5/1/2011
THE UNIVERSITY
OF AKRON
DESIGN AND CONSTRUCTION OF A VERTICAL
AXIS WIND TURBINE
Zack Carman
Ryan Ciganik
Ian Collins
Evan Gutshall
VAWT Senior Design Report
Page 0
Executive Summary
The Earth’s population is growing at a staggering pace and everyday requires more
energy than the previous day. To keep pace with the growing energy demand new forms of
energy generation and transmission are being developed and implemented. The current push
for energy generation is to harness renewable energy sources such as wind. Vertical axis wind
turbines provide renewable energy which can be harnessed to reduce environmental damage
produced by coal and other forms of nonrenewable energy.
This report will summarize two semesters worth of designing, testing and modifying a
vertical axis wind turbine, which will from this point on be referred to as a VAWT. Semester
one consisted of designing and selecting the components and materials that could withstand
the forces the turbine would experience along with having a good resistance to corrosion.
Construction of the turbine was done by using easily machinable materials such as
aluminum and foam insulation sheeting. To aid in foam shaping the team designed and
constructed a hot foam cutter. Foam was chosen because of its workability and also because of
its strength to weight ratio.
Initial turbine testing was done in moderate winds and proved successful. The turbine
easily and quickly spun up in almost no wind. Although no load was put on the turbine we were
able to prove that our initial calculations and assumptions were correct.
In Depth testing was accomplished with the use of a wind tunnel located in the
University of Akron’s Engineering building. During testing it was discovered that a purchased
inverter was damaged and not working correctly. Because of this we were not able to measure
the true efficiency of our inverter and all electrical output calculations will be theoretical.
The goal of this project was to create a functional VAWT that could be easily produced
while at the same time generate a usable amount of power.
We feel that we have
accomplished our goal and have created a low cost high efficiency VAWT that can easily be
adapted to work in nearly any environment.
VAWT Senior Design Report
Page 1
Contents
Executive Summary ................................................................................................................................. 1
Introduction ............................................................................................................................................ 4
Constraints/Specifications ....................................................................................................................... 5
Design ..................................................................................................................................................... 6
Airfoil Selection ....................................................................................................................................... 7
Materials ................................................................................................................................................. 8
Structural Analysis ................................................................................................................................... 8
Assumptions ........................................................................................................................................ 8
Equations ............................................................................................................................................ 9
Method ............................................................................................................................................... 9
Analysis ............................................................................................................................................. 14
Cost Analysis ......................................................................................................................................... 15
Electrical Analysis .................................................................................................................................. 15
Summary ............................................................................................................................................... 16
Appendix ............................................................................................................................................... 18
Materials & Components ................................................................................................................... 18
Structural Analysis Data ..................................................................................................................... 24
Turbine Cost ...................................................................................................................................... 27
Electrical Data ................................................................................................................................... 28
Airfoil Data ........................................................................................................................................ 29
VAWT Senior Design Report
Page 2
Formula List....................................................................................................................................... 32
Sample Calculations........................................................................................................................... 33
Sample Velocity Triangles .................................................................................................................. 34
VAWT Manufacture and Assembly..................................................................................................... 37
VAWT Senior Design Report
Page 3
Introduction
Vertical Axis Wind Turbines, VAWT, are a relatively new technology that is still being
developed and researched. VAWT’s have many advantages over the more common Horizontal
Axis Wind Turbines. The biggest advantage being that they are able to harness wind from any
direction rather than constantly having to be re-oriented to catch wind from a narrow field.
This is ideal for residential settings where wind can often be from any direction and also change
direction quite often.
Another advantage of a VAWT is that they operate at much lower
speeds than a traditional wind turbine. This results in VAWT’s being very quiet, which is also
ideal for residential settings where neighbors can be easily upset. VAWT’s also operate in very
low winds compared to traditional turbines. The cut-in speed of a VAWT is around half that of a
traditional turbine. We felt that a Vertical Axis Wind Turbine was a much smarter choice for
our current location and setting.
The goal of this project was to create a simple vertical axis wind turbine capable of
producing electricity in a residential setting. The project will focus on creating a turbine that is
simple to manufacture while at the same time highly efficient and cost effective.
Currently, vertical axis wind turbines have been manufactured and built. Although
turbines currently exist, there is no standard for production of VAWT’s. When a streamlined
manufacturing process is developed, it would be possible to mass produce VAWT’s. Mass
produced VAWT’s could be installed on commercial and residential buildings, greatly reducing
the amount of environmental pollution that is accumulating due to nonrenewable energy
production.
VAWT Senior Design Report
Page 4
Mass producing VAWT’s involves many challenges.
Currently a combination of
materials, electrical generation equipment, and other components are not designed to be
paired together in a cheap and efficient manner. The project will revolve around pairing
components together that, when combined, provide the best structural integrity, lowest cost,
highest efficiency, and simplest ability to manufacture. When strong components are paired
with low cost electrical generation systems, wind turbines become more attractive to
commercial and residential users.
Constraints/Specifications
Cost is an important constraint that the design team took into consideration when
theoretical design work was performed to construct a vertical axis wind turbine.
To be
marketable to commercial and residential users, VAWT’s must be low cost. Cost must be low
enough to buy VAWT’s so that initial capital invested for purchase is quickly recovered and the
turbine must produce enough power so that electrical costs are reduced when a turbine is in
use.
