sin αst

WIND TURBINE
DESIGN

Project: Wind Turbine Design – For Developing Countries
Project period: September 2010 - December 2010
Institution: Engineering College of Aarhus,
Supervisor: Hans Ole Nielsen
Department of Mechanical Engineering
Partner: Engineers Without Borders
Prepared by: ________________________________________
Jakob Vernersen
________________________________________
Søren Krag

ABSTRACT
At the request of the Engineers Without Borders the present project has been established
to facilitate the development of a wind turbine design that can be used in developing coun-
tries and potentially in disaster areas. The main objectives of the project are to determine
the most suitable wind turbine concept for use in developing countries and to develop a
wind turbine design, capable of producing 1500 W of generator power at a wind speed of
12 m/s. The work of the project is focused primarily on the mechanical and aerodynamic
design.
Through conceptualisation it is found that a horizontal-axis wind turbine is most suitable
for the present purpose. This concept thus forms the basis for the design proposal, which is
a three-bladed direct drive horizontal-axis wind turbine, with self-regulating capabilities
by means of a passive yaw orientation-system and a gravity-controlled furling system. The
technical specification of the wind turbine and associated engineering calculations are
documented in the form of the present project thesis and its attachments.
It is concluded that the proposed solution is viable for its purpose of producing electricity
in developing countries and that it is of considerable quality, as it meets the product de-
mands and wishes to a high degree. In closing remarks, several recommendations are
given with regards to the further development of the wind turbine design.

FOREWORD
The present project thesis has been prepared at the Engineering College of Aarhus (IHA)
from September 2010 to December 2010. The basis for the thesis has been established by
Engineers Without Borders (EWB) and its main intention is to facilitate the development
of a wind turbine design that can be used in developing countries. The target group of the
thesis is therefore mainly engineers at EWB and supervisors at IHA.
The structure of this thesis is in accordance with the guidelines provided by IHA and it is
thus divided into a main report accompanied by appendices, which include material that is
pertinent to the main report, but too detailed to be included in the main text. Secondary
documentation is provided as attachments in a separate binder and referenced in the main
report text.
Bibliographic references are structured according to a modified version the IEEE citation
style. In-text citations are given as a number enclosed in square brackets, frequently fol-
lowed by a page number, e.g. [1] or [26, p. 343]. Each citation corresponds to a numbered
reference in the bibliography, which contains detailed publication information about the
cited sources. Tables, figures and equations are numbered consecutively in each chapter,
i.e. so that figure 3.1 refers to figure 1 in chapter 3. Figures and tables without any source
reference are produced by the authors of this project thesis.
A nomenclature that defines the used terminology is provided at the end of the thesis
along with the bibliography and a list of attachments.
The writers would like to thank supervisor Hans Ole Nielsen (IHA) for his support and
encouragement during the project. Further acknowledgement goes to Nordic Folkecenter
for Renewable Energy, Søren Gundtoft (IHA) and Jesper Rost Villumsen (EWB).
Jakob Vernersen & Søren Krag
December 2010

CONTENTS
1 Introduction ........................................................................................................................................................ 1
1.1 Engineers Without Borders .................................................................................................................. 1
1.2 Past projects ................................................................................................................................................ 2
1.3 Present project ........................................................................................................................................... 4
2 Problem statement ........................................................................................................................................... 7
3 Methodology .................................................................................................................................................... 11
3.1 Calculation methods.............................................................................................................................. 14
4 Conceptualisation .......................................................................................................................................... 15
4.1 Terminology.............................................................................................................................................. 15
4.2 Survey of wind turbine concepts .................................................................................................... 17
4.2.1 Horizontal-axis wind turbines .................................................................................................. 19
4.2.2 Vertical-axis wind turbines ........................................................................................................ 21
4.2.3 Overview of wind turbine concepts ....................................................................................... 27
4.3 Evaluation .................................................................................................................................................. 28
4.4 Technical assessment ........................................................................................................................... 31
4.5 Principal solution ................................................................................................................................... 32
4.6 Summary .................................................................................................................................................... 34
5 Design presentation ...................................................................................................................................... 35
5.1 Summary .................................................................................................................................................... 40
6 Rotor .................................................................................................................................................................... 41
6.1 Number of blades ................................................................................................................................... 42
6.2 Blade design .............................................................................................................................................. 43
6.2.1 Material ............................................................................................................................................... 44
6.2.2 Airfoil and geometry ..................................................................................................................... 46
6.2.3 Manufacturing .................................................................................................................................. 52
6.2.4 Blade attachment ............................................................................................................................ 57
6.2.5 Structural calculations .................................................................................................................. 58
6.2.6 Alternative blade design .............................................................................................................. 58
6.3 Rotor performance ................................................................................................................................ 59
6.3.1 Annual energy production .......................................................................................................... 62

6.3.2 Self-starting capability ................................................................................................................. 64
6.4 Summary .................................................................................................................................................... 65
7 Generator and electrical system ............................................................................................................. 67
7.1 Generator ................................................................................................................................................... 67
7.2 Electrical system ..................................................................................................................................... 71
7.3 Summary .................................................................................................................................................... 74
8 Yaw and furling ............................................................................................................................................... 75
8.1 Yaw orientation system ....................................................................................................................... 75
8.2 Furling system ......................................................................................................................................... 80
8.3 Summary .................................................................................................................................................... 82
9 Tower .................................................................................................................................................................. 83
9.1 Tower options .......................................................................................................................................... 83
9.2 Design and height selection ............................................................................................................... 85
9.3 Tower design ............................................................................................................................................ 87
9.4 Installation ................................................................................................................................................. 89
9.5 Structural calculations ......................................................................................................................... 89
9.6 Summary .................................................................................................................................................... 90
10 Alternative blade design ............................................................................................................................. 91
10.1 Airfoil design .......................................................................................................................................... 92
10.2 Design evaluation ................................................................................................................................ 93
10.3 Summary .................................................................................................................................................. 94
11 Design evaluation .......................................................................................................................................... 95
11.1 Summary .................................................................................................................................................. 98
12 Further development ................................................................................................................................... 99
12.1 Summary ............................................................................................................................................... 101
13 Conclusion ...................................................................................................................................................... 103
14 Nomenclature ............................................................................................................................................... 105
15 Bibliography .................................................................................................................................................. 111
16 List of attachments ..................................................................................................................................... 115
A Basis for calculations................................................................................................................................. 119
A.1 Wind conditions ................................................................................................................................... 119
A.2 Other environmental conditions .................................................................................................. 121
A.3 Load cases ............................................................................................................................................... 122
A.4 Summary of loads ............................................................................................................................... 130
B Rotor theory .................................................................................................................................................. 131
B.1 BEM theory ............................................................................................................................................ 131
B.2 Optimum blade shape ....................................................................................................................... 135
C Rotor design tool ......................................................................................................................................... 139
D Airfoil ................................................................................................................................................................ 143
D.1 Profile shape .......................................................................................................................................... 146

E Structural analysis of blades .................................................................................................................. 147
E.1 Material description ........................................................................................................................... 147
E.2 Mechanical properties ...................................................................................................................... 150
E.3 Description of finite element model ........................................................................................... 152
E.4 Load case A ............................................................................................................................................. 156
E.5 Load case B ............................................................................................................................................. 160
E.6 Load case C ............................................................................................................................................. 164
E.7 Load case E ............................................................................................................................................. 167
E.8 Load case F ............................................................................................................................................. 171
E.9 Load case G ............................................................................................................................................. 174
E.10 Deflection analysis ........................................................................................................................... 178
E.11 Modal analysis .................................................................................................................................. 179
E.12 Longevity expectation .................................................................................................................... 180
E.13 Summary of analyses ...................................................................................................................... 182
F Blade attachment ........................................................................................................................................ 183
F.1 Dimensions ............................................................................................................................................. 187
G Structural verification of shaft .............................................................................................................. 189
H Tower analysis ............................................................................................................................................. 195
H.1 Load case G ............................................................................................................................................ 196
H.2 Flange assembly .................................................................................................................................. 198
H.3 Load case H ........................................................................................................................................... 200
I Furling and yaw analysis ......................................................................................................................... 201
I.1 Yaw system .............................................................................................................................................. 201
I.2 Furling mechanism .............................................................................................................................. 208
I.3 Bearing contact pressure .................................................................................................................. 210
J Alternative airfoil test ............................................................................................................................... 213
J.1 Purpose ..................................................................................................................................................... 213
J.2 Test equipment ...................................................................................................................................... 213
J.3 Test setup and preparations ........................................................................................................... 216
J.4 Test measurements ............................................................................................................................. 218
J.5 Data conversion and analysis ......................................................................................................... 218
K Compliance with IEC 61400-2 .............................................................................................................. 223

1
Introduction
This introductory chapter provides fundamental background information and describes
the scope and incentive for the present project.
1.1 Engineers Without Borders
The worldwide organisation Engineers Without Borders (EWB) is a technical humanitar-
ian organisation whose mission is to establish lifesaving arrangements, such as access to
drinking water, proper sanitation and emergency shelters to people in disaster affected
areas. This is mainly done by providing engineering experience and technical knowledge.
Even though the main focus of the organisation is on emergency relief a part of their mis-
sion is focused on improving long term living conditions. Thus the organisation helps with
general reconstruction, rebuilding roads and bridges, and installing solar electric lighting
or small scale wind turbines to produce electricity.
In the 1980s the first organisation within Engineers Without Borders was started in
France. At that time it was named Ingénieurs sans frontières (ISF). In the 1990s branches of
ISF were started in both Spain and Italy, and soon many other national branches followed.
Today EWB has more than 40 member groups worldwide. In 2004 Engineers Without
Borders – International (EWB-I) was started. The role of EWB-I is to enable cooperation
and exchange of information between its member groups. Several of the EWB and ISF
organisations are organised under EWB-I, but organisations that are not members of EWB-
I still collaborate with each other on occasion. The present report will not distinguish
thoroughly between the individual parts of the organisation and will often refer to them
simply as EWB.
The Danish branch of Engineers Without Borders (EWB-DK) was started in 2001 and it has
full membership of EWB-I. The EWB-DK organisation is a non-profit organisation that is
funded by contributions from public and private donators and from subscriptions from its
1

INTRODUCTION
members. Today EWB-DK comprises more than 500 members with 180 of them organised
in student chapters at four of the main Danish universities: Engineering College of Aarhus,
Aalborg University, University of Southern Denmark and Technical University of Denmark.
The purpose of the student chapters at the universities is to let the students contribute to
the projects with their engineering skills, as well as to develop their competences by let-
ting them identify and solve humanitarian problems of technical character.
This means that EWB-DK has three main focus areas:
2
� Emergency relief
� Development projects
� Student chapters
The Danish branch of EWB operates in close cooperation with most other Danish relief
organisations, e.g. Danish Red Cross and Danish Refugee Council, as well as universities
and private companies. Internationally EWB-DK collaborates with national branches of
EWB in Sierra Leone, India, Israel and Palestine at both a practical and an academic level.
1.2 Past projects
Recent examples of EWB-DK collaboration projects include:
� Re-housing 500 families in Haiti after the earthquake
� Establishing a school in Sierra Leone for children of war amputees
� Providing an engineer as team leader and site planner during the building of tem-
porary refugee camps in Southern Sudan
� Establishing solar and wind power supplies on the West Bank in Palestine
The latter example is a hybrid energy project where students from Aalborg University and
Engineering College of Aarhus collaborated with EWB-DK, the Israeli and Palestinian
branches of EWB, and the organisation COMET-ME (Community, Energy and Technology in
the Middle East). COMET-ME is a joint venture of Israeli and Palestinian communities.
Their mission is to facilitate social and economic empowerment in the most marginalised
and poorest communities in the occupied Palestinian territories. This is mainly done by
providing off-grid energy services in an environmentally and socially sustainable way.
The project was based in the beleaguered Palestinian community of Hareibat a Nabi, lo-
cated close to the Israeli border. The community’s roughly 60 permanent inhabitants make
their living by very traditional and non-mechanised agriculture and by herding goats and
sheep. Since its location is close to the border and due to the conflict between Palestine
and Israel, there are constant visits from the Israeli occupation administration to make
sure that nothing new is built. Moreover there is a constant presence of the Israeli army to
prevent Palestinian day-workers without a permit from crossing the border to Israel.

INTRODUCTION
There is no electrical power in the community even though there is a power grid line pass-
ing through the village as shown on figure 1.1.
Figure 1.1: Typical stone shed with a power line passing above it in the community of Harei-
bat a Nabi[1]
The collaborative project aimed to install a hybrid solar and wind power system in the
Southern Hebron Hills. The main purpose of the installation was to produce enough power
for an electrical butter churn to make butter from goat and sheep milk, as well as to sup-
port the power supply for three refrigerators that are used to store the dairy products that
villagers sell in nearby towns. Furthermore power was needed for indispensable basic
activities such as lighting, radio, television, running household appliances and charging
mobile phones.
Students from Aalborg University were involved in the preliminary part of the project
through a semester project, and afterwards travelled to the West Bank to help with the
practical installation of the system together with a student from Engineering College of
Aarhus.
The project result consists of 8 solar panels, each with a rated peak power of 135 W and a
wind turbine with a power output of 1 kW. Pictures of the installations are shown on figure
1.2.
3

INTRODUCTION
Figure 1.2: Left picture showing the erection of the wind turbine and the right picture show-
ing the installation of the solar panels in Hareibat a Nabi [1]
4
1.3 Present project
While the aforementioned hybrid energy project was initialised by EWB-DK, it is the Pales-
tinian/Israeli organisation COMET-ME that owns both the project and the installed equip-
ment. The present project has therefore been established by EWB-DK with the intention to
facilitate the development of an independent wind turbine design that can be used in de-
veloping countries, other than Palestine, and potentially in disaster areas.
Having a self-developed wind turbine will result in high flexibility compared to using ei-
ther an existing commercial solution or another non-profit design that is readily available.
It will render it possible to modify details of the wind turbine design according to the exist-
ing local technology level, including available manufacturing processes and obtainable
parts and materials. This greatly improves the possibility of servicing the wind turbines
locally. The development will furthermore increase the general knowledge of wind tur-
bines within the EWB organisation, making it possible to better educate local populations
in building and maintaining wind turbines. Thus it will also entail a potential for setting up
wind turbines in foreign destinations where import of technological equipment is prohib-
ited by legislation.
The need for small scale wind turbines is emphasised by the fact that 1.5 billion people, or
22% of the world population, are without access to electricity [2]. As shown on figure 1.3
the majority of the population without electricity is located in Africa and South Asia.

INTRODUCTION
Figure 1.3: Vertical axis showing percentage of the population with access to electricity (electri-
fication ratio) and horizontal axis indicating the number of people without access to electricity [2]
Approximately 85% of these people live in rural areas, which will be the key target of the
EWB wind turbines. It is expected that the units primarily will be used for charging batter-
ies that will power e.g. refrigeration, lighting and mobile phones. In Nigeria, for example,
the current per capita energy consumption is below 200 kWh annually [3]. Given 8760
hours per year and 50% availability a 100 W wind turbine would provide the required
power for 2 people. While this analysis is simplistic, it shows the impact that small scale
electrification projects can have in Africa [4].
The initial objective of the present project is to establish which wind turbine concept is
most suitable when taking into account the requirements specified by EWB-DK. With this
accomplished, the objective is to develop an overall wind turbine design with a power
output of 1500 W at a wind speed of 12 m/s. The detailed requirements for the listed ob-
jectives are elaborated in the following chapter, containing the problem statement of the
project.
5

INTRODUCTION
6

2
Problem statement
This chapter presents the results of the problem analysis that has been performed in the
early stages of the project. The objective of the problem analysis is to clearly elaborate the
project goals and the circumstances under which they have to be met.
The two overall goals of the project are described below.
� Selection of wind turbine concept
While it is not the intention of this project to develop a new method of harvesting wind
energy, it is however imperative for it to establish which existing wind turbine type is most
suitable for the present purpose, as this will constitute the basis of the further develop-
ment. There exist several types of wind turbine systems that can be classified according to
aerodynamic and mechanical characteristics. Selection of the most suitable type is to be
achieved by evaluation of each concept’s accommodation to the wishes of the requirement
specification and a general technical assessment of the concepts.
� Wind turbine design
The selected concept is to be developed into a wind turbine that is capable of producing
1500 W of generator power at a wind speed of 12 m/s. Focus is placed on the overall de-
sign of the wind turbine with significant emphasis on mechanical components and aerody-
namic analysis.
The wind turbine design should be producible at a typical local technological level, making
it possible to manufacture it in the majority of the rural areas that EWB operates in. It can
be assumed that conventional manufacturing processes such as milling, turning, drilling,
grinding and welding are available in close vicinity. In areas where this is not the case EWB
will provide the necessary facilities or ultimately bring manufactured components, al-
though this will minimise the local involvement. The intended wind turbine is flexible in
the sense that details of the construction can be easily modified in future design variants.
E.g. it is preferred that complex blades can be manufactured from different materials and
that the mechanical fastening techniques and design will allow for the wind turbine to be
7

PROBLEM STATEMENT
reconfigured with different types of blades and towers. This is considered vital as the
component and material availability in developing countries varies.
The above mentioned considerations to manufacturability and flexibility are to be made
without neglecting the overall quality of the proposed wind turbine, as it will function as a
fundamental design platform from which locally matched design variants may be created.
Further elaboration of the project goals is accomplished by translating the wishes and
needs of EWB into product requirements and subsequently compiling them in a require-
ment list. This thus represents the specification against which the success of the project
can be judged. The resulting product requirements are identified either as demands or
wishes. Demands are defined as requirements that must be met under all circumstances. In
other words, if any of these requirements are not fulfilled the solution is unacceptable.
Wishes are requirements that are to be taken into consideration whenever possible, thus
describing the quality of the solution. The demands are quantified to the extent that it is
possible, while wishes primarily are relative parameters, defined in the clearest possible
terms, and used as evaluation criteria in the conceptual phase. Both the quantitative and
qualitative requirements are tabulated in table 2.1 below.
8
ID D/W Requirements
Electrical / Performance requirements
1 D 1500 W ± 1% nominal power output from the generator a
2 D 48 V DC system voltage
Manufacturing requirements
3 W Ability to manufacture the wind turbine locally using standard operations b
4 W Flexibility in choice of blade materials
5 W Low manufacturing tolerance demands
6 W Low-cost materials and parts
Normative requirements
7 D Compliance with selected parts of IEC 61400-2 c
Service requirements
8 W Ability to perform localised maintenance
9 W Low maintenance requirements and high life expectancy
Design requirements
10 W Flexibility for reconfiguration with different components
11 D Ability to install wind turbine manually, i.e. without a crane
a) Under the conditions defined in appendix B.1 and using the generator specified in chapter 7
b) Milling, turning, drilling, grinding and welding
c) See appendix K for elaboration of the relevant parts of IEC 61400-2
Table 2.1: Requirement list containing demands and wishes for the wind turbine design

PROBLEM STATEMENT
The required compliance with selected parts of the international standard IEC 61400-2 [5],
comprises numerous additional design requirements for the wind turbine. The standard
deals with safety, quality assurance and engineering integrity for small wind turbines,
including design, calculation, installation, maintenance and operation under specified ex-
ternal conditions. The list of relevant standardised requirements is extensive and there-
fore not fully elaborated in this project thesis. Appendix K provides a summary of the
normative requirements and the extent to which they are met.
The major deliverables of this project include:
� The present project thesis containing justification for the chosen wind turbine
type and a technical description of the developed wind turbine design
� Verification of the structural integrity of key components
� Aerodynamic analyses
� Complete 3D model of wind turbine
The limits and exclusions of the deliverables are specified in section 4.5, which follows the
selection of wind turbine concept.
The present project is expected to be a platform for several future projects, which treat the
design subjects that are beyond its limits and exclusions. It should therefore define the
tasks that are necessary to fully complete the developed wind turbine design, as well as
relevant spin-off projects that may be carried out within the framework of EWB.
9

PROBLEM STATEMENT
10

3
Methodology
The purpose of this methodology chapter is to describe the methods by which the project
is approached and to clarify the overall structure of this project thesis.
To achieve an efficient product development process, this project thesis uses a systematic
engineering procedure based on VDI 2221 - Systematic approach to the development and
design of technical systems and products [6]. It is empirically shown that this systematic
approach provides an effective and problem-directed approach to design, which facilitates
and rationalises the establishment of optimum solutions [7, p. 10]. The guideline, devel-
oped by the Association of German Engineers (VDI), proposes a generic approach to the
design of technical systems and products. It aims for general applicability and has there-
fore been modified for the specific tasks of this project thesis.
Figure 3.1 shows the phases of the development process and the key results of each phase.
The detailed working procedures of each phase, including strategies and principles, are not
listed here. Special emphasis is placed on the iterative nature of the approach, and the
sequence of steps that is not to be considered rigid [7, p. 10].
11

METHODOLOGY
Figure 3.1: Flow chart showing the phases of the development process and the key results of
each phase
Each of the phases is documented in specific chapters of the present project thesis. Table
3.1 below links the phases and chapters, and provides a brief description of their contents.
12
Phase Chapter Description
I
II
1, 2
4
The main purpose of the preliminary phase is to clarify the objec-
tives of the project and the circumstances under which they are
met.
Chapter 1 describes the remote background and incentive for the
project, while chapter 2 elaborates the project goals. Chapter 2 also
contains the requirement list (specification) which is the main re-
sult of the task clarification phase.
In this project the key intention of the conceptual phase is to select
the most suitable existing wind turbine type for the present pur-
pose. VDI Guideline 2222-1 [8], which defines individual methods
for the conceptual design of technical products, is used in the selec-
tion process. The conceptualisation results in the specification of a
principal solution (concept), thus meeting the first project objec-
tive, established in the task clarification phase.

III 6-9
IV 5-9
METHODOLOGY
Chapter 4 describes various wind turbine types and documents the
selection process that leads to a principal solution. It also defines
important terminology that is necessary to comprehend basic wind
turbine characteristics.
The embodiment design phase involves further development of the
relatively abstract concept from phase II into a more concrete de-
sign proposal. The overall layout of the wind turbine is determined,
including arrangement of assemblies, components and their rela-
tive motions. Estimated dimensions, shapes and materials of indi-
vidual parts are established along with production processes.
The main result of the embodiment design is a preliminary layout
that is optimised and finalised in the detail phase. The documenta-
tion of this project thesis primarily focuses on the definite layout of
the wind turbine, but design decisions of the embodiment phase are
generally accounted for in the listed chapters.
For this project the detail design phase is the part of the develop-
ment process, which completes the embodiment of the wind tur-
bine, and thereby meets the second project objective.
The detail design phase overlaps considerably with the embodi-
ment design phase and involves e.g. definitive calculations, analyses
and documentation.
Chapter 5 provides an overall presentation of the wind turbine,
while the following chapters treat key components in greater detail.
Table 3.1: Coherence between development phases and chapters of the project thesis
The indicated further realisation on figure 3.1 refers to typical, mandatory parts of the
development process that are excluded from the present project. This comprises detailed
2D drawing of all components, specification of surfaces, tolerances and fits, as well as
preparation of part lists, manuals and instructions.
13

METHODOLOGY
14
3.1 Calculation methods
The basis for the calculations of this project is presented in appendix A, which contains the
definition of essential parameters, including:
� Environmental data
Temperature, humidity, air density
� Wind conditions
Speed, distribution
� Load cases
Based on the most significant operating or fault conditions which the turbine may
experience
Aerodynamic calculations are based on the environmental characteristics and the wind
conditions. The load cases are established in accordance with IEC 61400-2 and take into
account static and dynamic loads on the wind turbine resulting from e.g. inertia, vibration,
rotation and gyroscopic effect. The subsequent structural analyses use recognised meth-
ods, described in standards such as ISO 2394 and EN 1993 (Eurocode 3), to verify the
structural integrity of the wind turbine design, analytically and numerically.
The nomenclature in chapter 14 defines the symbols, subscripts, abbreviated terms and
graphical representations used throughout this project thesis.

4
Conceptualisation
This chapter begins with the definition of important terminology that is necessary to com-
prehend prior to reading the subsequent description of numerous different wind turbines
and their properties. The chapter continues with a systematic evaluation and technical
assessment of several wind turbine candidates and concludes with the selection of the
most suitable type of wind turbine.
4.1 Terminology
The following sections of this project thesis use several terms and expressions that are
mainly utilised within the field of wind turbine technology. With reference to making the
following sections more comprehendible to engineers without a background in wind tur-
bine technology, the present section gives a brief introduction to basic wind turbine theory
and defines significant terminology.
� Wind and wind power
The phenomenon wind is caused by movement of the air between low pressure and high
pressure regions. These regions arise due to uneven heating of the earth’s surface by the
sun. The air above a hot surface rises when it is heated and creates a low pressure zone.
The surrounding cold air flows towards the low pressure region and thus creates wind. For
the same reason wind energy is sometimes called indirect solar energy. Wind varies in
both intensity and direction as a function of time and it is greatly affected by factors such
as ground features and altitude [9, p. 1].
Distinction is generally made between the terms wind turbine and windmill. When the
energy is used directly for e.g. grinding, cutting and pumping, the machine is called a
windmill. When the energy is converted into electrical energy, the machine is called a wind
turbine [10, p. 57]. This project thesis will focus primarily on wind turbines, which harvest
15

CONCEPTUALISATION
the kinetic wind energy, transform it into mechanical energy in a shaft and finally into
electrical energy in a generator.
The maximum available power in the wind can be obtained if theoretically the wind speed
after the rotor is reduced to zero: Pmax,theo = ½ρAV 3 , where ρ is the air density, V is the wind
speed and A is the area where the wind speed is reduced [11, p. 3]. For a typical horizontal-
axis wind turbine the area is equal to the swept rotor area, without subtraction of the hub
area, as indicated on figure 4.1.
16
Figure 4.1: Swept rotor area of horizontal-axis wind turbine [11, p. 4]
In practice it is not possible to reduce the speed of the wind after the rotor to zero using a
wind turbine, so a power coefficient Cp is added to the before mentioned theoretical equa-
tion: Pmax = Cp½ρAV 3 . The power coefficient thus represents the ratio between the actual
power obtained and the maximum available power. It can also be seen as a parameter
indicating the size of the wind turbine, as a lower Cp will require a larger swept rotor area
to provide a given power output. The theoretical maximum for Cp is denoted the Betz limit
and is equal to 16/27 (or 0.593) [11, p. 4]. To this date there has not been designed any
wind turbine capable of exceeding this limit, which is named after the German aerody-
namicist, Albert Betz [3, p. 45].
� Lift and drag
When a body is exposed to an air flow it experiences an aerodynamic force. The force is
caused by pressure on the surface of the body and by viscous friction between the air and
the boundary layer around the object. The aerodynamic force that is in the direction of the
wind is called drag. When a streamlined body, such as an airfoil, is exposed to an air flow it
experiences a more complex resulting aerodynamic force that may be decomposed into
two components:
� Drag - The component parallel to the direction of the air flow
� Lift - The component perpendicular to the direction of the air flow
This is illustrated on figure 4.2, showing the forces and the moment that act on an airfoil
subjected to a two-dimensional flow [11, p. 6].
�
A�D 4
2

CONCEPTUALISATION
Figure 4.2: The forces and the moment acting on an airfoil subjected to a 2D air flow [12, p.
103]
The flow velocity on the convex upper surface of the airfoil is increased, creating a low
pressure zone above the airfoil in accordance with Bernoulli’s principle. This results in the
lift force that is perpendicular to the direction of the oncoming airflow. Both the lift force
and the drag force are considered acting on the chord line, ¼ of the chord length from the
leading edge. To describe the forces completely it is additionally necessary to identify the
pitching moment, which is generally placed at the same reference point as the force com-
ponents [11, p. 6].
Tip-speed ratio
The term tip-speed ratio (TSR) is defined as the ratio: � = Ut/V, where Ut is the tangential
velocity of the rotor blade tip and V the velocity of the wind. The tip-speed ratio is related
to the power coefficient that has an optimum at a specific TSR. For a drag-based device the
TSR will never exceed a value of 1, but it is higher for a lift-based device. [10, p. 69]
4.2 Survey of wind turbine concepts
This section contains a survey of numerous different wind turbines and their key proper-
ties. The survey focuses on the most prevailing types of wind turbines that have the poten-
tial of being used in rural areas. This means that so called fantasy turbines or
unconventional turbines that have not been effectively proven in practice are left out of the
survey. Examples include diffuser-augmented wind turbines (DAWT) and airborne wind
turbines, both shown on figure 4.3.
17

