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Coupled Dynamic Modeling of 

Floating Wind Turbine Systems 

Preprint 

E.N. Wayman and P.D. Sclavounos 

Massachusetts Institute of Technology 

S. Butterfield, J. Jonkman, and W. Musial 

National Renewable Energy Laboratory

To be presented at the Offshore Technology Conference 

Houston, Texas 

May 1–4, 2006 

Conference Paper 

NREL/CP-500-39481 

March 2006 
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OTC Paper Number 18287 

Coupled Dynamic Modeling of Floating Wind Turbine Systems 

E.N. Wayman and P.D. Sclavounos, Massachusetts Institute of Technology; S. Butterfield, J. Jonkman, and W. Musial, 

National Renewable Energy Laboratory 

Copyright 2006, Offshore Technology Conference 

This paper was prepared for presentation at the 2006 Offshore Technology Conference held in 

Houston, Texas, U.S.A., 1–4 May 2006. 

 

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Abstract 

This article presents a collaborative research program that the 

Massachusetts Institute of Technology (MIT) and the National 

Renewable Energy Laboratory (NREL) have undertaken to 

develop innovative and cost-effective floating and mooring 

systems for offshore wind turbines in water depths of 10−200 

m. Methods for the coupled structural, hydrodynamic, and 

aerodynamic analysis of floating wind turbine systems are 

presented in the frequency domain. This analysis was 

conducted by coupling the aerodynamics and structural 

dynamics code FAST [4] developed at NREL with the wave 

load and response simulation code WAMIT (Wave Analysis at 

MIT) [15] developed at MIT. 

Analysis tools were developed to consider coupled 

interactions between the wind turbine and the floating system. 

These include the gyroscopic loads of the wind turbine rotor 

on the tower and floater, the aerodynamic damping introduced 

by the wind turbine rotor, the hydrodynamic damping 

introduced by wave-body interactions, and the hydrodynamic 

forces caused by wave excitation. 

Analyses were conducted for two floater concepts coupled 

with the NREL 5-MW Offshore Baseline wind turbine in 

water depths of 10−200 m: the MIT/NREL Shallow Drafted 

Barge (SDB) and the MIT/NREL Tension Leg Platform 

(TLP). These concepts were chosen to represent two different 

methods of achieving stability to identify differences in 

performance and cost of the different stability methods. 

The static and dynamic analyses of these structures 

evaluate the systems’ responses to wave excitation at a range 

of frequencies, the systems’ natural frequencies, and the 

standard deviations of the systems’ motions in each degree of 

freedom in various wind and wave environments. This article 

explores the effects of coupling the wind turbine with the 

floating platform, the effects of water depth, and the effects of 

wind speed on the systems’ performance. 

An economic feasibility analysis of the two concepts was 

also performed. Key cost components included the material 

and construction costs of the buoy; material and installation 

costs of the tethers, mooring lines, and anchor technologies; 

costs of transporting and installing the system at the chosen 

site; and the cost of mounting the wind turbine to the platform. 

The two systems were evaluated based on their static and 

dynamic performance and the total system installed cost. Both 

systems demonstrated acceptable motions, and have estimated 

costs of $1.4−$1.8 million, not including the cost of the wind 

turbine, the power electronics, or the electrical transmission. 

1. Introduction 

A rich wind resource lies untapped off the coasts of the United 

States with an estimated capacity near 1 TW. This resource is 

available 5−50 miles off the coast in water depths mostly 

greater than 30 m. At these depths, the current practice of 

installing wind turbines on monopiles that are driven into the 

seabed becomes economically infeasible. The deployment of 

wind power technology on floating platforms offers a 

promising solution for offshore wind power at these depths, 

and a potential alternative to monopiles in shallower water. 

Previous simulation studies by J. E. Withee [16], K. H. Lee [8] 

and [9], and K. C. Tong [13] show promising results for the 

behavior of floating wind turbine systems. However the full 

coupling between the wind turbine and the floating platform 

has been observed only to a limited extent, and the optimal 

design concept for these systems remains unknown. 

Furthermore, the chore of installing a wind turbine onto a 

floating platform at sea may make the cost of this technology 

prohibitive. 

This study, therefore, has four goals: (1) to make a first 

step toward coupling proven codes from the wind power and 

oil and gas industries to create a tool to model and analyze the 

behavior of coupled wind turbine and floating platform 

systems; (2) to study and understand the behavior of these 

systems in various wind and wave environments; (3) to 

identify the most cost-effective structures that will provide a 

solution to the deep water problem; and (4) to avoid the need 

to install the wind turbine on the platform while at sea. 
2 OTC [18287] 

The approach was to first examine the mechanisms that 

provide stability, and propose two structures that practically 

isolate different stability mechanisms. The next step was to 

observe the dynamics of the coupled systems in various wind, 

wave, and water depth conditions, and evaluate those 

structures based on static and dynamic performance and an 

economic analysis. 

The two platform concepts presented are the 

Massachusetts Institute of Technology/National Renewable 

Energy Laboratory (MIT/NREL) Shallow Drafted Barge 

(SDB) and the MIT/NREL Tension Leg Platform (TLP). The 

MIT/NREL SDB achieves its restoring through high 

waterplane area, and is hence quite stable during the float-out 

and installation processes with the wind turbine already 

mounted. The mooring system of the SDB primarily provides 

station keeping, and does not contribute to the system’s 

stability in pitch and roll. Alternatively, the TLP achieves its 

restoring primarily through its tension leg mooring system, but 

also has enough hydrostatic and inertial restoring to provide 

stability during float-out and installation with the turbine 

already in place. 

The following sections outline this process by detailing the 

static design process and the static and dynamic analysis 

processes. The resulting structures and their respective static 

and dynamic behaviors are then presented and discussed, and 

then extreme wave events are considered. Finally, a summary 

of an initial economic analysis is presented that estimates the 

cost of each structure. The conclusion summarizes the key 

attributes of each structure and discusses their feasibility. 

2. Coordinate System and Modes of System Motion 

The combined wind turbine and floating platform system 

is assumed to undergo rigid body motions in the standard 

modes of motion that are considered in wave-body interaction 

theory. Modes 1−3 are the translational modes of surge, sway, 

and heave, and represent translation along the x, y, and z axes, 

respectively. Modes 4−6 are the rotational modes of roll, 

pitch, and yaw, and represent rotation about the x, y, and z 

axes, respectively. The origin of this coordinate system is 

taken as the x and y locations of the floating platform’s center 

of gravity; the z = 0 plane coincides with the calm water 

surface. Throughout the static and dynamic analyses, the wind 

and the ambient waves are assumed to be aligned and to 

propagate in the positive x direction. Four wind speeds and 

four water depths were considered for the MIT/NREL SDB. 

This coordinate system and the corresponding modes of 

motion are shown in Figure 1. 

Figure 1. Coordinate System and Modes of System Motion. 

3. NREL 5-MW Offshore Baseline Wind Turbine 

The wind turbine used in this study is the NREL 5-MW 

Offshore Baseline Wind Turbine model. This model does not 

correspond to an operating turbine, but is a realistic 

representation of a three-bladed upwind 5-MW wind turbine; 

its properties are drawn and extrapolated from operating 

machines and conceptual studies. Its general properties are 

described in Table 1. The details and rationale for this model 

are given by NREL in [5]. A rating of 5 MW was chosen 

because it is speculated to be the minimum rating at which a 

deepwater offshore wind turbine can be cost effective. 

Table 1. NREL 5-MW Offshore Wind Turbine

Rotor Orientation Upwind

Control Variable Speed, Collective Pitch

Rotor Diameter/Hub Diameter 126 m/3 m

Hub Height 90 m

Max Rotor/Generator Speed 12.1 rpm/1,173.7 rpm

Maximum Tip Speed 80 m/s

Overhang/Shaft Tilt/Precone 5 m/ 5°/ -2.5°

Rotor Mass 110,000 kg

Nacelle Mass 240,000 kg

Tower Mass 347,460 kg

Overall c.g. location

(x,y,z)t

 = (-.2,0,64)m

U

x

y

1: Surge

2: Sway 

3: Heave 

4: Roll 

5: Pitch 

6: Yaw 

z
OTC [18287] 3 

The systems were analyzed at four wind speeds to capture 

the coupled systems’ performance in representative wind 

speeds throughout the operational spectrum of the wind 

turbine. The wind speed of 9 m/s represents region 2 of the 

power curve. The turbine operates at roughly half of rated 

power at this wind speed. Its rated power is represented by 

11.2 m/s, where it first reaches its rated power. Fifteen m/s 

represents wind speeds beyond rated wind speed where the 

wind turbine feathers its blades to maintain rated power; 25 

m/s is the cut-out speed, or the highest sustained wind speed 

where the turbine is in operation. 

4. Overall Study Approach 

This study aims to advance the understanding and feasibility 

of floating wind turbine systems. Its goals are to study the 

effects of coupling a wind turbine with a floating structure on 

the dynamics of the floating system, to explore the effects of 

environmental conditions, and to identify the most costeffective floating structures to support a wind turbine that will 

demonstrate favorable operational performance. To avoid the 

uncertainty and the cost of mounting a wind turbine to a 

floating platform at sea, the study seeks to propose concepts 

for floating structures that will allow the wind turbine to be 

mounted on the platform on shore or in a shipyard and towed 

to its installation site already assembled. 

