INITIAL INVESTIGATION OF SHIP RESISTANCE AT RIVER MOUTH AREA
MUHAMMAD NASUHA MANSOR
UNIVERSITI TEKNOLOGI MALAYSIA
INITIAL INVESTIGATION OF SHIP RESISTANCE AT RIVER MOUTH AREA
MUHAMMAD NASUHA MANSOR
A dissertation submitted in partial fulfilment of the requirements for the award of the degree of Master of Engineering (Mechanical − Marine Technology)
Faculty of Mechanical Engineering Universiti Teknologi Malaysia
MAY 2009
iii
To my beloved wife Nordiana binti Jamil whose sacrifice a lot during this period of study and support that made me stronger every single day. For my family and friends who gave their utmost support.
iv
ACKNOWLEDGEMENT
Bismillahirrahmanirrahim...
All praise to Allah SWT, the Most Gracious and Most Merciful, Who has created the mankind with knowledge, wisdom and power. Being the best creation of Allah, one still has to depend on other for many aspects, directly and indirectly. This is, however, not an exception that during the course of study, I had received so much help, cooperation and encouragement that I need to duly acknowledge.
In the first place, I would like to express my sincere appreciation to my supervisor, Dr. Faizul Amri Adnan, for encouragement, guidance, and valuable comments in completion of this work. Without his continuous and supportive effort, this thesis would not have been materialised. I also came across several people who are very nice enough to offer help in term of ideas and physical assistance.
I also would like to relay a deep and warmest gratitude to my family and in law family for their understanding, patient and support in this period of study. Special dedication to my beloved wife Nordiana bt Jamil who experienced the most suffering and endure pain of sacrifice. Thank for the patient and supports.
Finally, special gratitude to my all colleagues in UniKL MIMET especially those who directly influence my thought in this thesis. Last but not least, many thanks for my friends who are unnamed here and were involved directly or indirectly during my study.
v
ABSTRACT
Lateral drift is one of the phenomenons when ship operates in open sea. It is possibly occurs due to waves and/ or wind and/ or current. In this study, the phenomenon of lateral drift effect onto ship resistance is investigated. As the early stage of this research, the study is focused on ship resistance prediction in calm water condition. In executing this research, the principle that will be used is by using the selected ship resistance prediction method as a basis. Any parameters in the formula which are influenced by drift effect will be reviewed. In this study, two cases are considered, namely Case 1 and Case 2. For Case 1 it is mainly considered the factor of ship velocity influencing the total resistance with lateral drift effect. For Case 2, other parameters are taken into account, which is length and breadth, as well as ship velocity. Due to the presence of drift angle, the velocity is separated into longitudinal and lateral component, and consequently, the process of total ship resistance determination is solved separately in longitudinal and lateral as well. At the end, the resultant of total ship resistance is determined using trigonometric solution. Thus, this becomes the total ship resistance, RTOTAL with lateral drift effect and it varies with the variation of drift angles. This principle of investigation considerably as an initial step in gaining some insights about this complicated problem. The result indicates that there is significant difference of total ship resistance, RTOTAL produced with lateral drift effect, comparing to the condition without lateral drift effect.
vi
ABSTRAK
Lateral drift merupakan salah satu fenomena yang berlaku ketika kapal beroperasi di laut terbuka. Ia berkemungkinan berlaku disebabkan oleh ombak dan/ atau angin dan/ atau arus. Di dalam kajian ini, fenomena kesan lateral drift terhadap rintangan kapal akan disiasat. Di peringkat awal, kajian ditumpukan ke atas anggaran rintangan kapal di air tenang. Dalam penyelesaian masalah ini, sebagai asas, prinsip yang akan digunakan ialah dengan menggunakan kaedah anggaran rintangan kapal sedia ada yang terpilih. Formula anggaran Holtrop dan Mennen dipilih dalam mengambil kira kesan lateral drift terhadap rintangan kapal. Semua parameter dalam formula ini yang dipengaruhi oleh lateral drift akan dikaji, dan dalam kajian ini, dua kes akan diambil kira. Untuk kes 1, faktor halaju kapal yang mempengaruhi nilai rintangan dengan kesan lateral drift hanya akan diambil kira. Untuk kes 2, parameter- parameter yang lain selain dari halaju diambil juga kira iaitu panjang dan lebar kapal. Disebabkan adanya sudut drift, halaju kapal di pecahkan kepada komponen memanjang dan sisian. Oleh yang demikian, proses penentuan nilai rintangan kapal juga akan diselesaikan secara berasingan, dalam keadaan memanjang dan melintang. Kemudian, paduan nilai rintangan kapal akan ditentukan dengan menggunakan penyelesaian trigonometri. Nilai paduan ini dikenali sebagai jumlah rintangan kapal, RTOTAL dalam keadaan kesan lateral drift. Nilai ini berbeza dengan kepelbagaian nilai sudut drift. Prinsip asas pengkajian ini adalah merupakan langkah awal dalam memperolehi gambaran awal mengenai masalah yang rumit ini. Keputusan yang diperolehi menunjukkan ianya terdapat perbezaan yang ketara terhadap jumlah rintangan kapal keseluruhannya, dengan mengambil kesan kira lateral drift, jika dibandingkan dengan keadaan tanpa kesan ini.
vii
TABLE OF CONTENTS
CHAPTER
1
2
TITLE
PAGE
DECLARATION
ii
DEDICATIONS
iii
ACKNOWLEDGEMENTS
iv
ABSTRACT
v
ABSTRAK
vii
TABLE OF CONTENTS
vii
LIST OF TABLES
x
LIST OF FIGURES
xii
LIST OF SYMBOLS
xiv
LIST OF APPENDICES
xvi
INTRODUCTION
1
1.1
Preface
1
1.2
Problems Statement
4
1.3
Research Objectives
5
1.4
Research Scopes
5
1.7
Significant of Research
6
LITERATURE REVIEW
7
2.1
Introduction
7
2.2
Resistance Theory
8
2.3
Components of Total Hull Resistance
9
2.3.1 Frictional Resistance
10
viii
2.4
2.5
2.6
3
4
5
2.3.2 Wave Making Resistance
13
2.3.3 Eddy Resistance
15
2.3.4 Air Resistance
16
Other Types of Resistance Not Included in Total Hull Resistance
17
2.4.1 Appendages Resistance
17
2.4.2 Steering Resistance
18
2.4.3 Wind and Current Resistance
18
2.4.4 Added Resistance Due to Waves
19
2.4.5 Increased Resistance in Shallow Water
19
Prediction of Ship Resistance
20
2.5.1 Holtrop’s and Mennen’s Method
22
2.5.2 Van Oortmerssen’s Method
26
2.5.3 Guldhammer’s and Harvald’s Method
29
2.5.4 DJ Doust’s Method
31
Lateral Drift Effect
33
RESEARCH METHODOLOGY
37
3.1
Introduction
37
3.2
Research Methodology
37
LATERAL DRIFT EFFECT
42
4.1
Introduction
43
4.2
Lateral Drift Factors
44
4.2.1 Current
44
4.2.2 Wind
45
4.3
Definition of Lateral Drift Effect
46
4.4
Lateral Drift Effect in Specific Case
48
4.5
Direction of Drift Factors
50
MATHEMATICAL DERIVATIONS
53
5.1
Introduction
53
5.2
Holtrop’s and Mennen’s Derivation
54
ix
6
7
COMPUTER PROGRAMMING
60
6.1
Introduction
60
6.2
Computer Programming Verification
60
6.3
Program Flowchart
61
6.4
Input and Output Data
61
6.4.1 User Input Data
61
6.4.2 Data in the Programming
62
6.4.3 Output Data
63
RESULTS AND DISCUSSION
65
7.1
Introduction
65
7.2
CASE 1: Severe Drift Effect on the Ship Total Resistance, RTOTAL
66
7.2.1 Ship Total Resistance, RTOTAL with the Drift Effect (due to wind)
70
7.2.2 Ship Total Resistance, RTOTAL with Current Effect
72
7.2.3 Ship Total Resistance, RTOTAL with Lateral Drift Effect Due to Combination of Wind and Current (Severe Case)
8
7.3
Analysis the Effect at Other Ship Velocities
7.4
CASE 2: Severe Drift Effect on the Total Ship
73 75
Resistance, RTOTAL
80
CONCLUDING REMARKS
87
8.1
Conclusion
87
8.2
Recommendation for Future Research
88
REFERENCES
89
Appendices A- B
91- 96
x
x
LIST OF TABLES
TABLE NO.
TITLE
PAGE
2.1
Limitation for Holtrop’s and Mennen’s method.
22
2.2
Limitation for Van Ootmersen method
28
2.3
Values of regression coefficient
29
2.4
Limitation of Guldhammer’s and Harvald’s method
30
2.5
Value for increament resistance coefficient at every ship displacement
31
2.6
Limitation for DJ Doust method.
32
2.7
Values of parameter ‘a’
33
3.1
Beaufort scale
46
5.1
Frictional Resistance Component due to Drift Angle, β
55
5.2
Frictional Resistance Component due to Current Direction angle,α (In severe case)
5.3
Wave Making Resistance Component due to Drift Angle, β
5.4
57
Immersed Transom Resistance Component due to Drift Angle, β
5.6
57
Bulbous Bow Resistance Component due to Drift Angle, β
5.5
56
58
Model Correlation Resistance Component due to Drift Angle, β
58
6.1
List of data’s set in the programming
62
7.1
CASE 1: Result of Ship Total Resistance with Lateral Drift Effect at Various Drift and Current Direction Angles
67
xi 7.2
Resultant ship total resistance at speed 25 knots with various drift angles
7.3
Comparison resistance
of
72 differences
produced
in
between
normal
total
ship
condition
with
maximum and minimum 7.4(a)
75
Total Ship Resistance Produced Due to Lateral Drift Effect (in Severe Case) at Various Ship Velocity in Heading Current, α = 0o
7.4(b)
76
Total Ship Resistance Produced Due to Lateral Drift Effect (in Severe Case) at Various Ship Velocity in Starboard Beam Current, α = 90o
7.4(c)
77
Total Ship Resistance Produced Due to Lateral Drift Effect (in Severe Case) at Various Ship Velocity in Following Current, α = 180o
7.4(d)
78
Total Ship Resistance Produced Due to Lateral Drift Effect (in Severe Case) at Various Ship Velocity in Port Beam Current, α = 270o
7.5
79
CASE 2: Longitudinal, Lateral and Resultant Total Resistance at Various Current Direction Angle and Drift Angle.
82
xii
LIST OF FIGURES
FIGURE NO.
TITLE
PAGE
1.1
Methods of ship resistance evaluation
2
2.1
Typical curve of total hull resistance
9
2.2
Components of total hull resistance
10
2.3
Boundary layer around ship hull at LWL
13
2.4
Lord Kelvin wave pattern
14
2.5
Schematic diagram of typical ship’s wave system
15
2.6
Pressure distributions around a ship hull given by Van Ootmersen
2.7
Wave system at fore and aft shoulder given by Van Ootmersen
2.8
27
27
Total resistance, CT, and drift moment, -CM of singlepropeller cargo/container model for a range of drift angle, β and Froude number, Fn
34
3.1
Flowchart of the research methodology
39
3.2
Definition of length, L and breadth, B in lateral direction for a laterally drifting ship
4.1
Typical nature of lateral drift effect due to wind and/ or current on travelling ship
4.2
49
Direction of current (for severe case) in several main cases
7.1
47
Schematic diagram of drift effect in severe case (due to current and wind) specifically at river mouth area
4.3
41
51
CASE 1: Result of total ship resistance with lateral drift effect at various drift and current direction angles 69
xiii 7.2
Total ship resistance, Rtotal at various ship speed, VS with lateral drift angles (due to wind).
71
7.3
Schematic diagram of lateral drift effect due to current 74
7.4(a)
Total ship resistance curve produced with drift effect (in severe case) at various ship velocity in heading current case, α = 0o
7.4(b)
76
Total ship resistance curve produced with drift effect (in severe case) at various ship velocity in starboard
77
beam current case, α = 90o 7.4(c)
Total ship resistance curve produced with drift effect (in severe case) at various ship velocity in following current case, α = 180o
7.4(d)
78
Total ship resistance curve produced with drift effect (in severe case) at various ship velocity in port beam current case, α = 270o
7.5
79
CASE 1: Lateral Total Resistance, RT(T) at Various Current Direction Angle, α and Various Drift Angle, β (at speed 25 knots)
7.6
83
CASE 1: Lateral Total Resistance, RT(T) at Various Current Direction Angle, α and Various Drift Angle, β (at speed 25 knots)
84
xiv
LIST OF SYMBOLS
VS
Ship velocity/ speed
β
Drift angle
VS (L)
Longitudinal ship velocity/ speed
VS (T)
Lateral ship velocity/ speed
VC
Current speed
α
Current direction angle
VC (L)
Longitudinal current velocity/ speed
VC (T)
Lateral current velocity/ speed
L
Length of ship
LWL
Length of waterline
LPP
Length perpendicular
LR
Length of run
LCB
Longitudinal centre of buoyancy
B
Breadth
T
Draught
S
Wetted surface area of the ship
Δ
Ship displacement (weight)
∇
Volume displacement
CP
Prismatic coefficient
CM
Midship coefficient
CWP
Waterplane area coefficient
CB
Block coefficient
SAPP
Wetted surface area of appendages
ABT
Transverse sectional area of the bulb at the position where the stillwater surface intersects the stem
xv hB
Position of the centre of the transverse area ABT above the keel line
iE
Half angle of entrance
AT
Immersed part of transverse area of transom at zero speed
ρSW
Density of salt water
νSW
Viscosity of salt water
G
Gravity acceleration
Rn
Reynold’s number
Fn
Froude’s number
FnT
Froude’s number based on the transom
Fni
Froude’s number based on the immersion
PE
Effective power
RT
Total Resistance
RTOTAL
Total ship resistance with lateral drift effect
RF
Frictional resistance
RAPP
Appendages resistance
RW
Wave- making resistance
RB
Additional resistance due to presence of bulbous bow
RTR
Additional pressure resistance due to immersed transom
RA
Model- ship correlation resistance
RR
Residuary resistance
CT
Total resistance coefficient
CF
Frictional resistance coefficient
CAS
Steering resistance coefficient
CAA
Air resistance coefficient
Ca
Correlation factor
CR
Residuary resistance coefficient
Corr
CR Correction factor
di
regression coefficient
xvi
LIST OF APPENDICES
APPENDIX A1
TITLE
PAGE
Flowchart of computer programming using FORTAN to calculate longitudinal total resistance with drift effect
A2
91
Flowchart of computer programming using FOTRAN to calculate lateral total resistance with drift effect
B1
93
Total ship resistance, RT determination in longitudinal and lateral component with drift effect caused by drift angle, β (due to wind)
B2
95
Total ship resistance at service speed 25 knots with lateral drift effect due to current (4 knots) at various current direction angles.
96
CHAPTER I
INTRODUCTION 1.1
Preface
In this research, the study about one of the ship performances in actual sea is carried out. It is about the initial investigation of ship resistance specifically at river mouth area. This river mouth area is highlighted since one of the main effect which experienced by a moving ship is a lateral drift. As an initial study, this effect will be focused and taken into account onto the ship resistance. This specific case of study is initiated due some previous researches about the effect of lateral drift on the other ship performances. One of the remarkable studies was carried out by Faizul A. A and Yakusawa H. (Faizul and Yakusawa, 2007), which about the influence of lateral drift on seakeeping performance. They found out and summarized that as far the ship motion study is concerned, the effect of lateral drift is not negligible. Due to this finding basically motivates this initial study, which considering on the ship resistance study. Before the discussing more about this lateral drift and the effect on ship resistance, an overview about introduction of this topic will be outlined first.
2 In ship design stage, there are a number of important scopes or disciplines that need to be concerned in detailed. All of the related scopes basically with one aim; to get an optimum performance of the ship that to be designed. For this particular project, one of the studies will be focused and discussed in deeper, which is the ship resistance. As we know, ship resistance study is one of the essential parts in ship design in order to determine the effective power, PE required by the ship to overcome the total resistance, RT and certain speed, VS. From there, total installed power then can be calculated and determined for that ship. Prediction in preliminary design stage is one of the important practices in ship design.
Concerning of fuel price growth basically increases the requirements to the quality of ship resistance and propulsion study on the design stage. To evaluate the resistance of a ship, in practice, designer has several options available. Figure 1.1 in general summarized four basic classes of approach to the ship resistance determination; the traditional and standard series, the regression based procedures, the computational fluid dynamics approach and the direct model test. The choice of method basically depend not only the capability available but also on the accuracy desired, the fund available and the degree to which the approach has been developed. Other than that, types of the ship and the limitation also are taking into account.
Ship resistance evaluation methods
Traditional and standard series methods
Regression based methods (statistical methods
Computational fluid dynamics (CFD)
Direct model test
Figure 1.1: Methods of Ship Resistance Evaluation (Carlton, 1994)
3 Traditional and standard series methods considerably more reflects to the application of the theory of ship resistance, which will be discussed more on the next chapter. The last method is considered the most accurate among others because it use model with geometrically similar to the ship and applicable to any kind of ships. The others are only can be used to predict ship resistance between certain limits or only for a ship that have similar particulars to such group.
