SOLAR SYSTEMS IN THE ECO VILLAGE AT THE UNIVERSITY OF ...bibeauel/research/... · The...

SOLAR SYSTEMS IN THE ECO‐VILLAGE

AT THE UNIVERSITY OF MANITOBA

Heather King

SOLAR SYSTEMS IN THE ECO‐VILLAGE

AT THE UNIVERSITY OF MANITOBA

Heather King

A thesis submitted in conformity with

the requirements for the degree of

BACHELOR OF SCIENCE (MECH. ENG)

at the University of Manitoba

Supervisor: Dr. E. Bibeau

Department of Mechanical and Manufacturing Engineering University of Manitoba

2007

ii

ABSTRACT Solar technologies are vastly emerging across the globe as a renewable, environmentally

acceptable alternative to fossil fuels and other non‐renewable energy resources. The

“eco‐village”, an old straw bale barn located on the University of Manitoba’s Ft. Garry

campus, is currently being used to study solar technologies; more specifically, to

examine the use and efficiency of solar air and water collectors. Once installed, data

must be logged from these solar collectors to enable the energy output and

instantaneous efficiency for each collector to be determined. This report discusses, in

detail, the various types of solar collectors that are to be installed at the “eco‐village”.

Calculations are carried out to determine the optimum location and position the solar

collectors should be installed at in order to maximize the amount of solar radiation

received by the collectors throughout the year. Research into the transfer of heat

throughout each collector allowed for instantaneous efficiency models to be created for

each collector, in which a user simply has to enter the required variable input data and

the efficiency of the collector is calculated. The report concludes by examining the

economical and environmental benefits of installing a system of solar collectors on the

University of Manitoba’s Ft. Garry campus and the capabilities this proposed system of

solar collectors would have in supplementing the university’s current district heating

system.

iii

ACKNOWLEDGEMENTS I would like to thank the following people for their assistance during the course of this

undergraduate research project:

Dr. Eric Bibeau Assistant Professor, Department of Mechanical

Engineering, University of Manitoba G. Paul Zanetel, P.Eng Associate Professor, Engineer‐in‐Residence, Department of

Mechanical Engineering, University of Manitoba Daniel Friesen, P. Eng Consultant, Daniel Lepp Friesen Consulting Mike Ferley, P.Eng Energy Advocate, Physical Plant, University of Manitoba Stephanie Zubriski Graduate Student, Faculty of Engineering, University of

Manitoba Dr. Kris Dick, P.Eng Adjunct Professor, Engineer‐in‐Residence, Design

Engineering, University of Manitoba

iv

NOMENCLATURE

sh = specific enthalpy of evaporation of steam at working pressure

bI = the direct radiation received by the collector

effI = the effective solar radiation on the collector

NI = the normal terrestrial solar radiation received at ground level

sm

= steam mass flow rate

aT = ambient air temperature

Q = heat transferred from the steam

LQ.

= thermal energy lost to the environment

LU = the overall heat loss coefficient

= Stefan‐Boltzmann constant = 5.67 x 10‐8 W/m²∙K4

= density of the heat transfer fluid

= viscosity of the heat transfer fluid

Σ = tilt angle of the flat plane of the collector Φ = direction of the angle of tilt Evacuated Tube Collector nomenclature:

icA , = inner tube diameter times collector length

ocA , = outer tube diameter times collector length

ihA , = heat pipe inner diameter times collector length

ohA , = heat pipe inner diameter times collector length

icD , = inner diameter of the collector tube

ocD , = outer diameter of the collector tube

ocondD , = outer diameter of the heat transfer condenser

ihD , = inner diameter of the heat transfer pipe

ohD , = outer diameter of the heat transfer pipe

evacF = the shape factor between the selectively coated outer surface of the

heat pipe and the inner surface of the collector tube

rF = flow rate factor

ch = heat transfer coefficient of the outer surface of the collector tube

eh = heat transfer coefficient of the inner surface of the collector tube

hmh = heat transfer coefficient between the heat pipe fluid and the manifold

fluid

v

phh = heat transfer coefficient between the fin plate and the heat transfer pipe

fluid

ck = thermal conductivity of the glass collector tube

hk = thermal conductivity of the copper heat transfer tube

fink = thermal conductivity of the fin plate

L = the length of the heat transfer pipe

fm

= flow rate of the fluid through the manifold

mPr = Prandtl number of the heat transfer fluid in the manifold

pPr = Prandtl number of the fluid within the heat transfer pipe

mRe = Reynolds number of the heat transfer fluid in the manifold

pRe = Reynolds number of the fluid within the heat transfer pipe

cT = mean temperature of the collector plate

hT = mean temperature of the heat pipe

ifT , = temperature of the fluid in the manifold before heating occurs

hmQ.

= thermal energy transferred from the heat pipe fluid to the manifold fluid

mU = mean velocity of the fluid within the heat pipe

V = mean velocity of the air flowing over the evacuated tube collector = kinematic viscosity of the liquid in the heat transfer pipe

c = emissivity of the collector tube

h = emissivity of the heat transfer pipe

Flat‐Plate Collector nomenclature:

cA = flat plate collector area

D = outer diameter of the fluid tube 'F = collector efficiency factor

RF = collector heat removal factor

h = convective heat transfer coefficient from the inner fluid tube to the fluid k = thermal conductivity of the fluid tube

m = flow rate of the heat transfer fluid through the heat transfer tubes

fT = mean temperature of the heat transfer fluid

W = distance between centre of two fluid tubes δ = thickness of the fluid tube = heat transfer tube absorptance ε = heat transfer tube emittance

vi

TABLE OF CONTENTS

ABSTRACT .............................................................................................................................ii ACKNOWLEDGEMENTS ....................................................................................................... iii NOMENCLATURE ................................................................................................................. iv LIST OF FIGURES ................................................................................................................ viii LIST OF TABLES .................................................................................................................... ix 1 INTRODUCTION ....................................................................................................... 1 1.1 Purpose and Scope.............................................................................................. 1 1.2 Layout of Thesis .................................................................................................. 2

2 REVIEW OF LITERATURE .......................................................................................... 3 2.1 Solar Energy ........................................................................................................ 3 2.2 Solar Collectors ................................................................................................... 5 2.2.1 Solar Evacuated Tube Collector .................................................................... 6 2.2.2 Solar Water Flat‐Plate Collector ................................................................... 9 2.2.3 Solar Air Flat‐Plate Collector ....................................................................... 10 2.2.4 Solar Wall Air Heating Solar Collector ........................................................ 11

3 SOLAR COLLECTOR LOCATION .............................................................................. 13 3.1 Geographical Location ...................................................................................... 14 3.2 Incident Angle ................................................................................................... 14 3.2.1 Methodology ............................................................................................... 15 3.2.2 Calculations ................................................................................................. 17

3.3 Solar Irradiance ................................................................................................. 24 3.3.1 Methodology ............................................................................................... 24 3.3.2 Calculations ................................................................................................. 25

3.4 Chapter Summary ............................................................................................. 29 4 HEAT TRANSFER ANALYSIS .................................................................................... 30 4.1 Evacuated Tube Collector Efficiency ................................................................... 30 4.1.1 Methodology ............................................................................................... 30 4.1.2 Calculations ................................................................................................. 38

4.2 Flat‐Plate Collector Efficiency ........................................................................... 40 4.2.1 Methodology ............................................................................................... 40 4.2.2 Calculations ................................................................................................. 43

vii

5 ECONOMIC ANALYSIS ............................................................................................ 47 5.1 Background ....................................................................................................... 47 5.2 Boiler Energy Analysis ....................................................................................... 49 5.3 Collector Energy Analysis .................................................................................. 49 5.4 Cost Analysis ..................................................................................................... 53 5.5 Chapter Summary ............................................................................................. 57

6 DISCUSSION OF RESULTS .............................................................................................. 58 6.1 Benefits of Installing Solar Collectors ............................................................... 58 6.2 Possible Collector Locations ............................................................................. 59 6.3 Evacuated Tube or Flat‐Plate? .......................................................................... 63

7 CONCLUSIONS AND RECOMMENDATIONS ........................................................... 65 7.1 Solar Collector Location .................................................................................... 65 7.3 Instantaneous Efficiency Calculators ................................................................ 66 7.4 Economic Analysis ............................................................................................. 66 7.5 Final Recommendations ................................................................................... 67

8 REFERENCES .......................................................................................................... 68 APPENDIX A – COLLECTOR SPECIFICATIONS ..................................................................... 70 APPENDIX B ‐ RETSCREEN DATA FOR WINNIPEG INT. AIRPORT ....................................... 83 APPENDIX C – OPTIMUM TILT ANGLES AND DIRECTIONS: JAN –DEC 2007 ..................... 85

viii

LIST OF FIGURES Figure 1: Earth's Energy Budget .......................................................................................... 3

Figure 2: Flat‐Plate Collector............................................................................................... 5

Figure 3: "Eco‐Village" Evacuated Tube Collector .............................................................. 6

Figure 4: Single Evacuated Tube Model .............................................................................. 7

Figure 5: Heat Pipe Schematic ........................................................................................... 8

Figure 6: Heat Transfer Schematic ...................................................................................... 8

Figure 7: EnerWorks Flat‐Plate Collector ............................................................................ 9

Figure 8: Flat‐Plate Collector Schematic ........................................................................... 10

Figure 9: Sunsiaray Northern Comfort Flat‐Plate Collector .............................................. 11

Figure 10: Solar Wall Schematic ....................................................................................... 12

Figure 11: Solar Geometry ................................................................................................ 13

Figure 12: Angle of Elevation of the Sun ‐ Sept 15/07 ...................................................... 19

Figure 13: Azimuth Angle of the Sun ‐ Sept 15/07 ........................................................... 21

Figure 14: Direct Radiation Received with a Tilt Angle of 45° ‐ Sept 15/07 ..................... 27

Figure 15: Varying Degrees of Tilt Angle ........................................................................... 28

Figure 16: Comparison of 40° ‐ 50° Tilt Angles ................................................................. 28

Figure 17: "Eco‐Village" Collector Schematic ................................................................... 30

Figure 18: Equivalent Thermal Circuit ............................................................................... 31

Figure 19: Evacuated Tube Efficiency Calculator .............................................................. 39

Figure 20: Flat‐Plate Collector Efficiency Calculator ......................................................... 45

Figure 21: Distribution of Powerhouse Boiler Usage........................................................ 47

Figure 22: University of Manitoba Campus Map .............................................................. 60

Figure 23: Hybrid Map of the University .......................................................................... 61

Figure 24: Rooftop Solar Collector Locations ................................................................... 62

ix

LIST OF TABLES

Table 1: Hour Angle ‐ Sept 15/07 ...................................................................................... 17

Table 2: Angle of Elevation of the Sun above the Eco‐Village ‐ Sept 15/07 ..................... 18

Table 3: Azimuth Angle of the Sun ‐ Sept 15/07 ............................................................... 20

Table 4: Direct Radiation Received by the Collector ‐ Sept 15/07 ................................... 26

Table 5: Summary of Location Results .............................................................................. 29

Table 6: Days of Operation in 2006 ‐ Boilers 5 and 6 ....................................................... 48

Table 7: Theoretical Collector Efficiencies ........................................................................ 50

Table 8: SRCC Heating Applications .................................................................................. 50

Table 9: Solar Radiation Values......................................................................................... 51

Table 10: Quantity of Collectors Needed.......................................................................... 52

Table 11: Collector Area Needed ...................................................................................... 52

Table 12: Cost to Substitute Boiler 5 with Solar Energy ................................................... 54

Table 13: Economic Analysis of a System of 10 Collectors ............................................... 56

Table 14: Rooftop Availability ........................................................................................... 62

Table 15: Optimum Tilt Angle ‐ January 2007 .................................................................. 86

Table 16: Optimum Tilt Angle ‐ February 2007 ................................................................ 86

Table 17: Optimum Tilt Angle ‐ March 2007..................................................................... 87

Table 18: Optimum Tilt Angle ‐ April 2007 ....................................................................... 87

Table 19: Optimum Tilt Angle ‐ May 2007 ........................................................................ 88

Table 20: Optimum Tilt Angle ‐ June 2007 ........................................................................ 88

Table 21: Optimum Tilt Angle ‐ July 2007 ......................................................................... 89

Table 22: Optimum Tilt Angle ‐ August 2007 .................................................................... 89

Table 23: Optimum Tilt Angle ‐ September 2007 ............................................................. 90

Table 24: Optimum Tilt Angle ‐ October 2007 .................................................................. 90

Table 25: Optimum Tilt Angle ‐ November 2007 .............................................................. 91

Table 26: Optimum Tilt Angle ‐ December 2007 .............................................................. 91

Solar Energy Systems in the Eco-Village at the University of Manitoba _________________________________________________________________________________________________

________________________________________________________________________ December 4th, 2007 1 Heather King

1 INTRODUCTION

The following chapter introduces the reader to this report, with the aim of clarifying the

purpose, scope, and layout the following undergraduate thesis presents.

1.1 Purpose and Scope The purpose of this thesis is to examine and discuss the energy potential of installing solar

collectors at the University of Manitoba. The primary intention of this report is to

conclude on whether it would be beneficial for the University of Manitoba to install solar

collectors on campus. If installed, these collectors would either 1) provide hot water that

would tie into the university’s district heating system or 2) heat air that could be

circulated as a heating source through campus buildings.

The “eco‐village”, a straw‐bale barn located on the University of Manitoba’s Fort Garry

campus, currently has a single evacuated tube collector installed onto its south facing

wall. Plans to install two flat‐plate collectors, both a solar water collector and a solar air

collector, as well as a solar wall collector, are in the works. Using manufacturer data for

the evacuated tube collector and the solar water flat‐plate collector, theoretical

efficiencies have been calculated. The results from these analyses were then applied to a

hypothetically larger quantity of collectors in order to study the economic potential of

installing a system of solar collectors on campus.

The scope of this project is limited to evacuated tube collectors and solar water flat plate

collectors. Solar air collectors, such as the second flat plate collector and the solar wall

collector, and photo‐voltaic (PV) systems could also be analyzed in the same manner;

however time and equipment constraints limited this report to the two solar technologies

mentioned.



1.2 Layout of Thesis Following the introduction to this report, a basic overview of solar energy and solar

energy technologies is provided. The schematics of the evacuated tube collector that is

currently mounted on the “eco‐village” and the proposed solar water flat‐plate collector

are provided and discussed in detail. Brief overviews of the solar air collector and solar

wall collector that the university plans to install along with the solar water collectors are

also given, however the scope of this thesis limits the discussion of these solar air

collectors, and therefore no analysis will be carried out on these collectors at this time.

