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Laboratory (NREL) at www.nrel.gov/publications.

Contract No. DE-AC36-08GO28308

Wind/Wave Misalignment in the 

Loads Analysis of a Floating 

Offshore Wind Turbine

Preprint

L. Barj and S. Stewart

The Pennsylvania State University

G. Stewart and M. Lackner

The University of Massachusetts

J. Jonkman and A. Robertson

National Renewable Energy Laboratory

Presented at AIAA SciTech 2014

National Harbor, Maryland

January 13-17, 2014

Conference Paper

NREL/CP-5000-61043

February 2014
NOTICE

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Wind/Wave Misalignment in the Loads Analysis of a 

Floating Offshore Wind Turbine

Lucie Barj* and Susan Stewart†

The Pennsylvania State University, University Park, PA, 16802

Gordon Stewart‡ and Matt Lackner§

The University of Massachusetts, Amherst, MA, 01003

Jason Jonkman** and Amy Robertson††

National Renewable Energy Laboratory, Golden, CO, 80401

and

Denis Matha‡‡

Endowed Chair of Wind Energy, University of Stuttgart, BW, 70569, Germany

Wind resources far from the shore and in deeper seas have encouraged the offshore wind 

industry to look into floating platforms. As a result, the International Electrotechnical 

Commission is developing a new technical specification for the design of floating offshore 

wind turbines that extends existing design standards for land-based and fixed-bottom 

offshore wind turbines. The work summarized in this paper supports the development of 

best practices and simulation requirements in the loads analysis of floating offshore wind 

turbines by examining the impact of wind/wave misalignment on the system loads under 

normal operation. 

We conducted simulations of a spar-type floating offshore wind turbine system under a 

wide range of wind speeds, significant wave heights, peak-spectral periods, and wind/wave 

misalignments using the aero-servo-hydro-elastic tool FAST. The extreme and fatigue loads 

were calculated for all of the simulations. The extreme and fatigue loading as a function of 

wind/wave misalignment are represented as load roses and a directional binning sensitivity 

study is performed. This study focused on identifying the number and type of wind/wave 

misalignment simulations needed to accurately capture the extreme and fatigue loads of the 

system in all possible meteorological and ocean conditions considered, and for a downselected set of conditions identified as the generic U.S. East Coast site. 

For this axisymmetric platform (except for the mooring lines), perpendicular wind and 

waves play an important role in the loading of the support structure. Therefore, including 

these conditions in the design loads analysis can improve the estimation of extreme and 

fatigue loads. However, most support-structure locations experience their highest extreme 

and fatigue loads when the wind and waves are aligned. These findings are specific to the 

spar-type platform, but we expect that the results presented here will be similar to other 

floating platforms. 

 

* Graduate Student (now graduated), Energy and Mineral Engineering, 157 Hosler, University Park, PA, 16802. † Assistant Professor and Research Associate, Aerospace Engineering, 230B Hammond, University Park, PA, 

16802, AIAA Professional Member. ‡ PhD Candidate, Department of Mechanical and Industrial Engineering, 160 Governors Dr., Amherst, MA, 01003, 

AIAA Student Member. § Assistant Professor, Department of Mechanical and Industrial Engineering, 160 Governors Dr. Amherst, MA, 

01003. ** Senior Engineer, NREL, 15013 Denver West Parkway, Golden, CO, 80401, AIAA Professional Member. †† Senior Engineer, NREL, 15013 Denver West Parkway, Golden, CO, 80401. ‡‡ Research Associate, Endowed Chair of Wind Energy, Allmandring 5B, Stuttgart, 70569, Germany.
2 