In executing this study, there are several stages that will be approached and discussed orderly. As well known, ship resistance can be evaluated either in calm water or in wave’s condition. Particularly in ship design practice, for the early stage, the prediction of ship resistance is highlighted more in calm water condition. Thus, power required to attain a certain speed in seaway have been determined from the still water performance after making allowance of 15 to 30% for wind or/ and waves or/and current. The prediction is applied (early stage) basically using a numerical/ statistical/ regression prediction method. There are a number of reliable methods that had been applied in predicting ship resistance in calm water and further discussion about that will be outlined later on Chapter II. Besides the ship resistance prediction in calm water, another approach is determining a ship resistance in wave. To this extent of ship resistance evaluation, in practice, experimental data of ship resistance in waves is necessary and contributes the most reliable and good result for predicting ship resistance in waves. The result is taken and summarized as an added resistance, where by subtracting the result of ship resistance in calm water with the results of ship resistance in waves.
However, from one point of view, effects of drift angle are important for all types of structures and vehicles, including those for land, sea, air, and space. Same goes to ship, where practically, when ship traveling at certain forward speed in actual sea or river, she experiences the effects of wind and current drifting forces. The ship will move with certain drift angle, considerably in this case influences on the ship resistance. This effect basically has not been studied in detail previously (ship resistance prediction). It is therefore important to capture the influence of lateral drift and investigate in ship resistance performance.
4
As far as lateral drift effects is concerned, there is a necessary and additional steps to be taken to extent those mentioned approach (ship resistance evaluation). In completing this research, for the first stage, ship resistance prediction in calm water will be studied first, by investigating the lateral drift effect. Thus, since this calm water condition is focused, the effect of lateral drift caused by wind and current will be concerned in this study. Due to that, several methods of ship resistance prediction will be detailed in and accompanying with basis ship resistance theory, extended study will be carried out to consider lateral drift effect for this ship resistance prediction (calm water). At this earlier stage of research, study and investigation of those prediction methods will be made, and a number of parameters or elements in those formulas will be identified and used as a basis in considering the influence of the lateral drift effects. This principal and approach basically is used in order to get some insight views on this topic. This could be regarded as an initiation and invantion of research activity.
1.2
Problem Statement
In practical, one of the natures when she operates in its real environment is traveling with the effect of current. This current effect exist either in open sea, coupled with effect of waves and strong winds, or in calm water condition. Focusing on calm water condition, for this present study, it can be viewed one of the area that could contribute very significant effect is at river mouth area. This area specifically can be seen especially during low and high tides time. One of the most important effects when she operates in these times and this area is a lateral drift effect. Due to this severe current effect which causes lateral drift, it considerably influences on the ship resistance. Hence, the captain has to reconsider the power required at the desired speed of his ship to travel at this area with a lateral drift effect. This effect basically
5 has not been studied previously and it is therefore important to capture the influence of lateral drift and investigate in ship resistance performance.
1.3
Research Objectives
The objectives of this present study are:
1. To investigate the effects of severe lateral drift on ship resistance. 2. To propose the suitable ship resistance prediction method by taking the effect of high speed current and/ or wind (lateral drift) into account. 3. To develop a calculation program based on the purpose ship resistance prediction method.
1.4
Research Scopes
In ensuring this study can be completed successfully, several scopes will be covered during completing this research. The scopes that have to be covered phase by phase are:
1. Literature review on ship resistance theory, ship resistance prediction method and lateral drift effect. 2. For lateral drift effect, literature is reviewed due to severe current effect, with a bigger drift angle will be specified. 3. Correlate the effect of lateral drift in ship resistance study. 4. Since prediction of ship resistance with lateral drift effect will be focused, the most suitable and applicable prediction method will be identified as a basis.
6 5. Derive the suitable ship resistance prediction method. 6. Develop the calculation software for predicting ship resistance with lateral drift effect in severe case. 7. Make a comparison between the computed result of ship resistance in severe lateral drift effect and ship total resistance in normal condition.
1.5
Significant of Research
During the design stage, designers/ naval architects perform their best effort in achieving as accurate as possible in designing the ship. This activity definitely includes in the ship resistance determination. Concerning this practice initially made this research significantly necessary, especially when it is considered in specific case. It is viewed that this effect of lateral drift could contribute very significant, specifically at river mouth area due to existing of current effect. Due to this current effect makes the lateral drift effect more severe, and it is believed it will influence on the ship resistance performance. This effect basically has not been studied previously in ship resistance point of view. Hence, by taking into account this specific condition in ship resistance determination, a better, specific and more accurate result possibly can be obtained at early of design stage.
CHAPTER II
LITERATURE REVIEW
2.1
Introduction
Prior to the start of the present study and development, several literature researches have been put in focus first. The main role of these literature basically to motivate the present study in ensuring the objectives is successfully achieved. Regarding to that purpose, the literature research will be divided into several parts of discussion. At first, the discussion and focus will be given onto the ship resistance part. The discussion including the basis theory related to ship resistance and the approach methods in predicting and evaluating ship resistance. Deeper understanding against methods of ship resistance prediction is very important in order to put directly the relationship with effects in lateral drift condition. The drift effects, as per discussed earlier might be due to wind or/ and waves.
Then, in second part of the literature research, lateral drift effect will be highlighted more, particularly which contributed to the ship resistance performance. The objective can be successfully achieved by digesting the relationship between ship resistance and the lateral drift effect of the ship when travelling through water.
8
Since the literature onto the ship resistance prediction methods is carried out, the initial investigation is highlighted in studying ship resistance with lateral drift effect.
2.1
Resistance Theory
When a body moves through a fluid it may experiences forces opposing the
motion. As a ship moves through water and air it experiences both water and air forces. This force is the water’s resistance to the motion of the ship, which is referred to as “total hull resistance” (RT). This resistance force consequently is used to calculate a ship’s effective horsepower. A ship’s calm water resistance is a function of many factors, including ship speed, hull form (draft, beam, length, wetted surface area), and water temperature. Total hull resistance increases as speed increases as shown below in Figure 2.1. Note that the resistance curve is not linear. The water and air masses may themselves be moving, the water due to currents and the air as a result of winds. These will, in general be of different magnitudes and directions. The resistance is studied initially in still water with no wind. Separate allowances are made for wind and the resulting distance travelled corrected for water movements. Unless the winds are strong the water resistance will be the dominant factor in determining the speed achieved.
9
Figure 2.1: Typical curve of total hull resistance
2.2
Components of Total Hull Resistance
As a ship moves through calm water, there are many factors that combine to form the total resistance force acting on the hull. The principle factors affecting ship resistance are the friction and viscous effects of water acting on the hull, the energy required to create and maintain the ship’s characteristic bow and stern waves, and the resistance that air provides to ship motion. In mathematical terms, total resistance can be written as: RT = RV + RW + RAA Where: RT
= total hull resistance
RV
= viscous (friction) resistance
RW
= wave making resistance
RAA
= resistance caused by calm air
(2.1)
10
Other factors affecting total hull resistance will also be presented. Figure 2.2 shows how the magnitude of each component of resistance varies with ship speed. At low speeds viscous resistance dominates, and at high speeds the total resistance curve turns upward dramatically as wave making resistance begins to dominate (Arizam, 2003)
Figure 2.2: Components of Total Hull Resistance
2.2.1
Frictional Resistance
As a ship moves through the water, the friction of the water acting over the entire wetted surface of the hull causes a net force opposing the ship’s motion. This frictional resistance is a function of the hull’s wetted surface area, surface roughness, and water viscosity. Viscosity is a temperature dependent property of a fluid that describes its resistance to flow. Although water has low viscosity, water produces a significant friction force opposing ship motion. Experimental data have shown that water friction can account for up to 85% of a hull’s total resistance at low speed (Fn ≤
11
0.12 or speed-to-length ratio less than 0.4 if ship speed is expressed in knots), and 40-50% of resistance for some ships at higher speeds. Naval architects refer to the viscous effects of water flowing along a hull as the hull’s frictional resistance (Bertram, 2000).
The flow of fluid around a body can be divided into two general types of flow: laminar flow and turbulent flow. A typical flow pattern around a ship’s hull showing laminar and turbulent flow is shown in Figure 2.3.
Laminar flow is
characterized by fluid flowing along smooth lines in an orderly fashion with a minimal amount of frictional resistance. For a typical ship, laminar flow exists for only a very small distance along the hull. As water flows along the hull, the laminar flow begins to break down and become chaotic and well mixed. This chaotic behaviour is referred to as turbulent flow and the transition from laminar to turbulent flow occurs at the transition point shown in Figure 2.3 (Harold, 1957).
Turbulent flow is characterized by the development of a layer of water along the hull moving with the ship along its direction of travel. This layer of water is referred to as the “boundary layer.” Water molecules closest to the ship are carried along with the ship at the ship’s velocity. Moving away from the hull, the velocity of water particles in the boundary layer becomes less, until at the outer edge of the boundary layer velocity is nearly that of the surrounding ocean. Formation of the boundary layer begins at the transition point and the thickness of the boundary layer increases along the length of the hull as the flow becomes more and more turbulent. For a ship underway, the boundary layer can be seen as the frothy white band of water next to the hull. Observation of this band will reveal the turbulent nature of the boundary layer, and perhaps we can see some of the water actually moving with the ship. As ship speed increases, the thickness of the boundary layer will increase, and the transition point between laminar and turbulent flow moves closer to the bow, thereby causing an increase in frictional resistance as speed increases.
12
Mathematically, laminar and turbulent flow can be described using the dimensionless coefficient known as the Reynolds Number in honor of Sir Osborne Reynolds’ (1883) contribution to the study of hydrodynamics (Harold, 1957). For a ship, the Reynolds Number is calculated using the equation below: Rn = VL / ν
(2.2)
Where: Rn
= Reynolds number
L
= length (ft)
V
= velocity (ft/sec)
ν
= kinematic viscosity of water (ft /sec)
2
For external flow over flat plates (or ship hulls), typical Reynolds number magnitudes are as follows: 5
Laminar flow: Rn < 5 x 10
Turbulent flow: Rn > 1 x 10
5
Values of Rn between these numbers represent transition from laminar to turbulent flow.
13
Figure 2.3: Boundary Layer around Ship Hull at LWL 2.2.2
Wave Making Resistance
A ship moving through still water surface will set up a very characteristic pattern of waves. There are essentially two primary points of origin of waves, which are at the bow and at the stern. However the bow wave train is more significant, because the waves generated here persist along the ship's hull. Generally the bow waves also larger and more predominant. These wave systems, bow and stern, arises from the pressure distribution in the water where the ship is acting and the resultant of net fore-and-aft force is the wave making resistance. Wave making resistance is the result of the tangential fluid forces. It’s depends on the underwater shape of a ship that moves through water. The size of wave created shows the magnitude of power delivered by the ship to the water in order to move forward.
14
Figure 2.4: Lord Kelvin Wave Pattern
Lord Kelvin (1887) has illustrated a ship’s wave pattern in order to explain the features. He considered a single pressure point at the front, moving in straight line over the water surface. The generated wave pattern consists of a system of transverse wave following behind the pressure point and a series of divergent waves radiating from the same pressure point. The envelope of the divergent wave crests makes an angle of 19° 28' for a thin disturbance travelling in a straight line, regardless of the speed. Figure 2.4 shows the wave pattern illustrated by Lord Kelvin (Edward, 1988).
Furthermore, the actual ship’s wave system is more complicated such that in Figure 2.5 below. A ship can be considered as a moving pressure field sited near the bow and moving suction field near the stern. The bow produces a series of divergent wave pattern and also the transverse wave in between on each side of the ship. Similar wave system is formed at the shoulder, and at the stern with separate divergent and transverse pattern.
15
In the case of a deeply submerged body, travelling horizontally at a steady speed far below the surface, no waves are formed, but the normal pressures will vary along the length. The magnitudes of the resistance reduce with increasing the depth of a submerged body. This force will be negligible when the depth is half-length of the body.
Figure 2.5: Schematic Diagram of Typical Ship’s Wave System (Edward, 1988).
2.2.3
Eddy Resistance or Viscous Pressure Resistance
In a non-viscous fluid the lines of flow past a body close in behind it creating pressures which balance out those acting on the forward part of the body. With viscosity, this does not happen completely and the pressure forces on the after body are less than those on the fore body. Also where there are rapid changes of section the flow breaks away from the hull and eddies are created. The effects can be minimized by streamlining the body shape so that changes of section are more gradual.
16
However, a typical ship has many features which are likely to generate eddies. Transom sterns and stern frames are examples. Other eddy creators can be appendages such as the bilge keels, rudders and so on. Bilge keels are aligned with the smooth water flow lines, as determined in a circulating water channel, to minimize the effect. At other loadings and when the ship is in waves the bilge keels are likely to create eddies. Similarly rudders are made as streamlined as possible and breakdown of flow around them is delayed by this means until they are put over to fairly large angles. In multi-hull ships the shaft bracket arms are produced wider streamlined sections and are aligned with die local flow. This is important not only for resistance but to improve the flow of water into the propellers.
Flow break away can occur on an apparently well rounded form. This is due to die velocity and pressure distribution in the boundary layer. The velocity increases where the pressure decreases and vice versa. Bearing in mind that the water is already moving slowly close into the hull, the pressure increase towards the stern can bring the water to a standstill or even cause a reverse flow to occur. That is the water begins to move ahead relative to the ship. Under these conditions separation occurs. The effect is more pronounced with steep pressure gradients which are associated with full forms.
2.2.4
Air Resistance
Air resistance is the resistance caused by the flow of air over the ship with no wind present. This component of resistance is affected by the shape of the ship above the waterline, the area of the ship exposed to the air, and the ship’s speed through the water. Ships with low hulls and small sail area will naturally have less air resistance than ships with high hulls and large amounts of sail area. Resistance due to air is typically 4-8% of the total ship resistance, but may be as much as 10% in high sided ships such as aircraft carriers. Attempts have been made reduce air resistance by streamlining hulls and
17
superstructures, however; the power benefits and fuel savings associated with constructing a streamlined ship tend to be overshadowed by construction costs.
2.3
Other Types of Resistance Not Included in Total Hull Resistance
In addition to frictional resistance, wave making resistance, eddy resistance and air resistance, there are several other types of resistance that will influence the total resistance experienced by the ship.
2.3.1
Appendage Resistance
Appendage resistance is the drag caused by all the underwater appendages such as the propeller, propeller shaft, struts, rudder, bilge keels, pit sword, and sea chests. Appendages will primarily affect the viscous component of resistance as the added surface area of appendages increases the surface area of viscous friction. Appendages include rudders, bilge keels, shaft brackets and bossings, and stabilizers. Each appendage has its own characteristic length and therefore, if attached to the model, would be running at an effective Reynolds' number different from that of the main model.
Thus, although obeying the same scaling laws, its resistance would scale differently to the full scale. That is why resistance models are run naked. This means that some allowance must be made for the resistance of appendages to give the total ship resistance. The allowances can be obtained by testing appendages separately and scaling to the ship. Fortunately the overall additions are generally relatively small,
18
say 10 to 15% of the hull resistance, and errors in their assessment are not likely to be critical.
2.3.2
Steering Resistance
Steering resistance is added resistance caused by the motion of the rudder. Every time the rudder is moved to change course, the movement of the rudder creates additional drag. Although steering resistance is generally a small component of total hull resistance in warships and merchant ships, unnecessary rudder movement can have a significant impact. Remember that resistance is directly related to the horsepower required to propel the ship. Additional horsepower is directly related to fuel consumed (more horsepower equals more fuel burned). A warship traveling at 15 knots and attempting to maintain a point station in a formation may burn up to 10% more fuel per day than a ship traveling independently at 15 knots.
2.3.3
Wind and Current Resistance
The environment surrounding a ship can have a significant impact on ship resistance. Wind and current are two of the biggest environmental factors affecting a ship. Wind resistance on a ship is a function of the ship’s sail area, wind velocity and direction relative to the ship’s direction of travel. For a ship steaming into a 20-knot wind, ship’s resistance may be increased by up to 25-30%. Ocean currents can also have a significant impact on a ship’s resistance and the power required to maintain a desired speed. Steaming into a current will increase the power required to maintain speed. For instance, the Kuroshio Current (Black Current) runs from South to North off the coast of Japan and can reach a speed of 4-5 knots. What is the impact of this
19
current? For a ship heading south in the current and desiring to travel at 15 knots it is not uncommon to have the propulsion plant producing shaft horsepower for speeds of 18-19 knots. Therefore, the prudent mariner will plan his or her voyage to avoid steaming against ocean currents whenever possible, and to steam with currents wherever possible.
2.3.4
Added Resistance Due to Waves
Added resistance due to waves refers to ocean waves caused by wind and storms, and is not to be confused with wave making resistance. Ocean waves cause the ship to expend energy by increasing the wetted surface area of the hull (added viscous resistance), and to expend additional energy by rolling, pitching, and heaving. This component of resistance can be very significant in high sea states.
2.3.4
Increased Resistance in Shallow Water
Increased resistance in shallow water (the Shallow Water Effect) is caused by several factors. i. The flow of water around the bottom of the hull is restricted in shallow water, therefore the water flowing under the hull speeds up. The faster moving water increases the viscous resistance on the hull. ii. The faster moving water decreases the pressure under the hull, causing the ship to “squat”, increasing wetted surface area and increasing frictional resistance.
20
iii. The waves produced in shallow water tend to be larger than do waves produced in deep water at the same speed. Therefore, the energy required to produce these waves increases, (i.e. wave making resistance increases in shallow water). In fact, the characteristic hump in the total resistance curve will occur at a lower speed in shallow water. The net result of resistance for ship traveling in shallow water is that it takes more horsepower (and fuel) to meet the required speed. Another more troublesome effect of high speed operation in shallow water is the increased possibility of running aground. Just as shallow water will adversely affect a ship’s resistance, operating in a narrow waterway such as a canal can produce the same effect. Therefore when operating in a canal, the ship’s resistance will increase due to the proximity of the canal walls and the decrease in pressure along the ships sides is likely to pull the ship towards the edge of the canal. The prudent mariner is advised to operate at moderate speeds when steaming in shallow and/or narrow waters (Harvald, 1983).
