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Contract No. DE-AC36-08GO28308

Investigation of Response 

Amplitude Operators for 

Floating Offshore Wind 

Turbines

Preprint

G. K. V. Ramachandran, A. Robertson, 

J. M. Jonkman, and M. D. Masciola

To be presented at the 23rd International Ocean, Offshore and 

Polar Engineering Conference – ISOPE 2013

Anchorage, Alaska

June 30 – July 5, 2013

Conference Paper

NREL/CP-5000-58098

July 2013
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Investigation of Response Amplitude Operators for Floating Offshore Wind Turbines

G. K. V. Ramachandran, A. Robertson, J. M. Jonkman, and M. D. Masciola

National Wind Technology Center, National Renewable Energy Laboratory, 

Boulder, CO, United States of America

ABSTRACT

This paper examines the consistency between response amplitude 

operators (RAOs) computed from WAMIT, a linear frequency-domain 

tool, to RAOs derived from time-domain computations based on whitenoise wave excitation using FAST, a nonlinear aero-hydro-servo-elastic

tool. The RAO comparison is first made for a rigid floating wind 

turbine without wind excitation. The investigation is further extended to 

examine how these RAOs change for a flexible and operational wind 

turbine. The RAOs are computed for below-rated, rated, and aboverated wind conditions. The method is applied to a floating wind system 

composed of the OC3-Hywind spar buoy and NREL 5-MW wind 

turbine. The responses are compared between FAST and WAMIT to 

verify the FAST model and to understand the influence of structural 

flexibility, aerodynamic damping, control actions, and waves on the 

system responses. The results show that based on the RAO computation 

procedure implemented, the WAMIT- and FAST-computed RAOs are 

similar (as expected) for a rigid turbine subjected to waves only. 

However, WAMIT is unable to model the excitation from a flexible 

turbine. Further, the presence of aerodynamic damping decreased the 

platform surge and pitch responses, as computed by both WAMIT and 

FAST when wind was included. Additionally, the influence of 

gyroscopic excitation increased the yaw response, which was captured 

by both WAMIT and FAST. 

KEY WORDS: Floating offshore wind turbines; OC3-Hywind spar; 

response amplitude operator; RAO. 

INTRODUCTION

Response amplitude operators (RAOs) are conventionally the 

frequency response functions, which are simply the ratio of the output 

to a given input. RAOs are used in the offshore oil and gas industry to 

assess the frequency-domain linear wave-body response of floating 

platforms during the design process. RAOs also have been applied in 

the design of floating platforms for wind turbines; but, in offshore 

floating wind turbines, in addition to the hydrodynamic loading, 

aerodynamics, structural dynamics (including blade and tower 

flexibility), and controller dynamics also are important effects. Due to 

the inherent nonlinearities of these dynamics, offshore floating wind 

turbines are designed and analyzed with nonlinear time-domain aerohydro-servo-elastic tools. It is important to understand how these 

additional dynamics affect the system responses. Due to sophistication 

of the nonlinear time-domain aero-hydro-servo-elastic tools, it also is 

essential that—before the models are applied in a design—the 

responses are verified as being meaningful. As such, it is important to 

compare the responses predicted from the complicated nonlinear timedomain tool to the responses predicted from a simpler model. 

As floating wind turbines are receiving more attention, it is necessary to 

determine measures to describe the motion characteristics of each of the 

concepts when subjected to both wind and wave loading. A popular 

tool for computing RAOs of offshore platforms is WAMIT (Lee and 

Newman, 2006), a three-dimensional panel code used to compute the 

linear wave forcing and motion characteristics of an offshore structure 

in the frequency domain. However, the motion characteristics of a 

floating platform for a deep-water wind turbine are also influenced by 

the structural flexibility and the operational conditions of the wind 

turbine, including aerodynamics and controller-induced motion. It is 

not possible in WAMIT to capture the interaction of the flexible wind 

turbine degrees of freedom (DOFs) with the platform motion in the 

computation of RAOs or system nonlinearities. This is overcome by 

interfacing WAMIT with the nonlinear time-domain aero-hydro-servoelastic code, FAST (Jonkman and Buhl, 2005), developed by the 

National Renewable Energy Laboratory (NREL). FAST can model the 

nonlinear dynamics of the flexible wind turbine subjected to 

hydrodynamic and aerodynamic excitation, and can compute the RAOs 

of the complete offshore wind system through white-noise wave 

excitation and the associated time-domain responses. 

