water efficiency is determined using the propeller design software: Propcalc. The known parameters for the Berezina s propeller are the P/D ratio, diameter and the number of blades. The PropCalc program provides a tool to match a standard propeller to the Berezina s propeller, see Appendix D for the details of this process. With the open water efficiency known, the open water power for the Berezina s propeller can be calculated: η O = P T P O (7.4) The open water power in combination with the number of revolutions the propeller has to make to achieve the required thrust are needed to calculate the torque delivered to the propeller: Q = P O 2π n p (7.5) The number of revolutions the propeller has to make is linearly proportional to the sailing speed, as can be seen in equation 7.6. n p = c 3 V S (7.6) Since the correlation between the number of revolutions and the sailing speed is linearly proportional, the factor c 3 has to be constant. The number of revolutions related to the maximum

48 CHAPTER 7. MATCHING OF LITERATURE AND SPEED TRIAL TESTS 46 sailing speed is known, so for this situation the c 3 factor can be calculated. This constant factor is needed to determine the number of revolutions for each sailing speed. The relative rotative efficiency describes the effect of the incoming disturbed water flow on the performance of the propeller, when compared to the open water situation. Therefore the relative rotative efficiency can be written as the ratio between the open water power and the power delivered by the propeller, resulting in the following equation: η R = P O P P = 2π Q n p 2π M p n p (7.7) A common range of values for the relative rotative efficiency is between 0,98 and 1,02 [11]. The relative rotative efficiency for the current propeller is calculated to be 1,02 according to Helm [24], who developed a method where he focused on small vessels. After simplification the remaining equation for the relative rotative efficiency can be found: η R = Q M p (7.8) Since the theoretical torque and the open water power are calculated in an earlier stage of the process, the relative rotative efficiency is determined to be equal to one, the propeller power and the related propeller torque M p can be calculated. Since the required power and torque for the propeller are determined, the focus changes to the rest of the drivetrain. The drivetrain of a vessel consists of an engine, gearbox, drive shaft and finally the propeller. In the previous section the focus was on the propeller and the influence of the incoming/outgoing water flow. From this point on, the focus will be on the transmission of torque and rotation from the engine to the propeller. Therefore, the efficiency of the drive shaft has to be determined. Transmission of energy is often not without dissipation losses. In this specific case shaft losses are taken account for by means of the shaft efficiency. η S = P p P S (7.9) Typical values for the shaft efficiency are ranged between 0,99 and 0,995 [11]. Since the Berezina s engine is located in the aft of the vessel, the drive shaft is small. Where a shaft efficiency of 0,99 could be used for large vessels with relatively long shafts, the shaft efficiency for the Berezina is determined to be 0,995. The power delivered to the transmission shaft is called the shaft power. The shaft power is equal to the for the shaft losses adapted propeller power. When the shaft power is determined the related shaft torque can be calculated. The shaft power is equal to the shaft torque times the propeller revolutions. P S = 2π M S n p (7.10) The second stage of the transmission process from engine to propeller is the gearbox. The gearbox reduces the engine speed to a matching propeller speed. To account for the losses in the gearbox the gearbox efficiency has been raised. This efficiency describes the losses between the power delivered by the prime mover and the power delivered to the drive shaft, as can be seen in equation 7.11 where k e is the number of installed engines. Common values for the gearbox

49 CHAPTER 7. MATCHING OF LITERATURE AND SPEED TRIAL TESTS 47 efficiency are 0,98 or 0,99 for simple gearboxes and 0,95 to 0,97 for more complex gearboxes [11]. The simplicity of a gearbox is dependent on the number of reduction stages in the gearbox. In the case of the Berezina a simple gearbox is used, so the efficiency is set to a value of 0,99. η GB = P S k e P B (7.11) When the gearbox efficiency is known, the power delivered by the prime mover can be calculated. The generated power is equal to the shaft power adapted for the gearbox losses. At last the engine s delivered torque M B can be calculated with equation 7.12: M B = P B 2π n e (7.12) The final step is to calculate the amount of injected fuel per second, related to the delivered power. In combination with the specific fuel consumption, which is given in the engine specifications [26], the amount of injected fuel can be calculated: ṁ f = sfc P B (7.13) The efficiencies and factor c 3 assumed for the calculation regarding the engine of the Berezina are given in table 7.4. An overview of the output of the calculation can be found in appendix E η H 1.04 η O η R 1.02 η S η GB 0.99 c Table 7.4: Efficiencies and constant assumed for the Berezina s engine. 7.3 Correction of the Speed Trial Results In the previous chapter the correction for the wind has been calculated. In this section the wind correction will be taken into account when calculating the resistance the Berezina experiences during the speed trials. The speed trial measurements include values for the depth of the water, the fuel consumption, the wind speed, the sailing speed, the heading and the rpm s. With table 6.1 the brake power corresponding to the used rpm s can be found. By using the method, as explained in section 7.2, the effective power corresponding with the brake power can also be found. By using equation 7.2 the resistance for each of the runs can be found. Table 7.6 shows the values for all the aforementioned parameters and corrects for the wind resistance to find the total resistance the Berezina experiences during the speed trials.

50 CHAPTER 7. MATCHING OF LITERATURE AND SPEED TRIAL TESTS 48 Figure 7.6: Corrected power and resistance for the Berezina s speed trial results. 7.4 Speed Trial Results Compared to Holtrop & Mennen Results In order to validate the results of the speed trials, the results are to be compared with the total resistance curve as obtained from the Holtrop & Mennen resistance prediction method. Since the Holtrop & Mennen resistance prediction method is purely based on deep water conditions, only the results from the deep water speed trials are discussed in this section. The results from the speed trials, corrected for influences of the wind, can be found in table 7.6. A complete overview of the Holtrop & Mennen results, as discussed in section 7.1, can be found in appendix C. To compare the results from both the speed trials and Holtrop & Mennen, the results are plotted in figure 7.7. Figure 7.7: Speed trials and Holtrop & Mennen resistance values.