To achieve these goals, this study first examines the 

mechanisms that provide restoring to a structure. With this 

knowledge, a static design process is carried out to provide 

two structures of relatively low cost and that promise to 

provide adequate restoring to allow the system to be floated 

out stably, and for the system to achieve an acceptable steadystate operating point once installed. These structures are 

passed to a static analysis phase where the steady-state 

operating point in various wind speeds is evaluated. Next, the 

systems and their steady-state operating conditions are passed 

to a dynamic analysis phase where their dynamic properties, 

including the systems’ response amplitude operators (RAOs), 

natural frequencies, and the standard deviations of motions in 

various wind speeds and sea states, are calculated. This 

general process is outlined in Figure 2. 

Figure 2. Flowchart Outlining the Study’s Approach. 

5. Static Design of MIT/NREL SDB and TLP Systems 

Design Approach 

The static performance of the combined wind turbine floating 

platform system is the initial criterion that drives the design of 

the floating platforms. The combined system is designed to 

demonstrate favorable steady-state static performance in its 

installed state, about which the system oscillates in response to 

random waves. Furthermore, the system must achieve a 

certain level of static stability during towing operations. 

The system’s position in steady-state operation is 

determined by the steady-state forces exerted on the system 

and the system’s restoring properties. Restoring is achieved 

through three general mechanisms: waterplane area moment, 

ballasting that creates vertical separation between the system’s 

center of gravity and center of buoyancy, and the mooring 

system. These mechanisms serve as a classification of 

floating structures, as developed in [1]. 

Conceptually, these three restoring mechanisms can be 

epitomized by three extreme structures: a shallow drafted 

barge that represents restoring by waterplane area moment, a 

ballasted deep drafted spar that represents vertical separation 

between the system’s center of gravity and center of 

buoyancy, and a TLP that represents restoring by the mooring 

STATIC 

ANALYSIS 

STATIC 

DESIGN 

DYNAMIC 

ANALYSIS 

Designs’ Steady-State 

Operating Point

RESULTS EVALUATED:

• Steady State Operation 

• System RAOs 

• Standard Deviation of System Motions 

• Natural Frequencies 

Promising Designs 

Designs’ Dynamic Performance 
4 OTC [18287] 

system. These restoring methods and their representative 

structures are shown in gray in Figure 3. 

Figure 3. Restoring Mechanisms and Representative Structures. 

This study examines the behavior and cost of the most 

practical representation of these extreme structures. Structures 

studied are the MIT/NREL SDB and the MIT/NREL TLP that 

achieve restoring primarily through waterplane area moment 

and the mooring system, respectively. These structures are 

shown in red in Figure 3. The extreme of ballasting was not 

presented here because an initial consideration of that 

structure type showed that the draft required to create enough 

inertial restoring rendered its construction infeasible for any 

realistic shipyard and port. 

The following sections outline the static design process 

used to arrive at the specifications for the MIT/NREL SDB 

and the MIT/NREL TLP. 

Static Design of the MIT/NREL SDB 

The MIT/NREL SDB is intended to represent the 

waterplane area method of achieving restoring. However, the 

structure also contains ballast to achieve a reasonable draft. 

Therefore, the MIT/NREL SDB achieves the required 

restoring through an optimal mix of waterplane area and 

ballast. 

A static design and analysis phase is initially carried out, 

calling on theory developed in [3] and [11], to determine the 

optimal size and shape of the MIT/NREL SDB that will 

provide sufficient stability in unmoored operating conditions. 

Once moored, the mooring lines are assumed to provide 

station-keeping functions only. Therefore, the MIT/NREL 

SDB system is assumed to experience restoring from its 

mooring lines only in surge, and is required to demonstrate 

acceptable static and dynamic behavior in all other modes of 

motion during full operation mode without additional restoring 

from mooring lines in those modes. 

The optimal size and shape are determined by solving for 

the platform geometry that limits the static steady-state pitch 

of the combined platform-wind turbine system to a pitch angle 

below a designated threshold value. The system must maintain 

an acceptable steady-state pitch angle in maximum wind 

loading conditions that it would experience during operation. 

The steady-state pitch is determined by the pitch moment 

on the system and the system’s restoring properties in pitch, as 

shown in the following equation. 

5

5

55

F

C ξ =

where F5 is the pitch moment about the origin of the 

coordinate system generated by the wind loading on the wind 

turbine, denoted by FThrust. This moment is given here. 

FFZ 5 = Thrust Hub

In the case of the MIT/NREL SDB, restoring is achieved 

through hydrostatics (waterplane area moment and the 

location of the center of buoyancy) and inertia (ballasting, and 

location of the center of mass). The hydrostatic and inertial 

restoring coefficient in pitch for a cylindrical, surface-piercing 

cylinder is shown in the following equation 

4

55, & 11 4 HI B B G

R C F Z M gZ g =− + ρ π

where FB and ZB represent buoyant force and center of 

buoyancy, M11, the total system mass, ZG, the center of 

gravity, ρ, the density of sea water, and R, the cylinder radius. 

It is speculated that beyond a pitch angle of 10 degrees, the 

wind turbine will lose substantial efficiency. Therefore, the 

threshold pitch value in this study was taken as 10 degrees. 

The maximum wind loading was taken as 800,000 N, which 

is the steady state thrust at a wind speed of 11.2 m/s and acts 

on the wind turbine hub, at ZHub = 91.5 m. The necessary 

restoring coefficient is found by solving for the restoring 

coefficient needed to limit the pitch to 10 degrees, as shown 

here. 

[ ] 5 8

55

5

800,000 91.5 4.2 10

.1745

F N m C N ξ rad

× − ⎡ ⎤ = = = − ⎢ ⎥ ⎣ ⎦  m

A sufficient restoring coefficient can be achieved by 

adjusting the draft and radius of the platform, and by pouring 

concrete inside the cylinder to add ballast. The resulting 

dimensions and properties of the MIT/NREL SDB are listed in 

Table 2. 
OTC [18287] 5 

Table 2. MIT/NREL SDB Properties 

Cylinder Radius 18 m

Cylinder Height 6.5 m

Concrete Ballast Height 1.65 m

Steel Thickness 0.01 m

Installed Draft 5 m

Deck Clearance 1.5 m

Steel Mass 218 metric ton

Concrete Mass 4299 metric ton

Turbine Mass 698 metric ton

Total Mass 5210 metric ton

Buoyant Mass 5210 metric ton

Reserve Buoyancy 0 kg

Center of Gravity 4.25 m

Center of Buoyancy -2.5 m

C55 4.84E+08 N-m

Static Design of the MIT/NREL TLP 

The MIT/NREL TLP is intended to represent a structure 

that achieves its restoring through a tension leg mooring 

system. This results in a system that is stiff in pitch relative to 

the MIT/NREL SDB, with significant force exerted by the 

tethers. A static design process along the lines of [16] and 

utilizing the theory developed in [3] and [11] is carried out to 

determine the tether tension and dimensions of the TLP. 

The restoring coefficient in pitch provided by the tethers is 

shown here. 

( ) ( )2

55, 2 Tethers

Tethers Tethers

Tethers

EA

C R

L

= + F T

where (EA)Tethers is the elastic modulus times the cross 

sectional area of the tethers, LTethers is the unstretched length of 

the tethers, R is the cylinder radius (or the radial distance to 

the tether fairlead), FTethers is the total force exerted by the 

tethers, and T is the cylinder draft (or the vertical distance to 

the tether fairlead). 

This equation shows the relationship of this restoring term 

to the elastic stiffness of the tethers. This study considers the 

rigid body motions, hence elastic modes of motion are out of 

the study’s scope, and the tethers are taken to be infinitely 

stiff. This assumption drives the restoring in pitch from the 

tethers toward infinity. 

( )Tethers EA → ∞

⇒ C55,Tethers → ∞

This stiffness prevents any significant motion in pitch, roll, 

and heave, and the platform’s motions are therefore limited to 

surge, sway, and yaw. The mooring system must be designed 

to adequately limit motions in these modes. 

A tension leg mooring system must also maintain 

reasonable tension in all of its tethers. With the steady-state 

wind force acting in the positive x direction, the tension in 

tether 3 increases and the tension in tether 1 decreases to 

provide a balance of forces and moments. The initial tether 

tension must be chosen to ensure that the tension in the 

windward tether does not exceed the maximum allowable 

tension and the tension in the leeward tether does not drop 

below the minimum allowable tension. 

A drawback of a conventional TLP is that the system has 

low or negative restoring properties without its mooring 

system, which renders it unable to float upright on its own. 

This attribute would require the wind turbine to be mounted to 

the floating platform only after the platform is installed and 

the tethers tensioned. 

To avoid mounting the wind turbine at sea, the size and 

shape of the floating platform must be chosen to provide the 

structure with significant restoring during towing and 

installation. The restoring during these processes is provided 

in part by water ballast inside the structure. Once the system 

reaches its installation site, it is hooked to its tethers, and 

deballasted to pretension the tethers. This pretensioning 

process requires the weight of the water ballast inside the 

structure to equal the total tension force desired. 

To summarize, the tether tension for this system must 

fulfill three requirements: (1) the tethers must provide 

sufficient restoring in surge to adequately limit the steadystate offset in surge; (2) the tension of the windward tether 

must never exceed the maximum allowable tension, and the 

leeward tether must never go slack or fall below the minimum 

allowable tension at any point during operation; and (3) the 

total force exerted by the tethers must match the weight of the 

water required to ballast the system for stability during 

installation. 

The operational scenario is shown in Figure 4. 

Figure 4. Steady-State Operational Configuration of the TLP. 
6 OTC [18287] 

Under steady-state conditions, the platform will achieve its 

steady-state displacement in surge. At this displacement, the 

tethers will form an angle with the vertical, shown as θ in 

Figure 4. The tethers must be of sufficient tension to provide 

adequate restoring to limit this angle to about 5 degrees to 

prevent the system from experiencing highly nonlinear 

restoring and displacement. 

