CHAPTER I.
VERTICAL MOTION OF FLOATING BODIES IN
REGULAR WAVES
I.1.
Introduction
1
I.2.
Heave motion of a buoy in regular waves
2
I.2.1.
I.2.1.1.
I.2.1.2.
I.2.1.3.
I.2.1.4.
I.2.2.
I.2.2.1.
I.2.2.2.
I.2.2.3.
I.2.3.
I.2.3.1.
I.2.3.2.
I.2.4.
Formulation of the equation of motion
Conventions
Representation of the heave motion of the buoy
Vertical forces
Equation of motion
Heave motion of a buoy in still water
Free damped motion
Captive oscillation
Work
Solution of the equation of motion
Exciting wave force
Heave motion
Important note
2
2
3
3
5
6
6
9
10
12
12
14
17
I.3.
Heave and pitch motions of a ship in regular waves
18
I.3.1.
I.3.2.
I.3.3.
I.3.3.1.
I.3.3.2.
I.3.3.3.
I.3.3.4.
I.3.3.5.
I.3.3.6.
I.3.3.7.
I.3.4.
I.3.4.1.
I.3.4.2.
I.3.4.3.
I.3.4.4.
I.3.4.5.
I.3.5.
I.3.5.1.
I.3.5.2.
I.3.5.3.
I.3.6.
I.3.7.
Conventions
Vertical motion of a point on the ship
Vertical force per length unit
Introduction
Inertia force
Hydrostatic force
Hydrodynamic force
Total force
Correction for depth effect
Note
Equation of motion for the ship
Differential equations
Coefficients of the differential equations
Exciting force and moment
Solution of the coupled differential equations
Representation of the results
Hydrodynamic coefficients
Added mass
Hydrodynamic damping
Algorithms for calculation of hydrodynamic coefficients
Encounter frequency in oblique waves
Limitations of the strip theory
18
19
21
21
21
21
22
23
23
24
25
25
26
31
34
36
37
37
41
42
43
46
CHAPTER II.
IRREGULAR WAVES
II.1.
Wave record
1
II.1.1.
II.1.2.
II.1.2.1.
II.1.2.2.
II.1.3.
Definitions
Wave record statistics
Apparent wave height
Apparent wave period
Characteristics of a sea state
1
1
1
2
2
II.2.
Energy spectrum
3
II.2.1.
II.2.2.
II.2.2.1.
II.2.2.2.
II.2.2.3.
II.2.3.
II.2.3.1.
II.2.3.2.
II.2.3.3.
II.2.4.
II.2.4.1.
II.2.4.2.
II.2.4.3.
II.2.4.4.
II.2.4.5.
II.2.5.
Definition
Relation between amplitude spectrum and wave record
Distribution of the wave record
Distribution of apparent wave heights
Characteristic wave heights
Shape of the wave spectrum
Factors affecting the shape
Moments of a wave spectrum
Band width of a spectrum
Theoretical wave spectra
Introduction
PIERSON-MOSKOWITZ spectrum
BRETSCHNEIDER spectrum
JONSWAP spectrum
OCHI six parameter spectrum
Directional wave spectrum
3
5
5
6
7
9
9
9
10
11
11
12
13
15
16
16
II.3.
Calculation of a wave spectrum from a wave record
17
II.3.1.
II.3.1.1.
II.3.1.2.
II.3.1.3.
II.3.2.
Autocorrelatiemethode
FOURIER-transformatie
Autocorrelatiefunctie
Praktische method (TUKEY)
Fast FOURIER transform (FFT)
18
18
20
22
27
II.4.
Indication of sea state
30
CHAPTER III.
III.1.
RESPONSE IN IRREGULAR WAVES
Spectrum of a response to an irregular sea
1
III.1.1. Principle of linear superposition
III.1.2. Encounter spectrum
III.1.2.1. Encounter frequency
III.1.2.2. Transformation of a wave spectrum
III.1.2.3. Special cases
III.1.3. Motion spectrum
III.1.3.1. Determination of a motion spectrum by means of the encounter spectrum
III.1.3.2. Determination of a motion spectrum by means of a wave spectrum from a fixed
wave recorder
III.1.3.3. Range of application
1
1
1
2
4
6
6
III.2.
