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The simulation of ship maneuvering and course keeping with escort tug Li, Ye 2004

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THE SIMULATION OF SHIP MANEUVERING AND COURSE KEEPING WITH ESCORT TUG By Ye Li B.Eng., Shanghai Jiaotong University P.R.CHINA, 2000 A THESIS SUBMITTED IN PARTIAL FULLFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF APPLIED SCIENCES THE FACULTY OF GRADUATE STUDIES DEPARTMENT OF MECHANICAL ENGINEERING We accept this thesis as conforming to required standard THE UNIVERSITY OF BRITISH COLUMBIA April 2004 © Y E LI,2004 Library Authorization In presenting this thesis in partial fulfillment of the requirements for an advanced degree at the University of British Columbia, I agree that the Library shall make it freely available for reference and study. I further agree that permission for extensive copying of this thesis for scholarly purposes may be granted by the head of my department or by his or her representatives. It is understood that copying or publication of this thesis for financial gain shall not be allowed without my written permission. Ye Li 20/04/2004 Name of Author (please print) Date (dd/mm/yyyy) Title of Thesis: The Simulation of Ship Maneuvering and Course Keeping with Escort Tug Degree: Master of Applied Sciences Department of Mechanical Engineering The University of British Columbia Vancouver, BC Canada Year: 2004 Abstract Ship maneuverability and its prediction in the early design stage become possible and important during the last 40 years as a result of some marine accidents involving large ships. Maneuverability standards were developed and proposed by the International Maritime Organization (IMO) which provides the ship maneuvering performance criteria. Ship simulation technology in particular simulation of ship maneuvering advanced well in recent years with the advent of computers. Computer programs using either numerically computed or experimentally determined hydrodynamics coefficients allowed for maneuverability simulations of different vessel types. Relatively good agreement was reported by various researchers between simulated results and those obtained from real ship trials. It seems that simulation can now identify acceptable ship maneuvering performance in calm seas. However the effects of the wind and the currents are not that well studied and reported while they are always important factors for ship maneuvering especially in restricted waters. The numerical simulation presented in this thesis classifies "good" ships and "bad" ships according to the IMO's most current standards for ship maneuverability. Subsequently, their course keeping ability in restricted area are studied in calm seas, shallow water, and under wind and current conditions. The simulation and validation work are done on ESSO OSAKA 278,000DWT Tanker, a well tested ship for regular maneuvering test in past few years. Good agreement has been obtained between results of simulation and sea trial. Since a large portion of disasters happened around coastal areas in the past few years, this Tanker's performance around Vancouver coast is simulated. ii Moreover, it is studied for the entrance in the Vancouver Harbor under wind and current conditions. The range of current and wind speeds for "successful" operation is then established. The effect of escort tugs on such an operation is also quantified. This thesis shows that a performance improvement index can be assigned to an escort tug for a given assignment. A detailed analysis and comparison with available experimental results are provided. Keyword: ship maneuvering, course keeping, IMO standard for ship maneuverability, marine vehicle, Tanker safety, ESSO OSAKA, wind and current effects, Vancouver Harbor, escort tug, ship simulation iii Contents Abstract ii Contents iv List of tables x List of figures xi Nomenclature xv English xv Greek , xviii Special xix Abbreviations xx Acknowledgements xxiii Chapter 1 Introduction 1 1.1 Background 1 1.2 Purpose of this work 5 1.3 Motivation 7 1.4 Overview of the thesis 10 1.5 Summary 12 Chapter 2 IMO Standards for Ship Maneuverability 13 2.1. History IMO Standards for Ship Maneuverability 13 2.2. Details of the four Ship Maneuverability Standards 17 2.2.1 Basic required tests 17 2.2.1.1 Turning tests 17 2.2.1.2 Zigzag tests 17 2.2.1.3 Full astern stopping tests 19 2.2.1.4 Test requirements 20 2.2.2 The detailed standard of the IMO criteria 22 2.2.2.1 Turning ability 22 iv 2.2.2.2 Initial turning ability 22 2.2.2.3 Yaw-checking and course-keeping abilities (zigzag) 22 2.2.2.4 Stopping ability 23 2.2.2.5 Difference between last standards 23 2.3 Summary 24 Chapter 3 Modeling and Maneuvering 25 3.1 Introduction 25 3.1.1 General 25 3.1.2 Previous work in Naval LAB at UBC 26 3.2 Modeling and Dynamics of Marine Vehicles 27 3.2.1 Reference frames and fundamental definitions 27 3.2.2 Basic equation 34 3.2.3 Inertia hydrodynamics forces, moments and Added Mass 36 3.2.4 Force derivatives and coefficients 39 3.2.5 Governing Equation 43 3.2.5.1 Abkowitz 43 3.2.5.2 Maneuvering Models Group (MMG) 45 3.2.5.3 Comparison of Abkowitz and MMG models 45 3.3 Detailed and specialized ship model 46 3.3.1 Container 46 3.3.1.1 Background 46 3.3.1.2 Basic data of the Container ship 47 3.3.2 ESSO OSAKA 49 3.3.2.1 Introduction 49 3.3.2.2 Maneuvering Equation for ESSO OSAKA 51 3.3.3 Mariner 52 3.4 Summary 54 Chapter 4 Course keeping and Simulation 55 4.1 External Forces 55 4.1.1 Environmental forces 57 4.1.1.1 Wind effect 58 4.1.1.2 Current effect 60 4.1.1.3 Restricted waterway 63 4.1.1.4 Waves 65 4.1.1.5 Other nature environmental forces 65 4.1.2 Manmade forces 65 4.1.2.1 Tug forces 66 4.1.2.2 Other manmade forces 67 4.1.3 Governing equation with environmental forces 68 4.2 System design and strategy for the ship sailing into a harbor 69 4.2.1 Analysis the real condition of the harbor 69 4.2.2 Analysis how the ship can sails into the harbor 71 4.2.3 Control system of this work 74 4.3 Detailed control algorithm 77 4.3.1 Introduction 77 4.3.2 PID strategy 80 4.3.3 The ship control equation 82 , 4.3.3.1 General 82 4.3.3.2 PID controller block 83 4.3.4 Filter 86 4.3.4.1 General 86 4.3.4.2 Filter block 86 4.3.5 Control parameters 87 4.4 Simulation 88 4.5 Summary 89 Chapter 5 Results Discussion and Analysis 90 5.1 Initial disturbance and perturbation 90 5.2 Simulation without external effects 90 5.2.1 Assumption according to IMO Standards 91 5.2.2 Container ship—"good" ship 91 vi 5.2.3 Mariner ship—"bad" ship 98 5.2.4 Simulation of ESSO OSAKA 99 5.2.4.1 Simulation of ESSO OSAKA based on IMO standard for Ship Maneuverability 99 5.2.4.2 Ship Speed Effect 107 5.2.4.3 Rudder Effect 108 5.2.4.4 Other Effects 110 5.3 Results under external forces 110 5.3.1 Basic assumption of the condition around Vancouver harbor 111 5.3.2 Discussion of the simulation results 112 5.3.2.1 Turning Circle 112 5.3.2.2 Zigzag 118 5.3.2.3 Comparison with real trial 122 5.3.2.4 Need for tug assistance 126 5.4 Results and discussions of Control work 128 5.5 Results and discussions of ship sailing into Vancouver Harbor 134 5.6 Summary 137 Chapter 6 Summary and Conclusion 139 6.1 Summary of the whole work 139 6.2 Conclusion 140 6.2.1 Existing maneuvering and course keeping model 141 6.2.2 Application of the model and the program in this thesis 141 6.3 Recommendations and future works 143 6.3.1 Recommendations 143 6.3.2 Future works 144 6.4 Commercial applications 145 6.4.1 General 145 6.4.2 Future works and recommendations for commercial application ..145 Bibliography 147 Appendix A Maneuvering characteristics 157 vii A.1 General Discussion 157 A.2 Detailed Fundamental Characteristics 158 A.2.1 Steady radius 158 A.2.2 Dynamically stable 158 A.2.3 Forces and moments during the maneuver 159 A.2.4 Trim effect 159 A.2.5 Unbalanced turn 159 A.2.6 The course-keeping ability and inherent stability 160 A.2.7 Hard-over turning ability ....163 A.2.8 The "crash-stop" ability 164 A. 3. Characteristics Defined 164 Appendix B Supplementary knowledge to Ship Maneuvering 167 B. 1 Frame Transformation 167 B.2 Definition 168 B.3 Derivation 169 B. 4 Propulsion forces 170 Appendix C Vessels data 172 C. 1 Container data 172 C.1.1 Hydrodynamic Force derivatives 172 C.1.2 Other Data 173 C.2 Mariner Class ship Data 174 C. 3 ESSO OSAKA Data 175 C.3.1 Hydrodynamic Force derivatives 175 C.3.2 Resistance data 176 C.3.3 Propulsion data 177 Appendix D External effects data 178 D. 1 Current data 178 D.2 Wind data 180 D.3Tug data 181 Appendix E Description and manual of the program 184 viii E.1 MATLAB part 184 E.2 SIMULINK part 187 Appendix F Explanation of softwares used in the thesis 188 ix List of tables Table 2-1 Evolution of IMO Standard of Ship Maneuvering 14 Table 2- 2 Other works related IMO Standard for Ship Maneuvering 16 Table 3-1 Definition of 6DOF of Marine Vehicle 32 Table 3-2 Major data of container ship 47 Table 3-3 Hull and Rudder data of ESSO OSAKA 49 Table 3-4 Propeller data of ESSO OSAKA 50 Table 3-5 Propulsion Machinery data of ESSO OSAKA 50 Table 3-6 Major data of Mariner Class ship 53 Table 4-1 Example of vehicle control 78 Table 4-2 History of modern ship control technology 78 Table 5-1 Ship Speed Vs. Turning Circle 107 Table 5-2 Basic data of ESSO OSAKA sea trial 122 Table 5-3 Initial value of the ESSO OSAKA sailing into the harbor 129 Table C-1 Hydrodynamic force derivatives data of Container 172 Table C-2 Other data of Container ship 173 Table C-3 Mariner Class ship data 174 Table C-4 Hydrodynamic force derivatives of ESSO OSAKA 175 Table C-5 Resistance data of ESSO OSAKA 176 Table C-6 Propulsion data of ESSO OSAKA 177 Table D-1 Current data 178 Table D-2 Wind data 180 Table D-3 Tug force data 1 181 Table D-4 Tug force data 2 182 Table D-5 Other data of the Tug 182 X List of figures Figure 1-1 An example of a manned-model simulator of Warsash Maritime Center, UK (From Marine Board 1996) 2 Figure 1-2 View of a whole room full-mission simulator of STAR center Florida USA (From Marine Board 1996) 3 Figure 1-3 View of control panel of a whole room full-mission simulator of STAR center Florida, USA (From Marine Board 1996) 3 Figure 1-4 Nautical disaster in Spanish Coastal 7 Figure 1-5 Vessel are going out from Vancouver Harbor 8 Figure 1-6 Two freights are waiting for docking into the Vancouver Harbor 8 Figure 2-1 Definition used on Turning Circle Test (from MSC/Circ 1053) 18 Figure 2-2 Definition used on Zigzag Test (from MSC/Circ 1053) 19 Figure 2-3 Definition used on Full Astern Stop Test (from MSC/Circ 1053) ....20 Figure 3-1 Near surface ocean vehicle—DOLPHIN 26 Figure 3-2 Stationary (Inertia) reference frame 28 Figure 3-3 Stationary (Inertia) reference frame (from PNA III) 29 Figure 3-4 Moving (Ship) reference frame 29 Figure 3-5 Moving (Ship) reference frame (from PNA III) 30 Figure 3-6 Ship dynamics 31 Figure 3-7 An aircraft carrier turning (from Naval Post School USA) 36 Figure 4-1-1 Ship under environmental external forces effects 56 Figure 4-1-2 Ship under manmade external forces effects 57 Figure 4-1-3 Coefficients of wind force OCIMF(1977) 60 Figure 4-1-4 Coefficient of Current force OCIMF(1977) 62 Figure 4-1-5 Tugs are assisting a large vessel grounded outside a navigation channel from Gray et al(2003) 66 Figure 4-1-6 Tug force model 67 Figure 4-2-1 Nautical Chart of Vancouver Harbor 70 Figure 4-2-2 Aerial view of the approach to Vancouver Harbor 70 Figure 4-2-3 Strategy of how a ship sailing into harbor 72 Figure 4-2-4 Lionsgate bridge at the first narrow 72 Figure 4-2-5 The control system 74 Figure 4-3-1 Control loop of ship autopilot by Segal (1960) 79 Figure 4-3-2 General feedback control loop 79 Figure 4-3-3 Non-interacting format PID 82 Figure 4-3-4 Interacting format PID 82 Figure 4-3-5 1st order Nomoto Equation 84 Figure 4-3-6 Autopilot system PID controller with Nomoto Equation 85 Figure 4-3-7 3rd order LP filter ...87 Figure 5-2-1 Initial Turning Test course of Container ship 93 Figure 5-2-2 Initial Turning Test yaw and speed of Container ship 94 Figure 5-2-3 Turning Circle Test course of Container ship 94 Figure 5-2-4 Turning Circle Test yaw and speed of Container ship 95 Figure 5-2-5 10/10 Zigzag Test yaw and speed of Container ship 95 Figure 5-2-6 10/10 Zigzag Test course of Container ship 96 Figure 5-2-7 20/20 Zigzag Test yaw and speed of Container ship 96 Figure 5-2-8 20/20 Zigzag Test course of Container ship 97 Figure 5-2-9 Full Astern Stopping test course of Container ship 97 Figure 5-2-10 Turning Circle Test course of Mariner 98 Figure 5-2-11 ESSO Turning Circle course 101 Figure 5-2-12 Speed and yaw of ESSO Turning Circle 102 Figure 5-2-13 Course of ESSO 20/20 Zigzag maneuver 102 Figure 5-2-14 Speed and yaw of ESSO 20/20 Zigzag maneuver 103 Figure 5-2-15 Course of ESSO 10/10 Zigzag maneuver 103 Figure 5-2-16 Speed and yaw of ESSO 10/10 Zigzag maneuver 104 Figure 5-2-17 Course of ESSO Initial Turning 104 Figure 5-2-18 Speed and heading angle of ESSO Initial Turning 105 xii Figure 5-2-19 Course of ESSO Full Astern Stop 105 Figure 5-2-20 Speed and yaw ESSO Full Astern Stop 106 Figure 5-2-21 Relationship between ship speed and some important values 108 Figure 5-2-22 Relationship between rudder and some important values 109 Figure 5-3-1 a Course of ESSO OSAKA turning under wind effect 114 Figure 5-3-1 b Speed and yaw of ESSO OSAKA turning under wind effect.. 114 Figure 5-3-1 c ESSO OSAKA turning under wind effect from Barr's result(1980) 115 Figure 5-3-2a ESSO OSAKA turning course under current effect 115 Figure 5-3-2b Speed and yaw of ESSO OSAKA turning speed under current effect 116 Figure 5-3-3a Course of ESSO OSAKA turning under overload wind and current effects 116 Figure 5-3-3b Speed and yaw ESSO OSAKA turning speed under overload wind and current effects 117 Figure 5-3-3c ESSO OSAKA turning under overload wind and wave effects from Barr's result(1980) 117 Figure 5-3-4a Speed and yaw of ESSO OSAKA zigzag under wind effect... 119 Figure 5-3-4b Course of ESSO OSAKA zigzag under wind effect 120 Figure 5-3-5a Speed and yaw ESSO OSAKA zigzag under current effect...120 Figure 5-3-5b Course of ESSO OSAKA zigzag under current effect 121 Figure 5-3-6a Speed and yaw of ESSO OSAKA zigzag under wind and current effects 121 Figure 5-3-6b Course of ESSO OSAKA zigzag under wind and current effects 122 Figure 5-3-7a Course of simulation compared with Crane (1979) 124 Figure 5-3-7b Speed and yaw of simulation compared with Crane (1979)... 125 Figure 5-3-7c Comparison result of Crane (1979) 126 XIII Figure 5-3-8a Breaking force and Steering force for ESSO OSAKA 127 Figure 5-3-8b ESSO OSAKA turning circle with Escort tug assistance 128 Figure 5-4-1 a Course of entering harbor at an initial required angle of 1.2(rad) 130 Figure 5-4-1 b Heading angle--^ > during the course 130 Figure 5-4-1c Yawing speed—r during the course 131 Figure 5-4-1d Rudder angle-<5 during the course 131 Figure 5-4-1 e x-distance during the course 132 Figure 5-4-1 f y -distance during the course 132 Figure 5-4-1 g Surge velocity u during the course..... 133 Figure 5-4-1 h Sway velocity v during the course 133 Figure 5-5-1 Possibility of ESSO OSAKA turning into the harbor 136 Figure 5-5-2 Zoom-in result of Possibility of ESSO OSAKA turning into the harbor without tug assistance 136 Figure 5-5-3 Possibility of ESSO OSAKA turning into the harbor with tug assistance 137 Figure A-1 Various kinds of motion stabilities (Arentzen, 1960) 161 Figure A-2 Ship stability performance after disturbance (From Fan 1988) ...162 Figure E-1 The flow chart of the program 186 xiv Nomenclature English Symbol Description A Area parameter a, (i = 1,2,3 or more) for propeller open water characteristics A L Longitudinal area of the hull Aj Transverse area of the hull \ Vertical area of the hull B Ship breath B Linear momentum B~(Bx,By,Bz) Bx Momentum in x direction By Momentum in y direction B_ Momentum in z direction C General constant or coefficient CB Block coefficient CT Total resistance coefficient CXc Current coefficient in x direction CYc Current coefficient in y direction C Z c Current coefficient in z direction CXwd Wind coefficient in x direction XV c Wind coefficient in y direction c Wind coefficient in z direction D Ship depth or Diameter DT Tactical diameter DP Propeller diameter F ForceF (X,Y,Z) vector f General function F Froude number " / , — s Acceleration due to gravity Center of Gravity of shipG (xc,yG,zG) or General center of reference frame h Water depth / General moment of inertial Ix Moment of inertial along x axis Iy Moment of inertial along y axis Iz Moment of inertial along z axis J Propeller advance ratio K moment of momentum K(KX,KY,KZ) K K coefficient of Nomoto Equation or Moment(see M) KT Integral coefficient of PID control algorithm KP p coefficient PID control algorithm KD D coefficient of PID control algorithm KT Thrust coefficient L General length or Ship length Lbp Length between perpendiculars L0A Over All Ship Length M Moment(see M) M Moment M (K,M,N) vector m Mass N Number of propeller blades or moment(see M) n Revolution per unit time P Ship rolling angular velocity Q Ship pitching angular velocity R General Radius r Ship yawing angular velocity T Ship Draught or T coefficent for Nomoto equation T, I coefficient for PID algorithm^ = K p / K Td D coefficient for PID algorithm^ = Kd/Kp t Time or thrust deduction factor V Ship speed V(u,v,w) vector V Ship nominal speed VA Advance speed of propeller u Ship serge speed v Ship sway speed w Ship heave speed wF Froude wake fraction coefficient wp Wake fraction coefficient X Force in x direction XP Propeller thrust force Y Force in y direction Z Force in z direction Greek Symbol Description a Angle of attack or Rotational angle along x axis fi Drift angle or Rotational angle along y axis 5 Rudder angle Sc Required rudder angle A Ship displacement or A finite increment <P Velocity Potential <f> Rolling angle 7 Rotational angle in z axis V Rudder& propulsion coefficient of governing equation X Added mass coefficients 2. (i, j = 1,2,3,4,5,6) n Natural number pi 6 Angle of pitch / trim xviii P General density or Sea water density pc Current density ,(Sea water density) psMp Ship density also written as ps pwd Density of air co Angular velocity co(p,q,r) con Natural frequency I Damping ratio W Heading/yawing angle Wd Desired heading angle y/r Required heading angle Special V Ship displacement volume A Aspect ratio Change from stationary frame to moving frame (See Chapter X 3 and Appendix B for details) X' Dimensionless of any value X x First time derivative of the variable x Second time derivative of the variable xix Abbreviations ABS American Bureau of Shipping ASCE American Society of Civil Engineers ASME American Society of Mechanical Engineers ASNE American Society of Naval Engineers ATTC American Towing Tank Conference AUV Autonomous Underwater Vehicle CHS Canadian Hydrographic Service DE Design Equipments (Sub organization of MSC) DOF Degree(s) Of Freedom OLPHIN D e e p O f f s n o r e Logging Platform for Hydrographic Instrumentation and Navigation DWT Deadweight FPSO Floating Production, Storage and Offshore loading units GNC Guidance Navigation and Control HSMB Hydronautics (Inc.) Ship Model Basin IEEE Institute of Electrical and Electronic Engineers IFAC International Federation of Automation Council IMD Institute of Marine Dynamics(Sub Organization of NRC) IMO International Maritime Organization ISE International Submarine Engineering Ltd. ISOPE International Society of Offshore and Polar Engineers ITTC International Towing Tank Conference KRISO Korea Research Institute of Ship and Ocean LCB Longitudinal Center of Buoyancy LCF Longitudinal Center of Floating LQG Linear Quadratic Gaussian LQR Linear Quadratic Regulator . . S N . I S N International Conference on Maneuvering and Control of MCMC . . . . . . . . Marine Vehicle MMG Maneuvering Model Group MSC Marine Safety Council(sub organization of IMO) NRC National Research Council(Canada) OCIMF the Oil Companies International Marine Forum . •- International Conference on Offshore Mechanics and Arctic OMAE _ . Engineering PID Proportional, Integral, Derivative(control) PNA Principle of Naval Architecture (Book) PMM Planar Motion Mechanism(test) RINA Royal Institution of Naval Architects RoRo Roll-On Roll-Off(Vessel) ROV Remotely Operated Vehicle RPM (Propeller)Revolution Per Minute SNAME Society of Naval Architects and Marine Engineers SNU Seoul National University SOLAS International Convention for the Safety of Life at Sea STAR Simulation, Training And Research T&R Technical and Research UBC University of British Columbia UK United Kingdom USA United States of America USCG USA Coast Guard UUV Unmanned Underwater Vehicle VLCC Very Large Crude Carrier WG Working Group (sub organization of DE) xxii Acknowledgements With the completion of this thesis, I feel a great sense of happiness and deep gratitude to all of the people who helped me to reach this point. First of all, the greatest and sincere appreciates are given to the my advisor who is also the chairman of the defense committee, Dr. Sander, M.Calisal, Professor of Department of Mechanical Engineering, University of British Columbia (UBC), for his kind supervision and guidance in both academic and non academic fields. He has been advising me to extend my knowledge and insight in naval architecture, general fluid mechanics and leading me into control fields. I also learned life attitudes and experiences from him which are also my important gains in my master studies. Many thanks are made to the other two committee members Dr. Roya, Rahbari from National Research Council and Mr. Jon, Mikkelson from Department of Mechanical Engineering, UBC for their precious time and suggestions on this work as they also kept showing interests the my work in its early stage. All the faculty and staff in the mechanical department deserve my sincere thanks and so do my colleagues in Naval Architecture and Offshore Engineering Lab. Several of these individuals made particularly valuable contributions at critical times throughout my Master studies. For example, Dr. Dunwoody, the associated Dean of Faculty of Applied Sciences, UBC, attended my presentations before the defense and gave me many useful and precious suggestions while he is a very busy person. I deeply appreciate and wish to acknowledge Dr. Kim and Dr.Choi from Korea Research Institute of Ship and Ocean (KRISO) for providing those xxiii precious old unpublished tanker tests data and explanation, the Canadian Hydrographic Service for providing the current data and Environment Canada for wind data in Vancouver Area. I also highly appreciate Mr. Alex C Landsburg, Maritime Administration Program Manager of Department of Transportation USA and Chairman of panel H-10 (ship controllability) of Society of Naval Architects and Marine Engineers (SNAME) for explaining some unclear notes and giving useful suggestion about ESSO OSAKA 278,000 DWT. Finally, I would deeply appreciate those people who had helped and encourage me during the work. Well, I can not list all their names and contributions. They are friends, relatives, colleagues, teachers and others. xxiv Chapter 1 Introduction 1.1 Background Ship maneuvering is a relatively young scientific discipline in the naval architecture and marine/ocean engineering field. However, there were some nonsystematic works before last century. Davidson (1946) gave out a set of complete maneuvering equations in which he addressed the complicated relationships between turning ability and course keeping ability. This work later became the milestone of ship maneuvering theory. In the following couple of decades, with the development of ship transportation and ship building, especially large tanker and container ships, the theory of ship maneuvering was also developed. There were two major theories, one is by Abkowitz (1964) and another is by (Maneuvering Models Group) MMG