CONCEPTUALISATION
Figure 4.3: (a) Diffuser-augmented wind turbine [13] and (b) airborne wind turbine [14]
The field of small wind turbines is characterised by experience-based and poorly docu-
mented knowledge, which is often contradictory and ambiguous. This survey therefore
strives to use only reliable academic sources and books by recognised authors. Moreover
collaboration with Nordic Folkecenter for Renewable Energy has been established to fur-
ther secure the quality of the survey. The Nordic Folkecenter is a non-profit organisation
that provides research, development of technology and training within the field of renew-
able energy technologies in Denmark and throughout the world. The organisation has been
involved in several projects committed to implementing renewable energy sources in de-
veloping countries and therefore have a great deal of experience that is relevant to the
present wind turbine project.
The following subsections contain descriptions of numerous wind turbine concepts that
have been categorised by their axis of rotation.
18
(a) (b)

4.2.1 Horizontal-axis wind turbines
CONCEPTUALISATION
Horizontal-axis wind machines have been known since the 10th century. Some of the earli-
est types were windmills, fixed permanently to face costal winds and used to grind cereals.
Later followed more versatile mills that functioned as sawmills, threshing mills and as
wind pumps, used for land drainage and for water supply. Several historical horizontal-
axis wind mills are shown on figure 4.4 [10, p. 1-13].
(a) (b) (c)
Figure 4.4: (a) Dutch windmill, (b) American wind pump and (c) Thai wind pump [15]
Today horizontal-axis wind turbines (HAWT), which produce electricity, are the most
commonly available wind machines. In fact all presently grid connected commercial wind
turbines are of this type [16, p. 2]. Figure 4.5 shows a modern commercial offshore wind
turbine and a small commercial household wind turbine.
Figure 4.5: On the left a 3 MW Vestas offshore wind turbine at Kentish Flats Offshore Wind
Farm [17]. On the right a 160 W battery charging small wind turbine [18]
The common denominator for modern HAWTs is that the rotor, shaft and generator are
mounted on the top of a vertical tower. Distinction is made between downwind and up-
wind rotors, see figure 4.6. Upwind rotors face the direction of wind and thereby avoid the
shade effect of the tower that exists on downwind rotors, which is known to create fatigue
19

CONCEPTUALISATION
issues due to turbulence. A yaw mechanism is needed to keep upwind rotors aligned with
the wind direction, while downwind rotors are self-aligning. The majority of HAWTs use
the upwind rotor design [12, p. 3].
Figure 4.6: Upwind and downwind rotors [19, p. 18]
HAWTs are equipped with a power control system that wastes excess energy to avoid
damage of the wind turbine in case of strong winds. Large commercial wind turbines use
either stall or pitch control. The latter involves pitching the blades slightly out of the wind
to reduce the power output. Stall control typically involves limiting the power output by
designing the geometry of the rotor blades so that flow separation is created on the down-
side of the blade when a critical wind speed is exceeded [16, p. 3-4]. Small wind turbines
often use a simple furling mechanism that will both limit the power production and func-
tion as a yaw system.
The power coefficient of horizontal-axis drag-based windmills is 0.3 at the most, while
modern lift-based HAWTs can achieve a Cp value of more than 0.5 [10, p. 78].
HAWTs are widely used for projects in developing countries. In the 1980s the
Nordic Folkecenter for Renewable Energy developed both windmills and wind turbines for
battery charging. The wind turbine used in the hybrid energy project, mentioned in section
1.2, is also of the horizontal-axis type. Pioneers within the field of small wind turbines for
developing countries, such as Hugh Piggott, advocate the use of HAWTs due to their high
power efficiency and technical superiority compared to other wind turbine concepts [20].
20
Upwind Downwind

4.2.2 Vertical-axis wind turbines
CONCEPTUALISATION
The first practical wind machines were vertical-axis windmills, invented in eastern Persia
in the 9th century. They had a number of struts on which sails, made from bundles of
reeds, were mounted, as shown on figure 4.7 [21, p. 54].
Figure 4.7: Vertical-axis windmill with sails from the 9th century [22]
In modern times several different vertical-axis wind turbines (VAWT) have been devel-
oped. The general advantages of the different types are that mechanical and electrical
components, such as gearbox and generator, can be installed close to the ground. This
provides a more economical tower design and makes maintenance easier. Additionally the
VAWTs are omnidirectional, meaning that they can receive wind from any direction, and
therefore do not need a yaw mechanism. The disadvantages of most VAWTs are that they
are not self-starting and therefore require an external starting mechanism. They may also
require a controlling mechanism to avoid dangerously high speeds that may cause system
failure [19, p. 19-20].
The efficiency of VAWTs is generally lower than that of HAWTs as the rotor blades pass
through aerodynamic dead zones during their rotation, see figure 4.8.
21

CONCEPTUALISATION
22
Figure 4.8: Typical vertical-axis wind turbine viewed from top [9, p. 4]
The rotation pattern of the VAWT causes the stress in each blade to change sign during the
rotation, increasing the stress range and thereby also the likelihood of blade failure by
fatigue.
Many of the unconventional turbines mentioned in section 4.2 are based on the vertical-
axis theme. The following descriptions focus on prevalent and proven subtypes of VAWTs
that are available in numerous variants. The main subtypes are:
� Savonius
� Darrieus
� Giromill
� Savonius
The Savonius turbine, named after its Finnish inventor, is among the simplest turbines. It is
an aerodynamic drag-type device that consists of two or three curved scoops (blades).
Looking down on the rotor from above, a two-scoop machine looks like an "S- shape” in
cross-section, as shown on figure 4.9 [19, p. 20].

Figure 4.9: Savonius wind turbine [10, p. 46]
CONCEPTUALISATION
Since the turbine is a drag-type device, its power coefficient is limited to about 0.15 when
the design is fully optimised. Moreover it is not efficient with respect to the ratio
weight/unit power output, as it requires a much larger surface area to output the same
amount of power as a HAWT [9, p. 17]. For this reason the Savonius turbine is only practi-
cal and economical when the power requirement is relatively low.
The technology required to manufacture Savonius turbines is very simple and they are
generally recommended for use in developing countries, and where cost or reliability is
more important than efficiency. For example most anemometers, used for measuring wind
speed, are Savonius turbines because efficiency is not an important factor for these appli-
cations. A simple version of a Savonius rotor may be manufactured by cutting an oil barrel
in half, inverting one of the halves, and welding the pieces together in an “S-shaped” cross-
section [9, p. 17]. Figure 4.10 shows a Savonius construction consisting of three stacked
rotors in a welded frame.
23

CONCEPTUALISATION
� Darrieus
24
Figure 4.10: Stacked Savonius rotor in a welded frame [20]
In 1925 the French engineer Darrieus proposed a new type of a VAWT with blades shaped
in a so-called troposkien pattern, as shown on figure 4.11 [10, p. 46]. The Darrieus rotor is
typically built with two or three blades, as in the case of horizontal-axis rotors. For obvious
reasons the original version of the Darrieus turbine is often referred to as the egg beater.
Figure 4.11: Original Darrieus wind turbine [10, p. 46]
The Darrieus vertical-axis design effectively utilises aerodynamic lift, making it possible to
achieve a power coefficient of more than 0.4 under ideal conditions [23, p. 106].

CONCEPTUALISATION
The combination of complex geometry and airfoils make the Darrieus turbine moderately
difficult to manufacture. In addition to the previously described pulsating loads, many
Darrieus designs have resonant modes at particular occurring rotational speeds, which
make the blades prone to structural fatigue problems [9, p. 4]. Another key disadvantage of
the classic Darrieus design is that the rotor is unable to start itself due to a low starting
torque and therefore requires external excitation. Both active and passive solutions to the
problem have been developed, but none of them have been proven beyond the research
stage [24].
Both the self-starting and the fatigue issues are improved when using a helical version of
the Darrieus turbine, see figure 4.12.
Figure 4.12: Helical Darrieus wind turbine [25]
Using a helical twist of 60 degrees has shown to spread the torque evenly over the entire
revolution, thus preventing destructive pulsations and furthermore enabling self-start of
the rotor [26, p. 94]. The helical version is commonly used in urban settings due to its ap-
pealing aesthetics and proclaimed low noise [59].
� Giromill
The patent that Darrieus filed in 1927 also covered other possible arrangements using
vertical airfoils. One of these is the Giromill or H-rotor that can be seen on figure 4.13.
25

CONCEPTUALISATION
26
Figure 4.13: Giromill with straight vertical airfoils [10, p. 46]
In this design the troposkien blades are replaced by straight vertical blade sections at-
tached to the central tower with horizontal supports. The Giromill design is simpler to
manufacture than the Darrieus since the blades do not need to be curved. Furthermore it
has more swept area than the Darrieus at the same height and diameter, thus generating a
higher power output [23, p. 87-88].
An augmented version of the Giromill is the Cycloturbine in which the blades are mounted
so that they can rotate about their vertical axis. A great advantage to this design is that the
rotor is able to self-start by pitching the downwind blades to generate a drag that will start
the rotor spinning. This construction requires a pitching mechanism, either active or pas-
sive, which inherently makes the design more complex. The efficiency of the Giromill and
Cycloturbine is approximately the same as the efficiency of the original Darrieus turbine.
The fatigue issues of the original Darrieus design exist in both the Giromill and the Cyclo-
turbine version.

4.2.3 Overview of wind turbine concepts
CONCEPTUALISATION
The main properties of the described wind turbine concepts are summarised in table 4.1
below.
Concept Properties
HAWT - Aerodynamic lift-device (drag design is possible)
- Commonly used in developing countries
- Proven design
Savonius - Simple design
- Design with the best power coefficient
- Drag-device
- Commonly used in developing countries
- Low power coefficient
Darrieus - Aerodynamic lift-device
- Complex blade geometry (troposkien shape)
- Unable to self-start (non-helical)
- Prone to structural and resonant fatigue issues (non-helical)
Giromill - Aerodynamic lift-device
- Straight blade design
- Cycloturbine design able to self-start
- Prone to fatigue issues
Table 4.1: Main properties of wind turbines in survey
The range of performance coefficients for the various wind turbine types is illustrated on
figure 4.14 as a function of tip-speed ratio.
27

CONCEPTUALISATION
Figure 4.14: Power coefficient as a function of tip-speed ratio for several wind turbine con-
cepts [10, p. 79]
A systematic evaluation of the concepts is carried out in the following section, which is
followed by a technical assessment in section 4.4.
28
4.3 Evaluation
All of the wind turbine concepts, described in the previous section, will theoretically fulfil
the demands of the requirement specification and thus provide a functioning solution for
the present purpose. Prior to assessing the quality of the concepts by evaluation it has
been decided to eliminate concepts without a proven self-starting mechanism, as lack of
such will render the solutions useless in practice. This means that the following wind tur-
bine concepts are selected for further evaluation:
� HAWT
� Cycloturbine
� Savonius
� Helical Darrieus
The selected wind turbine concepts are evaluated with reference to the wishes of the re-
quirement specification, table 2.1. The evaluation criteria are compiled in a decision-
matrix that enables a comparative and multi-dimensional analysis of the wind turbine

CONCEPTUALISATION
concepts. This approach assists in making subjective opinions, about one alternative solu-
tion versus another, more objective. The evaluation criteria do not vary markedly in im-
portance and they are thus not weighted in the conceptual phase. This is in accordance
with the recommendations of VDI Guideline 2225 [27] that suggests omitting the use of
weighting factors due to the fairly low level of information in this early development stage
[7, p. 194].
Each solution’s compliance to the evaluation criteria is rated on a 0-4 scale that is elabo-
rated on figure 4.15. Points 0 and 4 are only awarded if the solution characteristics are
excessive, that is, unsatisfactory or very good (ideal).
Pts. Meaning
0
Unsatisfactory
1 Just tolerable
2 Adequate
3 Good
4 Very good (ideal)
Figure 4.15: Meaning of the evaluation points (as recommended in VDI Guideline 2225) [27]
The qualitative evaluation criteria, adopted from the requirement specification, are listed
and rated for each wind turbine variant in table 4.2.
29

CONCEPTUALISATION
30
ID Requirement
3 Ability to manufacture the wind turbine locally using
standard operations
HAWT
Cyclo.
3 3 4 1
4 Flexibility in choice of blade materials 4 3 4 a 1
5 Low manufacturing tolerance demands 3 3 4 2
6 Low-cost materials and parts 3 3 4 2
8 Ability to perform localised maintenance 3 3 3 3
9 Low maintenance requirements and high life expectancy 4 1 3 b 3
10 Flexibility for reconfiguration with different components 4 4 4 3
24 20 26 15
a) The flexibility in choice of materials is less than that of the HAWT, but it is not considered as a disadvan-
tage due to the simplicity of the Savonius structure and due to the availability of e.g. oil barrels.
b) Due to the pulsating loads it is presumed that the Savonius is more prone to fatigue issues than the
HAWT.
Table 4.2: Decision-matrix with evaluation criteria and their rating for each wind turbine
concept
The following two-dimensional radar charts below provides an illustrative overview of the
multivariable data of table 4.2.
Figure 4.16: Graphical representation of the decision-matrix results
Savonius
Helical

CONCEPTUALISATION
From table 4.2 and figure 4.16 it is evident that the HAWT and the Savonius wind turbine
are the front-runner candidates when taking into consideration the relative evaluation
criteria. With a rating of 26 points the Savonius wind turbine is the quantitatively most
suitable concept, but it must be emphasised that the applied evaluation methods are mere
tools and not automatic decision mechanisms without uncertainties. In the next section the
two best candidates are therefore subjected to a technical assessment that explores further
aspects of the concepts than those used in the evaluation.
4.4 Technical assessment
The HAWT design is already widely used in developing countries and is a proven, reliable
and efficient concept for electrical production in the 1500 W size. The Savonius rotor on
the other hand has a less effective, but very simple and reliable design that can be built
from very basic components such as oil barrels. It is also commonly used in rural areas,
although usually in the power range of 200-500 W, which is less than needed for the pre-
sent project. If it is possible to scale the Savonius concept to the needed size it may prove
to be the most suitable candidate due to its simplicity.
Assuming a power coefficient Cp of 0.15 and an overall efficiency �tot of 45% for mechanical
components, generator and any possible transmission, it is possible to calculate the re-
quired swept rotor area of a Savonius rotor required to produce 1500 W power output at
wind speed V of 12 m/s (cf. table 2.1). The density � used in (4.1) is 1.225 kg/m 3 in accor-
dance with appendix A.2.
In comparison a lift-based HAWT with a Cp of 0.35 requires a swept area of only 9 m 2 (57%
less than the Savonius) under the same conditions. This is equivalent to a blade length of
approximately 1.7 m.
P
Asav 1
Cp 2 � V3 21 m
�tot 2
�
�
A 200-litre oil barrel sliced in half and welded in an S-shape has a swept area (cross-
sectional area) of 0.9 m 2 , which means that at least 23 oil barrels are needed to provide the
necessary swept rotor area. A similar sized structure is reached when using e.g. bend sheet
metal instead of oil barrels. This makes the Savonius wind turbine very impractical and
difficult to handle. Moreover it may actually produce less energy annually compared to a
HAWT, as it is placed by the ground where the wind speeds are lower due to surface drag.
Although the Savonius wind turbine satisfies both the demands of the requirement specifi-
cation and the evaluation criteria to a great extend, it must be considered unsuitable for
the present purpose. This is primarily due to the required size of the structure and its po-
tentially low annual energy production. The HAWT concept is therefore adopted as the
(4.1)
31

CONCEPTUALISATION
most suitable solution for the present purpose. The lift-based version is chosen due its
superior performance and its applicability for production of electricity.
32
4.5 Principal solution
The principal solution is a horizontal-axis wind turbine containing the subsystems shown
on figure 4.17.
R
o
t
o
r
Hub
Figure 4.17: Major components of the principal solution
The following paragraphs contain a brief description of each subsystem. It also identifies
the associated focal points, limitations and exclusions of the development phases that
follow the present conceptual phase. These are in accordance with the prioritisations of
EWB and the available project resources.
Control
Drive train Generator
Yaw system
T
o
w
e
r
Foundation
Nacelle
Electrical
system

Rotor and hub
CONCEPTUALISATION
The rotor consists of the blades and the hub of the wind turbine. These may well be con-
sidered the most important components of the turbine from both a performance and cost
perspective. This project thesis will focus on selection of blade material, mechanical de-
sign, manufacturing methods, as well as structural and aerodynamic analysis.
Drive train and generator
The drive train is the collective designation for the other rotating parts of the wind turbine.
It usually consists of a transmission, a generator, one or more shafts and bearings that are
all placed in a cover housing, commonly referred to as the nacelle. This project deals with
the mechanical design and dimensioning of the core drive train components, taking into
account the unique loading of the wind turbine. The generator is only treated peripherally.
Controls
The control system for a large commercial wind turbine includes wide range of controls
[12, p. 6]:
� Sensors – speed, position, flow, temperature, current, voltage etc.
� Power amplifiers – switches, electrical amplifiers, pumps and valves
� Actuators – motors, pistons, magnets and solenoids
� Controllers - mechanical mechanisms, electrical circuits
� Intelligence – computers and microprocessors
Generally these need to be avoided or reduced to a minimum for the present small wind
turbine that is to be used in developing countries. Relevant components will be treated to
the extent that it is necessary with focus on mechanical mechanisms.
Electrical system
The electrical system of the small wind turbine includes, but is not limited to, cables, trans-
formers, power converters and batteries. These will only the covered peripherally in this
project thesis, as emphasis is placed on mechanical and aerodynamic design.
Yaw system and nacelle
A yaw orientation system is required to keep the rotor properly aligned with the wind. The
design and dimensioning of the yaw system is covered by this project thesis, which also
treats the nacelle construction.
Tower and foundation
The tower of the wind turbine carries the nacelle and the rotor. This project thesis deals
with tower design and dimensioning. The supporting foundation is not treated thoroughly,
as knowledge of local soil properties is a requisite to the design of small wind turbine
foundations.
33

CONCEPTUALISATION
The embodiment design phase involves further development of the principal solution of
figure 4.17 into a design proposal, which is optimised and finalised in the detail design
phase. An overall presentation of the finalised layout is given in the following chapter. A
more thorough description of key design details such as rotor, tower and generator is
given in the subsequent chapters.
34
4.6 Summary
This chapter has defined basic wind turbine terms such as lift, drag and tip-speed ratio,
thus making its content more comprehensible to engineers without a background in wind
turbine technology.
A survey of numerous different wind turbines and their key properties was performed
with focus on proven HAWT and VAWT designs, including Savonius, Giromill and Darrieus
turbines.
It was found that the concepts without a proven self-starting mechanism are unfit for use
in developing countries and hence candidates in this category were eliminated. The re-
maining concepts were subjected to a systematic evaluation facilitated by a decision-
matrix. From this it was evident that the HAWT and the Savonius wind turbine are the
front-runner candidates when taking into consideration the relative evaluation criteria.
Through a technical assessment, exploring further aspects of the two best candidates, it
was concluded that the Savonius wind turbine is very impractical and difficult to handle
when it has the required structural size. The HAWT concept has therefore been adopted as
the most suitable solution for the present purpose.

5
Design presentation
This chapter introduces the wind turbine design proposal, which has been developed on
basis of the principal concept, described in section 4.5. A 3D illustration of the overall wind
turbine design is shown on figure 5.1.
Figure 5.1: 3D illustration of overall wind turbine design
35

DESIGN PRESENTATION
The main dimensions of the wind turbine are illustrated on figure 5.2.
36
Figure 5.2: Overall wind turbine design and main dimensions
Figure 5.3 contains a more detailed overview of the wind turbine and identifies its key
components. A full overview of the wind turbine components can be found in the compo-
nent diagram of att. 12. Reference is also made to the product drawing of att. 11, which
contains further technical details, including main dimensions, wind turbine data and detail
views.

Tower
Gin pole
Tower pivot base
Guy wire
Generator with integrated hub
Yaw system
Tail boom
Tail vane
Furling system
Generator rotor disc
Generator bearings
Nacelle cover
Base plate
Shaft
Generator stator disc
DESIGN PRESENTATION
Rotor
Figure 5.3: Diagram of wind turbine components and their designation
Chapters 6-9 contain a detailed presentation of the system components, which to varying
degrees have been the focal points of this project thesis (see the limits and exclusions of
section 4.5). The detail chapters include statement of the design considerations made dur-
ing the embodiment phase of the development process, and further contain a thorough
description of the functionality and specifications of the wind turbine components. To
some extent engineering calculations are also reported in the chapters, but the full details
of these are contained in the appendices.
In general terms the proposed wind turbine may be described as a three-bladed horizon-
tal-axis wind turbine, which operates at variable speed. It features an upwind design which
is self-regulating by means of a passive yaw orientation system and a gravity-controlled
furling system that controls the power output.
37

DESIGN PRESENTATION
The design proposal deviates from the principal system of figure 4.17 in that it uses a di-
rect drive concept, which eliminates the need for a transmission in the drive train. The
direct drive is rendered possible by an axial flux generator with permanent magnets
(AFPMG), which operates at rotational velocities that are low enough to omit any trans-
mission. This greatly simplifies the design and reduces the amount of production-wise
complex components, facilitating procurement in developing countries.
The overall design and its details are determined under great consideration to all demands
and wishes of the requirement list. A guyed tower, which may be installed manually with-
out a crane, is used in the design. The wind turbine components may be manufactured
using standard operations such as turning, milling and welding, hence enabling local
manufacturing. Even the generator may be produced locally by relatively simple means.
Common steel that is widely available is used for the majority of the wind turbine parts,
which eases localised maintenance and component replacement. Wood is used for the
rotor blades, but as requested the material choice is flexible and may be altered without
making extensive changes to the general design. The consideration to flexibility and manu-
facturability, as well as cost-consciousness is exhibited without compromising the overall
quality of the solution, as it will serve as a platform for future wind turbine designs. Fur-
ther statement of how the requirements are met is made in chapter 11.
The electrical power output of the wind turbine meets the performance requirement of
1500 W �1% at a rated wind speed of 12 m/s. The performance characteristics are fully
reported in section 6.3. The wind turbine is designed for a so-called IEC Class IV site, which
has the external conditions of a typical installation site in the areas where EWB operate
(see appendix A.1).
Table 5.1 provides an overview of the technical specifications of the wind turbine, some of
which may be marked on the turbines nameplate, as required by IEC 61400-2 [5, p. 121].
The overview further enables direct comparison with equivalent data for other wind tur-
bines.
38

DESIGN PRESENTATION
Product identification
Manufacturer Engineers Without Borders
Model EWB-IHA-1
Origin Denmark
Power
Rated electrical power 1506 W
Max. electrical power 2410 W
Annual energy output 935 kWh (On IEC Class IV site)
Rotor efficiency (Cp) 0.55 at rated wind speed
Overall efficiency 42% at rated wind speed
Wind speed
Cut-in wind speed 4 m/s
Rated wind speed 12 m/s
Furling wind speed 14 m/s
Cut-out wind speed Continuous operation up to survival wind speed
Survival wind speed 42 m/s
Rotor speed
Rated rotor speed 500 rpm
Max rotor speed 650 rpm
Rotor
No. of blades 3
Diameter 2.7 m
Rotor swept area 5.7 m 2
Blade material Wood
Airfoil NACA 4412
Orientation Upwind
Direction of rotation Clockwise
Generator / Electrical system
Type AFPMG
Phases 3-Phases
System voltage 48 V DC
Control system
Power control Furling
Orientation system Passive yaw control, tail vane
Protection system Shutdown switch, input breaker
Tower
Type Guyed tilt-up tower
Height 12 m
Foot print area 28 m 2
Tower-top mass 102 kg
IEC wind turbine class SWT Class IV
Base plate connection 300 x 300 mm, 4 x M16 bolts
Miscellaneous
Colour RAL 7035 a
Total mass 592 kg
Transmission Direct drive, no gearbox
Longevity 19 years minimum – Annual service inspection
Hub design Rigid, integrated in generator
Bill of material cost $1585 b
a) Where relevant, the wind turbine components are expected to be painted in the commonly used wind
turbine colour, RAL 7035, as a mean of protection against corrosion, moisture and UV-rays. Further
details of the surface treatment are not treated by this project thesis.
b) See att. 6
Table 5.1: Technical specifications of the wind turbine
39

DESIGN PRESENTATION
The background for the majority of the technical specifications of table 5.1 is provided in
the following detail chapters.
An overview of the development tasks, that are beyond the scope of this project, but
needed to fully complete the design proposal, is provided in chapter 12. This chapter addi-
tionally defines relevant spin-off projects that may be carried out within the framework of
EWB.
40
5.1 Summary
The developed design proposal was presented as a three-bladed HAWT with direct drive
and an upwind architecture, which uses a guyed tower as support structure. The wind
turbine was shown to be self-regulating by means of a passive yaw orientation system and
a gravity-controlled furling system.
The overall design was developed under great consideration to the demands and wishes of
the requirement list, thus fulfilling manufacturing, flexibility and performance require-
ments.

6
Rotor
This chapter describes the rotor, which may be considered the key component of the wind
turbine. The main components of the rotor are listed on figure 6.1.
Figure 6.1: Main components of the rotor
The chapter contains a detailed statement of the rotor design, including blades, airfoil and
manufacturing, in addition to structural and aerodynamic calculations.
A great part of the rotor design task is carried out using a rotor design tool that has been
developed as a part of this project thesis. The design tool is essentially a spreadsheet-
based program, which enables the iterative calculation of aerodynamic flow conditions,
forces, blade shape and performance. It is described further in appendix C and the theory
behind the tool is described in appendix B.2.
41

ROTOR
42
6.1 Number of blades
Modern wind turbines that are used for generating electricity normally have three blades,
although wind turbines with both fewer and more blades exist.
The influence of the number of blades on the rotor performance is illustrated on figure 6.2,
which shows the rotor power coefficient Cp as a function of tip-speed ratio � for different
blade numbers.
Figure 6.2: Influence of the number of blades on the rotor power coefficient [10, p. 93]
The dependency of the power coefficient on the number of blades emphasizes why two or
three blades generally are the preferred solutions for wind turbines. The power coefficient
of a wind turbine with just one blade is relatively low and it furthermore suffers from an
aesthetic imbalance as well as the need for a counterweight. The possible power increase
from three to four blades is less than 2%, which is not enough to justify the implicit higher
costs that are associated with an additional blade [10, p. 92].
A two-bladed wind turbine has a lower mass moment of inertia with respect to yawing
when the blades are vertical than when they are horizontal. This causes the inertial mo-
ment to have a pulsating profile during a revolution, which induces dynamic loads when
the wind turbine is yawing. A rotor with three blades, on the other hand, behaves like a
disc as far as the mass moment of inertia is concerned. It is symmetrical in terms of mass
and therefore has the advantage of a constant mass moment of inertia with respect to
yawing [12, p. 320]. Figure 6.3 illustrates the yaw moment of a specific rotor with different
numbers of blades.