Restoring in surge caused by the tethers is related to the 

tether tension and length through the following equation. 

11

Tethers

Tethers

F C

L =

Restoring results in steady-state displacement through the 

following relation. 

1

1

11 11

F FThrust

C C ξ = =

An initial limit for the tether tension is reached by limiting 

the system’s steady-state displacement. 

This tension must also satisfy the second requirement for 

the operational line tension. In operating conditions, the 

tension in each line is found by solving a balance of forces and 

moments for the tensions. As indicated in Figure 4, the tethers 

are numbered 1 through 4, where at rest the fairlead and 

anchor of tether 1 align with the positive x axis, tether 2, the 

positive y axis, tether 3, the negative x axis, and tether 4, the 

negative y axis. Assuming that the wind always propagates in 

the positive x direction, tether 3 is always the upwind tether 

and tether 1 is always the downwind tether. 

A balance of forces in the vertical direction requires the 

buoyancy force plus the additional buoyancy gained by the 

setdown of the structure as shown in Figure 4. The system 

weight must equal the downward component of the sum of the 

tether tensions. This balance of forces is shown in the 

following equation, where θ represents the angle that the 

tethers make with the vertical. 

( ) 2

11 , cos cos F g R L L Mg F B + − −= ρ π Tether Tether θ θ∑ T i

Employing the small angle approximation that cos θ is 

about equal to 1 and that sin θ is about equal to θ, this equation 

simplifies to 

F Mg F B − = 11 ∑ T i,

With four tethers spaced at 90-degree intervals around the 

structure, FT,ave, the average tether tension is found by dividing 

the total tension force by four. Because tethers 2 and 4 are not 

affected by the moment exerted on the structure, they are 

assumed to have tensions equal to the average tension. 

( ) 2

11

,2 ,4 ,

cos

4cos

B Tether Tether

T T T ave

F g RL L M g FFF ρ π θ

θ

+ −− == =

Again invoking the small angle approximation, the tension 

in tethers 2 and 4 is given by 

11

,2 ,4 , 4

b

T T T ave

F Mg FFF − == =

The tethers of concern are tethers 1 and 3, which are at risk 

of going slack or exceeding the maximum allowable tension, 

respectively. To balance the moment exerted on the system, 

tether 3 has a tension of FT,ave plus an additional tension, ∆F. 

To maintain the balance of forces in the vertical direction, 

tether 1 must then have a tension of FT,ave minus ∆F. This 

balance of moments is given by the following equation. 

5 ,3 ,1 ( )( ) , , cos cos cos cos F FR FR F FR F FR = − = +∆ − −∆ T θθ θ T T ave T ave θ

)

Employing the small angle approximation, this equation 

simplifies to the following equation. 

F FR FR F FR F FR 5 ,3 ,1 , = − = +∆ − −∆ T T ( )( T ave T ave ,

The initial line tension must be chosen to prevent the 

tensions in the individual tethers from going to zero or 

exceeding the maximum allowable tension. 

The final requirement is that this tether tension must be 

equal to the weight of the water used as ballast to stabilize the 

system during towing and installation. 

The maximum force that the system is expected to 

experience during towing is taken as the minimum thrust 

exhibited by the turbine during its operation, 250,000 N. The 

turbine will clearly not be operating during towing and 

installation, so the wind loading on the structure will certainly 

be lower than any wind loading during operation. Therefore, 

the minimum operational thrust serves as a definite upper 

bound to the installation wind loading. 

Again, the system is required to achieve adequate 

hydrostatic and inertial restoring to limit the steady-state pitch 

to less than 10 degrees during towing and installation. This 

limit was chosen to ensure that the system will remain almost 

vertical during installation processes, allowing the installers to 

tow the system with little stabilization required. To enforce 

this requirement, the minimum hydrostatic and inertial 

restoring coefficient required during towing can be found with 

the following equation. 

[ ] 5 8

55, & ,min

5

250,000 91.5 1.3 10

.1745 H I

F N m C N ξ rad

× − ⎡ ⎤ = = = − ⎢ ⎥ ⎣ ⎦  m

This restoring is achieved by adjusting the cylinder height 

and radius and the level of concrete ballast. 
OTC [18287] 7 

The requirements outlined above are considered together 

to arrive at the TLP’s size, shape, and tether tension. The 

system properties that result from this iterative static design 

process are summarized in Table 3. 

Table 3. Properties of the MIT/NREL TLP in 

Operating and Towing Conditions 

Ststem Properties

Radius 11.00 m

Cylinder Height 21.5 m

Concrete Ballast Height 4.5 m

Steel Thickness 0.01 m

Steel Mass 176 metric ton

Concrete Mass 4375 metric ton

Turbine Mass 698 metric ton

System in Towing Conditions

Water Ballast Height 6.55

Water Mass 2548 metric ton

Total Mass 7798 metric ton

Towing Draft 20.01

Deck Clearance 1.49

Center of Gravity -11.07

Center of Buoyancy -10.01

C55,Towing 1.97E+08 N-m

System in Installed, Operating Conditions

Number of Tethers 4

FTethers,Total 2.50E+07 N

FTethers,each 6.25E+06 N

FTethers,max [14] 2.38E+07 N

∆F 3.33E+06 N

FT,3 9.58E+06 N

FT,1 2.92E+06 N

Installed Draft 20.01 m

Deck Clearance 1.49 m

Total Mass 5249 metric ton

Buoyant Mass 7797 metric ton

Reserve Buoyancy 48.54%

Center of Gravity -9.40 m

Center of Buoyancy -10.01 m

6. Static and Dynamic Analysis Process 

The combined wind turbine and floating platform systems 

were analyzed in the frequency domain by following the 

process outlined in Figure 5. 

Figure 5. Flowchart for the Static and Dynamic Analysis Process. 

Inputs to this analysis process are shown in blue in this 

figure, analysis modules are shown in yellow, quantities 

passed between the modules are shown along the arrows, and 

the final outputs are shown in green. 

This process first takes the platform and wind turbine 

geometry and inertia, the steady-state thrust of the wind 

turbine, and the tether configuration into the STATIC 

ANALYSIS module. This module calculates the steady forces 

on the system and the system’s restoring, and computes the 

steady-state operating point, summarized by the six element 

vector, ξ. 

This steady-state operating point is passed to the FAST

module that calculates the linearized properties of the wind 

turbine. These include the wind turbine’s mass, damping, and 

stiffness matrices that incorporate contributions from 

aerodynamics and gyroscopics, shown in Figure 5 as MWT, 

BWT, CWT, respectively. The platform geometry and water 

depth are then passed to WAMIT, which calculates the 

platform’s mass, added mass, damping and stiffness matrices, 

and exciting forces MFP, AFP(ω), BFP(ω), CFP, and XFP(ω) at 

each frequency. 

The matrices for the wind turbine and the platform are then 

passed to the DYNAMIC ANALYSIS module, where they are 

combined to represent the coupled system, and the RAOs, 

natural frequencies, and standard deviations of motions of the 

combined system are calculated. 

The details of the calculations performed in each module 

are detailed in the following sections. 

Steady-State Operating Point 

A static analysis is first carried out to determine the 

steady-state operating configuration of the combined wind 

turbine-floating platform system in its moored condition. This 

configuration is governed by the static equilibrium equation, 

summarized in matrix form: 

[ ] H I Tethers Steady & Steady State State

CC F ⎛ ⎞⎛ + Ξ= ⎜ ⎟⎜ ⎝ ⎠⎝

⎞

⎟

⎠

R

where CH&I and CTethers represent the six-by-six restoring 

matrices from the hydrostatics and inertia from the tethers, 

respectively, Ξ represents the six-element steady-state 

displacement vector, and F represents the six-element steadystate force and moment vector exerted on the system by the 

wind. 

Assuming small rotations and displacements, the restoring 

coefficients are as follows. The hydrostatic and inertial 

restoring matrix for a surface-piercing cylinder contains all 

zeros except for the 33, 44, and 55 entries, which are defined 

here. 

2 C g 33, &H I = ρ π
8 OTC [18287] 

4

44, & 11 4 HI bb g

g R C F z M gz ρ π =− +

4

55, & 11 4 HI bb g

g R C F z M gz ρ π =− +

The restoring matrix for a tension leg mooring system 

contains all zeros except the following entries. As explained in 

Section 5, the tethers of the tension leg mooring system are 

modeled as infinitely stiff tethers to model purely rigid body 

motions. This drives C33,Tethers, C44,Tethers, and C55,Tethers toward 

infinity. 

11,

Tethers

Tethers

Tethers

F C

L =

22,

Tethers

Tethers

Tethers

F C

L =

33,

Tethers Tethers

Tethers

Tethers

E A C

L

= → ∞

( )2

44, 11 2 ( T T

Tethers Fairlead B

T

E A C RF M g L

= + − )T → ∞

( )2

55, 11 2 () T T

Tethers B

T

E A C RF M g L

= +− T → ∞

( ) ( )

2

66, 11

Fairleed

Tethers b

Tethers

R

C F

L = − M g

51, 42,

Tethers

Tethers Tethers

Tethers

F C C

L = =− T

ω

The MIT/NREL SDB is intended to represent a system that 

achieves stability through waterplane area. A mooring system 

is used with this design for station keeping only. Therefore, 

restoring is assumed to be provided only by the mooring lines 

in the mode of surge. 

Steady-state static displacement is then calculated as 

follows. 

[ ] 1

Steady H I Tethers Steady & State State

CC F − ⎛ ⎞ Ξ= + ⎜ ⎟ ⎝ ⎠

Response Amplitude Operators 

The RAOs are calculated in the DYNAMIC ANALYSIS

module for the combined wind turbine and floating platform 

system. 