Another important constraint that must be met to mass produce VAWT’s involves ease
of manufacture, long-term reliability and maintenance costs. Wind turbines must be easy to
manufacture so costs do not spike when producing large quantities of turbines. If costs are not
marketable, commercial and residential users will shy away from turbines due to high initial
investment costs. Reliability is another fundamental constraint that is of utmost importance. If
wind turbines are constantly breaking, commercial and residential users will stop purchasing
VAWT Senior Design Report
Page 5
the units. Turbines must be reliable so they consistently produce power to quickly pay for their
initial investment costs.
To be able to quickly recoup the costs of a turbine the unit must be efficient. The Betz
law states that no more than 60% of the energy in the wind can be harnessed and used to do
work. Our goal in designing this turbine is to come as close as we can to the Betz limit. For this
project we have set a goal of 40%. By combining low weight airfoils and materials with a high
efficiency generator this is an achievable goal.
Design
During initial design the team focused on the fundamentals listed in the constraints
section. The team decided that it was necessary to produce a VAWT that consisted of a main
center shaft. Attached to the shaft was a generator with a mounting plate. The mounting plate
housed three support arms spaced 120° apart from each other. The three support arms
attached to three individual airfoils. The airfoils chosen were NACA 0018 symmetric airfoils.
NACA 0018 airfoils were chosen because of the high coefficient of lift versus coefficient of drag
ratio (Cl/Cd). The team decided to use a main support shaft with a 1.5” outside diameter. This
main support shaft could be coupled to the ground or a roof top many different ways. A shaft
could be threaded and drilled to a roof which would allow the VAWT to operate in an
environment where optimal winds exist for maximum turbine efficiency. The 1.5” shaft could
also be set up using a tripod to allow simplistic turbine mobility.
The design specifications of the VAWT were achieved by decreasing the amount of CNC
machining time. Components of the VAWT were selected based on their structural strength
VAWT Senior Design Report
Page 6
and ease of machining. Components were selected that would be supplied ready to use,
lowering machining costs and lowering the assembly time of the turbine.
Airfoil Selection
A symmetric airfoil was chosen for this turbine because of the high variance in angle of
attack the airfoil would experience during each revolution of the turbine.
Choosing a
symmetric airfoil also resulted in the ability to generate lift on both faces of the airfoil which
allowed the airfoil to extract energy when the airfoil was experiencing both positive and
negative angles of attack. A NACA-0018 airfoil was chosen because of its high L/D coefficient
and also because its ability to deal with extreme angles of attack. Similar symmetric airfoils had
abrupt changes in their lift coefficient when the angle of attack was adjusted. Our team felt
that this could be potentially dangerous because of the sudden changes in angle of attack and
wind speed. The NACA-0018 airfoil has a max L/D ratio of 33.9. Although this is a relatively low
number when compared to non-symmetric airfoils, symmetric airfoils are far superior in this
application because of their ability to generate lift on both faces. More data on the NACA -0018
can be seen in the appendix section Airfoil Data.
Once the airfoil had been selected calculations were done to ensure that the turbine
would have a net positive torque. Having a net positive torque ensured that our turbine would
function in the way it was supposed to. An excerpt of the torque calculations can be seen in
the appendix as well as sample calculations in the Sample Calculation section of the appendix.
VAWT Senior Design Report
Page 7
Materials
Materials were chosen based on their strength and corrosion resistance. Parts that were
determined to be high stress were made out of aluminum. Aluminum was chosen because of its high
strength to weight ratio and also because it has good corrosion resistance.
The airfoils were made out of standard insulation foam with a main spar made of 6061-T6
aluminum. 6061-T6 aluminum was chosen because it was readily available as a thin walled tube. The
airfoil shapes were made out of standard insulation foam. Foam was chosen because of its strength to
weight ratio and also its workability.
The support arms and inserts were made out of 6063-T52 aluminum. This aluminum was
chosen because of its availability, cost and strength to weight ratio. Machining of the parts was
performed at The University of Akron.
Structural Analysis
Assumptions
A vertical axis wind turbine, like many machines, is subject to a very complex loading pattern that is
difficult to consider theoretically. To help simplify the process, a few assumptions were made that made
structural analysis of the vertical axis wind turbine less complex. The following assumptions were made:
1. The chosen airfoil was a NACA-0018 airfoil. The cross section of the NACA-0018 is symmetrical
with respect to its chord line. The NACA-0018 was chosen for its symmetry in addition to its
ability to create large lift forces with very small drag forces. Calculated drag forces for varying
wind speeds were much smaller than the lift forces and thus all drag forces were considered
negligible for stress analysis purposes.
VAWT Senior Design Report
Page 8
2. The air flow of the wind was considered to be one-dimensional. Wind speed was assumed
uniform in the x, y, and z planes and there were no wind forces in the y or z direction.
3. These calculations were made assuming that the wind seen by the turbine follows the function,
. A sample calculation can be seen the sample
calculation section of the appendix.
Equations
The following equations were used in calculating the factors of safety for the different loadings:
(Equation 1, Distortion Energy)
(Equation 2, Max Shear Stress)
(Equation 3, Bolt Factor of Safety)
(Equation 4, Joint Factor of Safety)
(Equation 5, Modified Goodman Factor of Safety)
(Equation 6, Modified Goodman for Bolts in Tension Factor of Safety)
In addition to the equations for the different factors of safety, equations for bending stress, axial stress,
shear stress, 1st moment area, 2nd moment area, stiffness of both bolts and members, area, and Mohr’s
Circle were used.