The purpose of this investigation is to verify the FAST/WAMIT model 

and to understand the influence of structural flexibility, aerodynamic 

damping, control actions, and waves on offshore floating wind system 

responses. To achieve this goal, RAOs generated from FAST/WAMIT 

are verified against WAMIT-only generated RAOs for a rigid offshore 

wind system. After the verification is completed, flexibility is added to 

the wind turbine in FAST and cases including wind excitation are used 

to understand the influence of these conditions on the RAOs.

The interaction of WAMIT and FAST for computing RAOs and 

performing the comparison process is shown in Figure 1. A detailed 

description of the RAO computation procedures using WAMIT and 

FAST is given in the next sections.
2 

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Figure 1. RAO computation flow chart

RESPONSE AMPLITUDE OPERATOR COMPUTATION 

PROCEDURE: WAMIT

WAMIT is a three-dimensional panel code used to compute the wave 

kinematics, wave forcing, and motion characteristics of an offshore 

structure in the frequency domain. WAMIT can provide the RAOs of a 

structure both in a freely floating condition and in a moored condition. 

Here, WAMIT is used to produce RAOs for the complete offshore wind 

system, including the influences of the wind turbine and moorings. To 

obtain these RAOs, the geometry of the floating platform is modeled in 

WAMIT, and the influences of the turbine and moorings are supplied 

through external mass, stiffness, and damping matrices linked to the 

WAMIT model. The process of deriving these external matrices 

involves using FAST.

The WAMIT model-building process is as follows. First, the geometry 

of the floating platform is modeled in WAMIT and the hydrostatic 

quantities (without body gravity), added mass, damping, and waveexcitation forces of the system are computed assuming the platform as 

a freely-floating body. This information is used as input for a FAST 

model of the system, and is represented as blocks (1), (2), and (4) in the 

flow chart. For this computation, the center of gravity position is 

assumed to be at the intersection of the still water level (SWL) and the 

centerline of the platform/tower, so that WAMIT neglects the body 

gravity term when calculating the hydrostatic stiffness matrix in pitch 

and roll. This is done to avoid double-booking the body gravity term 

when the hydrostatic quantities are used by FAST, which intrinsically 

accounts for these contributions. In the WAMIT calculation of block 

(2), WAMIT does not see the wind turbine on top of the platform and 

hence the hydrodynamic and hydrostatic quantities are purely due to the 

interaction of the platform with the fluid. 

Next, the complete floating system is modeled in FAST, which includes 

the hydrostatic quantities computed by WAMIT for a freely floating 

platform as input to the model. The FAST model is then used to derive

the mass (M), stiffness (K), and damping (C) matrices of the complete 

system including the platform, wind turbine (including aerodynamics 

and rotor gyroscopics), and moorings through a linearization process, 

as shown in block (6). The FAST linearization is performed using the 

hydrostatic quantities from the previous step (block (3)), but with the

hydrodynamics quantities (added mass and damping) zeroed out. Zeros 

are used for the hydrodynamic quantities to eliminate the 

hydrodynamic added mass and damping contribution and avoid double 

counting these contributions in the WAMIT RAO computation in block 

(9). The hydrostatic-restoring quantities, however, which don’t include 

the body gravity term but do include the contributions of buoyancy and 

water-plane area, are needed by FAST in block (6) to ensure that the 

system is in static equilibrium before linearizing. For the FAST 

linearization computation in block (6) no waves are applied, mimicking 

a still-water condition. Appropriate wind conditions are applied based 

on the cases under investigation; hence, the corresponding aerodynamic 

loads influence the damping and stiffness matrices. Additionally, in the 

FAST linearization computation of block (6) the wind turbine is treated 

as a rigid body with only the six rigid-body degrees of freedom of the 

floating platform enabled. The resulting M, C, and K matrices of size 

6 x 6 derived by FAST in block (6) contain the effects of body 

mass/inertia, aerodynamics, gyroscopics, hydrostatics (contributions 

from both buoyancy and body weight), and mooring stiffness (in block 

(7)). These matrices are azimuth averaged for models with a rotating 

rotor. 

