EXPERIMENTAL INVESTIGATION
OF
FISHING VESSEL STABILITY
IN A
TRANSVERSE SEAWAY
By
GERALD FRANCIS ROHLING
B.Sc. The University of Calgary, 1982
A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF
THE REQUIREMENTS FOR THE DEGREE OF
MASTER OF APPLIED SCIENCE
in
THE FACULTY OF GRADUATE STUDIES
DEPARTMENT OF MECHANICAL ENGINEERING
We accept this thesis as conforming
to the required standard
THE UNIVERSITY OF BRITISH COLUMBIA
September 1986
© Gerald Francis Rohling, 1986 In presenting this thesis in partial fulfillment of the requirements for an advanced degree at the University of British
Columbia, I agree that the Library shall make it freely available for reference and study. I furthur agree that permission for extensive copying of this thesis for scholarly purposes may be granted by the head of my department or by his or her representatives. It is understood that copying or publication of this thesis for financial gain shall not be allowed without my written permission.
Department of Mechanical Engineering
The University of British Columbia 2075 Wesbrook Place Vancouver, British Columbia Canada V6T 1W5
Date: October 6, 1986 ABSTRACT
The continuing loss of life at sea due to the capsizing of fishing vessels in inclement weather requires the research and design communities to continue their search to find methods for the prevention of further occurances. As part of this investigative process this thesis was prepared.
To gain an initial foothold on the dynamics of capsizing the area of transverse seaways was considered for its contribution to capsizing through the impact of breaking waves on the side of the ship. Two model fishing vessels, built without bulwarks or superstructure, were prepared for testing in a 220 foot test basin where, through the use of computer control, a repeatable sea environment could be created. The models were equipped with adjustable displacements and centers of gravity to allow testing of IMO stability guidelines and the simulation of wind induced decreases in general stability.
Tests were conducted in still water, regular waves and breaking waves of the plunging jet type. Motions, including roll, pitch, heave, sway and yaw, were measured and stored on media for analysis by computer. Along with the electronic monitoring of the vessel's motions a video tape was made of the tests to allow visual verification of motions at a later date.
From the results of the tests it was found that the single
ii - chine seiner exhibited greater intact stability in all transverse
sea conditions tested than did the west coast trawler. Under no
circumstance did the single chine seiner capsize while, in
breaking waves, the trawler exhibited repeated capsizing behaviour when at its heaviest displacement and lowest metacentric height.
This capsizing illustrates the need for greater stability
characterisitics and improved safety criterion for breaking waves
survival over that required in regular seas.
iii - TABLE OF CONTENTS
Abstract ii
Contents iv
List of Tables vii
List of Figures viii
Nomenclature xii
Acknowledgements xv
1.0 INTRODUCTION 1
1.1 HISTORY OF SAFETY REGULATIONS 1
2.0 MODEL DESCRIPTIONS 11
2.1 SINGLE CHINE SEINER 17
2.1.1 FULL SCALE SHIP DATA 17
2.1.2 SCALE MODEL DATA 21
2.2 WEST COAST TRAWLER 22
2.2.1 FULL SCALE SHIP DATA 22
2.2.2 SCALE MODEL DATA 28
3.0 DATA ACQUISITION 29
3.1 SINGLE CHINE SEINER 29
3.1.1 AUTO PILOT 30
3.1.2 ACCELEROMETERS 30
3.1.3 VERTICAL GYRO 31
3.1.4 ANALOG TO DIGITAL CONVERTER 31
3.1.5 LIGHT EMITTING DIODE DISPLAY 32
3.1.6 IBM PCjr. MICRO-COMPUTER 32
3.2 WEST COAST TRAWLER 33
4.0 TESTING 38 4.1 TEST FACILITIES 38
- iv 4.2 TESTING SEQUENCE 38
4.2.1 CALIBRATION 38
4.2.1.1 ROLL AND PITCH ANGLES 40
4.2.1.2 YAW 42
4.2.1.3 HEAVE AND SWAY ACCELERATIONS 42
4.2.1.4 WAVE HEIGHT 43
4.2.1.5 ZERO SETTINGS IN WATER 43
4.2.2 ROLL DECAY TESTS 44
4.2.3 REGULAR SEAWAY 45
4.2.4 BREAKING WAVES 47
5.0 ANALYSIS OF DATA 49
5.1 PRE-PROCESSING 49
5.1.1 SINGLE CHINE SEINER 49
5.1.2 WEST COAST TRAWLER 51
5.2 GENERAL PROCESSING 54
5.2.1 D.C. OFFSET REMOVAL 54
5.2.2 FOURIER FILTERING 55
5.2.3 DECOUPLING THE MOTIONS 57
5.3 ROLL DECAY TESTS 59
5.3.1 ROLL EXTINCTION CURVES 59
5.3.2 VIRTUAL MASS MOMENTS OF INTERTIA 68
5.4 REGULAR SEAS RESPONSE 70
5.4.1 WAVEMAKER CHARACTERISTICS 70
5.4.2 ROLL RESPONSE AMPLITUDE OPERATORS 75
5.5 REGULAR SEAS STABILITY FACTORS 77
5.6 BREAKING WAVE RESPONSE 93
5.7 BREAKING WAVES STABILITY FACTORS 101
5.7.1 STABILITY PARAMETER S' 101
- v - 5.7.2 STABILITY PARAMETER S* 102
6.0 RESULTS AND DISCUSSION Ill 6.1 FUNCTION OF METACENTRIC HEIGHT IN STABILITY 115
6.2 FUNCTION OF FREEBOARD IN STABILITY 117 6.3 EFFECTS OF SEVERE ACCELERATIONS ON SURVIVABILITY 118 7.0 CONCLUSIONS 120 REFERENCES 121 APPENDICES 123 A. SCHEMATICS 123
B. WEST COAST TRAWLER STABILITY REPORT 138 C. FOURIER SMOOTHING 152 D. BACKGROUND THEORY 162
- vi - LIST OF TABLES
Table I IMO Work on Stability for Small Crafts 8
Table II Scaling Parameters 14
Table III Single Chine Seiner Principle Dimensions 17
Table IV Single Chine Seiner Metacentric Heights 21
Table V Single Chine Seiner Model Characteristics 21
Table VI West Coast Trawler Principle Dimensions 26
Table VII West Coast Trawler Metacentric Heights 27
Table VIII West Coast Trawler Model Characteristics 28
Table IX Relevant ASCII Characters Used 51
Table X File Numbering Guide 52
Table XI Extinction Coefficients for the
Single Chine Seiner 61
Table XII Extinction Coefficients for the
West Coast Trawler 62
Table XIII Virtual Mass Moments of Inertia
Single Chine Seiner 69
Table XIV Virtual Mass moments of Inertia
West Coast Trawler 70
Table XV Breaking Wave Amplitudes 96
Table XVI Areas for Single Chine Seiner 106
Table XVII Areas for West Coast Trawler 107
Table XVIII Summary of Stability Requirements Compliance
Single Chine Seiner 112
Table XIX Summary of Stability Requirements Compliance
West Coast Trawler 113
Table XX Specifications of the Vertical Gyro 127
- vii - LIST OF FIGURES
Figure 1 Single Chine Seiner Layout 12
Figure 2 Single Chine Seiner Lines Drawing 13
Figure 3 Restoring Arm Curves for Single Chine Seiner
216.4 Tons Displacement 15
Figure 4 Restoring Arm Curves for Single Chine Seiner
249.6 Tons Displacement 16
Figure 5 West Coast Trawler Lines Plan 18
Figure 6 West Coast Trawler General Arrangement I 19
Figure 7 West Coast Trawler General Arrangement II 20
Figure 8 Restoring Arm Curve for West Coast Trawler
328.9 Tons Displacement 23
Figure 9 Restoring Arm Curves for West Coast Trawler
437.64 Tons Displacement 24
Figure 10 Restoring Arm Curves for West Coast Trawler
551.51 Tons Displacement 25
Figure 11 Test Facilities 39
Figure 12 Calibration Rig 41
Figure 13 Processing Sequence Flow Chart 56
Figure 14 Acceleration Vector Diagram 57
Figure 15 Roll Extinction Curves for Single Chine Seiner
216.4 Tons Displacement 63
Figure 16 Roll Extinction Curves for Single Chine Seiner
249.6 Tons Displacement 64
Figure 17 Roll Extinction Curves for West Coast Trawler
328.9 Tons Displacement 65
Figure 18 Roll Extinction Curves for West Coast Trawler
- viii - 437.64 Tons Displacement 66
Figure 19 Roll Extinction Curves for West Coast Trawler
551.51 Tons Displacement 67
Figure 20 Regular Seas Wave Amplitudes - Test Amplitude #1 .... 71
Figure 21 Regular Seas Wave Amplitudes - Test Amplitude #3 .... 72
Figure 22 Regular Seas Wave Amplitudes - Test Amplitude #4 .... 73
Figure 23 Regular Seas Wave Amplitudes - Test Amplitude #5 .... 74
Figure 24 Roll Response Amplitude Operator
Single Chine Seiner
216.4 Tons Displacement, GM = 0.2557 ft 78
Figure 25 Roll Response Amplitude Operator
Single Chine Seiner
216.4 Tons Displacement, GM = 1.1516 ft 79
Figure 26 Roll Response Amplitude Operator
Single Chine Seiner
216.4 Tons Displacement, GM = 2.1331 ft 80
Figure 27 Roll Response Amplitude Operator
Single Chine Seiner
249.6 Tons Displacement, GM = 0.2557 ft 81
Figure 28 Roll Response Amplitude Operator
Single Chine Seiner
249.6 Tons Displacement, GM = 0.5113 ft 82
Figure 29 Roll Response Amplitude Operator
Single Chine Seiner
249.6 Tons Displacement, GM = 1.1516 ft 83
Figure 30 Roll Response Amplitude Operator
Single Chine Seiner
249.6 Tons Displacement, GM = 2.1331 ft 84
- ix - Figure 31 Roll Response Amplitude Operator
West Coast Trawler
328.9 Tons Displacement, GM = 3.4154 ft.
(bilge keels removed) 85
Figure 32 Roll Response Amplitude Operator
West Coast Trawler
328.9 Tons Displacement, GM = 3.4154 ft.
(bilge keels attached) 86
Figure 33 Roll Response Amplitude Operator
West Coast Trawler
437.64 Tons Displacement, GM -= 0.2953 ft 87
Figure 34 Roll Response Amplitude Operator
West Coast Trawler
437.64 Tons Displacement, GM = 1.7960 ft 88
Figure 35 Roll Response Amplitude Operator
West Coast Trawler
437.64 Tons Displacement, GM = 3.8238 ft. 89
Figure 36 Roll Response Amplitude Operator
West Coast Trawler
551.51 Tons Displacement, GM = 0.2953 ft 90
Figure 37 Roll Response Amplitude Operator
West Coast Trawler
551.51 Tons Displacement, GM •= 1.7960 ft 91
Figure 38 Roll Response Amplitude Operator
West Coast Trawler
551.51 Tons Displacement, GM = 4.1468 ft 92
Figure 39 Regular Seas Stability Factor
Single Chine Seiner 94
- x - Figure 40 Regular Seas Stability Factor
West Coast Trawler 95
Figure 41 Breaking Waves Roll Response
Single Chine Seiner 97
Figure 42 Breaking Waves Roll Response
West Coast Trawler 98
Figure 43 Breaking Waves Sway Response
Single Chine Seiner 99
Figure 44 Breaking Waves Sway Response
West Coast Trawler 100
Figure 45 Breaking Waves Stability Factor (S')
Single Chine Seiner 103
Figure 46 Breaking Waves Stability Factor (S')
West Coast Trawler 104
Figure 47 Breaking Waves Stability Factor (S )
Single Chine Seiner 108
Figure 48 Breaking Waves Stability Factor (S )
West Coast Trawler 109
Figure 49 Schematic of the Vertical Gyro 126
Figure 50 Data Telemetry System 129
Figure 51 Shipboard Instrumentation 130
Figure 52 Typical Time Domain Signal 154
Figure 53 Typical Frequency Domain Representation of
Signal 155
Figure 54 The Dynamic Coordinate System 166
2 2 Figure 55 Wave Theory as a Function of H/gT and d/gT 178
Figure 56 Velocity Profile of a Breaking Wave 181
- xi - NOMENCLATURE
Note: A brief description is given each
term used in this thesis. Following the
description is a section number in brackets,
this designates the section where the symbol
is defined in full or first mentioned.
a : virtual mass moment of inertia about longitudinal axis
(§ D)
a : Acceleration (§ 2)
A : regular seas wave amplitude (§ 5) b : Damping coefficient (§ D) b^ : Damping coefficient related to roll velocity (§ D) b^ : Damping coefficient related to roll velocity squared (§ D)
B : Center of Buoyancy (§ D)
B : Beam of the vessel (§ 2)
B(#) : Righting moment in roll (§ 1)
c() : Restoring moment as a function of time and roll angle (§ D)
c^ : Restoring moment coefficient (first order) (§ D)
cz : Restoring moment coefficient (third order) (§ D)
c^ : Restoring moment coefficient (fifth order) (§ D)
C : Block coefficient (§ 2) b C : Midship section coefficient (§ 2) m C : Waterplane area coefficient (§ 2) wp d : Water depth (§ D)
D : Depth of the vessel (§ 2)
- xii - F : Force (§ 2)
FB : Effective freeboard (§ 2) g : Acceleration due to gravity (§ 1)
G : Center of Gravity (§ D)
GM : Metacentric height (§ 1)
GM o : Initial metacentric height (§ 1)
GZ : Righting arm (§ D)
GZ2oq: Righting arm at an angle of inclination of 20° (§ 1)
GZ : Maximum righting arm (§1) max h : Height of breaking wave at impact (§ 5)
H : Breaking wave height (§ D)
I' : Virtual mass moment of inertia about the longitudinal axis
(§ D) k : Wave number (§ D) k : Spring constant (§ 5) k : Radius of gyration of the vessel mass plus the added mass XX
(§ D)
K : Baseline (§ D)
KB : Distance from the baseline to the center of buoyancy (§ D)
KG : Distance from the baseline to the center of gravity (§ D)
L : wave length (§ D)
L : Length between perpendiculars (§ 2) BP m : Mass (§ 2)
M : Metacenter (§ D)
M() : External forcing function (§ D) p : Pressure (§ 2)
R : Average roll angle in regular seas (§ 5)
- xiii R : Maximum roll angle achieved in a breaking wave (§ 5)
S : Stability factor for regular seas (§ 6)
S' : Stability factor for breaking waves - version 1 (§ 6)
5 : Stability factor for breaking waves - version 2 (§ 6) t : Time (§ D)
T : Draft of the vessel (§ 3)
T : Period of oscillation (§ 5)
T, : Natural period of oscillation in roll (§ 6)
V : Velocity (§ 3) a : Instantaneous wave slope (§ D)
a' : Maximum effective wave slope (§ D) M
A : Displacement of the vessel (§ 1)
A' : Added displacement of the vessel (§ D)
: Total virtual displacement of vessel (§ D)
4> : Roll angle relative to water surface (§ 1)
4>^ : Angle of downflooding (§ 1)
4> : Angle of heel at maximum righting arm (§ 1)
$ : Maximum roll angle in regular seas (§ 6)
A : Scaling factor (§ 3)
n : Elevation of the water surface (§ D)
p : Water density (§ 3)
6 : Instantaneous angle of roll (§ 6)
u> : Encounter wave frequency (§ D) e w : Natural frequency (§ D)
xiv ACKNOWLEDGEMENTS
First and foremost I would like to thank my supervisor, Dr.
S.M. Calisal, for his patient guidance during the planning, construction and execution of these experiments and the writing of this thesis.
The experiments themselves would never have been possible without access to a towing tank and thus I would like to express my great appreciation to Gerry N. Stensgaard, Manager of the Ocean
Engineering Center, for the use of the facilities at B.C.
Research. In addition I would like to thank George Roddan and Gary
Novleski of the Ocean Engineering Center for their always excellent technical assistance during the building and testing of the models.
A number of other people lent invaluable assistance during the course of this work. In particular I would like to thank
Marcel LeFrancois for the software, and Steven Thompson for the electrical work, in the Seiner model. I also wish to thank Irene
Blank, Alejandro Allievi, Farshid Namiranian, Dan McGreer and
Gireesh Sadasivan, among others, for their assistance during the testing of the models.
Portions of this research were funded by the B.C. Science
Council, the Defense Research Establishment Atlantic (D.R.E.A.), and the National Research Council (N.R.C.). Their assistance is greatly appreciated.
- xv - 1.0 INTRODUCTION
1.1 HISTORY OF SAFETY REGULATIONS
The need for some type of guideline for the definition of ship safety is nearly as old as water-borne craft itself, the first formulation of a safety guideline was probably borne of experience and misfortune, ie: trial and error. When an early traveller encountered a body of water he searched for some manner of conveyance to transport him and his supplies across. The earliest of these craft was supplied by nature and may have been either logs or rafts. Rafts exhibited great stability but when man decided to streamline this craft by reducing it to a single log it was rapidly realized that the former stability had been sacrificed, as anyone who has tried standing on a floating log can testify.
Thinking of how to reduce this problem the potential sailor attempted to lower his center of gravity when he noticed that as his height reduced so did the rate at which he was rather unceremoniously dumped into the chilly waters. With the help of tools newly developed he was able to hollow the log out, and sit inside. This was a much more rewarding arrangement.
Over the millennia this rudimentary form of water-borne transportation developed through the transformation of the single log craft to a skin of material over a frame and from the motive forces of hands paddling in the water to oars and sails. Sailing ships were found to be in use in Egypt as early as 3500 B.C. and
- 1 - by 3000 B.C. [1] they were freely navigating the eastern
Mediterranean, and probably also the Arabian Sea. The use of sails once again presented a stability problem which was overcome this time by the storing of ballast weight in the lowest parts of the hull and later by the suspension of weights under the hull in the form of a ballasted keel.
From the fourth millennium to the later Middle Ages the steering mechanisms of these ships remained virtually unchanged.
Steering was still accomplished by the trailing of a long oar behind the vessel. In larger sailing ships the oar was attached to the stern and fitted with a lever to garner greater mechanical advantage. Little was done to change this system and galley slaves were used to aid in the steering of these vessels, a factor in the maintaining of slavery in vessels until the sixteenth century when, with the advent of naval artillery, it was necessary to make room for cannons on ships crowded with galley slaves.
In eighth-century China the vertical rudder came into use and over time this technology filtered back to Europe. By the fifteenth century European shipping was growing by leaps and bounds as the new rudder allowed greater speeds by allowing the ship to sail closer to the wind. Speed was also increased by the carrying of a much greater sail area. In 1492 the Atlantic was crossed.
All through this period of expanding commerce the safety of vessels was more or less a matter of experience and good fortune.
- 2 - As an example on July 19th, 1545, the 120 foot, 700 ton English battle ship Mary Rose sank in Portsmouth harbor after just hoisting sail for battle against the invading French [2]. The sudden capsizing and sinking of the vessel is still veiled in controversy (the French Naval Authorities claim they sank it) but it is known that it was in a serious breach of stability. At the time of its sinking it was 35 years old, originally built in 1510 and named after King Henry VIII's sister Mary Tudor. Because of the war it was brought in for refitting and rearmament with the latest equipment. At some point heavy bronze guns, which represented the latest in metallurgical technology, were added - guns she had not been originally designed to carry. In addition she carried 285 heavily armored soldiers on deck, over and above her regular crew of 415 men. This refitting was calculated to add another 24 to 25 tons to Mary Rose's displacement, all far above the waterline. Another addition, hoisted from deck level to about ten feet into the air around the perimeter of the ship, was an anti-boarding net.
Ready for battle the sails were hoisted and the sailors waited for that first gust of wind to carry them into battle. A swell in the wind filled the sails and she surged forward.