Method
The vertical axis wind turbine consists of three airfoils attached to support arms that are
attached to a generator. The generator has a built in brake function that locks the generator and keeps
VAWT Senior Design Report
Page 9
the turbine from spinning when the output wires are shorted together. This is necessary to keep the
generator from generating too high of a voltage that would cause the inverter to short. When the
generator is not locked, the wind turbine will rotate and turn the generator as wind blows past the
airfoils. The direction and velocity of wind relative to the airfoil changes as the airfoils rotate around the
generator. If the wind remains at constant direction and constant velocity, the lift force on an airfoil will
go from a maximum value, to the same maximum value in the opposite direction and back to that
maximum lift force value during a single revolution. For these reasons, it was decided that it would be
necessary to perform structural analyses under both static and cyclical loading (fatigue) conditions.
The maximum lift force an airfoil would experience for a given wind speed was calculated for
winds increments of 5 mph. This force was then carried throughout the wind turbine and its various
components.
For the all of the fatigue calculations, the endurance limit was used in combination with the
endurance limit modifying factors. The endurance limit modifying factors account for surface finish, size,
and type of loading (axial or bending). A machined surface was used for all components as it is the most
conservative and some surfaces were machined.
The airfoil consists of a solid foam air foil with an aluminum support rod running through the
center. It is attached to a support arm with a bolt that runs through a plastic standoff, the round
aluminum support tube and anchors into a machined aluminum insert in the support arm. The insert is
connected to the support arm with a bolt as well. The support arm is connected to the generator with
two bolts (Figure 1). Under both static and dynamic conditions, the wind acts over the surface of the
airfoil that is facing the wind. In Figure 1, the wind velocity is shown to be acting perpendicular to the
airfoil chord line. In practice, the wind velocity will act on each surface of the airfoil at some point in
one revolution.
VAWT Senior Design Report
Page 10
Figure 1 - Vertical Axis Wind Turbine, Complete Arm
The lift forces will cause a bending stress on the aluminum support rod through the foam air foil.
The distributed load caused by the wind force was converted into two point loads (magnitude of each
point load equal to half of the total lift force) at the 25% and 75% of the airfoil’s 4 ft height (Figure 2).
These point forces act with a 12 inch moment arm about the center. Using the moment and the second
moment area of the aluminum tube, the bending stress caused by the lift force at each wind speed was
calculated. This is the only stress on the airfoil and was used to calculate the factor of safety by the
distortion energy method for the static analysis. For a rotating wind turbine, the symmetry of the foil
mean that the maximum lift force will occur acting away from the center and acting towards the center
during a rotation. The mean stress will be 0 psi and the amplitude stress will be the bending stress
caused by the maximum lift force. Also included in the fatigue stress calculations was the stress
concentration caused by the hole used to attach the airfoil to the support arm. The factor of safety for
fatigue was evaluated using the modified Goodman theory.
VAWT Senior Design Report
Page 11
Figure 2 - Forces on Airfoil
The lift forces on the airfoil will act on the support arm as axial forces. Depending on the direction of the
lift force, this will cause either an axial tensile stress or an axial compressive stress on the support arm.
In addition to the axial stresses caused by the lift force, the weight of the airfoil causes a shear stress
and a bending stress on the support arm. The bending stress will constant be a tensile stress at the end
of the support arm that attaches to the generator. Mohr’s circle was used to calculate the principal
stresses and maximum shear stress from the multiple loads. The principal stresses were then used to
calculate the distortion energy stress to find the factor of safety. The maximum shear stress method was
also used in conjunction with the shear stresses determined from Mohr’s circle to find an alternate
factor of safety. The shear stresses were determined to be negligible compared to the normal stresses
and thus were not included in the fatigue analysis. The fatigue analysis included the stress concentration
factor from the transverse bolt holes as well as a mean stress from the weight of the airfoil. The lift
forces were then used to calculate the amplitude stress and the modified Goodman theory was used to
find the factors of safety.
VAWT Senior Design Report
Page 12
Figure 3 - Support Arm
The bolt holding the airfoil to the support arm is placed under alternating tensile and compressive
stresses in the axial direction as the wind turbine rotates. Both the factor of safety of the bolt and the
joint were calculated. The bolt grip is made up of a nylon 6/6 stand off, thin-wall, round, aluminum tube,
and an aluminum insert (Figure 4). The bolt used were assumed to have the properties of SAE Grade 1
because the grade was unknown and SAE Grade 1 is the lowest grade for which properties are known.
The stiffness of the joint was taken using Rotscher’s pressure cone method. It was necessary to calculate
the joint stiffness in three parts due to the two different materials. The aluminum section had to be
divided into two parts in order to get a matching condition at the center of the bolt length. The fatigue
factors of safety were again calculated using the modified Goodman theory.
Figure 4 - Bolt Attaching Airfoil to Support Arm (Top View)
One calculation was done to determine the maximum stresses in the other three bolts. The bolt holding
the insert in place on the support arm has two shear planes (Figure 5), thus the shear force at each
shear plane is half of the total shear force. Since all three bolts have the same diameter, this bolt will fail
after the bolts attaching the support arm to the generator, which have only one shear plane. The
bending stress is also higher at the end of the support arm attached to the generator. This causes the
VAWT Senior Design Report
Page 13
shear stress to be higher at this location and also results in a mean stress that is larger than zero for the
fatigue analysis.
Figure 5 - Bolt in Shear
Analysis
The static analysis determined that the support rod in the airfoil would be the first component
to fail. The support rod would have a design max speed of 25 mph. The bolt attaching the airfoil to the
support arm would be the next weakest point, being rated to speeds of approximately 40 mph. The
remaining bolts and the support arm would be rated for speeds in excess of 50 mph.
For fatigue, the calculations were to determine the wind speed at which infinite life could be
expected. The airfoil supporting rod would be the first to have a limited life, with speeds between 15-20
mph causing a large enough alternating stress load to not have infinite life. The bolts attaching the
support arm to the generator would be expected to have infinite life at wind speeds under 30 mph, the
bolt attaching the airfoil rod to the support arm would be rated for speeds under 40 mph, and the
support arm would once again not be expected to fail for speeds up to 50 mph.