The equations of motion that govern the linear dynamic 

motions of the system are summarized in matrix form: 

( ) ( ) () () () 2 ⎡ ⎤ − + + +Ξ = ω ω ωω ω M A iB C X ⎣ ⎦

where M, A(ω), B(ω), and C represent the 6 by 6 

combined mass, added mass, damping, and stiffness matrices, 

respectively, and X(ω), the six-by-one vector that contains the 

hydrodynamic exciting forces. These matrices are the 

superposition of the matrices calculated by the FAST module 

for the wind turbine and by the WAMIT module for the floating 

platform. 

The mass matrix can be found easily, while the added mass 

matrix, the damping matrix, and exciting forces are evaluated 

by WAMIT and FAST. The restoring matrix represents the 

restoring from hydrostatics and inertia, as developed in the 

previous section. 

The symbol Ξ(ω) represents the system’s dimensional 

response in each mode of motion at each frequency. The RAO 

is then reported as the dimensionless motion, made 

nondimensional. 

For the translational modes of motion, the RAO is given 

by 

( ) ( ) i

i

wave

w RAO w

A

Ξ = i = 1,2,3

and for the rotational modes of motion, the RAO is given by 

( ) ( ) /

i

i

wave

RAO

A R

ω

ω

Ξ = i = 4,5,6

where the subscript i denotes the mode of motion, Awave

represents the wave amplitude, and R is the cylinder radius. 

Although the RAOs are independent of the sea state, the 

damping and stiffness properties of the wind turbine depend 

on wind speed, which causes the RAOs of the combined 

system to depend on wind speed. 

Natural Frequencies 

The natural frequencies of the combined wind turbine and 

floating platform system can be estimated by considering the 

system’s restoring and inertial properties. 

*

(0)

ii

i

ii ii

C

M A

ω = +

where the subscript i indicates the mode of motion, and the 

0 indicates the zero-frequency limit of the added mass. 

In weakly restored modes of motion, the natural frequency 

will be calculated as zero. These modes of motion, however, 

pick up a natural frequency through cross coupling to other 

modes of motion. In this case, the natural frequencies can be 
OTC [18287] 9 

determined graphically, by examining the frequency at which 

the peak of the RAO occurs. 

Standard Deviation of System Motions 

By virtue of linear system theory, once the RAOs of the 

system have been determined, the variance and standard 

deviation of the system motions in various sea states can be 

ascertained [12]. An assumption of linear system theory is that 

given a Gaussian input signal, the output of the linear system 

will also be Gaussian with a variance determined by the 

Wiener-Khinchine theorem, which is shown in the following 

equation for the translational modes: 

( ) 2 2

i i S RAO d σ ω ξ ζ = ∫ ω i = 1,2,3, 

and by the equation below for the rotational modes, 

( )

2

2

i 2

RAOi S

R

σ ω ξ ζ = ∫ dω i = 4,5,6 

where 2

i σ ξ represents the variance of system motion in 

mode i, Sζ (ω), the spectral density of the ambient waves in 

the given sea state, ω , the wave frequency, and R, the radius 

that was used originally to make the RAO non-dimensional. 

The spectral density for fully developed seas has been 

defined by the International Ship Structures Committee (ISSC) 

and the International Towing Tank Conference (ITTC) [12]. 

( ) ( ) 5

2 .11 exp .44 22 2

m m

s m

T S HT ζω ω

ω

ππ π

−

⎛ ⎞⎛⎞ ⎛⎞ ⎧⎪ = ⎜ ⎟⎜⎟ ⎜⎟ ⎨ ⎬ ⎝ ⎠⎝⎠ ⎝⎠ ⎪⎩

4

T − ⎫⎪

⎪⎭

Hs and Tm represent significant wave height and mean 

period in the given sea state, respectively. The DYNAMIC 

ANALYSIS module performs this calculation to give the 

standard deviation of the system motion in 5 sea states defined 

in Table 4. 

Table 4. Sea State Definition 

Sea State Hs [m] Tm [s]

1 0.09 2.0

2 0.67 4.8

3 2.44 8.1

4 5.49 11.3

5 10.00 13.6

Analyses were performed by following this entire process 

for the MIT/NREL SDB and TLP in various wind, wave, and 

water depth conditions. Results are reported in the sections 

that follow to illustrate the effects of coupling the wind turbine 

with the floating platform, the effects of water depth, and the 

effects of wind speed. 

7. Static and Dynamic Analysis of the MIT/NREL SDB 

The MIT/NREL SDB is presented at water depths of 

10−100 m. An analysis at 10 m was performed to examine the 

SDB as a potential alternative to monopiles in shallow water. 

At 30 m, monopiles become technically and economically 

challenging to install. The NREL baseline water offshore site 

is 62.5 m deep. Finally, an analysis was performed at 100 m to 

illustrate the trends in behavior of the SDB as depth increases. 

The wind speed of 11.2 m/s and the water depth of 62.5 m 

were chosen as the base-case conditions for this analysis 

because they represent likely operating conditions that will be 

easily compared to other NREL studies. 

Static Analysis of the MIT/NREL SDB 

The steady-state static equation of motion was solved at 

four wind speeds that represent various zones of the power 

curve. The results of steady-state pitch in these wind speeds 

are summarized in Table 5. 

Table 5. Steady-State Pitch of the SDB in Various 

Steady Wind Speeds 

Wind Speed Thrust Restoring Pitch

[m/s] [kN] [N-m] [deg]

9 600 4.84E+08 6.499

11.3 800 4.84E+08 8.665

15 500 4.84E+08 5.416

25 400 4.84E+08 4.333

Dynamic Analysis of the MIT/NREL SDB 

The results of the dynamic analysis consist of the RAOs, 

the natural frequencies, and the standard deviations of the 

system motions. The RAOs for each analysis case will appear 

at the end of the section; the other results will be reported in 

the body of this section. 

Base-Case – Coupled System Effects 

The results of the dynamic analysis are first presented in 

Figure 6 for the base-case scenario of 11.2 m/s winds and 

62.5-m water depth. 

The RAOs of the combined wind turbine and floating 

platform are shown in Figure 6. Although the system is 

excited by wind and waves only in the modes of surge, heave, 

and pitch, it displays motion in the modes of sway, roll, and 

yaw as well. The system’s response in these modes indicates 

the effects of the coupling mechanisms that result from 

combining the wind turbine with the floating platform. The 

response in these modes, however, is quite small compared to 

the dominant modes. 

The RAOs also indicate a strong response at the system’s 

resonant frequencies. The resonant frequencies are listed in 
10 OTC [18287] 

Table 6. As explained in Section 6, although the modes of 

sway and yaw have no restoring, these modes of motion pick 

up a natural frequency through cross coupling effects, and are 

determined graphically from the system’s RAOs in Figure 6. 

Finally, the standard deviations of the system motions in 5 sea 

states are summarized in Table 7. 

Table 6. Natural Frequencies of the MIT/NREL SDB 

Mode Natural Frequency

Surge 0.769 [rad/s]

Sway 0.769 [rad/s]

Heave 0.650 [rad/s]

Roll 0.455 [rad/s]

Pitch 0.457 [rad/s]

Yaw 0.457 [rad/s]

Table 7. Standard Deviation of System Motions of 

the MIT/NREL SDB in Wind Speed of 11.2 m/s, Water 

Depth of 62.5 m, and Various Sea States 

Sea State 1 2 3 4 5

Hs [m] 0.09 0.67 2.44 5.49 10

Tm [s] 2 4.8 8.1 11.3 13.6

Surge [m] 0.00038 0.19875 1.32242 1.96520 2.66969

Sway [m] 0.00000 0.00006 0.01114 0.03916 0.06198

Heave [m] 0.00004 0.09430 0.62427 1.40341 2.53490

Roll [deg] 0.00000 0.00030 0.02239 0.07584 0.11748

Pitch [deg] 0.00002 0.01448 0.21819 0.62477 1.02926

Yaw [deg] 0.00000 0.00142 0.02994 0.10242 0.17075

For the MIT/NREL SDB, Table 7 shows increasing 

standard deviations of system motions with increasing severity 

of sea state. This can be attributed to the shape of the RAOs 

and the shape of spectral densities describing different sea 

states. At lower sea states, the spectral density has a large 

spread, and is centered around relatively high frequencies. As 

the severity of the sea state increases, its spectral density 

becomes more narrow-banded, and centered around lower 

frequencies. The standard deviation of system motions 

increase with increasing sea state because the MIT/NREL 

SDB’s natural frequencies are low compared to the 

frequencies where the peak of the spectral densities occur. As 

the sea state increases, the peak of the spectral density 

approaches the natural frequency, which results in an 

increasing response with increasing sea state. 

These results show the importance of considering the sea 

state properties of a site chosen for the installation of a 

floating structure. The structure must be tuned to achieve 

RAOs whose peaks are not coincident with the peak of the 

spectral density describing the likely sea state at that site. 

Wind Speed Effects 

The effects of various wind speeds on the combined 

system’s RAOs are shown in Figure 7. These RAOs are 

calculated at the base-case water depth of 62.5 m. 

The results plotted for the wind speed effects of the 

MIT/NREL SDB combined system once again show proof of 

coupling between the modes of motion. The RAOs in pitch 

and roll indicate that this coupling weakens in region 2 of the 

wind turbine power curve, as the wind turbine increases its 

power generated with wind speed to rated power, and 

strengthens beyond rated power. This effect is due to the 

cross coupling terms of the wind turbine matrices. Cross 

coupling damping terms are lowest at 15 m/s, and highest at 

11 m/s, while the cross coupling inertial terms are highest at 

15 m/s, and lowest at 11 m/s. 

