Optimal Mooring Pattern for a Semi-Submersible FOWT in a Typhoon Environment

Abstract

The scarcity of suitable shallow waters for fixed-bottom offshore wind turbines has prompted developers to explore deeper waters, albeit with caution due to the significant capital expenditure (CAPEX) associated with Floating Offshore Wind Turbines (FOWTs). A major cost component in FOWTs is the mooring system, a concern exacerbated in regions with the presence of typhoons, necessitating a more robust and therefore expensive 3 × 3 mooring solution compared to 3 × 1 in areas such as the North Sea. This study tried to propose a 3 × 2 mooring arrangement tailored for FOWTs in the typhoon region, offering a potential cost reduction of up to one-third compared to the original 3 × 3 configuration.
To achieve cost savings, an in-depth analysis of spreading angles from 10° to the widest angle of 126° is performed using the pre-tension-diameter vs offset-tension 3D response surfaces technique. The research reveals that, theoretically, a 60° mooring angle minimizes floater offset with the least tension. However, the discrepancy in safety factors between intact and damaged conditions makes grouped mooring a more cost-effective choice. Utilizing the American Bureau of Shipping (ABS) safety factor, a 10° spread angle mooring system’s chain cost emerges as roughly one-tenth cheaper than alternative configurations.
Additionally, the study explores an innovative V-Share mooring [1], wherein a single pile anchor connects to two different columns via two mooring lines. Depending on the anchoring conditions, it can be the most cost-effective.
In conclusion, a 3 × 2 mooring pattern for a 15MW semi-submersible FOWT in typhoon regions might be theoretically achieved on paper. However, it may not be practically achieved, if the size limit of the manufactured chain is considered.

Full text

1 © 2023 by ASME
Proceedings of the ASME 2024 43rd International
Conference on Ocean, Offshore and Arctic Engineering
OMAE2024
June 9-14, 2024, Singapore
OMAE2024-122874
OPTIMAL MOORING PATTERN FOR A SEMI-SUBMERSIBLE FOWT IN A TYPHOON ENVIRONMENT
Glib Ivanov
National Taiwan University
Taipei, Taiwan
Yongyan Wu
Aker Solutions
Houston, Texas, USA
DongHui Chen
Genesis Engineering
Houston, Texas, USA
Zhao-Yu Lai
National Taiwan University
Taipei, Taiwan
Jui-Chen Chen
National Taiwan University
Taipei, Taiwan
Nikolai Gladkov
Google
New Taipei, Taiwan
Kai-Tung Ma
National Taiwan University
Taipei, Taiwan
ABSTRACT
The scarcity of suitable shallow waters for fixed-bottom
offshore wind turbines has prompted developers to explore
deeper waters, albeit with caution due to the significant capital
expenditure (CAPEX) associated with Floating Offshore Wind
Turbines (FOWTs). A major cost component in FOWTs is the
mooring system, a concern exacerbated in regions with the
presence of typhoons, necessitating a more robust and therefore
expensive 3x3 mooring solution compared to 3x1 in areas such
as the North Sea. This study tried to propose a 3x2 mooring
arrangement tailored for FOWTs in the typhoon region, offering
a potential cost reduction of up to one-third compared to the
original 3x3 configuration.
To achieve cost savings, an in-depth analysis of spreading
angles from 10° to the widest angle of 126° is performed using
the pre-tension-diameter vs offset-tension 3D response surfaces
technique. The research reveals that, theoretically, a 60°
mooring angle minimizes floater offset with the least tension.
However, the discrepancy in safety factors between intact and
damaged conditions makes grouped mooring a more cost-
effective choice. Utilizing the American Bureau of Shipping
(ABS) safety factor, a 10° spread angle mooring system's chain
cost emerges as roughly one-tenth cheaper than alternative
configurations.
Additionally, the study explores an innovative V-Share
mooring [1], wherein a single pile anchor connects to two
different columns via two mooring lines. Depending on the
anchoring conditions, it can be the most cost-effective.
In conclusion, a 3x2 mooring pattern for a 15MW semi-
submersible FOWT in typhoon regions might be theoretically
achieved on paper. However, it may not be practically achieved,
if the size limit of the manufactured chain is considered.
Keywords: Floating Offshore Wind Turbines, FOWT, Mooring
System, Cost Optimisation, Minimum Break Load, Floating
Wind, V-Share Mooring, Mooring Chain.
1. INTRODUCTION
As pressure to de-carbonise intensifies, offshore wind power
emerges as one of the most efficient solutions to go green. As
sites suitable for fixed OWT are already scarce, Floating
Offshore Wind Turbines (FOWT) emerge as the technology to
save the day [2]. However, they are still 3-6 times more
expensive than fixed OWT, which doesn’t allow for mass
commercial application. There was a similar situation with fixed
turbines until their capital cost per MW went down by more than
50% in less than a decade[2].
This became possible due to 1) Economies of scale and
supply chain development, 2) technological advancements in all
parts of the turbines, including jacket foundations, tower
optimisation, nacelle and blades rotation control and components
made for easier installation procedures.
For Floating Wind, some of the systems are similar, but
there are unique parts, notably the mooring system that holds the
floater in place, the dynamic power export cable and port-side
integration. Also, FOWTs are generally much bigger, most now
designed to support 15 MW turbines. Big turbines add another

