1. IAN MCLEOD
PORTFOLIO
MASTER OF SCIENCE - MECHANICAL ENGINEERING
School of Engineering for Matter, Transport, and Energy
May 2016

2. EXECUTIVE SUMMARY
A requirement for obtaining a masters of science in mechanical engineering at Arizona State
University is a coursework portfolio. The following portfolio exemplifies what I consider to be
the two most outstanding projects performed in my graduate studies. The two papers included in
this portfolio are:
(1) the report submitted to Dr. Patrick Phelan for the project entitled “Calculating Loss
Coefficient of a Two-Cover Flat Plate Solar Collector” in the course of Solar Thermal
Engineering (MAE 585), and
(2) the report submitted to Dr. Ronald Calhoun for the project entitled “Statistical Methods of
Minimizing Risk for Small-Scale Wind Energy Investments” in the course of Wind Energy
(MAE 598).
The first paper included in this report, “Calculating Loss Coefficient of a Two-Cover Flat
Plate Solar Collector”, is notably multi-faceted. It involved an experimental set-up requiring
precise material manufacturing and assembly, presentation of complex theoretical equations in a
digestible format, and multiple packets of software coding in order to collect and analyze data.
Since the project drew upon so many skills learned throughout the mechanical engineering
curriculum, it effectively demonstrates the engineering acumen I have developed as a student.
Myself and two other graduate students performed this project as a group. Each of us worked
together during all stages of the project development. This ensured that each of us had the
opportunity to practice the variety of skills aforementioned, in addition to ensuring equal work
distribution. To summarize the project, a flat, two-cover solar panel was built that enabled
temperature measurements over time at varying key locations on the solar panel. My contribution
to the project can be explained in three stages: construction, modeling, and computation.
Constructing the solar panel necessitated use of several tools in the ASU machine shop. I
operated the drilling machine with a hollow cylindrical attachment to drill large holes, and a
circular saw to cut 2x4’s for structural support. I was also put in charge of coming up with a
blueprint in SolidWorks since I consider computer-aided design to be my specialty. This
blueprint can be viewed in figure 4 of the report. Lastly, I helped dremel cutouts in the PVC pipe
to allow lateral water flow between glass plates of the solar panel. The application of generous
quantities of sealant concluded the construction phase as our panel was securely watertight.
Validation of our group’s method was dependent upon the data we collected being in
agreement with theory. This goal required development of a list of equations that would enable
energy loss to be tabulated from temperature readings. I had to conduct a fair amount of research
in order to help flesh out the right equations for use with our model. The equations of thermal
resistance for use in the thermal network diagram shown in figure 2 were found in our course
book. I took these equations and applied the necessary simplifications to allow numerical
estimation based on the data we were going to collect. My colleague’s researched the equations
for convective heat transfer and loss coefficient dependency on both thermal resistances and heat
transfer coefficients. I also researched the available solar irradiance at the exact time, day and
latitude that the experiment was conducted. Together we built a derivation that led to an
estimation of the overall loss coefficient of the entire collector, meaning the total energy per unit
area lost by the collector for the time duration of the experiment.
Finally, thermocouple temperature data had to be digested in Matlab before being applied in
our model. I contributed to this process by developing a LabView code that recorded

3. temperatures from thermocouples placed on the solar collector and output them in a text file. I
then co-authored Matlab code that ultimately graphed overall loss coefficient based off of the
thermocouple temperature readings. Our experimental results were compared to theoretical
results published by Sekhar et al. as discovered by my teammate. Our numerical model proved to
be in agreement with their more lengthy experiment.
The second report included in this portfolio was what I consider to be my most creative
project out of my graduate courses. Professor Calhoun allowed full student autonomy in the
scope of the project so long as it was relative to wind energy in some way. I am especially
inspired by renewable energy technologies as the future power sources for the world. I found the
project to be both fascinating and practical as a means for any individual to calculate the amount
of energy able to be produced through wind power in a given region without the use of expensive
equipment. Additionally, this project was special because it employed statistical analyses in the
core of the project, which is a subject that is not heavily stressed in the mechanical engineering
curriculum. In this way, I consider this project to be one in which I “stepped outside the box” in
terms of creativity and development, and the results were encouraging.
The project was entitled “Statistical Methods of Minimizing Risk for Small-Scale Wind
Energy Investments”, and was also a group project. However, I only worked with one other
person, and I ended up producing the vast majority of the project alone. I solely authored the
Matlab code that produced the discriminant analyses and respective quadratic classifiers, the t-
test for comparing summer and winter data, and error estimation. The procedure for analyzing all
data was also my construction. My partner was tasked with helping research wind energy
empirical data in Cold Bay, Alaska, helping write up the report, and also conducting the multiple
linear regression involved that happened to fail based upon the variables that he used.
Nevertheless, the results of the project exemplified how simple statistical measures could reveal
a great deal regarding wind energy generation for the small-time financier. I may even recreate
this project in the near future if I am able to settle down in an area where wind energy could be
used for home power generation, and thus this report has become more than just an assignment
in my eyes.
On the next page starts the report “Calculating Loss Coefficient of a Two-Cover Flat Plate
Solar Collector” as given to Professor Phelan in the fall semester of 2015. Following that,
“Statistical Methods of Minimizing Risk for Small-Scale Wind Energy Investments” is included,
as given to Professor Calhoun in fall of 2014.

