EXTENDED TENSION LEG PLATFORM DESIGN FOR OFFSHORE WIND TURBINE
SYSTEMS
by
Nicholas W. Parker
B.S., Naval Architecture and Marine Engineering
United States Coast Guard Academy, 2003
Submitted to the Department of Mechanical Engineering in partial fulfillment of the
requirements for the degrees of
Master of Science in Naval Architecture and Marine Engineering
and
Master of Science in Mechanical Engineering
at the
MASSACHUSETTS INSTITUTE OF TECHNOLOGY
June 2007
©Nicholas W. Parker, 2007. All rights reserved.
The author hereby grants to MIT permission to reproduce and to distribute publicly paper
and electronic copies of this thesis document in whole or in part in any medium now
known or hereafter created.
Signature of Author......................................
Department of Mechanical Engineering
May .7, 2007
C ertified by .....................................................................................
Paul D. Sclavounos
Professor of Naval Architecture
Thesis Supervisor
A ccepted by ....................................................................................
Lallit Annand
-\ AC--H USETTS
INSTITUTE
i ECHNOLOGY
JUL 18 2007
BRARIES
Chairman, Departmental Committee on Graduate Students
Department of Mechanical Engineering
2
EXTENDED TENSION LEG PLATFORM DESIGN FOR OFFSHORE WIND TURBINE
SYSTEMS
by
Nicholas W. Parker
Submitted to the Department of Mechanical Engineering
on May 17, 2007, in partial fulfillment of the
requirements for the degrees of
Master of Science in Naval Architecture and Marine Engineering
and
Master of Science in Mechanical Engineering
ABSTRACT
The rise of reliable wind energy application has become a primary alternative to conventional
fossil fuel power plants in the United States and around the world. The feasibility of building
large scale wind farms has become increasingly dependent on location. The ideal locations
require placement in desolate areas with limited or no visibility from surrounding communities,
and with the presence of a consistent wind-enriched climate.
Deployments of wind turbines in an offshore environment where water depths exceed 30 meters
satisfy these requirements. Studies have shown that existing offshore wind turbine systems are
limited to shallower coastal waters by the cost of constructing and installing the support
structures. This thesis provides a continued parametric analysis of floating platforms for the
support of offshore wind turbine systems. In particular, the Tension Leg Platform design will be
optimized.
Optimization is achieved through the coupling of wave-body interaction theory for the platform
along with the aerodynamic performance of a 5-Megawatt wind turbine in the frequency domain.
The study provides comparisons over a variety of initial tether tensions and the dynamic
response and performance of the platform in several sea states. Statistical quantities are
evaluated to ensure these tensions provide adequate forces in storms for various sea states where
the significant wave heights can be expected to be 5 meters or greater. The Tension Leg
Platform is substantially resistant to heave, pitch and roll motions; therefore, methods of
damping the larger surge and sway responses are presented and discussed.
Thesis Supervisor:
Title:
Paul Sclavounos
Professor of Naval Architecture
3
4
ACKNOWLEDGEMENTS
I am sincerely thankful for the guidance of my thesis advisor, Professor Paul Sclavounos. His
distinguished knowledge and insight supplied the solid educational foundation on which this
thesis is based. The direction and encouragement he provided was invaluable throughout the
many challenges and transformations my thesis process underwent. I am ever grateful for the
opportunity extended by Professor Sclavounos to study in this exciting field.
To the 2N program, operated by the U.S. Navy, I am immensely grateful. The experience and
notable tutelage of Captain Patrick Keenan and Commander Joel Harbour were indispensable
sources of inspiration. My fellow Coast Guard and Naval officers provided a wealth of support
and intellect that contributed greatly to my own success.
I am especially thankful for the funding provided by the U.S. Coast Guard, and the opportunity
the service has given me to further my education. Without the daily support and financial
resources of this organization and the people in it, I would not be here today.
The Laboratory for Ship and Platform Flows offered a supportive and creative environment for
my research. I am particularly appreciative of the time, effort, and advice of Chris Tracy and
Adam Guttenplan.
Finally, I am continually thankful for the support of my wonderful friends, family, and friends at
WAKA; whose lives all present me with true inspiration.
5
6
CONTENTS
A BSTRA CT..................................................................................................................................................3
A CKN O W LED GEM EN TS ..........................................................................................................................
CONTENTS
...............................................................
LIST OF FIGU RES ......................................................................................................................................
5
7
9
LIST OF TA BLES......................................................................................................................................11
1.
BA CK GROUN D ................................................................................................................................
1.1
O ffshore W ind Turbine System s ...........................................................................................
1.2
N REL 5-M egaW att Turbine..................................................................................................
1.3
TLP Coordinate System .........................................................................................................
1.4
Design Characteristics and Dim ensions .................................................................................
1.5
W ave-Body Interaction Theory .............................................................................................
2.
DESIGN PRO CESS...........................................................................................................................22
3.
AD VAN CED TEN SION DESIGN ................................................................................................
3.1
Tension Principles .....................................................................................................................
3.2
Tension Optim ization ................................................................................................................
3.2.1
The Steady-State Force Balance ...................................................................................
3.2.2
Wave Induced Tensions from Wave-Body Interactions ..............................................
3.3
Com bined Dynam ic Analysis...............................................................................................
3.3.1
Response A m plitude Operators ...................................................................................
3.3.2
Spectral A nalysis and Standard Deviation....................................................................
3.3.3
Zero Tension Difference ...............................................................................................
4.
RESU LTS ..........................................................................................................................................
4.1
D esign Values for Iterations ..................................................................................................
4.2
Base Case Results......................................................................................................................
4.3
11 m Radius Base Case Com parison....................................................................................
4.3.1.
Draft A nalysis ..................................................................................................................
4.3.2
10 m Significant W ave H eight RA O A nalysis ............................................................
4.3.3
5 m Significant W ave Height RA O A nalysis .............................................................
4.3.4
10 m Significant W ave Height A cceleration Analysis ................................................
4.3.5
5 m Significant W ave Height Acceleration A nalysis ...................................................
4.3.6
Zero Tension Possibilities.............................................................................................
4.4
8 m Radius.................................................................................................................................52
4.4.1
Draft A nalysis ...................................................................................................................
4.4.2
8 m Radius D iscussion..................................................................................................
4.5
A lternative Platform Results (9 m , 10 m , and 12 m Radius).....................................................53
4.5.1
9 m Radius D iscussion..................................................................................................
4.5.2
10 m Radius D iscussion...............................................................................................
4.5.3
12 m Radius D iscussion...............................................................................................
5
CON CLU SION ..................................................................................................................................
5.1
D iscussion of Optim um TLP.....................................................................................................
5.2
Recom m endations for Future W ork .....................................................................................
Appendix A :
9 m Radius....................................................................................................................
A ppendix B :
10 m Radius..................................................................................................................67
A ppendix B :
12 m Radius..................................................................................................................76
References...................................................................................................................................................85
7
13
14
15
18
19
20
24
24
25
26
27
28
29
29
32
33
33
34
36
36
38
42
43
45
47
52
53
53
54
54
55
55
56
58
8
LIST OF FIGURES
Figure 1. Offshore Wind Turbine Systems (from left to right: shallow water monopile, Tensoin Leg
Platform, Spar Buoy, and Catenary M oored Barge)...............................................................................
15
Figure 2. NREL 5 M W Turbine Performance Curves [3] .........................................................................
17
Figure 3. TLP Coordinate System .........................................................................................................
18
Figure 4. Turbine, Rotor, and TLP Dimensions ...................................................................................
19
Figure 5. D esign Process............................................................................................................................23
Figure 6. Steady State Force D iagram .................................................................................................
26
Figure 7. W ave Induced Force Diagram ...............................................................................................
28
Figure 8. ITTC Sea Spectrum s...................................................................................................................30
Figure 9. Barge Spectral Analysis Example ..........................................................................................
31
Figure 10. Spectral Analysis of Tether Tensions .................................................................................
32
Figure 11. Base Case Surge, Sway and Yaw RAOs ..............................................................................
35
Figure 12. Wind Speed and Draft Effects, 11 m Radius, 10 m Tension Difference ..............................
37
Figure 13. Water Depth and Draft Effects, 11 m Radius, 10 m Tension Difference .............................
38
Figure 14. Wind Speed Effects on Surge RAOs, 11 m Radius, 10 m Significant Wave Height ........... 41
Figure 15. Water Depth Effects on Surge RAOs, 11 m Radius, 10 m Significant Wave Height .......... 41
Figure 16. Wind Speed Effects on Surge RAOs, 11 m Radius, 5.5 m Significant Wave Height .......... 42
Figure 17. Water Depth Effects on Surge RAOs, 11 m Radius, 5.5 m Significant Wave Height ......
43
Figure 18. Wind Speed Effects on Surge Acceleration RMS, 11 m Radius, 10 m Sig. Wave Height....... 44
Figure 19. Water Depth Effects on Surge Acceleration RMS, 11 m Radius, 10 m Sig. Wave Height......45
Figure 20. Wind Speed Effects on Surge Acceleration RMS, 11 m Radius, 5.5 m Sig. Wave Height ..... 46
Figure 21. Water Depth Effects on Surge Acceleration RMS, 11 m Radius, 5.5 m Sig. Wave Height.....47
Figure 22. Wind Speed Effects on Zero Tension Difference Trend Lines, 11 m Radius .....................
48
Figure 23. Water Depth Effects on Zero Tension Difference Trend Lines, 11 m Radius ..................... 48
Figure 24. Zero Tension Difference Surge RAOs and Ballast Heights based on Water Depth,
11 m Radius, 10 m Sig. W ave Height....................................................................................
50
Figure 25. Surge RAOs for Zero Tension Difference based on Water Depth, i m Radius .................. 50
Figure 26. Zero Tension Differences and Ballast Heights based on Wind Speeds, 11 m Radius,
10 m Sig. W ave H eight.........................................................................................................
51
Figure 27. Surge RAOs for Zero Tension Difference based on Wind Speed, i m Radius ................... 51
Figure 28. Wind Speed Effects on Draft, 8 m Radius, 10 m Sig. Wave Height ....................................
52
Figure 29. Surge, Sway, and Yaw RAO Comparison..........................................................................
56
Figure 30. Wind Speed and Draft Effects, 9 m Radius, 10 m Tension Difference ................................
58
Figure 31. Water Depth and Draft Effects, 9 m Radius, 10 m Tension Difference ...............................
58
Figure 32. Wind Speed Effects on Surge RAOs, 9 m Radius, 10 m Tension Difference ......................
59
Figure 33. Water Depth Effects on Surge RAOs, 9 m Radius, 10 m Tension Difference ....................
59
Figure 34. Wind Speed Effects on Surge RAOs, 9 m Radius, 5.5 m Tension Difference ..................... 60
Figure 35. Water Depth Effects on Surge RAOs, 9 m Radius, 5.5 m Tension Difference .................... 60
Figure 36. Wind Speed Effects on Surge Acceleration RMS, 9 m Radius, 10 m Sig. Wave Height ........ 61
Figure 37. Water Depth Effects on Surge Acceleration RMS, 9 m Radius, 10 m Sig. Wave Height........61
Figure 38. Wind Speed Effects on Surge Acceleration RMS, 9 m Radius, 5.5 m Sig. Wave Height ....... 62
Figure 39. Water Depth Effects on Surge Acceleration RMS, 9 m Radius, 5.5 m Sig. Wave Height.......62
Figure 40. Wind Speed Effects on Zero Tension Difference Trend Lines ...........................................
63
64
Figure 41. Water Depth Effects on Zero Tension Difference Trend Lines, 9 m Radius ......................
Figure 42. Zero Tension Difference Surge RAOs and Ballast Heights based on Water Depth,
65
9 m Radius, 10 m Sig. W ave Height...................................................................................
Figure 43. Surge RAOs for Zero Tension Difference 9 m Platforms ..................................................
65
9
Figure 44. Zero Tension Difference Surge RAOs and Ballast Heights based on Wind Speed,
66
9 m Radius, 10 m Sig. W ave Height....................................................................................
Figure 45. Wind Speed Effects on Surge RAOs for Zero Tension Difference Platforms, 9 m Radius ..... 66
67
Figure 46. Wind Speed and Draft Effects, 10 m Radius, 10 m Tension Difference ..............................
67
Figure 47. Water Depth and Draft Effects, 10 m Radius, 10 m Tension Difference .............................
Figure 48. Wind Speed Effects on Surge RAO, 10 m Radius, 10 m Sig. Wave Height.......................68
68
Figure 49. Water Depth Effects on Surge RAOs, 10 m Radius, 10 m Sig. Wave Height ....................
Figure 50. Wind Speed Effects on Surge RAOs, 10 m Radius, 5.5 m Sig. Wave Height .................... 69
Figure 51. Water Depth Effects on Surge RAOs, 10 m Radius, 5.5 m Sig. Wave Height .................... 69
Figure 52. Wind Speed Effects on Surge Acceleration RMS, 10 m Radius, 10 m Sig. Wave Height.......70
Figure 53. Water Depth Effects on Surge Acceleration RMS, 10 m Radius, 10 m Sig. Wave Height......70
Figure 54. Wind Speed Effects on Surge Acceleration RMS, 10 m Radius, 5.5 m Sig. Wave Height ..... 71
Figure 55. Water Depth Effects on Surge Acceleration RMS, 10 m Radius, 5.5 m Sig. Wave Height.....71
72
Figure 56. Wind Speed Effects on Zero Tension Difference Trend Lines, 10 m Radius .....................
Figure 57. Water Depth Effects on Zero Tension Difference Trend Lines............................................73
Figure 58. Water Depth Effects on Zero Tension Difference Surge RAOs and Ballast Heights,
74
10 m Radius, 10 m Sig. W ave Height.................................................................................
Figure 59. Surge RAOs for Zero Tension Difference Platforms based on Water Depth, 10 m Radius.....74
Figure 60. Wind Speed Effects on Zero Tension Surge RAOs and Ballast Heights, 10 m Radius,
10 m Sig. W ave Height.........................................................................................................
75
Figure 61. Surge RAOs for Zero Tension Difference Platforms base on Wind Speed, 10 m Radius ....... 75
76
Figure 62. Wind Speed Effects on Draft, 12 m Radius, 10 m Sig. Wave Height ..................................
76
Figure 63. Water Depth Effects on Draft, 12 m Radius, 10 m Sig. Wave Height ................................
77
Figure 64. Wind Speed Effects on Surge RAOs, 12 m Radius, 10 Sig. Wave Height .........................
Figure 65. Water Depth Effects on Surge RAOs, 12 m Radius, 10 Sig. Wave Height..........................77
78
Figure 66. Wind Speed Effects on Surge RAOs, 12 m Radius, 5.5 m Sig. Wave Height ....................
Figure 67. Water Depth Effects on Surge RAOs, 12 m Radius, 5.5 m Sig. Wave Height .................... 78
Figure 68. Wind Speed Effects on Surge Acceleration RMS, 12 m Radius, 10 m Sig. Wave Height.......79
Figure 69. Water Depth Effects on Surge Acceleration RMS, 12 m Radius, 10 m Sig. Wave Height......79
Figure 70. Wind Speed Effects on Surge Acceleration RMS, 12 m Radius, 5.5 m Sig. Wave Height ..... 80
Figure 71. Water Depth Effects on Surge Acceleration RMS, 12 m Radius, 5.5 m Sig. Wave Height.....80
81
Figure 72. Wind Speed Effects on Zero Tension Difference Trend Lines, 12 m Radius .....................
Figure 73. Water Depth Effects on Zero Tension Difference Trend Lines, 12 m Radius ..................... 82
Figure 74. Surge RAOs for Zero Tension Difference Platforms based on Water Depth, 12 m Radius.....83
Figure 75. Surge RAOs for Zero Tension Difference Platforms base on Water Depth, 12 m Radius.......84
10
LIST OF TABLES
Table
Table
Table
Table
Table
Table
Table
Table
Table
Table
Table
Table
Table
Table
Table
Table
Table
Table
Table
Table
Table
Table
Table
Table
N REL 5 M W Turbine Properties.................................................................................................16
30
Sea State Properties .....................................................................................................................
33
Base Case TLP Properties ..............................................................................................
Ranges of Design Iteration Values.....................................................................29
35
Base Case Natural Frequencies................................................................................................
35
Base Case Displacement, Velocity, and Acceleration Response ............................................
Water Depth Zero Tension Difference Options and Responses, 1 Im Radius,
39
10 m Significant W ave H eight...............................................................................................
8. Wind Speed Zero Tension Difference Options and Responses, 11 m Radius,
39
10 m Significant W ave H eight...............................................................................................
9. Water Depth Zero Tension Difference Options and Responses, 1 m Radius,
46
5.5 m Significant W ave H eight...............................................................................................
11
m
Radius,
and
Responses,
Options
Difference
Tension
Speed
Zero
10. Wind
47
5.5 m Significant W ave H eight .............................................................................................
TLP...........55
for
Optimum
values
(RMS)
Response
Acceleration
and
11. Displacement, Velocity,
56
12. Natural Frequencies of Optimum TLP .................................................................................
9
m
Radius,
13. Wind Speed Zero Tension Difference Options and Response,
63
10 m Significant W ave H eight.............................................................................................
14. Wind Speed Zero Tension Difference Options and Response, 9 m Radius,
63
5.5 m Significant W ave H eight.............................................................................................
15. Water Depth Zero Tension Difference Options and Responses, 9 m Radius,
64
10 m Significant W ave H eight.............................................................................................
16. Water Depth Zero Tension Difference Options and Responses, 9 m Radius,
64
5.5 m Significant W ave H eight.............................................................................................
17. Wind Speed Effects on Zero Tension Difference Options and Responses, 10 m Radius,
72
10 m Significant W ave Height.............................................................................................
18. Wind Speed Effects on Zero Tension Difference Options and Responses, 10 m Radius,
72
5.5 m Significant W ave H eight.............................................................................................
19. Water Depth Effects on Zero Tension Difference Options and Responses, 10 m Radius,
73
10 m Significant W ave Height.............................................................................................
20. Water Depth Effects on Zero Tension Difference Options and Responses, 10 m Radius,
73
5.5 m Significant W ave H eight.............................................................................................
21. Wind Speed Effects on Zero Tension Difference Options and Responses, 12 m Radius,
81
10 m Significant Wave H eight.............................................................................................
22. Wind Speed Effects on Zero Tension Difference Options and Responses, 12 m Radius,
81
5.5 m Significant W ave H eight.............................................................................................
23. Water Depth Effects on Zero Tension Difference Options and Responses, 12 m Radius,
82
10 m Significant Wave H eight.............................................................................................
24. Water Depth Effects on Zero Tension Difference Options and Responses, 12 m Radius,
82
5.5 m Significant W ave H eight.............................................................................................
1.
2.
3.
4.
5.
6.
7.
11
12
1.
BACKGROUND
The recognition of a need for renewable energies has increased dramatically within the past
decade as greenhouse gases from conventional power generation are believed to be flowing into
the atmosphere at an unprecedented rate. At the same time, technologies in wind energy have
grown tremendously, and with increased research, have become more competitive with
traditional fossil fuel energy. Harvesting energy from the wind differs from the production of
energy from the burning of fossil fuels in many important ways; the first of which is availability
and location.
Although this document will focus on specific types of geographical locations (Offshore in deep
water), the presence of wind is prevalent throughout the entire globe. This makes wind energy
virtually applicable to all countries of the world, whereas fossil fuels are segregated to a choice
group.
Next, wind energy is a cleaner source of power in that it does not directly impart negative side
effects back in to the environment. The emissions generated directly from wind turbines are
essentially zero when compared with the emissions of both conventional coal and gas electrical
power plants, and the indirect emissions associated with production are considerably smaller [5].
However, there exists a few drawbacks that may limit the feasibility of creating large scale wind
farms, but this paper will attempt to show that none of the negative impacts are great enough to
overcome the advantages. First, the transfer of energy from the turbine to the plant and from this
plant to the recipients must have a physical link. This distribution will cover a large distance
when considering that the concentration of current wind farms are located in the central plains of
the United States and the primary recipients (large scale cities requiring the majority of electrical
power) are located hundreds and thousands of miles away along the U.S. coasts. The magnitude
of distance equates to larger costs in delivering the power generated from the seemingly
advantageous wind farms on land. A justification, or verification, of the economics between
savings in wind energy production versus the cost of transport from the hub of wind farms must
13
be completed. A second drawback is that the aesthetics of wind farms are not visually appealing
to those living or operating in the vicinity of these wind farms.
An alternative to both of these considerations is the placement of wind turbines in an offshore
environment. At these locations, fetch is virtually uninterrupted providing an extremely reliable
source of wind, while also being located closer to the power demands.
However, current
offshore wind farms are limited by the water depths in which the supporting structures must be
erected. This in turn often limits the turbines' distance from shore and keeping them within sight
of coastal residents.
The offshore wind turbines in production today utilize monopiles, whose support extends all the
way to the ocean floor in depths ranging up to 30 meters. Along the coastline of Europe, and in
locations far from sight of land, water depths exceed 30 m, and monopiles become economically
infeasible to install. The introduction and study of floating wind turbine structures has become
of high interest to the industry, while also introducing equally intriguing challenges to overcome.
Therefore, the problem becomes how to design a cost-effective floating system to safely support
large-scale wind turbines in water depths of 30 to 300 meters.
Several studies and concept designs have been completed. As an extension to a collaborative
2006 study between Elizabeth Wayman and the National Renewable Energies Laboratory
(NREL), this study will focus on several features of a single concept system; the Tension Leg
Platform (TLP).
1.1
Offshore Wind Turbine Systems
The major types of support systems and platform designs that have been analyzed in the past will
be briefly presented here. The first of these systems is the current shallow water monopile on top
of which the turbine tower is attached (Figure 1, a). This system provides rigid support from
being completely secured in the seabed and is used in water depths less than 20-30 m. Next, are
the buoy-type platforms and moored systems consisting of spar, tethered, and catenary-type
barges. Each of these concepts are distinguished by three major components; the wind turbine,
14
the floating support platform, and the mooring system. All barges have a cylindrical planform
shape for encountering varying angles of wave headings while on station. The spar buoy in
Figure 1(c) provides stability primarily through ballast restoring and may or may not require
additional restoring forces from mooring lines. The catenary moored barge (Figure 1, d) and the
tension leg platform (Figure 1, b) both make use of stability and restoring through waterplane
area and ballast weight. In the catenary barge, the mooring lines are carefully designed to
provide an optimal weight distribution in order to minimize barge motions, while in the TLP, the
mooring lines are designed to pull the cylinder to a greater draft in order to provide additional
stiffness, which also minimizes barge motions.