from Japan. Professor Abkowitz is one of the pioneer scientists in ship maneuvering field. At the Danish Maritime Institute, he first measured the forces acting on the ship as a function of its motion. He then integrated the equations of motion to provide the path of the ship while it performed some predefined standard maneuvers. This thesis is based on Abkowitz's model. In the following years, mathematical modeling and experimental techniques have been advanced, some good works had been done by e.g. Eda and Crane (1965) and Bardarson et al (1967), but the methods applied to solve the equations of motions remained the same. In the 1970's, when the computers were first introduced into this field, real time simulation becomes possible. After the 1980's, ship simulation has always been considered as a prospective method to test a ship instead of a real trial at sea. These 1 simulations have evolved better and better. Consequently, the computer based simulators are used all over the world and they are able to describe most ship maneuverability problem in general level. Some good research were reported by Doerffer(1980), Miller et al (1984) and Biancardi (1988 ). However, it took a long time for the ship simulation technology to evolve as shown in Figure 1-1 to Figure 1-3. Figure 1-1 An example of a manned-model simulator of Warsash Maritime Center, UK (From Marine Board 1996) 2 Figure 1-2 View of a whole room full-mission simulator of STAR center Florida USA (From Marine Board 1996) Figure 1-3 View of control panel of a whole room full-mission simulator of STAR center Florida, USA (From Marine Board 1996) 3 The input data for simulation are normally partly obtained from captive model testing techniques and partly from the databases with information about the maneuvering coefficients and/or full scale maneuvers. In the meantime, researchers were still trying to improve the mathematical models and experimental methods e.g. Hirano (1981), Gou (1981), Inoue et al(1981), Son and Nomoto (1981), Kose (1982), Biancardi (1988), Pourzanjani(1990) and Nishimoto et al (1995). With the evolution and development of high speed computers and advance programming languages and software, programming simulation became the popular and easy way to replace or partly replace the traditional work with hardware and external experimental results. People did many comparisons and analysis with computer-based ship simulation and control work using super computers e.g. Govindaraj et al (1981), Miller et al (1984), Webster (1992), Barr (1993), Geer (1998) and Fossen (2000). Consequently, the simulation work was moved onto PC and good results were reported by Oltmann and Sharma (1984), Kobatashi (1988), Li and Wu (1990), Janke-Zhao(1994), Lauvdal(1994), Izadi-Zamanabadi and Blanke (1999) and Fossen (2001). Furthermore, the computer based programs have been used for ship maneuverability prediction work early in the design stage instead of former traditional analytical methods, e.g. Masayoshi (1981), Inoue et al(1981 b), Jiang and Schellin (1990) and Molland and Turnock(1994). The simulation on a PC is the main approach in this thesis. It became not only the method used to predict the behavior of complex ship system but also a method to understand such a complex system and phenomena. One of the important prediction techniques which will be used in this thesis, time domain simulation, lets one control and monitor the system by numerical integration of 4 a set of equations of motions. Normally the simulation quality will be affected by the following factors: 1) The quality of mathematical model we select. Normally, model A is suitable to test A while model B is suitable to test B. That is to say, an appropriate model should be introduced according to the requirement of the tests. 2) The complexity of the model we select. That is, the number of the independent variables and the formation of the equations. 3) The quality of the input data. This data may be subject to the test we did to obtain them. Normally, special coefficients are added to those equations in order to minimize the errors and improve the results. These coefficients depend on different rudder angle, heading angle, and so on. 1.2 Purpose of this work During the last four decades, the ship size, especially for tankers, has continuously increased. With that increase, the environmental risk, the ship safety, and especially the tanker safety, have become a major concern. As a result of these changes, many organizations and government offices became involved in ship safety ( Crane (1973), Eda et al (1979), Doerffer(1980) and Palomares(1994)). In particular, the International Maritime Organization (IMO) developed standards for ship maneuverability and these advisory standards are now accepted and used in a large number of countries. In additional, 5 individual countries have their own specific criteria. In this thesis, we will take the IMO requirements as the main criteria for ship maneuvering. The purpose of this thesis is to study the simulation of ship maneuvering and course keeping performance in a real sea condition. The results of this study are used to see if a ship (tanker) can enter into a harbor successfully with an example of entrance to Vancouver Harbor. The new IMO Standards for ship maneuverability is discussed and is the fundamental of the simulation done in the thesis. Utilizing the simulation package, any ship with proper hydrodynamic force coefficients can be evaluated and one can find out if she is a "good" ship according to the final IMO Standards for ship maneuverability. In summary, the purposes of this project can be written as following: • An investigation of an inclusion of external effects into the model of tanker maneuvering governing equations so as to understand and study the PC based program better for ship maneuverability and course keeping ability at sea. • A systematic study of the current IMO Standard for Ship Maneuverability and focus on tanker safety. Numerical simulation work is employed to test a ship for IMO Standard. • Investigation of the possibility that a ship can sail into the Vancouver Harbor. It is an interesting problem to study since Vancouver Harbor is one of the busiest and most important harbors in Western Northern America, around the pacific rim. 6 1.3 Motivation Various tanker accidents are well reported by the media as they usually cause extensive damage to the environment. Recent disasters had happened around touristic coastal areas of France and Spain as shown in figure 1-4 or in environmentally sensitive area in Alaska and they are of major concern to the public. The target of this study has been chosen as the Vancouver harbor, one of the biggest ports of Canada and the Pacific Rim. Every year, more than three thousand ships from all over the world and numerous yachts pass by or dock in here as shown in Figure 1-5 and Figure 1-6. As the tidal currents and wind conditions can be significant at the entrance to the harbor, the first narrow, we decided to simulate and investigate the ship navigational and maneuvering problems specifically around the Vancouver Harbor. Figure 1-4 Nautical disaster in Spanish Coastal 7 8 The numerical ship simulation is now well developed and it is a very useful design tool for naval architects. The problem to test and judge if a ship is a "good" ship before construction and without a sea trial in a real sea condition even in towing tank is always an attractive and challenging topic. It is good to know that the IMO Standard for Ship Maneuverability, was finalized in the year of 2002 (MSC 76), while its explanation might be further modified in March 2004 (DE 47). These IMO requirements were used to identify "good" ships by simulation for further studies. At the Department of Mechanical Engineering, University of British Columbia (UBC), Field (2000) and Ostafichuk (2004) worked on the simulation and control of submarine maneuvering in six degrees of freedom (6DOF) and Ratcliff (2004) worked on the escort tug performance. The experiences gained from these studies are used in this thesis. In the past few years, there are some work focusing on PC-based tanker maneuverability simulation according to part of IMO standards for ship maneuverability. Hasegawa and Sasaki (1997) did a java-based simulation using ESSO OSAKA Tanker (at unknown displacement) for ship maneuverability according to IMO interim standards for ship maneuverability and gained good experience. What's more, in the last decade, some modeling and experimental works concerning Floating Production, Storage and Offshore Loading units(FPSO) have been well reported by Martins et al(1999) and Sphaier et al (1998). All these works are good references for the tanker study in this thesis. 9 1.4 Overview of the thesis As a brief introduction and how to implement this work, an overview of the thesis is presented here and it could help and guide the reader to select which parts of this thesis the reader(s) like(s) to study. Chapter 1 is the introductory part of the thesis. It focus the purpose of this work and motivation why the author would like to do it. It also offers the reader a general background to the study of ship maneuverability and the driving forces which instigated the establishment of internationally standardized performance criteria. There is also an overview of the thesis that you are reading now. Chapter 2 address ship maneuvering and safety, especially tanker safety as well as the selection of an international standard concerning tanker safety was selected. Consequently, the IMO standards for ship maneuverability were employed and studied. The history of the IMO standards for ship maneuverability is reviewed at the beginning and the detailed criteria and the associated tests are discussed. The purpose of Chapter 3 is to simulate the ship maneuvering performance in on a PC. The modeling, maneuvering and dynamics of marine vehicles are the core of this chapter. In fact, the modeling work is based on a full 6DOF formulation for a marine vehicle, although the major test objective vessel is a 3DOF Tanker. Further more, the details of equations of three ships are given after general modeling of marine vehicle. The ESSO OSAKA 278,000DWT Tanker, the major test objective ship, is discussed more specifically as a fundamental work for later chapters. After the maneuvering studies in Chapter 3, Chapter 4 deal with the 10 modeling work for ship course keeping and control work. For the course keeping problem, real conditions in Vancouver Harbor were selected with the inclusion of external effects, both manmade and natural, namely tug assistance and wind and current effects. Therefore, the governing equations given in Chapter 3 are rewritten. With the new ESSO OSAKA governing equations with wind and current effects, the design of the control system for the ship entering into Vancouver Harbor was added. A pre distance and pre turn strategy has been designed for the whole process and a PID control has been employed as the core of the control loop. All the simulation results are discussed in Chapter 5. After the modeling, maneuvering, and control design work in Chapter 3 and Chapter 4, all discussions are given in Chapter 5. At first, simulations of IMO standards for ship maneuverability are given both "good" ships and a "bad" ship. The relationships between tanker performance and internal factors, rudder angle, ship speed and rudder rate are also discussed since they may also be included in the control loop. Then, the simulation work of tanker course keeping in Chapter 4 is shown and discussed. The simulations according to a set of similar conditions of sea trials are applied, simulated, discussed and compared with the sea trials and the results in section 5.2. Finally, the possibilities of a tanker entering the harbor with and without tug's assistance have been simulated and discussed in detail. After the completion of most works, the conclusion of simulation is presented in this chapter. Before the conclusions, a brief summary and review of Chapter 1 to Chapter 5 is given prior to the conclusion. Final conclusions are then presented based on discussion and analysis of the complete work. Finally, some outlook of future goals of this work and recommendations to related work are given as the ending of the main part of this thesis which exist as the Chapter 6, 11 1.5 Summary Considering the project is to study ship maneuvering and course keeping work, the background and history of modern maneuvering theory is briefly reviewed at beginning and purpose of the work has been given out secondly in details that this work will focus on ship maneuvering and course keeping performance around Vancouver Harbor based on the final IMO Standard for Ship Maneuverability. The motivation is explained as the personal interests. At last, the outline of every chapter of the thesis is listed that could help the reviewer to read the thesis and give their suggestions. 12 Chapter 2 IMO Standards for Ship Maneuverability 2.1. History IMO Standards for Ship Maneuverability Ship transportation is perhaps one of the most international of all the world's great industries and remains as one of the most dangerous. It has always been recognized that the best way of improving safety at sea is by developing international regulations that are followed by all shipping nations. Since the mid-19th century, a number of treaties were adopted. Historically, in the past thousand years, ship maneuvering performance had just traditionally received little attention during the design stages of a civil ship. That is to say, no one considered it as an important factor in the early design stages. Even for the navy warships, there was also no uniform, systematic criterion. The primary reason was the lack of maneuvering performance standards for the ship designer to design for and for, regulatory authorities to enforce. Consequently some ships were built with very poor maneuvering qualities that have resulted in marine disasters, casualties and pollutions. Designers have relied on the shiphandling abilities of human operators to compensate for the deficiencies inherent in the maneuvering qualities of the hull. The implementation of maneuvering standards will ensure that ships are designed to a uniform standard, so that an undue burden is not imposed on shiphandlers in trying to compensate for deficiencies in inherent ship maneuverability. However, that is not to say that people do not care about the ship maneuvering performance, especially when they are going to maneuver a new ship. The requirement of a ship with an excellent, or at least a good 13 maneuvering performance has been recognized long ago, but these performances were very difficult to be uniformly quantified and defined. With the development of large tankers, concerns about the environmental risks and ship safety increased. During the later 1960's, governments and public had started to express their concerns on the safety issues of these ships and these crew (Crane (1973), Eda et al (1979), Doerffer(1980) and Palomares(1994) ). In the United States of America (USA), the federal government passed the Ports and Waterways Safety Act in 1971 and Ports and Tanker Safety Act in 1978. After the accidents of the TOREY CANYON in 1967 and AMOCO CADIZ in 1978, the public and technical concerns increased and significant research on ship safety followed. From 1971 on, IMO published recommendations on rudder size standards mainly for ship maneuverability and ship safety. Statistically, in 1970's there were about 200 ship wrecks per year and in total 1,200,000 DWT corresponding to about 0.4% of the ships of the whole world, that is , about 50.000DWT was lost every two weeks. The prime reasons for these losses, about 48% of the total wreck DWT, were collision and grounding and most of them originating from maneuvering problems, Baquero (1982). The IMO started many special sub organizations for the ship maneuverability, such as Maritime Safety Committee (MSC), subcommittee Design and Equipment (DE) and the Working Group (WG). The major evolution events of IMO concerning the Standard for Ship Maneuverability are list in Table 2-1 as follows: Table 2-1 Evolution of IMO Standard of Ship Maneuvering Time Event Result Before 1968 N/A N/A 14 1968 DE 10 MSC.DE and WG started to concern ship maneuverability standards 1971 Assembly 7 of IMO IMO addressed A 209 (7) which is titled " Recommendation on information to be included in the maneuvering booklets" Jan 10th ,1985 MSC 50 of IMO IMO addressed MSC/Circ. 389 which is titled " Interim Guidelines for Estimating Maneuvering Performance in Ship Design" Nov., 1987 Assembly 15 of IMO IMO addressed resolution A.601(15), entitled "Provision and Display of Maneuvering Information on board Ships" Nov 1993 Assembly 18 of IMO IMO addressed resolution A.751 (18). "Interim Standards for Ship Maneuverability" June 4th 1994 MSC 63 of IMO IMO addressed MSC/Circ.644 titled Explanatory notes to the Interim Standards for ship maneuverability March 2002 DE 45 of IMO IMO addressed the Draft MSC/Circ of Explanatory Notes to the Standards for Ship Maneuverability which became MSC/Circ 1053 in the end of the year. Dec 4th 2002 MSC 76 of IMO IMO addressed Resolution MSC 137(76) which is titled "Final Standards for Ship Maneuverability" Dec 16th 2002 MSC 76 of IMO IMO addressed the new Explanatory Notes to the Standards for Ship Maneuverability-MSC/Circ 1053 March 2004 DE 47 of IMO IMO discussed the Explanatory Notes and finalize it. There are many other studies from all over the world which support or are separated from IMO's work, such as International Convention for the Safety of Life at Sea(SOLAS), United States Coast Guard(USCG), Society of Naval Architects and Marine Engineers(SNAME) e.g. Landsburg et al(1982) and Royal Institution of Naval Architects(RINA). 15 Some major events in the development of codes and standards are listed in the Table 2-2. Table 2- 2 Other works related IMO Standard for Ship Maneuvering Time Events 1972 Ports and Waterways Safety Act 1978 Ports and Tanker Safety Act Sept. 1979 Report to the President outline USCG program for considering maneuvering in design At MSC 76, the Maritime Safety Committee adopted the final Standards for Ship Maneuverability (Resolution MSC 136 (76)) on December 4, 2002. The MSC also adopted a new set of Explanatory Notes to the Standards for Ship Maneuverability (MSC/Circ. 1053) although there may be some changes in DE 47 which will be held in March 2004. These standards now supercede the original Interim Standards and Explanatory Notes (MSC/Circ.644). One can say now that the IMO Standard for Ship Maneuverability reached its current form. Designers and researchers wrote their understandings and expressed their concerns on IMO Standards for ship maneuverability. Some summary work of Palomares(1994) address the IMO's role in the standards, Daidola et al (2002) concerning MSC/Circ 644 and the prediction work of Gray et al (2003) is worth noting. In this thesis, the "IMO standard for ship maneuverability" will refer to the current version of IMO standard for ship maneuverability namely, "final Standards for Ship Maneuverability" (Resolution MSC.136 (76)) and new Explanatory Notes to the Standards for Ship Maneuverability (MSC/Circ.1053). Although it is called final standards, it might be changed in future as the world transportation and environmental are changing day by day. 16 2.2. Details of the four Ship Maneuverability Standards As it was mentioned in section 2.1, there are lots of maneuvering characteristic together with many tests, please refer to Appendix A or MSC/Circ 1053 for details. In this section, the detailed criteria of IMO standards for ship maneuverability will be discussed. 2.2.1 Basic required tests According to those measures in MSC/Circ 1053 as shown in Appendix A, following tests were considered as basic tests for the ship maneuvering performance at DE 45/Annex 4 and MSC/Circ 1053. 2.2.1.1 Turning tests A turning circle maneuver is to be performed to both starboard and port with 35° rudder angle or the maximum design rudder angle permissible at the test speed. The rudder angle is executed following a steady approach with zero yaw rates. The essential information to be obtained from this maneuver is tactical diameter, advance, and transfer as shown in Figure 2-1. 2.2.1.2 Zigzag tests A zigzag test should be initiated to both starboard and port and begins by applying a specified amount of rudder angle to an initially straight approach ("first execute"). The rudder angle is then alternately shifted to either side after a specified deviation from the ship's original heading is reached ("second execute" and following) as shown in Figure 2-2. Two kinds of zigzag tests are included in the Standards, the 10710° and 17 20720° zigzag tests. The 10710° zigzag test uses rudder angles of 10° to either side following a heading deviation of 10° from the original course. The 20720° zigzag test uses 20° rudder angles coupled with a 20° change of heading from the original course. The essential information to be obtained from these tests is the overshoot angles, initial turning time to second execute and the time to check yaw. f 3 TACTICAL OtAMETSH. t\ I j / \ 0Ht«a-i"v . -j Aepnaoft Qxna Figure 2-1 Definition used on Turning Circle Test (from MSC/Circ 1053) 18 mm Figure 2-2 Definition used on Zigzag Test (from MSC/Circ 1053) 2.2.1.3 Full astern stopping tests A full astern stopping test involves giving a full astern stopping order when the ship is sailing under full forward power and the ship should turn to either starboard or port with a very small rudder angle(normally, the value is 5°). This test is shown as Figure 2-3. It used to determine the track reach of a ship from the time an order for full astern is given until the ship is stopped dead in the water and detailed discussion is well addressed by Clarke and Hearn (1994). The full astern stopping test is the most complex test among the four standard tests. 19 Figure 2-3 Definition used on Full Astern Stop Test (from MSC/Circ 1053) 2.2.1.4 Test requirements These descriptions of the three major conditions above are selected from MSC/Circ 1053. There are also some other test requirements and the details description can be found in MSC/Circ 1053 or Appendix A. Compliance with the maneuvering criteria should be evaluated under certain standard conditions. The standard conditions provide a uniform and idealized basis against which the inherent maneuvering performance of all 20 ships may be assessed. These standards conditions are: 1) Deep, unrestricted water: Maneuverability of a ship is strongly affected by interaction with the bottom of the waterway, banks and passing ships. Trials should therefore be conducted preferably in deep, unconfined but sheltered waters. The water depth should exceed four times the mean draught of the ship. 2) Full load and even keel condition: The Standards apply to the full load and even keel condition. The term "fully loaded" refers to the situation where the ship is loaded to its summer load line draught (referred to hereafter as "full load draught"). This draught is chosen based on the general understanding that the poorest maneuvering performance of a ship occurs at this draught. The full load draught, however, is not based on hydrodynamic considerations but rather statutory and classification society requirements for scantlings, freeboard and stability. The result being that the final full load draught might not be known or may be changed as a design develops. 3) Calm environment: Trials should be held in the calmest weather conditions possible. Wind, waves and current can significantly affect trial results, having a more pronounced effect on smaller ships. The environmental conditions should be accurately recorded before and after trials so that corrections may be applied. Specific environmental guidelines are outlined in MSC/Circ 1053. 