Figure 6.3: Yaw moment of a given rotor with different numbers of blades [10, p. 167]
From the above figure it is clear that the alternating load of a two-bladed rotor is almost
ROTOR
levelled out in rotors with three blades. Figure 6.3 further emphasizes the disadvantages of
the one-bladed rotor. By process of elimination it is therefore concluded that the three-
bladed rotor concept is most suited for current purpose with regards to aerodynamic per-
formance, structural considerations, manufacturability and cost. It is therefore chosen for
the current rotor design.
6.2 Blade design
The developed blade design is illustrated on figure 6.4. The design is a compromise of
multiple considerations, including aerodynamic performance demands, structural re-
quirements, obtainable materials and available manufacturing methods.
43

ROTOR
44
Figure 6.4: Blade design shown with main dimensions and designations
6.2.1 Material
The following tabulated materials and associated manufacturing methods have been iden-
tified as design options.
Material Manufacturing method
Metal Steel or aluminium blades may be manufactured as solid shapes or from
rolled plates that are welded together on airfoil shaped support plates
Composite Blades of carbon or glass fibre reinforced polymer composites may be
manufactured in two-part moulds
Wood Wooden blades may be carved from a wood work-piece by mechanical
means or by hand
Table 6.1: Blade material options
Each of the abovementioned alternatives entails a number of relative advantages and dis-
advantages, some of which are listed qualitatively below.
Metal blades
� Heavy (steel)
� Light (aluminium)
� Expensive

� Widely available
� Demanding manufacturing processes
Composite blades
� Lightweight
� Strong
� High repeatability
� Good fatigue characteristics
� Low material availability
� Possibility for complex airfoil shape
Wooden blades
� Lightweight
� Abundant supply
� Cheap
� Strong
� Flexible
� Non-uniform when hand-carved
� Simple airfoil shape required
Quantitative engineering characteristics of the materials are listed in table 6.2. The data is
based on [10, p. 221] and it should only be used for the purpose of this comparison, as
many assumptions and simplifications are made to represent each property by a single
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value. The values will vary depending on factors such as manufacturing processes, material
purity, reinforcement material and environmental conditions.
Parameter
Material
Aluminium
(AlMg5)
Density
�
g/cm 3
Modulus
of elas.
E
GPa
Ultimate
strength
�
MPa
Spec.
breaking
strength
�/�
MPa/(g/cm 3 )
Spec.
modulus of
elasticity
E/�
GPa/(g/cm 3 )
Fatigue
strength
(10 7 )
2.7 70 236 87 26 20
Steel (St. 52) 7.85 210 520 66 27 60
CFRP a 1.4 44 550 393 31 100
GFRP a 1.7 15 420 247 9 35
Wood b 0.38 8 65 171 21 20
a) Epoxy matrix with 40 vol.%
b) Properties for Sitka Spruce (Picea sitchensis)
Table 6.2: Strength and stiffness parameters of materials available for rotor blades
��A
MPa
45

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Table 6.3 provides a material cost comparison based on approximate prices per tonne,
given in [58]. The prices are derived relatively to the price of steel in 2005, set to
$100/tonne. The actual values are out of date and they are unlikely to represent the prices
in development countries. However the prices are considered valid for a relative compari-
son of the price differences.
46
Material Steel Aluminium CFRP GFRP Wood
Relative material cost
($/tonne)
Relative volume cost
($/m 3 )
Table 6.3: Material cost comparison
100 400 20000 1000 200
785 1080 28000 1700 76
In addition to material cost, it is necessary to take into account manufacturing costs. As a
general rule it can be stated that manufacturing processes which require little or no auto-
matic machining are most advantageous. For the present project the price of manufactur-
ing is not scrutinised further, as the majority of it will be carried out by volunteers.
When taking into consideration the available data, the material selection is neither
straightforward nor unambiguous and the right choice of blade material will, to a great
extent, depend on the conditions at the specific destination where the wind turbine is to be
built. For the current wind turbine design wood is chosen as blade material, primarily due
to its generally high availability in developing countries, its low price and its low require-
ments for production facilities. The choice in material is further sustained by the fact that
wood in its nature is designed for resisting wind loads in bending, which is confirmed by
the overall excellent material properties in terms of strength and stiffness. Other material
options may prove superior in certain cases, e.g. where high quality wood is expensive or
difficult to find. The blade attachment method described in section 6.2.4 enables blades of
other materials to be attached in future designs without impacting the overall design con-
cept.
An in-depth description of the engineering properties of the chosen blade material may be
found in appendix E.
6.2.2 Airfoil and geometry
The cross-section of the wooden blades has the shape of an airfoil, which optimises the
aerodynamic performance. A number of terms are used to characterise airfoils, as shown
on figure 6.5. The geometric parameters have great influence on the aerodynamic per-
formance of the airfoil. Not shown on figure 6.5 is the span of the airfoil, which is perpen-
dicular to the shown cross-section.

Figure 6.5: Definition of typical airfoil parameters
� The chord line is a straight line connecting the leading and trailing edges on the
airfoil
� The mean camber line is a line drawn halfway between the upper and the lower
surfaces
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� The frontal surface of the airfoil is defined by the shape of a circle with the leading
edge radius. The centre of the circle is defined by the leading edge radius and a
line with a given slope relative to the chord line.
A NACA 4412 airfoil, which is an old design, used in e.g. Akron-Funk Model B aircrafts from
the 1930s [28, p. 61], is selected as the blade airfoil profile. The profile, shown on figure
6.6, is selected due to its performance characteristics and manufacturability. The high
pressure side of the profile is almost flat, which facilitates manufacturing by hand-carving.
This production method is assumed for the wooden blades, since it is available in all devel-
oping countries.
Figure 6.6: NACA 4412 airfoil
The NACA four-digit code defines the profile shape [10, p. 110]:
� 1st digit - maximum camber in percentage of the chord
� 2nd digit - location of maximum camber along chord line (from leading edge) in
tenths of the chord
� 3rd and 4th digit - describing maximum thickness of the airfoil in percentage of
the chord. The maximum thickness position of all four-digit airfoils amount to 30
% of the chord length.
Thus the NACA 4412 profile has a maximum camber of 4% located 40% of the chord from
the leading edge with a maximum thickness of 12% of the chord.
47

ROTOR
Figure 6.7 displays the lift coefficient Cl, drag coefficient Cd and glide ratio GR=Cl/Cd of the
NACA 4412 airfoil as a function of the angle of attack �. For a definition of the angle of
attack, see figure B.2.
Figure 6.7: Lift coefficient Cl, drag coefficient Cd and glide ratio GR=Cl/Cd of the NACA 4412
airfoil
Further details on the airfoil and calculation of its aerodynamic properties are available in
appendix D.
The chord length (i.e. width of the blade) and the length of the blade are functions of per-
formance requirements, airfoil properties, manufacturing method and structural strength
considerations. By means of the method described in appendix B.2, the optimum blade
shape is determined using Schmitz’ theory. Figure 6.8 illustrates the optimum chord length
and blade pitch, respectively, based on the following parameters:
48
� Wind speed V = 12 m/s
� Number of blades B = 3
� Blade radius R = 1.35 m
� Optimum angle of attack �opt = 5�
� Cl at �opt = 0.99
� Tip-speed ratio �opt = 5

Figure 6.8: Optimum blade chord and blade pitch as a function of the non-dimensionalised
blade radius
Note that no chord length or pitch angle is specified for the part of the blade that is closest
to the hub. This is due to the first element of each blade being left out in the BEM calcula-
tions, which underlie the optimum blade calculations. Further explanation can be found in
appendix C.
On figure 6.8 it is shown that the blade design for optimum power production has an in-
creasingly large chord and pitch angle when approaching the blade root. This hyperbolic
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contour of the theoretical optimal shape makes the fabrication of the blade difficult and the
design is therefore modified for ease of manufacturing using the optimum blade shape as a
guideline. An invariant pitch angle is chosen, as a twisted blade will complicate the manu-
facturing process. Figure 6.9 shows the rotor power output at V = 12 m/s as a function of a
fixed pitch angle.
49

ROTOR
Figure 6.9: Rotor power output at various fixed blade pitch angles. Curve shown for V = 12
m/s and � = 5
On basis of the above graph a fixed pitch angle of 2� is selected. At the rated point, V = 12
m/s and � = 5, the rotor power output is lowered by less than 1% when using an invariant
pitch angle rather the optimum pitch angle of figure 6.8.
A uniform tapering of the chord length is chosen, as it further simplifies the design and
removes a lot of material close to the blade root. The tapering shape is determined from
the slope of a straight line drawn between the span points at 70% and 90%, intersecting
the optimum shape midway at the 80% span point [29, p. 73]. This is illustrated on figure
6.10.
50

ROTOR
Figure 6.10: Uniform tapering of the chord compared to the optimum tapering according to
Schmitz
At a tip-speed ratio � of 5 the change in performance, when using a linear tapering, is less
than 4% compared to the optimum chord shape at a wind speed V of 12 m/s. Designing the
blade for a tip-speed ratio of 7 would theoretically render a higher performance, see figure
6.2. However this would also entail a more slender blade with problems of strength and
stiffness when using wood as blade material. The selected design tip-speed ratio is there-
fore a compromise between structural integrity and aerodynamic performance of the
blade.
The transition between the airfoil portion of the blade, shown above on figure 6.4, and the
hub junction of the blade, near root, is made smoothly in accordance with [10, p. 113-116].
The tip of the blade may be further optimised both aerodynamically and with regard to
noise emission. This optimisation is however beyond the scope of this project.
As a function of the chord length it is possible to calculate the complete shape of the NACA
4412 airfoil in any cross-section. In appendix D.1 the calculation is performed for 7 differ-
ent cross-sections and data output is used to generate a 3D CAD model of the blade.
Further airfoil and blade data can be found in the electronic version of the rotor design
tool and in appendix D.
51

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6.2.3 Manufacturing
During the process of airfoil selection and blade design, manufacturing has been a high
priority. This section contains a manufacturing guideline that describes the import consid-
erations that must be made when hand-carving the blades. Use of manual power tools or
machining centres provides a good alternative to hand-carving.
The raw material is cut from a single, solid work-piece of wood. It is important that the
direction of the fibres is along the z-axis on the blade as illustrated on figure 6.11.
52
Figure 6.11: Direction of fibres on the blade (left picture modified from [30])
It is recommended to use heartwood (centre wood from a tree trunk) as blade material
due to its ability to resist fungi and attacks from insects. It furthermore increases the mois-
ture content stability. Heartwood is commonly found 40-60 mm from the bark of the tree
and into the pith [30, p. 2-2].
The centreline of the hub junction is angled 2� with reference to the chord of the airfoil, so
that the blade has a fixed pitch angle of 2� when mounted on the front disc of the genera-
tor, see figure 6.12.
Figure 6.12: Angling of airfoil with respect to the hub junction
The series of pictures on figure 6.13 illustrates the manufacturing process from raw mate-
rial to a finished blade. It is stressed that the carving must be carried out with highest pos-
sible precision in order to minimise the imbalance of the rotor.

The raw material is cut, so that its outer
dimensions match the maximum outer
dimensions of the blade. The thickness of
the hub junction equals the maximum
thickness of the airfoil
The tapering of the blade is made solely
on the trailing edge of the blade. It is cut
according to the innermost and outer-
most chord length of the airfoil
The width of the hub junction and the
associated radius in the corner is cut
To guarantee equality of the hole-layout
in the three blades, a steel template is
made. By only having three sides on the
template, the dependency of the preci-
sion of the hub junction is minimised
Continues on next page
ROTOR
53

ROTOR
54
The three sides of the template are
clamped onto the blade root and the
holes are drilled. The feed should fit the
rpm when the holes are drilled to pre-
vent rough holes, as a smooth hole will
increase the embedding strength limit.
To prevent non-uniform bearing of the
bolt, the holes should fit the bolts, so that
they may be inserted by tapping slightly
with a mallet [30, p. 7-16].
The position of the trailing and the lead-
ing edge is marked. The blade is subse-
quently designed so the leading and the
trailing edges are parallel to the y-z-
plane. The airfoil is then divided into 9
(or more) equally sized sections.
Continues on next page

A set of 10 templates is made to facilitate
carving of the airfoil shape. They are
made from 1 mm sheet metal plates. Each
template is split at the trailing and lead-
ing edge of the blade. The shape of the
airfoil differs in every section along the
blade. The airfoil shape data needed to
create the templates for the sections is
described in appendix D.
The airfoil is carved according to the
templates. One template for each mark-
ing. The shape of the airfoil must pre-
cisely follow the template and the split-
line on the template must follow the
previously marked leading and trailing
edges on the blade.
When the airfoil-shape is carved, all that
is left is to chamfer the hub junction and
to carve the radius of the transition be-
tween the airfoil and the hub junction.
Figure 6.13: Blade manufacturing process
ROTOR
55

ROTOR
When the carving process is finished, three press-in connectors are mounted in each blade.
A press-in connector, illustrated on figure 6.14, is a plate with teeth along the perimeter,
which may be pressed into the wood.
56
Figure 6.14: Press-in connector [62]
The connectors enhance the bearing strength of the joint connection [31, p. 92]. It is rec-
ommended to install the press-in connectors by hammering them into the wood using a
stiff plate as support. It is important to ensure that the centre hole of the press-in connec-
tor is concentric to the bolt hole of the blade [31, p. 96].
When hand-carving the blades the repetitive accuracy is relatively low and it is therefore
necessary to verify the quality of the manufacturing process by inspecting the blade imbal-
ance. This is done in two steps: The first is to make sure that all three blades have the same
weight and the same weight-distribution. This is done by mounting a bracket with two
spikes on the root of the blade using two M12 bolts, as shown on figure 6.15. A third spike
is placed on a scale and its output reading is noted. If the blades have been carved thor-
oughly the output on the scale will be the same for all three blades.
Figure 6.15: Balancing the blade
When the individual blade balance has been checked, the blades are mounted onto the
front disc of the generator. Here it is checked that the distances L of figure 6.16 are all
equal.

Figure 6.16: Balancing of the assembled rotor
This project does not go into details regarding the imbalance limit states, e.g. determining
when a blade is considered in balance and when it is not. Some guidance for determining
these may be found in the load cases of appendix A.3, which states several loads of rotor
eccentricity. Practical rotor balancing is described in [20], which makes suggestions of
adding small weights on the rotor as a mean of balancing ii with regard to its centre of
rotation.
6.2.4 Blade attachment
The blades are mounted directly on the front disc of the generator, which therefore also
works as a hub. Each blade is mounted using 3 pcs. M12x60 bolts and a large washer,
which distributes the contact forces of the bolts, is used to secure the entire rotor in place,
as shown on figure 6.17.
ROTOR
57

ROTOR
58
Figure 6.17: Blade attachment components
The attachment method makes it relatively easy to mount rotor blades of other materials
and designs. If necessary an intermediate component may be fastened onto the plain front
disc, making virtually any connection interface possible.
The spacing between the bolt holes, their load capacities and the thickness of the washer
are in accordance with guidelines provided by the Danish Building Research Institute
(DBRI). Appendix F contains a verification of the structural integrity of the blade attach-
ment, which also complies with these guidelines.
6.2.5 Structural calculations
The structural integrity of the blades is verified through finite element analyses that are
documented in appendix E. The analyses are based on the ultimate and fatigue load cases
of IEC 61400-2, which are derived in appendix A.3.
Verification of the structural integrity of the blade attachment is carried out analytically in
appendix F.
A modal analysis, which predicts the rotating and non-rotating natural frequencies of the
blades, is performed in appendix E.11.
6.2.6 Alternative blade design
Chapter 10 contains a preliminary investigation of the option for an alternative blade de-
sign, which may be based on simple airfoils made from e.g. cut-out sections of plastic drain
pipes or from rolled steel plates.

6.3 Rotor performance
Aerodynamic rotor performance calculations are carried out using an iterative rotor de-
sign tool that has been developed as a part of this project on basis of the blade element
momentum (BEM) theory, described in appendix B.1. The rotor design tool enables calcu-
lation of aerodynamic flow conditions, forces, blade shape and rotor performance. It is
intended to be used by EWB in the development of future wind turbines and it is thus de-
signed with a spreadsheet interface that provides a certain degree of user-friendliness.
ROTOR
Details about the design tool, its functions, limitations and usage, can be found in appendix
C.
Performing analyses for a range of different wind speeds and rotational speeds enables the
rendering of rotor power curves that show rotor power output as a function of the rota-
tional speed. Figure 6.18 illustrates the power output for the developed rotor with a di-
ameter of 2.7 m at different wind speeds. Wind speeds are shown only up to 14 m/s, where
furling is initiated, see section 8.2.
Figure 6.18: Rotor power output as a function of rotational speed at wind speeds in the
range of 4 m/s to 14 m/s
The rotor power curves may be augmented to a system power curve by combining the
rotor power output of figure 6.18 with the linear characteristic of the generator, described
in section 7.1. An overlay plot of the rotor power output and the generator characteristic is
shown on figure 6.19.
59

ROTOR
60
Figure 6.19: Rotor power output and generator characteristics combined
Each intersection between the rotor power curves and the generator characteristic repre-
sents a point of operation for the wind turbine. Assuming a constant efficiency �g of the
generator of 45%, see section 7.1, both the generator input from the rotor Pr and the out-
put Pg may be established as a function of wind speed on figure 6.20.
Figure 6.20: Rotor power output Pr and generator output Pg within the wind speed range of
4 m/s to 14 m/s

Figure 6.20 shows the generator output to be 1506 W at the rated wind speed of 12 m/s.
The wind turbine thus meeting the demand of the requirement list, which commands a
nominal generator output of 1500 W �1%.
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The efficiency of the rotor for different wind speeds is expressed on figure 6.21 in terms of
�r and the power coefficient Cp, which are calculated from (B.16) and (B.17), respectively.
Figure 6.21: Rotor efficiency at different wind speeds expressed in terms of �r and the power
coefficient Cp
The efficiency �tot of the complete wind turbine is calculated by multiplying the rotor effi-
ciency �r by the generator efficiency �g, and shown on figure 6.22 for different wind
speeds.
61

ROTOR
62
Figure 6.22: Efficiency �tot of the complete wind turbine
Actual performance of the wind turbine is expected to exhibit divergence from the theo-
retical performance of figure 6.20, as the assumptions and idealisations of the BEM theory
(see appendix B.1) seldom occur in reality. The variations are further amplified by the
effects of manufacturing inaccuracies and varying surface properties that cause airfoil
characteristics to change from those described in appendix D.
6.3.1 Annual energy production
The average wind turbine power output is given by the wind turbine power curve of figure
6.20 and the wind regime probability function pR(V), described in appendix A.1 [12, p. 62]
P ave
V2
�
= �
�
V1
pR( V)
Pg( V)
Pg(V) is found through regression analysis of the power curve in figure 6.20 to be
dV
Pg( V)
0.3718V 3 0.9126V 2
=
� � 2.4588V
(6.1)
(6.2)

pR(V) is found in appendix A.1 to be
Where Vave is the average wind speed at the site, equal to 6 m/s.
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The integral of (6.1) is calculated from generator cut-in at V1 = 4 m/s to V2 = 14 m/s, where
furling is initialised (see section 7.1 and 8.2).
Multiplication of this by 8760 h yields the annual energy production for the site defined in
appendix A.1.
P ave
pR( V)
(6.3)
(6.4)
(6.5)
The above annual energy production is a conservative assessment, as the wind turbine still
produces power beyond 14 m/s, where furling is initiated. The produced power beyond
furling will presumably be less than the maximum power generated at 14 m/s. Moreover
wind speeds above 14 m/s only occur 1.4% of the time for the installation site specified in
appendix A.1, which renders the power produced above the furling limit negligible. The
annual energy production of the wind turbine can be optimised by trimming the character-
istics of the generator, to make the best possible fit to the characteristics of the rotor (or
vice versa). The cut-in wind speed of the generator, currently 4 m/s, may also be lowered
to improve annual energy production, although the power available at low wind speeds is
close to insignificant. It should be noted that the expected power output divergence, de-
scribed in the previous section, also is applicable to the annual energy output.
The average wind turbine power Pave (or the annual energy production) may also be used
to calculate a related performance parameter, the capacity factor, CF. The capacity factor is
the ratio of actual productivity to the rated productivity:
�
�
2
V
2
Vave e
2
� V
� � �
� �
4 � Vave �
4 m
14
s
m
� s
�
=
�
pR( V)
Pg( V)
dV
= 107W
�
E ann
= Pave8760h = 935kWh
Pave CF = =
0.07
1500W
A capacity factor of 7% is relatively low. Typical capacity factors for larger wind turbines
are 20-40%, with values in the upper end of the range in particularly favourable sites [32].
(6.6)
For the present turbine the low capacity factor is caused mainly by the generator efficiency
of 45% and the low average wind speed of the installation site. If hypothetically only con-
63

ROTOR
sidering the output from the rotor, and thus ignoring the efficiency of the generator, the
capacity factor increases to 35%.
6.3.2 Self-starting capability
For the wind turbine to start there must be a starting torque present, which is sufficient to
overcome frictional resistance in the bearings of the generator. Using the BEM theory,
described in appendix B.1, it is not possible to accurately calculate the torque at standstill.
It is however possible to calculate the torque at low rotational speeds and analyse the
tendency [33].
Figure 6.23 shows the rotor torque at low rotational speeds on basis of the rotor design
tool. The underlying calculations are made for a wind speed of 4 m/s, equivalent to the cut-
in wind speed mentioned in section 7.1.
64
Figure 6.23: Rotor torque at low rotational speeds and wind speed of 4 m/s
Extrapolation of the curve on figure 6.23 yields a starting torque of 100 Nmm at 0 rpm,
which is compared to the required starting torque of the bearings, which is 79.1 Nmm (att.
4). From this it is made probable that the wind turbine will self-start, as expected of a
HAWT design.

6.4 Summary
A three-bladed rotor with a diameter of 2.7 m has been developed for the present wind
turbine. Achieved through an iterative process, the rotor is a design compromise, which
takes into consideration aerodynamic performance, strength and stiffness requirements,
as well as material availability and production techniques.
Aerodynamic calculations have been carried out using a rotor design tool, which has been
developed as a part of this project. Structural calculations have been performed using a
combination of numerical finite element analyses and analytical calculations.
The rotor, in combination with the generator, yields a nominal system power output of
1506 W at a wind speed of 12 m/s, which is in agreement with the requirement specifica-
tion. The annual energy production has been calculated as 935 kWh at the targeted instal-
lation site.
An alternative blade design, involving the usage of curved plates as airfoils, was proposed
as a future design option that provides a simpler, but also less efficient rotor.
ROTOR
65

ROTOR
66

7
Generator and electrical system
The present chapter provides an overview of several generator options and explains the
selection made for the wind turbine design. Since the main focus of this project thesis in on
mechanical and aerodynamic design, the generator is only treated to a certain extent. The
chapter also contains a proposal for the components that should be included in the electri-
cal system.
7.1 Generator
The generator may be categorised as one of the key components in electricity producing
wind turbines. Its basic function is to convert mechanical energy into electrical energy by
means of a rotating magnetic field, which induces a voltage in the stator windings of the
generator. The generator has a high influence on the performance of the wind turbine and
its characteristics are important to the design of the wind turbine rotor.
Distinction is often made between the terms alternator and generator, where the first
commonly refers to a machine producing alternating current (AC) and the latter refers to a
machine producing direct current (DC). This project thesis does not make distinction be-
tween the two terms and denotes both types of machines as generators.
The most suitable type of generator is selected based on criteria such as simplicity, produ-
cability/availability and its impact on the rest of the wind turbine design.
Table 7.1 provides the results of a survey of different generator options that may be used
in small scale wind turbines. The listed technical properties, advantages and disadvantages
are subjective and based on assessments and information gathered during the survey.
67

GENERATOR AND ELECTRICAL SYSTEM
68
Type Advantages Disadvantages
Axial flux generator
with permanent
magnets (AFPMG) a
Asynchronous
generator (e.g. auto
generator)
DC generator
Induction motor as
PM generator b
� No transmission required
� No brushes required
� No cogging torque
� Can be build locally
� Availability
� Price
� Pre-assembled
� Simplifies the electrical
system
� Pre-assembled
� May not require transmission
� Price
� Availability
a) See description in the following paragraphs
� Availability of PM magnets
� Weight / size
� Transmission required
� Requires a current in the
field coils
� Brushes and slip rings
requires maintenance
� High maintenance
� Large sizes are hard to find
� Small sizes have limited
output
� Cogging torque
� High internal resistance
� Inefficient at high rpm
� Availability of PM magnets
b) Induction motor may converted to a generator and fitted with permanent magnets, e.g. from a hard
drive
Table 7.1: Results of generator survey
From the survey it is evident that the advantages of implementing an AFPMG in the wind
turbine are many. Its main disadvantage is the fact that it uses permanent magnets, e.g.
neodymium (NdFeB), samarium cobalt (SMCO) or ferrite magnets, as their availability in
developing countries is limited to some extent. In collaboration with EWB it is however
established that the advantages of the AFPMG design outweighs the availability issue and
the solution is therefore adopted for the wind turbine design. In situations where magnets
are unattainable they may either be provided by EWB or in cases of import prohibition one
of the listed alternatives may be implemented.

GENERATOR AND ELECTRICAL SYSTEM
A key advantage of the chosen generator design is that it operates at low rotational veloci-
ties compared to typical asynchronous generators, hence making it possible to utilise a
direct drive concept without any transmission. An additional advantage is that the genera-
tor can be built locally on-site, which facilitates production of replacement parts and in-
creases the design flexibility in that details may be changed to comply with varying local
needs.
As the name implies, the magnetic field of the axial flux permanent magnet generator is in
the axial direction, contrary to prevailing generators which have radial magnetic fields.
The generator output is 3-phased wild AC, referring to the varying output frequency and
voltage due to the variable speed of the wind turbine rotor. A rectifier, described in section
7.2, converts the wild AC into 48 V DC in agreement with the requirement of table 2.1.
Design of the generator, e.g. the sizing of magnets, wire dimensions and coils, is beyond the
scope of this project. However, since the generator has high influence on the overall wind
turbine design, its components, performance and loads it is necessary to establish a realis-
tic generator for the purpose design and calculation. This is done by using the dimensions
and principal layout of an existing commercial axial flux generator (att. 10) in the design
and by defining a characteristic for the generator which is achievable.
The generator consists of three main parts: stator, rotor and shaft as shown on the pro-
posed layout drawing of figure 7.1.
Figure 7.1: Cross section of the axial flux generator
69

GENERATOR AND ELECTRICAL SYSTEM
The rotor consists of a front disc (1) and a rear rotor disc (2), separated by a spacer (3).
The two discs and the spacer are held together by 6 pcs. M8 bolts (4). The blades of the
wind turbine rotor are attached directly to the front disc, as described in section 6.2.4.
Hence, when the blades rotate, the front disc and the rear both rotate. On the inside of the
front and rear rotor discs, the permanent magnets (5) are fitted into milled grooves. The
rotor discs are mounted on spherical roller bearings (6) and (7), which are fitted onto the
stationary shaft (8). The bearings are sealed at exposed endings and can absorb both axial
and radial forces. Details of bearing longevity and required starting torque are provided in
att. 4. To provide the option of disassembling the generator, a washer (12) is mounted in
the front disc with 6 pcs. M8x25 screws (13).
The stator disc (9) consists of a steel bushing (10) and several coils (11) with windings of
enamelled magnet wire, all of which is moulded together by a thermosetting plastic. The
stator disc is mounted on the stationary shaft with a pressure fitting. An ø20 mm hole is
drilled by the end of the shaft with the purpose of leading the stator wires to the electrical
system. Appendix G contains a verification of the structural integrity of the shaft in accor-
dance with IEC 61400-2.
It is expected that a future project will deal with the detailed design of the generator, as
described in chapter 12. The design may come to deviate from the above.
The characteristic of the generator will ideally have the shape of a cubic function that in-
tersects the vertices of the rotor power curves. This is shown on figure 7.2, which does not
take into account any cut-in speed.
70
Figure 7.2: Ideal characteristic of the generator

GENERATOR AND ELECTRICAL SYSTEM
In practice the generator is expected to be designed with a linear characteristic as shown
on figure 7.3.
Figure 7.3: Linear characteristic of the generator
The intended generator is designed to cut in at 250 rpm, meaning that the rectified DC
voltage at this angular velocity is high enough to produce power (see section 7.2 for more
information). The efficiency of the generator will vary as a function of the rotational speed,
but for the purpose of power calculations the total generator efficiency �g is assumed to
have a constant value of 45% [61]. The generator efficiency also takes into account any
losses in the electrical system.
7.2 Electrical system
Design of the electrical system is beyond the limits of this project thesis. A proposal of the
components that should be included in the system is however made, as several of these are
required to comply with various requirements of IEC 61400-2 and of the requirement list.
Figure 7.4 provides a schematic overview of the complete electrical system from the gen-
erator to the battery bank.
71

GENERATOR AND ELECTRICAL SYSTEM
Figure 7.4: Schematic overview of the electrical system. Three connecting lines between the
components indicate AC and two connecting lines indicate DC.
Shutdown switch
In case of an emergency, a shutdown switch is used to brake the wind turbine. It works by
short-circuiting the 3 phases of the generator, hence creating a high current load which
effectively stops the rotor. A further advantage of the shutdown switch is that it is possible
to manually park the wind turbine during maintenance and installation. For the present
wind turbine a shutdown switch is not required, but recommended by IEC 61400-2 [5, p.
93].
Slip ring
Since the wind turbine is able to yaw freely about its yaw axis, there would normally be a
risk of twisting the wires of the electrical system, which eventually would cause failure. A
slip ring, also known as a rotating electrical connector, prevents this problem from occur-
ring.
Rectifier
A rectifier is an electrical device used to convert the wild alternating current from the
generator, which periodically reverses direction, into direct current, which is in only one
direction. This is necessary to charge the battery bank that the wind turbine is assumed to
72

GENERATOR AND ELECTRICAL SYSTEM
be connected to. The result of the rectification is denoted ripple current and shown on
figure 7.5.
Figure 7.5: The result of 3-phased AC converted into DC ripple current [34]
As stated in the requirement list, ID 2, the system voltage must be 48 V DC. This means that
the rippled output voltage from the rectifier must be at least 48 V before any voltage is
transmitted to the batteries. The angular velocity of the generator, at which the voltage of
48 V is reached, is the cut-in speed, i.e. 250 rpm as described in section 7.1.
Input breaker
An input breaker, or circuit breaker, is an automatic switch, which protects the system
from damage caused by overload. If a fault condition is detected the input breaker imme-
diately discontinues the electric flow. When the breaker is activated the wind turbine is be
free spinning, as there is no resistance from the generator. The previously described shut-
down switch should therefore be activated once the input breaker is activated in order to
brake the wind turbine.
Battery Bank
It is recommended to use deep-cycle lead-acid batteries, which, contrary to normal lead-
acid automotive batteries, may be fully discharged without damage. The size of the battery
bank and the manner in which the individual batteries are connected depends on the spe-
cific needs and will therefore vary from site to site.
Earthing system
IEC 61400-2 requires that the wind turbine design includes a local earthing system,
which ensures that tower (including guy wires) are appropriately earthed to reduce
damage from lightning [5, p. 111].
73

GENERATOR AND ELECTRICAL SYSTEM
74
7.3 Summary
Several types of generators with different advantages and disadvantages were presented
as options for the wind turbine design. The AFPM generator was selected due to the fact
that it does not require any transmission and due to the possibility of building the gen-
erator locally in a developing country.
The working principle of the chosen generator was described and a peripheral descrip-
tion was made of the components of the electrical system. In-depth design of the genera-
tor and development of power control and energy storage devices was stated as beyond
the scope of this project thesis.