Figure 1. Offshore Wind Turbine Systems (from left to right: shallow water monopile, Tensoin Leg Platform,
Spar Buoy, and Catenary Moored Barge)
Each of the floating wind turbine concepts have been discussed in detail by Wayman in [9]. The
Tension Leg Platform (TLP) has proven to be a promising model for a deep-water floating wind
turbine platform, and will serve as the focus for the remainder of this study.
1.2
NREL 5-MegaWatt Turbine
The scale of the wind turbine is important in order to justify the cost effectiveness of deep water
offshore wind energy. Therefore, it is necessary to select a wind turbine with the largest power
15
density that is appropriate to what could be expected in the near future.
In this way, the
electricity generated can be produced at lower costs for larger turbines, making it necessary to
design a platform to support such larger systems.
The NREL Offshore Baseline 5 MW turbine is the wind turbine selected for this study. This
turbine is not an actual design that has been put in to production, but it serves as an excellent
representation of turbines with similar power ratings. NREL has referenced various mechanical,
structural, and aerodynamic properties of both fictitious and production wind turbines to develop
the specifics for a realistic 5 MW wind turbine [3]. Based on the models given in this reference,
the NREL offshore wind turbine has been designed to be a three-bladed Horizontal Axis Wind
Turbine (HAWT) with the following baseline turbine characteristics.
Table 1. NREL 5 MW Turbine Properties
Rating
Wind Regime
Rotor Orientation
Control
Rotor Diameter / Hub Diameter
Hub Height
Maximum Rotor/ Generator Speed
Maximum Tip Speed
5MW
IEC Class 1A / Class 6 winds
Upwind
Variable Speed, Collective Pitch
126m / 3m
90m
12.1rpm / 1,173.7rpm
80m/s
Overhang / Shaft Tilt / Precone
5m / 50 / -2.5*
Rotor Mass
Nacelle Mass
Tower Mass
110,000kg Overall c.g. location:
240,000kg (xt,yt,zt) = (-0.2m,0.0m,64.0m)
1347,460kg -
Once the baseline turbine parameters were established, the actual operational performance was
analyzed using the aeroelastic simulation code FAST (Fatigue, Aerodynamics, Structures and
Turbulence). The operational specifications of interest are generator speed (angular speed of the
high-speed shaft and generator), generator power (electrical generator power), rotor power
(mechanical rotor power), rotor thrust, and rotor torque. These relationships were evaluated as
functions of fixed wind speeds, and are plotted over the operational wind speeds at the hub
height in Figure 2 as given in [3].
16
60M -
6000
-nSpd
5000
-GenPwt
I
(rpm)
Rotor Power
(kW)
- RoThrust (kN)
I- Rofor (kN-m)
Generator Power
4000
Rotor Torque
3000
2000
Generator Speed
1000
Rotor Thrust
0
3
4
5
6
7
8
9
10
11
12
13
14
15
Wmd Speed (m/s)
16
17
18
19
20
21
22
23
24
25
Figure 2. NREL 5 MW Turbine Performance Curves [3]
The power curve above is specific to the NREL 5 MW turbine and provides a basic overview of
the turbine's general performance. For instance, because the turbine is designed to be selfstarting, power does not begin to be generated until the minimum wind speed, or cut-in velocity,
is reached in Region 2. Wind speeds below the cut-in velocity represent Region 1 of the power
curve where the turbine is not operational. As wind speed increases, so does the amount of
power generated. The rated velocity is the wind speed that is reached when the turbine first
produces the maximum rated power (beginning of Region 3). Beyond the rated velocity, the
NREL 5 MW turbine is designed to be pitch-regulated. Therefore, as wind speed increases
throughout Region 3, the pitch angle of each of the rotor blades is varied in order to maintain the
rated power until the cut-out velocity is reached. At this point, the blades are feathered, or
adjusted, in such a way that the turbine is taken out of operation in order to prevent excessive
loads and damage to the generator.
While the turbine is in operation it will induce forces and motions that must be coupled with the
motions of the platform concept structure. Therefore, several points along the power curve must
be analyzed for the purpose of this study. Four wind speeds were previously chosen by Wayman
in [9] to analyze the performance of the TLP wind turbine system at various operating regimes.
These speeds will continue to be the focus of this paper. First, a wind speed of 9 m/s produces
17
approximately 2500 KW, and serves as an initial test point for Region 2 of the power curve. The
next wind speed is 11.2 m/s, and provides data for the turbine's rated wind speed. A wind speed
of 15 m/s provides a location along Region 3. Finally, the cut-out wind speed of 25 m/s will be
investigated for maximum wind speed while the turbine is in operation.
1.3
TLP Coordinate System
The Tension Leg Platform designs were each analyzed for all translatory and rotational modes of
motion corresponding to linear wave-body interaction theory. The coordinate system assumes an
origin fixed at the center of gravity of the entire TLP-wind turbine system, with the x-y plane
coinciding with the barge's calm water surface, and the z-axis positive upwards. It is assumed
that regular waves will propagate in the positive x-axis direction. Wind direction will also be
assumed to be aligned with the positive x-axis, giving the upwind rotor scheme presented in
Figure 3.
Figure 3. TLP Coordinate System
The three standard modes of translational motion for the TLP system are surge, sway, and heave,
represented as 41, E, and E along the x, y, and z axes respectively. The three standard modes of
18
rotational motion are roll, pitch, and yaw, represented as
4,
4,
and E about the x, y, and z axes
respectively.
1.4
Design Characteristics and Dimensions
The Tension Leg Platform design is an ideal structure with many excellent seakeeping qualities,
especially with respect to heave motions [1]. Additionally, as shown in [9], the mooring tethers
provide stiffness at exceptionally large values, which also provides great resistance to pitching
(and rolling) motions. Therefore the remaining primary modes of motion that will be discussed
are surge, sway, and yaw.
The dimensions of the NREL 5 MW turbine for the tower, nacelle, and rotor are given in Table 1
and were not altered throughout the design iterations of this study. Only dimensions of the
platform and supporting tethers were adjusted to provide a complete iterative study of
performance. The following figures address the principal dimensions of the wind turbine and
TLP.
Figure 4. Turbine, Rotor, and TLP Dimensions
19
1.5
Wave-Body Interaction Theory
The steady state time-dependent form of the equations of motion for sinusoidal rigid-body
motions of a floating structure as presented by Faltinsen, Newman, and Principles of Naval
Architecture are given below.
(Mij + Aij)
j(t) + Bij
j(t) + CiJ 4j(t) = Re{aXie* t }
(ij = 1,...,6)
Where:
4 (t) = The amplitude of the barge's displacement responses in the jth mode of motion.
S(t) = The barge velocity response in the jth degree of freedom.
(t) = The barge acceleration response in the jth degree of freedom.
Mij= The barge mass(inertia) matrix.
Aij= The coefficients of added mass in the
Bij= The damping coefficients in the
ith
ith
direction due to a jth motion.
direction due to a jth motion.
Cij= The hydrostatic restoring force coefficients in the
ith
direction due to a jth motion.
a = The wave amplitude.
Xi= The complex amplitudes of the exciting forces and moments.
Aij and Bij are both functions of frequency (o), whereas Cij is independent of o and is defined by
body geometry. The coefficient matrices and exciting force amplitudes will be determined in the
frequency domain from the radiation diffraction panel program, Wave Analysis MIT (WAMIT).
Evaluating the equation of motion above in the frequency domain, while taking the wave
amplitude to be one, yields the following governing equation of motion.
L[-Wf (Mj + Ay) + iaBy + Cj]-:-j = X,(i=,.,)
j=1
Where:
4j(t) = Re{Eeis t }
j(t) = Re{ioEei' t }
j(t) = Re{-o 2EeiwtI
and Ej (o) represents the dimensional complex forms of the six modes of motion.
20
It is the responses of the TLP system that are to be analyzed for various configurations.
Translational and rotational accelerations are of the most importance in order to reduce
destructive forces on the wind turbine. The standard deviations of the displacement, velocity,
and acceleration of every platform and wind turbine system have been determined as per the
above equations using a short linear analysis code written for MATLAB.
21
2.
DESIGN PROCESS
The process of improving the Tension Leg Platform wind turbine system involves a static
analysis in the steady-state as well an advanced coupled analysis. A study of tether tensions is
the first priority and will serve as the basis of comparison for this research.
The initial
supporting structure is a TLP, which requires an initial pre-tension in the static phase to obtain
stability in calm water without a turbine in operation. Additional tether line tensions that must
be considered are those induced from the rotor thrust as well as the regular waves exhibited in
various sea states.
A large array of systems are analyzed iteratively in the linear code, and compared for various
wind speeds, water depths, and platform radii. The change in tether line tension is found, and the
standard deviations of these results are then computed to determine minimum and maximum
tension differences. Each different combination of system parameters is passed to the fully
coupled dynamic analysis, regardless of the outcome of unfavorable tether tension differences.
Trend lines are created in order to determine the best combination of characteristics (concrete
ballast height and initial tether tension) that produce optimum tension performance.
A sub-series of designs based on the trend lines just produced was studied next; each with
distinctive design arrangements, but meeting the same overall tension performance guidelines.
These systems are analyzed for their performance based on Response Amplitude Operators
(RAOs) and the standard deviations of the platform's motions, velocities, and accelerations in
several sea states.
Finally, the sub-set is broken down to identify the best TLP system that requires the least initial
tension and responds with the least amount of motion under the smallest acceleration.
overall design process is described in Figure 5.
22
The
i
I
Figure 5. Design Process
23
3.
ADVANCED TENSION DESIGN
Many of the initial design considerations have been taken from previous studies with minor
changes in order to better design a Tension Leg Platform for the NREL 5 MW turbine. These
studies have shown that TLP systems are enormously stiff from tension in their mooring
systems, and do not allow for large deviations in heave, pitch, or roll. However, it has been
shown that surge motions from head seas become a concern even in low sea states [9]. While a
TLP system mainly responds in surge, additional forces are introduced in all modes of motion.
The initial tension in the tethers of this system is of importance to ensure the lines never go
slack, as well as never exceed a maximum value.
3.1
Tension Principles
In the static, calm-water state, tension is created in the tethers, which provide the majority of
restoring forces in addition to the tethers' function as an anchor to the sea floor. The tension is a
product of the TLP weight being smaller than the submerged barge's buoyancy.
4
F
~M 11g = LF
=
FTtottl
1=1
In the force-balance equation above, FB is the buoyant force of the TLP, M is the entire mass of
the TLP system, g is the force of gravity, FT,i are the individual tether tensions and FT,totai is the
total tension force in all four tethers. The realistic procedure in creating this effect involves
ballasting the platform with removable weights, such as water, before connection is made with
the tethers, which are set in their suction piles (anchors) beforehand. When the platform is deballasted, the tethers are stretched taught to a pre-determined tension. This tension must be
carefully calculated to provide a balance above the minimum necessary restoring force and
below the point of failure.
24
It has been shown in Faltinsen, Newman, and Wayman that restoring coefficients of systems
with tensioned mooring systems depend heavily on the elastic modulus, cross-sectional area,
length, and radial location of the tether fairleads as described by:.
C55 ,Tethers =2
"'The (R
+ Leg )2 + FTethersT
Where E is the modulus of elasticity, A is the cross sectional area of the tethers,
LTethers
is the
length of an un-stretched tether, R is the platform radius, LLeg is the additional radial distance to
the tether fairlead due to attaching a leg, FTethers is the total tension force in the tethers, and T is
the platform draft. Assuming no elastic transformation takes place, the stiffness of the mooring
system can also be assumed to be infinite. The infinite stiffness is what limits the TLP's primary
motions to surge, sway, and yaw. The increase or decrease in tension created in the surge
direction from steady-state offsets as well as wave induced forces is the focus of this chapter.
3.2
Tension Optimization
Reliability in the TLP tether tensions is required to ensure the mooring lines will not go slack.
This involves the combination of a steady-state force balance as well as statistical expectations of
dynamic forces in various sea states. As will be shown, the four tethers of the TLP system may
experience variable changes in tension at the same time (for instance some tethers may have an
increase in tension, while at the same time, a decrease occurs in the other tethers). Therefore,
both the maximum and minimum tensions and changes in tensions have been calculated and
compared to limiting values.
Additionally, tension affects cost because other functions of the TLP are dependent on tension.
For instance, if tension and the height of concrete ballast are known, then the calculation of draft
follows directly. As the cost of concrete generally increases as draft (and consequently concrete
height) increases, the amount of ballast should be minimized [9]. Decreasing draft will also
decrease the amount of steel materials required, and lower tensions will require smaller diameter
tethers, again reducing the amount of material (and cost).
25
3.2.1 The Steady-State Force Balance
Figure 6 demonstrates the offset in surge at a steady-state operating point for a TLP with four
equally spaced tethers. Forces in the windward tether are expected to increase and forces in the
leeward tether will decrease, while forces in the middle tethers can be assumed to maintain an
average tension.
Figure 6. Steady State Force Diagram
The tensions in tethers 1 and 3 are aligned along the x-axis when the wave propagation and
thrust vectors are also aligned with the x-axis. The steady-state condition exists when the wind
turbine is in operation producing thrust in the surge direction with a calm water sea state. These
tethers will experience a change in tension, AT, which must not exceed the average total tension
in the steady-state in order to avoid going slack. Furthermore, the addition of AT to the average
tension must not exceed the maximum allowable force in the steady-state.
moments about point 0 provides the steady-state AT that must be considered.
IMO=FT',cosR-F 3 cosR-FThus -d=0
(Ff1
-
FT3)R = Frhrls, -d, where the small angle approximation gives cos 0 = 1.
26
Summing the
FTl, =FT + AT, FT,3
= FT
-ATand FTl,-FT,3 =FT +AT-FT +AT=2AT
4
F'
Where, Fr
AT -
4
FThrust d
2R
3.2.2 Wave Induced Tensions from Wave-Body Interactions
The wave body interaction was previously not taken into account in [9] and must be considered
for accurate calculations of maximum and minimum tensions. Although the mooring system
presented restrains the TLP in heave and pitch, forces are introduced in the tether lines from the
wave excitation forces and moments. Figure 7 describes the variables applied in the following
equations for forces and moments.
n =X-AT
=
-AT
F3= X3 - A
,i-AT,3
=0
nF= AT,,(R + L,,) - AT
3(R
+ Lg)- X5 = 0
Substituting the force balance equation into the pitch moment equation yields:
ATe =
AT
'
3
3
2
X
2
+
2(R + L,g)
X
2(R + Lg)
Where ATw,1 and ATw,3 represent the induced wave tensions in the windward and leeward tethers
respectively and are functions of frequency (w). X3 and X5 are the complex wave excitation
forces in the heave and pitch directions respectively. Lieg is the distance from the outer radius of
the TLP to the fairlead of each tether. The oscillatory wave induced tensions can be used to find
RAOs for the tension variations, which are then used to calculate standard deviations and other
statistical quantities of relevance discussed in section 3.3.2.
27
Figure 7. Wave Induced Force Diagram
3.3
Combined Dynamic Analysis
The dynamic analysis phase incorporates values from several aspects of the TLP system design.
Static offsets and quantities obtained from body geometry and tether initialization are first
required.
Additionally, the values from the governing equation for added mass, damping,
stiffness, and exciting forces are a compilation of hydrostatics, inertia, wave-body interaction,
and turbine operational influence. These values are obtained and combined in the following
manner.
Individual mass and inertial quantities are found separately for the platform and the wind turbine
and then combined.
The cylindrical platform's body mass matrix is determined in the
hydrostatic analysis using WAMIT, and the operational turbine's body mass matrix is
determined in the aerodynamic analysis using FAST. Similarly, the hydrostatic and aerodynamic
damping matrices are added together. Added Mass and the wave excitation forces are functions
of the platform's hydrostatics and wave-body interaction performance alone. And the combined
28
TLP system stiffness matrix includes the contributions from hydrostatic restoring coefficients,
aerodynamic restoring, and restoring forces from the tethers.
Mij= MHydro + MFAST
B ij, BHydro + BFAST
Cij = CHydro + CFAST + CTethers
3.3.1 Response Amplitude Operators
The Response Amplitude Operator (RAO) is the basic dynamic seakeeping value obtained from
the linear analysis code. RAOs are evaluated for the six principal modes of motion as well as the
derivative seakeeping quantities for wave induced tensions. The complex forms of the RAOs for
translational and rotational modes of motion are produced by the following equations.
(j=1,2,3)
RAO 1 (()=
RA 0, (co)=
EjA(W)I
=4,5,6)
(jR1
The responses are non-dimensionalized by the wave amplitude and platform radius.
The
responses of the wave-induced tether tensions are similarly found by forming RAOs from the
complex forms of the equations in section 3.2.2.
RAO, T'j(w) = IA T, j(a))
(j=1,3)
3.3.2 Spectral Analysis and Standard Deviation
There are several forms of standard wave spectra that are used to represent ambient wave records
for fully developed, or open, sea conditions that have unlimited fetch. The International Towing
29
Tank Conference (ITTC) recommends the use of a Modified Pierson-Moskowitz spectral density
equation.
0.11 (OT
r1
2H '.2fl
S (co) = H113 -T 2
e
-2n
Where H1 /3 represents the significant wave height and T1 represents the average wave period for
the following tables of sea states evaluated in this study.
Table 2. Sea State Properties
T1 (s)
Sea State H1,t (m)
1
0.09
2.0
2
0.67
4.8
3
4
5
2.44
5.49
10
8.1
11.3
13.6
ITTC Sea Spectrums
30
25 --- ------------ ----------
Sea State 1(xlO
5
Sea State 2(xl 0)
Sea State 3(xl)
--20 --------- -------- ---------
--
Sea State 4 (x2)
Sea State5
---- --------- ---------
15 ----
4
--------
10 ---
--- --------- --------
--------- -----
--
3
5 --
0
0
-
--------
2
1
---
2
-----
3
4
5
6
co(rad/s)
Figure 8. ITTC Sea Spectrums
Figure 8 demonstrates the increasing severity of sea states at lower oscillation frequencies.
However, the frequencies at higher sea states provide only a narrow band at which the responses
30
of the TLP can be excited, whereas lower sea states will excite the floating structure around a
broader range of frequencies with lower expected responses.
Particular interest in this case concerns a spectral analysis of the TLP in sea states 4 and 5 where
peak spectral frequencies interfere with the natural frequencies of the barge responses. Figure 9
illustrates how the overlap of the RAO and the ITTC spectral density produces a response
spectrum. The area under the response represents the variance of the mode of motion according
to the following equations.
fS(w)iRAO, 2 do
-=
a-
R2
= s,()
(i = 1,2,3)
(i = 4,5,6)
do)
Barge Spectral Analysis Example
Af%
35
CX
-
Response
RAO
Response
30
25
Sea Spectrum
(0
CD
E
0
20 - RAO
15
10
Co
5
nI
0
I
0.5
1.5
1
2
2.5
o(rad/s)
Figure 9. Barge Spectral Analysis Example
The changes in tension induced from the barge's interaction with waves also presents a similar
set of response curves as shown in Figure 10.
31
Spectral Analysis of Tether Tensions
X 1013
5
S( (x1 011)
RAO (xl 06)
Response
Response
0
ea Spectrum
2
2
RAO
0
0.5
1.5
2
2.5
n(rad/s)
Figure 10. Spectral Analysis of Tether Tensions
3.3.3 Zero Tension Difference
The standard deviation, as obtained from the variance will be used to ensure a 3a confidence
interval is maintained. As long as the 3a wave induced tension does not exceed the minimum
steady-state tension exhibited in either the leeward or windward tethers, it can be assumed that
the lines will have a 99.73% chance of not going slack at any particular moment. The zero
tension difference is therefore defined as the exact combination of TLP parameters (concrete
ballast height, initial tether tension, radius, water depth, and draft) which produces a maximum
3a wave induced tension that is equal and opposite of the minimum steady state tether tension.
32
4.
RESULTS
The results discussed here are a compilation of data, figures, and tables over a variety of barge
dimensions, ballast weights, tether tensions, water depths and wind speeds. The initial results
display every design iteration graphically for general comparisons between various quantities.
All cases have been run through the same coupled analysis phase to demonstrate performance at
different operating levels. The range of parameters was chosen around the base case as designed
by Wayman in [9].
4.1
Design Values for Iterations
The optimization of initial tether line tension force, which will be required for severe sea states,
is the primary objective of this study. Therefore, the values used for analysis of tensions are
more numerous than other parameters studied.
Water depths and wind speeds have been
analyzed for identical values in previous studies to allow for comparison of data. Several TLP
dimensions have also been introduced to the iterations, including barge radius and concrete
ballast height. The range of dimensions is centered about the base case design values as given in
Table 4
Table 3. Base Case TLP Properties
Base Case TLP Properties
Radius [m]
11
26
Cylinder Height [m]
4.5
Concrete Ballast Height [m]
Steel Thickness [m]
0.015
22.75
Installed Draft [m]
3.43E+07
Tension (total) [N]
200
Water Depth [m]
11.2
Wind Speed [m/s]
The following variables in Table 4 present the range of design values used in the iterative
analysis of the TLP-wind turbine system.
Previous studies by Wayman included the performance of a TLP with a radius of 11 meters,
ballast height of 5 meters, initial tether tension of 3.43x10 7 Newtons in various water depths and
wind speeds. The water depth of 62.5 m was included for comparison to other NREL studies
33
with identical
Table 4. Ranges of Design Iteration Values
baseline water depths.
The depths of 100, 200, and 300
were
meters
studied
in
evaluate
the
feasibility
of deploying
order to
the TLP
system in deeper waters, where the
offshore
locations
Bre Radius [m]
and
performance
become
Concrete Ballast
most
4
(Tital
valuable to this study.
10075
5.5
The wind speeds chosen were also
identical
to previous studies
comparison at different
turbine
operation.
[kn
9300
4.5
'A6.5
39525
40300
for
Wind Speeds [mis]
levels of
Each
10850
ater Depths
9
l
62.5
15
ll
200
[i]
speed
represents a different critical position
on the 5-MW turbine power curve.
At 9 m/s, the turbine produces approximately half of its rated power. At 11.2 m/s (rated wind
speed), the turbine is operating at maximum power. At 15 m/s, the turbine is operating in Region
3 of the power curve. Finally, at 25 m/s, the turbine's cut-out wind speed is reached.
Because the first phase of this study was totally iterative, many of the graphs display the absolute
or maximum value of a limiting quantity, such as maximum RAO.
These graphs are used to
distinguish trends as well as identify a superior group of analysis cases for further calculations.