4. 1 Copyright © 20xx by ASME
MAE 585: Solar Thermal Engineering Semester Project Report
Supervisor: Dr. Patrick Phelan
Arizona State University, Tempe, Arizona
December 4th, 2015
CALCULATING LOSS COEFFICIENT OF A TWO-COVER FLAT PLATE SOLAR
COLLECTOR
Principal Researchers:
Channing Ludden
Mechanical Eng. B.S.E.
Rachel Cook
Aerospace Eng. B.S.E.
Ian McLeod
Mechanical Eng. B.S.E.
ABSTRACT
The ratio of useful energy gain to total incident solar
energy over a period of time defines solar collector efficiency.
This article evaluates the energy losses of a flat plate solar
collector, which govern a collector’s ability to convert solar
energy into useful gain. Such an evaluation of flat plate
collector losses is primarily an exercise in thermodynamic
applications. Relationships between basic flat plate collector
components can be represented as a thermal resistance network.
This enables an examination of heat transfer modes as well as
thermal losses through convection and radiation throughout the
collector. It was determined that the flat plate collector overall
loss coefficient involved in this experiment was approximately
2.2375
𝑊
𝑚2. This calculation is in agreement with other
publications of note, and therefore the assumptions and
methodology detailed in the following report serve as an
accurate assessment of flat plate solar collector performance.
NOMENCLATURE
Symbols
 𝐴 𝑐 Collector area
 𝑐 𝑝 Specific Heat
 𝐻𝑇𝐹 Heat Transfer Fluid
 ℎ 𝑐 Convective heat transfer coefficient
 ℎ 𝑟 Radiative heat transfer coefficient
 ℎ 𝑤 Wind convective heat transfer coefficient
 𝑘 Thermal conductivity
 𝐿 Length, plate spacing
 𝑚̇ Mass flow rate
 𝑁𝑢 Nusselt number
 𝑅 Heat transfer resistance
 𝑅𝑎 Rayleigh number
 𝑆 Absorbed solar radiation per unit area
 𝑇 General surface temperature
 𝑇 𝑎 Ambient temperature
 𝑇𝑐1 Temperature of lower glass cover
 𝑇𝑐2 Temperature of top glass cover
 𝑇𝑠 Temperature of the sky
 𝑇𝑝 Temperature of absorber plate
 𝑈𝑏 Bottom loss coefficient
 𝑈𝑒 Edge loss coefficient
 𝑈𝐿 Collector overall heat loss coefficient
 𝑈𝑡 Top loss coefficient
 𝑣 Velocity
 𝛽 Collector tilt
 𝜀 𝑐 Cover emissivity
 𝜀 𝑝 Plate emissivity
 𝜎 Stefan-Boltzmann constant
INTRODUCTION
The flat plate solar collector is the simplest variation in
modern solar engineering practices. Its ease of construction and
operation enables consumers to capitalize on renewable energy
at a fraction of the cost of more sophisticated collector designs.
This makes flat plate collectors ideal for applications such as
solar water heating and passive building heating. Flat plate
collectors are also restricted in temperature range to 100℃
above ambient temperature [1]. Due to their relatively simple
design, flat plate collectors provide the background necessary
for understanding and harnessing energy from the sun.
Furthermore, it is from this understanding that researchers are
able to increase the capabilities of other forms of solar thermal
collectors. The abundance of solar insolation and the drive to
characterize system performance steered the principal
researchers to design an experiment that would better their
understanding of flat plate solar collectors.
The purpose of this experiment is to calculate the overall
loss coefficient of a two-cover flat plate solar collector. The flat
plate collector can be treated as a closed system with solar
irradiance as a conserved quantity passing through the system
boundary. Energy loss through the top, bottom, and sides of a
flat plate collector are a result of conduction, convection, and
radiation between all components of the collector. Construction
of a thermal resistance network is therefore necessary in
understanding the modes of heat transfer throughout the
system. A description of the geometry of flat plate collectors
serves to understand how the thermal resistance network is
constructed in this report.
Flat plate solar collector geometries typically involve a few
standard components:
 absorber plate
 one or more covers

