Technical Report

NREL/TP-500-38060

February 2009

Definition of a 5-MW Reference 

Wind Turbine for Offshore 

System Development

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

G. Scott
National Renewable Energy Laboratory

1617 Cole Boulevard, Golden, Colorado 80401-3393

303-275-3000 • www.nrel.gov

NREL is a national laboratory of the U.S. Department of Energy

Office of Energy Efficiency and Renewable Energy

Operated by the Alliance for Sustainable Energy, LLC

Contract No. DE-AC36-08-GO28308

Technical Report

NREL/TP-500-38060

February 2009

Definition of a 5-MW Reference 

Wind Turbine for Offshore 

System Development

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

G. Scott

Prepared under Task No. WER5.3301
NOTICE

This report was prepared as an account of work sponsored by an agency of the United States government. 

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recommendation, or favoring by the United States government or any agency thereof. The views and 

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iii

Acronyms and Abbreviations

ADAMS® = Automatic Dynamic Analysis of Mechanical Systems

A2AD = ADAMS-to-AeroDyn

BEM = blade-element / momentum

CM = center of mass

DLL = dynamic link library

DOE = U.S. Department of Energy

DOF = degree of freedom

DOWEC = Dutch Offshore Wind Energy Converter project

DU = Delft University

ECN = Energy Research Center of the Netherlands

equiripple = equalized-ripple

FAST = Fatigue, Aerodynamics, Structures, and Turbulence

GE = General Electric

IEA = International Energy Agency

MSL = mean sea level

NACA = National Advisory Committee for Aeronautics

NREL = National Renewable Energy Laboratory

NWTC = National Wind Technology Center

OCS = offshore continental shelf

OC3 = Offshore Code Comparison Collaborative

PI = proportional-integral

PID = proportional-integral-derivative

RECOFF = Recommendations for Design of Offshore Wind Turbines project

WindPACT= Wind Partnerships for Advanced Component Technology project

w.r.t. = with respect to
iv

Nomenclature

Ad = discrete-time state matrix

Bd = discrete-time input matrix

Cd = discrete-time output state matrix

Cφ = effective damping in the equation of motion for the rotor-speed error

Dd = discrete-time input transmission matrix

fc = corner frequency

GK = gain-correction factor

IDrivetrain = drivetrain inertia cast to the low-speed shaft

IGen = generator inertia relative to the high-speed shaft

IRotor = rotor inertia

KD = blade-pitch controller derivative gain

KI = blade-pitch controller integral gain

KP = blade-pitch controller proportional gain

Kφ = effective stiffness in the equation of motion for the rotor-speed error

Mφ = effective inertia (mass) in the equation of motion for the rotor-speed error

n = discrete-time-step counter

NGear = high-speed to low-speed gearbox ratio

P = mechanical power

P0 = rated mechanical power

∂ ∂ P θ = sensitivity of the aerodynamic power to the rotor-collective blade-pitch angle

t = simulation time

TAero = aerodynamic torque in the low-speed shaft

TGen = generator torque in the high-speed shaft
v

Ts = discrete-time step

u = unfiltered generator speed

x = for the control-measurement filter, the filter state

x,y,z = set of orthogonal axes making up a reference-frame coordinate system

y = for the control-measurement filter, the filtered generator speed

α = low-pass filter coefficient

Δθ = small perturbation of the blade-pitch angles about their operating point

ΔΩ = small perturbation of the low-speed shaft rotational speed about the rated speed

∆Ω = low-speed shaft rotational acceleration

ζφ = damping ratio of the response associated with the equation of motion for the 

rotor-speed error

θ = full-span rotor-collective blade-pitch angle

θK = rotor-collective blade-pitch angle at which the pitch sensitivity has doubled from 

its value at the rated operating point

π = the ratio of a circle’s circumference to its diameter

φ = the integral of φ with respect to time

φ = small perturbation of the low-speed shaft rotational speed about the rated speed



φ = low-speed shaft rotational acceleration

Ω = low-speed shaft rotational speed

Ω0 = rated low-speed shaft rotational speed

ωφn = natural frequency of the response associated with the equation of motion for the 

rotor-speed error
vi

Executive Summary

To support concept studies aimed at assessing offshore wind technology, we developed the 

specifications of a representative utility-scale multimegawatt turbine now known as the “NREL 

offshore 5-MW baseline wind turbine.” This wind turbine is a conventional three-bladed upwind 

variable-speed variable blade-pitch-to-feather-controlled turbine. To create the model, we 

obtained some broad design information from the published documents of turbine manufacturers, 

with a heavy emphasis on the REpower 5M machine. Because detailed data was unavailable, 

however, we also used the publicly available properties from the conceptual models in the 

WindPACT, RECOFF, and DOWEC projects. We then created a composite from these data, 

extracting the best available and most representative specifications. This report documents the 

specifications of the NREL offshore 5-MW baseline wind turbine—including the aerodynamic, 

structural, and control-system properties—and the rationale behind its development. The model 

has been, and will likely continue to be, used as a reference by research teams throughout the 

world to standardize baseline offshore wind turbine specifications and to quantify the benefits of 

advanced land- and sea-based wind energy technologies.
vii

Table of Contents

1 Introduction................................................................................................................................ 1

2 Blade Structural Properties...................................................................................................... 5

3 Blade Aerodynamic Properties................................................................................................. 7

4 Hub and Nacelle Properties.................................................................................................... 12

5 Drivetrain Properties............................................................................................................... 14

6 Tower Properties...................................................................................................................... 15

7 Baseline Control System Properties....................................................................................... 17

7.1 Baseline Control-Measurement Filter................................................................................17

7.2 Baseline Generator-Torque Controller ..............................................................................19

7.3 Baseline Blade-Pitch Controller ........................................................................................20

7.4 Baseline Blade-Pitch Actuator...........................................................................................26

7.5 Summary of Baseline Control System Properties..............................................................26

8 FAST with AeroDyn and ADAMS with AeroDyn Models................................................... 28

9 Full-System Natural Frequencies and Steady-State Behavior............................................. 30

10 Conclusions............................................................................................................................. 33

References.................................................................................................................................... 34

Appendix A FAST Input Files................................................................................................... 38

A.1 Primary Input File .............................................................................................................38

A.2 Blade Input File – NRELOffshrBsline5MW_Blade.dat...................................................40

A.3 Tower Input File – NRELOffshrBsline5MW_Tower_Onshore.dat .................................41

A.4 ADAMS Input File – NRELOffshrBsline5MW_ADAMSSpecific.dat............................42

A.5 Linearization Input File – NRELOffshrBsline5MW_Linear.dat......................................43

Appendix B AeroDyn Input Files.............................................................................................. 44

B.1 Primary Input File – NRELOffshrBsline5MW_AeroDyn.ipt...........................................44

B.2 Airfoil-Data Input File – Cylinder1.dat.............................................................................44

B.3 Airfoil-Data Input File – Cylinder2.dat.............................................................................44

B.4 Airfoil-Data Input File – DU40_A17.dat..........................................................................45
viii

B.5 Airfoil-Data Input File – DU35_A17.dat..........................................................................47

B.6 Airfoil-Data Input File – DU30_A17.dat..........................................................................48

B.7 Airfoil-Data Input File – DU25_A17.dat..........................................................................50

B.8 Airfoil-Data Input File – DU21_A17.dat..........................................................................52

B.9 Airfoil-Data Input File – NACA64_A17.dat ....................................................................54

Appendix C Source Code for the Control System DLL.......................................................... 57
ix

List of Tables

Table 1-1. Gross Properties Chosen for the NREL 5-MW Baseline Wind Turbine...................... 2

Table 2-1. Distributed Blade Structural Properties........................................................................ 5

Table 2-2. Undistributed Blade Structural Properties.................................................................... 6

Table 3-1. Distributed Blade Aerodynamic Properties.................................................................. 7

Table 4-1. Nacelle and Hub Properties........................................................................................ 13

Table 5-1. Drivetrain Properties .................................................................................................. 14

Table 6-1. Distributed Tower Properties ..................................................................................... 15

Table 6-2. Undistributed Tower Properties ................................................................................. 16

Table 7-1. Sensitivity of Aerodynamic Power to Blade Pitch in Region 3 ................................. 23

Table 7-2. Baseline Control System Properties........................................................................... 27

Table 9-1. Full-System Natural Frequencies in Hertz ................................................................. 30
x

List of Figures

Figure 3-1. Corrected coefficients of the DU40 airfoil.................................................................. 9

Figure 3-2. Corrected coefficients of the DU35 airfoil.................................................................. 9

Figure 3-3. Corrected coefficients of the DU30 airfoil................................................................ 10

Figure 3-4. Corrected coefficients of the DU25 airfoil................................................................ 10

Figure 3-5. Corrected coefficients of the DU21 airfoil................................................................ 11

Figure 3-6. Corrected coefficients of the NACA64 airfoil.......................................................... 11

Figure 7-1. Bode plot of generator speed low-pass filter frequency response............................. 18

Figure 7-2. Torque-versus-speed response of the variable-speed controller............................... 20

Figure 7-3. Best-fit line of pitch sensitivity in Region 3 ............................................................. 24

Figure 7-4. Baseline blade-pitch control system gain-scheduling law ........................................ 25

Figure 7-5. Flowchart of the baseline control system.................................................................. 27

Figure 9-1. Steady-state responses as a function of wind speed.................................................. 32
1

1 Introduction

The U.S. Department of Energy’s (DOE’s) National Renewable Energy Laboratory (NREL), 

through the National Wind Technology Center (NWTC), has sponsored conceptual studies aimed 

at assessing offshore wind technology suitable in the shallow and deep waters off the U.S. 

offshore continental shelf (OCS) and other offshore sites worldwide. To obtain useful 

information from such studies, use of realistic and standardized input data is required. This 

report documents the turbine specifications of what is now called the “NREL offshore 5-MW 

baseline wind turbine” and the rationale behind its development. Our objective was to establish 

the detailed specifications of a large wind turbine that is representative of typical utility-scale 

land- and sea-based multimegawatt turbines, and suitable for deployment in deep waters.

Before establishing the detailed specifications, however, we had to choose the basic size and 

power rating of the machine. Because of the large portion of system costs in the support 

structure of an offshore wind system, we understood from the outset that if a deepwater wind 

system is to be cost-effective, each individual wind turbine must be rated at 5 MW or higher 

[23].1

• Feasible floater configurations for offshore wind turbines scoped out by Musial, 

Butterfield, and Boone [

 Ratings considered for the baseline ranged from 5 MW to 20 MW. We decided that the 

baseline should be 5 MW because it has precedence:

23] were based on the assumption of a 5-MW unit.

• Unpublished DOE offshore cost studies were based on a rotor diameter of 128 m, which 

is a size representative of a 5- to 6-MW wind turbine.

• The land-based Wind Partnerships for Advanced Component Technology (WindPACT) 

series of studies, considered wind turbine systems rated up to 5 MW [19,24,29].

• The Recommendations for Design of Offshore Wind Turbines project (known as 

RECOFF) based its conceptual design calculations on a wind turbine with a 5-MW rating 

[32].

• The Dutch Offshore Wind Energy Converter (DOWEC) project based its conceptual 

design calculations on a wind turbine with a 6-MW rating [8,14,17].

• At the time of this writing, the largest wind turbine prototypes in the world—the 

Multibrid M5000 [5,21,22] and the REpower 5M [18,26,27]—each had a 5-MW rating.

We gathered the publicly available information on the Multibrid M5000 and REpower 5M 

prototype wind turbines. And because detailed information on these machines was unavailable, 

we also used the publicly available properties from the conceptual models used in the 

WindPACT, RECOFF, and DOWEC projects. These models contained much greater detail than 

was available about the prototypes. We then created a composite from these models, extracting 

the best available and most representative specifications.

 

1 A single 5-MW wind turbine can supply enough energy annually to power 1,250 average American homes.
2

The Multibrid M5000 machine has a significantly higher tip speed than typical onshore wind 

turbines and a lower tower-top mass than would be expected from scaling laws previously 

developed in one of the WindPACT studies [29]. In contrast, the REpower 5M machine has 

properties that are more “expected” and “conventional.” For this reason, we decided to use the 

specifications of the REpower 5M machine as the target specifications2

The wind turbine used in the DOWEC project had a slightly higher rating than the rating of the 

REpower 5M machine, but many of the other basic properties of the DOWEC turbine matched 

the REpower 5M machine very well. In fact, the DOWEC turbine matched many of the 

properties of the REpower 5M machine better than the turbine properties derived for the 

WindPACT and RECOFF studies.

for our baseline model.

3

The REpower 5M machine has a rotor radius of about 63 m. Wanting the same radius and the 

lowest reasonable hub height possible to minimize the overturning moment acting on an offshore 

substructure, we decided that the hub height for the baseline wind turbine should be 90 m. This 

would give a 15-m air gap between the blade tips at their lowest point when the wind turbine is 

undeflected and an estimated extreme 50-year individual wave height of 30 m (i.e., 15-m 

amplitude). The additional gross properties we chose for the NREL 5-MW baseline wind 

turbine, most of which are identical to those of the REpower 5M, are given in 

 As a result of these similarities, we made the heaviest use of 

data from the DOWEC study in our development of the NREL offshore 5-MW baseline wind 

turbine.

Table 1-1. The 

(x,y,z) coordinates of the overall center of mass (CM) location of the wind turbine are indicated 

in a tower-base coordinate system, which originates along the tower centerline at ground or mean 

 

2 Note that we established the target specifications using information about the REpower 5M machine that was

published in January 2005 [26,27]. Some of the information presented in Refs. [26] and [27] disagrees with more

recently published information. For example, the published nacelle and rotor masses of the REpower 5M are higher 

in the more recent publications.

3 This was probably because the REpower 5M prototype utilized blades provided by LM Glasfiber [18], a company 

that helped establish the structural properties of the blades used in the DOWEC study.

Table 1-1. Gross Properties Chosen for the NREL 5-MW Baseline 

Wind Turbine

Rating 5 MW

Rotor Orientation, Configuration Upwind, 3 Blades

Control Variable Speed, Collective Pitch

Drivetrain High Speed, Multiple-Stage Gearbox

Rotor, Hub Diameter 126 m, 3 m

Hub Height 90 m

Cut-In, Rated, Cut-Out Wind Speed 3 m/s, 11.4 m/s, 25 m/s

Cut-In, Rated Rotor Speed 6.9 rpm, 12.1 rpm

Rated Tip Speed 80 m/s

Overhang, Shaft Tilt, Precone 5 m, 5o, 2.5o

Rotor Mass 110,000 kg

Nacelle Mass 240,000 kg

Tower Mass 347,460 kg

Coordinate Location of Overall CM (-0.2 m, 0.0 m, 64.0 m)
3

sea level (MSL). The x-axis of this coordinate system is directed nominally downwind, the yaxis is directed transverse to the nominal wind direction, and the z-axis is directed vertically from 

the tower base to the yaw bearing.

The actual REpower 5M wind turbine uses blades with built-in prebend as a means of increasing

tower clearance without a large rotor overhang. Because many of the available simulation tools 

and design codes cannot support blades with built-in prebend, we chose a 2.5°-upwind precone 

in the baseline wind turbine to represent the smaller amount of precone and larger amount of 

prebend that are built into the actual REpower 5M machine.

The rotor diameter indicated in Table 1-1 ignores the effect of blade precone, which reduces the 

actual diameter and swept area. The exact rotor diameter in the turbine specifications (assuming 

that the blades are undeflected) is actually (126 m) × cos(2.5°) = 125.88 m and the actual swept 

area is (π/4) × (125.88 m)2 = 12,445.3 m2

.

We present other information about this model as follows:

• The blade structural properties in Section 2

• The blade aerodynamic properties in Section 3

• The hub and nacelle properties in Section 4

• The drivetrain properties in Section 5

• The tower properties in Section 6

• The baseline control system properties in Section 7

• The aero-servo-elastic FAST (Fatigue, Aerodynamics, Structures, and Turbulence) [11] 

with AeroDyn [16,20] and MSC.ADAMS® (Automatic Dynamic Analysis of Mechanical 

Systems) with A2AD (ADAMS-to-AeroDyn)4 [6,15] and AeroDyn models of the wind 

turbine in Section 8

• The basic responses of the land-based version of the wind turbine, including its fullsystem natural frequencies and steady-state behavior in Section 9.

Although we summarize much of this information5 for conciseness and clarity, Section 7

contains a high level of detail about the development of the wind turbine’s baseline control 

system. These details are provided because they are fundamental to the development of more 

advanced control systems.

The NREL offshore 5-MW baseline wind turbine has been used to establish the reference 

specifications for a number of research projects supported by the U.S. DOE’s Wind & 

Hydropower Technologies Program [1,2,7,12,28,33,34]. In addition, the integrated European 

 

4 Note that we use the term “ADAMS” to mean “MSC.ADAMS with A2AD” in this work.

5 Note that some of the turbine properties are presented with a large number (>4) of significant figures. Most of 

these were carried over from the turbine properties documented in the DOWEC study [8,14,17]—We did not 

truncate their precision to maintain consistency with the original data source.
4

Union UpWind research program6 and the International Energy Agency (IEA) Wind Annex 

XXIII Subtask 27 Offshore Code Comparison Collaboration (OC3) [13,25] have adopted the 

NREL offshore 5-MW baseline wind turbine as their reference model. The model has been, and 

will likely continue to be, used as a reference by research teams throughout the world to 

standardize baseline offshore wind turbine specifications and to quantify the benefits of 

advanced land- and sea-based wind energy technologies.

 

6 Web site: http://www.upwind.eu/default.aspx

7 Web site: http://www.ieawind.org/Annex%20XXIII/Subtask2.html
5

2 Blade Structural Properties

The NREL offshore 5-MW baseline wind turbine has three blades. We based the distributed

blade structural properties of each blade on the structural properties of the 62.6-m-long LM 

Glasfiber blade used in the DOWEC study (using the data given in Appendix A of Ref. [17]). 

Because the blades in the DOWEC study were 1.1 m longer than the 61.5-m-long LM Glasfiber 

blades [18] used on the actual REpower 5M machine, we truncated the 62.6-m blades at 61.5-m 

span to obtain the structural properties of the NREL 5-MW baseline blades (we found the 

structural properties at the blade tip by interpolating between the 61.2-m and 61.7-m stations 

given in Appendix A of Ref. [17]). Table 2-1 lists the resulting properties.

The entries in the first column of Table 2-1, labeled “Radius,” are the spanwise locations along 

the blade-pitch axis relative to the rotor center (apex). “BlFract” is the fractional distance along 

the blade-pitch axis from the root (0.0) to the tip (1.0). We located the blade root 1.5 m along the 

pitch axis from the rotor center, equivalent to half the hub diameter listed in Table 1-1.

“AeroCent” is the name of a FAST input parameter. The FAST code assumes that the bladepitch axis passes through each airfoil section at 25% chord. By definition, then, the quantity 

(AeroCent − 0.25) is the fractional distance to the aerodynamic center from the blade-pitch axis 

along the chordline, positive toward the trailing edge. Thus, at the root (i.e., BlFract = 0.0), 

AeroCent = 0.25 means that the aerodynamic center lies on the blade-pitch axis [because (0.25 −

0.25) = 0.0], and at the tip (i.e., BlFract = 1.0), AeroCent = 0.125 means that the aerodynamic 

center lies 0.125 chordlengths toward the leading edge from the blade-pitch axis [because (0.125

Table 2-1. Distributed Blade Structural Properties Radius BlFract AeroCent StrcTwst BMassDen FlpStff EdgStff GJStff EAStff Alpha FlpIner EdgIner PrecrvRef PreswpRef FlpcgOf EdgcgOf FlpEAOf EdgEAOf

(m) (-) (-) (o) (kg/m) (N•m2

) (N•m2

) (N•m2) (N) (-) (kg•m) (kg•m) (m) (m) (m) (m) (m) (m)

1.50 0.00000 0.25000 13.308 678.935 18110.00E+6 18113.60E+6 5564.40E+6 9729.48E+6 0.0 972.86 973.04 0.0 0.0 0.0 0.00017 0.0 0.0

1.70 0.00325 0.25000 13.308 678.935 18110.00E+6 18113.60E+6 5564.40E+6 9729.48E+6 0.0 972.86 973.04 0.0 0.0 0.0 0.00017 0.0 0.0

2.70 0.01951 0.24951 13.308 773.363 19424.90E+6 19558.60E+6 5431.59E+6 10789.50E+6 0.0 1091.52 1066.38 0.0 0.0 0.0 -0.02309 0.0 0.0

3.70 0.03577 0.24510 13.308 740.550 17455.90E+6 19497.80E+6 4993.98E+6 10067.23E+6 0.0 966.09 1047.36 0.0 0.0 0.0 0.00344 0.0 0.0

4.70 0.05203 0.23284 13.308 740.042 15287.40E+6 19788.80E+6 4666.59E+6 9867.78E+6 0.0 873.81 1099.75 0.0 0.0 0.0 0.04345 0.0 0.0

5.70 0.06829 0.22059 13.308 592.496 10782.40E+6 14858.50E+6 3474.71E+6 7607.86E+6 0.0 648.55 873.02 0.0 0.0 0.0 0.05893 0.0 0.0

6.70 0.08455 0.20833 13.308 450.275 7229.72E+6 10220.60E+6 2323.54E+6 5491.26E+6 0.0 456.76 641.49 0.0 0.0 0.0 0.06494 0.0 0.0

7.70 0.10081 0.19608 13.308 424.054 6309.54E+6 9144.70E+6 1907.87E+6 4971.30E+6 0.0 400.53 593.73 0.0 0.0 0.0 0.07718 0.0 0.0

8.70 0.11707 0.18382 13.308 400.638 5528.36E+6 8063.16E+6 1570.36E+6 4493.95E+6 0.0 351.61 547.18 0.0 0.0 0.0 0.08394 0.0 0.0

9.70 0.13335 0.17156 13.308 382.062 4980.06E+6 6884.44E+6 1158.26E+6 4034.80E+6 0.0 316.12 490.84 0.0 0.0 0.0 0.10174 0.0 0.0

10.70 0.14959 0.15931 13.308 399.655 4936.84E+6 7009.18E+6 1002.12E+6 4037.29E+6 0.0 303.60 503.86 0.0 0.0 0.0 0.10758 0.0 0.0

11.70 0.16585 0.14706 13.308 426.321 4691.66E+6 7167.68E+6 855.90E+6 4169.72E+6 0.0 289.24 544.70 0.0 0.0 0.0 0.15829 0.0 0.0

12.70 0.18211 0.13481 13.181 416.820 3949.46E+6 7271.66E+6 672.27E+6 4082.35E+6 0.0 246.57 569.90 0.0 0.0 0.0 0.22235 0.0 0.0

13.70 0.19837 0.12500 12.848 406.186 3386.52E+6 7081.70E+6 547.49E+6 4085.97E+6 0.0 215.91 601.28 0.0 0.0 0.0 0.30756 0.0 0.0

14.70 0.21465 0.12500 12.192 381.420 2933.74E+6 6244.53E+6 448.84E+6 3668.34E+6 0.0 187.11 546.56 0.0 0.0 0.0 0.30386 0.0 0.0

15.70 0.23089 0.12500 11.561 352.822 2568.96E+6 5048.96E+6 335.92E+6 3147.76E+6 0.0 160.84 468.71 0.0 0.0 0.0 0.26519 0.0 0.0

16.70 0.24715 0.12500 11.072 349.477 2388.65E+6 4948.49E+6 311.35E+6 3011.58E+6 0.0 148.56 453.76 0.0 0.0 0.0 0.25941 0.0 0.0

17.70 0.26341 0.12500 10.792 346.538 2271.99E+6 4808.02E+6 291.94E+6 2882.62E+6 0.0 140.30 436.22 0.0 0.0 0.0 0.25007 0.0 0.0

19.70 0.29595 0.12500 10.232 339.333 2050.05E+6 4501.40E+6 261.00E+6 2613.97E+6 0.0 124.61 398.18 0.0 0.0 0.0 0.23155 0.0 0.0

21.70 0.32846 0.12500 9.672 330.004 1828.25E+6 4244.07E+6 228.82E+6 2357.48E+6 0.0 109.42 362.08 0.0 0.0 0.0 0.20382 0.0 0.0

23.70 0.36098 0.12500 9.110 321.990 1588.71E+6 3995.28E+6 200.75E+6 2146.86E+6 0.0 94.36 335.01 0.0 0.0 0.0 0.19934 0.0 0.0

25.70 0.39350 0.12500 8.534 313.820 1361.93E+6 3750.76E+6 174.38E+6 1944.09E+6 0.0 80.24 308.57 0.0 0.0 0.0 0.19323 0.0 0.0

27.70 0.42602 0.12500 7.932 294.734 1102.38E+6 3447.14E+6 144.47E+6 1632.70E+6 0.0 62.67 263.87 0.0 0.0 0.0 0.14994 0.0 0.0

29.70 0.45855 0.12500 7.321 287.120 875.80E+6 3139.07E+6 119.98E+6 1432.40E+6 0.0 49.42 237.06 0.0 0.0 0.0 0.15421 0.0 0.0

31.70 0.49106 0.12500 6.711 263.343 681.30E+6 2734.24E+6 81.19E+6 1168.76E+6 0.0 37.34 196.41 0.0 0.0 0.0 0.13252 0.0 0.0