Suddenly, without warning, the vessel veered and water flooded in through the open gun ports. As the shocked King looked on the ship heeled over into the water and capsized, to sink like a stone. All this happened in under a minute and only 30 of the estimated 700 crew members survived.
- 3 - In the 1800's the advent of steam once again transformed the ships of the world. Still powered by paddles, now in the form of huge side mounted paddle wheels, they grew in power and versatility. One of the first steamships, the Charlotte Dundas, built in 1802, towed two 70-ton barges 19-j miles in 6 hours along the Dalswinton Loch in England against a headwind so strong no other vessel dared sail in it. Britain followed the Americans into the building of steam powered warships in 1833. Steam was still considered inadequate, though, for long voyages until in 1838 the
Sirius crossed the Atlantic in less than 20 days, a record held only a few hours when it was broken by the Great Western which made the same voyage in 15 days.
After the capsizing of the British warship Captain in 1870, while on a routine mission [3], it was decided that the dependence of the restoring moment on the angle of heel, not just on its upright position, as described by the relationship;
B(^) - gAGM^ (1.001)
where: g = acceleration
due to gravity
A = displacement
GM «= metacentric
height
4> = roll angle
was important and should be considered. This marked the starting point for the prescribing of minimum values for righting moments.
- 4 - In his 1939 doctoral thesis Rahola made a proposal for the stability requirements of small ships based on those of Benjamin
(1913) and Pierrottet (1935). This proposal was developed through
a survey of successful and unsuccessful ships of that time based
on casualty reports. From this he drew up the following
conclusions [4]:
(a) the values of the arms of statical stability must be:
i) at least 0.14m at an angle of 20° and,
ii) at least 0.20m at an angle of 30°;
(b) the "critical angle" of heel is meant the angle of heel
at which the curve of arms of statical stability reaches
its maximum value.
These requirements are referred to as the Rahola stability
criteria. A recent investigation of Raholas work has shown that
the sample size used for the development of the criteria was not
statistically significant. Nevertheless, this criterion is the
basis for many of the national regulations or recommendations
including the Intergovernmental Maritime consultative Organization
(IMO) recommendations for small passenger ships, fishing vessels
and, more recently, supply ships.
During the early years of IMO (then known as IMCO) analysis
of intact stability casualty records for both cargo ships and
fishing vessels were carried out by delegations from countries
such as Germany, Poland and France with proposals put forth for
- 5 - stability criterion by Poland, USSR, Denmark, Germany, France,
Sweden and others. For these initial studies 7 parameters were chosen for investigation to find which should be used for establishing stability guidelines. These parameters were:
(i) [GM ] initial metacentric height o (ii) [
(iii) [
(iv) [GZ ] maximum righting arm max
(v) [GZ2Q0] righting arm at an angle of inclination of 20°
(vi) [<£f ] angle of downflooding
(vii) [
Upon receipt of all the reports and recommendations four of the above parameters were chosen for further study by the various delegations at IMO:
(i) [GZ ] maximum righting arm max
(ii) ] angle of vanishing stability
(iii) [
From the results of these studies a number of stability parameters were finally selected and numerical values assigned to form the present day IMO recommended criteria.
IMO criterion as recommended for fishing vessels:
- 6 - A. The area under the GZ curve up to an angle of heel
of 30° must be greater than 0.055 meter-radians.
B. The area under the GZ curve up to an angle of heel
of 40°, or the angle of downflooding
40°, must be greater than 0.09 meter-radians.
C. The area under the GZ curve between 30° and 40° of
heel, or between 30° and d> if less than 40°, must be f
greater than 0.03 meter-radians.
D. The maximum righting arm beyond 30° of heel must
be greater than 0.2 meters.
E. The angle of heel where the righting arm is a
maximum must be greater than 30°.
F. The initial metacentric height, GM , must be o greater than 0.35 meters.
In some national regulations, the so-called weather criterion
is used, which includes the influence of wind induced heeling moments on the area under the still water righting lever curve. In addition a water-on-deck criterion has also been added to some criterion as small craft capsizings have been attributed to this phenomenon.
- 7 - Situation Cargo Vessels Fishing Vessels
1. Steady wind Calculation proced• General procedure given and wind ure worked out 1983 in T.C. gusts with Coefficients under severe consideration rolling
2.Following Calculation proced• As for cargo vessels waves ure under study. Criteria not yet - loss of Criteria proposal proposed stab, on by GDR. crest - broaching No calculation proc• As for cargo vessels edure available - Criteria not yet under study proposed
3. Breaking No calculation proc• No calculation procedure waves from edure available - available but under side under study study. Criteria proposal
by Norway (<£v> 80°)
4.Forces from Calculation procedure — fishing gear available but not under study. Criteria proposal by U.S.S.R.
5.Water on No Calculation proc• Calculation procedure deck edure available - given in principle in under study T.C - under study
6.Icing Under observation Calculation procedure in T.C. - under obser• vation
7.Flooding Probabilistic Not under study. concept recommended. Damage control plan concept worked out 1983 - under study.
Table I - IMO work on Stability for Small Crafts From Intact and Damaged Stability of Small Crafts with Emphasis on Design by Emil Aall Dahle, and Gunnar Edvin Nisja, University of Trondheim, 1984. (T.C. = Torremolinos Convention) [5]
The present trend in IMO is to supplement the minimum GZ requirements with functional requirements based on the operating
- 8 - conditions expected during the vessels lifetime. A summary of the
status of the IMO's "Sub-Committee on Stability, Load Lines and
Fishing Vessel Safety" is shown in Table I.
Stability criterion for the stability of fishing vessels when
subjected to breaking waves from the side is still under study as
illustrated by Table I. Up to the present time the only additional
criterion put into regulation expressly to counteract the effects
of breaking wave capsizing is to require a minimum angle for vanishing stability of 80°.
Fishing vessels offer a rather unique problem to the designer
in that it will be operated over a large range of displacement and
weight distributions thus creating the added inconvenience of not
being able to design for a certain operating condition as with
most other craft.
Despite the best efforts of a large number of research and
governing bodies there is still a recurring illustration of the
inadequacies of the fishing fleet with regards to safety by the
repeated accounts of ships lost at sea. Fishing being one of the most dangerous occupations, surpassing even such notably hazardous
occupations as coal mining.
Because of these continuing losses, many occurring in heavy weather, there is a push to more accurately define the mechanisms
involved in a capsizing due to breaking waves taken on the beam.
With this in mind a program for the investigation of fishing
- 9 - vessel dynamics was started at the University of British Columbia
Department of Mechanical Engineering. This program involves the dynamical response testing of scale model fishing vessels in a controlled environment with an emphasis on determining unstable operating conditions.
- 10 - 2.0 MODEL DESCRIPTIONS
Two fishing vessel designs were studied for this research. The first design was of a single chine fishing seiner designed for Cleaver and Walkingshaw of Vancouver by B.C. Research Ocean Engineering Center staff and represents the typical form of the vessel. The second design tested was of a fishing trawler designed by Peter S. Hatfield Ltd. of Vancouver. This design represents the latest design technology for this class of fishing vessel. The single chine design has not, as of the date of this thesis, been built and thus remains only a design consideration. The trawler, on the other hand, has been built and in now currently operating off the West Coast.
Both of the models were manufactured of wood by F.M. Pattern Works of Vancouver according to the original lines drawings of the respective Naval Architecture firms. The models were of the hull design only and thus excluded any bulwarks, deck fixtures or superstructure.
To determine the size of the model required a manner of being able to scale relevant properties is required. The method of determining the scaling factors is through a non-dimensionalizing procedure called the Buckingham Pi Theorem. This theorem allows the selection of what appear to be all the relevant parameters and then applying the theorems principles to obtain non- dimensionalized sets of these parameters. A table of the resulting scaling parameters is shown in Table II.
- 11 - cleaver & walklngehaw Jtd. I. naval architect* : V 1W
- 12 - - 13 - To make the table easier to understand the relations shown use two basic ratios determined from the non-dimensionalizing procedure, these are; A, the ratio of the ship length to the model length and c, the ratio of ship water density to model water density.
TABLE II
SCALING PARAMETERS
Parameter Full Scale Model
Length L L/A
Density P p/c
Time t t/A1/2
Mass m m/cA3
Velocity V V/A1/2
Acceleration a a
Force F F/cA3
Moment M M/cA*
Pressure P. p/cA
Frequency w wA1'2
The scaling for length is the same for all the other dimensions of the model, ie:
r = ir - r - A (2-001)
- 14 - RESTORING ARM CURVES SINGLE CHINE SEINER 216.4 TONS DISPLACEMENT
4.5
20 40 60 80 100 120 140 ANGLE OF HEEL (degrees)
Figure 3. Restoring Arm Curves for Single Chine Seiner 216.4 Tons Displacement
- 15 - RESTORING ARM CURVES SINGLE CHINE SEINER 249.6 TONS DISPLACEMENT
20 40 60 80 100 120 140 ANGLE OF HEEL (degrees) Figure 4. Restoring Arm Curves for Single Chine Seiner 249.6 Tons Displacement
- 16 - 2.1 SINGLE CHINE SEINER
2.1.1 FULL SCALE SHIP DATA
The full scale dimensions of the seiner are summarized in
Table III while a general arrangement plan and the lines drawing can be found in Figs. 4 and 5 respectively.
TABLE III
SINGLE CHINE SEINER
PRINCIPLE DIMENSIONS
LIGHT HEAVY
Length Overall (LOA) 77.0 ft. 77.0 ft.
Length Between Perpendiculars (L^) .... 69.9 ft. 69.9 ft.
Beam (B) 23.0 ft. 23.0 ft.
Depth (D) 15.0 ft. 15.0 ft.
Draft (T) 9.5 ft. 10.5 ft.
Displacement (A) 216.4 tons 249.6 tons
Block Coefficient (C ) 0.500 0.531
Midship Section Coefficient (C ) 0.756 0.775 m Waterplane Area Coefficient (C ) 0.850 0.862 wp KM 13.078 ft. 12.818 ft.
The metacentric heights used in the testing were determined from a review of existing vessels of similar design and displacement. From this survey it was found that metacentric heights of from 1% to 10% of the beam value would be appropriate.
- 17 -
Figure 6. West Coast Trawler General Arrangement I w*m DICK
Figure 7. West Coast Trawler General Arrangement II The actual values used are shown in Table IV and the righting arm curves for the two displacements tested are shown in Figs. 6 and
7.
TABLE IV
SINGLE CHINE SEINER
METACENTRIC HEIGHT TABLE
LIGHT HEAVY % B
GM # 1 0. .2557 ft. 0. .2557 ft. 1. .11
GM # 2 N/A 0. .5113 ft. 2, .22
GM # 3 1. .1516 ft. 1. .1516 ft. 5. .00
GM # 4 2. .1331 ft. 2. ,1331 ft. 9. .27
2.1.2 SCALE MODEL DATA
The model of the seiner was built on a scale of 13:1. The
dimensions of the model are given below in Table V. The model was built without bulwarks or superstructure.
TABLE V
SINGLE CHINE SEINER
SHIP MODEL CHARACTERISTICS
Light Heavy
Length Overall (LOA) 5.923 ft. 5.923 ft.
Length Between Perpendiculars (L ) 5.381 ft. 5.381 ft. bp
Beam (B) 1.769 ft. 1.769 ft. Depth (D) 1.154 ft. 1.154 ft.
- 21 - Draft (T) 0.730 ft. 0.808 ft.
Displacement (A) 220.6 lbs. 254.5 lbs
Block Coefficient (C ) 0.500 0.531 b Midship Section Coefficient (C ) 0.756 0.775 m Waterplane Coefficient (C ) 0.850 0.862 wp KM 1.006 ft. 0.986 ft.
GM # 1 0.236" or (1.11% B)
GM # 2 0.472" or (2.22% B)
GM # 3 1.063" or (5.00% B)
GM # 4 1.969" or (9.27% B)
2.2 WEST COAST TRAWLER
2.2.1 FULL SCALE SHIP DATA
The trawler form tested was taken from lines drawings of an
existing fishing vessel. It was therefore possible to obtain the
actual full scale operating configurations from the inclining
experiments done as per Canadian Coast Guard Safety regulations.
The stability booklet prepared from the experiments is shown in
Appendix C. A brief synopsis of the pertinent data can be found in
Table VI.
- 22 - RESTORING ARM CURVE WEST COAST TRAWLER 328.9 TONS DISPLACEMENT
4.5
Legend A GM = 3.4/ 54 ft. 3.5H
3H
2 CC 2.5 < i 2 o co 1.5 H LU tr
0.5 H
20 40 60 80 100 120 140 ANGLE OF HEEL (degrees) I Figure 8. Restoring Arm Curve for West Coast Trawler 328.9 Tons Displacement - 23 - RESTORING ARM CURVES WEST COAST TRAWLER 437.64 TONS DISPLACEMENT
40 60 80 100 140 ANGLE OF HEEL (degrees) Figure 9. Restoring Arm Curves for West Coast Trawler 437.64 Tons Displacement - 24 - RESTORING ARM CURVES WEST COAST TRAWLER 551.51 TONS DISPLACEMENT
4.5
Legend A GM = 4.1468 ft. X GM = /.796 /t. 3.5 • CA/ = 0.2953Jt.
3
< (D tZr o H CO UJ 1.5- * \ \ \ * \ \ \ \ * \ \ \ \
\ \ \ \ / 4 \ / / \ i
0.5- » \ \ \ I \
D 20 40 60 80 100 120 140 ANGLE OF HEEL (degrees) Figure 10. Restoring Arm Curves for West Coast Trawler 551.51 Tons Displacement
- 25 - TABLE VI
WEST COAST TRAWLER
PRINCIPLE DIMENSIONS
LIGHT MEDIUM HEAVY
Length Overall (LOA) 107.0 ft. 107.0 ft. 107.0 ft.
Length Between
Perpendiculars (L ) 99.75 ft. 99.75 ft. 99.75 ft.
Beam (B) 29.20 ft. 29.20 ft. 29.20 ft.
Depth (D) 28.50 ft. 28.50 ft. 28.50 ft.
Draft (T) 9.60 ft. 11.32 ft. 13.01 ft.
Displacement (A) 328.90 tons 437.64 tons 551.51 tons
Block Coefficient (C.) ... 0.3379 0.3823 0.4240 D Midship Section
Coefficient (C ) 0.5976 0.6374 0.6730 m Waterplane Area
Coefficient (C ) 0.7433 0.7851 0.8120 wp KM 16.183 ft. 15.763 ft. 15.500 ft.
The metacentric heights were not determined as a percentage of the beam but were taken from the actual measured values obtained during the inclining experiment. For comparison purposes the metacentric heights shown in Table VII are also given as the percentage of the beam. In addition the righting arm curves calculated for the configurations tested are shown in Figs. 11, 12 and 13.
- 26 - TABLE VII
WEST COAST TRAWLER
METACENTRIC HEIGHTS
LIGHT MEDIUM HEAVY % B
GM # 1 N/A 0.2953 ft. 0.2953 ft. 1.01
GM # 2 N/A 1.7960 ft. 1.7960 ft. 6.15
GM # 3 3.4154*ft. N/A N/A 11.70
GM # 4 N/A 3.8238^ft. N/A 13.10
GM # 5 N/A N/A 4.1468*ft. 14.20
design GM values.
GM # 1 was chosen as an arbitrary worst case scenario. This
GM represented the smallest GM value expected in operation under the most adverse loading conditions. GM # 2 is the minimum allowable design GM as defined by the Intergovernmental Maritime
Consultative Organization safety regulations regarding fishing vessels [6]. The minimum value can be found through the relationship,
GM = 0.53 + (2 x B x (GM + GM )) (2.002) MIN 12
GM - 0.075 - 0.37 x + 0.82 x [?|]2 (2.003)
GM = -0.014 x fjh (2.004)
where
B = maximum beam (meters)
FB —: effective freeboard (meters) T = draft of vessel (meters)
- 27 - The results are expressed in meters.
2.2.2 SCALE MODEL DATA
The model of the trawler was built to a scale of 15:1.
Following the configurations set above the following dimensions for the model were derived.
TABLE VIII
WEST COAST TRAWLER
MODEL PARAMETERS
Light Medium Heavy
Length Overall (LOA) 7.1 ft. 7.1 :ft . 7.1 ft.
Length Between Perpendiculars (L ) 6.65 ft. 6.65 ft. 6.65 ft. bp Beam (B) 1.95 ft. 1.95 ft. 1.95 ft.
Depth (D) 1.90 ft. 1.90 ft. 1.90 ft.
Draft (T) 0.64 ft. 0.75 ft. 0.87 ft.
Displacement (A) (in tons) 221.4 294. <6 371.0
Block Coefficient (C ) 0.3379 0.3823 0.4240 b Midship Section Coefficient (C ) 0.5976 0.6374 0.6730 m Waterplane Area Coefficient (C ) 0.7433 0.7851 0.8120 wp KM 1.08 ft. 1.05 ft. 1.03 ft.
GM # 1 N/A 0.02 ft. 0.02 ft.
GM # 2 N/A 0.12 ft. 0.12 ft.
GM # 3 0.23 ft. N/A N/A
GM # 4 N/A 0.25 ft. N/A
GM # 5 N/A N/A 0.28 ft.
- 28 - 3.0 DATA ACQUISITION
To accurately monitor and record the motions of the models
during the testing program a suitable system had to be developed.
Over the year and a half that was required to test the two models
the type of system used changed dramatically. The first model
tested, the single chine seiner, had a fully self contained system
on board. That is, all the equipment from sensors to data storage were all contained within the vessel. With the second model the
electronics had undergone a complete reworking with the purchase
of a remote data telemetry system which allowed the removal of a
large part of the on-board equipment to shore.
Each of the systems used will be described separately but the
emphasis will be on the second system as it was assembled and
developed under the supervision of the author. The earlier system, used in the single chine model, was already constructed and
operational when the model was received and therefore was used without alteration. A more complete description of the earlier
electronics system can be found in a thesis being written by
Alejandro Allievi of the Department of Mechanical Engineering,
University of British Columbia, entitled "Experimental and
Numerical Analysis of a Fishing Vessel's Motions and Stability in
a Longitudinal Seaway".
3.1 SINGLE CHINE SEINER
Motions necessary to define the full range of ship
- 29 - displacements included roll, pitch, heave, sway, surge and yaw.
Each of these displacements or rotations were measured by appropriate mechanisms and the information relayed to an analog-to-digital converter which sampled the data signals and fed the bit stream into the serial port of an IBM PCjr home computer.
This binary information was collected in a memory buffer until a preset level was reached and then transferred as a block to an analog tape recorder for subsequent retrieval and analysis.
A schematic of the electronics can be found in Fig. 51 showing the major components and their connections. Following is brief description of the components involved in the system.
3.1.1 AUTO PILOT
To measure the yaw of the model an autopilot/compass system developed by Wagner Engineering of North Vancouver was installed.
This system is identical to those found on many leisure craft throughout North America. The system represents the latest in technology for the company and has high frequency response characteristics ideal for use in model testing. Power required for the operation of the device was 12 VDC and this was supplied by the on-board batteries of the model.
3.1.2 ACCELEROMETERS
To measure the displacements in the heave and sway directions the model was instrumented with linear accelerometers oriented
- 30 - along the heave and sway axis of the model. The accelerometers were Schaevitz ± 2.0 g. servo type versions with a requirement of
± 13.0 Volts D.C. excitation. The excitation was supplied by two sets of 12 V.D.C. batteries each wired in series with their own
1.5 V.D.C. supplemental supply to provide approximately ± 13.0
V.D.C. .
3.1.3 VERTICAL GYRO
The motions of the model in rotation about two of its principle axis were of primary importance in this research work.
To provide direct measurement of this rotation a Humphry
VG24-0825-1 dual axis vertical gyro was installed to measure both roll and pitch. Output of the two axis was provided by potentiometers mounted on the shafts of the internal cage mechanism. Excitation was provided to each of these potentiometers by independent 9 V.D.C. batteries.