9
Absolute and relative vertical motions
7
8
III.2.1. Absolute vertical motion of a point of the vessel
III.2.1.1. Vertical motion
III.2.1.2. Vertical velocity
III.2.1.3. Vertical acceleration
III.2.2. Relative vertical motion of a point of the vessel
III.2.2.1. Conventions
III.2.2.2. Relative vertical motion
III.2.2.3. Relative vertical velocity
9
9
10
10
11
11
12
13
III.3.
15
Slamming
III.3.1. Description of the phenomenon
III.3.2. Theoretical considerations
III.3.2.1. Extending plate analogy
III.3.2.2. Hydrodynamic impact force
III.3.3. Causes of slamming
III.3.4. Probability of occurrence of slamming
III.3.4.1. Conditions for slamming occurrence
III.3.4.2. Threshold velocity
III.3.4.3. Acceptable frequency of occurrence
III.3.4.4. Number of slams per time unit
III.3.5. Slamming in het scheepsontwerp
III.3.5.1. Overzicht
III.3.5.2. Aanpassen van de scheepsvorm (OCHI & MOTTER)
III.3.5.3. Bepaling van de hydrodynamic belasting
15
16
16
21
24
24
24
26
27
28
30
30
30
31
III.4.
36
Shipping of water
III.4.1. Description of the phenomenon
III.4.1.1. Definition
III.4.1.2. Effective freeboard
III.4.1.3. Dynamic piling-up
III.4.2. Probability of shipping of water
III.4.3. Consequences of green water
36
36
36
37
38
38
III.5.
Wave induced loads
39
III.5.1.
General
39
III.5.2. Wave induced shear forces and bending moments
III.5.2.1. Determination of shear force and bending moment
III.5.2.2. Statistics
III.5.2.3. Comparison with traditional method
III.5.3. Maximum bending moment
39
39
41
41
42
III.6.
42
Behavior of a ship at sea
III.6.1. Pitch and heave response: determining factors
III.6.1.1. Response in regular waves
III.6.1.2. Response to irregular waves
III.6.1.3. Shape of the motion spectrum
III.6.2. Assessment of the seaworthiness of a ship
III.6.2.1. Relation between speed, encounter period and wave length at synchronism
III.6.2.2. Condition for synchronism with waves for which λ/L = 1
III.6.2.3. Natural pitch period
42
42
44
45
46
46
47
49
CHAPTER IV.
ROLL MOTION OF SHIPS
IV.1.
Linear equations of motion
1
IV.2.
Roll motion of a ship in calm water
2
IV.2.1. Equation of motion
IV.2.2. Roll axis
IV.2.3. Undamped motion
2
2
3
IV.3.
Moments induced by waves on a fixed ship
10
IV.4.
Roll response of a ship in regular beam waves
11
IV.4.1. Solution of the differential equation
IV.4.2. Discussion
11
14
IV.5.
15
Non-linear roll motion
IV.5.1. Introduction
IV.5.2. Non-linear restoring moment
IV.5.3. Periodic variation of GM in waves
15
15
17
IV.6.
20
Roll motion control
IV.6.1. Overview
IV.6.2. Free-surface tanks
IV.6.3. Stabilization fins
20
21
26
CHAPTER V.
STEERING AND MANOEUVRING
V.1.
COURSE STABILITY AND MANOEUVRABILITY
V.1.1.
Introduction
1
V.1.2.
Course stability
2
V.1.2.1.
V.1.2.2.
V.1.2.3.
V.1.2.4.
V.1.2.5.
V.1.2.6.
Definition
Different types of motion stability in the horizontal plane
Lineair theory
Criterion of straight-line stability
Choice of the origin of the ship-fixed coordinate system
Parameters determining the straight-line stability
2
3
3
11
19
23
V.1.3.
Manoeuvrability
24
V.1.3.1. Lineair equations of motion
V.1.3.2. Phases of a turning circle manoeuvre
V.1.3.3. Influence of the hydrodynamic derivatives on the manoeuvrability
24
25
28
V.1.4.
Standard manoeuvres
29
V.1.4.1.
V.1.4.2.