4.2
Base Case Results
The results for the NREL TLP surface system as determined by Wayman in [9] are reproduced
here for baseline comparisons. The graphs in Figure 11 show the RAOs for the primary modes
of motion that can be expected to be excited for this TLP. The natural frequencies are low, and
the RAOs at these frequencies show a strong response over a narrow band. The response of the
TLP in surge is the biggest concern, especially as the peak spectral frequency of larger sea states
approaches the natural frequencies of the TLP system. The RAOs in heave, roll, and pitch are
34
not presented as the maximum RAO in these cases is on the order of 10-7 and the natural
frequencies are far beyond the scope of the lowest sea state.
Surge RAO Base Case
Sway RAO Base Case
.0
9;i
--
--
-
--
-
0.025
20
-
-
0.02
-
- -
-
-
-
- -
I
-
-
-
-
-
-
15
0.015
10
------
- ----------------0
0.5
--
(o
--
-
0
2.5
2
1
1.5
1
0.5
om [rad/s]
[rad/s]
Yaw RAO Base Case
0.0
0.009------
+------
------
+------------ -
-
-
H
0.00
0.00 n--
-
-----
7-
---
-
'
I-
-
-
-
-
-
-
0.00
0.00
IL
0.00
1
- --
-
-
-
- J
-----
-
--
---
2
0.00
-
- -
-
-
-
-
-
-I
-H
0.00
0.00
0
--
-
0.005
1.5
1
-
- -
0.01
- - ----- ------ - - ---------- -----
5
-
0.5
2.5
2
1.5
1
co [rad/s]
Figure 11. Base Case Surge, Sway and Yaw RAOs
Table 5. Base Case Natural Frequencies
Natural Fmquency
Mode
Surge
0.1269 [rad/s]
Sway
Yaw
0.1269 [rad/s]
0.2925 [rad/s]
Table 6. Base Case Displacement, Velocity, and Acceleration Response
Sea State 4
20.54
5.98E+06
Sea State 5
20.54
7.06E+05
amax Surge Displacement [m]
1.373
2.907
ax Surge Velocity [mis]
ax Surge Acceleration [m/szl
0.663
0.369
1.182
0.568
Base Case Responses
Max Surge RAO
Tension Difference [N]
35
2
2.E
4.3
11 m Radius Base Case Comparison
A TLP with a radius of 11 m will be presented here as a direct comparison to the base case.
Analysis and discussion includes the effects from wind speeds, water depths, and initial tensions
on draft, motion responses, and accelerations.
4.3.1. Draft Analysis
The analyses presented in Figure 12 display the required drafts for various combinations of
initial tensions and concrete ballast heights based on the range of wind speeds and water depths
analyzed. Solid lines represent the 10 m significant wave height tension differences, which are
defined as the difference between the minimum steady state tension (in either the windward or
leeward line) and maximum tension that could be expected from three standard deviations of
wave induced tensions in sea state 5. For example, a negative tension difference represents a
combination of initial tension force and concrete ballast height that does not meet the
requirement, whereas positive differences exceed the requirement. It was a practice of this study
to analyze figures along the vertical line which intersects the tension difference data and the zero
crossing. For example, in Figure 12 for a wind speed of 9 m/s the 3.5 m concrete ballast height
intersects the zero crossing with an initial tension of 2.76x1 07 N, which corresponds to a required
TLP draft of only 18.52 m.
Referring back to the wind turbine power curve in Figure 2, turbine thrust increases as wind
speed increases up to the rated wind speed, and then begins to slowly drop off until the cut-out
wind speed. Because of the inclusion of steady-state thrust forces, it is shown that required
initial tensions and TLP drafts follow a similar trend, reaching a maximum at the rated wind
speed of 11.2 m/s. Since the wind turbine is producing a maximum thrust of 800 kN at this wind
speed, the tension differences are more affected. Although, the difference between the maximum
draft at 11.2 m/s and drafts at other wind speeds for zero tension difference is not as great as is
the case with the alternative platforms of lesser radius. Based on these comparisons, the range of
36
allowable ballast heights is now only available between 3.5 m and 5.5 m for a 10 m significant
wave height.
The results of drafts required over the range of water depths studied are less distinguishable than
those comparing wind speed effects, and also display the trend that greater water depths require
slightly shallower drafts for equivalent ballast heights. For this 11 m radius TLP, the 5.5 m
ballast height is limited by the 62.5 m water depth where the draft required for a zero tension
difference is above the platform depth of 26 m.
Draft relationships for Radius = 11m Wind Speed =
(multiple concrete ballast heights)
Draft relationships for Radius = 11 m Wind Speed = 11.2 m/s
(multiple concrete ballast heights)
9 m/s
x 106
30 -
25-
0
- - -
-
25--- - - - - - - - - - - - 252
0
--
0
-10=
S20-
x 106
5
30
0
.
15-
I-
10 0
0.5
- -
-
- -
&5m A Ten -
-4m
E
E
-10 !
-
3
2.5
2
1.5
Initial Tension [N]
1
-
-
3.5
15 - - -
10
4
A Ten
--
5m ATen
4.5m A Ten --
30
1
3
3.5
4
2.5
2
1.5
Initial Tension [N]
3
3.5
-- 15
4
x 107
6m A Ten
5-5M A Ten
-
2.5
6.5m A Ten
-
Draft relationships for Radius = 11m Wind Speed = 25 m/s
(multiple concrete ballast heights)
x 107
,11
x1
du
0.5 g
25
--
0.5
x 107
Draft relationships for Radius = 11m Wind Speed = 15 m/s
(multiple concrete ballast heights)
-T - -
0
2
25 - - - - - - - -
-- - -
15 - - - -- - - -.
- --
0.5
---
- - ---
---
-- ,-
0
2
0
41
15
0
0.5
1
2.5
2
1.5
Initial Tension [N]
3.5m draft
*
3
4m draft --
E
E
-0.5%5
1
3.5
0
4
0.5
x 107
4.5m draft
-
5m draft
--
- 5.5m draft
1
-
-
-
2.5
2
1.5
Initial Tension [N]
6m draft
-
6.5m draft
Figure 12. Wind Speed and Draft Effects, 11 m Radius, 10 m Tension Difference
37
-
-
3
-
-
3.5
x 10
--
.5
Draft relationships for Radius = Im Depth = 62.5 rn
(multiple concrete ballast heights)
25
--
20
- -- - -- -
Draft relationships for Radius = 1m Depth = 100 m
(multiple concrete ballast heights)
x 106
--- ----
0
25
-5
20
x 106
5
0
0
-
411'
15
-10
- 10 E
15
E
il
2.5
2
1.5
Initial Tension [N]
1
0.5
0
3
3.5
.13
2.5
2
1.5
Initial Tension [N]
1
0.5
0
4
x 107
n5m A
a T---- 4m4 A TM
e3.5m
Draft relationships for Radius = 11m Depth =200 m
(multiple concrete ballast heights)
6mATen --
5.SmATen
Ten -
3
3.5
'-~
-x
X 107
6.5m ATen
Draft relationships for Radius = 11 m Depth = 300 m
(multiple concrete ballast heights)
X 106
X 106
30
-
I--
-
0
25
0
25
-
- -
-- - -
20
20
0
----
--
-------
- ---
it),
0.5
i
L
1
1.5
- 1;j
2
2.5
3
Initial Tension [N]
3.5m draft
*
3.5
-10 E
15
-10
15
0.5
0
4
x 107
4m draft --
4.5m draft
5m draft
-
5.5m draft
1
2.5
2
1.5
Initial Tension [N]
6m draft
-
3
4
3.5
x 10
6.5m draft
Figure 13. Water Depth and Draft Effects, 11 m Radius, 10 m Tension Difference
4.3.2 10 m Significant Wave Height RAO Analysis
The figures presented below display the maximum Response Amplitude Operators (dotted lines)
that various combinations of TLP parameters exhibit in surge for a platform with a radius of 11
m. Analysis is performed over the range of wind speeds and water depths above, and should be
compared simultaneously with the same trend lines for a zero tension difference (solid lines) to
occur in sea states that have ambient waves with extreme significant wave heights. Table 7 and
38
Table 8 provide data for the exact combinations of parameters that produce a zero tension
difference at each operating point.
In addition to the objective of determining the response at the exact operating initial tension that
produces a zero tension difference, analysis was carried out on either side of the objective point
to present results for tensions that yield increasing or decreasing reliability in going slack. For
example, as Table 7 shows, for a ballast height of 3.5 m in a water depth of 300 m, the
corresponding initial tension which yields a zero tension difference is 3.005x10 7 N. If this point
is found in Figure 15, it can be seen that while a decrease in initial tension decreases the
maximum RAO, it also produces a negative tension difference (and increases the probability of
the tethers going slack).
Table 7. Water Depth Zero Tension Difference Options and Responses, 11m Radius, 10 m Sig. Wave Height
62.5 m
300 m
100 m
200 m
Tension Max RAO RMS Acc Tension Max RAO RMS Acc Tension Max RAO RMS Acc Tension Max RAO RMS Ace
Ballast
3.5
4
4.5
5
5.5
6
6.5
31884459
33431359
35338486
37637264
40267860
42475131
43506290
25.798
30.281
30.917
25.337
40.345
74.963
88.099
1.548
1.453
1.429
1.48
1.873
3.008
3.462
30606149
31796804
33258833
35006652
37046242
39380058
42250031
43.55
23.747
17.887
16.152
15.375
15.686
18.898
0.712
0.681
0.657
0.638
0.621
0.607
0.598
30090889
31147561
32444424
33991733
35792805
37843877
39882206
13.344
20.395
33.346
53.331
81.209
90.417
88.315
0.609
0.586
0.566
0.548
0.532
0.518
0.505
30047735
31092531
32374887
33904722
35685126
37711594
39911840
8.728
7.229
6.369
6.04
6.545
6.935
7.089
0.592
0.57
0.551
0.534
0.518
0.504
0.492
Table 8. Wind Speed Zero Tension Difference Options and Responses, 11 m Radius, 10 m Sig. Wave Height
9 mIs
Ballast
3.5
4
4.5
5
5.5
6
6.5
11.2 m/s
1_15
25 m/s
m/s
Tension Max RAO RMS Acc Tension Max RAO RMS Acc Tension Max RAO RMS Acc Tension Max RAO RMS Ace
27643795
28602466
29760773
31157845
32803077
34695640
36828067
21.458
44.201
85.155
53.946
37.978
32.084
30.225
0.604
0.581
0.561
0.544
0.529
0.515
0.502
30090889
31147561
32444424
33991733
35792805
37843877
39882206
13.344
20.186
32.299
53.331
79.607
92.168
88.315
0.609
0.586
0.566
0.548
0.532
0.518
0.505
26471625
27344053
28429570
29753615
31322742
33137486
35192731
32.65
162.187
60.672
33.056
25.288
22.285
21.322
0.601
0.579
0.559
0.542
0.527
0.513
0.501
24134903
24872488
25825394
27007194
28466232
30125561
32029824
127.105
36.001
21.249
16.377
14.308
13.305
12.986
0.596
0.574
0.555
0.538
0.523
0.51
0.498
Figure 14 shares the trend that the peaks of the RAOs are independent of wind speed and occur
at the same initial tension for a specific concrete ballast height. The maximum peak amplitudes
occur at the wind speed of 15 m/s. This figure shows how a zero tension difference for a 3.5 m
concrete ballasted TLP operating in 9 or 25 m/s of wind experiences a maximum surge RAO of
considerable proportion, whereas the zero tension crossings for 11.2 and 15 m/s wind speeds fall
within the lower limits of maximum RAO. It follows that the lowest RAO also occurs at the
39
same initial tension (for all concrete ballast heights) regardless of wind speed. Therefore, if an
acceptable upper limit for an RAO in a specific wind speed can be determined, there will also
exist an acceptable range of initial tensions to produce these smaller RAOs. It can then be
compared to the initial tension required to meet a zero tension difference level to see if that
initial tension is feasible. For example, if the maximum RAO in surge for a TLP with 6 m of
concrete ballast is 50, then the range of available tensions would be <1.3x1 07 N and 1.7x1 07 N<
Initial Tension < 3.6x107 N. When compared to the tension needed for zero tension difference
(3.012x10 7 N) at a wind speed of 25 m/s, it shows that this tension is feasible. However, because
the turbine should be expected to operate in all wind speeds up to 25 m/s, the operating ranges
must be verified.
The limiting case becomes the rated wind speed again where the tension
required for zero tension difference is 3.78x10 7 N. Since this initial tension is not within the
range for an acceptable RAO, this combination would be not be feasible.
Figure 15 displays a different trend for varying water depths; mainly, that changes in the initial
tension of TLPs deployed in deeper waters result in variations of maximum RAOs that are less
drastic than in shallow water.
Therefore, the range of initial tensions in order to produce
acceptable RAO limits is much broader for deeper water depths. Additionally, higher surge
RAOs are produced by TLPs situated in shallower waters. Finally, the graphs for 11.2 m/s in
Figure 14 and 200 m in Figure 15 are identical since the base case involves the combination of a
wind speed of 11.2 m/s and a water depth of 200 m.
40
RAO 1 for Radius = 11m Wind Speed = 9 m/s
(multiple concrete ballast heights)
RAO 1 for Radius = 1I1r Wind Speed = 11.2 m/s
(multiple concrete ballast heights)
x 107
,1
o
0
100 -
0
I
- -
0.5
1
- - .- -
-
- -
-
35beATon -
RAO 1
for Radius
00
0.5
I
1
17
4m6 Ten
-4.mi
Speed = 15
(multiple concrete ballast heights)
= 1Im Wind
A Ten
Ten -
-6mA
2.5
2
1.5
Initial Tension [N]
3
0A
TnI
fPA ATon
5.m Aen
rm/s
RAO 1
x 10
E
*
4
3.5
3
2.5
2
1.5
Initial Tension [N]
I
-- -1
-
-
K._
I
s
50-
x 10'
10
-
3.5
for Radius =
11m Wind Speed = 25 m/s
(multiple concrete ballast heights)
-
-
107
X
,1
200.
- -
2
4
107
-
0.5
0
200
E
-*
-0.59
50
0
0.5
1
1.5
2
Initial Tension
3.5m RAO
2.5
3
0
4
3.5
0.5
1.5
2
Initial Tension
1
1do
[N]
4m RAO
-
6m
5.5m RAO
5m RAO
4.5m RAO
-
-
RAO
2.5
[N]
6.5m
4
3.5
3
107
RAO
Figure 14. Wind Speed Effects on Surge RAOs, 11 m Radius, 10 m Significant Wave Height
62.5 m
for
RAO 1
Radius = 11 m Depth =
(multiple concrete ballast heights)
150.
RAO 1 tsr Radius = I1m Depth = 100
(multiple concrete ballast heights)
x1
m
x 10,
-100
0
--
7
-
*
-
so-
o'0
0.5
2.5
1.5
2
Initial Tension [N]
1
-
35,&STo
4m A Ton
-
-4.5m
-- -
00
7
aTon -~nTon
RAO I for Radius = 11m Depth = 200 m
(multiple concrete ballast heights)
100
1 50
4
3.5
3
100
-
m
I-,-
-
1
0.5
5.5m,&Ton
1 '.-~r
2
1.5
initial Tension
2.5
3
-
'
4
3.5
10
[N]
*mATn
Grn
A Ton -~~45,ATlfi
6.5m A Ton
RAO 1 for Radius = I1m Depth = 300 m
(multiple concrete ballast heights)
x
2
5Zero
60 - - - -'
50 -- - - - ---
- - - - - - --
-
n
0
-6
40
I
--- - -1
- T-
e-
- - - s-- - --- -
--
-100
20
0
0.5
2.5
2
1.5
Initial Tension [N]
1
-
RAO
m.5m
-
3.5
3
4
010
2
0.5
107
4m RAO
----
4.5m RAO
Sm RAO
5.5m RAO
1
1.5
2
3
2.5
Initial Tension [M
6m RAO
-
6.5m
3.5
4
107
RAO
Figure 15. Water Depth Effects on Surge RAOs, 11 m Radius, 10 m Significant Wave Height
41
Tension
Difference
4.3.3 5 m Significant Wave Height RAO Analysis
The same analysis conducted above was also completed for the alternative reliability of
designing a TLP system that can be expected only to survive seas with a 5.5 m significant wave
height without tethers going slack. As can be expected, the initial tensions required to maintain
this zero tension difference are much lower than for a 10 m significant wave height. The
maximum RAOs plotted below are identical to the figures above, while the new zero tension
lines are shifted left. Because the tensions required are much lower, the new intersections may
prove to be favorable to some combinations of TLP parameters or harmful to others. For
example, a zero tension difference combination for a 5 m ballast height in seas with a 10 m
significant wave height has a considerably high RAO at a wind speed of 11.2 m/s (and all other
wind speeds, since the ranges are independent). But the same 5 m ballast height in seas with a 5
m significant wave height produces an RAO that is practically lowest.
RAO 1 for Radius = 11m Wind Speed = 9 m/s
(multiple concrete ballast heights)
f
150
50
-
0
-
-
0.5
-
1
-
-
- -
-
1.5
2
2.5
Initial Tension [N]
3.5m& Ten -
X 106
10
1
3.5
011
0
4
0.5
1
4.5mA Ton -5m&
RAO 1 for Radius = 11m Wind Speed = 15 m/s
(multiple concrete ballast heights)
Ten -
5.5n
- - - - - - -
- - - - - -
--
- - -
-
- - - - - -----
0.5
1
1.5
2
2.5
Initial Tension [N]
3.5m RAO
.
3
4m RAO -
-- -
100-
C
A Ten
x 106
15
-
-
- -
-10
- - --
-
-
- 5
1
- - -
50--
0
4
1
*1
100 - - - - - - -
3.5
200
150---- - - - -
Sm A Ten -- +.5m
Ton
3
RAO 1 for Radius = 11m Wind Speed = 25 m/s
(multiple concrete ballast heights)
X 1
2
300
200 - - - - -
1.5
2
2.5
Initial Tension [N]
X 107
4--m-4
& Ton --
x 107
0
-
3
RAO 1 for Radius = 11m Wind Speed = 11.2 m/s
(multiple concrete ballast heights)
1 111 11
100
3.5
4
0
--
-
0.5
1
X 107
4.5m RAO
5m RAO
5.5m RAO
Figure 16. Wind Speed Effects on Surge RAOs, 11 m Radius, 5.5
42
- -0
--
1.5
2
2.5
Initial Tension [N]
6m RAO -.
3
.5
4
3.5
6.5m RAO
m Significant Wave Height
X 1d
"
RAO 1 for Radius = 11m Depth = 62.5 m
(multiple concrete ballast heights)
10
RAO 1 for Radius = 11m Depth = 100 m
(multiple concrete ballast heights)
X 107
1
X107
,1
----
E 100
-
0
#
0
0.5
1
1.5
2
2.5
Initial Tension [N]
[-
3.5m,& Ton
--
4m
3
I
3.5
4
1
0
X 107
A Ton
4.5m A Ton -
-
5m,&Ton
0.5
-
5.5m A Ton
RAO 1 for Radius = 11m Depth = 200 m
(multiple concrete ballast heights)
Vuu.
4
.7
50
1.5
2
2.5
Initial Tension [N]
8m A Ton ---
3
3.5
4
X17
6.5m,& TonI
RAO 1 for Radius = Im Depth = 300 m
(multiple concrete ballast heights)
80
1
1
X 107
11
60
0.5
40
U
r
.2
E
0
0.5
1
1.5
2
2.5
Initial Tension [N]
3.5m RAO
.
3
4m RAO ----
3.5
20
-0.5 E
Ln
,
4
0
0.5
g7
4.5m RAO
-
5m RAO -
5.5m RAO
1
1.5
2
2.5
Initial Tension [N]
6m RAO -
3
3.5
i
4
7
6.5m RAO
Figure 17. Water Depth Effects on Surge RAOs, 11 m Radius, 5.5 m Significant Wave Height
4.3.4 10 m Significant Wave Height Acceleration Analysis
The figures plotted in this section display the standard deviations for accelerations experienced
by the TLP in surge. The accelerations are presented in conjunction with the tension differences
in order to display the affects of TLP parameters other than those which produce a zero tension
difference.
Figure 18 shows how the surge accelerations vary only slightly over the change in wind speeds.
As a general rule, increases in initial tension result in increased acceleration responses. The key
becomes picking the initial tension that produces a zero tension difference and then analyzing the
corresponding acceleration. For instance, as has already been discussed, the limiting wind
condition for zero tension difference to occur is 11.2 m/s. This gives the maximum acceleration
43
standard deviation that could be expected for the ideal parameters selected. Table 8 above lists
all zero tension difference combinations for the wind speeds analyzed in seas with a 10 m
significant wave height.
Figure 19 presents the standard deviations for accelerations experienced by the TLP systems
which are deployed in varying water depths. The accelerations have a much wider range over
the scope of water depths selected, with maximum accelerations occurring at the lowest water
depth of 62.5 m. At this depth, the accelerations are minimized by smaller initial tensions, but
they become highly non-linear as initial tension is increased (where zero tension differences
occur for a 10 m significant wave height). As the water depth increases, the required initial
tension as well as the corresponding accelerations decrease. Table 7 above presents the exact
data for the combinations of TLP parameters that result in zero tension differences in sea state 5.
Surge Accelerations for Radius = Im Wind Speed = 9 m/s
(multiple concrete ballast heights)
0.65
..5
0.6
0
Surge Accelerations for Radius = 11m Wind Speed = 11.2 m/s
(multiple concrete ballast heights)
60
Ct
r~ 0.6
:0
-
0.55-
L|
0.5
1
1
i
2
2.5
1.5
Initial Tension [N]
3.5m A Ton -
-5
-10
0.5
.2
|
4
.45
Um
-
-
E
E
-10~
0.5-
-
~M 0.55 k
5
.-
100
x
0.65
3
4m A Ten --
3.5
4
X 107
'
1s
0
4.5m A Ten -5m
Surge Accelerations for Radius = 11 m Wind Speed = 15 m/s
(multiple concrete ballast heights)
0.5
1
1.5
2
2.5
Initial Tension [N]
4Ten -+-5.5m A T&nOm
X 107
A Ten
-+-6.5m
3
3.5
4
X17
A
Ten
Surge Accelerations for Radius = 11m Wind Speed = 25 m/s
h i ht
I
(mnultpleconcrete balast eg s)
0.65
0
X1
1
0.65
0.5
-
0.6 -- --
5
-
--
----
-0.
- --
----
5
Co.C
.9
0.55
0
------
Co
-e
rS
E
.5
0
0.5
1
2.5
2
1.5
Initial Tension [N]
3.5m Acc
.