33.70 0.52358 0.12500 6.122 253.207 534.72E+6 2554.87E+6 69.09E+6 1047.43E+6 0.0 29.14 180.34 0.0 0.0 0.0 0.13313 0.0 0.0

35.70 0.55610 0.12500 5.546 241.666 408.90E+6 2334.03E+6 57.45E+6 922.95E+6 0.0 22.16 162.43 0.0 0.0 0.0 0.14035 0.0 0.0

37.70 0.58862 0.12500 4.971 220.638 314.54E+6 1828.73E+6 45.92E+6 760.82E+6 0.0 17.33 134.83 0.0 0.0 0.0 0.13950 0.0 0.0

39.70 0.62115 0.12500 4.401 200.293 238.63E+6 1584.10E+6 35.98E+6 648.03E+6 0.0 13.30 116.30 0.0 0.0 0.0 0.15134 0.0 0.0

41.70 0.65366 0.12500 3.834 179.404 175.88E+6 1323.36E+6 27.44E+6 539.70E+6 0.0 9.96 97.98 0.0 0.0 0.0 0.17418 0.0 0.0

43.70 0.68618 0.12500 3.332 165.094 126.01E+6 1183.68E+6 20.90E+6 531.15E+6 0.0 7.30 98.93 0.0 0.0 0.0 0.24922 0.0 0.0

45.70 0.71870 0.12500 2.890 154.411 107.26E+6 1020.16E+6 18.54E+6 460.01E+6 0.0 6.22 85.78 0.0 0.0 0.0 0.26022 0.0 0.0

47.70 0.75122 0.12500 2.503 138.935 90.88E+6 797.81E+6 16.28E+6 375.75E+6 0.0 5.19 69.96 0.0 0.0 0.0 0.22554 0.0 0.0

49.70 0.78376 0.12500 2.116 129.555 76.31E+6 709.61E+6 14.53E+6 328.89E+6 0.0 4.36 61.41 0.0 0.0 0.0 0.22795 0.0 0.0

51.70 0.81626 0.12500 1.730 107.264 61.05E+6 518.19E+6 9.07E+6 244.04E+6 0.0 3.36 45.44 0.0 0.0 0.0 0.20600 0.0 0.0

53.70 0.84878 0.12500 1.342 98.776 49.48E+6 454.87E+6 8.06E+6 211.60E+6 0.0 2.75 39.57 0.0 0.0 0.0 0.21662 0.0 0.0

55.70 0.88130 0.12500 0.954 90.248 39.36E+6 395.12E+6 7.08E+6 181.52E+6 0.0 2.21 34.09 0.0 0.0 0.0 0.22784 0.0 0.0

56.70 0.89756 0.12500 0.760 83.001 34.67E+6 353.72E+6 6.09E+6 160.25E+6 0.0 1.93 30.12 0.0 0.0 0.0 0.23124 0.0 0.0

57.70 0.91382 0.12500 0.574 72.906 30.41E+6 304.73E+6 5.75E+6 109.23E+6 0.0 1.69 20.15 0.0 0.0 0.0 0.14826 0.0 0.0

58.70 0.93008 0.12500 0.404 68.772 26.52E+6 281.42E+6 5.33E+6 100.08E+6 0.0 1.49 18.53 0.0 0.0 0.0 0.15346 0.0 0.0

59.20 0.93821 0.12500 0.319 66.264 23.84E+6 261.71E+6 4.94E+6 92.24E+6 0.0 1.34 17.11 0.0 0.0 0.0 0.15382 0.0 0.0

59.70 0.94636 0.12500 0.253 59.340 19.63E+6 158.81E+6 4.24E+6 63.23E+6 0.0 1.10 11.55 0.0 0.0 0.0 0.09470 0.0 0.0

60.20 0.95447 0.12500 0.216 55.914 16.00E+6 137.88E+6 3.66E+6 53.32E+6 0.0 0.89 9.77 0.0 0.0 0.0 0.09018 0.0 0.0

60.70 0.96260 0.12500 0.178 52.484 12.83E+6 118.79E+6 3.13E+6 44.53E+6 0.0 0.71 8.19 0.0 0.0 0.0 0.08561 0.0 0.0

61.20 0.97073 0.12500 0.140 49.114 10.08E+6 101.63E+6 2.64E+6 36.90E+6 0.0 0.56 6.82 0.0 0.0 0.0 0.08035 0.0 0.0

61.70 0.97886 0.12500 0.101 45.818 7.55E+6 85.07E+6 2.17E+6 29.92E+6 0.0 0.42 5.57 0.0 0.0 0.0 0.07096 0.0 0.0

62.20 0.98699 0.12500 0.062 41.669 4.60E+6 64.26E+6 1.58E+6 21.31E+6 0.0 0.25 4.01 0.0 0.0 0.0 0.05424 0.0 0.0

62.70 0.99512 0.12500 0.023 11.453 0.25E+6 6.61E+6 0.25E+6 4.85E+6 0.0 0.04 0.94 0.0 0.0 0.0 0.05387 0.0 0.0

63.00 1.00000 0.12500 0.000 10.319 0.17E+6 5.01E+6 0.19E+6 3.53E+6 0.0 0.02 0.68 0.0 0.0 0.0 0.05181 0.0 0.0
6

− 0.25) = −0.125].

The flapwise and edgewise section stiffness and inertia values, “FlpStff,” “EdgStff,” “FlpIner,”

and “EdgIner” in Table 2-1, are given about the principal structural axes of each cross section as 

oriented by the structural-twist angle, “StrcTwst.” The values of the structural twist were 

assumed to be identical to the aerodynamic twist discussed in Section 3.

“GJStff” represents the values of the blade torsion stiffness. Because the DOWEC blade data did 

not contain extensional stiffness information, we estimated the blade extensional stiffness 

values—“EAStff” in Table 2-1—to be 107 times the average mass moment of inertia at each 

blade station. This came from a rule of thumb derived from the data available in the WindPACT 

rotor design study [19], but the exact values are not important because of the low rotational 

speed of the rotor.

The edgewise CM offset values, “EdgcgOf,” are the distances in meters along the chordline from 

the blade-pitch axis to the CM of the blade section, positive toward the trailing edge. We

neglected the insignificant values of the flapwise CM offsets, “FlpcgOf,” and flapwise and 

edgewise elastic offsets, “FlpEAOf” and “EdgEAOf,” given in Appendix A of Ref. [17]. 

Instead, we assumed that they were zero as shown in Table 2-1.

The distributed blade section mass per unit length values, “BMassDen,” given in Table 2-1 are 

the values documented in Appendix A of Ref. [17]. We increased these by 4.536% in the model 

to scale the overall (integrated) blade mass to 17,740 kg, which was the nominal mass of the 

blades in the REpower 5M prototype. In our baseline specifications, the nominal second mass 

moment of inertia, nominal first mass moment of inertia, and the nominal radial CM location of 

each blade are 11,776,047 kg•m

2

, 363,231 kg•m, and 20.475 m with respect to (w.r.t.) the blade 

root, respectively.

We specified a structural-damping ratio of 0.477465% critical in all modes of the isolated blade, 

which corresponds to the 3% logarithmic decrement used in the DOWEC study from page 20 of 

Ref. [14].

Table 2-2 summarizes the undistributed blade structural properties discussed in this section.

Table 2-2. Undistributed Blade Structural Properties

Length (w.r.t. Root Along Preconed Axis) 61.5 m

Mass Scaling Factor 4.536 %

Overall (Integrated) Mass 17,740 kg

Second Mass Moment of Inertia (w.r.t. Root) 11,776,047 kg•m2

First Mass Moment of Inertia (w.r.t. Root) 363,231 kg•m

CM Location (w.r.t. Root along Preconed Axis) 20.475 m

Structural-Damping Ratio (All Modes) 0.477465 %
7

3 Blade Aerodynamic Properties

Similar to the blade structural properties, we based the blade aerodynamic properties of the 

NREL 5-MW baseline wind turbine on the DOWEC blades (using the data described in Table 1 

on page 13 of Ref. [14] and in Appendix A of Ref. [17]). We set the FAST with AeroDyn and 

ADAMS with AeroDyn models to use 17 blade elements for integration of the aerodynamic and 

structural forces. To better capture the large structural gradients at the blade root and the large 

aerodynamic gradients at the blade tip, the 3 inboard and 3 outboard elements are two-thirds the 

size of the 11 equally spaced midspan elements. Table 3-1 gives the aerodynamic properties at 

the blade nodes, which are located at the center of the blade elements.

The blade node locations, labeled as “RNodes” in Table 3-1, are directed along the blade-pitch 

axis from the rotor center (apex) to the blade cross sections. The element lengths, “DRNodes,” 

sum to the total blade length of 61.5 m indicated in Table 2-2. The aerodynamic twist, 

“AeroTwst,” as given in Table 3-1, are offset by −0.09182° from the values provided in 

Appendix A of Ref. [17] to ensure that the zero-twist reference location is at the blade tip. 

Integrating the chord distribution along the blade span reveals that the rotor solidity is roughly 

5.16%.

As indicated in Table 3-1, we incorporated eight unique airfoil-data tables for the NREL offshore 

5-MW baseline wind turbine. The two innermost airfoil tables represent cylinders with drag 

coefficients of 0.50 (Cylinder1.dat) and 0.35 (Cylinder2.dat) and no lift. We created the

remaining six airfoil tables by making corrections for three-dimensional behavior to the twodimensional airfoil-data coefficients of the six airfoils used in the DOWEC study (as detailed in 

Table 3-1. Distributed Blade Aerodynamic Properties

Node RNodes AeroTwst DRNodes Chord Airfoil Table

(-) (m) (o) (m) (m) (-)

1 2.8667 13.308 2.7333 3.542 Cylinder1.dat

2 5.6000 13.308 2.7333 3.854 Cylinder1.dat

3 8.3333 13.308 2.7333 4.167 Cylinder2.dat

4 11.7500 13.308 4.1000 4.557 DU40_A17.dat

5 15.8500 11.480 4.1000 4.652 DU35_A17.dat

6 19.9500 10.162 4.1000 4.458 DU35_A17.dat

7 24.0500 9.011 4.1000 4.249 DU30_A17.dat

8 28.1500 7.795 4.1000 4.007 DU25_A17.dat

9 32.2500 6.544 4.1000 3.748 DU25_A17.dat

10 36.3500 5.361 4.1000 3.502 DU21_A17.dat

11 40.4500 4.188 4.1000 3.256 DU21_A17.dat

12 44.5500 3.125 4.1000 3.010 NACA64_A17.dat

13 48.6500 2.319 4.1000 2.764 NACA64_A17.dat

14 52.7500 1.526 4.1000 2.518 NACA64_A17.dat

15 56.1667 0.863 2.7333 2.313 NACA64_A17.dat

16 58.9000 0.370 2.7333 2.086 NACA64_A17.dat

17 61.6333 0.106 2.7333 1.419 NACA64_A17.dat
8

Appendix A of Ref. [14]).

8

9

 In these airfoil tables, “DU” refers to Delft University and “NACA” 

refers to the National Advisory Committee for Aeronautics. We used AirfoilPrep v2.0 [ ] to 

“tailor” these airfoil data. We first corrected the lift and drag coefficients for rotational stall 

delay using the Selig and Eggars method for 0° to 90° angles of attack. We then corrected the 

drag coefficients using the Viterna method for 0° to 90° angles of attack assuming an aspect ratio 

of 17. Finally, we estimated the Beddoes-Leishman dynamic-stall hysteresis parameters. We

made no corrections to the DOWEC-supplied pitching-moment coefficients. The resulting threedimensionally corrected airfoil-data coefficients are illustrated graphically in Figure 3-1 through 

Figure 3-6. The numerical values are documented in the AeroDyn airfoil-data input files that 

make up Appendix B.

 

8 C. Lindenburg of the Energy Research Center of the Netherlands (ECN) provided numerical values for these 

coefficients.
9

-1.5

-1.0

-0.5

0.0

0.5

1.0

1.5

2.0

2.5

-180 -150 -120 -90 -60 -30 0 30 60 90 120 150 180

Angle of Attack, °

Lift

Drag

Pitching-Moment

Figure 3-1. Corrected coefficients of the DU40 airfoil

-1.5

-1.0

-0.5

0.0

0.5

1.0

1.5

2.0

2.5

-180 -150 -120 -90 -60 -30 0 30 60 90 120 150 180

Angle of Attack, °

Lift

Drag

Pitching-Moment

Figure 3-2. Corrected coefficients of the DU35 airfoil
10

-1.5

-1.0

-0.5

0.0

0.5

1.0

1.5

2.0

2.5

-180 -150 -120 -90 -60 -30 0 30 60 90 120 150 180

Angle of Attack, °

Lift

Drag

Pitching-Moment

Figure 3-3. Corrected coefficients of the DU30 airfoil

-1.5

-1.0

-0.5

0.0

0.5

1.0

1.5

2.0

2.5

-180 -150 -120 -90 -60 -30 0 30 60 90 120 150 180

Angle of Attack, °

Lift

Drag

Pitching-Moment

Figure 3-4. Corrected coefficients of the DU25 airfoil
11

-1.5

-1.0

-0.5

0.0

0.5

1.0

1.5

2.0

2.5

-180 -150 -120 -90 -60 -30 0 30 60 90 120 150 180

Angle of Attack, °

Lift

Drag

Pitching-Moment

Figure 3-5. Corrected coefficients of the DU21 airfoil

-1.5

-1.0

-0.5

0.0

0.5

1.0

1.5

2.0

2.5

-180 -150 -120 -90 -60 -30 0 30 60 90 120 150 180

Angle of Attack, °

Lift

Drag

Pitching-Moment

Figure 3-6. Corrected coefficients of the NACA64 airfoil
12

4 Hub and Nacelle Properties

As indicated in Table 1-1, we located the hub of the NREL 5-MW baseline wind turbine 5 m 

upwind of the tower centerline at an elevation of 90 m above the ground when the system is 

undeflected. We also specified the same vertical distance from the tower top to the hub height 

used by the DOWEC study—that is, 2.4 m (as specified in Table 6 on page 26 of Ref. [14]). 

Consequently, the elevation of the yaw bearing above ground or MSL is 87.6 m. With a shaft tilt 

of 5°, this made the distance directed along the shaft from the hub center to the yaw axis 5.01910 

m and the vertical distance along the yaw axis from the tower top to the shaft 1.96256 m. The 

distance directed along the shaft from the hub center to the main bearing was taken to be 1.912 m

(from Table 6 on page 26 of Ref. [14]).

We specified the hub mass to be 56,780 kg like in the REpower 5M, and we located its CM at 

the hub center. The hub inertia about the shaft, taken to be 115,926 kg•m

2

, was found by 

assuming that the hub casting is a thin spherical shell with a radius of 1.75 m (this is 0.25 m 

longer than the actual hub radius because the nacelle height of the DOWEC turbine was 3.5 m,

based on the data in Table 6 on page 26 of Ref. [14]).

We specified the nacelle mass to be 240,000 kg like in the REpower 5M and we located its CM 

1.9 m downwind of the yaw axis like in the DOWEC turbine (from Table 7 on page 27 of Ref. 

[14]) and 1.75 m above the yaw bearing, which was half the height of the DOWEC turbine’s

nacelle (from Table 6 on page 26 of Ref. [14]). The nacelle inertia about the yaw axis was taken 

to be 2,607,890 kg•m

2

. We chose this to be equivalent to the DOWEC turbine’s nacelle inertia 

about its nacelle CM, but translated to the yaw axis using the parallel-axis theorem with the 

nacelle mass and downwind distance to the nacelle CM.

We took the nacelle-yaw actuator to have a natural frequency of 3 Hz, which is roughly 

equivalent to the highest full-system natural frequency in the FAST model (see Section 9), and a 

damping ratio of 2% critical. This resulted in an equivalent nacelle-yaw-actuator linear-spring 

constant of 9,028,320,000 N•m/rad and an equivalent nacelle-yaw-actuator linear-damping 

constant of 19,160,000 N•m/(rad/s). The nominal nacelle-yaw rate was chosen to be the same as 

that for the DOWEC 6-MW turbine, or 0.3°/s (from page 27 of Ref. [14]).

Table 4-1 summarizes the nacelle and hub properties discussed in this section.
13

Table 4-1. Nacelle and Hub Properties

Elevation of Yaw Bearing above Ground 87.6 m

Vertical Distance along Yaw Axis from Yaw Bearing to Shaft 1.96256 m

Distance along Shaft from Hub Center to Yaw Axis 5.01910 m

Distance along Shaft from Hub Center to Main Bearing 1.912 m

Hub Mass 56,780 kg

Hub Inertia about Low-Speed Shaft 115,926 kg•m2

Nacelle Mass 240,000 kg

Nacelle Inertia about Yaw Axis 2,607,890 kg•m2

Nacelle CM Location Downwind of Yaw Axis 1.9 m

Nacelle CM Location above Yaw Bearing 1.75 m

Equivalent Nacelle-Yaw-Actuator Linear-Spring Constant 9,028,320,000 N•m/rad

Equivalent Nacelle-Yaw-Actuator Linear-Damping Constant 19,160,000 N•m/(rad/s)

Nominal Nacelle-Yaw Rate 0.3 o/s
14

5 Drivetrain Properties

We specified the NREL 5-MW baseline wind turbine to have the same rated rotor speed (12.1 

rpm), rated generator speed (1173.7 rpm), and gearbox ratio (97:1) as the REpower 5M machine. 

The gearbox was assumed be a typical multiple-stage gearbox but with no frictional losses—a 

requirement of the preprocessor functionality in FAST for creating ADAMS models [11]. The 

electrical efficiency of the generator was taken to be 94.4%. This was chosen to be roughly the 

same as the total mechanical-to-electrical conversion loss used by the DOWEC turbine at rated

power—that is, the DOWEC turbine had about 0.35 MW of power loss at about 6.25 MW of

aerodynamic power (from Figure 15, page 24 of Ref. [14]). The generator inertia about the highspeed shaft was taken to be 534.116 kg•m

2

, which is the same equivalent low-speed shaft 

generator inertia used in the DOWEC study (i.e., 5,025,500 kg•m

2 from page 36 of Ref. [14]).

The driveshaft was taken to have the same natural frequency as the RECOFF turbine model and 

a structural-damping ratio—associated with the free-free mode of a drivetrain composed of a 

rigid generator and rigid rotor—of 5% critical. This resulted in an equivalent driveshaft linearspring constant of 867,637,000 N•m/rad and a linear-damping constant of 6,215,000 N•m/(rad/s).

The high-speed shaft brake was assumed to have the same ratio of maximum brake torque to 

maximum generator torque and the same time lag as used in the DOWEC study (from page 29 of 

Ref. [14]). This resulted in a fully deployed high-speed shaft brake torque of 28,116.2 N•m and 

a time lag of 0.6 s. This time lag is the amount of time it takes for the brake to fully engage once 

deployed. The FAST and ADAMS models employ a simple linear ramp from nothing to full 

braking over the 0.6-s period.

Table 5-1 summarizes the drivetrain properties discussed in this section.

Table 5-1. Drivetrain Properties

Rated Rotor Speed 12.1 rpm

Rated Generator Speed 1173.7 rpm

Gearbox Ratio 97 :1

Electrical Generator Efficiency 94.4 %

Generator Inertia about High-Speed Shaft 534.116 kg•m2

Equivalent Drive-Shaft Torsional-Spring Constant 867,637,000 N•m/rad

Equivalent Drive-Shaft Torsional-Damping Constant 6,215,000 N•m/(rad/s)

Fully-Deployed High-Speed Shaft Brake Torque 28,116.2 N•m

High-Speed Shaft Brake Time Constant 0.6 s
15

6 Tower Properties

The properties of the tower for the NREL offshore 5-MW baseline wind turbine will depend on 

the type support structure used to carry the rotor-nacelle assembly. The type of support structure

will, in turn, depend on the installation site, whose properties vary significantly through 

differences in water depth, soil type, and wind and wave severity. Offshore support-structure 

types include fixed-bottom monopiles, gravity bases, and space-frames—such as tripods, 

quadpods, and lattice frames (e.g., “jackets”)—and floating structures. This section documents 

the tower properties for the equivalent land-based version of the NREL 5-MW baseline wind 

turbine. These properties provide a basis with which to design towers for site-specific offshore 

support structures. For example, different types of offshore support structures for the NREL 5-

MW baseline wind turbine have been designed for—and investigated in—separate phases of the 

OC3 project [13,25].

We based the distributed properties of the land-based tower for the NREL 5-MW baseline wind 

turbine on the base diameter (6 m) and thickness (0.027 m), top diameter (3.87 m) and thickness 

(0.019 m), and effective mechanical steel properties of the tower used in the DOWEC study (as 

given in Table 9 on page 31 of Ref. [14]). The Young’s modulus was taken to be 210 GPa, the 

shear modulus was taken to be 80.8 GPa, and the effective density of the steel was taken to be 

8,500 kg/m3. The density of 8,500 kg/m3 was meant to be an increase above steel’s typical value 

of 7,850 kg/m3 to account for paint, bolts, welds, and flanges that are not accounted for in the 

tower thickness data. The radius and thickness of the tower were assumed to be linearly tapered 

from the tower base to tower top. Because the REpower 5M machine had a larger tower-top 

mass than the DOWEC wind turbine, we scaled up the thickness of the tower relative to the 

values given earlier in this paragraph to strengthen the tower. We chose an increase of 30% to 

ensure that the first fore-aft and side-to-side tower frequencies were placed between the one- and 

three-per-rev frequencies throughout the operational range of the wind turbine in a Campbell 

diagram. Table 6-1 gives the resulting distributed tower properties.

The entries in the first column, “Elevation,” are the vertical locations along the tower centerline 

relative to the tower base. “HtFract” is the fractional height along the tower centerline from the 

tower base (0.0) to the tower top (1.0). The rest of columns are similar to those described for the 

distributed blade properties presented in Table 2-1.

The resulting overall (integrated) tower mass is 347,460 kg and is centered at 38.234 m along the 

Table 6-1. Distributed Tower Properties

Elevation HtFract TMassDen TwFAStif TwSSStif TwGJStif TwEAStif TwFAIner TwSSIner TwFAcgOf TwSScgOf

(m) (-) (kg/m) (N•m2

) (N•m2) (N•m2) (N) (kg•m) (kg•m) (m) (m)

0.00 0.0 5590.87 614.34E+9 614.34E+9 472.75E+9 138.13E+9 24866.3 24866.3 0.0 0.0

8.76 0.1 5232.43 534.82E+9 534.82E+9 411.56E+9 129.27E+9 21647.5 21647.5 0.0 0.0

17.52 0.2 4885.76 463.27E+9 463.27E+9 356.50E+9 120.71E+9 18751.3 18751.3 0.0 0.0

26.28 0.3 4550.87 399.13E+9 399.13E+9 307.14E+9 112.43E+9 16155.3 16155.3 0.0 0.0

35.04 0.4 4227.75 341.88E+9 341.88E+9 263.09E+9 104.45E+9 13838.1 13838.1 0.0 0.0

43.80 0.5 3916.41 291.01E+9 291.01E+9 223.94E+9 96.76E+9 11779.0 11779.0 0.0 0.0

52.56 0.6 3616.83 246.03E+9 246.03E+9 189.32E+9 89.36E+9 9958.2 9958.2 0.0 0.0

61.32 0.7 3329.03 206.46E+9 206.46E+9 158.87E+9 82.25E+9 8356.6 8356.6 0.0 0.0

70.08 0.8 3053.01 171.85E+9 171.85E+9 132.24E+9 75.43E+9 6955.9 6955.9 0.0 0.0

78.84 0.9 2788.75 141.78E+9 141.78E+9 109.10E+9 68.90E+9 5738.6 5738.6 0.0 0.0

87.60 1.0 2536.27 115.82E+9 115.82E+9 89.13E+9 62.66E+9 4688.0 4688.0 0.0 0.0
16

tower centerline above the ground. This result follows directly from the overall tower height of 

87.6 m.

We specified a structural-damping ratio of 1% critical in all modes of the isolated tower (without 

the rotor-nacelle assembly mass present), which corresponds to the values used in the DOWEC 

study (from page 21 of Ref. [14]).

Table 6-2 summarizes the undistributed tower properties discussed in this section.

Table 6-2. Undistributed Tower Properties

Height above Ground 87.6 m

Overall (Integrated) Mass 347,460 kg

CM Location (w.r.t. Ground along Tower Centerline) 38.234 m

Structural-Damping Ratio (All Modes) 1 %
17

7 Baseline Control System Properties

For the NREL 5-MW baseline wind turbine, we chose a conventional variable-speed, variable 

blade-pitch-to-feather configuration. In such wind turbines, the conventional approach for 

controlling power-production operation relies on the design of two basic control systems: a 

generator-torque controller and a full-span rotor-collective blade-pitch controller. The two 

control systems are designed to work independently, for the most part, in the below-rated and 

above-rated wind-speed range, respectively. The goal of the generator-torque controller is to 

maximize power capture below the rated operation point. The goal of the blade-pitch controller 

is to regulate generator speed above the rated operation point.