8
Yaw and furling
This chapter describes the yaw and furling system, which are integral parts of the pro-
posed wind turbine design. The two systems are closely connected, but described sepa-
rately to the extent that it is possible.
8.1 Yaw orientation system
The fundamental purpose of the yaw orientation system is to keep the rotor facing into
the wind, that is, to align the rotor shaft with the wind direction. If the rotor is to fully
capture the power available in the wind, it must be properly oriented to the wind direc-
tion. Figure 8.1 illustrates an example of the decreased performance for various yaw
angles.
Figure 8.1: Decreased performance for various yaw angles [10, p.91]
75

YAW AND FURLING
For an upwind wind turbine design the basic options for a yaw orientation system are:
76
� Yawing by aerodynamic means (tail vane)
� Active yawing with motorised yaw drive
The first option is the obvious choice for small and simple wind turbines and the solution
is therefore adopted for the present wind turbine design. The design is illustrated in
figure 8.2. The wind force on the tail vane ensures that the turbine corrects its direction
as the wind changes intensity and direction.
Figure 8.2: Adopted tail vane design
Figure 8.3 shows the shows a cross-sectional view, revealing the inner components of the
yaw system. The figure is followed by a description of the components.
Figure 8.3: Section view of the yaw system

YAW AND FURLING
The inner layout of the yaw system consists of two main components: A stationary inner
part and an outer part that rotates freely about the inner part. The inner yaw pipe (1) is a
ø101.6x16 mm pipe, welded to a flange (2), which connects the yaw system to the upper
part of the tower by means of a flange assembly with 6 pcs. M16 bolts (11). On top of the
inner pipe there is an end cap (3), fitted with a thrust ball bearing with sphered housing
washer (4). The inner end cap has a centre hole, which allows the wires from the generator
to be run through the tower-top. The weight of the tower-top is transferred to the thrust
bearing through an outer end cap (8), which also has a centre hole, and is mounted with 8
pcs. M6 bolts (9). The nacelle cover, seen on figure 5.1, keeps water and dirt from entering
the assembly. The thrust ball bearing absorbs the load from the tower-top dead-weight
and minimises the frictional forces when the system is yawing. The spherical washer re-
duces misalignment between the inner and the outer parts of the complete yaw system. To
further reduce friction in the yawing mechanism, bronze bearings are mounted at the top
(7) and the bottom (6) of the outer yaw pipe (5), which is a ø127x12.5x580 mm pipe. The
lower bearing (6) is mounted with 8 pcs. M6 bolts (10). To meet tolerance and surface
roughness requirements in the bearing contact area, the outer diameter of the inner yaw
pipe is machined. The top and bottom parts of the inner diameter of the outer yaw pipe are
also machined to ensure a proper fit and alignment of the bearings in the pipe. The flange
components (12) and (13) secure the vertical movement of outer yaw pipe, and the entire
tower-top. During normal operation this preventive measure is not necessary as the dead-
weight of the tower-top will keep it in place. It is however needed during erection and
lowering of the tower, since the ball cage and the washer of the thrust bearing are separa-
ble. To minimise friction there is a vertical air gap between the upper flange part (12) and
bearing flange (6). The air gap is 2 mm, which is small enough to keep the bearing from
separating and considered large enough to absorb assembly and machining tolerances.
The outer components of the yaw system, which are directly attached to the tower, are
shown on figure 8.4. The figure is followed by a description of the components.
Figure 8.4: Isometric view of the outer yaw system
A 10 mm steel base plate (14) is welded to the outside of the outer yaw pipe and
strengthened by a 5 mm support plate (19). The shaft is mounted in two blocks (15) and
77

YAW AND FURLING
(16), which are bolted onto the base plate using two M16 bolts each. Rotation of the shaft
is prevented by parallel key connection between the shaft and the rear block (16). Axial
motion of the shaft is prevented with the retaining washer (17) that is connected to the
shaft with a M30x1.5 thread and bolted into the rear generator block with 4 pcs. M10
bolts (18). The tail boom of the wind turbine is mounted on an inclined pivot pin (20),
which has a lower and upper diameter of ø45 mm and ø35 mm, respectively. The diamet-
rical step is made with a 4 mm radius to reduce notch effect. A tail stop (21) is welded
onto the pivot pin with the purpose of limiting the movement of the tail vane. The entire
pivot system is welded onto the outer yaw pipe by means of two 5 mm fastening plates
(22). The pivot system is tilted backwards 40� and it is angled 45� about the z-axis with
reference to the xz-plane of figure 8.4. The inclinations are key parameters of the furling
system, which is described in section 8.2 and appendix I.2.
The remaining parts of the yaw system are shown below on figure 8.5, which is followed
by a component description.
78
Figure 8.5: Tail boom and tail vane
The tail boom (23) is a 1960 mm steel pipe with an outer diameter of 33.70 mm and a
wall thickness of 4.00 mm. The tail vane (24) is bolted onto the tail boom by means of two
8x30x800 mm brackets (26) and 8 pcs. M10 cup head bolts (25). The tail vane is a 10 mm
wooden plate, measuring 1300 mm by 900 mm. The sleeve (27) is a 45 mm cold-drawn
precision steel pipe with a wall thickness of 5 mm and a length of 220 mm, which is
welded onto the tail boom with an 8 mm support plate (31). The tail boom and the sleeve
are angled, so that the tail vane is vertical during normal operation. The bronze bearings
(28) and (29) are mounted in both ends of the sleeve to reduce friction. A tail stop (30),
equal to that of figure 8.4, is welded onto the bottom of the sleeve and a M6 bolt, not
shown on figure 8.5, is used to secure the entire tail vane system on the pivot.
Appendix I.1 contains a calculation of the yawing system, which validates the dimensions
of the tail vane and the ability of the wind turbine to approximately align itself in a situa-

YAW AND FURLING
tion where the wind speed changes from near zero to 4 m/s, where power production is
initiated. The worst case yaw error is calculated to 3.50�. A structural calculation of the
bearing contact pressure in the upper yaw bearing is carried out in appendix I.3. Other
structural calculations related to the yaw system may be found in appendix H.1 and H.2.
Analysis of the yaw behaviour during operation is beyond the scope of this project. While
theoretical calculation of the thrust on the rotor, in the case of perfect alignment with the
wind direction, can be performed using the BEM theory of the developed rotor design
tool, its calculation in the case of a yawed rotor is far from straightforward. The torque
generated by the thrust on the yawed rotor is further complicated by lift and drag forces
acting on the tail vane, which also generate a torque about the yaw axis. In addition to
this the wind seen by the tail vane, and thus the aerodynamic forces on it, are affected by
the wake of the rotor. For further information reference is made to the research of [35],
which presents advanced models of the dynamics of a gravity-controlled furling system,
similar to the present.
79

YAW AND FURLING
80
8.2 Furling system
Over-speed and power output control is needed to prevent the wind turbine from captur-
ing excessively high wind speeds that may overload mechanical and electrical compo-
nents. Among commonly used control mechanisms are stall control and furling control.
The present design uses a gravity-controlled furling system as shown on figure 8.6. This
furling mechanism is advantageous compared to other types of furling systems in that it
does not require counterweights or springs.
Figure 8.6: Top view of the furling and yaw system. Top: Normal operation. Bottom: Furled
operation
The simple appearing furling control mechanism is based on an eccentric positioning of
the rotor and the tail vane with respect to the yaw axis.
At wind speeds up to 14 m/s the tail vane properly orients the wind turbine, as described
in section 8.2. At higher wind speeds the tail vane remains approximately aligned with
the wind direction, while the increasing thrust force on the rotor creates a yawing mo-
ment, due to the lateral offset of the rotor, which tends to turn the rotor out of the wind in
the horizontal plane.

YAW AND FURLING
As shown on figure 8.7 the furling axis is tilted compared to the yaw axis. This inclination
causes the tail vane to rise during the furling action, thus creating an increase in the po-
tential energy of the tail vane.
Figure 8.7: Raising tail vane. Top: Normal operation. Bottom: Furled operation with inclined
tail vane.
The instantaneous position of the furled rotor is a balance between the gravity force on
the tail vane and the thrust force on the rotor. Equilibrium of the system is established
under stationary conditions when the torque around the yaw axis balances the gravity
torque around the furling axis. When the wind speed decreases below the critical value of
14 m/s, the rotor is automatically recovered from the furled position and realigned with
the wind direction by the restoring moment provided by gravity.
Appendix I.2 verifies the overall functionality of the furling mechanism by confirming
that furling is initiated at a wind speed of 14 m/s (equivalent to a thrust force of 872 N).
The power production beyond the onset of furling is not analysed in the present project,
as it is beyond the limitations of the BEM theory described in appendix B.1.
81

YAW AND FURLING
82
8.3 Summary
The functionality of the yaw orientation system, which is used to keep the rotor aligned
with the wind, was described in detail. The system basically consists of a stationary inner
part and an outer part that may rotate by means of a tail vane that is connected to it.
The gravity-controlled furling system was also described in detail. It functions as an over-
speed and power output control mechanism, which turns the rotor out of the wind at
wind speeds beyond 14 m/s.

9
Tower
The present chapter begins with a description of the various options that are available for
the tower, which constitutes the support structure of the wind turbine. It continues with
a selection of the most suited tower type and concludes with a description of its design
and installation.
9.1 Tower options
A brief description of the most prevailing tower types, including their advantages and
disadvantages, is given below.
Lattice tower
The lattice tower, or truss tower, is a simple design that provides the ability of creating a
both stiff and tall tower. For this reason the lattice tower was the preferred tower design
of the first experimental and small commercial wind turbines [36, p. 422]. The lattice
tower is manufactured using welded steel profiles. In countries where the labour costs
are low the lattice construction is an economical solution, as it only requires half as much
material to obtain the same stiffness as free standing tubular tower. In countries with
high labour costs the economical advantage is limited or non-existent [37, p. 35]. figure
9.1 shows a typical lattice tower.
83

TOWER
Concrete tower
84
Figure 9.1: Lattice tower [38]
In the 1930s steel-reinforced concrete was used for wind turbine towers in Denmark.
As with the lattice towers, the concrete towers are characteristic for the early large ex-
perimental wind turbines [36, p. 422]. Steel has been dominating the market for large
wind turbines, but due to increasing manufacturing costs and increasing hub heights,
concrete towers are becoming increasingly popular again [37, p. 35].
Free-standing tubular tower
The free-standing tubular tower of either steel or concrete is the most common tower
type. The structural mass, and thus the cost of the tower, is lowered considerably with
this design. The tower has a relatively soft design, which makes it necessary to have in-
depth knowledge of its vibrational behaviour. figure 9.2 shows a typical free-standing
tubular tower [36, p. 422].
Guyed towers
Figure 9.2: Free-standing pole tower [38]
Guyed tower constructions are by far the most common choice for small wind turbines.
They provide a good compromise between strength, ease of installation, cost and appear-

ance. Their disadvantage is that the foot-print area is large compared to that of freestand-
ing towers. Guyed towers basically consist of a pipe, a tube or a slender lattice tower, guy
wires and ground anchors. They are usually designed as tilt-up towers with a gin pole
[39, p. 155]. The typical guyed tower with two guy level is shown on figure 9.3.
Special tower designs
Figure 9.3: Guyed tower [38]
Besides the prevailing tower types mentioned, there are some special tower designs that
are either hybrids of the mentioned types or novel towers. The hybrids may be slender
lattice towers or concrete towers that are additionally fitted with guy wires [36, p. 423].
The novel towers include rooftops, silos, wooden poles and trees. None of them are very
suited as towers for wind turbines due to turbulence and vibrations in the structure on
which they are mounted [39, p. 156-159]. Furthermore they all require availability of the
particular structure at the desired site.
9.2 Design and height selection
Due to its many advantages as tower construction for small wind turbines, a guyed steel
pipe tower with a tilt-up gin pole design is chosen for the present wind turbine.
When selecting the tower height many factors must be taken into account and the opti-
mum height is highly dependent on the site of installation.
Turbulence is one of the key factors that must be considered when selecting the tower
height. Light turbulence will decrease performance since the wind turbine will be unable
to react to the rapid changes in wind direction, and heavy turbulence may reduce equip-
ment life or result in wind turbine failure. Hill tops that are high and rough can produce a
significant amount of turbulence in the airflow. The wind turbine on the top of the hill in
figure 9.4 is exposed to high wind speeds and to severe turbulence. The turbine on lower
grounds is free of most of the turbulent airflow, it will however be leeward when the
wind direction reverses.
TOWER
85

TOWER
86
Figure 9.4: Turbulent air flow on the top of a hill [40]
Trees and other obstacles, such as a sea cliff create turbulence as well. The closer to the
obstacles the wind turbine is located, the greater the height required by the tower if the
turbulent airflow is to be avoided. The airflow close to obstacles is illustrated in figure
9.5.
Figure 9.5: Turbulent airflow near to trees and sea cliffs [40]
Another key factor to consider is ground drag, or surface drag, which lowers wind speed
near the ground due to friction and thus restricts the performance of a wind turbine. Up
to a considerable height, the least expensive way to increase the performance of the wind
turbine is to increase the tower height [40]. An empirical model for calculating the in-
creasing wind speed with increasing tower height is known as the wind shear low [5, p.
25]:
V �
V0
Where V is the wind speed at the height H above the ground, and V0 is the wind speed at a
reference height H0. The power law exponent � depends on the surface roughness [39, p.
479]. For low grass prairies in the American Great Planes, it is often set to 1/7 [39, p.
489], while IEC 61400-2 defines it as 0.2 [5, p. 47].
Since the present wind turbine is targeted for a variety of different installation sites in
developing countries and not a specific site, it is not possible to take into consideration all
of the above factors. Instead the hub height is set to 12 m in collaboration with EWB, as it
is considered a likely minimum height in many terrains. It should be noted that the wind
speeds of the IEC Class IV site, described in appendix A.1, all apply at hub height.
�
�
�
H
H0
�
�
�
(6.7)

9.3 Tower design
The upper part of the guyed tower design is shown on figure 9.6:
Figure 9.6: Illustration of the upper part of the tower
TOWER
The tower (1) is a ø168.3x7.1 mm steel pipe with a length of 11.3 m. A flange (2) is welded
onto the top of the pipe, providing an interface for the yaw system. Due to the height of the
tower it may be necessary to weld the tower from shorter pieces of pipe.
The tower is mounted with three guy wires (3) in two levels. The upper attachment brack-
ets (4) are positioned as high up the tower as possible, but below the blade radius, as to
prevent collision between the brackets and the rotor blades during operation. The upper
guy wires are attached at an angle of approximately 30� to vertical while the angle for the
lower guy wires is approximately 50� to vertical. The lower brackets are positioned half-
way between the upper brackets and the ground with the intention of preventing buckling
of the tower. With a height of 12 m the foot-print radius of the guy wires is approximately
6 m.
87

TOWER
Figure 9.7 shows the tower base:
88
Figure 9.7: Tower base
The 6 m gin pole (5) has a diameter of ø101.6x6.30 mm and it is used in the erection of the
wind turbine, described in section 9.4. The two guy wires adjacent to the gin pole are at-
tached to it in order to prevent the joint between the tower and the gin pole from being
overloaded during erection and lowering of the wind turbine. The joint is strengthened
with a 6 mm support plate (6) that is welded on both sides.
The tower base hinge consists of a 20 mm tower base plate (8), upon which two 20 mm
steel plate hinges (9) are welded. The latter are supported by 6 mm triangular steel plates
(10) that are welded onto both the tower base plate and the hinges. A ø40x270 mm shaft
is used as pivot pin (7), which slides in a ø50.0x5.00 mm sleeve, welded to the tower. The
tower base plate is mounted onto the foundation with 4 pcs. M16 bolts that make up a
300x300 mm pattern. Design and dimensioning of the bolts and the foundation for both
the tower and the guy wires is very site specific and largely dependent on the structure of
the soil.

9.4 Installation
The design of wind turbine requires the installation to be manual, i.e. without the need of
a crane. The tower design complies with the requirement by using a tilt-up construction
with a gin pole. The principal installation method is shown on figure 9.8 and described
below:
Figure 9.8: Erection of the wind turbine
The wind turbine is fully assembled on the ground prior to erection. A gin pole is at-
tached to the base of the tower and positioned perpendicular to it. The tower base plate
is mounted onto the foundation and the tower is attached to the base plate using a pivot
pin. The gin pole is welded onto the tower and all guy wires are attached. The guy wires
that are adjacent to the gin pole are attached to it. Finally a towing wire is connected to
the end of the gin pole and attached to a pulley. The tower may now be erected by pulling
the wire attached to the towing point. When the tower is in vertical position the remain-
ing guy wires are attached to the foundation and tightened appropriately.
The maximum force needed to erect the turbine is 8.22 kN (att. 13). The needed force
may be reduced by adding pulleys to the block and tackle system.
9.5 Structural calculations
Structural calculations of the tower are performed in appendix H, which also contains
calculations for parts of the yaw system. The calculations are in accordance with the load
cases of IEC 61400-2 and thus comprise structural verification of the tower in survival
wind and during installation.
Further calculations are needed to fully verify the structural integrity of the tower. Al-
though these are beyond the limits of the present project thesis a few guidelines are given
below, which may be used by future projects that deal with tower dimensioning.
Generally speaking the analysis of guyed towers is complicated because of geometrically
non-linear behaviour. This is caused by the increase in axial stiffness of guy wires with
increasing tension and decreasing bending stiffness of the tower due to the compressive
forces from the guys. Analytical methods, which approximate the guyed tower as a beam-
column on nonlinear elastic supports, may be used for analysis a long with finite element
TOWER
89

TOWER
models [41, p. 111]. Under certain conditions the guyed tower may be analysed using
simplified models of EN 1993-3-1.
The future tower analyses should comprise
90
� Dimensioning of foundation base joint
� Dimensioning of guy wire attachments
� Dimensioning of guy wires in acc. with EN 1993-1-11
� Fatigue analysis of tower in acc. with EN 1993-1-9
� Buckling analysis
As with the rotor blades (see appendix E.11) the natural frequencies of the tower should
be determined in order to assess whether it is at risk of being subjected to dynamic am-
plifications. The most important consideration is to avoid natural frequencies of the
tower that are near rotor frequencies, i.e. 1P and 3P frequencies, as described in appen-
dix E.11. Distinction is made between soft towers, which have a natural frequency below
the blade-passing frequency (3P), and stiff towers that have a natural frequency above
that frequency [12, p. 197].
9.6 Summary
Several tower options were presented and a guyed tower construction with a height of 12
m was selected, as it constitutes a good compromise between strength, ease of installa-
tion, cost and appearance. The possibility of manual installation of the tower was docu-
mented through a description of the installation procedure.
Structural calculations of the tower were carried out and directions were given for the
further verification of the structural integrity, which is beyond the limits of this project.

10
Alternative blade design
The option for an alternative blade design, which is based on a simple airfoil, is investi-
gated in this chapter.
The blade geometry of the design proposal, described in section 6.2, is based on a NACA
airfoil which has good aerodynamic properties and decent manufacturability. It is however
possible to utilise simpler airfoils that have reduced aerodynamic properties, but superior
producability when considering the available manufacturing options in developing coun-
tries. Among home builders of wind turbines it is a widespread concept to use simple
curved airfoils, which enable the turbine blades to be made from e.g. cut-out sections of
plastic drain pipes or from rolled steel plates.
The considered potentials of using an alternative blade design based on a simple airfoil
are:
� Blade that may be produced easily and by simple means
� Increased flexibility as the alternative design may be used when the NACA-based
design is inconvenient
It is beyond the scope of this project thesis to fully design a blade other than the one al-
ready described in section 6.2. It will however perform a preliminary investigation of the
possibility of using simple airfoils. This is done firstly by testing lift and drag properties of
a simple airfoil. Although widely used, virtually no data is available on the simple airfoils
and it is therefore found necessary to design the test airfoil. Two different candidates are
designed and the best is selected from the test results. Secondly the test data is employed
in the rotor design tool with the aim of designing a rotor with performance equal to that of
the current NACA-based rotor at a wind speed of 12 m/s. This provides a preliminary view
of the resulting blade dimensions and the rotor efficiency when using a simple airfoil, and
thus gives an indication of whether it is applicable in the design.
91

ALTERNATIVE BLADE DESIGN
92
10.1 Airfoil design
The airfoil design candidates shown on figure 10.1 are inspired by a survey of different
existing designs [42], [43] and [44]. The airfoils are basically curved plates with different
radii and chamfered edges. Both may be manufactured either from pipe cut-outs or from
rolled plates.
Figure 10.1: Main dimensions of the two alternative airfoils. Wall thickness is 5 mm for both
airfoils. Left: Airfoil A. Right: Airfoil B.
It is incontestably possible to optimise the developed designs, but this is beyond the scope
of this project thesis.
The airfoil profiles are tested as described in appendix J, which also contains a full report
of the test results. The evaluation of section 10.2 is based on the test results.

10.2 Design evaluation
ALTERNATIVE BLADE DESIGN
From appendix J it is seen that profile A exhibits the best aerodynamic properties. These
are repeated on figure 10.1, which shows the lift coefficient Cl, the drag coefficient Cd and
the glide ratio GR of profile A. The error bars of figure 10.1 show the standard deviation
of three independent tests. This is further elaborated in appendix J.
Figure 10.2: Lift coefficient Cl, drag coefficient Cd and glide ratio GR of profile A
The glide ratio is approximately 10% of the NACA 4412 glide ratio, which indicates a
significantly lower aerodynamic performance.
The airfoil data is employed in the rotor design tool by the method described in Appendix
D. On basis of this, a three-bladed rotor is designed to have the same power output as the
NACA-based rotor at a wind speed of 12 m/s. Using a tip-speed ratio � of 4 and a fixed
blade pitch � of 6�, the resulting blade radius is 2.05 m and the rotor efficiency is 40% (Cp
= 0.24). This should be compared to the 1.35 m blade radius of the current design that
has an efficiency of 93% (Cp = 0.55). Full details of the rotor tool calculation are provided
as att. 5.
The more than 50% increase in blade length results in considerably higher loads on each
blade. Whether it is possible for the blade to structurally withstand the loads, depends on
the material used. It is considered unlikely that a section-cut plastic drain pipe of the
given length is strong and stiff enough, but a steel plate or a reinforced pipe section might
suffice. Further development of the airfoil and structural verification of the blades that
are based on it is left to a future project, as described in chapter 12.
93

ALTERNATIVE BLADE DESIGN
94
10.3 Summary
The option of using simple airfoils for the blade design was investigated, as it potentially
makes it possible to produce blades by even simpler means than with the current design.
Two different designs based on curved plates were subjected to wind tunnel tests and the
best candidate was selected. The test and subsequent analysis of the results showed that
to achieve the same power output with the simple airfoil as with the current, the blade
length would have to be increased from 1.35 m to 2.05 m. The possibility of creating a
blade of this length with sufficient structural strength was recommended to be investi-
gated in a future project.

11
Design evaluation
This chapter contains an evaluation of the developed wind turbine design. A statement of
how the wishes and demands of the requirement list are met is made in table 11.1.
ID D/W Requirements
1 D 1500 W ± 1% nominal power output from the generator a
The electrical power output of the wind turbine is 1506 W at a rated wind
speed of 12 m/s. The performance characteristics are fully reported in section
6.3.
2 D 48 V DC system voltage
The proposed electrical outputs a system voltage of 48 V DC by means of a
rectifier.
3 W Ability to manufacture the wind turbine locally using standard operations
The wind turbine components may be manufactured using standard operations
such as turning, milling and welding, which facilitates local manufacturing.
4 W Flexibility in choice of blade materials
Wood is used for the rotor blades, but as requested the material choice is
flexible and may be altered without making extensive changes to the general
design.
5 W Low manufacturing tolerance demands
The major part of the wind turbine components have tolerance demands
that are equal to those easily obtained when applying the necessary manufacturing
methods. Bearing surfaces have more rigorous tolerance requirements
in order to comply with engineering standards. Deviation from these
would decrease the product quality. Balancing methods that rectify the
obtainable tolerances from manual carving of the rotor blades are described
in section 6.2.3.
95

DESIGN EVALUATION
96
6 W Low-cost materials and parts
Common steel and wood are the main materials used in the wind turbine
design. Both are relatively inexpensive and widely available in developing
countries. The permanent magnets required for the generator are however
less available and relatively expensive.
7 D Compliance with selected parts of IEC 61400-2
The IEC standard defines the environmental conditions that are used for
aerodynamic performance calculations. It is further used for establishing
loads cases, which form the basis for structural calculations.
8 W Ability to perform localised maintenance
The common materials used for the wind turbine and the standard operations
needed for component manufacturing, ease localised maintenance and
component replacement.
9 W Low maintenance requirements and high life expectancy
Features such as corrosion protection, sealed bearings and a protectivenacelle
cover, yield generally low maintenance requirements. The longevity of
the wind turbine is estimated to at least 19 years (limited by the wooden
blades).
10 W Flexibility for reconfiguration with different components
If convenient several components, including tower and rotor blades, may be
replaced without changing the design as a whole. Exchanging the generator,
which is a highly integrated part of the proposed design, requires several
constructional modifications, but it is a valid option.
11 D Ability to install wind turbine manually, i.e. without a crane
A gin pole lifting system enables manual installation of the tower.
Table 11.1: Statement of how the product wishes and demands of the requirement list are
met
From table 11.1 it is concluded that the solution is functional for the intended purpose, as
the product demands are met. It is further concluded that the solution is of considerable
quality, as the product wishes generally are fulfilled to a high degree.
A SWOT analysis has been carried out as a supplement to the statement of table 11.1. The
purpose of the analysis, shown on figure 11.1, is to identify the overall the Strengths,
Weaknesses, Opportunities and Threats of the developed wind turbine design.

