SOLAR RADIATION – EQUATION OF TIME

PUNITHA A/P MARIMUTHOO

A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE

REQUIREMENTS FOR THE AWARD OF THE DEGREE OF BACHELOR OF

SCIENCE AND COMPUTER WITH EDUACATION (PHYSICS)

FACULTY OF SCIENCE

UNIVERSITY TECHNOLOGY MALAYSIA

MEI, 2006

ii

“I declare that this thesis is the result of my own research except as cited in the

references”

Signature : ………………………………….

Name : PUNITHA A/P MARIMUTHOO

Date : 25TH MARCH 2006

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I dedicate this thesis to my beloved parents ( R.Marimuthoo &

A.Meenachi ), sisters, brother, brother in law and my new born nephew

Avinash…..

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ACKNOWLEDGEMENT

There are countless of support and assistance from many parties throughout this

project. And thus, I would like to take is opportunity to express my highest appreciation

and deepest gratitude to those who have directly and indirectly helped me to complete

my final year project.

The first person I would like to thank is my supervisor, Prof. Dr Ramli Abu

Hassan, who has been guiding and supporting me throughout the duration of this

project. I would like to thank for all his constructive criticism and helpful suggestions,

which has lead to this thesis as presented here. He is indeed a dedicated lecturer as he

provides me with abundance of knowledge and advices. He is always there for me

whenever I need his consultation.

I would also like acknowledge my family members for their morale support and

encouragements throughout my life. Last, but not least, I would like to express my

sincerest thanks to my dearest friends especially; Aruneswaran, Usha, Tilaga, Sumathy,

Sakthiyavaani, Maliswairy, Vasantha and my coarse mates who were there for me all

the while I was pursuing my studies in UTM.

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ABSTRACT

The difference between true solar time and local mean time is known as the

Equation of Time. In a simplified manner the Equation of Time can be explained as the

difference in time between what your watch says and where the sun is in the sky. The

goal of this project is to study the Equation of Time in Kuala Lumpur for 2006. A set of

data on geometrical coordinates, solar time and the Equation of Time for a particular

local time was downloaded from a website as the source of this study. Since the focus is

placed on the Equation of Time, the extraction of data on Equation of Time from the

particular website was interpreted to a graph and compared with the theoretical model

to determine the reliability of the source. Then, a formula on Equation of Time for

Kuala Lumpur was created using Datafit Oakland Engineering software. The formula is,

E= (-5.6169448 E-5) * � + (-2.3254531 E-4) * � + 4.0005670 * H + 14.3259152

The error range for the output of this formula is 1± %. This formula was developed

based on three geometrical parameters which are Azimuth (�), Declination of Sun (�)

and Solar Hour Angle (H) as independent variables. Finally, a programme was

developed using the Qbasic programming language to determine the Equation of Time

throughout the year of 2006. From this study can be concluded that the solar time for

Kuala Lumpur at 1pm local standard time is approximately 12.15pm. The average time

for midday in Kuala Lumpur is at 1.10pm local standard time.

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ABSTRAK

Perbezaan di antara waktu suria dan waktu tempatan dikenali sebagai

persamaan waktu. Objektif projek ini adalah adalah untuk mengkaji Persamaan waktu

bagi Kuala Lumpur tahun 2006. Satu set data untuk parameter geometri, waktu suria,

dan Persamaan Waktu untuk masa tertentu telah dimuat turun dari laman web yang

merupakan sumber kajian bagi projek ini. Oleh kerana Persamaan Waktu merupakan

fokus utama dalam kajian ini, set data bagi Persamaan Waktu sepanjang tahun 2006

telah dimuat turun dari laman web yang terpilih dan diinterpretasikan kepada graf

untuk dibandingkan dengan teori. Tujuannya adalah untuk memastikan

kebolehpercayaan dan kejituan sumber yang telah dikaji. Kemudian, satu formula bagi

persamaan waktu telah dicipta dengan menggunakan perisian Datafit Oakland

Engineering. Formula yang diperoleh adalah seperti berikut:

E = (-5.6169448 E-5) * � +(-2.3254531 E-4) * � + 4.0005670 * H + 14.3259152

Peratus ralat yang diperoleh di antara Persamaan Waktu dari hasil pengiraan dan data

asal adalah dalam lingkungan -14.26 hingga 3.99 peratus. Formula ini telah dicipta

bersandarkan tiga parameter geometri iaitu Azimut,(�), Kodeklinasi,(�), dan Sudut

Jam,(H), sebagai pemalar tak bersandar. Akhirnya, satu program telah dibangunkan

dengan menggunakan bahasa pengaturcaraan Qbasic untuk mengira Persamaan Waktu

bagi sepanjang tahun 2006. Daripada kajian ini, boleh dirumuskan bahawa, waktu suria

pada pukul 1 petang waktu tempatan bagi Kuala Lumpur adalah 12.15pm. Purata

waktu tengahari bagi Kuala Lumpur adalah 1.10 petang.

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CONTENT

CHAPTER TITLE PAGE

SUPERVISOR’S AUTHENTICATION

THESIS TITLE i

DECLARATION ii

DEDICATION iii

ACKNOWLEDGEMENT iv

ABSTRACT v

ABSTRAK vi

CONTENT vii

LIST OF ABBREVATIONS/SYMBOL/

TERMINOLOGY x

LIST OF TABLES xi

LIST OF FIGURES xii

LIST OF APPENDIX xiii

CHAPTER 1 INTRODUCTION

1.1 Background 1

1.2 Project Objective 3

1.3 Project scope 3

1.4 Research problems 4

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CHAPTER 2 THEORY

2.1 Introduction 5

2.2 Universal Time 6

2.3 Time Zones 8

2.4 Solar Time 9

2.5 Solar and Local Standard Time 10

2.6 Equation of Time 11

2.6.1 Solar Angles 13

2.7 Sundial Theory 15

CHAPTER 3 METHODOLOGY RESEARCH

3.1 Introduction 16

3.2 Preface to the Research Procedure 17

3.3 Sources of Data 17

3.4 Data Collection Method 18

3.5 Data Manipulation Method 20

CHAPTER 4 MEASUREMENT AND DATA ANALYSIS

4.1 Introduction 23

4.2 Solar Radiation in Kuala Lumpur 23

4.3 The Data Evaluation 25

4.4 Analysis of Equation of Time 27

4.4.1 Data Collections and Manipulation 27

4.4.2 Formula of Equation of Time for

Kuala Lumpur 30

4.4.3 Comparisons with Other Sources 34

4.5 Equation of Time Model for

Kuala Lumpur 35

CHAPTER 5 CONCLUSION AND SUGGESTIONS

5.1 Conclusion 37

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5.2 Suggestion 38

REFERENCES 39

APPENDIX 40

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LIST OF ABBREVATIONS/SYMBOL/TERMINOLOGY