5. 2 Copyright © 20xx by ASME
 a fluid conduit
 thermal insulation
For the design presented in this paper, solar irradiance passes
through the collector geometry where it is first absorbed by a
thermally conductive absorber plate. Heat is transferred from
this plate via conduction through a glass cover where it then
encounters a fluid medium that converts the solar irradiance
into useful gain. A second glass cover serves to close the flat
plate collector system and help trap incident sunlight. Figure 1
depicts the collector geometry specific to this report:
Figure 1: Flat Plate Collector Geometry
An equivalent thermal resistance network was developed
to model the theoretical loss coefficient. Once a collector
representative of Fig. 1 was designed and constructed, the
researchers were able to design an experiment to obtain an
experimental loss coefficient. This experiment utilized several
thermocouples strategically placed to gather temperature
information about the system components. From these
temperatures, the researchers were able to produce an
experimental loss coefficient comparable to the theoretical
value. Through this process, the researchers gained an
understanding of the physics of heat transfer in a flat plate
collector and the system performance.
THEORETICAL MODEL
The development of an overall loss coefficient 𝑈𝐿 is a
useful characterization of the system losses that can simplify
other calculations, such as for the useful gain 𝑄 𝑢 of the system
[1]. The method to solve for an overall loss coefficient is by the
utilization of thermal resistance networks. These thermal
resistance networks for solar collector systems can result in
non-linear equations because of the multiple methods of heat
transfer between system components. Figure 2 shows the
typical thermal resistance schematic of a two-cover, flat plate
collector system.
Figure 2. Thermal network for a two-cover flat plate
collector: (a) in terms of conduction, convection, and
radiation resistances; (b) in terms of resistances between
plates. [1]
Figure 2a is reduced to Fig. 2b to allow the series addition of
resistances for the calculation of one unified loss coefficient.
The resistances on either side of the 𝑇𝑝 node in Fig. 2b combine
to form the top loss coefficient 𝑈𝑡 and the bottom loss
coefficient 𝑈𝑏. The magnitude of the bottom loss coefficient is
approximately zero for most cases, and this yields the equation
for the top loss coefficient:
𝑈𝑡 =
1
𝑅1+𝑅2+𝑅3
(1)
The resistances 𝑅1, 𝑅2, and 𝑅3 represent heat transfer modes at
the outer cover, inner cover, and the absorber plate. For a
typical two-cover system, 𝑅1, 𝑅2, and 𝑅3 are expanded to yield
the equations:
𝑅1 =
1
ℎ 𝑤1+ℎ 𝑟,𝑐2−𝑎
(2)
𝑅2 =
1
ℎ 𝑐,𝑐1−𝑐2+ℎ 𝑟,𝑐1−𝑐2
(3)
𝑅3 =
1
ℎ 𝑐,𝑝−𝑐1+ℎ 𝑟,𝑝−𝑐1
(4)
The loss of heat by convection to ambient is encapsulated by
ℎ 𝑤1. The loss of heat by radiation to the environment is
incorporated into the expression for 𝑅1 with ℎ 𝑟,𝑐2−𝑎. The

6. 3 Copyright © 20xx by ASME
calculation of this coefficient utilizes equation (6.4.5) from
Duffie [1] and is listed as equation (5) below:
ℎ 𝑟,𝑐2−𝑎 =
𝜎𝜀 𝑐(𝑇𝑐2+𝑇𝑠)(𝑇𝑐2
2 +𝑇𝑠
2)(𝑇𝑐2−𝑇𝑠)
𝑇𝑐2−𝑇 𝑎
(5)
The experimental setup shown in Fig. 4 shows that
there will be differences in the calculation of 𝑅2 and 𝑅3. A
typical 2-cover system is evacuated or has air between the two
covers. The experimental setup shows that the HTF is pumped
between the two covers, changing the primary modes of heat
transfer associated with 𝑅2. This replaces the radiation between
the two covers ℎ 𝑟,𝑐1−𝑐2 and natural convection ℎ 𝑐,𝑐1−𝑐2 with a
forced convection term ℎ 𝑤2. The new equation for calculating
𝑅2 is:
𝑅2 =
1
ℎ 𝑤2
(6)
The forced convection coefficient is calculated with
the same methodology and is discussed in the results.
𝑅3 represents convection and radiation coefficients
between the first cover and the absorber plate. These terms
characterize the transfer of heat to the absorber plate before the
energy is transferred to the HTF in a typical 2-cover system.
The experimental setup shown in Fig. 4 changes 𝑅3 to a
component of the bottom loss coefficient 𝑈𝑏. The modified top
loss coefficient equation becomes:
𝑈𝑡 =
1
𝑅1+𝑅2
(7)
With the elimination of 𝑈𝑏, Fig. 2b can be simplified to Fig. 3
below [1].
Figure 3. Equivalent thermal network for flat plate
solar collector. [1]
Variable 𝑈𝑡 becomes 𝑈𝐿 in the diagram because of the
negligible bottom and edge effects assumption. Equations (1)
through (7) are presented in chapter 6, section 4 of Solar
Engineering of Thermal Processes [1].
The forced convective heat transfer coefficients ℎ 𝑤1
and ℎ 𝑤2 are found by two different methods. The variable ℎ 𝑤1
is estimated for still-air conditions to be 5
𝑊
𝑚2∗𝐾
for most flat
plate collectors. The variable ℎ 𝑤2 is calculated by using a
modified Dittus-Boelter equation from Kaminsky [3] for a
forced internal convection system. The equations for
calculating the ℎ 𝑤2 values depend on the physical
characterization of the flow with the Reynolds, Rayleigh, and
Nusselt numbers. The equations for these dimensionless
parameters are given in Kaminsky (equations 12-1, 12-2, 12-
28) as:
𝑅𝑒 =
𝜌𝑣𝐿
𝜇
(8)
𝑁𝑢 = 1 + 1.44 [1
−
1708(sin(1.8𝛽)1.6)
𝑅𝑎 ∗ cos(𝛽)
] [1
−
1708
𝑅𝑎 ∗ cos(𝛽)
]
+
[
𝑅𝑎 ∗ cos(𝛽)
5380
1
3
− 1]
+
(9)
ℎ 𝑤2 =
𝑁𝑢∗𝑘
𝐿
(10)
EXPERIMENT
To begin evaluating the top loss coefficient, the two-cover
flat plate solar collector must be designed and built. The
specific setup of the collector can be seen in Fig. 4:
Figure 4: Detailed Collector Drawing with Dimensions
The dimensions of the collector were driven by the size of
the glass as it is difficult to cut without cracking. Each of the
glass plates had a length of 36in and a width of 24in. From
these limiting dimensions, the size of the 5052 aluminum
absorber plate was cut to match. All three plates combined to
form the collector (including two 0.075in wooden spacers
placed lengthwise in between the glass plates for fluid transfer)
yielded an overall thickness of 0.125in. The aluminum absorber
plate was attached to the bottom glass cover using two-part
epoxy. To provide an even source of water flow across the
collector, two 1.5in diameter PVC pipes were slotted with a
dremel and secured to both ends. These were secured using hot
glue to form an airtight seal. The lengthwise edges of the glass
plates were also sealed using hot glue. At the front edge of the
collector, one end of the PVC pipe was attached to a hose and

