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Computer modelling of cumulative daylight availability within an urban site

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Computer modelling of cumulative daylight availability within an urban site

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Content COMPUTER MODELLING OF CUMULATIVE DAYLIGHT AVAILABILITY WITHIN AN URBAN SITE by June Lok-Mei Liang A Thesis Presented to the FACULTY OF THE SCHOOL OF ARCHITECTURE UNIVERSITY OF SOUTHERN CALIFORNIA In Partial Fulfillment of the Requirements for the Degree MASTER OF BUILDING SCIENCE May 1993 Copyright 1993 June Lok-Mei Liang UMI Number: EP41432 All rights reserved INFORMATION TO ALL USERS The quality of this reproduction is dependent upon the quality of the copy submitted. In the unlikely event that the author did not send a complete manuscript and there are missing pages, these will be noted. Also, if material had to be removed, a note will indicate the deletion. Dissertation Publishing UMI EP41432 Published by ProQuest LLC (2014). Copyright in the Dissertation held by the Author. Microform Edition © ProQuest LLC. All rights reserved. This work is protected against unauthorized copying under Title 17, United States Code ProQuest LLC. 789 East Eisenhower Parkway P.O. Box 1346 Ann Arbor, Ml 4 8 1 0 6 -1 3 4 6 UNIVERSITY O F SO U T H E R N CALIFORNIA THE SCHOOL O F ARCHITECTURE UNIVERSITY PARK LOS ANGELES. CALIFORNIA 90089-0291 This thesis, written by J u n e , loKrM e .I.. ............. under the direction of h t E k .... Thesis Committee, and approved by dll its members, has been pre sented to and accepted by the Dean of The School of Architecture, in partial fulfillment of the require ments for the degree of . .O f pO)U?\IN6f. SaC H C b Dean Date . THESIS COMMITTEE ! air. 12) u.. S . ■ R 3 L-6R2) 3 7 4 * 6 / ^ ? V ACK NO W LEDG EM ENT I would like to recognize and thank the following people for contributing to my thesis: Professor M arc Schiler, professor of the University of Southern California and my chief advisor, for his patience, guidance, encouragement, and entrusting his invaluable reference books to me. Professor Douglas Noble, professor of the University of Southern California, for his advice on my manuscript. Professor G. Goetz Schierle, director of the Master of Building Science program and professor of the University of Southern California, for his advice and encouragement throughout the past two years. Sammy Chong, for our discussion on how to use Microsoft Word and, with his family, sheltering me during the LA riot. My family and friends, for listening to my complaints. and lastly, to whom I dedicate my thesis, M ichael Yip, for being my personal computer consultant, for being my best friend and listen to me whine in the middle of the night, and most importantly, for being my better half. ii TABLE OF CONTENTS L LIST OF FIGURES vi H. LIST OF TABLES ix m . ABSTRACT X 1. INTRODUCTION 1 2. BASICS OF LIGHTING CALCULATION 6 2.1 Solid Angle 7 2.2 Luminous Energy 8 2.3 Luminous Flux 8 2.4 Luminous Intensity 8 2.5 Illuminance 10 2.6 Luminance 10 3. CONCEPTS OF DAYLIGHT AVAILABILITY 12 3.1 Geographical Location of the Site 13 3.1.1 Latitude 13 3.1.2 Longitude 13 3.1.3 Altitude above Sea Level 14 3.2 Astronomical Location of the Sun (Solar Access) 15 3.2.1 Julian Date 16 3.2.2 Declination Angle 16 3.2.3 Hour Angle 17 3.2.4 Solar Altitude 18 3.2.5 Solar Zenith 19 3.2.6 Solar Azimuth 19 3.2.7 Solar Time 20 3.3 Atmospheric Condition 22 3.3.1 Atmospheric Turbidity 22 3.3.2 Optical Air Mass 23 3.3.3 Sky Conditions 23 t iii 4. COMPONENTS OF DAYLIGHT 25 4.1 Sunlight 26 4.1.1 Solar Illumination Constant 26 4.1.2 Extraterrestrial Solar Illuminance 27 4.1.3 Direct Normal Solar Illuminance 27 4.1.4 Direct Horizontal Solar Illuminance 28 4.1.5 Direct Vertical Solar Illuminance 28 4.2 Skylight 29 4.2.1 Sky Luminance Models 29 4.2.1.1 Clear Sky Luminance Model 31 4.2.1.2 Partly Cloudy Sky Luminance Model 32 4.2.1.3 Overcast Sky Luminance Model 32 4.2.2 Exterior Illumination Models 33 4.2.2.1 Dogniaux Prediction Model 34 4.2.2.2 Gillette Prediction Model 37 4.2.2.3 EES Recommended Model 38 4.3 Reflected Light 41 4.3.1 Lumen Method 42 4.3.2 Daylight Factor Method 45 4.3.3 Flux Transfer Method 48 5. COM PUTER SIMULATION MODEL 52 5.1 Methodology 52 5.2 Input 54 5.2.1 Observed Weather Data File 54 5.2.2 Site and Boundary Information File 55 5.2.3 Date and Time 61 5.3 Algorithms and O utput 62 5.3.1 Solar Access Variables 62 5.3.1.1 Latitude 62 5.3.1.2 Julian Date 62 5.3.1.3 Declination Angle 63 5.3.1.4 Hour Angle 63 5.3.1.5 Solar Altitude Angle 63 5.3.1.6 Solar Azimuth Angle 64 5.3.1.7 Solar Access Tables 64 iv 5.3.2 Radiation Data 67 5.3.2.1 Direct Horizontal S olar Radiation 67 5.3.2.2 Difluse Horizontal Solar Radiation 67 5.3.2.3 Weather Information and Radiation Graph 68 5.3.3 Exterior Illumination of Site using the Dogniaux Model 71 5.3.4 Exterior Illumination of Site using the Gillette Model 76 5.3.5 Exterior Illumination of Site using the EES Model 80 5.3.6 Interreflected Illumination using the Flux Transfer Method 8 5 6. COMPARATIVE SITE STUDIES 87 6.1 Changing Urban Mass 88 6.2 Changing the East-West Length of the Site 106 6.3 Changing the North-South Length of the Site 108 6.4 Changing the Orientation of the Site 110 6.5 Changing the Width of the Surrounding Streets 111 6.6 Changing the Reflectances of the Surrounding Building Surfaces 115 7. CONCLUSIONS 119 8. FUTURE WORK 121 APPENDIX A Glossary of Abbreviations 124 APPENDIX B List of Latitudes for Different Cities 126 APPENDIX C Reflectances of Building Materials and Surfaces 128 APPENDIX D Transmittances of Glass 129 APPENDIX E List of Cities Using TMY Weather Data 131 REFERENCES 132 V 1.1 LIST OF FIGURES Longhouse Pueblo, Mesa Verde, Colorado. 2 2.1 The electromagnetic spectrum and the visible spectrum. 7 2.2 The relationship between luminous flux, intensity, and illuminance. 9 2.3 The relationship between illuminance and luminance. 10 3.1 Latitude. 13 3.2 Longitude. 14 3.3 Latitudes and longitudes of the United States, with magnetic adjustments. 14 3.4a Sun path diagrams for winter and summer solstices and equinox. 15 3.4b Sun path diagrams for different seasons and latitudes. 16 3.5 Declination angles of the solstices and equinoxes. 17 3.6 Hour angles of a day. 18 3.7 Altitude, zenith, and azimuth angles of the sun. 19 3.8 Equation of time. 21 3.9 Optical air mass. 23 4.1 Incident angle. 28 4.2 Uniform sky luminance model. 30 4.3 Sky angles. 31 4.4 Nonuniform clear sky luminance model. 31 4.5 Nonuniform overcast sky luminance model. 33 4.6 Sky fraction in the Gillette model. 38 4.7 Light reflected off surfaces. 41 4.8 Lumen input method. 43 4.9 Daylight factor method. 46 vi 4.10 Dividing surfaces for the flux transfer method. 49 4.11 Contribution of illumination of one surface to another. 50 5.1 Flow chart of the program LightSum. 53 5.2 Parameters of site. 57 5.3 Sample site. 59 5.4 Sample atrium. 60 5.5 Radiation graph for March 21, Portland, Oregon. 69 5.6 Radiation graph for June 21, Portland, Oregon. 70 5.7 Hourly exterior illumination on June 1, simulated with the Dogniaux model. 75 5.8 Hourly exterior illumination on June 1, simulated with the Gillette model. 79 5.9 Hourly exterior illumination on June 1, simulated with the IES model. 83 5.10 Comparison of the direct and diffuse illuminations of the three daylight simulation models. 84 5.11 Available exterior illumination on a site together with the interreffected illumination. 86 6.1 Changing urban mass, Dogniaux model. 88 6.2 Changing urban mass, Gillette model. 92 6.3 Changing urban mass, IES model. 96 6.4 Seasonal illumination simulated with the Dogniaux model. 100 6.5 Seasonal illumination simulated with the Gillette model. 101 6.6 Seasonal illumination simulated with the IES model. 102 6.7 Yearly illumination plots using the Dogniaux model. 103 6.8 Yearly illumination plots using the Gillette model. 104 6.9 Yearly illumination plots using the IES model. 105 6.10 Changing the East-West site length on a clear day. 106 vii 6.11 Changing the East-West site length on an overcast day. 107 6.12 Changing the North-South site length on a clear day. 108 6.13 Changing the North-South site length on an overcast day. 109 6.14 Changing the orientation of the site on June 1, clear day. 110 6.15 Changing the width of the north street. I l l 6.16 Changing the width of the south street. 112 6.17 Changing the width of the east street. 113 6.18 Changing the width of the west street. 114 6.19 Changing reflectance of the surface in the north boundary. 115 6.20 Changing reflectance of the surface in the south boundary. 116 6.21 Changing reflectance of the surface in the east boundary. 117 6.22 Changing reflectance of the surface in the west boundary 118 7.1 Suggested graphic user interface for DayLight. 121 viii LIST OF TABLES 4.1 D and F coefficients used in the Dogniaux model. 35 4.2 Regression coefficients ao, aj, and & 2 used in the Dogniaux model. 36 4.3 Turbidity and daylight availability constants. 39 5.1 Solar access table for March 21, Portland, Oregon. 65 5.2 Solar access table for June 21, Portland, Oregon. 65 5.3 Solar access table for September 21, Portland, Oregon. 66 5.4 Solar access table for December 21, Portland, Oregon. 66 5.5 Weather information table for March 21, Portland, Oregon. 68 5 .6 Weather information table for June 21, Portland, Oregon. 69 5.7 Hourly direct and diffuse exterior illumination in Portland, Dogniaux model. 72 5.8 Hourly direct and diffuse exterior illumination in Portland, Gillette model. 77 5.9 Hourly direct and diffuse exterior illumination in Portland, IES model. 81 ix ABSTRACT This research is an effort to encourage the use of daylighting in architectural design. Daylighting should be included, when possible, as one of the major design criteria for architects. However, some of the key information necessary for designing and analyzing daylighting systems is not commonly considered by architects. One of the reasons is that daylight- and sunlight- availability data is not easily available or comprehensible. This research first studies the methods available for analyzing daylight availability. Then with the intension of aiding the design process, a computer program, with output in table format and three-dimensional graphics, is developed to do the following: 1. Calculate the solar altitude and azimuth angles for a given site, at a given date and time. 2. Read in a TMY weather file to provide recorded weather data ror the specific site. 3. Calculate the direct, diffuse, and total horizontal radiation at an open site or atrium, given boundary conditions of the site or atrium. 4. Calculate the exterior illuminance from the direct sun and diffuse sky, using the solar radiation data, atmospheric turbidity, air moisture, and other weather data. 5. Calculate the total illuminance available over a defined period of time on a workplane of specified height, taking all boundary conditions into consideration. Parameters influencing the daylight availabilty on an open site or within an atrium are studied using the computer program. X 1. INTRODUCTION Daylight is one of the fundamental elements in all life forms. We evolved under the influence of sunlight. We obtain warmth from light. We obtain food derived from light, via plants, in our ecological system. We have developed physiological and psychological responses to daylight and its daily and seasonal variations. Without daylight, we would be disoriented and undernourished. The purpose of this study is to analyze the availability of daylight in response to the sun's rhythm, the atmosphere, the building site, and the urban environment. The source of daylight is, of course, the sun. Although it is just a very small star in the universe, the sun has a huge reservoir of energy. The sun's average surface temperature is 5750 degree-Kelvin. It emits radiant energy at the rate of 6.25 kilowatt/cm2. Its high temperature gives it a luminous efficacy of 90 lumen/Watt.1 The earth only receives about one in 10^ of the total energy radiated by the sun. However, this energy is ample for the survival of all life forms on earth. Because of the rotations of the earth around its own axis and around the sun, each particular point on the earth is accessed by the sun for a period of time that is subject to change daily and seasonally. However, the rhythm of the rotation of the earth is predictable. Our ancestors have taken advantage of this rhythm and the warmth from the radiant energy to achieve thermal comfort. They expressed the role of the sun in primitive architecture. The location and form o f buildings at Longhouse Pueblo, M esa Verde, Colorado, provided ancient residents with year-round 'Murdoch, Joseph B., Illumination Engineering— From Edison's Lamp to the Laser, 1985, p.88. 1 comfort. The pueblo demonstrates a remarkable ability to mitigate extreme environmental temperature variations by responding to the differential impact o f the sun during summer and winter, night and day. The settlem ent is sited in a large cave that fa ces south, and the built structures are nestled within. The brow o f the cave admits warming rays o f the low winter sun but shields the interior o f the cave from the rays o f the more northern summer sun. The interior structures stay within the summer shadow line, and they are arranged so that one structure steps up from another toward the back o f the cave. I t is thus the location o f the cave itself and the siting o f structures within the cave that ensured the com fort o f the pueblo dwellers. Because o f orientation, the irradiation o f the cave on a winter day is equivalent to that on a summer day. The energy performance o f buildings within the cave is remarkably efficient, with adequate winter heat gain and summer coolness. The seasonal adaptation at Longhouse is complemented by the pueblo's response to a daily rhythm as the sun moves from the eastern to the western sky, casting morning rays inside the west end o f the cave and twilight rays inside the east end. The thermal mass o f the cave itself, as well as the structure o f buildings within, helped to mitigate extreme daily variations, but a main adaptation fo r comfort may be best understood in the rhythms o f people's lives.2 Figure 1-1. Longhouse Pueblo, Mesa Verde, Colorado (Knowles, 1981) O SUMMER O WINTER 2Knowles, Ralph, Sun Rhythm Form, 1980, pp. 11-12. Architectural designs thus need to respond to the rhythm of natural light sources in order to achieve thermal comfort and illumination level. The term fo r the practice o f using light from outside to replace electrically generated light indoors is "daylighting. 'n There was little interest in North America in daylighting before the Arab oil embargo in 1973.4 Energy produced by fuel sources such as oil and electricity was cheap and plentiful. There was little concern for utilizing the heat and light from the sun. With the depleting oil supply, architects become more conscious about the issue of energy conservation. The access of daylight to a building could decrease the amount of electrical lights utilized, therefore saving the electrical energy needed to illuminate the building and lowering the cooling load created by the usage of electrical equipment. It would decrease the maintenance cost of the less efficient electrical lights. The quality of light is also important in architectural design. Daylight is natural light that is pleasing to the human eye and reflects the true color of intercepting surfaces, while electrical lights, with the exception of incandescent lights, has a lower color rendition index than daylight. Color rendition index (CRI) is an index ranging from 0 to 100 that measures whether all colors are properly rendered by a light source when compared with a reference source that represents the full spectrum of visible wavelengths at a given color temperature. Daylight is white light that contains the full spectrum of visible wavelengths, while many electrical lights, with the exception of incandescent lights, do not represent some 3SchiIer, Marc, Simplified Design of Building Lighting, 1992, p. 146. 4Murdoch, Joseph B., Illumination Engineering— From Edison's Lamp to the Laser, 1985, p. 88 . 