The first calculation to be discussed is that of the optimal collector location on campus in

regards to the sun. Methodology and calculations related to this objective are stated and

explained. A heat transfer analysis is then applied to both the evacuated tube system and

the flat‐plate collector system in order to determine the theoretical efficiencies of these

collectors.

Finally, an economic analysis is conducted on the proposed systems of collectors.

Discussion in this section includes the number of collectors needed, the proposed location

for these collectors on campus, and the potential energy they would provide in relation to

the amount of energy currently used to heat water on campus. A recommendation is

then presented on whether or not installing a system of evacuated tube collectors at the

University of Manitoba is economically and environmentally advantages.



2 REVIEW OF LITERATURE In order to provide the reader with an introductory lesson on solar collector technologies,

the following background section and literature review has been provided. This section

will discuss current solar technologies, with specific focus on the collectors that are to be

installed at the University of Manitoba’s “eco‐village”.

2.1 Solar Energy Solar energy is, in the simplest of descriptions, energy from the sun. This energy travels to

the earth in the form of electromagnetic radiation and is used to support virtually all life

on earth. Approximately 1367 W/m² of energy is available from the sun outside the

Earth’s atmosphere; however some of this energy is absorbed as it passes through the

Earth’s atmosphere. For instance, on a clear day, the amount of solar energy available

from the sun is in the region of 1000 W/m² [1].

The schematic below shows how the incoming solar radiation from the sun is divided as it

enters the Earth’s atmosphere [2].

Figure 1: Earth's Energy Budget



As the diagram shows, the majority of the incoming solar energy is absorbed by land and

oceans; this is a large amount of free, renewable energy which could be converted to heat

energy or stored for later use.

Heat and light, direct forms of energy from the sun, and solar based resources account for

more than 99.9 percent of the available flow of renewable energy [3]. Solar based

resources include wind power, hydroelectricity, biomass and solar collectors. This thesis

report will further discuss solar energy collection by the use of solar collectors, such as

evacuated tube collectors and flat‐plate collectors. Further discussion on these different

types of collectors follows in the proceeding sections.



2.2 Solar Collectors A solar collector is a device that extracts energy from the incident radiation of the sun and

converts it into a more useful form of energy, such as heat. Solar collectors can be used

to heat air or water and are often seen atop of homes and industrial buildings. The image

below shows a flat plate collector mounted to the roof top of a house in Australia [4].

Figure 2: Flat‐Plate Collector

The two most commonly found solar collectors are flat plate collectors and evacuated

tube collectors. A flat‐plate collector generally consists of a weatherproofed and durable

insulated box, containing an absorber sheet and built in heat transfer pipes. The collector

is placed in the path of sunlight, which allows the radiation incident on the plate to heat

up the water within the heat transfer pipes, causing it to circulate through the system by

natural convection. This heated water is usually then accumulated in a storage tank

above the collector.

Evacuated tube collectors operate on the same general principle as the flat plate

collector; however these collectors use evacuated tubes to absorb the sun’s incident rays.

More detail is provided on evacuated tube collectors and flat‐plate collectors in the

following sections.



Evacuated tube collectors and flat‐plate collectors are referred to as solar water heating

devices. However, solar collector technology is not limited to water heating; solar air

heating technology is also commonly seen. Solar air heating collectors operate with the

same general principles as water heating collectors, the only difference between the two

technologies being that air is the medium to be heated, not water or a heat transfer fluid.

2.2.1 Solar Evacuated Tube Collector The image below shows the evacuated tube collector that is currently installed on the

“eco‐village”. This collector was manufactured by Apricus Solar Co. and is installed at a tilt

angle of 45° on the buildings south facing wall. Collector specifications for the Apricus

solar collector are given in Appendix A.

Figure 3: "Eco‐Village" Evacuated Tube Collector



The evacuated tube collector works by absorbing radiation from the sun through a system

of 30 evacuated tubes. Each evacuated tube consists of two glass tubes made from

extremely strong borosilicate glass. The outer tube is transparent, which allows light rays

to pass through with minimal reflection and maximum absorption. The inner tube is

coated with a special selective coating, in this case Al‐N/Al, which gives the collector

excellent solar radiation absorption and minimal reflection properties. A vacuum is

created by fusing the top of these two tubes together and pumping out the air contained

in the space between the two layers of glass. A schematic of a single evacuate tube is

given below.

Figure 4: Single Evacuated Tube Model

As you can see from the above figure, a copper heat pipe is inserted into the inner

borosilicate tube. This heat pipe works as a condenser, based on this principle that liquids

boil at a lower temperature when the surrounding air pressure is decreased. The liquid

used in the heat pipe is purified water.

The heat pipes used in Apricus solar collectors have a boiling point of only 30°C, allowing

any liquid in the heat pipe to vaporize if the heat pipe is heated above 30°C. This water

vapor rapidly rises to the top of the heat pipe, transferring heat along the heat pipe and

exchanging it into the propylene glycol/water heat transfer fluid flowing in the manifold.

As the heat is lost at the top of the condenser, the water vapor condenses to form a liquid



and returns to the bottom of the heat pipe to once again repeat the process. The heat

transfer fluid used in our application is a 50:50 propylene glycol water solution, in order to

achieve the lower freezing point necessary for northern winters. This process is

diagramed in Figure 5.

Figure 5: Heat Pipe Schematic

Figure 6: Heat Transfer Schematic



The figure shown on the previous page illustrates the flow of heat through the evacuated

tube collector, from the incident solar energy from the sun collected by the evacuated

tubes, to the transfer of heat from the condenser into the water running through the

copper header. Once heated, the water in the copper header will be collected in a

storage tank for future distribution into the university’s district heating system.

2.2.2 Solar Water Flat‐Plate Collector

At the time of completion of this thesis, an EnerWorks solar water flat‐plate collector had

been ordered by the university, for installation in the “Eco‐Village”. The EnerWorks flat‐

plate collector is a high performance collector that boasts an absorbance rate of 94% of

the sun’s energy [14]. The figure below shows two EnerWorks flat‐plate collectors

mounted to a home in North America.

Figure 7: EnerWorks Flat‐Plate Collector

Solar hot water flat‐plate solar collectors follow the same general principle as an

evacuated tube collector; however, the heat transfer process within the collector is much

simpler than that of the evacuated tube collector. The diagram on the following page

illustrates how the flat‐plate collector works.



Figure 8: Flat‐Plate Collector Schematic

Energy from the sun strikes the flat, glazed surface of the collector, travelling through the

glass surface to be absorbed by the absorber plate. The heat obtained from this energy

absorption warms up the heat transfer fluid that is flowing through the collector. This

fluid flow enters the collector through an inlet pipe on one corner of the collector, travels

through the fluid flow tubes, and exits the collector through an outlet tube located at the

opposite corner of the collector. From the outlet tube, heat is transferred through a heat

exchanger into a water flow. This heated water is collected in a storage tank for future

use.

Detailed product specifications for the EnerWorks solar hot water flat‐plate collector to be

installed on at the “Eco‐Village” can be found in Appendix A.

2.2.3 Solar Air Flat‐Plate Collector

The solar air flat‐plate collector works with exactly the same principles are the solar water

flat‐plate collector, the one and only difference being that the fluid that circulates through

the collector is air, not a heat transfer fluid such as water or a propylene glycol solution.



A Sunsiaray Inc. Northern Comfort flat plate collector is to be installed at the “eco‐village”.

An image of this collector can be seen in Figure 9 below.

Figure 9: Sunsiaray Northern Comfort Flat‐Plate Collector

2.2.4 Solar Wall Air Heating Solar Collector

The solar wall is a solar system for heating or pre‐heating ventilation air for buildings. If

you were to look at a building which contained a solar wall, it would simply look like the

building was composed of conventional metal cladding. This metal cladding, however,

contains thousands of tiny perforations which allow fresh air to pass through on the way

to the building’s heating and ventilation (HVAC) system. As the air passes through these

holes into the building, it accumulates free heat from the cladding, which has been

warmed by the sun during the day. Ventilation fans installed inside the building create

negative pressure to draw air in through the perforations. Once the warmed up air has

passed through the solar wall it rises up to be collected into a distribution ducting system.

One of the biggest benefits of solar walls is that they even work at night, as the heat that



would otherwise escape freely from the building is captured within the face of the metal

cladding and reused for ventilation pre‐heat.

The image below shows a schematic of the principle of solar wall operation [16].

Figure 10: Solar Wall Schematic



3 SOLAR COLLECTOR LOCATION

The absolute value of solar radiation available for utilization in a particular site on Earth is

dependent on the relation between the location of the site and the location of the sun. In

order to maximize the amount of solar radiation available we must optimize the variables

in this relation.

The diagram below shows the variables that must be optimized [6]:

Figure 11: Solar Geometry



Where:

A = the angle of elevation of the sun

Z = the azimuth angle of the sun

Φ = the azimuth angle from due south

θ = the incident angle of the collector

Ψ = the elevation angle

Σ = the tilt angle of the plane

In order to show the variation in optimal solar collector location throughout the year,

each variable has been calculated for the 1st of each month for the year 2007. Appendix C

shows the results of these calculations. Step by step calculations for September 15th,

2007 are shown in the proceeding sections.

3.1 Geographical Location The first variable that must be specified is the position coordinates of the solar collector.

For calculation purposes we will use the coordinates of the eco‐village.

The eco‐village has the following coordinates [5]:

Location Straw Bale BuildingService Street 1 SW University of Manitoba Winnipeg, MB Canada

Latitude 49.81° N

Longitude 97.13° W

Elevation Above Sea Level

238 m (781 ft)

Table 3.1 ‐ Location of the Eco‐Village

3.2 Incident Angle

The following section discusses the methodology for calculating the incident angle upon

the evacuated tube collector installed on the “eco‐village”. Sample calculations for

September 15th, 2007 are also included. The incident angle calculated in the following



sections will apply to both evacuated tube and flat‐plate collectors mounted on the

University of Manitoba campus.

3.2.1 Methodology

The incident angle of the collector, θ, is the angle between the sun’s rays and the normal

to the plane surface of the collector. This angle is given by the following relation:

)])[cos()(sin(cos))(cos(sincos ZAA [3‐1]

By calculating the incident angle we can determine the optimum solar collector position

relative to the sun.

The following are the steps that must be followed to determine the incident angle of the

sun in relation to a solar collector located at the University of Manitoba. For example

purposes, calculations will be done for each step of the process for the date of September

15th, 2007.

Step 1: Calculate D, the angle of declination.

The angle of declination, D, represents the amount by which the Earth’s north polar axis is

tilted towards the sun. This value varies on a daily basis and can be approximated by the

following equation:

)284(

365

360sin45.23 nD [3‐2]

Where:

n = the nth day of the year

Step 2: Calculate H, the hour angle.

The hour angle, H, expresses the time of day in which one 24‐hour day is represented as

360 degrees of angle.



tH 15 [3‐3]

Where:

t = the time in hours (decimally) from solar noon

Step 3: Calculate A, the angle of elevation of the sun.

The angle of elevation of the sun above the eco‐village can be calculated, on an hourly

basis, by the following equation:

))(sin(sin))(cos)(cos(cossin LDLHDA [3‐4]

Where:

D = the declination angle, calculated above.

H = the hour angle, calculated above.

L = the latitude of the collector site.

The angle of elevation will be positive above the horizon and negative below the horizon.

Step 4: Calculate Z, the azimuth angle of the sun.

The azimuth angle of the sun, Z, can be calculated as follows:

A

HDZ

cos

sincossin

[3‐5]

Where:

D = the declination angle, calculated above.

H = the hour angle, calculated above.

A = the angle of elevation of the sun, calculated above.

The azimuth angle will be positive to the east and negative to the west, if measured from

the south.



Step 5: Determine the optimum tilt angle of the plane, Σ, and the optimum

direction of the angle of tilt, Φ, to maximize the incident angle, θ.

In order to maximize the amount of solar irradiance we want to get the incident angle

between the sun's rays and the normal to the plane surface of the collector to as close to

zero as possible.

Using equation [3‐1], where )])[cos()(sin(cos))(cos(sincos ZAA , we can see

that, in order to make equal to zero, we must set cos equal to 1. By setting cos

equal to 1, the solver function in Excel can be used to optimize Σ, the tilt angle of the

plane, and Φ, the direction of the angle of tilt.

3.2.2 Calculations

The following computations use the methodology

outlined in section 3.2.1 to optimize Σ, the tilt

angle of the plane, and Φ, the direction of the

angle of tilt, for September 15th, 2007.

Complete, tabulated data is available in

Appendix C for the 1st of every month from

January 2007 to December 2007.

Step 1: Calculate D, the angle of declination.

September 15th, 2007 is the 258th day of the year,

therefore 258n .

Using equation [3‐2],

)]25.365

258284(2[45.23

D

3616.23D [degrees]

Table 1: Hour Angle ‐ Sept 15/07

Hour t H

12:00 AM 10.60 159.00

1:00 AM 11.60 174.00

2:00 AM 12.60 189.00

3:00 AM 13.60 204.00

4:00 AM 14.60 219.00

5:00 AM 15.60 234.00

6:00 AM 16.60 249.00

7:00 AM 17.60 264.00

8:00 AM 18.60 279.00

9:00 AM 19.60 294.00

10:00AM 20.60 309.00

11:00AM 21.60 324.00

12:00 PM 22.60 339.00

1:00 PM 23.60 354.00

2:00 PM 0.60 9.00

3:00 PM 1.60 24.00

4:00 PM 2.60 39.00

5:00 PM 3.60 54.00

6:00 PM 4.60 69.00

7:00 PM 5.60 84.00

8:00 PM 6.60 99.00

9:00 PM 7.60 114.00

10:00 PM 8.60 129.00

11:00 PM 9.60 144.00



Step 2: Calculate H, the hour angle.

On September 15th, 2007, solar noon occurred at 1:24 pm [7]. Using equation [3‐3], the

hour angle can be calculated. The table to the on the previous page shows the values of

the hour angle, in degrees, for each hour of the 24‐hour clock for September 15th, 2007.

Step 3: Calculate A, the angle of elevation of the sun.

From Table 1, the latitude of the eco‐village is 49.81° N.