2 © 2023 by ASME
layer of complexity when manufacturing or assembling them;
this was already discussed in the author’s earlier research[3].
FIGURE 1.1: Schematic representations of different mooring patterns
that were examined in the study. (Not to scale)
S. Verde and E. N. Lages [3] have shown that FOWT
mooring line tension is governed mostly by wave loads in
operational and parked conditions, and there is a noticeable
impact of wind load in operational conditions. Xu et al [4] show
the cost-benefit of taut fibre rope mooring in shallow water.
However, in the current industry practice, fibre ropes remain
susceptible to potential harm from marine growth, UV exposure
near the sea surface, and soil ingress close to the sea bottom.
Consequently, in shallow waters, only a short part of the mooring
line can be fibre rope, so the elastic benefit of stretchy rope is
limited, while chain-rope connectors add installation cost and
fatigue susceptibility. Therefore, a full-chain catenary system is
explored in this paper due to its proven robustness with extensive
track records in the offshore industry.
This paper focuses on the most prominent, and most costly
difference of a FOWT – the mooring system. FOWT moorings
come in different shapes and sizes depending on the
environmental conditions and their cost varies, accordingly; they
are shown in Figure 1.1. For the most recently launched deep
water FOWT Guan Lan, it amounted to 7% of the project cost
[5]. However, many FOWTs find themselves in shallower water,
where it is generally more challenging to design a mooring
system and more chains will be used [6]. For example, for
TaidaFloat, which is designed to be moored at 70 m depth, the
mooring system weight is getting close to the hull steel weight
[7], this floater is used for in this paper, shown in Figure 1.2 .
FIGURE 1.2: TaidaFloat semi-submersible with a 3x2 mooring
system that is at 10° spread angle as the base case.
About half of the mooring cost comes not from the line’s
material but from the charter of installation vessels. The
installation time often takes more than estimated due to rough
weather or unforeseen circumstances [8]. Big Anchor Handling
Vessels (AHV) [9] are chartered for about 250,000 USD/day and
their supply around the world is sparse and they are
disproportionally located in Europe. If a developer wants to
charter a ship, it usually needs to pay for a whole year, while the
installation work can only be done during a 5-month weather
window in spring and summer (e.g. for Taiwan Strait).
Offshore Renewable Energy Catapult analysed different mooring
systems’ carbon footprint[10]. It was found that steel chain production
and transportation was by far the most significant emission source. They
also compare 3x1, 3x2 and 3x3 catenary moorings, finding that
switching from 3x1 to 3x2 significantly increased carbon footprint but
switching from 3x2 to 3x3 was only a slight increase. The monetary cost
was not reported.
A Floating Wind Farm cost items are shown in Figure 1.3.
As mooring and dynamic cable capital, installation and
decommissioning costs for FOWT contribute around 11% of the
total wind farm costaccording to data from European Projects
by BVG Associates[11], there is a big incentive to make FOWT
moorings non-redundant, especially as it is allowed by class rules
such as ABS rules for FOWT[12]. While it is a straightforward
way to reduce mooring costs, in that case, the prescribed safety
factor (2) is higher resulting in much thicker and heavier chains,
that need to be operated by bigger vessels, which can offset some
or much of the benefits.