3 colors. Colors seen under a fluorescent light source are different than those seen under daylight. Studies have also shown that human beings are psychologically fitter when exposed to daylight. Human beings are glad to be connected with the nature. If not exposed to enough light for a long enough period of time, a form of depression known as seasonal affective disorder (SAD) affects people, especially in the winter months.5 Since life evolved under the influence of sunlight, a variety of physiological responses to the solar spectrum were developed by many animals, including man. There is growing evidence that fundamental biochemical and hormonal rhythms of the body are synchronized, directly or indirectly, by the daily cycle of light and dark. For example, the daily rhythm in the rate at which normal human subjects excrete melatonin, a hormone synthesized by the pineal organ of the brain, is affected by the amount of light seen by the individual. In man, the amount of the adrenocortical hormone cortisol in the blood also varies with a 24-hour rhythm.6 The near ultraviolet spectrum of sunlight is also used by the body to produce vitamin D, the vitamin that is essential for the proper metabolism of calcium. Furthermore, light has been introduced as the standard treatment for neonatal jaundice, a sometimes fatal disease that is common among premature infants. Other therapeutic uses for light are also important to the human body. Exposure to sunlight is thus necessary for the metabolism of our bodies. It is important that 5Schiler, Marc, Simplified Design of Building Lighting, 1992, p. 8. 6Wurtman, Richard J., "The Effects of Light on the Human Body," Scientific American, Vol. 233, No. 1, p. 69. 4 architects are conscious about the availability of daylight when designing a building. Daylight availability is a factor of time, weather, and the urban environment. The rhythm of the sun is the origin of time as a determinant. Weather condition affects the intensity of sunlight. The urban environment, depending on the time, may intrude on the access of sunlight to the building site. Working with the restrictions of these factors, an architect should considei the daylight behavior on the site to best utilize what is available. Because of the numerous factors involved in daylight calculations and the complexity of the procedures, analyzing daylight availability on a building site is usually not a standard procedure in preliminary design. The variability of weather conditions on a particular site also contribute to the difficulty in predicting daylight. General information on the access of light is not available to the designers unless physical measurements of illumination levels using photometers are executed. To solve this problem, a computer program that will generate the illumination levels at an open site or atrium will save the designers a great amount of time and effort. The computer program will also generate cumulative illuminance received by the site. This can help the design of spaces for vegetation and other uses to insure the quantity of light needed for the activities. The advantage of a computer program is its speed and capacity to handle large amount of data. This makes research easier, faster, more quantitative and, through graphic visualization, more qualitative. 2. BASICS OF LIGHTING CALCULATIONS In discussing the simulation of daylight availability, a basic understanding of the definition of light, its behavior, its qualitative and quantitative measurements is necessary. Light, as defined by the Illuminating Engineering Society of North America, is the visually evaluated radiant energy,1 or simply, a form of energy that permits us to see. The sun reaches the earth in the form of radiant energy that is transmitted in an electromagnetic spectrum of particular wavelengths. ThL radiant energy may be evaluated in two ways. First, there is the heat flow rate, or radiant flux, of the wave spectrum. Second, there is the luminous flow rate of the radiant energy spectrum. Light is the portion of the electromagnetic spectrum which can be perceived by the human eye. The electromagnetic waves of this visible spectrum act upon the retina o f the eye and stimulate the optic nerves to produce the sensation of light. This spectrum lies between the wavelength limits of 380 nanometers, perceived as violet, and 780 nanometers, perceived as red (Figure 2- 1). Visually there may be some individual variation in these limits. Daylight produces energy over the whole visible spectrum in approximately equal quantities. This combination appears as white light. 7EES, EES Lighting Handbook, 5th Edition, 1972, p.2-1. 6 io" 0.1 1 0 1 0 : Ultraviolet Cosmic rays X -rays Inlrared Microwave Radio Gamma Television Power Visible spectrum Infrared uv-a Blue Green Red 200 ran 300 400 500 600 700 800 900 1000 nm Figure 2-1. The electromagnetic spectrum and the visible spectrum (Schiler, 1992) Light obeys certain laws and exhibits certain fixed characteristics. All light waves that strike a surface are either transmitted, reflected, or absorbed. In an open site, the architect or lighting designer must be aware of the behavior of light as affected by the urban environment. Surrounding buildings may cut off the transmittance of sunlight, while others may reflect certain spectrum of light. Both the quantity and quality of light received on the site may be affected immensely. Before discussing light in the quantitative manner, it is important to have an understanding of some physical concepts and terminology involved and their interrelations. The following definitions of lighting terms are paraphrased from Sim plified Design o f Building Lighting, chapter 2.5-2.8, by Marc Schiler and M echanical and Electrical Equipment fo r Buildings, chapter 18.5-18.8, by Benjamin Stein, John S. Reynolds, and William J. McGuinness. 2.1 Solid Angle A solid angle is a ratio of the area on the surface of a sphere to the square of the radius of the sphere. It is expressed in steradians. A sphere with a radius of one foot has an area of 47t square feet. Each one square foot on this sphere 7 subtends a solid angle of one square foot (area) per one foot (radius), and thus, ■one steradian. This sphere has a total of 4 71, or 12.57, steradians. The solid angle is a convenient way of expressing the relationship between the light source, treated as a point, and the light energy that it emits. 2.2 Luminous Energy Luminous energy, Q, is the amount of energy transmitted in the visual spectrum. It is measured in lumen-seconds (lm-sec) or sometimes in Talbots (T). This unit is rarely used in calculations. 2.3 Luminous Flux Luminous flux (O) is the time flow rate of light energy. If we take a light source and surround it with an imaginary sphere of a fixed distance, the luminous flux through a defined area on that sphere is the amount of luminous energy flowing through the defined area. Luminous flux can be expressed as: < D = dO/dt The unit for measuring this flow rate, in both the English system and the Systeme International (SI), is lumen-second per second or lumen (lm). 2.4 Luminous Intensity The amount of light emitted by a source in a specific direction is called the luminous intensity (/). It represents the force of the source that generates light. It is defined as the luminous flux on a surface of the imaginary sphere per unit solid angle: / = d < E > / da 8 There are two units of measure for the luminous intensity. The first one is candlepower (cp), which measures the amount of energy emitted in all directions by a single candle. The second unit is candela (cd), which measures the rate at which energy is leaving the source in a specific direction. The magnitude of a candela is the same as a candlepower, but the definition is more specific. A luminous intensity of one candlepower results in one lumen passing through one steradian of the sphere. More specifically, a luminous intensity of one candela results in a luminous flux of one lumen passing through the steradian in the direction normal to that steradian. Spherical surface j t • 1 in area 1 m radius radius Spherical surface 1 ft2 in area • Total flux of 1 lum en Total flux 12.57 lu m e n s . . Total flux _ of 1 lum en Light source 1 can d ela Illum inance 1 fc or 1 Im /ft2 or 10.76 lux Illum inance 1 lux or 1 1 m /m 2 or 0 .0929 fc Figure 2-2. The relationship between luminous flux, intensity, and illuminance (Stein, 1986). 9 2.5 Illuminance The light energy arriving at a surface is the illuminance (E). It is the flux density intercepted by a surface at a given distance from the light source; specifically, it is the luminous flux per area of the surface: E = d< D / dA The unit of measure is footcandle (fc) in the English system and lux (lx) in the SI system. One lumen of luminous flux, uniformly incident on one square foot of area, produces an illuminance of one footcandle. One lumen of luminous flux on one square meter of area produces one lux (Figure 2-3). The actual measurement of one lux is smaller than one footcandle by the ratio of square feet to square meters: 10.764 lux = 1 footcandle Illuminance: 100 fc or 100 lm/sq.ft. Light Source: '" 100 candelas or 1257 lumens output Luminance: (100 lux or 100 Im/sq.m) * Transmittance o f surface Figure 2-3. The relationship between illuminance and luminance (Stein, 1986). 2.5 Exitance and Luminance There are two ways to define the light energy leaving a surface. First, the exitance (M ) is the total luminous flux density leaving a surface without specifying the direction of emittance. 10 M = dO / dA The magnitude of the exitance depends on the reflectance of the surface if light is reflected, or the transmittance of the surface if light is transmitted. The term for the total luminous flux density leaving a surface in a given direction, per unit of area of the surface as viewed from that direction, is the luminance (L). It is expressed by the following equation: L = d2n / dca dA cos 0 0 is the angle between the direction of observation and the normal to the surface. The unit of measure for luminance is footlambert (fL) in the English units and candela/square meter in the SI units. One footlambert is equal to 1/xc candela per square foot. A surface reflecting, transmitting, or emitting one lumen per square foot of area, in the direction being viewed, has a luminance of one footlambert. Similarly, a surface emitting one lumen per square meter has a luminance of l/7t (cd/m2). Luminance can also be described physically as the brightness of a surface. A more general definition of the luminance is that it is the portion of the illuminance of the surface reflected or transmitted by the same surface: L = E * p or L = E * x where p is the reflectivity of the surface and x is the transmittance of the surface. 11 3. DAYLIGHT AVAILABILITY FACTORS In order to understand the amount of daylight available on a particular site, a complete understanding of the factors affecting the behavior of daylight is necessary. Daylight is the light energy arriving at the earth from the sun. It travels in the form of light waves through space and the earth's atmosphere. Through its course of travel, much of the original wave is intercepted and, thus, the resultant measured at the ground level varies. The availability of daylight on a particular site depends on three groups of variables, which are the geographical location of the site, the astronomical location of the sun with respect to the earth, and the atmospheric condition of the sky at a particular time. The description of the geographical location of the site includes the latitude, longitude, and the altitude of the site above sea level. These factors are fixed and, therefore, have predictable influence over the access of daylight. The astronomical location of the sun with respect to the earth is described in terms of solar altitude and solar azimuth, among other variables. These factors vary with time and have a daily and seasonal effect on the availability of daylight. The last group of factors, the atmospheric condition of the sky, is the most unpredictable element contributing to daylight access. The turbidity, moisture, optical air mass of the atmosphere, and sky clearness all affect the amount of daylight reaching the site after travelling through the atmosphere. 12 3.1 GEOGRAPHICAL LOCATION The first factor that effects the amount of usable solar energy and daylight is the geographical location of the site being considered. 3.1.1 Latitude Latitude, L, is the angular distance measured along a meridian from the equator, north or south, to a point on the earth's surface, in degrees. The latitude along the equator is zero degrees. Any location north of the equator has positive latitudes; any location south of the equator has negative latitudes. The north and south poles are at +90 and -90 degrees respectively (Figure 3-1). The latitude of the location is important in that different latitudes define different relationships with the sun. s Elevation S ection s Figure 3-1. Latitude. 3.1.2 Longitude Longitude, I, is the angular distance measured from the prime meridian through Greenwich, England, west or east to a point on the earth's surface. Any 13 location west of the prime meridian has positive longitude; any location east of the prime meridian has negative longitude (Figure 3-2). N West East -90 s Plan View Figure 3-2. Longitude. Figure 3-3. Latitudes and longitudes of the United States, with magnetic adjustments (Mazria, 1979). 3.1.3 Altitude from Sea Level The altitude of a location from sea level is measured in feet or meters. It is important in that locations with different altitudes have different atmospheric pressures which affect the transmittance of light. 14 3.2 ASTRONOMICAL LOCATION OF THE SUN After understanding the geographical location of the site, the geometrical relationship between the sun and the particular site on earth must be analyzed. This geometrical relationship can be described by the latitude of the site, the time of the year, the time of the day, the angle between the sun and the earth, and the altitude and azimuth angles of the sun. This geometrical relationship can also be graphically expressed as sun-path diagrams plotted for each specific site. The sun- path diagrams usually trace the path of the sun on the 21st day of each month. But sometimes only four days are represented: winter solstice (December 21) which has the lowest sun angle of the year, summer solstice (June 21) which has the highest sun angle, and equinox (March 21 and September 21) which marks the absolute midpoint between the two solstices. For sites with different latitudes, the sun follows different paths (Figure 3-4). Sum m er Fall and spring W inter W N Structure E e,<f A , + 2 3 .5 “ = A 2 Figure 3-4a. Sun path diagrams for winter and summer solstices and equinox (Stein, 1986). 15 Equinox 90“ (Pole) (Equator) Figure 3-4b. Sun path diagrams for different seasons and latitudes (Stein, 1986). The factors used to describe the geometrical relationship between the earth and the sun also determine the location of shadows cast on the site by the surrounding buildings, which in turn determine whether both direct and diffuse light fall on the site. 3.2.1 Julian Date The Julian date is the number of days since the first day of the year. January 1 has a Julian day of 1; December 31 has a Julian day of 365 except on a leap year, when it has a Julian day of 366. 3.2.2 Declination Angle The earth orbits the sun in an elliptical path, while rotating itself once a day on an axis that extends from the North Pole to the South Pole. This axis is tilted 23.45 degrees from a vertical to the plane of ecliptic. The declination of the sun 5S is the angle between the sun's rays and the zenith direction at noon on the earth's equator.8 Declinations north of the equator, that is, summer in the northern 8Kreith, Frank; Kreider, Jan F., Principles of Solar Engineering, 1978, p.46. hemisphere, are positive; those south of the equator are negative. At the summer and winter solstices, the declinations are at the extreme: on June 21, the declination angle is +23.45 degrees, whereas on December 21, it is -23.45 degrees (Figure 3-5). For most of the solar calculations the declination angle is considered to be constant throughout the whole day. The declination angle of the day is given by the following equation:9 5S = 23.45 * sin ((Julian date + 284) * 360 / 365) Sep 21 SUN Dec 21 June 21 Mar 21 Figure 3-5. Declination angle of the soltices and equinoxes. 3.2.3 Hour Angle The hour angle hs is the angular distance the earth has rotated in a day. It is equal to 15 degrees multiplied by the number of hours from local solar noon. This is based upon the nominal time, 24 hours, required for the earth to rotate 9Kreith, Frank; Kreider, Jan F., Principles of Solar Engineering, 1978, p. 45. 17 once, 360 degrees. The local solar noon is considered to be due south and is at 0 degrees. Values east of due south, that is, morning values, are positive; values west, that is, afternoon values, are negative (Figure 3-6).1 0 The hour angle is given by: hs = 15 * (12 - hour) 200 iso 100 W > < u Q -so so 17 18 19 20 21 22 23 -100 -150 -200 Hour Figure 3-6. Hour Angles of a day. 3.2.4 Solar Altitude The solar altitude angle a is the angle within the vertical plane measured from the local horizontal plane upward to the center of the sun. It is the sun's position at elevation view (Figure 3-7). Solar altitude affects the luminance of the sky vault and the amount of illuminance available on the work plane. The altitude angle relates to the latitude of the site, the declination angle, and the hour angle:1 1 sin a = sin L sin 8S + cos L cos 8S cos hs 10Kreith, Frank; Kreider, Jan F., Principles of Solar Engineering, 1978, p.45. u Kreith, Frank; Kreider, Jan F., Principles of Solar Engineering, 1978, p.50. 