2.4
Prediction of Ship Resistance
In the design stage, particularly at the preliminary stage, early estimation of total resistance of the ship contributes an important part. It is important to predict the total resistance of a ship during design stage for used of determination the installed power. As far as an early estimation of total resistance is concerned, regarding to the Figure 1.0 earlier, there are two methods of resistance evaluation is approached, which are standard series method and regression based method. Regression based method or also known as systematic series is a prediction method that base on the statistical analysis of resistance results from ad-hoc testing of models in the towing tank. The standard series prediction method is based on the testing of series of model
21
that carried out for the resistance prediction purposes. However these methods only applicable to be used for ship having similar characteristics. It should be emphasized that resistance prediction is not an exact science and that the algorithms implemented in this program, while they are useful for estimating the resistance of a hull, may not provide exact results (Carlton, 1994).
Since early 1900s, number of studies onto prediction of ship resistance were carried out and published. Various methods and approaches had been discovered and apart from that, this development process is still keep on improving for better satisfactory for the application. Particularly for the preliminary stage in ship design process, number of prediction methods for ship resistance had been developed and significantly applied. These variations basically applicable to various different families of hull shapes. For example, some of the algorithms are useful for estimating the resistance of displacement hull or planing hulls, while others are useful for estimating the resistance of sailing boat hulls.
Prediction methods such as Van Ootmersen’s method, Holtrop’s & Mennen’s method, Cedric Ridgely Nevitt’s Method, DJ Doust’s Method and Guldhammer’s and Harvald’s Method are among of the significantly useful methods in solving the study of ship resistance prediction. As a summary, most of these methods basically considered several elements in contributing to the prediction of total resistance of the ship. From the basis theory of ship resistance, as discussed previously, elements such as frictional resistance, wave making resistance and other components of resistance such as viscous pressure resistance and air resistance are viewed as major elements in formulating and development of ship resistance prediction. All of these elements mainly contribute as a forms and factors to correlate in ship resistance prediction. The relationship of those factors is applied differently for each type of prediction methods and can be discussed on the next sub- topic.
22
2.4.1 Holtrop’s and Mennen’s Method
In 1982 Holtrop has published results of resistance and propulsion tests with 191 models of various types of ship using statistical analysis. It was found that for 95 percent of the cases the accuracy of the statistically derived formulas is satisfactory in preliminary design work. Holtrop and Mennen extended then their method to include the Series 64 hull forms. Also better formulas were obtained for the higher speed ranges. After deriving formula from the statistical analysis of model data the next step was to use the regression equation to investigate the optimum of parameters to suit any given design requirements. The regression analysis was based on the results for 334 models (Holtrop and Mennen, 1982).
In their approach to establishing their formulas, Holtrop and Mennen assumed that the non-dimensional coefficients representing the components of resistance for a hull form might be represented by appropriate geometrical parameters, thus enabling each component to be expressed as a non-dimensional function of the sealing parameter and the hull form. The range of parameters for which the coefficients of the basic expressions are valid as following:
Table 2.1: Limitation for Holtrop’s and Mennen’s Method (Arizam, 2003). Ship types
Max. Froude
L/B
B/T
Min
Max
Min
Max
Min
Max
0.24
0.73
0.85
5.1
7.1
2.4
3.2
0.38
0.55
0.65
3.9
6.3
2.1
3.0
0.45
0.55
0.67
6.0
9.5
3.0
4.0
No. Tankers, bulk
CP
carriers Trawlers, coasters, tugs Containership.
23
Destroyers Cargo liners
0.30
0.56
0.75
5.3
8.0
2.4
4.o
RORO ships,
0.35
0.55
0.67
5.3
8.0
3.2
4.0
car ferries
Holtrop’s and Mennen’s method is suitable for resistance prediction of small vessel. However, there are still errors that exist in the final result. Therefore, all the factors below should be considered to determine the degree of uncertain parameters:
i. Increasing in Froude number which will create a greater residuary resistance (wave making resistance, eddy resistance, breaking waves and shoulder wave) is a common phenomenon in small ships. As a result, error in total resistance increases. ii. Small vessels are easily influenced by environmental condition such as wind and current during operational. iii. For smaller ship, the form size and ship type has a great difference. This method only limited to the Froude number below 0.5, (Fn < 0. 5) and also valid for TF/ LWL > 0.04. For an extrapolation that only carried out in two dimensions, there is a correlation allowance factor in model ship that will affect some 15% difference in the total resistance and the effective power. This method also limited to hull form resembling the average ship described by the main dimensions and form coefficients used in the method. Below are the procedures of calculation ship resistance using Holtrop’s and Mennen’s method (Holtrop and Mennen, 1982).: i.
Calculate Frictional Resistance R F = 0.5 ρV 2 S C F Where C F =
0.075 (log Rn − 2) 2
24
ii.
1 + k1 = c13 {0.93 + c12 ( B / L) 0.92497 (0.95 − C P ) −0.521448 (1 − C P + 0.0225lcb) 0.6906 }
iii.
LR = L(1 − C P + 0.06C P lcb /( 4C P − 1)
When T/L>0.05
c12 = (T L )
0.2228446
When 0.02
c12 = 18.20(T L − 0.02) 2.078 + 0.479948 When T/L<0.02
c12 = 0.479948 iv.
c13 = 1 + 0.003Cstern
v.
Calculate Wave- making Resistance,
{
(
RW = c1c 2 c5 ∇ρg exp m1 Fnd + m2 cos λFn−2
)}
Where c1 = 2223105cΓ3.78613 (T B )1.07961 (90 − i E ) −1.37565 When B/L<0.11 cΓ = 0.229577( B / L) 0.3333
When 0.11
When B/L>0.25 cΓ = 0.5 − 0.0625 L / B vi.
c 2 = exp(−1.89 c 3 ) c 3 = 0.56 A1BT.5 /{BT (0.31 ABT + T F − h B )}
vii.
c5 = 1 − 0.8 AT /( BTC M )
viii.
m1 = 0.0140407 L / T − 1.75254∇1 3 / L − 4.79323B / L − c16
When CP<0.8
c16 = 8.07981C P − 13.8673C P2 + 6.984388C P3
25
When CP>0.8 c16 = 1.73014 − 0.7067C ix.
m2 = c15 C P2 exp(−0.1Fn−2 )
When L3/∇<521, c15 = -1.69385
When 512
When L3/∇>1727 c15 = 0.0
x.
Calculate λ When L/B<12
λ = 1.446C P − 0.03L / B When L/B>12
λ = 1.446C P − 0.36 xi.
1. 5 Calculate Bulbous Bow Resistance, R B = 0.11 exp(−3PB−2 ) Fni3 ABT ρg /(1 + Fni2 )
Where PB = 0.56 ABT /(TF − 1.5hB )
And Fni = V /[ g (TF − hB − 0.2 ABT ) + 0.15V 2 ]1 2 xii.
Calculate Immersed Transom Resistance, RTR = 0.5 ρV 2 AT c6 When FnT<5
c6 = 0.2(1 − 0.2 FnT ) When FnT≥5
c6 =0 Where FnT = V /[ 2 gAT /( B + BCWP )]1 2 xiii.
Calculate Model Ship Correlation Resistance, R A = 0.5 ρV 2 SC A
26
C A = 0.006( L + 100) −0.16 − 0.00205 + 0.003 L / 7.5C B4 c 2 (0.04 − c 4 )
When TF/L≤0.04
c4=TF/L When TF/L>0.04
c4=0.04 xiv.
Calculate Total Resistance, RTotal = RF(1+k) + RAPP + RW + RB + RTR + RA
This method is based on a numerical regression, which is obtained with experiments from models of small ships, drag ships and tugboats "The Netherlands Ship Model Basin" in Wageningen. With this method is possible to predict the required power in small ships like trawler ships, fish boats, tugboats, etc. With a reliability level of 95%, consequently the error in the speed range is lower than 18%.
2.4.2
Van Oortmerssen’s Method
G. Van Oortmerssen derived a mathematical model to describe the resistance and propulsion properties of ships as function of the Froude number, Reynold number and other general parameters for small ships such as trawlers and tugs from random tank data. In addition, several assumptions were made for predicting resistance and powering of small craft such as follows: i. The approximation of the surface disturbance of the ship by a pressure distribution consisting of a positive and a negative pressure peak is very realistic. There are regions of high pressure at the bow and the stern, whilst there are regions of low pressure near the shoulders. This as shown in Figure 2.6.
27
ii. Small ship can be characterized by the absence of a parallel middle body, so the regions of low pressure and the wave systems of fore and after shoulder coincide and consequently the pressure distribution is as illustrated in Figure 2.7 iii. The summation of viscous resistance and wave-making resistance representing the components of the total resistance.
Figure 2.6: Pressure distributions around a ship hull given by Van
Ootmersen
Figure 2.7: Wave system at fore and aft shoulder given by Van
Ootmersen
The range of parameters for which the coefficients of the basic expressions are as follow:
28
Table 2.2: Limitation for Van Ootmersen method. Parameter
Limitation
LWL
8- 80 m
L/B
3 to 6.2
B/T
1.9 to 4.0
CP
0.50 to 0.73
CM
0.70 to 0.97
LCB
-7% L to +2.8% L
½ ie
10o to 46o
V/L1/2
0 to 1.79
Fn
0 to 0.50
Van Ootmersen suggested that the final form of the resistance equation is represented by the summation of viscous resistance and wave-making resistance as follows (Arizam, 2003).
−2 −2 −2 −2 RT = [C1e − (1 / 9) mFn + C 2 e − mFn + C 3 e − mFn sin( Fn − 2 ) + C 4 e − mFn cos( Fn − 2 )] Δ 0.075 ρSV 2 ] +[ 2(log Rn − 2) 2 Δ
Where i.
10 3 Ci = d i ,0 + d i ,1 LCB + d i , 2 LCB 2 + d i ,3 C P + d i , 4 C P 2 + d i ,5 ( LWL / B + d i ,6 ( LWL / B ) 2 + d i ,7 CWL + d i ,8 CWL 2 + d i ,9 B / T + d i ,10 ( B / T ) 2 + d i ,11C m
ii.
m = b1 − C P
( −b / 2)
or for small ships this can be represented by m = 0.14347 − C P iii.
( −2.1976 )
CWL is a parameter for the angle of entrance of the load waterline, ie where CWL = ie ( LWL / B )
iv.
Approximation for wetted surface area is represented by:
29
S = 3.223V 2 / 33 + 0.5402 LWLV 1 / 3 Table 2.3: Values of regression coefficient
2.4.3
i
1
2
3
4
di,0
79.32134
6714.88397
-908.44371
3012.14549
di,1
-0.09287
19.83000
2.52704
2.71437
di,2
-0.00209
2.66997
-0.35794
0.25521
di,3
-246.45896
-19662.02400
755.186600
-9198.80840
di,4
187.13664
14099.90400
-48.93952
6886.60416
di,5
-1.42893
137.33613
-9.86873
-159.92694
di,6
0.11898
-13.36938
-0.77652
16.23621
di,7
0.15727
-4.49852
3.79020
-0.82014
di,8
-0.00064
0.02100
-0.01879
0.00225
di,9
-2.52862
216.44923
-9.24399
236.37970
di,10
0.50619
-35.07602
1.28571
-44.17820
di,11
1.62851
-128.72535
250.64910
207.25580
Guldhammer’s and Harvald’s Method
This method is based on a group of model resistance test results that have been collected and analyse using International Towing Tank Conference (ITTC) 1957. The specific residual resistance coefficient CR has been expressed as a function of Froude number, Fn =
VM . CR then has been plotted against Froude number gLWLM
in a group according to length-displacement ratio, L/∇ 1/3. Here ∇ is the volumetric displacement which is φ= ∇/ LBTβ. Furthermore, the resistance curves diagram is only corresponds to vessel with standard form, which is standard position of location of buoyancy, standard B/T, normal shaped sections, moderate cruiser stern and raked stem. The limits of the hull form parameters covered by this method are:
30
Table 2.4: Limitation of Guldhammer’s and Harvald’s method Parameter
Limitation 4.0 – 8.0
L/∇1/3
0.15 – 0.45
Froude number Fn V/√L (knots/ft)
0.5 – 1.5 0.55 – 0.85
Prismatic coefficient, CP
This method is applicable to many types of vessels that fulfill the limitation given above. However, correction needs to be taken into consideration for ships having different standard form such mentioned in the concept and also for hull form shape and model-ship correlation factor, CA.
Below is the procedure of calculation ship resistance using Gulghammer’s and Harvald’s method. i.
Calculate wetted surface area, S = ρLPP (C B B + 1.7)
ii.
Calculate Reynold’s number, Rn = VL / ν
iii.
Calculate frictional resistance coefficient, C F =
0.075 (log Rn − 2) 2
Residuary resistance is a function of three parameters which are L/∇ 1/3, CP and Froude’s number, Fn iv.
Calculate parameter,
L L ∇1 / 3
v.
Calculate Froude’s number, V
vi.
Determine the residuary resistance coefficient from the graph residuary
gL
resistance coefficient against speed- length ratio vii.
Calculate increment resistance coefficient, 10 3 C R = 0.5 log ∇ − 0.1(log ∇) 2
viii.
Calculate CR correction for deviation from standard B/T= 2.5
31
Corr1, ΔC R = Where
LCB Std LCB Fn 90 ( 2 )( − ) 3 L L 10 C P + 1.1C P − 0.0875
LCB Std = 0.44 Fn − 0.094 L
xv.
Calculate air and steering resistance, CAAS = CAA + CAS
ix.
Calculate total resistance coefficient, CT CT = CR + CF + CA + Corr1 + Corr2 + CAAS and values for increment resistance can be referred to table 2.9 as a function of
ship displacement Table 2.5: Value for increment resistance coefficient at every ship
displacement
2.4.4
-3
Displacement (tonne)
CA (10 )
1000
0.6
10000
0.4
100000
0
1000000
-0.6
DJ Doust’s Method
DJ Doust’s method is a method that yields a regression equation that expresses ship resistance for a particular ship type in term of certain basic form parameters at any required Froude number. Evaluation of this regression equation for specific combinations of form parameters provides corresponding estimates of resistance for the vessel under consideration. Those parameters are L/B, B/T, o
Cm, Cp, LCB and ½ α e. All of these six design parameters can be calculated at an early stage of the design. Doust has plotted the graph of changes in all this
32
parameter for the standard ship length (200 ft). DJ Doust’s method is applicable to predict the resistance for fishing vessel and other ship that fulfill the limitation given above. However, correction needs to be taken into consideration for ships having different length compare to the standard ship length (200 ft). Table 2.5 shows the limitation for DJ Doust resistance prediction method (Arizam, 2003).
Table 2.6: Limitation for DJ Doust method. Parameter
L/B B/T Cm Cp LCB ½α
o
Limitation 4.4 – 5.8 2.0 – 2.6 0.81 – 0.91 0.6 – 0.7 0% - 6% aft of midship 5o – 30o
e
Procedures of calculation for DJ Doust method are as follows (Arizam, 2003). i.
Calculate three parameters required to determine factors used to calculate residuary resistance for the ship having standard length, 200 ft. These parameters are L/B, B/T and V / L
ii.
Calculate three factors used to calculate residuary resistance using graph given. These three factors are F1 = f (CP, B/T), F2 = f(CP, LCB) and F’3 = f(CP, ½ αoe, L/B)
iii.
Calculate residuary resistance, CR(200) = 100a(CM-0.875). The parameter ‘a’ is a function V / L and given by Table 2.6.
iv.
Calculate residuary resistance, CR(200) = F1 + F2 + F’3 + F6
v.
Calculate S = 0.0935 S
vi.
Calculate L' = 1.05V / L
vii.
Calculate Froude’s skin friction correction
viii.
Calculate Δ ( 200) = Δ (200 / LBP ) 3
Δ2! / 3
33
ix.
Calculate δ 1 = (152.5 × SFC )
x.
Calculate residuary resistance for the new ship, C R ( New) = C R ( 200 ) + δ 1
xi.
3 Δ1(/200 )
Calculate total resistance, RT =
C R ( New) ΔV 2 L
Table 2.7: Values of parameter ‘a’
2.5
V/√L
a
0.8 0.9 1.0 1.1
-0.045 -0.053 -0.031 -0.035
Lateral Drift Effect
Study about this lateral drift effects basically is initiated from successful study about the other ship performance that had been carried out before. The previous study discussed the motion of the ship which influenced by the effect of lateral drift, performed by Faizul A. A. (Faizul, 2006). The study of hydrodynamic forces and ship motions were carried out for various hull drift angles in regular head and beam waves and was found contributed significant differences and effects. The effects which influence ship performance in lateral drift condition such as amplitude of sway, roll and yaw motion is confirmed that is not negligible. Due to that relationship basically motivated further study on the effect of lateral drift, specifically for this case, onto ship resistance.
On top of that, another earlier study and investigation about the relationship between lateral drift effect and ship resistance was produced. (Longo and Stern,
34
2001) From the investigation onto the Series 60, with CB = 0.6 single-propeller cargo/container model ship flow, they concluded that resistance increases linearly with angle of drift for all Froude number, Fn. And the result of the investigation is represented by the Figure 2.8
Figure 2.8: Total resistance coefficient, CT, and drift moment coefficient, -CM of single- propeller cargo/container model for a range of drift angle, β and Froude number, Fn (Longo and Stern, 1999)
CHAPTER III
RESEARCH METHODOLOGY
3.1
Introduction
Upon completion of this research, a proper and sequence steps are developed in determining its successfulness. Concerning the earlier objectives and scopes, the research is divided into two parts. The first part of the research is carried out in semester one and the second part of the research is performed in the second semester.