The natural frequencies of the system, which are 

summarized in Table 8, remain fairly constant in various wind 

speeds. The standard deviations of system motions in various 

wind speeds are also summarized in Table 9. 

Table 8. Natural Frequencies of the MIT/NREL SDB in 

62.5-m Water Depth and Various Wind Speeds 

Wind Speed [m/s] 9 11.2 15 25

Surge [rad/s] 0.7689 0.7689 0.7689 0.7689

Sway [rad/s] 0.7689 0.7689 0.7689 0.7689

Heave [rad/s] 0.6496 0.6496 0.6496 0.6496

Roll [rad/s] 0.4522 0.4548 0.4526 0.4530

Pitch [rad/s] 0.4541 0.4568 0.4546 0.4539

Yaw [rad/s] 0.4541 0.4568 0.4546 0.4539

Table 9. Standard Deviations of System Motions of 

the NREL/MIT SDB in 62.5-m Water Depth and 

Various Wind Speeds 

Hs [m] 0.09 0.67 2.44 5.49 10

Tm [s] 2 4.8 8.1 11.3 13.6

9 m/s 0.000 0.200 1.324 1.967 2.673

11.2 m/s 0.000 0.199 1.322 1.965 2.670

15 m/s 0.000 0.200 1.326 1.988 2.715

25 m/s 0.000 0.200 1.332 1.977 2.676

9 m/s 0.000 0.000 0.012 0.042 0.066

11.2 m/s 0.000 0.000 0.011 0.039 0.062

15 m/s 0.000 0.000 0.113 0.484 0.790

25 m/s 0.000 0.000 0.053 0.241 0.439

9 m/s 0.000 0.094 0.623 1.403 2.535

11.2 m/s 0.000 0.094 0.624 1.403 2.535

15 m/s 0.000 0.094 0.622 1.404 2.539

25 m/s 0.000 0.094 0.622 1.405 2.540

9 m/s 0.000 0.000 0.019 0.071 0.112

11.2 m/s 0.000 0.000 0.022 0.076 0.117

15 m/s 0.000 0.001 0.189 0.768 1.235

25 m/s 0.000 0.003 0.112 0.374 0.608

9 m/s 0.000 0.015 0.225 0.675 1.118

11.2 m/s 0.000 0.014 0.218 0.625 1.029

15 m/s 0.000 0.015 0.215 0.653 1.089

25 m/s 0.000 0.015 0.163 0.320 0.517

9 m/s 0.000 0.001 0.021 0.081 0.142

11.2 m/s 0.000 0.001 0.030 0.102 0.171

15 m/s 0.000 0.002 0.076 0.304 0.494

25 m/s 0.000 0.002 0.042 0.137 0.230

Pitch 

[deg]

Yaw 

[deg]

Sea 

States

Surge 

[m]

Sway 

[m]

Heave 

[m]

Roll 

[deg]
OTC [18287] 11 

As the RAOs suggest, the standard deviations of the 

system motions decrease with wind speed in region 2 of the 

power curve, where the wind turbine damping plays an 

increasingly larger role. The standard deviations of motions 

increase in region 3, as the wind turbine begins to feather its 

blades, reducing its damping. The motions then decrease 

again at very high wind speeds. Again, the cross-coupling 

effects are visible in the standard deviations of the system 

motions, most notably in roll at the wind speed of 15 m/s. 

Water Depth Effects 

Due to the shallow draft of the SDB, this structure has 

potential to be deployed in very shallow water as a possible 

alternative to monopile foundations. This shallow draft could 

also lead to the potential for slamming and other nonlinear 

effects in deeper open water, where large waves are more 

likely to develop. The effects of water depth on the MIT/ 

NREL SDB system are shown in water depths of 10, 30, 62.5, 

and 100 m, at the base-case wind speed of 11.2 m/s for (see 

Figure 8). These numbers show once again the coupling 

between modes of motion, and also show that surge motions 

increase with water depth, where as pitch motions decrease 

with water depth. 

The natural frequencies for this system in the water depths 

listed above are apparent in the RAOs, and are summarized in 

Table 10. 

Table 10. Natural Frequencies of the MIT/NREL SDB 

in 11.2 m/s Wind Speeds and Various Water Depths 

Water Depth [m] 10 30 62.5 100

Surge [rad/s] 0.7270 0.7657 0.7689 0.7692

Sway [rad/s] 0.4403 0.4543 0.4548 0.4549

Heave [rad/s] 0.4024 0.5749 0.6496 0.6782

Roll [rad/s] 0.4403 0.4543 0.4548 0.4549

Pitch [rad/s] 0.4424 0.4563 0.4568 0.4569

Yaw [rad/s] 0.4424 0.4563 0.4568 0.4569

These natural frequencies remain fairly constant across 

water depths, increasing only slightly with increasing depth. 

The only term factoring into the natural frequencies that is 

affected by water depth is the zero-frequency added mass 

term. Because this term only varies slightly with water depth, 

the natural frequencies remain fairly constant. 

The RAOs of the SDB in various water depths result in the 

standard deviations of system motions summarized in Table 

11. 

The values of the standard deviations of motion for various 

water depths show that although the cross coupling in the 

system excites motion in modes not directly excited by the 

wind and waves, the motions excited by cross coupling alone 

are highly tuned to a certain frequency and do not result in 

large standard deviations of motion. Furthermore, the results 

over the water depths show that the standard deviations of 

motions generally decrease with water depth. This trend is 

due to decreasing added mass with increasing water depth. 

Table 11. Standard Deviations of System Motions of 

the NREL/MIT SDB in 11.2 m/s Wind Speeds and 

Various Water Depths 

Hs [m] 0.09 0.67 2.44 5.49 10

Tm [s] 2 4.8 8.1 11.3 13.6

10 m 0.000 0.186 1.107 1.872 2.886

30 m 0.000 0.204 1.350 2.042 2.826

62.5 m 0.000 0.199 1.322 1.965 2.670

100 m 0.000 0.198 1.316 1.945 2.626

10 m 0.000 0.000 0.019 0.073 0.119

30 m 0.000 0.000 0.013 0.047 0.075

62.5 m 0.000 0.000 0.011 0.039 0.062

100 m 0.000 0.000 0.011 0.037 0.058

10 m 0.000 0.056 0.613 1.526 2.759

30 m 0.000 0.094 0.627 1.411 2.547

62.5 m 0.000 0.094 0.624 1.403 2.535

100 m 0.000 0.094 0.624 1.402 2.533

10 m 0.000 0.000 0.030 0.111 0.175

30 m 0.000 0.000 0.026 0.090 0.140

62.5 m 0.000 0.000 0.022 0.076 0.117

100 m 0.000 0.000 0.021 0.072 0.111

10 m 0.000 0.013 0.304 1.143 2.041

30 m 0.000 0.015 0.245 0.760 1.276

62.5 m 0.000 0.014 0.218 0.625 1.029

100 m 0.000 0.014 0.212 0.587 0.956

10 m 0.000 0.001 0.044 0.186 0.335

30 m 0.000 0.001 0.035 0.126 0.213

62.5 m 0.000 0.001 0.030 0.102 0.171

100 m 0.000 0.001 0.029 0.096 0.158

Pitch 

[deg]

Yaw 

[deg]

Sea 

States

Surge 

[m]

Sway 

[m]

Heave 

[m]

Roll 

[deg]
12 OTC [18287] 

RAOs of the MIT/NREL SDB for Each Case 

Base Case – Coupled Effects 

Translational Modes

6(a) 

 

6(b) 

6(c) 

 

Rotational Modes

6(d) 

6(e) 

 

6(f) 

Figures 6(a) – 6(f). Coupling Effects: RAOs of the MIT/NREL SDB Platform only, and of the MIT/NREL SDB Combined Floating Platform and 

Wind Turbine System. 
OTC [18287] 13 

Wind Speed Effects 

Translational Modes

7(a) 

7(b) 

7(c) 

Rotational Modes

7(d) 

7(e) 

7(f) 

Figure 7(a) – 7(f). Wind Speed Effects: RAOs of the MIT/NREL SDB Combined System in Water Depths of 62.5 m and Wind Speeds of 9, 11.2, 

15, and 25 m/s. 
14 OTC [18287] 

Water Depth Effects 

Translational Modes

8(a)

8(b) 

8(c) 

Rotational Modes

8(d) 

8(e) 

8(f) 

Figure 8(a) – 8(f). Water Depth Effects: RAOs of the MIT/NREL SDB Combined System in Wind Speeds of 11.2 m/s and Various Water 

Depths. 
OTC [18287] 15 

8. Static and Dynamic Analysis of the MIT/NREL TLP 

As in the case of the MIT/NREL SDB, throughout the 

static and dynamic analyses of the MIT/NREL TLP, the wind 

and the ambient waves are assumed to be aligned and to 

propagate in the positive x direction. Four wind speeds and 

four water depths were also considered for the MIT/NREL 

TLP. 

The wind speeds chosen for the MIT/NREL SDB were 

employed again in the analysis of the MIT/NREL TLP. These 

wind speeds are 9, 11.2, 15, and 25 m/s, represent region 2 of 

the power curve, rated wind speed, region 3 of the power 

curve, and cut out wind speed for the NREL 5-MW Offshore 

Baseline Wind Turbine, respectively. 

Unlike the SDB, the MIT/NREL TLP is intended for 

deployment in deeper water. Thus, the TLP was analyzed in 

water depths of 62.5−200 m. 

