Dynamic Power Cable Layout Design for 15 MW Floating Offshore Wind Turbines: Part 2 - Evaluation of Ultimate Limit State Performance

Article information

J. Ocean Eng. Technol. 2025;39(4):431-444

Publication date (electronic) : 2025 August 20

doi : https://doi.org/10.26748/KSOE.2025.024

Doyoung Kwon ¹

, Dong Suk Hong ²

, Joonmo Choung ³

¹Master’s degree candidate, Department of Naval Architecture and Ocean Engineering, Inha University, Incheon, Korea

²Chief Research Officer, Research & Development Lab, Taihan Cable & Solution, Seoul, Korea

³Professor, Department of Naval Architecture and Ocean Engineering, Inha University, Incheon, Korea

Corresponding author Joonmo Choung: +82-32-860-7346, heroeswise2@gmail.com

Received 2025 June 2; Revised 2025 July 8; Accepted 2025 July 15.

Abstract

This study presents an ultimate limit state (ULS) assessment of two optimal dynamic cable layouts, previously proposed by the authors, for a 15 MW floating offshore wind turbine (FOWT). These configurations were evaluated under 50-years return period extreme conditions representative of the Ulsan offshore region. Dynamic cable was modeled using MoorDyn, and fully coupled time-domain simulations were conducted in OpenFAST, accounting for interactions among the FOWT, mooring system and cable. Each layout underwent twelve 3-hour simulations across four sub-DLCs with varying wind and wave phase combinations. Both layouts satisfied all design constraints, with horizontal offsets staying within the ULS criterion of 30% and tension and curvature remaining within acceptable ranges under a safety factor of 2. Higher hang-off tension and Ez angle occurred under upwind conditions, especially in the 230% buoyancy configuration. Sag and hog bend points showed inverse tension-curvature relationships influenced by horizontal offset, with the 230% layout exhibiting lower curvatures due to extended buoyancy distribution. At TDP (touchdown point), wave/current directions governed curvature while horizontal offset controlled tension. Statistical analysis of TDP variability determined optimal cable lengths for both configurations. Future work will extend to fatigue limit state (FLS) evaluation under normal operating conditions to ensure long-term durability.

Keywords: Floating offshore wind turbine; Dynamic power cable; Lazy wave; Ultimate limit state; Fully-coupled analysis

Nomenclature

A : cross section area

D : outer diameter of dynamic power cable

E : elastic modulus

EA : axial stiffness of dynamic power cable

EI : bending stiffness dynamic power cable

h : water depth

H_S : significant wave height

I : second moment of area

L_T : total length of dynamic power cable configuraion

L₁ : distance from hang-off point to DBMs section start

L₂ : DBMs section length

L₃ : length from end of DBMs section to touchdown point

L₄ : touchdown length

T_p : wave period

U_C : current speed at sea water level

V_hub : wind speed at hub height of wind turbine

x : horizontal position of dynamic power cable

z : vertical position of dynamic power cable

θ : Ez angle, between the initial hang-off angle and the instantaneous hang-off angle

γ : peak shape factor for JONSWAP wave spectrum

μ : average of dynamic cable responses

σ : standard deviation of dynamic cable responses

1. Introduction

Construction of a floating offshore wind farm is being planned in the waters off Ulsan, Republic of Korea (Hyun et al., 2024; Kim et al., 2019, 2021, 2023). Because existing fixed-type wind power generation is not suitable for the Ulsan offshore environment consisting of deep waters with depths of 50m or more, floating offshore wind turbine (FOWT) technology has been adopted as an alternative (Barter et al., 2020; Fuchs et al., 2024; Maness et al., 2017; Ruzzo et al., 2018; Shah et al., 2021).

The dynamic power cable responsible for power transmission in FOWT systems must operate stably in the installed offshore area during a design life of 25 years or more (WFO, 2024). That is, the layout of dynamic power cables must be designed to effectively accommodate extreme loads, cyclic loads, and long-period offsets. The catenary mooring system commonly adopted in FOWT significantly increases the horizontal offset of floating bodies under extreme environmental loads such as typhoons. This causes tension and bending moments exceeding design strength to act on dynamic power cables, causing fatigue damage and failure (CIGRE, 2022; Ferreira et al., 2022). Therefore, dynamic power cable layout design that can stably accommodate extreme environmental loads and offsets during the design life of dynamic power cables is necessary (Cerik and Huang, 2024; Guzmán, 2024; Wang et al., 2024).