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Abbreviations

Meteorological ocean parameters

Ws wind speed at hub height in m/s

Wd wind/wave misalignment in degrees

Hs significant wave height in m

Tp wave peak-spectral period in s

Structural locations§§ 

Anch1Ten anchor tension of the first mooring line

Anch2Ten anchor tension of the second mooring line

Anch3Ten anchor tension of the third mooring line

Fair1Ten fairlead tension of the first mooring line

Fair2Ten fairlead tension of the second mooring line

Fair3Ten fairlead tension of the third mooring line

IPDefl1 in-plane deflection of blade 1

OoPDefl1 out-of-plane deflection of blade 1

LSSGagMya rotating low-speed shaft-bending moment about the ya axis

LSSGagMza rotating low-speed shaft-bending moment about the za axis

RootMxc1 first blade in-plane root-bending moment about the xc1 axis

RootMyc1 first blade out-of-plane root-bending moment about the yc1 axis

TwrBsMxt tower-base roll bending moment about the xt axis

TwrBsMyt tower-base pitch bending moment about the yt axis

YawBrMxp yaw-bearing roll bending moment about the xp axis

YawBrMyp yaw-bearing pitch bending moment about the yp axis

I. Introduction

OST fixed-bottom offshore wind turbine support structures are axisymmetric and stiff enough to ensure that 

wave loads do not have a significant impact on the overall structural loads of the system above the water. It is 

often conservative to assume that the winds, waves, and currents are co-directional for fixed-bottom offshore 

wind turbines because fore-aft loadings, which drive the design of their support structures, are highest when the 

winds, waves, and currents are from the same direction. However, in a floating wind turbine system there is greater 

potential for motion of the support structure, which combined with a lack of aerodynamic damping in the side-toside direction, may cause wind, wave, and current directionality to more heavily impact both extreme and fatigue 

loading. 

The goal of this work is to examine the importance of wind/wave misalignment when assessing the extreme and 

fatigue loads in a floating wind turbine system. We focused on identifying the number and type of wind/wave 

misalignment simulations needed to accurately capture the loads of the system over a large range of possible 

meteorological ocean (met-ocean) conditions. Specifically, this paper addresses the impact of wind/wave 

misalignment on the extreme and fatigue loading for a spar-type floating platform. This work is affiliated with the 

International Electrotechnical Commission (IEC) working group 3-2, with the intent of informing an upcoming 

floating wind turbine design technical specification. 

To date, a few studies have been conducted that investigate the impact of wind/wave misalignment on the 

response of floating wind turbine platforms. Philippe et al.

1 studied the impact of wind/wave misalignment on a 

floating wind turbine located on a barge platform and discovered that the sway, roll, and yaw response amplitude 

operators (RAOs) increased with misaligned wind and waves, especially for a misalignment of 90o. Ramachandran

et al.

2 studied the importance of wind/wave misalignment on a tension-leg platform (TLP) platform under wind 

 

§§ See FAST documention4 for a definition of the different coordinate systems

M
3 

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excitation of 10 m/s, and showed the significance of 90o and 180o misalignments in both the spectral energy contents 

and the time series of the platform motions. Kokubun et al.

3 modeled a 1/34.5-scale prototype of a wind turbine with 

a spar-buoy platform in an ocean engineering basin and were able to recreate storm situationswith blades fully 

featheredusing aligned wind, waves, and current and misaligned wind and waves. In this paper, misalignment 

situations created higher platform motions. These studies show the impact of wind/wave misalignment on floating 

platforms, especially in the side-to-side direction caused by increased compliance of the floating support structure. 

II. Methods 

This study uses the wind turbine computer-aided engineering tool FAST4 to simulate the Offshore Code 

Comparison Collaboration (OC3)-Hywind spar-buoy platform5 supporting the National Renewable Energy 

Laboratory (NREL) 5-MW reference wind turbine.

6 FAST is a nonlinear aero-hydro-servo-elastic tool that uses 

AeroDyn7 to compute the rotor aerodynamics and HydroDyn8 to compute the platform hydrodynamics. FAST

models wind turbines as a combination of rigid and flexible bodies, and allows the user to turn individual degrees of 

freedom (DOFs) on or off. All relevant structural DOFs were enabled in the present simulations.

We performed an exhaustive series of simulations with the OC3-Hywind system to examine the met-ocean 

conditions that produce the largest motions and loads in the structure during power production according to the IEC 

wind turbine standard’s design load cases 1.1 and 1.2. No discrete-event, fault, start, stop, parked/idling, or transport

cases were considered in this study. Instead, we considered variations in mean wind speed at hub height, wave 

direction, significant wave height, and peak-spectral wave period (which define the wave spectrum; modeled using a 

modified Pierson Spectrum).9 The wind direction was fixed at 0o with no nacelle yaw so the wind/wave 

misalignment was equal to the wave direction. Future work will consider separate wind and wave direction 

distributions to more accurately characterize fatigue damage accumulation, but for the extreme load and preliminary 

fatigue analyses presented in this study, the simplification of fixed wind direction allows one less variable to be

considered. Figure 1 shows the different directions of importance in this study.