Strengths
1) Qualified selection of concept
2) Direct drive
3) Prevailing materials
4) Flexible choice in materials and com-
ponents
Opportunities
1) Full compliance with IEC 61400-2
2) Alternative blade design
3) Scaling of design
Figure 11.1: SWOT analysis
Weaknesses
DESIGN EVALUATION
1) Divergence of actual performance
2) Only designed for Class IV site
Threats
The items of the SWOT analysis are elaborated below
Strengths
1) Availability and price of permanent
magnets
2) Not all components are covered by the
present work
1) The HAWT concept is adopted on basis of through investigations in the conceptual
phase.
2) The direct drive principle makes it possible to omit the transmission, which would
otherwise complicate the design and the manufacturing process.
3) The use of prevailing materials, such as common steel and widely available wood
makes it probable that the wind turbine may be manufactured in most developing
countries.
4) Material selections may be altered and key components may be replaced without
compromising the overall design
97

DESIGN EVALUATION
Weaknesses
1) The wind turbine performance data is calculated from the BEM theory, which in-
98
volves assumptions and idealisations that do not occur in reality. The divergence be-
tween modelled performance and real performance is unknown, since no prototype
tests are performed as a part of the present project.
2) In accordance with the demands of EWB the wind turbine is designed for an IEC
Class IV site, which has an average wind speed of 6 m/s. If used at a site with a higher
average wind speed, the structural integrity of the wind turbine will have to be re-
verified
Opportunities
1) Full compliance with IEC 61400-2 may be obtained if the remaining tasks, defined in
chapter 12, are carried out in accordance with this standard.
2) An alternative airfoil design can potentially be used to achieve a production-wise
simpler blade.
3) The working principles of the wind turbine are highly scalable. Hence a 4 kW design
variant might be developed by scaling the components of the current design pro-
posal.
Threats
1) The permanent magnets used for the generator are relatively expensive and their
availability in developing countries may be low.
2) Certain parts of the wind turbine, e.g. the electrical system and the generator, are not
fully covered by this project thesis. These components may therefore cause problems
that cannot be foreseen at the current stage of development. Further elaboration of
what is not covered by the present work is be found in chapter 12.
11.1 Summary
A statement was made of how well the demands and wishes of the requirement list are
met by the proposed design. It was found that the demands were all met and it was thus
concluded that the design is useful for the intended purpose. It was further concluded
that the solution is of considerable quality as the product wishes are fulfilled to a high
degree.
A SWOT analysis was used to additionally identify strengths, weaknesses, opportunities
and threats of the design.

12
Further development
This chapter defines tasks that that must be completed in order to fully develop the wind
turbine design, but which are beyond the limits and exclusions of the present project the-
sis. The tasks are expected to be carried out as student chapter projects within EWB.
The identified tasks and associated future projects are listed below. Tasks marked with an
(S) are optional spin-off projects that are not mandatory to complete the proposed wind
turbine design.
� 2D drawings
Technical 2D drawings, which enable prototype manufacturing, should be produced. A
sample part drawing of the shaft is enclosed as att. 11.
� Generator
An axial flux permanent magnet generator with the characteristics described in sec-
tion 7.1 should be developed. A generator design tool, similar to the rotor design tool
developed as a part of this project thesis, would of great use in the development proc-
ess and in the creation of future variants. The design tool could use input variables
such as magnet strength, magnet size, wire dimensions, number of coils and number
of windings to output generator performance and efficiency. If the developed genera-
tor deviates from the intended, it may be necessary to initiate a project that trims the
rotor to fit the new generator.
� Electrical system
An electrical system of the wind turbine, with components similar to those described
in section 7.2, should be developed. Emphasis should be placed on selecting compo-
nents that are available in developing countries. It is additionally necessary to comply
with the requirements of IEC 61400-2 with regards to the electrical system in general
and to the protective system.
99

FURTHER DEVELOPMENT
� Foundation
100
A foundation support structure should be developed under proper consideration to
relevant soil properties. Specification of the foundation layout may be an integral part
of the tower design task below.
� Tower
Further verification of the structural integrity of the guyed tower is needed and modal
analysis is advised to forgo resonance excitation issues.
� Prototype
The development of a prototype serves multiple purposes: Firstly it enables verifica-
tion of the general operation of the wind turbine and its detail working principles of
e.g. the furling system. Secondly a prototype makes it possible to conduct materials
tests, performance tests and load measurements that will clarify current uncertainties
(e.g. the match between theoretical performance and actual performance, and the fa-
tigue strength of the wooden blades).
� Alternative blade design (S)
Using the alternative airfoil shape of chapter 10, or a further developed version of it, a
new blade design may be developed using the rotor design tool. Material options
should be investigated and the structural integrity of the blade is to be verified
� Dynamic modelling (S)
The behaviour of a yawed rotor and a furled rotor may be further analysed using dy-
namic modelling. This is a first step in enabling calculation of more precise perform-
ance when the incoming wind is not aligned with the rotor axis. The project is mainly
of academic interest.
� Full compliance with IEC 61400-2 (S)
The design proposal of the present project has been developed in accordance with IEC
61400-2. Full compliance with IEC 61400-2 may be obtained if the remaining tasks,
such as design of the electrical system, also comply with the specifications of the IEC
standard. The full compliance may be used in type certification of the wind turbine in
accordance with IEC WT01, IEC system for conformity testing and certification
of wind turbines - rules and procedures.

12.1 Summary
FURTHER DEVELOPMENT
Several tasks that must be completed to fully develop the wind turbine design were de-
fined. Special emphasis was placed on the design of an axial flux permanent magnet gen-
erator and the electrical system, as well as the development of a prototype.
Spin-off projects, which are not mandatory, but which may be of interest, were also de-
fined. These include dynamic modelling of a yawed and furled rotor, as well as the devel-
opment of an alternative blade design.
101

FURTHER DEVELOPMENT
102

13
Conclusion
This project thesis was initialised by EWB-DK with the intention to facilitate the develop-
ment of a wind turbine design that could be used in developing countries and potentially in
disaster areas. The main objectives of the project were to select the most suitable wind
turbine concept for the established purpose and to develop a viable wind turbine design,
capable of producing 1500 W of generator power at a wind speed of 12 m/s. The work of
this project thesis was focused primarily on the mechanical and aerodynamic design. It
was therefore further intended for it to define the future tasks needed to fully develop the
aspects of the wind turbine that were beyond its limits and exclusions.
A survey of numerous different wind turbines and their key properties was performed
with focus on already proven designs, including Savonius, Giromill and Darrieus turbines.
These were compared using conceptual engineering methodology and the horizontal-axis
wind turbine (HAWT) concept was found to be the most suitable type of wind turbine,
when taking into consideration the needed size of the wind turbine and the special re-
quirements for a wind turbine that is to be built and operated in a developing country.
A wind turbine design proposal was developed on the basis of the selected wind turbine
concept, which meets the performance requirement of 1500 W at 12 m/s. The proposed
design is an upwind three-bladed horizontal-axis wind turbine, which is self-regulating by
means of a passive yaw orientation system and a gravity-controlled furling system. A
guyed tower, which may be installed manually without a crane, is used as support struc-
ture. The wind turbine design features a direct drive concept that eliminates the need for a
transmission in the drive train. The development of this key feature was highly advanta-
geous as it simplified the design and reduced the amount of production-wise complex
components. The direct drive was made possible by the use of an axial flux generator with
permanent magnets (AFPMG), which may be produced by relatively simple means.
The details of the wind turbine were determined under great consideration to the estab-
lished design requirements. Hence, components are made from prevailing materials such
as steel and wood, and they may be manufactured using standard operations. The design
103

CONCLUSION
proposal is highly flexible in that blade material and certain components may be substi-
tuted without compromising the overall design. A high engineering quality of the solution
was maintained, so that the wind turbine may function as a viable platform for local de-
signs, which may deviate from the proposed.
The design of the rotor was carried out using a rotor design tool, which was developed as a
part of this project thesis on basis of the BEM theory. The tool enables iterative calculation
of aerodynamic flow conditions, forces, blade shape and rotor performance. Structural load
cases were established in accordance with IEC 61400-2 with the purpose of verifying the
integrity of key components, including blades, shaft and tower. The load cases take into
consideration all relevant loads with a reasonable probability of occurrence during normal
and faulty operation. The structural verification was carried out using analytical and nu-
merical methods, which included calculation of ultimate stresses, fatigue stresses, deflec-
tions and natural frequencies. All components were designed so that their limit states were
not exceeded.
The technical specification of the wind turbine and the calculations were documented in
the present project thesis and its appendices. Further documentation, including a complete
3D CAD model and various print-outs, were provided as attachments.
Through a design review it was established that the developed wind turbine design meets
the demands of the requirement list and thus is functional for the intended purpose of
producing electricity in developing countries. It was further found that the solution is of
considerable quality as the product wishes are fulfilled to a high degree. A SWOT analysis
was used to additionally identify the overall strengths, weaknesses, opportunities and
threats of the design.
In closure the work defined the tasks that are considered necessary to fully complete the
developed wind turbine design. These include the complete development of a generator,
an electrical control system and a foundation. It was recommended to develop a prototype,
which will add the possibility of verifying the working principles of the design and to make
performance measurements. It was additionally suggested to further investigate the de-
velopment of a blade design, which is based on a simple airfoil that have superior produ-
cability when considering the available manufacturing options in developing countries.
104

14
Nomenclature
The nomenclature provides an overview of the majority of the used symbols, subscripts,
abbreviated terms and coordinate systems. It should be noted that a dot is used as decimal
point, throughout the project thesis.
Three coordinates systems are defined for the wind turbine and its components.
Wind turbine
The wind turbine system is fixed to
the tower. x is positive in the
downwind direction, z is pointing
up, y completes right hand coordi-
nate system.
Shaft
The shaft axis system rotates with
the nacelle. x is such that a positive
moment about the x axis acts in the
rotational direction. z is pointing
up, y completes right hand coordi-
nate system.
Blade
The blade axis system rotates with
the rotor. x is such that a positive
moment about the x-axis acts in
the rotational direction. y is such
that a positive moment acts to
bend the blade tip downwind. z is
positive towards the blade tip.
105

NOMENCLATURE
Abbreviation Description
AFPMG Axial flux permanent magnet generator
BEM Blade Element Momentum
CCW Counter clockwise
CF Capacity factor
CW Clockwise
DBRI Danish Building Research Institute
EWB Engineers Without Borders
HAWT Horizontal-axis wind turbine
IHA Engineering College of Aarhus
MC Moisture content
PM Permanent magnet
RH Relative humidity
TSR Tip-speed ratio
VAWT Vertical-axis wind turbine
Subscript Description
ann Annually
B Blade
design Input parameter for the simplified load equations
dw Dead-weight
fr Friction
g Generator
h Embedding strength
i Incremental value
L,R,T Designate longitudal, radial and tangential direction to fibres on blades
M Moment
max Maximum
pi Press-in connector
r Rotor
S Shaft
T Tower
tf Thrust force
tot Total
v Tail vane
x x-component
y y-component
z z-component
106

Symbol Description Unit
a Axial interference factor [-]
A Rotor swept area [m 2 ]
a' Tangential interference factor [-]
NOMENCLATURE
Ab Bearing area [mm 2 ]
Aproj Component area projected on to a plane perpendicular to the
wind direction
AS Aspect ratio [-]
B Number of blades [-]
c Blade chord length [m]
Cd Drag coefficient [-]
Cd.st Coefficient of drag at the onset of stall [-]
Cf Force coefficient [-]
Cl Lift coefficient [-]
Cl.st Coefficient of lift at the onset of stall [-]
Cp Power coefficient [-]
CT Thrust coefficient [-]
Cx Coefficient of tangential forces [-]
Cy Coefficient of axial forces [-]
D Rotor diameter [m]
[m 2 ]
db Bolt diameter [mm]
Db Bearing diameter [mm]
Dpc Bolt pitch diameter [mm]
e Natural logarithm [-]
E Modulus of elasticity [MPa]
er Distance from centre of gravity of the rotor to the rotation axis [m]
Ev Potential energy of tail [J]
F Prandtl’s number [-]
f� Constant [-]
Fd Drag force [N]
fk Characteristic material strength [MPa]
Fk Characteristic capacity [N]
Fl Lift force [N]
FxS Axial shaft load [N]
FzB Force in z direction on the blade at the blade root [N]
g Acceleration due to gravity: 9.81 [m/s 2 ]
G Shear modulus [MPa]
GR Glide ratio [-]
IB Blade mass moment of inertia about rotation axis [kg·m 2 ]
K Factor [-]
kmod Modification factor [-]
Lfs Distance between tower flange and rotor axis [mm]
107

NOMENCLATURE
Lgs Distance between upper guy wire and rotor axis [mm]
Lrb Distance between rotor centre and first bearing [mm]
Lrt Distance between the rotor centre and the yaw axis [mm]
LTB Distance between tower and blade [mm]
M Moment [Nm]
mB Blade mass [kg]
mr Rotor mass incl. generator [kg]
MS Shaft bending moment at the first bearing [Nm]
Mst Starting torque in thrust bearing [Nmm]
MT Tower moment [Nm]
mv Mass of tail [kg]
MxB Blade root bending moment [Nm]
MxS Torsion moment on the rotor shaft at the first bearing [Nm]
MyB Blade root bending moment [Nm]
n Rotational speed [rpm]
nb Number of bolts [-]
p Bearing contact pressure [MPa]
Pave Average Power [W]
pd Dynamic pressure [bar]
Pg Electrical power from generator [W]
Pr Rotor power [W]
Q Rotor torque [Nm]
r Radial coordinate [m]
R Radius of the rotor [m]
RB Bearing reaction force [N]
Rcog Distance between COG of a blade and the rotor centre [m]
Rdw Reaction force from dead-weight [N]
Re Reynolds number [-]
Rtf Reaction force from thrust [N]
Td Design life [yr]
V Wind speed [m/s]
Vave Annual average wind speed at hub height [m/s]
Vdesign Design wind speed defined as 1.4Vave [m/s]
Ve50 Extreme wind speed with a recurrence time interval of 50 years [m/s]
Vhub Wind speed at hub height averaged over 10 min [m/s]
Vref Reference wind speed [m/s]
Vtip Speed of the blade tip [m/s]
W Relative wind speed [m/s]
Wr Work performed by furling rotor [J]
WS Section modulus of shaft [mm 3 ]
WT Section modulus of tower [mm 3 ]
108

� Angle of attack [°]
�st Angle of attack at the onset of stall [°]
� Pitch angle of the blade to rotor plane [°]
�f Furling angle [°]
� Angle of relative wind to rotor axis [°]
�f Partial safety factor for load [-]
�m Partial safety factor for material [-]
� Range [-]
NOMENCLATURE
�h Height difference [mm]
� Efficiency [-]
� Shear stress [MPa]
� Tip-speed ratio [-]
�50 Tip-speed ratio at Ve50 [-]
� Poisson’s ratio [-]
�m Mean value [-]
� Kinematic viscosity of air, assumed 14e-6 [m 2 /s]
� Air density, assumed 1.225 [kg/m 3 ]
� w Wood density [kg/m 3 ]
� water Water density, assumed 1000 [kg/m 3 ]
�’ Solidity ratio [-]
�design Design stress from load case [MPa]
�eq Equivalent stress [MPa]
�lim.f Fatigue limit state stress [MPa]
�lim.u Ultimate limit state stress [MPa]
� Angle of relative wind to rotor plane [°]
�st Standard deviation [-]
� Angular speed of the rotor [rad/s]
�yaw Yaw rate [rad/s]
109

NOMENCLATURE
110

15
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[61] S. Fahey, Performance Testing a Homebrew Axial Flux Generator. 2007. URL:
http://www.greenenergywindturbine.com/download/AXIAL_FLUX_Testing_V2%5B1%5D
.pdf.
[62] SIMPSON Strong-Tie, Bulldog Mellemlæg. Retrieved: 12/9/2010. URL:
http://www.strongtie.dk/page229.aspx?recordid229=134.
[63] NASA - National Aeronautics and Space Administration, Inclination Effects on Lift and
Drag. Retrieved: 12/10/2010. URL: http://www.grc.nasa.gov/WWW/K-
12/airplane/kiteincl.html.
[64] F. M. White, Fluid Mechanics. New York: McGraw-Hill Education, 2008.
[65] H. O. Nielsen, Uddrag Af Stålkonstruktioner M504: Dimensionering Af Cirkelformet
Flangeforbindelse. Engineering College of Aarhus.
[66] NASA - National Aeronautics and Space Administration, Open Return Wind Tunnel.
Retrieved: 12/10/2010. URL: http://www.grc.nasa.gov/WWW/K-
12/airplane/tunoret.html
114

115
Att. no. Description
1 Time schedule
2 CD
3 Thrust ball bearing
4 Spherical ball bearing
5 Alternative airfoil design
6 Cost calculation
7 Moment from dead-weight
8 Rotor design tool print-outs
9 Airfoil coordinate data
10 Generator data and drawings
11 2D drawings
12 Component diagram
13 Erection force
14 Johnson Metal
15 Presentation folder
16 Flange connection
16
List of attachments

LIST OF ATTACHMENTSBASIS FOR CALCULATIONS

117
APPENDICES
The following appendices include material that is pertinent to the main report, but which
has been found too detailed to be included in the main text.

LIST OF ATTACHMENTSBASIS FOR CALCULATIONS

A
Basis for calculations
Wind turbines are subjected to environmental conditions that effect their loading, durabil-
ity and operation. To ensure an appropriate level of safety and reliability these conditions
are explicitly defined in this appendix and taken into account in the design.
The environmental conditions are divided into wind conditions and other environmental
conditions. Section A.1 contains the wind conditions that are the primary external consid-
erations for structural integrity and aerodynamic performance. Section A.2 defines other
relevant environmental data, such as air density and temperatures.
Load cases, which form the basis for structural calculations in accordance with IEC 61400-
2, are established in section A.3. Reference is made to the nomenclature in chapter 14 that
defines the symbols, subscripts, abbreviated terms and graphical representations used in
the present appendix.
A.1 Wind conditions
The environmental conditions that are to be considered during design of a wind turbine
depend on the specific site of installation. The wind turbine designed in this project thesis
is however intended to be used in a variety of different sites around the world. Therefore a
typical design site, which represents the characteristic values of many different sites, has
been established with input from EWB and their collaborative partners. The site character-
istics cause the wind turbine to be classified a class IV in accordance with the standard
SWT classes of IEC 61400-2 [5, p. 45]. This class defines basic external conditions in terms
of wind speeds at hub height, as indicated in table A.1.
119

LIST OF ATTACHMENTSBASIS FOR CALCULATIONS
Wind speed Symbol Value
Average wind speed Vave 6 m/s
Reference wind speed Vref 30 m/s
Table A.1: External wind conditions for Class IV wind turbine
The present wind turbine configuration meets the requirements of IEC 61400-2, which
makes it possible to use simplified load and wind distribution models for calculations [5, p.
67]. The requirements are:
120
� Horizontal-axis
� 2 or more bladed propeller-type rotor
� Cantilever blades
� Rigid hub (not teetering or hinged hub)
Among other things the simplified models mean that wind speeds are assumed to be
Rayleigh distributed, whereby the wind distribution at hub height is given by the following
probability density function [12, p. 59]:
� V
pR( V)
2 2
Vave e
�
�
4
�
The statistical distribution of (A.1) is equal to a Weibull distribution with a so called shape
parameter of 2. With Vave equal to 6 m/s the function may be represented graphically:
�
�
�
V
Vave
�
�
�
2
(A.1)

BASIS FOR CALCULATIONS
Figure A.1: Rayleigh probability density function for wind speed with an average of 6 m/s.
The graph indicates the probability of the occurrence of a specific wind speed
The wind distribution is important as it indicates the frequency of occurrence of the indi-
vidual load conditions. It is also used for calculating the annual energy production, see
section 6.3.1.
The wind conditions are subdivided into normal and extreme conditions. The normal con-
ditions generally concern long-term structural loading and operating conditions that occur
frequently during normal operation, while the extreme conditions represent the rare, but
potentially critical external design conditions that are defined as having a 50 year recur-
rence period [5, p. 69]. The conditions are used in the load cases, described in appendix
A.3. It should be noted that the defined external conditions are not intended to cover wind
conditions experienced in tropical storms such as hurricanes, cyclones and typhoons.
A.2 Other environmental conditions
Like the wind conditions, the other external conditions for the wind turbine can be subdi-
vided into normal and extreme external conditions. The environmental properties of each
condition are listed below [5, p. 59]. These are used in design calculations where applica-
ble.
121

LIST OF ATTACHMENTSBASIS FOR CALCULATIONS
Normal condition
122
� Normal system operation ambient temperature range of –10 °C to +40 °C
� Relative humidity of up to 95 %
� Solar radiation intensity of 1000 W/m 2
� Air density of 1.225 kg/m 3
Extreme condition
� Extreme temperature range of –20 °C to +50 °C
Other extreme environmental conditions include lightning, ice loading and earthquakes.
IEC 61400-2 contains no minimum requirements for these conditions when using standard
SWT classes and these are therefore not taken into account in the present project.
A.3 Load cases
Actual wind turbine load conditions are quite complicated, as the loads are variable and as
the structure itself moves in ways that affect the loading. Very detailed mathematical mod-
els must be used to fully analyse these interacting load effects. As mentioned in section A.1
the present wind turbine configuration however makes it possible to use simplified and
conservative load models that provide insight into the response of the wind turbines to
steady and cyclic loads.
Several load cases have been established in accordance with IEC 61400-2 to verify the
structural integrity of the key components: blades, shaft and tower, respectively. These
take into consideration all relevant load cases with a reasonable probability of occurrence
within the categories:
� Turbine operation without fault and with normal external conditions
� Turbine operation without fault and with extreme external conditions
� Turbine operation with fault and extreme external conditions
� Turbine installation with normal external conditions
The simplified load model of IEC 61400-2 take into account stochastic variations in the
wind speed (wind turbulence), as well as sudden and brief increases of the wind speed
over its mean value (gusts). This is done conservatively by defining the wind inflow condi-
tions for each load case.
The design load cases are tabulated in table A.2. For each load case the appropriate type of
analysis is stated. F refers to analysis of fatigue loads, to be used in the assessment of fa-
tigue strength. U refers to the analysis of ultimate loads such as analysis of exceeding the
maximum material strength.

Load case Design situation Wind inflow Analysis Remarks
BASIS FOR CALCULATIONS
A Normal operation Vdesign F Vdesign = 1.4Vave
B Yawing Vdesign U
C Yaw error Vdesign U
D Maximum thrust 2.5 Vave U Vave of table A.1
E Maximum rotational speed - U
F Short at load connection Vdesign U
G Survival wind Ve50 U Ve50 = 1.4Vref
(table A.1)
H Installation - U
Table A.2: Design load cases
Each of the eight load cases are described in the following paragraphs. The intention of the
description is to create a general understanding of the background for the equations, thus
making clear what kind of physics is included in the equation and thus what is not. For
further derivation reference is made to IEC 61400-2. A summary of the load cases may be
found in appendix A.4.
Figure A.2 shows the coordinate systems and some distance variables used in several of
the load cases. Table A.3 defines the numerical values of key variables that are used in the
following equations.
Figure A.2: Coordinate system and distance variables used for load cases
123

LIST OF ATTACHMENTSBASIS FOR CALCULATIONS
Variable Symbol Numerical value Reference
Design wind speed Vdesign 8.4 m/s IEC 61400-2
Design torque Qdesign 32.5 Nm Rotor design tool
Design thrust Tdesign 276 N Rotor design tool
Design tip-speed ratio �design 5.6 Rotor design tool
Design rotational speed �design 35.1 rad/s Rotor design tool
Mass of blade mB 2.61 kg 3D model
Mass of rotor mr 45.2 kg a 3D model
Blade moment of inertia
about rotational axis
124
IB 0.317 kg m 2 3D model
Number of blades B 3 3D model
Projected blade area Aproj.B 0.230 m 2 3D model
Distance between COG of a
blade and rotor centre
Distance between rotor
centre and the first bearing
Distance between blade root
centre and the yaw axis
Rcog 434 mm 3D model / Figure A.2
Lrb 77.7 mm 3D model / Figure A.2
Lrt 217 mm 3D model / Figure A.2
a) Mass includes generator, blades, bolts, washers, bearings etc. in the rotor
Table A.3: Key variables used in load cases
Load case A: Normal operation
Load case A defines loads for the wind turbine blades and shaft. The load case is a fatigue
load case with constant range. The basic idea behind the range is that the turbine speed
cycles between 0.5 and 1.5 of the design value.
By varying �design from 0.5�design to 1.5�design the following centrifugal load range is achieved
for the blades
�F zB
� �2 mB Rcog �0.5�design �2 � mB Rcog 1.5�design The edgewise bending moment range consists of a term due to torque variation (from
0.5Qdesign to 1.5Qdesign equally divided among B blades) and a term due to the moment
caused by the pure alternating load of the blade weight:
� � 2.79 kN
Qdesign �M xB �
� 2mB g Rcog � 33.1 N m
B
(A.2)
(A.3)

The axial load on the rotor may be expressed as [5, p. 165]
BASIS FOR CALCULATIONS
From this a flap moment range is determined by varying Q from 0.5Qdesign to 1.5Qdesign and
further assuming that the load is applied at 2/3 R and acting equally on each blade.
�M yB
The axial load range on the shaft may also be determined from (A.4):
�F xS
The shaft torsion range consists of a torque term and an eccentricity term, which assumes
that the rotor centre of mass is offset from the shaft by 0.005R (er = 6.8 mm), causing a
gravity torque range. The last term amounts to 15% of the total load and assumes that the
shaft is rotating, which is not the case with the current wind turbine. The term is however
kept as a conservative assumption.
The shaft bending moment is assumed to be maximal at the first bearing (ref. distance Lrb
on figure A.2). The rotor mass and an axial load eccentricity are taken into account. The
latter is assumed to be equal to R/6 [5, p. 167].
Again, the above presumes that the shaft is rotating, which is not the case with the present
design. The load is maintained here, as the dynamic loading of the shaft is not critical (load
case B is more severe). The load may be removed in later design calculations, where the
dynamic shaft load is more significant.
�
�
3
2
3 � Q
Faxial =
2 R
� design Q design
B
� design Q design
R
� 61.1 N m
� 204 N
�M xS � Qdesign � 2mr g er � 38.5 N m
R
�M S 2mr g Lrb 6 �F �
� xS � 115 N m
(A.4)
(A.5)
(A.6)
(A.7)
(A.8)
125

LIST OF ATTACHMENTSBASIS FOR CALCULATIONS
Load case B: Yawing
For this load case the ultimate loads during yawing are calculated for the blades and shaft.
The flapwise bending moment acting on the blades is considered to consist of three terms:
126
� Centrifugal force
� Gyroscopic
� Eccentricity of axial load
The first two terms occur due to the maximum yaw speed �yaw which is considered to oc-
cur with �design.
The last term accounts for an offset of the axial force, similar to that of (A.8).
For each blade the formula for the flapwise bending moment is:
(A.9)
(A.10)
The centrifugal force due to the yaw rate is multiplied by the distance Lrt of figure A.2. The
gyroscopic term is elaborated further in [5, p. 165].
For the shaft the bending moment is given by:
(A.11)
The load consists of a gyroscopic load valid for a three bladed rotor and two terms adding
mass loads and axial load eccentricity.
Load case C: Yaw error
� �
�yaw 3 0.01 � R 2
= � � 2 2.96 rad
=
s
2 R
MyB mB �yaw Lrt Rcog � 2�yaw IB �design 9 �F �
� xS � 98.6 N m
R
MS B�yaw �design IB � mr g Lrb 6 �F �
� xS � 179 N m
All turbines operate with a certain yaw error. In this load case, a yaw error of 30° is con-
sidered to induce a blade root bending moment. It is derived using approximations that
simplify a condition, where an extreme load is caused by the combination of the instanta-
neous wind and the yaw error, which is thought to place the entire blade at the angle of
attack for maximum lift. Further details may be found in [5, p. 169].
1
MyB 8 � Aproj.B Cl.maxR 3 � 2 4
�
�design �1
� �
� 3�design �
�
�
1
� design
2
� �
� �
� �
� 200 N m
(A.12)

BASIS FOR CALCULATIONS
Cl.max is the maximum lift coefficient of 1.48 for the NACA 4412 airfoil, described in appen-
dix D.
Load case D: Maximum thrust
The maximum thrust on the rotor is considered to be a shaft load that acts parallel to the
rotor axis. The load consists of a force coefficient and a dynamic pressure:
CT is a thrust coefficient equal to 0.5. It is found in IEC 61400-2 to be in good agreement
with loads predicted by aeroelastic models when combined with a wind speed of 2.5Vave.
Load case E: Maximum rotational speed
This load case considers the blade and shaft loads at the maximum rotational speed �max.
The maximum speed is assumed to be 650 rpm (68.1 rad/s), which is equivalent to the
rotational speed at the point where furling is initiated.
For the blade, only the centrifugal load is considered:
(A.13)
(A.14)
For the shaft, the bending moment from the rotor mass is considered along with an imbal-
ance er of the rotor centre of mass, see (A.7).
Load case F: Short at load connection
(A.15)
This load case takes into consideration an electrical short-circuit in the generator, which is
assumed to create a high torque in the rotor shaft and in the blades. For both components
the design torque is multiplied by a coefficient G equal to 2.
Shaft torque:
Blade torque:
F xS
1
CT 2 � 2.5V �
ave
� � 2 � R 2
� 395 N
2
FzB � mB Rcog� max � 5.25 kN
2
MS � mr g Lrb � mr er �max Lrb � 144 N m
MxS � G Qdesign � 65.0 N m
G Qdesign MxB �
B
� mB g Rcog � 32.8 N m
(A.16)
(A.17)
127