Lazy wave configuration has been widely used as a dynamic power cable layout for inter-array. Through this layout, the tension and bending moment of dynamic power cables can be effectively reduced. That is, by placing distributed buoyancy modules (DBMs) between the hang-off point (HOP) and seabed touchdown point (TDP) to form a lazy wave, the load on dynamic power cables is reduced (Wang et al., 2019). The lazy wave layout can absorb long period offsets of floating bodies caused by resonance force and second-order wave excitation force to prevent cable damage (Kwon et al., 2019; Oh et al., 2018). The lazy wave layout is cost-effective because it does not require additional equipment other than DBMs (Doole et al., 2023; Ikhennicheu et al., 2020).

Therefore, the authors aim to perform the optimization of the dynamic power cable layout based on the lazy wave layout derived in Part I of this paper. In order to verify the performance of the lazy wave layout under ultimate limit state (ULS) conditions, a fully-coupled load analysis must be performed for the design load case (DLC) considering a 50-year return period environment. Since each sub-DLC must be analyzed through simulations of at least 3 hours, simulation tools based on potential flow theory, rather than computational fluid dynamics (CFD), have been mainly used for fully-coupled load analysis. Representative fully-coupled load analysis tools based on potential flow theory include OrcaFlex (Orcina Ltd., 2024), Simo/Riflex (DNVGL SINTEF Ocean, 2018), HAWC2 (Larsen and Hansen, 2023), and OpenFAST (NREL, 2024).

Researchers around the world are conducting studies on the lazy wave layout of dynamic power cables using OrcaFlex (Gao et al., 2024; Holcombe et al., 2025; Liu and Li, 2025; Su et al., 2024). Thies et al. (2012) presented that the lazy wave layout can effectively reduce the maximum tension and fatigue damage of the cable compared to the catenary layout. Boo and Yang (2019) analyzed the relationship between the Ez angle and HOP tension generated by the cable at the HOP and provided basic data for the design of the bend stiffener. Schnepf et al. (2023) analyzed the dynamic response of an inter-array dynamic power cable connecting two FOWTs. In addition, Taninoki et al. (2017) conducted a cable shape design considering the floater offset corresponding to extreme environmental loads. Ahmad et al. (2023) set the horizontal offset of the floater as a fitness factor and analyzed the shape optimization and cable response under extreme load conditions. Zhao et al. (2021) used Simo/Riflex (DNVGL SINTEF Ocean, 2018) to analyze the dynamic response of a lazy wave layout reflecting 50-year return period environmental conditions, setting the HOP angle, installation water depth, and the shapes of the sag bend and hog bend as key design parameters. Gözcü et al. (2021) and Verelst et al. (2024) evaluated the optimization and response characteristics under extreme environmental conditions of the lazy wave layout using HAWC2 (Larsen and Hansen, 2023). As the MoorDyn module of OpenFAST (Hall, 2017) provides the implementation function for bending stiffness, modeling of the dynamic power cable has become possible, and related studies are increasing. Hall et al. (2021) verified the accuracy by comparing the load response of the dynamic power cable derived from MoorDyn with OrcaFlex. In addition, Lozon et al. (2025) proposed mooring and dynamic power cable layouts for FOWTs that can be operated in offshore regions of the United States.

The authors aim to analyze the motion performance and load response under ultimate limit state conditions using OpenFAST for the two lazy wave configurations designed in Part I of this paper. For this purpose, a 3-hour long fully-coupled load analyses are performed reflecting the 50-year return period extreme environmental conditions of the Ulsan sea area, based on the UMaine VolturnUS-S 15MW semi-submersible reference platform FOWT (Allen et al., 2020). Through this, the minimum length required for the dynamic power cable under ULS conditions is estimated. In addition, the deformed shape of the layout when the maximum horizontal offset of the floater occurs is derived to examine whether it satisfies the design conditions. Furthermore, the maximum loads at the HOP, TDP, sag bend point (SBP), and hog bend point (HBP) are analyzed. As a result, a dynamic power cable layout applicable to a 15 MW-class FOWT expected to be operated in the Ulsan offshore area of the Republic of Korea is proposed.