In the third step, post-processing of the M, C, and K matrices from 

block (7) is done in block (8) to eliminate any sort of double-booking. 

The post-processed matrices from block (8) are designated as the 

external matrices, Mext, Cext, and Kext, required by WAMIT to perform 

RAO computations in block (9). They include the influences of the 

wind turbine and moorings identified in the previous paragraph. The 

post-processing of the M, C, and K matrices in block (8) is described 

next. 

The external mass matrix, Mext, which contains the mass/inertia of the 

turbine, tower, and platform, is the same as that obtained from the 

FAST linearization output, M, because the mass matrix does not 

include hydrodynamic added mass, as explained previously. If this was 

not the case, then the hydrodynamic mass matrix would need to be

subtracted from the mass matrix, M, to obtain the external mass matrix, 

Mext. 

The external damping matrix, Cext, which includes the contributions 

from aerodynamic damping and gyroscopic effects, is also the same as 

that obtained from the FAST linearization output. For a non-spinning 

wind turbine with no aerodynamic loading and no platform viscous 

drag, the result should be a zero damping matrix, which can be used as 

a sanity check. 

The stiffness matrix, K—obtained from the FAST linearization 

output—contains the contributions from aerodynamics, hydrostatics, 

and gravitational and mooring line restoring, which is illustrated in the 

following equation:

K = Kaero + Khydrostat + KgravRest + Kmooring (1) 

The external stiffness matrix, Kext, is obtained by excluding the 

hydrostatic stiffness contribution from the above equation. The 

hydrostatic restoring obtained from the first step in block (3) is used for 

this purpose. The computation of Kext is given in the following 

equation: 

Kext = K – KWAMIT (2)

where, KWAMIT = Khydrostat represents the hydrostatic stiffness matrix 

from block (3) obtained from the WAMIT computation of block (2). 
3 

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The WAMIT output is non-dimensional; hence, Khydrostat must be 

dimensionalized before applying the above equation. 

In the final step, the RAOs are obtained from WAMIT in block (9)

including the influences of the wind turbine and moorings. For this 

case, the external mass, damping, and stiffness matrices (Mext, Cext, and 

Kext) computed from FAST in block (6) and post-processed in block (8) 

are specified for setting up the equations of motion in WAMIT. 

Compared to the block (2) computation, the block (9) computation uses 

the Mext, Cext, and Kext matrices from block (8), representing the 

influence of the wind turbine and moorings. Solving the equations of 

motion in WAMIT gives rise to the linear motion responses of the 

structure. Each element in the external mass matrix is added to the 

corresponding added mass of the body (this addition is done by 

WAMIT internally) to obtain the complete mass matrix for the 

equations of motion. In the case of the damping and stiffness matrices, 

a similar process is performed, in which linear wave damping is added 

to the external damping matrix and the hydrostatic restoring contributions are added to the external stiffness matrix. The x, y, and z 

coordinates of the center of gravity (CG) location of the structure also 

must be specified in WAMIT, but are set to zero because the stiffness 

matrix from the third step (block (8)) contains the body gravity terms 

derived from FAST. The WAMIT computation in block (9) gives rise 

to the RAOs of block (10). 

RESPONSE AMPLITUDE OPERATOR COMPUTATION 

PROCEDURE: FAST

The aero-hydro-servo-elastic code FAST computes the loads and 

responses of both onshore and offshore wind turbines. The procedure 

for computing the RAOs for a floating system using FAST is explained 

below. 

FAST computes the system response nonlinearly in the time domain in 

block (11) of the flow chart, in contrast to the linearization in block (6)

described in the previous section. The FAST computation is performed 

with both a rigid (resulting in only 6 DOFs) and a flexible wind turbine. 