3 © 2023 by ASME
The other approach is a redundant mooring system, which
is designed with a failure in mind – an accident that cuts off one
of the mooring lines, the so-called one-line damaged case. There
are different safety factors applicable for all lines intact and one-
line damaged conditions. Due to lower safety factors and the
environmental force distributed over several lines, redundant
systems have considerably thinner and sometimes shorter chains.
Because of that, the governing design condition is the damaged
condition, usually resulting in much higher line tension and
platform offset (excursion) than intact.
FIGURE 1.3: Floating Wind Farm cost items. Installation cost in the
figure includes sub-station. When re-arranged, mooring and dynamic
cable capital, installation and decommissioning costs account for 11%.
[11].
However, this is not true for all mooring configurations. As
seen in Figure 1.1, when an outside force acts in a certain
direction, only lines making an angle of more than 90° with the
load direction are tensioned – while others are slack, because a
chain or rope can’t transfer compression loads. The amount of
mooring reaction the line provides is proportional to the cosine
of this angle’s supplement. Literature review shows many
designs fix on an angle of 10° between mooring lines without
much consideration of the consequences. This is fine in intact
condition, but in the case that the second most tensioned mooring
line is damaged, the highest tension line will have to bear the
whole disturbing force alone and will break if not made overly
thick.
A proposed way to retain the benefit of low cost is to allow
more mooring lines to counteract the outside force. Shown in
Figure 1.1 are some possible configurations with mooring spread
angles between 10° and the widest angle, 126°[1]. Note here that
at the 126°, there are two mooring lines connecting two platform
columns to the one anchor. This is the innovative mooring design
known as the V-Share mooring [1].
2. FLOATER AND MOORING MODEL
To put the configurations to a test, their maximum tensions
and offsets are calculated in a dynamic coupled hydro-aero-
servo-elastic simulation using the time domain simulation
software OrcaFlex.
The moorings are attached to TaidaFloat – an open-source
floater specifically designed for environmental (typhoons) and
industrial conditions of Taiwan Strait and East Asia[3][5][14],
as other open-source floaters would not be feasible in storm
conditions investigated in this paper. Actual data from a site in
Taiwan strait is used from authors’ previous research, shown in
Table 2.2.[13]. Please note, that for this floater and conditions,
max total wind force on floater, tower and turbine occurs when
the turbine is parked.[14]
The wind, wave and current’s magnitude are constant with
direction and they are collinear for a fair comparison. The mesh
with coordinate system is shown in Figure 2.1 and its principal
dimensions are in Table 2.1, a simulation snapshot from
OrcaFlex is shown in Figure 2.2. In OrcaFlex environmental
force’s 0° direction means wind/wave is propagating from 180°
towards 0°, contrary to wind data, where 0° means wind is
coming from 0° towards 180°, as seen in Figure 1.2. In the
figures, 0° means OrcaFlex wind/wave/current direction.
FIGURE 2.1: 2.5 meter calculation mesh model of TaidaFloat .
TABLE 2.1: TaidaFloat’s principal dimensions
Length
81.6 m
Breadth
94.2 m
Height
34.75 m
Draught
20 m
Total displacement
20 300 t
Hull weight
4142 t
Fairlead
3.75 m above keel
Origin
Pontoon centroid at
base plane
TABLE 2.2: Site environmental conditions for DLC 6.1
Wind/Wave/Current
50-Year return period
Wind speed at hub height
(10-min average)
57 m/s
Wind spectrum
Full-field IEC Kaimal
Significant wave height (Hs)
12.7 m
Peak enhancement factor (γ)
2.08
Wave period (Tp)
11.8 sec
Wave spectrum
JONSWAP
The current speed at the
surface
1.59m/s
Current profile
Power law method profile
Tides
3.13m to -2.8m
Water depth
70 m
Dev
2%
OSS
3%
Floater
18%
Turbine
25%
Cable
6%
Mooring
3%
Installation
7%
O&M
25y
33%
Decom
3%

4 © 2023 by ASME
FIGURE 2.2: OrcaFlex dynamic simulation of case 126. White
dots represent contact with the seabed.
RAOs were calculated in OrcaWave with a 2.5 m mesh and
an example is shown in Figure 2.3; natural periods for heave,
pitch and roll are coupled due to 2 different column sizes[15],
and the pitch eigenperiod is 23 s, much higher than the
environmental waves peak period Tp 12 s. The natural period of
the system is reasonably far from the wave period range.
Damping based on tank test results was added in the OrcaFlex
directly.
FIGURE 2.3: Damped RAOs of TaidaFloat platform
For all the simulations, at least 3 seeds were calculated for
each parameter set and their results were averaged. During the
cost comparison, 5 seeds per set were used.
The simulation duration was 3600 s (increased to 10800 s
for response surfaces simulations), and finally, the chain element
length was set to 10 m to save processing time without
compromising accuracy. A mesh sensitivity study was done on
the chain element length, results are shown in Figure 2.4
FIGURE 2.4: Mesh sensitivity of mooring line with OrcaFlex
Seed sensitivity study was performed after the completion of the
study. The chosen number of seeds (6) is slightly lower than
optimal (7-8), but still acceptable, as seen in Figure 2.5
FIGURE 2.5 Seed sensitivity in OrcaFlex
3. MOORING ANALYSIS TO COMPARE DIFFERENT
PATTERNS
3.1 Mooring Patterns of Various Spreading Angles
As the base case, 160 mm stud chain is used with anchor radius
840 m. In the first phase, where the most critical wave direction
is sought, a 160 mm diameter chain is used for all simulations,
as the absolute value of tension does not matter in this case. The
mooring analysis results for the 30°, 45°, 60°S, and 120° were
between the critical cases of 10°, 60°, and 126°, so only the latter
are shown for graphic clarity.
The purpose of the mooring system is to limit the offset,
the results for offset are shown in Figure 3.1.1, offset is defined
as the geometric sum of the platform’s X and Y axes
displacement from the initial position. The offset limit is
assumed at 20 m, i.e. 28 % of water depth, exceeding this value
might damage the dynamic power export cable [16].
The offset is directly connected to the pre-tension. In all
the simulations, all the lines were pre-tensioned to 2000 ± 100
kN i.e. 8% of MBL. First, the offset is limited by the catenary
shape of the chain, as the floater has to counteract the catenary
segment’s weight to move. The higher the pre-tension, the faster
the mooring line becomes taut, at this point, any further offset is
restrained, while the tension is increasing rapidly.
Limiting the offset in the intact condition is important for
protecting the dynamic cable and preventing its fatigue, offset
results are presented in Figure 3.1.1. The offset varies a lot
depending on the wave direction, also, case 10°’s peak offset
happens at wave direction for which case 126°’s offset is the
lowest and vice versa. This implies different cases would need to
be rotated when considering a wind farm arrangement with a
prevailing wind direction. The maximum offsets from 10°, 60°,
and 126° are 16.9m, 14m, and 15.7 m, respectively. Among these,
the 60° separate angle configuration exhibits the lowest
maximum offset while the 10° case results in the highest
0.00
0.20
0.40
0.60
0.80
1.00
020 40 60 80
RAO (m/m or 100*rad/m)
Period, s
Pitch Heave
23 s
15 s
0
10
20
30
0 5 10 15 20
Segment length, m
Tension, MN Time, h
Space, 100 MB