21 2.2.2 The detailed standard of the IMO criteria The final IMO standard for ship maneuverability, Resolution MSC137 (76) is considered satisfactory if the following criteria are complied with: 2.2.2.1 Turning ability The advance should not exceed four and half times the ship lengths (L) and the tactical diameter should not exceed five times the ship lengths in the turning circle maneuver. 2.2.2.2 Initial turning ability With the application of 10 degrees rudder angle to port/starboard, the ship should not have traveled more than two and half times ship lengths by the time the heading has changed by 10 degrees from the original heading. 2.2.2.3 Yaw-checking and course-keeping abilities (zigzag) 1) The value of the first overshoot angle in the 10710° zigzag test should not exceed: a) 10° if L/V is less than 10 s; b) 20° if L/V is 30 s or more; c) (5 + 1/2(L/V)) degrees if L/V is 10 s or more, but less than 30 s, where L and V are expressed in m and m/s, respectively. 2) The value of the second overshoot angle in the 10710° zigzag test should not exceed: a) 25°, if L/V is less than 10 s; b) 40°, if L/V is 30 s or more; and c) (17.5 + 0.75(L/V))°, if LA/ is 10 s or more, but less than 30 s. 22 3) The value of the first overshoot angle in the 20720° zigzag test should not exceed 25°. 2.2.2.4 Stopping ability The track reach in the full astern stopping test should not exceed fifteen times ship lengths. However, this value may be modified by the Administration or related organization where ships of large displacement make this criterion impracticable, but, as an upper limit, it should in no case exceed twenty ship lengths. For ships with non-conventional steering and propulsion systems, the Administration may permit the use of comparative steering angles to the rudder angles specified by this Standard. 2.2.2.5 Difference between last standards After discussion with many useful works results and evidences e.g. Japan Netherlands, Korea (See DE 44/4 DE45 and DE45/3), the standards were built so that they are simple, practical and do not require a significant increase in trial time or complexity over that of current trial practice. Complex work were not accepted (See DE 45/3/1). Comparing the Final Standard (Resolution MSC. 137(76)) and Interim Standard (Resolution A. 751(18)) the slight differences can be found as follows: 1) The value of the second overshoot angle in the 10 degrees/10 degrees zigzag test should not exceed: a) twenty degrees if L/V is less than ten seconds; 23 b) forty degrees if L/V is thirty seconds or more; c) (17.5+0.75(L/V)) degrees if L/V is ten seconds or more, but less than 30 seconds. 2) The recommended stopping distance is still not more than fifteen ship lengths, but now the standard requires that the stopping distance does not exceed twenty ship lengths. The sea trial reporting form now includes entries for recording trim and ballast condition. 2.3 Summary In this chapter, the background and the history of IMO Standard for Ship Maneuverability are reviewed. Then, major maneuvering characteristics are listed and discussed in details while more detailed discussion are listed in Appendix A. Those important terms were proposed into IMO Standards for Ship Maneuverability and defined as current IMO Criteria. The four IMO criteria, initial turning test, zigzag test, full astern stopping test and turning circle test are given with figure and definition which will be used for the simulation program to judge if the ship satisfies the current IMO Standard for Ship Maneuverability. These work become good fundamentals of IMO standards simulation, no external effect and the real sea condition trial simulation in Chapter 5. In addition, the mathematical models are also discussed in details in the next chapter. 24 Chapter 3 Modeling and Maneuvering 3.1 Introduction 3.1.1 General In this section, some background and previous work of marine vehicle modeling and simulation work will be given briefly. Mathematical modeling is always a fundamental and important part of vehicle simulation studies. It has been developed hundred of years ago since people consider the ship as a dynamics system. Human being started their work to control a marine vehicle in the early age, as the oar was employed to guide the heading of the ship. The world oldest ship oar system was found in Yuyao County, Zhejiang Province P.R.China which is built in around 5000 B.C. It indicates that human being's history of navigation is longer than 7000 years. The oldest word navigation log in China was written in around 3500 B.C. while there are also figured logs around the world. Guidance Navigation and Control (GNC) system for vehicle are major technologies to help the vehicle maneuver as required. Especially, GNC for Marine Vehicle have the longer history than airplane and car since marine transportation has a longer history. 25 3.1.2 Previous work in Naval LAB at UBC In the Naval Architecture and Offshore Engineering (NA&OE) Lab at UBC, there are some recent works of ocean vehicle simulation and modeling which are mainly dealing with near water surface underwater vehicle (AUV/ROV/UUV). These have been done by Ostafichuk et al(1999 & 2000) and Field et al(1999 & 2000). And two graduate students had completed their Master and PhD theses in this topic separately, which are Field's (2000) and Ostafichuk's (2004). The name of the underwater vehicle in NA&OE Lab is Deep Offshore Logging Platform for Hydrographic Instrumentation and Navigation (DOLPHIN) as shown in Figure 3-1. The DOLPHIN was conceived locally in 1981-1983 by International Submarine Engineering Ltd. (ISE) for the Bedford Institute of Oceanography, in Bedford, Nova Scotia, Canada. Figure 3-1 Near surface ocean vehicle—DOLPHIN However, their works mainly focused on the control of actuators, while this 26 work will be different from their work with following points: • The objective of the marine vehicle is different as this work considers surface ships which are mainly 3DOF and 4 DOF although the general modeling work is 6DOF. • This work is about maneuvering and course keeping problem while previous work focused on control. • The control part of this work is based on PID while their works are based on more advanced algorithms such as LQR and LQG. 3.2 Modeling and Dynamics of Marine Vehicles Before starting the simulation work, the model of the marine vehicle should be developed. In this part, marine vehicle modeling and hydrodynamics will be discussed in details. All the terminologies in the discussion are based on the ITTC ST02 (2002) and SNAME (1950). 3.2.1 Reference frames and fundamental definitions When a ship moves on the sea, she can be regarded as a normal rigid body which can be regarded as a 6DOF problem. In additional to normal linear movement of a ship under a constant speed, there are also some other motion such as in linear and angular accelerations. There might be two major conditions for the latter part. 1) Regular maneuvering movement: This means that the ship operator uses ship maneuvering and 27 control system, normally just the rudder and propeller, to change the heading of the ship regardless of the effects of wind, wave and current. 2) Irregular movement: This means those movements which are affected by disturbances from wind, wave and current. This is a really complex situation that is beyond the control and maneuvering of the ship operator. In order to study the motion of the ship, especially for those complex situations, the coordinate reference system has to be chosen appropriately. There are different reference systems and they will be discussed in the following parts. i Figure 3-2 Stationary (Inertia) reference frame 28 / _ jmrnmst* aets BSgpiw rut SAVT* V TRANSVERSE ^ cosine* \cooitoiNAre SHIP'S HWOtNC f>0«ItlCN fck '•OF 3HHF ft? Tl»&,t TINMWT no SHIP'S. p*rm Figure 3-3 Stationary (Inertia) reference frame (from PNA III) u (surge) Earth-fixed W \ \ \ Figure 3-4 Moving (Ship) reference frame 29 Figure 3-5 Moving (Ship) reference frame (from PNA III) Traditionally, there are three different systems, stationary, moving and semi stationary reference frame which are given as follows: 1) Stationary(inertial) reference frame: Figure 3-2 and Figure 3-3 show the stationary reference frame in 3D and 2D separately. Stationary reference frame means a Cartesian coordinates which is fixed on the earth, the x0y0plane is horizontal and z„axis is positive in the upward direction. 2) Moving(ship) reference frame: Figure 3-4 and Figure 3-5 show the moving reference frame in 3D and 2D separately. A moving reference frame means the Cartesian coordinates whose origin is at the center of gravity point of the marine vehicle. The x axis is located at the center line plane and is parallel with base plane and positive to the head of the vehicle and the z axis is positive in upward 30 direction. Approximately, x,y and z axis can be regarded as the moment's axis of the marine vehicle. 3) Semi Stationary Reference Frame: Semi Stationary Reference Frame means the Cartesian coordinates whose x axis is the same as marine vehicle speed-V. Obviously, it superimposes on the Moving Reference Frame when the vehicle in the equilibrium condition. In this thesis, only the first two reference frames are discussed and employed, although the last one is also useful. As was mentioned before, the vehicle can be considered as a rigid body with 6DOF, the difference between these two reference frames are listed in the following Table 3-1, and definitions of angles are given in Figure 3-6. u (surge) Figure 3-6 Ship dynamics 31 Table 3-1 Definition of 6DOF of Marine Vehicle Description Position and Angle Velocity Force and Moment Name DOF M S M s M s 1 X Xo u dx01 dt X Surge 2 y y0 V dya 1 dt Y Sway 3 z w dz01 dt z z. Heave 4 a p d(j)l dt K Roll 5 fi e q dQIdt M M0 Pitch/trim 6 7 r dyj 1 dt N No Yaw M=Moving frame S=Stationary frame There are also some other definition methods. For example, sometime people also use cb{cox,o)2,o)3) to representco(p,q,r), use the name "ship reference frame" instead of "moving frame" and use the name "inertia frame" instead of "stationary frame". Please refer to Appendix B and Nomenclature for details. Before the discussion of the basic equations of motions, there are some important fundamental equations and definitions that should be discussed. The mass of the marine vehicle is m. The velocity of center of gravity is V(w,vandw denote the components of V on the moving reference frameG - xyz). The angular velocities of the center of gravity are <y [p,qand r denote 32 the components of & on the moving reference frame G-xyz). The external forces are F(X,Y and Z , denote the components of F on the moving reference frame G-xyz). The moments of the external forces about the center of gravity is M (K,M and N, denote the components of M in the moving reference frame G-xyz). More detailed definition and supplementary descriptions are given in Appendix B. According to the fundamental relationship between moving and stationary frame as shown in the Appendix B, the relationship between the stationary (inertia) frame and moving (ship) frame can be written as follows: dB (IB _ -— = + COXB (3-2-1) dt dt ^ = ^  + cdxK+VxB (3-2-2) dt dt where B(Bx,By,Bz)tieno\e the linear momentum of the marine vehicle and k(Kx,Ky,Kz) denote the moment of momentum of the marine vehicle about the center of gravityG. B denotes the change of B from inertia frame to ship frame and K denotes the change of k from inertia frame to ship frame. Actually, it is easier to remember and to use tixB if it is written into matrix format as follows 33 coxB - \ J q k r = i(qBz-rBy)+](rBx-pBz) + k(pBy-qBx)(3-2-3) \B„ B.. B, According to the definition, the relationship of B and K with F and M can be written as follows: ^- = F (3-2-4) dt — = M (3-2-5) dt Using these basic definitions and relationships, together with those supplementary knowledge and derivations in Appendix B, the basic equations of motion can be obtained as in section 3.2.2. 3.2.2 Basic equation In this part, the derivation of basic equations of motion of rigid body will be given and discussed. According to the Newton's law, the basic equation of 6DOF vehicle motion in moving(ship) frame can be obtained and each of them is defined as follows, m(u + qw --rv) = X (surge) m(v + ru- pw) = Y (sway) m(w + pv - qu) = Z (heave) IXP + VZ-~Iy)qr = K (roll) -Iz)rp = M (pitch) V + (V Ix)pq = N (yaw) (3-2-6) where X denotes the total forces in the x direction; Y denotes the total forces in the y direction; 34 Z denotes the total forces in the z direction; ii: denotes the turning moments around the x axis; M denotes the turning moments around the y axis; N denotes the turning moments around the z axis; Ixdenotes the mass moment of inertia of the ship about the x axis; ly denotes the mass moment of inertia of the ship about the y axis; Iz denotes the mass moment of inertia of the ship about the z axis; u denotes the ship speed in the x axis which is surge velocity; v denotes the ship speed in the y axis which is sway velocity; w denotes the ship speed in the z axis which is heave velocity; p denotes the rolling velocity; <? denotes the pitching velocity; r denotes the yawing velocity. These equations are the fundamental equations used in this thesis and please refer to Appendix B for the supplementary knowledge and notation of the motion of marine vehicle. As the objective vessel is a big surface vessel ship and it is maneuvered on a calm water surface, the heave, roll and sway are expected to be very small so that they can be neglected in general. Consequently, Equation 3-2-6 can be further simplified into following expression as form of 3DOF: m(u - rv) = X m(v + ru) = Y Ir = N (surge) (sway) (3-2-7) (yaw) This form will be applied into the major vessel ESSO OSAKA 278,000DWT in this thesis. 35 Particularly, for some types of surface vessels, such as a container ships, a Ro/Ro vessel and high speed navy warships (as shown in Figure 3-7), the rolling angle is larger when the vessel is being maneuvered, therefore one should consider Equation 3-2-6 together with Equation 3-2-7, that is to say, 4DOF (w = q = 0); m(u — rv) = X m(y + ru) = Y Ixp = K Izr = N (surge) (sway) (roll) (yaw) (3-2-8) This 4DOF equation is applied in the container ship model which will be discussed later. Figure 3-7 An aircraft carrier turning (from Naval Post School USA) 3.2.3 Inertia hydrodynamics forces, moments and Added Mass As Equation 3-2-6, Equation 3-2-7 and Equation 3-2-8 will be used to solve 36 the marine vehicle maneuvering problem, the external effects (forces, moments) on the marine vehicle have to be known. These effects include mainly two parts: 1) The hydrodynamic forces and moments of the hull, propeller, rudder and so on when the vessel is in calm water. 2) With external effects, those hydrodynamic forces and moments induced by environmental effects such as wave, current, wind and manmade forces by towing line and so on. In the following part, those effects in calm water will be discussed and idea of added mass will be given briefly. As the objective ship is the ESSO OSAKA Tanker which is represented as a 3 DOF marine vehicle and so as to save some paper space, from section 3.2.3 to section 3.2.5, all the derivations focus on equation of 3DOF. Considering a surface marine vehicle moving in an infinite deep water along with G-xy plane, the momentum can be written as follows: By = A22v (3-2-9) where ^,-the virtual mass of the ship when the body accelerates in x direction; A 2 2-the virtual mass of the ship when body accelerates in y direction; A 6 6-the virtual mass moment of inertial of the ship when body rotate along with z axis. When the rigid body is moving in the ideal fluid, the hydrodynamic forces are proportional to the acceleration. This ratio is called, the virtual mass which 37 is the sum of added mass and real mass. No matter what kind of shape the rigid body has, the added mass coefficients (added mass, added mass moment, added mass momentum) can be written as a matrix: /I], A 1 3 Aj4 / l 1 5 ^ 1 6 X22 A23 ^ 2 4 ^-25 ^-26 ^31 ^32 ^ 3 4 ^ 3 5 ^ 6 K\ Kl ^-43 ^ 4 4 ^ 4 5 ^-46 K\ ^-52 A 5 3 A 5 4 ^-55 ^ 5 6 K\ ^ 6 2 ^ 6 3 ^-64 ^ 6 5 ^ 6 6 . If velocity potentials, <p, exist for various motions, one can define: J s an Where the first integer refer to the direction of force and the second integer refer to the direction of motion. S is the wetted surface area, <px,<p2and(p3 velocity potentials and g)^,<p5and<p6 are the rotational velocity potentials. Added mass coefficients can be also obtained by experiments or by empirical data approximation algorithms. Here, the idea of added mass will not be further discussed in detail as it can be easily found in many marine hydrodynamics text books such as Newman (1977) and the idea of added mass and detail theory is not the focus point in this thesis. The equation of the motion for marine vehicle maneuvering can be written as follows: 38 Rewriting Equation 3-2-1 and Equation 3-2-2, putting them together, we have Equation 3-2-11 as follows: dB dB _ -— = — + COXB dt dt dK _ dK dt dt + coxK+VxB (3-2-11) Using Equation 3-2-9 and Equation 3-2-11, Equation 3-2-10 can be rewritten into component form as follows: • X, = Anu-A22rv •Y, = A22v + Anru •N, = A66r + (A22 -An)uv (3-2-12) Although these equations can be easily simplified, it is hard to get the precise data for those added mass values. Normally, one can calculate the additional forces by using the forces which will be discussed in section 3.2.4. 3.2.4 Force derivatives and coefficients After the forces and the added mass coefficients are stated, it is obvious that it is important to find a good method to find the forces on a ship so as to solve those governing equation such as Equation 3-2-6 to Equation 3-2-8. Considering a ship moving in an infinitely open, deep and calm water, the force on the ship hull (not including rudder and propeller) depends on hull shape and ship moving performance. For a certain ship whose shape is rigid, the force will depend on the moving performance as follows: 3 9 F = f(y,m (3-2-13) The rudder forces depend on S and S and the propeller forces depend on the propeller revolutionary speed- n. Consequently, if ship-rudder-propeller is considered as an integrated system which is given firstly by Abkowitz (1964), the force equation can be written as follows: F = f(y,CD,8,8,n) (3-2-14) Regularly, the propeller forces will be considered and obtained by other tests as shown in section 3.3.2 the governing equation for ESSO OSAKA, Equation 3-3-3. Simply, the system can be regarded as a ship-rudder system as follows: F = f(V,cd,S) (3-2-15) To solve this problem, normally, these equations are expended by using Taylor series expansions, keeping the first order expansion, they can be written as follows: X =X0+XuAu Y=Y0+ YuAu + Nvv + Yrr + Ys8 N = N0+ NuAu + Nvv + Nrr + Ns8 (3-2-16) where X, dx " du u=uQtv=r=5=0 ou u-Ur. ,v=r=<5=0 O U \u=u0,v=r=S=0 are called force derivatives. 40 Because all those forces and parameters are dimensional, normally, it is necessary to represent them into dimensionless forms as follows: X' = X'0+X'uAu' Y' = F0' + Y'uAu' + N'vv' + Y'/ + Y^S N = N'0 + N'u A M ' + N'vv' + N'rr' + N'SS (3-2-17) where these dimensionless forces and moments are defined as follows: X' = -X -pV2L2 2 N' = --pV2L2 2 N -pV2L3 (3-2-18) The dimensionless velocities are defined as follows: V V r = r-V (3-2-19) The dimensionless force derivatives are defined as follows: Y Y V — u V — v Y Y y> _ r V' — S 2 r _ 1 1*8 1 pvu 1 pVL2 - p r t -PVL' (3-2-20) 41 where, L is the ship length, normally, it denotes Lbp, the length between perpendicular, p is the density of the sea water and V is the ship speed at the center of gravity. However, the first order equations are far from enough to describe a complex movement as the requirement of ship maneuvering and course keeping studies. Considering that the purpose of this thesis is to study some large rudder angle maneuvering, the nonlinear parameter items have to be considered. Empirically, 3rd order of Taylor series is enough and the Equation 3-2-17 can be written like follows: X=X0+Xvy+Xvrvr + Xrrri Y=Yrr + Yvy + Ywrv2r + Yvrrvr2 + Yrrrr3 N = Nvv + Nrr + Nvy + Nvvrv2r + Nvrrvr2 + Nrrrr3 (3-2-21) Where, 337 Y = ™ dv3 u=u0,v=r=0 N = d3N dv3 d3Y U=UQ ,v=r=0 Y = rrr dr3 d3N u=u0,v=r=0 Nr„ =• dr3 u=un,v=r=0 are odd force derivative 42 3 3 7 dv2dr w=Ho,v=r=0 TV...,. = d3N dv2dr Y - d ' Y vrr dvdr2 u=u0 ,v=r=0 «=M 0,v=r=0 d3N N = w r dvdr2 u=« o ,v=r=0 are even force items. Every force derivative has its own meaning that indicates a ship's characteristics. Normally they can be obtained from modeling tests or empirical approximation e.g. Abkowitz (1980) and Inoue et al (1981). 3.2.5 Governing Equation After the theory and method of how to get these forces and moments have been discussed in section 3.2.3 and section 3.2.4, the final form of the governing equations used in the program will be discussed in following part. As was discussed in Chapter 1 about the history and category of maneuvering model, the model can be classified as an integrated system and individual system by Abkowitz (1964) and MMG. 3.2.5.1 Abkowitz As it was discussed in Chapter 1 and section 3.2.4, Abkowitz (1964) considered the ship, rudder, propeller as an integrated system, Combining Equation 3-2-8 and Equation 3-2-15 we can have 43 (m-X.)u = fx(u,v,r,8) (m-Y-)v + (mxG -Y-)r = f2(u,v,r,8) (mxG -N.)v + (Iz -N.)r = f3(u,v,r,8) (3-2-22) where f{(u,v,r,8),f2{u,v,r,&) and / 3 (w, v , r , <5) are given as follows: fl(u,v,r,S) = X0+XuAu + j:XuuAu2+]:XuuuAu3+±Xvy 1_ 2 + (LXrr+mXGy+LXssS2+^Xmuv2Au + ^Xrrur2Au 1_ 2 + TX5SUS2AU + (Xvr + m)vr + XvSvS + XrSrS + XvruvrAu f2(u,v,r,S) = Y0 +YuAu + YuM + Yvv + jYwv3 + V r rvr 2 D 2 + \YvSSvS2 +YvuvAu + \YvuuvAu2+(Yr-mu)r + ^Yrry 2 2 6 + -F„.. ,rv 2 +-YrSSrS2 +Y„.rAu + -Y„,„rAu2 +YXS + -Y^S3 2 1 1 ' s 888*-6 + -Y^Sv2 +-Y^Sr2 + Yx,SAu + -Yx.,.SAu2 + Y„rXvrS Su1 Suu1 vrS' Mu,v,r,S) = N0+NuAu + NuM2+Nvv + j N v y + | iV v r r vr 2 o + ^ W v » v < * 2 + N V U V A U + -\NVUUVAU2 +(Nr -mxGu)r + \ N r r y 1 1 o + -\Nmrv2 + ^ NrSSrS2 +NrurAu + ^ -NruurAu2 +Nx8 + j N m S 3 2 2 2 o 1 + -N^vdy2+-N^Sr2+N^SAu + -Nx,,,SAu2+N^xvrS 1 ' Srr1 5uu ' vrS1 ( 3 - 2 - 2 3 ) u v SX . v dY , v dY . „ dN . n . Here, Xu = — = -All ,Y> = — = -A22 ,Y, = — = -A26, Nt = — = -A62 and du ov or ov AT d N 7 Normally these equations are used in the non-dimensional form and this model is used for most modeling work in this thesis. 44 3.2.5.2 Maneuvering Models Group (MMG) Here the MMG model will be discussed briefly while it is not used in this thesis for ESSO OSAKA. The governing equations for MMG will be given as following: m(u -rv) = X = XH+Xp+XR m(v + ru) = Y -YH +YR Izf = NH+NR (3-2-24) where the subscripts H, P and R refer to Hull Propeller and Rudder respectively. There are some good works using the MMG model, especially those Japanese papers, e.g. Hasegawa and Sasaki (1997) and so on. 3.2.5.3 Comparison of Abkowitz and MMG models Both Abkowitz and MMG focus on a marine vehicle system. Here, the comparison of these two models will be simply discussed. MMG considers the marine vehicle system based on ship hull, rudder and propeller respectively, that is to say, it is made up by the three single subsystems while Abkowitz model does not. Abkowitz model just considers the ship as one integrated system. Therefore, using the MMG model, it is easier and more concise to express the interaction between ship rudder, and propeller than using Abkowitz model. Also, it is easier to be revised for maneuverability design. However, using the Abkowitz model, it is easier to get the whole model and easier to get the hydrodynamic forces data. Therefore, if the purpose of the 45 work does not focus on the detailed interaction between hull and propeller and rudder effects, Abkowitz model is a better choice. In past couple of decades, there are more works focusing on propeller and rudder interaction, e.g. Oltmann and Sharma (1984) and Molland and Turnock (1994). Normally, with different experimental method and different simulation requirements, the hydrodynamic force derivatives people use might be a little bit different from Equation 3-2-23 and/or Equation 3-2-24, the specified equation will be given in section 3.3 for specific ship for these two models. 