We based the baseline control system for the NREL 5-MW wind turbine on this conventional 

design approach. We did not establish additional control actions for nonpower-production 

operations, such as control actions for normal start-up sequences, normal shutdown sequences, 

and safety and protection functions. Nor did we develop control actions to regulate the nacelleyaw angle. (The nacelle-yaw control system is generally neglected within aero-servo-elastic 

simulation because its response is slow enough that it does not generally contribute to large 

extreme loads or fatigue damage.)

We describe the development of our baseline control system next, including the controlmeasurement filter (Section 7.1), the generator-torque controller (Section 7.2), the blade-pitch 

controller (Section 7.3), and the blade-pitch actuator (Section 7.4). Section 7.5 shows how these 

systems are put together in the overall integrated control system.

7.1 Baseline Control-Measurement Filter

As is typical in utility-scale multimegawatt wind turbines, both the generator-torque and bladepitch controllers use the generator speed measurement as the sole feedback input. To mitigate 

high-frequency excitation of the control systems, we filtered the generator speed measurement 

for both the torque and pitch controllers using a recursive, single-pole low-pass filter with 

exponential smoothing [30]. The discrete-time recursion (difference) equation for this filter is

yn 1 un yn 1 [ ] =− + − ( α α ) [ ] [ ], (7-1)

with

s c 2 Tf e π α − = , (7-2)

where y is the filtered generator speed (output measurement), u is the unfiltered generator speed 

(input), α is the low-pass filter coefficient, n is the discrete-time-step counter, Ts is the discrete

time step, and fc is the corner frequency.

By defining the filter state,

xn yn 1 [ ] = − [ ], (7-3a)
18

or

xn 1 yn [ + =] [ ], (7-3b)

one can derive a discrete-time state-space representation of this filter:

[ ] [ ] [ ]

[ ] [ ] [ ]

d d

d d

x n 1 Ax n Bu n

y n Cx n Du n

+= +

= + , (7-4)

where Ad =α is the discrete-time state matrix, B 1 d = −α is the discrete-time input matrix, 

Cd =α is the discrete-time output state matrix, and D 1 d = −α is the discrete-time input 

transmission matrix.

The state-space representation of Eq. (7-4) is useful for converting the filter into other forms, 

such as transfer-function form or frequency-response form [31].

We set the corner frequency (the -3 dB point in Figure 7-1) of the low-pass filter to be roughly 

one-quarter of the blade’s first edgewise natural frequency (see Section 9) or 0.25 Hz. For a 

discrete time step of 0.0125 s, the frequency response of the resulting filter is shown in the Bode 

plot of Figure 7-1.

We chose the recursive, single-pole filter for its simplicity in implementation and effectiveness 

-18

-15

-12

-9

-6

-3

0

0.01 0.10 1.00

Frequency, Hz

Magnitude, dB

-90

-75

-60

-45

-30

-15

0

0.01 0.10 1.00

Frequency, Hz

Phase, 

Figure 7-1. Bode plot of generator speed low-pass filter frequency response
19

in the time domain. The drawbacks to this filter are its gentle roll-off in the stop band (-6

dB/octave) and the magnitude and nonlinearity of its phase lag in the pass band [30]. We

considered other linear low-pass filters, such as Butterworth, Chebyshev, Elliptic, and Bessel 

filters because of their inherent advantages relative to the chosen filter. Like the chosen filter, a 

Butterworth filter has a frequency response that is flat in the pass band, but the Butterworth filter 

offers steeper roll-off in the stop band. Chebyshev filters offer even steeper roll-off in the stop 

band at the expense of equalized-ripple (equiripple) in the pass band (Type 1) or stop band (Type 

2), respectively. Elliptic filters offer the steepest roll-off of any linear filter, but have equiripple 

in both the pass and stop bands. Bessel filters offer the flattest group delay (linear phase lag) in 

the pass band. We designed and tested examples of each of these other low-pass filter types, 

considering state-space representations of up to fourth order (four states). None were found to 

give superior performance in the overall system response, however, so they did not warrant the 

added complexity of implementation.

7.2 Baseline Generator-Torque Controller

The generator torque is computed as a tabulated function of the filtered generator speed, 

incorporating five control regions: 1, 11⁄2, 2, 21⁄2, and 3. Region 1 is a control region before cut-in 

wind speed, where the generator torque is zero and no power is extracted from the wind; instead, 

the wind is used to accelerate the rotor for start-up. Region 2 is a control region for optimizing 

power capture. Here, the generator torque is proportional to the square of the filtered generator 

speed to maintain a constant (optimal) tip-speed ratio. In Region 3, the generator power is held 

constant so that the generator torque is inversely proportional to the filtered generator speed. 

Region 11⁄2, a start-up region, is a linear transition between Regions 1 and 2. This region is used 

to place a lower limit on the generator speed to limit the wind turbine’s operational speed range. 

Region 21⁄2 is a linear transition between Regions 2 and 3 with a torque slope corresponding to 

the slope of an induction machine. Region 21⁄2 is typically needed (as is the case for my 5-MW 

turbine) to limit tip speed (and hence noise emissions) at rated power.

We found the peak of the power coefficient as a function of the tip-speed ratio and blade-pitch 

surface by running FAST with AeroDyn simulations at a number of given rotor speeds and a 

number of given rotor-collective blade-pitch angles at a fixed wind speed of 8 m/s. From these 

simulations, we found that the peak power coefficient of 0.482 occurred at a tip-speed ratio of 

7.55 and a rotor-collective blade-pitch angle of 0.0 ̊. With the 97:1 gearbox ratio, this resulted in 

an optimal constant of proportionality of 0.0255764 N•m/rpm2 in the Region 2 control law. With 

the rated generator speed of 1173.7 rpm, rated electric power of 5 MW, and a generator 

efficiency of 94.4%, the rated mechanical power is 5.296610 MW and the rated generator torque 

is 43,093.55 N•m. We defined Region 11⁄2 to span the range of generator speeds between 670 

rpm and 30% above this value (or 871 rpm). The minimum generator speed of 670 rpm 

corresponds to the minimum rotor speed of 6.9 rpm used by the actual REpower 5M machine 

[26]. We took the transitional generator speed between Regions 21⁄2 and 3 to be 99% of the rated 

generator speed, or 1,161.963 rpm. The generator-slip percentage in Region 21⁄2 was taken to be 

10%, in accordance with the value used in the DOWEC study (see page 24 of Ref. [14]). Figure 

7-2 shows the resulting generator-torque versus generator speed response curve.
20

Because of the high intrinsic structural damping of the drivetrain, we did not need to incorporate 

a control loop for damping drivetrain torsional vibration in our baseline generator-torque 

controller.

We did, however, place a conditional statement on the generator-torque controller so that the 

torque would be computed as if it were in Region 3—regardless of the generator speed—

whenever the previous blade-pitch-angle command was 1o or greater. This results in improved 

output power quality (fewer dips below rated) at the expense of short-term overloading of the 

generator and the gearbox. To avoid this excessive overloading, we saturated the torque to a 

maximum of 10% above rated, or 47,402.91 N•m. We also imposed a torque rate limit of 15,000 

N•m/s. In Region 3, the blade-pitch control system takes over.

7.3 Baseline Blade-Pitch Controller

In Region 3, the full-span rotor-collective blade-pitch-angle commands are computed using gainscheduled proportional-integral (PI) control on the speed error between the filtered generator 

speed and the rated generator speed (1173.7 rpm).

We designed the blade-pitch control system using a simple single-degree-of-freedom (singleDOF) model of the wind turbine. Because the goal of the blade-pitch control system is to 

regulate the generator speed, this DOF is the angular rotation of the shaft. To compute the 

required control gains, it is beneficial to examine the equation of motion of this single-DOF 

system. From a simple free-body diagram of the drivetrain, the equation of motion is

( ) ( ) 2

Aero Gear Gen Rotor Gear Gen 0 Drivetrain

d T NT I NI I

dt

− = + += Ω ∆Ω ∆Ω , (7-5)

0

10,000

20,000

30,000

40,000

50,000

0 200 400 600 800 1,000 1,200 1,400

Generator Speed, rpm

Generator Torque, N•m

Optimal

Variable-Speed Controller

Region 1 11⁄2 2 21⁄2► 3

Figure 7-2. Torque-versus-speed response of the variable-speed controller
21

where TAero is the low-speed shaft aerodynamic torque, TGen is the high-speed shaft generator 

torque, NGear is the high-speed to low-speed gearbox ratio, IDrivetrain is the drivetrain inertia cast to 

the low-speed shaft, IRotor is the rotor inertia, IGen is the generator inertia relative to the highspeed shaft, Ω0 is the rated low-speed shaft rotational speed, ∆Ω is the small perturbation of 

low-speed shaft rotational speed about the rated speed, ∆Ω is the low-speed shaft rotational 

acceleration, and t is the simulation time.

Because the generator-torque controller maintains constant generator power in Region 3, the 

generator torque in Region 3 is inversely proportional to the generator speed (see Figure 7-2), or

( ) 0

Gen Gear

Gear

P T N

N

Ω

Ω = , (7-6)

where P0 is the rated mechanical power and Ω is the low-speed shaft rotational speed.

Similarly, assuming negligible variation of aerodynamic torque with rotor speed, the 

aerodynamic torque in Region 3 is

( ) ( 0 )

Aero

0

P , Tθ Ω θ

Ω = , (7-7)

where P is the mechanical power and θ is the full-span rotor-collective blade-pitch angle.

Using a first-order Taylor series expansion of Eqs. (7-6) and (7-7), one can see that

0 0

Gen 2

Gear 0 Gear 0

P P T

N N

∆Ω

Ω Ω ≈ − (7-8)

and

0

Aero

0 0

P 1 P T ∆θ

ΩΩ θ

  ∂

≈ +     ∂ , (7-9)

where ∆θ is a small perturbation of the blade-pitch angles about their operating point. With 

proportional-integral-derivative (PID) control, this is related to the rotor-speed perturbations by

t

P Gear I Gear D Gear

0

∆θ ∆Ω ∆Ω =+ + K N K N dt K N ∫ ∆Ω , (7-10)

where KP, KI, and KD are the blade-pitch controller proportional, integral, and derivative gains, 

respectively.

By setting φ ∆Ω  = , combining the above expressions, and simplifying, the equation of motion 

for the rotor-speed error becomes
22

0

Drivetrain Gear D Gear P 2 Gear I

0 0 0 0

M CK

1P 1P P 1 P I N K N K NK 0

φ φφ

φ φφ Ωθ Ωθ Ω Ωθ

   ∂∂ ∂           +− + − − + − =               ∂∂ ∂         

 

  

. (7-11)

One can see that the idealized PID-controlled rotor-speed error will respond as a second-order 

system with the natural frequency, ωφn, and damping ratio, ζφ, equal to

n

K

M

φ

φ

φ

ω = (7-12)

and

n

C C

2 KM 2M

φ φ

φ

φ φ φ φ

ζ

ω = = . (7-13)

In an active pitch-to-feather wind turbine, the sensitivity of aerodynamic power to the rotorcollective blade-pitch angle, ∂ ∂ P θ , is negative in Region 3. With positive control gains, then, 

the derivative term acts to increase the effective inertia of the drivetrain, the proportional term 

adds damping, and the integral term adds restoring. Also, because the generator torque drops 

with increasing speed error (to maintain constant power) in Region 3, one can see that the 

generator-torque controller introduces a negative damping in the speed error response [indicated 

by the 2 − P0 0 Ω term in Eq. (7-11)]. This negative damping must be compensated by the 

proportional term in the blade-pitch controller.

In the design of the blade-pitch controller, Ref. [10] recommends neglecting the derivative gain, 

ignoring the negative damping from the generator-torque controller, and aiming for the response 

characteristics given by ωφn = 0.6 rad/s and ζφ = 0.6 to 0.7. This specification leads to direct 

expressions for choosing appropriate PI gains once the sensitivity of aerodynamic power to 

rotor-collective blade pitch, ∂ ∂ P θ , is known:

Drivetrain 0 n

P

Gear

2I

K

P N

Ωζ ωφ φ

θ

=   ∂   −

  ∂

(7-14)

and

2

Drivetrain 0 n

I

Gear

I

K

P N

Ω ωφ

θ

=   ∂   −

  ∂

. (7-15)

The blade-pitch sensitivity, ∂ ∂ P θ , is an aerodynamic property of the rotor that depends on the 

wind speed, rotor speed, and blade-pitch angle. We calculated it for the NREL offshore 5-MW 

baseline wind turbine by performing a linearization analysis in FAST with AeroDyn at a number 
23

of given, steady, and uniform wind speeds; at the rated rotor speed (Ω0 = 12.1 rpm); and at the 

corresponding blade-pitch angles that produce the rated mechanical power (P0 = 5.296610 MW). 

The linearization analysis involves perturbing the rotor-collective blade-pitch angle at each 

operating point and measuring the resulting variation in aerodynamic power. Within FAST, the 

partial derivative is computed using the central-difference-perturbation numerical technique. We

created a slightly customized copy of FAST with AeroDyn so that the linearization procedure

would invoke the frozen-wake assumption, in which the induced wake velocities are held 

constant while the blade-pitch angle is perturbed. This gives a more accurate linearization for 

heavily loaded rotors (i.e., for operating points in Region 3 closest to rated). Table 7-1 presents 

the results.

As Table 7-1 shows, the sensitivity of aerodynamic power to rotor-collective blade pitch varies 

considerably over Region 3, so constant PI gains are not adequate for effective speed control. 

The pitch sensitivity, though, varies nearly linearly with blade-pitch angle:

( ) ( )

K

P 0 P P 0

θ

θ θ θ

θθ θ

  ∂ = ∂ ∂   ∂   = +=     ∂ ∂     

(7-16a)

or

( )

K

1 1

P P 0 1 θ θ θ θ θ

= ∂ ∂  

= +   ∂ ∂  

, (7-16b)

Table 7-1. Sensitivity of Aerodynamic Power to Blade 

Pitch in Region 3

Wind Speed Rotor Speed Pitch Angle ∂P/∂θ

(m/s) (rpm) (o) (watt/rad)

11.4 - Rated 12.1 0.00 -28.24E+6

12.0 12.1 3.83 -43.73E+6

13.0 12.1 6.60 -51.66E+6

14.0 12.1 8.70 -58.44E+6

15.0 12.1 10.45 -64.44E+6

16.0 12.1 12.06 -70.46E+6

17.0 12.1 13.54 -76.53E+6

18.0 12.1 14.92 -83.94E+6

19.0 12.1 16.23 -90.67E+6

20.0 12.1 17.47 -94.71E+6

21.0 12.1 18.70 -99.04E+6

22.0 12.1 19.94 -105.90E+6

23.0 12.1 21.18 -114.30E+6

24.0 12.1 22.35 -120.20E+6

25.0 12.1 23.47 -125.30E+6
24

where ( ) P θ 0

θ

∂ = ∂ is the pitch sensitivity at rated and θK is the blade-pitch angle at which the 

pitch sensitivity has doubled from its value at the rated operating point; that is,

( K ) ( ) P P θθ θ 2 0

θ θ

∂ ∂ = = = ∂ ∂ . (7-17)

On the right-hand side of Eq. (7-16a), the first and second terms in square brackets represent the 

slope and intercept of the best-fit line, respectively. We computed this regression for the NREL 

5-MW baseline wind turbine and present the results in Figure 7-3.

The linear relation between pitch sensitivity and blade-pitch angle presents a simple technique 

for implementing gain scheduling based on blade-pitch angle; that is,

( )

( )

( ) Drivetrain 0 n

P

Gear

2I

K GK

P N 0

Ωζ ωφ φ θ θ

θ

θ

=   ∂ − =     ∂

(7-18)

and

-140E+6

-120E+6

-100E+6

-80E+6

-60E+6

-40E+6

-20E+6

000E+0

0 5 10 15 20

Rotor-Collective Blade-Pitch Angle, o

Pitch Sensitivity, watt/rad

Original Data

Best-Fit Line

0E+6

∂P /∂θ (θ =0o) = -25.52E+6 watt/rad

 θ k = 6.302336o

Figure 7-3. Best-fit line of pitch sensitivity in Region 3
25

( )

( )

( )

2

Drivetrain 0 n

I

Gear

I

K GK

P N 0

Ω ωφ θ θ

θ

θ

=   ∂ − =     ∂

, (7-19)

where GK (θ ) is the dimensionless gain-correction factor (from Ref. [10]), which is dependent 

on the blade-pitch angle:

( )

K

1 GK

1

θ θ

θ

=

+

. (7-20)

In our implementation of the gain-scheduled PI blade-pitch controller, we used the blade-pitch 

angle from the previous controller time step to calculate the gain-correction factor at the next

time step.

Using the properties for the baseline wind turbine and the recommended response characteristics 

from Ref. [10], the resulting gains are KP(θ = 0o) = 0.01882681 s, KI(θ = 0o) = 0.008068634, and 

KD = 0.0 s2. Figure 7-4 presents the gains at other blade-pitch angles, along with the gaincorrection factor. We used the upper limit of the recommended damping ratio range, ζφ = 0.7, to 

compensate for neglecting negative damping from the generator-torque controller in the 

determination of KP.

Unfortunately, the simple gain-scheduling law derived in this section for the proportional and 

integral gains cannot retain consistent response characteristics (i.e., constant values of ωφn and 

0.0

0.2

0.4

0.6

0.8

1.0

0 5 10 15 20

Rotor-Collective Blade-Pitch Angle, o

Gain-Correction Factor

0.000

0.005

0.010

0.015

0.020

0.025

Proportional and Integral Gains

Gain-Correction Factor, -

Proportional Gain, s

Integral Gain, -

Figure 7-4. Baseline blade-pitch control system gain-scheduling law
26

ζφ) across all of Region 3 when applied to the derivative gain. We, nevertheless, considered 

adding a derivative term by selecting and testing a range of gains, but none were found to give 

better performance in the overall system response. Instead, the baseline control system uses the 

gains derived previously in this section (without the derivative term).

We set the blade-pitch rate limit to 8°/s in absolute value. This is speculated to be the bladepitch rate limit of conventional 5-MW machines based on General Electric (GE) Wind’s longblade test program. We also set the minimum and maximum blade-pitch settings to 0° and 90°, 

respectively. The lower limit is the set blade pitch for maximizing power in Region 2, as 

described in Section 7.2. The upper limit is very close to the fully feathered blade pitch for 

neutral torque. We saturated the integral term in the PI controller between these limits to ensure 

a fast response in the transitions between Regions 2 and 3.

7.4 Baseline Blade-Pitch Actuator

Because of limitations in the FAST code, the FAST model does not include any blade-pitch

actuator dynamic effects. Blade-pitch actuator dynamics are, however, needed in ADAMS. To 

enable successful comparisons between the FAST and ADAMS response predictions, then, we

found it beneficial to reduce the effect of the blade-pitch actuator response in ADAMS. 

Consequently, we designed the blade-pitch actuator in the ADAMS model with a very high 

natural frequency of 30 Hz, which is higher than the highest full-system natural frequency in the 

FAST model (see Section 9), and a damping ratio of 2% critical. This resulted in an equivalent 

blade-pitch actuator linear-spring constant of 971,350,000 N•m/rad and an equivalent blade-pitch

actuator linear-damping constant of 206,000 N•m/(rad/s).

7.5 Summary of Baseline Control System Properties

We implemented the NREL offshore 5-MW wind turbine’s baseline control system as an 

external dynamic link library (DLL) in the style of Garrad Hassan’s BLADED wind turbine

software package [3]. Appendix C contains the source code for this DLL, and Figure 7-5

presents a flowchart of the overall integrated control system calculations. Table 7-2 summarizes 

the baseline generator-torque and blade-pitch control properties we discussed earlier in this

section.
27

Table 7-2. Baseline Control System Properties

Corner Frequency of Generator-Speed Low-Pass Filter 0.25 Hz

Peak Power Coefficient 0.482

Tip-Speed Ratio at Peak Power Coefficient 7.55

Rotor-Collective Blade-Pitch Angle at Peak Power Coefficient 0.0 o

Generator-Torque Constant in Region 2 0.0255764 N•m/rpm2

Rated Mechanical Power 5.296610 MW

Rated Generator Torque 43,093.55 N•m

Transitional Generator Speed between Regions 1 and 11⁄2 670 rpm

Transitional Generator Speed between Regions 11⁄2 and 2 871 rpm

Transitional Generator Speed between Regions 21⁄2 and 3 1,161.963 rpm

Generator Slip Percentage in Region 21⁄2 10 %

Minimum Blade Pitch for Ensuring Region 3 Torque 1 o

Maximum Generator Torque 47,402.91 N•m

Maximum Generator Torque Rate 15,000 N•m/s

Proportional Gain at Minimum Blade-Pitch Setting 0.01882681 s

Integral Gain at Minimum Blade-Pitch Setting 0.008068634

Blade-Pitch Angle at which the Rotor Power Has Doubled 6.302336 o

Minimum Blade-Pitch Setting 0 o

Maximum Blade-Pitch Setting 90 o

Maximum Absolute Blade Pitch Rate 8 o/s

Equivalent Blade-Pitch-Actuator Linear-Spring Constant 971,350,000 N•m/rad

Equivalent Blade-Pitch-Actuator Linear-Damping Constant 206,000 N•m/rad/s

Low-Pass 

Filter

Gene rator

Spe ed

Torque-Speed 

Lookup Table

Determine 

Control Region

Control Region

(1, 11⁄2, 2, 21⁄2, or 3) 

Gene rator

 Tor que

Torque Limit 

Saturation

Torque Rate 

Saturation

Generator

Torque

+ Rated

Speed

Filtered

Speed

-

Spe ed

Err or

Integrator

Integr ated

Speed Error

Saturate 

Integral

Gain 

Schedule Integral

Gain

Proportional 

Gain Gain

Factor

+

Inte gral

Te rm

Propo rtional

Te rm

Pitch Limit 

Saturation

Pitch Rate 

Saturation

Rotor-C ollective 

Blade-Pit ch Angle

Rotor-Collective

Blade-Pitch Angle

+

+ +

Integr ated

Speed Error

Rotor-C ollective 

Blade-Pit ch Angle

Gene rator

 Tor que

Figure 7-5. Flowchart of the baseline control system
28

8 FAST with AeroDyn and ADAMS with AeroDyn Models

Using the turbine properties described previously in this report, we put together models of the 

NREL offshore 5-MW baseline wind turbine within FAST [11] with AeroDyn [16,20]. The 

input files for these models are given in Appendix A and Appendix B, for version (v) 6.10a-jmj 

of FAST and v12.58 of AeroDyn, respectively. We then generated the higher fidelity ADAMS 

with AeroDyn models through the preprocessor functionality built into the FAST code.

The input files in Appendix A are for the FAST model of the equivalent land-based version of 

the NREL 5-MW baseline wind turbine. The input files for other versions of the model, such as 

those for different support structures, require only a few minor changes. These include changes 

to input parameters “PtfmModel” and “PtfmFile,” which identify the type and properties of the 

support platform, and modifications to the prescribed mode shapes in the tower input file, 

“TwrFile.”

Although most of the input-parameter specifications in Appendix A and Appendix B are selfexplanatory, the specifications of the prescribed mode shapes needed by FAST to characterize 

the flexibility of the blades and tower deserve a special explanation. The required mode shapes

depend on the member’s boundary conditions. For the blade modes, we used v2.22 of the Modes 

program [4] to derive the equivalent polynomial representations of the blade mode shapes

needed by FAST. The Modes program calculates the mode shapes of rotating blades, assuming 

that a blade mode shape is unaffected by its coupling with other system modes of motion. This 

is a common assumption in wind turbine analysis. For the tower modes, however, there is a 

great deal of coupling with the rotor motions, and in offshore floating systems, there is coupling 

with the platform motions as well. To take the former factor into account, we used the 

linearization functionality of the full-system ADAMS model to obtain the tower modes for the 

land-based version of the NREL 5-MW baseline wind turbine. In other words, we built an 

ADAMS model of the wind turbine, enabled all system DOFs, and linearized the model. Then 

we passed a best-fit polynomial through the resulting tower mode shapes to get the equivalent

polynomial representations of the tower mode shapes needed by FAST.

Not including platform motions, the FAST model of the land-based version of the NREL 5-MW 

baseline wind turbine incorporates 16 DOFs as follows:

• Two flapwise and one edgewise bending-mode DOFs for each of the three blades

• One variable-generator speed DOF and one driveshaft torsional DOF

• One nacelle-yaw-actuator DOF

• Two fore-aft and two side-to-side bending-mode DOFs in the tower.

Not including platform motion, the higher fidelity ADAMS model of the land-based version of 

the wind turbine incorporates 438 DOFs as follows:

• One hundred and two DOFs in each of the three blades, including flapwise and edgewise

shear and bending, torsion, and extension DOFs

• One blade-pitch actuator DOF in each of the three blades
29

• One variable-generator speed DOF and one driveshaft torsional DOF

• One nacelle-yaw actuator DOF

• One hundred and twenty-six DOFs in the tower, including fore-aft and side-to-side shear 

and bending, torsion, and extension DOFs.

The support platform motions in, for example, the floating-platform versions of the NREL 5-

MW baseline wind turbine add six DOFs per model.