51 CHAPTER 7. MATCHING OF LITERATURE AND SPEED TRIAL TESTS 49 As can be seen in the figure, there is a significant deviation between the results from the speed trials and the results from the theoretical calculation. Table 7.5 shows the numerical values for both methods, so a ratio between the two can be calculated. According to these results, it is clear that the ratio between the speed trial results and the Holtrop & Mennen results decreases when the sailing speed increases. V S R corrected R HM R corrected /R HM [kn] [kn] [kn] 3,41 2,53 0,50 5,11 4,09 3,27 0,70 4,68 5,47 5,11 1,27 4,02 5,69 5,24 1,39 3,76 7,04 6,41 2,57 2,49 7,34 6,25 3,01 2,08 Table 7.5: Numerical values and ratio of the Van Ootmerssen and the Holtrop & Mennen method. An explanation for this phenomenon can be found in the decomposition of the resistance. The total resistance can be divided into a wave making & breaking part and a viscous part. As discussed in chapter 7.1.3, the effect of the wave making resistance and wave breaking resistance becomes more relevant at high sailing speeds and starts to exceed the effect of the viscous resistance. However, for low speeds the viscous (frictional) resistance has the biggest impact on the total resistance. Since the deviation between the speed trial results and the theoretical resistance values is largest for low speeds, it is expected that the frictional resistance component as calculated with the Holtrop & Mennen method is too small for the Berezina s situation. The Holtrop & Mennen method is designed to predict the resistance of a vessel during its first trial run, which means that the assumption is made that the influence of the vessel s hull roughness on the total resistance is small. The hull roughness of the Berezina, built in 1908, can not be expected to satisfy this criterion. Another assumption of a first trial run is that the hull and propeller of the vessel are clean. This is certainly not the case for the Berezina. So there are multiple reasons [6] to expect why the frictional resistance component should be higher than calculated with the Holtrop & Mennen method: ˆ Biological Macro biological, animal and weed fouling Micro biological, slime fouling ˆ Physical Macro physical, plate waviness, plate laps, mechanical damage, corrosion, rivets, et cetera. Micro physical, steel profiles, minor corrosion, condition of coating The frictional resistance component can be described using equation 7.14 where C F is the frictional resistance coefficient. Since the other parameters are constant, the frictional coefficient must become higher to match the Holtrop & Mennen resistance with the speed trial results.

52 CHAPTER 7. MATCHING OF LITERATURE AND SPEED TRIAL TESTS 50 To give an indication of the influence of the frictional coefficient on the total resistance, the total resistance has been plotted in figure 7.8 for various values for C F. The friction coefficient has been raised by multiplication of the original value. R F = 1 2 ρ S V 2 S C F (7.14) Figure 7.8: Speed trial resistances compared with Holtrop & Mennen resistance curves, corrected for different values of C F. From the figure it can be seen that in compliance with the speed trial data points the resistance curves for the 3 C F and even 4 C F give the best approximation for the Berezina. The measurement tools all have their error margins which are not taken into account in these points. It is expected that when these error margins are taken into account, the 1.5 C F line is the best approximation of reality, and therefore this resistant curve is used for further calculations in this report. 7.5 Applying Shallow Water Correction Methods In this section the shallow water correction are applied to the results of the speed trials onboard the Berezina. Subsection contains a correction by Schlichting s method, subsection covers a correction by Lackenby s method. In subsection the correction by Millward s correction is applied and in subsection the correction by Kamar s method. Lastly, the results of the correction by JIang s method are given in subsection

53 CHAPTER 7. MATCHING OF LITERATURE AND SPEED TRIAL TESTS Schlichting (1934) Otto Schlichting developed an equation to predict the shallow water effects, more on this formula can be found in subsection This formula is used to calculate the increase in speed if the vessel were to sail in deep water. Then that deep water speed is used to determine the resistance according to the Holtrop and Mennen resistance curve. During the speed trials it was observed that the depth of the water varies a lot, in each run the average depth of the water was documented. The average depth will be calculated for all the shallow water runs and so a constant depth of the water will be used in the calculation of the corrected speed. The average depth that will be used is a depth of 2.3m. Table 7.6 shows the sailing speed, ranging from 1 to 10 knots with a stepsize of 0.5 knots, the corresponding Froude number, the corresponding corrected speed according to Schlichting s formula and the resulting total resistance. Also the effective power, the brake power and the fuel consumption are shown in this table. V S V S F n h V R T P E P B ṁ f [kn] [m/s] [kn] [kn] [kw ] [kw ] [g/h] E E E Table 7.6: Results after correction by Schlichting s method.

54 CHAPTER 7. MATCHING OF LITERATURE AND SPEED TRIAL TESTS Lackenby (1963) In this formula the method differs from that of Schlichting. Lackenby expanded Schlichting s formula, but Lackenby considers the deep water sailing speed as a known parameter and calculates a corresponding shallow water speed. Because the speed trials provide the shallow water sailing speed, the method of Lackenby will be worked out for a speed range of 1-10 knots with steps of Now the corresponding shallow water speeds will be determined for a range of 1-10 knots with steps of 0.5 knots and the resulting resistance will be found with help from the Holtrop & Mennen program. For this method the average depth of 2.3m will be used. Table 7.7 shows the deep water speed corresponding with the shallow water sailing speed and the resulting resistance. V S V R T P E P B ṁ f [kn] [kn] [kn] [kw ] [kw ] [g/h] E E E Table 7.7: Results after correction by Lackenby s method.