In addition to the rigid-body motion of the floater, a flexible wind 

turbine includes degrees of freedom corresponding to blade and tower 

bending, rotor rotation, and drivetrain torsion.

The aerodynamic loads are calculated based on the controller settings 

and the wind conditions used. For the hydrodynamic loads, the 

WAMIT data from the first step of the previous section (represented in 

block (4)) are used in place of the zero-valued WAMIT data used as 

input to the FAST linearization. This data provides the frequencydependent added mass and damping coefficients and the incident waveexcitation forces. The time-domain wave excitation for the RAO 

computation is described using a white-noise spectrum. Six sets of 

computations are carried out using white-noise excitations with six

different seed numbers. Each of the computations is performed for a

time duration of 8,000 s. The system responses from the six 

computations are averaged and the auto-spectral density of the input

(wave elevation) and the cross-spectral density of the input/output 

(system responses) are computed in block (12). The ratio of the crossspectral density of the surface elevation and the corresponding output to 

the auto-spectral density of the surface elevation gives rise to the 

frequency-response function (FRF), or the RAOs in block (12) 

(illustrated in the following equation:) 

RAO = H(ω) = Sxy(ω)

Sxx(ω)

 (3) 

where, H(ω) is the FRF, Sxy(ω) and Sxx(ω) are the cross-spectral and 

auto-spectral densities of the input x(t) and the output y(t), in the 

frequency domain, respectively. The post-processing of the time series 

results is performed by excluding the transients of the first 2,000 s from 

each computation. The process is repeated for different operational 

conditions (e.g., wind, wave) and degrees of freedom. These RAOs in 

block (12) are compared to those computed from WAMIT in block 

(10). 

CASE STUDY: OC3-HYWIND SPAR-BUOY

The methods described above are implemented for a floating offshore 

wind turbine concept, namely the OC3-Hywind spar buoy (Jonkman, 

2009), which is subjected to various wind and wave conditions. The 

NREL 5-MW reference wind turbine (Jonkman et al., 2009) is mounted 

on the platform, which consists of a deep-drafted slender spar buoy 

with three mooring lines. The mooring lines are attached to the 

platform through a delta connection to achieve higher yaw mooring 

stiffness. FAST currently is not capable of modeling the delta 

connection; hence, an additional yaw stiffness of 9.834E7 Nm/rad is 

used to account for the simplification. Further, additional linear 

damping for surge and sway (1.0E5 N/(m/s)), heave (1.3E5 N/(m/s)), 

and yaw motions (1.3E7 Nm/(rad/s)) is applied to account for mooring 

damping neglected by FAST and to match with tank test data. For all 

the computations, the platform viscous drag is not considered (platform 

Cd = 0). 

A schematic of the OC3-Hywind concept is shown in Figure 2. The 

specifications of the platform are presented in Table 1 (Jonkman, 2009)

and the platform and tower natural frequencies are presented in Table 2 

(Jonkman et al., 2010) of the Appendix. 

Figure 2. OC3-Hywind concept 

As a first step, the RAOs computed using FAST and WAMIT are 

compared for a rigid turbine subjected to no wind. In FAST, whitenoise waves with a significant wave height of 2 m are used, which is 

small enough that linear wave theory is valid. The results are shown in

Figure 3. The RAOs show considerable excitation only in the surge, 

heave, and pitch modes, therefore only these RAOs are presented in the 

figure. The excitation at the other natural frequencies (sway, roll, and 

yaw) is considerably less because of the zero-degree wave heading and 
4 

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the absence of wind forcing. The figure shows that the RAOs are in 

good agreement; however, a small frequency shift is present for the 

heave and pitch responses at their respective natural frequencies. The 

frequency shift could be due to a slight stiffening of the mooring lines 

in the FAST computation, wherein the nonlinearity of the catenary 

mooring is taken into account while the floater oscillates, which is not 

incorporated in the linearized WAMIT calculation. Further, the unity 

amplitude heave RAO corresponding to the zero-frequency limit—

predicted by both of the tools—agrees very well, which is a sanity 

check for RAO estimation. (For an extremely long-period wave (long 

wavelength), the structure follows the wave in heave, which means that 

the output is the same as that of the input (excitation). This might not 

be the case for a tension leg platform (TLP); however, because TLPs 

are stiff structures.) 