5 © 2023 by ASME
maximum offset.
FIGURE 3.2.1: Safety factors for mooring lines from ABS
[12] FOWT Rules, 8-3/3
In the previous simulations, the same chain diameter (160
mm) was used, and the resulting offset varied among mooring
patterns. To compare the cost fairly, the mooring systems must
achieve the same performance criteria – an offset limit
Also, in Figure 3.1.1, the tilt angle which is the geometric sum
of pitch and roll is shown. Generally, all the heel results are quite
similar among configurations – this is because the heel is most
impacted by the stability of the platform and the volume of added
buoyancy as the floater inclines. This volume is determined by
the hull configuration of the platform and the inclination
direction, which are only slightly influenced by the mooring
system, however, case 10° does have a considerably higher
average tilt.
Yaw motion is an important factor for the offshore wind
platform design. It is a leading contributor to wind turbine
system reliability failure, as well as wind tower design [17].
The yaw motions results are shown in Figure 3.1.2. The results
indicate a considerable reduction in yaw from the 126°
configuration, while the 10° case exhibits the largest yaw motion.
The maximum yaw angles from 10°, 60°, and 126° configuration
are 13.3°, 7.9°, and 6.5°, respectively. The 126° separate angle
configuration reduce the yaw motion by 52% compared with the
10° case. However, the added stiffness in Yaw also produces
tension to stop the yaw rotation, which is one of the reasons case
126° has higher tension.
FIGURE 3.1.2: Intact condition Yaw max values for different
spreading angles. The bow is facing the 0-degree direction.
While keeping the offset under the limit, the mooring
system should be as economical as possible. The smaller the
tension, the cheaper the system will be. The maximum tension is
also subject to a safety factor according to ABS rules [12]. In the
results for maximum tension shown in Figure 3.1.3, the safety
factor of 1.67 was applied to the intact condition tension and a
factor of 1.05 was applied to the damaged condition. The
maximum tensions from 10°, 60°, and 126° configurations are
22719kN, 25619kN, and 26397kN, respectively. The 10°
separate angle configuration gives the lowest maximum tension.
During the first stage of the numerical analysis, it was
found that damaged tension results seem more unpredictable, so
simulation time was increased from 1h to 3h per seed to ensure
reliability. It was shown that about 8.1 hours of total simulation
time is enough for mooring tension result being independent
from seed [18]. The cases, where the lines are grouped (10°, 126°)
are characterised by lower intact tension, and higher damaged
tension as compared to spread mooring (60°), because in
damaged condition, they only have 1 active line, while others are
slack. Damaged and intact tension SF graphs look similar, as
seen in Figure 3.1.3. Damaged tension results are not further
discussed, as for redundant systems, intact tension multiplied by
safety factor is always higher than damaged condition tension.
The tension values are shown in Figure 3.1.4.
However, this paper focuses on the mooring system design
and cost, and therefore only intact offset and damaged tension
will be considered in the cost comparison later.
Case 60°S is superior in offset, but having the chains stem
out of the middles of pontoons would make the dynamic power
cable design quite challenging, as it would have even less room
to move around so it was discarded.
FIGURE 3.1.3: Damaged and Intact Tension actual safety factors for
different spreading angles. The wave directions corresponding to
minimum values are used for tension response surfaces.