3.1.4 ANALOG TO DIGITAL CONVERTER
To transform the analog signals produced by the various sensors corresponding to the associated measured quantities it was necessary to install a device capable of converting these values.
The unit used was an ADC-1 which is capable of sampling at a rate of 70 samples per second. The channels are sampled concurrently and then fed into the serial port of the PCjr, micro-computer in series. Power for the unit was supplied by the 12 VDC battery on board.
- 31 - In addition to receiving data the unit was also capable of converting digital values read from the serial port and converting these into analog voltages. This was used to power the L.E.D. display on board the model.
3.1.5 LIGHT EMITTING DIODE DISPLAY
To be able to convey at all times the status of the electronics system aboard the model it was necessary for some type of display. Because there was no possible method of using a monitor to display the computer status a set of light emitting diodes (L.E.D.'s) was installed. The lights were illuminated according to the status being indicated. The status values were: i) system ready to record, ii) system recording, iii) system writing data to tape and iv) system resetting. One further condition was portrayed coincidentally, this condition was of electrical malfunction caused by insufficient electrical power and was indicated by any number of lights being lit in an arbitrary pattern.
3.1.6 IBM PCjr. MICRO-COMPUTER
To act as central control to the entire electrical data acquisition system an IBM Pcjr micro-computer was installed. This computer was chosen because of its compact size and relatively inexpensive cost proportional to its computing power, because it was capable of being controlled with a wireless infrared link
- 32 - keyboard and thirdly, because it was compatible with standard IBM desktop computers allowing us to demultiplex the cassette data easily and conveniently.
Because the computer was originally designed to operate on AC power the internal power transformer of the unit had to be modified such that it could function with a 24 VDC power supply.
Because the internal circuitry required only 12 VDC and 5 VDC supplies this posed no great problem.
3.2 WEST COAST TRAWLER
Experience with the single chine seiner, as well as listening to reports of earlier attempts at data collection with previous models in the department indicated that an upgrading of the equipment used in the sensing, collecting and storing of the data was in order. It was thus decided that, starting with the trawler model, a new electronics system would be developed.
With this in mind a study was made of the important aspects of the testing program and how they may affect the type of system we would require. The major point point of consideration was a planned set of experiments to be done outdoors in free running trials. Because of this no direct link between the model and any other unit was acceptable as umbilical cords, besides being awkward and cumbersome also adversely affected the true dynamical response of the vessel. The cord acting as both extra mass and a damper on the true motions of the model due to drag and inertia.
- 33 - Another factor found to be very important was the matter of weight. In previous tests, including the single chine seiner, it was found to be impossible to install all the required batteries, motors, servos, sensors, converters and recorders and still retain a displacement less than the design light ship condition. In parallel to this was the problem of space, with all the equipment required to be carried on board space became a premium and optimum placement of electronics could not always be accommodated. With this in mind it was decided that as much electronics as possible was to be left on shore.
Free running tests required external control of the model and
thus, just as in earlier configurations, a remote control system using components found in hobbyist applications was installed to
control propeller speed and direction as well as to control the
rudder angle. All controls were built as proportional controls with a high degree of resolution. To power the vessel a 24 VDC high torque electric motor was installed running through a 5:1
reduction gearbox. Voltage to the motor was supplied by two 12 VDC batteries through a regulator connected to the radio control
receiver. The receiver was powered in turn by its own 6 VDC
rechargeable battery supply.
Powering of the vessel now decided, the next step was to
allow measurement of the appropriate vessel displacements.
Installation of a vertical axis gyro, compass and linear
accelerometers was next. Excitation was required for these sensors
34 - and thus a means of reducing the number and variety of batteries was searched for. In the end a signal conditioner built by
Terrascience of Vancouver was selected. The signal conditioner played many roles in the vessel. It required a single power source providing anywhere from 10 to 40 VDC and can supply from eight different channels either variable (0 to 10 VDC) or fixed (±13
VDC) excitations. For the accelerometers fixed ± 13 VDC excitation were required and thus the fixed output was selected which is factory preset at exactly ±13 VDC. For the compass/autopilot a supply in the range of 12 VDC was required. This was beyond the scope of the signal conditioner but was equal to the input voltage to the conditioner so the supply was derived from the terminal strip supplying voltages to the internal electronics. Also along the same lines was the vertical gyro. This piece of equipment required 28 VDC to operate but was proven to work with reduced voltages without appreciable degradation in quality.
Since the motor powering the model required 24 VDC there was already a good source available. Tapping into the terminal strip we were able to provide sufficient voltage for the gyros operation. This reduced to two the number of batteries required to operate the model. In contrast the single chine seiner required 10 batteries ranging in size from 1.5 VDC to 12 VDC.
With the reduction in the number of batteries recharging the system was a simple operation requiring only the isolation of the batteries from the electronics, a matter of throwing two surface mounted switches, and connecting the charger jumper wires in
- 35 - parallel to the two batteries.
Other sensors mounted in the model included a rudder angle sensor installed for later testing in following seas. The rudder angle was measured by a potentiometer mounted above and mechanically connected to the rudder shaft. Excitation for the potentiometer was supplied by the signal conditioner.
Having installed all the sensing equipment a means of collecting and storing the data was still required. The signal conditioner acted as a main clearing centre for all the shipboard data. Each sensor was assigned a channel in the conditioner which each contained a circuit for filtering and amplifying the signal. Low pass filters were installed to eliminate any noise picked up by the wiring from sources such as electric motors or fluorescent lighting. Gains were selected such that each channel would provide a ±10 VDC full scale output. This made all the data channels uniform and easier to handle.
To keep the amount of electronics to a minimum it was decided that this was the maximum we wanted to carry on board the model, save one. To get the data from the model to shore some form of transmission was required. After a market search a telemetry system was found that seemed to fit the bill. This system, produced by Sigma Data of Surrey, B.C., allowed the simultaneous transmission of up to eight channels from a remote source to a receiver up to three miles away.
- 36 - The telemetry system required only that a transmitter and antenna be placed in the model. No other electronics was required.
To provide the ±5 VDC input the telemetry system was designed to accommodate the output of the signal conditioner was stepped down through the use of a voltage divider.
The signals were all fed into the telemetry system transmitter which assigned to each channel a unique frequency in the audio band. The amplitude of each of these frequencies was modulated in proportion to the voltage of the input signal. A +5
VDC offset was added to all the input signals so that they read from 0 to 10 VDC to facilitate this conversion.
Once the conversion was complete the audio signals were summed and attached to a UHF carrier frequency provided by the UHF radio transmitter built into the system. This signal was then fed to an internal ground plane omni-directional antenna capable of broadcasting from nearly any orientation making it suitable for a model which may, at times, be required to broadcast from angles of roll exceeding 90 degrees; or totally inverted. Power for the transmitter was supplied by one of the single 12 VDC lead acid batteries.
A more complete description of the electronics, including schematics and specifications can be found in Appendix A.
- 37 - 4.0 TESTING
4.1 TEST FACILITIES
To allow the testing of the model in a known repeatable wave environment a test basin was required. The Ocean Engineering
Center of B.C. Research provided access to the towing tank at their facility for the several months required for the stability testing.
The towing tank in the Ocean Engineering Center is 220 feet in length, 12 feet in width and 8 feet in depth. It is equipped with a programmable hydraulically operated wavemaker situated at one end of the tank and a preparation tank at the other. A movable beach can be raised to block the towing tank test section from the preparation tank. A schematic of the testing facilities is shown in Fig. 11.
4.2 TESTING SEQUENCE
A large amount of data was created during the testing program. This data gathering can be divided into three main groups or sections: still water response, regular seaway response and breaking wave response. This section will present the methods used to obtain the data.
4.2.1 CALIBRATION
- 38 - JANUARY 9, 1986 BEAM SEAS ROLL RESPONSE UNIVERSITY OF BRITISH COLUMBIA TEST FACILITIES DRAWN BY" GERRY RDHLING To be able to accurately measure the response of the models the instruments on the model had to calibrated so that the motions of the model would be correctly represented. To do this a calibration rig was devised. This rig, illustrated in Figure 12, allows the model, outside of the tank, to be rotated to any selected angle and the voltages output by the various sensors recorded. Briefly described here will be how each sensor was calibrated for its respective sense.
4.2.1.1 ROLL AND PITCH ANGLES
The model was placed on the calibration rig such that it was constrained to rotate only about an axis perpendicular to the centerplane of the model for roll and parallel to the centerplane for pitch. The instrumentation was then turned on and the equipment allowed to reach operating speed and temperature. Once the equipment was ready the boat was placed with the design waterline parallel to the horizontal. The voltage output by the gyroscope was measured and the offset in the Signal Conditioner adjusted such that the voltage received and displayed by the shore unit was zero. This value was then noted for zero degrees roll or pitch.
The model was then rotated 10 degrees in the clockwise direction and fixed. A reading was made of the voltage output by the shore unit and noted. This was repeated up to about 40 degrees of roll or pitch (the limits of the rig with a 300 pound model attached) and then repeated for the counter-clockwise direction. A
- 40 - JANUARY 10, 1986 BREAKING WAVE RESPONSE TESTS UNIVERSITY DF BRITISH COLUMBIA CALIBRATION RIG DRAWN BY* GERRY ROHLING full calibration file was then completed. In these cases the results were linear hence a straight line was fitted to the data and the slope and intercept determined.
4.2.1.2 YAW
The model was placed on a large table equipped with wheels and situated away from any strong magnetic sources. The equipment was turned on and allowed to reach operating temperature. The model was then rotated so that the bow of the model pointed due north according to the on-board compass. The autopilot was then zeroed at true north. The output of the autopilot to the shore unit should read zero at this point and the signal conditioner
offset was adjusted to produce the zero reading.
With the zero point noted the model was rotated 15 degrees and the output of the auto-pilot noted. The model was then rotated another 15 degrees and again the output noted. This was repeated every 15 degrees until the model had completed a yaw of 90 degrees. The model was then brought back to true north, the zero checked for repeatability and then the same procedure was done in the other direction to give a calibration range of ± 90°. The calibration was linear within this range so a slope-intercept was determined.
4.2.1.3 HEAVE AND SWAY ACCELEROMETERS
The procedure for heave and sway calibration follows very
- 42 - closely the procedure for roll. Instead of noting just the roll angle and then taking the acceleration readings the component of the gravitational vector acting upon the sensitive axis of the accelerometers was recorded and the calibration done against this acceleration. These values were also linear and provided a slope and intercept.
4.2.1.4 WAVE HEIGHT
The wave height was measured using a two-wire resistance wave probe suspended from a footbridge spanning the towing tank just
"upstream" from the model's location in the tank. (See Fig. 11
[Test Facilities]) The tank was allowed to settle such that the surface was smooth and then the wave probe was adjusted such that its center position was at the waters surface. The voltage output was recorded. The wave probe was then raised in steps of one inch
(signifying a drop in the water surface) and the output voltage at each step recorded up to 5 inches. The probe was then brought back to zero, the voltage output re-checked, and then the procedure was repeated with the wave probe being immersed in the water in one inch steps. The output was found to be linear so a slope and intercept was determined.
4.2.1.5 ZERO SETTINGS IN WATER
Despite having zeroed every instrument on the calibration rig there is still the possibility of instrument drift due to temperature, battery voltage and local geo-magnetic fluctuations.
- 43 - Because of this possible change in instrument zero before the start of each series of test runs the model was placed in the tank, instruments running, and allowed to settle to the desired rest position. Once the model was motionless the data acquisition was started to record a file of the voltage values output by the instruments. This file was then saved along with the data files collected in that set and used to remove any residual DC offset.
4.2.2 ROLL DECAY TESTS
To gather data on the damping of the hull form, the natural frequencies of the various configurations tested and the in-water roll moments of inertia a roll decay test was deemed necessary.
While the model was held at some arbitrary angle the water surface in the tank was allowed to settle down such that there were no perceptible waves present. When the surface had become sufficiently calm the model was released and allowed to oscillate unhindered. Upon release of the model data collection was initiated. In addition to the electronic data collection a stopwatch was used to measure the time required for 10 full cycles of oscillation to occur. A video record of the roll decay test was made for future reference.
A quick calculation was then made to determine the approximate value of the natural frequency through the relation,
- 44 - 10 (4.001) n T 10
where:
T 10 10 time for oscillations
and to = natural frequency (Hz . )
This process was repeated three times and the average value of the natural frequency measured was recorded for use in the regular seas segment of the test as the center value of the frequency range to be tested.
Each roll decay test was repeated three times, each one starting at a larger initial roll angle than the one before. It was attempted to have the last roll decay measured to start at the vanishing angle of stability. Care had to be taken during this final test as the model was just as likely to initiate roll in the capsizing directions as the restoring direction. Occasionally the motion had to be arrested and restarted if the model showed a tendency toward capsizing.
4.2.3 REGULAR SEAWAY
This section of the test matrix allowed the measurement of the response of the vessel to a regularly repeating wave forcing function of a pre-determined frequency and amplitude. This testing of the response in a very narrow-banded spectrum allowed the individual measurement of points on the response amplitude operator curves. From the roll decay tests conducted earlier it
- 45 - was known what the roll natural frequency was and thus the test frequencies chosen were arranged such that the natural frequency of the configuration being tested would fall halfway between the lowest frequency tested and the highest frequency.
Due to limits in the range of frequencies that the wavemaker could produce, typically in the range of 0.2 Hz. to 1.5 Hz., it was not always possible to centre the natural frequency within the band of frequencies selected. For example, the natural frequency for the trawler in its smallest metacentric height configuration typically fell in at approximately 0.21 Hz. with many at lower frequencies. This precluded us from being able to pick any frequencies lower than the natural frequency and thus we unfortunately were only able to produce the upper half of the response amplitude operator.
For each regular wave test the model was placed transversely
in the tank and allowed to settle down to a still water condition.
The computer controlling the wavemaker was then fed the parameters
for the wave desired, ie: the frequency and the amplitude, and the wavemaker started. When the waves reached the model the control lines holding the vessels position were relaxed and the model allowed to move freely. The data acquisition and the video recording are then started and the subsequent motion of the model recorded.
Occasionally the model would start to veer off from its beam on position to the waves and had to be brought back into line.
- 46 - This was done by applying a very gentle tension to the required control line. This was not done unless the vessel had deviated considerably from beam-on, if the yaw experienced by the model was only a few degrees the vessel was normally left alone.
The other occasion that may prompt control line use was if the model, due the action of the larger waves, was destined to be thrown against one of the walls of the test tank. For the preservation of the model this was not allowed to happen and much more severe control was allowed. When this occurred it was noted in the records for future reference.
Tests were done at each of three amplitudes for each of the frequencies chosen. The amplitudes were in terms of voltages and were 33%, 66% and 100% of the wavemakers full scale allowable driving voltage. The frequencies that were picked included one
frequency computed to be at the natural roll frequency of the vessel. Frequency steps were usually on the order of 0.1 Hz..
4.2.4 BREAKING WAVES
The last part of the testing matrix, and the most important from an investigative point of view, was the measuring of the response of the vessel to the impact of a breaking wave.
In these tests the wavemaker control was reprogrammed to allow the creation of a breaking wave through the action of a controlled frequency sweep. That is, a range of frequencies were
- 47 produced starting at slower moving high frequency waves and ending with faster moving low frequency waves. At some point, a distance from the wavemaker, the wave crests produced would synchronize and the resulting single wave would be of a magnitude sufficient to become unstable and break.
Each of the tests was started with the wavemaker run so that the point of wave breaking could be determined. With this knowledge the model was placed across the tank at a point where the jet of the breaking wave would be fully formed and be of its greatest velocity. The wavemaker was restarted and the control lines holding the position of the boat released. The breaking wave created was preceded by a trough and followed by a smaller trough as is typical of plunging jet type waves. The ship would roll into the trough and, depending on the size of the wave, either start to swing back into a vertical position or receive the impacted while still rotating into the wave.
The roll response of the vessel was measured from the time
the wave first started to form till after it had been satisfactorily determined that either the model had capsized or was in no danger of becoming unstable. This test was repeated several times at each amplitude and at least three different amplitudes were tested. The control lines were not used in any of the testing runs unless it was obvious that physical harm would come to the model, such as impacting the walls of the tank, from the actions of the wave.
- 48 - 5.0 ANALYSIS OF DATA
5.1 PRE-PROCESSING
The data obtained from the testing was in a number of formats. The motion data from the single chine seiner tests was in a compressed binary format on standard audio cassettes while it's wave data was in compressed binary format on 8 inch floppy disks.
The trawler had all its data stored in a multiplexed binary format on 8 inch floppies. To make the data accessible to the user it had to be translated into standard ASCII character files so it could be manipulated by conventional software means on a variety of computers, most importantly, the VAX VMS 11/750 of the Department of Mechanical Engineering at the University of British Columbia.
In this section the procedures required to produce the final, processing ready, data files will be discussed. This discussion will be broken down into two separate parts; Single Chine Seiner and Trawler as the procedure required for the Single Chine Seiner differs considerably from the Trawler methods. Once the data is in
ASCII format files the discussion will revert back to a single path of analysis as there is no further difference in the procedure (except for a difference in the file numbering scheme).
5.1.1 SINGLE CHINE SEINER
Upon completion of the testing for the day a number of audio cassettes and an 8 inch floppy disk remained containing the
- 49 - measured values for the day. The audio cassettes held the information for the motions of the vessel in files corresponding to the sequential numbering system of the data acquisition program. The data in the cassette files was in a multiplexed binary format. This had to be demultiplexed and translated into usable ASCII files. To do this a program was written to read the data in from the cassette through the cassette interface port of a
IBM PC computer where it was demultiplexed and translated into
ASCII characters and then written to 5.25" floppy disk files of the same file name. The file names were the same as given by the data acquisition program and started at A and went to Z, occasionally the number of tests exceeded 26 in which case the subsequent characters in the standard ASCII table shown in Table
IX were used. To differentiate which file contained the data on the roll angle versus the data on the heave acceleration, etc., it was required to append a number to the files. A summary of the motions and their associated file number suffixes can be found in
Table X.
After the data was all transferred onto 5.25" floppy disks the disks were taken to the Department of Mechanical Engineering where an IBM PC, using PCKERMIT terminal emulation software, was connected to the VAX 11/750. Each disk in turn was placed in the
IBM PC drive and using standard KERMIT data transfer protocol, sent via the terminal connection to files on the VAX. The files, labelled with filename extensions .DAT, now on the VAX, could be accessed by the programs resident on the computer.
50 - TABLE IX RELEVANT ASCII CHARACTERS USED
ASCII CODE CHARACTER ASCII CODE CHARACTER
097 a 116 t 098 b 117 u 099 c 118 V 100 d 119 w 101 e 120 X 102 f 121 y 103 g 122 z 104 h 123 { 105 i 124 1 106 J 125 } 107 k 126 ~ 108 1 127 109 m 128 Q 110 n 129 u 111 o 130 e 112 P 131 a 113 q 132 a 114 r 133 a 115 s 134 a
The data collected from the wave probe, residing on the 8 inch floppy disk, was processed by a separate procedure. Because this procedure is the same as for the data collected for the
Trawler testing it will not be explained here.
5.1.2 WEST COAST TRAWLER
With the replacement of the old data acquisition system with the new telemetry system it was possible to collect all the data on one device and thus make the later handling of the data far easier. The ship motions and wave data were all collected simultaneously by the Mine 11 computer mounted on the towing carriage of the tank at B.C. Research. This data, upon completion
- 51 - of a series of tests, was in multiplexed binary format on 8" floppy disks. To get this data transferred to the VAX 11/750 was only a matter of mounting the disks in the 8" drives of the VAX and specifying an RT11 foreign disk format specification in the command string of the disk read command before reading. The disk was read in bulk by the VAX 11/750 and unique files created in its memory according to the original disk file names. These files were then renamed by the author by adding 100 to the file-numbers to differentiate these files form the files created by the single chine seiner testing.