3
0.5
-
4
3.5
0.5
0
X10
4m Acc
*
4.5m Acc
5m Ac
.-
5.5m Acc
1
2.5
2
1.5
Initial Tension [N]
6m Acc -
3
3.5
4
X17
6.5m Ace
Figure 18. Wind Speed Effects on Surge Acceleration RMS, 11 m Radius, 10 m Sig. Wave Height
44
Surge Accelerations tbr Radius = 1 Im Depth = 62.5 m
(multiple concrete ballast heights)
F
3 - -----
F
X 10
6
-
0
-
Surge Accelerations for Radius = 11 m Depth = 100 m
(multiple concrete ballast heights)
.
.
ur
I
.
.
.
,
.
X 106
5
-0
0.7
c
to-'
0.6
2 - -
0
E
~ -
a
.
-1
- - 1
0!5
1
15
2
2.5
3
3.5
Initial Tension [N]
I-3,5m
A Ton
U
4
14
0.5
1
7
X
4m,&Ton --
--
-10 E
4.5M,&Ton
Surge Accelerations for Radius = Im Depth = 200 m
(multiple concrete ballast heights)
5m,& Ton
'
x 10a
-
.5m
0. EE
,
.
A Ton
i
i
1.5
2
2.5
Initial Tension [N]
r6m & Ton
3
3.5
I
4
X 107
6.5m A TonI
-
Surge Accelerations for Radius = 11 m Depth = 300 m
(multiple concrete ballast heights)
x 10
5
0.1-
U,
8
0.55
- --
-
----
0
2
-5 5,
-
.5.2
~
F-
0.50
0.45
0
E
0.5
F15
1
1.5
2
2.5
Initial Tension [N]
3.5m Acc
.
3
3.5
4m Acc ---
0. 4 5
4
X
-
0.5
0.5
7
4.5m Acc
-
5m Acc
--
5.5m Acc
1
- -
-
1.5
2
2.5
Initial Tension [N]
6m Acc
-
-
-- *
3
- - -10E
3.5
4
x 10
6.5m Acc
Figure 19. Water Depth Effects on Surge Acceleration RMS, 11 m Radius, 10 m Sig. Wave Height
4.3.5 5 m Significant Wave Height Acceleration Analysis
The figures presented in this section display the standard deviations of acceleration produced in
sea state 4 with a significant wave height of 5.5 m. The same trend occurs in this sea state as it
did with a significant wave height of 10 m except the magnitude of accelerations created is on
the order of one-quarter to three-quarters lower. Additionally, in the water depth of 62.5 m, the
accelerations begin to become non-linear at higher initial tensions than the 10 m sig. wave height
case. Table 9 and Table 10 list the properties of feasible TLP combinations in order to reach a
zero tension difference for this sea state.
45
The change in acceleration response between lower water depths is much steeper than between
deeper waters. Also, as was outlined in the sections above, surge accelerations do not vary
significantly based on changes in wind speed profiles alone.
Table 9. Wind Speed Zero Tension Difference Options and Responses, 11m Radius, 5.5 m Sig. Wave Height
25 m/s
16 MIS
11.2 mis
9 MIS
Tension Max RAO RMS Acc Tension Max RAO RMS Acc Tension Max RAO RMS Acc Tension Max RAO RMS Acc
Ballast
0.376
0.38 13249937 8.882
0.385 15366553 7.339
0.381 18681476 12.127
16460494 8.453
3.5
16972997
17646624
18404235
19276993
20256458
21331635
4
4.5
5
5.5
6
6.5
0.368
0.355
0.344
0.334
0.325
0.316
7.069
7.196
8.228
9.166
9.966
10.555
Surge Accelerations for Radius = 11m Wind Speed = 9 m/s
(multiple concrete ballast heights)
0.366
0.354
0.343
0.333
0.324
0.316
7.324
8.802
10.037
11.743
12.954
13.734
0.37 15877136
0.358 16472297
0.346 17188854
0.336 18021537
0.327 18961743
0.318 20037754
9.425
8.036
7.229
6.744
6.919
7.264
19274514
19993359
20833599
21825693
22882963
24032631
13644112
14158835
14794268
15585158
16447320
17409758
0.363
0.351
0.34
0.331
0.322
0.314
11.932
15.938
20.938
26.165
31.565
35.728
Surge Accelerations for Radius = 11 m Wind Speed = 11.2 m/s
(multiple concrete ballast heights)
X 107
x-
1-
0.45
0.4
---
--
5
-0.
-
-
50
.2
E
E
!
02
S
0.5
1
2
1.5
initial Tension
2.5
3.5
3
3.5mA Ten --
4.5m
4mA Ton --
Surge Accelerations for Radius = 11 m Wind Speed = 15 m/s
0.5
,
,
p
,
,
0.3
.
05
1
O
7
[N]
g
,
,
,
A Tn
5m A Tn
-
6m&aTn
5.5mA Ton
-
2.5
2
1.5
Initial Tension [N]
-+-
3
3.5
4
X17
6.5m& Tn
Surge Accelerations for Radius = 1m Wind Speed = 25 m/s
(multiple concrete ballast heights)
x 106
x
15
15
10
0.45 -
i~.
ii,
|
in
0.45
E
0.3 L
0
O.5
1
1.5
2
Initial Tension
3.5m Acc
2.5
[N]
.
3
3.5
S 0.35 -
0.
4
0
0W
0.5
7
4m Acc
*
tt
|7
0.4 -
0
-
- - -
- -- -- - ---
- - - - - - - -
10
4.5m Acc
-
5m Acc
5.5m Acc
1
2.5
2
1.5
Initial Tension [N]
6m Acc
--
3
4
3.5
X 107
6.5m Acc
Figure 20. Wind Speed Effects on Surge Acceleration RMS, 11 m Radius, 5.5 m Sig. Wave Height
46
Table 10. Water Depth Zero Tension Difference Options and Responses, 11m Radius,
5.5 m Sig. Wave Height
62.5 m
100 m
200 m
300 m
Ballast
Tension Max RAO RMS Acc Tension Max RAO RMS Acc Tension Max RAO RMS Acc Tension Max
RAO RMS Acc
3.5
19162426
13.809
0.463
4
4.5
18793335
19866530
20715581
21706719
22848433
24115087
25495051
71.239
18.46
23.018
25.571
24.684
21.343
17.311
0.408
0.445
0.43
0.417
0.407
0.398
0.391
18681476
19411974
20160764
21035685
22067510
23169125
24368949
12.127
39.101
24.39
19.078
16.867
15.737
15.374
0.385
0.392
0.378
0.366
0.355
0.346
0.337
18677378
19274514
19993359
20833599
21825693
22882963
24032631
14.284
9.425
8.036
7.229
6.744
6.919
7.624
0.38
0.37
0.358
0.346
0.336
0.327
0.318
19269137 23.038
19986420 39.375
20825276 54.31
21814881 47.012
22869905 36.73
24017000 30.654
0.366
0.354
0.343
0.332
0.323
0.314
5
5.5
6
6.5
Surge Accelerations for Radius - 11m Depth - 62.5 m
(multiple concrete ballast heights)
X 107
1
1
cc-
0.8
0.5
C.1)
-
0.6
------
-
--
W--
-0.5 E
0
0.5
1
1.5
2
2.5
Initial Tension [N]
3.5-
A Ton
-
4m
3
3.5
0.4
A Ton
---
4.5m
4
x
0.5
-
)
A Tn -
1
0
--
0.35.-
7
Surge Accelerations for Radius = 11 m Depth - 200 m
(multiple concrete ballast heights)
X107
0.45-
0
P
0.4
12
Cq-
0.
t
Surge Accelerations for Radius = 11m Depth = 100 m
(multiple concrete ballast heights)
0. 5 ,
5m A Ton
0.5
1
5.5m,& Ton
-
- -4-
1.5
2
2.5
Initial Tension [N]
Sm A Ton --
-
3
- -
-0.5 E
3.5
4
X17
6.5mA Ton
Surge Accelerations for Radius = 11m Depth = 300 m
(multiple concrete ballast heights)
10'
X 107
0.4
0.
- - - -t*
- -
I
E
0.35 - - - -
U)
0.3
0
0.5
1
1.5
Initial
- -
2
ension
3.5m Acc
2.5
3
3.5
I
4
1
0.3
0
0.5
[N]
.
4mAcc
4.5mAcc
.
5m Acc
--
5.5m Acc
1
1.5
2
2.5
Initial Tension [N]
6m Acc
6.5m Acc
3
3.5
47
X 107
Figure 21. Water Depth Effects on Surge Acceleration RMS, 11 m Radius, 5.5 m Sig.
Wave Height
4.3.6 Zero Tension Possibilities
The trends discussed above are summarized graphically in the figures of this section for both of
the sea states of interest. Figure 22 and Figure 23 demonstrate the relationship between
combinations of initial tension values and concrete ballast heights that yield a zero tension
difference between minimum steady state tensions and maximum dynamic wave-induced
tensions. In all figures lower concrete ballast heights require less initial tension (for a given
47
wind speed or water depth), and the slopes at a 5.5 m significant wave height are steeper than
those for 10 m. This demonstrates the stronger influence that lower sea states have on limiting
feasible combinations of TLP properties. As was noted before, zero tension possibilities are
limited by the rated wind speed at specific water depths. However, shallower depths also require
more tension for a given concrete ballast height, so a balance between the two must be found.
Radius = 11 Trend Lines for Zero Tension Differences (5.5m sig ware)
6.5
9 m/s
- -
__- -
-
11.2 m/s
15 m/s
25 m/s
------
6 - - - - - - - --- - - -
15 m/s
- - ---
_--
-
.
11.2 m/s
---
6 - _
Radius = 11 Trend Lines for Zero Tension Differences(l0m sig. wave)
1m/s
6.5
25 m/s
5-
- - -
-
Z5.5- - - -
- -
-
4
- -
-4-----
- -
3.5
1.2
--
----
--
4.----
1.6
1.4
5.5---
- - -
----
2
1.8
Initial Pre-Tension
- - -
---
--
-
-
- - -
5-
- - - - -
----
-
2.2
2.4
2.6
x 107
3.5
2.4
-
-
-------
----
4--
-
-
-
--
-
-
-
4
3.8
3.6
3.4
3.2
3
Initial Pre-Tension
2.8
2.6
x10
Figure 22. Wind Speed Effects on Zero Tension Difference Trend Lines, 11 m Radius
Radius =11 Trend Lines for Zero Tension Differences(10m sig. ware)
Radius =11 Trend Lines for Zero Tension Differences (5.5m sig ware)
6.5
-
-
62.5 m
6.5
62.5 m
-i-P1niom
-
6- - - -
a-- - 5
3.5
1.8
'
1.9
'
4 _e
Tension
Lis
-
-
100 m
200m
-300 m
i
- ---
2
n2m
300 m
'
2.1
'
2.2
2.3
2.4
2.5
Initial Pre-Tension
Figure 23. Water Depth Effects
2.6
X 107
3.5'
3
3.1
3.2
3.3
3.4
Initial
3.6
3.5
Pre-Tension
3.7
3.8
4
3.9
x 10
on Zero Tension Difference Trend Lines, 11 m Radius
Once viable combinations of initial tension and concrete ballast height are determined, the
responses of these structures can be more precisely analyzed. The figures below are essentially
the local magnifications of the figures presented in section 4.3.2 around the correct range of
initial pre-tension values. As described above, for a water depth of 62.5 m, the responses
become non-linear in the range of zero tension difference possibilities. Figure 24 presents the
7
local magnification of Figure 13 and demonstrates how the lowest RAOs occur close to 3.2x10
48
N and 3.7x 10 7 N for a water depth of 62.5 m, with corresponding concrete ballast heights close
to 3.5 m and 4.75 m respectively.
Because a wind analysis was not completed at this depth, a comparison to the limiting case at the
rated wind speed cannot be made.
But with Figure 23 for zero tension trendlines, an
interpretation can be assumed for wind effects at water depths other than 200 m. These show
that the ballast required for the same initial tension decreases with a decrease in water depth.
This means that at a specified initial tension, the resulting tension difference is positive when
ballast is decreased going from a 200 m water depth to a 62.5 m water depth. Because positive
tension differences provide more steady state tension than what could be expected within a
99.7th percentile from wave induced tensions, this interpretation is appropriate.
In addition,
Figure 21 shows how increases in ballast height result in decreases in accelerations.
For 100 m, Figure 24 displays a local magnification where the RAOs are sloping downwards
towards a minimum that is beyond the suitable range of initial tensions studied here. As long as
accelerations are kept below a desired threshold, the better (and cheaper) combination becomes a
product of low tension and less concrete ballast.
The 200 m depth in Figure 24 displays a local magnification where the RAOs begin to rise, and
at 300 m, the magnification shows RAOs reaching a minimum within the range of applicable
initial tensions.
49
Zero Tension Difference Surge RAO
3155
S
for Radius
= 11 m Depth =
62.5 m 10m Sig
Zero Tension Difference Surge RAO for Radius = 1 1m Depth = 100 m 10m Sig Height
55
Height
5
Balat Haigt
RAO
*
32
.
50
als egt
RAG
5
40-
Z
0 30
01
0
45
0
E0
1
4
28-
4. 55
-o
30 i5
E
.E
20o
24'
3.1
3
10,
3
3.9
3.8
3.7
3.6
3.5
3.4
Initial Tension [N]
3.3
3.2
0
o o*
1
3.4
3.3
Initial Tension [N]
3.2
3.1
x 10
Zero Tension Difference Surge RAO for Radius = 11m Depth = 200 m 10m Sig Height
3.6
3.5
35
3.7
x 107
Zero Tension Difference Surge RAO for Radius = 1rm Depth = 300 m 10m Sig Height
.
10
o
o
RAOBallast
RAOo
5.5
80
10
iI
E
E
o
3.
26-
0
1
4
I
20-
(5
d0
-
o
8
60
4
=
0 EE
oo *
20
03
o
4.52e E
40
o
3.
3.1
3.2
4n
o*oo ol
*
6
4
1|
4l
3.5
3.7
3!6
3.5
3.4
3.3
Initial Tension [N]
3
3.4
3.3
Initial Tension [N]
3.2
3.1
X 107
3.5
3.6
3.7
x 10
Figure 24. Zero Tension Difference Surge RAOs and Ballast Heights based on Water Depth, 11 m Radius,
10 m Sig. Wave Height
Surge RAOs for Zero Tension Difference Platforms 10m Sig Height
90
1 0
0
+
9
-
-- -0
60
*
?
50
(n 40
E
E
30
I-
---
0
0. 04.
-
-
0
.
.
..
3
3.
.
.
O3
3.1
3.2
3.3
100
|
- -I
I a " |C
.
-
- -
-
-
-
-
-
--
0
1
0
20
10
a
-
--- -- ----- --
70
62.5
100
200
300
+
-I- - - - - - *0 -
80
00
.
.5
.
4
d
.h
3.5
3.4
Initial Tension [N]
36
37
38
3.6
3.7
3.8
3
3.9
x 10
Figure 25. Surge RAOs for Zero Tension Difference based on Water Depth, 11m Radius
50
Inn
Zero Tension Difference Surge RAO for Radius = 11m Wind Speed = 9 m/s
o
50
0
4A
I
0C
1
o
E
11m Wind Speed = 11.2 m/s
6
--
-5.5
T
~
10
for Radius =
|
80
0
I1
0
e
1
-
I
100
BaMast Heqgt
RAO
0
Co
Zero Tension Difference Surge RAO
6
60
OO
E 40
o
-
011
xa
10b
0
0
m
00
3 5
20
17
2.8
3.1
3
Initial Tension [N]
2.9
3.3
3.2
3.3
3.4
Initial Tension [N]
3.2
3.1
3
3.4
x 107
Zero Tension Difference Surge RAO for Radius = 11 m Wind Speed = 15 m/s
3.7
3.6
3.5
x
10
Zero Tension Difference Surge RAO for Radius = 11m Wind Speed = 25 m/s
1m
1
0
100
5
200L
0
-
0
E
4
100-
2.7
CS
0000?ooo
0
00
2.6
40C
50
0
0
I0
T
OO
E
C1
EO
1
Mih
8als
b
1
2.8
100
00
0
0
3
2.9
Initial Tension [N]
0
0
0
3.3
3.2
3.1
0 0
0000
00
2.4
2.8
2.7
initial Tension [N]
2.6
2.5
x 117
3.1
2.9
x 10
Figure 26. Zero Tension Differences and Ballast Heights based on Wind Speeds, 11 m Radius, 10 m Sig.
Wave Height
Surge RAOs for Zero Tension Difference Platforms
-- - -- --- -- -- - -- --- ---- - ---
300-
9m/s
+
0
-
250 -
o
--------
+
200
150
-
I-
E
E
0
100
-.--
-
r -
-
-
-
- - - -
-
0 -
-
0
--
I
-------------
0
0
0
0 I
-
---
+00
100
1 %+
0
- - -0I;
II 0 0
2.6
2.8
-
I-
00
-
-000
/
001!
*%3%4.
0A0+6"++I
2.4
- - -
I
-
1.+*
50
,
11.2 m/s
15 m/s
25 m/s
+
3.2
3
Initial Tension [N]
3.4
3.8
3.6
x 10
7
Figure 27. Surge RAOs for Zero Tension Difference based on Wind Speed, 1im Radius
51
7
8 m Radius
4.4
For a TLP with a radius of 8 meters, the performance was not only found to be poor, but the
required barge dimensions become unreasonable. Therefore, only a limited discussion will be
made for this configuration.
4.4.1 Draft Analysis
Because of the nature of this study, certain combinations of initial tensions and concrete ballast
The relationships
heights yield drafts above the 26-meter fixed depth for the TLP floater.
between concrete ballast height, draft, and resulting tension differences are presented below for
the four wind speeds.
Draft relationships for Radius = 8m Wind Speed = 9 m/s
(multiple concrete ballast heights)
Draft relationships for Radius = 8m Wind Speed = 11.2 m/s
(multiple concrete ballast heights)
X 107
---- --- ---
30
-
20
-
2
-
3
0
- -
----
0.5
2
2.5
1.5
Initial Tension [N]
1
I-
3.5m
Tn ---
3
3.5
10
0
4
Draft relationships for Radius = 8m Wind Speed = 15 m/s
(multiple concrete ballast heights)
I
--
-
r.-t-
~
-
0.5
1
-
--
-
3
-10
4
3.5
X 10
65mATeni
Draft relationships for Radius = 8m Wind Speed = 25 m/s
(multiple concrete ballast heights)
107
30---------------
------
---
---
---
2.5
1.5
2
Initial Tension [N]
&m ATon ---.
5.5rn A Ten
X
qu
20
5mATon -
---
4.5mATon
--
E
x 107
4mA Ton--
-
--
x
-
E
10U
0
0.5
1
1.5
2
2.5
Initial Tension [N]
3
3.5m draft
4m draft
-
+
3.5
4
1
0
0.5
X 107
*
4.5m draft
-
5m draft
+
5.5m draft
1
1.5
2
2.5
Initial Tension [N]
6m draft -
6.5m draft
Figure 28. Wind Speed Effects on Draft, 8 m Radius, 10 m Sig. Wave Height
52
10
5
0
10
E
0
106
20
E
0
X
40
-I
u
3.5
4
X 107
4.4.2 8 m Radius Discussion
The same trends as the above TLP draft analyses are displayed for the range of wind speeds
covered
The optimum configuration for the smallest possible draft in order for the zero-slack
probability to exist requires a draft greater than the depth of the TLP. Although a TLP with a
radius of 8 m may be within all limits for the entire range of wind speeds in order to meet the
zero tension difference for a significant wave height of 5.5 m, this study is interested in the
performance at superior sea states, and further analysis will not be discussed here. Additionally,
the results for the design cases for a TLP radius of 9 m, 1 Om, and 12 m will be presented in
Appendices A, B, and C. Only the design iteration consisting of an 11 m radius is thoroughly
discussed, and conclusions on the entire design spectrum will be made at the end.
4.5
Alternative Platform Results (9 m, 10 m, and 12 m Radius)
The exact linear analysis performed above for the base case comparison was completed for a
TLP with a radius of 9 m, 10 m, and 12 m. Identical platform depths, water depths, ballast
heights, and initial tension ranges were used to complete the initial comparison. Trend lines
were determined for each new platform radius and a list of feasible parameter combinations was
made to further analyze. Because similar trends were found for each scenario, discussion will be
limited, and all tables and figures are presented in Appendices A-C.
4.5.1 9 m Radius Discussion
Analysis for a barge radius of 9 m is given in Appendix A: 9 m Radius. This TLP configuration
represents the smallest design structure within the scope of reasonable dimensions (drafts). The
effects of wind speeds, water depths, and initial tensions on draft, motion responses, and
acceleration follow the same trends as results for an 11 m radius present. The draft analysis was
completed to ensure appropriate values were within limits as compared to the structures height
(26 m) in order to allow for freeboard. The limiting wind speed of 11.2 m/s allows for TLPs
with ballast heights of 3.5 m and 4 m to be further analyzed. As a general observation, greater
water depths require slightly shallower drafts for equivalent ballast heights. It continues to be
53
shown that shallower water depths require more initial tension and produce the largest
acceleration responses. Therefore, it follows that optimum responses warrant the use of more
ballast with higher initial tension in deep water. For wind speed effects, at the limiting rated
wind speed, the minimum acceleration experienced is 0.511 m/s 2 at a ballast height of 6.5 m.
The lowest acceleration in the water depth results occurs at 300 m for a standard deviation of
0.493 m/s 2. The corresponding limits in seas with a significant wave height of 5.5 m are 0.322
m/s 2 and 0.317 m/s 2 respectively.
4.5.2 10 m Radius Discussion
At a radius of 10 m (Appendix B:
10 m Radius), the limiting results for acceleration RMS
vary only slightly from the 9 m case; however, the required tensions to match the zero tension
difference become larger. At a wind speed of 11.2 m/s, the minimum acceleration still occurs at
a ballast height of 6.5 m. Although the acceleration is only 0.002 m/s 2 less than at a 9 m radius,
the initial tension required involves a 3% increase in force. Similarly, the minimum standard
deviation in acceleration is reduced to 0.493 m/s 2 at a water depth of 300 m, but initial tension is
over 1000 kN greater.
4.5.3 12 m Radius Discussion
Appendix B:
12 m Radius, presents all data on the largest TLP analyzed with a radius of 12 m.
The advantage in decreased acceleration response from a radius of 11 m to 12 m involves a more
significant jump than between the TLPs of smaller radii. At the limiting wind speed of 11.2 m/s,
acceleration RMS is decreased from 0.505 at an 11 m radius to 0.498 m/s 2. And at a water depth
of 300 m, accelerations are decreased to 0.487 m/s 2.