By substituting values for D, H, and L into equation [3‐4] we can obtain a numerical result

for sinA, and thus are able to calculate the angle of elevation of the sun above the eco‐

village, A for September 15th, 2007. The following table shows these results:

Hour sinA A

12:00 AM ‐0.57 ‐34.92

1:00 AM ‐0.61 ‐37.72

2:00 AM ‐0.61 ‐37.40

3:00 AM ‐0.56 ‐34.02

4:00 AM ‐0.47 ‐28.14

5:00 AM ‐0.35 ‐20.46

6:00 AM ‐0.20 ‐11.63

7:00 AM ‐0.04 ‐2.17

8:00 AM 0.13 7.49

9:00 AM 0.29 16.97

10:00 AM 0.44 25.81

11:00 AM 0.55 33.45

12:00 PM 0.63 39.17

1:00 PM 0.67 42.13

2:00 PM 0.67 41.79

3:00 PM 0.62 38.22

4:00 PM 0.53 32.05

5:00 PM 0.41 24.12

6:00 PM 0.26 15.11

7:00 PM 0.10 5.56

8:00 PM ‐0.07 ‐4.09

9:00 PM ‐0.23 ‐13.46

10:00 PM ‐0.38 ‐22.10

11:00 PM ‐0.49 ‐29.48

12:00 AM ‐0.57 ‐34.92

Table 2: Angle of Elevation of the Sun above the Eco‐Village ‐ Sept 15/07



The graph shown on the following page shows how the sun rises and falls during the 24‐

hour period of September 15th, 2007. Sunrise occurs when the angle of elevation of the

sun crosses the zero axes from a negative value to a positive one. Likewise, sunset occurs

when the angle of elevation of the sun crosses the zero axes from a positive value to a

negative value.

Figure 12: Angle of Elevation of the Sun ‐ Sept 15/07



Step 4: Calculate Z, the azimuth angle of the sun.

By substituting values for D, H, and A into equation [3‐5] we can obtain a numerical result

for sinZ, and thus are able to calculate the azimuth angle of the sun, Z, for September 15th,

2007.

The table below shows these results.

Table 3: Azimuth Angle of the Sun ‐ Sept 15/07

Hour sinZ Z

12:00 AM ‐0.44 ‐25.90

1:00 AM ‐0.13 ‐7.59

2:00 AM 0.20 11.35

3:00 AM 0.49 29.37

4:00 AM 0.71 45.49

5:00 AM 0.86 59.63

6:00 AM 0.95 72.26

7:00 AM 0.99 83.98

8:00 AM 1.00 84.53

9:00 AM 0.99 81.89

10:00 AM 0.86 59.61

11:00 AM 0.70 44.75

12:00 PM 0.46 27.51

1:00 PM 0.14 8.10

2:00 PM ‐0.21 ‐12.10

3:00 PM ‐0.52 ‐31.15

4:00 PM ‐0.74 ‐47.90

5:00 PM ‐0.89 ‐62.34

6:00 PM ‐0.99 ‐81.89

7:00 PM ‐1.00 ‐86.84

8:00 PM ‐0.99 ‐81.68

9:00 PM ‐0.94 ‐69.82

10:00 PM ‐0.84 ‐56.95

11:00 PM ‐0.67 ‐42.43

12:00 AM ‐0.44 ‐25.90



Figure 13: Azimuth Angle of the Sun ‐ Sept 15/07

The graph shown above shows the oscillation of the azimuth angle of the sun for a 24‐

hour period on September 15th, 2007. It can be seen that the azimuth angle is at a

maximum to the east at sunrise, as the sun rises from the east. Likewise, the azimuth

angle is at a maximum to the west at sunset, as the sun sets to the west.

Step 5: Determine the optimum tilt angle of the plane, Σ, and the optimum

direction of the angle of tilt, Φ, to maximize the incident angle, θ.

Using equation [3‐1], the values for A, the angle of elevation of the sun, and Z, the

azimuth angle of the sun, which were calculated above, and the solver function in

Microsoft Excel, it was possible to determine optimum values for the tilt angle of the

plane, Σ, and the direction of the angle of tilt, Φ. The optimum values for Σ and Φ for

September 15th, 2007 are shown in the table on the following page.



Hour Opt Σ Opt φ Max cosθ Max θ

12:00 AM 124.92 ‐25.90 1.00 0.00

1:00 AM 127.72 ‐7.59 1.00 0.00

2:00 AM 127.40 11.35 1.00 0.00

3:00 AM 124.02 29.37 1.00 0.00

4:00 AM 118.14 45.49 1.00 0.00

5:00 AM 110.46 59.63 1.00 0.00

6:00 AM 101.63 72.26 1.00 0.00

7:00 AM 92.17 83.98 1.00 0.00

8:00 AM 82.51 84.53 1.00 0.00

9:00 AM 73.03 81.89 1.00 0.00

10:00 AM 64.19 59.61 1.00 0.00

11:00 AM 56.55 44.75 1.00 0.00

12:00 PM 50.83 27.51 1.00 0.00

1:00 PM 47.87 8.10 1.00 0.00

2:00 PM 48.21 ‐12.10 1.00 0.00

3:00 PM 51.78 ‐31.15 1.00 0.00

4:00 PM 57.95 ‐47.90 1.00 0.00

5:00 PM 65.88 ‐62.34 1.00 0.00

6:00 PM 74.89 ‐81.89 1.00 0.00

7:00 PM 84.44 ‐86.84 1.00 0.00

8:00 PM 94.09 ‐81.68 1.00 0.00

9:00 PM 103.46 ‐69.82 1.00 0.00

10:00 PM 112.10 ‐56.95 1.00 0.00

11:00 PM 119.48 ‐42.43 1.00 0.00

Table 3.4 – Optimizing the Tilt Angle and Direction of the Tilt Angle of the Evacuated Tube Collector on the “Eco‐Village”

If we were to plot the curves of the optimum tilt angle and the direction of the tilt angle

as the day progressed, we would see curves similar to the ones plotted on the following

page for September 15th, 2007.

The first plot shows the variation in optimum tilt angle. Please note that this graph only

shows the values of the tilt angle that are equal to or less than 90°. An angle greater than

90° occurs when the sun is below the horizon; a time when irradiance levels are zero.

The second plot shown is that of the change in the optimum direction of the angle of tilt

as the day progresses. It can be seen from the plot that the optimum tilt direction is 0°;

the time at which the optimum direction of the collector is to face directly south.



Figure 3.4 – Optimum Tilt Angle: Sept 15/07

Figure 3.5 – Optimum Direction of the Tilt Angle: Sept 15/07

Determining the most beneficial, constant tilt angle for the evacuated tube collector

however is not as simple. The optimization of this constant angle will be discussed to

further depth in the following section.



3.3 Solar Irradiance

The following section discusses the methodology for calculating the solar irradiance

directed upon a collector installed at the “eco‐village”. Sample calculations for September

15th, 2007 are also included.

3.3.1 Methodology

The amount of solar irradiance that reaches either the installed evacuated collector or the

proposed flat plate collector throughout the day is related to the incident angle of the

collector, θ. The incident angle of the collector is the angle that a direct beam of light

from the sun makes with the line normal to the plane of the collector, as seen in Figure

3.1.

As discussed in Section 3.2, in order to receive optimum solar radiation on the plane of

the collector, this angle should be set as close to zero as possible. However, due to the

fact that the sun is not a stationary object and rises and falls throughout the day, it is not

possible to keep this angle constantly at zero unless a pivoting solar collector was

probable, which is not the case. Thus, in order to optimize the amount of radiation

received by the collector, we must determine the tilt angle that accumulates the most

incident rays onto the plate throughout the day.

The following two formulas are utilized in the proceeding section to determine the best

tilt angle for the evacuated tube collectors. The first equation that we will use is Equation

[3‐1],

)])[cos()(sin(cos))(cos(sincos ZAA [3‐1]

In this equation A and Z are known values. The direction of the tilt angle, Φ, will be set to

0°, as discussed in Section 3.2.2. This leaves us with two variables, Σ, the tilt angle of the

plane, and θ, the incidence angle of the collector.



The second formula utilized relates the daily solar radiation values for Winnipeg to the

incidence angle of the collector [6]. This equation allows us to determine the irradiance

upon the collector as it varies throughout the day.

cosNb II [3‐6]

Where:

bI = the direct radiation received by the collector

NI = the normal terrestrial solar radiation received at ground level

Values for NI can be obtained from RETScreen. The RETScreen data for Winnipeg

International Airport is included in Appendix B.

3.3.2 Calculations The evacuated tube collector that is currently installed on the “eco‐village” is mounted so

that it faces directly south and has a tilt angle of 45°. Therefore, Σ = 45° and Φ = 0°. From

the RETScreen data in Appendix B we can see that, for the month of September, the daily

solar radiation, NI , is 3.61 kWh/m²/d or 0.300833 kWh/m²/h. Using Equations [3‐1] and

[3‐6] with the values of Σ, Φ, and NI noted above and the values of A and Z as calculated

in the previous sections, a curve of the direct radiation received by the collector, bI ,

throughout the day can be plotted for September 15th, 2007. This plot can be seen on

page 27.



Hour A Z Σ φ cosθ θ In

[kWh/m²/h] Ib

[kWh/m²/h]

12:00 AM ‐34.92 ‐25.90 45.00 0 0.116774 83.29406 0 0

1:00 AM ‐37.72 ‐7.59 45.00 0 0.12188 82.99939 0 0

2:00 AM ‐37.40 11.35 45.00 0 0.121307 83.03244 0 0

3:00 AM ‐34.02 29.37 45.00 0 0.115095 83.39089 0 0

4:00 AM ‐28.14 45.49 45.00 0 0.103666 84.04967 0 0

5:00 AM ‐20.46 59.63 45.00 0 0.0878 84.96296 0 0

6:00 AM ‐11.63 72.26 45.00 0 0.068577 86.06774 0 0

7:00 AM ‐2.17 83.98 45.00 0 0.047307 87.28847 0 0

8:00 AM 7.49 84.53 45.00 0 0.15901 80.85058 0.300833 0.05

9:00 AM 16.97 81.89 45.00 0 0.301765 72.43636 0.300833 0.09

10:00 AM 25.81 59.61 45.00 0 0.629878 50.95885 0.300833 0.19

11:00 AM 33.45 44.75 45.00 0 0.808808 36.02035 0.300833 0.24

12:00 PM 39.17 27.51 45.00 0 0.93284 21.11805 0.300833 0.28

1:00 PM 42.13 8.10 45.00 0 0.993521 6.525449 0.300833 0.30

2:00 PM 41.79 ‐12.10 45.00 0 0.986717 9.349024 0.300833 0.30

3:00 PM 38.22 ‐31.15 45.00 0 0.912891 24.09208 0.300833 0.27

4:00 PM 32.05 ‐47.90 45.00 0 0.777073 39.00663 0.300833 0.23

5:00 PM 24.12 ‐62.34 45.00 0 0.58852 53.94791 0.300833 0.18

6:00 PM 15.11 ‐81.89 45.00 0 0.280605 73.70371 0.300833 0.08

7:00 PM 5.56 ‐86.84 45.00 0 0.107324 83.8389 0.300833 0.03

8:00 PM ‐4.09 ‐81.68 45.00 0 0.051657 87.03896 0 0

9:00 PM ‐13.46 ‐69.82 45.00 0 0.07263 85.83495 0 0

10:00 PM ‐22.10 ‐56.95 45.00 0 0.09128 84.76275 0 0

11:00 PM ‐29.48 ‐42.43 45.00 0 0.106337 83.89582 0 0

Table 4: Direct Radiation Received by the Collector ‐ Sept 15/07



The plot below shows how the incident radiation upon the evacuated tube collector

increase as the day moves towards mid‐day, then falls again as the afternoon progresses.

Figure 14: Direct Radiation Received with a Tilt Angle of 45° ‐ Sept 15/07

One of the aims of this thesis was to determine the optimum tilt angle; the angle in which

the most irradiance would be collected by the evacuated tube collector throughout the

period of one day. In order to compare the potentials of different tilt angles, the above

calculations were done while varying the tilt angle, Σ. As with the example above, the

direction of tilt, Φ, was set to 0°.

The plot on the following page shows the direct radiation received by the evacuated tube

collector, bI , as the day of September 15th, 2007 progresses for tilt angles of 5°, 15°, 25°,

35°, 45°, 55° and 65°. From this it can be concluded that the optimum tilt angle is 50°,

however any tilt value in the range of 45° to 55° would produce optimal results.



Figure 15: Varying Degrees of Tilt Angle

Figure 16: Comparison of 40° ‐ 50° Tilt Angles



3.4 Chapter Summary Analysis on the location of the sun with regards to the evacuated tube collector currently

installed on the “eco‐village” has allowed me to determine the optimum mounting

location for an evacuated tube or flat plate collector.

The following table summarizes these results:

Location Flat, horizontal surface, such as a roof top or an empty field.

Tilt Angle, Σ 50°

Direction of Tilt Angle, Φ 0° (South Facing)

Table 5: Summary of Location Results



4 HEAT TRANSFER ANALYSIS

The following section examines the transfer of heat through the Apricus evacuated tube

collector and the EnerWorks flat‐plate collector. A heat transfer model is created for each

collector and the overall efficiencies of the individual collectors are determined.

4.1 Evacuated Tube Collector Efficiency

The proceeding section discusses and outlines the methodology used to calculate the

working efficiency of the Apricus evacuated tube collector that is installed at the “eco‐

village” at the University of Manitoba. In order for these calculations to be accurately

applied, the necessary data must be acquired from the solar collector system, through the

use of data acquisition equipment.

4.1.1 Methodology

Figure 17 below shows a schematic of a single evacuated tube, comparable to one of the

tubes used in the collector currently mounted at the “eco‐village”. This tube consists of

an outer glass cover which acts as an envelope around a fin plate, which is selectively

coated and attached to a heat pipe absorber. The energy obtained from the solar

radiation incident on the collector travels as heat and is transferred from the heat pipe

evaporator fluid to the heat pipe condenser, and finally to the fluid flowing through the

manifold.

Figure 17: "Eco‐Village" Collector Schematic



The heat flow through the evacuated tube to the manifold can be modeled as a thermal

circuit. This model allows us to simplify the system for use in the following calculations.

Shown below is the thermal circuit equivalent of an evacuated tube [8], as seen in the

“eco‐village” solar collector.

Figure 18: Equivalent Thermal Circuit

In the above diagram the nomenclature is as follows:

icA , = collector tube inner diameter times collector length

ocA , = collector tube outer diameter times collector length

ihA , = heat pipe inner diameter times collector length

ohA , = heat pipe outer diameter times collector length

och , = heat transfer coefficient of the outer surface of the collector tube

hmh = heat transfer coefficient between the heat pipe fluid and the manifold

fluid

aT = ambient air temperature

cT = mean temperature of the collector tube

hT = mean temperature of the heat pipe

ifT , = temperature of the fluid in the manifold before heating occurs

effI = the effective solar radiation on the collector

LQ.