We use a constant time step of 0.0125 s in FAST’s fixed-step-size time-integration scheme and a 

maximum step size of 0.0125 s in ADAMS’ variable-step-size time integrator. We have

AeroDyn perform aerodynamic calculations every other structural time step (i.e., 0.025 s) to 

ensure that there are at least 200-azimuth-step computations per revolution at 12 rpm. Data are

output at 20 Hz or every fourth structural time step. We made these time steps as large as

possible to ensure numerical stability and suitable output resolution across a range of operating 

conditions.
30

9 Full-System Natural Frequencies and Steady-State Behavior

To provide a cursory overview of the overall system behavior of the equivalent land-based 

version of the NREL 5-MW baseline wind turbine, we calculated the full-system natural 

frequencies and the steady-state response of the system as a function of wind speed.

We obtained the full-system natural frequencies with both the FAST model and the ADAMS

model. In FAST, we calculated the natural frequencies by performing an eigenanalysis on the 

first-order state matrix created from a linearization analysis. In ADAMS, we obtained the 

frequencies by invoking a “LINEAR/EIGENSOL” command, which linearizes the complete 

ADAMS model and computes eigendata. To avoid the rigid-body drivetrain mode, the analyses 

considered the wind turbine in a stationary condition with the high-speed shaft brake engaged. 

The blades were pitched to their minimum set point (0o), but aerodynamic damping was ignored. 

Table 9-1 lists results for the first 13 full-system natural frequencies.

The agreement between FAST and ADAMS is quite good. The biggest differences exist in the 

predictions of the blades’ second asymmetric flapwise yaw and pitch modes. By “yaw” and 

“pitch” we mean that these blade asymmetric modes couple with the nacelle-yaw and nacellepitching motions, respectively. Because of the offsets of the blade section CM from the pitch 

axis, higher-order modes, and tower-torsion DOFs—which are available in ADAMS, but not in 

FAST—ADAMS predicts lower natural frequencies in these modes than FAST does.

Bir and Jonkman have published [2] a much more exhaustive eigenanalysis for the NREL 5-MW 

baseline wind turbine. The referenced publication documents the natural frequencies and 

damping ratios of the land- and floating-platform versions of the 5-MW turbine across a range of 

operating conditions.

We obtained the steady-state response of the land-based 5-MW baseline wind turbine by running 

a series of FAST with AeroDyn simulations at a number of given, steady, and uniform wind 

speeds. The simulations lengths were long enough to ensure that all transient behavior had died 

out; we then recorded the steady-state output values. We ran the simulations using the bladeTable 9-1. Full-System Natural Frequencies in Hertz

Mode Description FAST ADAMS

1 1st Tower Fore-Aft 0.3240 0.3195

2 1st Tower Side-to-Side 0.3120 0.3164

3 1st Drivetrain Torsion 0.6205 0.6094

4 1st Blade Asymmetric Flapwise Yaw 0.6664 0.6296

5 1st Blade Asymmetric Flapwise Pitch 0.6675 0.6686

6 1st Blade Collective Flap 0.6993 0.7019

7 1st Blade Asymmetric Edgewise Pitch 1.0793 1.0740

8 1st Blade Asymmetric Edgewise Yaw 1.0898 1.0877

9 2nd Blade Asymmetric Flapwise Yaw 1.9337 1.6507

10 2nd Blade Asymmetric Flapwise Pitch 1.9223 1.8558

11 2nd Blade Collective Flap 2.0205 1.9601

12 2nd Tower Fore-Aft 2.9003 2.8590

13 2nd Tower Side-to-Side 2.9361 2.9408
31

element / momentum (BEM) wake option of AeroDyn and with all available and relevant landbased DOFs enabled. Figure 9-1 shows the results for several output parameters, which are 

defined as follows:

• “GenSpeed” represents the rotational speed of the generator (high-speed shaft).

• “RotPwr” and “GenPwr” represent the mechanical power within the rotor and the 

electrical output of the generator, respectively.

• “RotThrust” represents the rotor thrust.

• “RotTorq” represents the mechanical torque in the low-speed shaft.

• “RotSpeed” represents the rotational speed of the rotor (low-speed shaft).

• “BlPitch1” represents the pitch angle of Blade 1.

• “GenTq” represents the electrical torque of the generator.

• “TSR” represents the tip-speed ratio.

• “OoPDefl1” and “IPDefl1” represent the out-of-plane and in-plane tip deflections of 

Blade 1 relative to the undeflected blade-pitch axis.

• “TTDspFA” and “TTDspSS” represent the fore-aft and side-to-side deflection of the 

tower top relative to the centerline of the undeflected tower.

As planned, the generator and rotor speeds increase linearly with wind speed in Region 2 to

maintain constant tip-speed ratio and optimal wind-power conversion efficiency. Similarly, the 

generator and rotor powers and generator and rotor torques increase dramatically with wind 

speed in Region 2, increasing cubically and quadratically, respectively. Above rated, the 

generator and rotor powers are held constant by regulating to a fixed speed with active bladepitch control. The out-of-plane tip deflection of the reference blade (Blade 1) reaches a 

maximum at the rated operating point before dropping again. This response characteristic is the 

result of the peak in rotor thrust at rated. This peak is typical of variable generator speed 

variable blade-pitch-to-feather wind turbines because of the transition that occurs in the control 

system at rated between the active generator-torque and the active blade-pitch control regions. 

This peak in response is also visible, though less pronounced, in the in-plane tip deflection of the 

reference blade and the tower-top fore-aft displacement.

Start-up transient behavior is an artifact of computational analysis. To mitigate this behavior, we 

suggest using the steady-state values of the rotor speed and blade-pitch angles found in Figure 

9-1 as initial conditions in simulations.
32

0

1,000

2,000

3,000

4,000

5,000

6,000

3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25

Wind Speed, m/s

GenSpeed, rpm

RotPwr, kW

GenPwr, kW

RotThrust, kN

RotTorq, kN·m

Region 11⁄2 2 21⁄2 3

0

5

10

15

20

25

30

35

40

45

50

3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25

Wind Speed, m/s

RotSpeed, rpm

BlPitch1, o

GenTq, kN·m

TSR, -

Region 11⁄2 2 21⁄2 3

-2

-1

0

1

2

3

4

5

6

3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25

Wind Speed, m/s

OoPDefl1, m

IPDefl1, m

TTDspFA, m

TTDspSS, m

Region 11⁄2 2 21⁄2 3

Figure 9-1. Steady-state responses as a function of wind speed
33

10 Conclusions

To support concept studies aimed at assessing offshore wind technology, we developed the 

specifications of a representative utility-scale multimegawatt turbine now known as the “NREL 

offshore 5-MW baseline wind turbine.” This wind turbine is a conventional three-bladed upwind 

variable-speed variable blade-pitch-to-feather-controlled turbine. To create the model, we 

obtained some broad design information from the published documents of turbine manufacturers, 

with a heavy emphasis on the REpower 5M machine. Because detailed data was unavailable, 

however, we also used the publicly available properties from the conceptual models in the 

WindPACT, RECOFF, and DOWEC projects. We then created a composite from these data, 

extracting the best available and most representative specifications. This report documented the 

specifications of the NREL offshore 5-MW baseline wind turbine—including the aerodynamic, 

structural, and control-system properties—and the rationale behind its development. The model 

has been, and will likely continue to be, used as a reference by research teams throughout the 

world to standardize baseline offshore wind turbine specifications and to quantify the benefits of 

advanced land- and sea-based wind energy technologies.
34

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38

Appendix A FAST Input Files

A.1 Primary Input File

--------------------------------------------------------------------------------

------- FAST INPUT FILE --------------------------------------------------------

NREL 5.0 MW Baseline Wind Turbine for Use in Offshore Analysis.

Properties from Dutch Offshore Wind Energy Converter (DOWEC) 6MW Pre-Design (10046_009.pdf) and REpower 5M 5MW (5m_uk.pdf); C

---------------------- SIMULATION CONTROL --------------------------------------

False Echo - Echo input data to "echo.out" (flag)

 3 ADAMSPrep - ADAMS preprocessor mode {1: Run FAST, 2: use FAST as a preprocessor to create an ADAMS model, 3: do 

 1 AnalMode - Analysis mode {1: Run a time-marching simulation, 2: create a periodic linearized model} (switch)

 3 NumBl - Number of blades (-)

630.0 TMax - Total run time (s)

 0.0125 DT - Integration time step (s)

---------------------- TURBINE CONTROL -----------------------------------------

 0 YCMode - Yaw control mode {0: none, 1: user-defined from routine UserYawCont, 2: user-defined from Simulink} 

9999.9 TYCOn - Time to enable active yaw control (s) [unused when YCMode=0]

 1 PCMode - Pitch control mode {0: none, 1: user-defined from routine PitchCntrl, 2: user-defined from Simulink

 0.0 TPCOn - Time to enable active pitch control (s) [unused when PCMode=0]

 2 VSContrl - Variable-speed control mode {0: none, 1: simple VS, 2: user-defined from routine UserVSCont, 3: use

9999.9 VS_RtGnSp - Rated generator speed for simple variable-speed generator control (HSS side) (rpm) [used only when 

9999.9 VS_RtTq - Rated generator torque/constant generator torque in Region 3 for simple variable-speed generator co

9999.9 VS_Rgn2K - Generator torque constant in Region 2 for simple variable-speed generator control (HSS side) (N-m/r

9999.9 VS_SlPc - Rated generator slip percentage in Region 2 1/2 for simple variable-speed generator control (%) [us

 2 GenModel - Generator model {1: simple, 2: Thevenin, 3: user-defined from routine UserGen} (switch) [used only 

True GenTiStr - Method to start the generator {T: timed using TimGenOn, F: generator speed using SpdGenOn} (flag)

True GenTiStp - Method to stop the generator {T: timed using TimGenOf, F: when generator power = 0} (flag)

9999.9 SpdGenOn - Generator speed to turn on the generator for a startup (HSS speed) (rpm) [used only when GenTiStr=F

 0.0 TimGenOn - Time to turn on the generator for a startup (s) [used only when GenTiStr=True]

9999.9 TimGenOf - Time to turn off the generator (s) [used only when GenTiStp=True]

 1 HSSBrMode - HSS brake model {1: simple, 2: user-defined from routine UserHSSBr} (switch)

9999.9 THSSBrDp - Time to initiate deployment of the HSS brake (s)

9999.9 TiDynBrk - Time to initiate deployment of the dynamic generator brake [CURRENTLY IGNORED] (s)

9999.9 TTpBrDp(1) - Time to initiate deployment of tip brake 1 (s)

9999.9 TTpBrDp(2) - Time to initiate deployment of tip brake 2 (s)

9999.9 TTpBrDp(3) - Time to initiate deployment of tip brake 3 (s) [unused for 2 blades]

9999.9 TBDepISp(1) - Deployment-initiation speed for the tip brake on blade 1 (rpm)

9999.9 TBDepISp(2) - Deployment-initiation speed for the tip brake on blade 2 (rpm)

9999.9 TBDepISp(3) - Deployment-initiation speed for the tip brake on blade 3 (rpm) [unused for 2 blades]

9999.9 TYawManS - Time to start override yaw maneuver and end standard yaw control (s)

 0.3 YawManRat - Yaw rate (in absolute value) at which override yaw maneuver heads toward final yaw angle (deg/s)

 0.0 NacYawF - Final yaw angle for override yaw maneuvers (degrees)

9999.9 TPitManS(1) - Time to start override pitch maneuver for blade 1 and end standard pitch control (s)

9999.9 TPitManS(2) - Time to start override pitch maneuver for blade 2 and end standard pitch control (s)

9999.9 TPitManS(3) - Time to start override pitch maneuver for blade 3 and end standard pitch control (s) [unused for 2 

 8.0 PitManRat(1)- Pitch rate (in absolute value) at which override pitch maneuver for blade 1 heads toward final pitc

 8.0 PitManRat(2)- Pitch rate (in absolute value) at which override pitch maneuver for blade 2 heads toward final pitc

 8.0 PitManRat(3)- Pitch rate (in absolute value) at which override pitch maneuver for blade 3 heads toward final pitc

 0.0 BlPitch(1) - Blade 1 initial pitch (degrees)

 0.0 BlPitch(2) - Blade 2 initial pitch (degrees)

 0.0 BlPitch(3) - Blade 3 initial pitch (degrees) [unused for 2 blades]

 0.0 BlPitchF(1) - Blade 1 final pitch for override pitch maneuvers (degrees)

 0.0 BlPitchF(2) - Blade 2 final pitch for override pitch maneuvers (degrees)

 0.0 BlPitchF(3) - Blade 3 final pitch for override pitch maneuvers (degrees) [unused for 2 blades]

---------------------- ENVIRONMENTAL CONDITIONS --------------------------------

 9.80665 Gravity - Gravitational acceleration (m/s^2)

---------------------- FEATURE FLAGS -------------------------------------------

True FlapDOF1 - First flapwise blade mode DOF (flag)

True FlapDOF2 - Second flapwise blade mode DOF (flag)

True EdgeDOF - First edgewise blade mode DOF (flag)

False TeetDOF - Rotor-teeter DOF (flag) [unused for 3 blades]

True DrTrDOF - Drivetrain rotational-flexibility DOF (flag)

True GenDOF - Generator DOF (flag)

True YawDOF - Yaw DOF (flag)

True TwFADOF1 - First fore-aft tower bending-mode DOF (flag)

True TwFADOF2 - Second fore-aft tower bending-mode DOF (flag)

True TwSSDOF1 - First side-to-side tower bending-mode DOF (flag)

True TwSSDOF2 - Second side-to-side tower bending-mode DOF (flag)

True CompAero - Compute aerodynamic forces (flag)

False CompNoise - Compute aerodynamic noise (flag)

---------------------- INITIAL CONDITIONS --------------------------------------

 0.0 OoPDefl - Initial out-of-plane blade-tip displacement (meters)

 0.0 IPDefl - Initial in-plane blade-tip deflection (meters)

 0.0 TeetDefl - Initial or fixed teeter angle (degrees) [unused for 3 blades]

 0.0 Azimuth - Initial azimuth angle for blade 1 (degrees)

 12.1 RotSpeed - Initial or fixed rotor speed (rpm)

 0.0 NacYaw - Initial or fixed nacelle-yaw angle (degrees)

 0.0 TTDspFA - Initial fore-aft tower-top displacement (meters)

 0.0 TTDspSS - Initial side-to-side tower-top displacement (meters)
39

---------------------- TURBINE CONFIGURATION -----------------------------------

 63.0 TipRad - The distance from the rotor apex to the blade tip (meters)

 1.5 HubRad - The distance from the rotor apex to the blade root (meters)

 1 PSpnElN - Number of the innermost blade element which is still part of the pitchable portion of the blade for 

 0.0 UndSling - Undersling length [distance from teeter pin to the rotor apex] (meters) [unused for 3 blades]

 0.0 HubCM - Distance from rotor apex to hub mass [positive downwind] (meters)

 -5.01910 OverHang - Distance from yaw axis to rotor apex [3 blades] or teeter pin [2 blades] (meters)

 1.9 NacCMxn - Downwind distance from the tower-top to the nacelle CM (meters)

 0.0 NacCMyn - Lateral distance from the tower-top to the nacelle CM (meters)

 1.75 NacCMzn - Vertical distance from the tower-top to the nacelle CM (meters)

 87.6 TowerHt - Height of tower above ground level [onshore] or MSL [offshore] (meters)

 1.96256 Twr2Shft - Vertical distance from the tower-top to the rotor shaft (meters)

 0.0 TwrRBHt - Tower rigid base height (meters)

 -5.0 ShftTilt - Rotor shaft tilt angle (degrees)

 0.0 Delta3 - Delta-3 angle for teetering rotors (degrees) [unused for 3 blades]

 -2.5 PreCone(1) - Blade 1 cone angle (degrees)

 -2.5 PreCone(2) - Blade 2 cone angle (degrees)

 -2.5 PreCone(3) - Blade 3 cone angle (degrees) [unused for 2 blades]

 0.0 AzimB1Up - Azimuth value to use for I/O when blade 1 points up (degrees)

---------------------- MASS AND INERTIA ----------------------------------------

 0.0 YawBrMass - Yaw bearing mass (kg)

240.00E3 NacMass - Nacelle mass (kg)

 56.78E3 HubMass - Hub mass (kg)

 0.0 TipMass(1) - Tip-brake mass, blade 1 (kg)

 0.0 TipMass(2) - Tip-brake mass, blade 2 (kg)

 0.0 TipMass(3) - Tip-brake mass, blade 3 (kg) [unused for 2 blades]

2607.89E3 NacYIner - Nacelle inertia about yaw axis (kg m^2)

534.116 GenIner - Generator inertia about HSS (kg m^2)

115.926E3 HubIner - Hub inertia about rotor axis [3 blades] or teeter axis [2 blades] (kg m^2)

---------------------- DRIVETRAIN ----------------------------------------------

100.0 GBoxEff - Gearbox efficiency (%)

 94.4 GenEff - Generator efficiency [ignored by the Thevenin and user-defined generator models] (%)

 97.0 GBRatio - Gearbox ratio (-)

False GBRevers - Gearbox reversal {T: if rotor and generator rotate in opposite directions} (flag)

 28.1162E3 HSSBrTqF - Fully deployed HSS-brake torque (N-m)

 0.6 HSSBrDT - Time for HSS-brake to reach full deployment once initiated (sec) [used only when HSSBrMode=1]

 DynBrkFi - File containing a mech-gen-torque vs HSS-speed curve for a dynamic brake [CURRENTLY IGNORED] (quote

867.637E6 DTTorSpr - Drivetrain torsional spring (N-m/rad)

 6.215E6 DTTorDmp - Drivetrain torsional damper (N-m/(rad/s))

---------------------- SIMPLE INDUCTION GENERATOR ------------------------------

9999.9 SIG_SlPc - Rated generator slip percentage (%) [used only when VSContrl=0 and GenModel=1]

9999.9 SIG_SySp - Synchronous (zero-torque) generator speed (rpm) [used only when VSContrl=0 and GenModel=1]

9999.9 SIG_RtTq - Rated torque (N-m) [used only when VSContrl=0 and GenModel=1]

9999.9 SIG_PORt - Pull-out ratio (Tpullout/Trated) (-) [used only when VSContrl=0 and GenModel=1]

---------------------- THEVENIN-EQUIVALENT INDUCTION GENERATOR -----------------

9999.9 TEC_Freq - Line frequency [50 or 60] (Hz) [used only when VSContrl=0 and GenModel=2]

9998 TEC_NPol - Number of poles [even integer > 0] (-) [used only when VSContrl=0 and GenModel=2]

9999.9 TEC_SRes - Stator resistance (ohms) [used only when VSContrl=0 and GenModel=2]

9999.9 TEC_RRes - Rotor resistance (ohms) [used only when VSContrl=0 and GenModel=2]

9999.9 TEC_VLL - Line-to-line RMS voltage (volts) [used only when VSContrl=0 and GenModel=2]

9999.9 TEC_SLR - Stator leakage reactance (ohms) [used only when VSContrl=0 and GenModel=2]

9999.9 TEC_RLR - Rotor leakage reactance (ohms) [used only when VSContrl=0 and GenModel=2]

9999.9 TEC_MR - Magnetizing reactance (ohms) [used only when VSContrl=0 and GenModel=2]

---------------------- PLATFORM ------------------------------------------------

 0 PtfmModel - Platform model {0: none, 1: onshore, 2: fixed bottom offshore, 3: floating offshore} (switch)

 PtfmFile - Name of file containing platform properties (quoted string) [unused when PtfmModel=0]

---------------------- TOWER ---------------------------------------------------

 20 TwrNodes - Number of tower nodes used for analysis (-)

"NRELOffshrBsline5MW_Tower_Onshore.dat" TwrFile - Name of file containing tower properties (quoted string)

---------------------- NACELLE-YAW ---------------------------------------------

9028.32E6 YawSpr - Nacelle-yaw spring constant (N-m/rad)

 19.16E6 YawDamp - Nacelle-yaw damping constant (N-m/(rad/s))

 0.0 YawNeut - Neutral yaw position--yaw spring force is zero at this yaw (degrees)

---------------------- FURLING -------------------------------------------------

False Furling - Read in additional model properties for furling turbine (flag)

 FurlFile - Name of file containing furling properties (quoted string) [unused when Furling=False]

---------------------- ROTOR-TEETER --------------------------------------------

 0 TeetMod - Rotor-teeter spring/damper model {0: none, 1: standard, 2: user-defined from routine UserTeet} (swi

 0.0 TeetDmpP - Rotor-teeter damper position (degrees) [used only for 2 blades and when TeetMod=1]

 0.0 TeetDmp - Rotor-teeter damping constant (N-m/(rad/s)) [used only for 2 blades and when TeetMod=1]

 0.0 TeetCDmp - Rotor-teeter rate-independent Coulomb-damping moment (N-m) [used only for 2 blades and when TeetMod

 0.0 TeetSStP - Rotor-teeter soft-stop position (degrees) [used only for 2 blades and when TeetMod=1]

 0.0 TeetHStP - Rotor-teeter hard-stop position (degrees) [used only for 2 blades and when TeetMod=1]

 0.0 TeetSSSp - Rotor-teeter soft-stop linear-spring constant (N-m/rad) [used only for 2 blades and when TeetMod=1]

 0.0 TeetHSSp - Rotor-teeter hard-stop linear-spring constant (N-m/rad) [used only for 2 blades and when TeetMod=1]

---------------------- TIP-BRAKE -----------------------------------------------

 0.0 TBDrConN - Tip-brake drag constant during normal operation, Cd*Area (m^2)

 0.0 TBDrConD - Tip-brake drag constant during fully-deployed operation, Cd*Area (m^2)

 0.0 TpBrDT - Time for tip-brake to reach full deployment once released (sec)

---------------------- BLADE ---------------------------------------------------

"NRELOffshrBsline5MW_Blade.dat" BldFile(1) - Name of file containing properties for blade 1 (quoted string)

"NRELOffshrBsline5MW_Blade.dat" BldFile(2) - Name of file containing properties for blade 2 (quoted string)

"NRELOffshrBsline5MW_Blade.dat" BldFile(3) - Name of file containing properties for blade 3 (quoted string) 

---------------------- AERODYN -------------------------------------------------
40

"NRELOffshrBsline5MW_AeroDyn.ipt" ADFile - Name of file containing AeroDyn input parameters (quoted strin

---------------------- NOISE ---------------------------------------------------

 NoiseFile - Name of file containing aerodynamic noise input parameters (quoted string) [used only when CompNois

---------------------- ADAMS ---------------------------------------------------

"NRELOffshrBsline5MW_ADAMSSpecific.dat" ADAMSFile - Name of file containing ADAMS-specific input parameters (quote

---------------------- LINEARIZATION CONTROL -----------------------------------

"NRELOffshrBsline5MW_Linear.dat" LinFile - Name of file containing FAST linearization parameters (quoted 

---------------------- OUTPUT --------------------------------------------------

True SumPrint - Print summary data to "<RootName>.fsm" (flag)

True TabDelim - Generate a tab-delimited tabular output file. (flag)

"ES10.3E2" OutFmt - Format used for tabular output except time. Resulting field should be 10 characters. (quoted strin

 30.0 TStart - Time to begin tabular output (s)

 4 DecFact - Decimation factor for tabular output {1: output every time step} (-)

 1.0 SttsTime - Amount of time between screen status messages (sec)

 -3.09528 NcIMUxn - Downwind distance from the tower-top to the nacelle IMU (meters)

 0.0 NcIMUyn - Lateral distance from the tower-top to the nacelle IMU (meters)

 2.23336 NcIMUzn - Vertical distance from the tower-top to the nacelle IMU (meters)

 1.912 ShftGagL - Distance from rotor apex [3 blades] or teeter pin [2 blades] to shaft strain gages [positive for up

 1 NTwGages - Number of tower nodes that have strain gages for output [0 to 9] (-)

 10 TwrGagNd - List of tower nodes that have strain gages [1 to TwrNodes] (-) [unused if NTwGages=0]

 1 NBlGages - Number of blade nodes that have strain gages for output [0 to 9] (-)

 9 BldGagNd - List of blade nodes that have strain gages [1 to BldNodes] (-) [unused if NBlGages=0]

 OutList - The next line(s) contains a list of output parameters. See OutList.txt for a listing of available 

"WindVxi , WindVyi , WindVzi" - Longitudinal, lateral, and vertical wind speeds

"WaveElev" - Wave elevation at the platform reference point

"Wave1Vxi , Wave1Vyi , Wave1Vzi" - Longitudinal, lateral, and vertical wave particle velocities a

"Wave1Axi , Wave1Ayi , Wave1Azi" - Longitudinal, lateral, and vertical wave particle acceleration

"GenPwr , GenTq" - Electrical generator power and torque

"HSSBrTq" - High-speed shaft brake torque

"BldPitch1, BldPitch2, BldPitch3" - Pitch angles for blades 1, 2, and 3

"Azimuth" - Blade 1 azimuth angle

"RotSpeed , GenSpeed" - Low-speed shaft and high-speed shaft speeds

"NacYaw , NacYawErr" - Nacelle yaw angle and nacelle yaw error estimate

"OoPDefl1 , IPDefl1 , TwstDefl1" - Blade 1 out-of-plane and in-plane deflections and tip twist

"OoPDefl2 , IPDefl2 , TwstDefl2" - Blade 2 out-of-plane and in-plane deflections and tip twist