54
5
CONCLUSION
The results above provide good comparisons of water depth effects and wind effects, as well as
the effects of variations of ballast heights and initial tensions. As has been discussed above, the
absolute lowest acceleration RMS from the design group occurs with a radius of 12 m at the
greatest ballast height of 6.5 m in a water depth of 300 m. The final results presented here
discuss the overall response and performance of this structure within the scope of this research.
5.1
Discussion of Optimum TLP
After the optimum TLP dimensions and properties were determined from the absolute maximum
responses, a spectral analysis over the range of frequencies and sea states was performed to
provide detailed results. Figure 29 recreates the surge, sway, and heave response spectrum for
the base case scenario and compares it to this optimum TLP. As described already, the RAO
peaks are much lower than the base case plots, and the natural frequencies are even lower than
the already small natural frequencies for an 11 m radius. This fact defends the result for smaller
standard deviations due to the fact that the majority of the response is excited less and less from
the sea spectrums for sea states 4 and 5.
The final result is a success in terms of reducing
motions and accelerations, but the size and amount of supporting materials has grown. More
research will be required to narrow down the design of a truly optimum support platform for
floating offshore wind turbines.
Table 11. Displacement, Velocity, and Acceleration Response (RMS) values for Optimum TLP
Optimum TLP Response
Max Surge RAO
Tension Difference [N]
Sea State 4
13.264
23671018.35
Sea State 5
11.326
39708668
amax Surge Displacement [m]
1.19
2.46
amax Surge Velocity [m/s]
amax Surge Acceleration [m/s 2 ]
55
0.573
1.01
0.31
0.487
Surge RAO Comparison to Base Case
Sway RAO Comparison to Base Case
Base Case (R =11 m)
Optimum TLP (R = 12 m)
Base Case (R = 11 m)
Optimum TLP (R = 12 m)
20
-_
---
- - - - - -- - - -- -- - -- - ---
-- -- ---
- --
I--- -- - -
0.025
0.02
15
- -- - - - -- -
--
-
-
-
-
--
0.015
10
- - -
-
~-
- - - -
-
-
+
-
0.01
-
-
-
-
0.015
5
0
0.2
0.4
0.8
0.6
0
1.4
1.2
1
0.6
0.4
0.2
0
0o
w [rad/s]
0.8
1
1.2
1.4
[rad/s]
Yaw RAO Comparison to Base Case
0.01
0.009
--
Base Case (R =11 m)
OptimumTLP(R=12m)
-.-
-
0.008
---------
-
T--
0.007
0.006
--
--
-
-
--
-
-
--
-
--
L
-
-d
-
-
-
-
0.005
0.004
0.002
------
------
----------
0.003
-------
--
--
------.-
--
p
-
-
0.001
0
0.2
-
-
0.4
-
-
-
-
-
-
0.8
0.6
-
- -
1
1.2
1.4
0) [rad/s]
Figure 29. Surge, Sway, and Yaw RAO Comparison
Table 12. Natural Frequencies of Optimum TLP
Mode
Surge
Sway
Yaw
5.2
Natural Frequency
0.0894 [rad/s]
0.0894 [rad/s]
0.2028 [rad/s]
Recommendations for Future Work
The results of this study display a solid trend in the relationships of Tension Leg Platform
parameters and the effects they have on tension requirements and barge motions. The platform
system designed in this study is only "optimized" as far as motions and responses are concerned.
56
Additional research could result in a floating support system that is more capable and more cost
effective than the TLP concluded above.
Promising active control techniques could further reduce surge motions through alterations in
blade pitch, essentially imparting a thrust into the wind and counteracting the direction of motion
(assuming wind angle and wave propagation are in the same direction). Additionally, other
hydrodynamic dampers could be introduced. The scope of the design iteration pool could be
increased to include more wind speeds and water depths as well as introducing the effects of
viscous damping. Finally, the most important addition to the research presented here would be a
cost analysis. All of the modifications made here in formulation of an "optimum" TLP suggest
an increase in cost. A larger radius requires more steel, a higher ballast height requires more
concrete, and higher initial tensions in greater water depths require more and longer tether
cables.
Including cost in the design iterations would greatly improve the approach towards
determining a truly optimum TLP system.
57
Appendix A: 9 m Radius
Draft relationships for Radius = 9m Wind Speed = 9 m/s
(multiple concrete ballast heights)
Draft relationships for Radius = 9m Wind Speed = 11.2 m/s
(multiple concrete ballast
heights)
X 10
40
-
10
.
.
0
0 1
15
2
2
5
1
0.5 -
30
I
is
X 10
3-..
- 2-
- ---
-0
E
3
20
E
-
-
-
e-
-
-
- -
-
-
-
-
- -5
- -
00
101
0
Initial Tension [N]
I
3mA
-
Ton
A Ton
-4m
40
4C
20
I
---
4.5m
-
Draft relationships for Radius = Sm Wind Speed
(multiple concrete ballast heights)
1
=
0
1
1.5
2
2.5
draft
3.5m
3
3.5
4m drat
-
1
Om A
-
1.5
2
2.5
Initial Tension [N]
Tn
-
4
110
10
A Tam
.5m
K 10
-
-
- - - - - - - - - -0
-
20 - - - - -
E
5m draft
-
---
2.5
1.5
2
Initial Tension [N]
1
0.5
4
X 107
4.5m draft
sm A Ten
3.5
3
Draft relationships for Radius = 9m Wind Speed = 25 m/s
(multiple concrete ballast heights)
-- 1- -
20
E
I
Initial Tension [N]
Ton
X107
0
0.5
6mA
-
Ten
15 m/s
'--
0n
0.5
10
X
6m
5.5m draft
3
3.5
4
X
10
6.5m drat
draft -
Figure 30. Wind Speed and Draft Effects, 9 m Radius, 10 m Tension Difference
Draft relationships for Radius = 9m Depth =
(multiple concrete ballast heights)
62.5
Draft relationships for Radius = 9m Depth = 100 m
(multiple concrete ballast heights)
m
X
C
30
I
--
--
X le
--
I
20 - - -
10110
0
-
-
0.5
1
A Ten --
-
2.5
3
3.5
[N]
4mA
--
30-
----
20 - - - -
0
-
-
0.5
-
-
-
1
- -
-L10
3.5m draft
-
- -
3
0.5
0
3.5
1.5
2
Initial Tension
- -
--
5
OmATen -
-
--
FIE
5
I10
3.5
X
4
107
8.5meATenI
m
X 106
I
-
-
20 - - -
E
E
- - -
-
-
- - -
- - - - --
E
10,
05
0
4
4.5m draft
3
300-
5
1
1
X 107
4m draft
2.5
[N]
Draft relationships for Radius = 9m Depth = 300
(multiple concrete ballast heights)
0
-.-
- -
1
$.5.fmmTan
X 1C
-
2.5
1.5
2
Initial Tension [N]
1oL
5m & Ton
--
--------
20 - -
10
4.4mATn -
- -
--
FE
4
X
Ton
5
---
--
Draft relationships for Radius = 9m Depth = 200 m
(multiple concrete ballast heights)
4'5
10
1.5
2
Initial Tension
' -Sm
I
-
draft
.Sm
-
5.5m drat
6m
2
Initial Tension
draft -.
2 5
3
[N]
.m
.5
4 10
1107
draft
Figure 31. Water Depth and Draft Effects, 9 m Radius, 10 m Tension Difference
58
3
RAO 1 for Radius = 9m Wind Speed = 9 m/s
(multiple concrete ballast heights)
100
RAO 1 for Radius = 9m Wind Speed = 11.2 m/s
(multiple concrete ballast heights)
X 107
70- - -- -
-
40 - - - -
--
50
-
--
--
1-- ---
- -
-
- 4-
-
-2-2
ill
0
30- ---
-
-
20- - - - -
~
f-
- 40
x 10
6
-
__.4
- -
.;
-
10
0.5
1
1
15
2
Initial Tension
2.5
S3.m aTonRAO 1
for Radius
3
[M]
3.5
4m ATon -
-8
0
4
7
4.5Zm ATon -
0'5
5m aTon -
x 107
71
1
1.5
2
2.5
Initial Tension [N]
5.5mA Ton
= gm Wind Speed = 15 m/s
(multiple concrete ballast heights)
Gm A Ton
- - - - -- -- - - - - - --
-
-
--
zeu
- ----
i~i
0
--
I
-- - -
100-
5
II-
---
0.5
1
1.5
2
2.5
Initial Tension [N]
3.5m RAO
3
3.5
6.5m a~T
-
x 107
---
--
4
0
0.5
1
- -0.5
4.5m RAO
5m RAO
5.5m RAO
2.5
-
3
- -----0.5s
3.5
7
6.5m
6m RAO -
0
0
II
i!1
50
-
-
-
-
-0
i
1001
(
cnre
blast
50 - - - - - - --
E
4
[N]
RAO
Figure 32. Wind Speed Effects on Surge RAOs, 9 m Radius, 10 m Tension Difference
RAO 1 for Radius = gm Depth = 62.5 m
RAO 1 for Radius = 9m Depth = 100 m
m7t l
100
I
j
- --- -
1.5
2
Initial Tension
X 107
4m RAO --
41
X 107
-- - --
50
)
3.
I
E
0,
3
RAO 1 for Radius = Sm Wind Speed = 25 m/s
(multiple concrete ballast heights)
150-
2 0-
S
--
X107
hits)
--
0
S
010
0.5
1
1.5
2
2.5
Initial Tension [N]
Sm ATn
4mA Tn
-
3
3!.5
4.5m a Ton
--
-
----
0
--
- - -
0.t
1
3.5
4
X 107
5m 4 To
-.
x10
0
--
- - - - - - - - --
- -
-
i!1
-
I
IIS
-
10o - -
On & Ten
3
2
I
20-
1 .5
2
2.5
Initial Tension [N]
4
4 -
-----
Ten
-5.5mA
4
30-
1
RAO 1 for Radius = gm Depth = 300 m
(multiple concrete ballast heights)
j~1
I
0.5
x 1e
-
60 -- -- -
4 Ton
-m
RAO 1 for Radius = Sm Depth = 200 m
(multiple concrete ballast heights)
70-
0
4
x 107
20*
05
E
-8
1.5
2
2.5
'3!
35
.
4
Initial Tension [INX
3.0
RAO
.
4m RAO
~'.
0~~~~~
Initial Tension
---
4.5m
RAO
5m
RAO
-
5.5m RAO
6m RAO
-
0' '.
[M
6.5m RAO
Figure 33. Water Depth Effects on Surge RAOs, 9 m Radius, 10 m Tension Difference
59
010
.5
X
10
RAO I for Radius = 9m Wind Speed = 9 mis
(multiple concrete ballast heights)
RAO 1 for Radius = Sm Wind Speed = 11.2 m/s
(multiple concrete ballast heights)
X 107
x
T
I
0.5
60
;r
%%
50
0
107
- --- 0
- -- - --
-
- ---- -
40
E
-0.5 *)
20
I
2
1.5
Initial Tension
1
0.5
3SmA
Ten
----
-445mA
4mATen
00
I
OmA Ten -
1
-
[N]
3.5m RAO
*
x 10
I
50
1
-
4
100
-tia -- -- -io -N - -X--
--
-
-
7-
135
[ 2
i
0ni1 1T
4
3.5
3
2.5
2
1.5
Initial Tension
6.5m-ATonItr
I
11
0.5
10
E
- ----
- -
- - -
- -
4
3.5
2.5
[N]
RAO 1 for Radius = 9m Wind Speed = 25 m/s
(multiple concrete ballast heights)
x 10,
0
- - - - - - - - -
5mg&mTon
-.
-5mATn
Tn
110-
100
2
1.5
Initial Tension
1
0.5
x
RAO 1 for Radius = 9m Wind Speed = 15 m/s
(multiple concrete ballast heights)
I
I
4
3.5
3
2.5
[N]
X 107
4m RAO
RAO
.Sm
4.5m RAO
-
+
6.5m RAC
-
6m RAO
5.5m RAO
Figure 34. Wind Speed Effects on Surge RAOs, 9 m Radius, 5.5 m Tension Difference
RAO 1 for Radius = 9m Depth = 62.5 m
(multiple concrete ballast heights)
x
lv*
50 -
--
RAO I for Radius = Sm Depth = 100 m
(multiple concrete ballast heights)
107
X 107
100
I
0
L
50 S-
-
-
-
-
,
E
E
of0
0.5
2
1.5
Initial Tension
1
3IMTon --
4
3.5
3
2.5
11
0
Am
Ton
5m
4.
--
RAO I for Radius = 9m Depth = 200 m
(multiple concrete ballast heights)
0
20
-o.5 E
2.5
2
1.5
Initial Tension [N]
1
-
3.5m RAO
-
2
1.s
Initial Tension
1
4m RAO
x
-
4J-
x 10
6Am
OiAiTen -
3.5
TenI
RAO 1 for Radius = Sm Depth = 300 m
(multiple concrete ballast heights)
x 107
10
0
00
4
3.5
3
3
2.5
[N]
- - 0.5
40
0.5
0.5
5.5mA Ten
Tar
x 107
-11
- L-- - '
60
0
1
x
[N]
- - -0-
0.5
7
4.5m RAO
5m RAO
+
5.5m RAO
-
2
1
1
1
I.s
2
Initial Tension
6m RAO -
2.t
3
3.5
3
3.5
[N]
6.5m RAI
Figure 35. Water Depth Effects on Surge RAOs, 9 m Radius, 5.5 m Tension Difference
60
1
4
x 10
Surge Accelerations for Radius = 9m Wind Speed
(multiple concrete ballast heights)
9 m/s
=
x 10"
73-
Surge Accelerations for Radius = Sm Wind Speed
(multiple concrete ballast heights)
0.7
=
11.2 m/s
e
x 106
5
0.6-
- -
-- - -
-
-
-
-
4.'
*
0
-.
L-
J
--
0.5 - - - -
0
-
T
0.5
1
1.5
2
Initial Tension
.15m a Tn -
2.5
3
4m a
Ten -
0.5
7
x 167
4.5m A Ton -
for
0.6
"'"-
3.5
[N]
Surge Accelerations
Radius = Om Wind Speed
(multiple concrete ballast heights)
5m
5.5m
-
Ton
m/s
=15
- ....
-
X 107
1
0.6 -
.r-
.~
1i-
1
1.5
2
Sm &Tan
& Tn
2.5
Initial Tension
-
-
3
..5 E
0
--
3.5
X17
& m & Tan I
-
0.6 - - - - - - - -- - ---- - -
4
[N]
Surge Accelerations for Radius = gm Wind Speed
(multiple concrete ballast heights)
0.65
0.5
0.55 -
=
25 m/s
107
X
- -- - -
--0.5
0-
0.5 -- -- - - 0.5
-.
55
-
-
0
-
-
- - -
0.5
1
-0.5
1.5
2
Initial Tension
2.5
3
3.5
. *
3.5m Acc
4m Acc -
-
-- - --
- - 0.5
0.5
0.451
0
4
0.5
1
7
[N)
. *
4.5m Acc
Sm Acc
S
-
5.5m Ace
1.5
2
Initial Tension
2.5
3
3.5
4
7
[N]
Acc
tm Acc -..- tm
6m Ace 65m Ace
Figure 36. Wind Speed Effects on Surge Acceleration RMS, 9 m Radius, 10 m Sig. Wave Height
Surge Accelerations for Radius = 9m Depth
(multiple concrete ballast heights)
=
62.5 m
lo
1..
(4-
=
100 m
X 107
1
73-
I
I
~
-I
~
-I
-
I
-
0i
2
0
Surge Accelerations for Radius = 9m Depth
(multiple concrete ballast heights)
5
1
.
-5
-
0
0.5
1
--
1.5
2
Initial Tension
3.5m
A
Ten -
2.5
3
A
Ton
-----
0. 6 -
-- - - - - - - - - - -
=
S
Dpl
=30-
E5j
u0
4101
3.5
0.5
1
7
Surge Accelerations for Radius = 9m Depth
(multiple concrete ballast heights)
0.7
u--
[N]
4m
SugeAcelraios orRdis
4.5m A Ton -
5mA
Ton
5.5m
-
1.5
2
Initial Tension
6m A Ton -
-Ten
2.5
3
3.5
107
6.5m,&Ton
Surge Accelerations for Radius = 9m Depth =300
200 m
x 106
.5
"--'
J0.6
--- - - - - - - - -
-5
K
- - - - -
-- 0.5
m
(multiple concrete ballast heights)
0.7
0
_-
4
[N]
10
-
1--
-5
0.5
E
U -"
0.5
1
1.5
2
2.5
Initial Tension [N]
-
-
3.5m Acc
.
4m Acc
3
3.5
4
-10
u
.s1
0.5
7
1
1.5
2
Initial Tension
2.5
[N]
3
3.5
4
X107
4.5m Acc
-
Sm Acc
5.5m Acc
6m Acc
-
6.5m Acc
Figure 37. Water Depth Effects on Surge Acceleration RMS, 9 m Radius, 10 m Sig. Wave Height
61
ao
Surge Accelerations for Radius = Sm Wind Speed
(multiple concrete ballast heights)
=
9 m/s
X
Surge Accelerations for Radius = Sm Wind Speed
(multiple concrete ballast heights)
107
rt~
I
..
0.4 ---
0.3
- --
0.4- -
- -
11
E
0
-O
02--2-*e
-
.,
-
0.31
0.5
- - -
-
-
- - - -
-
0
=
L
15 m/s
11(multiple
0.5
10
44-
0.45-
----
0.3
0
1
0.5
2.5
2
1.5
Initial Tension [N]
3.5m Acc
-5
.5
35
3
0.3
4
Sm
5 Acc
4.5m Acc
-
-
-
2
1.5
Initial Tension
6m Acc
5.5m Acc
=
25 m/s
x
i---
-
1
0.5
0
Teon
Speed
'
2.5
4
3.5
3
5--
I-E
- - -O
-
[N]
6.5m
-
-
- - -
10o
-10
- - -
-
- - - -
X17
4m Acc
.
0.35 -- - -
- - - 1
-
107
ballast heights)
concrete
-
- - -
I
E
-
- -
- - - - - -----
A
9m Wind
- J - - - -L
I-
- - -
0.4----
0.35-
.m
=
4
X
[N]
---
Surge Accelerations for Radius
x106
- - -
OmATen
.5m A TeA
56MA Ten
3.5
3
2.5
2
1.5
1
Initial Tension
-4.SmATen
- - L-
-
1
4
7
3.5
3
2.5
2
1.5
Initial Tension [N]
1
0.5
Surge Accelerations for Radius = 9m Wind Speed
(multiple concrete ballast heights)
I
5
-0.
-
I
*
0
0.45-
0.4 -
- --
- -
-
-
- - -
-
X 107
I.......
I3.mATenO--4mATen
44-
0.45
or-
11.2 m/s
=
107
Acc
Figure 38. Wind Speed Effects on Surge Acceleration RMS, 9 m Radius, 5.5 m Sig. Wave Height
Surge Accelerations for Radius = gm Depth
(multiple concrete ballast heights)
=
x 107
2,
C5
NO-
0.5
1.5-
0.45
-
-
0.4
-
-0.5 E
0.35
-
0
0.51
1
0.5
-
5mA
3.
3
2.5
2
1.5
Initial Tension [N
Ten
---
4mA
Ten
x
Ten
4.5mA
--
UJ.
4
3.5
5mA
Surge Accelerations for Radius = Sm Depth = 200 m
(multiple concrete ballast heights)
0.5
44-
0.45
- -
.
- -
- --
-0
1
0.5
2
1.5
Initial Tension
Om A Ten
5.5mATen
-
2.5
[N]
4
3.5
3
X 107
8.5ma Ton
Surge Accelerations for Radius = 9m Depth
(multiple concrete ballast heights)
=
300 m
X10
et~
II
-
---
.e
-0.5 E
1
-
--
-
--
-
0 107
0.5
I
Ten
x 107
0.5
107
---
100 m
Surge Accelerations for Radius = Sm Depth
(multiple concrete ballast heights)
62.5 m
--
0 .35 ---
+..
...-
0
-.....
E
-05s E
- -
+++++.+..-...
0.5
1
2.5
2
1.5
Initial Tension [N]
3.5m Acc
+
4m Acc
3.5
3
-
0.3 0
4
X107
4.5m Acc
Sm Acc
0
0.5
5.5m Acc
1
2.5
2
1.5
Initial Tension [N]
6m Acc
-----
6.5m
3
4
3.5
X 107
Acc
Figure 39. Water Depth Effects on Surge Acceleration RMS, 9 m Radius, 5.5 m Sig. Wave Height
62
Radius = 9 Trend Lines for Zero Tension Differences (5.5m sig wae)
Radius = 9 Trend Lines for Zero Tension Differences(10Onsig. waw)
6.5-
6.5
-
-
9 mIs
11.2 m/s
-/ -
6-
-
15 m/s
25 m/s
- ---
---
- --
- -
-
--6
9 m/s
11.2 M/s
15 M/s
25 M/s
5.5
--
S5
4 .5-
5
-
-
-
-
-
+
4.5-
4.5
4
4
1
1.2
1.4
1.6
1.8
2
Initial Pre-Tension
-
-
---
-
-
-
--
- - - -
-
2.4
2.2
3.5'
1.8
2
2.2
2.4
2.6
2.8
3
3.2
3.4
Initial Pre-Tension
x 1d
3.6
3.E
x 16
Figure 40. Wind Speed Effects on Zero Tension Difference Trend Lines
Table 13. Wind Speed Zero Tension Difference Options and Response, 9 m Radius, 10 m Sig. Wave Height
25 m/s
15 mIs
11.2 m/s
9 m/s
Ballast Tension Max RAO RMS Acc Tension Max RAO RMS Acc Tension Max RAO RMS Acc Tension Max RAO RMS Acc
0.597
0.605 19130765 59.987
0.615 22285042 15.452
0.609 27352258 8.093
3.5
23927260 11.069
0.584 19902002 88.399
0.576
0.593 23204222 22.067
0.587 28555855 8.425
4
24937999 14.022
0.558
0.565 20805737 44.523
0.573 24316746 31.483
4.5
26146426 17.209
0.568 29939903 9.477
0.542
0.548 21873182 31.825
0.555 25573570 44.7
31523794 10.314
0.55
5
27502314 20.478
0.527
0.532 23129594 27.361
0.539 26996907 59.454
0.535 33249610 10.919
29024995 23.126
5.5
0.513
0.525 28606790 68.129
0.518 24520730 25.728
0.521 35131621 11.218
6
30732693 24.426
0.501
0.505 26064711 25.945
0.511 30341199 68.36
0.507 37157131 11.225
32563491 24.516
6.5
Table 14. Wind Speed Zero Tension Difference Options and Response, 9 m Radius, 5.5 m Sig. Wave Height
11.2 mIs
9 MIS
Ballast
3.5
4
5mIs
25 mis
Tension Max RAO RMS Acc Tension Max RAO RMS Acc Tension Max RAO RMS Acc Tension Max RAO RMS Acc
0.382
6.81
0.387 11259814
0.393 14067588 11.999
0.389 18460902 43.68
15511732 17.406
0.373 11666973 7.732
0.369
0.378 14576170 9.73
0.375 19148888 35.373
16072055 13.154
4.5
16712277
11.007
0.362
19890545
24.815
0.365
15191428
8.539
0.36
12181661
8.887
0.357
5
5.5
17451169
18229722
9.814
9.032
0.35
0.34
20705673
21599200
19.476
16.598
0.353
0.342
15855610
16587148
7.786
7.305
0.349
0.339
12747798
13402250
10.003
10.914
0.346
0.336
6
6.5
19074488
19979742
8.529
8.206
0.33
0.321
22524927
23509494
14.805
13.696
0.332
0.322
17405072
18249911
7.01
6.798
0.329
0.32
14111913
14870629
11.633
12.115
0.327
0.318
63
6. 5 .