18 SUN Zenith. Azimuth Figure 3-7. Altitude, zenith, and azimuth angles of the sun. 3.2.5 Solar Zenith Angle The zenith angle z is the complementary angle to the altitude angle a t, that is, (a + z) equals to 90 degrees. It is the angle within the vertical plane measured from zenith to the center of the sun (Figure 3-7). 3.2.6 Solar Azimuth The azimuth angle as is the angle within the horizontal plane measured from the vertical plane intersecting true south to the vertical plane, rotated about the zenith, intersecting the center of the sun. It is the sun's position in plan. The sign convention is positive east of south and negative west of south (Figure 3-7). The azimuth sets the angle of shadow by the surrounding buildings and can be described by the following formula:1 2 sin as = cos S£ sin h£ cos a 12Kreith, Frank; Kreider, Jan F., Principles of Solar Engineering, 1978, p.50. 19 3.2.7 Solar Time The hours used for the calculation of daylight in this study will be solar time. Solar time is the time that would be given by a sun dial oriented true south. Solar noon occurs when the sun reaches its maximum altitude. The length of a day, measured from solar noon to solar noon, is not uniform throughout the year because of the earth's nonuniform motion around the sun. This can skew the solar time with respect to the local time, which is measured with clocks moving at a uniform rate. The maximum length of time difference due to the earth's nonuniform motion is about 17 minutes. Furthermore, if the observer is not exactly on the time meridian for his time zone, his local time will be shifted further.1 3 If daylight savings time is in effect for the region, it also needs to be considered since it deviates the solar time further by one hour. Therefore all the factors described above have a cumulative effect on the difference between the local time of a particular site and its solar time. The user must input the solar time while entering the hours to be considered in the program. To find the corresponding solar time for a local time, the following procedure should be applied: . 1. Subtract one hour from the local time if daylight savings time is in effect. 2. Determine the correction for the earth's non uniform movement, called the equation o f time (ET), according to the day of the year (Figure 3-8). 13Johnson, Timothy, Solar Architecture, 1981, p. 20. 20 3. Find the longitude of the site, /, and the longitude of the time meridian, Im. 4. Use the following equation to find the solar time:1 4 Solar Time = ET + 4 minutes/degree {Im - 1) + Local Time -/O -/s Z )£ C J A M r £ B M A * A P A AH W J& M J tfU A i/G S £ P O C T M O t ' Figure 3-8. Equation of time (Johnson, 1981). 14Johnson, Timothy, Solar Architecture, 1981, p. 23. 21 3.3 ATMOSPHERIC CONDITION The atmospherical condition describes the sky condition at a particular time. The atmosphere has a significant effect on the amount of light that can pass through and on the amount of light that is scattered in the sky. The sky's unpredictable condition makes the prediction of daylight availability difficult. However, weather information for various cities has been recorded throughout the years. Some generalized patterns of sky condition are set up for each of these cities. 3.3.1 Atmospheric Turbidity The intensity of direct solar illumination for a given solar elevation depends on the variable amount of dust and haze in the atmosphere. The extinction produced by these constituents is called the atmospheric turbidity. However, the atmospheric turbidity sometimes also includes the effect of water vapor in the atmosphere, which is otherwise represented separately as the moisture content of the air. In the Dogniaux illumination simulation model discussed in the next chapter, the turbidity and moisture content are accounted for separately. In the Gillette simulation model, however, the turbidity and moisture content are treated as one variable. Turbidity observations have been made at individual stations around the world, starting with Linke and Boda (1922) and Angstrom (1929).1 5 In 1960-61, 15Flowers, E.C. et.al. "Atmospheric Turbidity over the United States, 1961-1966," Journal of Applied Meteorology, December 1969, p.955. 22 a network program was established in the United States to make routine measurements of turbidity with the Volz sunphotometer at various stations. Monthly average atmospheric turbidity is derived for these stations. These results can be used for calculation of solar illumination passing through the atmosphere. 3.3.2 Optical Air Mass The optical air mass ratio is the dimensionless path length of sunlight through the atmosphere. It varies inversely with the sine of the solar altitude angle (Figure 3-9). At the outer boundary of the atmosphere, the air mass ratio equals to zero since it does not travel through any atmosphere. When the sun is overhead, the air mass ratio is equal to 1; when the solar altitude angle is 30 degrees, the air mass ratio is equal to 2. NOON, SUN MORNING SUN a l t it u d ; [OSPHERE Figure 3-9. Optical air mass. 3.3.3 Sky Condition The sky condition is described in terms of a clear sky, a partly cloudy sky, or an overcast sky. There are two ways to determine the sky condition of a particular sky at a particular time, the sky cover method and the sky ratio method. 23 The sky cover method is used by the National Oceanic and Atmospheric Administration (NOAA).1 6 The sky cover is estimated by visual observation of the amount of cloud cover. Cloud cover is estimated in tenths and ranges from 0 for no clouds to 10 for a completely covered sky. The sky conditions are: clear = 0 to 3 tenths partly cloudy = 4 to 7 tenths cloudy = 8 to 10 tenths The sky ratio method is used by the National Bureau o f Standards (NBS). The sky ratio is the ratio of horizontal sky irradiance to global horizontal irradiance. Since the sky ratio approaches 1 when the solar altitude approaches 0, regardless of sky condition, this method is inaccurate at low solar altitudes. The sky conditions are: clear = sky ratio <0.3 partly cloudy = 0.3 < sky ratio < 0.8 cloudy = sky ratio >0.8 Either the sky cover method or the sky ratio method will give similar results for daylight calculations. 16IES Calculation Procedures Committee, Recommended Practice for the Calculation of Daylight Availability, December 1983. 24 4. COMPONENTS OF DAYLIGHT There are three components of daylight which contributes to the final illuminance available on a surface. These are the direct sunlight, diffuse light from the sky, and the reflected light from surrounding surfaces. The measurement of each of these components depends on the sky condition at a particular time and the location of the site. 25 4.1 Sunlight Sunlight is the direct light received from the sun. For the purpose of daylight calculation, the sun is considered to be a point source providing a constant illuminance at a fixed distance in free space. When calculating the sunlight reaching the ground, there are two factors to be considered: 1. The varying distance of the earth to the sun caused by the earth's elliptical orbit. 2. The attenuation of sunlight by the earth's atmosphere. 4.1.1 Solar Illumination Constant The solar illumination constant is the total solar illuminance on a surface in free space which is normal to the sun's rays, at the earth's mean distance from the sun. This "constant" is an average value of the extraterrestrial solar illuminance described in the next section. The solar illumination constant is expressed by the following equation: ESC = Km / Gl V2 . E§c = ^27.5 klux or 11850 fc. where E sc = s°lar illumination constant Km = spectral luminous efficacy of radiant flux = solar spectral irradiance at wavelength X = photopic vision spectral luminous efficiency at wavelength X ’ 2 6 4.1.2 Extraterrestrial Solar Illuminance The extraterrestrial solar illuminance is the total solar illuminance measured on a surface normal to the sun's rays at the earth's outer atmosphere. Since the earth moves in an elliptical path, not a circular one, around the sun, the extraterrestrial solar illuminance for any day of the year is different because the distance from the earth to the sun is different. The extraterrestrial solar illuminance is a variant of the solar illumination constant. On any day of the year, the extraterrestrial solar illuminance is: E x t = E s c { 1 + 0 0 3 4 c o s I 2 * / 3 6 5 ( J - 2 ) ] } where Ext = extraterrestrial solar illuminance E sc = s°lar illumination constant J = Julian date (1 <= J <= 365) 4.1.3 Direct Normal Solar Illuminance The direct normal solar illuminance, also referred to as the direct beam, is the solar illuminance that is measured on a surface normal to the sun's rays at ground level. This is the solar illuminance that reaches the ground after passing through the atmosphere and is given by the equation: Eo n = Ext exP (-cm) where Edn = direct normal solar illuminance Ext = extraterrestrial solar illuminance c = atmospheric extinction coefficient calculated from turbidity and moisture 27 m = optical air mass 4.1.4 Direct Horizontal Solar Illuminance The direct horizontal solar illuminance is the direct sunlight measured on horizontal plane. It is expressed by the equation: E d h = E d n s* n a where e dh = direct horizontal solar illuminance Edn = direct normal solar illuminance a = solar altitude 4.1.5 Direct Vertical Solar Illuminance The direct vertical solar illuminance is the direct sunlight measured on a vertical surface.' It is expressed by the equation: Epv — E dn ai where e Dv = direct vertical solar illuminance av ~ incident angle (Figure 4-1) Z E N IT H NORMAL TO / VERTICAL * SURFACE Figure 4-1. Incident angle (EES, 1983). 4.2 Skylight As sunlight passes through the atmosphere, a portion of the incident radiation is scattered by dust, water vapor, and other suspended particles in the atmosphere.1 7 The resultant is scattered light throughout the sky called skylight, or diffuse light. In order to calculate the amount of this skylight, the sky condition must be determined first. The three sky conditions, clear sky, partly cloudy sky, and overcast sky, have distinct luminance distribution in the sky; therefore, for each sky conditions, the brightness of the sky needs to be modeled first. The amount of skylight received at any point is a summation of all the luminance distribution of the sky seen from that point. 4.2.1 Sky Lum inance Models Skylight, or daylight, is theoretically evenly distributed over the sky dome, that is, it composes a uniform sky. A uniform sky assumes an infinite flat surface of uniform brightness.1 8 If the luminance from the horizon to horizon is integrated, the resulting illuminance on the horizontal surface is the same as the illuminance of the sky. A vertical surface, however, has an illuminance of half of the horizontal surface illuminance since the vertical surface only sees half of the sky hemisphere (Figure 4-2). In reality the sky luminance is almost never uniform. But the uniform model is a useful and efficient way of estimating the illuminance on surfaces. 17IES Calculation Procedures Committee, Recommended Practice for the Calculation of Daylight Availability, December 1983, p. 10. 18Schiler, Marc, Simplified Design of Building Lighting, 1992, p. 86. 29 - UNIFORM LUMINANCE V . \\#’ S .M ' u .____ i £ •= I E B n B B n : i n V iW ; V '- A .' i X ir . I______ Figure 4-2. Uniform sky luminance model (Stein, 1986). The luminance of the sky is a function of the absolute values of the zenith luminance and the luminance distribution with respect to the zenith luminance. Many researchers in the past had developed different formulations for the sky luminances.1 9 Among these formulations, the Illuminating Engineering Society of North America has accepted a set of equations as the standard formulas that describe the sky luminance of the clear, partly cloudy, and overcast skies. In order to understand the sky luminance equations, a set of angles must be identified (Figure 4-3). The point P is the point in the sky at which the sky luminance is calculated. The position of point P is given by the angles C , and as where C , = the zenithal point angle as = the azimuth angle from the sun Angle y is the angle between the sun and the point P on their intersecting plane, y = arccos (cos z0 cos Q Diffuse horizontal and vertical illuminances can be calculated by integrating the luminance models described in the following section over the sky angles seen by the planes: 19Some of these researchers include Richard Kittler, Moon and Spencer, Joseph Murdoch, P.J. Littlefair, R. McCluney, and H. J. Bomemann. 30 ^diffuse, horizontal S S ^ * * * * * ^ ^ dot 'diffuse, vertical - N Figure 4-3. Sky angles (IES, 1983). 4.2.1.1 Clear Sky Luminance Distribution A standard clear sky luminance distribution function was developed by Kittler and adopted by the International Commission on Illumination (CIE).2 0 This distribution is given by the following equation: L = Lz [.91 + 10 expf-3^) + .45 cos2 ^ IT - exp(-.32/cos D 1 [.91 + 10 exp(-3z0) + .45 cos2 z0] [1 - exp(-.32)] A simpler description of the clear sky luminance model is that the luminance at the horizon is generally three times brighter than the zenith luminance (Figure 4-4). Figure 4-4. Nonuniform clear sky luminance model (Stein, 1986). 20IES Calculation Procedures Committee, Recommended Practice for the Calculation of Daylight Availability, December 1983. J. CLEAR SKY* NONUNIFORM LUMINANCE E3 f-| E3 4.2.1.2 Partly Cloudy Sky Luminance Distribution The partly cloudy sky luminance distribution function adopted by CIE is similar to the clear sky distribution, with the exception of modified constants. The distribution is given by the following equation: L = Lz [.526 + 5 expf-l.SyVj [1 - exp(-.80/cos ^)] [.526 + 5 exp(-1.5z0)] [1 - exp(-,80)] 4.2.1.3 Overcast Sky Luminance Distribution For the overcast sky, the following equation best describes the data used by Moon and Spencer in their studies of the completely cloudy sky:2 1 L = Lz (.864 fexpf-.52/cos D1 + .136 H - exp(-.52/cos Of } [exp(-.52)] [1 - exp(-.52)] The first term in the above formula provides the luminance contribution of the cloud layer. The second term provides the luminance contribution of the atmosphere between the bottom of the cloud layer and the ground. Moon and Spencer had also developed an empirical equation for the overcast sky luminance distribution: L = Lz / 3 * (1 + 2 cos Q This equation describes a sky luminance distribution that is three times brighter at the zenith than at the horizon (Figure 4-5). This equation has been almost universally used to represent overcast skies since the mid 1940's and was adopted 21Moon, P. and Spencer, D., "Illumination from a Nonuniform Sky," Illuminating Engineering, vol. 37, No. 12, December 1942, p. 707. 32 by the CIE in 1955.2 2 There is very little numerical difference between the two equations given. Figure 4-5. Nonuniform overcast sky luminance model (Stein, 1986). 4.2.2 Exterior Illumination Models The illumination level necessary for architectural design is usually measured on a horizontal surface called the workplane. This workplane is specified ..or a particular function and can be located at any height from the ground. A particular illumination level is to be met for a given function on this workplane. The common workplane in the United States has a height of 30 inches. This first step in calculating the amount of daylight availability at a certain site is to determine how much horizontal illumination, E qH, is available at the site if there is no obstruction in the surroundings of the site. This illumination level is called the exterior illumination, consisting of the direct sunlight and diffuse skylight. The traditional approach to analyzing daylight availability has been to take detailed measurements for a given locale, and then to use the measured data to establish a locale-specific illuminance model,2 3 A number of models have been 22IES Calculation Procedures Committee, Recommended Practice for the Calculation of Daylight Availability, December 1983. 