3.3 Detailed and specialized ship model In the following part, the maneuvering governing equations of specified vessels will be given. The vessels are a Container ship and a Mariner ship and the major objective tanker ESSO OSAKA 278,000 DWT will be discussed in details. 3.3.1 Container 3.3.1.1 Background Before the code is tested for larger tanker, a high-speed single-screw container is chosen as a simple example. It is a container ship originally designed for SR 108 Project by Japan Shipbuilding Research Association (See SR Report No 211 1975). It is really a classical type large vessel because many maneuverability characteristics analysis and simulation works had been down on this type before such as Matsumoti and Suemitsu(1980), and Nomoto(1981). It is a good ship for old standards. Therefore, it is expected to satisfy the New IMO Standard for Ship Maneuverability. 46 3.3.1.2 Basic data of the Container ship Here is the basic data of the container ship that is going to be discussed and simulated: Table 3-2 Major data of container ship L 175.00m B 25.40m dF 8.00m dA 9.00m V 21,222 m3 KM 10.39m KB 4.6154m cB 0.559 AR 33.0376 m2 A 1.8129 DP 6.533m V 8m/s Maximum rpm for full astern stopping 72 Maximum rudder angle 35° This mathematical modeling governing equation of this container ship comes from Nomoto's work (1981). Here, the detailed maneuvering equations with hydrodynamic derivatives are given as follows: 47 (m + mx )ii - (m + my )vr = X (m + my)v + (m + mx)ur + myayr-myI y<p =Y (Iz + Jz)r + myayv = N-YxG (Ix+Jx)</>-myIyv-mxIxur + WGMcj) = K0 The governing Equation 3-3-1 is a little different from the Equation 3-2-9 since the center of gravity is at a different point from the center of the hull, therefore there are sure differences from standard reference frame. The right hand sides of above equation's hydrodynamic force derivatives equations for the Container ship are given as follows: x = | L 2 V 2[X '(«')+ a - tyr'(J)+ x'„vY+x;y2 + x y 2 + X'H><p,2+cRXF'NsmS] Y = ^L2v2[Yy+Yy+Y;f+Y;f+Y;vy3 +ry3 +Y;vy2r'+Y;ryr'2 + Y^ + Y'mv'<p'2 + Y'rr/2<P' + Y'mr>'2 + (l + aH )F'N cos S] N=^L2v2[Ny+N'y+N$+N;#+N'vvy3 + N'rry3 + N'vvy2r + Kryr'2 + N'vvy2<t>+AV>'2 + W + K^r'(p'2 + (x'R + aHx'H ) F ; COS S] K = ^ L2V2 [Ky+Ky+Ktf+w+K'vy3 + K'rry3 + * > ' V + K'„ v Y2 + K'vv/2<p + K'^v'4,'2 + K'rr/2<t>' + K'r'f2+(l + aHyRF^cosS] (3-3-2) The model above is MMG model. With all hydrodynamic force derivatives data, the equations were solved. These data are given in Appendix C. The results of simulation will be given in Chapter 5. 48 3.3.2 ESSO OSAKA 3.3.2.1 Introduction ESSO OSAKA 278.000DWT is a classical and well tested tanker ship used for many research works in the field of ship maneuverability. In this part, it will be discussed here in details. There are many research papers related to the ESSO OSAKA no matter what DWT they are, e.g. Williem and Thomas(1972) for ESSO OSAKA 190,000DWT, Crane (1979) for 278,000 DWT, some for 280,000DWT and others. The summary work was reported by Barr(1993) and The Specialist Committee on ESSO OSAKA(2002). According to the study reported in proceedings of the 23rd ITTC (2002) and after consultation with Mr. Alex Landsburg, the Maritime Administration Program Manager of Department of Transportation USA and Chairman of panel H-10 (ship controllability) of SNAME, ESSO OSAKA 278,000 DWT was selected as a major objective ship for the studies of ship maneuverability and course keeping ability. Table 3-3 to Table 3-5, give the major data of ESSO OSAKA 278.000DWT and are taken from Crane(1979). Table 3-3 Hull and Rudder data of ESSO OSAKA Hull and Rudder Length overall 343m Length between perpendiculars 325m Breadth molded 53m Depth molded • 28.30m 49 Assigned Summer Freeboard draft .extreme 22.09m Designed load draft molded 22.05m Full load displacement at assigned summer freeboard draft 328,880mt Block coefficient, summer freeboard draft 0.831 Bow Bulbous type Stern Transom type Number of rudders 1 Rudder area 119.817m2 Draft molded at trial 21.73m Draft extreme at trial 21.79m Trim in still water at trials 0 Displacement at trials 319,400mt Longitudinal CG at trials; Forward of amidships 10.30m Table 3-4 Propeller data of ESSO OSAKA Propeller Single, right-handed, 5 blades Diameter 9.1m Propeller pitch 6.5m Expanded area 44.33m2 Projected area 37.22m2 Disk area 65m2 Pitch ratio 0.715 Expanded area ratio 0.682 Projected area ratio 0.572 Rake angle 4 degree 24 min Table 3-5 Propulsion Machinery data of ESSO OSAKA Propulsion Machinery Hitachi Impulse 2 Cylinder Cross-Compound Main Steam Turbine Continuous full output 36,000hp at 82 rpm Service output 35,000hp at 81 rpm Main Turbine Contro s (Bridge Telegraph) Operation Program Control Revolution Feedback Control Note 50 Ahead Yes Yes below 60 rpm Inaccurate rpm indicator No 60 rpm and above Real rpm indicator Astern Yes Yes Real rpm indicator Crash astern No No Astern full revolutions quickly attainable 3.3.2.2 Maneuvering Equation for ESSO OSAKA As it is really a well studied tanker, the various mathematical models are well developed. The popular algorithms are the one reported by Hydronautics Ship Model Basin (HSMB 1980), the one reported by Dr. Kim (1988) in Korea Research Institution of Ship and Ocean (KRISO) and the one reported by Dr. Rhee et al (1993) in Seoul National University (SNU) (See ITTC 23rd 2002 for detail). From the discussion of the special committee of ESSO OSAKA(2002) and Ship Maneuverability in 22nd ITTC (1999) and 23rd ITTC (2002), it is observed that the formulation by from KRISO is suggested to be the best one for this ship. The mathematical model chosen is the one accepted by ITTC 1978 and the data used for validation are from Kim (1988) and KRISO, which is given as follows: 51 m(u-vr-xGr2) = X.u + Xvrvr + [Xvv + Xvvn (77 - l)]v + [Xrr + XrrTJ (77 - l ) ] r 2 + [Xss + XSSn (77 - 1)]S2 - (Re sis tan ce) + (Thrust) m(v -ur + xGr) = Ya+ Y0J] (77 - I) + y. v + Yfr + P"v + Yvn 07 - l)]v + 17, + 07" Vfr +vrM + YMn (77 - l)]v|v|+[F M + y r | r | l | (77 - l)]r + O f 2 +F | v | r | v | + [F, + (77 - 1 ) ] £ // + mxG (v + wv) = 7Y0 + 7V07? (77 - 1 ) + N-v + N-r + Wv + Nvr} (77 - l)]v + [Nr + Nr1J (77 - l)]r + [ ^ v | v | + NMn (77 - l)]v|v| + [TV | r | + NMn (77 - l)]r + i V v r r v r 2 + /V r | v | r |v | + [/V, + / V ^ (77 - 1)]S + NsmSS+NdvvSv2 ( 3 - 3 - 3 ) For the first of the above equations we assume that the ship resistance and propeller thrust can be obtained from towing tank tests. All published and unpublished data are given in Appendix C. 3.3.3 Mariner The Mariner Class Cruise ship is a popular sea going ship in past few years while it became near coastal ship and many people took it as a research ship especially for experiments and simulation, such as Chislett and Stroem-Tejsen (1965), Li and Wu (1990) Lauvdal (1994) and Skjetne and Fossen(2001). 52 Table 3-6 Major data of Mariner Class ship 171.80 m Lbp 160.93 m B 23.17 m T 8.23 m V 18541 m3 V 15 kn The governing equations by Chislett and Strom-Tejsen(1965) are given as follows: (m' - X'u ) A i i ' = X'uAu' + XuuAu'2 + X'umAu" + X'nAv'2 + X'rr Ar'2 + X r ' v A r ' A v ' + X'SSA8'2 + X'uSSAu'A S'2 + X'vSAv'AS' + X'uv5Au'Av'A5' (m'-Y-)Av' + (m'x'G -Y-)Ar = 7 > ' + T r ' A r ' + CA v ' 3 + T v ' v r A v ' 2 A r ' + y v ' „ A v ' A w ' + Y'n Ar'Au' + YgAd' + Y^AS" + Y^Au'AS' + Y.'„,xAu'2AS' + Y'^Av'AS'2 + Y'„xAv'2AS' ' uuS vS8L vv8L + (T 0 ' + F 0 ' „ A M ' + T 0 ' „ „ A M ' 2 ) (m'x'G - N'- ) A v ' + ( / ; - N'. )Ar' = N'vAv' + N'rAr' + N'vvvAv' + A M A v ' 2 A r ' + N'Av'Au + N'Ar'Au' + N'AS' + N' AS 888 + N'uSAu'AS' + N',...xAu'2AS' + N'^Av'AS'2 + NixAv'2AS' ' uuS v88L \vSL + (N'0+N'0uAu' + Kuu^ ) The simulation results are given in Chapter 5 and the hydrodynamics force derivative data are given in Appendix C. 53 3.4 Summary As the studies of modeling and maneuvering of ship in chapter 1, there are lots of modeling methods such as MMG and Abkowitz(1964) while the latter one is chosen for the objective ship test. At beginning of Chapter 3, the detailed mathematical work of the marine vehicle model is presented step by step from the choice of the reference frame to derivation of the governing equation. Through the study of Proceeding of ITTC 22nd,23rd and recent related papers, especially after consulting with Mr. Alex Landsburg, the Maritime Administration Program Manager of Department of Transportation USA and Chairman of panel H-10 (ship controllability) of SNAME, ESSO OSAKA 278,000DWT is selected as the objective ship for detailed and further studies. Based on the modeling and governing equation, three ships have been discussed and the governing equations with hydrodynamics derivatives have been available where the ESSO OSAKA has been discussed in more detail as Equation 3-3-3. Finally, using ESSO OSAKA as the test ship, simulation work based IMO Standard for Ship Maneuverability has been done which gives a good agreement with the sea trials although the environmental effects are not considered in this chapter and we know that the ship is a "good "IMO class Tanker that can be discussed for further studies in later chapters. 54 Chapter 4 Course keeping and Simulation In this chapter, the course keeping problem will be discussed as a further study for marine vehicle modeling and maneuvering in Chapter 3. What's more, as the objective for this work is to study the tanker performance entering into the Vancouver harbor, the control algorithm used will be discussed and a specified strategy will be designed for this case and the condition of Vancouver Harbor will be briefly studied concerning the requirements of this simulation. 4.1 External Forces All the forces in the differential equations in Chapter 3 are for the conditions when the ship sails in calm water. That is to say, all discussions above are ship generated forces. Besides those internal forces such as thrust, interactions between rudder and propeller, resistance in calm water and so on, there are other important class of forces acting on marine vehicles in the real condition. These are the external forces. Ship maneuverability and course keeping ability will be significantly affected by external forces which can be divided into two parts: 1) Environmental forces such as wind, current, wave and ice generate forces on the ship moments. Normally, as shown in Figure 4-1-1, they would be the disturbing factors on the marine vehicles playing a 55 negative role in maneuvering, although the marine vehicle can benefit from them sometimes. Figure 4-1-1 Ship under environmental external forces effects 56 Figure 4-1-2 Ship under manmade external forces effects 2) Manmade forces such as tugboat force and drag force to some near surfaces underwater vehicle, pulling force by boat tracker and so on. Normally, as shown in Figure 4-1-2, they are positive factors to the marine vehicles, playing a good role in maneuvering and course keeping. In the following part, these external forces will be discussed in details one by one. 4.1.1 Environmental forces In this part, environmental forces will be discussed in details. There are some general works concerning all the environmental forces e.g. Ewing (1990), Jiang and Schellin (1990), Li and Wu (1990) and Martins et al (1999). 57 4.1.1.1 Wind effect 1) Basic description Wind force is a common and important environmental force on the ocean surface. It is generated from the difference between air pressure and temperature in the atmosphere. It affects the ship structure above the waterline. However, those waves and currents induced by wind also affect some near surface underwater marine vehicle. Here only its direct effect to surface vessel, the part above the waterline will be discussed. 2) Wind model Generally, a wind (and/or current) force model is an experimentally and statistically determined algorithm based on a great deal of experimental data and statistical analysis. There are many published algorithm, such as the ones published by the Oil Companies International Marine Forum (OCIMF, 1977), Van Berlekon et al (1974), and Wagner (1967). Considering the marine vehicle in this project is a larger vessel-Tanker, the model of OCIMF (1977) will be employed. The OCIMF model is one of the best models for tanker studies since this algorithm focuses on Very Large Crude Carrier (VLCC), tanker and FPSO shapes. However, OCIMF (1977) only describes in the form of 3DOF. For the modeling work, it is necessary to have a more general model which is suitable to any type of marine vehicle. Consequently, the 6DOF model should be derived and finally given as follows: 58 f o A HWd 7600 xVWd xAj. Y\vd ~ ^Ywd x ^Wd ~ CZwd X 'V/d 7600 xV^xA, f o ^ HWd 7600 K\Vd ~ CKwd X M\vd ~ ^Mwd X ywd 7600 xV*d xAvxB r D ^ HWd 7600 xV^xAj-xT N-Wd ~ CNwd x r O A HWd 7600 xVjdxALxLbp (4-1-1) Where XWd,YWd, Zwd, KWd, MWd NWd denote the forces and moments affected by wind, CXwd,CYwd,CZwd,CKwd,CMwd,CNwd denote the coefficients of wind effects pWd density in wind medium, Vwd means wind velocity at 10 meter elevation.(refer to nomenclature for details) A sample of CXwd is shown in Figure 4-1-3 from OCIMF (1977), rest of the five wind effect coefficients can be also obtained by experiments or real trial. 59 WIND ANGLE OF ATTACK 0W Figure 4-1-3 Coefficients of wind force OCIMF(1977) 4.1.1.2 Current effect 1) Basic description Current force is another important environmental force to the surface and near surface marine vehicle. It is generated by the wind, tide, difference between temperatures of closed ocean areas. Mathematically, its simulation effect is stronger than that of the wind's, however wind can induce strong currents (also waves, but waves' 60 mechanics effect will not be discussed in this thesis) and it is hard to find a weather that there is only strong wind but no current and waves except experimental conditions. Therefore, it is hard to say which one affects the ship motion severely. Some good studies were reported by Bucher (1989), Grue (1986) and Sphaier et al (1998). 2) Current model Basically, the current model is the same form as the wind model that current model is also an experimental and statistical algorithm based on a great deal of experimental data and statistical analysis while it affects the part of the ship below the waterline. For the same reasons as for wind force calculation, OCIMF (1977) model will be employed and its 3DOF model can be extended to 6DOF form as follows: XC - Cxc X f Pc ^ v7600 y f_Pc_^ 7600 xVcfx Aj. xV*xAL ~ x K C - CKc X v7600 y ' Pc ' xV c 2x^, 7600 Mc =CMcx xVcfx Av xB J \ 7600 xV^xAj XT Nc=CNcx r_P^ 7600 xVGxAL xL BP (4-1-2) Where Xc,Yc,Zc,Kc,Mc>Nc denote the forces and moments generated by current, CXc,CYc,CZc,CKc,CMc,CNc denote the coefficients 61 of current effects pc means the density of the fluid, namely the sea water and Vc means the speed of currents. Just as the coefficient of wind force, a sample result of coefficient of current force, CYci is given in Figure 4-1-4. There are some differences between current coefficients and wind coefficients as the current coefficients are more complex as the depth of the water must be considered. Figure 4-1-4 Coefficient of Current force OCIMF(1977) 62 4.1.1.3 Restricted waterway 1) General: Normally, the restricted waterway means a shallow water area or a very confined channel, canal and so on. Basically, the waves and currents induced by the marine vehicle will not disperse completely that they will return as reflection and affect the ship. The ship can not do large range action in these areas and all condition would be different from open areas. It is a very interesting topic and many good works for ship maneuvering in confined channel and channel design had been well done. These include Kray(1973), Inglis et al (1981), Abkowitz and Zheng (1984), Webb and Hewlett (1992) and Varyani et al (1997a). Also, some good works for shallow water effects have been reported by Yeung (1978) and Varyani et al (1997b). Actually, even though the same ship is used, the hydrodynamic forces derivative coefficients are significantly different between open shallow water and deep water area, so be those coefficients of other restricted waterway. 2) Shallow water effect As the ESSO OSAKA 278,000 DWT is considered in this thesis, a famous tanker which is well trialed in shallow water area by Crane (1979), shallow water effect should be added into the mathematical modeling work. Not only the Kim's (1988) model from KRISO but also others models (SNU model and HSMB model) recommended by ITTC (2002) for ESSO OSAKA did not consider the shallow water effects. Since the comparison which will be given in chapter 5 is between the simulation and a real trial in the shallow water area, the shallow water 63 effects have to be considered. Mathematically, taking the sway term as an example, the left hand side of the governing equation is m(v+ru) and the right hand side should have the terms with derivative respect to z such as terms like Yrrzr2z . Since none of those models has it, we should add appropriate term in the right hand side. The solution in this thesis is to combine this problem with the current model together that use the current effect term to represent both current effect and shallow water effect which is shown as follows: Yc=f(Vc,CYc) CYc=g(H/D) where VC,H and D denote current speed, water depth and ship draft separately. As was shown in section AAA.2, the current effects strongly depend on the water depth, especially in the shallow water area. Therefore, the quasi zero speed current condition is employed to approximate the calm water shallow water effects. Mathematically, in this thesis, three items will be added in the right hand side, which are X = fl(Vc,CXc) Y = f2(Vc,CYc) N = f3(Yc,CNc) where Vc -> 0. Actually, in the real trial, there may have been some current and wave effects and it is not absolute calm (zero speed current and no 64 wave). 4.1.1.4 Waves Ocean surface wave is a complicated and interesting topic to a surface marine vessel or those underwater vehicles near the ocean surface. However, modeling surface wave is a very complex task. Some good works were reported by Eda and Crane (1965), Grue(1986), McCreight (1986), Griffin (1988), Ambrossovski and Rumyantsev(1994), Sphaier et al(1998), and Timour (2001). Basically, random wave noise model with or without a filter could be employed to simulate wave effects on ships. The mechanical effects to marine vehicle will not be discussed in this thesis. It will be the future work to discuss its in detail about wave's interaction and ship motions on it. 4.1.1.5 Other nature environmental forces Besides those four major environmental forces, there are many other different types of environmental forces, say, ice effect, indirect forces from interaction between other marine vehicles(for instance, the wave induces by other marine vehicle passing by), effects from marine animals and so on. They are all parts of environmental forces but not as important as those considered in this thesis. Consequently, they are not considered in this thesis. 4.1.2 Manmade forces Manmade forces were born with the ship as origin propulsion and guidance tools when ancient human being used their hand or wood sticks pull in the water to move the ships. They improve with human being's intelligence and requirements. 65 4.1.2.1 Tug forces As the ships became larger in recent years especially, tankers are built larger and are required to deliver goods faster, a greater demand is shown on the performance of the tugs which handle them. This is especially apparent in coastal area where ship system failure or human error such as bad maneuvering can lead to nautical disaster, such as grounding, collision and result in devastating environmental impact. A specialized class of tug, the escort tug, has been developed to assist the larger ship for maneuvering or mooring which is discussed by Gray (2003) as shown in Figure 4-1-5. Figure 4-1-5 Tugs are assisting a large vessel grounded outside a navigation channel from Gray et al(2003) As the goal of this work is to study a ship sailing around the outside Vancouver harbor, an open deep water area, tugs are employed by many transportation companies and ship builders such as Robert Allen Ltd. are also investigating and producing it. Therefore, in this thesis, tug effect will be considered as an assistance to the large tanker. 66 Regularly, the tug can provide a breaking force and a steering force which are shown in Figure 4-1-6. The tug employed in this work is produced locally by Robert Allen Ltd. and tested at the Institute of Marine Dynamics (IMD) and data are obtained from experiments of Ratcliff (2004). 4.1.2.2 Other manmade forces There are many different types of manmade forces to the marine vehicle such as towing forces by workers in the bank, drag force by workers in the bank, human power marine vehicle and so on. With the development of technologies and requirements of human being, the types of manmade forces are increasing. Generally speaking, they have the same characteristics no matter how they were made that they are serving for the marine vehicle or they help people and satisfy the requirements. Figure 4-1-6 Tug force model 67 4.1.3 Governing equation with environmental forces As the goal of this work is to study the ship maneuvering and course keeping at the entrance of the Vancouver Harbor, one must include the external effects of the wave and current forces on the ship. These forces need to be added to the early governing equations. As the purpose is to study the ship performance around Vancouver harbor, considering the real weather and bathymetric condition, wind and current effects are considered to be rather important. With Equation 4-1-1 and Equation 4-1-2 of wind and current models given in above paragraphs, the governing equation, Equation 3-2-8 can be changed into the basic equations as follows: m(u + qw — rv) = X + Xc + XWd m(v + ru — pw) = Y + Yc + YWd m(w + pv - qu) -Z + Zc + ZWd . I (4-1-3) Ixp + (Iz-Iy)qr = K + Kc+KWd ? V ' Iyq + (Ix-Iz)rp = M+Mc+ MWd Izr + (Iy-Ix)pq = N + Nc+NWd where X,Y,Z,L,M,N denote the forces and moments in calm water, Xc,Yc,Zc,Kc,Mc>Nc denote the forces and moments generated by currents and XWd,YWd,ZWd,Kwd,Mwd,NWd denote the forces and moments produced by the wind. For the same reason as before, for the large tanker, the equations can be simplified into the form of 3 DOF: 68 m(u - ru) = X + Xc + XWd m(v + ru) = Y +YC +Ywd Izr = N + Nc+Nwd (4-1-4) This would be the final governing equations which are used in this simulation program for course keeping. The tug force is not added into these equations for the study is to consider the tug force we need and the number of the tugs we need but not the detailed performance of tugs. 4.2 System design and strategy for the ship sailing into a harbor In this section, the plan to simulation is discussed. Most nautical disasters happen near the harbor or coastal area. Related problems have been studied by many researchers in past few years e.g. Webb and Hewlett (1992) and Gray et al (2003). Vancouver Harbor is taken as the example to study as we are more familiar with it. 4.2.1 Analysis the real condition of the harbor Normally, the control strategy has to be designed according to the real problem. Therefore, the real condition of the harbor should be studied in details. Actually, the coefficient of the current force in the governing equations (Equation 4-1-3) also have to be set according to the local depth of the water around Vancouver Harbor which can be found in Figure 4-2-1 and in section 4.1.1.2. 