Figure 3. OC3-Hywind: RAO comparison (no-wind, rigid turbine)

This rigid case has verified the technique for deriving RAOs within 

FAST/WAMIT. The next step is to examine how these RAOs change 

due to both wind and flexibility of the turbine or tower. To examine the 

effect of these modifications, the following wind conditions are used: 

• No wind (no aerodynamic loads are present)

• Below-rated steady wind speed at hub height, V = 8 m/s

• Rated steady wind speed at hub height, V = 11.4 m/s

• Above-rated steady wind speed at hub height, V = 18 m/s

A variable speed/variable pitch controller developed for the OC3-

Hywind system was used for the wind cases within FAST. 

The RAOs are computed for these four wind cases within WAMIT

alone by applying mass/stiffness/damping matrices that account for the 

influence of wind condition on the system. Eight different RAOs are 

computed in FAST, for each of the wind conditions and for both a rigid 

and flexible turbine/tower. The calculations in WAMIT are only for a 

rigid system. As in the previous example, a white-noise wave spectrum 

with a significant wave height of 2 m is used for the FAST 

computations. The results are shown in Figure 4 through Figure 9. In 

each, the main figure shows the low-frequency region of the RAO and 

the inset figure shows the relevant frequency of interest for each 

platform mode. The terms V0, V8, V11.4, and V18 represent the results 

corresponding to the steady wind speeds of V = 0 m/s, V = 8 m/s, 

V = 11.4 m/s, and V = 18 m/s, respectively. Further, the “flex” and 

“rigid” keywords for FAST represent that the wind turbine is 

considered “flexible” and “rigid”, accordingly. 

Figure 4 shows the comparison of surge RAOs. From the figure, as 

expected, all the RAOs compare well at around the surge natural 

frequency (0.008 Hz). Additionally, as compared to the other cases, the 

surge natural frequency for the flexible turbine RAO corresponding to 

the rated wind speed has slightly higher amplitude and a lower 

frequency. It can also be noted that the no-wind case RAO (both rigid 

and flexible turbines) shows only the surge-pitch coupling through the 

peak at the pitch natural frequency (0.034 Hz), whereas the RAOs at 

the operational conditions show both surge-heave and surge-pitch 

couplings through the excitation peaks at 0.032 Hz and 0.034 Hz, 

respectively. Further, the peak corresponding to the surge-pitch 

coupling of the no-wind case is much higher in amplitude than that of 

the operational condition RAOs, due to the absence of aerodynamic 

damping for the no-wind case RAOs. A smaller peak is observed (but is 

not shown in the figure) at about the first blade flap-wise natural 

frequency (0.63 Hz) for the flexible-turbine case in FAST (but not in 

WAMIT, which cannot model turbine flexibility). 

Similar to Figure 4, the sway RAOs are compared in Figure 5, which 

show small excitations at the sway natural frequency (0.008 Hz) and at 

the roll natural frequency (0.034 Hz), demonstrating the sway-roll 

coupling. For a zero-degree steady wind and wave heading, the sway 

response is expected to be minimal (and can be observed in the figure), 

because the sway motion is excited only by rotor torque and transverse 

aerodynamic loads brought about by rotor gyrocopics-induced yaw 

motion. The magnitudes of the no-wind RAOs are very small as 

compared to the operational cases, because of the absence of rotor 

loads. Further, the operational case responses (between the wind speed 

conditions of 8, 11.4, and 18 m/s) are comparable in magnitude, but 

increase slightly with increasing wind speed, which is the result of 

higher aerodynamic torque. Additionally, the influence of aerodynamic 

damping is not present in this degree of freedom. Smaller peaks at the 

first tower side-side frequency (0.46 Hz) and at the first coupled blade 

flap-wise bending frequency (0.65 Hz) are visible for the FAST RAOs 

in the case of a flexible turbine. 