TABLE X
FILE NUMBERING GUIDE
CHANNEL NUMBER
MOTION SINGLE CHINE SEINER WEST COAST TRAWLER
WAVE HT. 1 0 YAW 9 1 RUDDER 10 2 SWAY 14 3 PITCH 12 4 HEAVE 13 5 ROLL 11 6
The data files, though on the VAX, were still in compressed binary format and had still to be demultiplexed. To do this they
- 52 - were run through a program called ADMUX which demultiplexed the input files and created a series of output files, each corresponding to an individual motion or environment parameter measured. The numbering scheme of the output files can be found in
Table X.
The data obtained from the single chine data had already been provided in units usable by the processing routines, namely, they
2 were in such units as inches, meters/sec, and degrees. The data derived from the West Coast Trawler tests was provided in electrical units corresponding to the signals measured from the sensing equipment. The calibration of the sensing equipment of the
West Coast Trawler had been done and the files containing the calibration values resided on the VAX.
The conversion of the files created by ADMUX for the West
Coast Trawler into usable units was done by a series of programs entitled HEAVE, SWAY, ROLLANGLE, WAVE and YAW. Each of these programs converted its own file type from the voltage values originally provided into the actual physical quantities required.
The filename extensions of the new files created were .UNT instead of .DAT to reflect this change.
Because of an error in the initial calibration of the data acquisition program the voltage values measured were all inverted
^"The programs used in the course of this research are all mentioned in highlights. The number of programs used precluded listing the source code as it would have made this thesis a rather unwieldly item.
- 53 - resulting in surprising values being observed in the later analysis. This was an easy problem to correct and was accomplished by feeding all files created in the 101 and 102 series of tests through the program CALIB which inverted each of the voltage values recorded again.
5.2 GENERAL PROCESSING
The data was now ready for processing. For the data to be meaningful in later analysis it had to be conditioned to provide data acceptable for further processing and interpretation. This procedure involved correcting for any deficiencies in the original data collecting procedure (described in section 5.1), removing the
DC offsets found in the files, filtering out the extraneous noise produced and decoupling the motions of the vessel so that each file contained only the values associated with that unique displacement vector. A flow chart outlining the procedure followed to process the data can be found in Fig. 13.
5.2.1 D.C. OFFSET REMOVAL
The first manner of business was to eliminate the DC offsets from the data. This was accomplished by two methods. The first method was to remove the DC offset created by the signals from the boat. This was done be subtracting from the records the null values recorded in the NULL FILE created at the beginning of each test sequence. This value corresponded to the still water reading of the instruments when the vessel had no trim (outside of the
- 54 - trim due to the weight condition), no heave, no sway and no rolling motions coupled with no heel.
If there was a residual DC offset in the data, as was the case with the files created later in the test day due to drift of the electronics and the sensing equipment, this was removed with an averaging DC offset type of manipulation. This was done through the use of the program DCRMV.
This provided us with a fairly good set of data files. The exceptions to this were those files that were excessively noisy or corrupt in other manners. To provide us with a cleaner signal a filter was required to provide a better foothold for the residual
DC offset removal program.
5.2.2 FOURIER FILTERING
Filtering of the data was accomplished with the use of a numerical filter patterned after the standard Fast Fourier
Transform (FFT) . The filter used is an adaptation of the FFT by
Aubanel and Oldham [7] for use on personal computers where requirements of efficiency and flexibility are paramount. This program was found to be very appropriate for my use because it allows a filtering factor to be specified which acts somewhat like the value of the high end frequency of a low-pass filter, depending on the number of data points. A more complete description of the programs theory can be found in Appendix C.
- 55 - "3 H" c: PROCESSING SEQUENCE co
TJ O file.DAT file.DAT o fl> in i D REMOVE THE iQ ERRONEOUS VOLTAGE *• file. NEW VALUES IN THE CO fD FIRST TWO RUNS iQ DUE TO BAD C CALIBRATION CONVERT VOLTAGE fD FILES 3 VALUES TO THE O ACTUAL PHYSICAL ^ fiie.UNT cn fD UNITS USING NULL RECORDS AND THE i UNEAR CALIBRATION TEST RESULTS SMOOTH THE DATA o USING A FAST FOURIER TRANSFORM flie.FOU METHOD WITH END EFFECT REMOVAL BY 01 LINEAR SUBTRACTION i OF AVERAGE START AND DECOUPLE THE SWAY END VALUES AND HEAVE VALUES FROM EACH OTHER AS WELL AS REMOVING THE GRAVITY EFFECTS INDUCED BY THE ROLL MOTION OF THE MODEL
file.TRU A subroutine was created from the program after conversion of
its original source code, by the author, from BASIC to FORTRAN.
This subroutine, named SMOOTH, was then called by another program, named FILTER, to filter out any high frequency (above
approximately 5 Hz.) noise form the data. These new files output by the filtering program were appended with the extension .FOU.
5.2.3 DECOUPLING THE MOTIONS
The data contained in the Heave and Sway files do not
represent the actual accelerations of the model in the directions
of the world coordinate system. They contain contributions from
the perpendicular acceleration as well as the acceleration due to
gravity because of the influence of the roll motion of the vessel.
MHEAVE
GRAVITY
Figure 14. Acceleration vector diagram
To remove this effect the sway and heave files had to be
decoupled from each other through the roll angle file. This was
- 57 - done by a vector addition/subtraction of those components not
required. From Fig. 13 the following equations can be derived to produce actual acceleration values for the vessel.
letting nheave and nsway be the actual accelerations, and
letting heave and sway be the accelerations measured by the
sensors we get;
heave = nheave cos(0) + nsway sin(0) - g cos(0) (5.001)
sway = nsway cos(0) - nheave sin(0) + g sin(0) (5.002)
or, solving for the actual values;
nheave cos(0) = heave - nsway sin(0) + g cos(0) (5.003)
nsway cos(0) •» sway + nheave sin(0) - g sin(0) (5.004)
substituting for nsway in (5.003) and nheave in (5.004) we
get;
sway + nheave sin(g) - g sin(fl) nheave cos(0) = heave - cos(0)
sin(0) + g cos(0) (5.005)
heave - nsway sin(0) +g cos(6) nsway cos(0) = sway + cos(0)
sin(0) - g sin(0) (5.006)
simplifying, and bringing like terms to the same side, we
arrive at;
- 58 - i. /n . ^ 2//iw heave sway sin(0) ,, 2,„. nheave (1 + tan (5)) * + g (1 + tan (5) cos(0) cos2(«)
(5.007)
/i . 2//iw sway . heave sin(0) nsway (1 + tan (8)) = z— + (5.008) cos(0) COS (5)
knowing (1 + tan2(0)) = l/cos2(0) we arrive, finally, at the relation;
nheave = heave cos(0) - sway sin(0) + g (5.009)
nsway = heave sin(0) + sway cos(0) (5.010)
The programs that implemented this decoupling are named, for sway and heave, NSWAY and NHEAVE respectively.
5.3 ROLL DECAY TESTS
5.3.1 ROLL EXTINCTION CURVES
The extinction curves, as defined by the equation:
&4> = a
where: A
were determined by going through each roll decay test's roll file
- 59 - and compiling a list of the maximum roll angles measured in degrees. Pairing each set of consecutive roll angles (one positive and one negative to make a complete roll cycle) the mean roll angle of the absolute values was computed along with the change in roll angle. These values were tabulated separately for plotting the change in roll angle as a function of the mean roll angle. The points were then smoothed to provide a curve without inflection points. Three sets of data points were removed from each curve, one at the low end of the amplitude scale, one at about the middle, and one at the high end of the curve. These points were then plugged into the extinction coefficient matrix to obtain the coefficients of extinction using Cramers Rule of Determinants [8], in the early stages, and later, a solution was obtained through ® the use of a IBM PC application package entitled TK! SOLVER . The extinction curves can be found in Figures 15 through 19. In addition the actual coefficients of extinction are presented in tables XI and XII.
- 60 - TABLE XI EXTINCTION COEFFICIENTS FOR THE SINGLE CHINE SEINER
DISPLACEMENT G.M. EXTINCTION COEFFICIENTS (kg) (mm)
100.27 6.0 a - 0. 19538 b = 0. 00117
c • 0 00007
100.27 27.0 a - o.0738 9 b - o.0129 4 c =-0. 00005
100.27 50.0 a = 0 06093 b o 03283 c =-0 00053
115.68 6.0 a = 0 07463 b - o 01334 c =-0 00022
115.68 12.0 a - 0 23214 b =-0 00389 c = 0 00028
115.68 27.0 a - 0 .23474 b = 0 .01767 c =-0 .00013
115.68 50.0 a = 0 .29632 b = 0 .01220
c =-0 .00009
- 61 - TABLE XII EXTINCTION COEFFICIENTS FOR THE WEST COAST TRAWLER DISPLACEMENT G.M. EXTINCTION COEFFICIENTS (kg.) (mm)
101.15 69.3 a — 0 29856 b - 0 03660 c =-0 00054
101.15 69.0 a =-0 15169 b - 0 03835 c =-0 00070
133.36 106.0 a - 0 06900 b = 0 03140 c =-0 00067
133.36 36.0 a - 0 24350 b =-0 01379 c = 0 00079
133.36 6.0 a = -0 33179 b - o 07830 c =-0 00233
168.15 81.6 a = -0 20816 b - 0 03765 c =-0 00053
168.15 36.0 a =-0 19111 b - 0 03400 c = -0 00046
168.15 6.0 a =-0 23880 b = 0 .05520 c =-0 00087
- 62 - ROLL EXTINCTION CURVES SINGLE CHINE SEINER 216.4 TONS DISPLACEMENT
Legend GM = 2.1331 ft. GM = 1.1516 ft. GM = 0.2557 ft.
/ / / / S / / t ' r t
/ * / t / * / * / * x * / / / * / 4* y' / y '' * s
S ^0, V
1 1 1 1 1 10 20 30 40 50 MEAN ROLL ANGLE (degrees) igure 15. Roll Extinction Curves for Single Chine Se 216.4 Tons Displacement ROLL EXTINCTION CURVES SINGLE CHINE SEINER 249.6 TONS DISPLACEMENT
30-1
Legend cm = 2J331 ft. 25- GM = 0.6//3 fl. CM = 0.2557 ft. o» 20 0) T3 o I- 15- o
I- X UJ 10- O CC
10 20 30 40 50 MEAN ROLL ANGLE (degrees)
Figure 16. Roll Extinction Curves for Single Chine Seiner 249.6 Tons Displacement - 64 - ROLL EXTINCTION CURVES WEST COAST TRAWLER 328.9 TONS DISPLACEMENT
30
Legend
25- Without Bilge Keels With Bilge Keels co 0
»- 20 0) •o / / / O / I- 15 / o ' x" z y X • x^ / X I- • x X / X * /• X LU * / 10 / > / / / X / X • X o y X / X y X * X * 5- * > • _/ * s //
10 20 30 40 50 MEAN ROLL ANGLE (degrees) Figure 17. Roll Extinction Curves for West Coast Trawler 328.9 Tons Displacement
- 65 - ROLL EXTINCTION CURVES WEST COAST TRAWLER 437.64 TONS DISPLACEMENT
MEAN ROLL ANGLE (degrees) Figure 18. Roll Extinction Curves for West Coast Trawler 437.64 Tons Displacement ROLL EXTINCTION CURVES WEST COAST TRAWLER 551.51 TONS DISPLACEMENT
30
Legend GM = 4.1468 ft. 25 GM = 1.7960 ft. GM = 0.2953 ft. / oco / © 20- / D) © /
•o */ g *s H 15 / *y O ty */ / *y X LU -I 10 / y
*/ O y CC /
5- // f/
0 10 20 30 40 50 MEAN ROLL ANGLE (degrees) Figure 19. Roll Extinction Curves for West Coast Trawler 551.51 Tons Displacement - 67 - 5.3.2 MOMENT OF INERTIA
The virtual mass moment of inertia of the vessel in still water, assuming no damping, can be determined through the use of
small angle linear vibration theory. For an undamped single degree of freedom system the natural frequency of vibration can be expressed as,
(5.012)
where: k = spring
constant
m = mass
If we then solve for the mass, and include the added mass in the mass term such that m — m + m' — I' , as the vessel is X X accelerating in water, we obtain,
V = w2 • k (5.013) xx n
Substituting, for small angles, the restoring moment in roll we
get,
V = / ^ ) • A • GM (5.014) XX [_ Z7T J
Knowing the natural period of oscillation for the model
- 68 - configurations tested the virtual mass moments of inertia are calculated. The results are shown in Tables XIII and XIV for the model scale.
TABLE XIII VIRTUAL MASS MOMENTS OF INERTIA SINGLE CHINE SEINER
I' XX CONFIGURATION (seconds) 2 (kgomos )
A = 216.4 T 4.8309 0.3547 GM - 0.2557 ft
A - 216.4 T 2.6525 0.4455 GM - 1.1516 ft
A - 216.4 T 1.7699 0.3967 GM = 2.1331 ft
A - 249.6 T 4.5045 0.3546 GM - 0.2557 ft
A - 249.6 T 3.3784 0.4322 GM = 0.5113 ft
A = 249.6 T 2.3148 0.4212 GM - 1.1516 ft
A - 249.6 T 1.7361 0.4653 GM - 2.1331 ft
- 69 - TABLE XIV VIRTUAL MASS MOMENTS OF INERTIA WEST COAST TRAWLER
I' XX 2 CONFIGURATION (seconds) (kgomas )
A = 328.9 T 1.5256 0.4149 GM - 3.4154 ft
A = 328.9 T 1.5149 0.4091 GM = 3.4154 ft
A = 437.6 T 6.1576 0.7716 GM = 0.2953 ft
A - 437.6 T 2.2920 0.6503 GM = 1.7960 ft
A = 437.6 T 1.3165 0.4568 GM = 3.8238 ft
A = 551.5 T 4.7170 0.5701 GM = 0.2953 ft
A = 551.5 T 1.9916 0.6183 GM = 1.7960 ft
A = 551.51 T 1.3280 0.6349 GM - 4.1468 ft
5.4 REGULAR SEAS RESPONSE
5.4.1 WAVEMAKER CHARACTERISTICS
A compilation was made of all the regular wave height measurements from both the single chine seiner and trawler tests.
These values were sorted according to frequency and wave maker amplitude setting. A histogram was developed from this data which had a step size of 0.05 Hz. Each histogram had its mean and
- 70 - REGULAR SEAS WAVE AMPLITUDES TEST AMPLITUDE #1
0.16
0.14 Legend • Measured Values
Mean 0.12- eo
.2 0.10 E UJ Q 0.08-
• tr t # • • t 0.04-
o E 0.02- UJ o z <
0.00 0.0 0 1 2 3 4 5 6 WAVE FREQUENCY (rad/sec.) Figure 20. Regular Seas Wave Amplitudes - Test Amplitude #1
- 71 - REGULAR SEAS WAVE AMPLITUDES TEST AMPLITUDE #3
0.16
0.14- Legend # Measured Values Mean • 0.12 • co <2 0.10- © E • 7 ui 0.08 A Q J /** 3
Q. 0.06 • • < I •
0.04
• e •7 E 0.02 u z •• < 0.00 0.0 0 1 2 3 4 5 6 WAVE FREQUENCY (rad/sec.)
Figure 21. Regular Seas Wave Amplitudes - Test Amplitude #3
- 72 - REGULAR SEAS WAVE AMPLITUDES TEST AMPLITUDE #4
0.16
0.14 — • • • •Legen d • Measured Values Mean 0.12
(0 ® 0.10 E UJ 0.08
t> 0.04- 6.0 r
E 0.02- ui o
rr
0.00 1I 1I 1 0.0 0 1 2 3 4 5 6 WAVE FREQUENCY (rad/sec.) Figure 22. Regular Seas Wave Amplitudes - Test Amplitude #4
- 73 - REGULAR SEAS WAVE AMPLITUDES TEST AMPLITUDE #5
0.16-1 : : : : : 1
WAVE FREQUENCY (rad/sec.) Figure 23. Regular Seas Wave Amplitudes - Test Amplitude #5
- 74 - variance calculated for the points lying within its bounds [9] The mean for each histogram containing data points was then associated with the center frequency of that histogram. Histograms containing no data points were neglected. A plot was then made of the mean wave amplitude as a function of frequency for each of the five wave amplitude settings. The variance is also plotted on the same
graph to show the repeatability of the wave amplitudes. The
results can be seen in Figures 20 through 23.
The rise in the variance is very small over the range of wave
frequencies tested except for test amplitude #5 (Fig. 23) where
there is a sudden jump in the variance curve. This can be
attributed to the decay in the structural integrity of the
wavemaker. The mounting bolts connecting the hydraulic actuator to
its base came adrift allowing a large percentage of the excursion
of the hydraulic ram to be taken up by the mountings instead of
the panel. This was remedied after discovery and only a few
records are affected.
The amplitude response of the wavemaker over the range of
frequencies tested showed a considerable inconsistency. The wavemaker has an optimum range of operation where maximum wave height can be obtained, at lower frequencies the wavemaker cannot
execute a paddle excursion sufficient to maintain wave amplitudes while at high frequencies the hydraulics cannot respond quickly
enough to reach full excursion at the driving voltage peak.
5.4.2 ROLL RESPONSE AMPLITUDE OPERATORS From the roll and wave amplitude records the roll response amplitude operators could be determined. To accurately determine the roll angle and wave amplitude values the respective files were fed into a Fast Fourier transform routine that broke the signals down into their component frequencies. These spectrums were stored in separate files and from these files the amplitudes were scanned for the largest value recorded. The largest value, because of the prior filtering, could be confidently assumed to be associated with the desired motion or displacement. The associated frequency was also output and if the frequency was not within 5 percent of the test frequency it was discarded and the search repeated. These amplitudes were printed out along with the response amplitude operator for the given (measured) wave frequency of that file set.
The roll response amplitude operators were determined through the use of the following relationship [10],
ROLL (5.015)
where: $ = roll angle
g = acceleration due
to gravity
co wave encounter
frequency
A = wave amplitude
- 76 - The roll response amplitude operator data was created in much the same manner as the wave amplitude plots. All the values were sorted according to frequency and a mean and variance were computed for each division of the histogram used. These can be seen in Figures 24 through 38.
The variance is much more pronounced in the plots of the roll
R.A.O. as it illustrates the non-linearities introduced in large angle roll due to resonance and large amplitude waves.
5.5 REGULAR SEAS STABILITY FACTORS
The response of the vessels tested to the influence of a
regularly repeating wave function is described well by the
creation of roll response amplitude operators. This does not
necessarily help, though, in describing the safety of the vessel
in a certain seaway as we cannot tell how near the vessel is to
it's point of capsizing.