From these results, it is shown that increasing the strength of the air foil support rod by either using a
stronger material or by increasing the tube wall thickness would be the first step needed to allow the
wind turbine to operate safely in higher wind speeds. Increasing the bolt grade or bolt diameter would
be the next step to operating in higher speeds. Going the other way, it would be possible to reduce the
VAWT Senior Design Report
Page 14
thickness or strength of the support arm without problems since the other components are expected to
fail before the support arm.
Cost Analysis
In designing and building the turbine one of our major concerns was using materials that were
readily available and cheap. All shapes and sizes of materials are common sizes that are mass produced.
For components that could not be made, suppliers such as McMaster Carr and Lowes were used. The
final cost of the turbine was $889.32. At the beginning of our project we projected that we would spend
around $1000, it can be seen that we stayed well within our budget. We also feel that if we were to
mass produce these turbines we could reduce the cost significantly. All expenses were split equally
among the team with each group member contributing 25% of the final cost.
Electrical Analysis
The generator used in our turbine is a US-VAWT B100 permanent magnet axial generator. This
generator was chosen because of its ability to produce high power at lower rpm’s without the need for
gearing. The generator is rated at an output of 100 Watts. We were going to combine this generator
with a Power-Jack 300W DC to AC Pure Sine Wave Inverter. Due to complications we were not able to
measure output from the inverter due to damage during shipping. We were however able to measure
the voltage and amperage that our alternator put out. Below is a graph that illustrates the potential
power of our alternator. The power listed below is calculated based on the idea that our inverter should
have a resistance that matches the resistance of the generator. If the inverter has a resistance that is
lower than the generator, it could damage the generator by trying to pull too much current.
VAWT Senior Design Report
Page 15
From the graph it can be seen that even in moderate winds, 10-15 Mph, we were able to
generate usable electricity.
Assuming the inverter has an efficiency of 92%, this is the claimed
efficiency, real world values of 27.5-55 watts would be expected.
Summary
During the past two semesters our team designed and built a Vertical Axis Wind Turbine that
was used to generate electricity that could be used to power small home appliances or be put back into
the grid. During initial testing it was proven that our turbine worked in the way we had predicted. We
designed our turbine to operate at a max tip speed ratio of 3.5, this can be achieved but do to our
manufacturing techniques our turbine had a great deal more drag than we originally anticipated. During
testing we experienced tip speed ratios of just under 3. This proves that our turbine was acting in lift
mode and affirms our design worked.
The goal of this project was to generate usable electricity by harvesting energy from the wind.
The Betz limit states that no more 60% of the wind’s energy can be harnessed and used to perform
work. We had set a goal of 40% efficiency when the project was initially started. After testing and
VAWT Senior Design Report
Page 16
realizing that our inverter was damaged we can only speculate as to the efficiency of our turbine. Basic
calculations have shown that in 15 Mph winds we could generate 55 Watts. This gives our turbine an
efficiency of 14%. Although this a great deal off from our projected efficiency we were still able to
determine that our turbine will produce electricity which was the ultimate goal.
To achieve higher efficiencies our next step would be to modify our design. This could be done
by constructing new wings with better materials and techniques, and by also incorporating a trip strip on
the leading edge of our airfoils. To improve efficiency even more the next step would be to design a
new generator that would match the size and speed of our turbine, doing this would ensure that at the
peak power of our turbine we would also be at the pear power point of our alternator.
Final cost of our turbine came to $889.32. We had initially set a budget of $1000, as it can be
seen we were able to stay within our budget. If we were to begin mass producing these turbines we feel
that we could greatly reduce this cost by incorporating better materials and manufacturing techniques.
VAWT Senior Design Report
Page 17
Appendix
Materials & Components
A compiled list of the materials purchased in order to build the design is shown below:
1.