6 © 2023 by ASME
FIGURE 3.1.4: Damaged and Intact maximum line tension.
These cases can also be viewed through the lenses of
offset-stiffness relationship, shown in Figure 3.1.5. Due to the
platform’s triangle shape and the difference in spreading angles,
their stiffness in surge and sway direction can be different. The
graph indicates that the 10° and 126° patterns have a big gap
between their maximum and minimum stiffness, while for 60°
both are almost the same. 10° is slightly stiffer than 126°, but
have the same average stiffness.
FIGURE 3.1.5: Restoring force of mooring patterns, large difference
between max and min implies non-linear stiffness.
Another perspective of load difference between mooring
patterns is provided by the scale of each environmental force’s
impact. Even as the loads are omnidirectional, environmental
forces (2nd order wave forces, current and wind) contributions
change with load’s direction. Unlike a usual simplified approach
which takes force values from static analysis, here force values
are taken from dynamic simulation, allowing to compare means,
shown in Figure 3.1.5.
FIGURE 3.1.5: Mean environmental forces acting on the floater.
While the theoretical mean force in a regular wave is
assumed 0, in real and time-domain simulations of FOWT,
observing a non-zero mean first-order wave force can result from
several factors. Hydrodynamic damping and added mass effects
influence the dynamic response of the structure, potentially
leading to a non-zero mean due to phase differences.
Additionally, wave directionality and spread, if not perfectly
aligned with the FOWT's principal axes, may not allow wave
forces to symmetrically cancel out. Mooring and restoring forces
contribute to the structure's mean position, and inaccuracies in
wave modelling or spectrum representation, along with the
specific methods used for force analysis in the software, might
also contribute to discrepancies. OrcaFlex also employs
techniques like kinematic stretching to extend the linear wave
theory beyond its basic assumptions, further complicating the
direct application of the zero-mean expectation from linear
theory.
It can be seen that the 15 MW FOWT is not dominated by
wave, wind or current forces, wave force magnitude is
comparable to combined current and wind forces. 2nd order (drift)
force varies nonlinearly with environmental direction. The mean
forces are functions of the floater only and the mooring pattern
doesn’t affect them.
When the peak of environmental force sum coincides with
the mooring line direction – largest tension occurs. That’s the
second reason for tension difference between different mooring
patterns. The first and main reason is that the added stiffness in
Yaw also produces tension to stop the yaw rotation.
Worth noting, mean wind force distribution curve is very
smooth and magnitude almost always slightly larger than current
force. However, at angles where current flows directly into
column’s face, the current force can exceed the wind force; the
distribution curve is much more uneven, too.
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7 © 2023 by ASME
3.2 Offset as Function of Chain Size and Tension
In practice, the mooring lines are subject to a safety factor
set by the class society rules, such as ABS FOWT rules, shown
in Figure 3.2.1. As the designed 3x2 systems are redundant, the
tension results of all simulations, are multiplied by a safety factor
of 1.67 for intact condition and 1.05 for damaged condition.
Other class societies have different safety factors [19], and this
value is critical as the intact condition becomes the governing
design case, as opposed to the damaged condition being
governing in Oil & Gas.
Having a complete set of tension and offset results for all
wave headings for different spreading angles, for each spreading
angle configuration two wave headings were used: one resulting
in maximum tension in intact or damaged condition and one with
maximum offset in intact condition. These wave headings are
used in cost comparison as the chain diameter is chosen based on
the minimum breaking load (MBL). R4S chain from Vicinay
catalogue is chosen[20]. For the 160 mm specimen, this chain’s
MBL is 24 281 kN as per ABS rules.
FIGURE 3.2.1: Safety factors for mooring lines from ABS
[12] FOWT Rules, 8-3/3
In the previous simulations, the same chain diameter (160
mm) was used, and the resulting offset varied among mooring
patterns. To compare the cost fairly, the mooring systems must
achieve the same performance criteria – an offset limit.
FIGURE 3.2.2: Offset response surface for 10° case.
FIGURE 3.2.3: Tension response surface for 10° case. (pre-
tension subtracted)
FIGURE 3.2.4: Offset response surface for 60° case.
FIGURE 3.2.5: Tension response surface for 60° case. (pre-
tension subtracted)
120
140
160
180
200
220
5
10
15
20
25
30
35
40
753
1600
2400
3200
4000
4800
5600
5-10 10-15 15-20 20-25 25-30 30-35 35-40
Offset, m
120
155
190
12000
15000
18000
21000
24000
27000
30000
753
1400
2000
2600
3200
3800
4400
5000
5600
12000-15000 15000-18000 18000-21000
21000-24000 24000-27000 27000-30000
Line tension, kN
120
140
160
180
200
220
5
10
15
20
25
30
35
40
753
1600
2400
3200
4000
4800
5600
5-10 10-15 15-20 20-25 25-30 30-35 35-40
Offset, m
120
155
190
12000
15000
18000
21000
24000
27000
30000
33000
753
1400
2000
2600
3200
3800
4400
5000
5600
12000-15000 15000-18000 18000-21000 21000-24000
24000-27000 27000-30000 30000-33000
Line tension, kN

8 © 2023 by ASME
FIGURE 3.2.6: Offset response surface for 126° case.
FIGURE 3.2.7: Tension response surface for 126° case. (pre-
tension subtracted)
To make all the configurations have the same offset, pre-
tension was changed. For every case, simulations were run to
find the tension and offset with parameter combinations shown
in Table 3.2.1. Bxs and Sxb cases were added to ease the
response surface computation. A brute-force evolutionary solver
was used to fit the data to Equation 3.2.1[21] and draw response
surfaces for offset and tension for each case, as shown in Figures
3.2.2-7, coefficients shown in Table 3.2.2. The tensions in
Figures are shown with pre-tension not included, as the pre-
tension’s is an input variable. This part of tension is re-added at
the final step when chain cost is assessed.
While offset response surfaces are rather similar, the
tension surfaces’ shape differs. Mooring line’s stiffness consists
of elastic part which depends on the chain length and diameter
and of geometric stiffness, which depends on the pre-tension and
spreading angle. Spreading angle also impacts the elastic
stiffness by increasing line length, but only up to 2.5%, while the
geometric stiffness is changing considerably, that’s why the
shapes of tension response surfaces can be rather different.
              (3.2.1)
To find the minimal chain weight for a given configuration,
a nonlinear solver was used, varying pre-tension and diameter as
long as the offset is 23 m and the tension factored by the safety
factor is less than MBL.
A very interesting finding is that no matter the spreading
angle, the lowest required line weight is achieved when the
pre-tension is 4-5% of MBL, so this value can be recommended
for future design.
The fact that the four corners of each response surface are
all located at different height shows that a significant
interaction effect is present, so that linear prediction
approaches (when chain diameter and pre-tension are varied
separately) are not suitable to predict the performance of a
mooring system.
TABLE 3.2.1: Numerical analysis setup for cost comparison


















