55 CHAPTER 7. MATCHING OF LITERATURE AND SPEED TRIAL TESTS Millward (1989) Millward s method works with a change in the form factor. This will result in a new form factor that will be used to calculate a new resistance for the vessel. Just as for the other methods the depth will be taken at 2.3m. Table 7.8 shows the vessel s sailing speed in a range of 1-10 knots with steps of 0.5 knots, the corresponding resistance in deep water, the old total resistance coefficient with which the C W can be calculated, the new C F, the new C T and finally the corrected resistance. In table7.9 the corresponding P E, P B and ṁ f will be shown. V S V S R DEEP C T 1, 5 C F (1 + k + k) C W C T,SHALLOW R SHALLOW C F [kn] [m/s] [kn] [kn] Table 7.8: Results after correction by Millward s method.

56 CHAPTER 7. MATCHING OF LITERATURE AND SPEED TRIAL TESTS 54 V S V S R DEEP R SHALLOW P E P B ṁ f [kn] [m/s] [kn] [kn] [kw ] [kw ] [g/h] E E E E Table 7.9: Results after correction by Millward s method. (2)

57 CHAPTER 7. MATCHING OF LITERATURE AND SPEED TRIAL TESTS Kamar (1996) Kamar s structure is similar to that of Millward (1989). For this case the depth will also be taken as 2.3m. Table 7.10 and table 7.11 show the results of the calculation. V S V S R DEEP C T 1, 5 C F C W C T,SHALLOW R SHALLOW [kn] [m/s] [kn] [kn] Table 7.10: Results after correction by Kamar s method.

58 CHAPTER 7. MATCHING OF LITERATURE AND SPEED TRIAL TESTS 56 V S V S R DEEP R SHALLOW P E P B ṁ f [kn] [m/s] [kn] [kn] [kw ] [kw ] [g/h] E E E E Table 7.11: Results after correction by Kamar s method. (2)

59 CHAPTER 7. MATCHING OF LITERATURE AND SPEED TRIAL TESTS Jiang (2001) Literature provides numerous formulae which calculate the dynamic sinkage. The work of Briggs [1] gives an overview of these methods and provides clear criteria for which method works best in particular cases. The work of Briggs will be worked through step by step to come to a conclusion as to which method fits best with the Berezina and this research project. ˆ Determining the channel configuration There are three types of channels according to Briggs. Type 1 is an Unrestricted Channel, type 2 is a Restricted Channel and type 3 is a Canal (see figure 7.9). For the Berezina case the assumption is made that the only restricted parameter related to the waterway is the water depth, therefore the unrestricted channel type will be used for the calculation. Figure 7.9: Different channel types, according to Briggs. [1] The effective width of the waterway can be calculated following equation 7.15: W EF F = ( (1 C 2 wp) ) B (7.15) However, according to the Berezina s stability plan by Cadhead [2], the c w p is equal to at a draught of 1.3 m. Substituting this value and the Berezina s width in the equation for the effective width of the waterway provides a value for W EF F of 48.8 m. ˆ Determining the block coefficient, c b This value is also found in the stability plan provided by Cadhead [2] and is ˆ Determining the water depth- draught coefficient for the different speed trial attempts in shallow water These values can be found in table 7.12: Run Water depth [m] h/t [-] Run 1 (PS) Run 3 (PS) Run 5 (PS) Run 2 (SB) Run 4 (SB) Run 6 (SB) Table 7.12: Water depth draught coefficients.

60 CHAPTER 7. MATCHING OF LITERATURE AND SPEED TRIAL TESTS 58 Theory Barrass (1981) Eryuzlu & Hausser (1978) Eryuzlu et al (1994) Hooft (1974) Huuska & Guliev (1976) ICORELS (1980) Japan (2002) Millward (1990) Millward (1992) Norrbin (1986) Romishi (1989) Applicability X X X X X X X V X X V Table 7.14: Various methods and their applicability to calculate the dynamic sinkage. [1] ˆ Determining the length- water depth coefficient for the different speed trial attempts in shallow water Those values can be found in 7.13: Run Water depth [m] L P P /h [-] Run 1 (PS) Run 3 (PS) Run 5 (PS) Run 2 (SB) Run 4 (SB) Run 6 (SB) Table 7.13: Length - water depth coefficients. ˆ Checking the table in Briggs, for which method is best applicable Table 7.14 shows the applicability of various methods to calculate the dynamic sinkage. The method of Millward(1990) will be chosen to be used in the calculation of the dynamic sinkage because the Berezina s coefficients meet the requirements for three of the parameters of the method while only two parameters of Romishi s method are met. ˆ Using Millward s method (1990) to define the dynamic sinkage Briggs [1] states that Millward conducted model tests to prove his theory. In these tests it is assumed that the channel width is approximately twice the ship length between perpendiculars. Furthermore, the tests were conducted on a limited range of ships, which means that the new and longer ships are not included in his tests. However, the Berezina is neither a new ship nor a long ship so she is qualified to use this method. Millward s method is a rather conservative method that provides a relatively large squat value. Millward s formula for the maximum bow squat is defined in equation The results of this calculation can are shown in table It is assumed that the dynamic sinkage is equal to the measured sinkage. S bm = 0.01 L P P (15 c b 1 L P P B 0.55 ) F n 2 h F n h (7.16)

61 CHAPTER 7. MATCHING OF LITERATURE AND SPEED TRIAL TESTS 59 V S V S F n h S bm [kn] [m/s] [ ] [m] Table 7.15: Results for the maximum bow squat calculation, using Millward s equation. Now that the dynamic sinkage is calculated the formula of Jiang can be used to calculate the effective speed and the corresponding total resistance. Table 7.16 and table 7.17 show the results for the calculations performed with the Jiang correction method. V S V S F n h Measured V E R T [kn] [m/s] sinkage[m] [kn] [kn] Table 7.16: Results after correction by Jiang s method.