Radius =9 Trend Lines for Zero Tension Differences(1Om sig. wave)
Radius =9 Trend Lines for Zero Tension Differences (5.5m sig wave)
6.5
-
1
62.5 m
62.5 m
- -100 m
6
- - -
-
- - - -
T
- - - - ,-- -
--
,-.
100 m
6
200 m 300 m
-
a
0
0
- - -
- -
- - - -
-
200 m
- - - -
300 m
5.5K
m
-
---
5.5-
---
-
-
--
5
4.5-----
4.5 F
-----------
-------
-
4
3.5
1.
II
.
1.9
i
2
i
2.1
A
2.2
Initial Pre-Tension
2.3
2.4
2.E
1 3.5 2.6
x 107
2.8
3
3.2
3.4
3.6
Initial Pre-Tension
3.8
4
x 107
Figure 41. Water Depth Effects on Zero Tension Difference Trend Lines, 9 m Radius
Table 15. Water Depth Zero Tension Difference Options and Responses, 9 m Radius, 10 m Sig. Wave Height
300 m
100 m
200 m
1_
62.5 m
Ballast Tension Max RAO RMS Acc Tension Max RAO RMS Acc Tension Max RAO RMS Acc Tension Max RAO RMS Acc
0.594
0.755 27352258 8.093
0.615 27298918 14.693
3.725 27967863 16.542
3.5
29542070 63.449
0.573
0.727 28555855 8.425
0.593 28489064 11.844
4
31338284 47.808
3.03 29326297 19.943
4.5
33434744 26.564
2.419 30894391 21.95
0.704 29939903 9.477
0.573 29857126 10.301
0.554
5
35859490 48.988
3.704 32685814 21.626
0.687 31523794 10.314
0.555 31422289 9.415
0.537
0.539 33125992 8.866
0.521
5.5
38631811 32.969
2.982 34674482 19.408
0.673 33249610 10.919
0.507
0.663 35131621 11.218
0.525 34983349 8.542
5.178 36849522 16.381
6
41997873 59.686
6.5
45462538 51.81
5.13
39210263 13.394
0.657 37157131 11.225
0.511 36980663 8.368
0.493
Table 16. Water Depth Zero Tension Difference Options and Responses, 9 m Radius, 5.5 m Sig. Wave Height
52.5 m
100 m
200 m
300 m
Ballast Tension Max RAO RMS Acc Tension Max RAO RMS Acc Tension Max RAO RMS Acc Tension Max RAO RMS Acc
0.393 18455672 6.353
0.387
18980864 29.555
0.509 18580004 10.545
0.423 18460902 43.68
3.5
4
19782917 38.363
0.491 19295964 11.138
0.407 19148888 35.373
0.378 19142207 7.484
0.372
4.5
20651852 43.124
0.476 20066862 13.027
0.392 19890545 24.815
0.365 19882331 8.756
0.359
5
21606751 40.003
0.464 20910653 14.718
0.38 20705673 19.476
0.353 20696057 10.108
0.348
0.337
0.368 21599200 16.598
0.342 21587438 11.491
5.5
22667867 31.103
0.455 21845513 15.88
6
23775393 22.872
0.449 22811706 16.581
0.358 22524927 14.805
0.332 22511102 12.956
0.327
24949773 34.018
0.448 23829960 16.618
0.348 23509494 13.696
0.322 23493836 14.374
0.317
6.5
64
Zero Tension Difference Surge RAO for Radius = 9m Depth = 100 m 10m Sig Height
21
-
Zero Tension Difference Surge RAO for Radius = 9m Depth = 62.5 m 10m Sig Height
5
80 ,
F
RAO
Ba
RAO
Heft
4.2
20
0
C1
60
=
E
0~
3.8 t
oI
- 36
17
2.95
16
2.75
5
3.1
3.05
Initial Tension [N]
x 107
Zero Tension Diference Surge RAO for Radius = 9m Depth = 200 m 10m Sig Height
4.5
10
BaRAO
ast Haght
0
E
0
0
x 107
Zero Tension Difference Surge RAO for Radius = 9m Depth = 300 m 10m Sig Height
15
S
Bls
RAO
uh
T
I
'0
8-4
-3.4
3.05
3
2.95
2.9
Initial Tension [N]
2.85
2.8
.4
6
4E
(DE
0
6 L3.5
2.7
101
2.9
2.8
2.85
initial Tension [N]
2.75
2.95
x 107
0
2.95
2.9
2.85
2.8
Initial Tension [N]
2.75
2.7
X 107
Figure 42. Zero Tension Difference Surge RAOs and Ballast Heights based on Water Depth, 9 m Radius, 10
m Sig. Wave Height
Surge RAOs for Zero Tension Difference Platforms
Surge RAOs for Zero Tension Difference Platforms 10m Sig Height
45
70r
+
6
60k
-
+
61000
1
40
300
35
Sig Height
++
+ +
62.5
100
200
5m
1
62.5
+
01
-
100
0
200
300
.
-
50
030
-
-
-- 0-
-
-
I
6
-
*
-- -- -- --- -
40
.-
-
L&25
---
E
E
10
= 20
E
- - -
20
I
-
6 166
15
Dl 6
10
2.7
2.75
2.8
10
2.85
2.9
2.95
Initial Tension [N]
3
3.05
3.1
3.15
x 107
51
1.8
-
--
6Q6.0,
1.85
-
--
I 00
~
1
1.9
1.95
CI
- -
-
--
I
.
6660
--
-00
-
Io
I
2
2.05
Initial Tension [N]
Figure 43. Surge RAOs for Zero Tension Difference 9 m Platforms
65
0-
-I
R
1
6
1
2.1
2.15
2.2
2.2
x 10
7
Zero Tension Difference Surge RAO for Radius = 9m Wind Speed = 9 m/s
Zero Tension Difference Surge RAO for Radius =9m Wind Speed = 11.2 m/s
4.5
1
Ballast
19
oRAO
Bailast Hgt
1
18
4.8
17
4.6
16
4.4
15-
4.2
8 -
-
C/,
E
0
14-
4
12-
0
11
2.3 5
2.4
2.45
3E
0
2.5
2.55
Initial Tension [N]
2.6
2.65
l 0
6. L
2.7
2.7
100
3.5
2.95
2.9
x 10
55
0
5-
Ballast Haigt
RAO
5
0
-
4
*
0
120.
o
ii- 40 0
1
2.8
2.85
Initial Tension [N]
Zero Tension Difference Surge RAO for Radius = 9m Wind Speed = 25 m/s
5
Salast Height
RAO]
80
T
45
a,
0
E
E
0
2.75
x 107
Zero Tension Difference Surge RAO for Radius = 9m Wind Speed = 15 m/s
-
-
3.6
60
C/)
1 0
1
0
30
t
1
13
1 0
:15
Cl
M
20
60
-
0
4
E
40
OL
2.2
2.25
2.3
2.35
2.4
Initial Tension [N]
2.45
2.5
3.5
20'1.9
2.55
2
1.95
2
2.05
2.1
2.15
Initial Tension [N]
x 107
2.2
2.25
2.3
7
x 10
Figure 44. Zero Tension Difference Surge RAOs and Ballast Heights based on Wind Speed, 9 m Radius, 10 m
Sig. Wave Height
Surge RAOs for Zero Tension Difference Platforms
Surge RAOs for Zero Tension Difference Platforms
45
120-
-- 4
100-
+
9 m/s
0
0
.
11.2 m/s
15m/s
4
25 m/s
EP.
1
4- -
40k
9 m/s
11.2 m/s
15m/s
25 m/s
a
0
35-
800 30
0
+
60
.E
E
E
40
15
20
++
2
2.2
2.6
2.4
Thnsin
Initia
Initial Tension
+
[N}1
[N]
10
*
2.8
x 10
312
7
-1
20
-0
6'
- -1 ..
' 00
C4.
1.8
- - - -
2 25
L - - -- - --
7
--
-
- - --
-
-- 14
16
18
2
Initial Tension [N]
Figure 45. Wind Speed Effects on Surge RAOs for Zero Tension Difference Platforms, 9 m Radius
66
2.2
7
x 10
Appendix B:
10 m Radius
Draft relationships for Radius = 10m Wind Speed
(multiple concrete ballast heights)
9 m/s
=
Draft relationships for Radius = 1Om Wind Speed
(multiple concrete ballast heights)
X 10
1
-~
30 - - - -.
--
11.2 m/s
=
X 107
t2
0
I
20
2
10|
20 -
0
0.5
1
1.5
2
Initial Tension
3.5. A Ton
-
2.5
3
4,&
0-
0
4
7
-4.5m ATon -
Ton -
Draft relationships for Radius = 10m Wind Speed
(multiple concrete ballast heights)
40
3.5
[N]
=
-
m
Ton -
0.5
1
-
1.5
2
Initial Tension
5.mA Ton
X
3.5
.
4
107
4.5m A Ton
=
1Dm Wind Speed
(multiple concrete ballast
107
3
[N]
Gm A Ten
Draft relationships for Radius
15 m/a
2.5
E
1
heights)
25 o/s
=
X 1107
1
20 -
-
-
20
I
-- 0
1-
I
011
~
Ii
0I.5
1a
1
1.5
T1e
2
Initial Tension
2.5
3
3.5
0
4
0.5
2.5
1.5
2
Initial Tension IN]
1
X 10
[N]
3.5m draft
4m draft
5m draft
-- 4.5m draft
5.5m draft
-
3.5
3
4
107
6.5m draftj
Sm draft -
Figure 46. Wind Speed and Draft Effects, 10 m Radius, 10 m Tension Difference
Draft relationships for Radius - 10m Depth = 62.5
(multiple concrete ballast heights)
Draft relationships for Radius - 10m Depth = 100 m
(multiple concrete ballast heights)
m
X 10,
4C
10
4
-.-
101
0
0.5
1
1
2.5
20
3
3.5
10
4
0
2
1.5
Initial Tension
1
0.5
X 10
[N]
3~-=.5mJA Ton
-
-
-
----
0
E
---1
-2
1.5
2
Initial Tension
4m A Ton
Draft relationships for Radius - 10m Depth
(multiple concrete ballast heights)
30
--
20-
E
10
1
30 - - - -
*
20 - - - -22.5-3
X
1
-
4.5mA Tenl
200 m
5tmATon
I
0
6m A Ten -
30 -- - - -
- - --
2
-
-
L- - -
3.5
3
4
07
-2
G,5m A Ton I
Draft relationships for Radius = 10m Depth
(multiple concrete ballast heights)
X le7
- - -
A Ton
-55m
2.5
[N]
300 m
X
- - --
10
-0-- -
-
E
- - - -
E
10 0
0.5
1
1.5
2
Initial Tension
3.5m draft
-
2.5
3
3.5
4
2
10
0
0.5
X 10
[N]
4m draft
----
4.5m draft
-
5m draft
-
----
5.5m draft
1
2
Initial Tension
1.5
6m draft
-
2.5
3
[N]
6.5m draft
Figure 47. Water Depth and Draft Effects, 10 m Radius, 10 m Tension Difference
67
3.5
4
X 107
1
0
RAO 1 for Radius = 10m Wind Speed = 9 m/s
(multiple concrete ballast heights)
100
x
|i~
RAO 1 for Radius = 10m Wind Speed = 11.2 m/s
(multiple concrete ballast heights)
107
E
--
-|
50 - -
0
tit
x 10 7
E
52
0
0
0.5
1
1.5
2
2.5
Initial Tension
-
I
3.Am a Ten t-
RAO 1 fbr Radius
(multeple
400
=
3
3.5
[N]
4m A Tsn
10m Wind Speed
concrete ballast
=
0
4
X
7
4,5m A Ten
--
15 m/s
123
1
0.5
2.5
3
3.5
[N]
4
x 107
*.Sm A TenI
RAO 1 fbr Radius = 10m Wind Speed = 25 m/s
(multiple concrete ballast heights)
x1 107
heights)
1.5
2
Initial Tension
ImA Ten
A Ten
5m A Ten -5.'m
-
*2*
0
S107
0.5
150
I
I
.2
100
E
0
26'|
-0.5 2
50
o01
0
0.5
1
1.5
2
Initial Tension
[N]
3.5m RAO
*
-
2.5
3
3.5
u
4
0.5
0
1
X 107
4m RAO
--
4.5m RAO
5m
-
RAO
6m
5.5m RAO
.
1.5
2
2.5
Initial Tension [N]
RAO
3.5
3
.1
4
7
6.5m RAO
-
Figure 48. Wind Speed Effects on Surge RAO, 10 m Radius, 10 m Sig. Wave Height
RAO 1 for Radius
(multiple
100
=
10m Depth = 62.5 m
ballast heights)
concrete
RAO 1 for Radius = 1im Depth = 100 m
(multiple concrete ballast heights)
x2 107
10
I
50 ----
*
--
-
-
-
X 107
-
-0
0
-
FE
0
F
0
.
-2
01
0
0.5
1
1.5
2
2.5
Initial Tension [N]
SmA Ten ---
I -.
RAO 1 for Radius
(multiple
1010
=
ballest
3.5
C
4
0
0.5
1
7
Arn
10m Depth
concrete
3
Ten
=
-
A Tn -5.5m
4.5mA Ten -om
200 m
Om A Tim -
A Ten
RAO 1 for Radius
x2 10I
heights)
2
1.5
Initial Tension
603
=
40 - - - -1
-
-
2
3.5
2
6. 3 m, Ten
10m Depth
=
300 m
x1
5
0
-
-0
- - -
4
107
ballast heights)
(multiple cnerste
so
2.5
[N]
- 41
- -
20
---
-
-
5
E
E
0
S12
1
1
2
253
I
3.5m RAO
-
4m RAO
0
4 25
Initial Tension [N]
0
0.5
x 107
*
4.5m RAO
^
5m
RAO
-
5.5m RAO
1
2.5
1.5
2
Initial Tension [N]
6m RAO
--
3
6.5m RA0
Figure 49. Water Depth Effects on Surge RAOs, 10 m Radius, 10 m Sig. Wave Height
68
3.5
-10
4
107
RAO 1 tor Radius = 10m Wind Speed = 9 m/s
(multiple concrete ballast heights)
100 - - - -
1--
- - - - - - - - - - - - - - --
5
- - -
I
00
0
L
4. -*-
so
RAO 1 for Radius = 10m Wind Speed = 11.2 m/s
(multiple concrete ballast heights)
x 10"'
x
10
0
E
0
.
.
5
1.*
+1
0
0
0.5
1.5
2
Initial Tension
1
5mA
I
2.5
3
5.m5A
-
4.5lAT, -SmATn
RAO I for Radius = 1im Wind Speed = 15 rn/s
(multiple concrete ballast heights)
$uu
Initial Tension [N]
x 10
4mA Ton --
Ton --
4
3.5
[N]
x 107
heights)
150 - - - 200-
---
100
0
0
1--
- - - - - - - - - - -
-
0,
15
-10
- - -
-
- - -
i!1
I
-OATeen
S A TAn
6.5m A Till I
Grin A T- RAO 1 for Radius = 10m Wind Speed = 25 m/s
(multiple concrete ballast
Ton
200
2
x 10
2.5
1.5
2
Initial Tension [N]
1
0.5
-
3.5m RAO
I
+
3
4m RAO
n
4
3.5
7
Sm RAO
4.5m RAO
-
-
- -
- - - --
i
5
I
0---
----
- -
1100 -- - - - - - - -
0.5
0
6m
5.5m RAO
-
RAO -6.5m
3.5
3
2.5
2
1.5
Initial Tension [N]
1
4
107
5
RAOI
Figure 50. Wind Speed Effects on Surge RAOs, 10 m Radius, 5.5 m Sig. Wave Height
RAO I for Radius = 10m Depth = 62.5 m
(multiple concrete ballast heights)
X
10
I
5
01
0
RAO 1 for Radius = 1Oin Depth = 100 m
(multiple concrete ballast heights)
200
x 107
0
0-
I
107
1
0.5
2.5
1.5
2
Initial Tension [N]
I-=-3~inATn
3.5m A Ton
-
RAO 1 for Radius
3
-k.
1
T~.lt
-
4.5m,& Ton -
I
- - -,
- --
S
01
0
0.5
1
10
2.5
2
1.5
Initial Tens ion [N]
wt4Tefl -n-~Arns4T.n
5.5m Ton
5m a Ton -
T.. -
3
X 107
X
107
6.5mA-T7
X 107
I
II
II
4
3.5
RAO 1 for Radius = 10m Depth = 300 m
(multiple concrete ballast heights)
=
(multiple concrete ballast heights)
100
- -
100 -
4
3.5
X
-- 4plAT.n
4m A Ton 10m Depth = 200 m
I
5
/
I
\
50
0
0
0.5
1
2.5
1.5
2
Initial Tension [N]
3.5m RAO
+
4m RAO
3
0
3.5
1
0
4
0.5
X 10
--
4.5m RAO
Sm RAO
-
5.5m RAO
1
1.5
2.5
[N]
6.Sm RAO
-6.5m
RAO
2
Initial Tension
Sm
Sm FtAO
RAO
----
3
Figure 51. Water Depth Effects on Surge RAOs, 10 m Radius, 5.5 m Sig. Wave Height
69
3.5
4
x17
S
0.65
e;
Surge Accelerations for Radius = 10m Wind Speed
(multiple concrete ballast heights)
=
9 m/s
I~L
0.551
--
1
1.5
2
Initial Tension
3.5mATn
o-
2.5
3
-0.55
4mATTon --
- -
-
-
i-
0 1
0.55
-0.505
0 .5
--
- -- -- -.---
-- -
0.45
5m.
4.5mA Ten =
0
--
-
0.5
OmATon
3.5m Acc
3
I
'4-
0
=
25 m/s
X 107
0.6-
0.5
T - --
0.55-
0
-- --E
0.5-
-05-
U.4:0- I
4
35
0.5
1
1.5
2
Initial Tension
x 10
4m Acc
*
x 10
0.65,
5 7
0.
--
2
25
1.5
Initial Tension [N]
-15
4
3.5
I
4
.*
1
- -1
-
8.5m&Toi
---
0.5
3
Surge Accelerations for Radius = 10m Wind Speed
(multiple concrete ballast heights)
x 10
r
-
- -
1.5
2
2.5
Initial Tension [N]
1
j.5m A Ton
-
Ten
.5 5
0
-0
-
E
-
- -
15 m/s
0.5
0.45
x 10,
5
-5
X 107
I
0.6 --
0.6--
'I-
3.5
[N]
Surge Accelerations for Radius = 10m Wind Speed
(multiple concrete ballast heights)
*~
11.2 m/s
----
0.51
0.5
=
0.55
0.5
0.6k
D.1 '
Surge Accelerations for Radius = 10m Wind Speed
(multiple concrete ballast heights)
( 10,
4.5m Acc
5m Acc
-
5.5m Acc
6m Acc
-
2.5
3
3.5
[N]
4
S107
6.5m Acc
Figure 52. Wind Speed Effects on Surge Acceleration RMS, 10 m Radius, 10 m Sig. Wave Height
Surge Accelerations for Radius = 1Om Depth
(multiple concrete ballast heights)
=
62.5 m
Surge Accelerations for Radius = 10m Depth
(multiple concrete ballast heights)
x 10
=
100 m
X
,1
0
4
0.8 - -
- -
0.6--
----
- - -
- - -
-
107
- -0
14
01
0.5
1
1.5
2
2.5
Initial Tension [N]
3.mA Ton ----
0.65
I
4m
A Tn
3
.
--
4.5mA Ten =
0
0.5
5m
.
. 10
t
-10
1.5
2
Initial Tension
-
3.5m Acc
2.5
[N]
.
4m Acc
'
3
'
3.5
4
2
6.5in, Ten 1
=
300 m
x 106
-5
0.5
1
3
x 10
Surge Accelerations for Radius = 10m Depth
(multiple concrete ballast heights)
0.5 - -
'Is
Sm A Ton -
2.5
[N]
- -
*
0.5
1.5
2
Initial Tension
Or-
-
0.55k
U.10' )
1
aTen
0 .7
5
*
-...-...-J.
Ten -5.m
200 m
.
0.6
0.4
3.5
x 107
Surge Accelerations for Radius = 10m Depth
(multiple concrete ballast heights)
.
0
Owogd
.,Ess
3.5
'
-5
1
5?
1
5
-
- - -
-
-
5
0.4L
0
4
S10
4.5m Acc
- --
5m Acc
-
S
02
0.5
5.5m Acc
1
1.5
2
2.t
Initial Tension [N]
6m Acc ---
1
3L
1
4-10
3.t
X
10
6.5m Acc
Figure 53. Water Depth Effects on Surge Acceleration RMS, 10 m Radius, 10 m Sig. Wave Height
70
Surge Accelerations for Radius = 10m Wind Speed
(multiple concrete ballast heights)
9 m/s
=
Surge Accelerations for Radius = 10m Wind Speed
(multiple concrete ballast heights)
x 10,
2
0.45
0
0.4
---
0.5
2
2.5
1.5
Initial Tension [N]
1
3
I
05
-
-
4.5m
0.3
4 1
=
A Ten
5m&
ATen
-
5.5m A Ten
---
- -
0.3 0
1
0.5
-
- - -
- - '''
---
- -
-
.Sm A
-
0.5
4
x 107
TenI
Surge Accelerations for Radius = 10m Wind Speed
(multiple concrete ballast heights)
15 m/s
x 106
Gma Ten
3.5
3
2.5
2
1.5
Initial Tension [N]
1
0.5
=
25 m/s
x 10
15
I
- -- - - - - - - ---
-
- -
-o0 .in
X 107
15
1.4 - -
- - -
0.35
3.5
4m,& Ton ---
-
o.n
- - - - - - -
0.5
- - - - - - -
*
'
Surge Accelerations for Radius = 10m Wind Speed
(multiple concrete ballast heights)
0.45 -
x 107
04
-
--- -
0.3 1
11.2 m/s
--....-
.