GeneratorB100 9" Diameter, High Power, Low RPM Battery Charging Alternator / Hub Assembly
2. RectifierUS-VAWT 3 Phase AC to DC Rectifier with a 28V limiter
VAWT Senior Design Report
Page 18
3. GTIPowerjack 300W Pure Sine Wave Inverter
4. Square Tube for Airfoil Arms1" square, .750" ID, .125" Wall, 6063-T52 Aluminum
5. Round Tube for Inside Airfoils1" OD, .870" ID, .065" Wall, 6061-T6 Aluminum
VAWT Senior Design Report
Page 19
6. Aluminum Plate for Airfoil Arm Hub Plate9" diameter, .250" Thick, 6061-T651 Aluminum
7. Bolts for Airfoil Pipe to Suppport Arm Inserts 1/4"-20 x 2”, Phillips Head, Steel
8. Bolts with Nuts for Pipe Machined Insert Mounts to Arms1/4"-20 x 1.5”, Hex Head, Steel
VAWT Senior Design Report
Page 20
9. Round Support Inserts for Inside Arms at Hub Mount1/2”OD 1/4”ID x .870” Length
10. Bolts with Nuts for Arm to Plate Hub Mounting1/4"-20 x 2”, Flat Slotted Head, Steel
11. Bolts for Plate to Hub Mounting1/4"-20 x 2”, Flat Slotted Head, Steel
VAWT Senior Design Report
Page 21
12. Support Pipe For Generator Mounting7’ Stainless Steel Pipe
13. Tripod SupportWinegard SW-0010 Tripod Mount for Antenna, 38.5 x 6.2 x 6 inches
VAWT Senior Design Report
Page 22
14. Foam From Local Hardware Store for AirfoilsStandard home insulation
15. Support arm insert6061-T6 Aluminum
VAWT Senior Design Report
Page 23
16. Airfoil CoatingMonokote
17. Other Various MaterialsGlue and aluminum material for items such as the Support Arm Inserts
Structural Analysis Data
Wind [mph] Force [lb] Stress [psi] F.O.S., DE
5
10
15
20
25
30
35
40
45
50
5.48
21.92
49.33
87.70
137.03
197.32
268.57
350.79
443.97
548.11
1568.62
6274.46
14117.54
25097.85
39215.39
56470.16
76862.17
100391.40
127057.87
156861.57
25.5
6.4
2.8
1.6
1.0
0.7
0.5
0.4
0.3
0.3
Table 1- Airfoil Static Stress Calculations
VAWT Senior Design Report
Page 24
Wind [mph] Force [lb]
5
10
15
20
25
30
35
40
45
50
5.48
21.92
49.33
87.70
137.03
197.32
268.57
350.79
443.97
548.11
Mean
+Stress
Stress [psi] Concentration [psi]
1568.62
1594.26
6274.46
6377.04
14117.54
14348.33
25097.85
25508.15
39215.39
39856.48
56470.16
57393.33
76862.17
78118.70
100391.40
102032.59
127057.87
129134.99
156861.57
159425.92
F.O.S.,
Mod. Goodman
12.21
3.05
1.36
0.76
0.49
0.34
0.25
0.19
0.15
0.12
Table 2 - Airfoil Fatigue Stress Calculations
Axial
Shear
Axial
Shear (xy)
Bending
Normal Principal 1 Principal 2
Shear 1,2
DE
Force [lb] Force [lb] Stress [psi] Stress [psi] Stress [psi] Stress [psi] Stress [psi] Stress [psi] Stress [psi] Stress [psi]
5.48
1.50
12.53
15.57
560.43
572.96
573.38
-0.42
286.90
573.59
21.92
1.50
50.11
15.57
560.43
610.55
610.94
-0.40
305.67
611.14
49.33
1.50
112.75
15.57
560.43
673.19
673.55
-0.36
336.95
673.73
87.70
1.50
200.45
15.57
560.43
760.88
761.20
-0.32
380.76
761.36
137.03
1.50
313.21
15.57
560.43
873.64
873.92
-0.28
437.10
874.05
197.32
1.50
451.02
15.57
560.43
1011.45
1011.69
-0.24
505.96
1011.81
268.57
1.50
613.88
15.57
560.43
1174.31
1174.52
-0.21
587.36
1174.62
350.79
1.50
801.81
15.57
560.43
1362.24
1362.42
-0.18
681.30
1362.50
443.97
1.50
1014.79
15.57
560.43
1575.22
1575.37
-0.15
787.76
1575.45
548.11
1.50
1252.82
15.57
560.43
1813.25
1813.39
-0.13
906.76
1813.45
F.O.S.,
DE
36.6
34.4
31.2
27.6
24.0
20.8
17.9
15.4
13.3
11.6
F.O.S.,
MSS
36.6
34.4
31.2
27.6
24.0
20.8
17.9
15.4
13.3
11.6
Table 3 - Static Support Arm Stress Calculations
Wind [mph]
5
10
15
20
25
30
35
40
45
50
Axial
Axial
Bending
Mean
Force [lb] Stress [psi] Stress [psi] Stress [psi]
5.48
12.53
560.43
560.43
21.92
50.11
560.43
560.43
49.33
112.75
560.43
560.43
87.70
200.45
560.43
560.43
137.03
313.21
560.43
560.43
197.32
451.02
560.43
560.43
268.57
613.88
560.43
560.43
350.79
801.81
560.43
560.43
443.97
1014.79
560.43
560.43
548.11
1252.82
560.43
560.43
Amplitude
F.O.S.,
Stress Mod. Goodman
12.53
35.9
50.11
31.9
112.75
26.9
200.45
22.1
313.21
17.9
451.02
14.6
613.88
11.9
801.81
9.9
1014.79
8.3
1252.82
7.0
Table 4 - Fatigue Support Arm Stress Calculations
VAWT Senior Design Report
Page 25
Wind Speed
[mph]
5
10
15
20
25
30
35
40
45
50
Axial
Force [lb]
5.48
21.92
49.33
87.70
137.03
197.32
268.57
350.79
443.97
548.11
F.O.S.
Bolt
70.5
17.6
7.8
4.4
2.8
2.0
1.4
1.1
0.9
0.7
F.O.S.
Joint
447.7
111.9
49.7
28.0
17.9
12.4
9.1
7.0
5.5
4.5
Table 5 - Bolt in Tension Static Calculations
Wind [mph]
5
10
15
20
25
30
35
40
45
50
Axial Alternating
Mean
Force [lb] Stress [psi] Stress [psi]
5.48
58.54
24750.00
21.92
234.15
24750.00
49.33
526.85
24750.00
87.70
936.62
24750.00
137.03
1463.46
24750.00
197.32
2107.39
24750.00
268.57
2868.39
24750.00
350.79
3746.47
24750.00
443.97
4741.62
24750.00
548.11
5853.85
24750.00
Sa [psi]
3301.36
3301.36
3301.36
3301.36
3301.36
3301.36
3301.36
3301.36
3301.36
3301.36
F.O.S.