7. 4 Copyright © 20xx by ASME
the other end was sealed with an end cap to ensure that the only
medium for water to flow was between the glass covers. The
slotted PVC pipe was also sealed to the collector on both ends
using hot glue. At the back edge of the solar collector, the PVC
pipe also had one end sealed with an end cap and the other end
open to provide a single outlet for the water flow. To create
structural support, two wooden 2”x4”’s of 42in length were
placed on the outer edges of the solar collector. Two holes in
each plank were drilled to allow the PVC pipe to fit through as
demonstrated in Fig. 4.
The mass flow rate through the collector was evaluated by
measuring the length of time required to fill an empty container
with water from the hose. The weight of the volume of water
within the container was then determined with a scale
calibrated to zero with the weight of the container. To minimize
error, three iterations were conducted and then averaged. Table
1 in the results section shows the data from that process.
To obtain the temperature reading required for calculating
the top loss coefficient, an accurate measurement system must
be used. This experiment utilized a block code with LabView
software in parallel with a National Instruments cDAQ-9171
with thermocouple capabilities [6].
A total of 5 k-type (chromel-alumel) thermocouples were
placed at the fluid inlet, fluid outlet, top of the glass cover,
bottom of the absorber plate, and the edge of the collector. The
sensitivity of this type of thermocouple is 41
𝜇𝑉
℃
, which
exceeded the accuracy required for the scope of this project [2].
For surface temperature measurements, the thermocouple ends
were attached with good contact using electrical tape. For the
inlet and outlet water temperatures, the thermocouples were
placed directly into the fluid streams. These locations can be
seen in Fig. 5:
Figure 5. Thermocouple Locations
A photo of the actual two-cover flat plate solar collector
assembly can be seen in Fig. 6:
Figure 6. Assembled Two-Cover Flat Plate Solar
Collector
The experiment was conducted on November 11, 2015
from 4:00 pm to 4:15 pm in Tempe, Arizona. The global
horizontal insolation value for this time is 269 W/m^2. Time
was cut short due to shadow effects. Ambient temperature (𝑇𝑎)
was recorded as 18.99℃. The mass flow rate (𝑚̇ ) of water
passing through the collector is the average taken from Table 1,
0.0288
𝑘𝑔
𝑠
. Once these values were determined, the solar
collector was placed horizontally (𝛽 = 0) in direct sunlight
with thermocouples attached. The hose was then attached to
the inlet and was allowed five minutes to reach steady state
before data was recorded.
RESULTS AND DISCUSSION
The data from the calculation of the mass flow rate is
presented below:
Table 1. Mass Flow Rate Measurements
Trial Mass of 𝑯 𝟐 𝑶 Time to Fill Mass Flow Rate
1 0.151 kg 5.30 s 0.0281
𝑘𝑔
𝑠
2 0.175 kg 5.95 s 0.0294
𝑘𝑔
𝑠
3 0.165 kg 5.68 s 0.0290
𝑘𝑔
𝑠
Average 0.0288
𝑘𝑔
𝑠
The data from the test setup was also collected and was
processed in MATLAB. Fig. 7 shows the inlet and outlet HTF
temperatures over time.

8. 5 Copyright © 20xx by ASME
Figure 7. Fluid Inlet/Outlet Data
It is seen from Fig. 7 that the HTF gained energy as it
passed through the system. Near the 750 second mark is a
disturbance in the sensor readings that was smoothed out in
MATLAB. The resulting, processed temperature data for all of
the sensors is show below in Fig. 8
Figure 8. Temperature Data for System Components
This information is used to calculate the top loss
coefficient in accordance with the theoretical model and thus
the overall loss coefficient. The plot of 𝑈𝐿 calculated from
equation (7) over the duration of the experiment is given below.
Figure 9. Calculate Top (Overall) Loss Coefficient
This overall loss coefficient is lower than expected.
Previous example problems in class had utilized loss
coefficients near 10
𝑊
𝑚2∗𝐾
. Verification could be performed by
calculating the absorbed insolation with assumed KL values for
a two cover system. The absorbed radiation could then be used
to calculate the useful gain 𝑄 𝑢 with system component
temperatures to calculate a theoretical loss coefficient.
However, the prevalence of system characterization research
for flat-plate collectors is large. Sekhar et al. in 2009 published
“Evaluation of heat loss coefficients in solar flat plate
collectors” and graphed their system results for top loss
coefficients in a figure designated as Figure-5. This figure is
reproduced down below as Fig. 10 and shows results for a
similar flat-plate collector setup.
Figure 10. Variation of top loss coefficient with
absorber plate temperature.
For a given absorber plate emissivity, temperature is varied
and its effect on 𝑈𝑡 was observed. The approximate value of the
aluminum sheet metal used as the absorber plate was tabulated
0 100 200 300 400 500 600 700 800 900
21.4
21.6
21.8
22
22.2
22.4
22.6
22.8
23
Time (s)
Temperature(degC)
Fluid Inlet/Outlet Temperature Profile
Tin
Tout
0 100 200 300 400 500 600 700 800 900
20
21
22
23
24
25
26
27
Time(s)
Temperature(degC)
Sensor Data
Inlet
Outlet
Outer Cover
Absorber Plate
Side
0 100 200 300 400 500 600 700 800 900
2.2374
2.2375
2.2375
2.2376
2.2376
2.2377
2.2378
2.2378
2.2378
Time (s)
U
L
(W/(m2K))
Calculated Overall Loss Coefficient