69 Figure 4-2-1 Nautical Chart of Vancouver Harbor Figure 4-2-2 Aerial view of the approach to Vancouver Harbor Vancouver harbor is one of the biggest ports of Canada. Every year there are more than three thousand ships from all over the world and numerous yachts which passed by or docked here. Basically, all the characteristics of wind and current such as speed and direction change with the season. As the goal of this study is the ship course keeping performance, the worst case is employed as the condition in order to get a more general result to fit into any weather condition around Vancouver harbor. Statistically, according to the data from Canadian Hydrographic Services (CHS) and Environment Canada (refer to Appendix D) and the worst weather condition in Vancouver Harbor exists in February and November every year. Consequently, the maximum values in the system are 65kn for the wind speed while 5.5kn for the current speed. 4.2.2 Analysis how the ship can sails into the harbor Normally, in the good weather, a ship enters into the harbor along with the regular waterway as shown in Figure 4-2-1 or Figure 4-2-3 which has the most open water area, water depth and other conditions. However, there are also always some bad weather conditions around Vancouver harbor which may not let the ship be able to sail through the waterway. Basically, the ship will sail directly into harbor/channel, after she reaches an appropriate distance, then she will turn her heading angle. Finally, she will enter into the harbor/channel ( the first narrow as shown in Figure 4-2-4) straightly and successfully. 71 Figure 4-2-3 Strategy of how a ship sailing into harbor Figure 4-2-4 Lionsgate bridge at the first narrow 72 As the plan shown in Figure 4-2-3, a prediction of the time when the ship should turn and judgment to the relative position of the ship to the harbor is set, this is under the assumption that the original ship heading angle is heading directly to the harbor (first narrow). That is to say, the prediction subprogram will be executed before the simulation. Concretely, as the time of t = 0, the simulation system has known the relative position of the ship into the harbor and predicts an estimated time tp when ship should turn and angle y/p that ship should turn. Consequently, during the simulating, the ship will go as a quasi straight line (it will be a straight line if the environmental effects say wind and currents are ignored), when t = tp, the ship will turn for yrp. If everything is okay, the ship will be entering the harbor successfully. However, there are always some unpredictable and inherent bad factors which means the ship can not enter the harbor successfully: 1) Environmental effects such as wind and current; 2) Original ship position and speed; 3) Any other factors may cause the ship can not enter the harbor such as mechanical performance in the ship. Therefore, following assumptions have been made for the ship simulation: 1) There is no other marine vehicle in the water area, so there will not be any detour problem and no interaction from other marine vehicle. 2) The original ship's heading angle is directly heading into the 73 entrance of the harbor. 3) No sudden external effects and unpredictable mechanical or marine engineering problem exist. 4) No other special problem. Therefore, we just discuss the position and speed of the ship and their effect to the result if the ship can enter the harbor. 4.2.3 Control system of this work As the idea of ship entering into the harbor was discussed in above section, the detailed system should be designed according to the requirement of the design. Before the detailed control algorithm and individual blocks are discussed, the whole control system of this work will be discussed here. Initial Pertubation Esso Ossaka heading angle with noise output h:;;;n 1:;:;; all values and course Figure 4-2-5 The control system 74 As it is shown in Figure 4-2-5, the whole control system is made up of 5 major parts and they are listed as follows: 1) Initial Position The Initial Position part is the major input of the control system which provides the initial position of the marine vehicle according to the reference frame that the "first narrow" is the center the reference frame. Then the system can evaluate the time and distance before the vehicle turning into the harbor according to the strategy in section 4.2.2. That is to say, the input is the position of the marine vehicle and the output is the time and the required turning angle. 2) Reference Model (filter) This is an important part to the PID controller part. It works as the input of the PID Controller and the Nomoto equation, which will be discussed in section 4.3 in detail. The simple 3rd order low pass filter model has been employed as Equation 4-3-10 for this system; it is good for the non complex PID control loop and 1st order Nomoto's Equation. The input is the required turning angle and the output are the desired heading angle, desired heading speed and desired heading acceleration. The detailed discussion will be given in section 4.3. 3) PID Controller (Autopilot part) The PID Controller is the key part of this Control system. It will be introduced and discussed in section 4.3.2. It works together with the Nomoto equation as the autopilot part of the control system. The inputs are the desired heading angle, desired heading speed, desired heading 75 acceleration, feedback of heading angle and feedback of heading speed while last two terms are with noise. The output is the rudder angle. 4) Marine Vehicle Model(Vessel model) The Marine Vehicle Model is another major input of the system it is made up of two parts. One is the Objective (test) Vessel Model and another is the initial perturbation of the vehicle such as speed, acceleration, propeller rudder parameter. One can easily change to other marine vehicles as required. This block is just a MATLAB file shell to run the mathematical model of the marine vehicle which is the combination of Equation 3-3-3 and Equation 4-1-4 which is written in MATLAB file. The input is the desired rudder angle and the outputs which will be given in result output block are the heading angle~v , the yawing speed—r, the real rudder angle- 3 , the x -distance, the y -distance, the surge velocity—u and the sway velocity- v . 5) Result Output After two different feedbacks, the Result Output part can be obtained which is the last part of the system. One can easily find that it provides all the output results you want to see and can monitor every value of the Objective Vessel in time domain. The feedbacks are heading rate and heading angle with noise which work in the PID controller part. All the unknown values in Equation 3-3-3 can be obtained in output. 76 4.3 Detailed control algorithm As a next step in the study, the entrance to Vancouver harbor under wind and current is simulated. The control strategy to be used in the simulation of the decisions of the captain is of course one of the most important parts of the simulation of ship sailing the harbor. In this part, the control strategy used is presented. 4.3.1 Introduction Vehicle Control System (VCS) design is a procedure of dynamics creating. The whole system can mainly be divided into four parts which are 1) Plants The plant in VCS is the vehicle itself, also the dynamics system in the control loop. 2) Inputs The inputs of the VCS are the requirement orders from the captain or commander. Normally, there are two types of inputs: single input and multiple inputs, in this work, both single input and multiple inputs are employed. 3) Outputs The outputs of the VCS are the requirement order and related values of the vehicle. There are also two types of outputs: single output and multiple outputs, and the multiple outputs is employed in 77 my program. 4) Sensors The sensors in the VCS are the instruments to monitor how the vehicle follows the requirement order for feedback. Table 4-1 Example of vehicle control Plant Inputs Outputs Sensors Car Wheel angel Heading GPS Marine Vehicle Rudder angel Heading GPS Gyrocompass Aircraft Rudder, Elevator etc. Heading altitude GPS, Altimeter etc There are some other important parts in the whole system, for example, the disturbance. There are always disturbances in the whole feedback system. They will be discussed in details in later parts of this thesis. Modern ship control has been developed for more than one hundred years along with the control theory. From the end of 19th century, the first electrically driven gyroscope was demonstrated by G.M. Hopkins. Table 4-2 History of modern ship control technology Time People Event Early 1900 H.Anschutz North seeking gyro 1911 E. Sperry "Metal Mike" 1922 Minorsky PID 1963 Kalman LQG 1965—now Combination methods more and more Normally the control loop of ship, as shown in Figure 4-3-1 by Segal (1960) is regarded as the classical template of ship control, although there might be 78 slight change in different versions. ...tWFOBMAT>ONsON;;SHIP;S:PATW< . lOESlRED HELMSMAN 1 OR AUTOPILOT; RUBBER INGLE STEERING GEAR 6RUDOER RUDOER ANGLE INDICATION EXTERNAL- . DISTURBANCES Figure 4-3-1 Control loop of ship autopilot by Segal (1960) Feedback control loop shown in Figure 4-3-2 is a good algorithm for ship control compared with feed forward loop. Load disturbance Measurement noise C Z D G D CD ^Ch+j Input * 1 In Out In Out Controller Process Feedback Output Figure 4-3-2 General feedback control loop There are various popular and pioneering strategies applied in ship control problems such as robust control, fuzzy control, and neural network application etc. They are all very advanced and fine strategies based on general control theory and some very successful applications in ship simulation are reported by Amerongen(1984), Djouani and Hamam (1996), Kvam et al (2000), 79 Encarnacao et al (2000) and Whalley and Ebrahimi (2003). However, they are far beyond a Master thesis work with a non-control background student like this author doing thesis on ship maneuvering and course keeping field. In the following parts, the control system design of the simulation work will be discussed although it is a simple one especially for those reviewers with excellent control background. The core control algorithm which is used in the simulation is widely used Proportional Integral Derivative (PID) control. All the works concerning ship control in this thesis are based on PID. PID control is a classical and useful algorithm in modern control system. Dr. Minorsky started to use it from 1922 and it became popular since then. Normally, it is easy to find the standard "textbook" version of the PID algorithm in any reference book e.g. Seborg et al (1989) and Astrom and Hagglund (1988) which is described as: where u is the control variable and e is the control error that defined as e = yc - y. The control variable is then a sum of three items; 1) The first one is P-term : Proportional to the error 2) The second one is l-term: Proportional to the integral of the error 4.3.2 PID strategy (4-3-1) 80 3) The last one is D-term: Proportional to the derivative of the error The controller parameters are proportional gain Kp, integral time 7;and derivative time Td. Note: Normally, Kp is written asA: and these three parameters will be together defined as follows: KP=K Kd=KxTd However, in order to be differentiated from the K of Nomoto's model(1957) which is the classical definition of Ship Maneuvering coefficients in Equation 4-2-4, Kp with subscript will be used to replace K. Equation 4-3-1 given above was the standard "textbook" version; however, it is seldom used in practice field because the much better performance is obtained by modified algorithms with Laplace transfer function as following: G(s) = K, F 1 ^ 1 + + sTd V ^ j (4-3-2) Equation 4-3-2 has been selected as the form of PID control in this thesis. Also, there is a slightly different version from Equation 4-3-2 which is the most common one in the commercial controller. It is described as follows: 81 G'(s) = K' 1 + -ST; (4-3-3) Normally, there are two types of PID control loops, non-interacting and interacting versions which are shown in Figure 4-3-2 and Figure 4-3-4 separately. The non-interacting type is employed in this work. Input ' 1 J f ^ - ^ Output Non interacting Figure 4-3-3 Non-interacting format PID Input C 2 v Output Interacting Figure 4-3-4 Interacting format PID 4.3.3 The ship control equation 4.3.3.1 General After the discussion of PID control which is used in this control system, a ship response equation has to be selected. Based on the complicated maneuvering equations, control equation was 82 obtained by Nomoto et al (1957). The 1 order model is given as follows Ty) +y) = KS (4-3-4) Normally, it can also be written as follows Tr + r = Kb (4-3-5) Actually, the 1 order equation is the simplified version of 2 order Nomoto equation. For some complicated situations, such as extremely wandering channel, severe wind, current, waves with unstable directions, and some other situation requiring the vessel to turn the rudder frequently, the 1st order control equation was advanced into a 2n d order model by Nomoto et al(1957). The 2n d order model is given as follows Normally, like the 1 order equation, it can also be written as follows where the linear term y/ has been replaced with a function HB(y>) . Assuming that r = rss is constant in steady -state where subscript" ss" means steady-state, that is,r' = r = 6 - 0. This implies that the r-S curve will be a single-valued function. 4.3.3.2 PID controller block In the case of ship entering Vancouver harbor, a 1st order model is chosen T,T2yf + (Tj + T2 )f + KHB (iff) = K(8 + T3S) (4-3-6) TxT2r + (Tx +T2)f + KHB (r) = K(S + T3S) (4-3-7) 83 for this simulation. As the rudder angle S is the input of the Mathematical model of the Marine vehicle, the Equation 4-3-4 can be written as follows: S^f + ^ yr (4-3-8) K K The Equation 4-3-8 is the form of 1st order Nomoto equation in the PID controller (autopilot) block of the control system which is shown as Figure 4-3-5. heading speed Figure 4-3-5 1st order Nomoto Equation However, as it was stated above, the 1st Nomoto equation is a simplified version of Equation 4-3-6. Actually, both 1st order and 2n d order equations have somewhat difference with experimental data. Therefore, the PID controller is introduced into this block as follows r4 G(s) = KP where yi d means the desired heading angle &d-w)+—&j-v)+Tdtyd-v)\ (4-3-9) sT: J The Equation 4-3-9 is based on the Equation 4-3-2 while the difference is the differential — — term is known as y/d -y). Therefore, there is no dt 84 requirement to add an ' V in this transfer equation. Together with Equation 4-3-8 as shown in Figure 4-3-6, the final autopilot equation can be written as follows: f 1 >\ S = K, l I T Wd-v)+ — &d -wY^iWd-w) +—Y + —V (4-3-10) sTt J K K velocity acceleration Figure 4-3-6 Autopilot system PID controller with Nomoto Equation So, the problem is changed to decide K coefficient and T coefficient. Physically, the indices K and T represent ratios of nondimensional coefficients as follows: _ yaw inertia yaw damping ' is the time constant of the system and represent the ship course keeping ability and responsiveness to the rudder. _ turning moment yaw damping is related to the rudder effectiveness or strength and represent the ship turning ability. 85 They can be obtained from model tests such as zigzag test and other special maneuvering tests and/or solving the Equation 4-3-5. 4.3.4 Filter 4.3.4.1 General As it is known to all, a modern autopilot system like which is discussed in section 4.3.3, must have both course-keeping and course-changing capabilities which can be obtained by using the reference model to calculate the desire values of yd,tfd,yd (also can be written as y/d,rd and rjandso on (the first three states have been employed in the filter) which are required by course-keeping and course-changing, finally, y/d = constant (4-3-11) mathematically it is limy/d(t)=y/ (4-3-12) ( - > ° o 4.3.4.2 Filter block In this system, because only three statesyd,rd and rd have been employed for the requirement of PID control system, although there are many other filters can be selected, the 3 r d order Low Pass Filter is good and introduced in the system and it is given as follows. — {s) = T - ^ 5- (4-3-13) yrr (s + o)„)(s2 +2Ccons + co2n) where the reference y/r is the operator input (the required turning angle which is shown in section 4.3.3), £ is the relative damping ratio, and con is the natural frequency. 86 Figure 4-3-7 shows the reference block according to Equation 4-3-13. spring Figure 4-3-7 3 m order LP filter With yjd,rd and rd, the PID control which is shown in Figure 4-3-6 can be executed. 4.3.5 Control parameters As the whole system discussed above, there are some special parameters which should be decided in the control loop and marine vehicle model as ESSO OSAKA. They are obtained by tuning, following guideline and/or statistical database. 1) For the control system, the PID controller is employed. The P, I and D parameters Kp,Tt and Td for PID controller are decided as 10, 50 and 1000 after tuning. 2) Both feedbacks with noise are set as 1 for the control system which 87 indicates there is no noise. 3) For 1st order Nomoto Equation 4-3-5 of the ESSO OSAKA, K and T are 0.0185 and 110. 4) For the reference block, the relative damping ratio £ is 1, and con ,the natural frequency is 0.1. Actually, there are also some other parameters should be set or selected such as the propeller rpm, thrust coefficients and so on. However, they are fixed in the marine vehicle modeling part and no relationship with the control work. Therefore, they will not be discussed here ( see Appendix for details). 4.4 Simulation In order to fully examine and verify the quality of the mathematical model of an given marine vehicle, it is necessary to perform a simulation program based on it. In this thesis work, the ship maneuvering and course keeping simulation is a time domain package. Considering the ESSO OSAKA as an example, the governing Equations(Equation 3-3-3) combined with Equation 4-1-4 are solved and integrated in time that those dynamics variables are obtained as streams in the time domain. The core part, the governing Equation 3-3-3 combined with Equation 4-1-4 are coded and packaged as one file, using the simulation software MATLAB® provided by Mathworks Inc. All the IMO standards tests are obtained by accessing this core file as outside functions. The code was then validated by using published experimental data. The outputs are the IMO tests results as shown above. The convenience is that the ship data are input into a single file 88 while tests requirement are other files. Therefore, one can change it to any vessel as long as the ship data are available. Please refer to Appendix E for detailed description of the simulation package. MATLAB® is a very useful software that it provides lots of built-in functions and procedures which can be used for design and construction of the simulation work. And the control part is run under the circumstance of simulink® that is also provided by Mathworks Inc. It provides lots of useful blocks that can be useful design and tuning of control system and make the procedure easier and faster. 4.5 Summary As the further and complementary work of Chapter 3, the mechanics model of the marine vehicle is studied extensively here. The external forces have been analyzed and discussed at the beginning. Considering the thesis work focuses on Ship course keeping performance around Vancouver Harbor, wind and current effects are added and OCIMF Model was employed for the Tanker Governing Equation. Because the purpose of the work is to study the possibility of the tanker performance, investigate how to increase the possibility and safety, the tug assistance is discussed, and added into the mathematical model. It appears that there are many control algorithms and lots of them have been used for ship control studies. PID algorithm is employed and a control strategy of entering the harbor has been designed later. After this, all fundamental works of the project have been finished. 89 Chapter 5 Results Discussion and Analysis In this chapter, all the results of the simulation work in Chapter 3 and Chapter 4, especially the ship sails into Vancouver harbor are discussed and analyzed. As it has been mentioned before, ESSO OSAKA 278,000DWT is selected as the objective marine vehicle. Therefore, in the following parts, all the discussion and analysis concerning ESSO OSAKA is just about ESSO OSAKA 278,000DWT Tanker but not of other displacements DWT. 5.1 Initial disturbance and perturbation In this part, the initial disturbance and perturbation of the marine vehicle is discussed. As discussed in Chapter 4, Figure 4-4-4, in the marine vehicle model block, there is initial disturbance and perturbation as the inputs to the marine vehicle. Although user can take zero into all initial value, sometime in the real problem there always initial disturbance and perturbation. However, as the initial conditions of the vessel in this work are at a certain point of the vessel's way into the harbor but not come out from a dock or start from a stationary condition, the vessel is in its fairly equilibrium condition already. Therefore, there is no need to discuss this problem in detail here. The simple example of initial disturbance will be discussed in Figure 5-3-7b of section 5.3.2.3. 5.2 Simulation without external effects In this part, the simulation results without external forces will be discussed. 90 Those entire basic tests are without any external forces in the calm water, and the assumption according to current IMO standards for ship maneuverability will be given at the first. Then, the simulation of IMO standards for ship maneuverability will be discussed for three vessels, two "good" ships, the simple example container ship and detailed discussed example ESSO OSAKA and one "bad" ship, Mariner class ship. Particularly, for the major objective test vessel ESSO OSAKA, some other important factors are analyzed in detail as the fundamental discussion for course keeping work. 5.2.1 Assumption according to IMO Standards In order to evaluate the performance of a ship, maneuvering trials should be conducted to both port and starboard and at conditions specified below: 1) Deep and unrestricted water; 2) Calm environment; 3) Full load (summer load line draught), even keel condition; 4) Steady approach at the test speed. For the validation the program, the following assumptions have to be made: 1) The disturbance affected by the interaction between rudder propeller stern and other parts is negligible. 2) The changes of center of gravity induced by motion of liquids or other matters on the vessel are negligible. 5.2.2 Container ship—"good" ship As stated in Chapter 3, before the major test objective vessel, ESSO OSAKA is discussed; a simple example container ship is given in this 9 1 section first. 1) Initial Turning test: Figure 5-2-1 and Figure 5-2-2 show the results of simulation for initial turning test. From this simulation, we can easily find that the distance ship traveled is 271 m, 1.55 times the ship length which is 175m. This distance is much less than the IMO criteria which is two and half times ship lengths. So we decided that the ship satisfies IMO criteria for Initial Turning test. 2) Turning Circle test: Figure 5-2-3 and Figure 5-2-4 show the results of simulation for turning circle test. From this simulation, we can find that the tactical diameter of ship is 712m, 4.06 times the ship length which is 175m. This length is much less than the IMO criteria, five times ship lengths. The advance is 570m, or 3.25 times the ship length, which is much less than it in the IMO criteria four and half times ship lengths. Therefore we claimed that the ship satisfies IMO criteria for Turning Circle test. 3) Zigzag test: Figure 5-2-5 to Figure 5-2-8 show the results of simulation for zigzag test. From this simulation, we can easily find that the overshoots are less than 10 degrees both 10/10 and 20/20. They are both much less than IMO criteria. Consequently, we concluded that the ship satisfies IMO criteria for Zigzag Test. 92 Note: the rudder changing rate is set as infinite here for the comparing with rudder changing rate in later chapters. 