62 CHAPTER 7. MATCHING OF LITERATURE AND SPEED TRIAL TESTS 60 V S V S V E R T P E P B ṁ f [kn] [m/s] [m/s] [kn] [kn] [kn] [g/s] 1 0,514 0,566 86,5 0,044 0,090 5,422E-06 1,5 0,772 0, ,142 0,287 1,730E ,029 1, ,5 0,327 0,660 3,980E-05 2,5 1,286 1, ,5 0,627 1,267 7,639E ,543 1, ,5 1,070 2,164 1,304E-04 3,5 1,801 2, ,703 3,443 2,075E ,058 2, ,574 5,204 3,137E-04 4,5 2,315 2, ,792 7,665 4,620E ,572 3, ,597 11,314 6,820E-04 5,5 2,829 3, ,389 16,958 1,022E ,087 3, ,5 13,388 27,063 1,631E-03 6,5 3,344 4, ,5 20,888 42,222 2,545E ,601 4, ,5 34,021 68,771 4,145E-03 Table 7.17: Results after correction by Jiang s method. (2) 7.6 Results Now that all of the values are known for the various methods and the speed trials these can be compared to each other. This is shown in figure This figure depicts the resistance the Berezina experiences and the sailing speed. A depth of 2.3m is taken for all the methods because this is the average of all the shallow water runs. According to this figure the method of Jiang is the best approximation to the speed trial measurements. Knowing this the method of Jiang will be used in the scenario simulator. Figure 7.10: Berezina s resistance-speed curves at h = 2.3m.

63 Chapter 8 Scenario Simulation This section describes the design, the development and the results of the scenario simulator that was mentioned in section 3.2. In the previous chapters of this report, correction methods were considered which describe the influence of the change in water depth on the resistance of the vessel. These methods have been compared to the speed trial results to check their reliability. The first section of this chapter, section 8.1, contains the working of the simulator, the outcome of the matching process taken into account. In this simulator several simplifications have been made. Section 8.2 covers the results obtained from running the scenario simulator. 8.1 Simulator This simulator is created as a tool to test the influence of adapting the speed to the water depth on the resistance, and therefore on the amount of injected fuel per route. The main goal of the simulation is to find an educated answer to the main question of this report. In this section the simulator itself is discussed, with an overview of the necessary simplifications in subsection an explanation of the inner workings of the simulator in subsection 8.1.2, an in depth look at the speed advisory in subsection and the results that are expected in subsection Simplifications To demonstrate the amount of fuel saved for the various simulations, simplifications of reality are taken into account. Some of the simplifications are a result of the scope of the research project, see section 3.2. The simplifications, as implemented in the model, are stated in the following list. ˆ Influence of shallow water effects when F n h > 0.5 A distinction between shallow and deep water can be made according to the Froude depth number. The definition, as stated in section 5.1, describes that a vessel sails in shallow water when the Froude depth number exceeds 0.5. Therefore, the model considers a shallow water condition when the Froude depth number exceeds 0.5 and a deep water condition when the Froude number is lower than 0.5. For the shallow water condition the resistance is compensated using the shallow water correction method from Jiang. ˆ Instantaneous speed changes The instantaneous speed changes are implemented into the simulation model, because this model is only used to illustrate the effect of the varying speed at varying water depths. The effects of the acceleration is therefore neglected in this model. 61

64 CHAPTER 8. SCENARIO SIMULATION 62 ˆ No added resistance effects wind and current The speed trial results are corrected for the wind and the effect of the current on the total resistance was negligible. The results from the Holtrop & Mennen method are also free from wind and current effects, therefore the added effects from wind and current are neglected in the simulations. ˆ Simulated route Since no detailed depth charts are available of the waters where the speed trials were conducted, the choice has been made to simulate various routes. Simulation of these routes is useful to demonstrate the amount of fuel that can be saved. The routes have been composed according to the following simplifications: 1. The water depth on the route varies instantaneously. 2. The vessel s heading is constant and therefore the route is a straight line. 3. The depth on the route is known beforehand. 4. The width of the channel is infinite, therefore bank effects are neglected. ˆ Deep water resistance from Holtrop & Mennen, compensated for C F The deep water speed trial resistance and the deep water resistance, as predicted with the Holtrop & Mennen method, deviate from each other. Since this is caused by the influence of the frictional coefficient, the Holtrop & Mennen resistance a correction has been applied to the Holtrop & Mennen resistance (see section 7.2). This corrected resistance is used as input for the model. ˆ Wake- and thrust deduction factor from Holtrop & Mennen resistance prediction The wake- and thrust deduction factor are estimated using the Holtrop & Mennen resistance prediction method. This method uses statistical predicition equations to estimate the wakeand thrust deduction factor [5]. ˆ Shallow water effects corrected for with Jiang As discussed in chapter 7, Jiang s correction method will be used to correct for the added resistance effects of sailing in shallow waters. ˆ Estimated efficiencies for fuel consumption calculation The method to correlate the measured or predicted resistance to the fuel consumption, as discussed in section 7.1, will be implemented in the model. The efficiencies used in this calculation process are estimated, since efficiencies are often not included in product guides. ˆ Speed correction Jiang cannot exceed 15 knots The Berezina s maximum sailing speed is 9.2 knots. The effective speed corresponding to this maximum speed limit is somewhere around 15 knots, as determined by Jiang Inner Workings of the Scenario Simulator The sailing speed advisory is opened through running the GUI.m file from Matlab. The interface of the advisory when initially opened can be seen in figure 8.1. By pressing the button Import route the depth profile of a route can be loaded into the simulation. The desired duration can then be entered, after which the calculation can be started by pressing the Calculate button. After the Calculate button is pressed, the following steps take place:

65 CHAPTER 8. SCENARIO SIMULATION The route is loaded into the local workspace 2. The duration is loaded into the local workspace 3. The constants are defined 4. The average speed is calculated 5. The Froude depth number on each interval is calculated 6. The average Froude depth number is calculated 7. The advised speed on each interval is calculated 8. The resistance on each interval for both the average and the advised speed are calculated If the Froude depth number on the interval is greater than 0.5, the resistance correction of Jiang is applied. 9. The effective towing power (P E ) is on each interval is calculated for both speeds 10. The brake power (P B ) on each interval is calculated for both speeds 11. The fuel consumption on each interval is calculated for both speeds 12. The total fuel consumption is calculated for both speeds 13. The total fuel consumptions are compared to see if fuel is saved 14. The fuel consumptions are written into the GUI 15. The depth profile of the route and the average and advised speed on the route are plotted Figure 8.1: The Graphical User Interface of the simulator.