23Robbins, Claude L., Daylighting Design and Analysis, 1986, p. 29. COMPLETELY OVERCAST SKY: NONUNIFORM LUMINANCE 33 established for different cities all over the world in the past century. However, the primary limitation of these models is that they are applicable to only one locale. Another limitation is that most of these models only represent the global illuminance on a horizontal surface. From the late 1960's, several general illuminance models have been developed. These models break down the global illuminance into direct, diffuse, and reflected components of the daylight resource. They can be applied to a given locale by using recorded or calculated climatic data to describe the local atmospheric conditions. In the United States, the Typical Meteorological Year (TMY) in 244 cities and the Test Reference Year (TRY) climatic data can be used (Appendix E). 4.2.2.1 Dogniaux Prediction Model The Dogniaux model was developed for the CIE in 1967. It is one of the first major general illuminance prediction models ever developed. It has never been formally accepted as an Agreed CIE Recommendation, although it was approved by a majority of the CIE Daylighting Technical Committee.2 4 The Dogniaux model has two techniques for estimating the exterior illumination on a horizontal plane. The first one is a model of the clear sky illumination. The second one is for the overcast sky. For the clear sky model, the global illuminance on a horizontal surface, EqH c is defined in the following equation, expressed in lux: E GH, c = E DH, c + E dH,c 24Robbins, Daylighting Design and Analysis, p. 37. where Eqjj c is the direct illuminance and c is the diffuse illuminance of a clear sky. The direct illuminance is expressed as an attenuated value of the extraterrestrial solar illuminance effected by the atmosphere and the altitude of the sun, which combines the concepts introduced in sections 4.1.3 and 4.1.4: EDH,c = E sC j(e -amT) ESC j is the apparent extraterrestrial solar illuminance constant for any given day, y; a represents the atmospheric extinction coefficient; m is the optical air mass; and T is the turbidity factor. These values are defined in the following equations, expressed in lux: ESCj = 126,820 + 4,248 cos wJ + 0.0825 cos 2wJ - 0.0043 cos 3wJ + 0.1691 sin wJ + 0.00914 sin2w + 0.01726 sin 3wJ where 126,820 lux is the solar illuminance constant adopted by Dogniaux, w equals 0.0172, and J is the Julian day of the year. The atmospheric extinction coefficient a is defined by: a = D - F(T) where the D and F coefficients vary with the turbidity coefficient 3 (Table 4-1). Turbidity Coefficient (P) D F 0.05 0.1512 0.0262 0.10 0.1656 0.0215 0.20 0.2021 0.0193 Table 4-1. D and F coefficients used in the Dogniaux Model. The optical air mass m is a function of the solar altitude a: 35 m = 10.01 + {a -5 / [-1.217 + (a -11) / (-10.034 + (a - 24.5) / (150.343 -(a -4 0 )/ 1.821))]} The turbidity factor T is defined as: T = {[(a + 85) / (39.5e"w + 47.4)] + 0.1} + (16 + 0.22w)(3 where w is the precipitible moisture, in centimeters, in the atmosphere. The clear sky diffuse illuminance, c , is represented by: E dH, c = a0 + a1 a 2 + a2 a 3 Values for the a coefficients are found in Table 4-2, varying with turbidity coefficient 3. 3 = 0 .0 5 w I I o • 3 = 0.2C an a, a , an a, a2 ao a, a2 w = 0.5 0.9361 0.0020 .2*io-7 1.0239 0.0024 -2*10-7 1.1399 0.0030 -3*10-7 o I I £ 0.9093 0.0018 -1*10-7 1.0206 0.0022 -2*10-7 1.1499 0.0028 -3*10-7 w = 2.0 0.8727 0.0014 -0*10-7 1.0074 0.0019 -1*10-7 1.1698 0.0025 -2*10-7 w = 3.0 0.8547 0.0012 -0*10-7 1.0019 0.0017 -1*10-7 1.1833 0.0023 -2*10*7 o ■ r f ’ I I £ 0,8460 0.0011 -0*10-7 0.999 0.0016 -1*10-7 1.1899 0.0022 -2*10-7 w = 5.0 0.8410 0.0011 -0*10*7 0.998 0.0016 1 * 1 — » o 1.1968 0.0021 -2*10-7 Table 4-2. Regression coefficients a^ & l, and % used in the Dogniaux model. For the overcast condition, there is no direct illuminance. To find the overcast diffuse illuminance, Dogniaux used the CIE standard overcast sky equation for sky luminance: Lp 0 — Lz o [(1 + 2sin ot) / 3] 36 The diffuse illuminance is the integral of the sky luminance equation over the angles that define the whole sky vault. 4.2.2.2 Gillette Prediction Model The Gillette model was developed at the National Bureau of Standards in 1983, with support from the U.S. Department of Energy and the National Fenestration Council. It is based upon extensive measurements made at the NBS in Gaithersburg, Maryland.2 5 The principal parameters are: 1. solar location (solar altitude, azimuth, time) 2. global radiation on a horizontal surface, Ijjg 3. the ratio of diffuse to total horizontal radiation as effected by atmospheric turbidity and moisture content. Again, the global horizontal illumination is a summation of the direct and diffuse horizontal illumination: e GH, c = e DH, c + E dH, c • The direct component E ^ h c is expressed in lux as follows: e DH, c = (EDN) ( s i n ° 0 ( £ c l r ) where EDN is the direct normal illuminance: e d n = E SC D + 0 033 c o s (3 6 0 J 1 3 6 5 >] e ’a/sin a EgQ is the solar illuminance constant, which is 127,500 lux. J is the Julian date, and a is the atmospheric extinction coefficient. The £ variable is a clear or overcast sky fraction defined by Gillette that accounts for the effects of cloud cover upon clear sky direct and diffuse illuminance (Figure 4-6). The sky fractions can be determined by: 25Robbins, Daylighting Design and Analysis, p. 38. 37 £clr = [1 + cos (CR t t )] / 2 £ o v r = [ l - c o s ( C R t c ) ] / 2 SK Y PH A SIN G FUNCTION 0 .8 1.6 0 .6 1.0 0 .4 CLOUD R A T IO .6 Figure 4-6. Sky fraction in the Gillette model (Gillette, 1983). CR is the cloud ratio, or the ratio of diffuse to global solar radiation falling on a horizontal surface. CR is the same as the sky ratio defined in section 3.3.3. The diffuse illuminance, E ^ c can be determined from the diffuse solar radiation and a diffuse luminous efficacy value: E dH.c = 111 IdH, c Using the recorded radiation data for each TMY stations, hourly illuminance for each station and its surrounding area can be predicted. 4.2.2.3 IES Recommended Model The illumination prediction model recommended by the Illuminating Engineering Society is based on the luminance model studies by Richard Kittler, 38 Moon and Spencer, and on the illuminance studies by William Pierpoint. Empirical equations are used for the prediction of direct and diffuse light under the three sky conditions: clear, partly cloudy, and overcast sky. The direct illumination received on horizontal and vertical planes, e d h and Edv, is calculated using the same formulas described in chapter 4.1, where E DH= e DN s‘n a e DV= e DN cos ai e DN= e SC 0 + 0.034 c o s [2k / 365 ( J - 2)] } * exp (-cm ) In the model, the turbidity c is defined for the three sky conditions in Table 4-3. Sky Condition c A B C (klux) (klux) (klux) Clear 0.21 0.8 15.5 0.5 Partly Cloudy 0.80 0.3 45.0 1.0 Overcast * 0.3 21.0 1.0 * No direct sun; EDN = 0. Table 4-3. Turbidity and daylight availability constants. The horizontal diffuse illumination, E^jj, can be calculated using the following equation: E dH = A + B sinc a The constant A is the sunrise or sunset illuminance; B is the solar altitude illuminance coefficient; C is the solar altitude illuminance exponent; a is the solar !| j altitude. The constants A, B, and C varies with the sky conditions and can be I found in Table 4-3. For the diffuse illuminance on vertical surfaces, E^y, empirical formulas were developed by William Pierpoint:2 6 Clear Sky: E(jv = (4.0 a 1-3 + 12.0 sin0- 3 a cos1-3 a ) * [(2 + cos az)/(3 - cos a^] Partly Cloudy Sky: EdV = (12.0 a + 30.2 sin0-8 a cos a ) * [(1 + cos az)/(3 - cos az)] Overcast Sky: Edv =8.5 sin a In the above equations, az is the angle between the solar azimuth and the normal of the vertical surface. Because the IES model uses empirical equations based on studies made with the three sky conditions, the resulting illuminances are subject to errors under marginal sky conditions. A sky ratio of 0.3 is considered a clear sky and empirical turbidity and coefficients for the clear sky are used for the simulation of direct and diffuse illuminances. A sky ratio of 0.31 is considered a partly cloudy sky and therefore values for the partly cloudy sky are used for simulation. In reality the sky conditions with these two sky ratios should produce similar illuminances. However, with the IES simulation method, the two sky conditions produce a difference of up to 200 percent. 26Pierpoint, William, "A Simplified Sky Model for Daylighting Calculations," 1983 International Daylighting Conference General Proceedings, p.47. 40 4.3 Reflected Light (Daylight Analysis Methods) A light wave travels in a manner that, when it encounters a translucent or opaque surface, some of the light will bounce back while the rest will be absorbed or transmitted. The amount of light that will be bounced back depends on the property of the surface and the angle of incidence. In the urban environment, a site is surrounded by other buildings in most cases. The amount of illumination at any point on that site depends immensely on these surrounding surfaces. After the exterior illumination level is known, the portion of the exterior illumination falling on a particular point needs to be determined, which would be the initial illumination level. Then the light which is bounced between the surrounding surfaces to the point will be added to obtain the final illuminance (Figure 4-7). For architectural calculations, the angle of incidence in determining the change in the reflectivity of the surface may be ignored. This is because the reflectivity remains fairly constant to within an incidence angle of 15 degrees of parallel or 75 degrees of the surface normal. Figure 4-7. Light reflected off surfaces. Procedures for calculating illumination from natural sources in an interior space have been proposed in more than fifty different countries over the past 90 41 Incidence Angle years.2 7 All of these methods can be categorized into one of two general categories: methods o f analysis that determine the absolute illuminance and methods of analysis that determine the relative illuminance. Methods of analysis providing absolute illuminance allow the designer to predict the actual illumination level at a given point at a particular time and day. Two of these methods that are widely used are the lumen input method and the flux transfer method. Methods of analysis that determine relative illuminance allow the designer to make a prediction of the percentage of exterior illuminance provided by daylight at a given station point. The daylight factor method is the primary technique for establishing the relative illuminance values. 4.3*1 Lum en Input M ethod The lumen method was developed in the United States at Southern Methodist University in 1953 and modified by Griffith, Amer, and Conover in 195 5.2 8 This method can be used for four distinct sky conditions: 1. The CIE standard overcast sky 2. The clear sky, with no sun on the window 3. The clear sky, with direct sun on the window and internal shading device 4. The uniform sky, with internal shading device present It assumes that the exterior ground plane and the interior surface reflectances play an important part in determining the illuminance provided by 27Robbins, Claude L., Daylighting Design and Analysis, 1986, p. 157. 28Robbins, Claude L., Daylighting Design and Analysis, 1986, p. 157. 42 daylight. It also assumes that there is only one window wall in the interior space and that the wall is uniformly lit. In the lumen method, absolute illuminance can only be determined for three station points of a given space, each located at workplane 3 feet above the floor. The three station points are located along an axis centered on the aperture. The max point is located at 5 feet into the room from the aperture. The mid point is located at the center of the room, and the min point is located 5 feet from the back wall. The absolute illuminance at each station point is designated Emax, Emjd, and Emin, respectively (Figure 4-8). S U N W INDOW W O R K PL A N E MID MAX Figure 4-8. Lumen input method. The lumen method carefully describes the variables affecting the amount of daylight reaching the work plane in a space. The variables are: 1. Those affecting the light reaching the aperture form above the horizon: a. the illuminance from the clear or overcast sky, b. the angular position of the sun with respect to the aperture, c. the intensity of sunlight. 2. Those affecting the light reaching the aperture from below the horizon: 43 a. the illuminance striking the ground for clear and overcast skies, b. the reflectivity of the ground, pg. 3. Those affecting the light leaving the inner surface of the aperture: a. the area of the aperture, b. the transmission of the glazing, c. the ratio of actual glazing area to aperture area, d. the dirt depreciation factor. 4. Those affecting the utilization and distribution of light on the work plane: a. the distribution of interreflected light in the room, b. the geometric description of the aperture, c. the geometric description of the room. The final illumination of each of the three station points is the sum of the contribution of exterior illumination and ground reflectance falling on the uniformly lit window wall multiplied by factors that compensate for the geometry of the room and the aperture. The factors are empirically determined, based on pre-tested models and are only applicable to a limited range of reflectances and aspect ratios of the room. The lumen method is thus a method for more generalized daylight analysis. 44 4.3.2 Daylight Factor Method The daylight factor method was first developed in England during the 1920's.2 9 It was mainly developed for daylight calculation under an overcast sky. However, recent development has made it applicable to clear skies also. The daylight factor, DF, is defined as the percentage of interior illuminance on a horizontal surface, Ej, over the exterior illuminance on a horizontal surface, Ee, under an overcast sky: DF = (Ej / Ee) * 100% The daylight factor method is more of a first principle approach. In theory, it can consider an off-centered window in a room and can be calculated for any position in the room. In this approach, the daylight factor is the sum of the following three components: 1. The sky component, SC 2. The external reflectance component, ERC 3. The internal reflectance component, IRC The sky component is the relative illuminance striking a given station point received directly from the sky (Figure 4-9). The external reflectance component is the relative illuminance striking a station point received directly from external reflecting surfaces. The sky component and external reflected component can be obtained by integrating derived form factors over the view angle of the aperture from a station point; or they can be obtained from charts which pre-determined the relationship between the aspect ratios of the room or the obstruction angle and the sky component or external reflectance component. The internal reflectance component is the relative illuminance striking a station point received directly or 29Egan, M. David, Concepts in Architectural Lighting, 1983, p. 193. 45 indirectly from the daylight that is interreflected around the room. It is a factor that describes the average reflectances and surface areas of the interior surfaces, and an obstruction coefficient that depends on the external obstruction angle. B u ild in g G round Figure 4-9. Daylight factor method (Stein, 1986). An interior maintenance factor, MF, can be added to represent the frequency of cleaning of the space's interior surfaces. The daylighting factor is expressed as: DF = SC + ERC + (MF)(IRC) This equation can be used to analyze apertures with no glazing. The reduction in interior illuminance due to the glazing is represented by the factor Cg where Cg = (Tg / 0.85) (Dg) ( Fg) Tg is the glazing transmission; Dg is the dirt depreciation factor; and Fg is the ratio of glazed area to aperture area. DF then becomes DF = [SC + ERC + (MF)(IRC)] (Cg) With the above method and average exterior illuminance charts, the absolute illuminance at any station point in the room can be determined. However, 46 a typical application of the daylight factor method is to work backward from weather information and available illuminances in order to provide a desired daylight factor within a space so that minimum illuminance requirements can be met over a period of time.3 0 In this method, the window head height is assumed to be 1 ft. below the ceiling height, and the window sill is assumed to be at least 3 ft. from the floor. The following steps are taken to insure the light level in the space: 1. Determine the percentage of the workday during which a desired amount of exterior illuminance is available. 2. Determine the desired daylight factor and adjust the factor using the light loss factor for dirt accumulation on windows. 3. Determine the maximum permissible room depth to window height ratio for the desired daylight factor. 4. Correct the daylight factor for the occlusion of sky by external surfaces. 5. Repeat steps 4 and 5 to find the new permissible room depth ratio. 