9. 6 Copyright © 20xx by ASME
to be .09 [7]. The approximate temperature of the absorber plate
is 296K. Extrapolation of the data curves yields a 𝑈𝑡 value at
about 2.2, very near to the experimental results demonstrated in
Fig. 9. These results are consistent with each other, as well as
the low variation of the y-axis in Fig. 9.
It is important to note that edge and bottom losses do exist,
but their effects are not as prevalent as top losses. Utilizing
equation 6.4.11 from Duffie, an approximate edge loss
coefficient was calculated to be:
𝑈𝑒 =
𝑘 𝑎𝑖𝑟
𝑡 𝑖𝑛𝑠
∗ 𝑃 ∗
𝑡 𝑐𝑜𝑙
𝐴 𝑐
= .1437
𝑊
𝑚2∗𝐾
,
Where,
The difference in magnitude of the edge effects confirms
that they are negligible. This concept was reinforced by the fact
that the collector was built with only a 0.125in edge thickness,
and hot glue was used to seal the sides. Due to the fact that
0.125 inches is an extremely short side length, and only the
wooden 2x4’s used as framework for the collector served to
insulate the sides, the edge losses had the potential to be larger
but still were considerably smaller than the top losses. In
regards to bottom losses, only convection could be a viable
mode of heat loss, and even so it would pale in comparison to
convective losses at the top of the collector because of the test
setup’s proximity to the ground. The spacing of the absorber
plate from the ground results in an absence of conductive
mediums. This is because conductive heat transfer requires two
or more solids to be in contact [3]. The same assumption is
applicable to the top of the solar collector. Losses due to
radiation are also negligible at the bottom of the collector for a
few reasons. The net rate of heat transfer due to radiation is
given by equation (5), which demonstrates reliance on
temperature differences between the surface in question and the
surroundings [4]. The temperature difference between the
absorber plate and the surroundings was only a few degrees and
the structural components acted like a black box to contain all
the radiation. These conditions lead the radiative terms to be
very small.
CONCLUSIONS
The experimental results matched the results from other
flat-plate characterization research projects. The experimental
results also show the potential of solar thermal applications. A
simple two-cover flat-plate collector was able to be constructed
out of commonly available materials. Even with low sunlight
conditions in November, a marked increase in temperature was
able to be recorded. It was determined that losses through the
top of the collector dominated all other collector losses.
Neglecting edge and bottom losses means that calculation of
the overall collector loss coefficient can be performed readily,
which in turn allows for other useful information such as fluid
exit temperatures to be calculated easily. The experimental
results corresponding to 𝑈𝐿=2.2375
𝑊
𝑚2∗𝐾
illustrates the
reproducibility of this simple geometry.
Certain limitations impeded the ability to get higher
temperature differences and calculate other useful system
parameters. The experiment required significant planning and
budgeting by the three team members, who had limited
resources compared to other research groups. Those resources
could lead to greater accuracy and more distinct results with
access to more expensive materials. For example, commercially
built flat plate collectors typically maximize surface
absorptivity of absorber plates at 95%, while the surface
absorptivity of the aluminum absorber plate in this experiment
was 65% at best [7][8]. Increasing absorber plate absorptivity
without sacrificing low level emissivity requires special types
of glazing of which the researchers’ did not have access. Glass
cover transmittance could similarly have been optimized
through tempering, and usage of more specialized adhesives
could have further increased heat transfer efficiency within the
collector. Lastly, perhaps the most obvious experimental
improvement would be to test the collector in summer months
rather than winter to increase the levels of incident solar
irradiation. For future work, each of these limitations could be
addressed to benefit the experimental results from testing.
RECOMMENDATIONS
The test data shows an increasingly smaller temperature
difference around the time of 450 seconds. This is due to
shading from the sun’s movement. Any future tests would
require analysis of the testing stage to ensure proper operation
can continue for extended periods of time without moving the
experimental setup. It is recommended that additional research
be performed in order to characterize system parameters for
elaborate systems to better optimize new collector geometries,
such as “sea shell” geometry CPC’s.
REFERENCES
[1] J. A. Duffie and W. A. Beckman, “Flat-Plate Collectors,” in
Solar Engineering of Thermal Processes, 4th ed., Hoboken,
New Jersey: John Wiley and Sons, Inc, 2013, pp. 236–321.
[2] “Type K Thermocouple,” Thermometricscorp.com, 2014.
[Online]. Available at:
http://www.thermometricscorp.com/thertypk.html. [Accessed:
Dec-2015].
[3] D. Kaminski and M. K. Jensen, Introduction to Thermal and
Fluids Engineering. Hoboken, N.J.: Wiley, 2005.
[4] Y. A. Engel, Introduction to Thermodynamics and Heat
Transfer, International. New York: McGraw-Hill, 1997.
[5] “Emissivity Coefficients of Some Common Materials,”
2015. [Online]. Available at:
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d_447.html. [Accessed: Dec-2015].