LIST OF ATTACHMENTSBASIS FOR CALCULATIONS
Load case G: Survival wind
In this load case the rotor is spinning and the wind speed is Ve50 equal to 42 m/s, see table
A.2.
It is expected that Cl.max (see (A.12)) will occur on one of the blades due to variations in the
wind direction, creating a root bending moment:
128
(A.18)
This assumes a constant chord length and a triangular lift distribution which is equivalent
to Cl.max at the tip and zero at the root of the blade. Further derivation is available in [5, p.
175].
The shaft is loaded by a thrust force given by
The calculation of the thrust force is based on helicopter theory, where the thrust coeffi-
cient is based on tip-speed rather than wind speed. Its value of 0.17 is found to be near
constant for transient events [45]. The tip-speed ratio �e50 is determined by:
Where �max is the assumed maximum rotational speed of (A.14).
(A.19)
(A.20)
The shaft thrust force is combined with drag forces on the tower and the tail, resulting in a
maximum tower load. The tail is assumed to be perpendicular to the wind and fully ex-
posed. The area of the tower that contributes to drag is considered to be the part above the
upper guy wire attachment.
Drag force on tail:
Where the projected tail area Aproj.tail is 1.04 m 2 and the drag coefficient Cf.tail is 1.5.
Drag force on tower:
M yB
F xS
�
1
Cl.max 6 � Ve50 2 Aproj.B R � 166 N m
2 2
� 0.17BAproj.B� e50 � Ve50 � 12.0 kN
Ftail �
� e50
�
� max � R
V e50
� 6.9
1
Cf.tail 2 � Ve50 2 Aproj.tail � 1.68 kN
1
FT CfT 2 � Ve50 2 �
Aproj.T � 228 N
(A.21)
(A.22)

BASIS FOR CALCULATIONS
Where the projected area of the tower above the upper guy wires Aproj.T is 0.163 m 2 and the
drag coefficient CfT is 1.3.
The total tower load becomes:
Load case H: Installation
FT.tot � FT � Ftail � FxS � 13.9 kN
(A.23)
This load case calculates the tower tilt-up load during erection, as illustrated on figure A.3.
Figure A.3: Tower tilt-up during erection
The load is a basic bending moment at the lifting point, multiplied by a dynamic amplifica-
tion factor of 2. The positions of the mass centres are conservative approximations.
�
moverhang MT �
2�mtowertop �
2
�
�
�
� g L lt
(A.24)
Where mtowertop is the combined mass of the rotor, generator, yaw system and nacelle com-
ponents, equal to 102 kg. And moverhang is the mass of the inner yaw pipe and the tower
between the lifting point and the tower top, equal to 57 kg. The distance between the lift-
ing point and the top of the tower, Llt is 1479.5 mm.
� 3.79 kN m
129

LIST OF ATTACHMENTSBASIS FOR CALCULATIONS
130
A.4 Summary of loads
Table A.4 provides a summary of the loads in each of the eight load cases.
Load case Blade Shaft Tower
A
B
C
D
E
F
G
H
�F zB � 2.79 kN
�M xB � 33.1 N m
�M yB � 61.1 N m
M yB
Table A.4: Summary of load cases
�F xS � 204 N
�M xS � 38.5 N m
�M S � 115 N m
� 98.6 N m
MS � 179 N m
MyB � 200 N m
F zB
M xB
M yB
FxS � 395 N
� 5.25 kN
MS � 144 N m
� 32.8 N m
MxS � 65.0 N m
� 166 N m
FxS � 12.0 kN
FT.tot � 13.9 kN
MT �
3.79 kN m

B
Rotor theory
The first section of the present appendix describes the basic theory behind the engineering
models used for aerodynamic design and performance calculation. The second section
describes the methods used to calculate the theoretically optimum blade shape. Section
three contains a thorough description of the rotor design tool that has been developed as a
part of this project thesis.
B.1 BEM theory
The blade element momentum (BEM) analysis combines momentum theory and blade
element theory (also known as strip theory). Momentum theory refers to the analysis of
blade forces based on conservation of linear and angular momentum, while blade element
theory refers to the analysis of forces in concentric ring elements of a rotor. A schematic
illustration of blade divided into elements is shown on figure B.1.
Figure B.1: Schematic of blade elements
131

LIST OF ATTACHMENTSROTOR THEORY
This project thesis uses the BEM method in calculation of steady state rotor performance
and in aerodynamic design of the rotor blades. The following equations describe the basics
of BEM analysis and form the foundation for the developed rotor design tool described in
appendix C. For a complete derivation of the formulas refer to [12, p. 91-153] and [46, p.
20-24], which are to be considered as sources for the following unless otherwise stated.
Further reference is made to the nomenclature of chapter 14 that contains the definitions
of symbols and subscripts.
Figure B.2 shows important velocities, angles and forces acting a ring element of the blade
profile.
132
Figure B.2: Velocities, angles and forces on blade element
From figure B.2 it is evident that the angle of attack � is given by
And that the angle of relative wind � is given by
a and a’ refer to axial and tangential interference factors, respectively. For rotors with few
blades (B < 5) these are derived using the laws of conservation of momentum and angular
momentum
tan( �)
� = � � �
=
1 � a
1 � a'
V
r�
(B.1)
(B.2)

And
ROTOR THEORY
In the above F refers to a correction factor that takes into account tip losses, according to
Prandtl’s theory. Tip losses occur when air flows around the tip from the lower to upper
surface due to pressure difference.
Cx and Cy are the components of the lift and drag coefficients:
�’ in (B.3) and (B.4) is the solidity ratio, defined as
In case a of (B.3) becomes greater than ac = 0.2 it is no longer valid and the axial interfer-
ence factor is then recalculated by
Where
�
a' =
a =
(B.3)
(B.4)
(B.5)
(B.6)
(B.7)
(B.8)
(B.9)
(B.10)
Combining the above geometric and aerodynamic relations with element theory, it is pos-
sible to calculate the differential axial force and torque acting on a blade element. Using
this theory, the following assumptions are made:
F
1
4F sin ( �)
2
�' C y
1
� 1
4F sin ( �)
cos( �)
�' C x
�
� B R�r �
2 � �
2 r sin( �)
= acos e
�
�
�
� 1
�
��
��
�
Cx = Cl sin ( �)
� Cd cos( �)
Cy = Cl cos( �)
� Cd sin ( �)
�'
c B
=
2� r
1
a
2 2 K 1 2a = � � � � c�
� �� K 1 � 2ac K =
� � � 2
4F sin ( �)
2
�' C y
� �
�� 2
2
� 4 K ac � 1
�
�
133

LIST OF ATTACHMENTSROTOR THEORY
134
� There is no aerodynamic interaction between the elements (no radial flow)
� The forces on the blades are determined solely by the lift and drag characteristics
of the blade airfoil
The differential contribution to axial force (thrust) is
Whereby the total axial forces can be calculated from
The differential contribution to torque is
1
dT
2 � W2 = c B Cy dr
R
1
T B
r
2
0
� W 2 �
= � c Cy d
�
�
1
dQ
2 � W2 = c B Cx r dr
From which the total torque and the power may be calculated
R
1
Q B
r
2
0
� W 2 �
= � c Cx r d
�
�
R
1
Pr � B
r
2
0
� W 2 �
= � c Cx r d
�
�
The rotor efficiency may be calculated by
The efficiency may also be denoted by a Cp value
� r
C p
=
P r
P betz
16
27 � =
r
Using the described BEM theory and iterative calculation methods, it is possible to deter-
(B.11)
(B.12)
(B.13)
(B.14)
(B.15)
(B.16)
(B.17)
mine the axial force (thrust) and tangential force (torque) on annular sections of the rotor
as a function of flow angles and airfoil characteristics. This makes it possible to determine
the rotor performance for an arbitrary blade shape, which is done via the developed calcu-
lation tool, described in appendix C. It is additionally possible establish the ideal shape of a

ROTOR THEORY
blade for optimum performance under certain assumptions, which is elaborated in the
next section.
Notable assumptions when using the described BEM theory is that the prevailing wind is
uniform and aligned with the rotor axis, and that the blades rotate in the rotor plane, per-
pendicular to the rotor axis. Due to factors such as wind shear, yaw error and turbulence,
real performance may differ from the modelled performance. The force and power output
that is calculated using the BEM theory is referred to as nominal output in the present
project thesis.
B.2 Optimum blade shape
Using the BEM theory described in the previous section it is possible to approximate the
blade shape that would provide the maximum power given the following parameters:
� Tip-speed ratio (�)
� Number of blades (B)
� Radius (R)
� Lift (Cl) and drag (Cd) characteristics of the airfoil (at optimum angles of attack)
The approximation of the ideal blade shape can be carried out using different theories such
as Betz or Schmitz [12, p. 121-132]. Betz encloses several assumptions:
� No wake rotation (a’ = 0)
� No drag (Cd = 0)
� No tip loss (F = 1)
� Axial interference factor (a) of 1/3 in each annular element
Schmitz’ theory does not presume a value of zero for the tangential interference factor and
hence takes into account wake rotation, which originates from a rotating flow behind the
rotor. This theory can therefore be seen as an augmented and a more accurate version
than the Betz’ theory, and it is hence used in the determination of the blade shape for an
ideal rotor.
One can determine the angle of relative wind � and the chord of the blade c for each ele-
ment of the ideal rotor [12, p. 132]:
2 � 1 �
� = atan� �
3 � � �
8� r
c =
( 1 � cos( �)
)
B Cl (B.18)
(B.19)
135

LIST OF ATTACHMENTSROTOR THEORY
Choosing the optimum angle of attack � where glide ratio (Cl/Cd) is maximum, makes it
further possible to calculate the blade pitch �, see (B.1).
Figure B.3 and figure B.4 show the optimum non-dimensional chord and blade pitch ac-
cording to both Betz and Schmitz. The graphs are based on the following assumptions: Tip-
speed ratio � = 5, the airfoil lift coefficient Cl = 0.99, number of blade B = 3 and optimal
angle of attach � = 7�.
Figure B.3: Chord length according to Betz and Schmitz theory. Shown for tip-speed ratio � =
5, the airfoil lift coefficient Cl = 0.99, number of blade B = 3 and optimal angle of attach � = 7�
136

ROTOR THEORY
Figure B.4: Blade pitch angle according to Betz and Schmitz theory. Shown for tip-speed
ratio � = 5, the airfoil lift coefficient Cl = 0.99, number of blade B = 3 and optimal angle of
attach � = 7�
As shown on the above figures the blade design for optimum power production has an
increasingly large chord and pitch angle when approaching the blade root. This makes the
fabrication of the blade difficult and the present blade design, described in section 6.2, is
therefore modified for ease of manufacturing using the optimum blade shape as a guide-
line.
137

LIST OF ATTACHMENTSROTOR THEORY
138

C
Rotor design tool
The rotor design tool enables iterative calculation of aerodynamic flow conditions, forces,
blade shape and performance. It is used in the calculation of all numeric and graphed re-
sults reported in the main report and in the appendices. The tool is programmed in Micro-
soft Excel, making it difficult to fully document the code in this project thesis. Reference is
therefore made to electronic version available on the CD-rom, enclosed as att. 2. The code
is based on the theory of appendix B.1 and B.2, as well as code originating from [46].
The design tool divides the rotor into 8 annular elements. The inner element constitutes
only 1.6 % of the total swept rotor area and it is empirically dispensed from the calcula-
tions under the assumption that this element only contains the hub of the rotor and no
blades. Neglecting the inner part of the rotor is without any noticeable consequences on
the power output. Figure C.1 shows the remaining 7 elements of a blade.
Figure C.1: Blade divided into blade elements
139

LIST OF ATTACHMENTSROTOR DESIGN TOOL
With the current rotor diameter of 2.7 m, the element size is 168.75 mm. The calculations
are performed in the centre of each element.
Figure C.2 shows the main program window, which may be divided into four sections.
Below follows a description of each section with the intention of illustrating the functional-
ity of the rotor design tool.
140
Figure C.2: Main program window of the rotor design tool
SECTION 1
SECTION 2
SECTION 3
SECTION 4

Section 1
Contains the required input (highlighted blue):
� Blade radius (R)
� Wind speed (V)
� Rotational speed (n)
� Number of blades (B)
� Optimum tip-speed ratio (�opt)
The ring element size dr is automatically calculated, as 1/8 of the blade radius.
Section 2
Contains the main results for easy reference:
� Rotor power output (Pr)
� Rotor efficiency (�r, cp)
� Torque (Q)
� Axial thrust force (T)
� Average angle of attack (�m)
Section 3
Contains various design output that is useful during the design phase:
� Rotational speed at (�opt)
� Actual tip-speed ratio (�)
� Maximum power output (Pbetz)
� Swept rotor area (A)
� Actual angular velocity (�)
� Tip-speed (Vtip)
Section 4
ROTOR DESIGN TOOL
The first part of the section calculates the optimum blade shape according to Schmitz’
theory (see appendix B.2) and outputs the following for each blade element:
� Blade pitch (�)
� Chord length (c)
The calculation is based on the airfoil characteristics, also specified in the rotor design tool
(see appendix D). In the second part of the section the optimum chord is converted to a
linear chord shape, as described in section 6.2.2 and the pitch angle is inputted.
The second part of section 4 contains the iterative calculations for all blade elements.
These are based on the equations of the BEM theory, described in section B.1. All relevant
cells are referenced to the appropriate equation number of this project thesis in an attempt
of making the program code transparent.
141

LIST OF ATTACHMENTSROTOR DESIGN TOOL
The iterative calculation steps for every element of the model are listed below:
142
� Step 1: Start
� Step 2: a and a’ are set at arbitrary values as a first time guess
� Step 3: � is calculated from (B.2)
� Step 4: Cl and Cd are calculated from airfoil data
� Step 5: Cx and Cy are calculated from (B.6) and (B.7)
� Step 6: a and a’ are calculated by (B.3) and (B.4). If a > 0.2 it is calculated from
(B.9)
� Step 7: If a and a’ found in step 6 differ more than 1% from the values set in step
� Step 8: Stop
2, the calculation process is repeated through steps 2-7
In the rotor design tool the above iterative calculation process is automated using a macro,
which copies row E62:K62 to E50:K50 and row E63:K63 to E51:K51. Pressing CTRL + T
will make the program run through 1 calculation loop. The macro should be run multiple
times until the reported error is below the selected threshold of 1%.
Various print-outs of the rotor design tool are available in att. 8, but the electronic version
should be seen as the main documentation.

D
Airfoil
Figure D.1 displays the lift coefficient Cl, drag coefficient Cd and glide ratio GR = Cl/Cd of the
NACA 4412 airfoil as a function of the angle of attack �.
Coefficient of lift and drag, Cd, Cl [-]
Figure D.1: Lift coefficient Cl, drag coefficient Cd and glide ratio GR = Cl/Cd of the NACA 4412
airfoil
1.6
1.4
1.2
1.0
0.8
0.6
0.4
0.2
0.0
0 10 20 30 40 50 60 70 80 90
Angle of attack, � [�]
From figure D.1 it can be seen that the onset of stall is at an angle �st of 13�. For angles of
attack less than this the airfoil data is obtained from [47] and conveniently approximated
by following 4th degree polynomial equation in the rotor design tool:
Cd �� l k0 � k1� k2� 2
� k3� 3
� k4� 4
=
�
C_l
C_d
GR
180
160
140
120
100
80
60
40
20
0
Glide ratio, GR [-]
(D.1)
143

LIST OF ATTACHMENTSAIRFOIL
With the following constants
144
Coefficient Cl Cd
k0 4.002e-1 7.027e-3
k1 1.112e-1 -5.823e-4
k2 -3.778e-3 1.344e-4
k3 4.785e-4 1.970e-6
k4 -2.714e-5 0.000e-0
Table D.1: Polynomial constants for 0� < � < 13�
For angles in the post-stall region the lift and drag coefficient values are predicted using a
method developed by Viterna and Corrigan [16, p. 65]. The method assumes zero twist
angle and maximum drag coefficient Cd,max at an inflow angle � = 90�. The latter is set to 1
in accordance with [46, p. 18].
The drag coefficient Cd is defined by [16, p. 65]
Where
Cd.st is the drag coefficient at stall.
The lift coefficient Cl is given by
Where
Cl.st is the lift coefficient at stall.
Cd B1sin ( �)
2 = � B2cos ( �)
1
B2 =
cos �st B1 = Cd.max � �
� � Cd.st Cd.max sin ��st� 2
�
Cl = A1 sin ( 2�)
� A2 B1 A1 =
2
A2 =
Cl.st � Cd.max sin �st cos( �)
2
sin ( �)
� � � cos� �st�� sin � � st�
� �2 cos � st
(D.2)
(D.3)
(D.4)
(D.5)
(D.6)
(D.7)

Note that according to [16], the first term of (D.5) reads A1 sin(�) 2 . This is an incorrect
reproduction of the Viterna and Corrigan theory and it has therefore been corrected.
The airfoil data of figure D.1 is valid for a Reynolds number Re of 3 × 10 6 and for airfoils
with so-called NACA standard roughness. The Reynolds number for an airfoil is given by
The length of the chord c and the relative wind speed W varies throughout the blade and
there will thus be a variance of the Reynolds number, rendering the usage of airfoil data
for a specific Reynolds number an approximation. The Reynolds number at the blade tip
ranges from 3 × 10 5 to 7 × 10 5 at a wind speed of 4 m/s and 14 m/s, respectively.
The significance of the deviance between the actual Reynolds numbers on the blade and
AIRFOIL
the Reynolds number of the airfoil data may be assessed from figure D.2, which shows the
lift and drag coefficients for a NACA 4412 profile at various Reynolds numbers.
Figure D.2: NACA 4412 lift and drag coefficients for various Reynolds numbers [48]
(D.8)
Figure D.2 reveals an invariance of the lift coefficient Cl as a function of Re. It further shows
that the change in drag coefficient Cd is only 10% in the Re-range of 5 × 10 5 to 5 × 10 6 . For
these reasons the usage of airfoil data that is valid for Re = 3 × 10 6 is considered to be an
acceptable approximation.
Using data that is based on the NACA standard roughness ensures conservative values of
lift and drag, as it is generally considerably more severe than the roughness generally
obtainable on real blade surfaces [49]. Wind tunnel tests of the airfoil performance are not
carried out in the present project, as the surface properties of test specimens will vary
from those of a real blade. Testing should be performed when a prototype is build, ref.
chapter 12.
c W
Re =
�
145

LIST OF ATTACHMENTSAIRFOIL
Complete calculations of the airfoil data can be found in the rotor design tool. Printouts are
provided as att. 8.
146
D.1 Profile shape
The NACA 4412 airfoil profile shape in each blade element is described as a function of the
local chord length via geometrical data found in [50]. The rotor design tool uses the data to
describe the airfoil shape with 102 Cartesian coordinates per element, as shown on figure
D.3.
Profile height [m]
0.03
0.02
0.01
0.00
-0.01
-0.02
0.00 0.05 0.10 0.15 0.20 0.25
Figure D.3: NACA 4412 airfoil shape in all elements of the rotor design tool
The coordinate data, which is provided as att. 9, is further used as shape coordinates in the
3D CAD model of the blades.
Chord length [m]

E
Structural analysis of blades
This appendix contains a general description of the material used for the blades, followed
by a statement of its mechanical properties. It further encloses a verification of the struc-
tural integrity of blades through finite element analysis.
E.1 Material description
For purpose of analysis the engineering properties of pinus taeda are used. This type of
wood is commonly known as loblolly pine, native to the South-eastern United States and
widely available in regions such as Africa and South East Asia [51]. It is therefore a likely
material candidate in the countries targeted by the present wind turbine design.
For future designs the selected wood may be substituted by other types of wood, e.g. dif-
ferent wood species, jointed wood, glued laminated wood or wood composites. Substitu-
tion requires that the new material has equal or greater strength and stiffness, and that
proper consideration is taken to manufacturing issues, described in section 6.2.3.
The mechanical properties presented in the following section assume that the blades are
produced from wood pieces that are termed clear and straight grained, i.e. considered
homogeneous within wood mechanics. This implies that the wood has growth rings that
occur in consistent patterns and that it does not contain characteristics such as knots,
cross grain and splits.
147

LIST OF ATTACHMENTSSTRUCTURAL ANALYSIS OF BLADES
Orthotropy
Wood may be described as an orthotropic material, as it has unique and independent
properties in the three mutually perpendicular directions. The longitudinal axis is parallel
to the grain (fibre), the radial axis is normal to the growth rings and the tangential axis is
tangent to the growth rings. The axes are shown on figure E.1 and designated with coordi-
nates that are valid when the blade is manufactured from the directions given in section
6.2.3.
148
Figure E.1: Principal axes of wood with respect to fibre direction and growth rings
Moisture content
Wood is also a hygroscopic material, i.e. a material that takes in moisture from the sur-
rounding environment. The moisture content MC is the amount of water, in any of its
states, contained in wood. It is usually expressed as a weight percentage:
Where mwater is the mass of water in the wood and mwood is the mass of oven-dry wood. MC
includes water or water vapour absorbed into cell walls and free water within the hollow
centre of the cells.
The amount of water vapour wood absorbs depends on the relative humidity (RH) of the
surrounding air. If wood is stored at 0% RH, the MC will eventually approach 0%. If wood
is stored at 100% RH, the MC will eventually reach fibre saturation (approximately 30%
moisture). This moisture relationship has an important influence on wood properties and
performance. In general most mechanical properties will decrease with increase in mois-
ture content [30, p. 16-6].
mwater MC =
mwood (E.1)

STRUCTURAL ANALYSIS OF BLADES
For the purpose of the present structural analyses MC is set to 12%, which is a standard
moisture content at which many wood properties are tested. IEC 61400-2 defines envi-
ronmental conditions with up to 95% RH (see appendix A.2), which potentially yields a
moisture content that is higher than 12%. This value is however considered an educated
estimate of the moisture content when wood is used outdoors. If at a later point MC is re-
evaluated, the mechanical properties may be corrected using the following expression [30,
p. 133].
(E.2)
Where P is the material property at a moisture content M, P12 is the property at 12% MC, Pg
is the property for green wood and Mp is a tabulated value approximately equal to the fibre
saturation point. The equation above for moisture content adjustment is not recom-
mended for tensile strength perpendicular to grain, as this property is known to erratic in
response to moisture content change.
Temperature effects
In general, the mechanical properties of wood decrease when it is heated and increase
when it is cooled. At constant moisture content below approximately 150 °C, mechanical
properties are approximately linearly related to temperature. The material data stated in
the following sections of this appendix are derived at 21 °C. The mechanical strength prop-
erties at 12% moisture content change very little in the temperature range from -10 to 40
�C, which is equivalent to the temperature range of the normal environmental conditions
in IEC 61400-2 [30, p. 5-36]. Therefore the mechanical properties in the above tempera-
ture range are considered equivalent to those at 21 �C. The extreme environmental condi-
tions of IEC 61400-2 further require consideration to temperatures in the range of -20 to
50 C. However, as the extreme conditions are rare in occurrence and as the safety factors
applied in appendix E.2 are relatively high, it is decided to set the mechanical properties
under extreme conditions equal to those at 21 �C.
Surface protection
P =
P12 The properties of the blade material are expected to be valid throughout its service life-
time. To accommodate this assumption the wood should be treated with a preservative
that provide the required protection for the conditions of exposure. Detailed specification
of the preservative treatment processes is beyond the scope of this project thesis, but a few
general guidelines are provided below.
A chemical preservative with a formulation intended for use outdoors should be used to
provide resistance to deterioration factors such as attack of fungi and harmful insects.
Wood finishes such as paint will additionally protect the blade material and provide a
cleanable surface with the desired appearance. Furthermore the paint will protect the
surface from damaging UV-rays and retard the movement of moisture.
�
�
�
P 12
P g
�
�
�
�
�
�
12 �M
Mp�12 �
�
�
149

LIST OF ATTACHMENTSSTRUCTURAL ANALYSIS OF BLADES
150
E.2 Mechanical properties
Characteristic values for key mechanical properties of pinus taeda are listed in table E.1
[30, p. 5-2 to p. 5-26]. The stated strengths are ultimate, except for the compressive
strength perpendicular to the grain, which is reported as stress at the proportional limit,
since there is no clearly defined ultimate stress for this property.
Density
[kg/m 3]
Modulus of
elasticity
(EL)
[MPa]
Compressionparallel
to grain
[kPa]
Compression
perpendicular
to grain
[kPa]
Shear
parallel to
grain
[kPa]
Shear
perpendicular
to
grain
[kPa]
Tension
perpendicular
to grain
[kPa]
Tension
parallel
to grain
[kPa]
571 a 13530 b 49200 5400 c 9600 2688 d 3200 c 90400 e
a) The density is calculated from the specific gravity of the wood (Gx = 0.51), based on volume at the
moisture content of 12%: �12 = 1000 kg/m 3 Gx (1 + 0.12) [30, p. 4-10]
b) The modulus of elasticity is determined from beam bending tests, where the deflection is assumed to
be only flexural, i.e. due to compression and stretching of fibres parallel to the axis of the beam.
However shear stresses also contribute to the deflection and to correct for this, the modulus of elasticity
is increased by 10% [30, p. 5-2]
c) Values presented are average of radial and tangential strength
d) Calculated as 28% of the shear strength parallel to grain [30, p. 5-15]
e) Strength is increased by 13% to achieve a value that is valid for 12% moisture content [30, p. 5-26]
Table E.1: Mechanical properties for pinus taeda
Being an orthotropic material twelve constants are needed to describe the elastic behav-
iour of wood: three moduli of elasticity E, three moduli of rigidity G, and six Poisson’s ra-
tios μ. The modulus of elasticity of table E.1 is parallel to the grain and therefore denoted
EL. From this the additional moduli of elasticity and moduli of rigidity, tabulated in table
E.2, are determined [30, p. 5-2].
ET
[MPa]
ER
[MPa]
GLR
[MPa]
GLT
[MPa]
GRT
[MPa]
1055 1529 1109 1096 176
Table E.2: Moduli of elasticity and moduli of rigidity
The three moduli of rigidity denoted by GLR, GLT, and GRT are the elastic constants in the LR,
LT, and RT planes, respectively.
The Poisson's ratios of an orthotropic material are different in each direction. They are
denoted by μLR, μLT, μRL, μTL, μRT, and μTR. The first letter of the subscript refers to direction of
applied stress and the second letter to direction of lateral deformation. Only three of the

STRUCTURAL ANALYSIS OF BLADES
six Poisson’s ratios are independent, as the remaining depend on the other three and may
be obtained from relations found in [52]. The Poisson’s ratios used for structural analysis
are listed in table E.3 [30, p. 5-3].
�LR �LT �RT
0.328 0.292 0.382
Table E.3: Poisson’s ratios
The characteristic material properties of table E.1 are converted into limit state values
using partial safety factors of table E.4, set in IEC 61400-2. It is assumed that the material
is fully characterised, meaning that factors such as environmental effects and manufactur-
ing methods have been taken into consideration when determining the material proper-
ties.
Condition �m �f
Fatigue strength 10 1.0
Ultimate strength 1.1 3.0
Table E.4: Partial safety factors in accordance with IEC 61400-2
The limit states values are calculated as follows:
Where
fk is the characteristic material strength
�m is the partial safety factor for the material
�f is the partial safety factor for the load
The ultimate limit states are shown in table E.5.
Compression
parallel to
grain
[MPa]
Compression
perpendicular to
grain
[MPa]
�lim =
Shear parallel
to grain
[MPa]
Shear perpendicular
to
grain
[MPa]
Tension
perpendicular
to grain
[MPa]
(E.3)
Tension
parallel to
grain
[MPa]
15 1.6 2.9 0.82 1.0 27
Table E.5: Ultimate limit states for blade material
f k
� m � f
151