6. Determine the window height and the permissible room depth to insure the minimum illumination level in the space. Although the daylight factor method is more flexible than the lumen method under an overcast sky, the application of this method is still largely dependent on pre-tested results. But a good approximation of light level can be determined using this method. 30Schiler, Marc, Simplified Design of Building Lighting, 1992, p. 110. 47 4.3.3 Flux Transfer Method The flux transfer method was proposed as early as 1909. But it was primarily developed by Higbie and Levine (1926), Randall (1927), and Waldram (1923). The flux transfer method can be used with the CIE clear or overcast sky, and can work with either illuminance or luminance at the plane of the aperture in determining the illuminance at any given station point or on any surface in the space. This method focuses on determining the illuminance from the sky in the room and the internally reflected illuminance in the room. The variables accounted for in this method are: 1. The size and shape of the aperture. 2. The distance from the station point to a comer of the aperture. 3. The view of the sky from the station point or the illuminance at the plane of the aperture. 4. The climate, time of day, and solar location. The general formula for the flux transfer method at point Ep is: E p = E S + e SE + e ERE + ( e i r e ) ( m f ) Eg is the illuminance from the direct sunlight; Egg the illuminance from the sky; e ERE from external reflection; and Ejr^ from internal reflection. Numerous t researchers have developed empirical formulas for the calculation of each o f the four components. However, a simpler approach of the method is to understand the relationship between light and surface interception. The basic procedure of the flux transfer method is to divide the surfaces of the room into tiny surfaces and determine the obstruction of the sky vault and the contribution of reflective light by these surfaces (Figure 4-10). If there are objects 48 in the room, the surfaces of these objects should also be accounted for in the contribution o f reflected light. Figure 4-10. Dividing surfaces for the flux transfer method. The final luminous exitance of each of these surfaces contributes to the illumination measured at any point in the room depending on the relationship between the point and the surfaces. The final luminous exitance of a surface is the summation of the initial luminance and interreflected component between the surfaces in the room: Lf = L0 + ( l/7 t ) * p * E 1 + ( l/7 t ) * p * E 2 + ( l/7 t ) * p * E 3 + ... + ( l/7 i) * p * E n where Lf = final luminance of the surface L0 = initial luminance of the surface p = reflectance of the surface En = illuminance from surface n received by the original surface The initial luminance, L0, is the luminous flux received from sunlight and skylight emitted by the surface. Whether the surface receives any sunlight depends on the time of the day and the existence of obstructions between the sun and the surface. The portion of skylight received by the surface depends on the viewed angle of the sky vault and the sky luminance. The remaining terms from the above equation describe the luminous flux received from the other surfaces emitted by the receiving surface. The illuminance received from each surface is: En — flux/area — (tcLqAq/) / Agurface f in the above equation is the form factor between the two surfaces in consideration. It represents the percentage of the total flux emitted from the first surface that falls on the second surface (Figure 4-11). The form factor is expressed by the following equation: f = (cos 0 cos 4 > ) / r2 where r = the distance between the midpoints of the two surfaces 0 = the angle between the normal of the first surface and r ( j) = the angle between the normal of the second surface and r Figure 4-11. Contribution of illumination of one surface to another. Note that there is a loop of relationship between the luminous emittance of a surface and the illuminance of the other surfaces. This demonstrates the behavior of light, which bounces from one surface to another. Each surface receives reflection from other surfaces while reflecting light itself. A portion of the reflected light will bounce back to the same surface, via the course of other surfaces, until this portion is small enough to be neglected. The flux transfer method is thus a more accurate method in predicting the illumination level of any surface. It is also a first principles approach and does not rely on tables o f pre-measured data. It is therefore amenable to application in nearly any situation in which the geometry of the surfaces can be defined, not just limited to rectangular shaped boxes with certain aspect ratios. However, manual application of the flux transfer method is almost impossible because of the quantity and complexity of the calculation involved. It is therefore mostly used in computer programs, including the daylight availability program written for this thesis. 51 5. COMPUTER SIMULATION MODEL The name of this computer program written to study the availability of daylight on a given site is LightSum. It is written in the C language and currently executes on an IBM personal computer or an IBM compatible personal computer with VGA graphics capability. This chapter will discuss input method, calculation algorithms and output formats. 5.1 Methodology The main objective of LightSum is to generate a daylight availabilitv contour plot of a specific site for a duration o f time, using a daylight simulation model specified by the user, and considering the direct, diffuse, and reflected components of daylight (Figure 5-1). The daylight simulation models available to the user in this program are the Dogniaux model, the Gillette model, and the IES recommended model. The physical description of the site and the typical weather information of the location are required for the execution of the program. The designated site is divided into an appropriate grid along the two axes. For each point of the grid, either the radiation availability or the illumination level is calculated for a length of time of the year. Both obstruction and reflection are calculated based on vertical surfaces adjacent to the site. The result of the analysis can be best understood if the background information can be accessed by the user, which include the following: 1. Solar access information for a particular day, 2. Weather information for a particular day, 52 O f f l H « j p S 3. Radiation available on the site at a particular time, 4. Exterior illumination level simulated by the Dogniaux, Gillette, or IES prediction model, 5. Total illumination available simulated by the Dogniaux, Gillette, or EES prediction model and the flux transfer method. Simulation Model Input Output Solar Position Table L I Weather File Dogniaux Weather Info. Table Site File |» Date & Time 1l Gillette Direct Exterior Illumination IES Diffuse Total Illumination Direct + Diffuse + Reflected Figure 5-1. Flow chart of the program LightSum. 53 5.2 Input The input needed for the execution of LightSum include: 1. TMY or ETMY recorded weather file o f the location. 2. Site file containing the parameters of the site. 3. Dates and times to be analyzed. 5.2.1 Observed Weather Data Files The weather of a location has a definite impact on the amount of light that will travel through the atmosphere. It determines the sky condition and the atmospheric attenuation at any time being considered. Since the weather varies from day to day and hour to hour, it is very unpredictable. However, these weather data have been recorded at various stations throughout the world over the years. In the United States, long-term exterior illumination data are not available; therefore, other weather information are relied on to estimate the exterior illumination. As of 1986, there were 26 stations in the United States, called the SOLMET stations, which record measured irradiance data that would help estimate exterior illumination. These stations established Typical Meteorological Year (TMY) weather tapes which represent the hourly weather data of a typical year at each particular station. There are'217 other stations that are subdivided into climatic regions based upon the SOLMET irradiance data. The irradiance data for each of the 217 stations are estimated from the SOLMET stations, while all other weather data are recorded at each individual station. These 217 stations are called the Estimated Typical Meteorological Year (ETMY) stations.3 1 3bobbins, Claude L., Daylighting Design and Analysis, 1986, p.36. 54 The TMY and ETMY weather tapes are in a format that this computer program will understand. The user will need to have the TMY or ETMY weather tape of the designated location available in order to proceed with daylight analysis using the computer program. The program reads in the hourly irradiance data and air pressures that will be used for daylight availability analysis. These hourly irradiance data (described in chapter 4.1) include: 1. Extraterrestrial solar radiation, 2. Direct normal solar radiation, 3. Total horizontal solar radiation, 4. Air pressure at the sea level, 5. Air pressure at the weather station. 5.2.2 Site and Boundary Information Files The user will need to specify the dimensions of the site and the boundary conditions for the computer program to analyze daylight availability. This input is done by numerically completing a list of descriptions of the site which will be dicussed later in this section. The user has a choice of inputing the information of an open site or an atrium. For this program, the algorithm conditions have been set up to consider only rectangular, flat sites and atriums. However, the algorithm for calculation is suitable for irregular or hillside sites if additional testing conditions are set up in the future. In this program, the site and boundary information input by the user will be stored in a text file with the extension ".ste", while the atrium information will be stored in a text file with the extension ".atr". After creating a site file, the user can recall the file for future usage. In order to input site information, the user will need to choose the "File" option from the main menu. From the sub-menu under the "File" option, the user can either recall an existing site file or create a new site file. To recall an existing site file, choose the "Read Site/Atrium File" option from the menu, then indicate whether it is a site file or an atrium file and input the name of the file at the prompt: Site or Atrium File (S/A): Enter site file name to be read from: (Enter atrium file name to be read from: ) To create a new site file, choose the "Make New Site File" option from the menu. Questions inquiring the orientation, dimension of the site, dimension of the surrounding streets, and characteristics of the surrounding surface will be asked. The orientation of the site describes the degree of rotation of the site from the north. If the site rotates to east of north, it is a positive rotation angle. If the site rotates to west of north, it is considered a negative rotation angle. The dimension of the site and the streets can be expressed in feet or meters; however, illumination levels will be expressed in lux. A grid of rectangular building blocks is assumed (Figure 5-2); therefore, the surrounding building surfaces are assumed to reside in one of the eight surrounding blocks defined by the east, west, north, and south streets. Only the surfaces of the buildings that are facing the site will be considered as the major elements effecting the illumination level of the site. Therefore, only these surfaces need to be input. These surfaces are modeled as a planar surface, defined by four comer points. The algorithm only considers surfaces that are perpendicular to the ground. A slight modification of the algorithm in the future will be able to consider those surfaces that are slanted. The 56 characteristics of each surface include the setback of the surface from the street that it is facing, the starting point from one specified end o f the street, the 'ength of the surface, its height, and its reflectance. A list of reflectances of typical building materials can be accessed before inputing the site information. Height Setbad E-W N-S Length Figure 5-2. Parameters of site. The site information input screen looks like this: Do you need a list of surface reflectances? (Y/N): Enter site information: note: clockwise from north is positive angle counterclockwise from north is negative. Site orientation from north: East-West site length: North-South site length: East side street width: West side street width: North side street width: 57 South side street width: Ground Reflectance of Site (0-1): Enter boundary information: North block surfaces (Y/N): Setback from north street: Start point from west: Length of surface: Height of surface: Reflectance of surface (0-1): More surfaces? (Y/N): Northeast block E-W surfaces (Y/N): Northeast block N-S surfaces (Y/N): East block surfaces (Y/N): Setback from east street: Start point from north: Length of surface: Height of surface: Reflectance of surface (0-1): More surfaces? (Y/N): Southeast block N-S surfaces (Y/N): Southeast block E-W surfaces (Y/N): South block surfaces (Y/N): Southwest block E-W surfaces (Y/N): South west block N-S surfaces (Y/N): West block surfaces (Y/N): Northwest block N-S surfaces (Y/N): Northwest block E-W surfaces (Y/N): 58 It is important that the three-dimensional input of the site be verified for accuracy and pathological errors. For this reason, a site review image is provided at the end o f the first input sequence (Figure 5-3). Figure 5-3. Sample Site. The procedure to create a new atrium file is almost identical, with the exception of including the glass trasmittance of the atrium. The atrium information screen looks like: Do you need a list of surface reflectances? (Y/N): Do you need a list of glass transmittances? (Y/N): Enter atrium information: note: clockwise from north is positive angle counterclockwise from north is negative. Atrium orientation from north: East-West atrium length: North-South atrium length: Ground Reflectance of Atrium (0-1): Glass Transmittance of Atrium (0-1): 59 Enter boundary information: North boundary: Start point from northwest comer: Length of surface: Height o f surface: Reflectance of surface (0-1): More surfaces? (Y/N): East boundary: Start point from northeast comer: Length of surface: Height o f surface: Reflectance of surface (0-1): More surfaces? (Y/N): South boundary: West boundary: Figure 5-4 shows a sample atrium file when plotted out: After the site information is input or retrieved from an existing file, the site is divided into a 21*21 grid. Each grid point is assigned a real coordinate with the southwest comer being the origin (0,0,0). The location of the boundary surfaces are also stored in real coordinates with respect to the grid. Each boundary surface Figure 5-4. Sample Atrium 60 is defined by two points: the lower left comer of the surface in elevation view (x0, y0, z0) and the upper right comer of the surface (x1 ? yl5 Zj). 5.2.3 Date and Time For the calculation of the final illuminance of the site, a starting date, ending date, starting hour and ending hour of each day are required. The computer program will then simulate and sum the daylight available at each grid point of the site, at each hour o f the duration of days specified. For the solar access, weather, and exterior illumination information, only one date can be considered at a time. < 3 61 5.3 Algorithms and Output 5.3.1 Solar Position Variables For a selected day from the weather file, a table of altitude and azimuth for each solar hour of the day can be calculated and listed by choosing the "Print Altitude/Azimuth" option from the "Calculation" menu. This table helps the designer to understand the position of the sun with respect to the site. Variables related to the sun position are simulated as follows. 