3.2
Research Methodology
As for the first part of the study, the research work began with the understanding and familiarization of the background and conducting literature review on the ship resistance fundamental and theory, methods for predicting ship resistance as well as effect of lateral drift in ship resistance. All those materials of literature review are obtained through several different sources such as books, journals also electronic resources such as e-journal, internet, websites and online materials.
38
Consequently, with familiarization of research topic, and understanding the related and useful literature, in the second part, the next step is to identify and investigate the suitable parameters or factors in ship resistance prediction that can be correlated with the effect of lateral drift. This approach, will be the main principle of this research. It was decided purposely to get the first insight in relating the ship resistance determination with the effect of lateral drift. At this stage, it mainly will bring to the mathematical modification/ derivation of ship resistance prediction with lateral drift effect. A number of methods for ship resistance prediction will be reviewed and modified to correlate with lateral drift effect.
The modified
mathematical ship resistance prediction will then be developed in calculation program for further analysis. For this initial investigation, Microsoft Excel and FORTRAN program can be seen capable to be applied for calculation program. From there, the computed results can be analyzed by comparing the resistance performance between with and without lateral drift effect. Also the comparison with lateral drift effect can be investigated between forward speed and lateral speed on ship performance. The flow of the research methodology as described above can be referred to the Figure 3.1.
39
Identifying of Problem Statement
Literature Review
Ship Resistance Theory/ Ship Resistance Prediction
Lateral Drift Effect (River Mouth Area)
Identifying Applicable Ship Resistance Prediction Method
Mathematical Derivation
Calculation Program
Data Gathering/ Data Analysis
Figure 3.1: Flowchart of the research methodology
Based on the sequence of flow of the research methodology, it can be summarized that several main activities will be carried out in ensuring objectives and outcomes of this study are successfully achieved. The main activities are: i.
Identifying the applicable and suitable ship resistance prediction method
ii.
Familiarizing and specifying the lateral drift condition
iii.
Derivation of ship resistance prediction formula with the effect of high speed current and/ or wind
40
iv.
Computer Programming Development
All these summarized activities are explained in detail separately in the next Chapters.
In deriving the ship resistance prediction method by taking the lateral drift effects into account, there have two main methodologies that will be used, which are specified as Case 1 and Case 2. The methodologies applied are as follows;
i. Case 1; Effects of Ship Speed •
In this case, the assumption made is the drift effect due to drift angle considerably only has an effect on the ship velocity, VS.
•
Due to that, the ship velocity, VS is broke down into two separate components
which
are
longitudinal
component,
namely
as
longitudinal ship velocity, VS(L) and lateral component, known as lateral ship velocity, VS(T).
•
The detail discussion about Case 1 is explained in the next Chapters, which in Chapter IV and Chapter V.
ii. Case 2; Effects of Ship Speed, Length and Breadth •
In this case, the assumption made is drift effect due to drift angle considerably only has the effect on ship velocity, VS, length, L and breadth, B of the ship.
•
Similarly to the Case 1, the ship velocity, VS is broke down into separate components which are longitudinal component, namely as longitudinal ship velocity, VS(L) and lateral component, known as lateral ship velocity, VS(T).
41
•
The ship length, L and breath, B values basically are inverted in lateral component. The explanation for the Case 2 can be referred to the Figure 3.2.
Longitudinal velocity, VS (L)
L
Lateral velocity, VS(T)
B
B
L
Figure 3.2: Definition of length, L and breadth, B in lateral direction for a laterally drifting ship
Referring to the Figure 3.2, in longitudinal direction, the value of ship length and breadth certainly similar to the original ship coordination. This is because the direction of longitudinal velocity is the same as ship direction without lateral drift effect. In lateral direction, if we consider the direction of lateral speed, then the ship length becomes a ship breadth while the ship breadth becomes a ship length. The different of speed direction cause the changing values between ship length and breadth.
In Case 2, the main problem is due to the unsymmetrical of ship form, which possibly will bring the assumption and results slightly difference. However, for comparison purpose with the result in Case 1, the result for Case 2 will be analyzed as well. Both detail discussion about the results and analysis will be presented in the Chapter VI later.
CHAPTER IV
LATERAL DRIFT EFFECT
4.1
Introduction
In practical, when ship travels in real nature, there have several elements of nature which considerably cannot be neglected and will influence its operation. These environment elements which acting on the operated ship could contribute to the drift effect, which certainly will influence the ship performance. Before discussing further about the definition of the lateral drift effect, as well as its detail, it is certainly to overview first about the possible causes of lateral drift effect. These causes are essential to be identified in comprehending entirely the lateral drift effect.
4.2
Lateral Drift Factors
When dealing with real nature operation, there are several major factors or sources which can possibly cause a drift effect, depending on the situation. In general, lateral drift effect can be caused by individually or combination of action of following factors;
44 i.
Waves
ii.
Current
iii.
Wind
However, as far as the main scope is concerned (as outlined earlier) the concentration is given for the case of operated ship in calm water. Due to that, in this study the effect of lateral drift due to waves is excluded. Due to this, it considerably can be said this lateral drift effect is caused by combination these following factors;
4.2.1
i.
Current and/ or
ii.
Wind
Current
Current, in general is defined in two separate types, namely ocean current, and tidal current. Firstly, ocean current basically is continuous and generated by the forces acting upon the water, such as the earth rotation, wind, temperature and salinity differences. Current in the upper layers of the ocean or surface current are mainly generated by the atmospheric wind system over the sea surface. Surface current generally restricted to the upper 400 meters of the ocean.
The ocean current is also generated by the heat exchange at the sea surface together with the salinity changes, which preferably referred as thermohaline current or deep ocean current. These currents, which flow under the surface of the ocean and are thus hidden from immediate detection also called as submarine rivers.
Secondly, the other types of current, called tidal current basically is caused by the gravitational pull of the moon and the sun. This type of current preferably can be
45
seen at river, especially river mouth. In coastal region, this tidal current is obtained has a high speed current. In fact, speed between 2 to 3 knots or more certainly can be measured. Specifically referring to this research scopes, this type of current as well as the area will be mainly focused for this study.
4.2.2
Wind
A ship sailing on a smooth sea and in still air experiences air resistance but this is usually negligible and it may become appreciable only if wind is appear. Although the wind speed and direction are never constant, a constant speed and direction are usually assumed. The main influence of the wind is through the waves it generates on the surface of the sea. The effect of waves it generates depends on it velocity, the time it acts and the distance over which it acts
The strength of wind is classified by the Beaufort Scale. This scale numbers of 0 to 12 were introduced was introduced in 1806. Scale 0 referring to a calm water and scale 12 to a wind of hurricane force. There were no specific winds speeds related with these numbers but the values have now been adopted internationally. The values of the scale are shown in Table 3.1.
46 Table 3.1: Beaufort Scale (Edward, 1988).
Number
4.3
Description
Limits of Speed Knots
m/s
0
Calm
0-1
0-0.3
1
Light air
1-3
0.3-1.5
2
Light breeze
4-6
1.6-3.3
3
Gentle breeze
7-10
3.4-5.4
4
Moderate breeze
11-16
5.5-7.9
5
Fresh breeze
17-21
8.0-10.7
6
Strong breeze
22-27
10.8-13.8
7
Near gale
28-33
13.9-17.1
8
Gale
34-40
17.2-20.7
9
Strong gale
41-47
20.8-24.4
10
Storm
48-55
24.5-28.4
11
Violent storm
56-63
28.5-32.6
12
Hurricane
64- and over
32.7 and over
Definition of Lateral Drift Effect
First of all, when discussing about the lateral drift effect onto the ship, we need to clarify the definition as well as the coordination of the traveling ship with lateral drift effect. The basic feature of traveling ship with lateral drift effect are shown in Figure 4.1.
47
A
Wind and/ or current
B Vs(L
Vs(T
β
Vs
O
Figure 4.1: Typical Nature of Lateral Drift Effect Due to Wind and/ or Current on Traveling Ship
In general, the condition of ship travels from point O to A represents as an intended course with speed, VS, which traveling completely in longitudinal direction. At this condition, which no lateral drift effect, speed longitudinally, VS (L) is similar to the ship’s speed, VS. This course represents the condition of traveled ship without effect of lateral drift (ideal travel). The other condition (real sea) can be referred to the ship which travels from point O to point B. It represents the condition where the ship experiences the effect of lateral drift with angle β due to some reasons. It is known as an actual course and the traveled ship is drifted with the ship speed, VS becomes the average speed. This condition was happened due to the lateral drift force acting on the ship which produced lateral speed, VS (T). Another component of speed produced due to the drifting effect is longitudinal speed, VS
(L).
As initial
finding, these components of speed basically leads as part of the elements/ factors that will be investigated further in the next phase in correlating the effect of lateral drift in ship resistance prediction. This effect is found has not been studied in detail previously, particularly in ship resistance prediction. For the early stage of study, concentration is put in considering this effect in prediction method of ship resistance in calm water condition.
4.4
48 Lateral Drift Effect in Specified Case
Concerning the investigation in calm water condition, the lateral drift effect mainly is specified caused by the wind action. The action of wind naturally affects the traveled ship and produced the drift angle. It produces a range of drift angles, which represented by the β sign However, must be borne in mind that this action of wind is not able to give the extreme effect of drift onto the ship. The effect of drift (drift angle) is considerably small and has the limitation. Full scale measurement of a ship drift angle using GPS shows that the magnitude is about 10 degrees even though the wind speed is not so strong (Tanaka, 2003). In this case, the maximum drift angle, β is taken up to 10 deg. Apart of the wind factor, as far as the main research scopes and objectives are concerned, the lateral drift effect in this study is specified in the case of severe lateral drift effect. In detailing more about this severe lateral drift study, particularly onto ship resistance performance this drift effect which is caused by wind is considered incorporating with the other element, which is due to the high speed current.
This current is a tidal current and is said brought a severe case onto the lateral drift effect due to the existing of the high current velocity, VC. This current velocity, is known sometimes produces relatively higher speed at certain time and angle of directions, and could give significant effect onto ship resistance performance. Due to that, as mentioned earlier, the specific case of river mouth area is concerned. The river mouth is focused, since it is one of the sources which could provide significant current effect and consequently could cause more severe effect of lateral drift. Moreover, severe effect of current particularly can be considered during low and high tides, due to its flow and velocity at this period. During ebb and flood at typical river mouth region, the velocity of the current is measured can be up to 4 knots (2.058 m/s), depending on the situation and place. Depending on the direction and coordination of both current action and ship’s travel, a significant lateral drift effect might be happened and the overview of this severe lateral drift situation is simulated and shown in Figure 4.2.
49
50
Besides she is experienced by the drift effect due to wind, in severe case, the drift effect also is incorporated with the current acting in various direction angles. This current direction angle is represented by α and at certain α, it might contribute the significant drift effect in ship resistance performance. .
4.5
Direction of Drift Factors
In reviewing the condition of lateral drift effect in severe case as visualized in Figure 4.2, especially due to current factor, it can be observed that there are various possibilities of acting direction. In this severe case, the drifted ship due to wind (with a small drift angle, β) is experienced by the various direction of current as well, possibly ranging from α= 0o up to 360o. To investigate more specific these various direction angles, which is due to current, new terms of direction is created and it can summarized in several main cases below
i.
Heading current; when current experienced at 0o or 360o direction
ii.
Beam current (starboard); when current experienced at 90o direction
iii.
Following current; when current experienced at 180o direction
iv.
Beam current (port); when current experienced at 270o direction
These cases also are illustrated in Figure 4.3
51 Heading current
Vc
Vs Beam current (Stbd)
Beam current (Port)
β
Longitudinal axis, x
Lateral axis, y Following current
Figure 4.3: Schematic Diagram of Current Direction (for severe case) in Several Main Cases
Figure 4.3 was illustrated the condition of severe case of drift effect where the drifted ship at drift angle, β is then together experienced with the current action. This particular condition, which is due to the combination of two drift components considerably called as severe case of drift effect. In addition, it is specifically investigated in several main cases, namely as following current, beam current (either port or starboard) and following current.
In general, heading and following current, does not have effect of drift because the current experiences in same direction of ship axis (longitudinally). In these cases, however the effect of lateral drift is significantly can be seen at the total ship resistance produced. The traveled ship at these cases possibly produced extra of
52
less total resistance, and this will be discussed in detail in the next chapter. On the other hands, in the case of beam current (port or starboard), it illustrated that the current experiences entirely in lateral direction. The effect of severe lateral drift possibly might occur significantly in the beam current case. This will be discussed more detail as well later.
From one point of view, it is concerned that this effect can be taking into account and correlated with the study of ship performance, specifically in this particular case, ship resistance. It possibly can allocate room for element or effect of lateral drift to be considered in ship resistance. It is therefore important to capture the influence of lateral drift and investigate in ship resistance. More detail about this investigation will be discussed in next chapter.
47
Current direction angle, α Current
α
Vc
y
Up to 360o current direction angle
x
Vs(T)
y
Vs
Wind effect
Vs(L) x
Figure 4.2: Schematic Diagram of Drift Effect in Severe Case (due to Current and Wind) Specifically at River Mouth Area
CHAPTER V
MATHEMATICAL DERIVATIONS
5.1
Introduction
As discussed in the earlier chapter of this ship resistance study, which incorporate with the effect of lateral drift due to wind and/ or current (for severe case) as the main mission, an initial investigation will be concentrated first. As the early phase, the study about this ship resistance by taking the lateral drift effect is developed by approximate resistance prediction method. At this stage, method approached by Holtrop and Mennen is selected due to wider range of types, sizes and limitation of ships/ vessels can be applied.
5.2
Holtop’s and Mennen’s Derivation
As far as ship resistance prediction is concerned, the original ship resistance prediction formula which was developed by Holtrop and Mennen (1982) is used as the main reference and guidance.
54 RTotal = RF(1+k) + RAPP + RW + RB + RTR + RA
(5.1)
Where;
RF
: frictional resistance according to the ITTC 1957 friction formula
(1+k) : form factor describing the viscous resistance of the hull form in relation to RF RAPP
: resistance of appendages
RW
: wave- making and wave- breaking resistance
RB
: additional pressure resistance of bulbous bow near the water surface
RTR
: additional pressure resistance of immersed transom stern
RA
: model- ship correction resistance
Base on this mathematical formulation, together with the literatures, the effect of lateral drift in the ship resistance prediction using the method is investigated and developed. In deriving the ship resistance prediction with lateral drift effects formula, it is determined that the element/ parameter of ship’ velocity, VS principally is the main point of concerned. It is viewed that due to the severe lateral drift which is caused by the wind and/ or current, the vector of the ship’s velocity is modified, depending on the drift angle produced, β. As a result, there exists components of velocity, which represented by the longitudinal velocity, VS (L) and lateral velocity, VS (T).
The drift angle, β presents due to the effect of drift, and it will be the main
variables in influencing the velocity’s components. With the presence of lateral drift effect, it will modify the parameter of ship velocity (into longitudinal and lateral component) in the Holtrop’s and Mennen’s, and consequently, the related equations with the velocity parameter will be modified as well.
Modifying the existing formulae of the selected ship resistance prediction method, the ship’s velocity, VS parameter (due to the action of drift angle, β) started with the Frictional Resistance, RF. The Frictional Resistance, RF is broke down into
55
longitudinal component, RF (L) and lateral component, RF (T). With the same concept of frictional resistance determination, the ITTC 1957 is applied in determining the Frictional Resistance longitudinally and laterally. Table 5.1: Frictional Resistance Component due to Drift Angle, β R F = 0.5 ρV 2 S C F
CF =
0.075 (log Rn − 2) 2
Rn =
VL
ν
Longitudinal Component R F ( L ) = 0.5 ρ (VS cos β ) 2 S C F
CF = Rn =
0.075 (log Rn − 2) 2 (VS cos β ) L
ν
Lateral Component R F (T ) = 0.5 ρ (VS sin β ) 2 S C F
CF = Rn =
0.075 (log Rn − 2) 2 (VS sin β ) L
ν
Besides the effect of lateral drift (drift angle, β) due to wind, when concerning the case of severe effect, there has another element that need to be considered. The significant lateral drift effect (severe case) which is caused by current is to be highlighted as well. This current element is said gave a severe case in lateral drift due to its velocity which acts onto the moving ship. As a result, a part of Frictional Resistance, RF due to ship velocity, VS, it is identified that there has additional frictional resistance interacts with the ship’s hull which is due to the velocity of current, VC. It is known as Frictional Resistance due to current velocity, RF(C). The value will be taken into account and combined with the existing Frictional Resistance due to ship’s velocity, RF(S). The additional resistance which due to the current is said only affects at this frictional resistance component since at the other components of resistance, namely appendages resistance (RAPP), wave- making resistance (RW), bulbous bow resistance (RB), immersed transom resistance (RTR) and model- ship correlation resistance (RA) the effect is not so significant. It is found that
56
the values produced by these components of resistance are very small and considerably neglected.
Frictional Resistance due to current, RF(C), mainly is determined depending on the current velocity, VC, as well as the current direction angle. In this study, current direction angle is the direction of the current (with its velocity) acting on the moving ship and it is represented by α. The various values of current direction angle, α will break down the current velocity components into longitudinal current velocity, VC (L) and lateral current velocity, VC (T). Thus, it also will give the various effect of lateral drift (severe) with different current direction angle. Similarly applying the ITTC 1957 of frictional coefficient, the additional frictional resistance RF(C), which is due to the current velocity (longitudinally and laterally) is considered and determined as followed.