Figure 1. Schematic showing the floating offshore wind turbine and direction of the waves and wind. The 

wind is fixed at 0° so the wave propagation direction is equal to the wind/wave misalignment. (The 90 ̊ wave 

direction is shown.)
4 

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Instead of choosing values for these parameters (shown in Figure 1) that were site-specific, we chose a range of 

values for the expected conditions that an operating floating wind turbine could encounter almost anywhere offshore 

of the United States, as shown in Table 1. To consider all of the possible combinations of the four parameters’ 

values, 370,656 simulations are required per seed. For our study, only one time-domain realization (one seed) of the 

wind/wave spectrum for a given combination was used. We ran time-domain simulations that were 10 minutes in 

length (after removal of the first 60 seconds of transient behavior with initial conditions chosen properly for each 

wind speed).

10 In addition, we used random turbulent wind fields created in TurbSim.11 Furthermore, we examined 

the following system responses: the platform motions and the loads/moments in the blade root, low-speed shaft 

(LSS), yaw bearing, tower base, and fairlead and anchor connections of the mooring lines.

In order to run all of these simulations, we used the high-performance computing (HPC) resources at NREL (a 

cluster with about 200 cores available for simulations). A Perl script, RunIEC,12 was also used to create all of the 

FAST input files and batch files to submit to the HPC.

Table 1. Values for the different parameters of the met-ocean conditions.

 Bin 

width

Numbers 

of bins*

Minimum 

value

Maximum 

value

Wind speed at hub height (Ws) 2 m/s 11 3 m/s 25 m/s

Significant wave height (Hs) 0.5 m 26 0 m 13 m

Peak-spectral period (Tp) 0.5 s 54 0 s 27 s

Wave direction (Wd) 15° 24 -180° 180°

* The bins were simulated at their midpoints, except for the wave direction, which used the bin endpoints.

Once the simulations from all of the combinations of the four met-ocean parameters were complete, we 

interpreted the data for a given site’s specific conditions (and its associated probabilities). Specifically in this study, 

the results were interpreted at a generic site located on the East Coast of the United States. The site was created as 

part of a previous study (reference forthcoming) that examined data provided by buoys that were located offshore 

from all of the U.S. coasts. Buoys with at least 5 years of data containing both wind and wave direction were kept 

and grouped into coastal regions depending on their locations: East Coast, West Coast, and the Gulf of Mexico. For 

each buoy, conditional distributions related to the four parameters were fit, including: 

● the wind speed at hub height was fitted with a two-parameter Weibull distribution; 

● the wind/wave misalignment was fitted with a two-parameter Von Mises distribution with parameters 

conditioned on the wind speed; 

● the significant wave height was fitted with a two-parameter Gamma distribution with parameters conditioned 

on wind speed and wind/wave misalignment; 

● the peak-spectral wave period was fitted with a two-parameter Gamma distribution with parameters 

conditioned on wind speed and wave height.

For each coastal region, we created a “generic” site with the average parameters of all the buoys in the area. 

From this, a four-dimensional array was created containing the probabilities of each combination of met-ocean 

parameters for the East Coast generic site. This information was used to analyze the simulation outputs.

III. Extreme Load Results

The extreme loading (taken here as the maximum positive value) experienced on various components of the 

floating wind turbine system were extracted from the simulation outputs using MExtremes.13 When considering all 

of the possible met-ocean conditions (370,656 simulations), we found that the highest significant wave height (12.75 

m) caused the highest loads for the blade-root, LSS, yaw-bearing, and tower-base bending moments, as well as for 

the anchor and fairlead tensions of mooring line 1 (which is directed downwind), as shown in Table 2. Also, more 

than half of these extreme loads were caused with a misalignment higher than 75°. 

