Resistance Calculation

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.

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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.

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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

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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,

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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

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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.

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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

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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.

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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.

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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

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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