TABLE 3.2.2: Response surface coefficients




















































3.3 Preliminary Cost Comparison of Mooring System
The comparison of different system’s costs is shown in
Figure 3.3.1, also compared to the 3x3 mooring system [7] cost.
As the 3x3 system had offset of 23 m, 3x2 systems in this cost
compare also designed for maximum offset of 23 m, the mooring
chain was since updated due to floater modification, and the 3x3
system uses 171 mm chain.
120
135
150
165
180
195
210
5
10
15
20
25
30
35
40
753
1400
2000
2600
3200
3800
4400
5000
5600
5-10 10-15 15-20 20-25 25-30 30-35 35-40
Offset, m
120
155
190
12000
15000
18000
21000
24000
27000
30000
33000
36000
753
1400
2000
2600
3200
3800
4400
5000
5600
12000-15000 15000-18000 18000-21000 21000-24000
24000-27000 27000-30000 30000-33000 33000-36000
Line tension, kN

9 © 2023 by ASME
First step is calculating the chain cost with Eq. 3.3.1. For
3x2 systems, chain cost is the main contributor to the overall cost.
     (3.3.1)
      
Then, the overall cost of the mooring system including the
installation and anchor cost are added in Eq. 3.3.2.
s
     
 (3.3.2)

 
 󰇛

 󰇜  
, where installation time is half of the mooring unit pre-lay time
(3.9 days) and test time is anchor test time (2.5 days) from [8]
A shared anchor might need to withstand larger load. To
account for that, sharing coefficient is used, the anchor is
assumed to be larger, and the unit anchor cost is multiplied by
1.5 for anchor shared by two lines (126S and 10S), and by 2.0
for anchor shared by three lines (10S 3x3).
The installation cost is calculated in Eq. 3.3.3 with time
data from Japanese projects compiled by T. Hasumi [8]. It did
not consider anchor and line installation time separately, so it is
split in half here.
   
󰇡
 󰇢   (3.3.3)
,where hook-up time (0.5 days) is from [8]
Finally, as two-three nearby anchors only require one
geotechnical survey, soil test cost is number of anchor clusters
times unit cost of 100 000$. It is only different for case 60° as all
the anchors are far from each other.
The vessel cost is estimated at 0.25 mil. USD/day for a big
Anchor Handling Vessel and the mooring chain price as 1500
USD/t based on industry experience. The cost data is shown in
Table 3.3.1. Tension is shown in percent from the average among
all the configurations for easier comparison.
A companion paper [22] employing a different method
looked at the different spreading angles, but also different
mooring radii. For the same mooring radius, the results are
almost the same, however, it was found that the mooring
pattern’s response to different mooring radii varies somewhat. So,
the cost analysis here might only be precise for a mooring radius
of 840 m, which can be considered a medium value [22].
The results show that the 10° configuration is the cheapest
in terms of chain material costs. Only when anchor sharing is
used for 126°, it is cheaper than 10°. A 10° with a shared anchor
would be even cheaper, but it’s chains would clash and get
damaged if they were attached to a single column.
The 60° spread mooring configuration is the least cost-
effective. This is also the more troublesome case to arrange on-
site and connect the dynamic cable due to the mooring lines all
over the place. These factors make it the less-desired mooring
configuration overall.
FIGURE 3.3.1: Mooring cost comparison.
It was found that the total mooring system cost’s largest
contributor is the chain cost in the case of spread or V-Share
mooring (60° or 126°), and vessel cost in the case of clustered
mooring (10°). Anchor’s capital cost also contributes a large part,
more than the vessel cost in some anchor cases.
When compared to the reference 3x3 system, 10° 3x2
configuration is a fifth cheaper. Overall, 126° (V-Share)
mooring system was found to be the cheapest. However, there
may be some potential challenges when sharing one anchor
between different lines, such as out-of-plane bending of the
anchor loops or the anchor’s insufficient moment holding
capacity.
TABLE 3.3.1: Preliminary cost comparison of different
mooring patterns. Reduction for the maximum in each cost
category.
Pattern
10°
10°
60°
126°
126°S
No. of lines
3 x 3
3x2
3x2
3x2
3x2
Line
diameter
171
mm
234
mm
360
mm
274
mm
274
mm
No. of
anchors
9
6
6
6
3
Chain cost
-61%
-34%
-7%
0%
0%
Anchor
capital
0%
-33%
-33%
-33%
-50%
Anchors
install.
0%
-33%
-33%
-33%
-67%
Mooring
install.
0%
-33%
-33%
-33%
-33%
Soil test
-50%
-50%
0%
-50%
-50%
Total
0%
-17%
-5%
-3%
-20%
0
5
10
15
20
25
30
35
10°3x3 10° 60° 126° 126°S
Mooring cost, mil. USD
Chain cost Anchor capital cost
Anchor installation cost Mooring installation cost
Soil test cost
3x3
3x2

