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 : 25 TH MARCH 2006
iii I dedicate this thesis to my beloved parents ( R.Marimuthoo & A.Meenachi ), sisters, brother, brother in law and my new born nephew Avinash..
iv 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.
v 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.
vi 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.
vii CONTENT CHAPTER TITLE PAGE SUPERVISOR S AUTHENTICATION THESIS TITLE DECLARATION DEDICATION ACKNOWLEDGEMENT ABSTRACT ABSTRAK CONTENT LIST OF ABBREVATIONS/SYMBOL/ TERMINOLOGY LIST OF TABLES LIST OF FIGURES LIST OF APPENDIX i ii iii iv v vi vii x xi xii xiii CHAPTER 1 INTRODUCTION 1.1 Background 1 1.2 Project Objective 3 1.3 Project scope 3 1.4 Research problems 4
viii 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
ix 5.2 Suggestion 38 REFERENCES 39 APPENDIX 40
x LIST OF ABBREVATIONS/SYMBOL/TERMINOLOGY - Declination of sun - Azimuth angle H - Solar hour angle - Day angle - Hour angle d n - Day number - Pi λ Latitude
xi 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
xii 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
xiii 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
2 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/meter 2. 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/meter 2 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.
3 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.
4 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.