5.3.1.1 Latitude The latitude of the site is input by the user while calling the specific weather file. 5.3.1.2 Julian Date The user input the month and day of the year to be analyzed while calling the weather file. The corresponding Julian day is simulated as follows: [Julian date = j_day] int CalcJulDay(int month, int day) { int j_day; switch (month) { case 1: j_day=0+day; break case 2: j_day=31+day; break case 3: j_day=59+day; break case 4: j_day=90+day; break case 5: j_day=120+day; break case 6: j_day= 151 +day; break case 7: j_day= 181 +day; break case 8: j_day=212+day; break, case 9: j_day=243+day; break; 62 case 10:j_day=273+day; break; case 11 :j_day=304+day; break; case 12 :j_day=334+day; break; } return (j day); /* return Julian date to main function */ } 5.3.1.3 Declination Angle [Declination angle = d angle] double CalcDeclination(int j_day) { double d angle; /* implement equation discussed in section 3.2.2 */ d_angle=23.45*sin(((j_day+284.0) * 360.0/365.0) * TORADIAN); return (d_angle); /* return declination angle to main function */ } 5.3.1.4 Hour Angle [Hour angle = h_angle] double CalcHourAngle(int hour) { double h angle; h_angle=15.0 * (12.0-hour); /*equation discussed in section 3.2.3*/ return (h_angle); /* return hour angle to main function */ } 5.3.1.5 Solar Altitude Angle [Solar altitude angle = alt_d] double CalcAltitude(double latd, double decl d, double hour d) { double alt_d, lat_r, decl_r, hour_r, sin_alt_r; 63 lat_r=lat_d * TORADIAN; /* change latitude angle to radians */ decl_r=decl_d * TORADIAN; /* declination angle in radians */ hour_r=hour_d * TORADIAN; /* change hour angle to radians */ sin_alt_r = cos(lat_r)*cos(decl_r)*cos(hour_r)+sin(lat_r) *sin(decl_r); /* equation discussed in section 3.2.4 */ alt_d=asin(sin_alt_r) * TODEGREE; /* convert angle to degrees*/ return (alt_d); /* return altitude angle in degrees to main function*/ } 5.3.1.6 Solar Azimuth Angle [Solar azimuth angle = aziD] double CalcAzimuth(double declD, double hourD, double altD) { double aziD, declR, hourR, altR, sinAziR; declR = declD * TORADIAN; hourR = hourD * TORADIAN; altR = altD * TORADIAN; sinAziR = cos(declR) * sin(hourR) / cos(altR); /* section 3.2.6 */ aziD = asin(sinAziR) * TODEGREE; return (aziD); /* return azimuth angle in degrees to main function*/ 5.3.1.7 Solar Access Tables With the above algorithms, the position of the sun relative to the site can be calculated for each hour of any day. This information will be used to calculate the availability of daylight for each hour of the day. The computer program can also generate a solar access table, upon request of the user, for the understanding of the sun path. Tables 5-1, 2, 3, and 4 show the solar access tables for the four soltices of the year for Portland, Oregon. 64 Date: 3 21 Julian Day: 80 Declination: -0.40 Hour HourAngle Altitude Azimuth Hour HourAngle Altitude Azimuth 1 165.00 -42.91 159.31 13 -15.00 42.13 -20.42 2 150.00 -37.66 140.83 14 -30.00 36.93 -38.72 3 135.00 -29.98 125.28 15 -45.00 29.32 -54.19 4 120.00 -20.78 112.14 16 -60.00 20.17 -67.31 5 105.00 -10.73 100.56 17 -75.00 10.14 -78.88 6 90.00 -0.29 89.72 18 -90.00 -0.29 -89.72 7 75.00 10.14 78.88 19 -105.00 -10.73 -100.56 8 60.00 20.17 67.31 20 -120.00 -20.78 -112.14 9 45.00 29.32 54.19 21 -135.00 -29.98 -125.28 10 30.00 36.93 38.72 22 -150.00 -37.66 -140.83 1 1 15.00 42.13 20.42 23 -165.00 -42.91 -159.31 12 0.00 44.00 0.00 24 -180.00 -44.80 -180.00 Table 5-1. Solar Access Table for March 21, Portland, Oregon. Date: 6 21 Julian Day: 172 Declination: 23.45 Hour HourAngle Altitude Azimuth Hour HourAngle Altitude Azimuth 1 165.00 -19.61 165.40 13 -15.00 64.73 -33.80 2 150.00 -15.76 151.54 14 -30.00 57.16 -57.77 3 135.00 -9.76 138.83 15 -45.00 47.58 -74.08 4 120.00 -2.10 127.34 16 -60.00 37.25 -86.45 5 105.00 6.79 116.82 17 -75.00 26.77 -97.00 6 90.00 16.52 106.88 18 -90.00 16.52 -106.88 7 75.00 26.77 97.00 19 -105.00 6.79 -116.82 8 60.00 37.25 86.45 20 -120.00 -2.10 -127.34 9 45.00 47.58 74.08 21 -135.00 -9.76 -138.83 10 30.00 57.16 57.77 22 -150.00 -15.76 -151.54 11 15.00 64.73 33.80 23 -165.00 -19.61 -165.40 12 0.00 67.85 0.00 24 -180.00 -20.95 -180.00 Table 5-2. Solar Access Table for June 21, Portland, Oregon. 65 Date: 9 21 Julian Day: 264 Declination: -0.20 Hour HourAngle Altitude Azimuth Hour HourAngle Altitude Azimuth 1 165.00 -42.71 159.37 13 -15.00 42.32 -20.49 2 150.00 -37.48 140.95 14 -30.00 37.11 -38.83 3 135.00 -29.82 125.41 15 -45.00 29.49 -54.32 4 120.00 -20.63 112.28 16 -60.00 20.32 -67.44 5 105.00 -10.58 100.70 17 -75.00 10.29 -79.02 6 90.00 -0.14 89.86 18 -90.00 -0.14 -89.86 7 75.00 10.29 79.02 19 -105.00 -10.58 -100.70 8 60.00 20.32 67.44 20 -120.00 -20.63 -112.28 9 45.00 29.49 54.32 21 -135.00 -29.82 -125.41 10 30.00 37.11 38.83 22 -150.00 -37.48 -140.95 11 15.00 42.32 20.49 23 -165.00 -42.71 -159.37 12 0.00 44.20 0.00 24 -180.00 -44.60 -180.00 Table 5-3. Solar Access Table for September 21, Portland, Oregon. Date: 12 21 Julian Day: 355 Declination: -23.45 Hour Hour Angle Altitude Azimuth Hour HourAngle Altitude Azimuth 1 165.00 -64.73 146.20 13 -15.00 19.61 -14.60 2 150.00 -57.16 122.23 14 -30.00 15.76 -28.46 3 135.00 -47.58 105.92 15 -45.00 9.76 -41.17 4 120.00 -37.25 86.45 16 -60.00 2.10 -52.66 5 105.00 -26.77 83.00 17 -75.00 -6.79 -63.18 6 90.00 -16.52 73.12 18 -90.00 -16.52 -73.12 7 . 75.00 -6.79 63.18 19 -105.00 -26.77 -83.00 8 60.00 2.10 52.66 20 -120.00 -37.25 -86.45 9 45.00 9.76 41.17 21 -135.00 -47.58 -105.92 10 30.00 15.76 28.46 22 -150.00 -57.16 -122.23 11 15.00 19.61 14.60 23 -165.00 -64.73 -*46.20 12 0.00 20.95 0.00 24 -180.00 -67.85 -180.00 Table 5-4. Solar Access Table for December 21, Portland, Oregon. 66 5.3.2 Radiation Data The following radiation data are calculated for each hour of the days that the user specified from the information taken from the weather tape. 5.3.2.1 Direct Horizontal Solar Radiation The direct horizontal solar radiation is the irradiance from direct sunlight measured on a horizontal surface at ground level. It is simulated by the following code: double CalcDirHorRad(double dirNormRad, double altD) { double dirHorRad; double altR; if (altD<0) altD = 0; altR = altD * TORADIAN; dirHorRad = dirNormRad * sin(altR); retum(dirHorRad); } 5.3.2.2 Diffuse Horizontal Solar Radiation The diffuse horizontal solar radiation is the irradiance from the sky measured on a horizontal surface at ground level. It is simply the difference between the total horizontal irradiance and the direct horizontal irradiance: double CalcDiffRad(double dirHorRad, double totHorRad) { double diffuseRad; diffuseRad = totHorRad - dirHorRad; retum(diffuseRad); } 67 5.3.2.3 Weather Information and Radiation Graph A table that describes the solar radiation and sky ratio data for each hour of a day can also be accessed with the computer program (Tables 5-5, 5-6). Among the information provided in this table, the extraterrestrial radiation, direct horizontal radiation, diffuse horizontal radiation and the sky ratio are derived, whereas the direct normal radiation and the total horizontal radiation are observed by weather stations. Four line graphs that show the extraterrestrial radiation, direct normal radiation, direct horizontal radiation and diffuse horizontal radiation will help the user understand the weather conditions of the day, and whether it is a predominantly cloudy sky or a predominantly clear sky (Figures 5-5, 5-6). Date: 3 21 Average Sky Ratio: 0.89 Hour Extra terrestrial Direct Normal Total Horiz. Direct Horiz. Diffuse Horiz. Sky Ratio 4 0.00 0.00 0.00 0.00 0.00 -999999 5 0.00 0.00 0.00 0.00 0.00 -999999 6 0.00 0.00 0.00 0.00 0.00 -999999 7 456.00 7.00 88.00 1.23 86.77 0.99 8 1335.00 23.00 324.00 7.93 316.07 0.98 9 2122.00 9.00 324.00 4.41 319.59 0.99 10 2766.00 341.00 1100.00 204.90 895.10 0.81 11 3221.00 907.00 1604.00 608.39 995.61 0.62 12 3456.00 94.00 1019.00 65.29 953.71 0.94 13 3456.00 417.00 1431.00 279.71 1151.29 0.80 14 3221.00 395.00 1319.00 237.35 1081.65 0.82 15 '2766.00 344.00 1102.00 168.45 933.55 0.85 16 2122.00 249.00 800.00 85.85 714.15 0.89 17 1335.00 7.00 184.00 1.23 182.77 0.99 18. 456.00 2.00 51.00 0.00 51.00 1.00 19 0.00 0.00 0.00 0.00 ' 0.00 -999999 20 0.00 0.00 0.00 0.00 0.00 -999999 21 0.00 0.00 0.00 0.00 0.00 -999999 Table 5-5. Weather information table for March 21, Portland, Oregon. 68 Extra—ter rest r fal Ftadiat ion 0 . 0 0 0 0 0 0 Diffuse Horizontal Radiation 0 . 0 0 0 0 0 0 23.OOOOOO Direct Nomal Radiation Hour 23.000000 Direct Horizontal Radiation 23.000000 0 . 0 0 0 0 0 0 Figure 5-5. Radiation graph for March 21, Portland, Oregon. Date: 6 21 Average Sky Ratio: 0.94 Hour Extra terrestrial Direct Normal Total Horiz. Direct Horiz. Diffuse Horiz. Sky Ratio 4 0.00 0.00 0.00 0.00 0.00 -999999 5 211.00 0.00 2.00 0.00 2.00 1.00 6 963.00 29.00 201.00 8.25 192.75 0.96 7 1765.00 59.00 450.00 26.58 423.42 0.94 8 2540.00 98.00 715.00 59.32 655.68 0.92 9 3234.00 122.00 961.00 90.06 870.94 0.91 10 3801.00 135.00 1157.00 113.43 1043.57 0.90 11 4202.00 140.00 1291.00 126.61 1164.39 0.90 12 4410.00 142.00 1358.00 131.52 1226.48 0.90 13 4410.00 143.00 1362.00 129.32 1232.68 0.91 14 4202.00 142.00 1295.00 119.31 1175.69 0.91 15 3801.00 136.00 1160.00 100.39 1059.61 0.91 16 3234.00 123.00 962.00 74.45 887.55 0.r2 17 2540.00 98.00 716.00 44.14 671.86 0.94 18 1765.00 59.00 450.00 16.77 433.23 0.96 19 963.00 29.00 202.00 3.43 198.57 0.98 20 211.00 0.00 5.00 0.00 5.00 1.00 21 0.00 0.00 0.00 0.00 0.00 -999999 Table 5-6. Weather information table for June 21, Portland, Oregon. 69 Extra—ter i .trial Radiation 0 0 0 0 0 5 ' 23.000000 . Hour Direct Noma 1 Radiation Diffuse Horizontal Radiation 23.000050 0.000000 Hour 23.000000 Direct Horizontal Radiation 0 . 0 0 0 0 0 0 23.000000 Figure 5-6. Radiation graph for June 21, Portland, Oregon. 70 5 . 3 . 3 E x t e r i o r I l l u m i n a t i o n U s i n g t h e D o g n i a u x P r e d i c t i o n M o d e l The user may choose to simulate the exterior illumination with the Dogniaux model or the Gillette model. The user may also define the starting hour and the ending hour o f the day chosen to be analyzed for daylight availability. If the Dogniaux model is preferred, the Dogniaux clear sky simulation and the Dogniaux overcast sky simulation will be executed for each hour specified. Depending on the sky condition for each hour calculated using the sky ratio method, the illumination values o f the clear sky and the overcast are interpolated to obtain the final direct and diffuse illuminance for each hour: Function: CalcDogniauxIll() Description: Calculate the direct and diffuse illuminance for each hour and call CalcSiteExIllum( ) to calculate the total exterior illuminance on each grid point. /*illum.dirlllum and ilium.diffllum in klux.*/ void CalcDogniauxIll(int hi, int h2, double illu[21][21]) { char buflBUFSIZE]; int i, j; double cloudRatio, ovrDir, ovrDif, clrDir, clrDif; for (i=0; i<21; i++) for (j=0;j<21;j++) illu[i][j] = 0.0; /* initialize the array */ for (i=hl; i<=h2; i++) /* for each hour */{ if (data[ij.totHorRad=0) { CalcDognO(i); /* no illumination if not daytime */ } else { cloudRatio = data[i].diffuseRad/data[i]. totHorRad; ovrDir = 0; ovrDif=DognOvrDif(i); /* overcast diffuse */ clrDir = DognClrDir(i); /*clear direct illumination*/ clrDif = DognClrDif(i); /*elear diffuse illumination*/ 71 illum[i].dirlllum = CalcIntpo(cloudRatio, clrDir, ovrDir)/1000; /* convert to klux */ illum[i].diflllum = CalcIntpo(cloudRatio, clrDif, ovrDif)/1000; /* convert to klux */ } } /* calculate illumination for each grid point, for each hour */ CalcSiteExIllum(hl, h2, illu); return; } The values of the direct and diffuse illuminance for the hours specified will be shown in a tabular format: Dogniaux Model: Direct and Diffuse Illumination Data: Date: 6/ 1 Direct (klux)' Diffuse (klux) Hour 9 52.76 2.76 Hour 10 58.19 2.91 Hour 11 60.18 3.22 Hour 12 59.87 3.56 Hour 13 57.96 3.81 Hour 14 53.88 4.01 Hour 15 47.12 4.13 Date: 6/12 Direct (klux) Diffuse (klux) Hour 9 5.38 14.44 Hour 10 6.10 16.34 Hour 11 13.46 15.68 Hour 12 24.13 13.24 Hour 13 32.83 10.56 Hour 14 32.80^ 9.51 Hour 15 31.65 8.05 7 2 Dogniaux Model: Direct and Diffuse Illumination Data: Date: 6/21 Direct (klux) Diffuse (klux) Hour 9: 6.07 14.32 Hour 10: 6.87 16.19 Hour 11: 7.13 17.40 Hour 12: 7.12 17.84 Hour 13: 6.90 17.46 Hour 14: 6.46 16.29 Hour 15: 5.61 14.44 Table 5-7. Hourly direct and diffuse exterior illumination in Portland, Dogniaux model. The computer program will then take the surrounding buildings into consideration. For each grid point defined on the site, the program will check for shadow casting on the grid point by the surrounding buildings. If the grid point is being shadowed at a particular hour, the exterior illuminance available on the point will only be the diffuse illuminance, which is calculated with consideration of the surrounding buildings, their obstruction, reflectances, and component form factors. If the grid point is not shadowed, it is entitled to both direct and diffuse illuminance calculated for the hour. The sum of the available exterior illuminance for each grid point between the starting hour and ending hour specified is then expressed by an axonometric graph showing the outline of the site, the grid points on the site, and the resulting exterior illuminance. The outline of the site is scaled in the x and y direction to fit in the graphic screen, unless the user specify a maximum length of the site to be fit in the screen. The illuminance levels for the grid points are represented on the screen by the yellow contour plot. The 73 illuminance is scaled in the z direction to fit in the graphic screen, unless the user specify a maximum illuminance level to be fit in the screen. The maximum and minimum illuminances calculated appear on the graphic output to indicate the scale of the illuminance levels. Figure 5-7 shows the hourly exterior illumination on June 1 for Portland, Oregon, calculated with the Dogniaux simulation model. 12 noon Figure 5-7. Hourly exterior illumination on June 1, simulated with the Dogniaux model. 75 5.3.4 Exterior Illumination Using the Gillette Prediction Model The user will need to input the starting hour and ending hour to be analyzed. Calculation of the direct and diffuse exterior illuminance for each hour * based on the sky clearness ratio will then be executed. As with the simulation done with the Dogniaux model, a table showing the direct and diffuse illuminance (Table 5-8) and a plot showing the available exterior illuminance of the site based on shadow casting will be provided (Figure 5-8). Function: CalcGilletteIll() Description: Call CalGillette( ) to calculate the diffuse and direct illuminance of each hour and call CalSiteExIllum( ) to calculate the total exterior illuminance on each grid point, void CalcGilletteIll(int h i, int h2, double illu[21][21]) { char buftBUFSIZE]; in ti,j; for (i=0; i<21; i++) for (j=0; j<21;j++) illu[i][j] = 0.0; /* initialize the array */ for (i=hl; i<=h2; i++) CalcGillette(i); /* calculate the illumination for each hour */ /* calculate illumination for grid point */ CalcSiteExIllum(h 1, h2, illu); return; } Function: CalcGillette() Description: Calculate the direct and diffuse illuminance for the hour specified. /* ilium, dir Ilium and ilium, diflllum in klux.*/ void CalcGillette(int i) { double dirNorlllum; double cr, trans, mO, mz, altR; 76 double skyFraction; if (data[i].totHorRad==0) { illum[i].dirlllum=0; /* no illumination if not daytime */ illum[i]. difXllum=0; } else { /* implement equation discussed in section 4.2.2.2 */ altR = data[i]. alt Angle * TORADIAN; mO = sqrt(1229 + 614* sin(altR)*614*sin(altR)) - 614*sin(altR); mz = mO * data[i].stationPres / data[i].seaLevelPres; trans = 0.5 * (exp(-0.65*mz) + exp(-0.095*mz)); cr = data[i].diffuseRad / data[i],totHorRad; dirNorlllum - 127500 * (1 + 0.033 * cos((360.0 * data[i].julDay / 365.0) * TORADIAN))* trans; skyFraction = 0.5 ? (1 + cos(3.14159 * cr)); illum[i].dirIllum=dirNorIllum * skyFraction * sin(altR) / 1000; illum[i].diflllum = 111 * data[i].diffuseRad/3600; } return; } Table 5-8 shows the direct and diffuse illumination for Portland, Oregon: Gillette Model: Direct and Diffuse Illumination Data: Date: 6/ 1 Direct (klux) Diffuse (klux) Hour 9 53.55 12.52 Hour 10 64.84, 14.03 Hour 11 71.41 16.11 Hour 12 72.87 18.33 Hour 13 69.39 20.13 Hour 14 60.97 21.71 Hour 15 48.44 22.77 77 Gillette Model: Direct and Diffuse Illumination Data: Date: 6/12 Direct (klux) Diffuse (klux) Hour 9 1.00 27.03 Hour 10 1.31 32.48 Hour 11 6.37 39.99 Hour 12 19.44 41.28 Hour 13 32.84 39.20 Hour 14 31.60 37.69 Hour 15 28.40 33.80 Gillette Model: Direct and Diffuse Illumination Data: Date: 6/21 Direct (klux) Diffuse (klux) Hour 9 1.27 26.85 Hour 10 1.65 32.18 Hour 11 1.82 35.90 Hour 12 1.84 37.82 Hour 13 1.71 38.01 Hour 14 1.46 36.25 Hour 15 1.08 32.67 Table 5-8. Hourly direct and diffuse exterior illumination in Portland, Gillette model. 78 12 noon Figure 5-8. Hourly exterior illumination on June 1, simulated with the Gillette model. 