10. 7 Copyright © 20xx by ASME
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Emissivity Coefficients of some common Materials. [Online].
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absorptivity-d_1805.html. [Accessed: Dec-2015].

11. Statistical Methods of Minimizing Risk for
Small- Scale Wind Energy Investments
By Erik Misiak and Ian McLeod
Professor Calhoun
Dec. 2nd, 2014
Executive Summary
The purpose of this project is to explore ways in which the typical individual
could sample local data in order to better understand the available wind power in
their region. The project is focused on using past data to extrapolate on potential
returns in energy and money. This is intended as an alternative to expensive
meteorological software. The project purpose is accomplished using statistical
analyses in Matlab, such as discriminant analyses, multiple linear regressions, t-
tests for comparison, and other methods of estimating probabilities. An estimation
of potential power generation over a six-month period in Cold Bay, Alaska, is
achieved. An explanation of the business impact of operating small-scale, residential
turbines is also provided. It is recommended that the reader employ the methods in
this paper toward implementing their own turbine, and thus contributing to the
global shift toward renewable energy.

12. McLeod and Misiak 2
Introduction
A. Problem Statement
In the modern energy market, alternative energies such as solar and wind
power are becoming more and more competitive against fossil fuels. However,
reusable energy is not currently as reliable as fossil fuels for human needs. Of the
many issues brought about, it can be difficult to select a site to farm wind because of
inaccuracies in wind power estimation techniques. Advances in technology such as
lidar equipment and meteorological software have significantly reduced the risk
involved in commercial wind farm investments. However, these technologies are
still so rare and expensive that the average citizen cannot afford them. This limits
wind farming potential. The purpose of this project is to demonstrate how the
average individual might take published data and employ statistical methods
towards understanding the nature of wind speeds in their area. A theoretical utility
for this knowledge could be setting up a personal wind farm on a residential
property, or perhaps even designing a small-scale wind farm. The ability to use
statistical estimation to predict areas that can produce the most energy is a vital
resource for implementing personal wind turbines. Wind power is reliant on
sustained wind speeds.
The business aspects pushing alternative energies can also be complex and
multidimensional. State and federal agendas often conflict, and it appears that many
people are uneducated about the energy resources they have available. It is the
objective of this project to present the reader with simple energy policy knowledge
in addition to statistical techniques regarding wind energy. Understanding these
principles can empower the average citizen to defy the unpredictability in weather
and feel comfortable operating their own turbine.
B. Background Information
As global dependency on coal continues to threaten the environment,
alternative energy is on the rise. Many states have instituted a percentage quota of
renewable energy to reach within the next few decades. Wind energy has become a
leader in the pursuit of clean energy sources. New ideas are being explored every
day in terms of capturing wind power, however a significant portion of the business
aspect of energy relies on prediction. As any meteorologist can attest, it is very
difficult to predict wind speeds since they are a byproduct of global changes in
weather and chaotic variables. However, statistics can be employed in order to
determine locations where there is a high probability of sustained wind speeds. To
demonstrate this process, the selected location for this report was Cold Bay, Alaska
since it is a relatively unexplored area in terms of wind energy. Cold Bay rigorously
documents statistics in relation to wind energy in an online database as well. While
sustained wind speeds may be lower in Alaska than in the contiguous United States,
it is interesting to examine the possibility of lucrative power generation from a
conditional probability standpoint. Such results can be a testament to the true
versatility of wind energy.

13. McLeod and Misiak 3
C. Design Considerations
It is important to take caution when exploring statistics since false
interpretations can proliferate. As the law of large numbers states, the larger the
sample size the closer the statistics of the observations approach population
parameters. In this project, yearly data consisting of hundreds of data points was
examined. The data was taken from Alaska Energy Authority, which has an extensive
inventory of statistics. As with any statistical method, error must be accounted for ,
and the student’s took caution not to extrapolate results beyond reasonable
applications.
Procedure and Results
The project organization later expands in complexity, but first relevant
observations were noted from simple scatter plots. The following plot exemplifies
the average frequency of wind versus direction for an entire year in Cold Bay.
Higher frequencies are observed around the 150° and 300° directions.
The same quantity of data points were used to plot average wind speeds
versus direction for the same year in Cold Bay. One can observe a similar spike in
wind speed at the 150° mark as in the previous frequency plot. High frequency wind
with high velocity is good for power generation, so it is important to identify which
direction these conditions occur most often.