66 CHAPTER 8. SCENARIO SIMULATION 64 For an in-depth look, a copy of the code is provided in appendix F. After running the calculations, the results are either plotted or written into the GUI. An example can be seen in figure 8.2. Figure 8.2: The Graphical User Interface of the simulator after running calculations. Two graphs are plotted in the GUI. On the left the depth profile of the imported route is displayed. The y-axis of this graph is reversed, so that the top of the graph can be seen as the water surface and the plotted line can be seen as the canal floor. In the graph on the right both the mean and advised speed are plotted for the whole route. In the top right corner of the GUI the fuel consumptions and savings can be read. If fuel is saved, the percentage of fuel saved will be displayed as green text. If fuel is lost, the percentage of fuel lost will be displayed in red text Speed Advisory During step 7 of the step-by-step process outlined in subsection 8.1.2, the advised speed on the route is calculated. Optimally, this advised speed is optimized for the lowest total fuel consumption on the route within the time constraint. This optimization is based on the following hypothesis: On a route with different water depths and a constant duration fuel can be saved between the situation where speed is constant and the situation where speed is varied in such a way that when sailing in relative deep water the speed is increased and when sailing in relative shallow water the speed is decreased. The method used to achieve this is sailing on a constant Froude depth number. First, the Froude depth number for each interval with the mean speed is calculated. Then, the mean Froude depth number is calculated. Hereafter, the speed on each interval that must be sailed at to sail at this mean Froude depth number is calculated. This speed is the advised speed.

67 CHAPTER 8. SCENARIO SIMULATION Expectations Due to the nature of the speed advisory and the application of the resistance correction above a Froude depth number of 0.5 it is expected that the greatest fuel savings can be achieved when the mean Froude depth number of a route approaches 0.5 from below. When the mean Froude depth number crosses this threshold the shallow water resistance correction will be applied on the entire route for the advised speed. Fuel savings seem unlikely in this scenario. When the mean Froude depth number drops too far below 0.5 only a relative small portion off the voyage with the mean speed will be in shallow water, which means relative little fuel can be saved when sailing the advised speed, until here too a threshold is crossed and fuel is lost when sailing the advised speed. 8.2 Results of the Scenario Simulation In this section the results for four different routes are shown and discussed, with subsection trough subsection corresponding to route 1 through 4. All routes have a total distance of a 1000 m. This is sufficient to see notable changes in the total fuel consumed between the mean sailing speed and the advised sailing speed. Scaling up these routes would affect the total fuel consumption, but not the ratio of the fuel saved, and is as such deemed unnecessary Route 1 Figure 8.3: Route 1: Constant depth profile. The first route tested is a route with a constant depth profile, as can be seen in the figure above. As is expected of this route, the simulation shows that the advised speed is the same as the mean speed, and thusly no fuel is saved or lost in comparison.

68 CHAPTER 8. SCENARIO SIMULATION Route 2 Figure 8.4: Route 2: A single depth change of 2m. The second route has a single change in depth. With a length of 1000m and a duration of 400s, the mean speed is 2.5 m/s or 4.86 kn. This route was designed to have a mean Froude depth number of at this duration. In this scenario a fuel saving of 41.6 g, or 18.2%, is achieved. After the mean Froude depth number at with a duration of 400s was achieved the duration was varied between 260s and 700s, with an irregular time step, in order to identify the relation between the mean Froude depth number and the fuel saved in percentages. The results can be seen in graph 8.5:. As expected, there are fuel savings just below mean Froude depth number 0.5. These exist until the lower threshold at mean Froude depth number 0.44, after which only losses are encountered. Just above mean Froude depth number 0.5 there are also fuel losses, as was expected. However, above mean Froude depth number 0.63 fuel is again saved. The percentage of fuel saved steadily climbs, until at a mean Froude depth number of 0.77 the maximum speed of the Berezina is reached. While the fuel savings at mean Froude depth number 0.63 and above show that when sailing at high enough speeds in shallow water it is preferable to increase speeds in the relative deep parts and slow down on the relative shallow parts of the route, it should be noted that the total fuel consumption skyrockets at these speeds. When sailing at mean Froude depth number the percentage fuel saved is close to the percentage when sailing at mean Froude depth number , while the total fuel consumed has increased with a factor 5 to 955,7g.

69 CHAPTER 8. SCENARIO SIMULATION 67 Figure 8.5: Route 2: Fuel savings at different mean Froude depth numbers. Figure 8.6: Route 2: At mean Froude depth number

70 CHAPTER 8. SCENARIO SIMULATION Route 3 The third route is a route with three different depths. This route, when optimized for a mean Froude depth number at a duration of 400s, saves slightly less fuel than the route with only two different depths, respectively 18.20% and 17.45% (see figure 8.7. When the duration is varied in order to investigate the relation between mean Froude depth number and fuel savings figure 8.8 is found which is very similar to figure 8.5. Figure 8.7: Route 3: Varying water depth profile. Figure 8.8: Route 3: Fuel savings at different mean Froude depth numbers.