"OoPDefl3 , IPDefl3 , TwstDefl3" - Blade 3 out-of-plane and in-plane deflections and tip twist

"TwrClrnc1, TwrClrnc2, TwrClrnc3" - Tip-to-tower clearance estimate for blades 1, 2, and 3

"NcIMUTAxs, NcIMUTAys, NcIMUTAzs" - Nacelle IMU translational accelerations (absolute) in the nonr

"TTDspFA , TTDspSS , TTDspTwst" - Tower fore-aft and side-to-side displacements and top twist

"PtfmSurge, PtfmSway , PtfmHeave" - Platform translational surge, sway, and heave displacements

"PtfmRoll , PtfmPitch, PtfmYaw" - Platform rotational roll, pitch and yaw displacements

"PtfmTAxt , PtfmTAyt , PtfmTAzt" - Platform translation accelerations (absolute) in the tower-bas

"RootFxc1 , RootFyc1 , RootFzc1" - Out-of-plane shear, in-plane shear, and axial forces at the ro

"RootMxc1 , RootMyc1 , RootMzc1" - In-plane bending, out-of-plane bending, and pitching moments a

"RootFxc2 , RootFyc2 , RootFzc2" - Out-of-plane shear, in-plane shear, and axial forces at the ro

"RootMxc2 , RootMyc2 , RootMzc2" - In-plane bending, out-of-plane bending, and pitching moments a

"RootFxc3 , RootFyc3 , RootFzc3" - Out-of-plane shear, in-plane shear, and axial forces at the ro

"RootMxc3 , RootMyc3 , RootMzc3" - In-plane bending, out-of-plane bending, and pitching moments a

"Spn1MLxb1, Spn1MLyb1, Spn1MLzb1" - Blade 1 local edgewise bending, flapwise bending, and pitching 

"Spn1MLxb2, Spn1MLyb2, Spn1MLzb2" - Blade 2 local edgewise bending, flapwise bending, and pitching 

"Spn1MLxb3, Spn1MLyb3, Spn1MLzb3" - Blade 3 local edgewise bending, flapwise bending, and pitching 

"RotThrust, LSSGagFya, LSSGagFza" - Rotor thrust and low-speed shaft 0- and 90-rotating shear forc

"RotTorq , LSSGagMya, LSSGagMza" - Rotor torque and low-speed shaft 0- and 90-rotating bending mo

"YawBrFxp , YawBrFyp , YawBrFzp" - Fore-aft shear, side-to-side shear, and vertical forces at the 

"YawBrMxp , YawBrMyp , YawBrMzp" - Side-to-side bending, fore-aft bending, and yaw moments at the 

"TwrBsFxt , TwrBsFyt , TwrBsFzt" - Fore-aft shear, side-to-side shear, and vertical forces at the 

"TwrBsMxt , TwrBsMyt , TwrBsMzt" - Side-to-side bending, fore-aft bending, and yaw moments at the 

"TwHt1MLxt, TwHt1MLyt, TwHt1MLzt" - Local side-to-side bending, fore-aft bending, and yaw moments 

"Fair1Ten , Fair1Ang , Anch1Ten , Anch1Ang" - Line 1 fairlead and anchor effective tensions and vertical ang

"Fair2Ten , Fair2Ang , Anch2Ten , Anch2Ang" - Line 2 fairlead and anchor effective tensions and vertical ang

"Fair3Ten , Fair3Ang , Anch3Ten , Anch3Ang" - Line 3 fairlead and anchor effective tensions and vertical ang

"Fair4Ten , Fair4Ang , Anch4Ten , Anch4Ang" - Line 4 fairlead and anchor effective tensions and vertical ang

"Fair5Ten , Fair5Ang , Anch5Ten , Anch5Ang" - Line 5 fairlead and anchor effective tensions and vertical ang

"Fair6Ten , Fair6Ang , Anch6Ten , Anch6Ang" - Line 6 fairlead and anchor effective tensions and vertical ang

"Fair7Ten , Fair7Ang , Anch7Ten , Anch7Ang" - Line 7 fairlead and anchor effective tensions and vertical ang

"Fair8Ten , Fair8Ang , Anch8Ten , Anch8Ang" - Line 8 fairlead and anchor effective tensions and vertical ang

"TipSpdRat, RotCp , RotCt , RotCq" - Rotor tip speed ratio and power, thrust, and torque coefficien

END of FAST input file (the word "END" must appear in the first 3 columns of this last line).

--------------------------------------------------------------------------------

A.2 Blade Input File – NRELOffshrBsline5MW_Blade.dat

--------------------------------------------------------------------------------

---------------------- FAST INDIVIDUAL BLADE FILE ------------------------------

NREL 5.0 MW offshore baseline blade input properties.

---------------------- BLADE PARAMETERS ----------------------------------------

 49 NBlInpSt - Number of blade input stations (-)

False CalcBMode - Calculate blade mode shapes internally {T: ignore mode shapes from below, F: use mode shapes from b

 0.477465 BldFlDmp(1) - Blade flap mode #1 structural damping in percent of critical (%)

 0.477465 BldFlDmp(2) - Blade flap mode #2 structural damping in percent of critical (%)

 0.477465 BldEdDmp(1) - Blade edge mode #1 structural damping in percent of critical (%)

---------------------- BLADE ADJUSTMENT FACTORS --------------------------------
41

 1.0 FlStTunr(1) - Blade flapwise modal stiffness tuner, 1st mode (-)

 1.0 FlStTunr(2) - Blade flapwise modal stiffness tuner, 2nd mode (-)

 1.04536 AdjBlMs - Factor to adjust blade mass density (-)

 1.0 AdjFlSt - Factor to adjust blade flap stiffness (-)

 1.0 AdjEdSt - Factor to adjust blade edge stiffness (-)

---------------------- DISTRIBUTED BLADE PROPERTIES ----------------------------

BlFract AeroCent StrcTwst BMassDen FlpStff EdgStff GJStff EAStff Alpha FlpIner EdgIner PrecrvRef Pre

(-) (-) (deg) (kg/m) (Nm^2) (Nm^2) (Nm^2) (N) (-) (kg m) (kg m) (m) (m)

0.00000 0.25000 13.308 678.935 18110.00E6 18113.60E6 5564.40E6 9729.48E6 0.0 972.86 973.04 0.0 0.0

0.00325 0.25000 13.308 678.935 18110.00E6 18113.60E6 5564.40E6 9729.48E6 0.0 972.86 973.04 0.0 0.0

0.01951 0.24951 13.308 773.363 19424.90E6 19558.60E6 5431.59E6 10789.50E6 0.0 1091.52 1066.38 0.0 0.0

0.03577 0.24510 13.308 740.550 17455.90E6 19497.80E6 4993.98E6 10067.23E6 0.0 966.09 1047.36 0.0 0.0

0.05203 0.23284 13.308 740.042 15287.40E6 19788.80E6 4666.59E6 9867.78E6 0.0 873.81 1099.75 0.0 0.0

0.06829 0.22059 13.308 592.496 10782.40E6 14858.50E6 3474.71E6 7607.86E6 0.0 648.55 873.02 0.0 0.0

0.08455 0.20833 13.308 450.275 7229.72E6 10220.60E6 2323.54E6 5491.26E6 0.0 456.76 641.49 0.0 0.0

0.10081 0.19608 13.308 424.054 6309.54E6 9144.70E6 1907.87E6 4971.30E6 0.0 400.53 593.73 0.0 0.0

0.11707 0.18382 13.308 400.638 5528.36E6 8063.16E6 1570.36E6 4493.95E6 0.0 351.61 547.18 0.0 0.0

0.13335 0.17156 13.308 382.062 4980.06E6 6884.44E6 1158.26E6 4034.80E6 0.0 316.12 490.84 0.0 0.0

0.14959 0.15931 13.308 399.655 4936.84E6 7009.18E6 1002.12E6 4037.29E6 0.0 303.60 503.86 0.0 0.0

0.16585 0.14706 13.308 426.321 4691.66E6 7167.68E6 855.90E6 4169.72E6 0.0 289.24 544.70 0.0 0.0

0.18211 0.13481 13.181 416.820 3949.46E6 7271.66E6 672.27E6 4082.35E6 0.0 246.57 569.90 0.0 0.0

0.19837 0.12500 12.848 406.186 3386.52E6 7081.70E6 547.49E6 4085.97E6 0.0 215.91 601.28 0.0 0.0

0.21465 0.12500 12.192 381.420 2933.74E6 6244.53E6 448.84E6 3668.34E6 0.0 187.11 546.56 0.0 0.0

0.23089 0.12500 11.561 352.822 2568.96E6 5048.96E6 335.92E6 3147.76E6 0.0 160.84 468.71 0.0 0.0

0.24715 0.12500 11.072 349.477 2388.65E6 4948.49E6 311.35E6 3011.58E6 0.0 148.56 453.76 0.0 0.0

0.26341 0.12500 10.792 346.538 2271.99E6 4808.02E6 291.94E6 2882.62E6 0.0 140.30 436.22 0.0 0.0

0.29595 0.12500 10.232 339.333 2050.05E6 4501.40E6 261.00E6 2613.97E6 0.0 124.61 398.18 0.0 0.0

0.32846 0.12500 9.672 330.004 1828.25E6 4244.07E6 228.82E6 2357.48E6 0.0 109.42 362.08 0.0 0.0

0.36098 0.12500 9.110 321.990 1588.71E6 3995.28E6 200.75E6 2146.86E6 0.0 94.36 335.01 0.0 0.0

0.39350 0.12500 8.534 313.820 1361.93E6 3750.76E6 174.38E6 1944.09E6 0.0 80.24 308.57 0.0 0.0

0.42602 0.12500 7.932 294.734 1102.38E6 3447.14E6 144.47E6 1632.70E6 0.0 62.67 263.87 0.0 0.0

0.45855 0.12500 7.321 287.120 875.80E6 3139.07E6 119.98E6 1432.40E6 0.0 49.42 237.06 0.0 0.0

0.49106 0.12500 6.711 263.343 681.30E6 2734.24E6 81.19E6 1168.76E6 0.0 37.34 196.41 0.0 0.0

0.52358 0.12500 6.122 253.207 534.72E6 2554.87E6 69.09E6 1047.43E6 0.0 29.14 180.34 0.0 0.0

0.55610 0.12500 5.546 241.666 408.90E6 2334.03E6 57.45E6 922.95E6 0.0 22.16 162.43 0.0 0.0

0.58862 0.12500 4.971 220.638 314.54E6 1828.73E6 45.92E6 760.82E6 0.0 17.33 134.83 0.0 0.0

0.62115 0.12500 4.401 200.293 238.63E6 1584.10E6 35.98E6 648.03E6 0.0 13.30 116.30 0.0 0.0

0.65366 0.12500 3.834 179.404 175.88E6 1323.36E6 27.44E6 539.70E6 0.0 9.96 97.98 0.0 0.0

0.68618 0.12500 3.332 165.094 126.01E6 1183.68E6 20.90E6 531.15E6 0.0 7.30 98.93 0.0 0.0

0.71870 0.12500 2.890 154.411 107.26E6 1020.16E6 18.54E6 460.01E6 0.0 6.22 85.78 0.0 0.0

0.75122 0.12500 2.503 138.935 90.88E6 797.81E6 16.28E6 375.75E6 0.0 5.19 69.96 0.0 0.0

0.78376 0.12500 2.116 129.555 76.31E6 709.61E6 14.53E6 328.89E6 0.0 4.36 61.41 0.0 0.0

0.81626 0.12500 1.730 107.264 61.05E6 518.19E6 9.07E6 244.04E6 0.0 3.36 45.44 0.0 0.0

0.84878 0.12500 1.342 98.776 49.48E6 454.87E6 8.06E6 211.60E6 0.0 2.75 39.57 0.0 0.0

0.88130 0.12500 0.954 90.248 39.36E6 395.12E6 7.08E6 181.52E6 0.0 2.21 34.09 0.0 0.0

0.89756 0.12500 0.760 83.001 34.67E6 353.72E6 6.09E6 160.25E6 0.0 1.93 30.12 0.0 0.0

0.91382 0.12500 0.574 72.906 30.41E6 304.73E6 5.75E6 109.23E6 0.0 1.69 20.15 0.0 0.0

0.93008 0.12500 0.404 68.772 26.52E6 281.42E6 5.33E6 100.08E6 0.0 1.49 18.53 0.0 0.0

0.93821 0.12500 0.319 66.264 23.84E6 261.71E6 4.94E6 92.24E6 0.0 1.34 17.11 0.0 0.0

0.94636 0.12500 0.253 59.340 19.63E6 158.81E6 4.24E6 63.23E6 0.0 1.10 11.55 0.0 0.0

0.95447 0.12500 0.216 55.914 16.00E6 137.88E6 3.66E6 53.32E6 0.0 0.89 9.77 0.0 0.0

0.96260 0.12500 0.178 52.484 12.83E6 118.79E6 3.13E6 44.53E6 0.0 0.71 8.19 0.0 0.0

0.97073 0.12500 0.140 49.114 10.08E6 101.63E6 2.64E6 36.90E6 0.0 0.56 6.82 0.0 0.0

0.97886 0.12500 0.101 45.818 7.55E6 85.07E6 2.17E6 29.92E6 0.0 0.42 5.57 0.0 0.0

0.98699 0.12500 0.062 41.669 4.60E6 64.26E6 1.58E6 21.31E6 0.0 0.25 4.01 0.0 0.0

0.99512 0.12500 0.023 11.453 0.25E6 6.61E6 0.25E6 4.85E6 0.0 0.04 0.94 0.0 0.0

1.00000 0.12500 0.000 10.319 0.17E6 5.01E6 0.19E6 3.53E6 0.0 0.02 0.68 0.0 0.0

---------------------- BLADE MODE SHAPES ---------------------------------------

 0.0622 BldFl1Sh(2) - Flap mode 1, coeff of x^2

 1.7254 BldFl1Sh(3) - , coeff of x^3

 -3.2452 BldFl1Sh(4) - , coeff of x^4

 4.7131 BldFl1Sh(5) - , coeff of x^5

 -2.2555 BldFl1Sh(6) - , coeff of x^6

 -0.5809 BldFl2Sh(2) - Flap mode 2, coeff of x^2

 1.2067 BldFl2Sh(3) - , coeff of x^3

-15.5349 BldFl2Sh(4) - , coeff of x^4

 29.7347 BldFl2Sh(5) - , coeff of x^5

-13.8255 BldFl2Sh(6) - , coeff of x^6

 0.3627 BldEdgSh(2) - Edge mode 1, coeff of x^2

 2.5337 BldEdgSh(3) - , coeff of x^3

 -3.5772 BldEdgSh(4) - , coeff of x^4

 2.3760 BldEdgSh(5) - , coeff of x^5

 -0.6952 BldEdgSh(6) - , coeff of x^6

A.3 Tower Input File – NRELOffshrBsline5MW_Tower_Onshore.dat

--------------------------------------------------------------------------------

---------------------- FAST TOWER FILE -----------------------------------------

NREL 5.0 MW offshore baseline tower input properties.

---------------------- TOWER PARAMETERS ----------------------------------------

 11 NTwInpSt - Number of input stations to specify tower geometry

False CalcTMode - Calculate tower mode shapes internally {T: ignore mode shapes from below, F: use mode shapes from b
42

 1.0 TwrFADmp(1) - Tower 1st fore-aft mode structural damping ratio (%)

 1.0 TwrFADmp(2) - Tower 2nd fore-aft mode structural damping ratio (%)

 1.0 TwrSSDmp(1) - Tower 1st side-to-side mode structural damping ratio (%)

 1.0 TwrSSDmp(2) - Tower 2nd side-to-side mode structural damping ratio (%)

---------------------- TOWER ADJUSTMUNT FACTORS --------------------------------

 1.0 FAStTunr(1) - Tower fore-aft modal stiffness tuner, 1st mode (-)

 1.0 FAStTunr(2) - Tower fore-aft modal stiffness tuner, 2nd mode (-)

 1.0 SSStTunr(1) - Tower side-to-side stiffness tuner, 1st mode (-)

 1.0 SSStTunr(2) - Tower side-to-side stiffness tuner, 2nd mode (-)

 1.0 AdjTwMa - Factor to adjust tower mass density (-)

 1.0 AdjFASt - Factor to adjust tower fore-aft stiffness (-)

 1.0 AdjSSSt - Factor to adjust tower side-to-side stiffness (-)

---------------------- DISTRIBUTED TOWER PROPERTIES ----------------------------

HtFract TMassDen TwFAStif TwSSStif TwGJStif TwEAStif TwFAIner TwSSIner TwFAcgOf TwSScgOf

(-) (kg/m) (Nm^2) (Nm^2) (Nm^2) (N) (kg m) (kg m) (m) (m)

0.0 5590.87 614.343E9 614.343E9 472.751E9 138.127E9 24866.3 24866.3 0.0 0.0

0.1 5232.43 534.821E9 534.821E9 411.558E9 129.272E9 21647.5 21647.5 0.0 0.0

0.2 4885.76 463.267E9 463.267E9 356.495E9 120.707E9 18751.3 18751.3 0.0 0.0

0.3 4550.87 399.131E9 399.131E9 307.141E9 112.433E9 16155.3 16155.3 0.0 0.0

0.4 4227.75 341.883E9 341.883E9 263.087E9 104.450E9 13838.1 13838.1 0.0 0.0

0.5 3916.41 291.011E9 291.011E9 223.940E9 96.758E9 11779.0 11779.0 0.0 0.0

0.6 3616.83 246.027E9 246.027E9 189.323E9 89.357E9 9958.2 9958.2 0.0 0.0

0.7 3329.03 206.457E9 206.457E9 158.874E9 82.247E9 8356.6 8356.6 0.0 0.0

0.8 3053.01 171.851E9 171.851E9 132.244E9 75.427E9 6955.9 6955.9 0.0 0.0

0.9 2788.75 141.776E9 141.776E9 109.100E9 68.899E9 5738.6 5738.6 0.0 0.0

1.0 2536.27 115.820E9 115.820E9 89.126E9 62.661E9 4688.0 4688.0 0.0 0.0

---------------------- TOWER FORE-AFT MODE SHAPES ------------------------------

 0.7004 TwFAM1Sh(2) - Mode 1, coefficient of x^2 term

 2.1963 TwFAM1Sh(3) - , coefficient of x^3 term

 -5.6202 TwFAM1Sh(4) - , coefficient of x^4 term

 6.2275 TwFAM1Sh(5) - , coefficient of x^5 term

 -2.5040 TwFAM1Sh(6) - , coefficient of x^6 term

-70.5319 TwFAM2Sh(2) - Mode 2, coefficient of x^2 term

-63.7623 TwFAM2Sh(3) - , coefficient of x^3 term

289.7369 TwFAM2Sh(4) - , coefficient of x^4 term

-176.5134 TwFAM2Sh(5) - , coefficient of x^5 term

 22.0706 TwFAM2Sh(6) - , coefficient of x^6 term

---------------------- TOWER SIDE-TO-SIDE MODE SHAPES --------------------------

 1.3850 TwSSM1Sh(2) - Mode 1, coefficient of x^2 term

 -1.7684 TwSSM1Sh(3) - , coefficient of x^3 term

 3.0871 TwSSM1Sh(4) - , coefficient of x^4 term

 -2.2395 TwSSM1Sh(5) - , coefficient of x^5 term

 0.5357 TwSSM1Sh(6) - , coefficient of x^6 term

-121.2097 TwSSM2Sh(2) - Mode 2, coefficient of x^2 term

184.4151 TwSSM2Sh(3) - , coefficient of x^3 term

-224.9037 TwSSM2Sh(4) - , coefficient of x^4 term

298.5360 TwSSM2Sh(5) - , coefficient of x^5 term

-135.8377 TwSSM2Sh(6) - , coefficient of x^6 term

A.4 ADAMS Input File – NRELOffshrBsline5MW_ADAMSSpecific.dat

--------------------------------------------------------------------------------

---------------------- FAST 2 ADAMS PREPROCESSOR, ADAMS-SPECIFIC DATA FILE -----

NREL 5.0 MW offshore baseline ADAMS-specific input properties.

---------------------- FEATURE FLAGS -------------------------------------------

True SaveGrphcs - Save GRAPHICS output (flag)

False MakeLINacf - Make an ADAMS/LINEAR control / command file (flag)

---------------------- DAMPING PARAMETERS --------------------------------------

 0.01 CRatioTGJ - Ratio of damping to stiffness for the tower torsion deflection (-)

 0.01 CRatioTEA - Ratio of damping to stiffness for the tower extensional deflection (-)

 0.01 CRatioBGJ - Ratio of damping to stiffness for the blade torsion deflections (-)

 0.01 CRatioBEA - Ratio of damping to stiffness for the blade extensional deflections (-)

---------------------- BLADE PITCH ACTUATOR PARAMETERS -------------------------

971.350E6 BPActrSpr - Blade pitch actuator spring stiffness constant (N-m/rad)

 0.206E6 BPActrDmp - Blade pitch actuator damping constant (N-m/(rad/s))

---------------------- GRAPHICS PARAMETERS -------------------------------------

 20 NSides - Number of sides used in GRAPHICS CYLINDER and FRUSTUM statements (-)

 3.000 TwrBaseRad - Tower base radius used for linearly tapered tower GRAPHICS CYLINDERs (m)

 1.935 TwrTopRad - Tower top radius used for linearly tapered tower GRAPHICS CYLINDERs (m)

 7.0 NacLength - Length of nacelle used for the nacelle GRAPHICS (m)

 1.75 NacRadBot - Bottom (opposite rotor) radius of nacelle FRUSTUM used for the nacelle GRAPHICS (m)

 1.75 NacRadTop - Top (rotor end) radius of nacelle FRUSTUM used for the nacelle GRAPHICS (m)

 1.0 GBoxLength - Length, width, and height of the gearbox BOX for gearbox GRAPHICS (m)

 2.39 GenLength - Length of the generator CYLINDER used for generator GRAPHICS (m)

 1.195 HSSLength - Length of the high-speed shaft CYLINDER used for HSS GRAPHICS (m)

 4.78 LSSLength - Length of the low-speed shaft CYLINDER used for LSS GRAPHICS (m)

 0.75 GenRad - Radius of the generator CYLINDER used for generator GRAPHICS (m)

 0.2 HSSRad - Radius of the high-speed shaft CYLINDER used for HSS GRAPHICS (m)

 0.4 LSSRad - Radius of the low -speed shaft CYLINDER used for LSS GRAPHICS (m)

 0.875 HubCylRad - Radius of hub CYLINDER used for hub GRAPHICS (m)

 0.18 ThkOvrChrd - Ratio of blade thickness to blade chord used for blade element BOX GRAPHICS (-)

 0.0 BoomRad - Radius of the tail boom CYLINDER used for tail boom GRAPHICS (m)
43

A.5 Linearization Input File – NRELOffshrBsline5MW_Linear.dat

--------------------------------------------------------------------------------

---------------------- FAST LINEARIZATION CONTROL FILE -------------------------

NREL 5.0 MW offshore baseline linearization input properties.

---------------------- PERIODIC STEADY STATE SOLUTION --------------------------

True CalcStdy - Calculate periodic steady state condition {False: linearize about initial conditions} (flag)

 3 TrimCase - Trim case {1: find nacelle yaw, 2: find generator torque, 3: find collective blade pitch} (switch) 

 0.0001 DispTol - Convergence tolerance for the 2-norm of displacements in the periodic steady state calculation (rad 

 0.0010 VelTol - Convergence tolerance for the 2-norm of velocities in the periodic steady state calculation (rad

---------------------- MODEL LINEARIZATION -------------------------------------

 36 NAzimStep - Number of equally-spaced azimuth steps in periodic linearized model (-)

 1 MdlOrder - Order of output linearized model {1: 1st order A, B, Bd, C, D, Dd; 2: 2nd order M, C, K, F, Fd, Vel

---------------------- INPUTS AND DISTURBANCES ---------------------------------

 0 NInputs - Number of control inputs [0 (none) or 1 to 4+NumBl] (-)

 CntrlInpt - List of control inputs [1 to NInputs] {1: nacelle yaw angle, 2: nacelle yaw rate, 3: generator to

 0 NDisturbs - Number of wind disturbances [0 (none) or 1 to 7] (-)

 Disturbnc - List of input wind disturbances [1 to NDisturbs] {1: horizontal hub-height wind speed, 2: horizon
44

Appendix B AeroDyn Input Files

B.1 Primary Input File – NRELOffshrBsline5MW_AeroDyn.ipt

NREL 5.0 MW offshore baseline aerodynamic input properties; Compatible with AeroDyn v12.58.