Again, the wind speed of 11.2 m/s and the water depth of 

62.5 m were chosen as the base-case conditions for this 

analysis. These properties were chosen because they represent 

likely operating conditions that will be easily compared to 

other NREL studies. 

Static Analysis 

The TLP is constrained from motion in pitch by tethers 

modeled to be infinitely stiff, so the significant mode of 

motion for this system is surge. The restoring properties of the 

tethers in surge, however, change with water depth. The 

steady-state static equations of motion were solved at four 

water depths, four wind speeds, and the results in surge are 

summarized in Table 12. 

Table 12. Steady-State Surge Displacement of the 

TLP in Various Water Depths and Wind Speeds 

Wind Speed [m/s] 9 11.2 15 25

Thrust [N] 600000 800000 500000 400000

Water Depth Restoring Surge Surge Surge Surge

[m] [N] [m] [m] [m] [m]

62.5 588235.29 1.02 1.36 0.85 0.68

100 312500 1.92 2.56 1.6 1.28

200 138888.89 4.32 5.76 3.6 2.88

Base Case – Coupled Effects 

The effects of coupling the MIT/NREL TLP with the 

NREL Offshore Baseline 5-MW wind turbine are shown in 

Figure 9. The RAOs for the combined system are presented 

here, and demonstrate the effects of coupling the floating 

platform with a wind turbine through the small, but nonzero, 

response in yaw and sway. 

Base Case – Coupling Effects 

9(a) 

9(b) 

9(c) 

Figure 9(a) – 9(c). Coupling Effects: RAOs of the MIT/NREL TLP 

Combined Floating Platform and Wind Turbine System in Water 

Depths of 62.5 m and Wind Speeds of 11.2 m/s. 

Figure 9 shows the RAOs of the floating platform coupled 

with the wind turbine in the base-case conditions of 62.5-m 

water depth and 11.2-m/s wind speed. Although the system is 

excited by the wind and waves in surge, pitch, and heave, the 
16 OTC [18287] 

motions in heave and pitch are prohibited by the tension leg 

mooring system, and the motions in sway and yaw are excited 

by cross coupling mechanisms of the wind turbine. These 

cross coupling mechanisms result in the nonzero RAOs for 

sway and yaw. 

The RAOs also indicate a highly tuned resonant response 

for this system. The resonant frequencies are listed in Table 

13. 

Table 13. MIT/NREL TLP Natural Frequencies in 11.2 

m/s Wind Speed and 62.5 m Water Depth 

Mode Natural Frequency

Surge 0.2324 [rad/s]

Sway 0.2324 [rad/s]

Yaw 0.4945 [rad/s]

Finally, the standard deviations of the system motions in 

five sea states are summarized in Table 14. 

Table 14. Standard Deviations of the System Motion 

of the MIT/NREL TLP in Wind Speed of 11.2 m/s, 

Water Depth of 62.5 m, and Various Sea States. 

Sea State 1 2 3 4 5

Hs [m] 0.09 0.67 2.44 5.49 10

Tm [s] 2 4.8 8.1 11.3 13.6

Surge [m] 0.000 0.059 0.526 2.097 10.293

Sway [m] 0 0.000 0.000 0.001 0.042

Yaw [deg] 0 0.000 0.001 0.002 0.004

As the sea state grows more severe, the spectral density 

becomes narrower with a more defined and higher magnitude 

peak. The spectral density also centers around lower 

frequencies as the sea state increases in severity. At the 

highest sea state reported here, the peak of the spectral density 

occurs close to the resonant frequency for the MIT/NREL 

TLP, and yields a higher value for the standard deviations of 

the system motions. At the lower sea states, the spectral 

density has a higher spread, and the peak occurs at a higher 

frequency. This results in the lower standard deviations at the 

lower sea states. 

Wind Speed Effects 

The RAOs of the combined wind turbine TLP system in 

various wind speeds are shown in Figure 10. 

As for the MIT/NREL SDB, the RAOs for the TLP in 

various wind speeds show that motions tend to decrease from 

region 2 to region 3 of the power curve, increase from rated 

power to 15 m/s, then decrease from 15 to 25 m/s. Again, this 

is due to the cross coupling terms in the linearized wind 

turbine damping and inertia matrices. At 15 m/s, the cross 

coupling entries in the mass matrix are the lowest across the 

wind speeds, and the cross coupling entries in the damping 

matrix are the highest. This results in the greatest reaction at 

15 m/s. 

Wind Speed Effects 

10(a) 

 

10(b) 

10(c) 

Figure 10(a) – 10(c). Wind Speed Effects: RAOs of the MIT/NREL 

TLP Combined Floating Platform and Wind Turbine System in 

Water Depths of 62.5 m and Various Wind Speeds. 

The wind turbine stiffness matrix remains relatively 

constant across wind speeds. This causes the natural 

frequencies of the system to remain constant in various wind 

speeds (see Table 13). 
OTC [18287] 17 

The standard deviations of system motions in the wind 

speeds considered are summarized in Table 15. 

Table 15. Standard Deviations of System Motions of 

the NREL/MIT TLP in 62.5-m Water Depth and 

Various Wind Speeds. 

Hs [m] 0.09 0.67 2.44 5.49 10

Tm [s] 2 4.8 8.1 11.3 13.6

9 m/s 0.0 0.059465 0.52637 2.0981 11.087

11 m/s 0.0 0.059446 0.52629 2.0968 10.293

15 m/s 0.0 0.059525 0.52662 2.1099 17.577

25 m/s 0.0 0.059510 0.52656 2.1047 14.952

9 m/s 0 0.000002 0.00005 0.0015 0.096

11 m/s 0 0.000001 0.00002 0.0007 0.042

15 m/s 0 0.000012 0.00110 0.0648 4.147

25 m/s 0 0.000007 0.00133 0.0448 2.856

9 m/s 0 0.000049 0.00158 0.0055 0.012

11 m/s 0 0.000020 0.00057 0.0020 0.004

15 m/s 0 0.000520 0.02033 0.0709 0.163

25 m/s 0 0.000289 0.01758 0.0604 0.110

Sea 

States

Surge [m]

Sway [m]

Yaw 

[deg]

The standard deviations of the system motions reported in 

this table are consistent with the RAOs, in that the highest 

value in all modes of motion at the most severe sea state 

occurs for the wind speed of 15 m/s. 

Water Depth Effects 

The deeper draft of the MIT/NREL TLP and its stiff 

tension leg mooring system make it a more attractive system 

for installation in deep water. The effects of water depth on 

the dynamics of this system are shown in Figure 11 for water 

depths of 62.5, 100, and 200 m, in a wind speed of 11.2 m/s. 

In Figure 11, the RAOs for the MIT/NREL TLP in 11.2 

m/s wind speeds are shown in water depths of 62.5, 100, and 

200 m, by the red, yellow, and green, respectively. The most 

notable trend in these figures is the effect of water depth on 

the natural frequencies. As shown in Section 5, the water 

depth affects the length of the tethers, and therefore the 

restoring in surge, which shifts the natural frequencies of the 

system to lower frequencies with increasing depth. This result 

shows the potential for tuning a system to a certain frequency 

with restoring. The natural frequencies for this system at 

water depths of 62.5, 100, and 200 m are summarized in 

Table 16. 

Table 16. Natural Frequencies of the MIT/NREL TLP 

in 11.2 m/s Wind Speeds and Various Water Depths 

Water Depth [m] 62.5 100 200

Surge [rad/s] 0.232 0.170 0.113

Sway [rad/s] 0.232 0.170 0.113

Yaw [rad/s] 0.494 0.369 0.260

Water Depth Effects 

11(a) 

11(b) 

11(c) 

Figure 11(a) – 11(c). Water Depth Effects: RAOs of the MIT/NREL 

TLP Combined Floating Platform and Wind Turbine System in 

Wind Speeds of 11.2 m/s and Various Water Depths. 
18 OTC [18287] 

The RAOs for the system in various water depths, shown 

in Figure 11 result in the standard deviations of the system 

motions summarized in Table 17. 

Table 17. Standard Deviations of the System Motions 

of the NREL/MIT TLP in 11.2 m/s Wind Speeds and 

Various Water Depths 

Hs [m] 0.09 0.67 2.44 5.49 10

Tm [s] 2 4.8 8.1 11.3 13.6

62.5 m 0.000 0.059 0.526 2.097 10.293

100 m 0.000 0.058 0.472 1.533 3.560

200 m 0.000 0.057 0.449 1.330 2.762

62.5 m 0 0.000 0.000 0.001 0.042

100 m 0 0.000 0.000 0.000 0.000

200 m 0 0.000 0.000 0.000 0.000

62.5 m 0 0.000 0.001 0.002 0.004

100 m 0 0.000 0.000 0.002 0.004

200 m 0 0.000 0.000 0.001 0.003

Sway [m]

Yaw [deg]

Sea 

States

Surge [m]

The RAOs and the standard deviation of system motions 

show that the motions decrease with increasing water depths. 

This can be explained by the decrease in the magnitude of the 

RAOs with depth. These reduced motions with increasing 

water depth confirm that the TLP is a good candidate for deep 

water deployment. 

Viscous Damping Effects 

The RAO in surge of the MIT/NREL TLP shows a large 

spike concentrated around its natural frequency. This extreme 

spike can be explained by examining the damping around the 

system’s natural frequency. At low frequencies, the 

hydrodynamic damping is close to zero. The system’s natural 

frequency falls in this range of very small damping, which 

causes the system’s response at its natural frequency to spike 

to very large numbers. 