71 CHAPTER 8. SCENARIO SIMULATION Route 4 Figure 8.9: Route 4: A single depth change of 10m. The fourth route has the same depth profile as route 2, with the difference that the relative deep part of the route is 10m deep instead of 2m. This route clearly show the limitations of the used speed correction method. The mean Froude depth number is greatly influenced by the big difference in water depths, and thus the advised speed is different from route 2, resulting in a fuel loss on a seemingly very similar route. This scenario shows that the speed advisory works best when the depth differences on the route are relatively small.

72 Chapter 9 Conclusions The main question of this research is To which extent can the fuel consumption of the Berezina be reduced, when the vessel s sailing speed is varied in shallow waters on inland waterways, with respect to the water depth?. This question has been answered through literature study, speed trial tests and scenario simulation. In the literature study the works of Schlichting, Lackenby, Millward, Kamar and Jiang were researched and worked out for the Berezina, these scientists all derived methods that predict the shallow water effects a ship experiences. Speed trial tests were done on the Berezina according to the procedures and guidelines of the ITTC. The average water depth of the shallow water speed trial runs is used in the literature study. The speed trials and literature study were compared and the best method of the literature was chosen as starting point of the scenario simulation, this comparison shows that the method of Jiang is closest to the speed trials. In the scenario simulation different routes with varying water depth will be used as input and the program will provide a speed advisory for this route as well as the percentage of fuel consumption reduction for this route. The hypothesis states that a reduction of at least 10% will be reached. In the most optimum case in the scenario simulation the reduction of the fuel consumption is 18.2%, this is more than stated in the hypothesis and thus it can be said that the hypothesis has been proven. A series of sub-questions have been formulated to help adequately answer the main question. These were answered throughout the report and will be shortly answered here. 1. When is water shallow? Research concludes that water is shallow when the Froude depth number is more than 0.5. See section 5.1 for detailed information. 2. How does the water depth influence the resistance of the vessel? When a vessel sails in shallow water it experiences extra sinkage and trim, a different pressure distribution along the hull which leads to a different form factor and viscous flow and the squat effect. See section 5.2 for detailed information about the effects that a ship experiences when sailing in shallow water. 3. How can a correction, due to the variation in water depth, in the vessels resistance be calculated? Schlichting, Lackenby and Jiang have formulated methods that calculate a corrected sailing speed in deep water that corresponds with the sailing speed in shallow water. The deep water sailing speed found can then be used in a program like Holtrop & Mennen to find 70

73 CHAPTER 9. CONCLUSIONS 71 the corresponding vessel resistance. Millward and Kamar also formulated methods that calculate a change in the form factor. The new form factor can then be used to find a new resistance for the vessel. See section 4.1 and section 7.5 for detailed information on these subjects. 4. What is the influence of the change in water depth on the fuel consumption? With this change in resistance found in the previous sub-question the effective power can be calculated through the equation P E = R T V S. This in turn can be used in the program of Holtrop & Mennen to find the brake power. The brake power in turn can then be used with the equation ṁ f = sfc P B to calculate the fuel consumption. See section 7.2 for detailed information. 5. How can all these relations be combined to achieve reduction of fuel consumption? A scenario simulator is created that uses the method of Jiang to calculate the shallow water effects. The input for the simulator is a file with the variation of the water depth, the duration of the run and the length of the run. The program will then give a sailing speed advisory which leads to a reduction in fuel consumption. See chapter 8 for detailed information.

74 Chapter 10 Recommendations This chapter contains recommendations for further research. The recommendations are divided up into four categories. Validation of the results of speed trials is discussed in section 10.1, recommandations on shallow water correction methods for inland ships in particular are given in section 10.2, validation of the scenario simulator is discussed in section 10.3 and recommendations on an optimization in the scenario simulator can be found in section Validating the Speed Trial Results In section 7.1 it became apparent that there was a significant difference between the deep water speed trial results and the predicted deep water resistance. It is proposed that the main reason for this is a too low frictional resistance, and an effort is made to correct the difference by changing de frictional coefficient. However, inaccuracy in the speed trials is another important reason for the difference in the theoretically calculated resistance and the resistance calculated from the speed trials. Therefore new speed trials should be done with the Berezina to verify the current speed trial data used. In order to increase the accuracy of these new speed trials, the following additional steps should be taken: 1. Properly index the accuracy of all the measurement devices in order to quantify the uncertainty of the measurements. 2. Perform the speed trials on a day with ideal weather conditions, or as close to ideal as possible. The currently used speed trials were performed on a quite windy day, while a wind correction is used according to ITTC guidelines, it would be best to entirely remove this factor. 3. Ideally a new location for the shallow water speed trials is found, where the shallow water depth is constant all along the desired waterway. 4. The current speed trials measure the speed over ground sailing speed. The speed trough water should be measured and used in the relevant calculations. 72

75 CHAPTER 10. RECOMMENDATIONS Shallow Water Correction Methods During the literature study in chapter 5 it became clear that the current shallow water resistance methods are mainly based on or validated with seagoing vessels. A shallow water correction method especially developed for inland ships is desired, as these ships mainly encounter shallow water effects Validating the Scenario Simulator The scenario simulator discussed in chapter 8 is not yet validated. In order to validate the scenario simulator speed trials should be performed, during which the total fuel consumed for each run needs to be measured to be compared with the values calculated in the scenario simulator. The depth profile of the sailed route needs to be known or mapped during the speed trials Speed Optimization Algorithm The scenario simulator currently uses a limited algorithm for speed optimization. A more advanced optimization algorithm should be researched and implemented in order to increase the accuracy of the simulator for different kind of routes.