2. FOWT Components

2.1 FOWT

As seen in Fig. 1, a 15 MW class semi-submersible platform (Allen et al., 2020) is station-kept by a 2×3 catenary mooring system was used. Basic specifications of turbine and substructure are presented in Table 1 and Table 2, and basic specifications of substructure’s hydrostatic stiffness and mooring system are presented in Table 3 and Table 4 respectively.

Fig. 1

VolturnUS-S FOWT (Allen et al., 2020)

Table 1

Properties of turbine (Allen et al., 2020)

Table 2

Properties of semi-submersible substructure (Allen et al., 2020)

Table 3

Hydrostatic stiffness of FOWT

Table 4

Properties of mooring system

2.2 Dynamic Power Cable

2.2.1 Properties of the 66 kV dynamic power cable

The rated voltage of the dynamic power cable used in this study shown in Fig. 2 is 66 kV. It consists of 3 conductor cores, and each conductor core is protected by insulation and core sheath. The 3 conductor cores are insulated and protected once again by bedding and outer sheath. To secure sufficient tensile strength of the dynamic power cable, a number of steel armors are placed between the bedding and outer sheath. Also, the basic specifications of the dynamic power cable are shown in Table 5.

Fig. 2

Cross section of 66 kV dynamic power cable

Table 5

Properties of dynamic power cable

2.2.2 Lazy wave configuration

Based on the design layout presented in Fig. 3, in Part I of this paper, optimal lazy wave configurations were derived for two buoyancy states. Each buoyancy state meant 140% and 230% of the mass (displacement) of the initial suspended length calculated as 140 m of the dynamic power cable. Two layouts are presented combined with FOWT in Fig. 4. The two layouts are also presented in Fig. 5(a), and tension and curvature distribution according to distance of dynamic power cable from HOP are presented in Figs. 5 (b) and (c), respectively. And the section-wise length of each lazy wave layout and specifications of applied DBMs are summarized in Table 6 and Table 7, respectively. Design criteria for ULS performance evaluation are shown in Table 8. According to this design criteria, the maximum tension occurring in dynamic power cable cannot exceed MBL, the maximum curvature must be smaller than maximum allowable curvature MAC, and the maximum horizontal offset cannot exceed 30% of water depth.

Fig. 3

Design layout of lazy wave configuration

Fig. 4

Optimized lazy wave configurations

Fig. 5

Optimized lazy wave configurations at static state

Table 6

Section lengths of the lazy wave configurations at static state

Table 7

Properties of DBMs applied to configurations

Table 8

Design constraints for ultimate limit state

3. Numerical Setup and Environmental Conditions for ULS Analysis

3.1 Determination of ULS Environmental Condition

Observation data from Wangdolcho observation buoy located approximately 23 km east of Uljin, Republic of Korea was used to perform fully-coupled load analysis. Although the FOWT that is the subject of this study is scheduled to be installed in Ulsan waters, offshore environmental data obtained from meteorological observation buoy in Wangdolcho area was applied. Wangdolcho is known to show harsh environmental conditions as it is located relatively more offshore than Ulsan offshore area.

DLC 6.1 corresponding to turbine parked/idling condition presented in the standard (International Electrotechnical Commission, 2019a, 2019b) was selected. DLC 6.1 is a DLC corresponding to ULS, and 50-year return period wind speed and current speed were determined through statistical processing of observation data. 50-year return period significant wave height was also determined by the same method, and wave peak period dependent on significant wave height was also determined through inverse first order reliability method (iFORM) analysis. After assuming that current direction is the same as wave direction, 4 sub-DLCs were generated by combining wind direction and wave direction, and this is shown in Table 9.

Table 9

Environment conditions for ultimate limit state

Also, the wind direction, wave direction, and current direction of FOWT applied to dynamic analysis are shown in Fig. 6. For each sub-DLC, 3 random wind speed phases and wave height phases were considered. 3-hour load analysis was performed for each sub-DLC.

Fig. 6

FOWT environment layout

3.2 Modeling of Mooring Lines and Dynamic Cable System

In this study, fully-coupled load analysis was performed using OpenFAST (NREL, 2024). The mooring system and dynamic power cable layout were modeled using OpenFAST MoorDyn module (Hall, 2017). The unstretched length of mooring lines was 1 km, and this was discretized into uniform elements with 10 m intervals to generate a total of 100 line elements. The unstretched length of dynamic power cable was 700 m, and this was discretized into uniform elements with 1 m intervals to generate a total of 700 line elements. DBMs were modeled as point objects and the element spacing was 1m. Since the shape and mass of DBMs were assumed to be absent, drag coefficient and added mass coefficient were not considered. The drag coefficient and added mass coefficient of mooring lines and dynamic power cable are summarized in Table 10.