= thermal energy lost to the environment

hmQ.

= thermal energy transferred from the heat pipe fluid to the manifold fluid



LU = the overall heat loss coefficient

= the product of the absorptivity and transmitivity of the glass tube

Assuming steady‐state conditions, Norton (1992) and Tiwari (2002) describe the rate of

useful energy produced by the evacuated tube collector, in Watts, as:

)]()[(,

.

afiLeffocru TTUIAFQ [4‐1]

Where:

rF , the flow rate factor, is equal to:

)1()(

1

,

,

ph

L

ohhm

ocLr

h

U

Ah

AUF [4‐2]

And,

phh = heat transfer coefficient between the fin plate and the heat transfer

pipe Once the rate of useful thermal energy is determined, the efficiency of the evacuated

tube collector can be calculated as:

oceff

u

AI

Q

,

.

[4‐3]

The following outline the steps taken to calculate the efficiency of the evacuated tube

collector installed at the “eco‐village”:

Step 1: Calculate hc,o, the heat transfer coefficient of the outer surface of the

collector tube.

The heat transfer coefficient of the collector tube can be calculated as:



ihoc

acaccoc AA

TTTTVh

,,

22

,

))((8.37.5

[4‐4]

Where:

c = emissivity of the glass collector tube

= Stefan‐Boltzmann constant = 5.67 x 10‐8 W/m²∙K4

V = mean velocity of the air flowing over the evacuated tube collector

Step 2: Calculate hc,i, the heat transfer coefficient of the evacuated envelope

(inner surface of the collector tube).

The heat transfer coefficient of the inner surface of the collector tube can be calculated

as:

)ln(2 ,

,,,

ic

ocoh

cic

DDDk

h [4‐5]

Where:

ocD , = outer diameter of the collector tube

icD , = inner diameter of the collector tube

ohD , = outer diameter of the heat transfer pipe

ck = thermal conductivity of the glass collector tube

Step 3: Calculate hh,o, the heat transfer coefficient of the outer surface of the heat

transfer pipe.

The heat transfer coefficient of the outer surface of the heat transfer pipe can be

calculated as:

)()1(1)1(

))((

,

,

22

,

ic

ih

c

c

evach

h

chchoh

AA

F

TTTTh

[4‐6]

Where:

c = emissivity of the collector tube

h = emissivity of the heat transfer pipe



evacF = the shape factor between the selectively coated outer surface of the

heat pipe and the inner surface of the collector tube

Step 4: Determine the overall heat loss coefficient of the collector, LU .

The overall heat loss coefficient of the collector can be calculated as:

ocicoh

L

hhh

U

,,,

1111

[4‐7]

Where the heat transfer coefficients ohh , , ich , and och , were calculated in the previous

three steps.

Step 4: Calculate hhm, the heat transfer coefficient between the heat pipe

condenser and the fluid flowing through the manifold.

The heat transfer coefficient between the heat pipe condenser and the fluid flowing

through the manifold can be calculated as external flow over a cylinder in cross flow. This

heat transfer can be expressed as:

h

ocondD

hm k

DNuh , [4‐8]

Where:

ocondD , = outer diameter of the heat transfer condenser

hk = thermal conductivity of the copper condenser

DNu = Nusselt number of the fluid flowing through the manifold

In order to calculate DNu , the Nusselt number of the fluid flowing through the manifold,

we first need to calculate the Reynolds number of that fluid.



The Reynolds number, mRe , can be calculated as follows:

focond

fm D

m

,

4Re

[4‐9]

Where:

fm

= the flow rate of the fluid through the manifold

f = dynamic viscosity of the fluid within the heat pipe

Once the Reynolds number of the heat transfer fluid within the manifold has been

determined, the value can be substituted into the following Churchill and Bernstein [15]

correlation for a cylinder in cross flow:

5/48/5

4/13/2

3/12/1

282000

Re1

]Pr)/4.0(1[

PrRe62.03.0

DmD

DNu [4‐10]

Where:

mPr = Prandtl number of the heat transfer fluid in the manifold

Substituting the value for the average Nusselt number obtained by the above correlation

into equation [4‐8], the heat transfer coefficient between the heat pipe condenser and

the heat transfer fluid flowing through the manifold can be calculated.

Step 5: Calculate phh , the heat transfer coefficient between the fin plate and the

heat transfer pipe fluid. Flow between the fin plate and the heat transfer pipe fluid can be considered as flow over

a flat plate. This flow will be assumed to be laminar.

The first step to calculating this value is to determine the Reynolds number of the liquid

within the heat transfer pipe.



This can be done by using the following relations:

LU

pRe [4‐11]

Where:

U = the velocity of the liquid within the heat transfer pipe

L = the length of the heat transfer pipe

= the kinematic viscosity of the liquid in the heat transfer pipe.

Please note that since the velocity of the liquid within the heat transfer pipe, in this case

purified water, is not known, we will assume it to be very small (~0.0001 m/s).

Once the Reynolds number has been determined, the following relation can be used to

find the heat transfer coefficient between the fin and the heat transfer pipe.

L

kh finpp

ph

3/12/1 PrRe664.0 [4‐12]

Where:

pPr = the Prandtl number of the fluid within the heat transfer pipe

fink = the thermal conductivity of the fin plate

Step 6: Calculate rF , the flow rate factor of the evacuated tube collector.

Using equation [4‐2], as shown below, and the values calculated above for LU , hmh , and

phh , the flow rate factor of the evacuated tube collector can be calculated.

)1()(

1

,

,

ph

L

ohhm

ocLr

h

U

Ah

AUF [4‐2]



Step 7: Calculate

Q , the rate of useful energy produced by the collector.

Using equation [4‐1], as shown below, and the values calculated above for rF and LU ,

the rate of useful energy produced by the evacuated tube collector can be calculated.

)]()[(,

.

afiLeffocru TTUIAFQ [4‐1]

Step 8: Calculate , the instantaneous efficiency of the evacuated tube collector.

Using equation [4‐3], as shown below, and the value of uQ

calculated in step 7, the

instantaneous efficiency of the evacuated tube can be calculated.

oceff

u

AI

Q

,

.

[4‐3]

The eight steps described in the preceding section can be used to calculate the

instantaneous efficiency of the Apricus evacuated tube solar water collector that is

currently installed at the University of Manitoba’s “eco‐village”. As an alternative to

manually calculating each step of the sequence, a Microsoft Excel spreadsheet has been

derived which calculates the instantaneous efficiency of the Apricus evacuated tube

collector based on the variable input parameters of the solar collector system (mass flow

rate, wind velocity, collector temperature, ambient air temperature and manifold fluid

temperature). This program can be found in the disk attached to the appendix of this

thesis report.



4.1.2 Calculations As previously mentioned, a Microsoft Excel spreadsheet was created to calculate the

instantaneous efficiency of the Apricus evacuated tube collector. This spreadsheet takes

seven variable parameter inputs and, along with the known collector and heat transfer

fluid parameters, calculates the efficiency of the Apricus evacuated tube collector.

The seven variable inputs necessary for the spreadsheet to calculate the efficiency are:

1. The temperature of the ambient air surrounding the collector, in degrees K.

2. The temperature of the heat transfer fluid entering the manifold, in degrees K.

3. The mean temperature of the collector tube, in degrees K.

4. The mean temperature of the heat pipe, in degrees K.

5. The mass flow rate, in kg/s, of the liquid within the heat pipe.

6. The velocity of the air flow over the collector, in m/s.

7. The month of the year. A scroll down menu is available for the user to choose the

month of the year that the preceding three parameters were collected. Once the

month of the year is known, the spreadsheet can calculate the appropriate

incident radiation value received by the collector.

Unfortunately, since the data acquisition equipment necessary to log the required inputs

from the Apricus evacuated tube collector have not been received at the “eco‐village” at

this time, no data readings were available for the input values in order to run a test of the

program. In lieu of entering obtained data as the input values, a theoretical calculation

will be applied to test to efficiency calculator program.

For this theoretical calculation, the following input parameters will be used:

1. aT = 293 K = 20 °C 5.

m = 0.0001 kg/s

2. fT = 288 K = 15 °C 6. V = 0. 1 m/s

3. tubeT = 298 K = 25 °C 7. Month of the Year = September

4. pipeT = 303 K = 30 °C



The image below shows the results of this calculation using the excel spreadsheet:

Apricus Evacuated Tube Collector Efficiency Calculator

Required Inputs: Ambient Air Temperature: 293 [K]

Temperature of Fluid flowing into the Manifold: 288 [K]

Mean Temperature of the Collector Tube: 298 [K]

Mean Temperature of the Heat Transfer Pipe: 303 [K]

Air Flow Velocity over the Collector: 0.1 [m/s]

Flow Rate of Heat Transfer Fluid in the Heat Pipe: 0.0001 [kg/s]

Month of the Year: September

Known Collector Parameters:

Collector Tube Length: 1.8000 [m]

Heat Pipe Length: 1.8000 [m]

Collector Tube Outer Diameter: 0.0580 [m]

Collector Tube Inner Diameter: 0.0480 [m]

Heat Pipe Outer Diameter: 0.0080 [m]

Heat Pipe Inner Diameter: 0.0073 [m]

Condenser Outer Diameter: 0.0200 [m]

Shape Factor between Heat Pipe and Collector Surfaces: 0.5000

Emissivity of the Glass Collector Tube: 0.9250

Emissivity of the Copper Heat Transfer Pipe: 0.0500

Stefan‐Boltzmann Constant: 5.67E‐08 [W/m²∙K^4]

Thermal Conductivity of the Copper Fin Plate: 4.01E+02 [W/m‐K]

Thermal Conductivity of the Condenser: 4.01E+02 [W/m‐K]

Thermal Conductivity of the Glass Collector Tube: 1.4 [W/m‐K]

Heat Transfer Fluid Kinematic Viscosity: 0.00813 [N∙s/m²]

Prandtl Number of Manifold Heat Transfer Fluid: 1.39615

Prandtl Number of Heat Pipe Fluid: 5.5

Effective Radiation Incident on Collector: 285.9 [W/m²]

Velocity of Liquid in the Heat Transfer Pipe: 0.001 [m/s]

Kinematic Viscosity of Liquid in the Heat Transfer Pipe: 8.33E‐07 [m²/s] Collector Absorptance: 0.94

Calculated Collector Parameters:

Collector Tube Outer Surface Area: 0.1044 [m²]

Collector Tube Inner Surface Area: 0.0864 [m²]

Heat Transfer Pipe Inner Surface Area: 0.0131 [m²]

Condenser Outer Surface Area: 0.0006 [m²]

Collector Tube Outer Surface Heat Transfer Coefficient: 1.4466 [W/m²·K] Collector Tube Inner Surface Heat Transfer Coefficient: 1849.4837 [W/m²·K]

Heat Transfer Pipe Outer Surface Heat Transfer Coefficient: 13222.1196 [W/m²·K] Collector Overall Heat Loss Coefficient: 1.4453 [W/m²∙°C]

Manifold Heat Transfer Fluid Reynolds Number: 0.7831

Manifold Heat Transfer Fluid Nusselt Number: 0.8604

Heat Transfer Coefficient Between Heat Pipe Condenser and Manifold Fluid: 4.2915E‐05 [W/m²·K] Reynolds Number of Fluid in the Heat Transfer Pipe: 2160.0864

Heat Transfer Coefficient Between Fin Plate and Heat Pipe Fluid: 12135.6508 [W/m²·K] Flow Rate Factor: 0.7899

Rate of Useful Energy from the Collector: 22.7572 [W]

Efficiency: 76.24 %

Figure 19: Evacuated Tube Efficiency Calculator



4.2 Flat‐Plate Collector Efficiency

The proceeding section follows the same general principles in describing the methodology

and calculations used to determine the working efficiency of the EnerWorks flat‐plate

collector, as were used to determine the working efficiency of the Apricus evacuated tube

collector. Variation, however, can be seen in the formulae utilized for the flat‐plate

collector from those used in analyzing the efficiency of the evacuated tube collector.

As mentioned in the previous section, the necessary data must be acquired for the flat‐

plate system before any calculations can be carried out.

4.2.1 Methodology

Assuming steady‐state conditions and pump forced flow, Norton (1992) and Tiwari (2002)

describe the rate of useful energy from the collector, in Watts, as:

)]()[(.

afLeffcRu TTUIAFQ [4‐10]

Where:

cA = flat plate collector area

RF , the collector heat removal factor, is equal to:

f

LC

Lc

fR

mC

FUA

UA

CmF

'

exp1 [4‐11]

'F , the collector efficiency factor, is equal to:

))(

()(

1'

FDWD

W

hD

WUF

L

[4‐12]



F, the fin efficiency, is equal to:

2/)]([

2/)](tanh[

DWm

DWmF

[4‐13]

k

Um L [4‐14]

In which,

W = distance between centre of two tubes

D = outer diameter of the tube

k = thermal conductivity of the tube

δ = thickness of the tube

h = convective heat transfer coefficient from the inner tube to the fluid

Once the rate of useful thermal energy is determined, the efficiency of the flat‐plate

collector can be calculated as:

ceff

u

AI

Q.

[4‐15]

Unlike with evacuated tube collectors, the overall heat loss coefficient of the flat‐plate

collector, UL, is a known value. Tiwari and Ghosal (2005) state that the value of the overall

heat transfer coefficient for a flat plate collector with a single glass cover at an inclination

angle, in an operating range of ambient to 70°C, can be considered as UL = 7.5 W/m² °C.

Therefore, the only variable left to calculate is h, the convective heat transfer coefficient

from the inner tube to the fluid. The steps needed to calculate this value are shown on

the next page.



Step 1: Determine DRe , the Reynolds number of the heat transfer fluid within

the tube.

The Reynolds number within the inner heat transfer tubes of the flat‐plate collector can

be determined using the following formula:

D

mD

4

Re [4‐16]

Where:

m = flow rate of the heat transfer fluid through the heat transfer tubes

= viscosity of the heat transfer fluid

Step 2: Determine the Nusselt number of the heat transfer fluid within the tube.

Fluid flow within the inner tubes of the flat‐plate collector can be described as laminar

internal flow. In a circular tube that is characterized by a uniform surface heat flux and

laminar, fully developed flow, the Nusselt number is a constant; it is independent of DRe ,

Pr, and axial location. Therefore,

36.4Nu [4‐17]

Step 3: Determine h, the convective heat transfer coefficient from the inner tube

to the heat transfer fluid.