76 Bibliography [1] M.J. Briggs, Ship Squat Predictions for Ship/Tow Simulator. US Army Corps of Engineers, August [2] Cadhead Stability, Square Rigging & Yacht Design. Stabiliteitsberekening Energieschip Berezina. Enkhuizen, [3] T. Fujiwara, M. Ueno and Y. Ikeada. A New Estimation Method of Wind Forces and Moments acting on Ships on the basis of Physical Component Models. J. JASNAOE, Vol.2, [4] M. Godjevac and K.H. van der Meij. Performance Measurements of European Inland Ships, European Inland Waterway Navigation Conference. Budapest, Hungary, [5] J. Holtrop and G. G. Mennen. An Approximate Power Prediction Method. International Shipbuilding Progress. Vol.29, pp , [6] Hull Roughness - What Causes an Increase in Hull Roughness?. International Marine. Web. December 14, [7] ITTC. Recommended Procedures and Guidelines, Speed and Power Trials - Part 1: Preparation and Conduct, [8] ITTC. Recommended Procedures and Guidelines, Speed and Power Trials - Part 2: Analysis of Speed/Power Trial Data, [9] T. Jiang. A New Method for Resistance and Propulsion Prediction of the Ship Performance in Shallow Water. Proceedings 8th PRADS Symposium, Shanghai, [10] L. Kamar. Wassertiefe - Ihr Einfluss auf den Formfaktor von Seeschiffen. Schiff & Hafen 6, pp , [11] H. Klein Woud and D. Stapersma. Design of Propulsion and Electric Power Generation Systems. London: IMarEST, [12] R. van Koperen. Berezina, BP and V prediction. DAMEN, March [13] H. Lackenby. The Effect of Shallow Water on Ship Speed. Shipbuilder and Marine Engine Builder, pp , [14] S. J. Miller. The Method of Least Squares, Brown University, Mathematics Department, Providence, RI 02912,

77 BIBLIOGRAPHY 75 [15] Amitava Chakrabarty. How Squat, Bank and Bank Cushion Effects Influence Ships in Restricted Waters?. Marine Insight, April 29, Web. December 2, [16] A. Millward. The Effect of Water Depth on Hull Form Factor. International Shipbuilding Progress. Vol , pp , [17] I. Ortigosa, R. Lopez and J. Garcia. A Neural Networks Approach For Prediction Of Total Resistance Coefficients. Universistat Politècnica de Catalunya, Barcelona, [18] Principle of Naval Architecture, Ship Standardization Trials, no. Volume II, Section II, [19] H.C. Raven. A Computational Study of Shallow-Water Effects on Ship Viscous Resistance. 29th Symposium on Naval Hydrodynamics, Gothenburg, Sweden, August 26-31, [20] A. Robbins, G. Thomas and G. Macfarlane. When is water shallow?, International Journal of Maritime Engineering, pp. A , [21] A. Robbins, G. Thomas, M. Renilson, G. Macfarlane and I. Dand. Vessel Transcritical Wave Wake, Divergent Wave Angle and Decay, International Journal of Maritime Engineering, [22] E. Rotteveel. Investigation of Inland Ship Resistance, Propulsion and Manoeuvring using Literature Study and Potential Flow Calculations. Delft University of Technology, Septemer 24, [23] O. Schlichting. Schiffswiderstand auf Beschränkter Wassertiefe - Widerstand von Seeschiffen auf Flachem Wasser. STG Jahrbuch. Vol.35, [24] H. Schneekluth and V. Bertram. Ship Design for Efficiency and Economy. Ship Design for Efficiency and Economy. Oxford: Butterworth-Heinemann. p. 184, [25] Chapter VI: Resistance Predicion. Resistance-Prediction. August 4, Web. November 20, [26] Volkswagen Marine. Engines for displacing boats Salzgitter, Nedersaksen, Germany, pp , 2008.

78 Appendix A Berezina Engine Specifications The following specifications were provided by the owner of the Berezina, Mr. Ewald Vonk. The Berezina is equipped with a hydraulic gearbox with a reduction ratio of 3.031:1, a Jooren 28, 19 three bladed propeller and a Volkswagen TDI motor. The specifications of the engine are as follows: Number of cylinders [-] 5 Stroke volume [cm 3 ] 2461 Stroke [mm] 95.5 Bore [mm] 81. Compression ratio [-] 19.0 : 1 Nominal Power [kw] (at 3250 rpm) 88 Nominal Power [pk] (at 3250 rpm) 120 Specific Power [kw/l] 3508 Average piston speed [m/s] 10.2 Maximum Torque [Nm] (at 2500 rpm) 275 Miniumum Specific Fuel Consumption [g/kwh] 217 Table A.1: Specifications of the VW TDI [26] The engine s torque curve is given in figure A.1: Figure A.1: Torque curve of the VW TDI [26] 76

79 Appendix B Main Specifications, Form Coefficients and Stern B.1 Main Specifications The main dimensions are given in the drawing in figure B.1 and further explained in this appendix. Figure B.1: Main dimensions of a vessel. Length between perpendiculars (L P P ) The length between perpendiculars is the length between the forward and aft perpendiculars, measured along the summer load line. Waterline length (L W L ) The waterline length is the distance between the most forward and the most afterward point where the hull touches the water. Beam (B) The beam is the width of the hull. For the Berezina the measured beam is 4,59 meters at the widest point. 77

80 APPENDIX B. MAIN SPECIFICATIONS, FORM COEFFICIENTS AND STERN 78 Draught (T ) The draught of the vessel is the vertical distance from the baseline (keel) to the waterline. The draught of the vessel (without trim) is 1,30 meters. Displacement (volume) ( ) The displacement volume is the volume of the water the ship displaces when floating. Longitudinal center of buoyancy (L CB ) The longitudinal center of buoyancy is equal to the longitudinal distance from aft to the center of buoyancy. Half angle of entrance (α) The half angle of entrance is the angle the waterline makes at the bow with respect to the centerline (see figure B.2). Figure B.2: Definition of the half angle of entrance.