To better get a grip on the "safety" of the vessel a parameter was required that could quantify this response in such a manner that zones of safe operation could be defined. The key parameters considered essential for the quantifying of the vessels
stability were the following,
> A, the amplitude of the regularly repeating
sea the vessel is operating in
> R, the average maximum roll angle achieved by
- 77 - ROLL RESPONSE AMPLITUDE OPERATOR SINGLE CHINE SEINER 216.4 TONS DISPLACEMENT GM = 0.2557 ft. 350
Legend 300 # Measured Values
Mean
250
200
150
100
50
0 1 r—m »—fw w | | r- 0 0.5 1 1.5 2 2.5 ENCOUNTER FREQUENCY (rad/sec.) Figure 24. Roll Response Amplitude Operator Single Chine Seiner 216.4 Tons Displacement, GM = 0.2557 ft. - 78 - ROLL RESPONSE AMPLITUDE OPERATOR SINGLE CHINE SEINER 216.4 TONS DISPLACEMENT GM = 1.1516 ft. 700
Legend 600- # Measured Values
Mean
500- \ o < 400 CC
O 300 CC A 200 : #\ 100000
o z 60000 < rr
\ 0.5 1 1.5 2 2.5 ENCOUNTER FREQUENCY (rad/sec.) Figure 25. Roll Response Amplitude Operator Single Chine Seiner 216.4 Tons Displacement, GM = 1.1516 ft. - 79 - ROLL RESPONSE AMPLITUDE OPERATOR SINGLE CHINE SEINER 216.4 TONS DISPLACEMENT GM = 2.1331 ft. 30
Legend 25 • Measured Values
Mean
20
•i • 15
10
I A 5 • \ \ •
1 1 1 1 i r 0 0.5 1 1.5 2 2.5 ENCOUNTER FREQUENCY (rad/sec.) Figure 26. Roll Response Amplitude Operator Single Chine Seiner 216.4 Tons Displacement, GM = 2.1331 ft. ROLL RESPONSE AMPLITUDE OPERATOR SINGLE CHINE SEINER 249.6 TONS DISPLACEMENT GM = 0.2557 ft. 120-1
Legend 100- # Measured Values
Mean
80
60
40
• 20 I 0 1 1 y ww | w w—iv 1 r 0 0.5 1 1.5 2 2.5 ENCOUNTER FREQUENCY (rad/sec.) Figure 27. Roll Response Amplitude Operator Single Chine Seiner 249.6 Tons Displacement, GM = 0.2557 ft. ROLL RESPONSE AMPLITUDE OPERATOR SINGLE CHINE SEINER 249.6 TONS DISPLACEMENT GM = 0.5113 ft. 200
Legend Measured Values
Mean 150
100
50 10<
0.5 1 1.5 2 2.5 ENCOUNTER FREQUENCY (rad/sec.) Figure 28. Roll Response Amplitude Operator Single Chine Seiner 249.6 Tons Displacement, GM = 0.5113 ft.
- 82 - ROLL RESPONSE AMPLITUDE OPERATOR SINGLE CHINE SEINER 249.6 TONS DISPLACEMENT GM = 1.1516 ft. 120
Legend
100 # Measured Values
Mean
80 •
60
40
20 +
0 i 1 «—mr»— » 1 1 r 0 0.5 1 1.5 2 2.5 ENCOUNTER FREQUENCY (rad/sec.) Figure 29. Roll Response Amplitude Operator Single Chine Seiner 249.6 Tons Displacement, GM = 1.1516 ft. ROLL RESPONSE AMPLITUDE OPERATOR SINGLE CHINE SEINER 249.6 TONS DISPLACEMENT GM = 2.1331 ft. 30
Legend 25- # Measured Values
Mean
20- o 4 <• cc 15- o cc 10- w 4 * 60 L z < 2
•o 0.5 1 1.5 2 2.5 ENCOUNTER FREQUENCY (rad/sec.) Figure 30. Roll Response Amplitude Operator Single Chine Seiner 249.6 Tons Displacement, GM = 2.1331 ft. - 84 - ROLL RESPONSE AMPLITUDE OPERATOR WEST COAST TRAWLER 328.9 TONS DISPLACEMENT GM = 3.4154 ft. (bilge keels removed)
0.5 1 1.5 2 ENCOUNTER FREQUENCY (rad/sec.) Figure 31. Roll Response Amplitude Operator West Coast Trawler 328.9 Tons Displacement, GM = 3.4154 ft. (bilge keels removed) •- 85 - ROLL RESPONSE AMPLITUDE OPERATOR WEST COAST TRAWLER 328.9 TONS DISPLACEMENT GM = 3.4154 ft. (bilge keels attached) 20-i
Legend • Measured Values Mean 15
30 : \ J « 20
10
0 0.5 1 1.5 2 2.5 ENCOUNTER FREQUENCY (rad/sec.) Figure 32. Roll Response Amplitude Operator West Coast Trawler 328.9 Tons Displacement, GM = 3.4154 ft. (bilge keels attached) - 86 -• ROLL RESPONSE AMPLITUDE OPERATOR WEST COAST TRAWLER 437.64 TONS DISPLACEMENT GM = 0.2953 ft. 70-1 : : ! : 1
ENCOUNTER FREQUENCY (rad/sec.) Figure 33. Roll Response Amplitude Operator West Coast Trawler 437.64 Tons Displacement, GM = 0.2953 ft.
- 87 - ROLL RESPONSE AMPLITUDE OPERATOR WEST COAST TRAWLER 437.64 TONS DISPLACEMENT GM = 1.7960 ft. 80
70- Legend # Measured Values Mean 60-
50 • o < * 40
30- • /•\ 20- 1000
Ui % \ (J z 10 J A 4 BOO <
< '\-% ) 0.•A5 1 1.5 2 2.5 ENCOUNTER FREQUENCY (rad/sec.) Figure 34. Roll Response Amplitude Operator West Coast Trawler 437.64 Tons Displacement, GM = 1.7960 ft
- 88 - ROLL RESPONSE AMPLITUDE OPERATOR WEST COAST TRAWLER 437.64 TONS DISPLACEMENT GM = 3.8238 ft.
Legend # Measured Values Mean
ENCOUNTER FREQUENCY (rad/sec.) Figure 35. Roll Response Amplitude Operator West Coast Trawler 437.64 Tons Displacement, GM = 3.8238 ft.
- 89 - ROLL RESPONSE AMPLITUDE OPERATOR WEST COAST TRAWLER 551.51 TONS DISPLACEMENT GM = 0.2953 ft.
Legend # Measured Values
Mean
•
mA •
i i—-— 1 1 r 0 0.5 1 1.5 2 ENCOUNTER FREQUENCY (rad/sec.) Figure 36. Roll Response Amplitude Operator West Coast Trawler 551.51 Tons Displacement, GM = 0.2953 f
- 90 - ROLL RESPONSE AMPLITUDE OPERATOR WEST COAST TRAWLER 551.51 TONS DISPLACEMENT GM = 1.7960 ft.
- — Legend • Measured Values
Mean
• o < • cc A o • / \ cc
J # 1 400
O * \ z 4 • 200 < > /\\ tr. %
0 0.5 1 1.5 2 2.5 ENCOUNTER FREQUENCY (rad/sec.) Figure 37. Roll Response Amplitude Operator West Coast Trawler 551.51 Tons Displacement, GM = 1.7960 ft. - 91 - ROLL RESPONSE AMPLITUDE OPERATOR WEST COAST TRAWLER 551.51 TONS DISPLACEMENT GM = 4.1468 ft. 10-1
Legend • • Measured Values 8 Mean •
6 • /• \ /• \ / #\ 4 / # •
2
ENCOUNTER FREQUENCY (rad/sec.) Figure 38. Roll Response Amplitude Operator West Coast Trawler 551.51 Tons Displacement, GM = 4.1468 f - 92 - the vessel while operating in this sea
> Area, the area under the GZ curve for the
configuration of the vessel under
consideration
These three values could be combined into a ratio of the energies within the operating environment and the energy inherent within the vessel. Thus a stability factor, called S, could be defined, as follows [26],
A • R S = (5.016) Area
Plots of the stability parameters S as a function of the beam to wavelength ratio can be found in Figures 39 and 40 for the single chine seiner and the west coast trawler respectively. Each plot represents the total response data of the hull in regular seas.
5.6 BREAKING WAVE RESPONSE
Analysis of the breaking wave response started with a compilation of the maximum roll, sway and heave values experienced during each test run over the entire testing series. This compilation was done through the use of the program BREAKER which inspected the maxima and minima of each displacement curve, found the largest value, and output the maximum value, along with its corresponding event time to a file associated with each test
93 REGULAR SEAS STABILITY FACTOR SINGLE CHINE SEINER
Legend O 216.4 tons, CM=0.2S57 ft. • 216.4 Tons, CM=1.1S16 ft. V 216.4 tons. GM=2.13SI ft. O 249.6 7bns, CM=0.2S57 ft. 4- 249.6 7bn«, CM=0.51I3 ft. A 249.6 tons, CM=1.l5t6 ft. O 249.6 tone. CM=2.1331 ft.
O
O O
0.6 0.8 1.2 B/L Figure 39. Regular Seas Stability Factor Single Chine Seiner
- 94 - REGULAR SEAS STABILITY FACTOR WEST COAST TRAWLER
0.09
Legend S28S0 Ibn», CM=3.4tS4 ft. [a] 0.08- 32B.90 Tbns,CM=3.4I54 ft. [b] 437.64 Jbn«, ,CM-3.B238 ft. 437.64 Jbn«, ,CM=t.7960 ft. 437.64 7bn». ,Cit=0.2953 ft. 0.07 55/.5Z Tbns. CM=4J468 ft. 55/5* n>n«. CM=I.7960 ft. 55/.S7 Ibn«, CU=OJ2953 ft.
0.06-
0.05- o
0.04-
0.03-
0.3 0.4 0.5 0.6 B/L Figure 40. Regular Seas Stability Factor West Coast Trawler - 95 - configuration. These files were later printed out for analysis which included inspection of the maxima event timing to ensure
that the event recorded corresponded to the onset of the breaking wave and not some other external event. This was especially
important for the files which contained multiple testing results
from the Single Chine Seiner series as the drag back was also
included in the data file and had to be filtered out by trapping
the time span the maxima/minima search was to operate in.
TABLE XV
BREAKING WAVE AMPLITUDES
BREAKING WAVE AMPLITUDE
BREAKING WAVE SINGLE CHINE WEST COAST NUMBER SEINER TRAWLER
2 3.63 meters 4.19 meters
3 3.82 meters 4.40 meters
4 3.99 meters 4.60 meters
5 4.16 meters 4.80 meters
A plot of the maximum sway acceleration values as a function
of the breaking wave height number is made for each configuration
tested. These plots can be found in Figures 41 and 42 for the
single chine seiner and the west coast trawler respectively. The
maximum roll angles experienced due to the impact of the breaking
wave are shown in Fig. 43 for the single chine seiner and Fig. 44
for the west coast trawler.
- 96 - BREAKING WAVES ROLL RESPONSE SINGLE CHINE SEINER
200
oH 1 1 1 1 1 0 1 2 3 4 5 6 BREAKING WAVE NUMBER
Figure 41. Breaking Waves Roll Response Single Chine Seiner
- 97 - BREAKING WAVES ROLL RESPONSE WEST COAST TRAWLER
Legend 328.90 tons,CH=S.41S4 ft. [a] 32830 Ibne,CM=3.4tS4 ft. [&] 437.64 Rmt,, CM=3.B238 ft. 437.64 Jbn», CH=t.7980, ft. 437.64 tons,, CM=0.29SS ft. 5S1.5I ftma.CM=4J468 ft. 561.51 IbntGM=I.?960, ft. X 55/.5»Jbn«, CM=0J1953 ft. X
Or 0 1 2 3 4 5 6 BREAKING WAVE NUMBER
Figure 42. Breaking Waves Roll Response West Coast Trawler
- 98 - BREAKING WAVES SWAY RESPONSE SINGLE CHINE SEINER
Legend O 216.4 tons, CM=0.2557 ft. • 216.4 Tbns, CM=1.1S16 ft. V 216.4 Tbns, CM=2.1331 ft. O 249.6 Tbns, CM=0.25S7 ft. + 249.6 Tbm,CM=0.5113 ft. A 249.6 7bn», CM-1.1S16 ft. O 249.6 7bns, CM=2.1331 ft.
1 I I I I I I 0 1 2 3 4 5 6 BREAKING WAVE NUMBER Figure 43. Breaking Waves Sway Response Single Chine Seiner - 99 - BREAKING WAVES SWAY RESPONSE WEST COAST TRAWLER
12 X Legend 328.90 Tbns,CH=3.4I64 ft. a 328.90 Tbns,CM=3.4I64 fl. b CM 437.84 Tbns.Cti-3.8238 ft. X , CM=1.7980 ft. : 10 437.84 Tbns, CO Tbns,, CM=0.2953 ft. 551.51 Tbns.CM-4.1468 ft. 551.51 TbnsCM=1.7960, ft. CM=GJ953 ft. X 55/.5» 7bn«, r- 8
6
4-
2-
O-f 1 1 1 1 1 0 1 2 3 4 5 6 BREAKING WAVE NUMBER Figure 44. Breaking Waves Sway Response West Coast Trawler - 100 - 5.7 BREAKING WAVE STABILITY FACTORS
5.7.1 STABILITY PARAMETER S'
The stability of the vessels in breaking waves is considered to be a function of a number of parameters but it is generally considered that the following parameters are the most important:
> R, the roll amplitude achieved by the vessel
upon wave impact
> h, the height of the breaking wave when it
strikes the vessel
> Area, the area under the GZ curve for the
configuration of the vessel under
consideration.
Using the above parameters a basic energy balance can be made with the area under the GZ curve being proportional to the energy required to roll the vessel to the angle of vanishing stability and the height of the breaking wave proportional to the energy inherent in the breaking wave. The roll angle attained by the model is then an indication of the amount of energy transferred to the vessel by the breaking wave. Relating these energies in a ratio the following stability parameter is derived,
S' - R ' h (5.017) Area
- 101 - where the parameters R, h and Area are as defined in the discussion above.
A plot of the stability parameter, S' , for each vessel tested as a function of the beam to wave height ratio can be found in
Figures 45 and 46.
5.7.2 STABILITY PARAMETER S*
It became apparent from an investigation of the stability parameter that there was not a good correlation between the stability of the vessel and its S' factor. Thus, after an investigation of the data, it was discovered that no provision had been made to account for the roll response amplitude operator of the vessel. This curve gives an excellent indication of the bandwidth of the vessel (ie: that frequency range over which the vessel exhibited a roll response) and hence the amount of energy it can absorb from a spectrum. If the impulse of the breaking wave is assumed to contain all frequencies then that vessel which carries the larger roll response amplitude operator area will theoretically absorb more of the available energy in the breaking wave.
With this information in hand a new stability parameter was developed through non-dimensionalizing those factors most influential in the capsizing of the vessel. These were:
- 102 - BREAKING WAVES STABILITY FACTOR SINGLE CHINE SEINER
60
Legend O 249.6 Tbns, CM=0.2SS? ft. • 249.6 Tbns, CM=0.S1I3 ft. V 7bns, 50 249.6 CM=t.lSt6 ft. O 249.6 Tbns, CM=2J331 ft. 4 216.4 Tbns, CU=0.25S7 ft. A 216.4 Tbns. CM=t.1SI6 ft. O 216.4 Tbns, CU-Z.1331 ft.
40- .Tf.. CC o I- o LL 30- LU CC Q. CO 20- + o o o
10
T 4 4.5 5.5 6 6.5 B/f Figure 45. Breaking Waves Stability Factor (S') Single Chine Seiner
- 103 - BREAKING WAVES STABILITY FACTOR WEST COAST TRAWLER
900
Legend 328.90 Tbns,Gil=3.4tS4 ft. 800- 328.90 Tbns,Clt=3.4t54 ft. 437.84 Tbns,, CU-3.B238 ft. 437.84 Tbns,, CM=t.7960 ft. 437.84 Tbns. ,CH=0.29S3 ft. 700- 6SI.S1 TbnsCU-4.U68, ft. SSI.SI Tbns,Clt=t.7960 ft. 651.51 TbnsCM=0J1953, ft. cc 600- o CAPSIZING i- REGION o 500-
LU ? 400- CC CL m 300 NO CAPSIZING X REGION X 200 X
100
i —I— 0 10 15 20 25 30 B/f Figure 46. Breaking Waves Stability Factor (SM West Coast Trawler
- 104 - >
> (j> , the angle of vanishing stability (radians)
> H, the breaking wave height (meters)
> A , the area under the appropriate roll R.A.O. curve RAO RR R (seconds *)
> A , the area under the appropriate righting arm curve GZ (meters)
> At, the duration of impact of the breaking wave (seconds)
The resulting expression for S becomes;
RAO (5.018) At GZ
The duration of impact of the breaking wave was difficult to measure and thus an estimate was made of the time duration. This estimate is based on values measured for the duration of impact by
Dahle [11] and Balitskaja [12]. Both authors reached an estimate of 0.1 seconds duration for impact on the model scale. This value was used here also, scaled appropriately.
Another difficulty was in the measuring of the areas under the roll response amplitude operator curves. Due to the limitations of the tank it was not possible to extend test frequencies down to or below the natural frequencies of the smaller metacentric height configurations of the models. When the
R.A.O. curve was incomplete an extrapolation was done from those curves which were fully formed adjusting for the changes in
- 105 - metacentric height and resonance characteristics.
TABLE XVI
AREAS FOR SINGLE CHINE SEINER
CONFIGURATION A A GZ RAO A = 216.4 Tons 11.634 167.95 -1 GM = 0.2557 ft ft-deg. sec.
A = 216.4 Tons 36.536 50.86 -1 GM - 1.1516 ft ft-deg. sec.
A = 216.4 Tons 79.714 4.70 -1 GM = 2.1331 ft ft-deg. sec.
A = 249.6 Tons 11.481 17.52 -1 GM - 0.2557 ft ft-deg. sec.
A -= 249.6 Tons 17.708 5.60 -1 GM = 0.5113 ft ft-deg. sec.
A = 249.6 Tons 37.669 6.84 -1 GM = 1.1516 ft ft-deg. sec.
A = 249.6 Tons 85.220 2.70 -1 GM - 2.1331 ft ft-deg. sec.
The stability parameter S was calculated from these areas using the breaking wave amplitudes shown in Table XV. The results are shown in Figures 47 and 48 for the Single Chine Seiner and the
West Coast Trawler respectively. The capsizing events for the * trawler are at 4> /4> — 3 and an S value of 600. Though only one max v capsizing symbol appears on the figure it is in actual fact a * number of capsizing events. The S value and the
- 106 - TABLE XVII
AREAS FOR WEST COAST TRAWLER
CONFIGURATION A A GZ RAO A = 328.9 Tons 194.04 4.21 -1 WITHOUT KEELS ft-deg. sec.
A = 328.9 Tons 194.04 3.39 -1 WITH KEELS ft-deg. sec.
A = 437.6 Tons 278.04 2.78 -1 GM = 3.8238 ft ft-deg. sec.
A = 437.6 Tons 142.59 7.95 -1 GM - 1.7960 ft ft-deg. sec.
A = 437.6 Tons 60.50 3.85 -1 GM = 0.2953 ft ft-deg. sec.
A = 551.5 Tons 227.96 3.04 -1 GM = 4.1468 ft ft-deg. sec.
A = 551.5 Tons 81.304 10.06 -1 GM = 1.7960 ft ft-deg. sec.
A = 551.5 Tons 16.259 4.37 -1 GM = 0.2953 ft ft-deg. sec.
It is interesting to note that the S values calculated for
the Single Chine Seiner are, on average, much larger than that for
the West Coast Trawler. This can be attributed to the difference
in scale of the two models tested. The Single Chine Seiner was
tested at a scale of 1:13 while the West Coast Trawler was tested
at a scale of 1:15. Both models were roughly the same size and operating in identical environments. When the parameters are
extended to full scale numerical differences appear that cause the
S values for the seiner to be much greater.
The areas under the GZ curves for the seiner, on average, are
- 107 - BREAKING WAVES S* STABILITY FACTOR SINGLE CHINE SEINER
40000
Legend O 216.4 Tbna, CM=0.2SS7 ft. 35000- • 216.4 Tbns, GU=1.1S16 ft. V 216.4 Tbna, GM=2.1331 ft.
O 249.6 Tbna, CM=0.2S57 ft. + 249.6 Tbna, CM=0.S113 ft.
249.6 Tbna. CM=1.1516 ft. 30000- A O 249.6 Tbns, CM=2.I33I ft.
25000-1 CC O h-
O 20000
* to 15000-
10000-
5000
0 0.2 0.4 0.6 0.8 1 1.2 Maximum Roll/Vanishing Angle of Stability
Figure 47. Breaking Waves Stability Factor (S*) Single Chine Seiner
- 108 - BREAKING WAVES S* STABILITY FACTOR WEST COAST TRAWLER
1000
Legend 3Z8.90 Jbn»,Gtt=3.4154 ft.[a] 328.90 7bn«,CM=3.4IS4 /t.[6] 437.84 Tbns, ,Ck-3.8238 ft. 437.84 Tbns, ,01=1.7960 ft. 800 437.84 Tbns, ,GH=0.29S3 ft. SSI.SI Tbns.CM=4J468 fl. 55/.5Z Tbns. CM=I.7960 ft. SSI.SI TbnsCM=0J9S3. fl.