However, a 12.75-m significant wave height value is an extremely rare occurrence at most offshore sites, thus the 

simulation set was filtered to only include conditions that pass a 50-year return period threshold as shown in Table 

2. To create this subset of simulations, the individual joint probabilities from the East Coast generic site were sorted 

in descending order, and a cumulative sum array was created from this sorted list. The 50-year probability of 

3.7*10-8 (the probability of a 10-minute event in 50 years) could then be applied to the cumulative sum array such 
5 

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that all simulations with lower probability are considered to have a return period larger than 50-years. This analysis 

reduced the number of simulations from 370,656 to around 70,000. This process filtered out simulations with high 

significant wave heights and high wind/wave misalignments (wave heights at real offshore sites tend to diminish 

with increasing wind/wave misalignmnent). A more accurate way of finding the 50-year return period uses the 

inverse first-order reliability method (IFORM), which will be investigated in future work.

With simulations of the most extreme conditions no longer present, the extreme loads observed at the (filtered) 

East Coast generic site were significantly lower than previously found and now occur at milder conditions. The 

significant wave height that caused these extreme loads decreased from 12.75 m to between 3 and 8 m, and aligned 

wind and waves were responsible for more than half of the extreme loads shown in Table 2. Of particular note is the

reduction of the side-to-side tower-base moment from 322 MN-m to 173 MN-m and the 31% reduction in the foreaft tower-base moment. Also note that in Table 2, mooring line 1 is the downwind line, so higher wind speeds 

(corresponding to higher rotor thrust) relieve the tension on this line, hence the extreme tensions occur at the lowest 

wind speeds; the other two mooring lines will be examined in future work.

To determine the general importance of the wind/wave misalignment on the extreme loads of the system, we 

compared the extreme loads for each angle of wind/wave misalignment (presented in load roses in Figure 2). 

Generally, we observe the importance of the 90° and -90° wind/wave misalignment for the side-to-side wind turbine 

loadings; the anchor and fairlead tensions for the three mooring lines experienced more significant loads in waves 

directed along the mooring line (the three lines are positioned at the 0°, 120°, and 240° angles around the platform; 

see Figure 1). The yaw bearing side-to-side bending moment, as well as the blade-root bending moments, blade 

deflection, and LSS moments (not shown here) are more impacted by high waves as their load rose profiles changed 

significantly from all conditions to those of the East Coast site with the 50-year return threshold. For the East Coast 

site, the load rose profiles show a dominant direction between -30 and 30 degrees, except for the yaw-bearing sideto-side bending moment, in which the perpendicular directions are more important.

Table 2. Extreme loads for different components of the floating wind turbine and the corresponding metocean conditions that produced these extremes. A comparison is made between the extreme loads for all 

conditions and for the U.S. East Coast conditions with a 50-year threshold.

All Conditions 

(All)

East Coast 

(50-Year) % Decrease 

From All to 

50-Year

All 50-

Year All 50-Year All 50-Year All 50-Year

Locations Units Maximum 

loads

Maximum 

loads

Ws 

(m/s)

Ws 

(m/s) Hs (m) Hs (m) Tp (s) Tp (s) Wd (°) Wd (°)

RootMxc1 kN-m 12,422.0 11,743.3 5% 14 24 12.75 7.25 12.75 2.25 -105° -90

RootMyc1 kN-m 26,780.5 23,721.3 11% 10 10 12.75 4.75 20.75 12.75 -135° 15

YawBrMxp kN-m 13,920.5 10,662.0 23% 16 16 12.75 6.25 6.75 5.25 90° 90

YawBrMyp kN-m 18,517.8 15,674.6 15% 24 24 12.75 6.75 6.25 6.25 0° -15

TwrBsMxt kN-m 322,110.4 173,271.4 46% 16 18 12.75 7.75 6.75 5.25 90° 75

TwrBsMyt kN-m 391,964.1 269,252.2 31% 12 16 12.75 6.25 8.25 6.25 180° 0

Fair1Ten kN 1,554.3 1,360.0 13% 4 4 12.75 3.25 16.25 17.75 0° 0

Anch1Ten kN 1,291.9 1,098.8 15% 4 4 12.75 3.25 16.25 17.75 0° 0
6 

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ALL CONDITIONS EAST COAST (50-YEAR RETURN)