The convective heat transfer coefficient from the inner tube to the heat transfer fluid can

be determined by combining equation [4‐17] and the following relation.

36.4k

hDNuD [4‐18]



Once the heat transfer coefficient between the inner tube and the heat transfer fluid has

been determine, the fin efficiency, collector efficiency factor, and collector heat removal

factor can be determined. This then allows for the rate of useful energy from the

collector to be calculated, by utilizing equation [4‐10], as shown.

)]()[(.

afLeffcRu TTUIAFQ [4‐10]

The instantaneous efficiency of the EnerWorks flat‐plate solar water collector can thus be

determined by applying equation [4‐15]:

ceff

u

AI

Q.

[4‐15]

As an alternative to manually calculating each step of the sequence, a Microsoft Excel

spreadsheet has been derived which calculates the instantaneous efficiency of the

EnerWorks flat‐plate collector based on the variable input parameters of the solar

collector system (mass flow rate, ambient air temperature, and heat transfer fluid

temperature). This program can be found in the disk attached to the appendix of this

thesis report.

4.2.2 Calculations As mentioned above, a Microsoft Excel spreadsheet was created to calculate the

instantaneous efficiency of the EnerWorks flat‐plate collector. This spread sheet takes

four variable parameter inputs and, along with the known collector and heat transfer fluid

parameters, calculates the instantaneous efficiency of the EnerWorks flat‐plate collector.

The four variable inputs necessary for the spreadsheet to calculate the efficiency are:

1. The temperature of the ambient air surrounding the collector, in degrees K.

2. The temperature of the heat transfer fluid entering the collector, in degrees K.

3. The mass flow rate, in kg/s, of the heat transfer fluid entering the collector.



4. The month of the year. A scroll down menu is available for the user to choose the

month of the year that the preceding three parameters were collected. Once the

month of the year is known, the spreadsheet can calculate the appropriate

incident radiation value received by the collector.

Unfortunately, since the EnerWorks flat‐plate collector and the necessary data acquisition

equipment, have not been received and installed at the “eco‐village” at this time, no data

readings were available for the input values in order to run a test of the program. In lieu

of entering obtained data as the input values, a theoretical calculation will be applied to

test to efficiency calculator program.

For this theoretical calculation, the following input parameters will be used:

1. aT = 293 K = 20 °C 3.

m = 0.0001 kg/s

2. fT = 288 K = 15 °C 4. Month of the Year = September

The image on the next page shows the results of this calculation using the excel

spreadsheet.



EnerWorks Flat-Plate Collector Efficiency Calculator

Required Inputs:

Mass Flow Rate of Heat Transfer Fluid: 0.0001 [kg/s]

Ambient Air Temperature: 293 [K]

Mean Heat Transfer Fluid Inlet Temperature: 288 [K]

Month of the Year: September

Known Collector Parameters:

Outer Diameter of Heat Transfer Tube: 0.01 [m]

Heat Transfer Tube Length: 2.445 [m]

Viscosity of Heat Transfer Fluid: 0.00813 [N∙s/m²]

Nusselt Number of the Heat Transfer Fluid: 4.36

Thermal Conductivity of the Heat Transfer Tube: 401 [W/m·K] Overall Collector Heat Loss Coefficient: 7.5 [W/m²∙°C]

Distance Between Centre of 2 Heat Transfer Tubes: 0.02 [m]

Thickness of Heat Transfer Tube: 0.001 [m]

Specific Heat of the Heat Transfer Fluid: 795 [J/kg·K] Effective Radiation Incident on the Collector: 285.9 [W/m²]

Collector Absorptance: 0.94

Calculated Collector Parameters:

Flat‐Plate Collector Area: 0.02445 [m²] Reynolds Number of the Heat Transfer Fluid: 1.5661

Heat Transfer Coefficient from the Inner Tube to the Fluid: 174836 [W/m²·K] Fin Efficiency: 0.9994

Collector Fin Efficiency: 0.9997

Collector Heat Removal Factor: 0.3903

Rate of Useful Energy from the Collector: 2.9226 [W]

Collector Efficiency: 41.8 %

Figure 20: Flat‐Plate Collector Efficiency Calculator

From the efficiency calculator output shown in Figure 20, it can be seen that, during the

month of September, if the ambient air surrounding the collector is at 25°C and the heat

transfer fluid flowing through the collector at a mass flow rate of 0.0001 kg/s is measured

to have a mean temperature of 45°C, the efficiency of the collector at that instant is

41.8%.



It should be noted that the heat transfer fluid used in the EnerWorks flat‐plate collector is

a 50:50 propylene glycol water solution. All heat transfer fluid properties used in the

efficiency calculator spreadsheet are for a 50:50 propylene glycol water solution.



5 ECONOMIC ANALYSIS

In order to determine the energy potential of installing solar collectors on campus, an

economic analysis must be undertaken. This analysis will look at the cost of purchasing

and installing a system of solar collectors, the number of solar collectors needed to

substantially affect the current district heating system at the University of Manitoba, and

finally, the pay‐back period that installing a system of collectors would produce.

5.1 Background

The University of Manitoba’s powerhouse currently has 6 steam boilers in operation.

These boilers are mainly used for domestic hot water and reheat, with the distribution

being approximately as follows:

Figure 21: Distribution of Powerhouse Boiler Usage

Of the six boilers in operation at the powerhouse, boiler 5 and boiler 6 are summer

boilers, each with an operating capacity of 15,000 lbs of steam per hour. In order to look

at the potential of installing a system of solar collectors on campus, an analysis will be

undertaken in which the cost of replacing one of these boilers with solar energy will be

determined.



The following table summarizes the number of days boilers 5 and 6 were in operation in

2006, along with the quantity of steam produced each month [10].

Operating Days Boiler 5

Steam Produced [klbs]

Operating Days Boiler 6

Steam Produced [klbs]

JAN 0 0 0 0

FEB 0 0 0 0

MAR 0 0 0 0

APR 4 49 0 0

MAY 3 86 20 3129

JUN 2 246 2 246

JUL 21 4336 21 4336

AUG 31 7350 31 7350

SEP 9 2270 8 1954

OCT 7 511 8 574

NOV 0 0 0 0

DEC 0 0 0 0

TOTAL 77 14848 90 17589

Table 6: Days of Operation in 2006 ‐ Boilers 5 and 6

Both boilers 5 and 6 have an average operating efficiency of 81% and operate for roughly

the same amount of days per month [10]. For analysis sake, the following discussion will

determine the potential of replacing the heat obtained from boiler 5 with solar energy. By

taking the total pounds of steam produced by boiler 5 in August, as is the dominant

month for use of the boiler, it can be seen that the boiler produces, at most, 9879 lbs of

steam per hour during August.

The following shows the conversion used to obtain this value:

Convert to lbs/hour: hours

day

days

month

klbs

lbsklbs

24

1

31

110007350 = 9879 lbs/hour



5.2 Boiler Energy Analysis

In order to eliminate the use of boiler 5, the equivalent to 9879 lbs/hour of steam must be

able to be produced by a system of solar collectors. The following relation is used to

determine the amount of power, in KW, that this flow rate of steam produces:

3600es hm

Q

[5‐1]

Where:

sm

= steam flow rate (kg/h)

sh = specific enthalpy of evaporation of steam at working pressure (kJ/kg)

Q = heat transferred from the steam (kW)

Noting that 9879 lbs/hour is equivalent to 4481 kg/h, and that the specific enthalpy of

evaporation of steam at 100 psi (the working pressure) is 267.1 kJ/kg [11], we can see

that:

5.3323600

)1.267)(4481(Q kW

Therefore, a system of collectors must be able to produce ~332.5 kW in order for boiler 5

to be eliminated from the district heating system.

5.3 Collector Energy Analysis

As the solar collectors have not yet been tested to determine their working efficiencies, all

energy analysis calculations will be done using the theoretical efficiency of the collectors,

as given on their respective product specification sheets.



These efficiencies are as follows:

Product Efficiency

Apricus Evacuated Tube Collector 0.717

EnerWorks Flat‐Plate Collector I

TT

I

TT aiai2)(0187.0)(014.4

7166.0

Table 7: Theoretical Collector Efficiencies

The Solar Rating & Certification Corporation (SRCC) breaks the different heating

applications into the following categories:

(T inlet – T ambient) Heating Application

A ‐5 °C Pool heating in warm climate.

B 5 °C Pool heating in cool climate.

C 20 °C Water heating in warm climate.

D 50 °C Water heating in cool climate.

E 90 °C Industrial process water heating.

Table 8: SRCC Heating Applications

During the summer months, when boiler 5 is operational, the climate in Winnipeg can be

described as warm. Therefore, in order to determine the efficiency of the EnerWorks Flat‐

Plate collector, )( ai TT will be set to 20 °C.

From the RETScreen data for Winnipeg International Airport, provided in Appendix B, the

daily solar radiation, in W/m² can be calculated based on the average monthly hours of

sunlight. These values can be seen in Table 9.



Month Daily Solar Radiation

[kWh/m²/d] Average Monthly Hours of Sunlight

[W/m²]

JAN 1.39 8.75 158.9

FEB 2.39 10.15 235.5

MAR 3.75 12 312.5

APR 4.97 13.75 361.5

MAY 5.78 15.375 375.9

JUN 6.17 16.125 382.6

JUL 6.33 15.75 401.9

AUG 5.28 14.375 367.3

SEP 3.61 12.625 285.9

OCT 2.19 10.75 203.7

NOV 1.31 9.125 143.6

DEC 1.03 8.251 124.8

ANNUAL 3.69 12.25 301.2

Table 9: Solar Radiation Values

For the month of August, in which boiler 5 is most prominently used, it can be seen that

the daily solar radiation value is 367.3 W/m².

In order to estimate the theoretical efficiency of the EnerWorks solar collector during

August, I, the solar irradiance incident upon the collector, will be set as 367.3 W/m². The

efficiency can be calculated as:

I

TT

I

TT aiai2)(0187.0)(014.4

7166.0

3.367

)20(0187.0

3.367

)20(014.47166.0

2

4776.0



The following table summarizes the number of solar collectors needed to obtain enough

heat energy from solar radiation to eliminate the use of boiler 5.

Collector Solar

Radiation for August [W/m²]

Efficiency

Solar Energy Converted to Heat Energy [W/m²]

Collector Absorber Area [m²]

Solar Energy Converted to Heat Energy

[W]

Number of Collectors Needed to Produce 332.5

kW of Heat

Apricus Evacuated Tube Collector

367.3 0.7166 263.207 2.400 631.697 418

EnerWorks Flat‐Plate Collector

367.3 0.4776 175.422 2.691 472.062 560

Table 10: Quantity of Collectors Needed

As Table 10 shows, 418 evacuated tube collectors, or 560 flat‐plate collectors, would need

to be installed by the University of Manitoba in order for the powerhouse to eliminate the

use of boiler 5.

To put this value into perspective, the area required to house these collectors can be

calculated. Table 11 shows a brief calculation of the area needed to house these

theoretical solar collector systems. Please note that the area of a standard Canadian

football field is approximately equal to 1 acre.

Collector Number of Collectors Needed

Area of Land Needed per Collector [m²]

Total Area of Land Needed for

Collector System [m²]

Total Area of Land Needed for Collector

System [acres]

Equivalent Number of Football Fields


418 4.348 1817.464 0.449 ~0.45


560 2.873 1608.880 0.398 ~0.4

Table 11: Collector Area Needed

From this calculation it can be seen that, if you were to take an area of land approximately

the size of approximately half of a football field and fill it with side by side evacuated tube

solar collectors, enough energy would be accumulated to eliminate the use of boiler 5.

This land may seem like a slightly large area to put aside solely for use by solar collectors,

however it is not unreasonable.



The University of Manitoba recently purchased the land on which the Southwood Golf and

Country Club resides. This facility is located adjacent to the University of Manitoba and

consists of roughly 120 acres of land, 240 times the area needed to house the solar

collectors; land that could easily be home to a system of solar collectors.

5.4 Cost Analysis

A brief cost analysis will be carried out to determine if there is any financial benefit for the

university to install a system of solar collectors to replace boiler 5. This cost analysis will

compare the cost of purchasing the solar collectors to the cost of running boiler 5. As this

is a simplified cost analysis estimate, factors such as installation and maintenance costs

are not included in the calculation.

Carbon Finance Intel, a Canadian company which trades greenhouse gasses financial

incentives for both Canadian and international customers, states the current trading

prices of C02 reduction as ~ €22 per tonne of CO2 (stated 28 Nov 2007 [17]). This value

converts to approximately $32.40 CAD per tonne of CO2.

In order to determine the financial incentive the University of Manitoba would obtain by

reducing their CO2 emissions, it must be determined how much CO2 boiler 5 releases

during the month of august. Boiler 5 was in use for 31 days during august 2006 and

produced a total of 247,380 kWh’s of energy (332.5 kW x 31 days x 24 hours/day). As the

boiler is only 81% efficient, 305,407.4 kWh’s of energy from natural gas were used by the

boiler to produce this steam output. For every kWh of energy from a greenhouse gas that

is consumed, 0.21 kg’s of CO2 are released into the atmosphere. This means that boiler 5

released approximately 64,135.6 kg’s (64.14 tonnes) of CO2 into the surroundings during

its operating period. Based on the current trading values of CO2 ($32.40 CAD per tonne

CO2), the university would receive an incentive of approximately $2,078.14 during the

month of august if boiler 5 was replaced with solar energy. Over the course of one year



this reimbursement would equal $24,937.68. This financial incentive will be taken into

consideration in the following cost analysis.



Cost Per Collector [$] 2425.00 1750.00

Number of Collectors Needed

418 560

Amount of Energy Produced [kW]

332.5 332.5

Total Cost of Solar Collector System [$]

1,013,650.00 980,000.00

Cost of Boiler 5 Operation [$]

87,957 87,957

Carbon Dioxide Reduction Incentive

[S] 24,938 24,938

Annual Energy Savings

112,895 112,895

Simple Payback 9.0 years 8.7 years

Table 12: Cost to Substitute Boiler 5 with Solar Energy

The values in Table 12 were determined as follows:

1. Cost per collector: Estimate quoted by Apricus and EnerWorks reference collector

specifications.

2. Number of collectors needed: Calculated in Table 10.

3. Total cost of solar collector systems: Cost per collector x number of collectors

needed.

4. Cost of Boiler 5 Operation: Calculated based on an average natural gas price in

Winnipeg of $0.024/kWh. Boiler 5 used 305,407.4 kWh’s during august 2006, at a

cost of $7329.78. Over the course of one year this would equal $87,957.36.