79 5.3.5 Exterior Illumination Using the DES Model As with the Dogniaux and the Gillette models, the user will need to input the starting hour and ending hour to be analyzed. Calculation of the direct and diffuse exterior illuminance for each hour based on the sky condition will then be executed. A table showing the direct and diffuse illuminance (Table 5-9) and a plot showing the available exterior illuminance of the site based on shadow casting will be provided (Figure 5-9). Function: CalclESIll() Description: Call CalIES( ) to calculate the diffuse and direct illuminance o f each hour and call CalSiteExIllum( ) to calculate the total exterior illuminance on each grid point, void CalcIESIll(int hi, int h2, double illu[21][21]) { int i, j; for (i=0; i<21; i++) for (j=0; j<21; j++) illu[i][j] = 0.0; /* initialize the array */ for (i=hl; i<— h2; i++) CalcIES(i); /* calculate the illumination for each hour */ CalcSiteExIllum(hl, h2, iliu); /* illumination for each grid point */ return; } Function: CaicIES() Description: Calculate the direct and diffuse horizontal illuminance for the hour specified. Illuminance in klux. void CalcIES(int i) { double c, altR; if (data[i].skyRatio<0) { ilium[i].dirlllum=0, /* no illumination if not daytime */ ilium [i]. diflllum=0; } else { /* implement equations discussed in section 4.2.2.3 */ 80 altR = data[i]. alt Angle * TORADIAN; if ((data[i].skyRatio>=0) && (data[i].skyRatio<0.3)) { c = 0.21; illum[i].dirlllum= 127500 * (1 + 0.034 * cos((3 60.0* (data[i]. julDay-2)/3 65.0) * TORADIAN)) * exp(-c / sin(altR)) * sin(altR)/1000; } else { if ((data[i].skyRatio>=0.3) && (data[i].skyRatio<0.8)) { c = 0.8; illum[i].dirlllum= 127500 * (1 + 0.034 * cos((360.0*(data[i].julDay-2)/365.0) * TORADIAN)) * exp(-c / sin(altR)) * sin(altR)/1000; } else illum[i].dirlllum = 0.0; } if ((data[i].skyRatio>=0) && (data[i].skyRatio<0.3)) illum[i].diflllum = 0.8 + (15.5 * pow(0.5, sin(altR))); else { if ((data[i].skyRatio>=0.3) && (data[i].skyRatio<0.8)) illum[i].diflllum = 0.3 + (45.0 * sin(altR)); else illum[i].dirlllum = 0.3 + (21.0 * sin(altR)); } } return; } Table 5-9 shows the direct and diffuse illumination for Portland, Oregon: IES Model: Direct and Diffuse Illumination Data: Date: 6/ 1 Direct Diffuse (klux) (klux) Hour 9: 67,40 10.17 Hour 10: 79.77 9.52 Hour 11: 87.59 9.14 Hour 12: 90.26 9.01 Hour 13: 87.59 9.14 Hour 14: 79.77 9.52 Hour 15: 67.40 10.17 81 EES Model: Direct and Diffuse Illumination Data: Date: 6/12 Direct (klux) Diffuse (klux) Hour 9 15.75 10.17 Hour 10 17.90 9.52 Hour 11 19.25 9.14 Hour 12 48.02 41.89 Hour 13 45.90 40.90 Hour 14 39.83 38.01 Hour 15 30.63 33.41 EES Model: Direct and Diffuse Illumination Data: Date: 6/21 Direct (klux) Diffuse (klux) Hour 9 15.80 10.17 Hour 10 17.94 9.52 Hour 11 19.29 9.14 Hour 12 19.75 41.89 Hour 13 19.29 40.90 Hour 14 17.94 38.01 Hour 15 15.80 33.41 Table 5-9. Hourly direct and diffuse exterior illumination in Portland, EES model. 82 10am 12 noon Figure 5-9. Hourly exterior illumination on June 1, simulated with the IES model Clear Sky Direct niumination k lu x 10 11 12 13 14 IS H o u r Clear Sky Diffuse niumination 100 80 klux 40 20 H o u r Partly Cloudy Sky Direct niumination 100 r 80 - 60 - 9 10 11 12 13 14 15 H o u r Partly Cloudy Sky Diffuse niumination 1 0 0 1 - 80 - 60 - 9 10 11 12 13 14 15 H o u r Overcast Sky Direct niumination 100r 80 - 60 - klux 40 - 9 10 11 12 13 14 15 H our ill D o gn iau x U S Gillette fl IES Overcast Sky Diffuse niumination 100 80 60 klux 40 20 0 9 10 11 12 13 14 15 H our 11 D ogniaux B Gillette ESIES Figure 5-10. Comparison of direct and diffuse illuminations of the three daylight simulation models. 84 5.3.6 Interreflected Illumination Using the Flux Transfer Method The following procedures are used to calculate the portions of direct and diffuse illumination falling on each grid point of the site and the reflected illumination received from the surrounding building surfaces: 1. Calculation o f initial illuminance for each grid point using Dogniaux, Gillette, or EES model: a. Check if the direct sunlight component exist. b. Calculate the portion of the sky luminance that contribute to the diffuse component 2. For each point of the grid: a. Define four vision planes that lie on the boundary of the site. b. Project image of building surfaces seen onto these vision planes. c. Subdivide the projection of the building surfaces according to area seen and reflectance seen. d. Calculate the initial luminance of these surfaces. e. Calculate the luminance received by reflection from other surfaces. f. Repeat two times, or until change is minimal, to obtain the final luminance of each surface. g. Calculate the reflectance from each surface to obtain final illuminance. 3. Plot graph. Figure 5-11 shows an example of the total illumination level, that is, the available direct, diffuse, and interreflected illumination, for a site on June 1 of Portland, Oregon. 85 Site O Exterior Illumination 0 Total Illumination Figure 5-11. Available exterior illumination on a site together with the interreflected illumination. 8 6 6. COMPARATIVE SITE STUDIES The amount of daylight accessible to a particular point on a site or atrium is important to the design process of the site or atrium. There are certain tasks that require a minimum amount of daylight, for example, different kinds of plants require a certain level of daylight for their survival. In designing an atrium or buildings on the site, if the designer is informed of the pattern and the amount of daylight availability, he may optimize the form and materials used for the design. Certain variables that are determined by urban designers and architects contribute to the resulting illumination level on a site. These variables include the latitude of the site, the density of the urban mass, the shape of the site, the orientation of the site, the width of the surrounding streets or the setback of buildings in the surrounding blocks, and the reflectances o f the surrounding building surfaces. The studies on the following pages demonstrate the effect of these variables, except that of the latitude of the site, to the level of illumination on the site. The period of time during which illumination is calculated is also critical. In the summer in most United States cities, sun exposure is most important between 9 am and 3 pm, whereas in the winter, it is between 10 am and 2 pm. To keep this variable constant for comparison o f studies, all of the following studies are made between the hours of 9 am and 3 pm. All studies are based on the recorded weather data for a typical meteorological year for Portland, Oregon. 6.1 Changing Urban Mass The denser the urban mass, the more obstruction of daylight and therefore, the less availability of daylight. Figure 6-la. Boundary height: Site length Ratio = 2:1 Dogniaux model Data maximum: 380 klux June 1 Clear Day June 12 Partly Cloudy June 21 Overcast Exterior Illumination Total Illumination Figure 6-lb. Boundary height: Site length Ratio =1:1 Dogniaux model Data maximum: 550 klux June 1 Clear Day June 12 Partly Cloudy June 21 Overcast Exterior Illumination Total Illumination 89 Figure 6-lc. Boundary height: Site length Ratio = 1:2 Dogniaux model Data maximum: 580 klux June 1 Clear Day June 12 Partly Cloudy June 21 Overcast Exterior Illumination Total Illumination Figure 6-Id. Boundary height: Site length Ratio =1:4 Dogniaux model Data maximum: 600 klux June 1 Clear Day June 12 Partly Cloudy June 21 Overcast Exterior Illumination Total Illumination 91 Figure 6-2a. Boundary height: Site length Ratio = 2:1 Gillette model Data maximum: 450 klux June 1 Clear Day June 12 Partly Cloudy June 21 Overcast Exterior Illumination Total Illumination 92 Figure 6-2b. Boundary height: Site length Ratio —1:1 . Gillette model Data maximum: 600 klux June 1 Clear Day June 12 Partly Cloudy June 21 Overcast Exterior Illumination Total Illumination 93 Figure 6-2c. Boundary height: Site length Ratio = 1:2 Gillette model Data maximum: 670 klux June 1 Clear Day June 12 Partly Cloudy June 21 Overcast Exterior Illumination Total Illumination 94 Figure 6-2d. Boundary height: Site length Ratio =1:4 Gillette model Data maximum: 700 klux June 1 Clear Day June 12 Partly Cloudy June 21 Overcast Exterior Illumination Total Illumination 95 Figure 6-3 a. Boundary height: Site length Ratio = 2:1 IES model Data maximum: 500 klux June 1 Clear Day June 12 Partly Cloudy June 21 Overcast Exterior Illumination Total Illumination 96 Ml Figure 6-3 b. Boundary height: Site length Ratio =1:1 EES model Data maximum: 650 klux June 1 Clear Day June 12 Partly Cloudy June 21 Overcast Exterior Illumination Total Illumination Figure 6-3c. Boundary height: Site length Ratio =1:2 EES model Data maximum: 680 klux June 1 Clear Day June 12 Partly Cloudy June 21 Overcast Exterior Illumination Total Illumination Figure 6-3d. Boundary height: Site length Ratio = 1:4 EES model Data maximum: 720 klux June 1 Clear Day June 12 Partly Cloudy June 21 Overcast Total Illumination Exterior Illumination Data maximum: 10000 klux March June September December Boundary height:Site length=2:1 Height:Length =1:2 Figure 6-4. Seasonal Illumination simulated with the Dogniaux model. 1 0 0 jf ii A A Data maximum: 12000 klux March June September December Boundary height:Site length=2:1 Height:Length =1:2 Figure 6-5. Seasonal Illumination simulated with the Gillette model. 101 0 0 0 0 0 0 Data maximum: 13800 klux March June September December Boundary height:Site length=2:1 Height:Length = 1:2 Figure 6-6. Seasonal Illumination simulated with the EES model. 102 Data Maximum: 30000 klux Site o Total Illumination Figure 6-7. Yearly illumination plots using the Dogniaux model. 103 Data Maximum: 70000 klux Figure 6-8. Yearly illumination plots using the Gillette model 104 Data Maximum: 50000 klux Site Total Illumination Figure 6-9. Yearly illumination plots using the IES model. 105 6.2 Changing the East-W est Length of the Site The shape of the daylight availability contour plot is elongated along the East-West axis when the East-West length of the site is elongated. June 1 Clear Day Dogniaux mode 0 0 Gillette model Figure 6-10. Changing the East-West site length on a clear day. 106 June 21 Overcast Day Dogniaux model Gillette model Figure 6-11. Changing the East-West site length on an overcast day. The maximum and minimum levels of illumination on the site are basically unchanged as the length of the site is elongated. The shape of the illumination plot for the overcast sky is again smoother and lower than that for the clear sky. 107 6.3 Changing the North-South Length of the Site June 1 Clear Day Dogniaux mode Gillette model Figure 6-12. Changing the North-South site length on a clear day. 108 June 21 Overcast Day Dogniaux model Gillette model Figure 6-13. Changing the North-South site length on an overcast day. The shape of the daylight availability contour plot is elongated along the North-South axis as the North-South length of the site is elongated. The maximum and minimum illumination levels on the site are basically unchanged. 109 6.4 Changing the Orientation of the Site Changing the orientation of the site affects the pattern o f the obstruction of daylight and, therefore, the general shape of the daylight availability contour plot. 0 degrees 30 degrees 45 degrees 60 degrees Dogniaux model Gillette model Figure 6-14. Changing the orientation of the site on June 1, Clear Day. 110 6.5 Changing the Width of Surrounding Streets Increasing the width of North street decreases the obstruction of daylight in the North and the amount of reflected light from the North building surface. The net amount of illumination is more as the width of the North street increases. June 1 Clear Day Gillette Model Site O Total Illumination Figure 6-15. Changing the width of the North street. i l l Increasing the width of South street decreases the obstruction of daylight in the South and the amount o f reflected light from the South building surface. The net amount of illumination is more as the width of the South street increases. June 1 Clear Day Gillette Model m 0 m 0 0 Site Total Illumination Figure 6-16. Changing the width of the South street. 112 Increasing the width of East street decreases the obstruction of daylight in the East and the amount of reflected light from the East building surface. The net amount of illumination, especially on the East side of the site, is more as the width of the East street increases. June 1 Clear Day Gillette Model 0 'v / / Site Total Illumination Figure 6-17. Changing the width o f the East street. 113 Increasing the width of West street decreases the obstruction of daylight in the West and the amount of reflected light from the West building surface. The net amount of illumination, especially on the West side of the site, is more as the width of the West street increases. June 1 Clear Day Gillette Model Site Total Illumination Figure 6-18. Changing the width of the West street. 114 6.6 Changing the Reflectances of the Surrounding Building Surfaces Increasing the reflectances of the surrounding building surfaces in each direction has the effect of increasing the illumination and exaggerating the shape of the daylight availability contour plot in each direction. June 1 Clear Day Gillette Model Reflectance = 0.3 Reflectance = 0.5 A Jw Maximum level = 600 klux Maximum level = 610 klux Reflectance = 0.7 Reflectance = 0.9 VTaximum level = 635 klux Maximum level = 650 klux Figure 6-19. Changing reflectance of the surface in the North boundary. In increasing the reflectances of the building surfaces on the North boundary, the shape of the illumination contour plot remains generally the same. The illumination level o f the site increases generally, with an exaggeration of increase on the North side of the site. 115 June 1 Clear Day Gillette Model Reflectance = 0.3 Maximum level = 600 klux Maximum level = 608 klux Reflectance = 0.5 Reflectance = 0.7 Reflectance = 0.9 Maximum level = 620 klux Maximum level = 630 klux Figure 6-20. Changing reflectance of the surface in the South boundary. In increasing the reflectances of the building surfaces on the South boundary, the shape of the illumination contour plot remains generally the same. The illumination level of the site increases generally, with an exaggeration of increase on the South side of the site. However, the increase in total illumination is less when compared to the result of changing the reflectances of building surfaces on the North boundary. This is due to the greater amount of sunlight received by the North surfaces. 116 June 1 Clear Day Gillette Model Reflectance = 0.3 Maximum level = 600 klux Maximum level = 608 klux Reflectance - 0.5 Reflectance = 0.7 Reflectance = 0.9 Maximum level = 613 klux Maximum level = 620 klux Figure 6-21. Changing reflectance of the surface in the East boundary. In increasing the reflectances of the building surfaces on the East boundary, the shape of the illumination contour plot remains generally the same. There is a slight increase in the illumination level of the site. The fringe on the East side of the site becomes more visible and curvy. 117 June 1 Clear Day Gillette Model Reflectance = 0.3 Maximum level = 600 klux Reflectance = 0.7 Reflectance = 0.5 Vlaximum level = 607 Reflectance — 0.9 klux Maximum level = 612 klux Maximum level = 621 klux Figure 6-22. Changing reflectance of the surface in the West boundary. In increasing the reflectances of the building surfaces on the West boundary, the shape of the illumination contour plot remains generally the same. There is a slight increase in the illumination level of the site, especially on the West side of the site. The fringe on the West side of the site becomes more visible and curvy. 118 ______ 7. CONCLUSIONS Daylight is a continuously changing variable that is subjected to numerous factors. Researchers have spent years simulating the sky dome and studying the availability of daylight. The same studies should be applied to architectural design so that an optimal level of daylight can be achieved on a site to provide illumination and energy for humans, animals and plants. The program LightSum is designed to provide the information a designer needs to make some of these daylighting decisions. It is designed to provide information that is usually unavailable to non-researchers. LightSum takes into account the variables contributing to the weather condition of a location, the solar position, and the site condition. It is based on any of the three existing daylight simulation models to analyze the momentary and cumulative availability of daylight on an open site or within an atrium. It is hoped that the program will help professional designers and developers to become more aware of the issue of daylight access, and of using daylight as a source of energy for the building. The LightSum program may serve as a design tool to locate a building on the site and to provide enough illumination for certain tasks. It may serve as a research tool to investigate the response of the urban form and properties to the sun's rhythm and weather condition. The program improves the efficiency of studying daylight on a given site and provides an overall behavior of daylight on the site. It gives immediate response to variable inputs, making the study of different designs convenient. It provides graphic output, making the communication direct and comprehensive for intuitive visualization. 