.-
I
- - - - - - -
=
.
2
1.5
Initial Tension
-
S
-
-
- -- -
I 0.35-
-
-
-
-
O.5
1
1
4m Acc -
4.5m Acc
-
Sm Acc
L
I
5
-0
4
3.5
3
2.5
6.5m
-.
-'
--
-
Initial Tension [N]
6m Acc
5.5m Acc
-----
-- *-
2
1.5
7
-1
- - -
-
- - - - -
-
0.3 0
1-
4
3.5
[N]
3.5m Acc
0.4
5
-
- - - - -- -- -- - - ---
0 .45 - - - -
- -
3
2.5
- 10 E
X17
Acc
Figure 54. Wind Speed Effects on Surge Acceleration RMS, 10 m Radius, 5.5 m Sig. Wave Height
Surge Accelerations for Radius = 10m Depth
(multiple concrete ballast heights)
=
62.5 m
x
Surge Accelerations for Radius = 10m Depth
(multiple concrete ballast heights)
10,
(4-
F;
0.45
1
L-
1.5
2
2.5
3
Initial Tension [NJ
5M A Ton -
- - - - - - - - - - - - -
35
4
x
4m A Ten -~-
Surge Accelerations for Radius = 10m Depth
(multiple concrete ballast heights)
0.4 5 -
I
I
I
0
-
5mt
0.
I
-jT
0.5
1
107
4.5m A Ton~
=
10
I
0.35
I
OI5
x 107
0.5
I
I
100 m
-
0.4
- -
- - -
.
I -- - - -
=
0.5
1
2
5.5m ATon
Ton -
6m &Ton =~-
3
2.5
2
1.5
Initial Tension
X107
4
107
6,5m &TonI
Surge Accelerations for Radius = 10m Depth
(multiple concrete ballast heights)
200 m
3.5
N)
=
300 m
C 107
- 0.5
- - - - - - --
I
-
I
-I-,
-
I
0.35
.-.-..
-
0.3
0.5
1
-1.5 E
'n
.. .. T-
2
2.5
1.5
Initial Tension [N]
----
- -
- -
--..
-+-
3.5m Ace
+
3
0.31
0
4
3.5
0.5
4m Acc
--
+
4.5m Acc
Sm Acc
-+
1
1.5
2
3
2.5
Initial Tension [M
x17
5.5m Acc
6m Acc
-
6.5m Acc
3.5
4
X 107
I
Figure 55. Water Depth Effects on Surge Acceleration RMS, 10 m Radius, 5.5 m Sig. Wave Height
71
Radius = 10 Trend Lines for Zero Tension Differences(10m sig. wave)
- -9
S-
6-
--
-
Radius = 10 Trend Lines for Zero Tension Differences (5.5m sig wave)
M/S
11.2 mIs
1mIs
-
6
-- -
25 m/s
1
5.5-
5.5
5-
5
9 mIs
11.2 m/s
- - - 15 M/S
-- -25 m/s
- -_-- - - - -
-
~ ~-7
-
- -
- -
4.5-
- -- ----- -- -- ---
0
0 4.5
4
3.51
2
- - - -
4
2.2
2.4
2.6
2.8
3
3.2
3.4
3.6
4
3.8
Initial Pre-Tension
x1
1.2
1.4
1.6
1.8
2
2.2
Initial Pre-Tension
7
2..
x
10
Figure 56. Wind Speed Effects on Zero Tension Difference Trend Lines, 10 m Radius
Table 17. Wind Speed Effects on Zero Tension Difference Options and Responses, 10 m Radius, 10 m Sig.
Wave Height
Ballast
3.5
4
4.5
5
5.5
6
6.5
9 MIS
Tension Max RAO RMS Acc
25495054 15.708
0.607
26464225 24.209
0.585
27636748 38.988
0.565
28999590 63.434
0.548
30578210 86.831
0.533
32375233 94.571
0.518
34338539 98.663
0.505
11.2 mis
Tension Max RAO RMS Acc
28337370 10.042
0.613
29459706 12.929
0.59
30778788 16.462
0.57
32332921 20.256
0.552
34096346 23.761
0.537
36050147 26.372
0.522
38204549 27.266
0.509
15 M/s
Tension Max RAO RMS Acc
24123017 22.963
0.604
25010350 48.431
0.582
26088543 176.739
0.563
27380633 98.917
0.546
28883868 58.604
0.53
30571883 47.588
0.517
32467861 45.543
0.504
25 m/s
Tension Max RAO RMS Acc
21449270 100.35
0.597
22195552 48.177
0.576
23130305 26.942
0.557
24263535 20.524
0.541
25592447 17.795
0.526
27101566 16.604
0.512
28834842 16.412
0.5
Table 18. Wind Speed Effects on Zero Tension Difference Options and Responses, 10 m Radius, 5.5 m Sig.
wave Hei nt
9 m/s
Ballast
3.5
4
4.5
5
5.5
6
6.5
11.2 mIs
15 mIs
25 m/s
Tension Max RAO RMS Acc Tension Max RAO RMS Acc Tension Max RAO RMS Acc Tension Max RAO RMS Acc
15806903
16355923
17004531
17747560
18579390
19489584
20468672
10.813
8.806
7.706
7.038
6.649
7.046
7.351
0.386
0.372
0.359
0.348
0.338
0.328
0.319
18328484
18967551
19705769
20536961
21452441
22446014
23513776
19.859
14.076
11.398
9.922
9.023
8.448
8.073
0.39
0.375
0.362
0.35
0.34
0.33
0.321
72
14566265
15060673
15658193
16355128
17144707
18018282
18966169
8.756
7.38
6.797
7.601
8.297
8.865
9.264
0.384
0.37
0.358
0.347
0.337
0.327
0.318
12138807
12543334
13053898
13667231
14371268
15158931
16021945
7.763
9.765
12.019
14.361
16.586
18.405
19.647
0.38
0.366
0.354
0.344
0.334
0.325
0.317
I
Radius =10 Trend Lines for Zero Tension Differences(10m sig. wave)
Radius =10 Trend Lines for Zero Tension Differences (5.5m sig wave)
7
8
-62.5
m
6
-
200 m
-- ---------- - ---- - - --- -- - -------- -
.5
---
e
- - -- -
5
Ca
l4
--------
-
-------
------
625
100
-200
--- - 300
6
- --
- - - - - -
m_
m
m
m-
4
3 --- -- - - --
2
12
2. 5
--- ---
-- - - - - - - - -
---
- - - -
------------------------
3
3.5
Initial Pre-Tension
2
1L_
I
4
1.6
x 107
1.8
2
2.4
2.2
Initial Pre-Tension
2.6
2.8
3
x 10
Figure 57. Water Depth Effects on Zero Tension Difference Trend Lines
Table 19. Water Depth Effects on Zero Tension Difference
Wave Hei ht
100 m
62.5 m
Tension Max RAO RMS Acc Tension Max RAO RMS Acc
Ballast
0.729
2.737 28870580 59.899
30230179 63.825
3.5
0.7
2.929 30122988 76.782
31871377 70.391
4
0.676
2.374 31637234 53.83
33836677 52.319
4.5
0.657
1.891 33389437 46.247
36151643 28.859
5
0.641
2.552 35381508 48.468
38862092 40.814
5.5
0.629
2.568 37617959 63.196
6
44088055 29.354
0.621
4.246 40073416 106.021
61855342 36.644
6.5
Table 20. Water Depth Effects on Zero Tension Difference
Wave Hei ht
100 m
62.5 m
Tension Max RAO RMS Acc Tension Max RAO RMS Acc
Ballast
0.415
0.481 18437756 21.205
18810620 22.358
3.5
0.399
0.462 19101464 36.319
4
19554942 17.248
0.385
0.447 19868207 64.776
4.5
20420521 15.32
0.373
0.435 20731716 82.062
21401332 14.873
5
0.362
0.425 21687071 69.964
22489908 15.53
5.5
0.352
0.416 22729627 61.561
6
23677566 17.492
0.342
0.41
23844408 60.366
24945182 21.723
6.5
73
Options and Responses, 10 m Radius, 10 m Sig.
200 m
Tension Max RAO RMS Acc
0.613
28337370 10.042
0.59
29459706 12.929
0.57
30778788 16.462
0.552
32332921 20.256
0.537
34096346 23.761
0.522
36050147 26.372
0.509
38204549 27.266
300 m
Tension Max RAO RMS Acc
0.594
28290813 10.437
0.573
29402801 8.614
0.554
30707697 7.587
0.537
32241008 6.978
0.521
33987476 6.604
0.507
35912615 6.374
0.494
38045468 6.253
Options and Responses, 10 m Radius, 5.5 m Sig.
200 m
Tension Max RAO RMS Acc
0.39
18328484 19.859
0.375
18967551 14.076
0.362
19705769 11.398
0.35
20536961 9.922
0.34
21452441 9.023
0.33
22446014 8.448
0.321
23513776 8.073
300 m
Tension Max RAO RMS Acc
0.384
18324042 9.361
0.37
18961703 12.364
0.357
19698635 16.431
0.346
20528008 21.952
0.335
21441723 29.291
0.326
22432646 38.691
0.317
23498091 49.505
Zero Tension Difference Surge RAO for Radius =10m Depth =62.5 mn 10m
Sig Height
50
55
0
1
1
80
- 4. 8
I
E
50
E3
6
75
4. 4
0 70
3
3.2
3.1
-3.4
3.5
3.4
-o
3.6
2.9
2.95
-
11-54
b1
2.8
2.85
1
0
2.9
2.95
1
1
0
5
.5
9
0
1
10 1
1
|
3.15
3.2
3.25
3C)
3_5
12.8
3.5
x
a
4
7
|
|
1o
2
1
3
3.05 3.1
Initial Tension [N]
..5A
Ballast H;ig7M
0
8
1
3.4
3.35
3.3
x 10
RAO
E)
15
0
3.25
--
0
4
3.2
1
10
-f i
.0
!_20
E
3.1
3.15
3.05
Initial Tension [N]
3
1
5
0
- 3.8
r
[:
01
4
Zero Tension Difference Surge RAO for Radius = 10m Depth = 300 in 10m Sig Height
6
25~
4.2 A
0
--
452.85
3.6
Zero Tension Difference Surge RAO for Radius = 10m Depth = 200 m 10m Sig Height
1
4.4 .0
X 107
25
4.6
1
1
50-
30.6
3.3
Initial Tension [N]
1
4.8
-0
55 -
3
o[
-
-
1~
1
1
X
u
-3. 8
40
4
SE 0
1
45
-
65
-4. 22
4
1
Bailast Fieiglt
0A
Ballast Heigh
RAO
70
0
Zero Tension Difference Surge RAO for Radius = 10m Depth = 100 m 10m Sig Height
2.85
2.9
2.95
107
3
3.05
Initial Tension [N]
3.1
3.15
3
3.25
3.2
x
7
10
Figure 58. Water Depth Effects on Zero Tension Difference Surge RAOs and Ballast Heights, 10 m Radius,
10 m Sig. Wave Height
Surge RAOs for Zero Tension Difference Platforms 5m Sig Height
Surge RAOs for Zero Tension Difference Platforms 1in Sig Height
90r
,-- ---- -- -- -- ------ - ----- --- - --- - ,
62.5
100
801-
-
- 10+
---
q- -""
70-
+
C0
------
+
- -, -
9n0 r
70 -
-- --
80
200
300
- - -
- ,
--
,
-
- ----- r
+
62.5
100
0
200
300
OO0----
So
-- - 1--
-
+
----
-
""100
ii-
1' 0
- -- -- - 1 - 01I- -
60-
0
0
-T-- -
50-
-
e
60
-
u) 40E
E
30
0
+
-
-- - --
50
----+ ---
W4 440
-
E---
E
-
-- - - - - -
0
-
- -- 0 0
3
- - - -
10
+
20 - -+-++-
-
.
- -
01
2.9
3
- -
--40
+
- - ---
- -- *----
,
--
0
-s-
-
-
7
oo ooo- ooo
0880 0 I
-_00 .poo
I
00
0
I
- - - - I
_0oo
++.+.++
O'
2.8
--1
1
...0-
10
. . ..
-
- --
---0
.+009
- 0 *00000
I~
- - 0 1- - -
--
3.1
3.2
3.3
Initial Tension [N]
3.4
3.5
1.8
3.6
x 107
11
1.9
1
2.1
2.2
Initial Tension [N]
2.3
2.4
Figure 59. Surge RAOs for Zero Tension Difference Platforms based on Water Depth, 10 m Radius
74
2.5
x 10
Zero Tension Difference Surge RAO for Radius = 10m Wind Speed = 11.2 m/s
1
5.
Zero Tension Difference Surge RAO for Radius = 10m Wind Speed = 9 m/s
I
o
o
Bouts fgm
RAO
FkghM
RAOBallast
80
20
4 5 .) 0
0
0
2.6
2.65
1
4
2.9
2.8
2.85
2.75
Initial Tension [N]
2.7
wI
2.95
o*
3.05
x 107
3
Zero Tension Difference Surge RAO for Radius = 10m Wind Speed = 15 m/s
4
o
15-
o
in
2.55
E
*
I
oII
C X
M
0
20
0
3.25
3.2
3.15
3.1
3.05
3
Initial Tension [N]
2.95
2.9
2.85
2.8
x 1
Zero Tension Difference Surge RAO for Radius = 10m Wind Speed = 25 m/s
(3
i;n.
5
6
o
200
5.5
S150
5
last Height
AOBal
5
100
--
Bals Ho
0
1
0
E 100
4.52
50
4
-1- 00
4
50
2.4
2.5
2.45
2.7
2.65
26
Initial Tension [N]
2.55
2.75
2.8
2.85
u2.1
2.9
x 107
0000
2.5
2.6
2.4
Initial Tension [N]
2.3
2.2
I~~ 600
~oo~~o
o000
ooo
o
I
2.7
x
0
Figure 60. Wind Speed Effects on Zero Tension Surge RAOs and Ballast Heights, 10 m Radius, 10 m Sig.
Wave Height
Surge RAOs for Zero Tension Difference Platforms
250
-:---------
T -- - -,7--
r
- +
T-
a
200
+
Surge RAOs for Zero Tension Difference Platforms
-1
15sm
25 m/s
-
- - -
- -
-
+
0
.-
18
++
.
1 *0
-
-
-
-
o
-
0
-
+
9 m/s
11.2 m/s
1
/
15mr/s
25 m/s
0
~16
0
150-
- -
20
9 m/s
11.2 mis
0
.+
E 100-
-Tr-I0
-
- -
-
-T- - -
E
0.
01
50-
+I
+
0
0
0I
I+E
--
12
0
ol+
- - - --
__
1
-
-.
-
-
--
- -CI-O
I+
-
107
8
1
I
I
I cppa13CP--(-
0
I
2
2.2
2.4
2.8
2.6
Initial Tension [N]
I
3
3.4
3.2
x
10
1.2
1.4
1.6
1.8
Initial Tension [N]
2
Figure 61. Surge RAOs for Zero Tension Difference Platforms base on Wind Speed, 10 m Radius
75
2.2
2.4
Appendix B:
12 m Radius
Draft relationships for Radius - 12m Wind Speed
(multiple concrete ballast heights)
25 -- - - - - -
9
m/s
Draft relationships for Radius - 12m Wind Speed
(multiple concrete ballast heights)
X le
- - - - - - -- - - - - - -
11.2 m/s
-
X
194
-0
20
-5*.
F
20----
-- - - - - - - - -
- -
-5
-
ic
.15
E
15
10
- - --
0
* - - -
0.5
1
- - - - - - - - - - - - - -
1.5
2
2.5
Initial Tension [N]
3
- -10
3.5
15 -- - - -
.15
4
10
0
- - --
0.5
1
7
x 1d
&3.nATon -
A Ten
-4m
Draft relationships for Radius = 12m Wind Speed
(multiple concrete ballast heights)
au
L - -- -
--
A TOM
45m
15 m/s
10l
-5
20
-
-----
---- - -- -
15
0
25
Om A Ten
A Ton
3
3.5
i15
4
x
6.5m A Tan
-
Draft relationships for Radius = 12m Wind Speed
(multiple concrete ballast heights)
30.
oi
1.5
2
2.5
Initial Tension [N]
= 25 m/s
0.5
-,
20
S
5m
5m-ATen -
E
- 10
-10P
--
0
-----
15
E
-- -- 0.5-
- -- - - ------
L. -
0.5
1
1.5
2
2.5
Initial Tension [N]
3
,
4
5
1
X 107
3.5m draft
-
3.5
4m draft
4.5m draft
-
m draft
1
5
o
Initial Tension
[
[NJ
6m draft-
5.5m draft
-.
3
35
4
x0
Sm draft
Figure 62. Wind Speed Effects on Draft, 12 m Radius, 10 m Sig. Wave Height
Draft relationships for Radius = 12m Depth = 62.5 m
(multiple concrete ballast heights)
x
25-
Draft relationships for Radius = 12m Depth
(multiple concrete ballast heights)
10
20
-5
15-
0.5
1
1.5
2
2.5
Initial Tension [N]
3.mA
25 - - - -
---
Ten
4m
- - - - - -
- - - -
--- - - -
-
15 --- - - - --
0
20
E
-10
3
- ----
0.5
- -
-
-
--
-
-
-
A
-
-
4.m
10
0
-
.
A
Ton
-
5m,
1
5.5mATan
Ton -
--
3
4m draft
- -
3.5
.
1.5
2
Initial Tension
-5
+
Sm
A Ten
2.5
3
25 - - - -
-5
20--5
I
1i
- -10
10
-15
4
X 107
-
Sm
draft
- - - -
0.5
-
5.5m draft
=
300 m
1le
draft
--- +--
6.5m
0
-
1.5
2
2.5
Initial Tension [N]
6m
-15
-6.mATen
- - -- - - - - - - - ---
1
E
x 10
3
- -10
3.5
4
X
draft
Figure 63. Water Depth Effects on Draft, 12 m Radius, 10 m Sig. Wave Height
76
4
3.5
- - - - - - - - - --
- - - - - - --
0
- - -10
-
[N]
Draft relationships for Radius = 12m Depth
(multiple concrete ballast heights)
O
4.5m draft
-
-
- -T
0.5
1t0
- - - -
-
-15
4
200 m
-
1.5
2
2.5
Initial Tension [N]
3.5m draft
--
Ten
-0-- - --
- - -- - - -
1
3.5
-
15 - -
7
Draft relationships for Radius = 12m Depth
(multiple concrete ballast heights)
101
x_ 10,
- - ------ --- - --
-
20
100 m
0
2-
100
=
10
15
E
RAO 1 lbr Radius
=
12m Wind Speed
100 -
I
RAO 1 for Radius = 12m Wind Speed = 11.2 m/s
(multiple concrete ballast heights)
9 m/s
07
x
1
.
0
E
1-2I
1
0
I
0I
0
0
0.5
2
1.5
Initial
Tension
3.5mA
Ton --
1
-
0
1
1
0.5
0
4
3.5
3
2.5
[N]
1.5
initial
X 17
4mATaTn
4-
5m ATen
-
m>A Tn
RAO 1 for Radius = 12m Wind Speed = 15 m/s
(multiple concrete ballast heights)
4
x 107
[M
am A T.
5.5mATn
-
3.5
3
2.5
2
ension
6.5mA
-
T.n
RAO 1 for Radius = 12m Wind Speed = 25 m/s
(multiple concrete ballast heights)
x 107
x 10
1
200
-0.5
150 - - - --
--------
200 ---
1d7
x
0
-
-
----
-
-
=
heights)
ballast
(multiple concrete
150
100
j
------------
100----
- - - - - -
-
00
0.5
-
3.5m RAO
-
3.5
3
2.5
2
1.5
Initial Tension [N]
1
4m RAO
-
--
2
4
x 1 67
0
6m
5.5m RAO
5m RAO ---
-
4.5m RAO
-0.5
--
3
2.5
2
1.5
Initial Tension [N]
1
0.5
-
35
4
x07
6.5m RAO
RAO --
Figure 64. Wind Speed Effects on Surge RAOs, 12 m Radius, 10 Sig. Wave Height
RAO 1 for Radius
=
12m Depth
=
0.5
100
-52
1
RAO 1 for Radius = 12m Depth = 100 m
(multiple concrete ballast heights)
62.5 m
107
x
(multiple concrete ballast heights)
150
0
-
II107
x
10
0 -- - - -
-
-0--- -
-
1
-
--
C|
I
5
50-
0 -O~
*
-
-
o
E2
I
0.5
0
01
2.5
2
1.5
Initial Tension [N]
--
I-3.5mrAT
-
3
=
2
1.5
Initial Tension
1
0.5
5.5mA
5m A Ton -
Tan
-4.5mA
x2 107
2.5
A Te.
Ten
I
--
- -
I
0
|
u
E
00
0.5
2
2.5
1.5
Initial Tension [N]
1
---
3.5m RAO
-*
4m RAO
'
I
3
3.5
--
- -
-
- --
0
12
4
Sm RAO
0
0.5
1
2.5
2
1.5
Initial Tension [N]
---
5.Sm
RAO
6m
RAO
.-
3
6.5m RAO
Figure 65. Water Depth Effects on Surge RAOs, 12 m Radius, 10 Sig. Wave Height
77
5
-- 10
----
-----
*-2
e
4.Sm RAO
- - 0
-
40-
7
-*-
le
1
I
20
U
12
4
x 107
6.5n A T7
60 -- - - - - - - - - - - - - - - - - - -
50 - -
3.5
3
[N]
RAO 1 for Radius = 12m Depth = 300 m
(multiple concrete ballast heights)
200 m
heights)
100
00
4
X 10
4mt&Ton
RAO 1 for Radius = 12m Depth
(multiple concrete ballast
-2
3.5
3.5
-15
4
x 107
I
E
RAO 1 for Radius = 12m Wind Speed =
(multiple concrete ballast heights)
150 - -
- I- - - - -2
9 m/s
RAO 1 for Radius
x
- - - - - - - - - - - - -
-
- -
167
I
-
01
=
12m Wind Speed
(multiple concrete ballast
10 0 -
=
11.2 m/s
heights)
107
X
1
5
E
00
0.5
1
1.5
2
2.5
3
Initial Tension [N
S
4
1
0
0.5
1
1d
mA Ton --
-
3mTn
3.5
45m
A
m A
Ton
RAO 1 for Radius = 12m Wind Speed = 15 m/s
(multiple concrete ballast heights)
6m,& Ten -
ATn
-&5m
Ton
1.5
2
Initial Tension
2.5
3
3.5
[N]
4
X 107
6.;A Ten
RAO 1 for Radius = 12m Wind Speed = 25 m/s
(multiple concrete ballast heights)
x ()7
x lj
0J
I~1
5
---
- -
-
100 - - - - -
0
50-0
E
0E5
3.5m RAO
4m RAO
.