5. Carbon dioxide reduction incentive: As discussed above.



6. Annual Energy Savings: Equivalent to the cost of operating boiler 5 plus the CO2

reduction incentive received by the university.

7. Simple payback: The cost to purchase the system divided by the annual energy

savings, in years.

From the results shown in Table 12, it can be seen that installing a system of solar

collectors on campus to replace the use of boiler 5 is financially feasible. This conclusion

is made for two reasons:

1) The average life span of a solar collectors averages around 20 – 30 years, making

the simple payback period of purchasing the solar collectors shorter than the life

of the collectors themselves. This would mean that the university would finish

paying off the purchasing cost of the collectors before their life span had ended,

allowing the university to actually make a profit out of the use of solar collectors

over natural gas steam boilers.

2) Other financial benefits for installing a system of solar collectors exist, beyond that

of the CO2 reduction incentive. Federal government incentives, such as the

Renewable Energy Deployment Initiative (REDI). REDI provides funds for up to

25% of the purchase and installation cost of a system of collectors by a business or

institution, up to a maximum value of $80,000. If the full spectrum of available

government incentives is utilized in the installation of solar collectors on campus,

the simple payback period will drop even further, creating more revenue for the

university.

Installing 418 evacuated tube collectors or 560 flat‐plate collectors on campus is a large

risk for the university as no solar collector system is currently set up to test the results

with. It is good, in this case, to look into the advantages of installing a smaller system of

collectors on campus. Would the results, both financial and environmental, be the same?



The same analysis was carried out for a system of 100 solar collectors; both the Apricus

evacuated tube collector and the EnerWorks flat‐plate collector. The results of this

analysis are contained in Table 13.



Cost Per Collector [$] 2425.00 1750.00

Number of Collectors 100 100

Total Cost of Solar Collector System [$]

242,500.00 175,000.00

Average Annual Solar Radiation [kWh/m²/d]

3.690 3.690

Average Annual Solar Radiation [kW/m²]

0.301 0.301

Collector Absorber Area [m²]

2.400 2.691

Average Annual Incident Radiation [kW]

0.723 0.811

Collector Efficiency 0.717 0.478

Amount of Energy Produced By One Collector

[kW] 0.518 0.387

Amount of Energy Produced By 100 Collectors [kW]

51.802 38.711

% of District Heating System Supplemented

4.296 3.210

Cost to Produce Equivalent Heat by District

Heating System [$] 10622.31 7937.92

Carbon Dioxide Prevented from Entering the

Atmosphere [tonnes] 92.95 69.46

Carbon Dioxide Reduction Incentive [S]

3011.58 2250.50

Annual Energy Savings $13,633.89 $10,188.42

Simple Payback 17.8 years 17.2 years

Table 13: Economic Analysis of a System of 10 Collectors



The results in Table 13 show the same type of results for the system of 100 solar

collectors to that of the larger quantity of collectors; however the simple payback period

is about double to length. It should be noted, however, that the results from Table 13

analyze a system of collectors over the course of one year and use the average annual

daily solar radiation, whereas the larger system of collectors used to replace boiler 5

looked specifically at the summer months, where more solar radiation is available.

5.5 Chapter Summary

This chapter examined the economic potential that installing a system of solar collectors

at the University of Manitoba would produce. An analysis was carried out to determine

how many solar collectors, either evacuated tube or flat‐plate, would be needed to

eliminate the use of one of the smaller, summer load boilers, and what the economic

value of installing this theoretical system would be. As the previous sections determined,

it is both environmentally and financially advantages to replace one of the boilers from

the university’s powerhouse with solar energy. The payback period that installing a

system of collectors induced would be much less than the lifespan of the collectors

themselves, creating both a large reduction in CO2 emissions and a long‐term profit for

the university.



6 DISCUSSION OF RESULTS

After analyzing the potential of installing solar collectors at the University of Manitoba’s

“eco‐village”, many distinctive results and debates arose. These results are discussed in

the following sections.

6.1 Benefits of Installing Solar Collectors

There are two ways to view the theoretical addition of a system of solar collectors to the

University of Manitoba campus. The first view and most obvious view would be to look at

the cost that installing a system of collectors ensues and compare it to the payback period

installing the system of collectors holds. From the results seen in Section 5.4, it is

apparent that the installation of a system of collectors on campus in economically

advantages for the university in the long run, and should be highly regarded as an energy

conservation method.

The second view in which to regard the installation of solar collectors on campus is from

an environmental standpoint. The use of steam boilers emits CO2 into the atmosphere,

adding to the Earth’s already highly increasing level of greenhouse gasses and global

warming. Solar energy, on the other hand, is a completely harm free, renewable energy

source. Yes, the price we pay for these collectors now may be significantly higher than

that of a steam boiler or natural gas, but what about 50 years from now? Somewhere

down the line, whether our generation or the next, someone will have to pay the price for

global warming and other easily preventable man‐made disasters. Many government

incentives now exist in which funding for some, if not most, of the cost of purchasing and

installing the collectors is provided. Incentives also exist for the reduction of CO2 from the

environment, with some emission trading markets stating exchange rates of up to $32.40

CAD per tonne of CO2 reduced from release into the atmosphere.



It may be completely unreasonable to convert the entire University of Manitoba’s heating

system to solar energy, but how much would it really take to convert 5, or even 10% of

the university’s annual heating use? We can see from the example in Section 5.4 that

substituting even 4% of the university’s district heating system from boilers to solar

energy would prevent around 93 tonnes of CO2 from being released into the atmosphere

per year, not to mention benefitting the University’s appeal and environmental

conformity from a green stance.

6.2 Possible Collector Locations

The following page shows a map of the University of Manitoba. Also shown in the image

is the Southwood Golf and Country Club. As mention previously, these 120 acres of land

were recently purchased by the University of Manitoba and will be acquired for use by the

University in 2010. In order to supplement around 4% of the district heating system,

approximately 400m² (~0.1 acres) of land would be needed. Of the 120 acres about to be

acquired by the university, it must certainly be possible to set aside a tenth of an acre for

solar collectors.

One could argue that that by designating a certain area of land for solar collectors, the

University would be losing potential land for agriculture. This is not necessarily the case.

The land underneath the collectors would still be cultivatable; it would just not receive as

much sunlight as a fully exposed area of land. However, there are many plants and crops

that do not need the sun to thrive. Fungi, such as mushrooms, do not need chlorophyll to

grow, and potatoes, once their dormancy is broken, can be fully harvested in a shaded

area. In addition, plants, such as hostas, astillbies, ferns, and impatients, will bloom to

fully potential in a shaded environment.



Figure 22: University of Manitoba Campus Map



In order to show just how little land is needed to significantly contribute to the University

of Manitoba’s district heating system with solar energy, the results from the previous

chapters have been used to estimate how much solar energy could be obtained from

installing solar collectors on the engineering and agriculture building’s rooftops.

The image below shows a hybrid map of the agriculture building and the engineering

building, on the left and the right of the view respectively.

Figure 23: Hybrid Map of the University

From the image above it can be seen that a majority of the rooftops of these buildings are

flat and unused. The hatched red areas on the following image mark potential solar

collector system locations on the Architecture and Engineering building’s rooftops.

Architecture Building

EngineeringBuilding



Figure 24: Rooftop Solar Collector Locations

By estimating the area, in m², of rooftop contained in the hatched areas, the following

analysis was completed to determine the approximate percentage of the district heating

system that could be supplemented by installing solar collectors in the available rooftop

space.

Engineering Building Roof Architecture Building Roof

Evacuated Tube

Collectors Flat‐Plate Collectors

Evacuated Tube Collectors

Flat‐Plate Collectors

Roof‐top Area Available [m²] 1000 1000 1500 1500

Area Needed Per Collector [m²]

4.348 2.873 4.348 2.873

Max # of Collectors Possible 230 348 345 522

Energy Produced by 1 Collector [kW]

0.518 0.387 0.518 0.387

Energy Produced by Collector System [kW]

119.135 134.702 178.703 202.054

% of District Heating System Supplemented

9.9 11.2 14.8 16.8

Table 14: Rooftop Availability



This breakdown shows that, by installing a system of solar collectors in the un‐utilized

space on top of one or more campus buildings, the university could easily obtain enough

heat energy from the sun to significantly supplement the district heating system and

drastically reduce CO2 emissions.

6.3 Evacuated Tube or Flat‐Plate?

The two types of solar collectors that were studied in detail throughout this report were

evacuated tube collectors and flat‐plate collectors. Both operate on the same general

principle – utilizing energy from the sun to heat water. However, there are a few distinct

differences between the collectors that must be discussed.

1. Evacuated tubes, in general, have a higher efficiency than flat‐plate

collectors. This result was seen when the efficiency calculators were used

for both the evacuated tube collector and the flat‐plate collector under the

same conditions. The evacuated tube collector gave an efficiency of

76.24% while the flat‐plate collector gave an efficiency of 41.8%. These

results match up to the efficiencies stated on both collectors specification

sheets. The Apricus evacuated tube collector suggested a product

efficiency of 71.77%, while the EnerWorks flat‐plate collector was

estimated to have an efficiency of 47.78% in the summer months.

2. Of the two types of collectors, flat‐plate collectors tend to sell at a price

reasonably less than evacuated tube collectors. The cost of an Apricus

evacuated tube collectors is approximately $2425 per collector, while an

EnerWorks flat‐plate collector would cost around $1750 per collector.

3. As for weathering the elements and surviving a winter in Winnipeg, both

collectors should fair the same. However, if a problem were to occur, an

evacuated tube collector may be easier to fix. For instance, if a hailstorm



was to damage a flat‐plate collector, it is most likely that the whole

collector would have to be replaced. With an evacuated tube collector,

however, only one or two of the tubes may have been damaged, allowing

the individual tubes to be easily replaced.

If the University of Manitoba were to install a system of solar collectors on campus, it is a

matter of quantity over quality as to whether evacuated tube collectors or flat plate

collectors should be installed. The calculations and analysis completed during this study

confirmed that the payback periods for each system were equivalent; however

maintenance costs were not included in those calculations. Therefore, it is suggested that

evacuated tube collectors be installed over flat‐plate collectors, as they would save the

university money in the long run.



7 CONCLUSIONS AND RECOMMENDATIONS The aim of this thesis report was to study and analyze the potential, both economic and

environmental, that installing a system of solar collectors at the University of Manitoba

could provide. This study began by proposing the installation of four solar collectors at

the “eco‐village”; an evacuated tube collector, two flat‐plate collectors (water and air),

and a solar wall collector.

The scope of this thesis project, unfortunately, was limited as “eco‐village” solar collector

research project as a whole is in its beginning phase. The solar collectors have been

purchased by the university but these collectors, along with the necessary data acquisition

equipment, were not accessible for installation at the completion of this thesis project

time period.

Despite the lack of available equipment, this project studied and analyzed many aspects

of a proposed installation of solar collectors on campus. The following conclusion and

recommendations can be made upon the completion of this thesis project.

7.1 Solar Collector Location

By utilizing the theories of Tiwari & Ghosal, and the work done by Ametek Inc., the

optimum angular location of a solar collector at the University of Manitoba was

determined. It was found that, in order to receive the maximum amount of solar

radiation incident on the collector plane over the course of one year, the tilt angle of the

plane should be set to 50° with a tilt angle direction of 0° (facing directly south). It is

recommended to install the “eco‐village” collectors at these tilt angle coordinates.



7.3 Instantaneous Efficiency Calculators Analyzing the heat transfer flows through the Apricus evacuated tube collector and the

EnerWorks flat‐plate collectors allowed for the creation of a Microsoft Excel spreadsheet

for each collector. This collector requires the user to input the variable collector

parameters, such as temperatures and fluid flow, and calculates the instantaneous

efficiency of the collector. As there is currently no installed, operational solar collector, it

was not possible to verify the accuracy of these calculators through experimentation. It is

highly recommended that these formulae be verified once the applicable equipment is

installed.

From the efficiency calculator models created, it was determined that, during the summer

months, an evacuated tube collector located at the “eco‐village” would have an efficiency

of 76.2% while a flat‐plate collector would have an efficiency of 41.8%. These results are

accurate when compared to the solar collector efficiencies stated by the respective

manufacturers.

7.4 Economic Analysis A brief economic analysis was performed on several theoretical solar collector systems.

This analysis showed both pros and cons to the installation of a system of solar collectors

at the University of Manitoba. The following gives an overview of the conclusions

obtained.

By placing a system of evacuated tube collectors in 1000m² of empty space upon the

rooftop of the Engineering Building, approximately 10% of the university’s district heating

load could be supplemented. This would decrease the amount of CO2 released into the

atmosphere by roughly 220 tonnes a year.



By placing a system of flat‐plate collectors in 1500m² of empty space upon the rooftop of

the Architecture Building, approximately 16.8% of the university’s district heating load

could be supplemented. This would decrease the amount of CO2 released into the

atmosphere by roughly 372 tonnes a year.

The cost for installing enough evacuated tube solar collectors on campus to eliminate the

use of one of the U of M powerhouse’s smaller, summertime boilers is approx. $1.013

million; installing enough flat‐plate collectors would cost approx. $0.98 million. If we take

these costs, minus the financial incentives available for reducing CO2 emissions, and

compare them to the cost of running a boiler with natural gas, lead to payback periods of

9.0 and 8.7 years respectively. It was concluded that the switch from steam boiler heating

to that of solar energy is beneficial to the university in the long run.

Due to time constraints on this thesis project, different effects on solar radiation levels

were not examined. Factors such as the amount of cloudy days per year, snow coverage

on collectors, and collector maintenance should be studied before a system of solar

collectors is installed at the University of Manitoba.

7.5 Final Recommendations

This thesis report concluded that installing a system of solar collectors at the University of

Manitoba is both an economically and environmentally viable project. Further research

and analysis of the solar collectors to be installed at the “eco‐village” should be carried

out to reinforce this claim, and a full, economic and financial cost evaluation should be

initiated.