119 However, in order to folly understand the results given by the LightSum program, some background knowledge on solar access and daylight is necessary. Without the understanding of the process of calculating daylight, the output may not be comprehensible to first-time users. The output of the program should also be verified with physical mr del testing after numerous studies have been done on the computer. This will help the user to decide which daylight simulation model works best for a specific site location. The program provides first-hand knowledge of daylight on the site and helps eliminate certain variable combinations for the design of the site. But physical model testing is complementary to investigating the behavior of daylight. To summarize this investigation of daylight availability to a building site, the LightSum program is a computer tool to aid the investigation of solar access to a site. It demonstrates the daily and seasonal behavior of daylight. When the program is properly used, together with other existing tools, energy costs of the building can be saved by reducing the artificial lighting needed and the HVAC load. It can bring the ecological system into the buildings by supporting the access of daylight to plants and humans. It can bring nature back into more responsive buildings and improve the quality of life. 120 8. FUTURE WORK It is hoped that the program LightSum can be used as a tool for initial architectural and urban design decision making. The following suggests some improvement to the program to increase its capability and user-friendliness. . • GRAPHIC INTERFACE: There should be graphic interface to make the program more user-friendly. A window operation with pull-down menus and mouse control is one of today's most common software options. The current menu, with further reorganizing, can be put into a graphics screen to be accessed by the user with keyboard or mouse interaction (Figure 7-1). File Print Site Weather Calculation Model Scale Help Solar Position Radiation Exterior Ilium Start Date End Date Start Hour End Hour Total Ilium Figure 7-1. Suggested graphic user interface for LightSum. • SITE INPUT OPTIONS: The site information input should also be graphical. This would help the user to more effectively create different forms and surroundings of sites. There are two approaches to graphical input of sites: generate a separate graphic interface to be used within the program or import and interpret formats of existing Computer Aided Design and Drafting files, for example, AutoCAD files. Productivity can be highly increased if CADD files can be imported into the LightSum program. • IRREGULAR SITES: The current LightSum program only accepts a flat, rectangular site. However, since the calculation of site illumination are done on a set of grid points with real coordinates, the grid points can be reset to accommodate an irregular shaped or sloped site if certain boundary checking procedures are added. Algorithms checking for irregular shaped and sloping building surfaces also need to be added to analyze a more complex and realistic site. . MULTIPLE OUTPUT WINDOWS: Multiple windows that allow several tables or illumination plots to be shown at the same time would enable the user to compare the results. Studies of various designs would be made efficient. • ON-SCREEN HELP: Provide on-screen help. First-time users of the LightSum program especially would need instructions on how to use the program. Information on related topics made accessible to the user through the help screen would also help those who are unfamiliar to the issues of daylighting design. • PARAMETRIC VARIABLES: The current program provide the options to change just the dates for study and the orientation of the site. Options to change the other variables such as street width, ground reflectance, setback of buildings would ease the work load of the user. Instead of creating a new site, quick studies could be made with focus on one variable at a time. • LINK TO OTHER SOFTWARE: Linking the program to other related software such as DOE2, a program that analyzes energy in buildings, and SolVelop, a program that generates solar envelopes for sites, can broaden the use of the program and provide even more meaningful information for the user. Together with the related software, a complete lighting and energy study of sites could be done. The features listed in the preceding paragraphs are only a portion of those that would improve the capabilities of the program. A professional version of LightSum would need the help of users from different fields to make suggestions on improvement. This program is designed to provide lighting information for open sites and atriums. Design professionals for various facilities, developers, and home-owners can use this program to investigate the lighting and, to some extent, energy results of their projects and property. APPENDIX A. Glossary of Abbreviations A Area as Azimuth angle c Atmospheric extinction coefficient cd Candela cp Candlepower cm International Commission on Illumination E Illuminance EdH Diffuse horizontal solar illuminance Edv Diffuse vertical solar illuminance e dh Direct horizontal solar illuminance Edn Direct normal solar illuminance E D v Direct vertical solar illuminance E SC Solar illuminance constant Ext Extraterrestrial solar illuminance fc Footcandle fL Footlambert hs Hour angle / Luminous intensity IES Illuminating Engineering Society of North America L Luminance lm Lumen lx Lux M Exitance 124 Q Luminous energy SI Systeme International a Altitude angle 5S Declination angle < D Luminous flux P Reflectance X Transmittance a Solid angle 125 APPENDIX B. List of Latitudes for Different Cities3 2 CITY LATITUDE ALGIERS, Algeria 36.5 ATHENS, Greece ‘ 37.6 ATLANTA, Georgia 33.5 BAGHDAD, Iraq 33.2 BALTIMORE, Maryland 39.2 BANGKOK, Thailand 13.5 BERLIN, Germany 52.3 BIRMINGHAM, Alabama 33.5 BOSTON, Massachusetts 42.2 BUENOS AIRES, Argentina -34.5 BUFFALO, New York 42.5 CAIRO, Egypt 30.2 CALCUTA, India 22.3 CHICAGO, Illonois 41.5 CINCINNATI, Ohio 39.1 CLEVELAND, Ohio 41.3 COPENHAGEN, Denmark 55.4 DALLAS, Texas 32.5 DENVER, Colorado 39.4 DETROIT, Michigan 42.2 EL PASO, Texas f 31.6 ESSEN, Germany 51.3 FRESNO, California 36.7 HARTFORD, Connecticut 41.5 HONGKONG 22.2 HOUSTON, Texas 29.5 INDIANAPOLIS, Indiana 39.5 ISTANBUL, Turkey 41.0 JAKARTA, Indonesia -6.1 JOHANNESBURG, S.Africa -26.2 KARACHI, Pakistan 24.5 KINSHASA, Zaire -4.2 LIMA, Peru -12.0 LONDON, Great Britain 51.3 LOS ANGELES, California 34.5 MADRID, Spain 40.2 32DOE-2 Manual, p. VIII.3; Schiler, Marc, SOLARIS, 1988. 126 CITY LATITUDE MANILLA, Philappines 30.5 MELBOURNE, Australia -37.5 MEXICO CITY, Mexico 19.2 MIAMI, Florida 25.5 MILWAUKEE, Wisconsin 43.0 MINNEAPOLIS, Minnesota 44.6 MONTREAL, Canada 45.3 MOSCOW, Russia 55.5 NEW ORLEANS, Louisiana 29.6 NEW YORK CITY, New York 40.4 PARIS, France 48.5 PHILADELPHIA, Pennsylvania 39.6 PHOENIX, Arizona 33.3 PITTSBURG, Pennsylvania 40.3 PORTLAND, Oregon 45.6 RENO, Nevada 39.3 ROME, Italy 41.5 SACRAMENTO, California 38.0 SAN DIEGO, California 32.4 SAN FRANCISCO, California 37.5 SANTIAGO, Chile -33.3 SAO PAOLO, Brazil -23.3 SEATTLE, Washington 47.7 SEOUL, South Korea 37.7 SHANGHAI, China 31.1 ST. LOUIS, Missouri 38.4 TAIPEI, Taiwan 25.0 TEHRAN, Iran 35.4 TOKYO, Japan 35.4 TORONTO, Canada 43.4 WARSAW, Poland 52.2 WASHINGTON, D.C. 38.5 APPENDIX C. Reflectances of Building Materials and Surfaces: 33 MATERIAL REFLECTANCE MATERIAL REFLECTANCE Asphalt 0.07-0.15 Bluestone, Sandstone 0.18 Brick, Light Buff 0.48 Brick, Dark Buff 0.40 Brick, Dark Red Glazed 0.30 Cement 0.27 Concrete 0.20-0.40 Dark Gray Paint 0.20 Earth 0.10 Grass, Dark Grenn 0.06 Granite 0.40 Granolite Pavement 0.17 Gravel 0.13-0.15 Ivory Paint 0.65 Macadam 0.18 Marble, White 0.45 Sky Blue Paint 0.40 Slate or Dark Clay 0.08 Snow, New 0.75 Snow, Old 0.64 Tan Paint 0.40 Vegetation, Average 0.25 White Paint, New 0.75 White Paing, Old 0.60 33The Regents of University of California, DAYLIT, 1987. 128 APPENDIX D. Transm ittances of Glass3 4 SINGLE PANE SHEET GLASS CATALOG: Glass Thickness Solar Glass Reflective Thickness Solar Type (inches) Transmittance Type Coating (inches) Trans. Clear 3/32,1/8 .90 Clear Silver 1/8,1/4 .08-.20 Clear 5/32,3/16 .89 Clear Golden 1/8,1/4 .08-.20 Clear 1/4 .88 Clear Lt. Gold 1/4 .08 Blu/Gm 3/16 .78 Blu/Gm Silver 1/4 .08-.20 Blu/Gm 1/4 .74 Gray Silver 1/4 .08-.34 Gray 1/8 .62 Bronze Silver 1/4 .08-.34 Gray 3/16 .51 Bronze Lt. Gold 1/4 .08-.20 Gray 1/4 .42 Bronze 1/8 .68 Bronze 3/16 .58 Bronze 1/4 .50 DOUBLE PANE SHEET GLASS CATALOG: Glass Thickness Solar Glass Reflective Thickness Solar Type (inches) Transmittance 'Type Coating (inches) Trans. Clear 1/8 .82 Clear Silver 2 @ 1/4 .07-. 18 Clear 3/16 .80 Clear Golden 2 @ 1/4 .07-. 18 Clear 1/4 .78 Clear Lt.Gold 2 @ 1/4 .07 Blu/Gm 3/16 .70 Blu/Gm Silver 2 @ 1/4 .07-.18 Blu/Gm 1/4 .65 Gray . Silver 2 @ 1/4 .07-.30 Gray 1/8 .56 Bronze Silver 2 @ 1/4 .07-.30 Gray 3/16 .46 Bronze Lt.Gold 2 @ 1/4 .07 Gray 1/4 .37 Bronze 1/8 .61 Bronze 3/16 .52 Bronze 1/4 .44 34The Regents of University of California, DAYLIT, 1987. ■ t 129 PLASTIC SHEET GLASS CATALOG: Glass Solar Glass Solar Type Transmittance Type Transmittance Acrylic, Clear .90 Lexan (Polycarbonate) .64 Acrylic, Bright White .82 Mylar (Polyester) .86 Acrylic, Medium White .53 Sunlite (Fiberglass) .86 Acrylic, Soft White .32 Tedlar (Fluorocarbon) .92 Acrylic, Bronze .27 Teflon (Fluorocarbon) .92 SPECIAL SHEET GLASS: Glass Solar Type Transmittance Heat-Absorbing Plate Glass .70-. 80 Neutral Low-Trans Glass . 10-.60 130 APPENDIX E. List of Cities Using TMY W eather D ata3 5 ALBANY, New York ALBUQUERQUE, New Mexico ATLANTA, Georgia BIRMINGHAM, Alabama BOISE, Idaho BOSTON, Massachusetts BURLINGTON, Vermont CHARLESTON, South Carolina CHICAGO, Illinois CLEVELAND, Ohio COLUMBIA, Missouri DETROIT, Michigan DODGE CITY, Kansas EL PASO, Texas FRESNO, California GREAT FALLS, Montana HOUSTON, Texas INDIANAPOLIS, Indiana JACKSON, Mississippi JACKSONVILLE, Florida LOS ALAMOS, New Mexico LOS ANGELES, California 35DOE-2 Manual, p. VIII.3. LOUISVILLE, Kentucky MADISON, Wisconsin MEMPHIS, Tennessee MIAMI, Florida MINNEAPOLIS, Minnesota NASHVILLE, Tennessee NEW ORLEANS, Louisiana NEW YORK CITY, New York OKLAHOMA CITY, Oklahoma OMAHA, Nebraska PHOENIX, Arizona PITTSBURGH, Pennsylvania PORTLAND, Maine PORTLAND, Oregon RALEIGH, North Carolina RICHMOND, Virginia SACRAMENTO, California SALT LAKE CITY, Utah SAN DIEGO, California SAN FRANCISCO, California SEATTLE, Washington WASHINGTON, D C. 131 REFERENCES DiLaura, David L. "On the Computation of Equivalent Sphere Illumination." Journal o f the Illuminating Engineering Society. January 1975: pp. 129-149. DiLaura, David L.; Hauser, Gregg A. "On Calculating the Effects of Daylighting in Interior Spaces." Journal o f the Illuminating Engineering Society. October 1978: pp. 2-14. DiLaura, David L. "On a New Technique for Interreflected Component Calculations." Journal o f the Illuminating Engineering Society. October 1979: pp. 53-59. DiLaura, David L. "On the Development of a Recursive Method for the Solution of Radiative Transfer Problems." Journal o f the Illuminating Engineering Society. Summer 1992: pp. 108-112. DOE-2 Manual. Dogniaux, R.; Lemoine, M. "Classification of Radiation Sites in Terms of Different Indices of Atmospheric Transparency." 1983 International Daylighting Conference. Phoenix, Arizona: pp. 33-40. Egan, M. David. Concepts in Architectural Lighting. McGraw-Hill Book Company. 1983. Flowers, E.C.; McCormick, R.A.; Kurfis, K.R. "Atmospheric Turbidity over the United States, 1961-1966." Journal o f Applied Meteorology. December 1969: pp. 955-962. Gillette, Gary. A Daylighting Model for Building Energy Simulation. Washington, D . C.: U.S. Department of Commerce, National Bureau of Standards Building Science Series 152, 1983. Gillette, Gary; Kusuda, T. "A Daylighting Computation Procedure for Use in DOE-2 and Other Dynamic Building Energy Analysis Programs." Journal o f the Illuminating Engineering Society. January 1983: pp. 78-85. Higbie, H.H. "Prediction of Daylight from Vertical Windows." Transactions o f the Illuminating Engineering Society. May 1925: pp. 433-476. Higbie, H.H.; Levine, A. "Prediction of Daylight from Sloped Windows." Transactions o f the Illuminating Engineering Society. March 1926: pp. 273-324. Hopkinson, R.G; Longmore, J.; Petherbridge, P. "An empirical formula for the computation of the indirect component of the daylight factor. Transactions o f the Illuminating Engineering Society, 1954, Vol. 19: p. 201. Hulstrom, Roland L., Editor. Solar Resources. Cambridge, Massachusetts: The MIT Press. 1989. Hunt, D.R.G. Availability o f Daylight. Garston, England: Building Research Station. 1979. Illuminating Engineering Society Lighting Handbook Reference Volume. New York: Illuminating Engineering Society of North America. 1984. EES Calculation Procedures Committee. Recommended Practice for the Calculation o f Daylight Availability. Illuminating Engineering Society of North America. 1983. International Commission on Illumination. - Daylight— International Recommendations for the Calculation o f Natural Daylight. Committe Publication CEE No. 16 (E-3.2). Paris: Bureau Central. 1970. Johnson, Timothy E. Solar Architecture, the Direct Gain Approach. New York: McGraw-Hill Book Company. 1981. 133 Kittler, Richard. "Luminance Models of Homogeneous Skies for Design and Energy Performance Predictions." 1986 International Daylighting Conference. Proceedings I . Long Beach, California: pp. 18-22. Knowles, Ralph L. The Sun— Heat & Light. Los Angeles, California: School of Architecture and Fine Arts, University of Southern California. 1967. Knowles, Ralph L. Sun Rhythm Form. Cambridge, Massachusetts: The MIT Press. 1981. Kreith, Frank; Kreider, Jan F. Principles o f Solar Engineering. New York: Hemisphere Publishing Corporation. 1978. Littlefair, P.J. "The Luminous Efficacy of Daylight." 1986 International Daylighting Conference. Proceedings I . Long Beach, California: pp. 45-60. Mazria, Edward. The Passive Solar Energy Book. Emmaus, Pennsylvania: Rodale Press. 1979. Murdoch, Joseph B. Illumination Engineering. From Edison's Lamp to the Laser. New York: Macmillan Publishing Company. 1985. Nawab, M.; Karayel, M.; Ne'eman, E.; Selkowitz, S. "Daylight Availability." 1983 International Daylighting Conference. Phoenix, Arizona: pp. 43-46. Treado, S.; Gillette, G. 1983. "Measurements of Sky Luminance, Sky Illuminance, and Horizontal Solar Radiation." Journal o f the Illuminating Engineering Society. Vol. 12, No. 3: pp. 130-135. Pierpoint, William. "A Simple Sky Model for Daylighting Calculations." 1983 International Daylighting Conference. Phoenix, Arizona: pp. 47-52. 134 Pierpoint, William. "Accuracy of the Lune Protractor." 1986 International Daylighting Confereance. Proceedings I . Long Beach, California: pp. 97-103. Robbins, Claude L. Daylighting Design and Analysis. New York: Van Nostrand Reinhold Co. 1986. Robbins, C.L.; Carlisle, N.L.; Hunter, K.C.; Wortman, D.N. "A Simplified Flux Transfer Method for Designing Daylighting Systems under Clear and Overcast Skies." 1986 International Daylighting Confereance. Proceedings I . Long Beach, California: pp. 111-114. Schiler, Marc. Simplified Design o f Building Lighting. John Wiley & Sons, Inc. 1992. Stein, Benjamin; Reynolds, John S.; McGuinness, William J. Mechanical and Electrical Equipment for Buildings. 7th Edition. John Wiley & Sons, Inc. 1986. Walsh, John W.T. The Science o f Daylight. London: Macdonald & Co. 1961. Wurtman, Richard J. "The Effects of Light on the Human Body." Scientific American. Vol. 233, No. 1: pp. 68-77 135

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Asset Metadata

Creator Liang, June Lok-Mei (author)

Core Title Computer modelling of cumulative daylight availability within an urban site

Degree Master of Building Science

Degree Program Building Science

Publisher University of Southern California (original), University of Southern California. Libraries (digital)

Tag engineering, architectural,OAI-PMH Harvest

Language English

Contributor Digitized by ProQuest (provenance)

Advisor Schiler, Marc (committee chair), Noble, Douglas (committee member), Schierle, Goetz G. (committee member)

Permanent Link (DOI) https://doi.org/10.25549/usctheses-c17-784404

Unique identifier UC11348761

Identifier EP41432.pdf (filename),usctheses-c17-784404 (legacy record id)

Legacy Identifier EP41432.pdf

Dmrecord 784404

Document Type Thesis

Rights Liang, June Lok-Mei

Type texts

Source University of Southern California (contributing entity), University of Southern California Dissertations and Theses (collection)

Access Conditions The author retains rights to his/her dissertation, thesis or other graduate work according to U.S. copyright law. Electronic access is being provided by the USC Libraries in agreement with the au...

Repository Name University of Southern California Digital Library

Repository Location USC Digital Library, University of Southern California, University Park Campus, Los Angeles, California 90089, USA