LIST OF ATTACHMENTSSTRUCTURAL ANALYSIS OF BLADES
The fatigue limit states are shown in table E.6.
Compression
parallel to
grain
152
[MPa]
Compression
perpendicular to
grain
[MPa]
Shear parallel
to grain
[MPa]
Shear perpendicular
to
grain
[MPa]
Tension
perpendicular
to grain
[MPa]
Tension
parallel to
grain
[MPa]
4.9 0.54 0.96 0.27 0.32 9.0
Table E.6: Fatigue limit states for blade material
The high fatigue safety factor of 10 is applied to the characteristic ultimate strengths, as
there is no S-N curve available for the blade material, pinus taeda. The value is considered
highly conservative [5, p. 93].
The ultimate and fatigue limit states of table E.5 and table E.6 are compared to the design
stresses of the blade load cases. These are found through finite element analyses per-
formed in the following sections. Details of the applied computational model are stated in
appendix E.3 below.
E.3 Description of finite element model
Finite element modelling makes it possible to take into account the previously described
orthotropic material properties, enabling stress calculation parallel and perpendicular to
the fibre direction, as well as deflection analysis. The analyses are carried out using Solid-
Works Simulation.
The general computational model used for all load cases is described below.
Material
The material properties of appendix E.2 are applied to the model. These are:
Density
[kg/m 3]
EL
[MPa]
ET
[MPa]
ER
[MPa]
GLR
[MPa]
GLT
[MPa]
GRT
[MPa]
571 13530 1055 1529 1109 1096 176 0.328 0.292 0.382
Table E.7: Mechanical properties used in finite element model
Model information
The fibre direction is defined as described in section 6.2.3, i.e. in the direction of the z-axis
of figure E.2 below. The x- and y-axis are defined as the radial and tangential directions,
respectively.
�LR
[-]
�LT
[-]
�RT
[-]

Figure E.2: Blade coordinate system
STRUCTURAL ANALYSIS OF BLADES
The basis mesh for all analyses is created using higher-order (parabolic) tetrahedral ele-
ments. The mesh details are tabulated below:
Mesh / element property Value
Total nodes 97144
Total elements 59668
Element size 7.1 mm
Maximum aspect ratio 4.12
Elements with aspect ratio < 3 98.3%
Table E.8: Mesh details
In each analysis the mesh is refined using the adaptive h-method, which improves the
accuracy of the analysis by using more elements in critical regions. The target accuracy of
the h-method is set to 99%, which indicates intended accuracy in the convergence of the
strain energy norm. The maximum number of iterative loops is set to 5. The simulation
stops when the target accuracy is achieved or the maximum number of loops is reached.
The maximum energy norm error, which indicates the variation in strain energy at com-
mon nodes, is less than 5% for all performed analyses. The low error can be viewed to
represent similarly low stress errors in the model, which indicates a solution with a high
degree of accuracy.
Restraints
The blade is fixed as a cantilever blade by the root of the airfoil, see figure E.3. This cross-
section is considered weaker than the root of the hub junction [5, p. 69], which therefore is
left out of the model. The fixture sets all translational degrees of freedom to zero.
Figure E.3: Model restraints
153

LIST OF ATTACHMENTSSTRUCTURAL ANALYSIS OF BLADES
Loads
The blade loads are defined in the load cases of appendix A. They are repeated table E.9 for
easy reference:
154
Load case Blade
A
B
C
E
F
G
Table E.9: Loads applied to the model
The simplified and conservative load models consider the loads to be acting at the cross-
section by the airfoil root. Since the computational model is restrained in the same cross-
section the loads are applied as follows:
� Bending moments MyB and MxB are applied as forces at the blade tip. The value of
the forces FMyB and FMxB is equal to the moment divided by the distance from the
blade root to the blade tip.
� Normal forces FzB are applied as centrifugal loads that act at the mass centre of
the blade. To compensate for the removed blade hub junction, a remote mass of
0.450 kg is added to the blade root, causing correct positioning of the loads. The
rotational velocity is adjusted so that the correct values of the centrifugal loads
are achieved.
�F zB � 2.79 kN
�M xB � 33.1 N m
�M yB � 61.1 N m
MyB � 98.6 N m
MyB � 200 N m
FzB � 5.25 kN
MxB � 32.8 N m
MyB �
166 N m
When applying the loads in the above manner it is assumed that the moments are maximal
at the airfoil root and zero at the tip with, having a linear distribution.

The applied loads are illustrated on figure E.4.
Figure E.4: Model loads
STRUCTURAL ANALYSIS OF BLADES
The bending forces at the blade tip are applied at a point, which is a projection of the cen-
troid of the airfoil root. This ensures that the applied forces produce root bending mo-
ments that are equivalent to those of the load cases. The tip forces originating from MyB
and MxB are aligned parallel and perpendicular to the rotor axis, respectively. The centrifu-
gal loads are applied with reference to the rotor axis.
The following sections show six stress plots of each of the load cases. The upper view on
each figure shows the downwind part of the blade and the lower view shows the upwind
surface, which faces the incoming wind. All reported stresses are in MPa. Each section
concludes with a summary of the stresses and a validation of the limit states.
155

LIST OF ATTACHMENTSSTRUCTURAL ANALYSIS OF BLADES
156
E.4 Load case A
Figure E.5: Normal stress parallel to fibres in longtitudal (z) direction of the blade
Figure E.6: Normal stress perpendicular to fibres in radial (x) direction of the blade

STRUCTURAL ANALYSIS OF BLADES
Figure E.7: Normal stress perpendicular to fibres in tangential (y) direction of the blade
Figure E.8: Shear stress in perpendicular to fibres in tangential (y) direction of the blade
157

LIST OF ATTACHMENTSSTRUCTURAL ANALYSIS OF BLADES
Figure E.9: Shear stress perpendicular to fibres in radial (x) direction of the blade
Figure E.10: Shear stress parallel to fibres in longtitudal (z) direction of the blade
158

The stresses are summarised and compared to the limit states in table E.10.
Compressionparallel
to grain
[MPa]
Compressionperpendicular
to grain
[MPa]
Shear
parallel to
grain
[MPa]
Shear
perpendicular
to
grain
[MPa]
STRUCTURAL ANALYSIS OF BLADES
Tension
perpendicular
to
grain
[MPa]
Tension
parallel to
grain
[MPa]
Limit state stress 4.9 0.54 0.96 0.27 0.32 9.0
Design stress 5.7 0.14 0.20 0.05 0.15 0.25 0.22 0.32 6.3
Table E.10: Summary of results and comparison to limit states
The limit state for compression parallel to grain is exceeded by 16%. The location of the
maximum compressive stress is shown on figure E.11.
Figure E.11: Position of maximum compressive stress
The maximum stress is highly local as less than 0.01% of the element volume has a com-
pression stress that exceeds the limit state. The limit state is not exceeded in the cross-
section at the blade root, which is the cross section that the loads are originally derived for
in accordance with IEC 61400-2. When further taking into account the high material safety
factor of 10, due to lacking S-N curves, it is considered acceptable that the limit state is
exceeded by 16% for this load case.
159

LIST OF ATTACHMENTSSTRUCTURAL ANALYSIS OF BLADES
160
E.5 Load case B
Figure E.12: Normal stress parallel to fibres in longtitudal (z) direction of the blade
Figure E.13: Normal stress perpendicular to fibres in radial (x) direction of the blade

STRUCTURAL ANALYSIS OF BLADES
Figure E.14: Normal stress perpendicular to fibres in tangential (y) direction of the blade
Figure E.15: Shear stress in perpendicular to fibres in tangential (y) direction of the blade
161

LIST OF ATTACHMENTSSTRUCTURAL ANALYSIS OF BLADES
Figure E.16: Shear stress perpendicular to fibres in radial (x) direction of the blade
Figure E.17: Shear stress parallel to fibres in longtitudal (z) direction of the blade
162

The stresses are summarised and compared to the limit states in table E.11.
Compressionparallel
to grain
[MPa]
Compressionperpendicular
to grain
[MPa]
Shear
parallel to
grain
[MPa]
Shear
perpendicular
to
grain
[MPa]
STRUCTURAL ANALYSIS OF BLADES
Tension
perpendicular
to
grain
[MPa]
Tension
parallel to
grain
Limit state stress 15 1.6 2.9 0.82 1.0 27
[MPa]
Design stress 10.6 0.26 0.39 0.09 0.50 0.55 0.21 0.42 9.3
Table E.11: Summary of results and comparison to limit states
The limit state stresses are not exceeded by the design stresses and the structural integrity
of the blade is therefore verified for the loads of the present load case.
163

LIST OF ATTACHMENTSSTRUCTURAL ANALYSIS OF BLADES
164
E.6 Load case C
Figure E.18: Normal stress parallel to fibres in longtitudal (z) direction of the blade
Figure E.19: Normal stress perpendicular to fibres in radial (x) direction of the blade

STRUCTURAL ANALYSIS OF BLADES
Figure E.20: Normal stress perpendicular to fibres in tangential (y) direction of the blade
Figure E.21: Shear stress in perpendicular to fibres in tangential (y) direction of the blade
165

LIST OF ATTACHMENTSSTRUCTURAL ANALYSIS OF BLADES
Figure E.22: Shear stress perpendicular to fibres in radial (x) direction of the blade
Figure E.23: Shear stress parallel to fibres in longtitudal (z) direction of the blade
166

The stresses are summarised and compared to the limit states in table E.12.
Compressionparallel
to grain
[MPa]
Compressionperpendicular
to grain
[MPa]
Shear
parallel to
grain
[MPa]
Shear
perpendicular
to
grain
[MPa]
STRUCTURAL ANALYSIS OF BLADES
Tension
perpendicular
to
grain
[MPa]
Tension
parallel to
grain
Limit state stress 15 1.6 2.9 0.82 1.0 27
[MPa]
Design stress 11.5 0.28 0.43 0.09 0.59 0.60 0.23 0.45 10.1
Table E.12: Summary of results and comparison to limit states
The limit state stresses are not exceeded by the design stresses and the structural integrity
of the blade is therefore verified for the loads of the present load case.
E.7 Load case E
Figure E.24: Normal stress parallel to fibres in longtitudal (z) direction of the blade
167

LIST OF ATTACHMENTSSTRUCTURAL ANALYSIS OF BLADES
Figure E.25: Normal stress perpendicular to fibres in radial (x) direction of the blade
Figure E.26: Normal stress perpendicular to fibres in tangential (y) direction of the blade
168

STRUCTURAL ANALYSIS OF BLADES
Figure E.27: Shear stress in perpendicular to fibres in tangential (y) direction of the blade
Figure E.28: Shear stress perpendicular to fibres in radial (x) direction of the blade
169

LIST OF ATTACHMENTSSTRUCTURAL ANALYSIS OF BLADES
Figure E.29: Shear stress parallel to fibres in longtitudal (z) direction of the blade
The stresses are summarised and compared to the limit states in table E.13.
170
Compressionparallel
to grain
[MPa]
Compressionperpendicular
to grain
[MPa]
Shear
parallel to
grain
[MPa]
Shear
perpendicular
to
grain
[MPa]
Tension
perpendicular
to
grain
[MPa]
Tension
parallel to
grain
Limit state stress 15 1.6 2.9 0.82 1.0 27
[MPa]
Design stress 1.8 0.07 0.09 0.02 0.12 0.43 0.23 0.31 6.2
Table E.13: Summary of results and comparison to limit states
The limit state stresses are not exceeded by the design stresses and the structural integrity
of the blade is therefore verified for the loads of the present load case.

E.8 Load case F
STRUCTURAL ANALYSIS OF BLADES
Figure E.30: Normal stress parallel to fibres in longtitudal (z) direction of the blade
Figure E.31: Normal stress perpendicular to fibres in radial (x) direction of the blade
171

LIST OF ATTACHMENTSSTRUCTURAL ANALYSIS OF BLADES
Figure E.32: Normal stress perpendicular to fibres in tangential (y) direction of the blade
Figure E.33: Shear stress in perpendicular to fibres in tangential (y) direction of the blade
172

STRUCTURAL ANALYSIS OF BLADES
Figure E.34: Shear stress perpendicular to fibres in radial (x) direction of the blade
Figure E.35: Shear stress parallel to fibres in longtitudal (z) direction of the blade
173

LIST OF ATTACHMENTSSTRUCTURAL ANALYSIS OF BLADES
The stresses are summarised and compared to the limit states in table E.14
174
Compressionparallel
to grain
[MPa]
Compressionperpendicular
to grain
[MPa]
Shear
parallel to
grain
[MPa]
Shear
perpendicular
to
grain
[MPa]
Tension
perpendicular
to
grain
[MPa]
Tension
parallel to
grain
Limit state stress 15 1.6 2.9 0.82 1.0 27
[MPa]
Design stress 0.34 0.01 0.02 0.0 0.01 0.06 0.01 0.03 0.51
Table E.14: Summary of results and comparison to limit states
The limit state stresses are not exceeded by the design stresses and the structural integrity
of the blade is therefore verified for the loads of the present load case.
E.9 Load case G
Figure E.36: Normal stress parallel to fibres in longtitudal (z) direction of the blade

STRUCTURAL ANALYSIS OF BLADES
Figure E.37: Normal stress perpendicular to fibres in radial (x) direction of the blade
Figure E.38: Normal stress perpendicular to fibres in tangential (y) direction of the blade
175

LIST OF ATTACHMENTSSTRUCTURAL ANALYSIS OF BLADES
Figure E.39: Shear stress in perpendicular to fibres in tangential (y) direction of the blade
Figure E.40: Shear stress perpendicular to fibres in radial (x) direction of the blade
176

STRUCTURAL ANALYSIS OF BLADES
Figure E.41: Shear stress parallel to fibres in longtitudal (z) direction of the blade
The stresses are summarised and compared to the limit states in table E.15.
Compressionparallel
to grain
[MPa]
Compressionperpendicular
to grain
[MPa]
Shear
parallel to
grain
[MPa]
Shear
perpendicular
to
grain
[MPa]
Tension
perpendicular
to
grain
[MPa]
Tension
parallel to
grain
Limit state stress 15 1.6 2.9 0.82 1.0 27
[MPa]
Design stress 9.8 0.24 0.36 0.08 0.43 0.51 0.20 0.38 8.6
Table E.15: Summary of results and comparison to limit states
The limit state stresses are not exceeded by the design stresses and the structural integrity
of the blade is therefore verified for the loads of the present load case.
177

LIST OF ATTACHMENTSSTRUCTURAL ANALYSIS OF BLADES
E.10 Deflection analysis
According to IEC 61400-2 it shall be verified that no deflections affecting the wind tur-
bine’s safety occur in the design load cases. One of the most important considerations is to
verify that no mechanical interference between the blade and tower can occur, that is, no
part of the blade shall hit the tower under any of the design load cases. Verification is ac-
complished through a critical deflection analysis, which checks the serviceability limit
state by comparing the no-load clearance LTB of figure E.42 with the maximum tip deflec-
tion.
178
Figure E.42: No-load clearance between blade and tower
The largest radial blade deflection (in the x-direction of figure E.42) occurs in load case C.
Figure E.43 below shows the deflection in mm.
Figure E.43: Radial deflection (x) of the blade in load case C

STRUCTURAL ANALYSIS OF BLADES
Contrary to normal practice, IEC 61400-2 requires that the maximum tip deflection is mul-
tiplied by the partial load factor for ultimate loads [5, p. 67]. Multiplying the maximum
deflection of 42.4 mm with �f = 3, yields a design deflection of 127.2 mm. The limit state of
130 mm is not exceeded by the design value and it is thus verified that the maximum blade
deflection is not critical.
E.11 Modal analysis
Resonance excitation problems may occur if the natural frequencies of the rotor blades
coincide with rotational frequencies of the rotor and multiples of it. When passing the
tower, each blade experiences a pressure pulse due to the air flowing around the tower.
Since the blades are all joined at the hub, their individual vibration also affects the other
blades. To avoid resonance problems the blade natural frequency must not coincide with
the frequency at which the blade or it neighbours pass the tower. For a three bladed ro-
tor, these frequencies are referred to as 1P and 3P frequencies (i.e. 1 per revolution and 3
per revolution) [36, p. 411]. The present variable speed wind turbine operates in the
range of 0 to 650 rpm, which yields a maximum 1P frequency of 10.8 Hz and maximum
3P frequency of 32.5 Hz. The blade should be stiff and light enough to keep its natural
frequency above the 3P tower passing frequency.
A modal analysis is performed to determine the natural frequencies of the blade. The
blade is fixed by the root of the airfoil and the computational model is thus similar to the
model described in appendix E.3. The natural frequencies are calculated for both a non-
rotating and a rotating blade. The rotation frequency of the rotating blade is set to 650
rpm and simulated by a centrifugal load, applied about the rotor axis. The Direct Sparse
solver of SolidWorks is used for the analysis.
The first five natural frequencies for a rotating and a non-rotating blade are shown table
E.16.
Mode Non-rotating blade (0 Hz) Rotating blade (10.8 Hz)
1 34.75 37.35
2 124.73 125.57
3 147.59 149.73
4 219.83 220.21
5 265.41 265.98
Table E.16: Rotating and non-rotating natural frequencies
The natural frequencies for the rotating blade are expectably higher than those of the
non-rotating blade. The increased natural harmonic frequency is caused by an increased
stiffness of the blade due to the centrifugal inertia forces.
179

LIST OF ATTACHMENTSSTRUCTURAL ANALYSIS OF BLADES
The first resonance frequency is a flapwise natural bending frequency (about the y-axis),
whereas the others are twisting and edgewise frequencies, so high that they are of no
concern. Figure E.44 shows the first mode shapes for a rotating blade.
180
Figure E.44: First mode shape for rotating blade
The first flapwise natural frequency of the rotating blade exceeds the maximum 3P fre-
quency by more than 14%. There is thus no apparent concern for resonance excitation of
the rotor blade.
To further verify the vibrational stability of the wind turbine, it is necessary to take into
account the dynamic couplings that exist between the interacting components of the
wind turbine, e.g. the tower and the rotor. This is however beyond the scope of this pro-
ject thesis.
E.12 Longevity expectation
The fatigue strength (10 7 ) of the steel shaft has been verified in appendix G and no num-
ber of loads is therefore considered to cause its failure. Other components are considered
replaceable during routine maintenance and therefore do not limit the longevity of the
complete wind turbine. Maintenance may include, but is not limited to:
� Lubrication
� Periodic testing of emergency shutdown/overspeed system
� Replacement of bearings and slip-rings
Since the fatigue properties of the tower are beyond the scope of this project thesis, the
blades are considered the limiting factor when it comes to longevity.
No S-N curves are available for the blade material, which means that it is not immediately
possible to determine the longevity of the blades. An attempt is however made to conser-
vatively estimate their fatigue life. While S-N curves are not available for the used mate-
rial, IEC 61400-2 provides one for birch. Figure E.45 shows the tensile stress range
parallel to the fibres for birch.

Figure E.45: S-N curve with fatigue life data for birch [5, p. 149]
STRUCTURAL ANALYSIS OF BLADES
From figure E.45 it is seen that the allowable stress range for birch at 10 10 load cycles is
25% of the static strength. Assuming that this also applies to the blade material, it is evi-
dent the blade can withstand 10 10 load cycles (and in all probability more), since a safety
factor of 10 is applied in appendix E.2.
Using the simplified load models of IEC 61400-2, the design life Td with n number of load
cycles may be calculated from [5, p. 91]:
n
Td �
� 19 yr
B ndesign Where the number of blades B is equal to 3 and ndesign is equal to 335 rpm.
From the above conservative estimate the blade longevity is set to 19 years. It is advised
to inspect the blades and other key components in an annual service inspection.
(E.4)
181

LIST OF ATTACHMENTSSTRUCTURAL ANALYSIS OF BLADES
E.13 Summary of analyses
Through stress analyses the structural integrity of the blade was verified in all load cases.
In load case A the limit state for compression strength parallel to the wood fibres was
exceeded by 16%. Due to the usage of a high fatigue safety factor of 10 and the position of
the critical load, the stress level was however found to be acceptable. The limit states
were not exceeded in any of the other load cases.
Through deflection analysis it was verified that the maximum blade deflection does not
cause mechanical interference between the blade and the tower.
Modal characteristics of the rotor blade were investigated and it was found that the pos-
sible excitation frequencies of the turbine do not coincide with the natural frequencies of
the blade.
The blade longevity was conservatively estimated to 19 years.
182

F
Blade attachment
The present appendix contains detailed statement of the blade joint dimensions and a
verification of the structural integrity of the blade attachment. Both are in accordance with
guidelines of the Danish Building Research Institute (DBRI).
The blade attachment is assumed to be an asymmetrical single shear joint connection of
two wooden members with different thicknesses, in which the fibre direction is parallel to
the load direction. The joint connection is principally illustrated on figure F.1. As described
in section 6.2.4 the joint is reinforced with a press-in connector, which is not shown on
figure F.1.
Load case E of appendix A.3 is considered as the worst case loading sceanrio for the joint
connection.
Figure F.1: Shear joint connection with asymmetrical members
183

LIST OF ATTACHMENTSBLADE ATTACHMENT
The dimensions of the joint components are listed in table F.1.
Description Symbol Value
Bolt diameter db 12.0 mm
Thickness of member 1 t1 32.0 mm
Thickness of member 2 t2 63.0 mm
Table F.1: Dimensions the joint connection
The thickness of member 2 is set to 63 mm to simulate the relative stiffness of the steel
front disc of the generator, which is the actual component that the blades are attached to.
The thickness of 63 mm is selected, as the load capacity does not increase for thicknesses
larger than this [31, p. 69-70]. Due to the relative large thickness of member 2, it is as-
sumed that twisting in the bolted joint, as illustrated in figure F.2, will not occur.
184
Figure F.2: Twisting in a bolted connection
The load capacity in the calculations is based on un-tightened bolts, since wood creeps
during loading. This means that any pre-loading would eventually be reduces to zero as a
function of time, due to factors such as temperature, moisture and load variations [31, p.
67]. According to DBRI, the ultimate limit state for the joint connection is given by [31,
p.38]:
kmod Fk
Flim.u �
� m� f
Where kmod is a modification factor that compensates for load duration, moisture content,
and temperature. Fk is the characteristic capacity of the joint connection and γm is the ma-
terial partial coefficient, taking into account uncertainties in determining Fk. The values of
these variables are determined on basis of the assumptions listed in table F.2 [31, p. 68]:
(F.1)

Assumption Description
Medium term load-duration
class M
BLADE ATTACHMENT
States a load-duration from 1 week to 6 months of the
total life time a [53, p. 45]
Service class 3 The service class is used for components that are fully
exposed to wetting [53, p. 44]
High safety class Is used as failure may cause personal injury or consider-
able social consequences [53, p. 43]
Bolt quality 4.6 Implying a bolt yield strength of 240 MPa and an ulti-
mate strength of 400 MPa [31, p. 63]
a) Load case E occurs at a wind speed of 14 m/s. Using the probability function of appendix A.1, it may be
calculated that the load-duration over a period of 19 years, which is the estimated longevity of the
wind turbine, is 59 days.
Table F.2: Description of the assumptions used in the calculations
From the above correction factor kmod is set to 0.722 [53, p. 40]. The partial coefficient �m is
set to 1.80 [53, p. 48] and �f is set to 1.5 [53, p. 47]. This is equal to a summarised safety
factor of 3.7.
Fk of (F.1) is calculated from the combined load capacity of one bolt connection and one
press-in connector. This is multiplied by the number of bolts in the joint connection, under
the assumption that the load capacity is equal for all components in the connection [31, p.
92].
Where the variables are:
Fk � �Fpi � Fb�nb
� 21.4kN
Description Symbol Value
Rated load capacity for press-in connector Fpi 4.1 kN
Rated load capacity for bolt connection Fb 3.03 kN
Number of bolts in the connection nb 3
Table F.3: Load capacity for press-in connectors and bolts
From the above, the limit state is now calculated:
kmod Fk
Flim.u � � 5.71kN
� m� f
This is compared to the centrifugal load FzB of load case E, which is 5.25 kN.
FzB �
Flim.u
(F.2)
(F.3)
(F.4)
185

LIST OF ATTACHMENTSBLADE ATTACHMENT
The limit state is not exceeded so it is concluded that the load carrying capacity of the
blade joint connection is sufficient.
It is noted that the rated load capacity for the bolt connection is based on a density �w for
coniferous trees of 380 kg/m 3 and an embedding strength fh of 25 MPa. As stated in appen-
dix E.2 the density of the blade wood �w is 571 kg/m 3 , which increases the load capacity to
[31, p. 63]:
The 65% increase in load capacity is considered as an extra safety factor, which makes the
present calculation conservative.
186
� � w 41.2
fh � 0.082 1 � 0.01db � MPa
(F.5)

F.1 Dimensions
BLADE ATTACHMENT
The load capacities of the previous section are only valid when certain minimum spacing
requirements for the joint connection are met. Table F.4 lists the requirements and the
actual dimensions with reference to figure F.3 [31, p. 95].
Figure F.3: Dimensional requirements for joint connection
Description Symbol
Dimension
Minimum Actual
Diameter of press-in connector Dpi - 48.0 mm
Centre to centre
Parallel to fibre direction a1 60.0 mm 60.0 mm
Perpendicular to fibre direction a2 57.6 mm 58.5 mm
Centre to end
Parallel to fibre direction a3 60.0 mm 60.0 mm
Centre to side
Perpendicular to fibre direction a4 28.8 mm 29.0 mm
Table F.4: Dimensional requirements compared to actual dimensions in the joint connection
It is concluded that the load capacities used in appendix F are valid, since the minimum
spacing requirements are met.
187

LIST OF ATTACHMENTSBLADE ATTACHMENT
188

G
Structural verification of shaft
The present appendix contains a verification of the structural integrity of the rotor shaft.
The shaft loads are found in appendix A.3 to be:
Load case Shaft load
A
B
D
E
F
G
Table G.1: Shaft loads
�F xS � 204 N
�M xS � 38.5 N m
�M S � 115 N m
M S
� 179 N m
FxS � 395 N
M S
� 144 N m
MxS � 65.0 N m
FxS �
12.0 kN
The loads are considered at the rotor shaft on the location of the first bearing, nearest to
the rotor. Figure G.1 shows the studied cross-section and the geometric data for the shaft.
189

LIST OF ATTACHMENTSSTRUCTURAL VERIFICATION OF SHAFT
Figure G.1: Indication of studied cross-section and geometric data
For both fatigue and ultimate limit states, the following requirement must be met:
Where
�design is the design stress from the load case
fk is the characteristic material strength
�m is the partial safety factor for the material
�f is the partial safety factor for the load
The shaft is manufactured from steel S235, which has a characteristic ultimate strength of
360 MPa and a characteristic amplitude fatigue strength of 180 MPa [54 , TB 1-1]. The
stated fatigue strength is converted into an allowable stress range by multiplying the am-
plitude value by 2, thus making the fatigue strength 360 MPa. This is a conservative value,
as it is valid for a fatigue stress ratio of -1.
The values of the partial safety factors are established in accordance with IEC 61400-2
under the assumption of so called full characterisation of the material properties [5, p. 89].
This implies that factors such as environmental effects and manufacturing methods have
been taken into consideration when determining the material properties.
Condition �m �f
Fatigue strength 1.25 1.0
Ultimate strength 1.1 3.0
Table G.2: Partial safety factors in accordance with IEC 61400-2
From this the ultimate limit state is calculated:
190
�lim.u �
�design �
f k
� m � f
f k
� m � f
� 109 MPa
(G.1)
(G.2)

And the fatigue limit state:
STRUCTURAL VERIFICATION OF SHAFT
For purpose of the structural strength calculations, the following cross-sectional proper-
ties are established from the dimensions on figure G.1.
Cross-sectional area:
Section modulus:
The cross-sectional stresses from the forces and moments within each load case are calcu-
lated and compared with the limit values in the following paragraphs.
Load case A
W S
A S
�
� lim.f
The fatigue stress ranges are calculated individually from the thrust loading (�FxS), the
torsion moment (�MxS) and the bending moment (�MS):
�
�
32
� xS
� MS
� MS
�
f k
� m � f
�
4 D2 d 2
�
D 4
�
�
�
� 288 MPa
� � 393 mm 2
d 4
�
D
�F xS
A S
�M S
W S
�M xS
2W S
�
The resulting equivalent stress is calculated and compared to the design limit stress:
� � 2
�eq � �xS � �MS �
�eq �
�lim.f 2.13 10 3
� mm 3
� 0.52 MPa
� 53.9 MPa
� 9.05 MPa
2
� 3�MS � 56.7 MPa
(G.3)
(G.4)
(G.5)
(G.6)
(G.7)
(G.8)
(G.9)
(G.10)
191