SI SysUnits - System of units used for input and output [must be SI for FAST] (unquoted string)

BEDDOES StallMod - Dynamic stall included [BEDDOES or STEADY] (unquoted string)

USE_CM UseCm - Use aerodynamic pitching moment model? [USE_CM or NO_CM] (unquoted string)

EQUIL InfModel - Inflow model [DYNIN or EQUIL] (unquoted string)

WAKE IndModel - Induction-factor model [NONE or WAKE or SWIRL] (unquoted string)

 0.005 AToler - Induction-factor tolerance (convergence criteria) (-)

PRANDtl TLModel - Tip-loss model (EQUIL only) [PRANDtl, GTECH, or NONE] (unquoted string)

PRANDtl HLModel - Hub-loss model (EQUIL only) [PRANdtl or NONE] (unquoted string)

"WindData\90m_12mps" WindFile - Name of file containing wind data (quoted string)

 90.0 HH - Wind reference (hub) height [TowerHt+Twr2Shft+OverHang*SIN(ShftTilt)] (m)

 0.0 TwrShad - Tower-shadow velocity deficit (-)

9999.9 ShadHWid - Tower-shadow half width (m)

9999.9 T_Shad_Refpt- Tower-shadow reference point (m)

 1.225 AirDens - Air density (kg/m^3)

 1.464E-5 KinVisc - Kinematic air viscosity [CURRENTLY IGNORED] (m^2/sec)

 0.02479 DTAero - Time interval for aerodynamic calculations (sec)

 8 NumFoil - Number of airfoil files (-)

"AeroData\Cylinder1.dat" FoilNm - Names of the airfoil files [NumFoil lines] (quoted strings)

"AeroData\Cylinder2.dat"

"AeroData\DU40_A17.dat"

"AeroData\DU35_A17.dat"

"AeroData\DU30_A17.dat"

"AeroData\DU25_A17.dat"

"AeroData\DU21_A17.dat"

"AeroData\NACA64_A17.dat"

 17 BldNodes - Number of blade nodes used for analysis (-)

RNodes AeroTwst DRNodes Chord NFoil PrnElm

2.8667 13.308 2.7333 3.542 1 NOPRINT

5.6000 13.308 2.7333 3.854 1 NOPRINT

8.3333 13.308 2.7333 4.167 2 NOPRINT

11.7500 13.308 4.1000 4.557 3 NOPRINT

15.8500 11.480 4.1000 4.652 4 NOPRINT

19.9500 10.162 4.1000 4.458 4 NOPRINT

24.0500 9.011 4.1000 4.249 5 NOPRINT

28.1500 7.795 4.1000 4.007 6 NOPRINT

32.2500 6.544 4.1000 3.748 6 NOPRINT

36.3500 5.361 4.1000 3.502 7 NOPRINT

40.4500 4.188 4.1000 3.256 7 NOPRINT

44.5500 3.125 4.1000 3.010 8 NOPRINT

48.6500 2.319 4.1000 2.764 8 NOPRINT

52.7500 1.526 4.1000 2.518 8 NOPRINT

56.1667 0.863 2.7333 2.313 8 NOPRINT

58.9000 0.370 2.7333 2.086 8 NOPRINT

61.6333 0.106 2.7333 1.419 8 NOPRINT

B.2 Airfoil-Data Input File – Cylinder1.dat

Round root section with a Cd of 0.50

Made by Jason Jonkman

 1 Number of airfoil tables in this file

 0.0 Table ID parameter

 0.0 Stall angle (deg)

 0.0 No longer used, enter zero

 0.0 No longer used, enter zero

 0.0 No longer used, enter zero

 0.0 Zero Cn angle of attack (deg)

 0.0 Cn slope for zero lift (dimensionless)

 0.0 Cn extrapolated to value at positive stall angle of attack

 0.0 Cn at stall value for negative angle of attack

 0.0 Angle of attack for minimum CD (deg)

 0.50 Minimum CD value

-180.00 0.000 0.5000 0.000

 0.00 0.000 0.5000 0.000

180.00 0.000 0.5000 0.000

B.3 Airfoil-Data Input File – Cylinder2.dat

Round root section with a Cd of 0.35

Made by Jason Jonkman

 1 Number of airfoil tables in this file
45

 0.0 Table ID parameter

 0.0 Stall angle (deg)

 0.0 No longer used, enter zero

 0.0 No longer used, enter zero

 0.0 No longer used, enter zero

 0.0 Zero Cn angle of attack (deg)

 0.0 Cn slope for zero lift (dimensionless)

 0.0 Cn extrapolated to value at positive stall angle of attack

 0.0 Cn at stall value for negative angle of attack

 0.0 Angle of attack for minimum CD (deg)

 0.35 Minimum CD value

-180.00 0.000 0.3500 0.000

 0.00 0.000 0.3500 0.000

180.00 0.000 0.3500 0.000

B.4 Airfoil-Data Input File – DU40_A17.dat

DU40 airfoil with an aspect ratio of 17. Original -180 to 180deg Cl, Cd, and Cm versus AOA data taken from Appendix A of DOW

Cl and Cd values corrected for rotational stall delay and Cd values corrected using the Viterna method for 0 to 90deg AOA by 

 1 Number of airfoil tables in this file

 0.0 Table ID parameter

 9.00 Stall angle (deg)

 0.0 No longer used, enter zero

 0.0 No longer used, enter zero

 0.0 No longer used, enter zero

 -1.3430 Zero Cn angle of attack (deg)

 7.4888 Cn slope for zero lift (dimensionless)

 1.3519 Cn extrapolated to value at positive stall angle of attack

 -0.3226 Cn at stall value for negative angle of attack

 0.00 Angle of attack for minimum CD (deg)

 0.0113 Minimum CD value

-180.00 0.000 0.0602 0.0000

-175.00 0.218 0.0699 0.0934

-170.00 0.397 0.1107 0.1697

-160.00 0.642 0.3045 0.2813

-155.00 0.715 0.4179 0.3208

-150.00 0.757 0.5355 0.3516

-145.00 0.772 0.6535 0.3752

-140.00 0.762 0.7685 0.3926

-135.00 0.731 0.8777 0.4048

-130.00 0.680 0.9788 0.4126

-125.00 0.613 1.0700 0.4166

-120.00 0.532 1.1499 0.4176

-115.00 0.439 1.2174 0.4158

-110.00 0.337 1.2716 0.4117

-105.00 0.228 1.3118 0.4057

-100.00 0.114 1.3378 0.3979

-95.00 -0.002 1.3492 0.3887

-90.00 -0.120 1.3460 0.3781

-85.00 -0.236 1.3283 0.3663

-80.00 -0.349 1.2964 0.3534

-75.00 -0.456 1.2507 0.3394

-70.00 -0.557 1.1918 0.3244

-65.00 -0.647 1.1204 0.3084

-60.00 -0.727 1.0376 0.2914

-55.00 -0.792 0.9446 0.2733

-50.00 -0.842 0.8429 0.2543

-45.00 -0.874 0.7345 0.2342

-40.00 -0.886 0.6215 0.2129

-35.00 -0.875 0.5067 0.1906

-30.00 -0.839 0.3932 0.1670

-25.00 -0.777 0.2849 0.1422

-24.00 -0.761 0.2642 0.1371

-23.00 -0.744 0.2440 0.1320

-22.00 -0.725 0.2242 0.1268

-21.00 -0.706 0.2049 0.1215

-20.00 -0.685 0.1861 0.1162

-19.00 -0.662 0.1687 0.1097

-18.00 -0.635 0.1533 0.1012

-17.00 -0.605 0.1398 0.0907

-16.00 -0.571 0.1281 0.0784

-15.00 -0.534 0.1183 0.0646

-14.00 -0.494 0.1101 0.0494

-13.00 -0.452 0.1036 0.0330

-12.00 -0.407 0.0986 0.0156

-11.00 -0.360 0.0951 -0.0026

-10.00 -0.311 0.0931 -0.0213

 -8.00 -0.208 0.0930 -0.0600

 -6.00 -0.111 0.0689 -0.0500

 -5.50 -0.090 0.0614 -0.0516

 -5.00 -0.072 0.0547 -0.0532

 -4.50 -0.065 0.0480 -0.0538
46

 -4.00 -0.054 0.0411 -0.0544

 -3.50 -0.017 0.0349 -0.0554

 -3.00 0.003 0.0299 -0.0558

 -2.50 0.014 0.0255 -0.0555

 -2.00 0.009 0.0198 -0.0534

 -1.50 0.004 0.0164 -0.0442

 -1.00 0.036 0.0147 -0.0469

 -0.50 0.073 0.0137 -0.0522

 0.00 0.137 0.0113 -0.0573

 0.50 0.213 0.0114 -0.0644

 1.00 0.292 0.0118 -0.0718

 1.50 0.369 0.0122 -0.0783

 2.00 0.444 0.0124 -0.0835

 2.50 0.514 0.0124 -0.0866

 3.00 0.580 0.0123 -0.0887

 3.50 0.645 0.0120 -0.0900

 4.00 0.710 0.0119 -0.0914

 4.50 0.776 0.0122 -0.0933

 5.00 0.841 0.0125 -0.0947

 5.50 0.904 0.0129 -0.0957

 6.00 0.967 0.0135 -0.0967

 6.50 1.027 0.0144 -0.0973

 7.00 1.084 0.0158 -0.0972

 7.50 1.140 0.0174 -0.0972

 8.00 1.193 0.0198 -0.0968

 8.50 1.242 0.0231 -0.0958

 9.00 1.287 0.0275 -0.0948

 9.50 1.333 0.0323 -0.0942

 10.00 1.368 0.0393 -0.0926

 10.50 1.400 0.0475 -0.0908

 11.00 1.425 0.0580 -0.0890

 11.50 1.449 0.0691 -0.0877

 12.00 1.473 0.0816 -0.0870

 12.50 1.494 0.0973 -0.0870

 13.00 1.513 0.1129 -0.0876

 13.50 1.538 0.1288 -0.0886

 14.50 1.587 0.1650 -0.0917

 15.00 1.614 0.1845 -0.0939

 15.50 1.631 0.2052 -0.0966

 16.00 1.649 0.2250 -0.0996

 16.50 1.666 0.2467 -0.1031

 17.00 1.681 0.2684 -0.1069

 17.50 1.699 0.2900 -0.1110

 18.00 1.719 0.3121 -0.1157

 19.00 1.751 0.3554 -0.1242

 19.50 1.767 0.3783 -0.1291

 20.50 1.798 0.4212 -0.1384

 21.00 1.810 0.4415 -0.1416

 22.00 1.830 0.4830 -0.1479

 23.00 1.847 0.5257 -0.1542

 24.00 1.861 0.5694 -0.1603

 25.00 1.872 0.6141 -0.1664

 26.00 1.881 0.6593 -0.1724

 28.00 1.894 0.7513 -0.1841

 30.00 1.904 0.8441 -0.1954

 32.00 1.915 0.9364 -0.2063

 35.00 1.929 1.0722 -0.2220

 40.00 1.903 1.2873 -0.2468

 45.00 1.820 1.4796 -0.2701

 50.00 1.690 1.6401 -0.2921

 55.00 1.522 1.7609 -0.3127

 60.00 1.323 1.8360 -0.3321

 65.00 1.106 1.8614 -0.3502

 70.00 0.880 1.8347 -0.3672

 75.00 0.658 1.7567 -0.3830

 80.00 0.449 1.6334 -0.3977

 85.00 0.267 1.4847 -0.4112

 90.00 0.124 1.3879 -0.4234

 95.00 0.002 1.3912 -0.4343

100.00 -0.118 1.3795 -0.4437

105.00 -0.235 1.3528 -0.4514

110.00 -0.348 1.3114 -0.4573

115.00 -0.453 1.2557 -0.4610

120.00 -0.549 1.1864 -0.4623

125.00 -0.633 1.1041 -0.4606

130.00 -0.702 1.0102 -0.4554

135.00 -0.754 0.9060 -0.4462

140.00 -0.787 0.7935 -0.4323

145.00 -0.797 0.6750 -0.4127

150.00 -0.782 0.5532 -0.3863

155.00 -0.739 0.4318 -0.3521

160.00 -0.664 0.3147 -0.3085

170.00 -0.410 0.1144 -0.1858

175.00 -0.226 0.0702 -0.1022
47

180.00 0.000 0.0602 0.0000

B.5 Airfoil-Data Input File – DU35_A17.dat

DU35 airfoil with an aspect ratio of 17. Original -180 to 180deg Cl, Cd, and Cm versus AOA data taken from Appendix A of DOW

Cl and Cd values corrected for rotational stall delay and Cd values corrected using the Viterna method for 0 to 90deg AOA by 

 1 Number of airfoil tables in this file

 0.0 Table ID parameter

 11.50 Stall angle (deg)

 0.0 No longer used, enter zero

 0.0 No longer used, enter zero

 0.0 No longer used, enter zero

 -1.8330 Zero Cn angle of attack (deg)

 7.1838 Cn slope for zero lift (dimensionless)

 1.6717 Cn extrapolated to value at positive stall angle of attack

 -0.3075 Cn at stall value for negative angle of attack

 0.00 Angle of attack for minimum CD (deg)

 0.0094 Minimum CD value

-180.00 0.000 0.0407 0.0000

-175.00 0.223 0.0507 0.0937

-170.00 0.405 0.1055 0.1702

-160.00 0.658 0.2982 0.2819

-155.00 0.733 0.4121 0.3213

-150.00 0.778 0.5308 0.3520

-145.00 0.795 0.6503 0.3754

-140.00 0.787 0.7672 0.3926

-135.00 0.757 0.8785 0.4046

-130.00 0.708 0.9819 0.4121

-125.00 0.641 1.0756 0.4160

-120.00 0.560 1.1580 0.4167

-115.00 0.467 1.2280 0.4146

-110.00 0.365 1.2847 0.4104

-105.00 0.255 1.3274 0.4041

-100.00 0.139 1.3557 0.3961

-95.00 0.021 1.3692 0.3867

-90.00 -0.098 1.3680 0.3759

-85.00 -0.216 1.3521 0.3639

-80.00 -0.331 1.3218 0.3508

-75.00 -0.441 1.2773 0.3367

-70.00 -0.544 1.2193 0.3216

-65.00 -0.638 1.1486 0.3054

-60.00 -0.720 1.0660 0.2884

-55.00 -0.788 0.9728 0.2703

-50.00 -0.840 0.8705 0.2512

-45.00 -0.875 0.7611 0.2311

-40.00 -0.889 0.6466 0.2099

-35.00 -0.880 0.5299 0.1876

-30.00 -0.846 0.4141 0.1641

-25.00 -0.784 0.3030 0.1396

-24.00 -0.768 0.2817 0.1345

-23.00 -0.751 0.2608 0.1294

-22.00 -0.733 0.2404 0.1243

-21.00 -0.714 0.2205 0.1191

-20.00 -0.693 0.2011 0.1139

-19.00 -0.671 0.1822 0.1086

-18.00 -0.648 0.1640 0.1032

-17.00 -0.624 0.1465 0.0975

-16.00 -0.601 0.1300 0.0898

-15.00 -0.579 0.1145 0.0799

-14.00 -0.559 0.1000 0.0682

-13.00 -0.539 0.0867 0.0547

-12.00 -0.519 0.0744 0.0397

-11.00 -0.499 0.0633 0.0234

-10.00 -0.480 0.0534 0.0060

 -5.54 -0.385 0.0245 -0.0800

 -5.04 -0.359 0.0225 -0.0800

 -4.54 -0.360 0.0196 -0.0800

 -4.04 -0.355 0.0174 -0.0800

 -3.54 -0.307 0.0162 -0.0800

 -3.04 -0.246 0.0144 -0.0800

 -3.00 -0.240 0.0240 -0.0623

 -2.50 -0.163 0.0188 -0.0674

 -2.00 -0.091 0.0160 -0.0712

 -1.50 -0.019 0.0137 -0.0746

 -1.00 0.052 0.0118 -0.0778

 -0.50 0.121 0.0104 -0.0806

 0.00 0.196 0.0094 -0.0831

 0.50 0.265 0.0096 -0.0863

 1.00 0.335 0.0098 -0.0895

 1.50 0.404 0.0099 -0.0924

 2.00 0.472 0.0100 -0.0949

 2.50 0.540 0.0102 -0.0973
48

 3.00 0.608 0.0103 -0.0996

 3.50 0.674 0.0104 -0.1016

 4.00 0.742 0.0105 -0.1037

 4.50 0.809 0.0107 -0.1057

 5.00 0.875 0.0108 -0.1076

 5.50 0.941 0.0109 -0.1094

 6.00 1.007 0.0110 -0.1109

 6.50 1.071 0.0113 -0.1118

 7.00 1.134 0.0115 -0.1127

 7.50 1.198 0.0117 -0.1138

 8.00 1.260 0.0120 -0.1144

 8.50 1.318 0.0126 -0.1137

 9.00 1.368 0.0133 -0.1112

 9.50 1.422 0.0143 -0.1100

 10.00 1.475 0.0156 -0.1086

 10.50 1.523 0.0174 -0.1064

 11.00 1.570 0.0194 -0.1044

 11.50 1.609 0.0227 -0.1013

 12.00 1.642 0.0269 -0.0980

 12.50 1.675 0.0319 -0.0953

 13.00 1.700 0.0398 -0.0925

 13.50 1.717 0.0488 -0.0896

 14.00 1.712 0.0614 -0.0864

 14.50 1.703 0.0786 -0.0840

 15.50 1.671 0.1173 -0.0830

 16.00 1.649 0.1377 -0.0848

 16.50 1.621 0.1600 -0.0880

 17.00 1.598 0.1814 -0.0926

 17.50 1.571 0.2042 -0.0984

 18.00 1.549 0.2316 -0.1052

 19.00 1.544 0.2719 -0.1158

 19.50 1.549 0.2906 -0.1213

 20.00 1.565 0.3085 -0.1248

 21.00 1.565 0.3447 -0.1317

 22.00 1.563 0.3820 -0.1385

 23.00 1.558 0.4203 -0.1452

 24.00 1.552 0.4593 -0.1518

 25.00 1.546 0.4988 -0.1583

 26.00 1.539 0.5387 -0.1647

 28.00 1.527 0.6187 -0.1770

 30.00 1.522 0.6978 -0.1886

 32.00 1.529 0.7747 -0.1994

 35.00 1.544 0.8869 -0.2148

 40.00 1.529 1.0671 -0.2392

 45.00 1.471 1.2319 -0.2622

 50.00 1.376 1.3747 -0.2839

 55.00 1.249 1.4899 -0.3043

 60.00 1.097 1.5728 -0.3236

 65.00 0.928 1.6202 -0.3417

 70.00 0.750 1.6302 -0.3586

 75.00 0.570 1.6031 -0.3745

 80.00 0.396 1.5423 -0.3892

 85.00 0.237 1.4598 -0.4028

 90.00 0.101 1.4041 -0.4151

 95.00 -0.022 1.4053 -0.4261

100.00 -0.143 1.3914 -0.4357

105.00 -0.261 1.3625 -0.4437

110.00 -0.374 1.3188 -0.4498

115.00 -0.480 1.2608 -0.4538

120.00 -0.575 1.1891 -0.4553

125.00 -0.659 1.1046 -0.4540

130.00 -0.727 1.0086 -0.4492

135.00 -0.778 0.9025 -0.4405

140.00 -0.809 0.7883 -0.4270

145.00 -0.818 0.6684 -0.4078

150.00 -0.800 0.5457 -0.3821

155.00 -0.754 0.4236 -0.3484

160.00 -0.677 0.3066 -0.3054

170.00 -0.417 0.1085 -0.1842

175.00 -0.229 0.0510 -0.1013

180.00 0.000 0.0407 0.0000

B.6 Airfoil-Data Input File – DU30_A17.dat

DU30 airfoil with an aspect ratio of 17. Original -180 to 180deg Cl, Cd, and Cm versus AOA data taken from Appendix A of DOW

Cl and Cd values corrected for rotational stall delay and Cd values corrected using the Viterna method for 0 to 90deg AOA by 

 1 Number of airfoil tables in this file

 0.0 Table ID parameter

 9.00 Stall angle (deg)

 0.0 No longer used, enter zero

 0.0 No longer used, enter zero

 0.0 No longer used, enter zero
49

 -2.3220 Zero Cn angle of attack (deg)

 7.3326 Cn slope for zero lift (dimensionless)

 1.4490 Cn extrapolated to value at positive stall angle of attack

 -0.6138 Cn at stall value for negative angle of attack

 0.00 Angle of attack for minimum CD (deg)

 0.0087 Minimum CD value

-180.00 0.000 0.0267 0.0000

-175.00 0.274 0.0370 0.1379

-170.00 0.547 0.0968 0.2778

-160.00 0.685 0.2876 0.2740

-155.00 0.766 0.4025 0.3118

-150.00 0.816 0.5232 0.3411

-145.00 0.836 0.6454 0.3631

-140.00 0.832 0.7656 0.3791

-135.00 0.804 0.8807 0.3899

-130.00 0.756 0.9882 0.3965

-125.00 0.690 1.0861 0.3994

-120.00 0.609 1.1730 0.3992

-115.00 0.515 1.2474 0.3964

-110.00 0.411 1.3084 0.3915

-105.00 0.300 1.3552 0.3846

-100.00 0.182 1.3875 0.3761

-95.00 0.061 1.4048 0.3663

-90.00 -0.061 1.4070 0.3551

-85.00 -0.183 1.3941 0.3428

-80.00 -0.302 1.3664 0.3295

-75.00 -0.416 1.3240 0.3153

-70.00 -0.523 1.2676 0.3001

-65.00 -0.622 1.1978 0.2841

-60.00 -0.708 1.1156 0.2672

-55.00 -0.781 1.0220 0.2494

-50.00 -0.838 0.9187 0.2308

-45.00 -0.877 0.8074 0.2113

-40.00 -0.895 0.6904 0.1909

-35.00 -0.889 0.5703 0.1696

-30.00 -0.858 0.4503 0.1475

-25.00 -0.832 0.3357 0.1224

-24.00 -0.852 0.3147 0.1156

-23.00 -0.882 0.2946 0.1081

-22.00 -0.919 0.2752 0.1000

-21.00 -0.963 0.2566 0.0914

-20.00 -1.013 0.2388 0.0823

-19.00 -1.067 0.2218 0.0728

-18.00 -1.125 0.2056 0.0631

-17.00 -1.185 0.1901 0.0531

-16.00 -1.245 0.1754 0.0430

-15.25 -1.290 0.1649 0.0353

-14.24 -1.229 0.1461 0.0240

-13.24 -1.148 0.1263 0.0100

-12.22 -1.052 0.1051 -0.0090

-11.22 -0.965 0.0886 -0.0230

-10.19 -0.867 0.0740 -0.0336

 -9.70 -0.822 0.0684 -0.0375

 -9.18 -0.769 0.0605 -0.0440

 -8.18 -0.756 0.0270 -0.0578

 -7.19 -0.690 0.0180 -0.0590

 -6.65 -0.616 0.0166 -0.0633

 -6.13 -0.542 0.0152 -0.0674

 -6.00 -0.525 0.0117 -0.0732

 -5.50 -0.451 0.0105 -0.0766

 -5.00 -0.382 0.0097 -0.0797

 -4.50 -0.314 0.0092 -0.0825

 -4.00 -0.251 0.0091 -0.0853

 -3.50 -0.189 0.0089 -0.0884

 -3.00 -0.120 0.0089 -0.0914

 -2.50 -0.051 0.0088 -0.0942

 -2.00 0.017 0.0088 -0.0969

 -1.50 0.085 0.0088 -0.0994

 -1.00 0.152 0.0088 -0.1018

 -0.50 0.219 0.0088 -0.1041

 0.00 0.288 0.0087 -0.1062

 0.50 0.354 0.0087 -0.1086

 1.00 0.421 0.0088 -0.1107

 1.50 0.487 0.0089 -0.1129

 2.00 0.554 0.0090 -0.1149

 2.50 0.619 0.0091 -0.1168

 3.00 0.685 0.0092 -0.1185

 3.50 0.749 0.0093 -0.1201

 4.00 0.815 0.0095 -0.1218

 4.50 0.879 0.0096 -0.1233

 5.00 0.944 0.0097 -0.1248

 5.50 1.008 0.0099 -0.1260

 6.00 1.072 0.0101 -0.1270

 6.50 1.135 0.0103 -0.1280
50

 7.00 1.197 0.0107 -0.1287

 7.50 1.256 0.0112 -0.1289

 8.00 1.305 0.0125 -0.1270

 9.00 1.390 0.0155 -0.1207

 9.50 1.424 0.0171 -0.1158

 10.00 1.458 0.0192 -0.1116

 10.50 1.488 0.0219 -0.1073

 11.00 1.512 0.0255 -0.1029

 11.50 1.533 0.0307 -0.0983

 12.00 1.549 0.0370 -0.0949

 12.50 1.558 0.0452 -0.0921

 13.00 1.470 0.0630 -0.0899

 13.50 1.398 0.0784 -0.0885

 14.00 1.354 0.0931 -0.0885

 14.50 1.336 0.1081 -0.0902

 15.00 1.333 0.1239 -0.0928

 15.50 1.326 0.1415 -0.0963

 16.00 1.329 0.1592 -0.1006

 16.50 1.326 0.1743 -0.1042

 17.00 1.321 0.1903 -0.1084

 17.50 1.331 0.2044 -0.1125

 18.00 1.333 0.2186 -0.1169

 18.50 1.340 0.2324 -0.1215

 19.00 1.362 0.2455 -0.1263

 19.50 1.382 0.2584 -0.1313

 20.00 1.398 0.2689 -0.1352

 20.50 1.426 0.2814 -0.1406

 21.00 1.437 0.2943 -0.1462

 22.00 1.418 0.3246 -0.1516

 23.00 1.397 0.3557 -0.1570

 24.00 1.376 0.3875 -0.1623

 25.00 1.354 0.4198 -0.1676

 26.00 1.332 0.4524 -0.1728

 28.00 1.293 0.5183 -0.1832

 30.00 1.265 0.5843 -0.1935

 32.00 1.253 0.6492 -0.2039

 35.00 1.264 0.7438 -0.2193

 40.00 1.258 0.8970 -0.2440

 45.00 1.217 1.0402 -0.2672

 50.00 1.146 1.1686 -0.2891

 55.00 1.049 1.2779 -0.3097

 60.00 0.932 1.3647 -0.3290

 65.00 0.799 1.4267 -0.3471

 70.00 0.657 1.4621 -0.3641

 75.00 0.509 1.4708 -0.3799

 80.00 0.362 1.4544 -0.3946

 85.00 0.221 1.4196 -0.4081

 90.00 0.092 1.3938 -0.4204

 95.00 -0.030 1.3943 -0.4313

100.00 -0.150 1.3798 -0.4408

105.00 -0.267 1.3504 -0.4486

110.00 -0.379 1.3063 -0.4546

115.00 -0.483 1.2481 -0.4584

120.00 -0.578 1.1763 -0.4597

125.00 -0.660 1.0919 -0.4582

130.00 -0.727 0.9962 -0.4532

135.00 -0.777 0.8906 -0.4441

140.00 -0.807 0.7771 -0.4303

145.00 -0.815 0.6581 -0.4109

150.00 -0.797 0.5364 -0.3848

155.00 -0.750 0.4157 -0.3508

160.00 -0.673 0.3000 -0.3074

170.00 -0.547 0.1051 -0.2786

175.00 -0.274 0.0388 -0.1380

180.00 0.000 0.0267 0.0000

B.7 Airfoil-Data Input File – DU25_A17.dat

DU25 airfoil with an aspect ratio of 17. Original -180 to 180deg Cl, Cd, and Cm versus AOA data taken from Appendix A of DOW