180°

-165°

-150°

-135°

-120°

-105°

-90°

-75°

-60°

-45°

-30°

-15°

0°

15°

30°

45°

60°

75°

90°

105°

120°

135°

150°

165°

YawBrMxp (MN*m)

180°

-165°

-150°

-135°

-120°

-105°

-90°

-75°

-60°

-45°

-30°

-15°

0°

15°

30°

45°

60°

75°

90°

105°

120°

135°

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165°

YawBrMyp (MN*m)

180°

-165°

-150°

-135°

-120°

-105°

-90°

-75°

-60°

-45°

-30°

-15°

0°

15°

30°

45°

60°

75°

90°

105°

120°

135°

150°

165°

TwrBsMxt (MN*m)
7 

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180

-165

-150

-135

-120

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-90

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-45

-30

-15

0

15

30

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TwrBsMyt (MN*N)

180

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0

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Fair1Ten (MN*m)

180°

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-15°

0°

15°

30°

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60°

75°

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120°

135°

150°

165°

Anch1Ten (MN)

Figure 2. Loads roses representing the extreme loads as a function of the wave direction. From top to bottom: 

yaw-bearing side-to-side and fore-aft bending moments; tower-base side-to-side and fore-aft bending 

moments; anchor and fairlead tensions of mooring line 1. The roses on the left correspond to the complete 

range of met-ocean conditions and the roses on the right correspond to the generic U.S. East Coast site.
8 

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IV. Extreme Loading Directional Binning Sensitivity

In this study, we addressed a second issue: the minimum resolution of the wind/wave misalignment needed to 

accurately capture the extreme loads. To investigate this issue, we used the results from the East Coast generic site

(provided in the previous section), and examined the extreme loads for varying numbers of simulated wave 

directions. In Figure 3, the various bars represent different directional binning schemes, with each configuration 

having the number of bins specified with even bin spacing around 360°. The loads are normalized by the 24-bin 

case.

Figure 3. Comparison of the extreme loads when considering different numbers of wave direction bins. The 

extreme loads are normalized by the 50-year extremes with all 24 misalignment bins.

For most of the loads, aligned wind and waves produced the maximum values, therefore only one bin (0 degrees) 

was needed to capture the extreme load. However, for the tower-base side-to-side loading, considering only aligned 

wind and waves resulted in an extreme load that is three times less than what would be experienced when 

wind/wave misalignment is considered. Still, tower-base fore-aft bending moments are higher in magnitude than 

tower-base side-to-side bending moments. Finally, the lower extreme loads for the offset 4-bin case (-135°, -45°, 

45°, 135°) for most channels can be explained by the absence of the important bins of 0°, 90°, and -90° wind/wave 

misalignment. From these initial results, considering 0° as well as either -90° or 90° should be sufficient to 

characterize the extreme load for this system. More work needs to be done concerning this question however, 

because this study only included one 10-minute simulation for each combination of met-ocean parameters, and 

extreme loads may change with the addition of more seeds.

V. Fatigue Load Results 

Similar analyses were conducted to investigate the impact of wind/wave misalignment on the fatigue loads 

considering the set of simulations that represent the East Coast generic site with a 50-year return period. The goal of 

this analysis was to determine the necessary simulations needed to accurately characterize the fatigue of this floating 

platform. We used a customized version of the postprocessor MLife14 that includes the capability to consider a fourparameter probability distribution in the fatigue calculations. With this addition, MLife is able to use the fourparameter conditional probability distribution derived from our East Coast generic site to calculate lifetime fatigue.

From the various MLife runs, the fatigue lifetime damage was obtained as a function of the wind/wave 

misalignment. We calculated the lifetime fatigue damage by determining the short-term fatigue damage from each 

separate simulation using a rainflow-counting algorithm, and summing these short-term fatigue damage values 

weighted by their probability. Load roses for the fatigue lifetime damage similar to those used for the extreme loads 

 RootMxc1 RootMyc1 TwrBsMxt TwrBsMyt Anch2Ten
9 

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are shown in Figure 4. The Wöhler exponents used are 10 for the blade root-bending moments and 4 for the other 

structural locations (typical Wöhler exponents are 3−5 for steel and 8−12 for fiberglass blade materials).15 Figure 4 

shows that similar trends were found: the side-to-side tower-base and yaw-bearing loadings experience their highest 

lifetime damage towards the 90° and -90° directions and the other locations experience their highest lifetime damage 

towards the 0° direction.