LIST OF ATTACHMENTSSTRUCTURAL VERIFICATION OF SHAFT
Load case B
The bending stress is calculated from (G.11) and subsequently compared to the design
limit stress:
Load case D
The axial stress is calculated below and compared to the design limit stress:
Load case E
The shaft bending stresses are calculated from (G.15) and subsequently compared to the
design limit stress:
Load case F
The shaft torsion stress is calculated from (G.17):
The stress is compared to the shear strength of the material [55, p. 45]
Where f� is equal to 0.58.
192
� MS
� xS
� MS
� MS
�
�
M S
W S
� 84.2 MPa
�MS � �lim.u �
�
� xS
F xS
A S
M S
W S
� 1.0 MPa
� �lim.u � 67.9 MPa
�MS � �lim.u M xS
2W S
� 15.3 MPa
f� �lim.u � 63.3 MPa
�MS �
f� �lim.u (G.11)
(G.12)
(G.13)
(G.14)
(G.15)
(G.16)
(G.17)
(G.18)
(G.19)

Load case G
The axial stress is calculated below and compared to the design limit stress:
Summary
� S
F xS
A S
STRUCTURAL VERIFICATION OF SHAFT
(G.20)
(G.21)
In neither of the load cases is the limit state exceeded. The structural integrity of the rotor
shaft is there considered to be verified.
�
� 30.6 MPa
�S �
�lim.u 193

LIST OF ATTACHMENTSSTRUCTURAL VERIFICATION OF SHAFT
194

H
Tower analysis
The present appendix contains a verification of the structural integrity of the tower in
accordance with IEC 61400-2. The tower loads are found in appendix A.3 to be:
Load case Tower load
G
H
Table H.1: Tower loads
In both load cases the loads are ultimate and the tower components should thus meet the
following requirement:
Where
�design �
�design is the design stress from the load case
fk is the characteristic material strength
�m is the partial safety factor for the material
�f is the partial safety factor for the load
FT.tot � 13.9 kN
MT � 3.79 kN m
(H.1)
The tower is manufactured from steel S355, which has a characteristic ultimate strength of
510 MPa. The values of the partial safety factors are established in accordance with IEC
61400-2 under the assumption of so called full characterisation of the material properties
[5, p. 89]. This implies that factors such as environmental effects and manufacturing meth-
ods have been taken into consideration when determining the material properties. �m is set
to 1.1 and �f to 3.0. This results in the following ultimate limit state:
f k
� m � f
195

LIST OF ATTACHMENTSTOWER ANALYSIS
The tower stresses from the load cases are calculated below and compared to the limit
state.
196
H.1 Load case G
�lim.u �
The load case combines a shaft thrust load with drag forces on the tail vane and the tower
to a maximum tower load in survival wind. In accordance with [5, p. 77], the maximum
bending moment is assumed to occur at the upper guy wire attachment.
The position of the load is considered at the centre of the rotor shaft, as this is the posi-
tion of the dominating part of the combined load. Figure H.1 shows the load position and
the dimensions used in the stress calculation.
f k
� m � f
� 155 MPa
Figure H.1: Load position and dimensions used in calculations
The bending moment at the guy wire attachment (cross-section 1) is calculated by:
’
(H.2)

Where Lgs is found in the 3D CAD model to be 1479.5 mm.
The resulting stress in cross-section 1 is:
Where WT is the section modulus, defined as:
Where D1 of figure H.1 is 168.3 mm and d1 is 154.1 mm.
The limit state is not exceeded in that:
TOWER ANALYSIS
The structural integrity by the flange is further checked, as the tower diameter is smaller
in cross-section 2.
W T
The bending moment in cross-section 2 is:
With Lfs found to be 564.5 mm in the 3D CAD model.
The section modulus is:
W T
With D2 of 93 mm and d2 of 69.6 mm.
The cross-sectional stress is thereby:
�
�
MyT � FT.tot Lgs � 20.6 kN m
� T
�
32
�
D 1 4
M yT
W T
4
� d1 D 1
� T
� 148 MPa
�
� �lim.u 1.39 10 5
� mm 3
MyT � FT.tot Lfs � 7.85 kN m
�
32
� T
D 2 4
�
4
� d2 D 2
M yT
W T
�
5.42 10 4
� mm 3
� 145 MPa
�T �
�lim.u (H.3)
(H.4)
(H.5)
(H.6)
(H.7)
(H.8)
(H.9)
(H.10)
197

LIST OF ATTACHMENTSTOWER ANALYSIS
The stresses in the bolts of the flange assembly under load case G are checked in a separate
calculation below.
198
H.2 Flange assembly
This appendix carries out a verification of the structural integrity of the bolts in the flange
assembly, which connects the upper part of the tower to the yaw system, as shown on
figure H.2.
Figure H.2: Bolt connection in flange assembly
The moment MyT =7.85 kNm, calculated in (H.7), is considered to act as a tension load in
some of the bolts and as a compression load in a part of the flange. The calculation is
performed in accordance with [65]. The basic concept of the calculation method is to
divide the flange into two parts: One part that represents the tension loaded bolts (a) and
one part that represents the compressed part of the flange (b), as shown on figure H.3.

Figure H.3: Division of the flange into part a and part b
TOWER ANALYSIS
The neutral axis y-y of the connection is located at the position of equilibrium between
the static moments of the areas a and b. The area moment of inertia for the tension
loaded bolts, about the neutral axis of the bolt connection, is determined from:
(H.11)
Where Dpc is the bolt pitch diameter of 210 mm and a is 1.43, calculated from [65, p. 91]. �
is a function of the ratio between the width of the flange and the tension stress area of the
bolt, divided with the arc length between each bolt. It is found to be 0.6 in [65]. This
yields:
Iy.a �
�
�
�
The area moment of inertia of the compression loaded flange is determined to be:
Iy.b �
�
�
�
Dpc
2
Where b is 38.4 mm, calculated from [65, p. 93].
The two contributions are added and total area moment of inertia for the bolt connection
is calculated:
Dpc
�
�
�
2
3
b
�
�
�
�
�
�
3
a� �
�
�
1
2
� sin( 2 ) � 4 cos ( ) sin( ) � 2( � ) cos ( )
2
Iy.a 1.20 10 7
� mm 4
=
1
2
� sin( 2 ) � 4 cos ( ) sin( ) � 2 cos ( )
2
Iy Iy.a � Iy.b 1.30 10 7
� mm 4
�
�
�
�
�
�
�
�
�
1.07 10 6
� mm 4
(H.12)
(H.13)
(H.14)
199

LIST OF ATTACHMENTSTOWER ANALYSIS
The highest tension stress occurs in at the greatest distance from the neutral axis.
The above tension stress is used to calculate the maximum bolt tension force, which is
compared to the limit state of the bolt. This is done in att. 16, using prevalent methods
described in [55]. From this it is verified that the limit states of the most stressed bolt is
not exceeded.
200
t.bolt
MyT
H.3 Load case H
�
�
�
�
Dpc Dpc
cos ( )
2 2 �
In load case H the bending moment at the lifting point, i.e. the upper guy wires, is:
The equivalent moment from load case G in cross-section 1 is multitudes higher and it is
therefore not necessary to check the tower stresses of this load case.
Iy
MT �
3.79 kN m
�
�
�
� 114 MPa
(H.15)
(H.16)

I
Furling and yaw analysis
This appendix contains a calculation of the yaw orientation system, which validates the
ability of the wind turbine to approximately align itself in a situation where the wind speed
changes from near zero to 4 m/s, where power production is initiated. The appendix also
contains a verification of the overall functionality of the furling mechanism, which con-
firms that furling is initiated at a wind speed of 14 m/s. Finally the appendix contains a
calculation of the contact pressure in the bearings of the yaw system.
I.1 Yaw system
For the yaw system to turn the wind turbine into the wind, the frictional forces in the
mechanism must be overcome. The following frictional forces are considered:
� Bearing frictional forces due to dead-weight of components, e.g. tail, rotor and
generator
� Bearing frictional forces due to thrust on the rotor
In the calculations it is assumed that the rotor is positioned at an arbitrary angle and is at
standstill due to a wind speed of 0 m/s. It is checked that the forces on the tail vane will
properly align the rotor with the wind when the wind speed is suddenly increased to 4
m/s, where power production is initiated. Analysis of the yaw behaviour during operation
is beyond the scope of this project for the reasons mentioned in section 8.1.
The following paragraphs contain calculation of bearing forces due to the various loads.
These are followed by calculation of the frictional moment that must be overcome by the
yaw mechanism.
201

LIST OF ATTACHMENTSFURLING AND YAW ANALYSIS
Reaction moments due to dead-weight
The mass of the tower-top components induces dead-weight loads on the bearings in the
yaw system. SolidWorks is used to find the mass centres of the components that create
bearing reaction moments about the x-axis and y-axis, shown on figure I.1.
Figure I.1: Moment about x-axis (top) and y-axis (bottom) due to dead-load of components
These dead-weight loads lead to a positive moment about the y-axis and a negative mo-
ment about the x-axis, according to a positive clock-wise direction of calculating. The val-
ues calculated in att. 7, are shown in table I.1.
202

Moment and direction (CW) Value
Mx -4.86 Nm
My 202 Nm
FURLING AND YAW ANALYSIS
Table I.1: Reaction moments due to dead-weight load of the top of the wind turbine
Reaction force due to thrust load
The reaction force in the bearings due to the thrust loading at a wind speed of 4 m/s is
calculated:
Where Ar is the projected area of the rotor equal to 0.691 m 2 , V is the wind speed of 4 m/s
and Cf is a force coefficient of 2 according to IEC 64100-2 [5, p. 79].
Bearing forces
From the dead-weight reaction moments and the thrust load, the bearing reaction forces
are calculated. The moments from the dead-weight load are converted in to force couple,
as illustrated in figure I.2. The directions of the arrows show the actual directions of the
forces.
1
Ftf.x
2 Ar V 2 �
Cf � 13.5N
Figure I.2: Illustration of moments and force couples due to loading on the bronze bearings
(I.1)
203

LIST OF ATTACHMENTSFURLING AND YAW ANALYSIS
The dead-load induced bearing reaction forces:
Where L1 is 275 mm
The thrust induced reaction forces:
Where L2 is 3.00 mm.
The sum of the reaction forces in the x-direction and the y-direction is:
The sum of the reaction forces in the x-direction and the reaction force in the y-direction
are summed geometrically into a reaction force in each bearing.
204
My
Rdw.x.A � � 367 N
2L1
My
Rdw.x.B � � 367 N
2L1
Mx
Rdw.y.A � � 8.83N
2L1
Mx
Rdw.y.B � � 8.83N
2L1
Rtf.x.B �
Ftf.x� 2L1 � L2�
2L1
� 13.6N
Rtf.x.A Ftf.x � Rtf.x.B 7.39 10 2 �
�
� � N
Rx.A � Rdw.x.A � Rtf.x.A � 367N
Rx.B � Rdw.x.B � Rtf.x.B � 353N
Ry.A � Rdw.y.A � 8.83N
Ry.B � Rdw.y.B � 8.83N
RA Rx.A 2 Ry.A 2
�
� � 367 N
(I.2)
(I.3)
(I.4)
(I.5)
(I.6)
(I.7)
(I.8)
(I.9)
(I.10)
(I.11)
(I.12)

Friction forces and moments
FURLING AND YAW ANALYSIS
(I.13)
The friction force in the bearings is calculated from the sum of the reaction force in the two
bearings, which is:
Using a friction coefficient µs of 0.2, the friction force becomes:
This is recalculated into a frictional resistance moment:
A total frictional resistance moment is calculated by further adding the required starting
(I.14)
(I.15)
(I.16)
torque for the thrust bearing Mst, which is 28.8 Nmm. The calculation, which is documented
in att. 3, uses the following input:
� Bearing load: 997 N
� The number of rotations per minute: 1 rpm
� Friction coefficient in full-film condition: 0.1 µEHL, which corresponds to grease
used as lubrication in the bearing.
Yawing moment
The aerodynamic lift and drag forces on the tail vane will tend to align the rotor with the
wind, whereas the thrust force on the rotor and the above calculated frictional resistance
(I.17)
moment will oppose the tendency. Using principles of equilibrium it is possible to calculate
a steady state yaw offset.
The lift force is perpendicular to the wind direction and the drag is parallel to the wind
direction, which is shown on the free body diagram of the tail vane and the rotor on figure
I.3.
RB Rx.B 2 Ry.B 2
� � � 354 N
Rtot � RA � RB � 721N
Ffr � Rtot s � 144N
Mfr �
Db
Ffr
2
� 6.70Nm
Mfr.tot �
Mst � Mfr � 6.73Nm
205

LIST OF ATTACHMENTSFURLING AND YAW ANALYSIS
206
Figure I.3: Free Body Diagram of the tail vane and rotor
Both the lift and drag forces may be divided into components along the x-axis and the y-
axis. It is seen that both the lift and drag forces contribute to a moment (CW) about the
yaw axis, which is:
Where Av is the area of the tail vane equal to 1.04 m 2 and:
Aerodynamically the tail vane is considered a thin flat plate. The drag coefficient is there-
(I.18)
(I.19)
(I.20)
(I.21)
(I.22)
fore approximated as Cd = 1.28 sin(�) and the lift coefficient as Cl = 2��, see [63] and [64, p.
557], respectively.
Mv � FxLv.y � FyLv.x
Fx � Fdcos ( �)
� Flsin( �)
Fy � Fdsin( �)
� Flcos ( �)
Mv � Fx Lv.x � Fy Lv.y
Fl �
1
2 V2 Av Cl
1
Fd
2 V2 �
Av Cd
The moment from the rotor thrust force about the yaw axis is calculated as (positive CCW):

1
Mr
2 Ar V 2 �
cos ( ) Lr.y Cf
FURLING AND YAW ANALYSIS
(I.23)
Where cos(�) is the projection of the rotor area onto a plane, which is perpendicular to the
wind direction. The variables equate those of (I.1).
Using the derived moment equations, the alignment of the wind turbine is calculated in
two different scenarios, as illustrated on figure I.4. In the first scenario the wind turbine
aligns with the wind by rotating clockwise and in the second it rotates counter clockwise.
Figure I.4: Alignment of the wind turbine Top: CW rotation. Bottom: CCW rotation
207

LIST OF ATTACHMENTSFURLING AND YAW ANALYSIS
For the first scenario of CW rotation the equilibrium equation is:
Which yields a yaw error � of 3.50°.
For the second scenario of CCW rotation the equilibrium equation is:
Which yields a yaw error � of 2.24°.
The largest yaw error of 3.50° occurs during CW rotation for alignment. The error is con-
sidered low enough to be acceptable.
208
I.2 Furling mechanism
The present calculation verifies the overall functionality of the furling mechanism, by
checking that furling is initiated at a wind speed of 14 m/s.
The calculation is based on the principle of energy conservation. It is assumed that the
amount of work performed by the furling rotor is translated into an increased potential
energy of the tail, see description in section 8.2. The energy conversion is expressed
mathematically by:
Mv � Mr � Mfr.tot � 0
Mfr.tot � Mr � Mv � 0
Where Wr is the work performed by the rotor:
Wr
And Ev is the potential energy of the tail:
Ev � Wr
� Ftf Lr.y�f
Ev �
mv g h
Ftf is the rotor thrust force, which is found using the rotor calculation tool calculated. Lr.y is
the moment arm of 107.5 mm shown on figure I.3 and �f is the furling angle of figure 8.6.
mv is the tail mass of 17.5 kg and Δh is the gained height of the tail’s mass centre.
(I.24)
(I.25)
(I.26)
(I.27)
(I.28)

The following assumptions are made when using the above calculation principle:
� The rotor plane is perpendicular to the direction of the wind
� Friction in the tail pivot is neglected
� The mass of welds in the tail is neglected
� The tail vane is parallel to the air flow
FURLING AND YAW ANALYSIS
The gain height Δh of the tail is analysed in SolidWorks as a function of the furling angle �f
in the range of 0-5�, using 1� steps.
Furling angle, �f [�] Height gained, Δh [mm]
Table I.2: Results of the tail motion analysis
0 0
1 9.28
2 18.8
3 28.4
4 38.3
5 48.3
The rotor thrust Ftf is calculated for wind speeds 13 m/s, 14 m/s and 15 m/s as shown in
table I.3.
Wind speed V [m/s] 13 14 15
Thrust force Ftf [N] 718 872 1050
Table I.3: Rotor thrust force as different wind speeds
The work performed by during furling Wr may now be calculated as a function of the furl-
ing angle �f at the three wind speeds of table I.3. Correspondingly the potential energy of
the tail may be calculated as a function of the furling angle �f. The result is illustrated on
figure I.5 below.
209

LIST OF ATTACHMENTSFURLING AND YAW ANALYSIS
Figure I.5: Potential energy of the tail and worked performed during furling. Both as a func-
tion of the furling angle �f
From the graph of figure I.5 it is seen that the work performed by the furling operation at a
wind speed of 13 m/s is less than the energy required to increase the height of the tail.
Hence the wind turbine will not furl at a wind speed of 13 m/s. At a wind speed of 14 m/s
the work performed and the energy required is approximately equal, which indicates that
furling is initiated at a wind speed very close to this, and certainly below one of 15 m/s
where the work performed is much greater.
210
I.3 Bearing contact pressure
The maximum contact pressure in the bearing is compared to the allowable contact pres-
sure.
Where
pdesign �
pdesign is the design stress from the load case
fk is the characteristic material strength
�m is the partial safety factor for the material
�f is the partial safety factor for the load
fk
� m� f
(I.29)

FURLING AND YAW ANALYSIS
The bearing material is bronze alloy with a characteristic limited contact pressure of 50
MPa, see att. 14. The values of the partial safety factors are established in accordance with
IEC 61400-2 under the assumption of so called full characterisation of the material proper-
ties [5, p. 89]. This implies that factors such as environmental effects and manufacturing
methods have been taken into consideration when determining the material properties. �m
is set to 1.1 and �f to 3.0. This results in the following yield limit state:
plim
The contact area Ab in the bearing is calculated on basis of the bearing diameter Db = 93.0
mm and the bearing height Lb = 10.0 mm.
(I.30)
(I.31)
The 13.9 kN tower load of load case G is assumed to be applied directly at the centre of the
upper bearing in the yaw system. This yields a maximum contact pressure of:
It is concluded that the limit state for the material is not exceeded.
�
fk
� m� f
� 15.2MPa
Ab LbDb 930 mm 2
� �
Pmax
�
RB
Ab
� 14.6MPa
pmax �
plim
(I.32)
(I.33)
211

LIST OF ATTACHMENTSFURLING AND YAW ANALYSIS
212

J
Alternative airfoil test
This appendix contains a description of the tests performed on the alternative airfoil de-
sign, described in chapter 10.
J.1 Purpose
The main purpose of the tests is to establish the aerodynamic properties, in terms of lift
and drag coefficients, for airfoil A and B of chapter 10.
J.2 Test equipment
The aerodynamic properties of the airfoils are established through wind tunnel tests. The
tests are performed in the Vestas Lab at the Engineering College of Aarhus. The utilised test
equipment is described in the following.
213

LIST OF ATTACHMENTSALTERNATIVE AIRFOIL TEST
Wind tunnel
The wind tunnel is an open return, subsonic wind tunnel, also denoted an Eiffel tunnel. The
schematic of figure J.1 shows the principle layout of the wind tunnel.
214
Figure J.1: Principle layout of the wind tunnel [66]
The air that passes through the test section is gathered from the laboratory where the
wind tunnel is located. Since it is an open return tunnel, the flow has to turn the corner of
the bell-mouth, which may produce asymmetries and turbulence in the airflow of the test
section. There is no technical data available on the wind tunnel.
Pitot tube
The airflow in the wind tunnel is measured using a pitot tube, illustrated on figure J.2,
which is positioned in the test section.
Figure J.2: Pitot tube
The tube is pointed directly into the air. The difference between the stagnation pressure
and the static pressure is the dynamic pressure, which is used to calculate the air flow

ALTERNATIVE AIRFOIL TEST
velocity. The height difference �h is measured on the liquid gauge column and the velocity
of the air flow is calculated from:
Where the dynamic pressure pd is:
Load cell
The load cell is used to measure the lift and drag forces exerted on the airfoils.
Key data:
Brand: Hottinger Baldwin Messtechnik
Type: Z6FC3
Accuracy class: C3
Max capacity: 10 kg
Tolerance on sensitivity: < ± 0.1 %
Display
The digital display shows the measurements of load cell.
Key data:
Brand: Hottinger Baldwin Messtechnik
Type: MVC2510
Setting accuracy: 0.33
3D Printer
The 3D printer is used to print the airfoils from a 3D CAD model. The printer software
automatically prepared the model for printing and adds necessary support material to the
model. The airfoils are printed in ABS plastic in layers with a thickness of 0.178 mm [56].
Key data:
Brand: Dimension
Type: SST 1200es
Model material: ABSplus
Support material: Soluble Support Technology
V
�
2pd
pd �
g h water
(J.1)
(J.2)
215

LIST OF ATTACHMENTSALTERNATIVE AIRFOIL TEST
216
J.3 Test setup and preparations
The dimensions of the printed airfoils are shown on figure J.3.
Figure J.3: Main dimensions of the two alternative airfoils. Left: Airfoil A. Right: Airfoil B. The
airfoil thickness is 5 mm.
The support material is removed from the printed airfoils and the surface is smoothened
using sandpaper (grit 200). The airfoils are mounted on a ø16 mm steel shaft. A ø3 mm
steel wire, which is used to measure the angle of attack, is attached to the shaft. Finally, 1
mm steel plates are glued to both ends of the airfoils. Figure J.4 shows the airfoils prepared
for testing.
Figure J.4: Airfoils prepared for testing

ALTERNATIVE AIRFOIL TEST
The steel endplates are mounted to reduce vortices, produced at the edges of the airfoil,
which affect the lift characteristics [57, p. 8]. The vortices are illustrated on figure J.5:
Figure J.5: Trailing vortices at the ends of an airfoil
The prepared airfoils are mounted on a test bed, which is placed in the test section of wind
tunnel, as shown on figure J.6. Dependent on whether the lift or the drag force is being
measured, the test bed is rotated, so that the load cell measures either the force perpen-
dicular or parallel to incoming wind speed. To retain a laminar airflow, the test bed is posi-
tioned as close to the outlet of the contractor as possible.
Figure J.6: Airfoil mounted on test bed
The test airfoil is aligned with the mutual centre line of the contractor and the diffuser, so
that the airfoil chord is parallel to the centre line. The alignment is facilitated by the use of
the protractor and the steel wire, seen on figure J.6.
217

LIST OF ATTACHMENTSALTERNATIVE AIRFOIL TEST
218
J.4 Test measurements
The lift and drag force measurements are performed for angles of attack in the range of 0°-
20°, using 2� steps. The drag force is measured in the direction of the air flow. The lift force
is measured perpendicular to the air flow.
A temperature of 20.5 °C was measured in the laboratory at the beginning of the test. A
wind speed of 44.9 m/s was used, resulting in a Reynolds number Re of 3.2 × 10 5 .
The raw results may be found in att. 5, which also contains the data conversion, described
in the following appendix.
J.5 Data conversion and analysis
The load cell outputs that are logged during the tests are report in kg. The output is con-
verted forces and the lift and drag coefficients are calculated as follows:
1 2
Since p � �V
both the equations can be rewritten to:
d
2
0
Where b is the span of the test airfoil, c is the chord length and FL,D are the lift and drag
forces, respectively. The air density � is set to 1.225 kg/m 3 as in all other calculations,
which is a good assumption for the measured temperature of 20.5 °C.
The lift coefficient calculated in (J.5) is made valid for an airfoil of infinite length in (J.7),
which is valid for small aspect ratios, AS = b/c [60, p. 20].
Cl
Cd
�
�
Cl
Cd
�
Fl
c b 1
� V2
2
�
Fd
c b 1
� V2
2
Fl
c bpd
�
�
Fd
c bpd
2
Cl.inf �
Cl�1 �
AS
�
�
�
(J.3)
(J.4)
(J.5)
(J.6)
(J.7)

Glide ratio is calculated from
ALTERNATIVE AIRFOIL TEST
Three independent tests are performed for each airfoil to account for the uncertainties of
the measurements. On the result charts of figure J.7and figure J.8, the arithmetic mean of
the test results are shown with error bars that indicate � 1 standard deviation �st. The
standard deviation is calculated from:
�st =
Where σst is the standard deviation, N is the number of data points, xi is the reading and µm
is the mean value. Assuming that the data is normally distributed about 68% of the values
lie within 1 standard deviation of the mean.
The charted results for airfoil A:
Cl
GR �
Cd
N
1
�x i � �m�
N
i 1
2
�
�
Figure J.7: Measured lift coefficient, drag coefficient and glide ratio for profile A
(J.8)
(J.9)
219

LIST OF ATTACHMENTSALTERNATIVE AIRFOIL TEST
The charted results for profile B:
Figure J.8: Measured lift coefficient, drag coefficient and glide ratio for profile B
Profile A stalls at an angle of attack of 10�, while profile B stalls at 13�. Both profiles have
an optimum angle of attack of 4.5�, where the glide ratio is maximal. Profile A however has
a higher glide ratio and it is therefore considered the better of the two profiles.
The variation of the test results are primarily ascribed to uncertainties in the adjustment
of the angle of attack. Another factor that has contributed to the result variance is the lack
of stiffness of the test airfoil, which vibrated slightly during the performed tests, resulting
in fluctuating measurements of load.
The measured aerodynamic properties of profile A are added to the rotor design tool using
the method described in appendix D. Figure J.9 shows the lift coefficient, drag coefficient
and glide ratio for the airfoil in the angle of attack range of 0�-90�. The properties are de-
rived using Viterna and Corrigan (see appendix D) and with �opt of 4.5�, �st of 10 and Cd.max
= 1.11+0.018AS [16].
220

Figure J.9: Lift coefficient, drag coefficient and glide ratio for profile A
ALTERNATIVE AIRFOIL TEST
From the above airfoil properties a new three-bladed rotor is designed with the same
rated power output as the one based on the NACA-4412 profile. The result is described in
chapter 10.2 and a print-out of the calculations from the rotor design tool is provided in
att. 5.
221

LIST OF ATTACHMENTSALTERNATIVE AIRFOIL TEST
222

K
Compliance with IEC 61400-2
This appendix concerns the partial compliance with IEC 61400-2, which is a requirement
for the present wind turbine design.
The demands of the IEC standard may be divided into the following main categories:
� External conditions
� Structural design
� Protection and shutdown system
� Testing
� Electrical system
� Support structure
� Documentation
� Wind turbine markings
Each of the eight categories contains numerous demands, which are fully accounted for in
the standard and therefore not repeated here. Table K.1 lists the categories and summa-
rises the extent to which the normative requirements are met by the design.
223

LIST OF ATTACHMENTSCOMPLIANCE WITH IEC 61400-2
Category Compliance
External conditions The external conditions of IEC 61400-2 include
224
wind and environmental conditions. These are
used to establish structural load cases and they
further form the basis for aerodynamic perform-
ance calculations.
Structural design The structural design loads are based on simplified
IEC load models and safety factors. The structural
integrity of key components is verified.
Protection and shutdown system The design complies with the protection system
requirements of the IEC standard if it is used with
an electrical system with the same properties as
those described in section 7.2.
Testing No tests are performed due to the lack of a proto-
type.
Electrical system Design of the electrical system is beyond the scope
of this project and its compliance with the IEC
standard is therefore not treated. The general
guidelines of section 7.2 however provide a good
starting point.
Support structure The wind turbine tower is treated to some extent,
but further validation is needed. The foundation is
not treated.
Documentation IEC requires product manuals to be provided.
While manuals are not produce, much of the infor-
mation of this project thesis may be used to pro-
duce manuals containing clear description of
assembly, installation and operation of the wind
turbine.
Wind turbine markings All required marking information may be found in
Table K.1: Categories of IEC 61400-2
table 5.1, except for full details of the electrical
system.