Table 5.2: Frictional Resistance Component due to Current Direction angle,α (In severe case) R F = 0.5ρVC 2 S C F
CF =
0.075 (log Rn − 2) 2
Rn =
VC L
ν
Longitudinal Component
RFC ( L ) = 0.5ρ VC cos α
CF =
0.075 (log Rn − 2) 2
Rn C ( L ) =
VC cos α L
ν
2
S CF
Lateral Component
RFC ( L ) = 0.5ρ VC sin α CF =
2
0.075 (log Rn − 2) 2
Rn C ( L ) =
VC sin α L
ν
S CF
57 By referring to the main reference of ship resistance prediction method, the
other component of resistance which will be influenced by the modified ship’s velocity is the wave making and wave breaking resistance, RW. In RW calculation, the component of ship’s velocity mainly influences the Froude’s number, Fn parameter and also coefficient of m2 as shown below.
Table 5.3: Wave Making Resistance Component due to Drift Angle, β
{
(
RW = c1c 2 c5 ∇ρg exp m1 Fnd + m2 cos λFn−2 Longitudinal Component Fn ( L ) =
(VS cos β ) L
Lateral Component Fn (T ) =
ν
)}
(VS sin β ) L
ν
m2 = c15 C P2 exp(−0.1Fn−2 ) Longitudinal Component
Fn ( L ) =
(VS cos β ) L
Lateral Component
Fn (T ) =
ν
(VS sin β ) L
ν
The other component of resistance prediction which is modified due to the ship’s velocity parameter is called additional pressure resistance of bulbous bow near the water surface, or indicated as RB. In this component of resistance, it is affecting the parameter of Fni and the modified equation related as followed; Table 5.4: Bulbous Bow Resistance Component due to Drift Angle, β 1.5 RB = 0.11exp(−3PB−2 ) Fni3 ABT ρg /(1 + Fni2 )
Fni = V /[ g (TF − hB − 0.2 ABT ) + 0.15V 2 ]1 2
Longitudinal Component
Lateral Component
Fni ( L ) = (V S cos β ) /[ g (TF − hB
Fni (T ) = (V S sin β ) /[ g (TF − hB −
− 0.2 ABT ) + 0.15(V S cos β ) 2 ]1 2
0.2 ABT ) + 0.15(V S sin β ) 2 ]1 2
58
Same goes to the resistance component due to the additional pressure resistance of immersed transom stern, RTR. The additional resistance due to the immersed transom part is modified due to the modified c6 coefficient, which is influenced by the FnT as described below. Table 5.5: Immersed Transom Resistance Component due to Drift Angle, β
RTR = 0.5ρV 2 AT c6 when FnT<5 c6 = 0.2(1 − 0.2 FnT )
when FnT≥5 c6 =0
Longitudinal Component FnT = (V cos β ) /[ 2 gAT /( B + BCWP )]1 2
Lateral Component FnT = (V sin β ) /[2 gAT /( B + BCWP )]1 2
The ship’s velocity also one of the parameters in predicting the model-ship correlation resistance, known as RA. Due to that, it also modifies the model-ship correction resistance, RA as stated below;
Table 5.6: Model Correlation Resistance Component due to Drift Angle, β R A = 0.5 ρV 2 SC A
Longitudinal Component R A( L ) = 0.5 ρ (V S cos β ) 2 SC A
Lateral Component R A (T ) = 0.5 ρ (V S sin β ) 2 SC A
By taking into account and modifying all the related resistance components, coefficients and functions which influenced by the ship’s velocity due to drift angle, β, and the additional frictional resistance due to acting current velocity, RF(C) at various angle, α, the problem of ship resistance prediction with lateral drift effect can be solved. There are slightly differences with the original procedure, which due to the presence of ship’s and current velocity component (longitudinal and lateral). The
59
prediction of ship resistance using the proposed prediction formula can be performed by solving it separately; longitudinally and laterally. Applying the original Holtrop’s and Mennen’s prediction approach as the guideline, it is explored by considering the lateral drift effect due to wind and severe current. Both of these effects (small drift angle due to wind and severe drift angle due to current) are calculated separately at each component (longitudinal and lateral). The modified procedure in determining the total ship resistance, RTotal are written as follows: RTotal (longitudinally) = RF (L)’ (1+k) + RAPP + RW + RB + RTR + RA RF (L)’= RFS (longitudinal) + RFC (longitudinal)
Where
RTotal (lateral) = RF (T)’ (1+k) + RAPP + RW + RB + RTR + RA RF (T) ‘= RFS (lateral) + RFC (lateral)
Where
RFS
= Frictional Resistance due to ship’s velocity, VS
RFC
= Frictional Resistance due to current’s velocity, VC
(5.2)
(5.3)
(5.4)
(5.5)
The results of each component are combined in view of trigonometric relationship to obtain the Total Ship Resistance, RTOTAL with severe drift effects (at various angles). The proposed trigonometric relation for this Total Ship Resistance, RTOTAL is written as follows:
RTOTAL=
( RTotal ( longitudinally ) 2 + ( RTotal ( laterally ) ) 2
(5.6)
CHAPTER VI
COMPUTER PROGRAMMING
6.1
Introduction
At this stage, a calculation programming are essentials due to the complication of the calculation itself. Therefore, calculation template using Microsoft Excel and FORTRAN were developed. The results from both calculation tools will be used for comparison and verification purpose and to further confirm the correctness of the proposed ship resistance prediciton method.
6.2
Computer Programming Verification
The developed calculation program (FORTRAN) certainly requires to be verified in order to ensure its validity. The verification of this developed programming is started upon the source code is written. Stage by stage each of the derived equation is verified by running the program and comparing the output result with the result calculated by the Microsoft Excel. Must be borne in mind that in performing these two mode of calculation, some data is required. In this study, those
61 data are taken similarly with example data provided by Holtrop’s example calculation (Holtrop J.and Mennen G. G. J.,1982).
6.3
Program Flow Chart
Upon development of this program, the flow chart is produced in visualizing the flow of this calculation program. The flowchart is available in Appendix A.
6.4
Input and Output Data
As an input, the data in this program is divided into two categories, namely user input data and data’s set in the programming.
6.4.1
User Input Data
For this particular calculation program, in executing the problem of ship resistance with lateral drift effect, incorporating the severe case, it requires ship velocity, VS and current velocity, VC as user input data. These two data are defined as user input data since they will be the main variables in determining total ship resistance with lateral drift effect, especially in severe case (due to current).
62 6.4.2
Data in the Programming
This type of data is required and initially is set in the programming. Means, these data is a fixed and can only be modified or changed by changing the source code. In performing this particular calculation, main particulars of any proven ships, are needed, as long as it is within the scopes and limitations of the Holtrop’s and Mennen’s criteria range. In this case, main particulars data of container ship type is used, since it is provided by Holtrop’s and Mennen’s example calculation (as mentioned previously). Apart of the main ship particulars, the main hydrostatics data of corresponding ship also is required to complete the calculation. Other than that, properties of water, as a medium for the ship to operate also are necessary data to be set for the calculation program. The list of data which is set initially in the program are shown in the Table 6.1.
Table 6.1: List of data’s set in the programming (Holtrop, J. and Mennen, G. G. J.). MAIN PARTICULARS Length of Waterline, LWL 205.000 Breadth Moulded, B 32.000 Draught Moulded, T 10.000 Volume displacement, Ñ 37500 Wetted surface Area, S 7381.45 Wetted Surface Area of Appendages, SAPP 50 Prismatic Coeff., CP 0.5833 Midship Area Coeff., CM 0.98 Block Coefficient, CB 0.586 Waterplane. Area Coeff., 0.75 CWP LCB from zero pt. (+ve fwd) -0.75 Transverse sectional area of bulb, ABT 20 1/2 angle of entrance, iE 12.080 Transverse area of immersed transom, AT 16 Centre of bulb area above keel line, hB 4 Stern shape coefficient, CStern
10.0
Density of salt water, ρSW
1.026
UNIT m m m m3 m2 m2
m m2 degree m2 m tonne/m3
63
6.4.3
Viscosity of salt water, νSW
1.19-06
m2/s
Gravity Acceleration, g
9.81
m/s2
Drift Angle, β
0-10
deg
Current Direction Angle, α
0-360
deg
Output Data
The output data from this computer programming are listed as follows:
1) Parameters, Coefficients, Functions and Sub- components of Total Resistance • Longitudinal Ship Velocity, Vs(L) and Lateral Ship Velocity, Vs(T) • Longitudinal Current Velocity, Vc(L) and Lateral Current Velocity, Vc(T) • Length of run, Lr • Coefficient of C1, C2, C3, C4, C5, C6(L), C6(T), C7, C12, C13, C15, C16, PB and CA • Wetted Surface Area, S • Reynold Number (longitudinal), Rn(L) and (lateral), Rn(T) • Frictional Resistance Coefficient, CF, (longitudinal), CF(L) and (lateral), CF(T) • Froude’s Number, (Fn), (longitudinal), Fn(L) and (lateral), Fn(T) • Lambda, λ • Coefficient of m1, m2, m2(L) and m2(T) • Immersion Froude’s Number, Fni, (longitudinal), Fni(L) and (lateral), Fni(T) • Transom Froude’s Number, Fnt, (longitudinal), Fnt(L) and (lateral), Fnt(T)
64 2) Total Resistance Components •
Form factor, (1+k)
•
Frictional Resistance, RF, (longitudinal), RF(L) and (lateral), RF(T)
•
Frictional Resistance (due to current), RFC, (longitudinal), RFC(L) and (lateral), RFC(T)
•
Appendages Resistance, RAPP, (longitudinal), RAPP(L) and (lateral), RAPP(T)
•
Wave- making Resistance, RW, (longitudinal), RW(L) and (lateral), RW(T)
•
Bulbous Bow Resistance, RB, (longitudinal), RB(L) and (lateral), RB(T)
•
Immersed Transom Resistance, RTR, (longitudinal), RTR(L) and (lateral), RTR(T)
•
Model- Ship Correlation Resistance, RA, (longitudinal), RA(L) and (lateral), RA(T)
•
Resultant Frictional Resistance, RF(Total)
•
Resultant Appendages Resistance, RAPP(Total)
•
Resultant Wave- making Resistance, RW(Total)
•
Resultant Bulbous Bow Resistance, RB (Total)
•
Resultant Immersed Transom Resistance, RTR (Total)
•
Resultant Model- Ship Correlation Resistance, RA (Total)
3) Final Results •
Total Resistance with Severe Drift Case
CHAPTER VII
RESULTS AND DISCUSSION
7.1.
Introduction
Based on the proposed ship resistance prediction formulae that were discussed in previous chapter and the calculation tools which is based on Microsoft Excel and FORTRAN, the output results are calculated and analyzed. In this chapter, it presents and discusses in more detail and wider about the results obtained. Data of related results are presented effectively in tables and several necessary graphs are produced to illustrated clearly about the results and related analysis. In this study, the analysis and discussion also remarks about two case of study as highlighted earlier.
7.2.
CASE 1: Severe Drift Effect on the Total Ship Resistance, RTOTAL
As discussed in the earlier chapter, it clearly highlighted that the assumption of this lateral drift with severe effect are due to two separate elements, wind and current (maintaining the calm water condition). First effect of lateral drift which
66
caused by wind is considerably limited up to 10 degrees drift angle, β, assuming relatively wind effect is small comparing to the forward speed of the ship. However, as severe lateral drift effect is concerned, it is incorporated with the current cause. This current is said could give a severe drift effect due to the current velocity (as set earlier) acts on the moving ship, which considerably gives more severe lateral drift effect. In measuring wider about this lateral drift effect, the current velocity acting on the moving ship, especially at river mouth area is varied in term of direction angle. The current direction angle (with fixed velocity) is represented by α and varies from 0o (also known as heading current) up to 360o, with 10o intervals.
As results, it can be summarized that this lateral drift investigation on the ship resistance is influenced by two types of variables with fixed values of current velocity, VC. Consideration is given on the variables from range of drift angles, β, as well as range of current direction angles, α. The calculated result of the lateral drift effect on the ship total resistance, RTOTAL is shown in Table 7.1. According to this result, the total ship resistance is calculated at various drift angles incorporating with the various current direction angles. The ship’s velocity, VS is set at 25 knots (service speed) and current velocity, VC is assumed 4 knots (considerably the typical maximum value). The mathematical calculation for this total ship resistance, RTOTAL is executed by solving the proposed ship resistance prediction formulae separately into two components of total ship resistance, namely longitudinally (RT(longitudinal)) and laterally (RT(lateral)). Both values are then combined by applying the trigonometric solution as described in previous chapter. These results are plotted and visualized in Figure 7.1
67
Table 7.1: CASE 1: Result of Ship Total Resistance with Lateral Drift Effect at Various Drift and Current Direction Angles Drift angle, β(deg) 2
0
4
Current direction angle, α (deg)
RTOTAL(L)
RTOTAL(T)
R (TOTAL)
RTOTAL(L)
RTOTAL(T)
R (TOTAL)
RTOTAL(L)
RTOTAL(T)
R (TOTAL)
0
1824.859
0.000
1824.859
1822.333
2.510
1822.334
1814.751
9.250
1814.774
10
1823.946
1.081
1823.946
1821.420
3.760
1821.424
1813.838
10.499
1813.868
20
1821.308
3.797
1821.311
1818.781
6.900
1818.794
1811.199
13.640
1811.251
30
1817.232
7.692
1817.248
1814.706
11.404
1814.742
1807.124
18.144
1807.215
40
1812.168
12.279
1812.209
1809.642
16.710
1809.719
1802.060
23.449
1802.212
50
1806.675
17.029
1806.755
1804.149
22.203
1804.285
1796.567
28.942
1796.800
60
1801.370
21.408
1801.497
1798.844
27.266
1799.051
1791.262
34.006
1791.585
70
1796.867
24.931
1797.040
1794.341
31.340
1794.615
1786.759
38.080
1787.165
80
1793.728
27.211
1793.935
1791.202
33.977
1791.524
1783.620
40.716
1784.085
90
1792.481
27.998
1792.700
1789.955
34.887
1790.295
1782.373
41.627
1782.859
100
1791.229
27.207
1791.436
1788.703
33.972
1789.025
1781.121
40.712
1781.586
110
1788.086
24.924
1788.260
1785.560
31.332
1785.835
1777.978
38.072
1778.386
120
1783.581
21.399
1783.709
1781.055
27.255
1781.263
1773.473
33.995
1773.799
130
1778.275
17.018
1778.357
1775.749
22.190
1775.888
1768.167
28.930
1768.404
140
1772.782
12.268
1772.825
1770.256
16.697
1770.335
1762.674
23.437
1762.830
150
1767.720
7.681
1767.736
1765.194
11.393
1765.230
1757.612
18.132
1757.705
160
1763.647
3.789
1763.651
1761.121
6.891
1761.135
1753.539
13.631
1753.592
170
1761.013
1.076
1761.013
1758.486
3.754
1758.490
1750.904
10.494
1750.936
180
1760.104
0.000
1760.104
1757.578
2.510
1757.580
1749.996
9.250
1750.020
190
1761.021
1.085
1761.021
1758.495
1.255
1758.495
1750.913
7.995
1750.931
200
1763.663
3.805
1763.667
1761.137
-1.890
1761.138
1753.555
4.850
1753.562
210
1767.741
7.702
1767.758
1765.215
-6.396
1765.227
1757.633
0.343
1757.633
220
1772.807
12.290
1772.850
1770.281
-11.703
1770.320
1762.699
-4.963
1762.706
230
1778.301
17.040
1778.382
1775.775
-17.195
1775.858
1768.193
-10.456
1768.224
240
1783.604
21.417
1783.733
1781.078
-22.257
1781.217
1773.496
-15.518
1773.564
250
1788.105
24.938
1788.278
1785.578
-26.328
1785.773
1777.996
-19.589
1778.104
260
1791.240
27.214
1791.446
1788.714
-28.961
1788.948
1781.132
-22.221
1781.270
270
1792.481
27.998
1792.700
1789.955
-29.867
1790.204
1782.373
-23.128
1782.523
280
1793.739
27.204
1793.945
1791.213
-28.948
1791.447
1783.631
-22.209
1783.769
290
1796.885
24.917
1797.058
1794.359
-26.304
1794.552
1786.777
-19.565
1786.884
300
1801.393
21.389
1801.520
1798.867
-22.225
1799.005
1791.285
-15.485
1791.352
310
1806.700
17.007
1806.780
1804.174
-17.158
1804.256
1796.592
-10.418
1796.622
320
1812.193
12.257
1812.234
1809.667
-11.664
1809.704
1802.085
-4.924
1802.091
330
1817.254
7.671
1817.270
1814.728
-6.361
1814.739
1807.146
0.378
1807.146
340
1821.323
3.781
1821.327
1818.797
-1.862
1818.798
1811.215
4.877
1811.222
350
1823.954
1.071
1823.955
1821.428
1.271
1821.429
1813.846
8.011
1813.864
360
1824.859
0.000
1824.859
1822.333
2.510
1822.334
1814.751
9.250
1814.774
68
Drift angle, β(deg) 8
6
10
Current direction angle, α (deg)
RTOTAL(L)
RTOTAL(T)
R (TOTAL)
RTOTAL(L)
RTOTAL(T)
R (TOTAL)
RTOTAL(L)
RTOTAL(T)
R (TOTAL)
0
1802.097
19.808
1802.206
1784.332
33.924
1784.655
1761.371
51.370
1762.120
10
1801.184
21.058
1801.307
1783.419
35.173
1783.766
1760.459
52.620
1761.245
20
1798.546
24.198
1798.709
1780.781
38.314
1781.193
1757.820
55.760
1758.704
30
1794.471
28.702
1794.700
1776.706
42.818
1777.222
1753.745
60.264
1754.780
40
1789.406
34.008
1789.729
1771.641
48.123
1772.295
1748.680
65.570
1749.909
50
1783.913
39.501
1784.350
1766.148
53.616
1766.962
1743.187
71.062
1744.635
60
1778.608
44.564
1779.167
1760.843
58.680
1761.821
1737.883
76.126
1739.549
70
1774.106
48.638
1774.772
1756.341
62.754
1757.461
1733.380
80.200
1735.234
80
1770.967
51.275
1771.709
1753.202
65.390
1754.421
1730.241
82.837
1732.223
90
1769.720
52.185
1770.489
1751.955
66.301
1753.209
1728.994
83.747
1731.021
100
1768.467
51.270
1769.210
1750.702
65.386
1751.923
1727.742
82.832
1729.726
110
1765.325
48.630
1765.994
1747.560
62.746
1748.686
1724.599
80.192
1726.462
120
1760.819
44.553
1761.383
1743.054
58.669
1744.042
1720.094
76.115
1721.777
130
1755.514
39.488
1755.958
1737.749
53.604
1738.575
1714.788
71.050
1716.259
140
1750.021
33.995
1750.351
1732.256
48.110
1732.924
1709.295
65.557
1710.552
150
1744.958
28.691
1745.194
1727.193
42.806
1727.723
1704.232
60.253
1705.297
160
1740.886
24.189
1741.054
1723.121
38.305
1723.546
1700.160
55.751
1701.074
170
1738.251
21.052
1738.378
1720.486
35.168
1720.845
1697.525
52.614
1698.340
180
1737.342
19.808
1737.455
1719.577
33.924
1719.912
1696.617
51.370
1697.394
190
1738.259
18.553
1738.358
1720.494
32.668
1720.805
1697.534
50.115
1698.273
200
1740.902
15.408
1740.970
1723.137
29.524
1723.390
1700.176
46.970
1700.824
210
1744.980
10.902
1745.014
1727.215
25.017
1727.396
1704.254
42.464
1704.783
220
1750.046
5.595
1750.055
1732.281
19.711
1732.393
1709.320
37.157
1709.724
230
1755.539
0.103
1755.539
1737.774
14.218
1737.832
1714.813
31.665
1715.106
240
1760.843
-4.959
1760.850
1743.078
9.156
1743.102
1720.117
26.603
1720.323
250
1765.343
-9.030
1765.366
1747.578
5.085
1747.585
1724.617
22.532
1724.764
260
1768.478
-11.663
1768.517
1750.713
2.453
1750.715
1727.752
19.899
1727.867
270
1769.720
-12.569
1769.764
1751.955
1.546
1751.955
1728.994
18.993
1729.098
280
1770.977
-11.650
1771.016
1753.213
2.465
1753.214
1730.252
19.912
1730.366
290
1774.124
-9.006
1774.147
1756.359
5.109
1756.366
1733.398
22.556
1733.545
300
1778.632
-4.927
1778.639
1760.867
9.189
1760.891
1737.906
26.635
1738.110
310
1783.939
0.140
1783.939
1766.174
14.256
1766.231
1743.213
31.702
1743.501
320
1789.431
5.634
1789.440
1771.666
19.749
1771.776
1748.705
37.196
1749.101
330
1794.492
10.937
1794.526
1776.727
25.052
1776.904
1753.766
42.499
1754.281
340
1798.562
15.436
1798.628
1780.797
29.551
1781.042
1757.836
46.998
1758.464
350
1801.193
18.569
1801.289
1783.428
32.684
1783.727
1760.467
50.131
1761.181
360
1802.097
19.808
1802.206
1784.332
33.923
1784.655
1761.371
51.370
1762.120
69
1850
Total Resistance,R
TOTAL
(kN)
1800
1750
1700 R(t) with 0 deg drift R(t) with 2 deg drift
1650
R(t) with 4 deg drift R(t) with 6 deg drift
1600
R(t) with 8 deg drift 1550
R(t) with 10 deg drift
1500 0
20
40
60
80
100 120 140 160 180 200 220 240 260 280 300 320 340 360
Current Angle, a (deg)
Figure 7.1: CASE 1: Result of Total Ship Resistance with Lateral Drift Effect at Various Drift and Current Direction Angles
Referring to the calculated and analyzed result in Table 7.1 and Figure 7.1, it is showed that the total ship resistance, RTOTAL incorporating with the effect of lateral drift decreased with increase of drift angle, β. However, the values of total ship resistance incorporating with severe drift effect showed decrease trend with the increase of current direction angle until α = 180o. After 180o, total resistance starts to increase until current direction angle, α= 360o. From β=0o to 10o and from α=0o to 180o shows that the values of total ship resistance linearly decrease. Must be borne in mind that this severe drift effect is caused by combination of two types of sources; due to wind, which produces drift angle, β and due to current, which at its speed of 4 knots (max.) acts at various current direction angle, α.