4) Full Astern Stopping Test: Figure 5-2-9 shows the result of simulation for full astern stopping test. From this simulation, we can find that the distance ship traveled is 1282m, 7.33 times the ship length which is 175m. This value is much less than it in the IMO criteria fifteen times ship lengths. We can say that the ship satisfies IMO criteria for Full Astern Stopping test. Generally Speaking, this container ship is a good ship that satisfies IMO criteria; we can conclude that she can go well in normal sea condition. initialtuming test 100 -80 — -60 • j;-"••••• :,v..,,W ,, ;,,....„..4;:..v;.,,..v -100 h - ^ ~ - ^ - ^ . v . : . - i ' - : - . . 0 50 100 150 200 250 x-position Figure 5-2-1 Initial Turning Test course of Container ship 93 yaw angle y (cleg) 8.02 15 20 time (s) speed U (m/s) 15 20 time (s) Figure 5-2-2 Initial Turning Test yaw and speed of Container ship Turning circle (* = rudder execute, o • 90 deg heading) 600 800 x-position Figure 5-2-3 Turning Circle Test course of Container ship Zig-zag test 1 r 0 500 1000 1500 2000 2500 3000 3500 4000 4500 x-position Figure 5-2-6 10/10 Zigzag Test course of Container ship yaw angle v (cleg) I — *c . - / \ ... r \ \ ... \ \ \ I I i )• I I I i I I 0 100 200 300 400 500 600 time (s) speed U (m/s) time (s) Figure 5-2-7 20/20 Zigzag Test yaw and speed of Container ship Zig-zag test 500: 1000 1500 .2000: 2500. 3000" 3500 4000 4500 x-position Figure 5-2-6 10/10 Zigzag Test course of Container ship yaw engle v (ccg) :igure 5-2-7 20/20 Zigzag Test yaw and speed of Container ship Zig-zag test 1500} 1000, 500 -500 -1000 500 1CC0 '1500 2000 2500 3000 3500 x-position Figure 5-2-8 20/20 Zigzag Test course of Container ship astemstop test 600 500 400 300 "1 200jr 100 -100 -200 200; 400 600 x-position 1000. Figure 5-2-9 Full Astern Stopping test course of Container ship 5.2.3 Mariner ship—"bad" ship As a "good" IMO class ship has been stated, a "bad" ship example could be given for comparison. The ship length is 160.93meter. According to the IMO criteria, the tactical diameter should not exceed five times the ship length, nearly 805m, which is less than the simulation result of the Mariner 1100m in Figure 5-2-10. Obviously, the Mariner does not satisfy the IMO criteria for turning circle test. That is to say, we can conclude that the Mariner Class ship is not a good ship under the final IMO Standard for ship maneuverability. However, its rudder size might be changed and could possibly satisfy the IMO Standards. Bad ship Turning :circle;(*;=.rudder:execute,;p = 90 deg heading); x-position Figure 5-2-10 Turning Circle Test course of Mariner 98 5.2.4 Simulation of ESSO OSAKA This thesis is based on IMO Standard for Ship maneuverability which has been discussed in chapter 2. The major test objective vessel is ESSO OSAKA. In this section, the simulation of ESSO OSAKA of IMO Standard for ship maneuverability and other tests without external effect will be discussed. What's more, from this section, all discussions are focused on ESSO OSAKA tanker. 5.2.4.1 Simulation of ESSO OSAKA based on IMO standard for Ship Maneuverability ESSO OSAKA is always the highlight vessel of many ship maneuvering research group or technical committees. Its performances under the tests set by IMO for the Standard of Ship Maneuverability are discussed in following parts In the following part, we do the similar simulation test for IMO Standard for Ship Maneuverability as the results shown for the container ship in Section 5.2.2 while the rudder effects are concerned. However, as ESSO OSAKA is selected as the major test objective ship for the program of course keeping and other programs, it is further discussed. 1) Turning Circle: Figures 5-2-11 and Figure 5-2-12 show the results of simulation for Turning Circle test. From this simulation, we calculated that the tactical diameter of ship is 1488m, 4.33 times the ship length, 343m. This length is much less than the required IMO criteria of five times the ship length. 99 The advance is 922m or 2.69 times the ship length. This value is also much less than the IMO criteria of four and half times the ship length. So we concluded that the ship satisfies the Turning Circle test of IMO criteria. 2) Zigzag Test a) General discussion Figure 5-2-13 to Figure 5-2-16 show the results of the simulation for the Zigzag test. From this simulation, we can easily find that the overshoots are less than 10 degrees for both 10/10 degree and 20/20 degree zigzag test. The overshoots are much less than the values required by the IMO criteria. So we decided that the ship satisfies the requirements of IMO criteria for Zigzag Test. b) Rudder rate effect Compared with Figure 5-2-5 to Figure 5-2-8 of the Container ship in section 5.2.2, we can see the difference that the rudder rate in this simulation is set at a regular value, while in section 5.2.2 is nearly infinite. It is obvious that the slower is the rudder rate, the larger is the overshoot. 3) Initial Turning Test Figure 5-2-17 and Figure 5-2-18 show the results of the simulation for Initial Turning tests. From this simulation we found that the distance the ship traveled is 588 m, or 1.72 times the ship length. This distance is 100 much less than the requirement of the IMO criteria which is two and half times the ship length. Therefore, we conclude that the ship satisfies the Initial Turning test of IMO criteria. 4) Full Astern Stop Figure 5-2-19 and Figure 5-2-20 show the results of the simulations for full astern stop. From this simulation we found that the distance ship traveled is 2311 m or 6.74 times the ship length. This value is much less than the requirement of the IMO criteria which is fifteen times the ship length. Our conclusion was that the ship satisfies the Full Astern Stopping test of IMO criteria. Esso Osaka Turning circle (* = rudder execute, o = 90 deg heading) x-position Figure 5-2-11 ESSO Turning Circle course 101 Figure 5-2-12 Speed and yaw of ESSO Turning Circle 2000 r Esso QsakaZig-zag test 1 5 0 0 ; 1000J-. 500} -500 ;-1000+-15004 I 2000 500- 1000 1500 2500 3000 3500 4000 4500 x-position Figure 5-2-13 Course of ESSO 20/20 Zigzag maneuver 30 20 10 0 -10 -20 -30 I 4.2 yaw angle v (deg) — V — 5 c " 100r / \ / A \ 1/ X \ j / N . 1 \ 1 / • \ \ ; / \ \ / / \ V X L i i T - ^ 200 400 600 800 time (s) speed U (m/s) 1000 1200 1400 I I I | speed m/s | j ] r ~ 3.8 3.6f 3.4 200 400 600 800 time (s) 1000 1200 1400 Figure 5-2-14 Speed and yaw of ESSO 20/20 Zigzag maneuver 2000 1500 1000 500 J 1 s -500 -1000 -1500 Zig-zag test ~T~. 1—: r~ r 0 500 1000 1500 2000 2500 3000 3500 4000 4500 5000 x-position Figure 5-2-15 Course of ESSO 10/10 Zigzag maneuver 103 yaw angle (deg) 1 1 — V A is 1 \ / A 100r \ / \ / / \ / / _ \ \ / • / \ / \ : V / i \ / \ _ v / i i > * t 4.05 200 400 600 800 time (s) speed U (m/s) 1000 1200 1400 j speed m/s | i i i i < 3.95 h 3.9 3.85 200 400 600 800 time (s) 1000 1200 1400 Figure 5-2-16 Speed and yaw of ESSO 10/10 Zigzag maneuver Esso initialturnlng test 200 150 100 50 8 i o -50 -100 h -150 -200 100 200 300 x-position 400 500 Figure 5-2-17 Course of ESSO Initial Turning 104 .yaw angle n>. (deg) 4:01 3.99 h 3 98--3.97 time (s) speed U (m/s) time (s) 150 -150 Figure 5-2-18 Speed and heading angle of ESSO Initial Turning Esso Osaka astemstop test 1Q00J-800 1000 x-position 1500 Figure 5-2-19 Course of ESSO Full Astern Stop Figure 5-2-20 Speed and yaw ESSO Full Astern Stop With the results of simulations for the four IMO standard tests, we established that this tanker can be claimed to satisfy the requirements of IMO Standard for maneuverability. This ship can be considered to be a "good" ship. These results are also used as a validation of the numerical simulation code. Generally saying, following conclusions can be drawn: 1) The objective ship, ESSO OSAKA 278,000DWT Tanker is a "good" IMO Class ship according to the current IMO Standard for Ship Maneuverability. 2) The Code can not only work for 4 DOF ship (Container) but also 3DOF ship, Tanker and Mariner. Actually the code can work well for 6 DOF marine vehicles such as ROV, AUV and UUV. While in general one 106 prefers comparison of the experimental results with the numerical predictions, the code was considered to be able to identify "good" ships for maneuvering. 5.2.4.2 Ship Speed Effect As the objective area is the quasi open water area, the relationship between ship speed and the tanker performance is not difficult to find. Figure 5-2-21 and Table 5-1 show that the simulation results of relationship between ship speed and important values of turning circle tests. We can see that the tactical diameter, advance and transfer do not change (there is less than 0.1 percent change per knot) with the ship speed to a large extent. That is because the ship speed will affect the turning speed, therefore in regular speed, the diameter will not change much. Actually, it even does not change. The only value changing much is the steady radius Rs which is defined as^/ while the faster the ship speed, the smaller steady radius, because of the changing speed of yawing rate is higher than changing speed of serge speed. Mathematically, it can be written as follows: Therefore, the steady radius is larger when the speed is higher. Table 5-1 Ship Speed Vs. Turning Circle Ship speed Transfer advance diameter 2 729 917 1498 3 729 919 1498 4 730 920 1499 5 731 923 1500 6 732 925 1501 7 733 927 1502 8 734 929 1504 107 4.5 A , „ - A - = — - A = i i = A . Transfer '= Advance Tactical Diameter « • = :.•= • — • , — — ^ ^ - p a ^•V ' | '• | ' | ' :| • .1 ' I. ••' ;1 1 2 3 4 5 6 7 8 Ship Speed (m/s) Figure 5-2-21 Relationship between ship speed and some important values 5.2.4.3 Rudder Effect Rudder effect is another important factor of the surface marine vehicle especially tanker. In earlier chapters, the effect of rudder changing rate had been discussed and it can be also found in SNAME T&R Report R-22(1976) for some other similar test. In this part, the relationships between rudder angle and the three values, Tactical Diameter, Transfer and Advance are discussed. As the performance of ESSO OSAKA is well known, there is no need to do test in port side since the value of port side always smaller than them in starboard side because of the E' CD I ,.CL m 3.5-B 3.0 a> f TO I— 2.5 108 geometry's characteristics of the ship. Figure 5-2-22 shows the simulation results of relationship between rudder angle and three important values of turning circle test. We can see the all three values decrease when rudder angle increases and the changes are bigger and faster in 5 degree to 10 degree. What's more, from Figure 5-2-22, we can see that, the ship satisfies IMO Standards for Ship Maneuverability when the rudder angle is smaller than 35 degree but bigger than 27 degree. That is good news for ship owner since the tanker can have more reserve ability if its maximum rudder angle is 35 degree. Actually, 35 degree is the minimum maximum rudder angle for larger tanker and the regular maximum rudder angle is around 5 degree larger than 35 degree. 28-, 5 10 15 20 25 30 35 Rudder Angle (degree); Figure 5-2-22 Relationship between rudder and some important values 109 5.2.4.4 Other Effects There are some other internal effects which affect the ship performance in the maneuvering and course keeping action such as hull rudder and propeller interaction, which is a little bit complex topic. Mathematically, as MMG model, the force can be divided into parts, Hull, Rudder, Propeller and interaction between them. The modeling work can be then made and equations can be derived. Basically, in this program, one can get this kind of results by changing the hydrodynamics derivatives of rudder, propeller and hull such as Y0 , Ys > Y & v > N 6 v r a r i ( i s 0 o n t 0 approximate the change of the interaction or add coefficients to approximate better results to reduce the difference between the experimental and simulation's value just as 77, in Equation 3-3-3. However, this is not a precise method although it works well in some cases. Therefore, it would not be discussed in this thesis in details. 5.3 Results under external forces In this part, the simulation results of some basic tests under external effect will be discussed and compared with some experimental and authorized results to see if the program runs well with the external effects model given in Chapter 4. 110 5.3.1 Basic assumption of the condition around Vancouver harbor As the governing equations had been discussed in the course keeping part of Chapter 4, the importance of wind and current effects were presented and tanker safety problems are always related to the external effect. We will directly discuss the result here. Before detailed discussion, some assumptions specify for the Vancouver Harbor have to be made as follows: 1) Actually there might be little difference between the current angle and wind angle of attack, normally, one degree or two. However, as the wave effect and interaction between wind and current are both ignored, their effective angles of attack can be considered as the same value. The wind and current direction is -30 degree. 2) The worst wind and current speed is 65kn and 5.5kn based on the results from Canadian Hydrographic Service and Canadian Department of Environment. 3) As there is no obvious current and wind speed variation in time in this specified area, both speed values have been set as constants. 4) The water depth data are obtained from the nautical chart by the Canadian Hydrographic Service. Actually for assumption 3, those values can also be set as function of position as follows: 111 where V means those speed values such as current speed and wind speed. It just takes some more lines code of judgment subroutine in the program, but constants will make the results have more representatives as they are shown in later part of the thesis. 5.3.2 Discussion of the simulation results As it known, the turning circle test is a very important test for the ship both with external forces and without external forces. And as it had been discussed in Chapter 4, the strategy for the tanker to entering the harbor is a pre distance and pre turn calculation with the turning into the harbor, therefore, the turning circle is more important in this work. 5.3.2.1 Turning Circle In this section, the turning circle test with external forces will be discussed. The result of ESSO OSAKA turning under the wind effect is shown at first. Figure 5-3-1 a and Figure 5-3-1 b show the simulation results of turning circle test under wind effect that wind direction is -30 degree, which is a regular direction of the wind near the Vancouver harbor during the heavy weather times, the wind speed is set 50kn and the ship speed is set as 4m/s(7.8 kn). It is easy to see that under the wind effect the ship turns in an elliptic path and it trends to the left compared with Figure 5-2-11. That is an evidence to support the wind effect especially its direction. What's more, we can see that second turn is more elliptical than the first one. 112 Figure 5-3-2a and Figure 5-3-2b show the simulation results that of turning circle test under current effect that current direction is -30 degree which is the regular direction of the current near the Vancouver harbor during the bad weather times, the current speed is set as 1kn and the ship speed is 4m/s(7.8kn). The shape of the ship course does not change as much as it's under wind effect but the speed and yaw rate change more and oscillatory. Figure 5-3-3a and Figure 5-3-3b show the simulation results that the tanker can not complete the circle when combined wind and current effects are too strong. As it is mentioned before, there are lots of published papers and research works focusing on this tanker. The results of Figure 5-3-1 a and Figure 5-3-3a can be, at least compared qualitatively with results shown in Figure 5-3-1 c and Figure 5-3-3c separately, representing the results of Barr and Martin (1980) which discuss its performance under the wind effects. It is hard to compare those couples published results quantitatively and get a percentage error as the authors did not provide enough data. 113 ESSO OSAKA Turn Circle under Wind effect of 30 degree@50kn -4 500 xfposition-Figure 5-3-1 a Course of ESSO OSAKA turning under wind effect yaw rate r (deg/s) speed U (m/s) 3 5 3 2.5 2 1:5 500 1000 1500 2000 2500 time (s) •3000 3500 4000 Figure 5-3-1 b Speed and yaw of ESSO OSAKA turning under wind effect 114 Figure 5-3-1 c ESSO OSAKA turning under wind effect from Barr's result(1980) ESSO OSAKA Turn circle under Current Effect of 30 degree© 1kn :XrpOSitJOrt; Figure 5-3-2a ESSO OSAKA turning course under current effect yaw rate r (deg/s) -0:4., ' 0 : 500 1000 1500 2000 2500 3000 3500 4000 time (s) speed U (m/s) .500 1000; 1500 ,2000 2500 3000 3500 4000 time (s) Figure 5-3-2b Speed and yaw of ESSO OSAKA turning speed under current effect ESSO tring Turning Circle under.strong wind:and^current .combined,effect -200 -400 -600 -800 '-1000: -1200-•-1400 -1600h -400 -200 0 200 400 600 800 1000 1200 1400 1600 ;x-position Figure 5-3-3a Course of ESSO OSAKA turning under overload wind and current effects 116 yaw rate r (deg/s) 150O 4.5 time (s) speed U (m/s) 24-1,5 4 3.5 2;:5. 500: 1000 1500 time (s) Figure 5-3-3b Speed and yaw ESSO OSAKA turning speed under overload wind and current effects Figure 5-3-3c ESSO OSAKA turning under overload wind and wave effects from Barr's result(1980) 117 5.3.2.2 Zigzag In this part, some same simulations under wind and current effects will be done for zigzag test, which is another important ship test (see chapter 2 and chapter 3 for detailed description and discussion). According to those maneuvering tests in IMO Standard for ship Maneuverability, there are two types of zigzags test, 10/10 and 20/20. 10/10 Zigzag Test for the external effects simulation will be shown here. Figure 5-3-4a and Figure 5-3-4b show the simulation results of the zigzag performance of ESSO OSAKA under wind effect that wind direction is 30 degrees while wind speed is 50kn. Obviously, the second starboard overshoot increases more due to the wind effect, when compared with Figure 5-2-5 and Figure 5-2-6 without external effect. Figure 5-3-5a and Figure 5-3-5b show the simulation results of zigzag performance of ESSO OSAKA under current effect. The current direction is 30 degrees while the current speed is 1kn. Obviously, the speed change is rather oscillatory due to the current effect, when compared to Figure 5-2-5 and Figure 5-2-6 without external effects. And the yaw rate and overshoot change slightly compared with the results without external effects in section 5.2.4. Figure 5-3-6a and Figure 5-3-6b show the simulation results of the zigzag performance of ESSO OSAKA under combined wind and current effects. The wind direction is 30 degrees while wind speed is 50kn and current direction is 30 degrees while current speed is 2kn. Obviously, the ship can not turn back after second overshoot of starboard due to the overload external effects. Generally saying, we can see that the simulation program runs well and at 118 least quantitatively has a good agreement with other simulation results which had been regarded as good results compared with real situation. The wind force change the shape of the ship's course more while current force changes the ship speed and yaw rate more and make them much more oscillatory. yaw angle v (deg) 1 1 1 1 — w i / \ } \ i r 5c 100r \ ' / 1 1 1 1 0 200 400 600 800 1000 1200 1400 time (s) speed U (m/s) 1 1 1 1 1 | speed m/s [ ! ; — : -i i i i 11 i  i i i : I '0 200 400 600 800 1000 1200 1400 time (s) Figure 5-3-4a Speed and yaw of ESSO OSAKA zigzag under wind effect 119 Zig-zag test under wind effect of 30 degree@50kn 1500 1000 500 o Q. *. 0 -500 -1000 500 1000 1500 2000 2500 3000 3500 x-position Figure 5-3-4b Course of ESSO OSAKA zigzag under wind effect yaw angle iy (deg) 15 10 5 0 -5 -10 -15 i 4.02 4 3.98 3.96 3.94 3.92 — <v — 8 c " 100r / /.' I 200 400 600 800 time (s) speed U (m/s) 1000 1200 1400 speed m/s 200 400 600 800 1000 1200 1400 time (s) Figure 5-3-5a Speed and yaw ESSO OSAKA zigzag under current effect 120 Zig-zag test under current effect 2000 1500 1000h 500 -500 -1000 -1500 500 1000 1500 2000 2500 3000 3500 4000 4500 5000 x-position Figure 5-3-5b Course of ESSO OSAKA zigzag under current effect yaw angle iy (deg) 20 10 0 -10 -20 200 400 600 800 time (s) speed U (m/s) 600 800 time (s) I — " M> — 8 c 100r l/\ \ 1000 1200 1400 1200 1400 Figure 5-3-6a Speed and yaw of ESSO OSAKA zigzag under wind and current effects 121 Zig-zag test under combined effect of overload wind and current 15004-1000 -100Q - 1 5 0 0 H 500; 1000 1500 2000 2 5 0 0 3000 3500: 4000 ^position-Figure 5-3-6b Course of ESSO OSAKA zigzag under wind and current effects 5.3.2.3 Comparison with real trial In section 5.2, the four tests of IMO Standards for Ship Maneuverability have been done. Especially, the turning circle tests results of ESSO OSAKA were shown in Figure 5-2-11 and Figure 5-2-12 and discussed in section 5.2.4. As a next step of the validation, the results of the simulations are compared with the experimental ship trials. The external wind effect and other condition as shown in Table 5-2 are included in the simulation in order to try to make the simulation closer to the real trials studied and reported by Crane (1979). Table 5-2 Basic data of ESSO OSAKA sea trial Wind Effects 11.9kn and - 15 degree Tanker Speed 7.2 kn Propeller 39 rpm as constant Tanker rudder -34 degree 122 Mathematically, this is similar to the simulation done earlier and presented in Figure 5-2-11 and Figure 5-2-12 in section 5.2.4, but the wind effect and the changes in rudder angles are properly represented in this case. The tactical diameter obtained with these conditions is 1564 meter. This value is obtained from Figure 5-3-7a. The simulation results are then compared with the experimental tactical diameter reported by Crane (1979) in Figure 5-3-7c, which is 1591 meter. The difference between these numbers is 1.7 percent. One can claim that a good agreement has been obtained between the results of simulation done at UBC and the full scale experimental results. There are obviously still some differences possibly due to following reasons: 1) The test is in a shallow water area that water depth to draft ratio is equal to 1.2. However, the governing equation model by Kim (1988) did not consider the shallow water effects. Actually, none of the mathematical models for ESSO OSAKA recommended by ITTC (2002) considers the shallow water effects. We introduced shallow water effects into the formulation by using OCIMF (1977) current model which considering the water depth in details. We used the quasi zero speed current condition to approximate the calm water shallow water effects. Consequently, there might be some difference between this methodology and the result of sea trial (refer to Chapter 4 for detailed methodology). 2) There should be some current effects which at least generated by the wind, but the possible current strength was not reported. The wind and current effects are then increased substantially to quantify the effects of these parameters on ship maneuvering. 