81 APPENDIX B. MAIN SPECIFICATIONS, FORM COEFFICIENTS AND STERN 79 B.2 Form Coefficients Midship coefficient (c m ) The midship coefficient is given by the ratio between the cross sectional area and the product of the beam and draught. It describes the shape of the cross sectional area. c m = A m B T (B.1) Block coefficient (c b ) The block coefficient describes the fullness off the vessel s hull. The block coefficient is given by the ratio between the volume of the displaced water and the product of the length, beam and draught. V c b = (B.2) L W L B T Prismatic coefficient (c p ) The prismatic coefficient describes the shape of the waterline area of the vessel compared to a rectangular area. The prismatic coefficient gives the ratio between the immersed volume and the product of the length between perpendiculars and the waterline area. V c p = L P P A m (B.3) Waterplane coefficient (c wp ) The waterplane coefficient is given by the ratio between the waterline area and the product of length between perpendiculars and width of the hull. c wp = A w L P P B (B.4)

82 APPENDIX B. MAIN SPECIFICATIONS, FORM COEFFICIENTS AND STERN 80 B.3 Stern The resistance of a vessel depends on the shape of the vessels immersed volume. Therefore, it is important to define the shape of the cross sectional areas. Standard shapes for cross sectional areas are shown in figure B.3. The frames of the Berezina are V-shaped. Figure B.3: Standard shapes for cross sectional areas.

83 Appendix C Numerical Results of the Resistance Methods Figure C.1: Numerical overview of the results of the Holtrop & Mennen method. 81

84 APPENDIX C. NUMERICAL RESULTS OF THE RESISTANCE METHODS 82 Figure C.2: Numerical overview of the results of the Van Oortmerssen method.

85 Appendix D PropCalc The computer software PropCalc is used to match the Berezina s current propeller with a theoretical standard propeller. The matching is performed in order to make an educated guess for the open water efficiency of the current propeller design. Typical values for the open water efficiency range between 0.3 for inland ships and 0.7 for frigates [11]. Since the Berezina is a small vessel with a relatively low sailing speed, the open water efficiency for this propeller is expected not to exceed 50%. The process of matching the current propeller to a standard series propeller will be explained in this section. The output of the program is based on two standard propeller series: the Wageningen B-series and a series of ducted propellers. These series are developed by MARIN, the Maritime Research Institute Netherlands. Each series contains a large numbers of propellers with varying numbers of blades and A e /A 0 ratios. D.1 Fixed Parameters Since the Berezina already has a propeller, there are some parameters which are known. Due to earlier research performed by DAMEN Shipyards [12] these parameters are documented, see table D.1. Since these parameters are fixed, a propeller design has to be found that has similar parameters. Diameter [inch] 28 Diameter [m] P/D ratio [-] 0.79 Table D.1: Fixed parameters of the current propeller design. D.2 Method The program uses four methods to calculate the optimal propeller for a specific load condition. The four optimization methods are based on velocity, power, propeller diameter, thrust and/or number of revolutions. Each method requires three known parameters, see figure D.1. 83

86 APPENDIX D. PROPCALC 84 Since propeller diameter, thrust and the number of revolutions at the maximum sailing speed [12] are known for this propeller, the choice could be made between the second and the fourth method. The fourth method is used to calculate the propeller characteristics, as displayed above. The thrust at this velocity is calculated using the Holtrop & Mennen resistance results. Figure D.1: Optimization methods PropCalc. D.3 Input The input parameters for the program depend on the chosen calculation method. The chosen method, which is based on the optimization of the thrust coefficient (K T ), requires the vessel s speed, the number of revolutions of the propeller related to that speed and the thrust force as input parameters. The input values are partly based on the research document by DAMEN [12], and partly based on the calculations performed with the Holtrop & Mennen method (thrust, thrust deduction and wake factor). The draft at the propeller is the vertical distance between the propeller hub and the waterline. Figure D.2 shows the input as used for the PropCalc calculation. Figure D.2: Input for PropCalc. D.4 Matching The parameters which determine the shape and size of the propeller are the propeller diameter, the number of blades and the P/D ratio. Therefore the choice has been made to match the theoretical propeller to these parameters. Since the propeller has 3 blades and is not ducted, the range of possible matches reduces to four propellers, see table D.2.

87 APPENDIX D. PROPCALC 85 Type A e /A 0 B B B B Table D.2: Range of possible propeller designs. For each of these propeller designs there has been tried to match the diameter and the P/D ratio with the current propeller design. The results can be seen in table D.3. From these results it can be seen that the difference in propeller diameter is somewhere around 0.01 meters for the B3-35, -50 and -60 propeller designs. The B3-80 deflects the most from the Berezina s propeller and is therefore considered not to be a suitable design to determine the open water parameters for the Berezina s propeller. D p P/D Current Design B B B B Table D.3: Diameter and P/D ratios for various propellers. Since the range in propeller diameter of the other three designs is small, the design with the best matching P/D ratio is chosen to determine the open water efficiency of the Berezina s propeller. The final design is the B3-65, figure D.3 and table D.4 show the open water diagram of this design and the final design parameters. According to these results the open water efficiency for the Berezina s propeller is determined to be η O =0,494. This complies with the expected values for the open water efficiency as stated in the introduction of this Appendix.

88 APPENDIX D. PROPCALC 86 Figure D.3: Open water diagram for propeller B3-65. K T K Q η O Q 1 knm P/D A e /A J Table D.4: Estimated design parameters for propeller B3-65.

89 Appendix E Output of the Power Estimation This appendix contains an extended overview of the output of the power estimation as explained in section 7.2 on the next page. 87

90 APPENDIX E. OUTPUT OF THE POWER ESTIMATION 88 Figure E.1: Output of the power estimation.