In discussing more about this effect, we might view the effect of both causes of severe drift effect separately. In other words, first, we possibly discuss the effect of lateral drift due wind which causes drift angle, β.
7.2.1
70 Ship Total Resistance, RTOTAL with the Drift Effect (due to wind)
Appendix B1 shows that the trend of total ship resistance is decrease with the increase of drift angle, β. The total ship resistance determination at this case is made by solving it in separate components; longitudinally and laterally. As a result, total ship resistance is calculated as Longitudinal Total Ship Resistance, RT (L) and Lateral Total Ship Resistance, RT (T) as shown in Table 7.1. From there, as a resultant of total ship resistance, it is combined and solved by applying a trigonometric solution.
As indicated in Table 7.2, the total resistance with lateral drift effect due to drift angle is influenced by component of ship’s velocity parameter, which is ship longitudinal velocity, VS
(L)
and ship lateral velocity, VS
(T).
Due to that, ship
resistance determination is made by breaking down into longitudinal and lateral component as well, where all the component of resistances, coefficients and functions are solved separately in longitudinal and lateral direction (as per discussed in Chapter V). As the result, from the table, it shows that longitudinal total resistance of the ship, RT(L) decrease with the increase of drift angle, β, whereas in lateral component, the trend of total resistance, RT(T) is proportionally increase with the increment of drift angle. It explains that with the increase of drift angle, from β = 0o to 10o, the resistance acting longitudinally becomes less, but the magnitude increases in lateral component point of view.
However, we also find out that although the total ship resistance laterally, RT(T) is proportionally increase, the resultant value of total ship resistance, RTOTAL still decrease with the increase of drift angle (refer to Table 7.2). This is due to the increasing values of total resistance in lateral direction, RT (T), which is relatively small comparing the decreasing values of total resistance in longitudinal component with the increase of drift angle. This trend are looked similarly with other range of ship speed values, as shown in Figure 7.2
71
Table 7.2: Resultant Ship Total Resistance at Speed 25 knots with Various Drift Angles Ship Velocity= 25 knots RTOTAL(L) RTOTAL(T) R (TOTAL) Drift angle, β(deg) (kN) (kN) (kN) 0
1792.48
0.00
1792.48
2
1789.96
2.51
1789.96
4
1782.37
9.25
1782.40
6
1769.72
19.81
1769.83
8
1751.95
33.92
1752.28
10
1728.99
51.37
1729.76
Ship speed,v=5 knots
ship speed,v=10 knots
Ship speed,v=15 knots
Ship speed,v=20 knots
Ship speed,v=25 knots
Ship speed,v=30 knots
Total Resistance, RT (kN)
3500 3000 2500 2000 1500 1000 500 0 0
1
2
3
4
5
6
7
8
9
10
Drift Angle,β (deg)
Figure 7.2: Total Ship Resistance, RTOTAL at Various Ship Speed, Vs with Lateral Drift Angles (due to wind).
7.2.2
72 Ship Total Resistance, RTOTAL with Current Effect
On the other hand, besides drift effect due to wind which produces drift angles, since concerning the severe lateral drift effect at the river mouth, it also is caused by the current acting on the ship. This factor of lateral drift is said to give severe effect to the ship, due to the presence of current velocity itself. The mathematical investigation due to this current speed on the ship resistance is made by approaching the so called a relative solution. With the fixed value of current velocity, VC = 4 knots (approx.), the analysis is made by considering various direction of angles, α. The varying of current direction angles begin at 0o, which also namely as heading current, with 10o of interval up to 180o (following current), then continues until α = 360o (which considerably back to heading current). At these various current direction angles, a wider effect of drift on the ship resistance can be analyzed. For the analysis of total ship resistance with drift effect only caused by current itself, is shown in Appendix B2.
In reviewing the total ship resistance at 25 knots with lateral drift due to 4 knots current from point view of longitudinal and lateral component, it shows that the total ship resistance produced longitudinally, RT(L) decrease with increase of current direction angle until α = 180o. However, the trend then indicates linearly increase from α = 190o until reach up to α = 360o (which considerably back to heading current). There also indicates that the total ship resistance is determined as maximum value at current direction angles, α= 0o or α = 360o with RT (L) is 1824.86 kN. Whilst, the value of total ship resistance laterally, RT (T) at this angle is zero. This situation happened since at α= 0o, the current is said in the position of heading current. Means, the traveled ship at 25 knots is encountered by the current with 4 knots speed completely in longitudinal component and in opposite direction of traveled ship, and there is absence of lateral component at this direction. Relatively, at this condition, ship total resistance is added by the resistance produced due to the heading current at 4 knots and the resistance due to the current is found at highest value at the α= 0o or α = 360o (heading current).
73 As passed with the increment of current angle, the longitudinal component of
total resistance starts decreasing, while in lateral component proportionally increase. This increasing value of lateral component came to the highest point when the current direction angle, α= 90o, also namely as starboard beam current. The lateral total resistance, RT (T) is determined 28 kN at this angle. This due to the magnitude of lateral velocity component at 90o is the maximum magnitude, since there only has the absolute lateral component, without longitudinal current velocity. This condition also occurs in the case of port beam current. The only difference is that the total resistance laterally, RT
(T)
produced is in the opposite direction of the case of
starboard beam current. After current direction angle passing starboard beam current (90o), both total resistance produced longitudinally and laterally decrease till reaching 180o. This trend can be explained that at this range of angle current, the longitudinal resistance is encountered in opposite direction of current, which is the same direction with traveled ship. As a result, it is found that the longitudinal resistance due to current effect is produced in negative values, hence brought the total ship resistance lesser as compared to the total ship resistance produced in normal condition. These negative reading of resistance can be interpreted and converted into the additional force or thrust in moving the ship forward (longitudinally). The traveled ship is gained a merit in term of powering requirement at this range of current angles. The peak of this merit was achieved when the current angle, α at 180o. At this direction (following current) resistance due to this current produced absolutely in longitudinal component, same direction with the traveled ship direction. In other words, it produced the maximum value of additional force/ thrust (negative resistance) for the traveled ship forward. The comprehension of this various condition of current action in effecting lateral drift is shown in Figure 7.3 below.
74
Current velocity, Vc Current direction angle Vc(T)
α
Vc(L) Vc X
Ship velocity, Vs
Y
Up to 360o
Figure 7.3: Schematic Diagram of Lateral Drift Effect Due to Current
7.2.3
Ship Total Resistance, RTOTAL with Lateral Drift Effect Due to Combination of Wind and Current (Severe Case)
In general discussion about total ship resistance produced with the effect of severe drift; these two causes are combined together. The severe lateral drift due to combination of wind (due to drift angle) and current (current direction angle), it can be summarized that the trend is decreased with increase of these angles. In this case, at ship service speed of 25 knots, the maximum value of total ship resistance produced is RTOTAL = 1824.86 kN, at the condition when she is encountered by the heading current (α= 0o or α= 360o) and no drift effect due to wind (β= 0o). Whereas, the lowest value produced is RTOTAL =1697.39 kN when she is drifted by wind at maximum drift angle, β= 10o incorporating with the following current (α= 180o). It is possibly clearer to view the comparison and difference between the total ship resistance calculated using original Holtrop;s and Mennen’s formula (at normal
75
condition), with maximum and minimum total ship resistance produced due to the effect of severe drift (caused by combination of wind and current). The exact values are shown in Table 7.3 Table 7.3: Comparison of differences between total ship resistance produced in normal condition with maximum and minimum total ship resistance produced due to drift effect
Condition at service speed 25 knots
Total ship resistance at normal condition Maximum of total ship resistance produced due to drift effect (caused by combination of wind and current) Minimum of total ship resistance produced due to drift effect (caused by combination of wind and current)
7.3
Total Resistance,
Percentage of
RTOTAL (kN)
difference
1792.48
1824.86
1.81 %(added)
1697.39
5.31 % (reduced)
Analysis the Effect at Other Ship Velocities
Furthermore, in reviewing the total ship resistance with this drift effect, it also can be further reviewed at other ship velocities. Result in Table 7.4 (a), (b), (c) and (d) and graphs in Figure 7.4 (a), (b), (c) and (d) visualized the totals ship resistance calculated at various ship velocities. It is evaluated by taking into account the increase of drift angle (β up to 10o) incorporating with current direction angle. On the whole, the curve of total resistance still follows the ideal trend of total resistance curve, which increases proportionally when the ship velocity increased. However, in relating the total ship resistance with drift angles case, the trend of result at other ship velocities remarkably showed similar with the result discussed earlier, (particularly at VS = 25 knots). The total ship resistance, R (TOTAL) curves produced at velocity 5, 10, 15, 20 and 30 knots individually decreases with the increase of drift angle, β. The
76
results specifically are overviewed in four main cases, which is in heading current (α = 0o), starboard beam current (α = 90o), following current (α = 180o) and port beam current (α = 270o) and most of them, the total ship resistance produced with the effect of drift, are decreased when the drift angle is increased. Table 7.4 (a): Total Ship Resistance Produced Due to Lateral Drift Effect (in Severe Case) at Various Ship Velocity in Heading Current, α = 0o Drift angle, β (deg) 0
2
4
6
8
10
Ship Velocity, Vs (knot) 0 5 10 15 20 25
R (TOTAL) (kN) 0.000 99.27 273.83 546.51 981.20 1824.86
R (TOTAL) (kN) 0.000 99.19 273.57 545.90 979.81 1822.33
R (TOTAL) (kN)) 0.000 98.96 272.76 544.06 975.67 1814.78
R (TOTAL) (kN) 0.000 98.59 271.43 541.05 968.91 1802.21
R (TOTAL) (kN) 0.000 98.07 269.60 536.89 959.70 1784.66
R (TOTAL) (kN) 0.000 97.41 267.30 531.67 948.27 1762.12
30
3025.49
3018.45
2997.52
2963.26
2916.59
2858.74
Total Resistance, R TOTAL (kN)
3500 Drift Drift Drift Drift
3000 2500
angle, angle, angle, angle,
β (deg) 0 β (deg) 2 β (deg) 4 β (deg) 6
Drift angle, β (deg) 8 Drift angle, β (deg) 10
2000 1500 1000 500 0 0
5
10
15
20
25
30
Ship Velocity, Vs (knot)
Figure 7.4 (a): Total Ship Resistance Curve Produced with Drift Effect (in Severe Case) at Various Ship Velocity in Heading Current Case, α = 0o
77 Table 7.4 (b): Total Ship Resistance Produced Due to Lateral Drift Effect (in Severe Case) at Various Ship Velocity in Starboard Beam Current,
α = 90o Drift angle, β (deg) Ship Velocity, Vs (knot) 0 5 10 15 20 25 30
0
2
4
6
8
10
R (TOTAL) (kN) 0.000 66.89 241.45 514.13 948.82 1792.48
R (TOTAL) (kN) 0.000 74.21 243.41 514.10 948.04 1790.29
R (TOTAL) (kN)) 0.000 74.24 242.77 512.93 944.06 1782.85
R (TOTAL) (kN) 0.000 74.13 241.71 510.18 937.54 1770.48
R (TOTAL) (kN) 0.000 73.97 240.25 506.39 928.67 1753.10
R (TOTAL) (kN) 0.000 73.76 238.41 501.63 917.67 1731.02
2993.11
2986.28
2965.45
2931.36
2884.93
2827.38
Total Resistance, R TOTAL (kN )
3500 3000
Drift Drift Drift Drift
angle, angle, angle, angle,
β (deg) 0 β (deg) 2 β (deg) 4 β (deg) 6
2500
Drift angle, β (deg) 8 Drift angle, β (deg) 10
2000 1500 1000 500 0 0
5
10 15 20 Ship Velocity, Vs (knot)
25
30
Figure 7.4 (b): Total Ship Resistance Curve Produced with Drift Effect (in Severe Case) at Various Ship Velocity in Starboard Beam Current Case, α = 90o
78
Table 7.4(c): Total Ship Resistance Produced Due to Lateral Drift Effect (in Severe Case) at Various Ship Velocity in Following Current, α = 180o
Ship Velocity, Vs (knot) 0 5 10 15 20 25 30
0
2
R (TOTAL) (kN) 0 34.51 209.07 481.75 916.44 1760.10 2960.73
R (TOTAL) (kN) 0 34.43 208.80 481.14 915.05 1757.58 2953.69
Drift angle, β (deg) 4 6 R (TOTAL) (kN) 0 34.21 208.00 479.31 910.92 1750.02 2932.76
R (TOTAL) (kN) 0 33.84 206.68 476.30 904.16 1737.45 2898.50
8
10
R (TOTAL) (kN) 0 33.34 204.87 472.16 894.96 1719.91 2851.83
R (TOTAL) (kN) 0 32.72 202.59 466.96 883.55 1697.39 2794.00
3500 Drift angle, β (deg) 0 Drift angle, β (deg) 2
Total Resistance, R TOTAL (kN)
3000
Drift angle, β (deg) 4 Drift angle, β (deg) 6 Drift angle, β (deg) 8
2500
Drift angle, β (deg) 10
2000 1500 1000 500 0 0
5
10 15 20 Ship Velocity, Vs (knot)
25
30
Figure 7.4 (c): Total Ship Resistance Curve Produced with Drift Effect (in Severe Case) at Various Ship Velocity in Following Current Case, α = 180o
79 Table 7.4 (d): Total Ship Resistance Produced Due to Lateral Drift Effect (in Severe Case) at Various Ship Velocity in Port Beam Current, α = 270o
Ship Velocity, Vs (knot) 0 5 10 15 20 25 30
0
2
R (TOTAL) (kN) 0 66.89 241.45 514.13 948.82 1792.48 2993.11
R (TOTAL) (kN) 0 74.19 243.28 514.47 947.92 1790.20 2986.20
Drift angle, β (deg) 4 6 R (TOTAL) (kN) 0 73.84 242.33 512.48 943.64 1782.52 2965.17
R (TOTAL) (kN) 0 73.28 240.76 509.22 936.64 1769.76 2930.75
8
10
R (TOTAL) (kN) 0 72.51 238.61 504.73 927.11 1751.95 2883.85
R (TOTAL) (kN) 0 71.54 235.90 499.08 915.28 1729.09 2825.72
3500 Drift angle, β (deg) 0
3000 Total resistance, R TOTAL (kN)
Drift angle, β (deg) 2 Drift angle, β (deg) 4
2500
Drift angle, β (deg) 6 Drift angle, β (deg) 8
2000
Drift angle, β (deg) 10
1500 1000 500 0 0
5
10 15 20 Ship velocity, Vs (knots)
25
30
Figure 7.4 (d): Total Ship Resistance Curve Produced with Drift Effect (in Severe Case) at Various Ship Velocity in Port Beam Current Case, α = 270o
80
7.4
CASE 2: Severe Drift Effect on the Total Ship Resistance, RTOTAL
The total ship resistance in Case 2 is solved and approached similarly as in Case 1 which treated as resultant of longitudinal and lateral component. Comparing to the Case 1, based on the methodology, the values of total resistance is totally depend on the lateral resistance component, since the longitudinal resistance values is similar with the values in Case 1. So that, in this particular section, the discussion is focused more on the result of total resistance in lateral direction. The difference in Case 2 is that, besides the effect of ship velocity, VS the other main modified parameters including ship length and breadth as well.