Table 10

Drag and added mass coefficients of mooring line and dynamic power cable

4. Result of ULS Simulation and Discussion

4.1 Horizontal Offset of Lazy Wave Configurations

The maximum horizontal offset that occurred in each sub-DLC is presented in Table 11. Also, the maximum deformation of the two layouts is shown in Fig. 7. In Case 1 and Case 2, positive offset (near offset) occurred, and in Case 2 and Case 4, negative offset (far offset) occurred. This means that aerodynamic load determined the direction of offset and means that aerodynamic load is the most dominant load in offset. And the two layouts satisfied the condition within 30% of water depth (within 44.4 m) in the 4 load cases.

Table 11

Maximum horizontal offset

Fig. 7

Deformed configurations

4.2 Determination of Dynamic Cable Length

If the initial length of the dynamic power cable is set too short, the touchdown length L₄ may be insufficient, resulting in excessive tensile force at the end of the dynamic power cable. Therefore, in this study, the initial length of the dynamic power cable was set sufficiently long at 700 m. It was confirmed from the fully-coupled load analyses that sufficient touchdown length was secured in both layouts. To estimate the total required length of the dynamic power cable, the authors analyzed the variation of L₄. For each layout, the mean (μ) and standard deviation (σ) of L₄ were derived, and μ+ 2σ was considered the minimum L₄. The total length L_T based on the minimum L₄ is presented in Table 12.

Table 12

Determined L₄ and L_T for each buoyancy levels

The total length L_T that simultaneously satisfies the four sub-DLCs is confirmed from Table 12 to be 254.82 m for the Buoyancy 140% layout and 338.16 m for the Buoyancy 230% layout. In other words, the longest L_T was obtained in Case 3. The three-dimensional shapes

Fig. 8

Updated lazy wave configurations

4.3 Dynamic Responses

The time histories of tension at the HOP for the two layouts were grouped according to the cases with near offset and far offset and are presented in Fig. 9. The maximum values of these time history responses are provided in Table 13. Additionally, the maximum Ez angles are also presented in Table 13. For a more detailed analysis, the results of Table 13 are summarized and shown in Fig. 10. From the analysis of the maximum tension and maximum Ez angle at the HOP, the following results were obtained:

Fig. 9

Tension history of each layout at HOP

Table 13

Maximum cable response comparison at HOP

Fig. 10

Heatmap of responses at HOP

(1) Max. tension @HOP: In both layouts, near offset of the floater occurred in Case 1 and Case 2 due to upwind conditions, and as a result, the offset decreased and the maximum tension was reduced. On the other hand, under downwind conditions (Case 3 and Case 4), far offset occurred, and consequently, increased offset caused higher tensile forces.
(2) Ez angle @HOP: Larger Ez angles were observed in the Buoyancy 230% layout compared to the Buoyancy 140% layout. As the buoyancy of the DBMs increased, L₂ was positioned closer to the water surface, resulting in an increase in the Ez angle. Wave/current direction significantly affected the Ez angle, and an increase in Ez angle was observed when the wave/current direction was 0° (Case 1 and Case 3).

The maximum tension and maximum curvature at the SBP and HBP of the dynamic power cable are presented in Table 14/Fig. 11 and Table 15/Fig. 12, respectively. The results can be summarized as follows:

Table 14

Maximum cable response comparison at SBP

Fig. 11

Heatmap of responses at SBP

Table 15

Maximum cable response comparison at HBP

Fig. 12

Heatmap of responses at HBP

(1) Max. tension @SBP & HBP: As buoyancy increases, the DBMs are positioned closer to the water surface, resulting in increased tension. When near offset occurs, curvature increases and the DBMs become concentrated within a narrower space. This causes the DBMs to rise toward the water surface, decreasing tensile forces.
(2) Max. curvature @SBP & HBP: The offset of the floater governs the curvature at the SBP and HBP. That is, near offset increases the curvature, while far offset reduces it at both the SBP and HBP. Since the L₂ in the Buoyancy 230% layout is longer than that in the Buoyancy 140% layout (as the buoyancy acts over a longer segment), the curvature at the SBP is relatively alleviated. Therefore, as buoyancy increases, a decreasing trend in curvature was observed.