Cl and Cd values corrected for rotational stall delay and Cd values corrected using the Viterna method for 0 to 90deg AOA by 

 1 Number of airfoil tables in this file

 0.0 Table ID parameter

 8.50 Stall angle (deg)

 0.0 No longer used, enter zero

 0.0 No longer used, enter zero

 0.0 No longer used, enter zero

 -4.2422 Zero Cn angle of attack (deg)

 6.4462 Cn slope for zero lift (dimensionless)

 1.4336 Cn extrapolated to value at positive stall angle of attack

 -0.6873 Cn at stall value for negative angle of attack

 0.00 Angle of attack for minimum CD (deg)

 0.0065 Minimum CD value
51

-180.00 0.000 0.0202 0.0000

-175.00 0.368 0.0324 0.1845

-170.00 0.735 0.0943 0.3701

-160.00 0.695 0.2848 0.2679

-155.00 0.777 0.4001 0.3046

-150.00 0.828 0.5215 0.3329

-145.00 0.850 0.6447 0.3540

-140.00 0.846 0.7660 0.3693

-135.00 0.818 0.8823 0.3794

-130.00 0.771 0.9911 0.3854

-125.00 0.705 1.0905 0.3878

-120.00 0.624 1.1787 0.3872

-115.00 0.530 1.2545 0.3841

-110.00 0.426 1.3168 0.3788

-105.00 0.314 1.3650 0.3716

-100.00 0.195 1.3984 0.3629

-95.00 0.073 1.4169 0.3529

-90.00 -0.050 1.4201 0.3416

-85.00 -0.173 1.4081 0.3292

-80.00 -0.294 1.3811 0.3159

-75.00 -0.409 1.3394 0.3017

-70.00 -0.518 1.2833 0.2866

-65.00 -0.617 1.2138 0.2707

-60.00 -0.706 1.1315 0.2539

-55.00 -0.780 1.0378 0.2364

-50.00 -0.839 0.9341 0.2181

-45.00 -0.879 0.8221 0.1991

-40.00 -0.898 0.7042 0.1792

-35.00 -0.893 0.5829 0.1587

-30.00 -0.862 0.4616 0.1374

-25.00 -0.803 0.3441 0.1154

-24.00 -0.792 0.3209 0.1101

-23.00 -0.789 0.2972 0.1031

-22.00 -0.792 0.2730 0.0947

-21.00 -0.801 0.2485 0.0849

-20.00 -0.815 0.2237 0.0739

-19.00 -0.833 0.1990 0.0618

-18.00 -0.854 0.1743 0.0488

-17.00 -0.879 0.1498 0.0351

-16.00 -0.905 0.1256 0.0208

-15.00 -0.932 0.1020 0.0060

-14.00 -0.959 0.0789 -0.0091

-13.00 -0.985 0.0567 -0.0243

-13.00 -0.985 0.0567 -0.0243

-12.01 -0.953 0.0271 -0.0349

-11.00 -0.900 0.0303 -0.0361

 -9.98 -0.827 0.0287 -0.0464

 -8.98 -0.753 0.0271 -0.0534

 -8.47 -0.691 0.0264 -0.0650

 -7.45 -0.555 0.0114 -0.0782

 -6.42 -0.413 0.0094 -0.0904

 -5.40 -0.271 0.0086 -0.1006

 -5.00 -0.220 0.0073 -0.1107

 -4.50 -0.152 0.0071 -0.1135

 -4.00 -0.084 0.0070 -0.1162

 -3.50 -0.018 0.0069 -0.1186

 -3.00 0.049 0.0068 -0.1209

 -2.50 0.115 0.0068 -0.1231

 -2.00 0.181 0.0068 -0.1252

 -1.50 0.247 0.0067 -0.1272

 -1.00 0.312 0.0067 -0.1293

 -0.50 0.377 0.0067 -0.1311

 0.00 0.444 0.0065 -0.1330

 0.50 0.508 0.0065 -0.1347

 1.00 0.573 0.0066 -0.1364

 1.50 0.636 0.0067 -0.1380

 2.00 0.701 0.0068 -0.1396

 2.50 0.765 0.0069 -0.1411

 3.00 0.827 0.0070 -0.1424

 3.50 0.890 0.0071 -0.1437

 4.00 0.952 0.0073 -0.1448

 4.50 1.013 0.0076 -0.1456

 5.00 1.062 0.0079 -0.1445

 6.00 1.161 0.0099 -0.1419

 6.50 1.208 0.0117 -0.1403

 7.00 1.254 0.0132 -0.1382

 7.50 1.301 0.0143 -0.1362

 8.00 1.336 0.0153 -0.1320

 8.50 1.369 0.0165 -0.1276

 9.00 1.400 0.0181 -0.1234

 9.50 1.428 0.0211 -0.1193

 10.00 1.442 0.0262 -0.1152

 10.50 1.427 0.0336 -0.1115

 11.00 1.374 0.0420 -0.1081
52

 11.50 1.316 0.0515 -0.1052

 12.00 1.277 0.0601 -0.1026

 12.50 1.250 0.0693 -0.1000

 13.00 1.246 0.0785 -0.0980

 13.50 1.247 0.0888 -0.0969

 14.00 1.256 0.1000 -0.0968

 14.50 1.260 0.1108 -0.0973

 15.00 1.271 0.1219 -0.0981

 15.50 1.281 0.1325 -0.0992

 16.00 1.289 0.1433 -0.1006

 16.50 1.294 0.1541 -0.1023

 17.00 1.304 0.1649 -0.1042

 17.50 1.309 0.1754 -0.1064

 18.00 1.315 0.1845 -0.1082

 18.50 1.320 0.1953 -0.1110

 19.00 1.330 0.2061 -0.1143

 19.50 1.343 0.2170 -0.1179

 20.00 1.354 0.2280 -0.1219

 20.50 1.359 0.2390 -0.1261

 21.00 1.360 0.2536 -0.1303

 22.00 1.325 0.2814 -0.1375

 23.00 1.288 0.3098 -0.1446

 24.00 1.251 0.3386 -0.1515

 25.00 1.215 0.3678 -0.1584

 26.00 1.181 0.3972 -0.1651

 28.00 1.120 0.4563 -0.1781

 30.00 1.076 0.5149 -0.1904

 32.00 1.056 0.5720 -0.2017

 35.00 1.066 0.6548 -0.2173

 40.00 1.064 0.7901 -0.2418

 45.00 1.035 0.9190 -0.2650

 50.00 0.980 1.0378 -0.2867

 55.00 0.904 1.1434 -0.3072

 60.00 0.810 1.2333 -0.3265

 65.00 0.702 1.3055 -0.3446

 70.00 0.582 1.3587 -0.3616

 75.00 0.456 1.3922 -0.3775

 80.00 0.326 1.4063 -0.3921

 85.00 0.197 1.4042 -0.4057

 90.00 0.072 1.3985 -0.4180

 95.00 -0.050 1.3973 -0.4289

100.00 -0.170 1.3810 -0.4385

105.00 -0.287 1.3498 -0.4464

110.00 -0.399 1.3041 -0.4524

115.00 -0.502 1.2442 -0.4563

120.00 -0.596 1.1709 -0.4577

125.00 -0.677 1.0852 -0.4563

130.00 -0.743 0.9883 -0.4514

135.00 -0.792 0.8818 -0.4425

140.00 -0.821 0.7676 -0.4288

145.00 -0.826 0.6481 -0.4095

150.00 -0.806 0.5264 -0.3836

155.00 -0.758 0.4060 -0.3497

160.00 -0.679 0.2912 -0.3065

170.00 -0.735 0.0995 -0.3706

175.00 -0.368 0.0356 -0.1846

180.00 0.000 0.0202 0.0000

B.8 Airfoil-Data Input File – DU21_A17.dat

DU21 airfoil with an aspect ratio of 17. Original -180 to 180deg Cl, Cd, and Cm versus AOA data taken from Appendix A of DOW

Cl and Cd values corrected for rotational stall delay and Cd values corrected using the Viterna method for 0 to 90deg AOA by 

 1 Number of airfoil tables in this file

 0.0 Table ID parameter

 8.00 Stall angle (deg)

 0.0 No longer used, enter zero

 0.0 No longer used, enter zero

 0.0 No longer used, enter zero

 -5.0609 Zero Cn angle of attack (deg)

 6.2047 Cn slope for zero lift (dimensionless)

 1.4144 Cn extrapolated to value at positive stall angle of attack

 -0.5324 Cn at stall value for negative angle of attack

 -1.50 Angle of attack for minimum CD (deg)

 0.0057 Minimum CD value

-180.00 0.000 0.0185 0.0000

-175.00 0.394 0.0332 0.1978

-170.00 0.788 0.0945 0.3963

-160.00 0.670 0.2809 0.2738

-155.00 0.749 0.3932 0.3118

-150.00 0.797 0.5112 0.3413

-145.00 0.818 0.6309 0.3636

-140.00 0.813 0.7485 0.3799
53

-135.00 0.786 0.8612 0.3911

-130.00 0.739 0.9665 0.3980

-125.00 0.675 1.0625 0.4012

-120.00 0.596 1.1476 0.4014

-115.00 0.505 1.2206 0.3990

-110.00 0.403 1.2805 0.3943

-105.00 0.294 1.3265 0.3878

-100.00 0.179 1.3582 0.3796

-95.00 0.060 1.3752 0.3700

-90.00 -0.060 1.3774 0.3591

-85.00 -0.179 1.3648 0.3471

-80.00 -0.295 1.3376 0.3340

-75.00 -0.407 1.2962 0.3199

-70.00 -0.512 1.2409 0.3049

-65.00 -0.608 1.1725 0.2890

-60.00 -0.693 1.0919 0.2722

-55.00 -0.764 1.0002 0.2545

-50.00 -0.820 0.8990 0.2359

-45.00 -0.857 0.7900 0.2163

-40.00 -0.875 0.6754 0.1958

-35.00 -0.869 0.5579 0.1744

-30.00 -0.838 0.4405 0.1520

-25.00 -0.791 0.3256 0.1262

-24.00 -0.794 0.3013 0.1170

-23.00 -0.805 0.2762 0.1059

-22.00 -0.821 0.2506 0.0931

-21.00 -0.843 0.2246 0.0788

-20.00 -0.869 0.1983 0.0631

-19.00 -0.899 0.1720 0.0464

-18.00 -0.931 0.1457 0.0286

-17.00 -0.964 0.1197 0.0102

-16.00 -0.999 0.0940 -0.0088

-15.00 -1.033 0.0689 -0.0281

-14.50 -1.050 0.0567 -0.0378

-12.01 -0.953 0.0271 -0.0349

-11.00 -0.900 0.0303 -0.0361

 -9.98 -0.827 0.0287 -0.0464

 -8.12 -0.536 0.0124 -0.0821

 -7.62 -0.467 0.0109 -0.0924

 -7.11 -0.393 0.0092 -0.1015

 -6.60 -0.323 0.0083 -0.1073

 -6.50 -0.311 0.0089 -0.1083

 -6.00 -0.245 0.0082 -0.1112

 -5.50 -0.178 0.0074 -0.1146

 -5.00 -0.113 0.0069 -0.1172

 -4.50 -0.048 0.0065 -0.1194

 -4.00 0.016 0.0063 -0.1213

 -3.50 0.080 0.0061 -0.1232

 -3.00 0.145 0.0058 -0.1252

 -2.50 0.208 0.0057 -0.1268

 -2.00 0.270 0.0057 -0.1282

 -1.50 0.333 0.0057 -0.1297

 -1.00 0.396 0.0057 -0.1310

 -0.50 0.458 0.0057 -0.1324

 0.00 0.521 0.0057 -0.1337

 0.50 0.583 0.0057 -0.1350

 1.00 0.645 0.0058 -0.1363

 1.50 0.706 0.0058 -0.1374

 2.00 0.768 0.0059 -0.1385

 2.50 0.828 0.0061 -0.1395

 3.00 0.888 0.0063 -0.1403

 3.50 0.948 0.0066 -0.1406

 4.00 0.996 0.0071 -0.1398

 4.50 1.046 0.0079 -0.1390

 5.00 1.095 0.0090 -0.1378

 5.50 1.145 0.0103 -0.1369

 6.00 1.192 0.0113 -0.1353

 6.50 1.239 0.0122 -0.1338

 7.00 1.283 0.0131 -0.1317

 7.50 1.324 0.0139 -0.1291

 8.00 1.358 0.0147 -0.1249

 8.50 1.385 0.0158 -0.1213

 9.00 1.403 0.0181 -0.1177

 9.50 1.401 0.0211 -0.1142

 10.00 1.358 0.0255 -0.1103

 10.50 1.313 0.0301 -0.1066

 11.00 1.287 0.0347 -0.1032

 11.50 1.274 0.0401 -0.1002

 12.00 1.272 0.0468 -0.0971

 12.50 1.273 0.0545 -0.0940

 13.00 1.273 0.0633 -0.0909

 13.50 1.273 0.0722 -0.0883

 14.00 1.272 0.0806 -0.0865

 14.50 1.273 0.0900 -0.0854
54

 15.00 1.275 0.0987 -0.0849

 15.50 1.281 0.1075 -0.0847

 16.00 1.284 0.1170 -0.0850

 16.50 1.296 0.1270 -0.0858

 17.00 1.306 0.1368 -0.0869

 17.50 1.308 0.1464 -0.0883

 18.00 1.308 0.1562 -0.0901

 18.50 1.308 0.1664 -0.0922

 19.00 1.308 0.1770 -0.0949

 19.50 1.307 0.1878 -0.0980

 20.00 1.311 0.1987 -0.1017

 20.50 1.325 0.2100 -0.1059

 21.00 1.324 0.2214 -0.1105

 22.00 1.277 0.2499 -0.1172

 23.00 1.229 0.2786 -0.1239

 24.00 1.182 0.3077 -0.1305

 25.00 1.136 0.3371 -0.1370

 26.00 1.093 0.3664 -0.1433

 28.00 1.017 0.4246 -0.1556

 30.00 0.962 0.4813 -0.1671

 32.00 0.937 0.5356 -0.1778

 35.00 0.947 0.6127 -0.1923

 40.00 0.950 0.7396 -0.2154

 45.00 0.928 0.8623 -0.2374

 50.00 0.884 0.9781 -0.2583

 55.00 0.821 1.0846 -0.2782

 60.00 0.740 1.1796 -0.2971

 65.00 0.646 1.2617 -0.3149

 70.00 0.540 1.3297 -0.3318

 75.00 0.425 1.3827 -0.3476

 80.00 0.304 1.4202 -0.3625

 85.00 0.179 1.4423 -0.3763

 90.00 0.053 1.4512 -0.3890

 95.00 -0.073 1.4480 -0.4004

100.00 -0.198 1.4294 -0.4105

105.00 -0.319 1.3954 -0.4191

110.00 -0.434 1.3464 -0.4260

115.00 -0.541 1.2829 -0.4308

120.00 -0.637 1.2057 -0.4333

125.00 -0.720 1.1157 -0.4330

130.00 -0.787 1.0144 -0.4294

135.00 -0.836 0.9033 -0.4219

140.00 -0.864 0.7845 -0.4098

145.00 -0.869 0.6605 -0.3922

150.00 -0.847 0.5346 -0.3682

155.00 -0.795 0.4103 -0.3364

160.00 -0.711 0.2922 -0.2954

170.00 -0.788 0.0969 -0.3966

175.00 -0.394 0.0334 -0.1978

180.00 0.000 0.0185 0.0000

B.9 Airfoil-Data Input File – NACA64_A17.dat

NACA64 airfoil with an aspect ratio of 17. Original -180 to 180deg Cl, Cd, and Cm versus AOA data taken from Appendix A of D

Cl and Cd values corrected for rotational stall delay and Cd values corrected using the Viterna method for 0 to 90deg AOA by 

 1 Number of airfoil tables in this file

 0.0 Table ID parameter

 9.00 Stall angle (deg)

 0.0 No longer used, enter zero

 0.0 No longer used, enter zero

 0.0 No longer used, enter zero

 -4.4320 Zero Cn angle of attack (deg)

 6.0031 Cn slope for zero lift (dimensionless)

 1.4073 Cn extrapolated to value at positive stall angle of attack

 -0.7945 Cn at stall value for negative angle of attack

 -1.00 Angle of attack for minimum CD (deg)

 0.0052 Minimum CD value

-180.00 0.000 0.0198 0.0000

-175.00 0.374 0.0341 0.1880

-170.00 0.749 0.0955 0.3770

-160.00 0.659 0.2807 0.2747

-155.00 0.736 0.3919 0.3130

-150.00 0.783 0.5086 0.3428

-145.00 0.803 0.6267 0.3654

-140.00 0.798 0.7427 0.3820

-135.00 0.771 0.8537 0.3935

-130.00 0.724 0.9574 0.4007

-125.00 0.660 1.0519 0.4042

-120.00 0.581 1.1355 0.4047

-115.00 0.491 1.2070 0.4025

-110.00 0.390 1.2656 0.3981

-105.00 0.282 1.3104 0.3918
55

-100.00 0.169 1.3410 0.3838

-95.00 0.052 1.3572 0.3743

-90.00 -0.067 1.3587 0.3636

-85.00 -0.184 1.3456 0.3517

-80.00 -0.299 1.3181 0.3388

-75.00 -0.409 1.2765 0.3248

-70.00 -0.512 1.2212 0.3099

-65.00 -0.606 1.1532 0.2940

-60.00 -0.689 1.0731 0.2772

-55.00 -0.759 0.9822 0.2595

-50.00 -0.814 0.8820 0.2409

-45.00 -0.850 0.7742 0.2212

-40.00 -0.866 0.6610 0.2006

-35.00 -0.860 0.5451 0.1789

-30.00 -0.829 0.4295 0.1563

-25.00 -0.853 0.3071 0.1156

-24.00 -0.870 0.2814 0.1040

-23.00 -0.890 0.2556 0.0916

-22.00 -0.911 0.2297 0.0785

-21.00 -0.934 0.2040 0.0649

-20.00 -0.958 0.1785 0.0508

-19.00 -0.982 0.1534 0.0364

-18.00 -1.005 0.1288 0.0218

-17.00 -1.082 0.1037 0.0129

-16.00 -1.113 0.0786 -0.0028

-15.00 -1.105 0.0535 -0.0251

-14.00 -1.078 0.0283 -0.0419

-13.50 -1.053 0.0158 -0.0521

-13.00 -1.015 0.0151 -0.0610

-12.00 -0.904 0.0134 -0.0707

-11.00 -0.807 0.0121 -0.0722

-10.00 -0.711 0.0111 -0.0734

 -9.00 -0.595 0.0099 -0.0772

 -8.00 -0.478 0.0091 -0.0807

 -7.00 -0.375 0.0086 -0.0825

 -6.00 -0.264 0.0082 -0.0832

 -5.00 -0.151 0.0079 -0.0841

 -4.00 -0.017 0.0072 -0.0869

 -3.00 0.088 0.0064 -0.0912

 -2.00 0.213 0.0054 -0.0946

 -1.00 0.328 0.0052 -0.0971

 0.00 0.442 0.0052 -0.1014

 1.00 0.556 0.0052 -0.1076

 2.00 0.670 0.0053 -0.1126

 3.00 0.784 0.0053 -0.1157

 4.00 0.898 0.0054 -0.1199

 5.00 1.011 0.0058 -0.1240

 6.00 1.103 0.0091 -0.1234

 7.00 1.181 0.0113 -0.1184

 8.00 1.257 0.0124 -0.1163

 8.50 1.293 0.0130 -0.1163

 9.00 1.326 0.0136 -0.1160

 9.50 1.356 0.0143 -0.1154

 10.00 1.382 0.0150 -0.1149

 10.50 1.400 0.0267 -0.1145

 11.00 1.415 0.0383 -0.1143

 11.50 1.425 0.0498 -0.1147

 12.00 1.434 0.0613 -0.1158

 12.50 1.443 0.0727 -0.1165

 13.00 1.451 0.0841 -0.1153

 13.50 1.453 0.0954 -0.1131

 14.00 1.448 0.1065 -0.1112

 14.50 1.444 0.1176 -0.1101

 15.00 1.445 0.1287 -0.1103

 15.50 1.447 0.1398 -0.1109

 16.00 1.448 0.1509 -0.1114

 16.50 1.444 0.1619 -0.1111

 17.00 1.438 0.1728 -0.1097

 17.50 1.439 0.1837 -0.1079

 18.00 1.448 0.1947 -0.1080

18.50 1.452 0.2057 -0.1090

 19.00 1.448 0.2165 -0.1086

 19.50 1.438 0.2272 -0.1077

 20.00 1.428 0.2379 -0.1099

 21.00 1.401 0.2590 -0.1169

 22.00 1.359 0.2799 -0.1190

 23.00 1.300 0.3004 -0.1235

 24.00 1.220 0.3204 -0.1393

 25.00 1.168 0.3377 -0.1440

 26.00 1.116 0.3554 -0.1486

 28.00 1.015 0.3916 -0.1577

 30.00 0.926 0.4294 -0.1668

 32.00 0.855 0.4690 -0.1759

 35.00 0.800 0.5324 -0.1897
56

 40.00 0.804 0.6452 -0.2126

 45.00 0.793 0.7573 -0.2344

 50.00 0.763 0.8664 -0.2553

 55.00 0.717 0.9708 -0.2751

 60.00 0.656 1.0693 -0.2939

 65.00 0.582 1.1606 -0.3117

 70.00 0.495 1.2438 -0.3285

 75.00 0.398 1.3178 -0.3444

 80.00 0.291 1.3809 -0.3593

 85.00 0.176 1.4304 -0.3731

 90.00 0.053 1.4565 -0.3858

 95.00 -0.074 1.4533 -0.3973

100.00 -0.199 1.4345 -0.4075

105.00 -0.321 1.4004 -0.4162

110.00 -0.436 1.3512 -0.4231

115.00 -0.543 1.2874 -0.4280

120.00 -0.640 1.2099 -0.4306

125.00 -0.723 1.1196 -0.4304

130.00 -0.790 1.0179 -0.4270

135.00 -0.840 0.9064 -0.4196

140.00 -0.868 0.7871 -0.4077

145.00 -0.872 0.6627 -0.3903

150.00 -0.850 0.5363 -0.3665

155.00 -0.798 0.4116 -0.3349

160.00 -0.714 0.2931 -0.2942

170.00 -0.749 0.0971 -0.3771

175.00 -0.374 0.0334 -0.1879

180.00 0.000 0.0198 0.0000
57

Appendix C Source Code for the Control System DLL

!=======================================================================

SUBROUTINE DISCON ( avrSWAP, aviFAIL, accINFILE, avcOUTNAME, avcMSG )

!DEC$ ATTRIBUTES DLLEXPORT, ALIAS:'DISCON' :: DISCON

 ! This Bladed-style DLL controller is used to implement a variable-speed

 ! generator-torque controller and PI collective blade pitch controller for

 ! the NREL Offshore 5MW baseline wind turbine. This routine was written by

 ! J. Jonkman of NREL/NWTC for use in the IEA Annex XXIII OC3 studies.