10 © 2023 by ASME
4. DISCUSSION
The results show, that for FOWT in a typhoon region, a
grouped 10° system is the most cost-efficient. However, in the
Oil & Gas (O&G) Industry, spread 60° moorings are widely used
for a 6-line mooring system. The difference comes down to the
required safety factors between the two industries, FOWT and
O&G. As there is no danger of accidents involving human lives
or oil spills, safety factors required by class societies for
damaged conditions are smaller for FOWT (1.05) than for O&G
(1.25), making the intact condition the governing case for
mooring design, as opposed to the damaged condition being
governing for O&G platforms. The safety factors change as rules
are updated, and are different among class societies, therefore the
governing case and best mooring patterns are also subject to
change.
Mooring radius is another main design factor for mooring
systems. Companion paper showed that different mooring
patterns have different sensitivity to it, so this cost comparison’s
limitation is its applicability to medium mooring radius only
(840 m).
When it comes to anchor sharing between lines, there is a
lot of uncertainty on its feasibility. Potential problems include
anchor fatigue and difficulty of installation. The way these
problems are solved will impact the cost of the mooring system.
Also, the shared anchor will most probably be a pile anchor
[4][13], while drag anchors can be used for unshared systems. In
the present paper, pile anchors were used for all cases, as the
site’s soil condition might not allow drag anchors. It follows that
whether shared anchors are economically viable depends on the
site’s soil condition and anchor design. Installation vessel cost is
the largest part of the 3x3 mooring system cost, and it is prone to
much more severe changes than material costs. In Taiwan, vessel
hire costs rose more than 2 times after more wind farm projects
were announced, due to a spike in demand with slowly growing
supply. In case the vessel prices fall by a large margin, the 3x3
system might become less expensive than 3x2 due to its lower
chain cost, which is less subjected to a volatile market. The
bottom line is, based on supply constraints, the available chain
size is limited, so a 3x3 system must be used even if 3x2 could
be cheaper theoretically. At the time of writing, only one
company on Earth – Vicinay – claimed to have made chain with
diameter of 220 mm, as seen in Table 4.1, and no bigger chain
could be used. Chains so big had never been tested yet, so their
use for a large-scale project soon is unlikely.
TABLE 4.1: Worldwide Offshore Mooring Chain
Manufacturing Capability. R3-6 refer to metal grade.
American Petroleum Institute
Approved Vendor List:
Country of
supplier
Production
capability
Asian Star
China
R6 up to 200 mm
Zheng Mao
China
R6 up to 208 mm
Vicinay
Spain
R6 up to 220 mm,
capacity 40 000
t/year
Hamanaka Chain
Japan
R3 up to 132 mm
Ramnas
Sweden
R5 up to 177 mm
Other suppliers:
Daihan
Korea
R3 up to 162 mm
DeYuan Marine
China
Up to 162 mm
SOTRA
Norway
R4 up to 178 mm
Marit
France
R3 - 200 mm R4 -
180 mm
Tullyn
China
R4 up to 162 mm
It shall be noted here that the mooring technologies for
floating wind are evolving quickly, including new mooring
configurations (V-Share mooring, shared mooring lines), new
mooring components such as polymer spring load reduction
devices, new mooring materials such as HMPE rope [6, 19]. New
mooring anchors for floating wind are also emerging quickly, e.g.
the multiline ring anchor, helical anchor. The direction these
new mooring technologies take will influence the overall
mooring system cost.
In this study, the 126° case, i.e. the V-Share mooring [1],
demonstrates over a 50% reduction in maximum yaw motion,
and 16% higher tension than the 10° case. The main reason for
the higher tension is the much-increased yaw stiffness. It's
expected that the performance of the V-Share mooring might
vary across different floaters, especially considering variations
in pontoon size (smaller or deeper) which directly impact the
dominant wave loads and platform length, impacting yaw
stiffness.
Given the substantial chain size used in this study,
significantly increasing the chain size becomes necessary to
achieve the targeted tension safety factor and offset in the 126°
case. Yet, enlarging the chain size might be not the most cost-
efficient approach for this objective. Consequently, it is
anticipated that the V-Share mooring will showcase more
advantages in mooring systems that allow for more parameter
adjustments, including variations in component size and lengths,
azimuth angles, and material grades.
A shared anchor connecting two or three mooring lines
among different floaters is a field-proven design, such as the
Hywind Tampen project. However, connecting two mooring
lines from a single floater to one anchor is novel. The V-Share
mooring system also provides an opportunity to optimize the
mooring installation procedure [1]. The evolution of V-Share
mooring technology is expected to influence the cost of the
mooring system for floating wind.
Finally, this paper primarily focuses on assessing the
mooring system. The influence of the mooring system on hull
and turbine size remains unexplored. This study employs an all-
chain mooring system in shallow water with a specified radius.
It was found that the optimal pre-tension for such system is 4-
5%, making chain size the sole adjustable parameter to attain the
desired performance. Concerning performance, the focus is on
tension and offsets. Recent engineering observations show that
fatigue might govern the mooring design, especially because of
the impact of dynamic wind turbine loads on top of wave
frequency fatigue damage. These are all topics that deserve to be
further studied.
5. CONCLUSION
In summary, the economic viability of a mooring system is
intricately tied to both installation expenses and material costs.
Among the various components, the mooring chain plays a major
role alongside anchors, clump weight, shackles, and connectors.
Interestingly, the cost dynamics reveal a counterintuitive
relationship — as installation vessel prices soar, employing