14. McLeod and Misiak 4
Discriminant analyses were used for this purpose. Discriminant analyses can
be used to help identify associations between pairs of variables. In order to prepare
for a discriminant analysis, variables must be selected that are somehow related. In
this case, average wind speed per direction was plotted against frequency per
direction. Both variables are related in that they were recorded by direction. This
yielded a plot of average wind speeds per frequency.
The purpose of this set up was to identify directions in Cold Bay where high
frequency of wind and high wind speeds occur simultaneously. Naturally, this

15. McLeod and Misiak 5
combination is ideal for wind energy production. Normally, sustained wind speeds
of 12 mph are typical constraints for wind farm investment. However, as observed
in the previous plot, most wind speeds average below 9 mph in Cold Bay. Thus, it
may not be economical to operate a wind turbine throughout the entire year. The
goal of subsequent discriminant analyses is to identify directions and times of year
where the probability of sustained wind speed occurring above 9 mph is high. This
is similar to a conditional probability analysis. In other words, it is desirable to
identify directions where the probability of wind speed occurring above 9 mph
exists given also that a high frequency of wind exists in that direction. Quadratic
discriminant classifiers were employed towards toward this end as well.
The following plot groups the data by four quadrants of direction. It is clear
that the highest frequencies with simultaneous high wind speeds occur most often
in the second quadrant. This implicates that an individual would have the best odds
of generating quality power in Cold Bay by facing their turbine between 90° and
180°. The plot also shows that the lowest frequencies in combination with low wind
speeds occur in the third quadrant, between 180° and 270°. The quadratic
classifiers display decision boundaries. These decision boundaries account for the
flexibility in approximation, and identify regions of the plot that belong to the same
category. An individual could use these boundaries as probabilistic guidelines for
sustained wind speed and frequency. There is confidence that the classifiers are
reasonably accurate because the resubstitution losses of the classifiers in both plots
were as low as the cross-validated losses.

16. McLeod and Misiak 6
qerror =0.4468
cverror = 0.4514
The following plot displays the same quadratic discriminant analysis,
however the data is grouped by season instead of direction. It is evident that the
boundaries in this analysis are much less clear-cut as with the directional grouping.
However, the trend generally demonstrates that higher wind speeds and
frequencies are observed in the fall and winter seasons rather than the spring and
summer seasons.
qerror = 0.6319
cverror =0.6435
Combining the results of the two discriminant analyses concludes that
operating a turbine between the months of October and March facing in a direction
between 90° and 180° yields the highest probability of generating the most power.
In the interest of saving money and effort, a small-scale turbine operator in Cold Bay
could activate their turbine for these few months of the year and not have to worry
about creating a responsive system that constantly adjusts the turbine into the face
of the wind. For the spring and summer seasons, the wind energy density may not
be high enough and the operator may desire to switch to solar energy due to the
extended daylight that occurs in areas close to the north pole.
In order to decisively conclude that wind speed averages in the summer of
Cold Bay are significantly different than those in winter, a two-sample t-test can be
implemented. A two-sample t-test involves two hypotheses: a null hypothesis that
the sample means are not significantly different, and an alternative hypothesis that

17. McLeod and Misiak 7
the sample means are significantly different. The t-test uses a 95% confidence
interval that false acceptance or rejection of the null hypothesis does not occur.
Using the matlab function “ttest2”, comparing wind speed averages in the winter
versus the summer validated the null hypothesis. This means that the average wind
speeds in the winter were significantly different than those in the summer. A plot of
the day of the season versus average wind speed was created to compare the two
data sets to better visualize their differences.
A final statistical tool that can be used by the average individual is multiple
linear regression. Multiple linear regression is a tool that allows multiple
independent predictor variables to be tested for relationship to a categorical
dependent variable. In this project, the variables of time of sunrise (IV), time of
sunset (IV), maximum temperature (IV), and minimum temperature (IV) from
January, February, and March of 2006 were tested in order to determine if any of
these individual variables could be used to predict wind speed (DV) in Cold Bay. The
results are as follows:
Show results of b-matrix and interpret meaning.
b=
0.4024
0.0109
-0.0094
0.0010
0.0023

18. McLeod and Misiak 8
Show results of stats and interpret meaning.
R^2 =[0.0062]
Fstat =[0.1319]
Prob =[0.9703]
Variance =[1.443]
Construct a normal probability plot of the residuals and interpret this graph.
The normal plot of the residuals does not show any evidence of nonlinearity,
which concludes that the regression results are trustworthy. Each [b] coefficient
represents the magnitude of correlation between wind speed and each variable
listed above, accordingly. The first [b] coefficient is simply the intercept of the
equation, while the remaining four [b] coefficients represent the magnitude of the
relationship between each variable and wind speed. It is evident that each
independent variable had almost zero correlation with wind speed, as each [b]
coefficient was especially small. The stats results also indicated a low value of
coefficient of determination (𝑅2
), meaning that the data was not fitted very
effectively. The highest correlation involved minimum daily air temperature.
Maximum daily air temperature was negatively correlated to wind speed, meaning
that lower maximum temperature correlated to higher wind speed in Cold Bay. The
time of sunset was about twice as much of a predictor as the time of sunrise. Using
the minimum daily air temperature and time of sunset, a surface fit plot was created
to demonstrate their correlation with wind speed.