X 600 X X X tr XK o o if 400- * CO
200
O
0 12 3 4 Maximum Roll/Vanishing Angle of Stability
Figure 48. Breaking Waves Stability Factor (S*) West Coast Trawler
- 109 - smaller than for the trawler. The duration of wave impact, using
0.1 seconds model scale for both, scales up to a smaller impact duration on the seiner at full scale and the area under the respective roll response amplitude operator curves is generally smaller for the seiner.
* Inspecting the equation for S (5.018) it can be seen that all these scaling differences cause the factor to grow. To allow * direct numerical comparison of the S parameters between different vessels would require an adjustment for the type of vessel as the * seiner operated safely at large S (seiner) values while the * trawler capsized at much smaller S (trawler) values.
A comparison of the S' and S values plotted shows that the
S parameter gives a better representation of the behaviour of the two vessels. As an example Fig. 45 shows the seiner, with a displacement of 216 tons and metacentric heights of 0.2557 ft. and
2.1331 ft., to be more unstable than other configurations (highest
S' values). Fig. 47 gives a better illustration of this tendency * with the S values. Similarly with the trawler. From Fig. 46 the lower metacentric height configurations show larger S' values and from Fig. 48 there is a much more marked differentiation between these configurations and the higher metacentric heights tested.
- 110 - 6.0 RESULTS AND DISCUSSION
The two models tested exhibited stable responses in most of the testing program, with the exception of one configuration of the west coast trawler in breaking waves, regardless of the configuration of the model. To illustrate how severely some of the configurations violated existing stability requirements tables listing the vessel configurations and marking the stability criteria violations made were drawn up.
To recap the stability criterion of concern in this testing they are listed here, with an alphabetic coding. These letters correspond to the stability criteria letters found in Tables XV and XVI.
A. The area under the GZ curve up to an angle of heel of
30° must be greater than 0.055 meter-radians.
B. The area under the GZ curve up to an angle of heel of
40° must be greater than 0.09 meter-radians.
C. The area under the GZ curve between 30° and 40° of heel
must be greater than 0.03 meter-radians.
D. The maximum righting arm beyond 30° of heel must be
greater than 0.2 meters.
E. The angle of heel where the righting arm is a maximum
must be greater than 30°.
F. The initial metacentric height must be greater than 0.35
meters.
G. The vanishing angle of stability must be greater than
-111 - 80° •
TABLE XVIII SUMMARY OF STABILITY REQUIREMENTS COMPLIANCE SINGLE CHINE SEINER
STABILITY REQUIREMENT
CONFIGURATION A B C D E F G
A = 216.4 T • • • • • • • GM = 0.2557 ft
A = 216.4 T • • • • • • • GM - 1.1516 ft
A = 216.4 T • • • • • • • GM = 2.1331 ft
A = 249.6 T • • • • • • • GM - 0.2557 ft
A - 249.6 T • • • • • • • GM = 0.5113 ft
A = 249.6 T • • • • • • GM = 1.1516 ft
A - 249.6 T • • • • • • • GM = 2.1331 ft
• : does not meet criterion • : meets criterion
112 - TABLE XIX SUMMARY OF STABILITY REQUIREMENTS COMPLIANCE WEST COAST TRAWLER
STABILITY REQUIREMENT
CONFIGURATION A B C D E F G
A - 328.9 T • • • • • • • GM = 3.4154 ft
A - 437.6 T • • • • • • • GM = 0.2953 ft
A - 437.6 T • • • • • • • GM - 1.7960 ft
A = 437.6 T • • • • • • • GM = 3.8238 ft
A - 551.5 T • • • • • • • GM = 0.2953 ft
A - 551.5 T • • • • • • • GM = 1.7960 ft
A = 551.5 T • • • • • • • GM = 4.1468 ft
• : does not meet criterion • : meets criterion
The West Coast Trawler more readily met the stability requirements as the initial area under the GZ curve for the greatest GM value was much greater than that for the Single Chine
Seiner. From Table XIX it can be seen that there are only two configurations that actually do violate some of the stability requirements. These two are the 437.6 tons displacement configuration with a metacentric height of 0.2953 feet that only violated the initial metacentric height requirement and the configuration that capsized: 551.51 tons displacement with a metacentric height also of 0.2953 feet. The configuration that
- 113 - capsized violated not only the minimum initial metacentric height requirement but also violated every other requirement save the requirement for having the peak of the GZ curve beyond 30° of heel. The design configurations meet, as is to be expected, all the stability requirements including the minimum vanishing angle of stability.
The Single Chine Seiner, on the other hand, much more readily violated the stability requirements. The only two configurations that met all the stability requirements were the 216.4 and the
249.6 tons displacement configurations, both with a metacentric height of 2.1331 feet. All other configurations tested violated one or more of the stability requirements.
When the Single Chine Seiner's metacentric height was reduced from the levels that fulfilled all the stability requirements the first criterion to be violated was the minimum vanishing angle of stability. This was followed closely by the violation of all minimum area requirements. The only stability requirement that was not violated was, again, the requirement of the peak GZ value being beyond 30° of heel.
With this knowledge it is interesting to discover that the vessel which showed the most dangerous breaking wave response, the
West Coast Trawler, was also the vessel that most readily met the stability requirements as set forth by IMO and others. This illustrates the need for ensuring that vessels which originally meet all stability requirements remain in compliance throughout
- 114 - their working life.
6.1 FUNCTION OF METACENTRIC HEIGHT IN STABILITY
As the metacentric height was reduced, for a given displacement, both vessels exhibited greater roll response amplitudes to regular wave forcing, as can be seen by the much greater roll R.A.O. peak values in Figures 24 through 39. The reduction of metacentric height did not necessarily imply that the vessel was on the verge of capsizing as the smallest metacentric height tested, 0.2557 ft., was found on the single chine seiner which did not, at any time, exhibit capsizing tendencies.
As the metacentric height decreased the areas under the GZ curves for the respective configurations also reduced. In addition the vanishing angle of stability became smaller. Because of this reduction in area under the GZ curves, and the increased roll angles attributed to lower metacentric height values, the * stability parameters S, S' and S all grow in relation. The S, S' and S parameters are then indicators of the energy content within the vessel configuration.
With some knowledge of the type of environment a vessel is to operate in the stability parameters S and S' could be used in conjunction with the most severe sea spectra from that environment to determine a minimum requirement for the area under the GZ curve.
- 115 - Balancing the energy within the sea spectra to the energy required to capsize the vessel (known from model tests) a resulting minimum value for the area under the GZ curve could be arrived at.
This method, for a regular seaway, can be described as follows: let S be the maximum value of the parameter S corresponding to the limit of ship stability for a given class of ships (in this case single chine seiners). Then, as the ship load condition is considered fixed, the denominator of the fraction defining S can be considered to be known. The numerator of S has yet two unknowns to be determined for a given sea state. While average wave amplitude and average roll amplitude are inter-related, they can be determined for a given sea spectrum.
Experimental testing of a model, as was done here, will give statistically averaged roll motions. Under these conditions a ship that can operate satisfactorily would be expected to have a minimum dynamic stability (area under the general stability diagram) in a given sea spectrum to:
(6.001)
where:
area under the m o
sea spectrum
m = area under the or roll spectrum
- 116 - K = constant
If K is a universal constant for a given class of ships, regulatory agencies can specify a dynamic stability for the expected average wave conditions. These rules, while still related to the existence of a wave spectrum, would be more flexible and would require stability depending on the statistical prediction of environmental conditions.
After the values of m and m are obtained, the minimum area o or required under the general stability diagram can be estimated for the specified environmental conditions the ship would operate in.
If an ITTC wave spectrum with a significant wave height of 11 feet and a value of 5 for the parameter S is assumed, a proposed approximate value of K is 0.8.
With the stability parameter S the method would be altered to include the area under the roll response amplitude operator as well as the area under the general stability diagram.
6.2 FUNCTION OF FREEBOARD IN STABILITY
The only capsizing of the West Coast Trawler in breaking waves occurred when the vessel was in its greatest displacement and hence in its minimum freeboard configuration. From this it would appear that the amount of freeboard, in itself, does not account for the capsizing.
- 117 - What does become apparent is that, from an investigation of
the sway accelerations recorded, the freeboard does have a measurable effect on the amount of sway acceleration experienced by the vessel. As the freeboard is increased the measured sway
accelerations also increased. This trend was true so long as the breaking waves were smaller in amplitude than the freeboard of the vessel. If the jet of the breaking wave was able to pass
unhindered over the deck of the vessel the recorded sway
accelerations began to drop. The largest amplitude breaking wave
used in the tests was greater than any of the freeboards tested as
can be seen by the consistent trend by all configurations to a
reduced sway acceleration at the largest breaking wave, breaking
wave number 5.
6.3 EFFECTS OF SEVERE ACCELERATIONS ON SURVIVABILITY
Accelerations experienced by the two vessels in breaking
2 waves were both averaging on the order of 3 m/sec . In some
2
instances, with the West Coast Trawler, up to 5 m/sec
accelerations were measured. This is remarkable as it implies a
great deal of force is being exerted on all fixtures in the boat
hull as well as providing an opportunity for an appreciable free
surface effect^. If either the fish holds or the fuel tanks hold a
The free surface effect is the roll moment induced by the sloshing of a fluid to one side within a container. Calculations indicate that for a 5 m/sec sway acceleration and no roll there would be a slope change of the fluid surface of 26 degrees.
- 118 - significant amount of fluid or catch and there is room for it to shift there is the possibility of great heeling moments being produced.
Heave accelerations, though measured, are not shown as the values determined fell as a random function of the vessels configuration. The heave accelerations were in the range of 1
2 2 m/sec to 3 m/sec when impacted by a breaking wave.
- 119 - 7.0 CONCLUSIONS
The stability requirements of the IMO and various other governmental regulatory bodies, if met, prevented the vessel, without bulwarks or superstructure, from developing hazardous motion characteristics in roll. When the stability requirements were violated, and then only if they were severely violated, did any model tested show a tendency to capsize.
With this in mind it would appear that the most pragmatic approach would be to ensure that vessels operating at sea meet all the present IMO stability requirements. The stability requirement of
S calculations show that in addition to the need for a large value of
- 120 - REFERENCES
[I] Lilley, S., Men, Machines and History, Lawrence & Wishart, London, England, 1965.
[2] Rule, M. , The Search for MARY ROSE, National Geographic Magazine, National Geographic Society, Washington, D.C., May, 1983, pp. 654 - 675.
[3] Hocking, CA. , F.L.A. , Dictionary of Disasters During the Steam Age 1842 - 1962, Vol I., Lloyds Register of Shipping, London, England, 1969.
[4] Morrall, A, Intact Ship Stability Criteria, Proceedings of Small Ships Survival Seminar, Ship and Marine Technology Requirements Board, Department of Industry, London, England, 1979.
[5] Dahle, E.A., and Nisja, G.E., Intact and Damaged Stability of Small Crafts with Emphasis on Design, University of Trondheim, 1984.
[6] Inter-Governmental Maritime Consultative Organization, Code of Safety for Fishermen and Fishing Vessels, Part B, Safety and Health Requirements for the Construction and Equipment of Fishing Vessels, London, 1977.
[7] Aubanel, E.E. and Oldham, K.B., Fourier Smoothing Without the Fast Fourier Transform, BYTE Magazine, February 1985, McGraw-Hill Inc., Peterborough, NH., pp. 207 to 218.
[8] Thomas Jr.,G.B., Calculus and Analytic Geometry, Addison- Wesley Publishing Company, Reading, Mass., 1968.
[9] Walpole, R.E., and Myers, R.H., Probability and Statistics for Engineers and Scientists, Second Edition, Macmillan Publishing Co., Inc., New York, N.Y., 1978.
[10] Bhattacharyya, R., Dynamics of Marine Vehicles, John Wiley & Sons, New York, N.Y., 1978.
[II] Dahle, A.D. and Kjaerland, 0., The Capsizing of M/S HELLAND-HANSEN, The investigation and recommendations for preventing similar accidents, Proceedings of The Royal Institution of Naval Architects, London, England, 1979.
[12] Balitskaja, E.O., Results of Experimental Investigation for Capsizing in Breaking Waves, University of Michigan, College of Engineering, No. 048, March 1970.
[13] Terrascience Signal Conditioner Reference Manual, Terrascience Ltd., Vancouver, B.C., 1985.
[14] Bhattacharyya, R., Dynamics of Marine Vehicles, John Wiley & Sons, New York, N.Y., 1978.
- 121 - [15] Himeno, Y. , Prediction of Ship Roll Damping - State of the Art, Department of Naval Architecture and Marine Engineering, College of Engineering, The University of Michigan, Ann Arbor MI, 1981.
[16] Ibid.
[17] Ibid.
[18] Sarpkaya, T and Isaacson, M. , Mechanics of Wave Forces on Offshore Structures, Van Nostrand Reinhold Company Inc., New York, NY, 1981.
[19] Ibid.
[20] Dahle, A.D. and Kjarland, 0., The Capsizing of M/S HELLAND-HANSEN, The investigation and recommendations for preventing similar accidents, Proceedings of The Royal Institution of Naval Architects, London, England, 1979.
[21] LeBlond, P.H. and Mysak, L.A., Waves in the Ocean, Elsevier Scientific Publishing Company, Amsterdam, The Netherlands, 1978.
[22] Pizer, S.M. and Wallace, L.V., To Compute Numerically. Concepts and Strategies, Little, Brown Computer Systems Series, Little, Brown & Company, Ltd., Boston, Ma., 1983.
[23] Doebelin, E.O., Measurement Systems, Application and Design, McGraw-Hill Book Company, New York, N.Y., 1975.
[24] Burden, R.L., Faires, J.D. and Reynolds, A.C., Numerical Analysis, Second Edition, Prindle, Weber & Schmidt, Boston, Ma., 1981.
[25] Tse, F.S., Morse, I.E., and Hinkle, R.T., Mechanical Vibrations, Theory and Applications, Second Edition, Allyn and Bacon, Inc., Boston, Mass., 1978.
[26] Allievi, A.G., Calisal, S.M., Rohling, G.F., Motions and Stability of a Fishing Vessel in Transverse and Longitudinal Seaways, STAR Symposium, Society of Naval Architects and Marine Engineers, New York, N.Y., 1986.
122 APPENDIX A
SCHEMATICS OF THE
ELECTRONIC SYSTEMS
- 123 - APPENDIX A. SCHEMATICS OF THE ELECTRONIC SYSTEMS
The electronics used in the testing of the two vessel differed considerably. Because the electronics used in the single chine seiner were not developed by myself I will refrain here from presenting more than a cursory over-view of the electronics. A block diagram is shown illustrating the layout of the components and the power supplies.
The West Coast Trawler benefited from a complete redesign of the data acquisition system. A survey was conducted of the methods used by others in the ship model testing industry to help evaluate what does and doesn't work. From this survey it was gleaned that a remotely controlled vessel with a fully self contained data transmission system would not only be feasible but desirable.
Especially when considering we were going to conduct outdoor sea trials of the model.
A block diagram was drawn up indicating the components we would like to incorporate in the data acquisition system. This included the types and number of sensors required, the means of powering the sensors and gathering their output, and finally a means of relaying this information to a data storage unit which would hold the information received for later retrieval for processing.
- 124 - A.l VERTICAL GYRO
The list of sensors required was easily filled as most of the desired equipment was already available for the single chine seiner tests. One piece of equipment that was not available was the unit to measure roll and pitch of the vessel. An old military style vertical gyro was available from previous tests but this unit was found to be both bulky and poor in quality. The output was far noisier than specifications permitted. The search for a replacement finally netted us the Humphry vertical gyro described here.
After consultation with the suppliers of gyroscopes to the aircraft industry it had been settled on Humphry as a supplier of the gyro. Their range of gyros and their reputation in the industry gave some reassurance that the piece would be reliable and robust. This was later proven to be somewhat misleading as we found that the marine test environment, even with all the extra precautions taken, proved to be a very hostile one for the gyro.
Deterioration of the pick-off quality due to high humidity and shock loadings became a problem later in the test program, culminating in the returning of the unit to the service department for an overhaul and the repetition of a small set of experiments found to have been too badly affected by the malfunction to be usable.
The model selected was a VG24-0825-1 vertical gyro with a range of +/- 60° in pitch and +/- 90° in roll. The frequency
- 125 - •rH
- 126 - 1
- 127 - response of the unit was adequate for the anticipated test range.
A summary if its relevant statistics can be found in Table XVII
and a blueprint of the dimensions of the gyroscope can be found in
Fig. 48.
A.2 LINEAR ACCELEROMETERS
The measurement of the accelerations of the vessel in heave
and sway required the installation of two linear servo-style
accelerometers. The accelerometers used are the same as have been
used for many years by the staff of B.C. Research Ocean
Engineering Center for the measuring of test vessel accelerations.
The units used were Schaevitz model linear accelerometers with a
range of +/- 2.0 g.
A.3 AUTO-PILOT/COMPASS SYSTEM
The need for some means to measure the yaw of the vessel,
plus provide some additional control in the running of the model
in open waters led us to decide on the inclusion of an auto-pilot
unit. This unit would allow us to both measure the yaw as a
deviation from a set direction on the compass and incorporate an
autopilot system in the control of the heading of the vessel to
help keep unintentionally large angle rudder motions from being
introduced in an attempt to maintain a desired course heading.
A local search of suppliers in the Lower Mainland ultimately
led us to the doors of Wagner Engineering. The engineers at this
- 128 - DEMODULATOR
RECEIVER EASTWARD HO MDDEL
WAVE PROBE STORAGE DECEHBER 10, 1985 EASTWARD HQ MODEL SCHEMATICS DATA TELEMETRY SYSTEM UNIVERSITY OF BRITISH COLUMBIA DRAVN IY» GERRY ROHUNG Figure 51. Shipboard Instrumentation
- 130 - firm were most helpful and understanding of our needs and were able to suggest a new auto-pilot unit they had finished developing
for small recreational craft which would satisfy both our needs for light weight and quick response. Because of our need for such a unit and the interest shown in our testing Wagner Engineering donated an entire autopilot unit, minus hydraulics, to our test program.
A. 4 RUDDER ANGLE SENSOR
Other sensors were installed in the vessel, notably a sensor
for determining the rudder angle at any given time. This was not
required for the beam seas testing that comprise this thesis but
was installed for the following seas tests anticipated for the
vessel in the summer of 1986. The sensor consisted primarily of a
potentiometer mounted above, and secured to, the rudder shaft.
A.5 SIGNAL CONDITIONER
The information presented by the various sensors on board the
ship had to be relayed through a central processing point prior to
entering the data telemetry system to bring the signals to the
same standards in regards to amplitude and offset. In addition, a
number of units required a very stable excitation to ensure
accurate motion sensing.
The signal conditioner used is an ST41B dual channel board mounted, along with three identical boards in a unit equipped with
- 131 - a power supply designed to operate from a 10 to 40 VDC power supply. The signal conditioner was supplied by Terrascience of
Vancouver. Principle features of the unit, plus its specifications, are shown below.
Independently variable regulated excitation for each
channel (2 to 10 V d.c.)
- Independent regulated positive and negative excitation per
dual channel unit (+/- 13 V d.c.)
- Independent switch selectable gain (1 to 1000) for each
channel
- Provision for bridge completion components to accept 1/4,
1/2 or full bridge inputs to each channel
- Four pole Butterworth low pass filter on each channel
- All supplies and outputs fully short circuit protected.