In practice, however, damping will occur at very low 

frequencies due to viscous effects [7]. Viscous damping can 

be achieved and tuned in the structure by, for example, adding 

damping plates or other drag elements. Although these 

physical mechanisms were not modeled here, viscous damping 

was added to the model to observe the effects on the system’s 

response, which is defined by the viscous damping ratio, γ. 

* 2( )

BViscous

M A γω = +

The RAOs for the MIT/NREL TLP are shown in Figure 12

for various levels of viscous damping, with values of γ from 0 

to .10. 

Viscous Damping Effects 

12(a) 

 

12(b) 

12(c) 

Figure 12(a) – 12(c). Viscous Damping Effects: RAOs of the 

MIT/NREL TLP Combined Floating Platform and Wind Turbine 

System in Water Depths of 62.5 m, Wind Speeds of 11.2 m/s, and 

Various Values of gamma. 

As expected, these RAOs show the mitigation of the 

system response at its natural frequency. As viscous damping 

increases, the peak response decreases. 
OTC [18287] 19 

The natural frequencies of the system remain unaffected 

by damping (see Table 13). 

The results of viscous damping on the standard deviations 

of the system motions are summarized in Table 18. 

Table 18. Standard Deviation of System Motions of 

the NREL/MIT TLP in 62.5-m Water Depth and 11.2 

m/s Wind Speed, with Various Viscous Damping 

Ratios. 

Hs [m] 0.09 0.67 2.44 5.49 10

Tm [s] 2 4.8 8.1 11.3 13.6

N = 0 0.000 0.059 0.526 2.097 10.293

N = .05 0.000 0.059 0.523 2.069 6.513

N = .10 0.000 0.058 0.518 2.025 5.822

N = 0 0.000 0.000 0.000 0.001 0.042

N = .05 0.000 0.000 0.000 0.000 0.008

N = .10 0.000 0.000 0.000 0.000 0.004

N = 0 0.000 0.000 0.001 0.002 0.004

N = .05 0.000 0.000 0.001 0.002 0.004

N = .10 0.000 0.000 0.001 0.002 0.004

Yaw 

[deg]

Sea 

States

Surge [m]

Sway [m]

As suggested by the RAOs, the standard deviations of 

motions decrease with higher levels of viscous damping. This 

is especially apparent in the more extreme sea states where the 

peak of the wave spectrum aligns with the peak of the RAOs. 

This indicates the great potential for the practical tuning of the 

system’s response at resonance. 

9. Loads and Responses in Extreme Waves 

The study presented in this article is based on linear theory 

and the use of standard simulation tools that are routinely used 

by the wind industry to analyze wind turbine loads and 

performance and the offshore industry to analyze floating 

structures. Within the limitations of linear wave body 

interaction theory (namely, moderate ambient wave slopes, 

small amplitudes of the system rectilinear motions, and small 

angular displacements that are comparable to the ambient 

wave slopes), the predictions of the theory are likely to offer 

reliable guidance for the responses of the floating wind turbine 

system in realistic wave environments. 

The overall dynamic responses of both MIT/NREL system 

concepts predicted by the linear analysis are very favorable 

and underscore their promise for commercial applications. 

Yet, extreme waves of large amplitude are often present in 

severe storms and a robust floating wind turbine system must 

be designed for such conditions. This analysis is beyond the 

scope of the present study, but it would be carried out as 

outlined here. 

Extreme or breaking waves may be responsible for 

slamming loads on the overhangs of the SDB and TLP 

floaters, and may cause bottom slamming of the SDB floater 

when its draft is small. Moreover, the SDB floater may 

experience a large pitch response caused by an ambient wave 

of large amplitude. This would not be the case for the TLP 

floater, which is constrained in pitch. 

Possible ways to mitigate such extreme wave effects 

would be to increase the freeboard of both floaters and 

consider a conically shaped superstructure with negative flare 

that may mitigate slamming loads. For the SDB floater, 

bottom slamming may be mitigated by increasing its draft. 

The TLP floater may be able to absorb extreme waveinduced responses and loads via its setdown, which occurs 

naturally because of its stiff tether system. Moreover, 

excessive setdown is unlikely because of the buoyancy effect, 

which acts naturally to restore the system to its mean position. 

So the TLP floater appears to be an attractive design for 

extreme wave environments. This is less obvious for the SDB 

floater, which is compliant in pitch and therefore exposed to 

extreme motions in pitch. Therefore, the SDB may be a better 

design for sheltered and shallower coastal waters where 

extreme waves are less likely. An SDB floater that is tethered 

to the sea floor like a TLP is possible with design attributes 

that may vary depending on water depth and wave 

environment. This study has developed the basic methodology 

on how such a design would be created and evaluated. 

Approximate wave body interaction tools can be used to 

analyze the responses of floating structures in steep ambient 

waves. Their predictions would need to be validated against 

tank tests which are quite possible for the floater concepts 

considered in the present study. Moreover, the responses of 

the wind turbine system would also need to be considered and 

modeled. A detailed design analysis, which accounts for 

turbulent winds, stochastic and extreme waves, turbine 

flexibility, and the action of the control and protection system, 

would need to be carried out in the time domain along the 

lines of Jonkman and Sclavounos [6]. 

10. Cost Analysis 

A cost analysis was performed on the MIT/NREL SDB and 

TLP to estimate the total cost of the floating structure, 

mooring systems, and installation processes associated with 

each design. The costs estimated here do not include the wind 

turbine, power electronics, or transmission system. 

Several assumptions were made about the construction and 

installation process, and the costs of labor, materials, and 

equipment. These assumptions were based on quotes from 

manufacturers, consultants, and contractors in the marine 

industry, and are detailed in Table 19. 

Floating wind turbine systems are intended for deployment 

in a wind farm setting, consisting of many individual units. 

Because the MIT/NREL SDB and TLP may be deployed with 

the wind turbine already mounted, each unit is assumed to be 

produced by an assembly line style process in a shipyard and 

towed to its installation site for commissioning. The platforms 

will first be fabricated in the shipyard. Next the turbines will 

be installed to the platform using a crane at the shipyard. The 

mooring system will then be installed and the floating wind 
20 OTC [18287] 

turbine units will then be towed to their installation sites and 

attached to their mooring lines. 

It is also assumed that these structures are intended for 

deployment in U.S. coastal waters, and are therefore 

manufactured and commissioned in the United States. 

The cost of steel and concrete were estimated by 

considering quotes from manufacturers, and were taken to 

reflect unfinished steel and batch concrete produced in the 

United States. 

The cost of mounting the wind turbine to the floating 

platform was estimated for mounting the wind turbine at the 

shipyard and at sea. For the option of mounting the wind 

turbine at sea, a costly crane would be required, and with a full 

crew manning the process 24 hours a day, 2 installations could 

be accomplished in 24 hours. This option is subject to 

unpredictable weather windows and requires a large crew to 

be stationed at sea during the entire installation process. For 

the option of mounting the wind turbine at the shipyard, it is 

assumed that a crane would be on site that would charge a 

lifting fee per wind turbine. Once the platforms are 

manufactured, mounting the wind turbine at the shipyard 

would then be an assembly line process utilizing the crane on 

site. Due to the assembly line style of this process, mounting 

wind turbines to platforms in a shipyard is estimated to be 

even less expensive than mounting a wind turbine onto a 

foundation on land. 

Anchor and mooring line costs were taken from quotes 

from the offshore industry and from product manuals. Two 

alternative anchoring technologies were considered, the drag 

embedment vertical load anchor (VLA) and the suction pile. 

The VLA is a patented, proprietary technology, and is 

installed either by 1 or 2 anchor handling vehicles (AHVs) 

that drag the anchor into the sea bed. Once the AHV loads the 

anchor to its installation load, the anchor snaps into its vertical 

load-bearing orientation, and installation is complete. This 

installation technique avoids the need for subsea equipment, 

but can result in anchor placement that is difficult to control or 

predict, and necessitates thorough geotechnical data of a large 

footprint of the sea floor. Suction pile anchors are cylindrical 

caissons that become embedded into the sea floor through 

suction. The caissons are lowered to the sea floor, and suction 

is applied to a valve at the top of the caisson. A combination 

of suction and the exterior hydrostatic pressure drive the pile 

into the sea floor. This installation process requires the use of 

subsea pumps, and sometimes divers. The caissons, however, 

are easily manufactured, and avoid the retail fees associated 

with the VLA. A cost of $25 and $15 per kN of vertical load, 

or a minimum anchor cost of $50,000 and $25,000 were 

estimated for the VLA and the suction pile, respectively. 

Two methods of anchor installation were outlined as well. 

Installation Option 1 employs a barge and a tug, and 

Installation Option 2 requires an AHV. While Installation 

Option 1 has a lower cost on a daily rate, Installation Option 2 

promises a lower cost per anchor. It is assumed that floating 

wind turbine systems will be installed in a wind farm array, 

and will require enough anchor installations to make 

Installation Option 2 more economical. 

The cost of transporting the assembled system to its 

installation site, and installing it to its mooring lines was 

estimated assuming an installation site of 100 miles from the 

shipyard. 

The tables and figures to follow detail these estimates and 

show the total cost breakdown for each system. 