Bolt
56.4
14.1
6.3
3.5
2.3
1.6
1.2
0.9
0.7
0.6
Table 6 - Bolt in Tension Fatigue Calculations
Wind Speed
Normal
Normal
Shear [psi]
[mph] Stress [psi] Force [psi]
5
572.96
250.67
4659.30
10
610.55
267.11
4964.94
15
673.19
294.52
5474.33
20
760.88
332.89
6187.48
25
873.64
382.22
7104.40
30
1011.45
442.51
8225.07
35
1174.31
513.76
9549.49
40
1362.24
595.98
11077.68
45
1575.22
689.16
12809.62
50
1813.25
793.30
14745.33
F.O.S.,
MSS
3.9
3.6
3.3
2.9
2.5
2.2
1.9
1.6
1.4
1.2
Table 7 - Bolt in Shear Static Calculations
VAWT Senior Design Report
Page 26
Wind [mph]
5
10
15
20
25
30
35
40
45
50
Axial
Stress [psi]
560.43
560.43
560.43
560.43
560.43
560.43
560.43
560.43
560.43
560.43
Axial
Force [lb]]
245.19
245.19
245.19
245.19
245.19
245.19
245.19
245.19
245.19
245.19
Wind
Mean Amplitude
Force [lb] Stress [psi] Stress [psi]
5.48
9114.84
203.76
21.92
9114.84
815.03
49.33
9114.84
1833.82
87.70
9114.84
3260.13
137.03
9114.84
5093.95
197.32
9114.84
7335.29
268.57
9114.84
9984.15
350.79
9114.84
13040.52
443.97
9114.84
16504.41
548.11
9114.84
20375.81
F.O.S.,
Mod. Goodman
3.6
3.0
2.2
1.7
1.3
1.0
0.8
0.6
0.5
0.4
Table 8 - Bolt in Shear Fatigue Calculations
Turbine Cost
Item
Store
Cost
Total Spent
Balsa
Michaels
24.43
24.43
Bolts
Foam/Saw/Blades/Glue
Gen/Rectifier/GTI
Aluminum Tube
Lowes
Lowes
US-Vawt
Speedy
Metals
Speedy
Metals
Lowes
Radio Shack
Lowes
Woodsy’s
Akron Music
Lowes
McMaster
Lowes
Lowes
Amazon
2.51
48.56
549
33.93
26.94
75.5
624.5
658.43
56.93
715.36
10.58
20.21
28.97
4.27
8.52
8.5
11.33
6.37
22.95
52.26
725.94
746.15
775.12
779.39
787.91
796.41
807.74
814.11
837.06
889.32
Aluminum Tube
Hot Wire Supplies
Hot Wire Supplies
Kill a Watt
Hot Wire Strings
Hot Wire Strings
Epoxy/Sandpaper
Standoffs
Epoxy
Epoxy/Bolts
Monokote
VAWT Senior Design Report
Page 27
Electrical Data
Wind
(Mph)
3.15
4.69
6.23
7.49
9.1
10.36
11.27
12.53
VAWT Senior Design Report
Volt
3.1
4.8
6.1
7.5
9
10.16
11.5
12.76
Amp
0.024
0.033
0.043
0.053
0.062
0.071
0.081
0.089
Resistance
86
86
86
86
86
86
86
86
RPM
44.00
62.00
76.29
90.00
107.14
122.57
139.71
154.29
TSR
2.99
2.83
2.62
2.57
2.52
2.53
2.66
2.64
Page 28
Airfoil Data
Figure 1 – Cross Section of NACA 0018 Symmetric Airfoil
VAWT Senior Design Report
Page 29
Figure 2 – Graph of Lift Coefficient versus Drag Coefficient
Figure 3 – Graph of Lift Coefficient versus Angle of Attack
VAWT Senior Design Report
Page 30
AOA
Re 350000
Cl
Cd
15
0.8405
0.145
14
0.8803
0.094
13
0.9104
0.0259
12
0.9279
0.0235
11
0.9249
0.0213
10
0.8983
0.0194
9
0.8526
0.0176
8
0.7879
0.0159
7
0.71
0.0145
6
0.6228
0.0132
5
0.524
0.0121
4
0.44
0.0112
3
0.33
0.0107
2
0.22
0.0104
1
0.11
0.0102
0
0
0.0101
Table 1 – Coefficients of lift and drag based on Angle of Attack
Degree Angle TSR Wind (Ft/S) Vel Mag App Mag
360
270 3.5
14.70
51.45
53.51
359
269 3.5
14.70
51.45
53.26
358
268 3.5
14.70
51.45
53.01
357
267 3.5
14.70
51.45
52.76
356
266 3.5
14.70
51.45
52.51
355
265 3.5
14.70
51.45
52.26
354
264 3.5
14.70
51.45
52.01
353
263 3.5
14.70
51.45
51.76
352
262 3.5
14.70
51.45
51.50
351
261 3.5
14.70
51.45
51.25
350
260 3.5
14.70
51.45
51.00
349
259 3.5
14.70
51.45
50.74
348
258 3.5
14.70
51.45
50.48
347
257 3.5
14.70
51.45
50.23
346
256 3.5
14.70
51.45
49.97
345
255 3.5
14.70
51.45
49.72
344
254 3.5
14.70
51.45
49.46
343
253 3.5
14.70
51.45
49.20
342
252 3.5
14.70
51.45
48.95
341
251 3.5
14.70
51.45
48.69
340
250 3.5
14.70
51.45
48.43
339
249 3.5
14.70
51.45
48.18
338
248 3.5
14.70
51.45
47.92
337
247 3.5
14.70
51.45
47.67
App Dir
-74.05
-74.98
-75.91
-76.85
-77.78
-78.73
-79.67
-80.63
-81.58
-82.54
-83.51
-84.48
-85.45
-86.43
-87.42
-88.41
-89.40
-90.40
-91.40
-92.41
-93.43
-94.45
-95.48
-96.51
Lift Dir
15.95
15.02
14.09
13.15
12.22
11.27
10.33
9.37
8.42
7.46
6.49
5.52
4.55
3.57
2.58
1.59
0.60
-0.40
-1.40
-2.41
-3.43
-4.45
-5.48
-6.51
Drag Dir AOA
105.95
16
105.02
16
104.09
16
103.15
16
102.22
16
101.27
16
100.33
16
99.37
16
98.42
16
97.46
16
96.49
16
95.52
17
94.55
17
93.57
17
92.58
17
91.59
17
90.60
17
89.60
17
88.60
17
87.59
17
86.57
17
85.55
17
84.52
17
83.49
16
Cl
0.5567