S .05
1
X
5m
4.5m RAO
RAO
+
1
5.5m RAO
15
..
2
6m RAO -
-
3.
25
Initial Tension [N]
7~
6..m RAO
Figure 66. Wind Speed Effects on Surge RAOs, 12 m Radius, 5.5 m Sig. Wave Height
RAO 1 for Radius = 12m Depth = 62.5 m
(multiple concrete ballast heights)
200
RAO 1 for Radius = 12m Depth = 100 m
(multiple concrete ballast heights)
-x1 107
100
x 107
0I
-
--
0
0.5
1
1.5
2
2.5
Initial Tension [N]
rATen
3-,&
RAO 1 for Radius
3
12m Depth
=
LI
LI
0
1
3.5
0
05
1
x 107
T.-4mATen
-
(multiple concrete ballast
100
-
.---
-
=
5
45mnTan
A Ten
5.5mA
-
Tn
200 m
x 1)7
heights)
1x
1.5
2
2.5
Initial Tension [N]
3
3.5
x 10
--mA Tn
m A Ten -
RAO 1 for Radius = 12m Depth = 300 m
(multiple concrete ballast heights)
80
X 107
1
1
i
50 --
010
-
-
0.5
1
- --
1.5
-0
*7
2
Initial Tension
3.5m RAO
+
2.5
[N]
4m RAO
3
-
4
x 107
4.5m RAO
0.5
40
0
20
-0.5E
0
3.5
5mRAO
-
60
0.5
5.5m RAO
1
2
2.5
1.5
Initial Tension [N]
6m RAO -
3
6.5m RAO
Figure 67. Water Depth Effects on Surge RAOs, 12 m Radius, 5.5 m Sig. Wave Height
78
4
3.5
x1
7
Surge Accelerations for Radius = 12m Wind Speed
(multiple concrete ballast heights)
--- -
0.55
--
106
x
*- - - -
- -5
0.5
1
1.5
2
2.5
Initial Tension [N]
3.5 &
-
Ton
3
3.5
X 10
&Ton -o-
4m
4.m
Surge Accelerations for Radius = 12m Wind Speed
(multiple concrete ballast heights)
=
-5
0.5
-- - ---- - -- - -1- - - - - - - - - -
A Ton -
-m
x
- --
10
-- --
0.5
-
1.
,
-
-
--
3.5m Ace
+
0.
07
4m Ace
4.5m Ace
--
6.5m,
-
5m Ace
-
Ton i
=
25 m/s
x
0. 5
- -
-
10
-
-
|
---
-0
-
.5
.5 -
[N]
4
107
1
-.
0
-- 10
-215
Initial Tension
3.5
- - -
0.5
0
.5 -
-*
05 L
3
2.5
E
[N]
0 .6 - - - -
-5
- -
.-
Surge Accelerations for Radius = 12m Wind Speed
(multiple concrete ballast heights)
0. 65
-0
0.55
Om4 Ton
A Ton
5.5m
-e--~ -- ---
2
1.5
Initial Tension
1
0.5
15 m/s
0.65
0.6
0.45 0
74
A Tn
--0
-
0.55
-1o-
0.451'0
11.2 m/s
x 10
-- -- - -- - -- -- - -- -- -.--
c,0.6
41
0.5
=
n FUS
0
oe
-1
-
Surge Accelerations for Radius = 12m Wind Speed
(multiple concrete ballast heights)
9 m/s
-- -- -- --
----- -
0.6
=
4510
----
-
-
0.5
1
5.5m Ace
-
- -
1.5
Initial
6m Ace
-
2.5
2
Tension
- -,
- - - - -
-
4
107
1
3.5
3
[N]
6.5m Ace
-
Figure 68. Wind Speed Effects on Surge Acceleration RMS, 12 m Radius, 10 m Sig. Wave Height
Surge Accelerations for Radius = 12m Depth
(multiple concrete ballast heights)
=
- - - - -- -- - -
3
--- --
2
--- - - - - - - - - -
--
- - -e
1x5 100
0.8
-0
0.7
.
)
0.5
1
100 m
x 10,
0
-5
0.5
E
-1o E
-I
1
1.t
2
Initial Tension
2.5
[N]
35m A Ten --
3
4m
A
- - - - -- -- - -- - - - - - -
-
3.5
Ton
Surge Accelerations for Radius = 12m Depth
(multiple concrete ballast heights)
S0.6-- -
=
-0.6
-10
1
1
Surge Accelerations for Radius = 12m Depth
(multiple concrete ballast heights)
62.5 m
4,
---.
0.4
15
4
X 107
5.m A Ton
5m& To-
4Am A T
10
65m&
ATenI
Om A Ton
=
300 m
x
0.65
- -o
-
4
3.5
x 10
Surge Accelerations for Radius = 12m Depth
(multiple concrete ballast heights)
200 m
x
3
2
2.5
1.5
Initial Tension [N]
1
0.5
1
-
0.6
-
-- -
-
-
-
--
-
-
106
-
0
0.55
-5
0.55
-6
- -.
- --
0.5 -- - - -- --
0
0.5
1
*
-
3.5m Ace
+
4m Ace
3
----
3.5
au
4
x 107
4.5m Ace
-
---
-- 1o
0.5
-10,
1.5
2
2.5
Initial Tension [N]
---
5m Ace
I
0.5
5.5m
Ace
1
1.5
2
2.5
Initial Tension [N]
6m Ace
6-5m
3
3.5
4
X 107
Ace
Figure 69. Water Depth Effects on Surge Acceleration RMS, 12 m Radius, 10 m Sig. Wave Height
79
Surge Accelerations for Radius = 12m Wind Speed = 9 m/s
(multiple concrete ballast heights)
Surge Accelerations
x 107
I
I
0.3
--
0
-
1
1.5
2
Initial Tension
3.6
0.4(multiple
2.5
3
3.5
[N]
X
107
a
I
Tan
----
12m Wind Speed
=
concrete ballast
2
4
0. 31
0
0.5
1
1.5
15 m/s
heights)
2
3
2.5
3.5
4
Initial Tension [N]
A Tn -56ATmn
4.5m ATen -5m
=
I
0.3
107
X
A Ton -4MA
Surge Accelerations for Radius
11.2 m/s
=
heights)
rI~
0
-
0.5
12m Wind Speed
=
.
..*.
...
T
0.35
for Radius
(multiple concrete balast
0. 4
10 7
x
6mA ton
TToo
m
Surge Accelerations for Radius
X
A
=
107
Ten
12m Wind Speed
=
25 m/s
-
(multiple concrete ballast heights)
0.4
1107
*
W)
0.35 - - - -0
0.35
.
2
0.
L- 0..-
2
2
.
25
.+.
** 1-24.
.5
E
0.3
0
0.5
1
1.5
2
Initial Tension
2.5
3
3.5
[N]
3.5m Acc
4m Acc
+
2
4
0.3
Initial Tension [N]
X 107
4.Sm Acc
5m Ac
-
5.5m Acc
107
6.5mAcc
6m Acc -.
Figure 70. Wind Speed Effects on Surge Acceleration RMS, 12 m Radius, 5.5 m Sig. Wave Height
Surge Accelerations for Radius = 12m Depth
(multiple concrete ballast heights)
0.7
62.5 m
0.5
-
Surge Accelerations for Radius = 12m Depth
(multiple concrete ballast heights)
107
x
1
0.6 -- ----- --- ---- -
I
=
If
0. 5
- - - - - - ---
-
0
0
- -
-
0.5
,
1
--
1 .5
2
2.5
Initial Tension [N]
3.m& Top ---
3
3.5
4mA Tn --
Surge Accelerations for Radius = 12m Depth
(multiple concrete ballast heights)
0
-0.5 E
U.
4
0.5
1
1.5
2
Initial Tension
A TnT 5m
4,mA Teon
x
-
- --w -*-
0.35-
200 m
=
x
0.5
7
X 10
- 10,
0.4 -
0.5 E
---
100 m
0.45-
0.4 - -
=
Gm &Too
2.5
3
X
-
10
Ton
.
Surge Accelerations for Radius = 12m Depth
(multiple concrete ballast heights)
107
4
3. 5
[N]
=
300 m
X
107
it=|
-
-----.
*-
:5
'I-
1*r
0.35
I
..
--
--
4--- -
01
-T
0.35-
-
-
-
-7
-
.
E
E
So
0. 3
310
0.5
1
1.5
2
2.5
Initial Tension [N]
3.5m Acc
+
4m Acc
3
3.5
-
.
4
107
X
4.5m Ace
1
0.31
0
0.5
1
1.5
2
2.5
Initial Tension [N]
5m Acc
5.5m Ace
6m Acc
--
3
3.5
4
X 107
6.5m Acc
Figure 71. Water Depth Effects on Surge Acceleration RMS, 12 m Radius, 5.5 m Sig. Wave Height
80
Radius = 12 Trend Lines for Zero Tension Differences(10m sig. wave)
Radius = 12 Trend Lines for Zero Tension Differences (5.5m sig wave)
6. 5.
m/s
11.2 m/s
15 m/s
25 m/s
__
6
6
55
9
-
5.5 F
9 m/s
11.2 m/s
- 15 m/s
25 m/s
----------
S4.5
.5
4)
e-
-
5
/
-I - -. .
- -. .
4.5 k
4
4
1
3. I3.5
2.6
-
2.8
3
3.2
3.4
Initial Pre-Tension
3.6
3.8
4
1.4
- -
1.6
- - -
1.8
-
-
2
-
2.2
Initial Pre-Tension
x 107
-
-
-
-
-
- -
-
--
2.6
2.4
x 1d
Figure 72. Wind Speed Effects on Zero Tension Difference Trend Lines, 12 m Radius
Table 21. Wind Speed Effects on Zero Tension Difference Options and Responses, 12 m Radius, 10 m Sig.
Wave Hei ht
Ballast
3.5
4
4.5
5
5.5
6
6.5
9 mis
Tension Max RAO RMS Acc
29631963 33.996
0.598
30353408 81.982
0.575
31238321 32.966
0.555
32392421 21.043
0.538
33735864 16.441
0.522
35363814 14.337
0.508
37186197 13.207
0.496
11.2 mIs
Tension Max RAO RMS Acc
31737758 19.332
0.603
32507819 43.713
0.579
33516974 73.627
0.559
34758429 37.781
0.541
36216568 25.667
0.525
37963734 20.927
0.511
39807487 18.356
0.498
15 mIs
Tension Max RAO RMS Acc
28615521 63.276
0.596
29291131 62.046
0.573
30126595 24.964
0.553
31227891 17.224
0.536
32514726 13.954
0.521
34046715
12.34
0.507
35847097
11.53
0.495
25 mis
Tension Max RAO RMS Acc
26610168 90.209
0.591
27162052 24.908
0.569
27936318 15.672
0.549
28888132 12.167
0.533
30109869 10.507
0.518
31519738 9.569
0.504
33209846 9.098
0.492
Table 22. Wind Speed Effects on Zero Tension Difference Options and Responses, 12 m Radius, 5.5 m Sig.
Wave Hei ht
9 mIs
11.2 mis
1I mIs
25 mis
Ballast
3.5
4
4.5
5
5.5
6
6.5
Tension Max RAO RMS Acc
29631963 7.056
0.376
30353408 7.975
0.362
31238321 10.045
0.35
32392421 12.587
0.339
33735864 15.495
0.329
35363814 18.405
0.32
37186197 21.398
0.312
Tension Max RAO RMS Acc Tension Max RAO RMS Acc
31737758
8.9
0.379 28615521 7.212
0.374
32507819 7.222
0.365 29291131 9.569
0.361
33516974 7.255
0.352 30126595 12.604
0.349
34758429 8.584
0.341
31227891 16.749
0.338
36216568
9.88
0.331
32514726 22.111
0.328
37963734 11.214
0.322 34046715 28.042
0.32
39807487 12.307
0.313 35847097 34.944
0.311
81
Tension
26610168
27162052
27936318
28888132
30109869
31519738
33209846
Max RAO RMS Acc
10.508
0.371
15.962
0.358
26.073
0.346
46.878
0.336
106.572
0.326
172.411
0.318
112.268
0.31
Radius =12 Trend Lines for Zero Tension Differences (5.5m sig wave)
Radius =12 Trend Lines for Zero Tension Differences(10m sig. wave)
6.5
62.5 m
m
200 m
300 m
-6
-100
7
5.5
J- -
5
-
- 1
- - ---
---
-
---
--
+-
-
- - - -
-
- - --- 6
62. m
.~4.5
4
-
3.5
3
-- --
- - -
- -~ - ~ - -
-
- -
200 m
300 m
- - -
3
-
- -T-
-~~~
- -- ~ ~
2.5
-- - -- -- - - - -
2
3
3.1
3.2
3.3
3.4
3.5
--
3.6
Initial Pre-Tension
3.7
- -3.8
-
--
-
- - --
-
--
2
4
3.9
..
1.
7
2
2.2
2.4
2.8
2.6
Initial Pre-Tension
3.2
3
x 10
Figure 73. Water Depth Effects on Zero Tension Difference Trend Lines, 12 m Radius
Table 23. Water Depth Effects on Zero Tension Difference Options and Responses, 12 m Radius, 10 m Sig.
Wave Hei ht
300 m
200 m
100 m
62.5 m
Ballast
3.5
4
4.5
5
5.5
6
6.5
Tension Max RAO RMS Acc
2.27
33300019 90.671
1.389
34460016 43.249
1.197
35973309 31.584
1.16
37777836 30.008
1.206
39801041 34.259
1.076
38283143 49.143
0.668
27515630 48.127
Tension Max RAO RMS Acc
0.695
32195042 20.333
0.664
33073158 13.355
0.638
34238272 10.671
0.617
35616642 10.607
0.6
37311552 11.568
0.585
39238302 12.018
0.576
42702380 10.209
Tension Max RAO RMS Acc
0.603
31737758 19.332
0.579
32507819 43.713
0.559
33516974 73.627
0.541
34758429 37.781
0.525
36216568 25.667
0.511
37963734 20.927
0.498
39807487 18.356
Tension Max RAO RMS Acc
0.586
7.516
31700066
0.564
6.216
32460653
0.545
6.814
33454453
0.528
7.993
34685500
0.513
36127130 9.201
0.499
37854375 10.298
0.487
39708668 11.326
Table 24. Water Depth Effects on Zero Tension Difference Options and Responses, 12
Wave Hei ht
200 m
_
100 m
62.5 m_
Ballast
3.5
4
4.5
5
5.5
6
6.5
Tension Max RAO RMS Acc
0.448
38.7
19504084
0.429
20092902 99.33
0.414
20780531 55.771
0.401
21613910 37.931
0.391
22634910 34.083
0.382
23747947 35.024
0.374
25035605 43.543
Tension Max RAO RMS Acc
0.399
19150834 26.014
0.384
19663557 15.711
0.37
20260619 11.952
0.358
20988457 10.157
0.348
21888824 9.239
0.338
9.59
22864354
0.33
23996847 9.908
82
Tension Max RAO RMS Acc
0.379
8.9
19042667
0.365
19532487 7.222
0.352
20102583 7.255
0.341
20799034 8.584
0.331
9.88
21663323
0.322
22598261 11.214
0.313
23685055 12.307
m Radius, 5.5 m Sig.
300 m
Tension Max RAO RMS Acc
0.374
19039334 25.89
0.361
19527856 50.168
0.348
20096601 34.063
0.338
20791429 22.199
0.328
21653795 17.335
0.319
22586658 14.697
0.31
23671018 13.264
Zero Tension Difference Surge RAO for Radius = 12m Depth = 62.5 m 10m Sig Height
aa Hg
RAO
S
Zero Tension Difference Surge RAO
12m Depth = 100 mn 10m
Sig
Height
Balast Heigt
RAO
100
6.5
80
-
0
-
0
21 60-
-
E
2
5.5
40
5
20-
0
11
E
E
for Radius =
IoI
o
8Q
ooo
8
10
5
o-
0oo o
o0
4
I
o4
45
20-
0
02.
2.8
3.4
3.2
Initial Tension [N]
3
3.6
x 1O
.
3.8
3.5
3.6
3.7
Initial Tension [N]
3
4
3.9
x 107
Zero Tension Difference Surge RAO for Radius = 12m Depth = 300 m 10m Sig Height
8
12
7
0
Balast Height
| 0
3.4
7
Zero Tension Difference Surge RAO for Radius = 12m Depth = 200 mu 10m Sig Height
00RAO
3.3
3 .2
4
3.8
RAO
BallastH
kght
0
60
6
S
_
I
1
E
1 10
1
0
2
0
0
0|
C)0
0
b
0
40
52
P10
~~
11 0 1
4
1
0
C)
8
C
20
0
*
00
00 0
01
o
*
3.1
3.2
3.3
3.4
3.6
3.5
Initial Tension [N]
3.7
3.8
x
3.2
3.1
3.9
107
Surge RAOs for Zero Tension Difference Platforms 1n Sig Height
120
100
3.5
3.6
3.4
Initial Tension [N]
3.3
3.7
3
2
3.9
3.8
x 10
Surge RAOs for Zero Tension Difference Platforms 5m Sig Height
100
L
62.5
100
200
300,
+
o
0
*
90
--
-
+
4
80
-
62.5
100
-200
. 300
70
80
0+
++
0
60
U,
50
+
60
+
-
U,
- - - - -++
E
:3
+
0
E
E
0+I
- -
40
-
1,+++
-*
-.
- -
40
-+
- -- -
+
~ ~~
-
-
+
-
-
-
-
-
-
-
+ +
*r1
20
0-
- -T
-
-
1
+ +
-- - -, - - - -L
30
-
20
-
++
.1 +
10
0'2.6
2.8
3
3.2
3.4
Initial Tension [N]
3.6
3.8
O'
4
1.9
x 107
I
2
I
2.1
I
I
2.2
2.3
Initial Tension [N]
2.4
2.5
2.6
x 1o
Figure 74. Surge RAOs for Zero Tension Difference Platforms based on Water Depth, 12 m Radius
83
Zero Tension Difference Surge RAO for Radius = 12m Wind Speed = 9 m/s
Zero Tension Difference Surge RAO for Radius = 12m Wind Speed = 11.2 m/s
7
80
.
10
o
.
RAOf
RAOBailast-Height
31
1
- I
6
60
0
T
0
t
|
I
o I
o
50
-
LM 40
5
E
DE
0
0
o
|
o
3
52
1
1
io
0
1
I
1
I
e
x
4c
4 e oo 9
0
|
2.9
I
3.1
?01
|1
|
3.3
3.2
3.4
3.5
3.6
Initial Tension [N]
Zero Tension Difference Surge RAO for Radius
=
3.3
3.2
3.1
3.7
X107
3.6
3.5
3.4
3.7
3.8
Initial Tension [N]
12m Wind Speed = 15 m/s
3.9
x 107
Zero Tension Difference Surge RAO for Radius = 12m Wind Speed = 25 m/s
3M0
10(
.10
1
Salast Haigit
200 k
0
011
5.5
M
50
2
Eo
(DE
100k
4
0o
9
.0
2.9
3.2
I
999
909699909
oo o"P9
o 0o
3.1
0
I
0
99
0
2.8
8
3.3
0o
0
3.4
3.5
Initial Tension [N]
3.6
2.6
2.9
2.8
2.7
3.1
3
x 10
Surge RAOs for Zero Tension Difference Platforms
Surge RAOs for Zero Tension Difference Platforms
180-
250-
+
9 m/s
11.2 m/s
15 m/s
25 m/s
0
200-
140-
+
120-
-
0
+
0
15 m/s
+
25 m/s
-1 -1 -
100 -
---- ---- ----
9 m/s
11.2 m/s
160-
0 150
--- ---- ---
3.4
3.3
3.2
Initial Tension [N]
x 107
T
7
80
Eo
E
oo
=3 100E
60
50
-
40
-
-1
--I
4-
-
-
-1---
4
---
I---
C;'P0100
OCPO
20
---
I-
C6
EM
0C
2.6
2.8
3
3.2
3.4
Initial Tension [N]
3.6
3.8
1.4
4
1.5
1.6
1.7
1.8
1.9
2
2.1
2.2
Initial Tension [N]
x 107
Figure 75. Surge RAOs for Zero Tension Difference Platforms base on Water Depth, 12 m Radius
84
2.3
2.4
x 10
7
References
1
Faltinsen, 0. M. Sea Loads on Ships and Offshore Structures. Cambridge, UK.
Cambridge University Press. 1999.
2
Jonkman, J. M., Buhl, M. L. FAST User Guide. Golden Colorado. National Renewable
Energy Laboratory. 2005.
3
Jonkman, L. M. NRELOffshrBsline5MWUpdatedControlsDocumentation. Golden,
CO. National Renewable Energy Laboratory. March 13, 2007.
4
Lewis, E. V., Editor. Principles of Naval Architecture, Second Revision, Volume III
Motions in Waves and Controllability. Jersey City, NJ. The Society of Naval Architects
and Marine Engineers. 1989.
5
Manwell, J. F., McGowan, J. G., and Rogers, A. L. Wind Energy Explained: Theory,
Design and Application. University of Massachusetts, Amherst, USA. John Wiley &
Sons Ltd. 2002.
6
Newman, J. N. Marine Hydrodynamics. Cambridge, MA. The MIT Press. 1977.
7
Sclavounos, P. D. 13.022 Surface Waves and Their Interaction with Floating Bodies.
Lecture Notes. Cambridge, MA. Massachusetts Institute of Technology.
8
WAMIT@ User Guide. Cambridge, MA. WAMIT, Inc. and MIT. 1998.
9
Wayman, E. Coupled Dynamics and Economic Analysis of Floating Wind Turbine
Systems. Cambridge, MA. Massachusetts Institute of Technology. 2006.
85