11 © 2023 by ASME
fewer mooring chains proves more cost-effective. This
phenomenon stems from the environmental load being
distributed thinly over larger chains, even as the individual chain
cost increases.
The research findings underscore the advantages of a
clustered mooring system featuring a 10° spreading angle
between lines. This configuration emerges as the most cost-
efficient choice when compared to traditional alternatives such
as the spread 60° mooring, which shows a small offset in both
damaged and intact conditions. Note that the 60° spread is more
common for applications like offloading buoys and small
production vessels in the oil and gas industry. Moreover, the
prospect of sharing anchors between two neighbouring lines in
126° configuration (V-Share) holds promise for even more
substantial cost savings. This strategy becomes particularly
relevant in cases where site soil conditions present challenges to
the use of drag anchors.
It is imperative to address the feasibility of a 3x2 mooring
pattern for a 15MW semi-submersible FOWT in typhoon-prone
regions. Regrettably, this configuration currently proves
unfeasible for the typhoon condition of the site, when
considering the 180 mm practical size limit of mooring chain.
However, a strategic shift to a 3x2 pattern would yield
considerable advantages, reducing the total cost by utilizing
three fewer mooring lines compared to a 3x3 pattern in typhoon
regions.
In conclusion, the optimal mooring pattern for a 15MW
semi-submersible FOWT in typhoon-prone regions involves a
clustered arrangement with either a 10° or 126° spreading angle.
These configurations emerge as the top choices, outperforming
alternatives like 45° and 60° options. The findings may help
economic viability of mooring systems for floating wind, but
also contribute to the advancement of sustainable and cost-
effective offshore wind energy solutions.
ACKNOWLEDGEMENTS
The authors highly appreciate the funding support from the
government agency, the Taiwan (ROC) Ministry of Science and
Technology, for the FOWT research, and thank the Taiwan (ROC)
Ministry of Education’s Yushan fellowship programme.
REFERENCES
         A New
Mooring System for Floating Offshore Wind Turbines:
Theory, Design and Industrialization  Offshore
Technology Conference
 

 Prospects of offshore wind power in
Taiwan and the development of semi-submersible
floating platformsTaiwan Wind Energy Symposium
    



 Design Considerations
on Semi-Submersible Columns, Bracings and Pontoons
for Floating Wind.     
    

     Design and comparative analysis of
alternative mooring systems for floating wind turbines
in shallow water with emphasis on ultimate limit state
design.

    New Energy Generation Equipment
Business Study    



     Mooring System Engineering for
Offshore Structures    



     Design Of Mooring System For a
15mw Semi-Submersible, Taidafloat,inTaiwan Strait
42nd International Conference on Ocean, Offshore and
Arctic Engineering
 








     ESTIMATION FOR EFFICIENCY OF
OFFSHORE INSTALLATION PROCESS OF FLOATING
OFFSHORE WIND TURBINES IN JAPAN  42nd
International Conference on Ocean, Offshore and Arctic
Engineering
 Harvest Wind - Offshore Engineering
      
     


     WP4 Innovation in Low Carbon
Design and Manufacturability
Task 4 – Mooring and Anchoring SystemsCORNWALL FLOW
ACCELERATOR    
  



   Guide to a Floating Offshore Wind
Farm       
    
 



 Guide for Building and Classing Floating Offshore

12 © 2023 by ASME
Wind Turbine InstallationsThe American Bureau of
Shipping, Houston (TX), USA   



 Optimization of Semi-Submersible Hull
Design for Floating Offshore Wind Turbines  41st
International Conference on Offshore Mechanics and
Arctic Engineering (OMAE 2022)  
    
 
  

     Overview of FOWT
Demo Projects Cost and Analyses of Hull Design
Features  3rd World Conference on Floating
Solutions (WCFS2023)    
 



 Investigation report. Column size influence
on RAO peaks.    
   

 Review of the state of the art of
mooring and anchoring designs, technical challenges
and identification of relevant DLCs
  



      Yaw Systems for wind
turbines – Overview of concepts, current challenges
and design methods.    
     

     Sensitivity analysis of numerical
modeling input parameters on floating offshore wind
turbine loads. 

 Mooring Designs for Floating Offshore
Wind Turbines Leveraging Experience From the Oil &
Gas Industry  41st International Conference on
Offshore Mechanics and Arctic Engineering (OMAE
2021)     
  

   The Future of Mooring (Brochure)
 


     Polynomial Regression with
Response Surface Analysis: A Powerful Approach for
Examining Moderation and Overcoming Limitations of
Difference Scores.
    

     Mooring Anchor radius and Spread-
angle Optimization for a 2 MW Semi-Submersible
Floating Wind Turbine in Taiwan StraitInternational
Conference on Ocean, Offshore and Arctic Engineering
(OMAE 2024)   