19. McLeod and Misiak 9
Although the results had little correlation, an individual could select different
independent variables in order to discover variables that actually predict wind
speed. Understanding how such variables correlate to wind speed would allow the
individual to operate their turbine with greater confidence. Due to time limitations,
the students were not able to identify such variables, however the method is still
useful to learn for an individual interested in estimating wind speeds.
Returning to the discriminant analyses, it is possible to roughly estimate the
amount of power an individual turbine could generate while operating throughout
fall and winter and facing only in directions between 90° and 180° in Cold Bay,
Alaska. A Tycon Power Systems turbine was selected for this analysis since it is
affordable and designed for residential use. The rotor swept area of this turbine is
0.665𝑚3
. The following plot displays the wind speeds during Fall and Winter
between 90° and 180°.

20. McLeod and Misiak 10
A power curve was generated for this data according to the following
formula:
𝑃𝑜𝑤𝑒𝑟 =
1
2
∗ 𝜌 ∗ 𝑉3
∗ 𝐴
The startup wind speed for a Tycon Power Systems turbine is 2.1 m/s, so all
values are included.
Speed (m/s) Approx
Frequency
5.5 10
6 15
6.5 14
7 29
7.5 28
8 42
8.5 17
9 18
9.5 14
10 11
Total 198

21. McLeod and Misiak 11
𝑃𝑜𝑤𝑒𝑟 𝑃𝑟𝑜𝑑𝑢𝑐𝑒𝑑 = Σ𝑃𝐷𝐹𝑤𝑖𝑛𝑑𝑠𝑝𝑒𝑒𝑑 ∗ 𝑐𝑜𝑟𝑟𝑒𝑠𝑝𝑜𝑛𝑑𝑖𝑛𝑔 𝑝𝑜𝑤𝑒𝑟
𝑃𝑜𝑤𝑒𝑟 = (
10
198
∗ 70.55) + (
15
198
∗ 91.6) + (
14
198
∗ 116.5) + (
29
198
∗ 145.5)
+ (
28
198
∗ 178.9) + (
42
198
∗ 225.4) + (
17
198
∗ 260.4) + (
18
198
∗ 309.1)
+ (
14
198
∗ 363.6) + (
11
198
∗ 436.9)
𝑃𝑜𝑤𝑒𝑟 = 213.6 𝑊𝑎𝑡𝑡𝑠
𝑃𝑜𝑤𝑒𝑟 𝑃𝑟𝑜𝑑𝑢𝑐𝑒𝑑 𝑂𝑣𝑒𝑟 𝐹𝑎𝑙𝑙 & 𝑊𝑖𝑛𝑡𝑒𝑟 = 213.6 𝑊𝑎𝑡𝑡𝑠 ∗ 4335 𝐻𝑜𝑢𝑟𝑠
𝑃𝑜𝑤𝑒𝑟 𝑃𝑟𝑜𝑑𝑢𝑐𝑒𝑑 𝑂𝑣𝑒𝑟 𝐹𝑎𝑙𝑙 & 𝑊𝑖𝑛𝑡𝑒𝑟 = 0.926 𝑀𝑊 ∗ ℎ𝑟𝑠
Conclusion and Recommendations
The major take-away from this project is that wind energy has great
potential to spread into residential environments. The statistical methods involved
in this project demonstrate how an individual could optimize a personal wind
turbine. Provided that past wind data is available, employing discriminant analyses
can help the user to identify the best times of year and directions to operate their
turbine. Multiple linear regressions can be employed to identify the magnitude and
nature of correlations between independent variables and wind speed. The reader
should take time to identify independent variables that are better correlated than
those presented in this project if they intend to minimize risk with this method. T-
tests and data plotting further helps to verify significant differences in wind speeds.
This improves the researcher’s confidence in their results. It is recommended that
the reader reproduce the procedure of this project using data from their hometown
in order to calculate how much energy and money they can generate by purchasing
a personal turbine such as those offered by Tycon Power Systems. Further
recommendations are to stay up to date with federal and local government
incentives and tax breaks, as these are sure to shift each year.
References
Cold Bay Longterm Data. (2007, August 3). Retrieved December 2, 2014, from
http://www.akenergyauthority.org/PDF files/Wind Resource
Assessment/Cold-Bay_longterm-data.txt
Conditional Probability. (2012, July 31). Retrieved December 2, 2014, from
http://www.epa.gov/caddis/da_exploratory_4.html
Decision Boundaries. (2001, April 7). Retrieved December 2, 2014, from
http://www.cs.princeton.edu/courses/archive/fall08/cos436/Duda/PR_sim
p/bndrys.htm

22. McLeod and Misiak 12
Discriminant Analysis. (n.d.). Retrieved December 2, 2014, from
http://www.mathworks.com/help/stats/discriminant-
analysis.html?refresh=true#brah8i2
Horizontal Wind Turbine. (2010, December 14). Retrieved December 2, 2014, from
http://www.flyteccomputers.com/ext/Tycon Power/TPW-200-12.pdf
Joint, Marginal & Conditional Frequencies: Definitions, Differences & Examples.
(n.d.). Retrieved December 2, 2014, from http://education-
portal.com/academy/lesson/joint-marginal-conditional-frequencies-
definitions-differences-examples.html#transcript
Multiple Regression. (2009, September 19). Retrieved December 2, 2014, from
http://peoplelearn.homestead.com/MULTIVARIATE/Module11MultipRegres
s1.html
Wind Power: A Clean and Renewable Energy. (2014, June 17). Retrieved December
2, 2014, from http://www.renewableenergyst.org/wind.htm