Referring to the Table 7.5, it is indicated that the values of total resistance (laterally), RT (L) is remarkably large in comparison to the values in Case 1. However, from point view of lateral total resistance, it still follows the trend in Case 1. The obvious difference is about the values obtained. Comparing to the Case 1, in Case 2, the lateral total resistance calculated gave a drastic increase. Even though with the same trend, the values obtained are very big in comparison to Case 1. Taking one point as an example, when the ship is drifted at β = 10 degrees incorporating with the current direction angle, α = 90 degrees, it is obtained that the lateral total resistance, RT
(L)
is 828.03 kN for the Case 2. If compared to the Case 1, the lateral total
resistance produced at this point is just about 83.75. kN. In comparison these two values, which is taken at maximum point, the lateral total resistance determined at Case 2 almost 43.19% of total ship resistance (resultant of total resistance). Whereas, the percentage of the maximum lateral total resistance obtained in Case 1 is only.4.84% of the resultant of total resistance.. Figure 7.5 and Figure 7.6 illustrated clearer about the comparison between Case 1 and Case 2, as far as lateral total resistance is concerned. In overall, the large differences of lateral total resistance obtained between Case1 and 2 might be due to some assumptions decided earlier, which possibly could contribute to the error. One of reason, maybe due to the unsymmetrical form of ship in Case 2. By changing inversely the length and breadth, it created the form of ship unsymmetrical. Obviously the solution of this unsymmetrical condition is a complicated problem to be executed.
81
Table 7.5: CASE 2: Longitudinal, Lateral and Resultant Total Resistance at Various Current Direction Angle and Drift Angle. Drift angle, β(deg) 0 Current direction angle, α (deg)
2
R RT (L)
4
R
R
RT (T)
(TOTAL)
RT (L)
RT (T)
(TOTAL)
RT (L)
RT (T)
(TOTAL)
0
1824.86
0.00
1824.86
1822.33
23.61
1822.49
1814.75
84.31
1816.71
10
1823.95
15.00
1824.01
1821.42
38.61
1821.83
1813.84
99.31
1816.55
20
1821.31
51.88
1822.05
1818.78
75.49
1820.35
1811.20
136.19
1816.31
30
1817.23
104.26
1820.22
1814.71
127.87
1819.21
1807.12
188.57
1816.94
40
1812.17
165.61
1819.72
1809.64
189.22
1819.51
1802.06
249.92
1819.31
50
1806.67
228.89
1821.12
1804.15
252.50
1821.73
1796.57
313.20
1823.66
60
1801.37
287.07
1824.10
1798.84
310.67
1825.47
1791.26
371.38
1829.35
70
1796.87
333.79
1827.61
1794.34
357.40
1829.59
1786.76
418.10
1835.02
80
1793.73
364.00
1830.29
1791.20
387.61
1832.66
1783.62
448.31
1839.10
90
1792.48
374.43
1831.17
1789.96
398.03
1833.68
1782.37
458.73
1840.46
100
1791.23
363.95
1827.83
1788.70
387.56
1830.21
1781.12
448.26
1836.66
110
1788.09
333.70
1818.96
1785.56
357.31
1820.96
1777.98
418.01
1826.46
120
1783.58
286.94
1806.52
1781.05
310.55
1807.93
1773.47
371.25
1811.91
130
1778.28
228.74
1792.93
1775.75
252.35
1793.59
1768.17
313.05
1795.67
140
1772.78
165.46
1780.49
1770.26
189.07
1780.32
1762.67
249.77
1780.28
150
1767.72
104.13
1770.78
1765.19
127.74
1769.81
1757.61
188.44
1767.68
160
1763.65
51.78
1764.41
1761.12
75.38
1762.73
1753.54
136.08
1758.81
170
1761.01
14.94
1761.08
1758.49
38.54
1758.91
1750.90
99.24
1753.71
180
1760.10
0.00
1760.10
1757.58
23.61
1757.74
1750.00
84.31
1752.03
190
1761.02
-15.06
1761.09
1758.49
8.54
1758.52
1750.91
69.25
1752.28
200
1763.66
-51.99
1764.43
1761.14
-28.38
1761.37
1753.56
32.32
1753.85
210
1767.74
-104.40
1770.82
1765.22
-80.79
1767.06
1757.63
-20.09
1757.75
220
1772.81
-165.76
1780.54
1770.28
-142.15
1775.98
1762.70
-81.45
1764.58
230
1778.30
-229.03
1792.99
1775.77
-205.43
1787.62
1768.19
-144.72
1774.11
240
1783.60
-287.19
1806.58
1781.08
-263.59
1800.48
1773.50
-202.88
1785.06
250
1788.10
-333.88
1819.01
1785.58
-310.28
1812.34
1778.00
-249.58
1795.43
260
1791.24
-364.05
1827.86
1788.71
-340.44
1820.82
1781.13
-279.74
1802.97
270
1792.48
-374.43
1831.17
1789.96
-350.82
1824.01
1782.37
-290.12
1805.83
280
1793.74
-363.90
1830.28
1791.21
-340.30
1823.25
1783.63
-279.59
1805.41
290
1796.89
-333.61
1827.59
1794.36
-310.00
1820.94
1786.78
-249.30
1804.09
300
1801.39
-286.82
1824.08
1798.87
-263.21
1818.02
1791.29
-202.51
1802.70
310
1806.70
-228.60
1821.11
1804.17
-204.99
1815.78
1796.59
-144.29
1802.38
320
1812.19
-165.32
1819.72
1809.67
-141.71
1815.21
1802.08
-81.01
1803.90
330
1817.25
-103.99
1820.23
1814.73
-80.39
1816.51
1807.15
-19.69
1807.25
340
1821.32
-51.67
1822.06
1818.80
-28.06
1819.01
1811.22
32.64
1811.51
350
1823.95
-14.87
1824.01
1821.43
8.73
1821.45
1813.85
69.44
1815.17
360
1824.86
0.00
1824.86
1822.33
23.61
1822.49
1814.75
84.31
1816.71
82
Drift angle, β(deg) 6 Current direction angle, α (deg)
8
R
10
R
R
RT(L)
RT (T)
(TOTAL)
RT (L)
RT (T)
(TOTAL)
RT (L)
RT (T)
(TOTAL)
0
1802.10
177.70
1810.84
1784.33
301.42
1809.61
1761.37
453.60
1818.84
10
1801.18
192.70
1811.46
1783.42
316.42
1811.27
1760.46
468.60
1821.76
20
1798.55
229.58
1813.14
1780.78
353.30
1815.49
1757.82
505.48
1829.06
30
1794.47
281.97
1816.49
1776.71
405.68
1822.43
1753.74
557.87
1840.34
40
1789.41
343.32
1822.04
1771.64
467.03
1832.17
1748.68
619.21
1855.08
50
1783.91
406.59
1829.66
1766.15
530.31
1844.05
1743.19
682.49
1872.03
60
1778.61
464.77
1838.33
1760.84
588.49
1856.58
1737.88
740.67
1889.13
70
1774.11
511.50
1846.37
1756.34
635.21
1867.68
1733.38
787.39
1903.84
80
1770.97
541.70
1851.96
1753.20
665.42
1875.23
1730.24
817.60
1913.69
90
1769.72
552.13
1853.85
1751.95
675.85
1877.79
1728.99
828.03
1917.04
100
1768.47
541.65
1849.56
1750.70
665.37
1872.88
1727.74
817.55
1911.41
110
1765.32
511.40
1837.91
1747.56
635.12
1859.39
1724.60
787.30
1895.81
120
1760.82
464.65
1821.09
1743.05
588.36
1839.68
1720.09
740.54
1872.73
130
1755.51
406.45
1801.95
1737.75
530.16
1816.82
1714.79
682.35
1845.56
140
1750.02
343.17
1783.35
1732.26
466.88
1794.07
1709.29
619.07
1817.95
150
1744.96
281.83
1767.57
1727.19
405.55
1774.17
1704.23
557.73
1793.17
160
1740.89
229.48
1755.94
1723.12
353.20
1758.95
1700.16
505.38
1773.68
170
1738.25
192.64
1748.89
1720.49
316.36
1749.33
1697.53
468.54
1761.00
180
1737.34
177.70
1746.41
1719.58
301.42
1745.80
1696.62
453.60
1756.21
190
1738.26
162.64
1745.85
1720.49
286.36
1744.16
1697.53
438.54
1753.26
200
1740.90
125.71
1745.43
1723.14
249.43
1741.10
1700.18
401.61
1746.97
210
1744.98
73.30
1746.52
1727.21
197.02
1738.42
1704.25
349.20
1739.66
220
1750.05
11.94
1750.09
1732.28
135.66
1737.58
1709.32
287.84
1733.39
230
1755.54
-51.33
1756.29
1737.77
72.39
1739.28
1714.81
224.57
1729.46
240
1760.84
-109.49
1764.24
1743.08
14.23
1743.14
1720.12
166.41
1728.15
250
1765.34
-156.18
1772.24
1747.58
-32.46
1747.88
1724.62
119.72
1728.77
260
1768.48
-186.34
1778.27
1750.71
-62.63
1751.83
1727.75
89.55
1730.07
270
1769.72
-196.72
1780.62
1751.95
-73.01
1753.48
1728.99
79.18
1730.81
280
1770.98
-186.20
1780.74
1753.21
-62.48
1754.33
1730.25
89.70
1732.58
290
1774.12
-155.91
1780.96
1756.36
-32.19
1756.65
1733.40
119.99
1737.55
300
1778.63
-109.12
1781.98
1760.87
14.60
1760.93
1737.91
166.78
1745.89
310
1783.94
-50.90
1784.66
1766.17
72.82
1767.67
1743.21
225.00
1757.67
320
1789.43
12.39
1789.47
1771.67
136.10
1776.89
1748.71
288.28
1772.31
330
1794.49
73.71
1796.01
1776.73
197.43
1787.66
1753.77
349.61
1788.27
340
1798.56
126.03
1802.97
1780.80
249.75
1798.23
1757.84
401.93
1803.20
350
1801.19
162.83
1808.54
1783.43
286.55
1806.30
1760.47
438.73
1814.31
360
1802.10
177.70
1810.84
1784.33
301.42
1809.61
1761.37
453.60
1818.84
83
RT (T) Current Angle, α
Figure 7.5: CASE 1: Lateral Total Resistance, RT
(T)
at Various Current
Direction Angle, α and Various Drift Angle, β (at speed 25 knots)
84
RT (T) Current Angle, α
Figure7.6: CASE 2: Lateral Total Resistance, RT
(T)
at Various Current
Direction Angle, α and Various Drift Angle, β (at speed 25 knots) On the whole, even though the longitudinal total resistance, RT
(L)
values
similar with Case 1, with the remarkable values of total resistance (laterally), RT(L) produced in Case 2, it consequently will reflect the resultant total resistance, RTOTAL. Due to that, the end result of total ship resistance (applying the described methodology) gave a certain difference between Case 1 and Case 2, where the result for the Case 1 is significantly higher. It considerably can be concluded that the result obtained in Case 1 is preferable and more acceptable. It is said so since the values of lateral total resistance obtained in Case 2 were too large at every current angle. Referring to the Figure 7.6, the maximum lateral total resistance obtained is at drift angle, β = 10 degrees with the current experienced at α = 90. At this point, the values is up to 828.027 kN, which approaching almost half of the longitudinal total resistance, and considerably a large value. The values in this lateral component preferably should not be at this range because the ship has a forward velocity, which definitely contribute the major influence in total resistance. Other than that, although it is said as severe lateral drift due to the combination of wind and current, in the
85
assumption of no effects of waves, there is not possible to the values obtained up to this range. In fact, although in the condition of extreme sea, the influence is still small because the main effect is come from ocean waves.
CHAPTER VIII
CONCLUDING REMARKS
8.1
Conclusion
On the whole, concerning about the earlier objectives of this research, it can be summarized that they are successfully achieved. As far as this preliminary study is concerned, base on the literature reviewed, the mathematical derived and calculated results, this research potentially could contribute significant differences in certain condition in this ship resistance study. In this particular study, with specific case of severe lateral drift, instead of existing ship resistance prediction formulas, it is viewed that more detail and specific value can be calculated and predicted.
Although the condition of severe lateral drift effect due to wind and current is not entirely experienced by the ship in actual operation, but for a specific case of river mouth area (as discussed on the earlier part), it also can be considered that the predicted value would be more practical for a ship which travelling in this case. It is viewed that this matter is practical especially in ship operations which economy issue become the priority. This is because determining engine power requirement correctly at this particular condition will determine the correct fuel consumption for the engine to be used. As discussed in the previous chapter, in certain case (Case 1) such as
88 when ship traveled at her service speed (25 knots) with drift angle (β = 0 deg) in heading current (α = 0 deg), it produced the maximum of total ship resistance (RTOTAL = 1824.86 kN). This can be interpreted that about 1.806 % of total ship resistance is added in comparison to the normal condition of operation (with no drift effect). Another case is when ship is experienced a maximum drift angle (β = 10 deg) and traveled in following current, the total resistance produced is reduced up to 5.305 % of total ship resistance. Meaning, there exists an additional thrust or force for the ship when operating at this specific condition.
As far as the first initiative of research is concerned in this study, an investigation which is made by using Holtrop’s and Mennen’s prediction formulae as a guideline and main basis is considerably promising. A few information and understanding about this complicated problem are gained in initiating more detail studies in the near future. Some argument possibly will arise here regarding the principle used in this problem determination, since Holtrop’s approach is considerably a statistical method. However, it is highlighted that, at earlier of the Holtrop’s finding, an attempt also was made to extend the method by adjusting the original numerical prediction model to test data obtained in specific case, because the accuracy of the method was reported to be insufficient when unconventional combination of main parameters were used. Due to this adaption of the method has resulted this set of Holtrop’s formulae with a wider range of application (Holtrop and Mennen, 1982).
8.2
Recommendation for Future Research
Lastly, it is viewed that there have a large rooms of research opportunity possibly be explored and studied for the next stage of investigation. This initial investigation possibly can be made onto other methods of ship resistance prediction, as well as another types of ships and hull forms. Besides, as the future research, more
89 study is needed and developed especially for strong verification of this initial investigation. In this nearer period of time, computer simulation approach, such as Computer Fluid Dynamics (CFD) could provide a better promising result in solving the lateral drift effect onto ship resistance. Other than that, a specific model experiment is seen one of the approaches that possibly to be focused in the near future, which can further verify the proposed ship resistance prediction formulae.
REFERENCES
Arizam, A. W. (2003) “ Resistance Prediction of the Tugboat” Undergraduate Thesis. University Technology Malaysia, Skudai
Bertram, V. (2000). Practical Ship Hydrodynamics. Butterworth- Heinemann. Linacre House, Jordan Hill, Oxford.
Carlton, J. S. (1994). Marine Propellers and Propulsion. ButterworthHeinemann. Linacre House, Jordan Hill, Oxford.
Takao I. (1962). Wave – Making Resistance of Ships. The Society of Naval Architects and Marine Engineers, 70. pg 283-353.
Edward, V. L. (1988). Principles of Naval Architecture, Volume II. Resistance, Propulsion and Vibration. Jersey City, NJ: The Society of Naval Architectures and Marine Engineers.
Faizul A. A. (1996). A Study of Ship Resistance Prediction Method. Undergraduate Thesis. University Technology Malaysia, Skudai.
Faizul A. A, (2006). A Strip Method for a Laterally Drifting Ship in Waves. Ph.D Thesis. Hiroshima University, Japan.