� - Declination of sun

� - Azimuth angle

H - Solar hour angle

� - Day angle

� - Hour angle

dn - Day number

� - Pi

λ − Latitude

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LIST OF TABLES

TABLE NO. TITLE PAGE

2.1 Regions and time zones 8

2.2 Equation of time 11

3.1 Simple Sunrise and Sunset Calculator 20

3.2 The declarations of the variables 22

4.1 Sunrise, Sunset, Solar Time and Equation of Time

for Kuala Lumpur 25

4.2 Azimuth, Declination of Sun and Solar Hour Angle 29

4.3 Regression variable results 31

4.4 Comparisons between downloaded Equation of Time

and calculated Equation of Time for Kuala Lumpur 31

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LIST OF FIGURES

FIGURE NO TITLE PAGE

2.1 Altitude (h) and Azimuth (�) 13

2.2 Declination of Sun (�) and Hour Angle (�) 14

2.3 Graph of the Equation of Time 16

3.1 Datafit Sotware 22

4.1 Graph of Equation of Time versus Date/

Months (2006) – (Downloaded data) 27

4.2 Graph of Equation of Time versus Date/Months

(2006) - Theory [3] 28

4.3 Graph of Equation of Time versus Date/Months

(2006)- (Formula results) 34

4.4 Graph of Equation of Time versus Months

(2006)– (Comparison) 35

4.5 Flowchart shows the calculation process for

Equation of Time 36

4.6 Window of QBasic Programming 37

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LIST OF APPENDIX

APPENDIX NO TITLE PAGE

1 QBasic Source Code for Equation of Time 40

Model

2 Data Table from Datafit Software 41

3 Data for Comparisons 43

4 Declination of Sun 45

5 Datafit software (Calculation for Declination of Sun)-

For QBasics Application 46

6 Solar Hour Angle 48

7 Datafit software (Calculation for Solar Hour Angle)-

For QBasics Application 49

CHAPTER 1

INTRODUCTION

1.1 Background

Solar radiation is a term used to describe visible and near-visible (ultraviolet and

near-infrared) radiation emitted from the sun. The different regions are described by

their wavelength range within the broad band range of 0.20 to 4.0 µm (microns).

Terrestrial radiation is a term used to describe infrared radiation emitted from the

atmosphere. The following is a list of the components of solar and terrestrial radiation

and their approximate wavelength ranges:

Ultraviolet: 0.20 - 0.39 µm

Visible: 0.39 - 0.78 µm

Near-Infrared: 0.78 - 4.00 µm

Infrared: 4.00 - 100.00 µm

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Approximately 99% of solar, or short-wave, radiation at the earth's surface is

contained in the region from 0.3 to 3.0 µm while most of terrestrial, or long-wave,

radiation is contained in the region from 3.5 to 50 µm.

Outside the earth's atmosphere, solar radiation has an intensity of approximately 1370

watts/meter2. This is the value at mean earth-sun distance at the top of the atmosphere

and is referred to as the Solar Constant. On the surface of the earth on a clear day, at

noon, the direct beam radiation will be approximately 1000 watts/meter2 for many

locations.

The availability of energy is affected by location (including latitude and

elevation), season, and time of day. All of which can be readily determined. However,

the biggest factors affecting the available energy are cloud cover and other

meteorological conditions which vary with location and time.

Historically, solar measurements have been taken with horizontal instruments

over the complete day. In the Northern US, this results in early summer values 4-6

times greater than early winter values. In the South, differences would be 2-3 times

greater. This is due, in part, to the weather and, to a larger degree, the sun angle and the

length of daylight.

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1.2 Project Objective

For this project, the geometrical dataset for solar position for Kuala Lumpur will

be downloaded from a website by using the local time.

Firstly, the purpose of this project is to study the shadow of the sunlight which

contributes to building design and solar energy applications. Besides that, the Equation

of Time for Kuala Lumpur throughout the year 2006 will be identified by using the

related website. The formula for Equation of Time then will be generated by using the

geometrical parameters and Datafit software courtesy of Oakland Engineering. Then the

results from the formula will be used to plot a graph to get the best fitting and compared

with the theory to measure the reliability of the source (website) before the study is

carried out any further. Besides that this study is conducted to analyze the

characteristics of the sun on how it influences the solar time and local time.

1.3 Project scope

In this project, geometrical dataset for the solar position was downloaded from

http://www.jgiesen.de/deot for the entire year 2006. 4 days have been chosen per month

to get the solar position particulars to invent own formula for equation of time. This

experiment is based at latitude 3˚10’N and longitude 101˚42’ E for Kuala Lumpur. The

important geometrical parameters that will be considered from the downloaded solar

position results are azimuth, declination of the sun, solar hour angle, sunset, sunrise and

equation of time.

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1.4 Research Problems

The main source of this project is internet. Dataset were collected from internet

to develop the equation. Initially the procedure of this research is by using a sundial to

get the reading for the position of the sun in angle and manipulate the data to develop a

formula for equation of time.

But since the weather did not allow furthering the research, the idea of getting

the information from internet had to be considered. Even though there are ample of

websites that can provide the required information, but only a right website was chosen

after doing a few evaluations to assist in this project.