The heave RAO comparison is shown in Figure 6. The heave RAOs 

compare well at the heave natural frequency (0.032 Hz). This is 

because the heave response at its natural frequency is unaffected by the 

aerodynamic damping. 

Figure 7 presents the roll RAO comparison. It shows a behavior similar 

to that of the sway response. The roll-sway coupling is also visible. 

The pitch RAOs are compared in Figure 8. Similar to the surge, the nowind case RAOs compare well at the pitch natural frequency

(0.034 Hz). The operational case RAOs also compare well at the pitch 

natural frequency, but with a smaller magnitude as compared to that of 

the no-wind case RAOs. This shows the influence of the aerodynamic 

damping. All the RAOs show the surge-pitch coupling through the peak 

at the surge natural frequency. Further, all the operational case RAOs 

show the heave-pitch coupling through a peak at the heave natural 

frequency. This is not present for the no-wind case RAO, as seen in the 

surge response case. The flexible turbine RAOs show a peak at about 

0.47 Hz, corresponding to the first fore-aft tower frequency. Further, 

the peak at the tower frequency is slightly shifted in cases that include

wind compared to that of the no-wind condition, which may be 

attributed to the additional aerodynamic stiffness or stiffening of the 

mooring system to the aerodynamic-thrust-induced mean surge offset. 

Figure 9 shows the yaw RAO comparison. None of the WAMITcomputed RAOs has an excitation at the yaw natural frequency

0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2

5

10

15

20

25

Frequency [Hz]

RAO(surge) [m/m]

0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2

1

2

3

Frequency [Hz]

RAO(heave) [m/m] 0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2

1

2

3

4

Frequency [Hz]

RAO(pitch) [deg/m]

FAST

WAMIT
5 

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(0.121 Hz), which is due to the fact that hydrodynamic yaw forcing is 

zero for a cylindrical structure and the main cause for this excitation 

should come from the rotor aerodynamics, especially the rotor 

flexibility. This is clearly visible for the FAST-computed RAOs as 

excitation at the yaw natural frequency. All the RAOs show excitations 

at the surge / sway and roll / pitch natural frequencies demonstrating 

the yaw coupling with these DOFs. Further, all the FAST-computed 

RAOs during operational conditions show an excitation close to 0.6 Hz, 

corresponding to the 3p excitation (a rated rotor speed of 12.1 rpm 

gives rise to a 1p frequency at around 0.2 Hz) from the rotor. This

effect is more predominant for the rated and above rated wind speed 

conditions. The flexible turbine RAOs show a peak at around 0.46 Hz, 

corresponding to the first tower side-side frequency and demonstrating 

the coupling between the platform yaw motion and the tower bending 

flexibility.

CONCLUSIONS

Two procedures are explained for computing the RAOs of floating 

wind turbines using WAMIT and FAST. A comparison of RAOs 

computed for a rigid turbine by both WAMIT and FAST (using whitenoise wave excitation) shows that WAMIT can be used as a verification 

tool for the modeling of floating wind turbines in FAST. The RAOs for 

a flexible turbine, however, cannot be estimated using WAMIT. 

Further, the comparison of RAOs for different wind conditions shows 

the influence of aerodynamic damping and gyroscopic effect. Although 

the presence of aerodynamic damping decreased the surge and pitch

responses, the influence of gyroscopic loading increased the yaw 

response. The rigid and flexible turbine responses also are comparable, 

but the high-frequency excitations observed for the flexible turbine are 

larger than that of the rigid turbine.

The results also show different platform degrees of freedom coupling 

effects, such as surge-heave, surge-pitch, sway-roll, rotor gyroscopics–

platform yaw, and platform yaw–tower bending flexibility. Most of the 

platform–turbine coupling is captured only using FAST, because the 

turbine flexibility could not be included in the WAMIT computation. 