V.1.4.3.
V.1.4.4.
V.1.4.5.
V.1.4.6.
V.1.4.7.
V.1.4.8.
V.1.4.9.
Introduction
Turning circle manoeuvres
Zigzag manoeuvres
Initial turning test
Spiral manoeuvres: control on the course stability
Pull out manoeuvre
Course change test
Stop tests
Criteria by IMO
29
29
31
34
34
36
36
37
37
V.2.
FORCES AND MOMENTS ACTING ON THE SHIP’S HULL
V.2.1.
Theoretical considerations
41
V.2.1.1. Basic equations: slender body theory
V.2.1.2. Acceleration dependent terms
V.2.1.3. Velocity dependent terms
V.2.1.4. Longitudinal forces
V.2.1.5. Separation of the transverse flow
V.2.1.6. Linear hydrodynamic derivatives
V.2.1.6.1. Full theory
V.2.1.6.2. Slender-body theory
V.2.1.6.3. Ship with a rectangular longitudinal profile
V.2.1.7. Alternative interpretation
V.2.1.7.1. Sway velocity derivatives
V.2.1.7.2. Yaw velocity derivatives
V.2.1.8. Lift effects
V.2.1.8.1. Introduction
V.2.1.8.2. Forces on a fin
V.2.1.8.3. Hydrodynamic derivatives of the hull
41
42
43
46
46
47
47
49
50
50
50
52
53
53
54
56
V.2.1.8.4. Influence of a fixed fin on the hydrodynamic derivatives
58
V.2.2.
Empirical formulas
62
V.2.2.1.
V.2.2.2.
V.2.2.3.
V.2.2.4.
Introduction
Formulas of CLARKE
Formulas of INOUE
Other formulas
62
63
64
65
V.2.3.
Experimental methods
66
V.2.3.1. Overview
V.2.3.2. Stationary rectilinear tests
V.2.3.2.1. History
V.2.3.2.2. Execution
V.2.3.3. Stationary rotating arm tests
V.2.3.3.1. General
V.2.3.3.2. Principle
V.2.3.4. Harmonic oscillating tests or PMM tests
V.2.3.4.1. Principe
V.2.3.4.2. Overview of PMM-systems
V.3.
66
67
67
67
68
68
69
70
17
72
RUDDER DESIGN
See appendix passive control devices
V.4.
AUTOMATIC COURSE CONTROL
V.4.1.
Introduction
100
V.4.2.
PD-control
100
V.4.2.1. Equations of motion
V.4.2.2. Solution
V.4.2.3. Influence of the dynamics of the steering engine
100
101
102
V.4.3.
PID-control
103
V.4.4.
Optimisation of the steering behaviour
104
V.4.4.1. Resistance components
V.4.4.2. Cost function
V.4.4.3. Filter characteristic
104
104
105
V.4.5.
Fuzzy logics
105
V.5.
SHIP MANOEUVRING SIMULATION
V.5.1.
Introduction
106
V.5.1.1. Macroscopic approach: traffic simulation
V.5.1.1.1. Capacity models
V.5.1.1.2. Vessel traffic models
V.5.1.2. Microscopic approach: manoeuvring simulation
106
106
106
106
V.5.2.
Bridge
108
V.5.3.
Outside view
109
V.5.3.1. Generation
109
V.5.3.2. Sight angle
109
V.5.4.
109
Mathematical model
V.5.4.1. Principle
V.5.4.2. Types of mathematical models
V.5.4.3. Models on apure mathematical basis, regression models
V.5.4.3.1. General
V.5.4.3.2. ABKOWITZ model
V.5.4.3.3. NORRBIN model
V.5.4.4. Models on a physical basis, modular models
V.5.4.4.1. General
V.5.4.4.2. The model of the Group-MMG (JTTC, Japan)
V.5.4.4.3. The modular manoeuvring model of Hamburg
V.5.4.5. NOMOTO model
V.5.4.5.1. Linear equations
V.5.4.5.2. Simplified linear equations
V.5.4.5.3. Indices K and T
V.5.4.5.4. Non-linear equations
109
110
111
111
111
112
114
114
115
117
118
118
119
120
121
V.5.5.
121
Numerical integration