SPECIFICATIONS
Excitation
Plug selectable excitation of either;
1) separate 2 - 10 V d.c. (60 mA maximum load) per channel
or
2) single +/- 13 V d.c. (+/- 60 mA maximum load) per dual
channel
Line Regulation
- 132 - 2 -10 V dc less than 0.02% for +/" 10% input change
+/- 13 V dc less than 0.2% for +/- 10% input change
Load Regulation
2 - 10 V dc less than 0.05% for 5 mA to 60 mA load
variation
+/- 13 V dc less than 0.2% for 5 mA to 30 mA load
variation
Ripple
either source less than 1 mV peak to peak DC - 100 Hz.
Amplifier
Input - true differential instrumentation amplifier greater
than 10 megaohms impedanc
Maximum common mode input +/- 15 V dc - no damage
Maximum differential input +/- 30 V dc - no damage
Common mode rejection better than 90 dB DC - 60 Hz
Gain - switch selectable as follows:
LEGEND: X: closed 0: open
GAIN Sl/1 Sl/2 Sl/3 S3/1 S3/2
X 1 0 0 0 0 0
X 2 0 0 0 X 0
X 5 0 0 0 X X
- 133 - X 10 X 0 0 0 0
X 20 X 0 0 X 0
X 50 X 0 0 X X
X 100 X X 0 0 0
X 200 X X X 0 0
X 500 X X 0 X X
X1000 X X X X X
Switches kept open: Sl/4
Switches kept closed: S3/3 and S3/4
BRIDGE COMPLETION Sl/4, S2/4 p.c. mounted switches that connect the positive amplifier input (S+) to a bridge network for use in 1/4 and 1/2 bridge application. Note J3, J4 jumper need to be in place for 1/4 and 1/2 bridge applications.
BALANCE RANGE S3/3, S4/3 pc mounted switches that when closed double the balance range of the SET BALANCE control (authors note: at the expense of a slight loss in precision)
BALANCE OFF S3/4, S4/4 p.c. mounted switches that when opened disconnect the SET BALANCE control from the amplifier.
SELECT EXCITATION SOURCE Jl a p.c. mounted male header which on odd channel numbers only allows the selection of either variable excitation (2 to 10 V dc) or fixed excitation of +/-
13 V dc.
set as follows:
- 134 - connect a to b for variable excitation (2 to 10 V dc)
connect b to c for fixed excitation (+/- 13 V dc)
Connectors:
Inputs are Bendix PT02A 12-10S military style connectors pin connections are as follows:
PIN # FUNCTION
A S- signal negative
B P+ excitation positive
C P- excitation negative
D S+ signal positive
E N.C.
F SHIELD cable shield
G 1/4 B quarter bridge
H N.C.
J N.C.
K V- excitation negative
(odd channels numbers only)
Outputs are standard BNC (isolated from chassis) connectors
Power Supply Requirements:
This version of the signal conditioner comes with transformer
option number 01 which requires 10.6 to 40 V dc supply and provides a regulated +/- 15 V dc to the boards,
pin connections are as follows:
FUNCTION
PIN # D.C. INPUT AC INPUT
- 135 - A positive live
B common neutral
C chassis chassis
Signal Conditioner Board Dimensions:
Size: 250 mm X 170 mm X 110 mm
Weight: 3.2 kg.
Further information can be found in the owners manual supplied by the manufacturer [13].
A.6 TRANSMITTER/MODULATOR
The signals passed through the signal conditioner are fed into the modulator-transmitter for transmission to the remote receiving station. The input range of the transmitter was +/- 5 V dc thus, if the output of the signal conditioner was expected to exceed this value a voltage divider was installed in-line with the signal conditioner feed to ensure no saturation of the input to
the modulator-transmitter would occur.
The function of the transmitter can be described as follows;
the incoming signals are all voltage shifted 5 volts to render the
+/- 5 V dc signal into a 0 to 10 V dc signal. Each of the incoming
signals are then assigned a unique frequency in the audio band.
This frequency is then modulated proportional to the amplitude of
the incoming signal. The individual audio frequencies are then
summed and attached to a UHF radio wave carrier wave for
- 136 - transmission from an omni-directional antenna mounted within the model.
A.7 RECEIVER
The radio signal sent from the model is intercepted by the onshore receiver which removes the carrier wave from the radio signal and sends the remaining audio signal out a standard coaxial link.
A.8 DEMULTIPLEXER/DEMODULATOR
This unit takes the audio signal and selectively filters each respective frequency to create 8 channels of data. These frequencies are then demodulated to regain their 0 to 10 V dc range. A -5 V dc offset is again applied to the data and the output is 8 channels of +/- 5 V dc data.
A.9 MINC COMPUTER
The data acquisition was done with the use of a MINC 11 mini-computer running B.C. RESEARCH data acquisition software. The output of the demodulator/demultiplexer as well as the feed from the wave probe were fed into the input strip of the computer where
it was sampled and stored on 8 inch floppy disk for subsequent analysis.
- 137 - APPENDIX B
WEST COAST TRAWLER
STABILITY REPORT
- 138 - STABILITY REPORT
M.V. "EASTWARD HO"
•NELSON BROS. FISHERIES
INCLINING EXPERIMENT '
In accordance with Owners instructions and C.S.I, regulations, the subject vessel was inclined when nearing completion at the Builder's yard. The following conditions existed at the time of the inclining experiment:
Location: Star Shipyard (Mercer's) Ltd. New Westminster, B. C.
Date: June 4, 1969
Representatives: Mr. B. Smith - C.S.I. Kr. G. Mercer- Builder Mr. P. S. Hatfield
Total men on board: Seven
Wind and tide: Calm, no current
Water Density: Fresh
Bilges: Pumped dry
Condition of tanks:
Fuel oil - Fwd. S Pressed Full - 4400 gal. cap. Day Tank Operating level-150 gal. cap. Fresh water - Aft P Pressed Full - 2100 gal. cap. S Pressed Full - 2100 gal. cap. Hydraulic Oil Tank Fwd. 100 gals. - 260 gal. cap. Lube Oil Tank Fwd. 175 gals. - 260 gal. cap. Hydraulic Reservoir Tanks P & S Operating level Inclining weights used: 4 © 1000 lbs. (total 4000 .lbs.) Distance weights moved: 27'-0" Pendulum position Shaft tunnel Pendulum length 99" - 139 - Drafts of vessel as Inclined: Fwd. P B'-3" S 8'-3" Aft P ll'-ll" s ll»-7" Mean Draft 10'-O" Minimum freeboard as inclined:' P 47" 5 51" Mean 49" Trim as inclined: 6" by stern Displacement of vessel as inclined: 345.5 L. Tons (S.W.) Record of deflections: Shift Direction Deflection 1 P to S 14/16 0.8750 2 P to S 14/16 0.8750 3 5 to P 14/16 0.8750 4 S to P 14/16 0.8750 5 S to P 13/16 0.8125 6 S to P 14/16 0.8750 7 P to S 14/16 0.8750 8 P to S 13/16 0.8125 6.875 Mean deflection 6.875/8 - 0.859" GM as inclined: GM - w x d x 1 - .447 x 27 x 99 - 4.06 feet disp. x a 345.5 x .B59 LCG & KG as inclined: From Hydrostatic Curves at 345.5 L. Tons (S.W.) KM 15.97 feet GM 4.06 feet Therefore KG - 11.91 feet MCT 1" - 30.05 ft. tons LCB 3.90 feet aft LEVER - 6 x 30.05 - .52 feet 345.5 Therefore LGG 4.42 feet aft " 140 - 0 o 4 to a o 3 "an 0 0 S j j t T + * t t O o u o o o o * O c 0 2 rt)s i A a ii 6 6 o eft N 10 ifl CD d> 14 w r \ •<»• n •5 j in j M ro ? * i» •t I V \ t V5 I t IL IL L I o a. a 0 o o 0 0 0 0 0 0 o o w o 0 o 0 o 0 r M o w ! /- u (0 il 0 t i ! i i i id v : z 1 i • J 0 1 vi to J 0 0 p» "* UJ t J 1L 0 •i •i w w' u. iL IL I 2 2 2 2 z z 14 1 : ITEM —— VJT. U.T&nS MOME(JT WIOMENT . VCSS.EL A% U4C*_lMe-C» 34-5.SO 4-US.OO •'.4.42 l5-L--".00 .*"£A.U_I>J.G OEL5W\ . Ol«C-iE • to l.s-B •-- .TO T(£>J-SC t> e-\ >M kOivte t. OO n.-s n is • i.oo •¥ ~) .CO .S". oo i en."so .* zio.oo Sewer t4. itei l.co u.oo 11- CO -t-4-0£ - tA-.co _ -IMCLJ M<*JC oTs> : C-} 14 75 •» Z.fcS -V.Tl LDIU. v_ •:. *st=-r. F*S :" C-0." - 5V -fp \Z.OO . - -to(. OO - ISSiP-OO ~rvso • pis J-J - 2.P.--0 I.Uo - is-s-.feo -n.tfo + 356 .B© 7 camera. (.-J fe. 2.CL.SO- .- W.TP - t r.nr 15 ir - ZS"7.-*0 - .TOTALS •JS07 •r 11" . 55 t-XcxJ DRftPT AFT "3'- a* © . S^s" p-r. 6'- LCF ( AxFT « c JSS rr. 5UW - LCQ 1 KM ,t»p -—r. ( — v...... i~> rr. LCT3. . . 3 • (6 *T. KG fed 1 • 89 "T. GM .. . 530 1 FT. T-.JS FR"£. &ORPA.C& • — WVCT- 1A . 00 rT. T»u< Ar • oo rr. TRIM £«y HEAD) 1\• 57 INCHK. 'HEEL. CO' «so- . *£CC D 7071 l.t>DC CM &>N» © 2. DP 34-4. :. - - "t-V -l.lZ - «..c4- (£>5 ITU (.11 t.ro •*2- - .04- - 142 - ~e ~ t* ie ST • «n *» ;rrEMr— VJT. L-.TOMS MOMEUT MOMEUT . UJCHT -&HtT» wen .t<» JTR6&H. WAT« .. APT : » is tine • *s-|. "FUEL "OIU ":r' :.' rwe> *»4i .so ISS.6o -SSB.eo ~ ."- : :. cewTsn. ..&.£<• LSO Aono - "M.-ic - . UCD • CKI=40 <;eFP«e.t5','.. .7..*...... ~ "t -PO 10.0P t-O-OO -2».0£> - Z.»". OD "STOnuEfc i;:_ : •; •:. Z..OP \1.DD -2.7.00 - tf"4- OO — — - -- —• • • • - - . •• ...... •• • • ...... , ." -- ToTALt | 32-B 4- D < S". UCs *IC7 see.so i-.Tou DRfcFT AFT .< .HEEL . IS" so" CO* -&IK4 © •ires .ffOOP .7071 I.COO CM & Z.PS> Z.UU " - -.X.O -t.e^ -•STB cz. : fRic^mKiG UEv/eft) •ssr i.us l.fel ."71 - .It - 143 - -JTE.M . VT. L.TOKS! KG MOMEWT \_CC . DEPARTURE .TO. SRAJViDS : 41-97 tC^ta. 59 4CE ~:_ •.• -. .. . avis. VL SO 500-65 '. " -—"" ...... : ..... • -— i:- ;; —_ ... . .:...... — .... _ .. • - • ' • - •• . "-v.: . — .... !. 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AFT 14-05 13 io 164-05 .50 (.0 710-^0 FUEL OIL " 15-36 7-16 no-oo -17-35 - 7i>4> • SO CENTRE 4-70 5-90 27-70 -34•'30 . no to CREvO ft." fcFFlCTS" i -09 OD-00 *XO .00 2&.00 ITORfc* 1-50 1700 75-50 -27.00 ±0-50 "OTALt 3>7 -01 12-23 3&T4-- 51 rlfco * 54,9- 90. Ci\£.?=>i_ACG.»-'\E>-lT 31-7 • OX L.Tetfs 5R6FT AFT IC- MEA.g . ORA.FT . 4© FT. Es«AP*T F"W O £>- LCF. : (AFT «•) 7 . 17 (FT. M.'MiMyyi r"R£E.E»OA,UO A' •9" LCG . « . 6O »T KM IG»- IS FT. LCB. - < — > 3 • fcl *T. KG I-2- 13 FT B.G. 1 • 62 rr. »wo. GM 3- 95 .FT. TKlSrl w\c»Me>JT .. 576. • 96 rr. •hit. E.URt=ACe. O •20 FT. a7 • 75 FT.TMJ. OKA tortwECTae» 3- 75. FT. TRIM 2.0 •75 Mcaii HEEL. IS" • SO' JE>IKI e> . 1536 . SfffO •7 - 145 - TAALF LOAD cpw'PiTiPN: Q&o'/p L.IBUHI>*- 4 &TC*<«» , sr>% CARGO) ~e IK ie *T • tx. «« *s ' ITEM "~" •WT. u.Te> -FtfcefcH WATER : AFT 9."S7 11.80 MOW •>- "Fotc:". oa~ *.'"~ fc.SD -n-io - 17S\ *o — - ,— . — .oosiTKe. 3 . 15> 4.75 (464. -ace© — 1 it. OO "_ej£t=w 4-~crr&i.TW;. ..-'.—ir.."- ''... : 1. 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OO •*- ao4&.oo . .— — —— - ,"„ 1. „ ''. '.... „ . — — - _ ; • • •;• - • - - — •.— •• "-- • .'. :.' .TOTALt 5S-2. .Ol 11.06 6.2.3*.% 1 Dl£.PuA,CEME»JT LCF (AFT #) 6 .r»£> FT. MlMlMUM* PR£EB*Ano 1'- LCG .... ( — ) — • Cat... rr. KM IS". 3.6 FT. Lf& . < — ) S-.-7&: PT. KG ' ' U . ©e IT. .. . ;• 0.4.5 ,.TG. M . 4- ' 3o FT- TRM V\0**E>JT . 3.5 "& •'3 ^T.-roMS FRce. £,uFtr=/vee. • 14- PT. MCT GM C.OP5«EC.Ti£B lt> FT. TRINA HEEl . " " IS" ^0° 45" GO* 75" ..£>tKi . e .ti»66 .S0OO .-7071 .•Stele O (. OOO c M &«Ni e lofc z 3-foo 4-.it> Mto " " "' " '. . - .1*. -.LB -ZOl -z.es -3.S3 GZ. fRiGfcrnKlG 1.40 (-74, Mi .<*3 - 147 - TfcgeiVAl *>T PORT ftp*/ L'tfOlOt <> «5TORE5, FULL CARGO]). "8" .48-- " ' • si.- -•-«*,. ... 41« ES . IITEM VJT. L..TOK&! KG MOMEtJT l_ce> MOwiEMT "~" • 260-39 12-50 S501-2C * 1-26 •t-.34,1-99 _FRESW VWtTER, : if T' < • ee U.30 .. .' 21 -25 +5000 • 94-00 roti. CIL F-WD RfcS. 2.05 6>-10 a-5o -\4rfcO - 54-42 — .— . — .. 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U.TOKS) KG MOMEUT .LIGHTSHIP ".: ;~ " 11-50 3S01--Z4. * 1 -16+ .".3 ic& . _:: • _ 17 50 — —r.. . .. • :— - - • - • - - — - ... .": • . __r ' ". - - _ " V" ... — • —' - - _•- • - •'• .... -• *" • TOTALS 30B--4-I i3'ie 4- \ '10 3 01 £.F> «ACE«\ E>JT 3oB • 4-t L.-tow* D^feFT AFT 9'. .MEASI . OW.FT s • as FT. 5RA!»T FWD LCF .- ( AFT tf ) £> • V7 »T. MIMIWIDM FReCLB^A^O LCG : •...(.-• V 1 • xo rr. KM ... •. 16- •22. rr. LGB. 3-51 FT. KG 13- 19 rr B.G 1.31 rr. FWD. GM a-t?3 FT 712-43 rr.-swt FRit 6URFA.C& 0- OB fr. M\C_T- 47- ©8 rr TOKS GM contra ECTiS.'O 1 95 fT. TRlM t_ev UEM?) 26-1© >MCMf« HEEL. - • IS" | 3>0P -US' GO* «>0" . i»6<5 . Z9SO •lei I 1 •DOOO CM £>INI © 9 76 1-49 IM i-55 S-65 1-95 M&o ' - Ml -1-04 -7-67 o-to . I-V7 -C 01 cr (RicurtKjG ueve*:) - 149 - . JOT " STE.Rkl TRKWLER J..MV.' EASTWARD MO* ^o^^'^E1 (MpS) CURVES ~' "WOrVTvJ VAUCOOVEK B.C. APPENDIX C FOURIER SMOOTHING - 152 - Cl FOURIER SMOOTHING The smoothing technique used in the processing of the experimental data to eliminate high frequency noise from the signals was developed by Eric E. Aubanel and Keith B. Oldham of Trent University, Peterborough, Ontario. The technique they developed smooths data obtained at regular intervals and containing any number of data points. The discussion that follows is based primarily on an article they published in the February 1985 issue of BYTE magazine. The discussion will be broken into two parts. First, a little explanation of the Fourier transformation is given with how the high frequencies can be removed and, secondly, an explanation of the algorithm used for the smoothing technique. C.l.l THE FOURIER TRANSFORM Fourier transformation of a number of data points produced in the time domain remaps the energy contained within the signal into the frequency domain. As an example, if the input signal to be transformed was a pure sinusoid with a frequency of 1.0 Hz. and an amplitude of 10.0 units the frequency domain representation would be a single spike at 1.0 Hz. with an amplitude of 10.0 units. If there was a second signal, let's say a 5 Hz. sine wave of amplitude 20.0 units, superimposed upon the original 1.0 Hz. signal we would have what is shown in Fig. 52 as the time domain - 153 - signal. When this is transformed into the frequency domain the resulting map becomes what is shown in Fig. 53. TYPICAL REPEATING FUNCTION 40 T : ! -40 H 1 "1 : 1 1 0 12 3 4 TIME (seconds) Figure 52 Typical Time Domain Signal From the illustration in Fig. 53 it can easily be seen that the removal of high frequency components becomes almost a trivial matter involving the truncation of the components on the frequency axis beyond some chosen cut-off point and then transforming the resulting waveform back into the time domain. This remaping to the time domain is called Fourier inversion. - 154 - The performing of a Fourier transform on a series of real TYPICAL FREQUENCY DOMAIN REPRESENTATION OF REPEATING FUNCTION 40 30 111 Q • 20-| Q_ < 10 2 4 6 8 10 FREQUENCY (Hertz) Figure 53 Typical Frequency Domain Representation of Signal data points, x^ , produces two sets of transforms: N-1 1 v f 2jrjk>, k =0,1,2 N-1 (C.001) N!XJ cos(-iH N-1 k =0,1,2 N-1 (C.002) J-o The elimination of high frequency components from the frequency domain can be represented as a multiplication, - 155 - (C.003) by a function, f^, which is called the digital filter function. The filter function can take any number of forms. The most obvious type of filter function is the rectangular filter which cuts off all transforms for k>E. The problem with using this form of filtering is that it can lead to false accentuations of frequencies corresponding to transform points near where the filter begins. The method proposed in the paper was to use a quadratic filter function which produces a gradual attenuation of the frequencies at the high end. The filter function can be represented as the mathematical function; 1-(|] k-1,2,3 E-l fk = (C.004) 0 k=E,E+l,. . . The smaller the chosen value of E, the greater the high frequency attenuation. The closer E is to (~~~) tne less affected the inverted signal. To reduce the amount of computational work required the two equations for the Fourier transforms can be inspected for terms that repeat and that are equal to zero. With this reduction in terms the two equations become: N-1 R (C.005) j = o - 156 - \ = ~lr + Ir I xj cosC^) k=1-2 E-1 (c-006> N-l = sin \ ~4 I Xj C^3 k=l,2,...,E-l (C.007) j-i E - 1 \-\ + 2lfA (c-008) E- 1 k= 1 j-l,2,...,N-l (C.009) where Xj is the high-frequency-stripped analog of x^. The term for I is zero because the sine of 0 is 0. The factor of 2 found in o equations (C.008) and (C.009) is there because of the restriction of E being less than or equal to ^ and by taking advantage of the symmetries (R^ ^ = R^, 1^ ^ = -1^) already noted. This simplification still leaves a considerable amount of number crunching to be done. It was because of this that a further reduction in computation was developed using an algorithm called the Fast Fourier Transform (FFT). This approach to the problem applies the properties of sines and cosines such that the number of computations is significantly reduced. Similarly, this allows a reduction in the number of multiplications required, replacing a large number of them with additions instead. The storage space required for transform and inversion is greatly reduced as the new - 157 - numbers computed can over write the original values. On the negative side of the FFT coin the algorithm requires that the number of data points to be processed be a power of 2. This restriction requires the user to usually "pad" the input data by adding a number of zero data points to the end of his record to meet the power of 2 requirement. This method is called "zero-filling". Besides creating additional demands on memory allocation the addition of zeros to the end can cause undesired high frequencies to be added to the signal due to possible discontinuities between the real data and the zero line extension. Also working against the use of the FFT for smoothing purposes is that it is an inherently square method, ie: it requires the computation of 2N outputs from 2N inputs. Thus, it cannot exploit the advantages of being able to produce E outputs from N inputs. With all these factors involved in the use of the FFT for data smoothing the process was taken one step further by Aubanel and Oldham to produce the algorithm used for the smoothing of the data in this thesis. Further reductions in computation could be realized by inspection of equations (C.006), (C.007) and (C.009). It can be seen that all of these equations are of the form; M |-27rml-> + V sin (C.010) m m=l - 158 - where G, m, U^, Vm,M and 1 are appropriately interpreted. To evaluate expression (C.010) the sum was split into odd-m and even-m terms, M or M-1 _ r«T T r27r(m+l)l 2TT1^ i . r27r(m+l)l 27rl>, G = ) U cosf— - —i-=—J + V sin — VT -jH m=l , 3 M or M-1 /-27rml-v . r27rml-N ,Y U cos [—^3 + V 51nl—N~J (C.011) m m m = 2 , 4 and the arguments of the trigonometric terms are modified in the odd-m moeity. Additional formulas were added to expand the modified functions and the m is then replaced by 2m-1 in the first summation and by 2m in the second. After collecting terms it was found that, M + l Int- 2 r G !1 - I »2,.I-(T)-VI . f4fnil>, :ln U0 Sinf%i) J +V9 cosf^+V l— J (C.012) 2m-1 *- N 2m-1 N •> m N~ If M is odd, equation (C.012) calls for the values of V^+^ and U"M+1' which were not present in equation (C.011); the authors interpreted these terms as zero. A comparison of this method with the earlier FFT form shows there are two extra terms to compute but the number of summed - 159 - terms has been condensed by a factor of two. If this condensation procedure is repeated P times, where P=Int{log2(2M-l)} , then a single (m=l) term, G = newest U coefficient co + newest V coefficient sin (C.013) remains from which G can be computed. The use of this procedure reduces the number of sines and cosines needed to be computed from M to P+l each. C.l.2 FOURIER INVERSION To recreate the time domain data the frequency components are summed together as powers of sines and cosines, with their associated phases, to produce the time domain curve. The operation can be written as follows: N-l N-l (C.014) C.l.3 OPERATION OF THE ALGORITHM The data that is to be smoothed is stored in an array named X(J) ,J=1 N, where N is the number of points in the input waveform. The number of iterations that the routine has gone - 160 - through, Q, is set to zero. From an average of the first ten points and the last ten points a straight line is subtracted from the data to eliminate the possible end effects of introducing unwanted high frequency information into the data. The amount