The analysis presently is being extended for tension-leg and semisubmersible platforms. It is expected that the impact of the turbine 

(especially tower) flexibility will be much more important for tensionleg platforms due to the strong coupling between platform-pitch and 

tower-bending (Matha, 2009). 

ACKNOWLEDGEMENTS

This work was supported by the U.S. Department of Energy, under 

Contract No. DE-AC36-08GO28308 with the National Renewable 

Energy Laboratory. 

REFERENCES

Jonkman, JM (2009). Definition of the Floating System for Phase IV of 

OC3, TP-500-47535. Golden, CO: National Renewable Energy 

Laboratory. 

Jonkman, JM, and Buhl, ML (August 2005). FAST User’s Guide, EL500-38230. Golden, CO: National Renewable Energy Laboratory.

Jonkman, J, Butterfield, S, Musial, W, and Scott, G (February 2009). 

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

Development, TP-500-38060. Golden, CO: National Renewable 

Energy Laboratory.

Jonkman, J, Larsen, T, Hansen, A, Nygaard, T, Maus, K, 

Karimirad, M., Gao, Z, Moan, T, Fylling, I, Nichols, J, 

Kohlmeier, M, Pascual Vergara, J, Merino, D, Shi, W, and Park, H 

(2010). “Offshore Code Comparison Collaboration Within IEA 

Wind Task 23: Phase IV Results Regarding Floating Wind 

Turbine Modeling,” Proceedings of the European Wind Energy 

Conference—EWEC2010, Warsaw, Poland. 

Lee, CH, and Newman, JN (2006). WAMIT User Manual, Versions 6.4, 

6.4PC, 6.3S, 6.3S-PC, WAMIT, Inc., 343 pp.

Matha, D (2009). Model Development and Loads Analysis of an 

Offshore Wind Turbine on a Tension Leg Platform, with a 

Comparison to Other Floating Turbine Concepts, MS Thesis, 

Endowed Chair of Wind Energy, Universität Stuttgart, Germany. 

Available at http://www.nrel.gov/docs/fy10osti/45891.pdf 

(accessed March 15, 2013). 

APPENDIX

Table 1. OC3-Hywind Platform Specifications1

Parameter Value

Water depth (m) 320

Diameter (m) 6.5 to 9.4 (tapered)

Draft (m) 120

Water displacement (m3) 8029

Mass, including ballast (kg) 7,466,000

Center of gravity location of the platform 

below still water level (m)

89.92

Roll inertia about center of gravity (kg- 2

)

4,229,000,000

Pitch inertia about center of gravity (kg- 2

)

4,229,000,000

Yaw inertia about center of gravity (kg- 2

)

164,200,000

Number of mooring lines 3

Depth to fairleads, anchors (m) 70

320 Radius to fairleads, anchors (m) 5.2

Unstretched line length (m) 902.2

Line diameter (m) 0.09

Line mass density (kg/m) 77.71

Line extensional stiffness (N) 384,200,000

1. The mass, center of gravity, and inertia values are for the 

platform alone (not including the tower and turbine).

Table 2. OC3-Hywind Platform and Tower Natural Frequencies

Mode Natural Frequency (Hz)

Surge 0.008

Sway 0.008

Heave 0.032

Roll 0.034

Pitch 0.034

Yaw 0.121

Tower first side-side 0.457

Tower first fore-aft 0.473
6 

This report is available at no cost from the 

National Renewable Energy Laboratory (NREL) 

at www.nrel.gov/publications.

Figure 4. OC3-Hywind: Surge RAO comparison (main figure shows the low-frequency region of the RAO; inset figure shows relevant frequency)

Figure 5. OC3-Hywind: Sway RAO comparison (main figure shows the low-frequency region of the RAO; inset figure shows relevant frequency)

0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2 10-2

10-1

100

101

Frequency [Hz]

RAO(surge) [m/m]

0 0.01 0.02 0.03 0.04 0.05 0.06 10-2

10-1

100

101

WAMIT RAO - V0

WAMIT RAO - V8

WAMIT RAO - V11.4

WAMIT RAO - V18

FAST RAO - V0, rigid

FAST RAO - V8, rigid

FAST RAO - V11.4, rigid

FAST RAO - V18, rigid

FAST RAO - V0, flex

FAST RAO - V8, flex

FAST RAO - V11.4, flex

FAST RAO - V18, flex

0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2 10-10

10-8

10-6

10-4

10-2

100

Frequency [Hz]