8 REFERENCES

[1] “About Solar Energy”, Canadian Renewable Energy Network, [Online Document], 2000 Jul 10, [cited 2007 Oct 27], Available HTTP: http://www.canren.gc.ca/tech_appl/index.asp?CaId=5&PgId=121 [2] “Cheaper and Efficient Energy”, Solar Benefits, [Online Document], no date given, [cited 2007 Oct 27], Available HTTP: http://www.solar‐benefits.com/ [3] “Solar Energy”, Wikipedia, [Online Document], no date given, [cited 2007 Oct 27], Available HTTP: http://en.wikipedia.org/wiki/Solar_energy [4] “The Facts about Solar Hot Water”, World of Energy, [Online Document], 2007 Feb 27, [cited 2007 Oct 27], Available HTTP: http://www.worldofenergy.com.au/factsheet_solarhotwater/07_fact_solarhotwater_how.html [5] “Winnipeg”, Wikipedia, [Online Document], no date given, [cited 2007 Oct 28], Available HTTP: http://en.wikipedia.org/wiki/Winnipeg [6] Ametek, Inc., Solar Energy Handbook: Theory and Applications, 2nd Edition, Chilton Book Company, 1984. [7] “Sunrise and Sunset in Winnipeg”, Time and Date AS, [Online Document], no date given, [cited 2007 Sept 29], Available HTTP: http://www.timeanddate.com/worldclock/astronomy.html?n=265&month=9&year=2007&obj=sun&afl=‐11&day=1 [8] Tiwari, G. N., Solar Energy Technology Advances, 1st Edition, Nova Science Publishers, 2006. [9] “Technical Information”, Apricus Solar Co., [Online Document], 2007, [cited 2007 Nov 15], Available HTTP: http://www.apricus.com/html/solar_collector_technical_info.htm [10] “University of Manitoba Powerhouse Annual Report 2006”, University of Manitoba, 2006. [11] Çengel, Y.A. & Boles, M.A., Thermodynamics: An Engineering Approach, 4th Edition, McGraw‐Hill Higher Education, 2002. [12] “Solar Collector Efficiency”, Energistic Systems, [Online Document], no date given, [cited 2007 Nov 21], Available HTTP: http://www.energisticsystems.us/pdfs/ce_brochure.pdf



[13] “Profitability Index Calculator”, MONEY‐zine.com, [Online Document], 2006, [cited 2007 Nov 22], Available HTTP: http://www.money‐zine.com/Calculators/Investment‐Calculators/Profitability‐Index‐Calculator/ [14] “Residential Products”, EnerWorks Inc., [Online Document], 2007, [cited 2007 Nov 24], Available HTTP: http://www.enerworks.com/Res_Products_Collectors.asp [15] Incropera et al, Fundamentals of Heat and Mass Transfer, 6th Edition, John Wiley & Sons, 2007. [16] “World's Largest Solar Wall at Canadair Facility”, Natural Resources Canada, [Online Document], 2005 Sep 26, [cited 2007 Nov 27], Available HTTP: http://www.oee.nrcan.gc.ca/publications/infosource/pub/ici/caddet/english/r336.cfm?attr=20 [17] “Carbon Finance Intel”, Carbon Finance Intel, [Online Document], 2006, [cited 2007 Nov 28], Available HTTP: www.carbonfinance.ca



APPENDIX A – COLLECTOR SPECIFICATIONS This appendix lists the technical specifications of the two collectors studied throughout

this report.

The Apricus Evacuated Tube Collector specifications can be found at the following site: http://www.trendsetterindustries.com/pdf/FTD‐801‐APCollectorSpecificationsRev.1.6.pdf The EnerWorks Flat‐Plate Collector specifications can be found at the following site: http://www.enerworks.com/Res_Products.asp



Apricus Solar Collector Specifications:





















EnerWorks Flat‐Plate Collector Specifications:





APPENDIX B ‐ RETSCREEN DATA FOR WINNIPEG INT. AIRPORT This appendix gives the RETScreen data for Winnipeg International Airport that was

utilized throughout this report.

RETScreen International can be accessed at www.retscreen.net.





APPENDIX C – OPTIMUM TILT ANGLES AND DIRECTIONS: JAN –DEC 2007

The following appendix calculates the optimum tilt angles and tilt directions for a solar

collector installed at the University of Manitoba’s Ft. Garry campus for the months of

January to December 2007.