Faizul A. A. and Yasukawa, H. (2007). Strip Method for a Laterally Drifting ship in Waves. J Mar Sci Technol. 12: 139–149
90 Gillmer, C and Johson, B. (1982). Introduction to Naval Architecture. London: E. & F. N. Spon Ltd.
Harold, E. S. (1957). Hydrodynamics in Ship Design. (Vol III). New York: The Society of Naval Architectures and Marine Engineers.
Harvald, S. V. (1983). Resistance and Propulsion of Ships. Lyngby, Denmark: John Wiley & Sons.
Holtrop, J. and Mennen, G. G. J. (1982). An Approximate Power Prediction Method. Netherlands Ship Model Basin, (Marin), Netherland
Holtrop, J. (1984), A Statistical Re-Analysis of Resistance and Propulsion Data. International Shipbuilding Progress, Vol. 31, No. 363,
Iwasaka, N. and K. Hanawa (1990). Climatologies of marine meteorological variables and surface fluxes in the North Pacific computed from COADS. Tohoku Geophys. J., 33, 188–239.
Longo, J. and Stern, F. (2001). Effects of Drift Angle on Model Ship Flow. University of Iowa, USA Tupper, E.C. (1996). Introduction to Naval Architecture. (3rd ed.) Formerly Muckle’s Naval Architecture for Marine Engineers.
APPENDIX A1 Flowchart of Computer Programming to Calculate the Longitudinal Total Resistance with Drift Effect. Cont A
START
Ship Velocity, Vs Current velocity, Vc
Cp = 0.5833 LCB = -0.75 L = 205 T = 10 B = 32 Cb = 0.5860 Cm = 0.98 Cwp = 0.75 Abt = 20 rho = 1.025 V = Speed*0.5144 Vc = Speed_c*0.5144 Visc = 0.0000011906 S = 7381.45 Sapp = 50 Vdisp = 37500 Tf = 10 Hb = 4 At = 16 gvt = 9.81
10
true
true
C7 = 0.229577*(B/L)**0.33333
true
C7 = (B/L)
x5=(Lr/B)**0.34574*(100*Vdisp/ L**3)**0.16302 x4=-(L/B)**0.80855*(1Cwp)**0.30484*(1-Cp0.0225*LCB)**0.6367*x5 ie = 1+89*EXP(x4) C1= 2223105*(C7**3.78613)*(T/ B)**1.07961*(90-ie)**(-1.37565) x6 = B*T*(0.31*Abt**0.5+Tf-Hb) C3 = 0.56*Abt**1.5/x6 C2 = EXP(-1.89*C3**0.5) C5 =1-(0.8*At)/(B*T*Cm) Fn = V/(gvt*L)**0.5
else
true
else
C7 = 0.5-0.0625*(L/B)
Lr = (1-Cp+(0.06*Cp*LCB)/ (4*Cp-1))*L
If(T/L .GT. 0.05)
elseIF (0.11 .LT. B/L .AND. B/L .LT. 0.25)
IF (B/L .GT. 0.25)
IF (0.02 .LT. T/L .AND. T/L .LT. 0.05)
C12 = 48.20*(T/L0.02)**2.078 + 0.479948
else IF (L/B .GT. 12) true
false
Lamda = 1.446*Cp-0.03*L/B
Lamda = 1.446*Cp-0.36
C12 = (T/L)**0.2228446 C12 = (T/L)**0.2228446 Cstern=10 C13 = 1 + 0.003*Cstern
IF (Cp .GT. 0.8) else true
x1 = (1-Cp+0.0225*LCB)**0.6906 k1 = C13*(0.93+(C12*(B/ Lr)**0.92497*(0.95-Cp)**(0.521448)*x1))
C16 = 1.73014-0.7067*Cp C16 = 8.07981*Cp13.8673*Cp**2+6.98 4388*Cp**3
Beta = Angle*3.142/180 Alfa = Angle_2*3.142/180 V = V*cos(Beta) Vc = ABS(Vc*cos(Alfa)) Rn = V*L/Visc Rnc = Vc*L/Visc Cf = 0.075/(ALOG10(Rn)-2)**2 Cfc = 0.075/(ALOG10(Rnc)-2)**2 RFs = 0.5*rho*S*(V**2)*Cf RFc = 0.5*rho*S*(Vc**2)*Cfc
IF (270 .GE. Angle_2 .AND. Angle_2 .LE.360)
else IF (90 .GE. Angle_2 .AND. Angle_2 .LE.270)
m1=0.0140407*L/T(1.75254*Vdisp**(0.33333)/L)(4.79323*B/L)-C16
IF (L**3/Vdisp .GT. 1727)
else
else
else
true
IF (L**3/Vdisp .GT. 1727) true
C15 = -1.69385+(L/ Vdisp**0.66667-8)/2.36
C15 = 0
true true
RFL = RFs - RFc RFL = RFs + RFc
k2 = 1.5 k2eq = k2*Sapp/Sapp RAPPL = 0.5*rho*(V**2)*Sapp*K2eq*Cf
Cont A
C15 = -1.69385
m2 = C15*Cp**2*EXP(-0.1*Fn**(-2)) x3 = m1*Fn**(-0.9)+m2*cos(Lamda*Fn**(-2)) RWL = C1*C2*C5*Vdisp*rho*gvt*EXP(x3)
Cont B
APPENDIX A1 Flowchart of Computer Programming to Calculate the Longitudinal Total Resistance with Drift Effect. Cont B
10
else
x7 = gvt*(Tf-Hb-0.25*(Abt**0.5))+0.15*V**2 Fni = V/x7**0.5 Pb = (0.56*Abt**0.5)/(Tf-1.5*Hb) RBL = (0.11*EXP(-3*Pb**(2))*Fni**3*Abt**1.5*rho*gvt)/(1+Fni**2)
Current Angle_2 <=350
true Angle_2 = Angle_2 +10
Fnt = V/(2*gvt*At/(B+B*Cwp))**0.5
IF (Fnt .LT. 5)
else
else
Drift Angle Value <= 8
true true C6 = 0.2*(1-0.2*Fnt)
C6 = 0
Angle = Angle +2 RTRL = 0.5*rho*V**2*At*C6
IF (Tf/L .GT. 0.04) else true C4 = 0.04
x8 = 0.003*(L/ 7.5)**0.5*Cb**4*C2*(0.04C4) Ca = 0.006*(L+100)**(0.16)-0.00205+x8 RAL = 0.5*rho*V**2*S*Ca
RTL = RFL*(k1) + RAPPL + RWL + RBL + RTRL + RAL
C4 = Tf/L
END
APPENDIX A2 Flowchart of Computer Programming to Calculate the Lateral Total Resistance with Drift Effect. Cont A
START
Ship Velocity, Vs Current velocity, Vc
10
Cp = 0.5833 LCB = -0.75 L = 205 T = 10 B = 32 Cb = 0.5860 Cm = 0.98 Cwp = 0.75 Abt = 20 rho = 1.025 V = Speed*0.5144 Vc = Speed_c*0.5144 Visc = 0.0000011906 S = 7381.45 Sapp = 50 Vdisp = 37500 Tf = 10 Hb = 4 At = 16 gvt = 9.81
true
true
true
true
C7 = 0.229577*(B/L)**0.33333
C7 = (B/L)
x5=(Lr/B)**0.34574*(100*Vdisp/ L**3)**0.16302 x4=-(L/B)**0.80855*(1Cwp)**0.30484*(1-Cp0.0225*LCB)**0.6367*x5 ie = 1+89*EXP(x4) C1= 2223105*(C7**3.78613)*(T/ B)**1.07961*(90-ie)**(-1.37565) x6 = B*T*(0.31*Abt**0.5+Tf-Hb) C3 = 0.56*Abt**1.5/x6 C2 = EXP(-1.89*C3**0.5) C5 =1-(0.8*At)/(B*T*Cm) Fn = V/(gvt*L)**0.5
else
else
C7 = 0.5-0.0625*(L/B)
Lr = (1-Cp+(0.06*Cp*LCB)/ (4*Cp-1))*L
If(T/L .GT. 0.05)
elseIF (0.11 .LT. B/L .AND. B/L .LT. 0.25)
IF (B/L .GT. 0.25)
IF (0.02 .LT. T/L .AND. T/L .LT. 0.05)
C12 = 48.20*(T/L0.02)**2.078 + 0.479948
else IF (L/B .GT. 12) true
false
Lamda = 1.446*Cp-0.03*L/B
Lamda = 1.446*Cp-0.36
C12 = (T/L)**0.2228446 C12 = (T/L)**0.2228446
Cstern=10 C13 = 1 + 0.003*Cstern
IF (Cp .GT. 0.8) else
true x1 = (1-Cp+0.0225*LCB)**0.6906 k1 = C13*(0.93+(C12*(B/ Lr)**0.92497*(0.95-Cp)**(0.521448)*x1))
IF (180 .GE. Angle_2 .AND. Angle_2 .LE.360)
m1=0.0140407*L/T(1.75254*Vdisp**(0.33333)/L)(4.79323*B/L)-C16
IF (L**3/Vdisp .GT. 1727)
else
else
else
true
IF (L**3/Vdisp .GT. 1727) true
C15 = -1.69385+(L/ Vdisp**0.66667-8)/2.36
C15 = 0
true RFT = RFs - RFc RFT = RFs + RFc
C16 = 8.07981*Cp13.8673*Cp**2+6.98 4388*Cp**3
Beta = Angle*3.142/180 Alfa = Angle_2*3.142/180 V = V*sin(Beta) Vc = ABS(Vc*sin(Alfa)) Rn = V*L/Visc Rnc = Vc*L/Visc Cf = 0.075/(ALOG10(Rn)-2)**2 Cfc = 0.075/(ALOG10(Rnc)-2)**2 RFs = 0.5*rho*S*(V**2)*Cf RFc = 0.5*rho*S*(Vc**2)*Cfc
C16 = 1.73014-0.7067*Cp
k2 = 1.5 k2eq = k2*Sapp/Sapp RAPPT = 0.5*rho*(V**2)*Sapp*K2eq*Cf
Cont A
C15 = -1.69385
m2 = C15*Cp**2*EXP(-0.1*Fn**(-2)) x3 = m1*Fn**(-0.9)+m2*cos(Lamda*Fn**(-2)) RWT = C1*C2*C5*Vdisp*rho*gvt*EXP(x3)
Cont B
APPENDIX A2 Flowchart of Computer Programming to Calculate the Lateral Total Resistance with Drift Effect.
Cont B
10
else
x7 = gvt*(Tf-Hb-0.25*(Abt**0.5))+0.15*V**2 Fni = V/x7**0.5 Pb = (0.56*Abt**0.5)/(Tf-1.5*Hb) RBT = (0.11*EXP(-3*Pb**(2))*Fni**3*Abt**1.5*rho*gvt)/(1+Fni**2)
Current Angle_2 <=350
true
Angle_2 = Angle_2 +10 Fnt = V/(2*gvt*At/(B+B*Cwp))**0.5
IF (Fnt .LT. 5)
else
else
Drift Angle Value <= 8
true true C6 = 0.2*(1-0.2*Fnt)
C6 = 0
Angle = Angle +2 RTRT = 0.5*rho*V**2*At*C6
IF (Tf/L .GT. 0.04) else true C4 = 0.04
x8 = 0.003*(L/ 7.5)**0.5*Cb**4*C2*(0.04C4) Ca = 0.006*(L+100)**(0.16)-0.00205+x8 RAT = 0.5*rho*V**2*S*Ca
RTT = RFT*(k1) + RAPPT + RWT + RBT + RTRT + RAT
C4 = Tf/L
END
APPENDIX B1: Total Ship Resistance, RT Determination in Longitudinal and Lateral Component with Drift Effect Caused by Drift Angle, β (due to wind) Ship Speed, V(knot)
25
Ship Speed, V(m/s)
12.86
Fn
0.286767239 Longitudinal Component Longi. Ship Speed, VL(m/s)
Fn(L)
RF
m2
RW
FnT
C6
RTR
RAPP
Fni
RB
0
12.86000
0.28677
869.62581
-0.170823598
557.2074
5.4316
0.00
0.00
8.8359
1.50826
0.0492
2
12.85216
0.28659
868.62892
-0.170570408
556.1132
5.4283
0.00
0.00
8.8258
1.50766
0.0492
4
12.82867
0.28607
865.64271
-0.169810624
552.8204
5.4183
0.00
0.00
8.7955
1.50584
6
12.78953
0.28520
860.68048
-0.168543633
547.2940
5.4018
0.00
0.00
8.7450
8
12.73481
0.28398
853.76434
-0.166768499
539.4617
5.3787
0.00
0.00
8.6748
10
12.66458
0.28241
844.92512
-0.164484096
529.1939
5.3490
0.00
0.00
Drift angle, β(deg)
CA
RA
RTOTAL(L)
3.52E-04
220.7493
1792.4813
3.52E-04
220.4803
1789.9552
0.0491
3.52E-04
219.6748
1782.3732
1.50280
0.0490
3.52E-04
218.3367
1769.7198
1.49854
0.0487
3.52E-04
216.4724
1751.9548
8.5850
1.49304
0.0484
3.52E-04
214.0912
1728.9939
Lateral Component Lateral Ship Speed, VT(m/s)
Fn(T)
RF
0
0.00000
0.00000
0.00000
2
0.44887
0.01001
1.64827
4
0.89718
0.02001
6
1.34441
8
1.79000
10
2.23340
Drift angle, β(deg)
m2
RW
FnT
C6
RTR
RAPP
Fni
RB
CA
RA
RTOTAL(L)
0
0.0000
0.0000
0.20000
0.0000
0.0000
0.00000
0.0000
0.0003525
0.0000
0.0000
0
0.0000
0.1896
0.19242
0.3182
0.0167
0.06484
0.0000
0.0003525
0.2689
2.5100
5.96096
-1.8078E-109
0.0000
0.3789
0.18484
1.2212
0.0606
0.12948
0.0001
0.0003525
1.0744
9.2496
0.02998
12.65676
-2.74644E-49
0.0000
0.5678
0.17729
2.6301
0.1286
0.19372
0.0003
0.0003525
2.4126
19.8080
0.03992
21.58593
-3.17767E-28
0.0000
0.7560
0.16976
4.4645
0.2193
0.25737
0.0008
0.0003525
4.2768
33.9235
0.04980
32.63145
-1.7831E-18
0.0000
0.9433
0.16227
6.6436
0.3316
0.32024
0.0014
0.0003525
6.6581
51.3698
APPENDIX B2: Total Ship Resistance at Service Speed 25 Knots with Lateral Drift Effect due to Current (4 knots)at Various Current Direction Angles. Ship Speed, v(knot) Fn
25 0.287
Current speed, VC(knot)
4
Current Direction, a
Ship Speed, v(m/s)
0.00001 10 20 30 40 50 60 70 80 90 100 110 120 130 140 150 160 170 180
12.860 12.860 12.860 12.860 12.860 12.860 12.860 12.860 12.860 12.860 12.860 12.860 12.860 12.860 12.860 12.860 12.860 12.860 12.860
RF (due to current) component
Current speed, Vc component VC(L) 4.000 3.939 3.759 3.464 3.064 2.571 2.000 1.367 0.694 0.001 0.695 1.369 2.001 2.572 3.065 3.465 3.759 3.939 4.000
VC(T) 0.000 0.695 1.368 2.000 2.571 3.064 3.464 3.759 3.939 4.000 3.939 3.758 3.464 3.063 2.570 1.999 1.367 0.693 0.002
RF 869.626 869.626 869.626 869.626 869.626 869.626 869.626 869.626 869.626 869.626 869.626 869.626 869.626 869.626 869.626 869.626 869.626 869.626 869.626
RFC(L) 27.998 27.209 24.927 21.403 17.024 12.274 7.686 3.793 1.078 0.000 1.083 3.801 7.697 12.285 17.035 21.413 24.934 27.213 27.998
RFC(T) 0.000 1.081 3.797 7.692 12.279 17.029 21.408 24.931 27.211 27.998 27.207 24.924 21.399 17.018 12.268 7.681 3.789 1.076 0.000
RTOTAL (due to current effect) RW 557.207 557.207 557.207 557.207 557.207 557.207 557.207 557.207 557.207 557.207 557.207 557.207 557.207 557.207 557.207 557.207 557.207 557.207 557.207
RTR 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000
RAPP 8.836 8.836 8.836 8.836 8.836 8.836 8.836 8.836 8.836 8.836 8.836 8.836 8.836 8.836 8.836 8.836 8.836 8.836 8.836
RB 0.049 0.049 0.049 0.049 0.049 0.049 0.049 0.049 0.049 0.049 0.049 0.049 0.049 0.049 0.049 0.049 0.049 0.049 0.049
RA 220.749 220.749 220.749 220.749 220.749 220.749 220.749 220.749 220.749 220.749 220.749 220.749 220.749 220.749 220.749 220.749 220.749 220.749 220.749
RTOTAL(L) 1824.859 1823.946 1821.308 1817.232 1812.168 1806.675 1801.370 1796.867 1793.728 1792.481 1791.229 1788.086 1783.581 1778.275 1772.782 1767.720 1763.647 1761.013 1760.104
RTOTAL(T) 0.000 1.081 3.797 7.692 12.279 17.029 21.408 24.931 27.211 27.998 27.207 24.924 21.399 17.018 12.268 7.681 3.789 1.076 0.000
RTOTAL 1824.859 1823.946 1821.311 1817.248 1812.209 1806.755 1801.497 1797.040 1793.935 1792.700 1791.436 1788.260 1783.709 1778.357 1772.825 1767.736 1763.651 1761.013 1760.104