RAO(sway) [m/m]

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 10-10

10-5

100

WAMIT RAO - V0

WAMIT RAO - V8

WAMIT RAO - V11.4

WAMIT RAO - V18

FAST RAO - V0, rigid

FAST RAO - V8, rigid

FAST RAO - V11.4, rigid

FAST RAO - V18, rigid

FAST RAO - V0, flex

FAST RAO - V8, flex

FAST RAO - V11.4, flex

FAST RAO - V18, flex
7 

This report is available at no cost from the 

National Renewable Energy Laboratory (NREL) 

at www.nrel.gov/publications.

Figure 6. OC3-Hywind: Heave RAO comparison (main figure shows the low-frequency region of the RAO; inset figure shows relevant frequency)

Figure 7. OC3-Hywind: Roll RAO comparison (main figure shows the low-frequency region of the RAO; inset figure shows relevant frequency)

0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2 10-3

10-2

10-1

100

101

Frequency [Hz]

RAO(heave) [m/m]

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2

10-4

10-3

10-2

10-1

100

101

WAMIT RAO - V0

WAMIT RAO - V8

WAMIT RAO - V11.4

WAMIT RAO - V18

FAST RAO - V0, rigid

FAST RAO - V8, rigid

FAST RAO - V11.4, rigid

FAST RAO - V18, rigid

FAST RAO - V0, flex

FAST RAO - V8, flex

FAST RAO - V11.4, flex

FAST RAO - V18, flex

0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2 10-10

10-8

10-6

10-4

10-2

100

Frequency [Hz]

RAO(roll) [deg/m]

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 10-10

10-5

100

WAMIT RAO - V0

WAMIT RAO - V8

WAMIT RAO - V11.4

WAMIT RAO - V18

FAST RAO - V0, rigid

FAST RAO - V8, rigid

FAST RAO - V11.4, rigid

FAST RAO - V18, rigid

FAST RAO - V0, flex

FAST RAO - V8, flex

FAST RAO - V11.4, flex

FAST RAO - V18, flex
8 

This report is available at no cost from the 

National Renewable Energy Laboratory (NREL) 

at www.nrel.gov/publications.

Figure 8. OC3-Hywind: Pitch RAO comparison (main figure shows the low-frequency region of the RAO; inset figure shows relevant frequency)

Figure 9. OC3-Hywind: Yaw RAO comparison (main figure shows the low-frequency region of the RAO; inset figure shows relevant frequency)

0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2 10-3

10-2

10-1

100

101

Frequency [Hz]

RAO(pitch) [deg/m]

0 0.1 0.2 0.3 0.4 0.5 0.6 10-4

10-3

10-2

10-1

100

WAMIT RAO - V0

WAMIT RAO - V8

WAMIT RAO - V11.4

WAMIT RAO - V18

FAST RAO - V0, rigid

FAST RAO - V8, rigid

FAST RAO - V11.4, rigid

FAST RAO - V18, rigid

FAST RAO - V0, flex

FAST RAO - V8, flex

FAST RAO - V11.4, flex

FAST RAO - V18, flex

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 10-10

10-8

10-6

10-4

10-2

100

Frequency [Hz]

RAO(yaw) [deg/m]

0 0.005 0.01 0.015 0.02 0.025 0.03 0.035 0.04 0.045 0.05 10-10

10-8

10-6

10-4

10-2

100

WAMIT RAO - V0

WAMIT RAO - V8

WAMIT RAO - V11.4

WAMIT RAO - V18

FAST RAO - V0, rigid

FAST RAO - V8, rigid

FAST RAO - V11.4, rigid

FAST RAO - V18, rigid

FAST RAO - V0, flex

FAST RAO - V8, flex

FAST RAO - V11.4, flex

FAST RAO - V18, flex