Table 15: Optimum Tilt Angle ‐ January 2007

01‐Feb‐07

n = 32

Solar Noon: 12:42 PM

Hour L D t H sinA A sinZ Z Opt Σ Opt φ

6:00 AM 49.81 ‐17.52 17.30 259.50 ‐0.34 ‐20.00 1.00 86.25 110.00 86.25

7:00 AM 49.81 ‐17.52 18.30 274.50 ‐0.18 ‐10.47 0.97 75.19 100.47 75.19

8:00 AM 49.81 ‐17.52 19.30 289.50 ‐0.02 ‐1.40 0.90 64.05 91.40 64.05

9:00 AM 49.81 ‐17.52 20.30 304.50 0.12 6.81 0.79 52.33 83.19 52.33

10:00 AM 49.81 ‐17.52 21.30 319.50 0.24 13.77 0.64 39.62 76.23 39.62

11:00 AM 49.81 ‐17.52 22.30 334.50 0.33 19.00 0.43 25.73 71.00 25.73

12:00 PM 49.81 ‐17.52 23.30 349.50 0.38 22.04 0.19 10.81 67.96 10.81

1:00 PM 49.81 ‐17.52 0.30 4.50 0.38 22.56 ‐0.08 ‐4.65 67.44 ‐4.65

2:00 PM 49.81 ‐17.52 1.30 19.50 0.35 20.50 ‐0.34 ‐19.87 69.50 ‐19.87

3:00 PM 49.81 ‐17.52 2.30 34.50 0.28 16.10 ‐0.56 ‐34.21 73.90 ‐34.21

4:00 PM 49.81 ‐17.52 3.30 49.50 0.17 9.77 ‐0.74 ‐47.38 80.23 ‐47.38

5:00 PM 49.81 ‐17.52 4.30 64.50 0.04 2.01 ‐0.86 ‐59.46 87.99 ‐59.46

6:00 PM 49.81 ‐17.52 5.30 79.50 ‐0.12 ‐6.76 ‐0.94 ‐70.78 96.76 ‐70.78

7:00 PM 49.81 ‐17.52 6.30 94.50 ‐0.28 ‐16.15 ‐0.99 ‐81.80 106.15 ‐81.80

8:00 PM 49.81 ‐17.52 7.30 109.50 ‐0.44 ‐25.81 ‐1.00 ‐86.88 115.81 ‐86.88

Table 16: Optimum Tilt Angle ‐ February 2007

01‐Jan‐07

n = 1



6:00 AM 49.81 ‐23.01 17.47 262.05 ‐0.38 ‐22.38 0.99 80.35 112.38 80.35

7:00 AM 49.81 ‐23.01 18.47 277.05 ‐0.23 ‐13.05 0.94 69.66 103.05 69.66

8:00 AM 49.81 ‐23.01 19.47 292.05 ‐0.08 ‐4.34 0.86 58.82 94.34 58.82

9:00 AM 49.81 ‐23.01 20.47 307.05 0.06 3.40 0.74 47.38 86.60 47.38

10:00 AM 49.81 ‐23.01 21.47 322.05 0.17 9.77 0.57 35.06 80.23 35.06

11:00 AM 49.81 ‐23.01 22.47 337.05 0.25 14.38 0.37 21.75 75.62 21.75

12:00 PM 49.81 ‐23.01 23.47 352.05 0.29 16.84 0.13 7.64 73.16 7.64

1:00 PM 49.81 ‐23.01 0.47 7.05 0.29 16.91 ‐0.12 ‐6.78 73.09 ‐6.78

2:00 PM 49.81 ‐23.01 1.47 22.05 0.25 14.59 ‐0.36 ‐20.92 75.41 ‐20.92

3:00 PM 49.81 ‐23.01 2.47 37.05 0.18 10.10 ‐0.56 ‐34.28 79.90 ‐34.28

4:00 PM 49.81 ‐23.01 3.47 52.05 0.07 3.82 ‐0.73 ‐46.67 86.18 ‐46.67

5:00 PM 49.81 ‐23.01 4.47 67.05 ‐0.07 ‐3.84 ‐0.85 ‐58.16 93.84 ‐58.16

6:00 PM 49.81 ‐23.01 5.47 82.05 ‐0.22 ‐12.50 ‐0.93 ‐69.02 102.50 ‐69.02

7:00 PM 49.81 ‐23.01 6.47 97.05 ‐0.37 ‐21.81 ‐0.98 ‐79.70 111.81 ‐79.70

8:00 PM 49.81 ‐23.01 7.47 112.05 ‐0.52 ‐31.44 ‐1.00 ‐89.21 121.44 ‐89.21



Table 17: Optimum Tilt Angle ‐ March 2007

01‐Apr‐07

n = 91

Solar Noon: 1:33 PM


6:00 AM 49.81 4.02 16.45 246.75 ‐0.20 ‐11.57 0.94 69.32 101.57 69.32

7:00 AM 49.81 4.02 17.45 261.75 ‐0.04 ‐2.23 0.99 81.10 92.23 81.10

8:00 AM 49.81 4.02 18.45 276.75 0.13 7.42 1.00 87.44 82.58 87.44

9:00 AM 49.81 4.02 19.45 291.75 0.29 16.98 0.97 75.64 73.02 75.64

10:00 AM 49.81 4.02 20.45 306.75 0.44 26.02 0.89 62.80 63.98 62.80

11:00 AM 49.81 4.02 21.45 321.75 0.56 33.99 0.74 48.15 56.01 48.15

12:00 PM 49.81 4.02 22.45 336.75 0.64 40.16 0.52 31.02 49.84 31.02

1:00 PM 49.81 4.02 23.45 351.75 0.69 43.68 0.20 11.41 46.32 11.41

2:00 PM 49.81 4.02 0.45 6.75 0.69 43.85 ‐0.16 ‐9.36 46.15 ‐9.36

3:00 PM 49.81 4.02 1.45 21.75 0.65 40.65 ‐0.49 ‐29.16 49.35 ‐29.16

4:00 PM 49.81 4.02 2.45 36.75 0.57 34.70 ‐0.73 ‐46.55 55.30 ‐46.55

5:00 PM 49.81 4.02 3.45 51.75 0.45 26.88 ‐0.88 ‐61.43 63.12 ‐61.43

6:00 PM 49.81 4.02 4.45 66.75 0.31 17.92 ‐0.96 ‐74.42 72.08 ‐74.42

7:00 PM 49.81 4.02 5.45 81.75 0.15 8.39 ‐1.00 ‐86.28 81.61 ‐86.28

8:00 PM 49.81 4.02 6.45 96.75 ‐0.02 ‐1.27 ‐0.99 ‐82.25 91.27 ‐82.25

Table 18: Optimum Tilt Angle ‐ April 2007

01‐Mar‐07

n = 60



6:00 AM 49.81 ‐8.29 17.32 259.75 ‐0.22 ‐12.93 1.00 87.56 102.93 87.56

7:00 AM 49.81 ‐8.29 18.32 274.75 ‐0.06 ‐3.29 0.99 81.03 93.29 81.03

8:00 AM 49.81 ‐8.29 19.32 289.75 0.11 6.06 0.94 69.48 83.94 69.48

9:00 AM 49.81 ‐8.29 20.32 304.75 0.25 14.70 0.84 57.20 75.30 57.20

10:00 AM 49.81 ‐8.29 21.32 319.75 0.38 22.16 0.69 43.66 67.84 43.66

11:00 AM 49.81 ‐8.29 22.32 334.75 0.47 27.86 0.48 28.52 62.14 28.52

12:00 PM 49.81 ‐8.29 23.32 349.75 0.52 31.21 0.21 11.88 58.79 11.88

1:00 PM 49.81 ‐8.29 0.32 4.75 0.53 31.75 ‐0.10 ‐5.53 58.25 ‐5.53

2:00 PM 49.81 ‐8.29 1.32 19.75 0.49 29.39 ‐0.38 ‐22.57 60.61 ‐22.57

3:00 PM 49.81 ‐8.29 2.32 34.75 0.41 24.49 ‐0.62 ‐38.30 65.51 ‐38.30

4:00 PM 49.81 ‐8.29 3.32 49.75 0.30 17.60 ‐0.79 ‐52.41 72.40 ‐52.41

5:00 PM 49.81 ‐8.29 4.32 64.75 0.16 9.33 ‐0.91 ‐65.10 80.67 ‐65.10

6:00 PM 49.81 ‐8.29 5.32 79.75 0.00 0.20 ‐0.97 ‐76.84 89.80 ‐76.84

7:00 PM 49.81 ‐8.29 6.32 94.75 ‐0.16 ‐9.39 ‐1.00 ‐88.23 99.39 ‐88.23

8:00 PM 49.81 ‐8.29 7.32 109.75 ‐0.33 ‐19.02 ‐0.99 ‐80.11 109.02 ‐80.11



01‐May‐07

n = 121

Solar Noon: 1:26 PM


6:00 AM 49.81 14.90 16.57 248.50 ‐0.03 ‐1.84 0.90 64.11 91.84 64.11

7:00 AM 49.81 14.90 17.57 263.50 0.13 7.23 0.97 75.43 82.77 75.43

8:00 AM 49.81 14.90 18.57 278.50 0.29 16.78 1.00 86.60 73.22 86.60

9:00 AM 49.81 14.90 19.57 293.50 0.45 26.43 0.99 81.75 63.57 81.75

10:00 AM 49.81 14.90 20.57 308.50 0.58 35.78 0.93 68.78 54.22 68.78

11:00 AM 49.81 14.90 21.57 323.50 0.70 44.25 0.80 53.36 45.75 53.36

12:00 PM 49.81 14.90 22.57 338.50 0.78 50.96 0.56 34.21 39.04 34.21

1:00 PM 49.81 14.90 23.57 353.50 0.82 54.69 0.19 10.91 35.31 10.91

2:00 PM 49.81 14.90 0.57 8.50 0.81 54.41 ‐0.25 ‐14.21 35.59 ‐14.21

3:00 PM 49.81 14.90 1.57 23.50 0.77 50.20 ‐0.60 ‐37.02 39.80 ‐37.02

4:00 PM 49.81 14.90 2.57 38.50 0.68 43.20 ‐0.83 ‐55.61 46.80 ‐55.61

5:00 PM 49.81 14.90 3.57 53.50 0.57 34.57 ‐0.94 ‐70.63 55.43 ‐70.63

6:00 PM 49.81 14.90 4.57 68.50 0.42 25.15 ‐0.99 ‐83.36 64.85 ‐83.36

7:00 PM 49.81 14.90 5.57 83.50 0.27 15.49 ‐1.00 ‐85.10 74.51 ‐85.10

8:00 PM 49.81 14.90 6.57 98.50 0.10 5.98 ‐0.96 ‐73.94 84.02 ‐73.94

Table 19: Optimum Tilt Angle ‐ May 2007

01‐Jun‐07

n = 152

Solar Noon: 1:26 PM


6:00 AM 49.81 22.04 16.57 248.50 0.07 3.87 0.86 59.81 86.13 59.81

7:00 AM 49.81 22.04 17.57 263.50 0.22 12.65 0.94 70.71 77.35 70.71

8:00 AM 49.81 22.04 18.57 278.50 0.38 22.03 0.99 81.47 67.97 81.47

9:00 AM 49.81 22.04 19.57 293.50 0.53 31.68 1.00 87.29 58.32 87.29

10:00 AM 49.81 22.04 20.57 308.50 0.66 41.23 0.96 74.69 48.77 74.69

11:00 AM 49.81 22.04 21.57 323.50 0.77 50.13 0.86 59.33 39.87 59.33

12:00 PM 49.81 22.04 22.57 338.50 0.84 57.48 0.63 39.19 32.52 39.19

1:00 PM 49.81 22.04 23.57 353.50 0.88 61.76 0.22 12.81 28.24 12.81

2:00 PM 49.81 22.04 0.57 8.50 0.88 61.43 ‐0.29 ‐16.65 28.57 ‐16.65

3:00 PM 49.81 22.04 1.57 23.50 0.84 56.64 ‐0.67 ‐42.23 33.36 ‐42.23

4:00 PM 49.81 22.04 2.57 38.50 0.75 49.01 ‐0.88 ‐61.60 40.99 ‐61.60

5:00 PM 49.81 22.04 3.57 53.50 0.64 39.98 ‐0.97 ‐76.49 50.02 ‐76.49

6:00 PM 49.81 22.04 4.57 68.50 0.51 30.39 ‐1.00 ‐88.85 59.61 ‐88.85

7:00 PM 49.81 22.04 5.57 83.50 0.35 20.75 ‐0.98 ‐80.02 69.25 ‐80.02

8:00 PM 49.81 22.04 6.57 98.50 0.20 11.43 ‐0.94 ‐69.28 78.57 ‐69.28

Table 20: Optimum Tilt Angle ‐ June 2007



Table 21: Optimum Tilt Angle ‐ July 2007

01‐Aug‐07

n = 213

Solar Noon: 1:35 PM


6:00 AM 49.81 17.91 16.42 246.25 ‐0.01 ‐0.71 0.87 60.58 90.71 60.58

7:00 AM 49.81 17.91 17.42 261.25 0.14 8.14 0.95 71.81 81.86 71.81

8:00 AM 49.81 17.91 18.42 276.25 0.30 17.57 0.99 82.81 72.43 82.81

9:00 AM 49.81 17.91 19.42 291.25 0.46 27.23 1.00 85.81 62.77 85.81

10:00 AM 49.81 17.91 20.42 306.25 0.60 36.73 0.96 73.22 53.27 73.22

11:00 AM 49.81 17.91 21.42 321.25 0.71 45.55 0.85 58.26 44.45 58.26

12:00 PM 49.81 17.91 22.42 336.25 0.80 52.84 0.63 39.38 37.16 39.38

1:00 PM 49.81 17.91 23.42 351.25 0.84 57.34 0.27 15.56 32.66 15.56

2:00 PM 49.81 17.91 0.42 6.25 0.85 57.71 ‐0.19 ‐11.18 32.29 ‐11.18

3:00 PM 49.81 17.91 1.42 21.25 0.81 53.83 ‐0.58 ‐35.75 36.17 ‐35.75

4:00 PM 49.81 17.91 2.42 36.25 0.73 46.90 ‐0.82 ‐55.43 43.10 ‐55.43

5:00 PM 49.81 17.91 3.42 51.25 0.62 38.27 ‐0.95 ‐70.93 51.73 ‐70.93

6:00 PM 49.81 17.91 4.42 66.25 0.48 28.83 ‐0.99 ‐83.82 61.17 ‐83.82

7:00 PM 49.81 17.91 5.42 81.25 0.33 19.17 ‐1.00 ‐84.66 70.83 ‐84.66

8:00 PM 49.81 17.91 6.42 96.25 0.17 9.68 ‐0.96 ‐73.64 80.32 ‐73.64

Table 22: Optimum Tilt Angle ‐ August 2007

01‐Jul‐07

n = 182

Solar Noon: 1:33 PM


6:00 AM 49.81 23.12 16.45 246.75 0.07 3.77 0.85 57.87 86.23 57.87

7:00 AM 49.81 23.12 17.45 261.75 0.21 12.40 0.93 68.74 77.60 68.74

8:00 AM 49.81 23.12 18.45 276.75 0.37 21.70 0.98 79.41 68.30 79.41

9:00 AM 49.81 23.12 19.45 291.75 0.52 31.32 1.00 89.53 58.68 89.53

10:00 AM 49.81 23.12 20.45 306.75 0.66 40.92 0.98 77.23 49.08 77.23

11:00 AM 49.81 23.12 21.45 321.75 0.77 50.00 0.89 62.35 40.00 62.35

12:00 PM 49.81 23.12 22.45 336.75 0.85 57.70 0.68 42.80 32.30 42.80

1:00 PM 49.81 23.12 23.45 351.75 0.89 62.54 0.29 16.63 27.46 16.63

2:00 PM 49.81 23.12 0.45 6.75 0.89 62.79 ‐0.24 ‐13.67 27.21 ‐13.67

3:00 PM 49.81 23.12 1.45 21.75 0.85 58.34 ‐0.65 ‐40.49 31.66 ‐40.49

4:00 PM 49.81 23.12 2.45 36.75 0.78 50.85 ‐0.87 ‐60.64 39.15 ‐60.64

5:00 PM 49.81 23.12 3.45 51.75 0.67 41.87 ‐0.97 ‐75.89 48.13 ‐75.89

6:00 PM 49.81 23.12 4.45 66.75 0.53 32.29 ‐1.00 ‐88.38 57.71 ‐88.38

7:00 PM 49.81 23.12 5.45 81.75 0.39 22.65 ‐0.99 ‐80.48 67.35 ‐80.48

8:00 PM 49.81 23.12 6.45 96.75 0.23 13.31 ‐0.94 ‐69.80 76.69 ‐69.80



01‐Sep‐07

n = 244

Solar Noon: 1:29 PM


6:00 AM 49.81 7.72 16.52 247.75 ‐0.14 ‐8.02 0.93 67.85 98.02 67.85

7:00 AM 49.81 7.72 17.52 262.75 0.02 1.26 0.98 79.50 88.74 79.50

8:00 AM 49.81 7.72 18.52 277.75 0.19 10.89 1.00 89.10 79.11 89.10

9:00 AM 49.81 7.72 19.52 292.75 0.35 20.49 0.98 77.30 69.51 77.30

10:00 AM 49.81 7.72 20.52 307.75 0.49 29.62 0.90 64.32 60.38 64.32

11:00 AM 49.81 7.72 21.52 322.75 0.61 37.71 0.76 49.31 52.29 49.31

12:00 PM 49.81 7.72 22.52 337.75 0.69 43.99 0.52 31.43 46.01 31.43

1:00 PM 49.81 7.72 23.52 352.75 0.74 47.48 0.19 10.66 42.52 10.66

2:00 PM 49.81 7.72 0.52 7.75 0.74 47.42 ‐0.20 ‐11.39 42.58 ‐11.39

3:00 PM 49.81 7.72 1.52 22.75 0.69 43.82 ‐0.53 ‐32.08 46.18 ‐32.08

4:00 PM 49.81 7.72 2.52 37.75 0.61 37.47 ‐0.76 ‐49.85 52.53 ‐49.85

5:00 PM 49.81 7.72 3.52 52.75 0.49 29.32 ‐0.90 ‐64.78 60.68 ‐64.78

6:00 PM 49.81 7.72 4.52 67.75 0.34 20.17 ‐0.98 ‐77.70 69.83 ‐77.70

7:00 PM 49.81 7.72 5.52 82.75 0.18 10.57 ‐1.00 ‐89.49 79.43 ‐89.49

8:00 PM 49.81 7.72 6.52 97.75 0.02 0.94 ‐0.98 ‐79.11 89.06 ‐79.11

Table 23: Optimum Tilt Angle ‐ September 2007

01‐Oct‐07

n = 274

Solar Noon: 1:18 PM


6:00 AM 49.81 ‐4.22 16.70 250.50 ‐0.27 ‐15.72 0.98 77.59 105.72 77.59

7:00 AM 49.81 ‐4.22 17.70 265.50 ‐0.11 ‐6.12 1.00 89.29 96.12 89.29

8:00 AM 49.81 ‐4.22 18.70 280.50 0.06 3.50 0.98 79.24 86.50 79.24

9:00 AM 49.81 ‐4.22 19.70 295.50 0.22 12.76 0.92 67.36 77.24 67.36

10:00 AM 49.81 ‐4.22 20.70 310.50 0.36 21.21 0.81 54.44 68.79 54.44

11:00 AM 49.81 ‐4.22 21.70 325.50 0.47 28.31 0.64 39.91 61.69 39.91

12:00 PM 49.81 ‐4.22 22.70 340.50 0.55 33.40 0.40 23.50 56.60 23.50

1:00 PM 49.81 ‐4.22 23.70 355.50 0.59 35.83 0.10 5.54 54.17 5.54

2:00 PM 49.81 ‐4.22 0.70 10.50 0.58 35.22 ‐0.22 ‐12.85 54.78 ‐12.85

3:00 PM 49.81 ‐4.22 1.70 25.50 0.52 31.65 ‐0.50 ‐30.29 58.35 ‐30.29

4:00 PM 49.81 ‐4.22 2.70 40.50 0.43 25.67 ‐0.72 ‐45.94 64.33 ‐45.94

5:00 PM 49.81 ‐4.22 3.70 55.50 0.31 17.96 ‐0.86 ‐59.77 72.04 ‐59.77

6:00 PM 49.81 ‐4.22 4.70 70.50 0.16 9.13 ‐0.95 ‐72.20 80.87 ‐72.20

7:00 PM 49.81 ‐4.22 5.70 85.50 ‐0.01 ‐0.32 ‐0.99 ‐83.85 90.32 ‐83.85

8:00 PM 49.81 ‐4.22 6.70 100.50 ‐0.17 ‐9.99 ‐1.00 ‐84.68 99.99 ‐84.68

Table 24: Optimum Tilt Angle ‐ October 2007



01‐Nov‐07

n = 305

Solar Noon: 1:12 PM


6:00 AM 49.81 ‐15.36 16.80 252.00 ‐0.39 ‐23.25 1.00 86.47 113.25 86.47

7:00 AM 49.81 ‐15.36 17.80 267.00 ‐0.23 ‐13.59 0.99 82.17 103.59 82.17

8:00 AM 49.81 ‐15.36 18.80 282.00 ‐0.07 ‐4.19 0.95 71.04 94.19 71.04

9:00 AM 49.81 ‐15.36 19.80 297.00 0.08 4.59 0.86 59.53 85.41 59.53

10:00 AM 49.81 ‐15.36 20.80 312.00 0.21 12.36 0.73 47.19 77.64 47.19

11:00 AM 49.81 ‐15.36 21.80 327.00 0.32 18.63 0.55 33.66 71.37 33.66

12:00 PM 49.81 ‐15.36 22.80 342.00 0.39 22.92 0.32 18.88 67.08 18.88

1:00 PM 49.81 ‐15.36 23.80 357.00 0.42 24.77 0.06 3.19 65.23 3.19

2:00 PM 49.81 ‐15.36 0.80 12.00 0.41 23.97 ‐0.22 ‐12.67 66.03 ‐12.67

3:00 PM 49.81 ‐15.36 1.80 27.00 0.35 20.61 ‐0.47 ‐27.89 69.39 ‐27.89

4:00 PM 49.81 ‐15.36 2.80 42.00 0.26 15.07 ‐0.67 ‐41.93 74.93 ‐41.93

5:00 PM 49.81 ‐15.36 3.80 57.00 0.14 7.85 ‐0.82 ‐54.72 82.15 ‐54.72

6:00 PM 49.81 ‐15.36 4.80 72.00 ‐0.01 ‐0.58 ‐0.92 ‐66.51 90.58 ‐66.51

7:00 PM 49.81 ‐15.36 5.80 87.00 ‐0.17 ‐9.78 ‐0.98 ‐77.72 99.78 ‐77.72

8:00 PM 49.81 ‐15.36 6.80 102.00 ‐0.33 ‐19.38 ‐1.00 ‐88.92 109.38 ‐88.92

Table 25: Optimum Tilt Angle ‐ November 2007

01‐Dec‐07

n = 335



6:00 AM 49.81 ‐22.11 17.70 265.50 ‐0.33 ‐19.54 0.98 78.53 109.54 78.53

7:00 AM 49.81 ‐22.11 18.70 280.50 ‐0.18 ‐10.28 0.93 67.80 100.28 67.80

8:00 AM 49.81 ‐22.11 19.70 295.50 ‐0.03 ‐1.73 0.84 56.78 91.73 56.78

9:00 AM 49.81 ‐22.11 20.70 310.50 0.10 5.78 0.71 45.08 84.22 45.08

10:00 AM 49.81 ‐22.11 21.70 325.50 0.21 11.84 0.54 32.42 78.16 32.42

11:00 AM 49.81 ‐22.11 22.70 340.50 0.28 16.03 0.32 18.77 73.97 18.77

12:00 PM 49.81 ‐22.11 23.70 355.50 0.31 17.97 0.08 4.38 72.03 4.38

1:00 PM 49.81 ‐22.11 0.70 10.50 0.30 17.48 ‐0.18 ‐10.20 72.52 ‐10.20

2:00 PM 49.81 ‐22.11 1.70 25.50 0.25 14.60 ‐0.41 ‐24.34 75.40 ‐24.34

3:00 PM 49.81 ‐22.11 2.70 40.50 0.17 9.62 ‐0.61 ‐37.61 80.38 ‐37.61

4:00 PM 49.81 ‐22.11 3.70 55.50 0.05 2.93 ‐0.76 ‐49.87 87.07 ‐49.87

5:00 PM 49.81 ‐22.11 4.70 70.50 ‐0.09 ‐5.04 ‐0.88 ‐61.25 95.04 ‐61.25

6:00 PM 49.81 ‐22.11 5.70 85.50 ‐0.24 ‐13.92 ‐0.95 ‐72.10 103.92 ‐72.10

7:00 PM 49.81 ‐22.11 6.70 100.50 ‐0.40 ‐23.36 ‐0.99 ‐82.87 113.36 ‐82.87

8:00 PM 49.81 ‐22.11 7.70 115.50 ‐0.54 ‐33.02 ‐1.00 ‐85.77 123.02 ‐85.77

Table 26: Optimum Tilt Angle ‐ December 2007

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