0.4896
0.4896
0.4896
0.4896
0.4896
0.4896
0.4896
0.4896
0.4896
0.4896
0.4896
0.4896
0.4896
0.4896
0.4896
0.4896
0.4896
0.4896
0.4896
0.4896
0.4896
0.4896
0.4896
Cd Lift (Lb) Drag (Lb) Torque (+) Torque (-) Torque (Ft*Lb)
0.177 11.37
3.61
0.27
0.96
7.67
0.196
9.90
3.96
0.28
0.96
5.34
0.196
9.81
3.93
0.28
0.96
5.39
0.196
9.72
3.89
0.28
0.96
4.72
0.196
9.63
3.85
0.28
0.96
4.78
0.196
9.54
3.82
0.28
0.96
4.49
0.196
9.44
3.78
0.28
0.96
4.54
0.196
9.35
3.74
0.28
0.96
4.58
0.196
9.26
3.71
0.28
0.96
3.96
0.196
9.17
3.67
0.28
0.96
1.87
0.196
9.08
3.63
0.28
0.96
1.90
0.196
8.99
3.60
0.28
0.96
1.93
0.196
8.90
3.56
0.28
0.96
1.36
0.196
8.81
3.53
0.29
0.96
1.41
0.196
8.72
3.49
0.29
0.96
-2.15
0.196
8.63
3.45
0.29
0.96
-2.15
0.196
8.54
3.42
0.29
0.96
-2.16
0.196
8.45
3.38
0.29
0.96
-2.53
0.196
8.36
3.35
0.29
0.96
-2.51
0.196
8.28
3.31
0.29
0.96
-2.49
0.196
8.19
3.28
0.29
0.96
-3.93
0.196
8.10
3.24
0.28
0.96
-4.29
0.196
8.02
3.21
0.28
0.96
-4.27
0.196
7.93
3.18
0.28
0.96
-4.26
Table 2 – Turbine torque calculations
VAWT Senior Design Report
Page 31
Formula List
Area of Turbine:
Definitions:
Tip Speed Ratio:
Reynolds Number:
Density of Air:
Betz Limit:
Available Power in Wind:
Apparent magnitude experienced by airfoil:
Planform Area:
VAWT Senior Design Report
Page 32
Direction of apparent wind relative to X-axis:
Direction of lift:
Direction of drag:
Angle of attack:
Lift:
Drag:
Torque Generated:
Force on Pole:
Sample Calculations
Area of Turbine:
VAWT Senior Design Report
Page 33
Reynolds Number:
Maximum Apparent magnitude experienced by airfoil:
Direction of apparent wind relative to X-axis:
Planform Area:
Lift:
Drag:
Sample Velocity Triangles
Lift forces (L) act perpendicular to the apparent wind (W) and drag (D) forces act parallel to the
Apparent Wind (W).
VAWT Senior Design Report
Page 34
L
U
W
V
D
Airfoil Support
Velocity Triangle for Airfoil at 1500
L
D
V
W
U
Airfoil Support
Velocity Triangle for Airfoil at 210
VAWT Senior Design Report
Page 35
L
D
Airfoil Support
V
W
U
Velocity Triangle for Airfoil at 3150
VAWT Senior Design Report
Page 36
VAWT Manufacture and Assembly
1. Assembly figure 1 depicts a 1/8” thick 6061 Aluminum template. This template was first drawn in
AutoCAD, plotted, then glued to a piece of 1/8” thick 6061 Aluminum. A band saw was used to cut the
sheet of Aluminum down to the symmetric NACA-0018 cross section profile. Hand sanding took place
prior to band saw cutting to reduce rough edges. Two identical templates were created first used to cut
balsa ribs. Originally the design team decided to build airfoils using a combination of balsa wood
supports and foam. After further design and research the team decided that insulation foam would be
sufficient for airfoil construction thus eliminating the need for balsa wood supports. The 1/8” thick
aluminum templates main usage occurred when insulation foam was cut using a hot wire foam cutter.
The two 1/8” inch aluminum templates were clamped on each side of the insulation foam. After
clamping the hot wire was run around the outside perimeter of the aluminum templates, yielding an
insulation foam with the geometry of a symmetric NACA-0018 profile.
Figure 1: 1/8” Aluminum NACA-0018 cross section templates
VAWT Senior Design Report
Page 37
2. Figure 2 shows a representation of the generator, mounting plate, 3 airfoil support arms, and
respective hardware used to secure the supports to the generator. The finalized design involved
features the design team felt were advantageous to residential turbine applications. The amount of
hardware is low, thus allowing for simple assemblage if the turbine was sold in a kit. The 3 support
arms are simply attached with two bolts each allowing for quick assemble and disassembly. The
mounting plate consists of 1/16” deep channels machined in the plate to secure the airfoil support
arms and reduce play. The reduction in play decreases the losses the wind turbine experiences in
operation due to friction, thus increasing the overall efficiency and reliability of the turbine.