123 Figure 5-3-7b shows the simulation results of yaw rate and speed. As the requirement propeller rpm is 37 and the expected trial speed is 7.2 kn. The initial disturbance and perturbation can be found at the beginning part of the speed that the speed is rather constant after about 100 second and it has a strong perturbation at very beginning seconds. That is because the initial speed is set a somewhat higher than 7.2 kn. ESSO turning circle under 11.9kn wind and 34 degree of rudder -200 0 200/ 400; 600 800 1000 '1200 1400" x-position Figure 5-3-7a Course of simulation compared with Crane (1979) 124 -o.i :• -0:2 -0.3r--0:4.', ' 0 3 7 3.695I 3.69 r yaw rate r (deg/s) 500: 1000 time (s) speed U (m/s) 1500 r ~ 1 \ _ 3.685 3.68 3.675 500 1000 time (s) 1500 Figure 5-3-7b Speed and yaw of simulation compared with Crane (1979) 125 -4— 2 Km "I I ' l l j. i i r !, f I Figure 5-3-7c Comparison result of Crane (1979) 5.3.2.4 Need for tug assistance As it had been discussed in Chapter 4, a tug is a great help for a ship in bad conditions. In this part, the result of the need for tug assistance will be discussed with as example. In this section, one escort tug, designed locally by Robert Allan Ltd. is included in this work. Figure 5-3-8a shows the breaking force and steering force that a tug can provide to ESSO OSAKA when it is turning under the 126 conditions given in Table-5-2(refer to Figure 5-3-7a Figure 5-3-7b and Figure 5-3-7c). Figure 5-3-8b shows the result of ESSO OSAKA turning circle with escort tug assistance. The tactical diameter is 1547m here compared with 1564m in Figure 5-3-7a. In this case, the escort tug compensates all forces in x and y direction but not the torque. With the tug's assistance, the tanker can now maintain a better performance and increase its safety limitation in bad weather. Through this simulation, the number of escort tug necessary for safe maneuvering can be estimated. 3 2-1 -Q--1 o -2-1 -3--4--5:-Steering force Breaking force -200; 0 ,200 400 600 800 1000 1 200 1400 1600 1800 2000 Time(Second) Figure 5-3-8a Breaking force and Steering force for ESSO OSAKA 127 Tuming;circle with tug assistance-underthe sea trial condition x-position Figure 5-3-8b ESSO OSAKA turning circle with Escort tug assistance 5.4 Results and discussions of Control work The control strategy is the one of the most important parts in the entering harbor work. In this part, the performance of the control strategy will be discussed. During the simulation, ESSO OSAKA was required to turn 1.2 (rad) in to the harbor under conditions of wind and current combined effects. The wind speed chosen for simulation was 30 kn and coming from -30 degrees and current speed is 1 kn coming from 30 degrees as well. The initial conditions for the ship are given in Table 5-3. 128 Table 5-3 Initial value of the ESSO OSAKA sailing into the harbor u 4 m/s (7.8 kn) V 0 m/s W 0 rad r 0 rad/s Pre turn time 1 s Normally, we can see that the tanker sails straight at beginning until the turning time. Figure 5-4-1 a shows the ship course as a result of simulation for the ship entering in the harbor. In this case, the ship sails straight only just in the very first second and enters in the regular turning water way as shown in Figure 4-3-3. The heading angle used in simulation is given in Figure 5-4-1 b. The yawing rate used in simulation is given in Figure 5-4-1 c. The rudder angle used in simulation is given in Figure 5-4-1 d. The travel lengths in jtand y direction of the simulation are shown in Figure 5-4-1 e and Figure 5-4-1 f. The speeds of u and v of the simulation are shown in Figure 5-4-1 g and Figure 5-4-1 h. From the pre-turning analysis, we know that the angle the ship should turn is 1.2(rad) shown in Figure 5-4-1 b. From the result of simulation, we can see that the heading angle is about 1.24(rad) after the 300th second. If we take the 300th second as a measure, we know that the error is about 3.3 percent in turning angle. What's more, the error will be smaller as the time increases. 129 X Y Plot 1800 2000 XAxis Figure 5-4-1 a Course of entering harbor at an initial required angle of 1.2(rad) ' 0 100 200 300 400 500. 600" 700 800 900 1000 time (second) Figure 5-4-1 b Heading angle-^ during the course 130 1000 time(second) Figure 5-4-1 c Yawing speed—r during the course 0.7, 0.6 0.5 0 .g -j I I i L ! j L 1 1 1 1 * 0 100 200 300 400 500 600 700 800 900 1000 time (second) Figure 5-4-1 d Rudder angle-S during the course 131 .3000 -E time (second)' Figure 5-4-1 e x-distance during the course Figure 5-4-1 f y -distance during the course 132 il L j ii i i i J i i I 0 100; 200 300: 400: 500. 600 700 800 900 1000 time(second) Figure 5-4-1 g Surge velocity u during the course 0.25 _0 •) I ( i 1 L ii ii j i i 1 : 0 100 200 300 400 : 500 600; 700 800 900 1000 time(second) Figure 5-4-1 h Sway velocity v during the course 5.5 Results and discussions of ship sailing into Vancouver Harbor After selecting various combinations of wind and current strengths, for entering the harbor, one can obtain the possibility of a safe entrance into the harbor by a given ship based on the strategy of pre turning discussed in Chapter 4. A safe entrance means that the vessel is able to enter into the harbor successfully through an appropriate waterway. The possibility if the tanker can turn into the harbor is discussed here. As it is stated before, the reported severe maximum wind condition around Vancouver harbor is 65 kn from (-30 degrees) and the strength of tidal current is around 5.5kn (-30 degrees). In Figure 5-5-1, consequently, the upper limit of wind and current speeds are selected somewhat higher than maximum data values as 80 kn and 6 kn as the scales of vertical and horizontal axes. Figure 5-5-1 shows three distinct areas which are labeled as safe, unsafe and unknown. One can see that the "unknown" area covers a band where the current speed is in the interval from 1.8 kn to 2.4 kn while wind speed is 0 kn. And this unknown band can be defined as the limit of the safe operation. In order to obtain more precise results, one can take more combinations of current and wind effects in a certain area as shown Figure 5-5-2 which is called finer mesh of the combination. Figure 5-5-2 shows a zoom-in area result where wind speed is 0 kn to 20 kn and current speed is 1.75 kn to 1.95 kn. The limit of the safe operation is 1.825 kn to 1.85 kn of current speed compared with 1.8 kn to 2.4 kn in Figure 5-5-1 while the wind speed is Okn. That is to say, we can obtain a more precise result if we make a finer mesh of the combination. As the tug's assistance was discussed in section 5.3.2.4, with the tug's assistance, the tanker can, now maintain a better performance and increase its 134 safety limitation in bad weather. As a final simulation, Figure 5-5-3 shows that such a tug can provide great assistance to ship course keeping and increases the maneuvering performance of a ship at the entrance to a harbor. The limit of the safe operation increases to 2.15 kn to 2.175 kn of current speed while the wind speed is Okn compared with 1.825 kn to 1.85 kn without tug assistance which is shown in Figure 5-5-2. Roughly, considering the difference of the whole area between Figure 5-5-1 and Figure 5-5-3, the possibility of safe operation increases about thirty-six percent with one escort tug compared to the results obtained without help by escort tug under the same condition. Generally saying, the possibilities of safe entrance into Vancouver harbor with and without escort tug assistance can be obtained through Figure 5-5-1 and Figure 5-5-3. And from these results of the simulation, it is easy to find that the current effect is stronger than wind effect for the ESSO OSAKA tanker in Vancouver Harbor. It is difficult for ESSO OSAKA to enter into Vancouver Harbor nearly 2/3 of the current condition even without wind. On the other hand, it can enter in all condition of wind if no current in Vancouver harbor. 135 Possibility of ESSO Osaka Turning into Vancouver Harbor 6.0 i 1 1 1 1 1 1 5.4 -4.8 -4.2 -£ 3 . 6 \-0 0 i 1 1 1 1 1 1 ' 0 10 20 30 40 50 60 70 80 Wind Speed(kn) Figure 5-5-1 Possibility of ESSO OSAKA turning into the harbor Possibility of ESSO Osaka Turning into the Vancouver Harbor 1.951 1 1 r 1 i 1 1.925 f-1.9k ; l I I I I I i I J 0 2.5 5 7.5 10 12.5 15 17.5 20 Wind Speed(kn) Figure 5-5-2 Zoom-in result of Possibility of ESSO OSAKA turning into the harbor without tug assistance 136 2.3 Possibility with assistance from one tug 2.275 -2.25 -2.225 -Wind Speed(kn) Figure 5-5-3 Possibility of ESSO OSAKA turning into the harbor with tug assistance 5.6 Summary As the final results discussion chapter, all results of simulation have been discussed. Some effects induced by important factors such as ship speed and rudder angle were analyzed and discussed in detail. From all the results above, following summaries can be obtained: 1) The simulation results without external effects were given at the beginning. With hydrodynamic force derivatives data and governing equations, some ships are tested in the simulation program based on the final IMO Standard for Ship Maneuverability. After these simulations, the test ships can be identified as "good" and "bad" IMO 137 class ships. In addition, some important factors to ship performance are also discussed. 2) The modeling work is good not only for the no external force effects but also with external force effect. The result has good agreement with the sea trial and a qualitatively good agreement with experimental trial and other authorized simulation. 3) With PID control, the control loop works well the error is 3.3 percent at the 300 second under a regular speed. 4) The possibilities of safe entrance for a tanker going into the harbor have been obtained with and without escort tugs assistance. 138 Chapter 6 Summary and Conclusion All the works from Chapter 1 to Chapter 5, have been presented step by step, from the basic introduction, fundamental theory, modeling and maneuvering theory, course keeping simulation and control until the final result. In this chapter, summary and conclusion of the whole work above will be finalized and drawn. In this chapter, all summary, conclusion and future works are in technical work and/or related field. The commercial content will be discussed in Appendix E. 6.1 Summary of the whole work As the results of this study have been finalized at Chapter 5, all the main results will be reviewed again here. 1) At the beginning, in Chapter 1, in the introduction section, the background, motivation and purpose of the thesis are given. 2) In Chapter 2, IMO Standards for ship Maneuverability were reviewed and discussed. Starting from the evolution and original conception of IMO Standard, the detailed criteria and tests have been discussed. 3) In Chapter 3, Modeling and Maneuvering of Marine Vehicle were discussed. Starting from definitions of reference frames, the marine vehicle is considered as a 6 DOF rigid body, the basic equations have been given. With the added mass and hydrodynamic force 139 derivatives, the governing equations were given later in their standard format. The detailed governing equations were given for the 3 test ships while ESSO OSAKA was discussed much more in detail. 4) In Chapter 4, Course keeping and Control of the simulation were discussed. Starting from the discussion of external forces on the ship, the OICMF (1977) model is employed together with the Equation 3-3-3 in Chapter 3, the final governing equations for course keeping were derived in this chapter and the tug model was added as well. A pre distance and pre turn strategy and PID, the core algorithm in the control system were designed for simulating a ship entering into a harbor at the end of this chapter. 5) In Chapter 5, All results of simulation were discussed in this chapter. Simulation results of two "good" and one "bad" IMO Class Ships are given at the beginning of this chapter. Then, important course keeping results and the simulation of ESSO OSAKA entering the Vancouver Harbor were discussed. Starting from discussion and comparison to some standard tests under wind and current effect with some published results. The whole simulation system has been proved as a good combination of current and wind prediction program. With the strategy designed in Chapter 4, the conditions for a ship sail safely into the Harbor with and without escort tug are given at last at this Chapter. 6.2 Conclusion As the displacements of tanker disaster become larger and larger in recent years as well as the transport of biohazard substances rises, attention has 140 been increasingly focused on the requirements of proper prediction of ship maneuverability and course keeping performance in order to enhance the safety. This thesis, of course, increases the interest in the numerical maneuvering and course keeping simulation programs, which are powerful engineering tools for the investigation of the ship maneuverability and course keeping performance especially the performance around harbor. 6.2.1 Existing maneuvering and course keeping model The conclusion of this study of different kinds of maneuvering and course keeping simulation theories applied nowadays, is that state of art method for ship maneuvering and course keeping simulation covers the full mission simulators, based on numerical solution of the governing equations with full hydrodynamics data from experiments. These data can be obtained regularly from the tests done with a Planar Motion Mechanism (PMM). Considering the most current IMO Standard for Ship Maneuverability, the well studied and documented tanker ESSO OSAKA 278,000 DWT is employed as an objective vessel. The available mathematical models are mainly the three, SNU, KRISO and HSMB models. The model of KRISO is selected and revised for the IMO Standard test. 6.2.2 Application of the model and the program in this thesis This simulation program based on suitable captive model test data appears to be capable of simulating and predicting with suitable accuracy the ship maneuvering and course keeping performance. 141 The simulation program produces valid results using comparisons with experimental data for all four IMO Standard ship maneuvering tests, namely: the turning circle test, the zigzag maneuver test, the full astern test, and the initial turning test. The simulations for the above tests are all performed at calm water conditions, with no external wind and current effects. Specifically, the test results for ESSO OSAKA 278,000DWT have been used for validation. This ship can be judged to be a "good" ship as the simulation suggests that she satisfies all of the IMO requirements. The previous studies of PC based maneuvering simulation had worked on turning circle and zigzag but were not specific enough. Rudder effects and propeller effects have been considered into this study and the simulation results have been advanced and are more close to the real trial. This advance work is not only done to ESSO OSAKA, it also can be used to other vessel as long as the hydrodynamics data are provided. Other simulation results of "good" ship example and "bad" ship example are also given. Concerning the ship course keeping performance under external effects, the wind and current forces have been considered in detail, as one of the goals of this study is to identify the limits of safe entrance into Vancouver Harbor, where the wind and current forces could be significant. The model of OCIMF has been used for the simulation of the wind and current forces together with the maneuvering equations which were reported by Kim (1998). The simulation results and the results of real trials showed a good agreement and the error is about 1.7 percent for significant lengths. The important factors which might affect ship performance are discussed. With the help of PID control, the simulation of safe entrance of a tanker into the Vancouver harbor was done, including wind and current forces. The conditions used included the worst weather conditions reported for the Vancouver Harbor in recent years. The current effect is found to be more 142 important and severe than the wind effects for this harbor. The tug assistance that was simulated proved to be significant, improving the safety at harbor entrance. The simulation is able to quantify the effectiveness of an escort tug in wind and current conditions. 6.3 Recommendations and future works The simulation work presented in this paper can not only benefit those seeking to learn about ship maneuvering but it can also be used as a building block for future simulation programs. 6.3.1 Recommendations There are lots of researchers doing related work in the ship maneuvering fields as shown in the references in earlier chapters. Some recommendations of this thesis might be useful for their reference. 1) Rudder and propeller interaction should be considered in the governing equation. The adjustment of rudder and/or propeller would be easy to apply into the vessel so as to improve its maneuverability or change a "bad" ship into a "good" ship. 2) Wave effect could be added into the governing equation as so to make the result of simulation more close to the sea trial. 3) The control strategy could be advanced although PID is a good algorithm for ship autopilot problem. 4) The control strategy of the tug can be studied for improving the assistance to the tanker entering into the harbor. 143 5) Ship model test in towing tank could be done as the data in this work is somewhat old and not precise enough in some parts. This test must be done if one plans to re do the modeling work especially for multiple rudders or propellers assistance and MMG model can be employed. 6.3.2 Future works As the extension of this thesis' work, the numerical simulation of a "good" tanker entering into a harbor successfully, some of the future works are listed as follows and the recommendations above might be considered as well: 1) The ship maneuverability and course keeping ability in Fraser River approaches to Juan de Fuca Strait for various weather conditions should be quantified. 2) As the continuity work of this thesis, the ship maneuvering and course keeping problems in the restricted waterway, insider the harbor should be studied. 3) The mooring and docking problem could be studied as the final stage of a ship entering a harbor. 4) The interaction between ships should be studied as there are normally at least two ships in the area of inside harbor as shown in Figure 1-5 and Figure 1-6. 144 6.4 Commercial applications As stated in section 6.2 and section 6.3, the program can be used for simulating ship planar motion with wind and current effects together with escort tug assistance. All technical conclusions and recommendations were covered. In additional, in this section, the commercial applications and value will be discussed. 6.4.1 General At present time, the program might not be used as a commercial software as it does not yet have user friendly pre and post processes. However, after some improvements or those future works, the software can be upgraded. The software can be used for education in the fields of ship maneuvering, course keeping and ship dynamics. It can be used for testing if a ship is a "good" ship. It can be used for ship maneuverability prediction. What's more, it might be used as a simple game. 6.4.2 Future works and recommendations for commercial application In this section, the future works and recommendations for commercial applications are given: • With more detailed data, compared with sea trial and captain's experience, expertise system could be developed. 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Vol 85 1978 156 Appendix A Maneuvering characteristics In this part, those important maneuvering characteristics are discussed and most of them selected from MSC/Circ 1053 or other official documents. Practically, there are really hundreds of maneuvering characteristics in the whole world no matter in which ocean and country and it is also an important reason why the standard was not uniform in the past time, therefore IMO tried to make select some regular as the major characteristics. Those addressed by the new IMO Standards for ship maneuverability and the Explanatory Notes to the Standards for Ship Maneuverability are typical measures of performance quality and handling ability that are of direct nautical interest. Every one of them can be reasonably well predicted at the early design stage and measured or evaluated from simple trial-type maneuvers and tests. A.1 General Discussion According to the MSC/Circ1053, in the following part of discussion, the assumption of these topics is made that the ship has normal actuators for the control of forward speed and heading (i.e., a stern propeller and a stern rudder). However, most of the definitions and conclusions also apply to ships with other types of control actuators although they will not be discussed in this thesis. In accepted terminologies, discussion mainly concerned with two problem: one is the stability of steady-state motion with "fix controls" and another is the time-dependent modify steady motion, make the ship follow a prescribed path or initiate an emergency maneuver. 157 A.2 Detailed Fundamental Characteristics These detail fundamental characteristics have been discussed and selected by DE of IMO times by times since MSC/Circ 389 though MSC/Circ 644 till MSC/Circ 1053. It seems the results now are finalized although they will be slightly changed after DE 47 March 2004. In this part, some of them will be given and discussed here while most of which are selected from MSC/Circ1053: A.2.1 Steady radius At a given propeller speed rpm and rudder angle 5, the ship may take up a certain steady motion. In general, this will be a turning motion with constant yaw rate r, speed V and drift angle B (please refer to Chapter 3 for detail symbol definitions with illustrations). The radius of the turn is then defined by the following relationship, expressed in consistent unit: R = y/r. Obviously, this particular ship-rudder angle configuration can be regarded as "dynamically stable in a turn of radius R". Consequently, a straight course may be viewed as part of a very wide circle with an infinite radius, corresponding to zero yaw rate. A.2.2 Dynamically stable Most ships, perhaps, are "dynamically stable on a straight course" (usually referred to as simply "dynamically stable") with the rudder in a neutral position close to midship. In the case of a single screw ship with a right-handed propeller, this neutral helm is typically of the order of rudder angle is one degree (i.e., one degree to starboard). Other ships which are dynamically unstable, however, can only maintain a straight course by repeated use of 158 rudder control. While some instability is fully acceptable, large instabilities should be avoided by suitable design of ship proportions and stern shape. A.2.3 Forces and moments during the maneuver The motion of the ship is governed mainly by the propeller thrust and the hydrodynamic and mass forces acting on the hull and these are the key things in the simulation problem. During a maneuver, normally, the side force due to the rudder is often small compared to the other lateral forces. However, the introduced controlling moment is mostly sufficient to balance or overcome the resultant moment of these other forces. In a steady turn there is complete balance between all forces and moments acting on the hull. Some of these forces seem to "stabilize" and others to "destabilize" the motion. Thus the damping moment due to yaw, which always resists the turning, is stabilizing and the moment associated with the side force due to sway is destabilizing. Any small disturbance of the equilibrium attitude in the steady turn causes a change of the force and moment balance. If the ship is dynamically stable in the turn (or on a straight course) the net effect of this change will strive to restore the original turning (or straight) motion. A.2.4 Trim effect It is well understood that a change of trim will have a marked effect mainly on the location of the centre-of-pressure of the side force resulting from sway. This is easily seen that a ship with a stern trim, a common situation in ballast trial condition, is likely to be much more stable than it would be on an even draught. A.2.5 Unbalanced turn If motion is not in an equilibrium turn, which is the general case of motion, 159 there are not only unbalanced damping forces but also hydrodynamic forces associated with the added inertia in the flow of water around the hull. Therefore, if the rudder is left in a position the ship will search for a new stable equilibrium. If the rudder is shifted (put over "to the other side") the direction of the ship on the equilibrium turning curve is reversed and the original yaw tendency will be checked. By use of early counter-rudder it is fully possible to control the ship on a straight course with helm angles and yaw rates well within the loop. A.2.6 The course-keeping ability and inherent stability The course keeping ability is a very important characteristic in ship maneuvering research, which is also called "path keeping" or "directional stability" sometimes and it is a major topic in this thesis. The concept of course keeping is strongly related to the concept of inherent stability. Obviously, it depends on the performance of the closed loop system including not only the ship and rudder but also the course error sensor and control system. Therefore, the acceptable amount of inherent dynamic instability decreases as ship speed increases and covers more ship lengths in a given period of time. And it is because a human helmsman will face a certain limit of conceptual capacity and response time. This fact is reflected in the IMO Standards for ship maneuverability where the criterion for the acceptable first overshoot in a zigzag test includes a dependence on the ratio L/V, a factor characterizing the ship "time constant" and the time history of the process which will be discussed in the later part of this chapter. The various kinds of motion stability associated with ships are classified by attributes of their initial state of equilibrium that are retained in the final path of their centers of gravity. It is well classified as 6 types by Arentzen(1960) which is shown in Figure A-1. 