IMPLICIT NONE

 ! Passed Variables:

REAL(4), INTENT(INOUT) :: avrSWAP (*) ! The swap array, used to pass data to, and r

INTEGER(4), INTENT( OUT) :: aviFAIL ! A flag used to indicate the success of this 

INTEGER(1), INTENT(IN ) :: accINFILE (*) ! The address of the first record of an array

INTEGER(1), INTENT( OUT) :: avcMSG (*) ! The address of the first record of an array 

INTEGER(1), INTENT(IN ) :: avcOUTNAME(*) ! The address of the first record of an array

 ! Local Variables:

REAL(4) :: Alpha ! Current coefficient in the recursive, singl

REAL(4) :: BlPitch (3) ! Current values of the blade pitch angles, r

REAL(4) :: ElapTime ! Elapsed time since the last call to the con

REAL(4), PARAMETER :: CornerFreq = 1.570796 ! Corner frequency (-3dB point) in the recurs

REAL(4) :: GenSpeed ! Current HSS (generator) speed, rad/s.

REAL(4), SAVE :: GenSpeedF ! Filtered HSS (generator) speed, rad/s.

REAL(4) :: GenTrq ! Electrical generator torque, N-m.

REAL(4) :: GK ! Current value of the gain correction factor

REAL(4) :: HorWindV ! Horizontal hub-heigh wind speed, m/s.

REAL(4), SAVE :: IntSpdErr ! Current integral of speed error w.r.t. time

REAL(4), SAVE :: LastGenTrq ! Commanded electrical generator torque the l

REAL(4), SAVE :: LastTime ! Last time this DLL was called, sec.

REAL(4), SAVE :: LastTimePC ! Last time the pitch controller was called,

REAL(4), SAVE :: LastTimeVS ! Last time the torque controller was called, 

REAL(4), PARAMETER :: OnePlusEps = 1.0 + EPSILON(OnePlusEps) ! The number slighty greater than unity in si

REAL(4), PARAMETER :: PC_DT = 0.00125 ! Communication interval for pitch controlle

REAL(4), PARAMETER :: PC_KI = 0.008068634 ! Integral gain for pitch controller at rated

REAL(4), PARAMETER :: PC_KK = 0.1099965 ! Pitch angle were the the derivative of the 

REAL(4), PARAMETER :: PC_KP = 0.01882681 ! Proportional gain for pitch controller at r

REAL(4), PARAMETER :: PC_MaxPit = 1.570796 ! Maximum pitch setting in pitch controller, 

REAL(4), PARAMETER :: PC_MaxRat = 0.1396263 ! Maximum pitch rate (in absolute value) in 

REAL(4), PARAMETER :: PC_MinPit = 0.0 ! Minimum pitch setting in pitch controller, 

REAL(4), PARAMETER :: PC_RefSpd = 122.9096 ! Desired (reference) HSS speed for pitch con

REAL(4), SAVE :: PitCom (3) ! Commanded pitch of each blade the last time 

REAL(4) :: PitComI ! Integral term of command pitch, rad.

REAL(4) :: PitComP ! Proportional term of command pitch, rad.

REAL(4) :: PitComT ! Total command pitch based on the sum of the

REAL(4) :: PitRate (3) ! Pitch rates of each blade based on the curr

REAL(4), PARAMETER :: R2D = 57.295780 ! Factor to convert radians to degrees.

REAL(4), PARAMETER :: RPS2RPM = 9.5492966 ! Factor to convert radians per second to rev

REAL(4) :: SpdErr ! Current speed error, rad/s.

REAL(4) :: Time ! Current simulation time, sec.

REAL(4) :: TrqRate ! Torque rate based on the current and last t

REAL(4), PARAMETER :: VS_CtInSp = 70.16224 ! Transitional generator speed (HSS side) bet

REAL(4), PARAMETER :: VS_DT = 0.00125 ! Communication interval for torque controlle

REAL(4), PARAMETER :: VS_MaxRat = 15000.0 ! Maximum torque rate (in absolute value) in 

REAL(4), PARAMETER :: VS_MaxTq = 47402.91 ! Maximum generator torque in Region 3 (HSS s

REAL(4), PARAMETER :: VS_Rgn2K = 2.332287 ! Generator torque constant in Region 2 (HSS 

REAL(4), PARAMETER :: VS_Rgn2Sp = 91.21091 ! Transitional generator speed (HSS side) bet

REAL(4), PARAMETER :: VS_Rgn3MP = 0.01745329 ! Minimum pitch angle at which the torque is 

REAL(4), PARAMETER :: VS_RtGnSp = 121.6805 ! Rated generator speed (HSS side), rad/s. --

REAL(4), PARAMETER :: VS_RtPwr = 5296610.0 ! Rated generator generator power in Region 3

REAL(4), SAVE :: VS_Slope15 ! Torque/speed slope of region 1 1/2 cut-in t

REAL(4), SAVE :: VS_Slope25 ! Torque/speed slope of region 2 1/2 inductio

REAL(4), PARAMETER :: VS_SlPc = 10.0 ! Rated generator slip percentage in Region 2

REAL(4), SAVE :: VS_SySp ! Synchronous speed of region 2 1/2 induction 

REAL(4), SAVE :: VS_TrGnSp ! Transitional generator speed (HSS side) bet

INTEGER(4) :: I ! Generic index.

INTEGER(4) :: iStatus ! A status flag set by the simulation as foll

INTEGER(4) :: K ! Loops through blades.

INTEGER(4) :: NumBl ! Number of blades, (-).
58

INTEGER(4), PARAMETER :: UnDb = 85 ! I/O unit for the debugging information

INTEGER(1) :: iInFile ( 256) ! CHARACTER string cInFile stored as a 1-byt

INTEGER(1) :: iMessage ( 256) ! CHARACTER string cMessage stored as a 1-byt

INTEGER(1), SAVE :: iOutName (1024) ! CHARACTER string cOutName stored as a 1-byt

LOGICAL(1), PARAMETER :: PC_DbgOut = .FALSE. ! Flag to indicate whether to output debuggin

CHARACTER( 256) :: cInFile ! CHARACTER string giving the name of the par

CHARACTER( 256) :: cMessage ! CHARACTER string giving a message that will

CHARACTER(1024), SAVE :: cOutName ! CHARACTER string giving the simulation run 

CHARACTER( 1), PARAMETER :: Tab = CHAR( 9 ) ! The tab character.

CHARACTER( 25), PARAMETER :: FmtDat = "(F8.3,99('"//Tab//"',ES10.3E2,:))" ! The format of the debugging data

 ! Set EQUIVALENCE relationships between INTEGER(1) byte arrays and CHARACTER strings:

EQUIVALENCE (iInFile , cInFile )

EQUIVALENCE (iMessage, cMessage)

EQUIVALENCE (iOutName, cOutName)

 ! Load variables from calling program (See Appendix A of Bladed User's Guide):

iStatus = NINT( avrSWAP( 1) )

NumBl = NINT( avrSWAP(61) )

BlPitch (1) = avrSWAP( 4) 

BlPitch (2) = avrSWAP(33)

BlPitch (3) = avrSWAP(34) 

GenSpeed = avrSWAP(20)

HorWindV = avrSWAP(27)

Time = avrSWAP( 2)

 

 ! Initialize aviFAIL to 0:

aviFAIL = 0

 ! Read any External Controller Parameters specified in the User Interface

 ! and initialize variables:

IF ( iStatus == 0 ) THEN ! .TRUE. if were on the first call to the DLL

 ! Convert byte arrays to CHARACTER strings, for convenience:

 DO I = 1,MIN( 256, NINT( avrSWAP(50) ) )

 iInFile (I) = accINFILE (I) ! Sets cInfile by EQUIVALENCE

 ENDDO

 DO I = 1,MIN( 1024, NINT( avrSWAP(51) ) )

 iOutName(I) = avcOUTNAME(I) ! Sets cOutName by EQUIVALENCE

 ENDDO

 ! Inform users that we are using this user-defined routine:

 aviFAIL = 1

 cMessage = 'Running with torque and pitch control of the NREL offshore '// &

 '5MW baseline wind turbine from DISCON.dll as written by J. '// &

 'Jonkman of NREL/NWTC for use in the IEA Annex XXIII OC3 ' // &

 'studies.'

 ! Determine some torque control parameters not specified directly:

 VS_SySp = VS_RtGnSp/( 1.0 + 0.01*VS_SlPc )

 VS_Slope15 = ( VS_Rgn2K*VS_Rgn2Sp*VS_Rgn2Sp )/( VS_Rgn2Sp - VS_CtInSp )

 VS_Slope25 = ( VS_RtPwr/VS_RtGnSp )/( VS_RtGnSp - VS_SySp )

 IF ( VS_Rgn2K == 0.0 ) THEN ! .TRUE. if the Region 2 torque is flat, and thus, the denominator in the ELSE condition is 

 VS_TrGnSp = VS_SySp

 ELSE ! .TRUE. if the Region 2 torque is quadratic with speed

 VS_TrGnSp = ( VS_Slope25 - SQRT( VS_Slope25*( VS_Slope25 - 4.0*VS_Rgn2K*VS_SySp ) ) )/( 2.0*VS_Rgn2K )

 ENDIF

 ! Check validity of input parameters:

 IF ( CornerFreq <= 0.0 ) THEN

 aviFAIL = -1
59

 cMessage = 'CornerFreq must be greater than zero.'

 ENDIF

 IF ( VS_DT <= 0.0 ) THEN

 aviFAIL = -1

 cMessage = 'VS_DT must be greater than zero.'

 ENDIF

 IF ( VS_CtInSp < 0.0 ) THEN

 aviFAIL = -1

 cMessage = 'VS_CtInSp must not be negative.'

 ENDIF

 IF ( VS_Rgn2Sp <= VS_CtInSp ) THEN

 aviFAIL = -1

 cMessage = 'VS_Rgn2Sp must be greater than VS_CtInSp.'

 ENDIF

 IF ( VS_TrGnSp < VS_Rgn2Sp ) THEN

 aviFAIL = -1

 cMessage = 'VS_TrGnSp must not be less than VS_Rgn2Sp.'

 ENDIF

 IF ( VS_SlPc <= 0.0 ) THEN

 aviFAIL = -1

 cMessage = 'VS_SlPc must be greater than zero.'

 ENDIF

 IF ( VS_MaxRat <= 0.0 ) THEN

 aviFAIL = -1

 cMessage = 'VS_MaxRat must be greater than zero.'

 ENDIF

 IF ( VS_RtPwr < 0.0 ) THEN

 aviFAIL = -1

 cMessage = 'VS_RtPwr must not be negative.'

 ENDIF

 IF ( VS_Rgn2K < 0.0 ) THEN

 aviFAIL = -1

 cMessage = 'VS_Rgn2K must not be negative.'

 ENDIF

 IF ( VS_Rgn2K*VS_RtGnSp*VS_RtGnSp > VS_RtPwr/VS_RtGnSp ) THEN

 aviFAIL = -1

 cMessage = 'VS_Rgn2K*VS_RtGnSp^2 must not be greater than VS_RtPwr/VS_RtGnSp.'

 ENDIF

 IF ( VS_MaxTq < VS_RtPwr/VS_RtGnSp ) THEN

 aviFAIL = -1

 cMessage = 'VS_RtPwr/VS_RtGnSp must not be greater than VS_MaxTq.'

 ENDIF

 IF ( PC_DT <= 0.0 ) THEN

 aviFAIL = -1

 cMessage = 'PC_DT must be greater than zero.'

 ENDIF

 IF ( PC_KI <= 0.0 ) THEN

 aviFAIL = -1

 cMessage = 'PC_KI must be greater than zero.'

 ENDIF

 IF ( PC_KK <= 0.0 ) THEN

 aviFAIL = -1

 cMessage = 'PC_KK must be greater than zero.'

 ENDIF

 IF ( PC_RefSpd <= 0.0 ) THEN

 aviFAIL = -1

 cMessage = 'PC_RefSpd must be greater than zero.'

 ENDIF

 

 IF ( PC_MaxRat <= 0.0 ) THEN

 aviFAIL = -1

 cMessage = 'PC_MaxRat must be greater than zero.'

 ENDIF

 IF ( PC_MinPit >= PC_MaxPit ) THEN

 aviFAIL = -1

 cMessage = 'PC_MinPit must be less than PC_MaxPit.'

 ENDIF

 ! If we're debugging the pitch controller, open the debug file and write the
60

 ! header:

 IF ( PC_DbgOut ) THEN

 OPEN ( UnDb, FILE=TRIM( cOutName )//'.dbg', STATUS='REPLACE' )

 WRITE (UnDb,'(/////)')

 WRITE (UnDb,'(A)') 'Time '//Tab//'ElapTime'//Tab//'HorWindV'//Tab//'GenSpeed'//Tab//'GenSpeedF'//Tab//'RelSpdErr'//Tab

 'SpdErr '//Tab//'IntSpdErr'//Tab//'GK '//Tab//'PitComP'//Tab//'PitComI'//Tab//'PitComT'//Tab// 

'PitRate1'//Tab//'PitCom1'

 WRITE (UnDb,'(A)') '(sec)'//Tab//'(sec) '//Tab//'(m/sec) '//Tab//'(rpm) '//Tab//'(rpm) '//Tab//'(%) '//Tab

 '(rad/s)'//Tab//'(rad) '//Tab//'(-)'//Tab//'(deg) '//Tab//'(deg) '//Tab//'(deg) '//Tab// 

 '(deg/s) '//Tab//'(deg) '

 ENDIF

 ! Initialize the SAVEd variables:

 ! NOTE: LastGenTrq, though SAVEd, is initialized in the torque controller

 ! below for simplicity, not here.

 GenSpeedF = GenSpeed ! This will ensure that generator speed filter will use the initial value of 

 PitCom = BlPitch ! This will ensure that the variable speed controller picks the correct contr

 GK = 1.0/( 1.0 + PitCom(1)/PC_KK ) ! This will ensure that the pitch angle is unchanged if the initial SpdErr is 

 IntSpdErr = PitCom(1)/( GK*PC_KI ) ! This will ensure that the pitch angle is unchanged if the initial SpdErr is 

 LastTime = Time ! This will ensure that generator speed filter will use the initial value of 

 LastTimePC = Time - PC_DT ! This will ensure that the pitch controller is called on the first pass 

 LastTimeVS = Time - VS_DT ! This will ensure that the torque controller is called on the first pass 

ENDIF

 ! Main control calculations:

IF ( ( iStatus >= 0 ) .AND. ( aviFAIL >= 0 ) ) THEN ! Only compute control calculations if no error has occured and we are 

 ! Abort if the user has not requested a pitch angle actuator (See Appendix A

 ! of Bladed User's Guide):

 IF ( NINT(avrSWAP(10)) /= 0 ) THEN ! .TRUE. if a pitch angle actuator hasn't been requested

 aviFAIL = -1

 cMessage = 'Pitch angle actuator not requested.'

 ENDIF 

 ! Set unused outputs to zero (See Appendix A of Bladed User's Guide):

 avrSWAP(36) = 0.0 ! Shaft brake status: 0=off

 avrSWAP(41) = 0.0 ! Demanded yaw actuator torque

 avrSWAP(46) = 0.0 ! Demanded pitch rate (Collective pitch)

 avrSWAP(48) = 0.0 ! Demanded nacelle yaw rate

 avrSWAP(65) = 0.0 ! Number of variables returned for logging

 avrSWAP(72) = 0.0 ! Generator startup resistance

 avrSWAP(79) = 0.0 ! Request for loads: 0=none

 avrSWAP(80) = 0.0 ! Variable slip current status

 avrSWAP(81) = 0.0 ! Variable slip current demand

!=======================================================================

 ! Filter the HSS (generator) speed measurement:

 ! NOTE: This is a very simple recursive, single-pole, low-pass filter with

 ! exponential smoothing.

 ! Update the coefficient in the recursive formula based on the elapsed time

 ! since the last call to the controller:

 Alpha = EXP( ( LastTime - Time )*CornerFreq )

 ! Apply the filter:

 GenSpeedF = ( 1.0 - Alpha )*GenSpeed + Alpha*GenSpeedF

!=======================================================================

 ! Variable-speed torque control:
61

 ! Compute the elapsed time since the last call to the controller:

 ElapTime = Time - LastTimeVS

 ! Only perform the control calculations if the elapsed time is greater than

 ! or equal to the communication interval of the torque controller:

 ! NOTE: Time is scaled by OnePlusEps to ensure that the contoller is called

 ! at every time step when VS_DT = DT, even in the presence of

 ! numerical precision errors.

 IF ( ( Time*OnePlusEps - LastTimeVS ) >= VS_DT ) THEN

 ! Compute the generator torque, which depends on which region we are in:

 IF ( ( GenSpeedF >= VS_RtGnSp ) .OR. ( PitCom(1) >= VS_Rgn3MP ) ) THEN ! We are in region 3 - power is constant

 GenTrq = VS_RtPwr/GenSpeedF

 ELSEIF ( GenSpeedF <= VS_CtInSp ) THEN ! We are in region 1 - torque is zero

 GenTrq = 0.0

 ELSEIF ( GenSpeedF < VS_Rgn2Sp ) THEN ! We are in region 1 1/2 - linear ramp in to

 GenTrq = VS_Slope15*( GenSpeedF - VS_CtInSp )

 ELSEIF ( GenSpeedF < VS_TrGnSp ) THEN ! We are in region 2 - optimal torque is pro

 GenTrq = VS_Rgn2K*GenSpeedF*GenSpeedF

 ELSE ! We are in region 2 1/2 - simple induction 

 GenTrq = VS_Slope25*( GenSpeedF - VS_SySp )

 ENDIF

 ! Saturate the commanded torque using the maximum torque limit:

 GenTrq = MIN( GenTrq , VS_MaxTq ) ! Saturate the command using the maximum torque limit

 ! Saturate the commanded torque using the torque rate limit:

 IF ( iStatus == 0 ) LastGenTrq = GenTrq ! Initialize the value of LastGenTrq on the first pass only

 TrqRate = ( GenTrq - LastGenTrq )/ElapTime ! Torque rate (unsaturated)

 TrqRate = MIN( MAX( TrqRate, -VS_MaxRat ), VS_MaxRat ) ! Saturate the torque rate using its maximum absolute value

 GenTrq = LastGenTrq + TrqRate*ElapTime ! Saturate the command using the torque rate limit

 ! Reset the values of LastTimeVS and LastGenTrq to the current values:

 LastTimeVS = Time

 LastGenTrq = GenTrq

 ENDIF

 ! Set the generator contactor status, avrSWAP(35), to main (high speed) 

 ! variable-speed generator, the torque override to yes, and command the

 ! generator torque (See Appendix A of Bladed User's Guide):

 avrSWAP(35) = 1.0 ! Generator contactor status: 1=main (high speed) variable-speed generator

 avrSWAP(56) = 0.0 ! Torque override: 0=yes

 avrSWAP(47) = LastGenTrq ! Demanded generator torque

!=======================================================================

 ! Pitch control:

 ! Compute the elapsed time since the last call to the controller:

 ElapTime = Time - LastTimePC

 ! Only perform the control calculations if the elapsed time is greater than

 ! or equal to the communication interval of the pitch controller:

 ! NOTE: Time is scaled by OnePlusEps to ensure that the contoller is called

 ! at every time step when PC_DT = DT, even in the presence of

 ! numerical precision errors.

 IF ( ( Time*OnePlusEps - LastTimePC ) >= PC_DT ) THEN

 ! Compute the gain scheduling correction factor based on the previously

 ! commanded pitch angle for blade 1:

 GK = 1.0/( 1.0 + PitCom(1)/PC_KK )
62

 ! Compute the current speed error and its integral w.r.t. time; saturate the

 ! integral term using the pitch angle limits:

 SpdErr = GenSpeedF - PC_RefSpd ! Current speed error

 IntSpdErr = IntSpdErr + SpdErr*ElapTime ! Current integral of speed error w.r.t. time

 IntSpdErr = MIN( MAX( IntSpdErr, PC_MinPit/( GK*PC_KI ) ), &

 PC_MaxPit/( GK*PC_KI ) ) ! Saturate the integral term using the pitch angle li

 ! Compute the pitch commands associated with the proportional and integral

 ! gains:

 PitComP = GK*PC_KP* SpdErr ! Proportional term

 PitComI = GK*PC_KI*IntSpdErr ! Integral term (saturated)

 ! Superimpose the individual commands to get the total pitch command;

 ! saturate the overall command using the pitch angle limits:

 PitComT = PitComP + PitComI ! Overall command (unsaturated)

 PitComT = MIN( MAX( PitComT, PC_MinPit ), PC_MaxPit ) ! Saturate the overall command using the pitch angle 

 ! Saturate the overall commanded pitch using the pitch rate limit:

 ! NOTE: Since the current pitch angle may be different for each blade

 ! (depending on the type of actuator implemented in the structural

 ! dynamics model), this pitch rate limit calculation and the

 ! resulting overall pitch angle command may be different for each

 ! blade.

 DO K = 1,NumBl ! Loop through all blades

 PitRate(K) = ( PitComT - BlPitch(K) )/ElapTime ! Pitch rate of blade K (unsaturated)

 PitRate(K) = MIN( MAX( PitRate(K), -PC_MaxRat ), PC_MaxRat ) ! Saturate the pitch rate of blade K using its maximu

 PitCom (K) = BlPitch(K) + PitRate(K)*ElapTime ! Saturate the overall command of blade K using the p

 ENDDO ! K - all blades

 ! Reset the value of LastTimePC to the current value:

 LastTimePC = Time

 ! Output debugging information if requested:

 IF ( PC_DbgOut ) WRITE (UnDb,FmtDat) Time, ElapTime, HorWindV, GenSpeed*RPS2RPM, GenSpeedF*RPS2RPM, &

 100.0*SpdErr/PC_RefSpd, SpdErr, IntSpdErr, GK, PitComP*R2D, PitComI*R2D, &

 PitComT*R2D, PitRate(1)*R2D, PitCom(1)*R2D

 ENDIF

 ! Set the pitch override to yes and command the pitch demanded from the last

 ! call to the controller (See Appendix A of Bladed User's Guide):

 avrSWAP(55) = 0.0 ! Pitch override: 0=yes

 avrSWAP(42) = PitCom(1) ! Use the command angles of all blades if using individual pitch

 avrSWAP(43) = PitCom(2) ! "

 avrSWAP(44) = PitCom(3) ! "

 avrSWAP(45) = PitCom(1) ! Use the command angle of blade 1 if using collective pitch

!=======================================================================

 ! Reset the value of LastTime to the current value:

 LastTime = Time

ENDIF

 ! Convert CHARACTER string to byte array for the return message:

DO I = 1,MIN( 256, NINT( avrSWAP(49) ) )

 avcMSG(I) = iMessage(I) ! Same as cMessage by EQUIVALENCE

ENDDO
63

RETURN

END SUBROUTINE DISCON

!=======================================================================
F1147-E(10/2008)

REPORT DOCUMENTATION PAGE Form Approved

OMB No. 0704-0188

The public reporting burden for this collection of information is estimated to average 1 hour per response, including the time for reviewing instructions, searching existing data sources, 

gathering and maintaining the data needed, and completing and reviewing the collection of information. Send comments regarding this burden estimate or any other aspect of this 

collection of information, including suggestions for reducing the burden, to Department of Defense, Executive Services and Communications Directorate (0704-0188). Respondents 

should be aware that notwithstanding any other provision of law, no person shall be subject to any penalty for failing to comply with a collection of information if it does not display a 

currently valid OMB control number.

PLEASE DO NOT RETURN YOUR FORM TO THE ABOVE ORGANIZATION.

1. REPORT DATE (DD-MM-YYYY)

February 2009

2. REPORT TYPE

technical report

3. DATES COVERED (From - To)

4. TITLE AND SUBTITLE

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

Development

5a. CONTRACT NUMBER

DE-AC36-08-GO28308

5b. GRANT NUMBER

5c. PROGRAM ELEMENT NUMBER

6. AUTHOR(S)

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

5d. PROJECT NUMBER

NREL/TP-500-38060

5e. TASK NUMBER

WER5.3301

5f. WORK UNIT NUMBER

7. PERFORMING ORGANIZATION NAME(S) AND ADDRESS(ES)

National Renewable Energy Laboratory

1617 Cole Blvd.

Golden, CO 80401-3393

8. PERFORMING ORGANIZATION

REPORT NUMBER

NREL/TP-500-38060

9. SPONSORING/MONITORING AGENCY NAME(S) AND ADDRESS(ES) 10. SPONSOR/MONITOR'S ACRONYM(S)

NREL

11. SPONSORING/MONITORING

AGENCY REPORT NUMBER

12. DISTRIBUTION AVAILABILITY STATEMENT

National Technical Information Service

U.S. Department of Commerce

5285 Port Royal Road

Springfield, VA 22161

13. SUPPLEMENTARY NOTES

14. ABSTRACT (Maximum 200 Words)

This report describes a three-bladed, upwind, variable-speed, variable blade-pitch-to-feather-controlled 

multimegawatt wind turbine model developed by NREL to support concept studies aimed at assessing offshore wind 

technology.

15. SUBJECT TERMS

offshore wind energy development; wind turbine design model; wind turbine specifications

16. SECURITY CLASSIFICATION OF: 17. LIMITATION 

OF ABSTRACT

UL

18. NUMBER 

OF PAGES

19a. NAME OF RESPONSIBLE PERSON

a. REPORT

Unclassified

b. ABSTRACT

Unclassified

c. THIS PAGE

Unclassified 19b. TELEPHONE NUMBER (Include area code)

Standard Form 298 (Rev. 8/98)

Prescribed by ANSI Std. Z39.18