180 -165 -150

-135

-120

-105

-90

-75

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-30 -15 0 15 30

45

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YawBrMxp (kN·m)

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-30 -15 0 15 30

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60

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TwrBsMyt (kN·m)

Figure 4. Lifetime fatigue damage roses for the U.S. East Coast generic site. 
10 

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VI. Fatigue Loading Directional Binning Sensitivity

We analyzed several directional bin sizes, which was the same analysis conducted for the extreme loads. Figure 

5 shows the effect of changing the wind/wave misalignment bins on the lifetime fatigue damage-equivalent loads of 

the edgewise and flapwise blade root-bending moment, fore-aft and side-to-side tower-bending moment, and anchor 

tensions. A two-bin case was added for this analysis, in which only 0° and 90° bins were considered, but the 

probability of the 0° bin was combined with the probability of the 180° bin, and the -90° bin probability was added 

to the 90° bin to ensure that the total probability remained equal. From Figure 5, it can be determined that blade and 

anchor tension loads are not strongly affected by wave misalignment. Of note is that the only anchor tension 

considered in Figure 5 is the mooring line directed along the wind; future work will look at the other two mooring 

lines as well. The side-to-side and fore-aft tower loads show the importance of considering wind/wave 

misalignment; with only one bin (aligned wind/waves), side-to-side tower damage is underpredicted by 

approximately 50%, and fore-aft tower fatigue is overpredicted by more than 5%.

Figure 5. Comparison of the damage-equivalent loads when considering different numbers of wind/wave 

misalignments for the U.S. East Coast generic site. The loads are normalized by the case with all 24 

misalignment bins.

VII. Conclusions 

This study investigates the importance of wind/wave misalignment in predicting the loads for an offshore 

floating wind turbine with a spar-type floating platform. A wide range of met-ocean conditions were investigated 

and the extreme loads were found to occur at the maximum significant wave height and for high wind/wave 

misalignments. The set of simulations was then filtered by using a four-parameter joint probability distribution 

representing a generic site on the U.S. East Coast with a 50-year return period. Once filtered, the extreme loads 

occurred mostly during aligned wind and waves or low misalignment values and lower significant wave heights. 

Tower-base side-to-side bending moments showed a strong dependency on the perpendicular wind and waves cases. 

This finding was demonstrated by a sensitivity study in which the extreme side-to-side tower loads were three times 

smaller when considering only aligned wind and waves. For other structural locations, extreme loads can be well 

estimated by aligned wind and wave situations. The fatigue analysis for the same U.S. East Coast generic site 

showed similar trends. However, considering only aligned wind and waves leads to an underestimation of the towerbase side-to-side bending moment by approximately 50% and an overestimation of the tower-base fore-aft bending 

moment by about 5%. Based on these results, we recommend considering at least two wave directions (aligned with 

the wind and 90 ̊ misaligned) to precisely capture the extreme and fatigue characteristics of a spar-type platform.

 RootMxc1 RootMyc1 TwrBsMxt TwrBsMyt Anch1Ten
11 

This report is available at no cost from the National Renewable Energy Laboratory (NREL) at www.nrel.gov/publications.

Future work will consider separate wind and wave direction distributions to increase the accuracy of the fatigue 

damage calculation, as well as investigate the validity of the 50-year return period approach with joint probability 

distributions. Other floating platforms must be investigated to fully understand the impact of wind/wave 

misalignment, especially for nonaxisymmetric platforms.

Acknowledgments

The authors would like to thank the staff at the National Wind Technology Center in Boulder, Colorado, for 

helping with HPC issues, especially Torri Lopez and Marshall Buhl. The University of Massachusetts authors were 

funded by an Integrative Graduate Education and Research Traineeship (IGERT) grant, number 1068864. The 

NREL authors performed this work in support of the U.S. Department of Energy, under contract number DE-AC36-

08GO28308.

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