1 6 0 \ 1 w I 1 ; QftlOtMAt STHAIBWT ">_C I STRAIGHT U N € STftfilHTY S. MNAL PATH IS STRAIGHT BUT X^OtRECTlOM CHANGED ORIGINAL STftAJCHT LINE PATH ^""V >>^" FINAL "ATM,!AM« _ OiRCCTION AS H DIRECTIONAL STABILITY _ (WITH COMRJEX STABILITY INDEXES) ORIGINAL. *ATM 8UT OlFTEftKNT v«J5iriON ORtGINAt STRAIGHT FINAL'PATH. SAME AS CASE * Tj DIRECTIONAL STA8lli|TYc ; (VWH ftBit STA8ILTY INDEXES) FINAL PATH, SAM€ ~ ^ OmtC T\QN ANO f»OS< TlOW A3 tlMt-PATM; "*>v >^ ^ S ^ - ^ ' o f N G i N A L PATH JSf POSITIONAL MOTION STABILITY —" INDICATES INSTANTANEOUS DISTURBANCE ^ Figure A-1 Various kinds of motion stabilities (Arentzen, 1960) Mathematically, in Figure A-2, the motion stability can be classified by Fan(1988) as follows: 1) The ship can keep its original way after the disturbance. Mathematically, t -><*>,Ar -> 0,Ay/ -> 0 and AyG —> 0 which is called "position stability". 2) The heading angle is the same as the original angle but the way is not the same( that is to say the final way is parallel to the original 161 one. Mathematically, t - > oo,Ar -> 0,Ay/ -> 0 but AjG * 0 namely "directional stability". . 3) The ship keeps the direction of a new water way. Mathematically, t -> °°,Ar -> o,Ay> -> constant and AyG^0 namely, "linear stability". 4) The ship goes in a curvilinear waterway, t^><*>,Ar *0,Ay/ *0 and AyG * 0. Figure A-2 Ship stability performance after disturbance (From Fan 1988) Obviously, a ship with position stability must have linear stability and directional stability. A ship with directional stability must have linear stability. The ship without linear stability does not have either of position stability and directional stability. In terms of control engineering, the acceptable inherent instability or stability may be expressed by the "phase margin" available in the open loop. If the rudder is oscillated with a certain amplitude, ship heading also oscillates at the same frequency with a related amplitude. Due to the inertia and damping in 162 the ship dynamics and time delays in the steering engine, this amplitude will be smaller with increasing frequency, meaning the open loop response will lag further and further behind the rudder input. At some certain frequency, the "unit gain" frequency, the response to the counter-rudder is still large enough to check the heading swing before the oscillation diverges (i.e., the phase lag of the response must then be less than 180°). If a manual helmsman takes over the heading control, closing the steering process loop, a further steering lag could result but, in fact, he will be able to anticipate the swing of the ship and thus introduce a certain "phase advance". Various studies suggest that this phase advance may be of the order of 10° to 20°. At present time, there is no straightforward method available for evaluating the phase margin from routine trial maneuvers. Obviously, the course-keeping ability will depend not only upon the counter-rudder timing but also on how effectively the rudder can produce a yaw checking moment large enough to prevent excessive heading error amplitudes. The magnitude of the overshoot angle alone is a poor measure for separating the opposing effects of instability and rudder effectiveness, additional characteristics should therefore be observed. So, for instance, "time to reach second execute", which is a measure of "initial turning ability", is shortened by both large instability and high rudder effectiveness. A.2.7 Hard-over turning ability Hard over turning ability always exists in aircraft maneuver or ship maneuver problem. It is mainly an asset when maneuvering at slow speed in confined waters. However, a small advance and tactical diameter will be of value in case emergency collision avoidance maneuvers at normal service speeds are required. 163 A.2.8 The "crash-stop" ability The crash stop is also a pretty important performance of a marine vehicle which is known "crash-astern" maneuver as well. It is mainly a test of engine functioning and propeller reversal. The stopping distance is essentially a function of the ratio of astern power to ship displacement. A test for the stopping distance from full speed has been included in the Standards in order to allow a comparison with hard-over turning results in terms of initial speed drop and lateral deviations. A.3. Characteristics Defined From the description in Chapter A, one can find that there are still too many characteristics to be considered although IMO had selected them from much more larger number of maneuvering characteristics. However, one have to choose what is important from them to save work and get a better efficient. Therefore, the IMO Standards for ship maneuverability identify significant qualities for the evaluation of ship maneuvering characteristics. Each has been discussed above and is finally selected and defined below as written in MSC/Circ 1053: 1) Inherent dynamic stability: A ship is dynamically stable on a straight course if it, after a small disturbance, soon will settle on a new straight course without any corrective rudder. The resultant deviation from the original heading will depend on the degree of inherent stability and on the magnitude and duration of the disturbance. 2) Course-keeping ability: 164 The course-keeping quality is a measure of the ability of the steered ship to maintain a straight path in a predetermined course direction without excessive oscillations of rudder or heading. In most cases, reasonable course control is still possible where there exists an inherent dynamic instability of limited magnitude. 3) Initial turning/course-changing ability: The initial turning ability is defined by the change-of-heading response to a moderate helm, in terms of heading deviation per unit distance sailed (the P number) or in terms of the distance covered before realizing a certain heading deviation (such as the "time to second execute" demonstrated when entering the zigzag maneuver). 4) Yaw checking ability: The yaw checking ability of the ship is a measure of the response to counter-rudder applied in a certain state of turning, such as the heading overshoot reached before the yawing tendency has been cancelled by the counter-rudder in a standard zigzag maneuver. 5) Turning ability: Turning ability is the measure of the ability to turn the ship using hard-over rudder. The result being a minimum "advance at 90° change of heading" and "tactical diameter" defined by the "transfer at 180° change of heading". Analysis of the final turning diameter is of additional interest. 165 6) Stopping ability: Stopping ability is measured by the "track reach" and "time to dead in water" realized in a stop engine-full astern maneuver performed after a steady approach at full test speed. Lateral deviations are also of interest, but they are very sensitive to initial conditions and wind disturbances. 166 Appendix B Supplementary knowledge to Ship Maneuvering In this part, the supplementary knowledge, fundamental equations and derivation of chapter 3 are given here and all definition are based on work in chapter 3. B.1 Frame Transformation Considering a certain vector(point) from the stationary frame to moving frame, the time derivatives can be expressed as follows: — = —+ d)x (B-1) dt dt the position vector for the point on the body can be written as follows: 7=7 + 7 (B-2) Equation B-1 represents the relationship between stationary (inertia) frame and moving (ship) frame which is the most important equation used for the derivation of governing equations. If the translation of the moving frame is excluded from the motion, the moving frame and the stationary frame can be assumed to coincide at a given time,t. if the moving frame is then rotated by an angle of a the relationship between stationary and moving frame can be expressed as follows: fx } *<> I 0 0 y0 0 cos a: -sin a y 0 sin a cos a 167 B.2 Definition Some important definitions are given mathematically, The ship mass is one of the important values in the governing equations which is expressed as follows: The center of gravity is given as follows: III***™ _v (B-5) Normally, a ship hull can be described as follows: z = ±f(x,y) (B-6) By the choice of coordinates, moments and product of inertias are: ^-jj\(y2 + z2}>shipdv' iyy=jj!(x2 + z2)ysupdv U =]]]& + i^\\\xyPshiPdv lyz = jJjyZPsHipdV Ivc=\\\zxpshipdV (B-7) For symmetrical ships about the centerplane one can assume that lyz = o. However, the above statement is based on the assumption that 168 pshjp is a symmetrical function which may not always be the case. Simply, people always use Ixlo replace,I y to replace Iw and Iz to replace lzz. B.3 Derivation Before the derivation, a useful relationship in vector calculation is given as follows: <yx((f5x?G)=(<y-FG)y-(0^-60% (B-8) Using the equation B-1, the momentum is expressed as follows: — (mV )=mV + mcdxV (B-9) dt mV + mdJxV=F (B-10) Together with equation B-10, the Equation 3-2-6 can be derived. Considering Equation 3-3-3 and Equation 3-3-4, the change of the left hand side is stated as the change of the center of the frame from center of the gravity to center of the hull, the form of the governing equations are changed. This is also used in Equation 3-3-2 while it is expressed as mx,my,Jx and J as the change of the center of frame. The complete governing equations with the center of the frame at the center of hull are given as follows: 169 m\u + qw-rv + qzG-ryG+(qyG + yzG)p-(q2 +r2)cG]=X m\y + ru-pw + rxG-pzG + (rzG + pxG)q-(r2 + p2)yG ]=Y m\w + pv -qu + pyG - qxc + (pxG + qyG)--(p2 + q2 )zG ]= z I,P + 'l^ + I J + Vz-Iy)qr + IyM2-r2) + I*zpq-IxyPr + m[yG (w + pv- qu)- zG (y + ru- pw)]= K IyXP + Iyq + lyj + (/, - h W + I*z(r2-P2)+ txyV - lyiVP + m\zG (u + qw- rv)- xG (w + pv - qu )]= M KP + M + lJ- + Uy ~h)P4 + lyzPr - h z q r + m[xG (y + ru — pw)- yG (u + qw — rv)]= ./V B.4 Propulsion forces As it stated in Equation 3-3-3 in Chapter 3, the thrust force can be obtained from tests and the calculation method is explained here: Xp = (1 - t)T = pD^n2 (1 - t)KT (B-12) T = KTpn2D* (B-13) KT = al+a1J + a3J2 (B-14) 7 = - ^ _ (B-15) nDp VA=U(l-wP) (B-16) w F = - ^ - (B-17) l — Wp where t denotes the thrust deduction factor, n denotes the propeller revolution, Dp denotes the propeller diameter, J denotes the propeller advance ratio,KT denotes the thrust coefficient, a,,a2 and a3 denote the constants for propeller open characteristics parameter. (surge) (sway) (heave) ( " H ) (B-11) (pitch) (yaw) 170 VA is the advance speed of propeller and wp denotes the wake fraction and wF is Froude wake fraction. Sometime, people also use up replace the With the experiment data of KT from open channel test, the thrust xp can be obtained. 171 Appendix C Vessels data In this part, all ship hydrodynamics data and other major data will be given separately. C.1 Container data C.1.1 Hydrodynamic Force derivatives Table C-1 Hydrodynamic force derivatives data of Container valuexlu 5 valuexlO 5 ValuexlO"5 ValuexlO-5 -42.26 -1160 K -385.45 K 30.26 K -386 K -311 Y' 4605 N' -1905.8 K' A vvtp -120.12 Y' 304 N' -537.66 V 7.93 Y' vvv -10900 149.2 K'wv 284.3 Y; 242 K -222 K -30.26 x'rr 20 Y' rvv 2140 Km -4240 K'rw -55.8 Y' rrv -4050 156 KL 105.65 Y' rrr 177 N'rrr -229 -4.62 Y' 932.5 -385.92 K' "-rrip -24.3 172 Y' -136.8 N' 241.95 V 3.57 -6.3 -14.24 K 0 0 Ni 21.3 K -2.1 -20 C. 1.2 Other Data Table C-2 Other data of Container ship n 79.1 Fn 0.2 aH 0.237 e 0.921 118.6 Fn 0.3 f xH -0.48 K 0.631 158.2 Fn 0.4 CRX 0.71 } 0.088 (v'>0) (1-0 0.825 t Zr 0.033 0.193(v'<0) (1-",) 0.816 0 -0.156 x' -0.5 Cpr 0 CRrrr -0.275 K -0.526 I 1.09 CRrrv 1.96 m 0.00792 K 0.0000176 K 0.000419 m'x 0.000238 K 0.0000034 < 0.05 0.007049 K 0.000456 K 0.0313 0.1(F„<0.1) K 0.0313 0.2(F„ >0.2) 0.527-0.4557 F„(0.1<F„ <0.2) 173 C.2 Mariner C lass ship Data Table C-3 Mariner Class ship data ValuexlO-5 valuexlu 5 ValuexlO"5 -840 Y; -1546 -23 Y; 9 m -83 K -184 -110 Y' 1uS -556 -278 X'uuu -215 Y' 1uuS 278 Kus -139 X'UVS 93 X'uss -190 Y; -1160 K -264 K -1160 K -264 xi -899 x:s 93 Y' vvv -8078 Km 1636 Y' vvr 15356 K r -5483 Y' 1190 -489 Y' -4 Kss 13 174 Y; -499 AC -166 Y;U -499 K -166 798 18 Y' 278 K -139 -95 Y' 1S55 -90 N' n8S8 45 Y' 1 0 -4 K -3 Y' l0u -8 N 0 u 6 Y' -4 3 C.3 E S S O O S A K A Data C.3.1 Hydrodynamic Force derivatives Table C-4 Hydrodynamic force derivatives of ESSO OSAKA ValuexlO-5 valuexlO 5 ValuexlO-5 K -138.5 Y; -1423.5 K -29.1 Y; 39.7 K -47.5 Y; -1930.9 K -761.2 K 0 Y;V -4368.1 K 118.2 K 1530.1 175 561.4 K -322.0 X'rr 133.1 r rr 206.5 K -113.6 Y' 326.7 K -147.6 X'ss -134.0 Y' 1 ss 0 0 Y' vrr -3428.2 Krr 338.2 -148.6 Y' rv 321.8 K -361.7 Y' -2281.3 NL -109.9 Y" 1 0 2 K -1.0 Y' -349.2 K -28.7 X'vvr, 0 Y' VVTJ 0 24.1 Y' 54.7 Kn -9.6 0 Y' 0 Km 0 Y' ISr, 411.4 -163.7 XSSn -158.7 Y' I0rj 2.0 K -1.0 C.3.2 Resistance data Table C-5 Resistance data of ESSO OSAKA V (knot) CT xlO"3 N (rpm) 1.993 2.287 10.87 2.999 2.198 16.14 4.000 2.140 21.34 176 4.990 2.097 26.45 6.997 2.035 36.78 8.375 2.003 43.85 9.856 1.976 51.45 12.403 1.961 64.79 15.207 2.005 80.29 C.3.3 Propulsion data Table C-6 Propulsion data of ESSO OSAKA J 0.050 0.3309 0.100 0.3142 0.150 0.2956 0.200 0.2756 0.250 0.2554 0.300 0.2347 0.350 0.2135 0.400 0.1917 0.450 0.1687 0.500 0.1447 0.550 0.1208 0.600 0.0962 0.650 0.0708 0.700 0.0439 Appendix D External effects data In this appendix, all the external effects data in this thesis are given separately. D.1 Current data The data of November 5th 2002 are listed here as a sample, the full data will be available upon request. Table D-1 Current data Date time angle speed (m/s) 2002-11-5 0:00 315 0.086 2002-11-5 0:15 135 0.227 2002-11-5 0:30 135 0.535 2002-11-5 0:45 135 0.833 2002-11-5 1:00 135 1.118 2002-11-5 1:15 135 1.386 2002-11-5 1:30 135 1.633 2002-11-5 1:45 135 1.856 2002-11-5 2:00 135 2.051 2002-11-5 2:15 135 2.216 2002-11-5 2:30 135 2.349 2002-11-5 2:45 135 2.449 2002-11-5 3:00 135 2.514 2002-11-5 3:15 135 2.544 2002-11-5 3:30 135 2.539 2002-11-5 3:45 135 2.5 2002-11-5 4:00 135 2.427 2002-11-5 4:15 135 2.322 2002-11-5 4:30 135 2.187 2002-11-5 4:45 135 2.025 2002-11-5 5:00 135 1.839 2002-11-5 5:15 135 1.632 2002-11-5 5:30 135 1.407 2002-11-5 5:45 135 1.168 2002-11-5 6:00 135 0.92 178 2002-11-5 6:15 135 0.666 2002-11-5 6:30 135 0.411 2002-11-5 6:45 135 0.158 2002-11-5 7:00 314 0.088 2002-11-5 7:15 315 0.323 2002-11-5 7:30 315 0.544 2002-11-5 7:45 315 0.748 2002-11-5 8:00 315 0.931 2002-11-5 8:15 315 1.09 2002-11-5 8:30 315 1.224 2002-11-5 8:45 315 1.33 2002-11-5 9:00 315 1.407 2002-11-5 9:15 315 1.455 2002-11-5 9:30 315 1.472 2002-11-5 9:45 315 1.46 2002-11-5 10:00 315 1.418 2002-11-5 10:15 315 1.349 2002-11-5 10:30 315 1.254 2002-11-5 10:45 315 1.134 2002-11-5 11:00 315 0.993 2002-11-5 11:15 315 0.833 2002-11-5 11:30 315 0.658 2002-11-5 11:45 315 0.471 2002-11-5 12:00 315 0.276 2002-11-5 12:15 315 0.076 2002-11-5 12:30 135 0.124 2002-11-5 12:45 135 0.32 2002-11-5 13:00 135 0.509 2002-11-5 13:15 135 0.687 2002-11-5 13:30 135 0.851 2002-11-5 13:45 135 0.996 2002-11-5 14:00 135 1.12 2002-11-5 14:15 135 1.22 2002-11-5 14:30 135 1.294 2002-11-5 14:45 135 1.341 2002-11-5 15:00 135 1.358 2002-11-5 15:15 135 1.345 2002-11-5 15:30 135 1.302 2002-11-5 15:45 135 1.228 2002-11-5 16:00 135 1.124 2002-11-5 16:15 135 0.992 2002-11-5 16:30 135 0.834 2002-11-5 16:45 135 0.65 2002-11-5 17:00 135 0.445 2002-11-5 17:15 135 0.22 2002-11-5 17:30 315 0.02 2002-11-5 17:45 315 0.273 2002-11-5 18:00 315 0.534 2002-11-5 18:15 315 0.799 2002-11-5 18:30 315 1.064 2002-11-5 18:45 315 1.325 2002-11-5 19:00 315 1.577 2002-11-5 19:15 315 1.818 2002-11-5 19:30 315 2.042 2002-11-5 19:45 315 2.246 2002-11-5 20:00 315 2.426 2002-11-5 20:15 315 2.58 2002-11-5 20:30 315 2.704 2002-11-5 20:45 315 2.797 2002-11-5 21:00 315 2.856 2002-11-5 21:15 315 2.88 2002-11-5 21:30 315 2.869 2002-11-5 21:45 315 2.821 2002-11-5 22:00 315 2.738 2002-11-5 22:15 315 2.62 2002-11-5 22:30 315 2.468 2002-11-5 22:45 315 2.284 2002-11-5 23:00 315 2.07 2002-11-5 23:15 315 1.83 2002-11-5 23:30 315 1.566 2002-11-5 23:45 315 1.281 D.2 Wind data The data of November 5th 2002 are listed here as a sample, the full data will be available upon request. Table D-2 Wind data Date Time Degree Speed (m/s) 2002-11-5 0am 50 4 2002-11-5 1am 320 4 2002-11-5 2am N/A 0 180 2002-11-5 3am N/A 0 2002-11-5 4am 130 4 2002-11-5 5am 90 6 2002-11-5 6am 120 6 2002-11-5 7am 140 4 2002-11-5 8am 90 6 2002-11-5 9am 90 7 2002-11-5 10am 90 15 2002-11-5 11am N/A 0 2002-11-5 12pm 340 4 2002-11-5 1pm 180 4 2002-1175 2pm 230 13 2002-11-5 3pm 200 4 2002-11-5 4pm 300 4 2002-11-5 5pm 60 6 2002-11-5 6pm 190 9 2002-11-5 7pm 90 11 2002-11-5 8pm 80 20 2002-11-5 9pm 60 17 2002-11-5 10pm 110 11 2002-11-5 11pm 60 13 D.3 Tug data According to the discussion in Chapter 4 the breaking force and steering force can be obtained from following table: Table D-3 Tug force data 1 6kn 8kn R theta beta R theta Beta tonnes deg deg tonnes deg Deg 98 0 60 133 0 45 105 5 65 136 5 50 103 10 75 130 10 50 102 15 80 134 15 55 102 20 85 130 20 60 106 25 90 126 25 65 109 30 95 122 30 70 112 35 100 119 35 75 181 114 40 105 116 40 80 115 45 110 115 45 90 116 50 115 130 50 100 116 55 120 135 55 105 116 60 125 139 60 110 116 65 130 141 65 115 117 70 135 144 70 120 111 75 145 139 75 120 109 80 150 146 80 125 107 85 155 147 85 135 104 90 175 140 90 135 Table D-4 Tug force data 2 10 kn 12 kn R theta beta R theta Beta tonnes deg deg tonnes deg Deg 151 0 35 126 0 20 146 5 35 205 5 30 154 10 40 209 10 35 183 15 45 205 15 35 187 20 50 209 20 40 183 25 50 257 25 45 184 30 55 255 30 45 178 35 55 263 35 50 174 40 60 258 40 55 168 45 65 254 45 55 166 50 50 251 50 50 167 55 50 252 55 50 169 60 50 255 60 45 175 65 45 265 65 45 178 70 45 273 70 45 188 75 45 275 75 50 198 80 45 270 80 55 199 85 50 252 85 80 197 90 55 271 90 90 Table D-5 Other data of the Tug Item Lwl T AL Bwl D CB SKEG Value 38.196 3.8052 125.5151 14.202 1243.382 0.587158 TRUE Item Tmax Be cr I AL AR L Value 6.7986 3.929445 10.17 0.703 32.01765 0.964501 23 182 Item GMt Y FB FBr f max PROP PPx Value 2.63988 30.5 2.43 0 18.89122 TRUE 9.882 Item LP BPmax TPx TPz hmax R N Value 2.7 100 5.7 4.41 130 1025.9 1.19E-06 183 Appendix E Description and manual of the program The program is made up of and running two parts MATLAB® and SIMULINK®. E.1 MATLAB part The four tests of the final IMO standards for ship maneuverability are simulated on the console of MATLAB. One can choose the test ship and which criteria to be tested. The core marine vehicle file named ESSO.m is written in MATLAB according to Equation 3-3-3 and Equation 4-1-4 together with Tug assistance. What's more, there are four switches in this ESSO OSAKA ship The first switch is current effect. This switch can decide if there is current effect. The second is wind effect. This switch can decide if there is current effect. The third one is the propeller switch. This switch can decide if there is propeller speed change. The last one is tug assistance. This switch can decide if there is tug assistance. model file: 1) 2) 3) 184 One can select which effect is applied into the vessel. With these three switches, one can test the vessel compare with real trial and analyze the tug assistance. According to the IMO standards for ship maneuverability, there are four files (Eturncircle.m, Einitial.m, Ezigzag.m and Estop.m) to access if and they ask ESSO OSAKA to do appropriate simulation. One can write other files to ask ESSO OSAKA to do other tests as their requirements. Figure E-1 shows the simple flow chart of the program as a supplementary explanation for the description of the program. 185 Decide a test and its condition Check the test requirement Yes it is No No, Check if it is standard test Standard tests Yes No Modify the IMO Test Simulation file As the requirement Create new Test file Open the ESSO.m file Setting Internal Values Initial Velocity, Propeller revolution and so on Set Environmental Effects Wind Effect, Current Effect Tug Assistance Modify ESSO.m Run Desired Test simulation file Change all files to standard format Yes Quit Figure E-1 The flow chart of the program E.2 SIMULINK part As the control system is well discussed in Chapter 4, the system will not be discussed here more. With the PID control system, the vessel can goes into the harbor. Considering a certain vessel e.g. ESSO OSAKA in the thesis, the marine vehicle MATLAB file is set in the marine vehicle block, K and T are set together with the certain vessel, the only input is the initial position and then the user can see the result after running Simulink. Finally, with the possibility analysis file, the result can be obtained. All files will be available after thesis submission. 187 Appendix F Explanation of softwares used in the thesis Besides the acknowledgements in the beginning of the thesis, there are some other individuals (software) should be credited. The thesis is written with Microsoft® Office XP and Office 2000 Word and Excel by Microsoft Corporation. The final file is made into Portable Document Format (PDF) using Adobe® Acrobat 5.0 by Adobe systems Inc. Some figures in the thesis are made by hands and AUTOCAD® 2002 by Autodesk Inc. The data analysis and process are made by using Origin® 6.1 by OriginLab Corporation. The simulation programs were being coding and running in MATLAB® 6.5 and SIMULINK® 5.0 release 13 by MATHWORKS Inc together with the Simulink toolbox and Aerospace GNC toolbox by MATHWORKS Inc and Marine GNC toolbox by Marine Cybernetics AS. The operating systems used in this process are Microsoft® Windows XP Home Edition and Windows 2000 by Microsoft Corporation. Some other softwares were used during the processing of the thesis, although they are not listed. 188 

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