Table 19. Platform Cost Tables 

Platform Construction and Materials

Steel Material Cost $700 /ton

HSM Steel Structures (Aug 2005) $1,100 /ton

US Steel Corp (July 2005) $1,233 /ton finished steel

US Steel Corp (July 2005) $633 /ton flat rolled

Baoshan, China: Predicted Cut $560 /ton flat rolled

Concrete $100 /ton

HSM Steel Structures (Aug 2005) $80 /ton from mill

HSM Steel Structures (Aug 2005) $1,100 /ton in place

Construction Labor $40 /hour

Wind Turbine Installation In Shipyard

Hours per Installation 6 hours/turbine

Workers Per Installation 5 workers/turbine

Labor Rate $40 /hour

Crane Fee per Tower $6,250 /turbine

Inst. Cost Per Turbine: $7,450 /turbine

Wind Turbine Installation at Sea

Installations per Day 2 /day

Labor $16,800 /day

Crane $500,000 /day

Barge $10,000 /day

Tug $30,000 /day

Inst. Cost Per Turbine $278,400 t

Drag Embedment Anchors

Steel Wire Rope $60 /meter

Chain $270 /meter

Anchor Cost per Load $25 /kN vertical load

Minimum Anchor Cost $50,000 /anchor

Installation Option 1

Barge $10,000 /day

Tug $30,000 /day

Labor $7,000 /day

Anchors Installed 3 anchors/day

Inst. Cost per Anchor: $15,666.67 /anchor

Installation Option 2

AHV $65,000 /day

Labor $7,000 /day

Anchors Installed 7 anchors/day

Inst. Cost per Anchor: $10,285.71 /anchor
OTC [18287] 21 

Suction Pile Anchors

Synthetic Rope $120 /meter

Anchor Cost per Load $15 /kN vertical load

Minimum Anchor Cost $25,000 /anchor

Installation Option 1

Barge $10,000 /day

Tug $30,000 /day

Labor $7,000 /day

Pumps + Divers $7,000 /day

Anchors Installed 3 anchors/day

Installation per Anchor: $18,000.00 /anchor

Installation Option 2

AHV $65,000 /day

Labor $7,000 /day

Pumps + Divers $7,000 /day

Anchors Installed 7 anchors/day

Installation per Anchor: $11,285.71 /anchor

Platform Transportation and Installation

Mileage Fee $200 /mile

Total Miles per Turbine 100 miles/turbine

Tug $30,000 /day

Labor per day $11,760 /day

Days for T&I 3 days/turbine

T&I Cost per Turbine $145,280 /turbine

The total costs for the MIT/NREL SDB and TLP based on 

these assumptions are estimated to be $1.81 and $1.41 million, 

respectively. The general cost breakdown for each structure is 

shown in Figure 13. More detailed cost breakdowns of each 

general category are shown in Figures 14, 15, and 16. 

Total Cost Breakdown

$0.0

$0.2

$0.4

$0.6

$0.8

$1.0

$1.2

$1.4

$1.6

$1.8

$2.0

TLP SDB

Million Dollars

Construction Anchoring

Transportation & Installation Wind Turbine Installation

Figure 13. Total Estimated Cost Breakdown for the MIT/NREL TLP 

and SDB. 

Constuction Costs

$0.00

$0.50

$1.00

$1.50

TLP SDB

Million Dollars

Steel Concrete Labor

Figure 14. Breakdown of the Estimated Construction Costs of the 

MIT/NREL TLP and SDB. 

Transportation and Installation Costs

$0.00

$0.02

$0.04

$0.06

$0.08

$0.10

$0.12

$0.14

$0.16

$0.18

TLP SDB

Million Dollars

Transportation Installation Equimpent

Installation Crew Wind Turbine Installation

Figure 15. Breakdown of the Estimated Transportation and 

Installation Costs of the MIT/NREL TLP and SDB. 

Mooring System and Mooring System Installation Costs

$0.00

$0.10

$0.20

$0.30

$0.40

$0.50

$0.60

$0.70

TLP SDB

Million Dollars

Lines Anchors Mooring System Installation

Figure 16. Breakdown of the Estimated Mooring System Costs of 

the MIT/NREL TLP and SDB. 

The MIT/NREL TLP and SDB are somewhat comparable 

in cost. However, the TLP is estimated to cost less. One 

reason is that although the structures are comparable in mass, 

the TLP’s boxy shape will probably be constructed more 

easily than the very wide and flat shape of the SDB. Also, the 

TLP requires suction pile anchors that can be fabricated in the 

process of the floater construction. These devices are 

estimated to be less expensive than proprietary drag anchors 

that are available through anchor manufacturers. The TLP also 

will require less line than the SDB, which will be moored 
22 OTC [18287] 

through a catenary system that will fill a large footprint, thus 

using significantly more line. 

11. Conclusions 

A complete analysis of static and coupled dynamic analysis of 

floating wind turbine systems was conducted with linear 

theory and standard tools that are used by the wind and 

offshore industries. 

Two floater concepts have been considered: a TLP and an 

SDB that may be deployed in offshore environments with 

water depths of 10−200 m. A critical consideration that was 

factored into the development of both designs is that they are 

statically stable in their nonmoored condition, which allows 

them to be assembled at a near shore facility and towed to the 

offshore site. The dynamic response properties of both 

concepts in their moored condition have been very favorable. 

Their responses in extreme wave conditions will be considered 

in a future study. 

A baseline cost analysis estimates the total costs for these 

structures to be $1.4−$1.8 million. These figures include the 

construction, labor, mooring system, and installation costs of 

the platform, as well as the cost of mounting the wind turbine 

to the platform. These figures do not include the cost of the 

wind turbine, power electronics, or the transmission system. 

These estimates offer promising figures and encourage further 

consideration of floating wind turbine systems. 

12. Acknowledgments 

This study was undertaken as a collaborative effort between 

MIT and NREL and funded by NREL (Subcontract No. 

XAM-4-33200-04). This financial support is gratefully 

acknowledged. 

Also contributing to the cost analysis reported in this study are 

the following individuals and groups. 

• Professor Rob Randal, TAMU 

• Jens Rasmussen, GVA Consultants 

• Koos Krispijn, HSM Steel Structures 

• Mike Lane, Poseidon 

• Ralph Plummer, Spectra International, Inc. 

• Evan Zimmerman, DelMar Systems 

• Roderick Ruinen, Vryhof Anchors 

• Nick McKenna, BP/MIT 

13. References 

 [1] Butterfield, S., Musial, W., Jonkman, J., Sclavounos, P., 

Wayman, E., “Engineering Challenges for Floating Offshore 

Wind Turbines,” Copenhagen Offshore Wind 2005 Conference 

and Expedition Proceedings, 25-28 October 2005, Copenhagen, 

Denmark (to be published). 

 [2] Eltaher, A., Rajapaksa, Y., Chang, K. “Industry Trends for 

Design of Anchoring Systems for Deepwater Offshore 

Structures,” Offshore Technology Conference, 2003. 

 [3] Faltinsen, O. M. Sea Loads on Ships and Offshore Structures, 

Cambridge, UK: Cambridge University Press, 1999. 

 [4] Jonkman, J. M., Buhl, M. L., FAST User Guide, Golden, CO: 

National Renewable Energy Laboratory, 2005. 

 [5] Jonkman, J, Butterfield, S., Musial, W., and Scott, G., 

“Definition of a 5-MW Reference Wind Turbine for Offshore 

System Development,” NREL/TP-500-38060, Golden, CO: 

National Renewable Energy Laboratory, January 2006 (to be 

published). 

 [6] Jonkman, J. M., Sclavounos, P. D., “Development of Fully 

Coupled Aeroelastic and Hydrodynamic Models for Offshore 

Wind Turbines,” Proceedings of the 44th AIAA Aerospace 

Sciences Meeting and Exhibit, 9-12 January 2006, Reno, NV,

Washington D.C.: American Institute of Aeronautics and 

Astronautics, January 2006; NREL/CP-500-39066. 

 [7] Kim, S., Sclavounos, P. D., “Fully Coupled Response 

Simulations of Theme Offshore Structures in Water Depths of 

up to 10,000 Feet,” Proceedings of the Eleventh International 

Offshore and Polar Engineering Conference, 2001. 

 [8] Lee, K. H., Responses of Floating Wind Turbines to Wind and 

Wave Excitation, Master of Science Thesis, Massachusetts 

Institute of Technology, 2004. 

 [9] Lee, K. H., Sclavounos, P. D., Wayman, E. N., “Floating Wind 

Turbines,” Workshop on Water Waves and Floating Bodies, 

May 29, 2005. 

[10] Musial, W., Butterfield, S., Boone, A., “Feasibility of Floating 

Platform Systems for Wind Turbines,” 23rd SSME Wind Energy 

Symposium, 2004. 

[11] Newman, J. N., Marine Hydrodynamics, Cambridge, MA: The 

MIT Press, 1977. 

[12] Sclavounos, P. D., Surface Waves and their Interaction with 

Floating Bodies, Lecture Notes, Massachusetts Institute of 

Technology, Cambridge, MA. 

[13] Tong, K.C., “Technical and Economic Aspects of a Floating 

Offshore Wind Farm,” Journal of Wind Engineering and 

Industrial Aerodynamics, 1998. 

[14] Vryhof Anchor Manual, Vryhof Systems, 2000. 

[15] WAMIT® User Guide, Cambridge, MA: WAMIT, Inc. and 

MIT, 1998. 

[16] Withee, J. E., Fully Coupled Dynamic Analysis of a Floating 

Wind Turbine System, Doctoral Thesis, Massachusetts Institute 

of Technology, 2004. 
F1147-E(12/2004) 

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Coupled Dynamic Modeling of Floating Wind Turbine Systems: 

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This paper presents a collaborative research program that the Massachusetts Institute of Technology (MIT) and the 

National Renewable Energy Laboratory (NREL) have undertaken to develop innovative and cost-effective floating 

and mooring systems for offshore wind turbines in water depths of 10−200 m. Methods for the coupled structural, 

hydrodynamic, and aerodynamic analysis of floating wind turbine systems are presented in the frequency domain. 

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