The maximum load responses at the TDP of the dynamic power cable are presented in Table 16 and Fig. 13, and the following results were obtained. At the TDP, the minimum tension was examined to assess the occurrence of compressive force.

Table 16

Maximum cable response comparison at TDP

Fig. 13

Heatmap of responses at TDP

(1) Min. tension @TDP: It was anticipated that near offset would cause the cable to contact the TDP in a nearly vertical manner, potentially resulting in compressive force; however, no compression was actually observed. Small tensile forces occurred under near offset conditions, while large tensile forces were generated under far offset conditions.
(2) Max. curvature @TDP: When near offset occurred, the dynamic power cable contacted the TDP in a more vertical orientation, leading to an increase in the maximum curvature at the TDP. Even with increased buoyancy, the same phenomenon was observed – that is, the cable approached the TDP more vertically, resulting in large curvature.

In conclusion, both layouts satisfied all the design constraints presented in Table 8, and it was confirmed that the tensile forces and curvatures occurring in the cable remained within the allowable limits even with a safety factor of 2.0 applied.

5. Conclusion

In this study, the structural safety of two dynamic power cable layouts applicable to a 15 MW-class FOWT under extreme environmental conditions was evaluated. The main findings are as follows:

(1) A total of twelve 3-hour fully-coupled load analyses were performed using OpenFAST for four sub-DLCs reflecting the offshore conditions at Wangdolcho, by combining three different wind speeds and wave phases. As a result of the analysis, the maximum horizontal offset for both layouts remained within 30% of the water depth, and even with a safety factor of 2.0 applied, the tension and curvature of the power cable satisfied the MBL and MAC criteria.
(2) A statistical analysis of the variation in the touchdown length at the TDP of the dynamic power cable was conducted to estimate the actual required cable length. By adding two times the standard deviation to the mean value of the touchdown length variation, the design L₄ length was determined to be 4.82 m for the Buoyancy 140% and 10.16 m for the Buoyancy 230% configuration.
(3) A heatmap analysis of the load response characteristics was performed for HOP, SBP, HBP, TDP which are important points of the layout. The results showed that the horizontal offset of the floater was the most influential factor affecting structural response overall. Additionally, the Ez angle at the HOP and the tension at the TDP were found to be responsive to the wave/current direction.

In future research, fatigue limit state assessments under normal turbine operating conditions (DLC 1.2) will be performed to verify fatigue safety over the design life. This study presents a design and evaluation methodology for dynamic power cables under site-specific extreme load conditions, which is expected to serve as a practical reference for the future design of floating offshore wind farms.

Notes

Joonmo Choung serves as an editorial board member of the Journal of Ocean Engineering and Technology. However, he was not involved in the decision-making process for the publication of this article. The authors have no potential conflicts of interest related to this article.

This research was supported by the Korea Institute of Energy Technology Evaluation and Planning (KETEP) grant funded by the Korea government (MOTIE) (20213000000020, Development of core equipment and evaluation technology for construction of subsea power grid for offshore wind farm).

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Item	Unit	Value
Turbine rating	MW	15
Hub height	m	150
Excursion (Length, Width, Height)	m	90.1, 102.1, 290.0
Platform type	n/a	Semi-submersible
Water depth h	m	148
Total FOWT mass	t	20,093
Platform mass	t	17,839
RNA mass	t	991
Tower mass	t	1,263

Item	Unit	Value
Hull displacement	m³	20,206
Tower interface mass	t	100
Freeboard	m	15
Draft	m	20
Vertical center of gravity from SWL	m	−14.94
Roll inertia about center of gravity	kg·m²	1.251 × 10¹⁰
Pitch inertia about center of gravity	kg·m²	1.251 × 10¹⁰
Yaw inertia about center of gravity	kg·m²	2.367 × 10¹⁰

Item	Unit	Value
Heave	N/m	4.470 × 10⁶
Roll	N·m/rad	2.190 × 10⁹
Pitch	N·m/rad	2.190 × 10⁹

Item	Unit	Value
Mooring system	-	Six-line chain catenary
Chain link type	-	Studless
Material grade	-	R5
Chain diameter	mm	105.00
Minimum breaking load (MBL)	kN	12580.00
Unstretched length	m	1000.00
Vertical distance from fairlead to water line	m	14.00
Horizontal distance from fairlead to anchor	m	966.00