Another important design feature to note involves the ability to assemble the turbine with common,
inexpensive tools and uncomplicated technical detail.
Figure 2: Generator, mounting plate, and support arms assembled together
VAWT Senior Design Report
Page 38
3. Green insulation foam was utilized in the construction of symmetric NACA-0018 airfoils. Insulation
foam was chosen because this material exhibited many positive design features. Insulation foam is
widely available for purchase and is obtainable at a low cost. This foam is easily workable, as a hot wire
was constructed to shape the foam to a NACA-0018 profile. Foam is easily bonded together or adhered
to various types of other materials. Strength to weight ratio of the foam allows lightweight rigid airfoils
to be constructed increasing turbine efficiency and decreasing turbine weight. Figure 3 depicts multiple
pieces of foam which were adhered together with foam glue. The foam was adhered together so the
team would need to make less cuts with the hotwire reducing manufacturing time.
Figure 3: Green insulation foam, bonded, prior to cutting with hot wire
4. After green insulation foam was adhered together, the foam was positioned in a vice. Once properly
oriented in the vice, a drill press with a 1” spade bit was used to drill through the foam. The 1” wide
VAWT Senior Design Report
Page 39
thru hole was positioned so the foam could be mounted onto a 1” wide thin walled Aluminum tube. The
thin walled Aluminum tube added structural support as well as crucial alignment to NACA-0018 airfoils.
Figure 4: Drill 1” thru hole in green foam to allow positioning of thin walled Aluminum tube
5. A key design decision was reached when the VAWT team decided to fabricate NACA-0018 airfoils
using green insulation foam. The most difficult manufacturing step involved shaping the green
insulation foam to a specific, smooth, symmetrical NACA-0018 shape. If airfoil geometry was
inconsistent the entire VAWT would be in serious trouble. Vibration and rotational imbalances could
occur which could cause the turbine to self destruct, possibly injuring testing personnel and losing
money. A hot wire was created to aid in the shaping of the green insulation foam. A hot wire passes an
electrical current through a small diameter exposed wire. As current passes through the wire, the wire
VAWT Senior Design Report
Page 40
heats creating a small diameter cutting surface that easily slices through green insulation foam. The hot
wire was a key piece of equipment utilized in the manufacturing process to create the VAWT.
Figure 5: VAWT design member Ian Collins testing newly created hot wire foam cutter.
6. Figure 6 displays green insulation foam being cut with hot wire cutter. Notice 1/8 Aluminum
templates clamped on each side of green insulation foam creating an exact perimeter to cut. The 1”
wide thin walled circular Aluminum tubing is also placed in the 1” wide thru hole in the green insulation
foam further ensuring alignment of 1/8” Aluminum templates.
VAWT Senior Design Report
Page 41
Figure 6: Foam cutter cutting through green insulation foam creating NACA-0018 profile
7. After foam was cut to proper geometry, green insulation foam resembled NACA-0018 profile. The
wire cutter did an excellent job of creating a smooth outer profile resembling the NACA-0018 profile.
Little final finish work was necessary after completion of cuts hot wire cutter.
VAWT Senior Design Report
Page 42
Figure 7: Green insulation foam after cut to shape with hot wire cutter.
8. After the NACA-0018 shape was cut into green insulation foam final finish sanding was performed to
smooth the surface . Sanding blocks and a Dremel tool were utilized to create the smoothest most
uniform surface finish possible. Individual portions of green insulation foam were then placed on 1”
diameter thin walled circular tubing. Any surface imperfections were sanded down, prepping the
surface for the application of the Monokote covering. After all surfaces were smooth and no rough
edges existed, adhesive glue was applied inside the green foam 1” wide thru holes and on the outer
diameter of the 1” wide thin circular tubing. The green foam insulation was then slide onto the 1” wide
thin walled circular tubing.
VAWT Senior Design Report
Page 43
Figure 8: VAWT design member Evan Gutshall performing final finish work to green insulation foam
9. After allowing adhesive to dry, 1” square Aluminum tubing, with a threaded insert placed in the outer
portion of the arm, was aligned with the newly created airfoil. A plastic standoff was placed inside the
outermost surface of the airfoil which will eventually hold the airfoil to the square support arm after
Monokote is adhered to the airfoils outer surface. The standoff was adhered in place then the square
tubing was removed.
VAWT Senior Design Report
Page 44
Figure 9: Square Aluminum support arm being aligned with 1” circular thin walled tubing
10. The final manufacturing step involved adhering Monokote to the outside surface profile of the
green insulation foam airfoil. Monokate shrinks when heated, furthering increasing the structural
rigidity of the airfoils while adding a very small cost and weight. Monokote was first placed by adhering
a 4” section above the trailing edge of the airfoil, wrapping around the trailing edge, finally going around
the leading edge then adhering where the Monokote overlapped. Finesse was employed applying
Monokote as too much heat can melt through the Monokote, too little pulling pressure would leave the
Monokote loose and flappy, and applying too much pulling pressure to the Monokote would tear the
coating.
VAWT Senior Design Report
Page 45
Figure 10: VAWT design members Ryan Cigank, Zack Carman, and Evan Gutshall apply monokote
11. Fully assembled VAWT placed in a park for initial prototype testing. It is important to note that
turbine began spinning with no outside forces other than wind acting on the airfoils at a very low
velocity. Please note that finalized tripod was not available at the time of this initial testing.
VAWT Senior Design Report
Page 46
Figure 11: VAWT design members Ryan Cigank, Zack Carman, and Ian Collins performing initial testing
of VAWT
VAWT Senior Design Report
Page 47