of smoothing to be done is determined by the specification of the smoothing factor, E. This factor must be an integer greater than 1 and less than or equal to ^. The first transform calculated is R , followed by the evaluation of R and o J k I for k=Q to E-l. After this the first inverse transform is k performed. This is to calculated the value of Xq using the quadratic filter function and R^. Following this the rest of the new values, x^, j=l N, are computed in turn using R^, 1^ and the quadratic filter function, f All the transformed data values, representing the smoothed data, are stored in array X1(J),J=1 N. The iteration counter,Q , is set to Q+l and another pass is performed if the smoothing was insufficient. With the new pass the degree of smoothing specified by E can be changed. Once the data is smoothed to satisfaction the straight line removed at the start of the process is added back into the data for final output. - 161 - APPENDIX D BACKGROUND THEORY - 162 - D.O BACKGROUND THEORY D.l SOME BASIC DEFINITIONS To be able to better understand the characteristics of a vessel in a marine environment some means was necessary to describe the pertinent aspects of the vessels design and motion. In this section the notation used will be explained and some background given to the basic equations of motion and how the parameters computed relate to the ships motion. D.l.l DISPLACEMENT Displacement is the measure of the weight of water corresponding to the volume of the vessel below the surface of the water. This value is equal to the weight of the vessel when it is suspended from a scale in air. The standard symbol used for displacement is A. D.1.2 TRIM Trim is the longitudinal inclination of the vessel. This may be expressed as the angle between the baseline of the ship and the waterplane. Usually the trim is expressed as the difference between fore and aft drafts. D.l.3 DRAFT - 163 - Draft is the measure of the lowest point of the vessel from the surface of the water. Draft values quoted for a vessel are usually given for the fore and aft sections of the vessel as the trim is not always 0 degrees from the design trim. For the sake of comparison most drafts, when compared, are either the average of the fore and aft drafts or the largest draft measured along the length of the vessel. There are two types of draft measures quoted. These are the molded draft and the keel draft. The molded draft is measured from the waterline down to the molded baseline. The keel draft is measured from the waterline to the lowest point on the keel. The second is usually the one operators of the vessel will quote when asked the draft of their vessel. D.l.4 BASELINE The baseline is a design aid used by the naval architect to define the datum elevation of the vessel and from which all elevations are measured. This line does not necessarily have to coincide with the lowest point of the hull as any arbitrary plane is just as adequate. The baseline is usually placed such that it intersects the centerpoint of the vessel at its lowest point. This line is referred to in nomenclature as K. D.1.5 CENTER OF GRAVITY The center of gravity is a point from which a mass of - 164 - equivalent magnitude to the vessel could be placed to produce identical moments about all three exclusive axis. The position of this center of gravity is usually along the longitudinal axis of the vessel (provided it has no heel) and is measured in the other two planes as the distance from the center-line of the hull longitudinally and its height from the baseline. This point is normally marked with the symbol G. D.1.6 CENTER OF BUOYANCY The center of buoyancy of a vessel is the point within the vessel that all the hydrostatic buoyancy forces appear to be acting. This position is normally denoted by the symbol B. D.1.7 METACENTER The metacenter is a point located above the baseline where, at some angle 6 D.1.8 KM KM refers to the distance from the baseline, K, to the metacenter, M. This value is a function of the displacement and draft of the vessel. - 165 - D.l.9 KG KG refers to the distance of the center of gravity, G, from the baseline, K. This varies with the vertical position of the center of gravity. D.l.10 GM GM is called the metacentric height and is equal to KM minus KG. D.l.11 GZ GZ is also named the righting arm and is the distance between the center of gravity, G, and the vector produced by the buoyant force acting on the hull at an angle 8 y FIXED COORDINATE SYSTEM y k MOVING COORDINATE SYSTEM Figure 54. The Dynamic Coordinate System - 166 - D.2 THE DYNAMIC COORDINATE SYSTEM To represent the motions of the vessel mathematically two sets of coordinate systems had to be developed. These are illustrated in Fig. 54. D.2.1 WORLD COORDINATES The world coordinates are fixed in space externally to the vessel. These coordinates give the absolute displacements of the vessel with reference to its surroundings. The reference frame is assumed to be fixed in space. Normally this reference frame, though fixed in space, is, for the study of ship motions, allowed to exist in one point relative to the surface of the Earth as it is unnecessary to include the Earths rotation. D.2.2 LOCAL COORDINATES The local coordinates are fixed to the vessel and usually have their intersection, 0, as the location of the center of gravity, G, of the vessel. The z axis runs longitudinally through the hull parallel to the center line of the vessel. The x-axis extends horizontally from the center of gravity and the y-axis rises vertically from the center of gravity. D.3 EQUATIONS OF MOTION - 167 - D.3.1 Equation of Roll Motion (Uncoupled) The motion of a ship in a transverse seaway can be described by a relationship of the roll angle of the ship, the restoring moments and the exciting forces. For small roll angles a simplifying approach of linear equations of motion is usually considered sufficient and produces acceptable results. When the roll motions of the ship become large the non-linearities involved in the motions can become very important. These non-linearities could eventually magnify some small variation in excitation to the point where restoring moments are not only insufficient but may actually contribute to the capsizing of the vessel. To develop the non-linear equation of roll motion (uncoupled) we first start with the standard linear form of the equation of motion. This equation is of the form, it a I' H + hp. + AGity - 0 (D.002) dt2 dt where a virtual mass moment of inertia about the longitudinal axis = I' -[(A+A')/g]k2 XX A = displacement of the vessel - 168 - A' /g= added mass of the vessel for rolling k = radius of gyration of the vessel mass plus added mass term for the rolling motion b = damping coefficient GM = metacentric height (transverse) (j> = angle of roll (in still water) if the vessel is not in still water the angle of roll considered above is relative to the instantaneous surface of the water. That is, the difference in angles between the roll angle of the vessel and the angle defining the slope of the water surface, a. If the damping and inertia terms are assumed to be functions of then the equation of motion can be expressed as, I' or A k2 A k2 A k2 1 XX 1 XX 1 XX where A = A + A' l In many cases the waveform defining the surface of the water can be expressed as a simple sinusoid of the form, - 169 - a = a'sinw t (D.005) M e where maximum effective wave slope encounter wave e frequency Substituting these assumptions into the the equation for simple linear motion (D.004) we obtain the general equation of linear rolling in a sinusoidal seaway. After simplification of coefficients we obtain, which is a linear second order differential equation that can be solved using conventional techniques for an exact solution. This relationship is only adequate, though, for roll angles of less than around 8 degrees [14]. Non-linear rolling can be caused by a number of factors, these are divided into two primary categories; those that affect the roll damping of the vessel and those that affect the restoring moment of the vessel. These non-linearities can be expressed as, (D.007) where a represents the virtual mass moment of inertia as a 170 - function of the encounter frequency and b^ and b^ are damping coefficients related to the roll velocity and roll velocity squared, respectively. The absolute value of one of the terms in the velocity squared roll damping is included to retain the sign of the force such that it is always opposing the roll motion. The c( •both the instantaneous roll angle and time. It can be expressed as the series expansion, 3 5 c(*,t) - c^t)* + c3(t)^ + c5(t)«4 + ... (D.008) The last term in the non-linear roll motion equation is M(w ,t) which varies with both the encounter frequency and elapsed e time. D.3.1.1 Non-Linear Damping Coefficients Returning to the single degree of freedom equation of motion, AA + B.(^) + CA - M.(wt) (D.009) The damping moment can be expressed as a series expansion of and |^| in the form B^ = B which is the non-linear representation as described earlier. To - 171 obtain values of the non-linear damping coefficients from testing the most popular technique is to conduct free-roll tests. In the free-roll tests the model is rolled to a certain angle and then released. The motion initiated is such that there is no sway or yaw as these would affect the values of the damping obtained. The heave and pitch motions, on the other hand, are allowed in so much as they are a part of the rolling process of the model as it attempts to maintain a constant displacement and trimming moment at all roll angles. The pitch and heave are to be results of the natural hydrostatics of the vessel and not of the initial motion. If we denote by A where the angle of roll is given in degrees. and the values of and A^ = )/2- (D.013) m n-l n The coefficients of polynomial (D.011), a, b and c, are - 172 - called the coefficients of extinction. The relationship between these coefficients of extinction and the damping coefficients shown in equation (D.010) can be derived by integrating the equation of motion shown in (D.009), without the external-force term, over the time for a half roll cycle to complete. The energy dissipated due to damping is then equated to the work done by the restoring moment. This result can be expressed in the form, B + f-w Comparing this relationship to that shown in (D.011) and relating terms the extinction coefficients can be expressed in terms of the damping coefficients as follows: a=f^Bi (D.015) 9 2 b - wm § B2 For the above relationships to hold the coefficients B , and B3 must remain independent of the roll angle. From other investigations [16] it has been found that the the value of B2 is a function of the roll amplitude and that the effects of bilge keels are expressed primarily in B2. Only that part of B2 that remains constant is proportional to b. The part of B2 that is inversely proportional to the roll amplitude is apparently - 173 - transferred to coefficient a, and that part of B that is proportional to the roll amplitude is found in coefficient c. Thus it can be seen that to be able to give a true representation of the roll damping for all angles of roll a continuous function cannot adequately define the value as the coefficients of the relationship vary over the range of roll angles achieved. Thus it has been suggested that equivalent linear damping coefficients be developed of the form, a - a + b^ + c Using the expression for roll extinction developed by Bertin [17], Ad, = tty2 (deg.) (D.019) we can take the coefficient N as a form of an equivalent non-linear damping coefficient. This term has been called the "N-coefficient". Rewriting in terms of the extinction coefficients we get: N = + b + cd, (deg.) (D.020) 0 m m where N depends strongly on the mean roll angle, ^ , and is usually given in terms of the - 174 - D.3.1.2 Non-Linear Restoring Moments The restoring moment for a water-borne vessel is a function of its displacement, its geometry, the position of its center of gravity and the angle of roll. For small angle theory the restoring moment can be assumed to be linear, like the typical coil spring where the resisting force is proportional to the change in length of the spring. For angles of roll less than about 8° this approximation is adequate. From inspection of a typical righting arm curve^ it can be seen that the slope of the curve at small angles can be represented by a straight line. If this line is extended until it reaches the intersection with the M = AGM<£ (D.021) When the roll angles become large it is very important to consider non-linear coefficients as the restoring moment actually decreases after the vessel has rolled beyond its critical angle. The restoring moment should then be a function such as: Righting arm curves for the models tested are shown in chapter 3 - 175 - M = AGZ(^) (D.022) The values for GZ(^) can be readily found through the use of available computer routines for ship design or by hand following the procedures outlined in the Principles of Naval Architecture published by The Society of Naval Architects and Marine Engineers. D.4 WAVE DYNAMICS The types of waves found in the ocean depend upon wind, temperature, geographic and atmospheric conditions. This does not lend itself easily to modeling. To be able to gain some insight into the response of vessels to these wave conditions a number of simplifications, or approximations, are made. The first approximation is that the waves found in the ocean can be represented by the summation of a number of discrete regular wave trains of varying frequency, amplitude and phase at various angles of incidence to each other. This is defined as a sea spectrum and a number of methods have been devised by Oceanographers to both measure these in the field and to represent them numerically through mathematical relationships. Beyond this there is also the problem of wave shape, though the sea spectrum is defined as a summation of a number of regular sinusoidal waves it is not always possible to create these waves in a test environment. Because the wave forms are a function of their environment they change as the depth they are in varies in - 176 - relation to the wavelength of that wave frequency. Waves can thus deviate from the regular sinusoidal form and become more trochoidal, ie: flatter troughs and sharper peaks, until the point where the wave slope at the peak is sufficiently steep that collapsing of the crests occurs. D.4.1 Regular Waves Regular waves are defined as those waves whose crests are equidistant and all travelling at the same phase velocity. The simplest approximation to a regular wave is the sinusoidal wave, a product of linear wave theory. The relationship for a sinusoidal wave is: n = A cos(kx-wt) (D.025) where: r/ = elevation of water surface at time, t, and distance x A = amplitude of the wave form k = wave number — 2n/L a) = wave frequency (radians) The existence of sinusoidal waves depends on both its frequency and the water depth. Figure 55 illustrates the regions of existence of the various wave types. Typically the region of linear waves is where the depth of the water is much greater than the wave height, as is the wavelength, ie: d > L > n. The zone demarcated by the crosshatching represents the range of wave types used during the testing computed from their wavelengths, - 177 - amplitudes and the known depth of the tank. D.4.2 Non-Linear Waves The non-linear waves types are numerous, examples include Stokes Ilnd order, Stokes Vth order, Cnoidal, Hyperbolic and Trochoidal wave theories. [18] These theories are all expansions of the wave theory from its linear approximations to include higher order terms. 0.0000510.001 0.002 0.005 0.01 0.02 005 0.1 0.2 d Figure 55. Wave theory as a function of H/gT2 and d/gT2 - 178 - From the figure of wave types as a function of the wave length and water depth we can see that each wave theory has a unique area of application where it best describes the wave environment. There is some overlap of the theories in parts of the wave type spectrum. D.4.3 Breaking Waves When an individual wave exceeds the hydrostatic and hydrodynamic limits the wave falls apart. This is known as wave breaking. There are a number of different styles of breaking waves; they include the spilling breaker, the plunging jet, the collapsing breaker,and the surging breaker. Breaking waves can be expected when the wave height to wave length ratio becomes a certain ratio as a function of the water depth. This ratio, put forth by Miche (1944) [19], can be expressed as, - - 0.142 tanh(kd) (D.026) L where: H — wave height L = wave length k «= wave number d = water depth This only provides an indicator of the conditions required - 179 - for a breaker to form. If the water becomes sufficiently shallow almost any waveform will break. The type of breaking wave to expect when a wave train encounters a beach can be computed through the parameter B .Galvin (1968), which is expressed as: 8 = H /(L m2) (D.027) o o where: H /L — deep water wave o o slope m = beach slope with the different types of breakers designated by: B > 5 : spilling breaker 5 > B > 0.1 : plunging breaker B « 0.1 : collapsing breaker B < 0.1 : surging breaker. D.4.4 Energy Content of Waves The waves, as they progress, transfer energy to their surroundings. Regular waves dissipate energy at a regular and controlled rate while a breaking wave expends much greater energy over a shorter period of time. D.4.4.1 Regular Waves The energy flux P, which is the average rate of transfer of energy per unit width across a plane perpendicular to the direction of wave propagation, can be expressed by integrating - 180 - over the depth and taking the time average of the instantaneous rate at which work is done and the kinetic and potential energy transfer across this plane. This can be expressed as; 2 2 [P + 2 P (u + w ) + pgz] u dz (D.028) -d which, for steady, progressive waves, reduces to: P = pc u2 dz (D.029) H / I / y / [ 0 V_ 1 VELOCITY PROFILE C' Figure 56. Velocity profile of a breaking wave D.4.4.2 Breaking Waves - 181 - The energy transmitted from a breaking wave is a function of the amplitude of the wave and the point of impact of the wave as well as the time from initial breaking that the wave strikes the object. A typical velocity profile of a breaking wave is shown in Fig. 56 [20] . From this profile it can be seen that a great deal of the energy transferred by a breaking wave is contained within the high velocity jet of water at its crest. The transfer of energy to a vessel on impact with a breaking wave can be expressed through an energy balance. The energies involved can be broken into four main components, these are: : the energy dissipated by damping max (BJ + B |£|?)d4 (D.030) 44 V1 1 where: B = non-linear V damping B = linear damping 44 $ •= roll velocity E : the energy transferred from the wave slope - —2 1 M dt 2 0 E = (D.031) 2 2 I' XX - 182 - where: M 2 = moment induced by wave slope I' «= virtual mass XX moment of inertia At 2= duration of exposure to the wave the energy transferred from the jet .At M dt 3 (D.032) 2 I' where: M = moment induced 3 by plunging jet I' = virtual mass XX moment of inertia At = duration of 3 exposure to the jet the energy content of the heeled vessel - 183 - 9 , max E •= A (D.033) 4 GZ cty o where: GZ •= righting arm A = displacement The balance then becomes: E = E + E = E + E (D.030) 2 3 14 - 184 -S07 .14. * 5