Item	Unit	Value
Rated voltage	kV	66
Outer diameter D	mm	188.16
Mass per unit length in the air	t	0.073
Mass per unit length in the water	t	0.044
Minimum bend radius (MBR)	m	2.50
Minimum breaking load (MBL)	kN	150
Maximum allowable curvature (MAC)	rad/m	0.40
Axial stiffness (EA)	MN	750
Bending stiffness (EI)	kN·m²	16.0

Item	Unit	Buoyancy 140%	Buoyancy 230%
Number of DBMs	n/a	49	105
DBMs volume	m³	0.121	0.095
Total buoyancy of DBMs	N	59850	99750

DLC 6.1		Unit	Case 1	Case 2	Case 3	Case 4
Wind	Direction	deg	0	0	180	180
Wind	Speed at hub	m/s	50	50	50	50
Wave	Direction	deg	0	180	0	180
	Significant height	m	8.49	8.49	8.49	8.49
	Peak period	s	13.51	13.51	13.51	13.51
	Peakness factor	n/a	1.52	1.52	1.52	1.52
Current	Direction	deg	0	0	180	180
Current	Surface speed	m/s	1.69	1.69	1.69	1.69
Safety factor		n/a	2.0	2.0	2.0	2.0
Yaw misalignment		deg	0	0	0	0
Seeds		n/a	3	3	3	3
Simulation period		h	3	3	3	3

Parameter	Components	Normal	Tangential
Drag coefficient	Mooring line	2.0	1.15
Drag coefficient	Dynamic power cable	1.2	0.0
Added mass coefficient	Mooring line	0.8	0.2
Added mass coefficient	Dynamic power cable	1.0	0.0

Load case	Unit	Buoyancy 140%	Buoyancy 230%
Case 1	%	12.15	12.60
Case 2	%	11.07	11.25
Case 3	%	−14.87	−14.60
Case 4	%	−18.43	−19.09

Layout	Load case	L₄ (m)	L_T (m)
Buoyancy 140%w	Case 1	0.16	250.16
	Case 2	0.58	250.58
	Case 3	4.82	254.82
	Case 4	3.84	253.84

Buoyancy 230%	Case 1	5.58	333.58
	Case 2	0.52	328.52
	Case 3	10.16	338.16
	Case 4	8.67	336.67

Layout	Load case	Tension (kN)	Ez angle (deg)
Buoyancy 140%	Case 1	53.43	28.36
	Case 2	52.44	14.85
	Case 3	56.29	23.84
	Case 4	56.25	13.76
	μ	54.60	20.20
	σ	1.97	7.07

Buoyancy 230%	Case 1	52.12	35.90
	Case 2	48.13	21.78
	Case 3	56.95	31.97
	Case 4	55.73	22.19
	μ	53.23	27.96
	σ	3.97	7.09

Layout	Load case	Tension (kN)	Curvature (rad/m)
Buoyancy 140%	Case 1	10.026	0.058
	Case 2	9.886	0.059
	Case 3	15.286	0.044
	Case 4	16.895	0.039
	μ	13.023	0.050
	σ	3.603	0.010

Buoyancy 230%	Case 1	20.106	0.039
	Case 2	15.679	0.044
	Case 3	26.440	0.031
	Case 4	23.882	0.031
	μ	21.527	0.036
	σ	4.687	0.006

Layout	Load case	Tension (kN)	Curvature (rad/m)
Buoyancy 140%	Case 1	8.350	0.115
	Case 2	10.138	0.095
	Case 3	14.315	0.079
	Case 4	16.815	0.069
	μ	12.405	0.090
	σ	3.859	0.020

Buoyancy 230%	Case 1	13.470	0.051
	Case 2	15.387	0.045
	Case 3	20.750	0.040
	Case 4	21.953	0.032
	μ	17.890	0.042
	σ	4.102	0.008

Layout	Load case	Tension (kN)	Curvature (rad/m)
Buoyancy 140%	Case 1	4.478	0.058
	Case 2	9.066	0.035
	Case 3	7.081	0.043
	Case 4	12.426	0.028
	μ	8.263	0.041
	σ	3.352	0.013

Buoyancy 230%	Case 1	6.242	0.046
	Case 2	13.840	0.026
	Case 3	10.695	0.033
	Case 4	17.421	0.021
	μ	12.050	0.032
	σ	4.748	0.011